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2 

2.1 A global view of vegetation

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We start with the observation that the global distribution of plants and characteristic assemblies of different plant species is not random, but relates to climate. Around the beginning of the 19th century, Alexander von Humboldt pursued expeditions to different places on Earth and connected the multitude of his local observations into a global view of biogeography. He was the first to realize that vegetation zones along elevational gradients were shifted across different mountain ranges on different continents and located on different latitudes, and that the elevational and latitudinal patterns in vegetation were related to climate - in much the same way across the earth. This finding is visualised by the schematic scientific drawing in Figure 2.1. The figure illustrates, for example, that the treeline increases from the high northern latitudes of Lapland at 68\(^\circ\)N to the Alps and Pyrenees at 42-46\(^\circ\)N and to the Himalaya at 29-32\(^\circ\)N. Or that the elevation at which Betula alba (birch) grows varies from 1000-2000 ft in Lapland, to 4000-5000 ft in the Alps, and about 15,000 ft in the Himalaya. Figure 2.1 also illustrates that the treeline doesn’t increase monotonically with decreasing latitude. Although not spelled out in the figure, this is a hint at the importance of water, along with temperature, for controlling vegetation. We’ll revisit this observation later in this book. Humboldt’s integration of globally distributed observations into his global view of climate as a driver of vegetation was pioneering and forms the basis of our modern approach to understanding and modelling global vegetation patterns and how they are influenced by climate change.

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We start with the observation that the global distribution of plants and characteristic assemblies of different plant species is not random, but relates to climate. Around the beginning of the 19th century, Alexander von Humboldt pursued expeditions to different places on Earth and connected the multitude of his local observations into a global view of biogeography. He was the first to realize that vegetation zones along elevational gradients were shifted across different mountain ranges on different continents and located at different latitudes, and that the elevational and latitudinal patterns in vegetation were related to climate - in much the same way across the Earth. This finding is visualised by the schematic scientific drawing in Figure 2.1. The figure illustrates, for example, that the treeline increases from the high northern latitudes of Lapland at 68\(^\circ\)N to the Alps and Pyrenees at 42-46\(^\circ\)N and to the Himalaya at 29-32\(^\circ\)N. Or that the elevation at which Betula alba (birch) grows varies from 1000-2000 ft in Lapland, to 4000-5000 ft in the Alps, and about 15,000 ft in the Himalaya. Figure 2.1 also illustrates that the treeline doesn’t increase monotonically with decreasing latitude. Although not spelled out in the figure, this is a hint at the importance of water, along with temperature, for controlling vegetation. We’ll revisit this observation later in this book. Humboldt’s integration of globally distributed observations into his global view of climate as a driver of vegetation was pioneering and forms the basis of our modern approach to understanding and modelling global vegetation patterns and how they are influenced by climate change.

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Click on the biome names below to open a tab that lists some key characteristics and provides a Walter-Lieth climate diagram for a representative site, located in that biome. The sites are locations where ecoystem water and carbon fluxes, along with meteorological variables, are measured. We will revisit data from these same sites in later chapters, then with a focus on water and carbon fluxes and the phenology. The locations of the sites are indicated on the map in Figure 2.2.

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Walter-Lieth climate diagrams show monthly climatologies of average temperature and precipitation on the same axis and scaled such that months where the blue curve (precipitation, mm month-1) is above the red curve (temperature, \(^\circ\)C) indicates humid periods and the opposite relative curve positions indicates dry periods. Dry periods are roughly indicating when potential evapotranspiration is higher than precipitation (see Chapter 7). Blue bars along the x-axis indicate months with likely frost. Annotations on the top of the graph indicate the observation period (left), the mean annual temperature (center), and the mean annual precipitation (right). The average temperatures of the warmest and coldest months are given to the left of the temperature axis.

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Click on the biome names below to open a tab that lists some key characteristics and provides a Walter-Lieth climate diagram for a representative site, located in that biome. The sites are locations where ecosystem water and carbon fluxes, along with meteorological variables, are measured. We will revisit data from these same sites in later chapters, then with a focus on water and carbon fluxes and the phenology. The locations of the sites are indicated on the map in Figure 2.2.

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Walter-Lieth climate diagrams show monthly climatologies of average temperature and precipitation on the same axis and scaled such that months where the blue curve (precipitation, mm month-1) is above the red curve (temperature, \(^\circ\)C) indicates humid periods, while the opposite relative curve position indicates dry periods. Dry periods are roughly characterized by a potential evapotranspiration higher than precipitation (see Chapter 7). Blue bars along the x-axis indicate months with likely frost. Annotations on the top of the graph indicate the observation period (left), the mean annual temperature (center), and the mean annual precipitation (right). The average temperatures of the warmest and coldest months are given to the left of the temperature axis.

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Chapter 11). This association is highly relevant for the N economy of the plant and its productivity and competitiveness under different levels of N availability.

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Plants can also be distinguished into the botanical classification of angiosperms (flowering plants) and gymnnosperms (seed-producing plants that include conifers, cycads, and Ginkgo). The distinction between angiosperms and gymnosperms largely aligns with the distinction between needle-leaved and broadleaved plants (but see Ginkgo). The two groups are not only distinguished by their phylogenetic heritage, but also by essential characteristics that relate to the efficiency by which they photosynthesise and transpire water. Angiosperm leaves typically exhibit higher photosynthesis and transpiration rates and are thinner and shorter-lived than leaves of gymnosperms. These differences relate to differences in how the water transport system (plant hydraulics) is built. A larger number and a wider diameter of water transport organs in angiosperms enable a higher water conductivity - essential for sustaining higher photosynthetic rates than in gymnosperms.

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Global vegetation models use PFTs as their basic unit for distinguishing plants. The exact delineation of PFTs implemented in such models may vary from the list given above. Further distinctions may be made and are relevant in a global vegetation and carbon cycle modelling context. For example, only a relatively small subset of plants is known to associate with symbiotic nitrogen (N)-fixing bacteria that live in root nodules of the host plant (“N-fixing plants”, see also Chapter 11). This association is highly relevant for the N economy of the plant and its productivity and competitiveness under different levels of N availability.

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Plants can also be distinguished into the botanical classification of angiosperms (flowering plants) and gymnosperms (seed-producing plants that include conifers, cycads, and Ginkgo). The distinction between angiosperms and gymnosperms largely aligns with the distinction between needle-leaved and broadleaved plants (but see Ginkgo). The two groups are not only distinguished by their phylogenetic heritage, but also by essential characteristics that relate to the efficiency by which they photosynthesise and transpire water. Angiosperm leaves typically exhibit higher photosynthesis and transpiration rates and are thinner and shorter-lived than leaves of gymnosperms. These differences relate to differences in how the water transport system (plant hydraulics) is built. A larger number and a wider diameter of water transport organs in angiosperms enable a higher water conductivity - essential for sustaining higher photosynthetic rates than in gymnosperms.

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2.4 Traits

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The physiological, morphological, and life history characteristics of different plants determine their productivity and competitiveness in a given climate. Such characteristics are referred to as plant functional traits, or often just traits. Plant species can be described by a set of traits and a subset of certain traits yields the distinction into PFTs described above: leaf habit (deciduous vs. evergreen), leaf form (needle-leaved vs. broadleaved), and the life history strategy distinguising annual vs. perennial. A range of additional traits are commonly described and investigated scientifically. Here, we will not consider additional ones. The concept of a plant functional trait is that it describes a largely immutable characteristic of a plant species that determines metabolic rates (photosynthesis, respiration) and their relationship to the abiotic environment (e.g., temperature), nutrient and water demand, and ultimately its demographic rates (growth, fecundity, mortality) and thus competitiveness.

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The physiological, morphological, and life history characteristics of different plants determine their productivity and competitiveness in a given climate. Such characteristics are referred to as plant functional traits, or often just traits. Plant species can be described by a set of traits and a subset of certain traits yields the distinction into PFTs described above: leaf habit (deciduous vs. evergreen), leaf form (needle-leaved vs. broadleaved), and the life history strategy distinguishing annual vs. perennial. A range of additional traits are commonly described and investigated scientifically. Here, we will not consider additional ones. The concept of a plant functional trait is that it describes a largely immutable characteristic of a plant species that determines metabolic rates (photosynthesis, respiration) and their relationship to the abiotic environment (e.g., temperature), nutrient and water demand, and ultimately its demographic rates (growth, fecundity, mortality) and thus competitiveness.

Today’s global distribution of species and biomes (assuming no intervention by human land use and forest management) is the outcome of competition and thus reflects the combination of plant functional traits that optimises competitiveness of a species under the present-day climate. The distribution of biomes and PFTs is thus a direct reflection of the climate.

For example, whether a region is dominated by deciduous or by evergreen trees and forests is determined by the benefits and costs for a plant of maintaining leaves year-round. Evergreen trees benefit from the ability to photosynthesise and gain carbon around the year. For example, in Mediterranean regions, although light levels are lower in winter than in summer, ample moisture and non-negligible light enables evergreen trees to assimilate carbon also during winter months. However, leaves and needles of evergreen plants have to be built for lasting several years. Such leaves are typically much thicker than those of deciduous trees and thus require more carbon per unit leaf area for their construction. The leaf mass per unit leaf area is commonly referred to as the leaf mass per area, LMA, and is an important additional plant trait as it is directly linked to a plant’s carbon balance. Over the leaf lifespan, the initial high construction costs of high-LMA leaves are outweighed by the additional carbon assimilation during periods when deciduous trees shed their leaves.

Leaf-shedding of deciduous trees, in contrast, is a strategy to avoid having to build costly long-lasting leaves and maintaining them year-round (which also incurs an additional respiration cost, also in the form of carbon). Leaves are shed during periods when the climate is unfavourable for photosynthesis - during cold and dark winter months, or during excessively dry periods.

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Note that plant functional traits are often not entirely immutable. Instead, traits may vary also within a species and these variations are often driven by the environment. This is called acclimation. Such variations can even arise over the course of a season. For example, photosynthetic traits can rapidly acclimate to the large changes in light availability over the course of a year. Some traits are more plastic than others. For example, a tree is either needle-leaved or broadleaved. There is no continuum between the two leaf forms. In contrast, the nitrogen content per unit leaf mass is relatively plastic within a species.

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A changing environment changes the competitiveness of a given species, i.e., of a given trait combination. As a result, some traits may acclimate to some extent within a weeks to years. Over longer time scales, the altered demographic rates in a new climate affect the competitiveness of a species (even after some of its traits may have acclimated to a new climate) and ultimately shift demographic rates and the community composition. In grasslands, where the demographic cycle is short, such community composition changes may unfold over time scales of a few years. In forests, the longevity of an individual tree is on the order of decades to centuries and community composition changes unfold on correspondingly long time scale.

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Note that plant functional traits are often not entirely immutable. Instead, traits may vary also within a species, and these variations are often driven by the environment. This is called acclimation. Such variations can even arise over the course of a season. For example, photosynthetic traits can rapidly acclimate to the large changes in light availability over the course of a year. Some traits are more plastic than others. For example, a tree is either needle-leaved or broadleaved. There is no continuum between the two leaf forms. In contrast, the nitrogen content per unit leaf mass is relatively plastic within a species.

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A changing environment changes the competitiveness of a given species, i.e., of a given trait combination. As a result, some traits may acclimate to some extent within weeks to years. Over longer time scales, the altered demographic rates in a new climate affect the competitiveness of a species (even after some of its traits may have acclimated to a new climate) and ultimately shift demographic rates and the community composition. In grasslands, where the demographic cycle is short, such community composition changes may unfold over time scales of a few years. In forests, the longevity of an individual tree is on the order of decades to centuries and community composition changes unfold on a correspondingly long time scale.

2.5 Global vegetation patterns

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The biome classification is a way to discretize vegetation based on several characteristics (e.g., tree cover fraction). However, many of these characteristics describe observable variables that vary more or less gradually across environmental gradients and each of these variables can be mapped across the globe thanks to Earth observation data. These global patterns of different observable variables reflect how the climate influences vegetation structure and functioning across the globe (independent of a classification into biomes). In much of the remainder of this course, we will investigate these vegetation-climate relationships without considering the biome classification. These relationships are informative for understanding how different processes of terrestrial ecology, plant physiology, the carbon cycle, and land-climate interactions are driven by the environment and vary across the globe.

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The biome classification is a way to discretize vegetation based on several characteristics (e.g., tree cover fraction). However, many of these characteristics describe observable variables that vary more or less gradually across environmental gradients, and each of these variables can be mapped across the globe thanks to Earth observation data. These global patterns of different observable variables reflect how the climate influences vegetation structure and functioning across the globe (independent of a classification into biomes). In much of the remainder of this course, we will investigate these vegetation-climate relationships without considering the biome classification. These relationships are informative for understanding how different processes of terrestrial ecology, plant physiology, the carbon cycle, and land-climate interactions are driven by the environment and vary across the globe.

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2.8 Hillslope-scale heterogeneity

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Topography shapes microclimates and drives small-scale variations in hydrology. In mountain regions, vegetation may thus vary strongly along small spatial scales - on the order of 10-103 m. This scale - from the river channel to the ridge - is referred to as the hillslope scale. In much the same way as climate drives vegetation across biomes, so it does across the hillslope scale. The incident solar radiation and - as a consequence of that - near-surface air temperatures are affected by the local slope, aspect, and shading by the surrounding topography. Soil moisture and the groundwater table depth are affected by lateral subsurface flow of water, driven by gradients in water potentials along topographical gradients. Subsurface water flow converges in depressions and concave terrain (e.g., in valley bottoms) and diverges in convex terrain. (e.g., on ridges and hilltops). As a consequence, the water table is shallow in valley bottoms and deep under ridges. Radiation and hydrology thus create microclimates and plant water availability conditions that are shaped by topography and variations in vegetation that are shaped by the microclimates and hydrological conditions.

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These hillslope-scale variations “intersect” with the the background climate (average climate across larger spatial scales, on the order of 104-105 m). A shallow groundwater table and moist soils in valley bottoms can promote plant productivity in arid regions and seasons. In contrast, in a humid climate, a very shallow water table in valley bottoms inhibits plant productivity due to anaerobic conditions in waterlogged soils and the inability of roots to penetrate into permanently water-saturated soil. Similarly, the influence of radiation in promoting versus inhibiting plant productivity depends on the background climate. In cold climates of the high northern latitudes, the solar zenith angle is relatively also, even in mid-summer. This creates a strong influence of the local slope and aspect. In the northern hemisphere, south-facing slopes receive more radiation - a difference to north-facing slopes that can be critical for sustaining tree growth in high northern regions. In contrast, elevated incident solar radiation in south-facing slopes can aggravate water limitation and suppress vegetation productivity in more arid climates of the subtropics and mid-latitudes of the northern hemisphere.

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Topography shapes microclimates and drives small-scale variations in hydrology. In mountain regions, vegetation may thus vary strongly along small spatial scales - on the order of 10-103 m. This scale - from the river channel to the ridge - is referred to as the hillslope scale. In much the same way that climate drives vegetation across biomes, so it does across the hillslope scale. The incident solar radiation and - as a consequence of that - near-surface air temperatures are affected by the local slope, aspect, and shading by the surrounding topography. Soil moisture and the groundwater table depth are affected by lateral subsurface flow of water, driven by gradients in water potentials along topographical gradients. Subsurface water flow converges in depressions and concave terrain (e.g., in valley bottoms) and diverges in convex terrain. (e.g., on ridges and hilltops). As a consequence, the water table is shallow in valley bottoms and deep under ridges. Radiation and hydrology thus create microclimates and plant water availability conditions that are shaped by topography, from which result variations in vegetation.

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These hillslope-scale variations “intersect” with the background climate (average climate across larger spatial scales, on the order of 104-105 m). A shallow groundwater table and moist soils in valley bottoms can promote plant productivity in arid regions and seasons. In contrast, in a humid climate, a very shallow water table in valley bottoms inhibits plant productivity due to anaerobic conditions in waterlogged soils and the inability of roots to penetrate into permanently water-saturated soil. Similarly, the influence of radiation in promoting versus inhibiting plant productivity depends on the background climate. In cold climates of the high northern latitudes, the solar zenith angle is relatively also, even in mid-summer. This creates a strong influence of the local slope and aspect. In the northern hemisphere, south-facing slopes receive more radiation - a difference to north-facing slopes that can be critical for sustaining tree growth in high northern regions. In contrast, elevated incident solar radiation in south-facing slopes can aggravate water limitation and suppress vegetation productivity in more arid climates of the subtropics and mid-latitudes of the northern hemisphere.

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Figure 2.1). Radiation levels are elevated at high altitudes due to a shorter path length of solar radiation travelling across the atmosphere and, consequently, a reduced attenuation of the radiation intensity. Atmospheric pressure and thus the partial pressure of oxygen declines with elevation. This implies reduced respiration and an increased efficiency of photosynthesis.

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Small-scale variations in vegetation may also be driven my variations in soil characteristics and bedrock lithology which influences drainage and soil chemistry (pH, nutrient availability). Where the ground is seasonally snow-covered, very small-scale terrain features (100-102) and dominant wind directions drive snow accumulation and dispersion, leading to substantial small-scale variations in maximum snow depth and the duration of seasonal snow cover - with implications for plants (Körner and Hiltbrunner 2021).

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Small-scale variations in vegetation may also be driven my variations in soil characteristics and bedrock lithology which influences drainage and soil chemistry (pH, nutrient availability). Where the ground is seasonally snow-covered, very small-scale terrain features (100-102 m) and dominant wind directions drive snow accumulation and dispersion, leading to substantial small-scale variations in maximum snow depth and the duration of seasonal snow cover - with implications for plants (Körner and Hiltbrunner 2021).

2.9 Species distribution modelling and ecological niche

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Hutchinson (1957; Araújo and Guisan 2006), each species has a fundamental niche that can be conceived as a domain in a multi-dimensional space defined by the environmental conditions. Environmental filtering yields the fundamental niche which is generally a subset of the Earth’s climate space (Figure 2.26). The actual, or realized niche is smaller as it is additionally constrained by biotic interactions with other species. Natural selection yields the realized niche. Several challenges for species distribution modelling exist (Zimmermann et al. 2010). For example, the species distribution is hardly ever in equilibrium with the environment, given that climate has been constantly changing (although not as rapidly as today for millions of years); topographic heterogeneity, climatic history, and ecological refugia affect the species distribution and how it varies under climate change; genetic adaptation can lead to populations within species that exhibit different responses to the environment; and niche stability over long time scales may be undermined not only by genetic adaptation, but also by physiological effects of CO2 which fundamentally alters photosynthesis and transpiration and will therefore shift water availability-related niche limits observed today.

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The approach to species distribution modelling is fundamentally rooted in the ecological niche concept. As formulated by Hutchinson (1957; Araújo and Guisan 2006), each species has a fundamental niche that can be conceived as a domain in a multidimensional space defined by the environmental conditions. Environmental filtering yields the fundamental niche which is generally a subset of the Earth’s climate space (Figure 2.26). The actual, or realized niche is smaller as it is additionally constrained by biotic interactions with other species. Natural selection yields the realized niche. Several challenges for species distribution modelling exist (Zimmermann et al. 2010). For example, the species distribution is hardly ever in equilibrium with the environment, given that climate has been constantly changing (although not as rapidly as today for millions of years); topographic heterogeneity, climatic history, and ecological refugia affect the species distribution and how it varies under climate change; genetic adaptation can lead to populations within species that exhibit different responses to the environment; and niche stability over long time scales may be undermined not only by genetic adaptation, but also by physiological effects of CO2 which fundamentally alters photosynthesis and transpiration and will therefore shift water availability-related niche limits observed today.

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2.10 Temporal variations of vegetation

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Spatial patterns in vegetation are influenced by how climate varies across different areas. Similarly, changes in vegetation are influenced by how climate changes over time. Vegetation change at temporal scales of thousands of years is recorded, for example, by pollen deposited in layered sediments. Given that they are preserved and that the sediment layers can be dated, the vegetation composition over time can be reconstructed. An example is given for the Moossee, near Bern in Figure 2.27. The pollen diagram documents how vegetation on the Swiss Plateau unterwent several major changes since the last Glacial. At around 19 kyr BP, a steppe tundra established, replaced around 16 kyr BP by a shrub tundra. At around 15 kyr BP, a boreal forest established before it was replaced by a temperate mixed oak forest at the beginning of the Holocene - the current warm period at 11,600 yr BP. A beech-dominated temperate forest, as it is common for this region today, established around 8200 yr BP. Figure 2.27 also shows that these biome replacements coincided with rapid climatic shifts and that the vegetation change was largely instantaneous. This instantaneous response of species composition is interpreted as a reflection of the importance of glacial refugia from which a species may rapidly expand upon climate change (Rey et al. 2020).

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Spatial patterns in vegetation are influenced by how climate varies across different areas. Similarly, changes in vegetation are influenced by how climate changes over time. Vegetation change at temporal scales of thousands of years is recorded, for example, by pollen deposited in layered sediments. Given that they are preserved and that the sediment layers can be dated, the vegetation composition over time can be reconstructed. An example is given for the Moossee, near Bern in Figure 2.27. The pollen diagram documents how vegetation on the Swiss Plateau underwent several major changes since the last Glacial. At around 19 kyr BP, a steppe tundra established, replaced around 16 kyr BP by a shrub tundra. At around 15 kyr BP, a boreal forest established before it was replaced by a temperate mixed oak forest at the beginning of the Holocene - the current warm period at 11,600 yr BP. A beech-dominated temperate forest, as it is common for this region today, established around 8200 yr BP. Figure 2.27 also shows that these biome replacements coincided with rapid climatic shifts and that the vegetation change was largely instantaneous. This instantaneous response of species composition is interpreted as a reflection of the importance of glacial refugia from which a species may rapidly expand upon climate change (Rey et al. 2020).

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Figure 2.29, bottom panel). The difference in climate and CO2 (global mean temperatures were around 6°C lower than at present; CO2 was at around 180 ppm, today it’s at over 420 ppm) caused forest biomes to recede and grasslands to expand across most of the globe. The upper panel of Figure 2.29 shows the simulated biome distribution. These simulation results are not based on a species distribution model, but on a Dynamic Global Vegetation Model that accounts for both climate and CO2 effects and simulates the distribution of PFTs from which biomes were derived here. The simulation of vegetation distribution at the level of PFTs instead of species is less affected by biotic interactions that are hard to simulate at global scale.

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diff --git a/ecohydrology.html b/ecohydrology.html index 6a99bca..eef4028 100644 --- a/ecohydrology.html +++ b/ecohydrology.html @@ -372,15 +372,15 @@

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Water cycles in the Earth system between the atmosphere, the ocean, the land biosphere and the cryosphere. The evaporation of water (H2O) from its liquid form to (gaseous) water vapour consumes energy (Section 7.2) and its condensation releases the same amount of energy in the form of heat again. Hence, the global water cycle is coupled to large energy transfers. For the Earth as a whole and as an annual average, 80 W m–2 are consumed for evaporation – more than three-quarters of the 98 W m–2 net radiation at the surface (Bonan 2015).

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Water cycles in the Earth system between the atmosphere, the ocean, the land biosphere and the cryosphere. The evaporation of water (H2O) from its liquid form to (gaseous) water vapor consumes energy (Section 7.2) and its condensation releases the same amount of energy in the form of heat again. Hence, the global water cycle is coupled to large energy transfers. For the Earth as a whole and as an annual average, 80 W m–2 are consumed for evaporation – more than three-quarters of the 98 W m–2 net radiation at the surface (Bonan 2015).

The vast majority (ca. 98%) of water on Earth is saline and is stored in the Oceans, inland seas, and saline groundwater (Figure 8.1 a). Among the total amount of freshwater, the vast majority is stored as ice. Only a small fraction of water on Earth cycles between the atmosphere, the ocean and land. However, this cycling is relatively rapid (see Exercise below).

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Oceans dominate in total evaporation (470 km3 yr-1, vs. 74 km3 yr-1 from land, Figure 8.1 b) and the majority of precipitation falls over oceans. However, since precipitation over oceans is smaller than evaporation from oceans (424 km3 yr-1 vs. 470 km3 yr-1), a net transfer of water from oceans to land exists. Almost all of the surplus of the land’s water balance runs off as river discharge back into the ocean. A small fraction is discharged into the ocean through groundwater.

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Oceans dominate in total evaporation (470 km3 yr-1, vs. 74 km3 yr-1 from land, Figure 8.1 b) and the majority of precipitation falls over oceans. However, since precipitation over oceans is smaller than evaporation from oceans (424 km3 yr-1 vs. 470 km3 yr-1), a net transfer of water from oceans to land exists. Almost all the surplus of the land’s water balance runs off as river discharge back into the ocean. A small fraction is discharged into the ocean through groundwater.

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Figure 8.1: Depiction of the present-day water cycle. In the atmosphere, which accounts for only 0.001% of all water on Earth, water primarily occurs as a gas (water vapour), but it is also present as ice and liquid water within clouds. The ocean is the primary water reservoir on Earth: it comprises mostly liquid water across much of the globe but also includes areas covered by ice in polar regions. Liquid freshwater on land forms surface water (lakes, rivers) and, together with soil moisture and mostly unusable groundwater stores, accounts for less than 2% of global water. Solid terrestrial water that occurs as ice sheets, glaciers, snow and ice on the surface, and permafrost currently represents nearly 2% of the planet’s water. Water that falls as snow in winter provides soil moisture and streamflow after melting, which are essential for human activities and ecosystem functioning. Note that these best estimates do not lead to a perfectly closed global water budget and that this budget has no reason to be closed given the ongoing human influence through both climate change (e.g., melting of ice sheets and glaciers, see Chapter 9) and water use (e.g., groundwater depletion through pumping into fossil aquifers, see Figure 8.10). Figure and caption from Douville et al. (2021).
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Figure 8.1: Depiction of the present-day water cycle. In the atmosphere, which accounts for only 0.001% of all water on Earth, water primarily occurs as a gas (water vapor), but it is also present as ice and liquid water within clouds. The ocean is the primary water reservoir on Earth: it comprises mostly liquid water across much of the globe but also includes areas covered by ice in polar regions. Liquid freshwater on land forms surface water (lakes, rivers) and, together with soil moisture and mostly unusable groundwater stores, accounts for less than 2% of global water. Solid terrestrial water that occurs as ice sheets, glaciers, snow and ice on the surface, and permafrost currently represents nearly 2% of the planet’s water. Water that falls as snow in winter provides soil moisture and streamflow after melting, which are essential for human activities and ecosystem functioning. Note that these best estimates do not lead to a perfectly closed global water budget and that this budget has no reason to be closed given the ongoing human influence through both climate change (e.g., melting of ice sheets and glaciers, see Chapter 9) and water use (e.g., groundwater depletion through pumping into fossil aquifers, see Figure 8.10). Figure and caption from Douville et al. (2021).
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We have encountered the vapour pressure deficit (VPD) and its control on transpiration in Section 4.4 and on evapotranspiration in Section 7.2.2. VPD is a measure of atmospheric humidity. This box is to explain how VPD relates to other metrics of atmospheric humidity and to the physics of moist air.

+

We have encountered the vapor pressure deficit (VPD) and its control on transpiration in Section 4.4 and on evapotranspiration in Section 7.2.2. VPD is a measure of atmospheric humidity. This box is to explain how VPD relates to other metrics of atmospheric humidity and to the physics of moist air.

The total pressure of a gas can be expressed as the sum of partial pressures of different components of a gas mixture. For moist air, we can distinguish the partial pressures of water vapor (\(e_a\)) and dry air (\(P_d\)) and write the total pressure of moist air as \[ P = P_d + e_a \;. -\] Both, the dry air and water vapour follow the ideal gas law. Expressed in molar form, it is \[ +\] Both, the dry air and water vapor follow the ideal gas law. Expressed in molar form, they are \[ P_d = \rho_d \frac{RT}{M_d} \\ +\text{ and } \\ e_a = \rho_v \frac{RT}{M_v} = \rho_v \frac{RT}{0.622 M_d} -\tag{8.1}\] Here, \(\rho_d\) is the density of dry air; \(\rho_v\) is the density of water vapor, \(R\) is the universal gas constant (8.314 J K-1 mol-1); \(T\) is temperature (in K). The factor 0.622 relates the molecular mass of water ($M_v = $ 18.02 g mol–1) to that of dry air ($M_d = $28.97 g mol–1).

+\tag{8.1}\]

+

Here, \(\rho_d\) is the density of dry air; \(\rho_v\) is the density of water vapor, \(R\) is the universal gas constant (8.314 J K-1 mol-1); \(T\) is temperature (in K). The factor 0.622 relates the molecular mass of water (\(M_v = 18.02\) g mol–1) to that of dry air (\(M_d = 28.97\) g mol–1).

The specific humidity \(q\) can be derived from Equation 8.1 as \[ q = \frac{\rho_v}{\rho_v + \rho_d} = \frac{0.622 e_a}{P-(1-0.622)e_a} -\] The vapour pressure deficit (\(D\)) is the difference between the actual vapour pressure \(e_a\) and the vapour pressure at saturation \(e_s(T)\) (where water condensates). \[ +\] The vapor pressure deficit (\(D\)) is the difference between the actual vapor pressure \(e_a\) and the vapor pressure at saturation \(e_s(T)\) (where water condensates). \[ D = e_s - e_a -\] The saturation vapour pressure is a function of air temperature (\(T\) in °C). This relationship is related to the Clausius-Clapeyron relation of the temperature dependence of vapor pressure. A relatively accurate, yet simple empirical equation for this relationship is the following. \[ +\] The saturation vapor pressure is a function of air temperature (\(T\) in °C). This relationship is related to the Clausius-Clapeyron relation of the temperature dependence of vapor pressure. A relatively accurate, yet simple empirical equation for this relationship is the following. \[ e_s(T) = 611.0 \; \exp \left( \frac{17.27 \; T}{T + 237.3} \right) -\] This equation calculates the the saturation vapour pressure \(e_s(T)\) in units of Pa.

+\] This equation calculates the the saturation vapor pressure \(e_s(T)\) in units of Pa.

Code @@ -443,14 +445,14 @@

geom_function(fun = calc_e_sat) + xlim(0, 35) + labs(x = "Temperature (°C)", - y = "Saturation vapour pressure (Pa)") + + y = "Saturation vapor pressure (Pa)") + theme_classic()

-
Figure 8.2: Saturation vapour pressure as a function of air temperature.
+
Figure 8.2: Saturation vapor pressure as a function of air temperature.
@@ -499,7 +501,7 @@

The different components to ET draw water from separate stores - from moisture in the root zone of vegetation for \(T\), from moisture in the top few centimeters of soil for \(E_S\), and from moisture adsorbed on canopy surfaces. Therefore, their evolution over time during dry (rain-free) phases is very different. While \(E_I\) drops to zero within 1-3 days as canopy surfaces become dry, \(E_S\) declines more slowly since the top soil takes longer to dry out to a degree where \(E_S\) becomes zero. In contrast, \(T\) takes much longer to decline as plants may draw moisture from much larger belowground stores - from water stored in the soil and sub-soil across the entire rooting zone.

8.2.1 Cumulative water deficits

-

The latent heat flux and precipitation have clear seasonal variations in most biomes. As described above, for annual totals, \(P \geq E\). However, over shorter periods of time, ET may exceed precipitation (\(E > P\)). Of course, on a rain-free day \(P=0\), while \(E>0\). In some climates, \(E > P\) may also be sustained over several weeks to months. For example, in Mediterranean or Monsoonal climates the asynchroneity of precipitation and solar radiation (and thus net radiation) can create a seasonal imbalance of water and energy availability and thus of water inputs and losses. As an example, Figure 8.4 a shows the multi-year average monthly total precipitation (\(P\)) and ET (the same as \(E\)) for an ecosystem in a Mediterranean climate - a woody savannah in California (eddy covariance measurement site US-Ton). It shows that \(E>P\) on average for May-Sep each year. The difference in monthly totals is relatively small - on the order of 10 mm or less. However, considering the cumuluative sum of daily \(E-P\) during the dry summer months for calculating the cumulative water deficit (Figure 8.4 b) shows that the maximum attained seasonal water deficit is 40-80 mm for this site (and varies between years). This is a substantial amount. Where does this water come from? Of course, it’s drawn by plants through their roots from the rooting zone, including the soil and potentially also the sub-soil or even the groundwater. How much water can be stored in the soil is the topic of the next section.

+

The latent heat flux and precipitation have clear seasonal variations in most biomes. As described above, for annual totals, \(P \geq E\). However, over shorter periods of time, ET may exceed precipitation (\(E > P\)). Of course, on a rain-free day \(P=0\), while \(E>0\). In some climates, \(E > P\) may also be sustained over several weeks to months. For example, in Mediterranean or Monsoonal climates, the asynchroneity of precipitation and solar radiation (and thus net radiation) can create a seasonal imbalance of water and energy availability and thus of water inputs and losses. As an example, Figure 8.4 a shows the multi-year average monthly total precipitation (\(P\)) and ET (the same as \(E\)) for an ecosystem in a Mediterranean climate - a woody savannah in California (eddy covariance measurement site US-Ton). It shows that \(E>P\) on average for May-Sep each year. The difference in monthly totals is relatively small - on the order of 10 mm or less. However, considering the cumulative sum of daily \(E-P\) during the dry summer months for calculating the cumulative water deficit (Figure 8.4 b) shows that the maximum attained seasonal water deficit is 40-80 mm for this site (and varies between years). This is a substantial amount. Where does this water come from? Of course, it’s drawn by plants through their roots from the rooting zone, including the soil and potentially also the sub-soil or even the groundwater. How much water can be stored in the soil is the topic of the next section.

@@ -573,13 +575,13 @@

The matric potential is commonly expressed in units of mm or Pa. It can also be expressed as the suction head which is the negative of the matric potential.

-

Imagine you stick a straw into the soil and try to suck out the water. When the soil is wet, you initially don’t have to suck hard to withdraw water. The suction head has a small positive value. The matric potential has a small negative value. After you have sucked out some amount water from the soil, you have to start sucking “harder” to extract the same amount again as the soil dries out. That’s because the matric potential declines to more negative numbers (and the suction head increases to larger positive numbers) for drier soils. Staying with the straw analogue, -1 mm matric potential (or 1 mm suction head) is equivalent sucking from your straw such that that 1 mm of water doesn’t drain out of the straw (ignoring capillary forces).

+

Imagine you stick a straw into the soil and try to suck out the water. When the soil is wet, you initially don’t have to suck hard to withdraw water. The suction head has a small positive value. The matric potential has a small negative value. After you have sucked out some amount water from the soil, you have to start sucking “harder” to extract the same amount again as the soil dries out. That’s because the matric potential declines to more negative numbers (and the suction head increases to larger positive numbers) for drier soils. Staying with the straw analogue, -1 mm matric potential (or 1 mm suction head) is equivalent sucking from your straw such that 1 mm of water doesn’t drain out of the straw (ignoring capillary forces).

The same can also be expressed as a pressure - the gravitational force per unit area: \[ p = \frac{F_G}{A} = \frac{mg}{A} -\] 1 mm corresponds to 1 kg m-2 and \(g =\) 9.81 m s-2. Therefore \[ +\] 1 mm corresponds to 1 kg m-2 and \(g =\) 9.81 m s-2. Therefore, \[ 1 \; \text{mm} = 9.81 \; \text{kg m}^{-1} \text{s}^{-2} = 9.81 \; \text{Pa} \]

-

The soil matric potential \(\psi_s\) is related to the soil volumentric water content \(\theta\) in a highly non-linear fashion. It stays near zero for a wide range \(\theta\) and drops off sharply as \(\theta\) falls below a certain range. Reflecting the large variation in how strongly water is bound to the soil matric across different soil texture classes, the relationship \(\psi_s(\theta)\) varies strongly across soil types. An empirical equation for this relationship is given by Clapp and Hornberger (1978) as: \[ +

The soil matric potential \(\psi_s\) is related to the soil volumetric water content \(\theta\) in a highly non-linear fashion. It stays near zero for a wide range \(\theta\) and drops off sharply as \(\theta\) falls below a certain range. Reflecting the large variation in how strongly water is bound to the soil matric across different soil texture classes, the relationship \(\psi_s(\theta)\) varies strongly across soil types. An empirical equation for this relationship is given by Clapp and Hornberger (1978) as: \[ \psi_s = \psi_\text{SAT} \left( \frac{\theta}{\theta_\text{SAT}} \right)^{-b} \tag{8.4}\] Here, \(\psi_\text{SAT}\) is the soil matric potential at saturation, that is when \(\theta = \theta_\text{SAT}\). The exponent \(b\) determines how rapidly the matric potential declines towards low \(\theta\). These parameters have different values depending on the soil texture class, resulting in different functional forms of the relationship between volumetric water content and the matric potential.

@@ -907,7 +909,7 @@

\(\rho\) is the density of water (kg m-3), \(g\) is the gravitational constant (9.81 m s-2), and \(h\) is the height of the tree (m), measured from the average depth of the roots to the average height of the leaves. With the units of \(\psi_l\) and \(\psi_s\) in Pa and \(T\) in units of (kg m-2 s-1), \(G_p\) is in units of (s m-1). Equation 8.6 expresses the “supply” of water from the soil. From Equation 4.11, we know how the “demand” for water is determined by the vapor pressure deficit \(D\) and the stomatal conductance \(g_s\). The \(T\) in Equation 8.6 thus has to be equal to the \(T\) from Equation 4.11 (where it was called \(E\)): \[ T = 1.6 \; g_s \; D -\tag{8.7}\] These equations illustrate some important points. First, a positive (upward) transpiration stream \(T\) that satisfies the demand from the atmosphere (Equation 8.7) can only be maintained if the leaf water potential is more negative than the soil water potential. Second, as the soil water potential becomes more negative, the leaf water potential also has to become more negative to transport the amount of water that is “demanded” by the atmosphere and determined by \(D\) and \(g_s\). Third, tall trees have to sustain more negative leaf water potentials than short for a given soil dryness and transpiration rate. By setting the two equations for \(T\) equal and solving for the leaf water potential \(\psi_l\) also illustrates how soil moisture (\(\psi_s\)) and VPD (\(D\)) have an interactive effect on \(\psi_l\).

+\tag{8.7}\] These equations illustrate some important points. First, a positive (upward) transpiration stream \(T\) that satisfies the demand from the atmosphere (Equation 8.7) can only be maintained if the leaf water potential is more negative than the soil water potential. Second, as the soil water potential becomes more negative, the leaf water potential also has to become more negative to transport the amount of water that is “demanded” by the atmosphere and determined by \(D\) and \(g_s\). Third, tall trees have to sustain more negative leaf water potentials than short ones for a given soil dryness and transpiration rate. By setting the two equations for \(T\) equal and solving for the leaf water potential \(\psi_l\) also illustrates how soil moisture (\(\psi_s\)) and VPD (\(D\)) have an interactive effect on \(\psi_l\).

Responses of plants to water stress are physiologically triggered through the sensing of leaf water potentials. In other words, \(\psi_l\) is the central quantity that drives water stress responses of plants. Understanding how \(\psi_l\) responds to environmental factors is thus key to understanding how water stress (stomatal closure, damaging drought stress) is a function of soil and air dryness, modified by plant hydraulic traits determining \(G_p\).

@@ -1008,8 +1010,8 @@

-

Sustaining very negative water potentials along the transport pathway can be dangerous for the plant. As described in the box above, the whole-plant conductance declines with increasingly negative negative water potentials. This is because the very negative water potentials can only be sustained if no air is in contact with the water inside the xylem. As pressures become very negative, air may seep in and create embolisms. If the conductance was to drop towards zero, transpiration would collapse and embolisms would be excessive - creating potentially irreversible damage and triggering branch and eventually tree mortality due to hydraulic failure.

-

Plants can avoid such water stress and hydraulic failure through stomatal regulation (see also Section 4.4.3). To avoid embolisms, stomata close (stomatal conductance is reduced) when the soil water potential declines to increasingly negative values. As a consequence transpiration, and also CO2 assimilation, are decline. Once soil moisture across the rooting zone is depleted and the soil water potential reach very negative values, vegetation activity (transpiration and assimilation) comes to a halt. However, this rarely happens since water loss cannot be fully avoided even if stomata are fully closed and plants have evolved adaptations and are adjusted through plasticity in various traits to avoid a complete depletion of moisture stores across the rooting zone and to limit water losses. Variations in rooting depth are an expression of this adaptation and acclimation. Leaf properties with thick, waxy leaves that prevent water loss, or a drought-deciduous strategy are other examples.

+

Sustaining very negative water potentials along the transport pathway can be dangerous for the plant. As described in the box above, the whole-plant conductance declines with increasingly negative water potentials. This is because the very negative water potentials can only be sustained if no air is in contact with the water inside the xylem. As pressures become very negative, air may seep in and create embolisms. If the conductance was to drop towards zero, transpiration would collapse and embolisms would be excessive - creating potentially irreversible damage and triggering branch and eventually tree mortality due to hydraulic failure.

+

Plants can avoid such water stress and hydraulic failure through stomatal regulation (see also Section 4.4.3). To avoid embolisms, stomata close (stomatal conductance is reduced) when the soil water potential declines to increasingly negative values. As a consequence, transpiration, as well as CO2 assimilation, decline. Once soil moisture across the rooting zone is depleted and the soil water potential reach very negative values, vegetation activity (transpiration and assimilation) comes to a halt. However, this rarely happens since water loss cannot be fully avoided even if stomata are fully closed and plants have evolved adaptations and are adjusted through plasticity in various traits to avoid a complete depletion of moisture stores across the rooting zone and to limit water losses. Variations in rooting depth are an expression of this adaptation and acclimation. Leaf properties with thick, waxy leaves that prevent water loss, or a drought-deciduous strategy are other examples.

Different plant species respond differently to water stress (variations in soil water potential) and are characterised with different hydraulic traits that determine the stomatal response to soil and leaf water potentials. Two examples are shown in Figure 8.12

@@ -1462,7 +1464,7 @@

<

8.7 Energy and water limitation across the globe

Ecosystems are commonly distinguished into energy-limited and water-limited systems. This notion relates to the dominant limiting resource and to the relations described in Section 8.5. When the bucket is full, the system is energy-limited. When it gets depleted, the system becomes water-limited. Of course, this is a simplification. The relations described in Section 8.5 really refer to a spectrum, rather than a binary classification.

-

Furthermore, water-limited conditions may be temporally limited and interspersed by energy-limited periods. Also, the water bucket model, as formulated above, suggests that water-limitation sets in at the point when soil moisture falls below the field capacity. However, as long as the net radiation and the atmospheric vapour pressure deficit are not “excessive”, the demand for transpiration (Equation 8.7) may be met by the supply (Equation 8.8) without substantial stomatal closure during the daytime.

+

Furthermore, water-limited conditions may be temporally limited and interspersed by energy-limited periods. Also, the water bucket model, as formulated above, suggests that water-limitation sets in at the point when soil moisture falls below the field capacity. However, as long as the net radiation and the atmospheric vapor pressure deficit are not “excessive”, the demand for transpiration (Equation 8.7) may be met by the supply (Equation 8.8) without substantial stomatal closure during the daytime.

A common classification of ecosystems into aridity classes is given in Table 8.1 based on Middleton and Thomas (1992). This considers the moisture index as defined by P/PET.

@@ -1509,7 +1511,7 @@

Section 8.5. The green vegetation cover, measured by fAPAR, initially increases linearly with increasing P/PET for low values of the latter. Beyond a certain value, fAPAR no longer shows a relationship with P/PET (Figure 8.23).

-

The slope of the initial linear increase of fAPAR vs. P/PET reflects the water-carbon coupling. The amount of active green and transpiring foliage area is limited by water availability. research has shown that the relationship shown in Figure 8.23 is shifting such that the slope of the initial increase tends to steepen over time (Donohue et al. 2013; Ukkola et al. 2016). This is related to the fact that under rising CO2, stomatal conductance tends to be reduced (Figure 4.11) and the water use efficiency is enhanced (Section 4.4.1). In other words, a larger area of green leaves per unit ground area can be sustained for a given level of aridity.

+

The slope of the initial linear increase of fAPAR vs. P/PET reflects the water-carbon coupling. The amount of active green and transpiring foliage area is limited by water availability. research has shown that the relationship shown in Figure 8.23 is shifting such that the slope of the initial increase tends to steepen over time (Donohue et al. 2013; Ukkola et al. 2016). This is related to the fact that under rising CO2, stomatal conductance tends to increase (Figure 4.11) and the water use efficiency is enhanced (Section 4.4.1). In other words, a larger area of green leaves per unit ground area can be sustained for a given level of aridity.

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Chapter 3, we conceived the global carbon cycle as a system of three pools (atmosphere, land, ocean). The C dynamics in the land biosphere were modeled using a 1-box model which receives C inputs through photosynthesis and loses C through a constant turnover. In Chapter 4, we focused on the processes driving terrestrial CO2 uptake. In this chapter, we are unboxing the 1-box model and introduce the processes that determine C flows in ecosystems and their C balance. We will describe the C dynamics of an ecosystem, not as a single box with a single and constant turnover, but as a cascade of C, made of of multiple pools with different turnover rates, and where the partitioning (allocation) of the cascading C into the different pools is influenced by the environment and by the ecosystem state.

+

In Chapter 3, we conceived the global carbon cycle as a system of three pools (atmosphere, land, ocean). The C dynamics in the land biosphere were modeled using a 1-box model which receives C inputs through photosynthesis and loses C through a constant turnover. In Chapter 4, we focused on the processes driving terrestrial CO2 uptake. In this chapter, we are unboxing the 1-box model and introduce the processes that determine C flows in ecosystems and their C balance. We will describe the C dynamics of an ecosystem, not as a single box with a single and constant turnover, but as a cascade of C, made of multiple pools with different turnover rates, and where the partitioning (allocation) of the cascading C into the different pools is influenced by the environment and by the ecosystem state.

5.1 Ecosystem carbon flows and pools

At the ecosystem-level, C dynamics can be described as the flows (fluxes) between carbon pools that represent C in non-structural forms, leaves (foliage), (stem) wood, fine roots, litter, and soil (Figure 5.1). C is respired by plants (autotrophic respiration) and by soil microbes (heterotrophic respiration). C in live vegetation biomass is turned over to produce litter (litterfall) as trees shed their leaves and lose branches (over years) and as they die (over decades to centuries). Plant mortality is related to the size and age of a tree and may be driven by disturbances (fire, pests, extreme drought and heat). Within years, litter is respired or transformed into soil organic C where it may be stabilized for centuries and more. Heterotrophic respiration originates from litter and soil C decomposition by microbes (fungi and bacteria).

@@ -443,7 +443,7 @@

\(C_\mathrm{VOC}\) and \(C_\mathrm{exu}\) are difficult to measure in the field and tend to be smaller than the other terms. Therefore, the biomass productivity is more commonly quantified from observations. \[ \mathrm{BP} = \Delta C_\mathrm{leaves} + \Delta C_\mathrm{roots} + \Delta C_\mathrm{wood} -\tag{5.3}\] Note that there is often some ambiguity in definitions of in the literature and ‘NPP’ is used instead of ‘BP’. BP is expressed as a flux of C per unit square meter (for example gC m-2 yr-1). It measures the amount of biomass C produced per unit ground area and time. NPP is expressed in the same units and additionally includes C produced and released as volatie organic compounds and exudates. These do not contribute to biomass of the plant itself and are relatively short-lived. However, they are not in the form of oxidized C (as is \(R_a\)) and therefore are counted towards NPP.

+\tag{5.3}\] Note that there is often some ambiguity in definitions in the literature and ‘NPP’ is often used instead of ‘BP’. BP is expressed as a flux of C per unit square meter (for example gC m-2 yr-1). It measures the amount of biomass C produced per unit ground area and time. NPP is expressed in the same units and additionally includes C produced and released as volatile organic compounds and exudates. These do not contribute to the biomass of the plant itself and are relatively short-lived. However, they are not in the form of oxidized C (as is \(R_a\)) and therefore are counted towards NPP.

The ratio of NPP:GPP is commonly referred to as the ecosystem carbon use efficiency (CUE), and BP:GPP as the biomass production efficiency (BPE).

\[ \begin{aligned} @@ -549,7 +549,7 @@

Soil organic matter (SOM) refers to the organic mass fraction in soils. It consists of litter at advanced stages of decomposition and of microbial biomass and necromass. The decomposition rate of organic matter in soil can be strongly reduced compared to the decomposition rate of litter. This is due to stabilisation processes. Stabilisation of SOM arises from the chemical transformation through soil micro and macro-fauna and through physical protection in the soil matrix (association to minerals, occlusion in soil aggregates). Yet, the decomposition of SOM is rarely fully suppressed (except under fully anoxic conditions).

-

SOM exposed to decomposition is consumed by microbes (fungi and bacteria) and fuels their growth. As they consume organic matter - like humans - they use the chemical energy “stored” in organic matter and oxidise the carbohydrates to CO2. The CO2 is respired away in gaseous form and leaves the soil volume and is referred to as heterotrophic respiration (\(R_h\)). The rate of microbial activity and hence \(R_h\) increases with temperature in a similar way as the temperature dependency of \(R_a\). \(R_h\) also depends on soil moisture and has a peaked relationship. It initially increases with increasing soil moisture until a point where the oxygen availability in the soil probihits activity by heterotrophic microorganisms. At this point, \(R_h\) drops sharply. Under water-logged soil conditions, SOM decomposition and \(R_h\) are suppressed. The temperature dependency of \(R_h\), implemented in the LPJ vegetation model is the same as described for \(R_m\) by Equation 5.1.

+

SOM exposed to decomposition is consumed by microbes (fungi and bacteria) and fuels their growth. As they consume organic matter - like humans - they use the chemical energy “stored” in organic matter and oxidise the carbohydrates to CO2. The CO2 is respired away in gaseous form and leaves the soil volume and is referred to as heterotrophic respiration (\(R_h\)). The rate of microbial activity and hence \(R_h\) increases with temperature in a similar way as the temperature dependency of \(R_a\). \(R_h\) also depends on soil moisture and has a peaked relationship. It initially increases with increasing soil moisture until a point where the oxygen availability in the soil prohibits activity by heterotrophic microorganisms. At this point, \(R_h\) drops sharply. Under water-logged soil conditions, SOM decomposition and \(R_h\) are suppressed. The temperature dependency of \(R_h\), implemented in the LPJ vegetation model is the same as described for \(R_m\) by Equation 5.1.

SOM plays important roles for global biogeochemical cycles and for land-climate interactions. SOM is a vast store of C (~1700 PgC, see Figure 3.1). The soil organic matter content is an important measure for nutrient availability, and strongly influences the water holding capacity of the soil (Chapter 7). C in soil organic matter (SOM) has a turnover time on the order of years to centuries. Under anoxic conditions, the turnover time of SOM can attain millennia. As for litter decomposition, the rate of SOM decomposition (\(k\) in Equation 5.6) is controlled by the soil temperature and moisture.

@@ -568,7 +568,7 @@

where \(t\) is time. Indeed, the litter mass shown in Figure 5.5 exhibits an exponential decline over time.

Also SOM decay can be represented following Equation 5.6. In words, the amount of SOM C that gets decomposed in a given amount of time is proportional to the SOM C pool size. The input into that pool is independent of the pool itself.

-

Litter and SOM pools in terrestrial biosphere models are most commonly represented by an array of pools that are characterized by different turnover times and that are connected following a specific structure. The litter pools receive inputs from biomass turnover. Decomposed litter is diverted to SOM pools. Fast-decomposing litter is diverted too a SOM pool with a short turnover time (high \(k\)), slow-decomposing litter is diverted to a SOM pool with a long turnover time. C is respired away as CO2 during litter and SOM decomposition. The microbial carbon use efficiency (\(e\)) determines the ratio of the decomposed C contributing to microbial biomass growth. \((1-e)\) is respired as CO2.

+

Litter and SOM pools in terrestrial biosphere models are most commonly represented by an array of pools that are characterized by different turnover times and that are connected following a specific structure. The litter pools receive inputs from biomass turnover. Decomposed litter is diverted to SOM pools. Fast-decomposing litter is diverted to a SOM pool with a short turnover time (high \(k\)), slow-decomposing litter is diverted to a SOM pool with a long turnover time. C is respired away as CO2 during litter and SOM decomposition. The microbial carbon use efficiency (\(e\)) determines the ratio of the decomposed C contributing to microbial biomass growth. \((1-e)\) is respired as CO2.

@@ -591,7 +591,7 @@

(Odum 1969).

@@ -603,8 +603,8 @@

(Luyssaert et al. 2008). Biometric data (forest inventories) and eddy covariance flux measurements from forests do not show a clear decline of NEP towards zero with increasing stand age, but rather show a sustained positive NEP over several decades to centuries since forest stand development.

-

Will forests accumulate C infinitely? Tracking soil C stocks over millennia is per se not possible but clear patterns of a positive influence of soil age on SOM content would have to be evident in data - but are not. Biomass C stocks do not increase indefinitely, either. Individual trees in maturing forest stands continue accumulating biomass but the lifetime of a tree is limited due to hydraulic, mechanical, or C balance constraints whereby increasing respiratory costs pose limits to further growth and may trigger mortality. Self-thinning drives the exclusion of individual trees based on the competition for limited resources and leads to a negative relationship between the number and the average size of trees in a maturing forest stand (see Section 5.4). Therefore, although individual trees may accumulate C in the form of biomass for centuries, the biomass C accumulation at the stand level is much lower due to the declining tree number and the associated mortality, turnover, and decomposition of affected trees.

+

However, field data of biomass stocks in mature forests seem to contradict Odum’s steady state (and zero NEP) model (Luyssaert et al. 2008). Biometric data (forest inventories) and eddy covariance flux measurements from forests do not show a clear decline of NEP towards zero with increasing stand age, but rather show a sustained positive NEP over several decades to centuries since forest stand development.

+

Will forests accumulate C indefinitely? Tracking soil C stocks over millennia is per se not possible but clear patterns of a positive influence of soil age on SOM content would have to be evident in data - but are not. Biomass C stocks do not increase indefinitely, either. Individual trees in maturing forest stands continue accumulating biomass but the lifetime of a tree is limited due to hydraulic, mechanical, or C balance constraints whereby increasing respiratory costs pose limits to further growth and may trigger mortality. Self-thinning drives the exclusion of individual trees based on the competition for limited resources and leads to a negative relationship between the number and the average size of trees in a maturing forest stand (see Section 5.4). Therefore, although individual trees may accumulate C in the form of biomass for centuries, the biomass C accumulation at the stand level is much lower due to the declining tree number and the associated mortality, turnover, and decomposition of affected trees.

Very old stands are dominated by few very large individual trees that contribute strongly to the total ecosystem biomass. However, also these individuals are inevitably affected by mortality. Once they fall, the ecosystem C stock rapidly declines (NEP is negative) and they create a forest gap that enables younger and smaller individuals to benefit from increased light levels. Smaller individuals around the newly formed gap accelerate growth, reach the canopy, and eventually fill the gap.

These dynamics imply that the NEP is rarely zero, but is positive for most of the time, except when affected by rare mortality events of large individuals. The spatial extent of a forest gap is on the order of 100-101 m and the maximum tree longevity is on the centuries (and the probability of a tree dying in a given year is its inverse - on the order of 10-2). This implies that the probability of observing a gap formation within a given areal extent is a function of the size of the areal extent. The larger the areal extent, the larger the probability that the influence of gap formation on NEP is captured and the large negative NEP of the gap is balanced by the small positive NEP of the remaining forest area. With an increasing size of the areal extent, the mean NEP should therefore tend to zero.

Forest monitoring plots are usually on the order of 20-50 m in radius. Hence, such data is sensitive to whether the observed plots are a representative sample of forest dynamics and forest gap formation across the landscape.

@@ -648,7 +648,7 @@

Figure 5.9 illustrates the pivotal role of BPE in determining how much C enters more long-lived storage as biomass vs. its largely immediate loss through respiration, of allocation in diverting C streams along cascades of very different turnover times (e.g., leaf vs. wood allocation), of microbial carbon use efficiency, and of processes determining the partitioning of C into (protected) slowly decomposing SOM pools and more rapidly decomposing SOM pools.

In Chapter 3, we simulated the response of terrestrial C storage to an increased GPP using a 1-box model and 1st-order decay. In this Chapter, we have “unboxed” C storage in terrestrial ecosystems, distinguishing a suite of pools and fluxes, arranged in a cascading order. When considering the response of this system to a change in GPP, how does the more complex representation affect the dynamics?

-

A key characteristic of the 1st order decay model is that the steady-state C pool size \(C^\ast\) is proportional to (is linearly dependent on) the input flux (Equation 3.4). Hence, with an change in the input flux of \(x = I/I_0\), the steady-state pools size changes also by \(x = C^\ast/C^\ast_0\).

+

A key characteristic of the 1st order decay model is that the steady-state C pool size \(C^\ast\) is proportional to (is linearly dependent on) the input flux (Equation 3.4). Hence, with a change in the input flux of \(x = I/I_0\), the steady-state pools size changes also by \(x = C^\ast/C^\ast_0\).

It can be demonstrated (see Box ‘Simulating the C cascade’ below) that when considering the following properties for the C cascade model:

  • 1st-order decay dynamics of all pools
    • @@ -656,7 +656,7 @@

    …, the same linear dependency of the total system C storage \(\sum_i C_i^\ast\) emerges: \[ \frac{I}{I_0} = \frac{\sum_i C_i^\ast}{\sum_i C_{i,0}^\ast} = \frac{C_i^\ast}{C_{i,0}^\ast}, \; \forall i -\] The symbol \(\forall\) means ‘for all’. However, whether a model with constant \(\alpha\), \(k_i\), \(e\), and \(f_\mathrm{fast}\) is a good representation of real ecosystems’ responses to environmental change is questionable. It is well established, for example, that \(\alpha\) is very sensitive altered soil nutrient availability and changes in CO2 experiments (Poorter et al. 2012). The turnover rate of biomass in forests (or tree longevity) may be affected by accelerated self-thinning if environmental change positively influences tree-level growth (e.g., through CO2 fertilization or an extension of the growing season) (Marqués et al. 2023). This implies a departure from the linear systems behavior of the C cascade model described by the two points above.

    +\]     The symbol \(\forall\) means ‘for all’. However, whether a model with constant \(\alpha\), \(k_i\), \(e\), and \(f_\mathrm{fast}\) is a good representation of real ecosystems’ responses to environmental change is questionable. It is well established, for example, that \(\alpha\) is very sensitive to altered soil nutrient availability and changes in CO2 experiments (Poorter et al. 2012). The turnover rate of biomass in forests (or tree longevity) may be affected by accelerated self-thinning if environmental change positively influences tree-level growth (e.g., through CO2 fertilization or an extension of the growing season) (Marqués et al. 2023). This implies a departure from the linear systems behavior of the C cascade model described by the two points above.

- +@@ -518,18 +519,18 @@

Table 3.1: Pre-industrial pool sizes, input fluxes, and turnover times of major pools of the global carbon cycle. The preindustrial input flux into the atmosphere is calculated as the sum of fluxes from volcanism, total respiration and fire, freshwater, and ocean-atmosphere gas exchange from Figure 3.1. The input flux into the surface ocean is the sum of ocean-atmosphere gas exchange and the flux from intermediate and deep sea. The flux from marine biota is not additional to the ocean-atmosphere exchange flux. The pool size of the biosphere is taken as the sum of vegetation and soils. The permafrost C pool is relatively inert. The size of the lithosphere C pool includes C in the form of sedimentary (carbonate) rocks and kerogens (solid, insoluble organic matter in sedimentary rocks). Its estimate is based on Falkowski et al. (2000). The input flux into the lithosphere is calculated as the sum of burial on land, rock weathering, and ocean floor sedimentationTable 3.1: Pre-industrial pool sizes, input fluxes, and turnover times of major pools of the global carbon cycle. The pre-industrial input flux into the atmosphere is calculated as the sum of fluxes from volcanism, total respiration and fire, freshwater, and ocean-atmosphere gas exchange from Figure 3.1. The input flux into the surface ocean is the sum of ocean-atmosphere gas exchange and the flux from intermediate and deep sea. The flux from marine biota is not additional to the ocean-atmosphere exchange flux. The pool size of the biosphere is taken as the sum of vegetation and soils. The permafrost C pool is relatively inert. The size of the lithosphere C pool includes C in the form of sedimentary (carbonate) rocks and kerogens (solid, insoluble organic matter in sedimentary rocks). Its estimate is based on Falkowski et al. (2000). The input flux into the lithosphere is calculated as the sum of burial on land, rock weathering, and ocean floor sedimentation.
-

It should be noted that the turnover time \(\tau\) describes the average time that an atom of C resides in the respective pool. This is a simplification. In the C pool ‘terrestrial biosphere’, not every C atom has the same probability of being oxidized and respired as CO2. Hence, in reality, \(\tau\) is a wide distribution, ranging from seconds to years for non-structural carbon derived from photosynthesis, decades to centuries for C in woody biomass, and to millennia for a small fraction of soil organic matter, especially if the C is protected from oxidation, for example in water-logged soils. The turnover time should therefore be understood as a diagnostic, useful for describing the average systems dynamics in a simplified way, and subsuming multiple processes that operate at different time scales, contributing to different portions of C conversion to CO2.

-

The range of turnover times (e.g., within the terrestrial biosphere) arise because C is transferred between multiple pools within the biosphere and the ocean. Going to the next more detailed level of abstraction (model representation), multiple C pools in terrestrial ecosystems can be distinguished (e.g., non-structural C, leaves, roots, wood, litter, soil organic matter, microbes). Some C “cascades” through multiple pools, some is quickly respired back into the atmosphere. The interpretation that \(k\) equals the inverse of the turnover time \(\tau\), and that the turnover time equals the mean age of all C atoms in that pool, and that the mean transit time (the time it takes between an atom of C entering a pool until it exits that pool again) equals \(\tau\) is only valid for certain cases, and not for “C cascades” with fluxes between multiple pools. Requirements are that we’re dealing with a single well-mixed pool, that this pool is at steady-state, that it has been so for an infinitely long time, that \(I\) and \(k\) are constant over time, and the flux leaving the pool is a linear function of the pool size (\(O=kC\)) (Sierra et al. 2017). The transit time is the same as residence time - a term used more commonly in hydrology.

+

It should be noted that the turnover time \(\tau\) describes the average time that an atom of C resides in the respective pool. This is a simplification. In the C pool ‘terrestrial biosphere’, not every C atom has the same probability of being oxidized and respired as CO2. Hence, in reality, the residency time of each C atom follows a wide distribution, ranging from seconds to years for non-structural carbon derived from photosynthesis, decades to centuries for C in woody biomass, and to millennia for a small fraction of soil organic matter, especially if the C is protected from oxidation, for example in water-logged soils. The turnover time should therefore be understood as a diagnostic, useful for describing the average systems dynamics in a simplified way, and subsuming multiple processes that operate at different time scales, contributing to different portions of C conversion to CO2.

+

The range of turnover times (e.g., within the terrestrial biosphere) arises because C is transferred between multiple pools within the biosphere and the ocean. Going to the next more detailed level of abstraction (model representation), multiple C pools in terrestrial ecosystems can be distinguished (e.g., non-structural C, leaves, roots, wood, litter, soil organic matter, microbes). Some C “cascades” through multiple pools, while some is quickly respired back into the atmosphere. The interpretation that \(k\) equals the inverse of the turnover time \(\tau\), and that the turnover time equals the mean age of all C atoms in that pool, and that the mean transit time (the time it takes between an atom of C entering a pool until it exits that pool again) equals \(\tau\) is only valid for certain cases, and not for “C cascades” with fluxes between multiple pools. Requirements are that we’re dealing with a single well-mixed pool, that this pool is at steady-state, that it has been so for an infinitely long time, that \(I\) and \(k\) are constant over time, and the flux leaving the pool is a linear function of the pool size (\(O=kC\)) (Sierra et al. 2017). The transit time is the same as residence time - a term used more commonly in hydrology.

3.3 The anthropogenic perturbation

-

Although fossil fuels are formed by natural processes of the C cycle, their combustion can be regarded as an external input of C into the (modern) global C cycle. This is because the time scale at which the reservoir of fossil fuels is depleted (102 yr) stands in stark contrast to the time scale at which it was formed (108 yr, see turnover time of C in the lithosphere in Table 3.1). The C is added in the form of CO2 to the atmosphere from where it is taken up by the ocean through diffusion and equilibration of the ocean surface water’s CO2 partial pressure with the atmosphere’s CO2 partial pressure, and by the terrestrial biosphere through photosynthesis. It is important to note that CO2 in the atmosphere does not decay through physical or chemical processes, nor are there C sinks on land or in the ocean that remove C away from the “fast” C cycle - except the burial into sediments (see Figure 3.1 and Table 3.1). However the magnitude of the burial fluxes are dwarfed by the magnitude of C inputs through the combustion of fossil fuels and deforestation. Hence, the present-day C emissions drive an accumulation of the total amount of C cycling in the “fast” C cycle and the added C gets redistributed between the spheres. The net fluxes from the atmosphere into land ecosystems and the ocean arise because the total terrestrial and oceanic C pools are increasing as CO2 is emitted into the atmosphere and the atmospheric CO2 concentration is rising. In subsequent chapters (Chapter 4 and Chapter 14), we will learn about the processes driving the CO2 uptake by land and ocean and the dynamics of the C redistribution in the Earth system. In this chapter, we will look at the global C budget - how much C has been emitted by the combustion of fossil fuels and deforestation and how much of this C has accumulated in the atmosphere and how much has been taken up by the ocean and the terrestrial biosphere?

+

Although fossil fuels are formed by natural processes of the C cycle, their combustion can be regarded as an external input of C into the (modern) global C cycle. This is because the time scale at which the reservoir of fossil fuels is depleted (102 yr) stands in stark contrast to the time scale at which it was formed (108 yr, see turnover time of C in the lithosphere in Table 3.1). The C is added in the form of CO2 to the atmosphere from where it is taken up by the ocean through diffusion and equilibration of the ocean surface water’s CO2 partial pressure with the atmosphere’s CO2 partial pressure, and by the terrestrial biosphere through photosynthesis. It is important to note that CO2 in the atmosphere does not decay through physical or chemical processes, nor are there C sinks on land or in the ocean that remove C away from the “fast” C cycle - except the burial into sediments (see Figure 3.1 and Table 3.1). However, the magnitude of the burial fluxes is dwarfed by the magnitude of C inputs through the combustion of fossil fuels and deforestation. Hence, the present-day C emissions drive an accumulation of the total amount of C cycling in the “fast” C cycle and the added C gets redistributed between the spheres. The net fluxes from the atmosphere into land ecosystems and the ocean arise because the total terrestrial and oceanic C pools are increasing as CO2 is emitted into the atmosphere and the atmospheric CO2 concentration is rising. In subsequent chapters (Chapter 4 and Chapter 14), we will learn about the processes driving the CO2 uptake by land and ocean and the dynamics of the C redistribution in the Earth system. In this chapter, we will look at the global C budget - how much C has been emitted by the combustion of fossil fuels and deforestation, how much of this C has accumulated in the atmosphere, and how much has been taken up by the ocean and the terrestrial biosphere.

The global C budget can be defined for globally aggregated fluxes as the balance between emissions from fossil fuels \(E_\mathrm{FF}\) and land use change \(E_\mathrm{LUC}\) on the left side of the equation and the redistribution of C among the atmosphere, land and ocean. \(G_\mathrm{atm}\) is the atmospheric growth rate, \(S_\mathrm{ocean}\) is the net ocean C uptake (also referred to as the ocean sink) and \(S_\mathrm{land}\) is the net land C uptake (or land sink). A net flux from the atmosphere into the ocean or into land C storage is positive.

\[ E_\mathrm{FF} + E_\mathrm{LUC} = G_\mathrm{atm} + S_\mathrm{ocean} + S_\mathrm{land} \tag{3.6}\]

This terminology is adopted from the Global Carbon Budget (Friedlingstein et al. 2023) and is expressed as global annual total fluxes. The separation of \(E_\mathrm{LUC}\) and \(S_\mathrm{land}\) is not straight-forward, but can be understood in a simplified fashion as spatially separated fluxes, whereby the land sink occurs only on areas that are not affected by land use change (LUC). In reality, LUC affects the land sink which complicates a separation of the two components. This is further resolved in Chapter 10.

-

The values of the global carbon budget components are given in Figure 3.1 for an average across years 2010-2019, where \(S_\mathrm{ocean}\) corresponds to the ‘net ocean flux’ and \(S_\mathrm{land}\) corresponds to the the ‘net land flux’ in Figure 3.1. \(E_\mathrm{LUC}\) corresponds to ‘net land-use change’. The ‘net’ indicates that \(E_\mathrm{LUC}\) is the net effect between CO2 emissions from deforestation and C uptake by re-growing forests and afforestations. Note that the annual atmospheric growth rate is not resolved in Figure 3.1. The most recent update of the global carbon budget from Friedlingstein et al. (2023) is given in Table 3.2 as 10-year averages of annual fluxes for years 2013-2022 and cumulative fluxes for the industrial era - years 1750-2022.

+

The values of the global carbon budget components are given in Figure 3.1 for an average across years 2010-2019, where \(S_\mathrm{ocean}\) corresponds to the ‘net ocean flux’ and \(S_\mathrm{land}\) corresponds to the ‘net land flux’ in Figure 3.1. \(E_\mathrm{LUC}\) corresponds to ‘net land-use change’. The ‘net’ indicates that \(E_\mathrm{LUC}\) is the net effect between CO2 emissions from deforestation and C uptake by re-growing forests and afforestation. Note that the annual atmospheric growth rate is not resolved in Figure 3.1. The most recent update of the global carbon budget from Friedlingstein et al. (2023) is given in Table 3.2 as 10-year averages of annual fluxes for years 2013-2022 and cumulative fluxes for the industrial era - years 1750-2022.

@@ -574,8 +575,8 @@

\(B_\mathrm{IM}\) can be defined. A value of zero indicates that models of the land and ocean C uptake exactly match the (better known) emission terms minus the atmospheric growth rate. \[ B_\mathrm{IM} = E_\mathrm{FF} + E_\mathrm{LUC} - (G_\mathrm{atm} + S_\mathrm{ocean} + S_\mathrm{land}) \tag{3.7}\]

-

Today, the global carbon budget is well specified thanks to reliable estimates of its individual components. The budget imbalance is only a fraction of the total emissions. Until recently, “bottom-up” estimates of \(S_\mathrm{land}\) by land C cycle models were deemed insufficient for providing reliable estimates. Instead, \(S_\mathrm{land}\) was estimated as the budget residual by neglecting \(B_\mathrm{IM}\) and rearranging terms in Equation 3.7 to solve for \(S_\mathrm{land}\). In fact, when the IPCC First Assessment Report was published in 1990, the existence of C sink on land was not known and it was treated as the budget imbalance and referred to as the ‘missing sink’. It was stated that “there are possible processes on land which could account for the missing CO2 (but it has not been possible to verify them)”.

-

It was only later that the existence of a terrestrial C sink could be more firmly established and quantified thanks to parallel measurements of the atmospheric O2 and CO2 concentrations (Keeling, Piper, and Heimann 1996). (In fact, the ratio O2/N2 is measured to avoid the much larger measurement uncertainty in absolute O2 measurements). The ratios of O2:CO2 are known from the stoichiometric molecular formulae for photosynthesis (O2:CO2 = 1.1), fossil fuel combustion (O2:CO2 = 1.4) and ocean uptake (O2:CO2 = 0). An ocean O2 source from marine organisms has to be factored in. Given the total C emissions from fossil fuel combustion, the net land C balance can thus be calculated and the calculation visualized geometrically (Figure 3.2). Note that net emissions from land use change are not considered and the what is termed the “Sland” in Figure 3.2 is actually the net \((S_\mathrm{land} - E_\mathrm{LUC})\) in Equation 3.6.

+

Today, the global carbon budget is well specified thanks to reliable estimates of its individual components. The budget imbalance is only a fraction of the total emissions. Until recently, “bottom-up” estimates of \(S_\mathrm{land}\) by land C cycle models were deemed insufficient for providing reliable estimates. Instead, \(S_\mathrm{land}\) was estimated as the budget residual by neglecting \(B_\mathrm{IM}\) and rearranging terms in Equation 3.7 to solve for \(S_\mathrm{land}\). In fact, when the IPCC First Assessment Report was published in 1990, the existence of C sink on land was not known, and it was treated as the budget imbalance and referred to as the ‘missing sink’. It was stated that “there are possible processes on land which could account for the missing CO2 (but it has not been possible to verify them)”.

+

It was only later that the existence of a terrestrial C sink could be more firmly established and quantified thanks to parallel measurements of the atmospheric O2 and CO2 concentrations (Keeling, Piper, and Heimann 1996). (In fact, the ratio O2/N2 is measured to avoid the much larger measurement uncertainty in absolute O2 measurements). The ratios of O2:CO2 are known from the stoichiometric molecular formulae for photosynthesis (O2:CO2 = 1.1), fossil fuel combustion (O2:CO2 = 1.4) and ocean uptake (O2:CO2 = 0). An ocean O2 source from marine organisms has to be factored in. Given the total C emissions from fossil fuel combustion, the net land C balance can thus be calculated and the calculation visualized geometrically (Figure 3.2). Note that net emissions from land use change are not considered and what is termed the “Sland” in Figure 3.2 is actually the net \((S_\mathrm{land} - E_\mathrm{LUC})\) in Equation 3.6.

@@ -752,9 +753,9 @@

3.4.1 Processes

As challenging as it was to locate the “missing C sink” in the terrestrial biosphere in the 1990s (see above), it remains a great challenge to locate the C sink within the terrestrial biosphere and attribute it to processes. Three processes are considered to be particularly influential for the terrestrial C balance, and they each affect ecosystems’ C balances in different regions across the globe - land use change, the relief of temperature limitations on photosynthesis and growth, and the CO2 fertilization effect.

-

The land C balance from land use change is the net of a flux to the atmosphere due to deforestation and a flux from the atmosphere to the land biosphere due to regrowth after deforestation. Land use change trends are very different across regions globally. While large C losses due to land use change are currently occurring in the tropics, northern extra-tropical regions generally gain C as forests are recovering from more intense wood harvesting in the past - prior the the mid-20th century. Chapter 10 delves deeper into the role of land use change on the carbon cycle and climate. The net C flux from land use change is accounted for in the global carbon budget by the term \(E_\mathrm{LUC}\) (Equation 3.6) and should reflect also effects by C accumulation in recovering forests. However, past land use changes are uncertain and the impact of pre-1950 wood harvesting in temperate regions may be underestimated by models that supply estimates for \(E_\mathrm{LUC}\). \(S_\mathrm{land}\), when defined as the budget residual, may thus be driven by the C sink in recovering forests. A recent estimate suggests that about a quarter of the land sink, or 1.3 PgC yr-1, is due to recovery from past forest disturbances (fire, wind, and wood harvesting) (Pugh et al. 2019).

+

The land C balance from land use change is the net sum of a flux to the atmosphere due to deforestation and a flux from the atmosphere to the land biosphere due to regrowth after deforestation. Land use change trends are very different across regions globally. While large C losses due to land use change are currently occurring in the tropics, northern extra-tropical regions generally gain C as forests are recovering from more intense wood harvesting in the past - prior the mid-20th century. Chapter 10 delves deeper into the role of land use change on the carbon cycle and climate. The net C flux from land use change is accounted for in the global carbon budget by the term \(E_\mathrm{LUC}\) (Equation 3.6) and should reflect also effects by C accumulation in recovering forests. However, past land use changes are uncertain and the impact of pre-1950 wood harvesting in temperate regions may be underestimated by models that supply estimates for \(E_\mathrm{LUC}\). \(S_\mathrm{land}\), when defined as the budget residual, may thus be driven by the C sink in recovering forests. A recent estimate suggests that about a quarter of the land sink, or 1.3 PgC yr-1, is due to recovery from past forest disturbances (fire, wind, and wood harvesting) (Pugh et al. 2019).

Warming trends due to anthropogenic climate change are relieving temperature limitations on photosynthesis and tree growth, enabling an extension of the growing season (Ruehr et al. 2023), and an expansion of forest areas and vegetation greenness in high northern latitudes - as sensed from space (T. F. Keenan and Riley 2018). The associated land C sink, as the one driven by forest recovery from past land use change, is located in the northern extra-tropics.

-

Rising atmospheric CO2 stimulates leaf-level photosynthetic rates. The additional C assimilated likely drives increases in ecosystem C storage. However, a multitude of processes and ecosystem feedbacks are involved and affect the link between the leaf-level CO2-fertilization of photosynthesis and ecosystem-level C storage (nutrient limitation, tree longevity reduction due to accelerated growth, soil organic C loss due to plant-soil interactions). Free-Air-CO2-Experiments, where plots of outdoor growing vegetation are exposed to elevated CO2 during multiple years indicate a stimulation of photosynthesis and growth, but evidence for gains in biomass and soil C stocks is mixed. Yet, C gains in mature forest growth, biomass, and ecosystem C stocks are documented and, particularly in the tropics, CO2-fertilization appears to be the main driver of this trend. This is consistent with Dynamic Global Vegetation Models that attribute about 60-85% of the total land sink to CO2-fertilization (Schimel, Stephens, and Fisher 2015; Trevor F. Keenan et al. 2016). Published review studies (Ruehr et al. 2023; Walker et al. 2021) provide a more detailed account of the complex role of CO2-fertilization in driving the land C sink.

+

Rising atmospheric CO2 stimulates leaf-level photosynthetic rates. The additional C assimilated likely drives increases in ecosystem C storage. However, a multitude of processes and ecosystem feedbacks are involved and affect the link between the leaf-level CO2-fertilization of photosynthesis and ecosystem-level C storage (nutrient limitation, tree longevity reduction due to accelerated growth, soil organic C loss due to plant-soil interactions). Free-Air-CO2-Experiments, where plots of outdoor growing vegetation are exposed to elevated CO2 during multiple years, indicate a stimulation of photosynthesis and growth, but evidence for gains in biomass and soil C stocks is mixed. Yet, C gains in mature forest growth, biomass, and ecosystem C stocks are documented and, particularly in the tropics, CO2-fertilization appears to be the main driver of this trend. This is consistent with Dynamic Global Vegetation Models that attribute about 60-85% of the total land sink to CO2-fertilization (Schimel, Stephens, and Fisher 2015; Trevor F. Keenan et al. 2016). Published review studies (Ruehr et al. 2023; Walker et al. 2021) provide a more detailed account of the complex role of CO2-fertilization in driving the land C sink.

Theory suggests that the CO2 effect on photosynthesis should be higher under warm than under cold temperatures. Therefore, a CO2-driven land sink should be strongest in the tropics. As mentioned above, a C sink that is driven predominantly by either growing season extensions and cold limitation reliefs or by recovery from past land use change would be located mainly in the northern extra-tropics. How to discriminate between these drivers and their associated C sink regions? Once more, atmospheric CO2 measurements provide a constraint. While the total terrestrial C sink is relatively well-constrained through the global carbon budget, contributions from the tropics (and southern hemisphere) vs. the northern extra-tropics requires an additional constraint. Atmospheric CO2 measurements, in combination with known CO2 sources and their location and with atmospheric transport fields (atmospheric inversions) enable a split of the global land C sink into contribution from the two regions, while their sum is constrained by the global carbon budget. This approach is visualized in Figure 3.5. The combination of the two constraints indicates that model simulations where the CO2-fertilization effect was “turned off” tend to be outside the range of plausible combinations of tropical and northern-extratropical land C sinks. This indicates the importance of a strong CO2-fertilization-driven C sink in the tropics. Hence, the hypothesis that the land C sink is driven exclusively by forest recovery from past land use and the extension of the growing season in cold-limited regions of the northern extra-tropics is not compatible with the C budget and the inter-hemispheric split of land C uptake inferred from atmospheric inversions.

@@ -798,9 +799,9 @@

\(\Delta x = x - x_0\). The sensitivity of the total terrestrial photosynthetic CO2 uptake to atmospheric CO2 has been estimated by T. F. Keenan et al. (2023) as \(\beta = 0.59 \pm 0.16\). With this, we can model \(I\) as a function of \(c_a\) using Equation 3.9.

The 1-box model can be implemented numerically by discretization in time (i.e., considering time steps \(\Delta t\)). To simulate the terrestrial C pool over time (\(C(t)\)), Equation 3.2 can thus be written as \[ -C(t+\Delta t) = C(t) + I(t) - \tau^{-1}C(t) +C(t+\Delta t) = C(t) + (I(t) - \tau^{-1}C(t)) * \Delta t \]

-

We further assume that \(C(t)\) was at steady-state in year 1850 - the first year of the CO2 time series used here. \(\tau\) could be estimated by using values of terrestrial C pools (sum of vegetation C and soil C) and the gross photosynthesis flux from Figure 3.1 (\(\tau = (450\; \mathrm{GtC} + 1700\; \mathrm{GtC})/113\; \mathrm{GtC\;yr}^{-1} = 19.0 \; \mathrm{yr}\)). However, the resulting land C sink would be strongly overestimated when compared to the residual sink \(S_\mathrm{land}\) from the Global Carbon Budget. When choosing \(\tau = 9 \; \mathrm{yr}\), a better fit between the 1-box model-derived land sink and the observed land sink emerges. This could indicate that CO2-fertilization drives additional C storage that is more short lived than on average in vegetation and soil biomass. It probably also indicates that not all of the C assimilated by photosynthesis stays in the system for more than a few minutes to weeks. A substantial fraction of that C is respired by plants (autotrophic respiration, see also Chapter 4) before it is synthesized into longer-lived plant tissue biomass. The resulting evolution(s) of the land C cycle are illustrated in Figure 3.7.

+

We further assume that \(C(t)\) was at steady-state in year 1850 - the first year of the CO2 time series used here. \(\tau\) could be estimated by using values of terrestrial C pools (sum of vegetation C and soil C) and the gross photosynthesis flux from Figure 3.1 (\(\tau = (450\; \mathrm{GtC} + 1700\; \mathrm{GtC})/113\; \mathrm{GtC\;yr}^{-1} = 19.0 \; \mathrm{yr}\)). However, the resulting land C sink would be strongly overestimated when compared to the residual sink \(S_\mathrm{land}\) from the Global Carbon Budget. When choosing \(\tau = 9 \; \mathrm{yr}\), a better fit between the 1-box model-derived land sink and the observed land sink emerges. This could indicate that CO2-fertilization drives additional C storage that is more short-lived than on average in vegetation and soil biomass. It probably also indicates that not all of the C assimilated by photosynthesis stays in the system for more than a few minutes to weeks. A substantial fraction of that C is respired by plants (autotrophic respiration, see also Chapter 4) before it is synthesized into longer-lived plant tissue biomass. The resulting evolution(s) of the land C cycle are illustrated in Figure 3.7.

diff --git a/globalcarbonpatterns.html b/globalcarbonpatterns.html index b3d1e06..6cc6e1a 100644 --- a/globalcarbonpatterns.html +++ b/globalcarbonpatterns.html @@ -403,7 +403,7 @@

6.1.1 Solar geometry

Let’s first step outside the atmosphere and focus on the solar geometry to understand \(I_\mathrm{TOA}\). Solar geometry describes the cyclical movement of the Earth around the sun and how the resulting cyclically varying amount of solar energy that reaches the Earth. The top-of-the atmosphere perspective is relevant to separate atmospheric effects from planetary effects.

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\(I_\mathrm{TOA}\) scales in proportion with the solar constant \(I_S\) (1360.8 W m-2) and is inversely proportional to the square of the distance between the Earth and the sun (\(r_E\)). \[ +

\(I_\mathrm{TOA}\) scales in proportion to the solar constant \(I_S\) (1360.8 W m-2) and is inversely proportional to the square of the distance between the Earth and the sun (\(r_E\)). \[ I_\mathrm{TOA} = I_S r_E^{-2} \cos \theta_z \tag{6.3}\] \(\theta_z\) is the solar zenith angle. The term \(\cos \theta_z\) accounts for the dependence of the solar radiation on the angle at which the sun’s rays reach the Earth surface (no terrain considered). It varies cyclically over the course of a day (with hour-of-day) and over the course of a year (with day-of-year). The zenith angle is zero when the sun is directly above the observer - in the zenith (Figure 6.2). At this point, the intensity of the solar radiation is at its maximum.

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\(I_\mathrm{TOA}\):

  • The diurnal variation of the instantaneous flux is largest in the tropics.
    • -
  • The seasonal variation of the daily total flux is largest at the north pole.
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  • At the summer solstice, the daily total solar radiation is largest at the north pole, …
    • -
  • … but the daily maximum instantaneous and the daytime mean radiation flux are lower at the north pole than at the equator at the summer solstice.
    • +
  • The seasonal variation of the daily total flux is largest at the North Pole.
    • +
  • At the summer solstice, the daily total solar radiation is largest at the North Pole, …
    • +
  • … but the daily maximum instantaneous and the daytime mean radiation flux are lower at the North Pole than at the equator at the summer solstice.

The biology of plants is attuned to the solar radiation patterns across different latitudes. The photosynthetic apparatus is constructed to make best use of the light, even during the hours of peak light intensity at mid-day. The phenological phases of plant growth reflect the light distribution over the seasons - evergreen plants dominate in the moist tropics to make use of the light year-round, while deciduous leaf strategies and annual life history strategies dominate in the northern latitudes where the seasonal fluctuation of light is large.

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\(I_S\) isn’t actually constant but varies on the order of 0.1% of the course of a solar cycle. One cycle is approximately 11 years. The cyclic behavior is related to the periodic flip of the sun’s magnetic field and the number of sunspots. The radiation emitted from the sun and the number of sunspots are at their minimum after a magnetic flip. There is also a small long-term trend in the solar radiation, having increased by <0.1% since the Maunder Minimum (1645–1715). Solar irradiance is measured at high altitude to minimize the influence of the atmosphere (\(\tau\) in Eq. Equation 6.1) and get information about how \(I_S\) varies. Reconstructions of solar irradiance changes for the pre-instrumental period are based on the relationship between \(I_S\) and the (easily observable) sunspot number. Variations in \(I_S\) are small and do not have a dominant effect on climate and the carbon cycle that would override other forcings, especially for the industrial period (IPCC 2021).

Volcanic activity

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Volcanic eruptions can influence the solar radiation at the Earth surface. Events that reduce solar radiation by more than 1 W m-2 occur approximately every 35-40 years (Gulev et al. 2021) and affect climate and the carbon cycle for up to a few years after very large eruptions. The increased aerosol load in the atmosphere reduces the total radiative energy flux (reducing \(\tau\) in Eq. Equation 6.1). However, through the strong positive effect of the aerosol load on the share of diffuse versus direct radiation, volcanic aerosols can affect the terrestrial carbon cycle, (somehow surprisingly) leading to a greater land C sink following years of large volcanic eruptions (Section 4.2).

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Volcanic eruptions can influence the solar radiation at the Earth’s surface. Events that reduce solar radiation by more than 1 W m-2 occur approximately every 35-40 years (Gulev et al. 2021) and affect climate and the carbon cycle for up to a few years after very large eruptions. The increased aerosol load in the atmosphere reduces the total radiative energy flux (reducing \(\tau\) in Eq. Equation 6.1). However, through the strong positive effect of the aerosol load on the share of diffuse versus direct radiation, volcanic aerosols can affect the terrestrial carbon cycle, (somehow surprisingly) leading to a greater land C sink following years of large volcanic eruptions (Section 4.2).

Orbital parameters

The largest changes in \(I_\mathrm{TOA}\) arise over millennial time scales and are related to variations in Earth’s orbit around the sun. These Milankovic cycles are the trigger for the large climate swings between ice ages and warm periods over the course of ~100,000 years. Variations in the orbital parameters affect the latitudinal and seasonal distribution of \(I_\mathrm{TOA}\). Orbital parameters that vary periodically are:

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    Figure 6.6). During this period, temperatures and solar irradiance during the growing season were elevated relative to the pre-industrial period and precipitation patterns shifted. This had profound effects on vegetation and the carbon cycle. Testimony to this change are reconstructions that document a “Green Sahara” and a northward shift temperate and boreal forest biomes (MacDonald et al. 2000; Prentice, Jolly, and Participants 2000) during this period.

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    About 6000 years ago, during the Mid-Holocene Warm Period, a summer maximum insolation for the northern hemisphere was reached (Figure 6.6). During this period, temperatures and solar irradiance during the growing season were elevated relative to the pre-industrial period and precipitation patterns shifted. This had profound effects on vegetation and the carbon cycle. Testimonies to this change are reconstructions that document a “Green Sahara” and a northward shift temperate and boreal forest biomes (MacDonald et al. 2000; Prentice, Jolly, and Participants 2000) during this period.

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    6.2 Phenology

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    In general, phenology refers to the study of periodic events of biological activity. In most cases, such periodic events are linked the seasonal variations of the climate. In the context of terrestrial photosynthesis and land-climate interactions, the most important phenological event is the leaf unfolding and leaf senescence and shedding in response to seasonal variations in temperature, radiation, and water availability. The presence (or absence) of active green leaves has major implications for CO2, water vapour, and energy exchange between the land surface and the atmosphere.

    +

    In general, phenology refers to the study of periodic events of biological activity. In most cases, such periodic events are linked to the seasonal variations of the climate. In the context of terrestrial photosynthesis and land-climate interactions, the most important phenological event is the leaf unfolding and leaf senescence and shedding in response to seasonal variations in temperature, radiation, and water availability. The presence (or absence) of active green leaves has major implications for CO2, water vapor, and energy exchange between the land surface and the atmosphere.

    The presence of green leaves is recorded by optical satellite remote sensing and documents the Earth’s greenness dynamics that follows the seasons - differently across the globe, as the video below illustrates.

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    Leaf phenology is either controlled by temperatures and light availability in temperate, boreal, and tundra ecosystems, or by water availability in warm, seasonally dry climates elsewhere. The water control on vegetation and leaf phenology will be discussed in Chapter 8.

    -

    In winter-cold climates (temperate, boreal, and tundra climate zones C, D, and E, see Figure 2.22), leaf phenology of deciduous plants is driven by the seasonal fluctuations of temperature and radiation. Leaves are shed before winter to avoid damage by cold temperatures and because the limited gains by C assimulation during dark and cold winter months does not outweigh the costs for maintenance of vital functions. In seasonally dry climates (mainly climate zones Am, Aw, see Figure 2.22), leaves are shed to avoid water loss and avoid dangerous desiccation of the plant. Leaf area also varies more gradually in response to seasonal variations in climate. LAI can have a seasonal cycle also in evergreen forests and shrublands. In grasslands, LAI typically has a strong seasonal cycle, with rapid foliage development and senescence during the typically relatively short vegetation period - but without the typical budbreak, leaf unfolding, and leaf shedding as in deciduous trees.

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    Photosynthesis and the exchange of CO2 between the land surface and the atmosphere are very directly affected by the amount of active green leaves - as measured by fAPAR (Equation 4.1). Coupled to this exchange is the exchange of water vapour and the surface energy balance. Therefore, leaf phenology is a primary control on land-climate interactions and the carbon cycle. Leaf phenology is not only a driver of land-climate interactions, but is also driven by climate. Different controls act on the leaf unfolding and leaf senescence dates.

    +

    In winter-cold climates (temperate, boreal, and tundra climate zones C, D, and E, see Figure 2.22), leaf phenology of deciduous plants is driven by the seasonal fluctuations of temperature and radiation. Leaves are shed before winter to avoid damage by cold temperatures and because the limited gains by C assimilation during dark and cold winter months does not outweigh the costs for maintenance of vital functions. In seasonally dry climates (mainly climate zones Am, Aw, see Figure 2.22), leaves are shed to avoid water loss and avoid dangerous desiccation of the plant. Leaf area also varies more gradually in response to seasonal variations in climate. LAI can have a seasonal cycle also in evergreen forests and shrublands. In grasslands, LAI typically has a strong seasonal cycle, with rapid foliage development and senescence during the typically relatively short vegetation period - but without the typical budbreak, leaf unfolding, and leaf shedding as in deciduous trees.

    +

    Photosynthesis and the exchange of CO2 between the land surface and the atmosphere are very directly affected by the amount of active green leaves - as measured by fAPAR (Equation 4.1). Coupled to this exchange is the exchange of water vapor and the surface energy balance. Therefore, leaf phenology is a primary control on land-climate interactions and the carbon cycle. Leaf phenology is not only a driver of land-climate interactions, but is also driven by climate. Different controls act on the leaf unfolding and leaf senescence dates.

    6.2.1 Leaf unfolding

    In winter-cold (temperate and boreal) deciduous forests, the timing of leaf unfolding (bud-burst) is sensitive to temperatures prior to the leaf unfolding date. Warm temperatures in early spring accelerate leaf unfolding and can lead to a shift of spring phenology dates by several days or even weeks. Phenology models commonly use the concept of growing degree days (GDD) (Basler 2016) and consider a critical GDD (GDD*) for predicting leaf unfolding. Growing degree days on day \(j\) is defined as the cumulative sum of temperatures above a specified threshold (\(T_0\), most commonly \(T_0 = 5^\circ\)C), counting from a given start date \(M\).

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Here in Switzerland, most trees start leaf unfolding in the second half of April. Why are leaves of winter-cold deciduous trees not unfolding earlier in the year (given that there is light available for photosynthesis)? Leaf shedding is a protection of plants against frost. At temperatures below freezing, costly cell protection measures against frozen water and excessive photosynthetic light harvesting are required to avoiding damage. Delayed leaf unfolding is a strategy to avoid such damage.

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Here in Switzerland, most trees start leaf unfolding in the second half of April. Why are leaves of winter-cold deciduous trees not unfolding earlier in the year (given that there is light available for photosynthesis)? Leaf shedding is a protection of plants against frost. At temperatures below freezing, costly cell protection measures against frozen water and excessive photosynthetic light harvesting are required to avoid damage. Delayed leaf unfolding is a strategy to avoid such damage.

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6.2.2 Leaf senescence

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Leaf senescence in temperate and boreal deciduous forests is - similarly as leaf unfolding - a strategy to avoid stress and damage by low temperatures in winter. Before leaf abscission (leaf shedding), the leaf nutrients are resorbed and photosynthetic activity starts declining. Leaves are rich in nutrients. A large fraction of nutrients contained in leaf biomass, in particular nitrogen (N), are linked to photosynthesis - mostly Rubisco. These nutrients are re-mobilised before leaf abscission and resorbed into plant-internal storage compartments. Thereby, the loss of “costly” nutrients can be avoided. A side effect of the nutrient resorption is the change of the leaf color to yellow, reddish, or brown.

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Environmental controls on leaf senescence are not the same as for leaf unfolding and vary between tree species. Model predictability for leaf senescence dates is generally lower than for leaf unfolding dates, observed global trends are less clear (Piao et al. 2019), and drivers less well understood (Richardson et al. 2013) than for spring phenology. Photoperiod and temperature are considered important abiotic controls on leaf senescence dates. While photoperiod sets the induction of the end-of-season phenology, temperature modulates its progression with cold temperatures accelerating leaf senescence (Christian Körner and David Basler 2010). Also the timing of leaf unfolding can appears to affect the timing of leaf senescence [Keenan and Richardson (2015); marques23natee]. An earlier leaf unfolding in spring appears to induce an earlier leaf senescence in autumn. Processes driving this pattern may be related to cell aging and a conserved leaf longevity, but may also be related to the ecosystem water balance and premature defoliation as a response to dry soil conditions (after vegetation has started consuming water earlier in spring).

+

Leaf senescence in temperate and boreal deciduous forests is - similarly as leaf unfolding - a strategy to avoid stress and damage by low temperatures in winter. Before leaf abscission (leaf shedding), the leaf nutrients are resorbed and photosynthetic activity starts declining. Leaves are rich in nutrients. A large fraction of nutrients contained in leaf biomass, in particular nitrogen (N), is linked to photosynthesis - mostly Rubisco. These nutrients are re-mobilised before leaf abscission and resorbed into plant-internal storage compartments. Thereby, the loss of “costly” nutrients can be avoided. A side effect of the nutrient resorption is the change of the leaf color to yellow, reddish, or brown.

+

Environmental controls on leaf senescence are not the same as for leaf unfolding and vary between tree species. Model predictability for leaf senescence dates is generally lower than for leaf unfolding dates, observed global trends are less clear (Piao et al. 2019), and drivers less well understood (Richardson et al. 2013) than for spring phenology. Photoperiod and temperature are considered important abiotic controls on leaf senescence dates. While photoperiod sets the induction of the end-of-season phenology, temperature modulates its progression with cold temperatures accelerating leaf senescence (Christian Körner and David Basler 2010). Also, the timing of leaf unfolding can appear to affect the timing of leaf senescence [Keenan and Richardson (2015); marques23natee]. An earlier leaf unfolding in spring appears to induce an earlier leaf senescence in autumn. Processes driving this pattern may be related to cell aging and a conserved leaf longevity, but may also be related to the ecosystem water balance and premature defoliation as a response to dry soil conditions (after vegetation has started consuming water earlier in spring).

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Figure 6.13 a). In this case, GPP is equal to the product of the quantum yield (\(\varphi_0\)), a factor \(\tilde{a}\) that accounts for the incomplete utilization of absorbed light by the light reactions, and the photosynthetically active radiation received at the top of the atmosphere (PARTOA in Figure 6.13, corresponds to ITOA in Equation 6.1). In this (hypothetical) case, the global distribution of GPP varies along latitudes, but not along longitudes and is estimated by Wang, Prentice, and Davis (2014) at 2960 PgC yr-1.

Next, we consider the attenuation of solar radiation by the atmosphere, considering cloud cover and the elevation of the land surface. This considers Equation 6.2 and reflects the geographic pattern of distribution of solar radiation, incident at the land surface (Figure 6.1). Note that \(\varphi_0\) and \(\tilde{a}\) are considered here to be global constants. Atmospheric attenuation of photysnthetically active solar radiation reduces terrestrial GPP by over 50% (from 2960 to 1442 PgC yr-1, Wang, Prentice, and Davis (2014)).

Not all solar radiation that reaches the land surface is absorbed by active green vegetation. The highest radiation intensities coincide with sparsely vegetated land, including major desert regions. The effect of reduced vegetation cover on GPP is quantified by the factor fAPAR which accounts for the fraction of absorbed photosynthetically active radiation (Section 4.2). Limited vegetation cover and light absorption reduces terrestrial GPP further by over 75% (from 1442 to 322 PgC yr-1, Wang, Prentice, and Davis (2014)).

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At the global scale, temperature has a relatively weak effect on GPP. Considering that photosynthesis is inhibited by freezing temperatures (below 0°C) does not substantially reduce total terrestrial GPP (from 322 to 300 PgC yr-1, corresponding to a 7% reduction, Wang, Prentice, and Davis (2014)). This is because low temperatures coincide with low PAR (or \(I_0\)) and . Situations of high light and low temperatures are relatively rare.

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Finally, physiological effects of CO2, temperature, vapour pressure deficit, and the atmospheric pressure are considered. Note that the effect of temperatures below freezing is treated separately by the step described above. The potential maximum rate of the conversion of absorbed photosynthetically active radiation is reduced by the limited diffusion rate of CO2 through stomatal openings (thus reducing \(c_i\) relative to \(c_a\), Figure 6.13 e) and is further reduced by the effects of photorespiration as accounted for by the factor \((c_i - \Gamma^\ast)/(c_i + 2\Gamma^\ast)\). This represents the effect of leaf-internal CO2 concentration on the electron transport-limited assimilation rate \(A_J\) in the FvCB model (Equation 4.9). These physiological effects reduce terrestrial GPP from 300 to 211 PgC yr-1, corresponding to a 30% reduction (Wang, Prentice, and Davis 2014). Note that the range of published total annual terrestrial GPP estimates is lower - between 110 and 140 PgC yr-1 (Benjamin D. Stocker et al. 2019).

+

At the global scale, temperature has a relatively weak effect on GPP. Considering that photosynthesis is inhibited by freezing temperatures (below 0°C) does not substantially reduce total terrestrial GPP (from 322 to 300 PgC yr-1, corresponding to a 7% reduction, Wang, Prentice, and Davis (2014)). This is because low temperatures coincide with low PAR (or \(I_0\)). Situations of high light and low temperatures are relatively rare.

+

Finally, physiological effects of CO2, temperature, vapor pressure deficit, and the atmospheric pressure are considered. Note that the effect of temperatures below freezing is treated separately by the step described above. The potential maximum rate of the conversion of absorbed photosynthetically active radiation is reduced by the limited diffusion rate of CO2 through stomatal openings (thus reducing \(c_i\) relative to \(c_a\), Figure 6.13 e) and is further reduced by the effects of photorespiration as accounted for by the factor \((c_i - \Gamma^\ast)/(c_i + 2\Gamma^\ast)\). This represents the effect of leaf-internal CO2 concentration on the electron transport-limited assimilation rate \(A_J\) in the FvCB model (Equation 4.9). These physiological effects reduce terrestrial GPP from 300 to 211 PgC yr-1, corresponding to a 30% reduction (Wang, Prentice, and Davis 2014). Note that the range of published total annual terrestrial GPP estimates is lower - between 110 and 140 PgC yr-1 (Benjamin D. Stocker et al. 2019).

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Figure 6.14 shows the overall pattern of highest aboveground biomass C being located in tropical forests, it hides “pockets” of exceptionally high biomass in temperate forests. Some of the worlds highest biomass densities (average biomass per unit ground area in a forest plot) are found in cool and moist temperate forests, including Eucalyptus regnans-dominated forests in southeast Australia, Sequoia-dominated forests in coastal California, Oregon and Chile, and Agathis australis-dominated forests in New Zealand (Keith, Mackey, and Lindenmayer 2009).

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While the global biomass map in Figure 6.14 shows the overall pattern of highest aboveground biomass C being located in tropical forests, it hides “pockets” of exceptionally high biomass in temperate forests. Some of the world’s highest biomass densities (average biomass per unit ground area in a forest plot) are found in cool and moist temperate forests, including Eucalyptus regnans-dominated forests in southeast Australia, Sequoia-dominated forests in coastal California, Oregon and Chile, and Agathis australis-dominated forests in New Zealand (Keith, Mackey, and Lindenmayer 2009).

6.4.3 Global distribution of soil carbon

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Controls on soil C stocks

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Allocation Root inputs are approximately five times more likely than an equivalent mass of aboveground litter to be stabilized as soil organic matter (SOM) (Jackson et al. 2017). Thus, allocation and plant growth in different tissues is an important factor determining the link between vegetation productivity, litter production, and soil C. In grasslands and shurblands, a much larger fraction of C is allocated to roots than in forests. Thus, soil C stocks are often higher in natural grasslands and shrublands than in forests. This is also visible in Figure 6.15 which indicates high soil C stocks in the Earth’s grassland and shrubland-dominated regions.

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Climate The activity of soil organic matter-decomposing microbes (fungi and bacteria) is strongly controlled by abiotic factors in the soil. Under low temperatures, their activity is reduced and soil and litter decomposition rates are slowed (see also Section 5.1.5). This is reflected in Figure 6.15 by the generally high soil organic C stocks in the cold climates of the high northern latitudes - despite the generally low productivity of vegetation in these regions.

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Stabilisation and saturation of soil organic C depends on the mineralogy of the soil. This suggests that not (only) the C inputs determine stocks, but also the capacity of soil mineral surfaces to sorb organic matter.

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Plant-soil interactions via fungi and bacteria strongly influence C and nutrient cycling in soils. Inputs of fresh litter and labile C through root exudates can stimulate the decomposition (priming) of stable C in the soil. These relationships are complex and implications for the global distribution of soil C is not clear, but can undermine a positive and linear relationship between vegetation productivity, litter inputs, and soil C stocks.

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Allocation Root inputs are approximately five times more likely than an equivalent mass of aboveground litter to be stabilized as soil organic matter (SOM) (Jackson et al. 2017). Thus, allocation and plant growth in different tissues is an important factor determining the link between vegetation productivity, litter production, and soil C. In grasslands and shurblands, a much larger fraction of C is allocated to roots than in forests. Thus, soil C stocks are often higher in natural grasslands and shrublands than in forests. This is also visible in Figure 6.15 which indicates high soil C stocks in the Earth’s grassland and shrubland-dominated regions.

+

Climate The activity of soil organic matter-decomposing microbes (fungi and bacteria) is strongly controlled by abiotic factors in the soil. Under low temperatures, their activity is reduced, and soil and litter decomposition rates are slowed (see also Section 5.1.5). This is reflected in Figure 6.15 by the generally high soil organic C stocks in the cold climates of the high northern latitudes - despite the generally low productivity of vegetation in these regions.

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Soil mineral composition Stabilisation and saturation of soil organic C depends on the mineralogy of the soil. This suggests that not (only) the C inputs determine stocks, but also the capacity of soil mineral surfaces to adsorb organic matter.

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Plant-soil interactions Plant-soil interactions via fungi and bacteria strongly influence C and nutrient cycling in soils. Inputs of fresh litter and labile C through root exudates can stimulate the decomposition (priming) of stable C in the soil. These relationships are complex and implications for the global distribution of soil C is not clear, but can undermine a positive and linear relationship between vegetation productivity, litter inputs, and soil C stocks.

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Global soil C stocks

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The total C stock in soils up to 2 m is estimated 2273 PgC by Jackson et al. (2017) - higher than the number provided in the IPCC AR6 (Canadell et al. 2021) and Figure 3.1. Global soil C estimates are based on soil organic C content measurements which are available mostly from the top soil and are thus sensitive to assumptions regarding the soil C distribution across the soil profile. In general, the organic matter and thus soil C content declines with depth but the rate of decline depends on vegetation and the distribution of roots. The global soil C stock of 0-3 m is even higher and estimated by Jackson et al. (2017) at 2800 PgC. The soil depth-to-bedrock puts a constraint on soil C storage at depth in many places, is very uncertain, and may lead to a substantial reduction of the total 0-2 and 0-3 m soil C estimates.

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The high soil C density in high northern latitudes (Figure 6.15) reflects also the particular functioning and soil C dynamics dynamics and stabilization under conditions where temperatures are below freezing for a large part of the year (in permafrost regions) and under permanently water-logged soil conditions (in peatlands). Contributions of soil C stocks in peatland and permafrost regions are substantial (see Section 6.4.4 and Section 6.4.5).

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The total C stock in soils up to 2 m is estimated 2273 PgC by Jackson et al. (2017) - higher than the number provided in the IPCC AR6 (Canadell et al. 2021) and Figure 3.1. Global soil C estimates are based on soil organic C content measurements which are available mostly from the top soil and are thus sensitive to assumptions regarding the soil C distribution across the soil profile. In general, the organic matter and thus soil C content declines with depth but the rate of decline depends on vegetation and the distribution of roots. The global soil C stock of 0-3 m is even higher and estimated by Jackson et al. (2017) at 2800 PgC. The soil depth-to-bedrock puts a constraint on soil C storage at depth in many places, which is very uncertain, and may lead to a substantial reduction of the total 0-2 and 0-3 m soil C estimates.

+

The high soil C density in high northern latitudes (Figure 6.15) reflects also the particular functioning and soil C dynamics and stabilization under conditions where temperatures are below freezing for a large part of the year (in permafrost regions) and under permanently water-logged soil conditions (in peatlands). Contributions of soil C stocks in peatland and permafrost regions are substantial (see Section 6.4.4 and Section 6.4.5).

Peatland history

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Due to the very slow decay, oldest peat present at a peat dome’s base may date back millennia. Indeed, dated carbon in peatlands across the globe indicate a peak in the initiation of northern peatlands in the early Holocene around 11-9 kyr BP and of tropical peatlands even before - around 20 kyr BP (Yu et al. 2010; MacDonald et al. 2006) and. The timing of the rapid initiation of northern peatlands coincides with the retreat of the major ice sheets after the Last Glacial Maximum and with a peak in summer insolation (Figure 6.6 and Figure 6.18) and climate seasonality with warm summers in the northern hemisphere, supporting vegetation growth. As new peatlands formed in the early Holocene, old ones that established in the glacial climate, disappeared due to climatic change (Müller and Joos 2020) and were lost to rising sea levels during the melting of the ice sheets (Dommain et al. 2014).

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Due to the very slow decay, the oldest peat present at a peat dome’s base may date back millennia. Indeed, dated carbon in peatlands across the globe indicates a peak in the initiation of northern peatlands in the early Holocene around 11-9 kyr BP and of tropical peatlands even before - around 20 kyr BP (Yu et al. 2010; MacDonald et al. 2006). The timing of the rapid initiation of northern peatlands coincides with the retreat of the major ice sheets after the Last Glacial Maximum and with a peak in summer insolation (Figure 6.6 and Figure 6.18) and climate seasonality with warm summers in the northern hemisphere, supporting vegetation growth. As new peatlands formed in the early Holocene, old ones that established in the glacial climate disappeared due to climatic change (Müller and Joos 2020) and were lost to rising sea levels during the melting of the ice sheets (Dommain et al. 2014).

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6.4.5 Permafrost

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About 24% of the northern hemisphere’s exposed land surface contains ground that remains frozen for at least two consecutive years - the definition of permafrost (Schuur and Mack 2018). The global distriution of permafrost in the northern hemisphere is shown in Figure 6.19. Organic matter in frozen soils is protected from decomposition - as long as the ground remains frozen. The total amount of C stored in permafrost soils (0-3 m depth) is estimated at 1,035 ± 150 PgC (Tarnocai et al. 2009; Hugelius et al. 2014) and substantial additional C (400-500 PgC) is stored at greater depth in particular locations (river sediments) (Schuur and Mack 2018). This amount of C adds another 50-100% to the total amount of C stored in soils (Figure 3.1) and suggests that the distribution of permafrost is an important determinant for the global distribution of soil C (Figure 6.15).

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About 24% of the northern hemisphere’s exposed land surface contains ground that remains frozen for at least two consecutive years - the definition of permafrost (Schuur and Mack 2018). The global distribution of permafrost in the northern hemisphere is shown in Figure 6.19. Organic matter in frozen soils is protected from decomposition - as long as the ground remains frozen. The total amount of C stored in permafrost soils (0-3 m depth) is estimated at 1,035 ± 150 PgC (Tarnocai et al. 2009; Hugelius et al. 2014) and substantial additional C (400-500 PgC) is stored at greater depth in particular locations (river sediments) (Schuur and Mack 2018). This amount of C adds another 50-100% to the total amount of C stored in soils (Figure 3.1) and suggests that the distribution of permafrost is an important determinant for the global distribution of soil C (Figure 6.15).

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Permafrost occurs (roughly) where the mean annual temperature is below freezing. During summer, the upper soil layers, the active layer, thaw. However, the seasonal fluctuation of soil temperature is attenuated deeper in the soil due to constraints on the rate of thermal diffusion across the soil. At a certain depth, the seasonal cycle of soil temperature disappears and the soil temperature is largely constant and equal to the mean annual air temperature on the ground (\(Z^\ast\) in Figure 6.20). Towards greater depth, the temperature increases again due to the geothermal heat flux. Permafrost is zone where temperatures never rise beyond 0°C.

+

Permafrost occurs (roughly) where the mean annual temperature is below freezing. During summer, the upper soil layers, the active layer, thaw. However, the seasonal fluctuation of soil temperature is attenuated deeper in the soil due to constraints on the rate of thermal diffusion across the soil. At a certain depth, the seasonal cycle of soil temperature disappears, and the soil temperature is largely constant and equal to the mean annual air temperature on the ground (\(Z^\ast\) in Figure 6.20). Towards greater depth, the temperature increases again due to the geothermal heat flux. Permafrost is the zone where temperatures never rise beyond 0°C.

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Table of contents

  • 4.3.4 Summary
  • 4.3.5 Response to light and CO2
  • 4.3.6 Response to temperature
    • -
  • 4.3.7 Adptation and acclimation of Topt
    • +
  • 4.3.7 Adaptation and acclimation of Topt
  • 4.3.8 C4 photosynthesis
  • 4.4 Transpiration and leaf water-carbon coupling @@ -384,7 +384,7 @@

    4.2 Canopy light absorption

    Photosynthetic CO2 uptake only operates if active (green) leaves are out. The relationship between the amount of leaves and GPP is introduced here. Active leaf area varies across the seasons and space in response to the seasonality of temperature, light and water availability. The seasonal fluctuation of leaf area, most visible for deciduous trees, is referred to as (leaf) phenology. The drivers of temporal and spatial variations of phenology and leaf area are introduced in Section 6.2.

    -

    The fraction of absorbed photosynthetically active radiation (fAPAR) increases with the projected (one-sided) surface area of leaves per unit ground area (the leaf area index, LAI). The total surface area of leaves is roughly twice the projected surface area. The LAI is an ecosystem-level variable and reflects the leaf area density of the whole canopy. The canopy may be composed of multiple species and organised in multiple canopy layers (Figure 4.1). While temperate and boreal forests commonly form a single understorey and attain LAI values of 4-6 m2 m-1, tropical moist forests may have multiple canopy layers and an LAI of over 6 m2 m-1 (Figure 2.16).

    +

    The fraction of absorbed photosynthetically active radiation (fAPAR) increases with the projected (one-sided) surface area of leaves per unit ground area (the leaf area index, LAI). The total surface area of leaves is roughly twice the projected surface area. The LAI is an ecosystem-level variable and reflects the leaf area density of the whole canopy. The canopy may be composed of multiple species and organised in multiple canopy layers (Figure 4.1). While temperate and boreal forests commonly form a single understorey and attain LAI values of 4-6 m2 m-2, tropical moist forests may have multiple canopy layers and an LAI of over 6 m2 m-2 (Figure 2.16).

    @@ -398,13 +398,13 @@

    While the intensity of shortwave (solar) radiation is highest at the top of the canopy, it is progressively attenuated as it penetrates into the canopy. Radiation gets reflected, absorbed and transmitted by individual leaves. The penetration of radiation into a canopy is referred to as canopy radiative transfer. Each of the processes - reflection, absorption, and transmittance - affects light differently in different wavelengths, depends on the solar zenith angle, on the three-dimensional arrangement of leaves in the canopy (angles, “clumping”), and on the pigments on the leaf surfaces that are responsible for light absorption. Pigments change across species and may vary in response to stress (e.g., by frost, heat, or water limitation).

    In brief, canopy radiative transfer is complex. A simple model for how (solar) radiation (light) is attenuated as it penetrates into the canopy is given by the Beer-Lambert law. To apply it for canopy radiative transfer, we assume that a leaf only absorbs light, but does not reflect or transmit it. Following this model, the light intensity \(I\) at the bottom of the canopy (\(z_0\)) is an exponential function of LAI (\(L\)). The rate of decline of the light intensity is given by the light extinction coefficient \(k\). A typical value of \(k\) in the visible (photosynthetically active) wavelength spectrum is 0.5. \[ I(z_0) = I_0 \; e^{-kL} -\] We have assumed that no light is reflected. Therefore the reduction of light levels at the bottom of the canopy tells us how much light was absorbed by the canopy (and used for photosynthesis). The fraction of absorbed (photosynthetically active) radiation therefore is \[ +\] We have assumed that no light is reflected. Therefore, the reduction of light levels at the bottom of the canopy tells us how much light was absorbed by the canopy (and used for photosynthesis). The fraction of absorbed (photosynthetically active) radiation therefore is \[ \begin{align} \mathrm{fAPAR} &= 1 - I(z_0)/I_0 \\ &= 1 - e^{-kL}\;. \end{align} \]

    -

    The shape of this function is illuatrated in Figure 4.2 (a). This implies a dependency of light levels on canopy depth \(z\), as illustrated in Figure 4.2 (b) - consistent with the observation shown in Figure 4.1 (b).

    +

    The shape of this function is illustrated in Figure 4.2 (a). This implies a dependency of light levels on canopy depth \(z\), as illustrated in Figure 4.2 (b) - consistent with the observation shown in Figure 4.1 (b).

    Code @@ -532,7 +532,7 @@

    -
    Figure 4.3: CO2 diffuses into the leaf through stomata, while water vapour diffuses out of the leaf. The water vapour diffusion out of the leaves (transpiration) is introduced in Chapter 7.
    +
    Figure 4.3: CO2 diffuses into the leaf through stomata, while water vapor diffuses out of the leaf. The water vapor diffusion out of the leaves (transpiration) is introduced in Chapter 7.

    @@ -540,7 +540,7 @@

    Once inside the leaf, CO2 diffuses across mesophyll cells to the chloroplasts - the site of photosynthetic reactions. The conductance to this diffusion step - mesophyll conductance - is often ignored for modelling photosynthesis. Reflecting this, we are referring to “leaf-internal” CO2 concentration, \(c_i\)” here, instead of a more correct CO2 concentration at the chloroplast.

    -

    Photosynthesis can be considered as a sequence of three processes that are serially connected - the three processes run one after the other and the rate of the slowest of the three processes determines the overall process rate of photosynthesis. The following is a condensed description, based on Lambers, Chapin, and Pons (2008) and Bonan (2015).

    +

    Photosynthesis can be considered as a sequence of three processes that are serially connected - the three processes run one after the other, and the rate of the slowest of the three processes determines the overall process rate of photosynthesis. The following is a condensed description, based on Lambers, Chapin, and Pons (2008) and Bonan (2015).

    @@ -568,11 +568,11 @@

    4.3.4 Summary

    The chemical summary equation of photosynthesis is: \[ n\mathrm{CO}_2 + 2n\mathrm{H}_2\mathrm{O} \rightarrow (\mathrm{CH}_2\mathrm{O})_n + n\mathrm{O}_2 + n\mathrm{H}_2\mathrm{O} -\tag{4.6}\] A total of eight photons is consumed to assimilate one molecule of CO2. For each molecule of CO2, one molecule of O2 is produced. And for each molecule of CO2, one molecule of H2O is consumed (net). Note however, that this water consumption is not the primary reason for why plants use water. A much larger amount of water is consumed by the diffusion of water vapour from the water-saturated air inside the leaves out of the stomata. This transpiration flux is further explained in Chapter 7.

    +\tag{4.6}\] A total of eight photons is consumed to assimilate one molecule of CO2. For each molecule of CO2, one molecule of O2 is produced. And for each molecule of CO2, one molecule of H2O is consumed (net). Note however, that this water consumption is not the primary reason for why plants use water. A much larger amount of water is consumed by the diffusion of water vapor from the water-saturated air inside the leaves out of the stomata. This transpiration flux is further explained in Chapter 7.

    • 4.3.5 Response to light and CO2

    -

    The three steps described above operate in series and each step is potentially rate-limiting and responds differently to the environment. The rates of the processes are coordinated such that they are roughly equal and co-limiting for average environmental conditions to which a leaf is exposed during a day. An imbalance of rates can lead to an excess production of electrons and can cause damage to the photosynthetic apparatus. This happens for example when leaves are exposed to very cold temperatures and high light during a frost event, or when you move your indoor plant that has been sitting in a dark corner for years suddenly into full sunlight outdoors.

    +

    The three steps described above operate in series, and each step is potentially rate-limiting and responds differently to the environment. The rates of the processes are coordinated such that they are roughly equal and co-limiting for average environmental conditions to which a leaf is exposed during a day. An imbalance of rates can lead to an excess production of electrons and can cause damage to the photosynthetic apparatus. This happens, for example, when leaves are exposed to very cold temperatures and high light during a frost event, or when you move your indoor plant that has been sitting in a dark corner for years suddenly into full sunlight outdoors.

    The response of photosynthetic CO2 assimilation (\(A\)) to light (PPFD) and leaf-internal CO2 (\(c_i\)) reflects the serial nature of how the light and dark reactions are connected. \(A\) saturates both in response to increasing PPFD as well as to increasing \(c_i\). When a leaf is exposed to increasing PPFD, \(A\) initially increases and eventually saturates (Figure 4.5). The slope of the initial linear increase reflects the efficiency at which photons are used for CO2 assimilation in the light reactions (the quantum yield \(\varphi_0\)). Under these conditions, light, i.e. the rate of the light reactions, is limiting, not CO2 inside the leaf. Under conditions of very high light, the dark reactions of the Calvin cycle become limiting. The assimilation rate attained under saturating light is commonly referred to as \(A_\mathrm{sat}\).

    The level at which the light response of \(A\) saturates (\(A_\mathrm{sat}\)) varies within a species and across different plant species. Variations within species arise through the acclimation of the light reaction capacities to the typical light intensities to which a leaf is exposed. Acclimation of photosynthesis evolves over time scales of weeks to months. (Thus, your indoor plant suffers because the change to high-light conditions happened to fast.) \(A_\mathrm{sat}\) also varies across species, reflecting the adaptation through evolution of different plant species to the environment in which they commonly grow. A typical light adaptation to different light levels is expressed by plants that commonly grow in the shady understorey versus plants that grow in the sun-exposed upper canopy.

    @@ -585,7 +585,7 @@

    \(A\) to \(c_i\) initially increase and saturates at high \(c_i\). This is reflected by the so-called “A-ci curve” (Figure 4.6). Commonly, net assimilation \(A_n = A - R_d\) is considered when analysing A-ci curves. \(A_n\) is initially negative until the photorespiratory compensation point (\(\Gamma^\ast\)) is reached. Then, \(A_n\) increases steeply with \(c_i\) as it is limited by the rate of RuBP carboxylation by Rubisco. This Rubisco carboxylation-limited functional response of assimilation is commonly denoted \(A_C\).

    +

    In a similar fashion, the response of \(A\) to \(c_i\) initially increases and saturates at high \(c_i\). This is reflected by the so-called “A-ci curve” (Figure 4.6). Commonly, net assimilation \(A_n = A - R_d\) is considered when analysing A-ci curves. \(A_n\) is initially negative until the photorespiratory compensation point (\(\Gamma^\ast\)) is reached. Then, \(A_n\) increases steeply with \(c_i\) as it is limited by the rate of RuBP carboxylation by Rubisco. This Rubisco carboxylation-limited functional response of assimilation is commonly denoted \(A_C\).

    As \(c_i\) increases further, \(A\) is no longer limited by RuBP carboxylation, but by the rate at which RuBP becomes available. This, in turn, is governed by the rate at which ATP and NADPH are produced and thus by the rate of electron transport \(J\). This functional response of assimilation is commonly denoted \(A_J\). A limiting electron transport rate may be due to limiting light or a limiting capacity of electron transport (\(J_\mathrm{max}\)). A slower further increase of \(A\) with \(c_i\) in the electron transport-limited range is due to the suppression of RuBP oxygenation at high concentrations of CO2 (relative to O2). The effective assimilation rate across the full range of \(c_i\) is the minimum of the electron transport-limited and the RuBP carboxylation-limited rate: \[ A_n = \min(A_C, A_J) - R_d \tag{4.7}\]

    @@ -927,9 +927,9 @@

    4.3.6 Response to temperature

    -

    All processes involved in photosynthesis are strongly affected by temperature. Enzymatic rates, like Rubisco carboxylation, have a temperature at which reaction rates have a maximum. As a consequence, assimilation rates also attain a maximum at a certain temperature - the temperature optimum (Topt). In contrast, dark respiration (\(R_d\)) monotonically increases with temperature. That is, it continues to rise as temperatures go up - without attaining a maximum. As a consequence, the decline of net assimilation rates is even faster at towards high temperatures than that of gross assimilation rates.

    +

    All processes involved in photosynthesis are strongly affected by temperature. Enzymatic rates, like Rubisco carboxylation, have a temperature at which reaction rates have a maximum. As a consequence, assimilation rates also attain a maximum at a certain temperature - the temperature optimum (Topt). In contrast, dark respiration (\(R_d\)) monotonically increases with temperature. That is, it continues to rise as temperatures go up - without attaining a maximum. As a consequence, the decline of net assimilation rates is even faster towards high temperatures than that of gross assimilation rates.

    The temperature dependency of leaf CO2 assimilation rates can be measured in the field by exposing a leaf to a range of temperatures (within a relatively short period of time) and measuring assimilation rates for each temperature. When looking at such measurements, a temperature optimum of net photosynthesis is evident.

    -

    The Farquhar-von Caemmerer Berry model for C3 photosynthesis (see Box ‘Farquhar von Caemmerer Berry model’) and the mathematical description of temperature dependencies of factors therein (\(V_\mathrm{cmax}\), \(J_\mathrm{max}\), \(K_c\), \(K_o\), and \(\Gamma^\ast\), temperature dependencies not shown here) provide a basis for modelling the temperature dependency of assimilation rates. Such modelled temperature dependencies are shown in Figure 4.9.

    +

    The Farquhar-von Caemmerer Berry model for C3 photosynthesis (see Box ‘Farquhar von Caemmerer Berry model’) and the mathematical description of temperature dependencies of factors therein (\(V_\mathrm{cmax}\), \(J_\mathrm{max}\), \(K_c\), \(K_o\), and \(\Gamma^\ast\), temperature dependencies not shown here) provide a basis for modelling the temperature dependency of assimilation rates. Such modelled temperature dependencies are shown in Figure 4.9.

    Code @@ -1047,9 +1047,9 @@

    -
    -

    4.3.7 Adptation and acclimation of Topt

    -

    The temperature dependencies shown in Figure 4.9 are instantaneous responses. That is, they represent the responses to changes in temperature that evolve over short time scales - minutes to hours. Over longer time scales, the shapes of the instantaneous temperature responses change. The temperature optimum of photosynthesis (Topt) tends to be higher for plant species that grow in warm climates than for plants that can be found in cold climates (Figure 4.10 a). Such variations of Topt across different plant species reflects species’ adaptation to their growth environment which makes them perform well and compete effectively under certain environmental conditions and is related to their genes and is thus passed on from generation to generation. Topt can be considered as a plant trait (see Section 2.4).

    +
    +

    4.3.7 Adaptation and acclimation of Topt

    +

    The temperature dependencies shown in Figure 4.9 are instantaneous responses. That is, they represent the responses to changes in temperature that evolve over short time scales - minutes to hours. Over longer time scales, the shapes of the instantaneous temperature responses change. The temperature optimum of photosynthesis (Topt) tends to be higher for plant species that grow in warm climates than for plants that can be found in cold climates (Figure 4.10 a). Such variations of Topt across different plant species reflect species’ adaptation to their growth environment which makes them perform well and compete effectively under certain environmental conditions and is related to their genes and is thus passed on from generation to generation. Topt can be considered as a plant trait (see Section 2.4).

    Topt not only varies between species growing in different climates, but can also vary within a given species and even within a given plant when it is exposed to different temperatures for a longer period (Kumarathunge et al. 2019). Given enough time, the instantaneous temperature response and Topt will shift to higher temperatures as a result of persistent exposure to warmer temperatures. Such variations in a plant trait (here Topt) within species and an individual plant is referred to as acclimation. Figure 4.10 b shows how Topt varies within different species (distinguished by color) over the course of the seasons - a demonstration of acclimation.

    @@ -1061,7 +1061,7 @@

    \(V_\mathrm{cmax}\) in the FvCB model - or the maximum rate of electron transport - \(J_\mathrm{max}\)) acclimate over the course of seasons (Jiang et al. 2020). Other plant traits are less plastic or not plastic at all. For example phenological strategies (e.g., deciduousness) does not acclimate. The acclimation of physiological traits is important for understanding vegetation and land carbon cycle responses to long-term trends in climate. While it may be exected that plants have a certain capacity for acclimation to a new climate, limits to acclimation must be better understood.

    +

    Acclimation is relatively common to observe also for other physiological traits than Topt. For example, photosynthetic capacities (the maximum rate of Rubisco carboxylation - \(V_\mathrm{cmax}\) in the FvCB model - or the maximum rate of electron transport - \(J_\mathrm{max}\)) acclimate over the course of seasons (Jiang et al. 2020). Other plant traits are less plastic or not plastic at all. For example, phenological strategies (e.g., deciduousness) do not acclimate. The acclimation of physiological traits is important for understanding vegetation and land carbon cycle responses to long-term trends in climate. While it may be expected that plants have a certain capacity for acclimation to a new climate, limits to acclimation must be better understood.

    @@ -1071,19 +1071,19 @@

    4.4 Transpiration and leaf water-carbon coupling

    -

    The opening of stomata is highly sensitive to environmental factors and the CO2 assimilation rate feeds back to stomatal opening. By opening and closing stomata, plants regulate the conductance to CO2 diffusion from the ambient air into the leaves and to the photosynthesis reaction sites. Simultaneously, when stomata are open, water vapour diffuses out of the leaf - transpiration. This link between CO2 and water loss is at the core of stomatal regulation to balance C uptake and desiccation.

    +

    The opening of stomata is highly sensitive to environmental factors, and the CO2 assimilation rate feeds back to stomatal opening. By opening and closing stomata, plants regulate the conductance to CO2 diffusion from the ambient air into the leaves and to the photosynthesis reaction sites. Simultaneously, when stomata are open, water vapor diffuses out of the leaf - transpiration. This link between CO2 and water loss is at the core of stomatal regulation to balance C uptake and desiccation.

    The diffusive supply of CO2 to the photosynthetic reaction sites is determined by a series of conductances. The description of the diffusive CO2 uptake in Equation 4.5 resolves this as a single conductance. However, stomatal conductance is only one chain in this series. More realistically, the leaf boundary layer conductance and the mesophyll conductance are treated separately from the stomatal conductance. However, because the leaf boundary layer conductance is much larger than the stomatal conductance, it is not limiting. Furthermore, actively regulated plant physiological responses to the environment arise through the stomatal conductance \(g_s\). As described in Section 4.3, mesophyll conductance is often ignored due to practical limitations for separating it from stomatal conductance in measurements and due to very poorly known dependencies to the environment. Hence, we focus on \(g_s\) here and describe the diffusive CO2 supply to photosynthesis by Equation 4.5.

    -

    The diffusive water vapour flux out of the leaf - transpiration - is driven by the difference of water vapour pressure in the leaf-interior air spaces (\(e_i\)) and the the water vapour pressure at the leaf surface (\(e_s\)). Their difference is commonly referred to as the vapour pressure deficit (VPD), here denoted as \(D = e_s - e_i\). Leaf-interior air spaces are water vapour-saturated, while the surrounding air is not. Fick’s law predicts that a diffusive flux occurs in presence of a concentration difference, hence transpiration can be described as \[ +

    The diffusive water vapor flux out of the leaf - transpiration - is driven by the difference of water vapor pressure in the leaf-interior air spaces (\(e_i\)) and the the water vapor pressure at the leaf surface (\(e_s\)). Their difference is commonly referred to as the vapor pressure deficit (VPD), here denoted as \(D = e_s - e_i\). Leaf-interior air spaces are water vapor-saturated, while the surrounding air is not. Fick’s law predicts that a diffusive flux occurs in presence of a concentration difference, hence transpiration can be described as \[ E = 1.6 \; g_s \; D \tag{4.11}\] The factor 1.6 arises due to the lower diffusivity of CO2 compared with H2O. Hence, \(g_s\) has to be understood as a conductance to CO2 diffusion (mol CO2 m-2 s-1). Note that \(g_s\) regulates both transpiration (Equation 4.11) and assimilation (Equation 4.5) at the leaf-level. A tight coupling between water and carbon fluxes at the leaf-level follows from the physical principle of diffusion.

    -

    Water loss through transpiration poses risks and incurs costs for a plant. The diffusive water vapour flux through stomata has to be maintained by root water uptake from the soil and transport along the xylem in the plant. When the water content in the rooting zone declines, it becomes increasingly hard for plants to extract water from the soil - they have to “suck” out the water with a increasingly negative water potential - a negative pressure. The hydraulic relationships of water transport along the soil-plant-atmosphere continuum will be introduced later. What matters here is that such negative water potentials along the water transport pathway are dangerous for the plant and can lead to lethal desiccation of cells, leaves, branches, or entire plants.

    -

    Avoidance of dangerous desiccation is enabled by responses at the level of leaves and the plant which operate at a range of time scales. At time scales of seconds to minutes and at the level of a leaf, stomatal conductance is reduced in response to dry air and dry soil conditions. At time scales of weeks to months, or even years, the the leaf area of a plant may decline under dry conditions. At even longer time scales (albeit this time scale is subject to large unknowns and active research), plants are genetically adapted (or may acclimate within their lifetime) to dry conditions by resistant water transport (resistant xylem) and effective water uptake organs (deeper roots).

    +

    Water loss through transpiration poses risks and incurs costs for a plant. The diffusive water vapor flux through stomata has to be maintained by root water uptake from the soil and transport along the xylem in the plant. When the water content in the rooting zone declines, it becomes increasingly hard for plants to extract water from the soil - they have to “suck” out the water with a increasingly negative water potential - a negative pressure. The hydraulic relationships of water transport along the soil-plant-atmosphere continuum will be introduced later. What matters here is that such negative water potentials along the water transport pathway are dangerous for the plant and can lead to lethal desiccation of cells, leaves, branches, or entire plants.

    +

    Avoidance of dangerous desiccation is enabled by responses at the level of leaves and the plant which operate at a range of time scales. At time scales of seconds to minutes and at the level of a leaf, stomatal conductance is reduced in response to dry air and dry soil conditions. At time scales of weeks to months, or even years, the leaf area of a plant may decline under dry conditions. At even longer time scales (albeit this time scale is subject to large unknowns and active research), plants are genetically adapted (or may acclimate within their lifetime) to dry conditions by resistant water transport (resistant xylem) and effective water uptake organs (deeper roots).

    Obviously, such adaptations and the largely instantaneous stomatal response incurs a cost - the opportunity cost of reduced CO2 assimilation when stomatal conductance is reduced and the construction cost of building water-stress adapted organs. Hence, plants always have to balance carbon uptake and water loss and a tight carbon-water coupling at the level of plants, and ecosystems arises from these leaf-level processes.

    4.4.1 Water use efficiency

    The trade-off between transpiration and assimilation can be measured by considering their ratio by combining Equation 4.5 and Equation 4.11 to define the instantaneous water-use efficiency: \[ \frac{A_n}{E} = \frac{c_a(1 - \chi)}{1.6\;D}\;, -\tag{4.12}\] where \(\chi = c_i/c_a\). The instantaneous water-use efficiency is proportional to \(D^{-1}\). In other words, the drier the air, the more transpiration per unit net CO2 assimilation a leaf “suffers”. This demonstrates the strong effect of atmospheric dryness on the water-carbon trade-off. To remove the effect of vapour pressure deficit (\(D\)) on transpiration and focus on the biological component of the water-carbon trade-off, the intrinsic water-use efficiency (iWUE) is defined by relating net assimilation to stomatal conductance: \[ +\tag{4.12}\] where \(\chi = c_i/c_a\). The instantaneous water-use efficiency is proportional to \(D^{-1}\). In other words, the drier the air, the more transpiration per unit net CO2 assimilation a leaf “suffers”. This demonstrates the strong effect of atmospheric dryness on the water-carbon trade-off. To remove the effect of vapor pressure deficit (\(D\)) on transpiration and focus on the biological component of the water-carbon trade-off, the intrinsic water-use efficiency (iWUE) is defined by relating net assimilation to stomatal conductance: \[ \frac{A_n}{g_s} = \frac{c_a}{1.6}(1 - \chi) \tag{4.13}\] Note that Equation 4.12 and Equation 4.13 are written as being proportional to \(c_a(1-\chi)\). Of course, this term is mathematically equivalent to \((c_a - c_i)\). However, there is a reason for expressing it this way. First, it reflects the direct influence of \(c_a\) ambient (atmospheric) CO2 concentration on the water-carbon trade-off - less water is lost for a given amount of C assimilation under elevated CO2. Second, observations suggest that \(\chi\) is regulated by plants to remain relatively constant under a wide range of CO2 levels (Ainsworth and Long 2005) and Figure 4.11. The near constancy of \(\chi\) is also reflected by the observation that \(A_n\) and \(g_s\) vary in near proportion across a wide range of light levels (Bonan 2015).

    @@ -1091,7 +1091,7 @@

    -
    Figure 4.11: Constancy of leaf-internal to ambient CO2. (a) Relationship between net photosynthesis (An) and stomatal conductance (gs) of one species (Jack pine) over a range of light conditions. A linear relationship is reflective of a constant ci:ca. Figure from Bonan (2015). (b) Response of multiple photosynthesis-related variables to elevated CO2 from free-air carbon dioxide enrichment experiments. Figure from Ainsworth and Long (2005). ci:ca
    +
    Figure 4.11: Constancy of leaf-internal to ambient CO2. (a) Relationship between net photosynthesis (An) and stomatal conductance (gs) of one species (Jack pine) over a range of light conditions. A linear relationship is reflective of a constant ci:ca. Figure from Bonan (2015). (b) Response of multiple photosynthesis-related variables to elevated CO2 from free-air carbon dioxide enrichment experiments. Figure from Ainsworth and Long (2005).

    @@ -1104,7 +1104,7 @@

    4.4.3 Stomatal regulation

    The closing of stomates and the reduction of stomatal conductance \(g_s\) under dry conditions prevents plants from dangerous desiccation. However, a reduced \(g_s\) also leads to a reduction in CO2 diffusion into leaves and thus a reduction of photosynthetic CO2 assimilation. Hence, plants have to balance a trade-off between carbon gain and the risk of desiccation. A complete stomatal closure under moderately dry conditions (low soil moisture, high VPD) may be safe in terms of desiccation avoidance but comes at an excessive cost in terms of foregone CO2 uptake (and similarly vice-versa). An optimal strategy must lie somewhere in between these extreme strategies.

    -

    Observations of leaf and ecosystem fluxes CO2 and water vapour fluxes document how stomatal conductance responds to increasing VPD and decreasing soil moisture. Figure 4.12 shows this for measurements taken at the ecosystem-level, quantifying the canopy stomatal conductance (denoted by an uppercase \(G_s\)), representative for the collective behaviour of all leaves in the canopy. Three important aspects of this relationship stand out. First, \(G_s\) declines in response to VPD in a non-linear fashion (high sensitivity to VPD at low VPD, lower sensitivity towards higher VPD). Second, there is an interaction between the effect of VPD and soil moisture. Under conditions of dry soils, \(G_s\) is reduced compared to wet soils, given the same VPD. Third, at the most moist site (Figure 4.12 a), \(G_s\) under moist conditions (moist soils, low VPD) is highest but declines most rapidly with VPD.

    +

    Observations of leaf and ecosystem fluxes CO2 and water vapor fluxes document how stomatal conductance responds to increasing VPD and decreasing soil moisture. Figure 4.12 shows this for measurements taken at the ecosystem-level, quantifying the canopy stomatal conductance (denoted by an uppercase \(G_s\)), representative for the collective behaviour of all leaves in the canopy. Three important aspects of this relationship stand out. First, \(G_s\) declines in response to VPD in a non-linear fashion (high sensitivity to VPD at low VPD, lower sensitivity towards higher VPD). Second, there is an interaction between the effect of VPD and soil moisture. Under conditions of dry soils, \(G_s\) is reduced compared to wet soils, given the same VPD. Third, at the moistest site (Figure 4.12 a), \(G_s\) under moist conditions (moist soils, low VPD) is highest but declines most rapidly with VPD.

    @@ -1130,7 +1130,7 @@

    -

    The aspect that plants regulate stomatal conductance to balance the trade-off between carbon gain and water loss lends itself to modelling the stomatal response considering optimality principles. Indeed, there is empirical evidence that optimality models are a good representation of how stomata are regulated. Following this notion, it can be assumed that stomatal conductance is optimised such that the net between the carbon gain by increasing stomatal conductance and the carbon cost by the resulting increased transpiration and is maximized.

    +

    The aspect that plants regulate stomatal conductance to balance the trade-off between carbon gain and water loss lends itself to modelling the stomatal response considering optimality principles. Indeed, there is empirical evidence that optimality models are a good representation of how stomata are regulated. Following this notion, it can be assumed that stomatal conductance is optimised such that the net between the carbon gain by increasing stomatal conductance and the carbon cost by the resulting increased transpiration is maximized.

    \[ A - aE - bV_\mathrm{cmax} = \arg \max \tag{4.14}\]

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  • 1.2 Why we study the land
    • @@ -328,7 +328,7 @@

    1  Falkowski et al. (2000)

    +

    As we drift further away from the domain that characterized the pre-industrial Earth system, we severely test the limits of our understanding of how the Earth system will respond. – Falkowski et al. (2000)

    The Earth system can be regarded as a coupled system in which its elements (atmosphere, ocean, cryosphere, biosphere, pedosphere, lithosphere) are interacting on various time scales. A primary goal of Earth System research is to understand the interactions occurring on time scales that are relevant for society in the context of anthropogenic climate change. It is now established with overwhelming evidence that anthropogenic CO2 emissions from the combustion of fossil fuels have caused a rise in atmospheric CO2 concentrations beyond levels reached over the past 800,000 years, and that this concentration increase is the dominant driver of climate change as observed over the last decades.

    The terrestrial biosphere - land - is at the core of the Earth system. It connects all spheres. Atmospheric humidity and near-surface heating of the atmosphere are determined by how much water vegetation transpires and how much radiation it reflects or absorbs. Its carbon balance determines the accumulation of anthropogenic CO2 in the atmosphere and thus affects the CO2 gas exchange between the ocean and the atmosphere. The activity of plants is the driver for processes in the soil, the weathering of rocks. Any projection of climate change and climate impacts for the coming decades, centuries and millennia relies on an understanding of how the terrestrial biosphere responds and feeds back to climate and the Earth system. The carbon cycle of the terrestrial biosphere has a strong influence on how fast anthropogenic CO2 emissions will accumulate in the atmosphere. And it is through land ecosystems - both natural and agricultural - that climate impacts will be most clearly expressed. Understanding how climate influences the terrestrial biosphere is thus key to understanding climate impacts and projecting Earth system change.

    This book focuses on the terrestrial biosphere, how its structure and functioning are shaped by climate, and how it affects atmospheric CO2 and climate change. The following set of phenomena, observations, and popularised concepts are an expression of the key role of the land in the Earth system. Over the course of this book, we will revisit these phenomena, observations, and concepts, introduce the underlying processes and principles for understanding them, and provide a scientific basis to address questions of immanent societal relevance. What is the role of the land biosphere in accelerating climate change (think positive feedbacks and tipping points), and in providing solutions for mitigating it (think forest restoration and other land-based mitigation options).

    @@ -369,8 +369,8 @@

    1.1.3 Responses to rapid climate change in the past

    -

    The climate of the past 11,000 years (11 ka) until the Industrial Revolution was relatively stable, at least in comparison to the climate of the Last Glacial period. This period was marked by millennial-scale climate oscillations where temperatures rose by up to 16\(^\circ\)C within a few decades (Oeschger et al. 1984; Dansgaard et al. 1993). When first discovered in measurments of an ice core recovered from Greenland, the massive excursions of the \(\delta^{18}\)O signal - a proxy for air temperature - were considered a measurement error. But the correspondence of similar excursions measured on a different Greenland ice core and the coincidence of the most recent such excursion with a similar pattern found in the \(\delta^{18}\)O signal of carbonate in the lake sediment of Gerzensee (near Bern) (Oeschger et al. 1984) confirmed the robustness of these rapid climate change events in the past. Reflecting this, these rapid climate swings between about 80 and 10 ka BP were named Dansgaard-Oeschger events. Today, Dansgaard-Oeschger events are undersood to be oscillations of the Earth system that occurr without external triggers, but arise from the interaction of ocean and ice sheet dynamics, and are confined to Earth system states corresponding to the glacial periods of the late Pleistocene (Stocker and Johnsen 2003; Vettoretti et al. 2022).

    -

    The terrestrial biosphere was strongly affected by these large and rapid climate changes and left its imprints in several palaeo records (Figure 1.3). In response to the climate warming, atmospheric methane (CH4) concentrations increased rapidly. Natural CH4 sources almost exclusively in land ecosystems (wetlands, fire). In parallel, the amount of dust transported to Greenland declined rapidly as climate warmed. This reflects an expansion of vegetation cover into dust-forming regions (e.g., deserts and peri-glacial areas). Also in parallel, nitrous oxide (N2O), another greenhouse gas, increased. This increase unfolded more gradually and reflects both oceanic and terrestrial sources. Furthermore, fire activity in the northern hemisphere, measured by charcoal deposits in Greenland ice cores, increased as the climate warmed.

    +

    The climate of the past 11,000 years (11 ka) until the Industrial Revolution was relatively stable, at least in comparison to the climate of the Last Glacial period. This period was marked by millennial-scale climate oscillations where temperatures rose by up to 16\(^\circ\)C within a few decades (Oeschger et al. 1984; Dansgaard et al. 1993). When first discovered in measurements of an ice core recovered from Greenland, the massive excursions of the \(\delta^{18}\)O signal - a proxy for air temperature - were considered a measurement error. But the correspondence of similar excursions measured on a different Greenland ice core and the coincidence of the most recent such excursion with a similar pattern found in the \(\delta^{18}\)O signal of carbonate in the lake sediment of Gerzensee (near Bern) (Oeschger et al. 1984) confirmed the robustness of these rapid climate change events in the past. Reflecting this, these rapid climate swings between about 80 and 10 ka BP were named Dansgaard-Oeschger events. Today, Dansgaard-Oeschger events are understood to be oscillations of the Earth system that occur without external triggers, but arise from the interaction of ocean and ice sheet dynamics, and are confined to Earth system states corresponding to the glacial periods of the late Pleistocene (Stocker and Johnsen 2003; Vettoretti et al. 2022).

    +

    The terrestrial biosphere was strongly affected by these large and rapid climate changes and left its imprints in several palaeo records (Figure 1.3). In response to the climate warming, atmospheric methane (CH4) concentrations increased rapidly. Natural CH4 sources originate almost exclusively from land ecosystems (wetlands, fire). In parallel, the amount of dust transported to Greenland declined rapidly as climate warmed. This reflects an expansion of vegetation cover into dust-forming regions (e.g., deserts and peri-glacial areas). Also in parallel, nitrous oxide (N2O), another greenhouse gas, increased. This increase unfolded more gradually and reflects both oceanic and terrestrial sources. Furthermore, fire activity in the northern hemisphere, measured by charcoal deposits in Greenland ice cores, increased as the climate warmed.

    @@ -392,7 +392,7 @@

    -
    Figure 1.4: An overview of physical and biogeochemical feedbacks in the climate system. (a) Synthesis of physical, biogeophysical and non-carbon dioxide (CO2) biogeochemical feedbacks that are included in the definition of equilibrium climate sensitivity (ECS) assessed in this Technical Summary. These feedbacks have been assessed using multiple lines of evidence including observations, models and theory. The net feedback is the sum of the Planck response, water vapour and lapse rate, surface albedo, cloud, and biogeophysical and non-CO2 biogeochemical feedbacks. Bars denote the mean feedback values, and uncertainties representvery likely ranges; (b) Estimated values of individual biogeophysical and non-CO2 biogeochemical feedbacks. The atmospheric methane (CH4) lifetime and other non-CO2 biogeochemical feedbacks have been calculated using global Earth system model simulations from AerChemMIP, while the CH4 and nitrous oxide (N2O) source responses to climate have been assessed for the year 2100 using a range of modelling approaches using simplified radiative forcing equations. The estimates represent the mean and 5–95% range. The level of confidence in these estimates is lowowing to the large model spread. (c) Carbon-cycle feedbacks as simulated by models participating in the C4MIP of the Coupled Model Intercomparison Project Phase 6 (CMIP6). An independent estimate of the additional positive carbon-cycle climate feedbacks from permafrost thaw, which is not considered in most C4MIP models, is added. The estimates represent the mean and 5–95% range. Note that these feedbacks act through modifying the atmospheric concentration of CO2 and thus are not included in the definition of ECS, which assumes a doubling of CO2 , 4 but are included in the definition and assessed range of the transient climate response to cumulative CO2 emissions (TCRE). {5.4.7, 5.4.8, Box 5.1, Figure 5.29, 6.4.5, Table 6.9, 7.4.2, Table 7.10}. Figure and caption text from the IPCC Assessment Report 6, Technical Summary, Figure TS.17 (Arias et al. 2021).
    +
    Figure 1.4: An overview of physical and biogeochemical feedbacks in the climate system. (a) Synthesis of physical, biogeophysical and non-carbon dioxide (CO2) biogeochemical feedbacks that are included in the definition of equilibrium climate sensitivity (ECS) assessed in this Technical Summary. These feedbacks have been assessed using multiple lines of evidence including observations, models and theory. The net feedback is the sum of the Planck response, water vapor and lapse rate, surface albedo, cloud, and biogeophysical and non-CO2 biogeochemical feedbacks. Bars denote the mean feedback values, and uncertainties representvery likely ranges; (b) Estimated values of individual biogeophysical and non-CO2 biogeochemical feedbacks. The atmospheric methane (CH4) lifetime and other non-CO2 biogeochemical feedbacks have been calculated using global Earth system model simulations from AerChemMIP, while the CH4 and nitrous oxide (N2O) source responses to climate have been assessed for the year 2100 using a range of modelling approaches using simplified radiative forcing equations. The estimates represent the mean and 5–95% range. The level of confidence in these estimates is lowowing to the large model spread. (c) Carbon-cycle feedbacks as simulated by models participating in the C4MIP of the Coupled Model Intercomparison Project Phase 6 (CMIP6). An independent estimate of the additional positive carbon-cycle climate feedbacks from permafrost thaw, which is not considered in most C4MIP models, is added. The estimates represent the mean and 5–95% range. Note that these feedbacks act through modifying the atmospheric concentration of CO2 and thus are not included in the definition of ECS, which assumes a doubling of CO2 , 4 but are included in the definition and assessed range of the transient climate response to cumulative CO2 emissions (TCRE). {5.4.7, 5.4.8, Box 5.1, Figure 5.29, 6.4.5, Table 6.9, 7.4.2, Table 7.10}. Figure and caption text from the IPCC Assessment Report 6, Technical Summary, Figure TS.17 (Arias et al. 2021).

    @@ -402,7 +402,7 @@

    1.1.5 Tipping points

    -

    Tipping points in the Earth system are points at which of a part of the Earth system transitions into a new state in response to a relatively small external forcing. They are inherently hard to predict using Earth System Models. Surprises cannot be excluded. Several potential tipping points have been identified in terrestrial systems (Armstrong McKay et al. 2022). Their reliable simulation in models relies on accurate models of processes in land ecosystems. Once more, land ecosystems and their response to climate change may be a critical element for the future of the Earth system. However, relatively large uncertainties remain for modelling key processes and further research is needed to consolidate the current understanding (and hand-drawn map) of potential tipping elements in the land biosphere (Armstrong McKay et al. 2022).

    +

    Tipping points in the Earth system are points at which a part of the Earth system transitions into a new state in response to a relatively small external forcing. They are inherently hard to predict using Earth System Models. Surprises cannot be excluded. Several potential tipping points have been identified in terrestrial systems (Armstrong McKay et al. 2022). Their reliable simulation in models relies on accurate models of processes in land ecosystems. Once more, land ecosystems and their response to climate change may be a critical element for the future of the Earth system. However, relatively large uncertainties remain for modelling key processes and further research is needed to consolidate the current understanding (and hand-drawn map) of potential tipping elements in the land biosphere (Armstrong McKay et al. 2022).

    @@ -414,9 +414,9 @@

    -
    -

    1.1.6 Carbon dixide removal through land ecosystems

    -

    For the climate to be stabilized at 1.5°C or 2.0°C, rapid and large CO2 emission cuts are needed. Alongside the reduction of fossil fuel combustion, climate stabilization scenarios rely - to a varying degree - on carbon dioxide removal (CDR). Most CDR options deployed to date and available for scaling to meet climate stabilization needs rely on land ecosystems for sequestering (net uptake and long-term storage) additional C. Afforestation and reforestation have been estimated to be a potent solution for climate change mitigation (Walker et al. 2022; Mo et al. 2023) and tree planting has moved to center stage in the public perception and in policy efforts to avert dangerous climate change. But can we rely on trees or other land ecosystems as a solution for the climate crisis?

    +
    +

    1.1.6 Carbon dioxide removal through land ecosystems

    +

    For the climate to be stabilized at 1.5°C or 2.0°C, rapid and large CO2 emission cuts are needed. Alongside the reduction of fossil fuel combustion, climate stabilization scenarios rely - to a varying degree - on carbon dioxide removal (CDR). Most CDR options deployed to date and available for scaling to meet climate stabilization needs rely on land ecosystems for sequestering (net uptake and long-term storage) additional C. Afforestation and reforestation have been estimated to be a potent solution for climate change mitigation (Walker et al. 2022; Mo et al. 2023) and tree planting has moved to center stage in the public perception and in policy efforts to avert dangerous climate change. The figure below shows an example of stylised net-zero pathway.

    @@ -427,7 +427,8 @@

    (Deprez et al. 2024). For example, the carbon stored in a tree is susceptible to a range of threats, including wildfires, deforestation, and tree mortality by aggravating climatic stress (Anderegg et al. 2020). Moreover, surface properties, relevant for land-climate interactions, and their differences between forests and grasslands imply that forests may heat the local climate more than a grassland would - despite the additional C stored in a forest (Bala et al. 2007).

    +

    But can we rely on trees or other land ecosystems as a solution for the climate crisis? Ecological principles and multiple aspects of the role of land ecosystems and their interaction with climate and the carbon cycle have to be considered - apart from conflicts with biodiversity and sustainability goals and social, economic, and cultural aspects of land use (Deprez et al. 2024). For example, the carbon stored in a tree is susceptible to a range of threats, including wildfires, deforestation, and tree mortality by aggravating climatic stress (Anderegg et al. 2020). Moreover, surface properties, relevant for land-climate interactions, and their differences between forests and grasslands imply that forests may heat the local climate more than a grassland would - despite the additional C stored in a forest (Bala et al. 2007).

    +

    Understanding the technical potential of land-based CDR will have to consider the full complexity of land-Earth system interactions. This course introduces these interactions.

    @@ -435,7 +436,7 @@

    1.2 Why we study the land

    -

    The examples for given above are attest to the key role of the terrestrial biosphere in the Earth system and for understanding the risks and mitigation options in the context of anthropogenic climate change. With climate change and its impacts moving into the centre of public attention and becoming an increasingly important boundary condition for policy making, it is crucial to have a basic understanding of the Earth system and how the terrestrial biosphere works. That’s why we study Land in the Earth System.

    +

    The examples given above illustrate the key role of the terrestrial biosphere in the Earth system and the importance of understanding the risks and mitigation options in the context of anthropogenic climate change. With climate change and its impacts moving into the centre of public attention and becoming an increasingly important boundary condition for policymaking, it is crucial to have a solid understanding of the Earth system and how the terrestrial biosphere works. That’s why we study Land in the Earth System.

    @@ -520,7 +523,7 @@

    The longwave radiation components are a substantial fraction of net radiation. In Figure 7.2, they are referred to as “thermal”. The outgoing longwave radiation \(L\uparrow\) is on average 398 W m-2 and is a function of the Earth’s surface temperature and emissivity, following the Stefan-Boltzmann law (Equation 7.3), plus the incident longwave radiation reflected (not absorbed) by the surface: \[ L\uparrow = \varepsilon \sigma T^4 + (1-\varepsilon) L\downarrow \tag{7.4}\] Note that \(\varepsilon\) is used in Equation 7.4 as the absorbtivity and in Equation 7.3 as the emissivity. This is because the two are equal.

    -

    Clouds absorb radiation emitted by the earth surface and re-emit a large fraction of it. In absence of clouds, much less radiation is absorbed and re-emitted by the atmosphere. Therefore, the incoming longwave radiation depends strongly on the presence of clouds.

    +

    Clouds absorb radiation emitted by the Earth’s surface and re-emit a large fraction of it. In the absence of clouds, much less radiation is absorbed and re-emitted by the atmosphere. Therefore, the incoming longwave radiation depends strongly on the presence of clouds.

    @@ -531,7 +534,7 @@

    -

    Using Equation 7.2 and Equation 7.4, the net radiation at the earth surface (Equation 7.1) can be expressed as \[ +

    Using Equation 7.2 and Equation 7.4, the net radiation at the Earth surface (Equation 7.1) can be expressed as \[ R_n = (1-\alpha) S\downarrow + \varepsilon L\downarrow - \varepsilon \sigma T^4 \]

    @@ -558,7 +561,7 @@

    The energy available from radiative fluxes is converted into a sensible heat flux (\(H\)), a latent heat flux (\(\lambda E\)), and a ground heat flux (\(G\), Figure 7.1 b). Following energy conservation, net radiation is equal to the sum of these three heat fluxes. \[ R_n = H + \lambda E + G \tag{7.5}\]

    -

    The components of the surface energy balance (Equation 7.5) are commonly expressed in energy units (W m-2). Sensible heat is determined by the temperature of air. Latent heat is the energy contained by evaporated water. The latent heat flux (\(\lambda E\)) can also be expressed as a mass flux of water vapour (\(E\)). \(E\) is the mass flux of water vapor, e.g., expressed in units of g m-2 s-1. \(\lambda\) is the latent heat of vaporization and converts the mass units into energy units. It measures how much energy (Joules, J) is needed vapourize 1 g of water at constant temperature. \(\lambda\) is 2.466 MJ kg-1 at 15°C and has a slight dependence on temperature, decreasing linearly by about 3% from an air temperature of 0°C to 30°C.

    +

    The components of the surface energy balance (Equation 7.5) are commonly expressed in energy units (W m-2). Sensible heat is determined by the temperature of air. Latent heat is the energy contained by evaporated water. The latent heat flux (\(\lambda E\)) is the product of the mass flux of water vapor (\(E\)), expressed in units of g m-2 s-1, and the latent heat of vaporization (\(\lambda\)), converting the mass units back into energy units. \(\lambda\) measures how much energy (Joules, J) is needed to vaporize 1 g of water at constant temperature. \(\lambda\) is 2.466 MJ kg-1 at 15°C and has a slight dependence on temperature, decreasing linearly by about 3% from an air temperature of 0°C to 30°C.

    @@ -595,14 +598,15 @@

    -

    The sensible and latent heat fluxes are transported vertically, away from or to the land surface through convective transport. That is, through turbulences that mix the air and lead to a net vertical transport of heat and water vapor. Whether net fluxes are pointed upwards or downwards depends on the sign of the net radiation (see Figure 7.11 and Figure 7.12) and typically changes between night and daytime. Note that the latent heat flux can be negative, leading to a net flux of water vapor towards the surface. The respective water mass condensates at the surface (of leaves) and can be a considerable fraction of the ecosystem water balance. The ground heat flux \(G\) buffers variations of net radiation, absorbing energy and removing heat from the surface during the day and summer and releasing heat during night and winter.

    - +

    The sensible and latent heat fluxes are transported vertically, away from or to the land surface through convective transport. That is, through turbulences that mix the air and lead to a net vertical transport of heat and water vapor. Whether net fluxes are pointed upwards or downwards depends on the sign of the net radiation (see Figure 7.11 and Figure 7.12) and typically changes between night and daytime. Note that the latent heat flux can be negative, leading to a net flux of water vapor towards the surface. The respective water mass condensates at the surface (of leaves) and can be a considerable fraction of the ecosystem water balance.

    +

    Finally, the ground heat flux \(G\) buffers variations of net radiation, absorbing energy and removing heat from the surface during the day and summer and releasing heat during night and winter.

    +

    7.2.1 Potential evapotranspiration

    -

    Physical and biological properties of the land surface determine not only the net radiation through (mainly) effects of the albedo, but also strongly influence the partitioning of net radiation into sensible and latent heat fluxes in Equation 7.5. In particular, the availability of water for evaporation from the land surface through transpiration or directly from wet surfaces, is decisive for the partitioning of net radiation into \(H\) and \(\lambda E\).

    -

    A useful quantity for understanding the surface energy partitioning and the influence of limiting factors (e.g., water limitation) is the potential evapotranspiration (PET). Evapotranspiration is equivalent to the latent heat flux, but expressed in water vapour mass units. (You will learn more about evapotranspiration in Chapter 8). PET can be understood as the maximum possible \(E\), attained under conditions where water supply to evaporation is not limiting. Different methods are available for estimating PET. A physically based and widely used method is the one by Priestley and Taylor (1972) which relates PET to net radiation, considering that net radiation is consumed by the water vapor flux from a water-saturated surface into an air parcel at constant temperature and pressure. \[ +

    Physical and biological properties of the land surface determine not only the net radiation through (mainly) effects of the albedo, but also strongly influence the partitioning of net radiation into sensible and latent heat fluxes in Equation 7.5. In particular, the availability of water for evaporation from the land surface through transpiration, or directly from wet surfaces, is decisive for the partitioning of net radiation into \(H\) and \(\lambda E\).

    +

    A useful quantity for understanding the surface energy partitioning and the influence of limiting factors (e.g., water limitation) is the potential evapotranspiration (PET). Evapotranspiration is equivalent to the latent heat flux, but expressed in water vapor mass units. (You will learn more about evapotranspiration in Chapter 8). PET can be understood as the maximum possible \(E\), attained under conditions where water supply to evaporation is not limiting. Different methods are available for estimating PET. A physically based and widely used method is the one by Priestley and Taylor (1972) which relates PET to net radiation, considering that net radiation is consumed by the water vapor flux from a water-saturated surface into an air parcel at constant temperature and pressure. \[ \mathrm{PET} = \alpha \frac{s}{s + \gamma} \frac{R_n}{\lambda} -\tag{7.6}\] Here, \(s\) (Pa K-2) is the slope the change in saturation vapor pressure with respect to temperature. \(\gamma\) is the psychrometric constant (a representative value is 66.5 Pa K–1). The coefficient \(\alpha\) is an empirically determined value and is taken to be 1.26 for a wet surface. However, for vegetated surfaces, it is substantially lower, even if the plants are not water-limited. It ranges between 0.82 for tropical and temperate broadleaf forests and 0.55 for boreal conifer forests (G. Bonan 2015).

    +\tag{7.6}\] Here, \(s\) (Pa K-2) is the slope of the change in saturation vapor pressure with respect to temperature. \(\gamma\) is the psychrometric constant (a representative value is 66.5 Pa K–1). The coefficient \(\alpha\) is an empirically determined value and is taken to be 1.26 for a wet surface. However, for vegetated surfaces, it is substantially lower, even if the plants are not water-limited. It ranges between 0.82 for tropical and temperate broadleaf forests and 0.55 for boreal conifer forests (G. Bonan 2015).

    7.2.2 Metrics of energy partitioning

    @@ -625,8 +629,8 @@

    7.2.3 Combining energy, atmospheric, and biophysical controls on \(\lambda E\)

    -

    Not only the availability of water for evaporation, but also the atmospheric condition (specifically, the vapour pressure deficit) and biophysical surface properties determine the latent heat flux and the surface energy partitioning. The key biophysical surface properties are the aerodynamic conductance to heat transfer (\(G_\mathrm{ah}\)) and the surface conductance to water vapor transport (\(G_\mathrm{sw}\)). How energy, atmospheric, and biophysical controls drive the latent heat flux \(\lambda E\) is described by the Penman-Monteith equation (Equation 7.7), as shown in the box below and Figure 7.9. The aerodynamic conductance depends on the roughness of the surface and on wind speed. Taller vegetation has a higher roughness and a higher aerodynamic conductance. Roughness also increases with LAI.

    -

    On vegetated surfaces, the surface conductance to water vapor transport is strongly influenced by the stomatal conductance (\(g_s\), Equation 4.5 and Equation 4.11) and by the LAI. Water evaporation from rock, soil, leaf, or branch surfaces contributes to surface conductance and occurs also from non-vegetated surfaces. In a closed canopy, surface conductance is dominated by the signal by stomatal conductance. When leaves are active and photosynthesizing (high light), and when water stress is low (high soil moisture, low VPD), stomatal conductance is high. How water availability and vegetation regulate stomatal conductance and thus the latent heat flux and energy partitioning at the land surface is introduced in Chapter 8.

    +

    Not only the availability of water for evaporation, but also the atmospheric condition (specifically, the vapor pressure deficit) and biophysical surface properties determine the latent heat flux and the surface energy partitioning. The key biophysical surface properties are the aerodynamic conductance to heat transfer (\(G_\mathrm{ah}\)) and the surface conductance to water vapor transport (\(G_\mathrm{sw}\)). How energy, atmospheric, and biophysical controls drive the latent heat flux \(\lambda E\) is described by the Penman-Monteith equation (Equation 7.7), as shown in the box below and Figure 7.9. The aerodynamic conductance depends on the roughness of the surface and on wind speed. Taller vegetation has a higher roughness and a higher aerodynamic conductance. Roughness also increases with LAI.

    +

    On vegetated surfaces, the surface conductance to water vapor transport is strongly influenced by the stomatal conductance (\(g_s\), Equation 4.5 and Equation 4.11) and by the LAI. Water evaporation from rock, soil, leaf, or branch surfaces contributes to surface conductance and occurs also from non-vegetated surfaces. In a closed canopy, surface conductance is dominated by the signal by stomatal conductance. When leaves are active and photosynthesizing (high light), and when water stress is low (high soil moisture, low VPD), stomatal conductance is high. How water availability and vegetation regulate stomatal conductance, and thus the latent heat flux and energy partitioning at the land surface is introduced in Chapter 8.

    @@ -673,7 +677,7 @@

    calc_le_pm <- function(netrad, vpd, temp, g_ah, g_sw){ # ARGUMENTS # netrad: net radiation - # vpd: vapour pressure deficit + # vpd: vapor pressure deficit # temp: ambient air temperature # patm: atmospheric pressure (kPa) # aerodynamic conductance to heat transport, in mass units (m s-1) @@ -813,7 +817,7 @@

    Figure 7.9 shows an interesting interactive effect of aerodynamic conductance and the VPD of ambient air. At low VPD, plant transpiration is reduced, thus limiting the latent heat flux (\(\lambda E\)). Under such conditions, the \(\lambda E\) declines with increasing aerodynamic conductance. This is because \(H\) rises faster than \(\lambda E\) with increasing aerodynamic conductance and consumes a larger share of the net radiation. Under moderate-to-high VPD (above $$1 kPa in this example), \(\lambda E\) rises with increasing aerodynamic conductance.

    +

    Figure 7.9 shows an interesting interactive effect of aerodynamic conductance and the VPD of ambient air. At low VPD, plant transpiration is reduced, thus limiting the latent heat flux (\(\lambda E\)). Under such conditions, the \(\lambda E\) declines with increasing aerodynamic conductance. This is because \(H\) rises faster than \(\lambda E\) with increasing aerodynamic conductance and consumes a larger share of the net radiation. Under moderate-to-high VPD (above ~1 kPa in this example), \(\lambda E\) rises with increasing aerodynamic conductance.

    Under conditions of very low aerodynamic conductance (e.g., in a short-statured grassland that has a low surface roughness and under stable atmospheric conditions, e.g., during an inversion), the latent heat flux does not approach zero. This is because as long as there is positive net radiation (here 400 W m-2), the surface (skin temperature) heats up relative to the ambient air and creates a positive VPD at the leaf surface (even if VPD of ambient air is zero). These aspects drive a continued positive \(H\) and \(\lambda E\) and the rise of the surface boundary layer.

    @@ -822,7 +826,7 @@

    7.3 Energy fluxes across biomes

    -

    As for C fluxes in Chapter 6, we turn to investigating diurnal and seasonal patterns in fluxes - this time the energy fluxes. The patterns observed at the same sites as used before illustrate general differences across biomes and how different characteristics of the vegetation cover affect the surface energy balance and flux partitioning. In addition to the temperate broadleaved forest site (Hainich Forest, DE-Hai), we consider a coniferous forest (DE-Tha) and a grassland site (DE-Gri) that are located closeby (and thus experience largely identical meterological conditions, ignoring feedbacks from vegetation-atmosphere fluxes that affect near-surface climate).

    +

    As for C fluxes in Chapter 6, we turn to investigating diurnal and seasonal patterns in fluxes - this time the energy fluxes. The patterns observed at the same sites as used before illustrate general differences across biomes and how different characteristics of the vegetation cover affect the surface energy balance and flux partitioning. In addition to the temperate broadleaved forest site (Hainich Forest, DE-Hai), we consider a coniferous forest (DE-Tha) and a grassland site (DE-Gri) that are located close by (and thus experience largely identical meteorological conditions, ignoring feedbacks from vegetation-atmosphere fluxes that affect near-surface climate).

    Code @@ -949,7 +953,7 @@

    The diurnal course of energy fluxes is considered for an average day in July for each site. Describe key patterns and differences between sites and relate them to your knowledge about radiation, energy partitioning, and land surface and vegetation properties.

      -
    1. How does net radiation compare across sites in the top row of Figure 7.11? What component of the net radiation (Figure 7.1 a) do you think is responsible for the observed differences? What surface property may contribute to the differences in net radiation and does it explain why the tropical site has a higher mid-day net radiation peak than the boreal site?
      2. +
    2. How does net radiation compare across sites in the top row of Figure 7.11? What component of the net radiation (Figure 7.1 a) do you think is responsible for the observed differences? What surface property may contribute to the differences in net radiation, and does it explain why the tropical site has a higher mid-day net radiation peak than the boreal site?
    3. How does net radiation compare across the three sites in the temperate biome? Can vegetation properties that affect the reflectance explain why the mid-day peak net radiation is lower for DE-Gri han for DE-Tha?
    4. During night-time, net radiation is negative at all sites. Which of the four components of net radiation is largest during nighttime?
    5. Is the land surface losing or gaining energy during the night? What flux drives this gain/loss (\(H\) or \(\lambda E\))?
      6. @@ -959,7 +963,7 @@

      Assuming all sites had the same aerodynamic and surface conductances, which site may have the highest mid-day VPD? Is this a valid assumption? If not, how do you expect conductances to differ among sites?
    6. The temperate coniferous forest site (which one?) has the higher mid-day net radiation than the temperate broadleaved fores site (which one?). Yet, its latent heat flux is lower than for the latter. Assuming they had the same VPD and aerodynamic conductance, what other surface property may explain this difference?
    7. The temperate grassland has a higher latent heat flux than the two temperate forest sites. Can the difference in vegetation height explain the difference in the latent heat flux?
      8. -
    8. What site has the highest sensible heat flux? If you were a paraglider, over which site do you expect to find the strongest up-lift to take you to your next destination?
      9. +
    9. What site has the highest sensible heat flux? If you were a paraglider, over which site do you expect to find the strongest uplift to take you to your next destination?

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    - + diff --git a/search.json b/search.json index ad8cb5c..830a558 100644 --- a/search.json +++ b/search.json @@ -4,7 +4,7 @@ "href": "index.html", "title": "Land in the Earth System", "section": "", - "text": "About this book\nThis online navigatable book serves as the material for the course with the same name - Land in the Earth System. It is written by Prof. Benjamin Stocker, Institute of Geography, University of Bern.\nThis book introduces processes of the terrestrial biosphere and how they drive Earth system dynamics. The course starts with identifying general patterns in vegetation, carbon, and water fluxes and stocks, and connects them with underlying principles, governing controls, and quantitative frameworks for their description and prediction. A special focus will be put on introducing the role of terrestrial biosphere in driving and being driven by climate change and global environmental change.\nThe book covers a diverse thematic ground - as diverse as the processes of the biosphere. Topics range from biogeography, the global carbon cycle, land-climate interactions, ecohydrology, to Earth system dynamics." + "text": "About this book\nThis online navigable book serves as the material for the course with the same name - Land in the Earth System. It is written by Prof. Benjamin Stocker, Institute of Geography, University of Bern.\nThis book introduces processes of the terrestrial biosphere and how they drive Earth system dynamics. The course starts with identifying general patterns in vegetation, carbon, and water fluxes and stocks, and connects them with underlying principles, governing controls, and quantitative frameworks for their description and prediction. A special focus will be put on introducing the role of terrestrial biosphere in driving and being driven by climate change and global environmental change.\nThe book covers a diverse thematic ground - as diverse as the processes of the biosphere. Topics range from biogeography, the global carbon cycle, land-climate interactions, ecohydrology, to Earth system dynamics." }, { "objectID": "index.html#links", @@ -25,14 +25,14 @@ "href": "intro.html#examples-for-the-terrestrial-biospheres-role-in-the-earth-system", "title": "1  Introduction", "section": "1.1 Examples for the terrestrial biosphere’s role in the Earth system", - "text": "1.1 Examples for the terrestrial biosphere’s role in the Earth system\n\n1.1.1 Annual swings in atmospheric CO2\nThe longest-running record of direct measurements of atmospheric CO2 is from the Mauna Loa Observatory, atop a volcano on Hawaii. This record has become iconic for documenting the rapid rise of atmospheric CO2 - a greenhouse gas - since the great economic acceleration after the Second World War. This has provided a basis for understanding the relationship between emissions of anthropogenic CO2 and its accumulation in the atmosphere and for estimating the climate impact of this important greenhouse gas.\n\n\n\n\n\nFigure 1.1: Atmospheric CO2 from Mauna Loa Observatory, Hawaii. The red curve represents monthly mean values. The black curve represents the same after removing an average seasonal cycle. Source: Dr. Pieter Tans, NOAA/GML (gml.noaa.gov/ccgg/trends/) and Dr. Ralph Keeling, Scripps Institution of Oceanography (scrippsco2.ucsd.edu/).\n\n\n\n\nThe time series in Figure 1.1 shows not only the accelerating rise in atmospheric CO2 over the past decades, but also its regular annual swings - the “breathing of the Earth”. This is the result of the seasonal cycles in CO2 uptake and release by terrestrial ecosystems. CO2 uptake peaks in early early summer in the northern extra-tropics - driven by the high light availability and high photosynthetic rates of young leaves in the early summer months. CO2 release by respiring plants and soil microbes has a shifted seasonality and tends to have a smaller amplitude, compared to CO2 uptake. The net of the two drives changes in atmospheric CO2 which are measured here in the free atmosphere - unaffected by local anthropogenic sources - atop a volcano on Hawaii.\nThe processes responsible for the breathing of the Earth will be introduced in Chapter 4 and Chapter 5.\n\n\n1.1.2 Year-to-year changes of the global carbon budget\nAnthropogenic carbon emissions in the form of CO2, resulting from the combustion of fossil fuels and from land use change, are partly taken up by the ocean and partly by terrestrial ecosystems. The remainder remains in the atmosphere and drives the atmospheric CO2 growth (see Figure 1.1). Each of these components gets estimated and updated each year as the Global Carbon Budget. The latest scientific publication is Friedlingstein et al. (2023).\nEstimates of each component are largely independent and rely on different types of observations, data, and methods. Fossil emissions are based on energy statistics and cement production data, land use emissions are based on land-use and land-use change data and forest carbon “bookkeeping models”. Atmospheric CO2 concentration, and hence the accumulation of C in the atmosphere, is measured directly. The ocean sink is estimated from global ocean biogeochemistry models and observation-based products. The land sink is estimated from dynamic global vegetation models (Friedlingstein et al. 2023).\n\n\n\n\n\nFigure 1.2: Annual carbon emissions (positive) and their redistribution between the ocean, land, and atmosphere (negative). The black line in the positive domain represents total emissions and is mirrored by the black line in the negative domain which represents the total of the land sink, ocean sink, and atmospheric growth. Design and data are based on the Global Carbon Budget. In contrast to Friedlingstein et al. (2023), the land sink is defined here as the carbon budget residual (introduced in Chapter 3). The budget imbalance term - the difference between Sland calculated as the budget residual vs. bottom-up using land C cycle models - is shown by the separate fine grey line.\n\n\n\n\nFigure 1.2 shows that the largest year-to-year variations in the redistribution of anthropogenic CO2 emissions is in the land sink component. While variations in the ocean sink and in emissions are relatively small, the carbon balance of the terrestrial biosphere varies strongly between years. This leads to substantial variations in annual atmospheric CO2 growth rate. Annual variations in the land C balance have been found to originate mostly from semi-arid regions, where large year-to-year variations in precipitation, often linked to El-Nino-Southern-Oscillation climate variability, alter water limitation of vegetation and drought-related disturbances, including fire activity (Ahlström et al. 2015; Humphrey et al. 2018). This leads to large year-to-year variability in CO2 uptake and release by land ecosystems and leaves an imprint on the rise in atmospheric CO2. This also demonstrates the sensitivity of terrestrial C storage to climatic variations and that the response of the land biosphere to climate extremes can drastically alter the accumulation of anthropogenic CO2 in the atmosphere and thus the rate of climate change.\nThe global carbon budget will be introduced in Chapter 5.\n\n\n1.1.3 Responses to rapid climate change in the past\nThe climate of the past 11,000 years (11 ka) until the Industrial Revolution was relatively stable, at least in comparison to the climate of the Last Glacial period. This period was marked by millennial-scale climate oscillations where temperatures rose by up to 16\\(^\\circ\\)C within a few decades (Oeschger et al. 1984; Dansgaard et al. 1993). When first discovered in measurments of an ice core recovered from Greenland, the massive excursions of the \\(\\delta^{18}\\)O signal - a proxy for air temperature - were considered a measurement error. But the correspondence of similar excursions measured on a different Greenland ice core and the coincidence of the most recent such excursion with a similar pattern found in the \\(\\delta^{18}\\)O signal of carbonate in the lake sediment of Gerzensee (near Bern) (Oeschger et al. 1984) confirmed the robustness of these rapid climate change events in the past. Reflecting this, these rapid climate swings between about 80 and 10 ka BP were named Dansgaard-Oeschger events. Today, Dansgaard-Oeschger events are undersood to be oscillations of the Earth system that occurr without external triggers, but arise from the interaction of ocean and ice sheet dynamics, and are confined to Earth system states corresponding to the glacial periods of the late Pleistocene (Stocker and Johnsen 2003; Vettoretti et al. 2022).\nThe terrestrial biosphere was strongly affected by these large and rapid climate changes and left its imprints in several palaeo records (Figure 1.3). In response to the climate warming, atmospheric methane (CH4) concentrations increased rapidly. Natural CH4 sources almost exclusively in land ecosystems (wetlands, fire). In parallel, the amount of dust transported to Greenland declined rapidly as climate warmed. This reflects an expansion of vegetation cover into dust-forming regions (e.g., deserts and peri-glacial areas). Also in parallel, nitrous oxide (N2O), another greenhouse gas, increased. This increase unfolded more gradually and reflects both oceanic and terrestrial sources. Furthermore, fire activity in the northern hemisphere, measured by charcoal deposits in Greenland ice cores, increased as the climate warmed.\n\n\n\n\n\nFigure 1.3: Ice core and biomass burning records of Earth system changes during Dansgaard-Oeschger events - rapid climate change events during the last Glacial period, between 80 and 10 ka BP (kilo-years, 10\\(^{3}\\) years before present). Shading indicates significant patterns in the response of the time series to the events of abrupt warming and rapid cooling. (a) \\(\\delta^{18}\\)O signal is a proxy for air temperature. (b-f) Time series of reconstructed atmospheric greenhouse gas concentrations, dust and fire, temporally aligned and aggregated from subsets of the time series covering multiple Dansgaard-Oeschger events. BYRD: Byrd station, Antarctica; EDC: EPICA Dome C; NGRIP: North Greenland Ice Core Project. Figure from Arneth et al. (2010).\n\n\n\n\nThese variations in land-mediated greenhouse gases, dust, and fire are attest to the large and hemisphere-scale changes in terrestrial biosphere functioning in response to climate variations. Of course, greenhouse gases, dust, and fire-related emissions of CO2 and aerosols are radiative forcing agents themselves and thus affect the climate. These changes during Dansgaard-Oescher events therefore demonstrate the important role of the land biosphere in mediating Earth system changes.\nThe sources of multiple land-mediated greenhouse gases will be introduced in Chapter 12.\n\n\n1.1.4 Feedbacks\nLand ecosystems are a major sink for anthropogenic CO2. Between a quarter and a third of the C emitted by the combustion of fossil fuels and by land use change is taken up again by land ecosystems (Chapter 3). This uptake flux partly buffers the anthropogenic disturbance of the Earth system. This is called a negative feedback (Chapter 9). Without it, the rise in atmospheric CO2 would be about 30-50% more rapid. The terrestrial carbon cycle is steered by a multitude of processes, operating at very different scales, and it is characterised by an enormous heterogeneity in space - across ecosystem types, climate and soil conditions. There is not just a single process responsible for this apparent negative global-scale climate-land biosphere feedback and the negative feedback is partly compensated by positive feedbacks.\n\n\n\n\n\nFigure 1.4: An overview of physical and biogeochemical feedbacks in the climate system. (a) Synthesis of physical, biogeophysical and non-carbon dioxide (CO2) biogeochemical feedbacks that are included in the definition of equilibrium climate sensitivity (ECS) assessed in this Technical Summary. These feedbacks have been assessed using multiple lines of evidence including observations, models and theory. The net feedback is the sum of the Planck response, water vapour and lapse rate, surface albedo, cloud, and biogeophysical and non-CO2 biogeochemical feedbacks. Bars denote the mean feedback values, and uncertainties representvery likely ranges; (b) Estimated values of individual biogeophysical and non-CO2 biogeochemical feedbacks. The atmospheric methane (CH4) lifetime and other non-CO2 biogeochemical feedbacks have been calculated using global Earth system model simulations from AerChemMIP, while the CH4 and nitrous oxide (N2O) source responses to climate have been assessed for the year 2100 using a range of modelling approaches using simplified radiative forcing equations. The estimates represent the mean and 5–95% range. The level of confidence in these estimates is lowowing to the large model spread. (c) Carbon-cycle feedbacks as simulated by models participating in the C4MIP of the Coupled Model Intercomparison Project Phase 6 (CMIP6). An independent estimate of the additional positive carbon-cycle climate feedbacks from permafrost thaw, which is not considered in most C4MIP models, is added. The estimates represent the mean and 5–95% range. Note that these feedbacks act through modifying the atmospheric concentration of CO2 and thus are not included in the definition of ECS, which assumes a doubling of CO2 , 4 but are included in the definition and assessed range of the transient climate response to cumulative CO2 emissions (TCRE). {5.4.7, 5.4.8, Box 5.1, Figure 5.29, 6.4.5, Table 6.9, 7.4.2, Table 7.10}. Figure and caption text from the IPCC Assessment Report 6, Technical Summary, Figure TS.17 (Arias et al. 2021).\n\n\n\n\nAn example for an important positive feedback arising from land biosphere processes is that of permafrost melting. As the climate warms, previously frozen soil that is very rich in organic matter content melts and the C becomes exposed to decomposers (heterotrophic soil bacteria and fungi). CO2 is produced. This climate warming-induced CO2 from melting permafrost amplifies the warming, which triggered it in the first place, due to its greenhouse effect - a positive feedback. Melting permafrost soil often becomes water-logged. The anaerobic conditions promote the production of methane (CH4) - an even stronger greenhouse gas than CO2. The positive feedback gets further amplified.\nThe land biosphere is connected with the Earth system through a multitude of positive and negative feedbacks, leading to complex interactions. While Earth System Models resolve many of these feedbacks and aid our understanding of the systems response to the anthropogenic forcing, translating these concepts into verbal and mental models of how climate change unfolds is challenging. A positive feedback is often described as a “vicious cycle” and sometimes vaguely conflated with a tipping point. A solid understanding of terrestrial biosphere processes, clear definitions, and a concise formalism, grounded on known physical relationships, helps to clarify concepts and the contextualization and communication of the risks of climate change. Chapter 9 will serve this purpose.\n\n\n1.1.5 Tipping points\nTipping points in the Earth system are points at which of a part of the Earth system transitions into a new state in response to a relatively small external forcing. They are inherently hard to predict using Earth System Models. Surprises cannot be excluded. Several potential tipping points have been identified in terrestrial systems (Armstrong McKay et al. 2022). Their reliable simulation in models relies on accurate models of processes in land ecosystems. Once more, land ecosystems and their response to climate change may be a critical element for the future of the Earth system. However, relatively large uncertainties remain for modelling key processes and further research is needed to consolidate the current understanding (and hand-drawn map) of potential tipping elements in the land biosphere (Armstrong McKay et al. 2022).\n\n\n\n\n\nFigure 1.5: The location of climate tipping elements in the cryosphere (blue), biosphere (green), and ocean/atmosphere (orange), and global warming levels at which their tipping points will likely be triggered. Figure and caption text from Armstrong McKay et al. (2022).\n\n\n\n\n\n\n1.1.6 Carbon dixide removal through land ecosystems\nFor the climate to be stabilized at 1.5°C or 2.0°C, rapid and large CO2 emission cuts are needed. Alongside the reduction of fossil fuel combustion, climate stabilization scenarios rely - to a varying degree - on carbon dioxide removal (CDR). Most CDR options deployed to date and available for scaling to meet climate stabilization needs rely on land ecosystems for sequestering (net uptake and long-term storage) additional C. Afforestation and reforestation have been estimated to be a potent solution for climate change mitigation (Walker et al. 2022; Mo et al. 2023) and tree planting has moved to center stage in the public perception and in policy efforts to avert dangerous climate change. But can we rely on trees or other land ecosystems as a solution for the climate crisis?\n\n\n\n\n\nFigure 1.6: Roles of CDR in global or national mitigation strategies. Stylised pathway showing multiple functions of CDR in different phases of ambitious mitigation: (1) further reducing net CO2 or GHG emissions levels in near-term; (2) counterbalancing residual emissions to help reach net zero CO2 or GHG emissions in the mid-term; (3) achieving and sustaining net-negative CO2 or GHG emissions in the long-term. Figure and caption text from IPCC Assessment Report 6, Working Group III, Cross-Chapter Box 8 (IPCC 2022).\n\n\n\n\nHowever, ecological principles and multiple aspects of the role of land ecosystems and their interaction with climate and the carbon cycle have to be considered - apart from conflicts with biodiversity and sustainability goals and social, economic, and cultural aspects of land use (Deprez et al. 2024). For example, the carbon stored in a tree is susceptible to a range of threats, including wildfires, deforestation, and tree mortality by aggravating climatic stress (Anderegg et al. 2020). Moreover, surface properties, relevant for land-climate interactions, and their differences between forests and grasslands imply that forests may heat the local climate more than a grassland would - despite the additional C stored in a forest (Bala et al. 2007).\nUnderstanding the technical potential of land-based CDR will have to consider the full complexity of land-Earth system interactions. This course introduces these interactions." + "text": "1.1 Examples for the terrestrial biosphere’s role in the Earth system\n\n1.1.1 Annual swings in atmospheric CO2\nThe longest-running record of direct measurements of atmospheric CO2 is from the Mauna Loa Observatory, atop a volcano on Hawaii. This record has become iconic for documenting the rapid rise of atmospheric CO2 - a greenhouse gas - since the great economic acceleration after the Second World War. This has provided a basis for understanding the relationship between emissions of anthropogenic CO2 and its accumulation in the atmosphere and for estimating the climate impact of this important greenhouse gas.\n\n\n\n\n\nFigure 1.1: Atmospheric CO2 from Mauna Loa Observatory, Hawaii. The red curve represents monthly mean values. The black curve represents the same after removing an average seasonal cycle. Source: Dr. Pieter Tans, NOAA/GML (gml.noaa.gov/ccgg/trends/) and Dr. Ralph Keeling, Scripps Institution of Oceanography (scrippsco2.ucsd.edu/).\n\n\n\n\nThe time series in Figure 1.1 shows not only the accelerating rise in atmospheric CO2 over the past decades, but also its regular annual swings - the “breathing of the Earth”. This is the result of the seasonal cycles in CO2 uptake and release by terrestrial ecosystems. CO2 uptake peaks in early early summer in the northern extra-tropics - driven by the high light availability and high photosynthetic rates of young leaves in the early summer months. CO2 release by respiring plants and soil microbes has a shifted seasonality and tends to have a smaller amplitude, compared to CO2 uptake. The net of the two drives changes in atmospheric CO2 which are measured here in the free atmosphere - unaffected by local anthropogenic sources - atop a volcano on Hawaii.\nThe processes responsible for the breathing of the Earth will be introduced in Chapter 4 and Chapter 5.\n\n\n1.1.2 Year-to-year changes of the global carbon budget\nAnthropogenic carbon emissions in the form of CO2, resulting from the combustion of fossil fuels and from land use change, are partly taken up by the ocean and partly by terrestrial ecosystems. The remainder remains in the atmosphere and drives the atmospheric CO2 growth (see Figure 1.1). Each of these components gets estimated and updated each year as the Global Carbon Budget. The latest scientific publication is Friedlingstein et al. (2023).\nEstimates of each component are largely independent and rely on different types of observations, data, and methods. Fossil emissions are based on energy statistics and cement production data, land use emissions are based on land-use and land-use change data and forest carbon “bookkeeping models”. Atmospheric CO2 concentration, and hence the accumulation of C in the atmosphere, is measured directly. The ocean sink is estimated from global ocean biogeochemistry models and observation-based products. The land sink is estimated from dynamic global vegetation models (Friedlingstein et al. 2023).\n\n\n\n\n\nFigure 1.2: Annual carbon emissions (positive) and their redistribution between the ocean, land, and atmosphere (negative). The black line in the positive domain represents total emissions and is mirrored by the black line in the negative domain which represents the total of the land sink, ocean sink, and atmospheric growth. Design and data are based on the Global Carbon Budget. In contrast to Friedlingstein et al. (2023), the land sink is defined here as the carbon budget residual (introduced in Chapter 3). The budget imbalance term - the difference between Sland calculated as the budget residual vs. bottom-up using land C cycle models - is shown by the separate fine grey line.\n\n\n\n\nFigure 1.2 shows that the largest year-to-year variations in the redistribution of anthropogenic CO2 emissions is in the land sink component. While variations in the ocean sink and in emissions are relatively small, the carbon balance of the terrestrial biosphere varies strongly between years. This leads to substantial variations in annual atmospheric CO2 growth rate. Annual variations in the land C balance have been found to originate mostly from semi-arid regions, where large year-to-year variations in precipitation, often linked to El-Nino-Southern-Oscillation climate variability, alter water limitation of vegetation and drought-related disturbances, including fire activity (Ahlström et al. 2015; Humphrey et al. 2018). This leads to large year-to-year variability in CO2 uptake and release by land ecosystems and leaves an imprint on the rise in atmospheric CO2. This also demonstrates the sensitivity of terrestrial C storage to climatic variations and that the response of the land biosphere to climate extremes can drastically alter the accumulation of anthropogenic CO2 in the atmosphere and thus the rate of climate change.\nThe global carbon budget will be introduced in Chapter 5.\n\n\n1.1.3 Responses to rapid climate change in the past\nThe climate of the past 11,000 years (11 ka) until the Industrial Revolution was relatively stable, at least in comparison to the climate of the Last Glacial period. This period was marked by millennial-scale climate oscillations where temperatures rose by up to 16\\(^\\circ\\)C within a few decades (Oeschger et al. 1984; Dansgaard et al. 1993). When first discovered in measurements of an ice core recovered from Greenland, the massive excursions of the \\(\\delta^{18}\\)O signal - a proxy for air temperature - were considered a measurement error. But the correspondence of similar excursions measured on a different Greenland ice core and the coincidence of the most recent such excursion with a similar pattern found in the \\(\\delta^{18}\\)O signal of carbonate in the lake sediment of Gerzensee (near Bern) (Oeschger et al. 1984) confirmed the robustness of these rapid climate change events in the past. Reflecting this, these rapid climate swings between about 80 and 10 ka BP were named Dansgaard-Oeschger events. Today, Dansgaard-Oeschger events are understood to be oscillations of the Earth system that occur without external triggers, but arise from the interaction of ocean and ice sheet dynamics, and are confined to Earth system states corresponding to the glacial periods of the late Pleistocene (Stocker and Johnsen 2003; Vettoretti et al. 2022). \nThe terrestrial biosphere was strongly affected by these large and rapid climate changes and left its imprints in several palaeo records (Figure 1.3). In response to the climate warming, atmospheric methane (CH4) concentrations increased rapidly. Natural CH4 sources originate almost exclusively from land ecosystems (wetlands, fire). In parallel, the amount of dust transported to Greenland declined rapidly as climate warmed. This reflects an expansion of vegetation cover into dust-forming regions (e.g., deserts and peri-glacial areas). Also in parallel, nitrous oxide (N2O), another greenhouse gas, increased. This increase unfolded more gradually and reflects both oceanic and terrestrial sources. Furthermore, fire activity in the northern hemisphere, measured by charcoal deposits in Greenland ice cores, increased as the climate warmed.\n\n\n\n\n\nFigure 1.3: Ice core and biomass burning records of Earth system changes during Dansgaard-Oeschger events - rapid climate change events during the last Glacial period, between 80 and 10 ka BP (kilo-years, 10\\(^{3}\\) years before present). Shading indicates significant patterns in the response of the time series to the events of abrupt warming and rapid cooling. (a) \\(\\delta^{18}\\)O signal is a proxy for air temperature. (b-f) Time series of reconstructed atmospheric greenhouse gas concentrations, dust and fire, temporally aligned and aggregated from subsets of the time series covering multiple Dansgaard-Oeschger events. BYRD: Byrd station, Antarctica; EDC: EPICA Dome C; NGRIP: North Greenland Ice Core Project. Figure from Arneth et al. (2010).\n\n\n\n\nThese variations in land-mediated greenhouse gases, dust, and fire are attest to the large and hemisphere-scale changes in terrestrial biosphere functioning in response to climate variations. Of course, greenhouse gases, dust, and fire-related emissions of CO2 and aerosols are radiative forcing agents themselves and thus affect the climate. These changes during Dansgaard-Oescher events therefore demonstrate the important role of the land biosphere in mediating Earth system changes.\nThe sources of multiple land-mediated greenhouse gases will be introduced in Chapter 12.\n\n\n1.1.4 Feedbacks\nLand ecosystems are a major sink for anthropogenic CO2. Between a quarter and a third of the C emitted by the combustion of fossil fuels and by land use change is taken up again by land ecosystems (Chapter 3). This uptake flux partly buffers the anthropogenic disturbance of the Earth system. This is called a negative feedback (Chapter 9). Without it, the rise in atmospheric CO2 would be about 30-50% more rapid. The terrestrial carbon cycle is steered by a multitude of processes, operating at very different scales, and it is characterised by an enormous heterogeneity in space - across ecosystem types, climate and soil conditions. There is not just a single process responsible for this apparent negative global-scale climate-land biosphere feedback and the negative feedback is partly compensated by positive feedbacks.\n\n\n\n\n\nFigure 1.4: An overview of physical and biogeochemical feedbacks in the climate system. (a) Synthesis of physical, biogeophysical and non-carbon dioxide (CO2) biogeochemical feedbacks that are included in the definition of equilibrium climate sensitivity (ECS) assessed in this Technical Summary. These feedbacks have been assessed using multiple lines of evidence including observations, models and theory. The net feedback is the sum of the Planck response, water vapor and lapse rate, surface albedo, cloud, and biogeophysical and non-CO2 biogeochemical feedbacks. Bars denote the mean feedback values, and uncertainties representvery likely ranges; (b) Estimated values of individual biogeophysical and non-CO2 biogeochemical feedbacks. The atmospheric methane (CH4) lifetime and other non-CO2 biogeochemical feedbacks have been calculated using global Earth system model simulations from AerChemMIP, while the CH4 and nitrous oxide (N2O) source responses to climate have been assessed for the year 2100 using a range of modelling approaches using simplified radiative forcing equations. The estimates represent the mean and 5–95% range. The level of confidence in these estimates is lowowing to the large model spread. (c) Carbon-cycle feedbacks as simulated by models participating in the C4MIP of the Coupled Model Intercomparison Project Phase 6 (CMIP6). An independent estimate of the additional positive carbon-cycle climate feedbacks from permafrost thaw, which is not considered in most C4MIP models, is added. The estimates represent the mean and 5–95% range. Note that these feedbacks act through modifying the atmospheric concentration of CO2 and thus are not included in the definition of ECS, which assumes a doubling of CO2 , 4 but are included in the definition and assessed range of the transient climate response to cumulative CO2 emissions (TCRE). {5.4.7, 5.4.8, Box 5.1, Figure 5.29, 6.4.5, Table 6.9, 7.4.2, Table 7.10}. Figure and caption text from the IPCC Assessment Report 6, Technical Summary, Figure TS.17 (Arias et al. 2021).\n\n\n\n\nAn example for an important positive feedback arising from land biosphere processes is that of permafrost melting. As the climate warms, previously frozen soil that is very rich in organic matter content melts and the C becomes exposed to decomposers (heterotrophic soil bacteria and fungi). CO2 is produced. This climate warming-induced CO2 from melting permafrost amplifies the warming, which triggered it in the first place, due to its greenhouse effect - a positive feedback. Melting permafrost soil often becomes water-logged. The anaerobic conditions promote the production of methane (CH4) - an even stronger greenhouse gas than CO2. The positive feedback gets further amplified.\nThe land biosphere is connected with the Earth system through a multitude of positive and negative feedbacks, leading to complex interactions. While Earth System Models resolve many of these feedbacks and aid our understanding of the systems response to the anthropogenic forcing, translating these concepts into verbal and mental models of how climate change unfolds is challenging. A positive feedback is often described as a “vicious cycle” and sometimes vaguely conflated with a tipping point. A solid understanding of terrestrial biosphere processes, clear definitions, and a concise formalism, grounded on known physical relationships, helps to clarify concepts and the contextualization and communication of the risks of climate change. Chapter 9 will serve this purpose.\n\n\n1.1.5 Tipping points\nTipping points in the Earth system are points at which a part of the Earth system transitions into a new state in response to a relatively small external forcing. They are inherently hard to predict using Earth System Models. Surprises cannot be excluded. Several potential tipping points have been identified in terrestrial systems (Armstrong McKay et al. 2022). Their reliable simulation in models relies on accurate models of processes in land ecosystems. Once more, land ecosystems and their response to climate change may be a critical element for the future of the Earth system. However, relatively large uncertainties remain for modelling key processes and further research is needed to consolidate the current understanding (and hand-drawn map) of potential tipping elements in the land biosphere (Armstrong McKay et al. 2022).\n\n\n\n\n\nFigure 1.5: The location of climate tipping elements in the cryosphere (blue), biosphere (green), and ocean/atmosphere (orange), and global warming levels at which their tipping points will likely be triggered. Figure and caption text from Armstrong McKay et al. (2022).\n\n\n\n\n\n\n1.1.6 Carbon dioxide removal through land ecosystems\nFor the climate to be stabilized at 1.5°C or 2.0°C, rapid and large CO2 emission cuts are needed. Alongside the reduction of fossil fuel combustion, climate stabilization scenarios rely - to a varying degree - on carbon dioxide removal (CDR). Most CDR options deployed to date and available for scaling to meet climate stabilization needs rely on land ecosystems for sequestering (net uptake and long-term storage) additional C. Afforestation and reforestation have been estimated to be a potent solution for climate change mitigation (Walker et al. 2022; Mo et al. 2023) and tree planting has moved to center stage in the public perception and in policy efforts to avert dangerous climate change. The figure below shows an example of stylised net-zero pathway.\n\n\n\n\n\nFigure 1.6: Roles of CDR in global or national mitigation strategies. Stylised pathway showing multiple functions of CDR in different phases of ambitious mitigation: (1) further reducing net CO2 or GHG emissions levels in near-term; (2) counterbalancing residual emissions to help reach net zero CO2 or GHG emissions in the mid-term; (3) achieving and sustaining net-negative CO2 or GHG emissions in the long-term. Figure and caption text from IPCC Assessment Report 6, Working Group III, Cross-Chapter Box 8 (IPCC 2022).\n\n\n\n\nBut can we rely on trees or other land ecosystems as a solution for the climate crisis? Ecological principles and multiple aspects of the role of land ecosystems and their interaction with climate and the carbon cycle have to be considered - apart from conflicts with biodiversity and sustainability goals and social, economic, and cultural aspects of land use (Deprez et al. 2024). For example, the carbon stored in a tree is susceptible to a range of threats, including wildfires, deforestation, and tree mortality by aggravating climatic stress (Anderegg et al. 2020). Moreover, surface properties, relevant for land-climate interactions, and their differences between forests and grasslands imply that forests may heat the local climate more than a grassland would - despite the additional C stored in a forest (Bala et al. 2007).\n\nUnderstanding the technical potential of land-based CDR will have to consider the full complexity of land-Earth system interactions. This course introduces these interactions." }, { "objectID": "intro.html#why-we-study-the-land", "href": "intro.html#why-we-study-the-land", "title": "1  Introduction", "section": "1.2 Why we study the land", - "text": "1.2 Why we study the land\nThe examples for given above are attest to the key role of the terrestrial biosphere in the Earth system and for understanding the risks and mitigation options in the context of anthropogenic climate change. With climate change and its impacts moving into the centre of public attention and becoming an increasingly important boundary condition for policy making, it is crucial to have a basic understanding of the Earth system and how the terrestrial biosphere works. That’s why we study Land in the Earth System.\n\n\n\n\nAhlström, Anders, Michael R. Raupach, Guy Schurgers, Benjamin Smith, Almut Arneth, Martin Jung, Markus Reichstein, et al. 2015. “The Dominant Role of Semi-Arid Ecosystems in the Trend and Variability of the Land CO2 Sink.” Science 348 (6237): 895–99.\n\n\nAnderegg, William R. L., Anna T. Trugman, Grayson Badgley, Christa M. Anderson, Ann Bartuska, Philippe Ciais, Danny Cullenward, et al. 2020. “Climate-Driven Risks to the Climate Mitigation Potential of Forests.” Science 368 (6497): eaaz7005. https://doi.org/10.1126/science.aaz7005.\n\n\nArias, P. A., N. Bellouin, E. Coppola, R. G. Jones, G. Krinner, J. Marotzke, V. Naik, et al. 2021. “Technical Summary.” Book Section. In Climate Change 2021: The Physical Science Basis. Contribution of Working Group i to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, edited by V. Masson-Delmotte, P. Zhai, A. Pirani, S. L. Connors, C. Péan, S. Berger, N. Caud, et al. Cambridge, UK; New York, NY, USA: Cambridge University Press. https://doi.org/10.1017/9781009157896.002.\n\n\nArmstrong McKay, David I., Arie Staal, Jesse F. Abrams, Ricarda Winkelmann, Boris Sakschewski, Sina Loriani, Ingo Fetzer, Sarah E. Cornell, Johan Rockström, and Timothy M. Lenton. 2022. “Exceeding 1.5°C Global Warming Could Trigger Multiple Climate Tipping Points.” Science 377 (6611): eabn7950. https://doi.org/10.1126/science.abn7950.\n\n\nArneth, A., S. P. Harrison, S. Zaehle, K. Tsigaridis, S. Menon, P. J. Bartlein, J. Feichter, et al. 2010. “Terrestrial Biogeochemical Feedbacks in the Climate System.” Nature Geoscience 3 (8): 525–32. https://doi.org/10.1038/ngeo905.\n\n\nBala, G., K. Caldeira, M. Wickett, T. J. Phillips, D. B. Lobell, C. Delire, and A. Mirin. 2007. “Combined Climate and Carbon-Cycle Effects of Large-Scale Deforestation.” Proceedings of the National Academy of Sciences 104 (16): 6550–55. https://doi.org/10.1073/pnas.0608998104.\n\n\nDansgaard, W., S. J. Johnsen, H. B. Clausen, D. Dahl-Jensen, N. S. Gundestrup, C. U. Hammer, C. S. Hvidberg, et al. 1993. “Evidence for General Instability of Past Climate from a 250-Kyr Ice-Core Record.” Nature 364 (6434): 218–20. https://doi.org/10.1038/364218a0.\n\n\nDeprez, Alexandra, Paul Leadley, Kate Dooley, Phil Williamson, Wolfgang Cramer, Jean-Pierre Gattuso, Aleksandar Rankovic, Eliot L. Carlson, and Felix Creutzig. 2024. “Sustainability Limits Needed for CO2 Removal.” Science 383 (6682): 484–86. https://doi.org/10.1126/science.adj6171.\n\n\nFalkowski, P., R. J. Scholes, E. Boyle, J. Canadell, D. Canfield, J. Elser, N. Gruber, et al. 2000. “The Global Carbon Cycle: A Test of Our Knowledge of Earth as a System.” Science 290 (5490): 291–96. https://doi.org/10.1126/science.290.5490.291.\n\n\nFriedlingstein, P., M. O’Sullivan, M. W. Jones, R. M. Andrew, D. C. E. Bakker, J. Hauck, P. Landschützer, et al. 2023. “Global Carbon Budget 2023.” Earth System Science Data 15 (12): 5301–69. https://doi.org/10.5194/essd-15-5301-2023.\n\n\nHumphrey, Vincent, Jakob Zscheischler, Philippe Ciais, Lukas Gudmundsson, Stephen Sitch, and Sonia I. Seneviratne. 2018. “Sensitivity of Atmospheric CO2 Growth Rate to Observed Changes in Terrestrial Water Storage.” Nature 560 (7720): 628–31. https://doi.org/10.1038/s41586-018-0424-4.\n\n\nIPCC. 2022. Climate Change 2022: Mitigation of Climate Change. Contribution of Working Group III to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change. Book. Edited by P. R. Shukla, J. Skea, R. Slade, A. Al Khourdajie, R. van Diemen, D. McCollum, M. Pathak, et al. Cambridge, UK; New York, NY, USA: Cambridge University Press. https://doi.org/10.1017/9781009157926.\n\n\nMo, Lidong, Constantin M. Zohner, Peter B. Reich, Jingjing Liang, Sergio de Miguel, Gert-Jan Nabuurs, Susanne S. Renner, et al. 2023. “Integrated Global Assessment of the Natural Forest Carbon Potential.” Nature, November, 1–10. https://doi.org/10.1038/s41586-023-06723-z.\n\n\nOeschger, H., J. Beer, U. Siegenthaler, B. Stauffer, W. Dansgaard, and C. C. Langway. 1984. “Late Glacial Climate History from Ice Cores.” Climate Processes and Climate Sensitivity, 299–306. https://doi.org/10.1029/gm029p0299.\n\n\nStocker, Thomas F., and Sigfùs J. Johnsen. 2003. “A Minimum Thermodynamic Model for the Bipolar Seesaw.” Paleoceanography 18 (4). https://doi.org/10.1029/2003PA000920.\n\n\nVettoretti, Guido, Peter Ditlevsen, Markus Jochum, and Sune Olander Rasmussen. 2022. “Atmospheric CO2 Control of Spontaneous Millennial-Scale Ice Age Climate Oscillations.” Nature Geoscience 15 (4): 300–306. https://doi.org/10.1038/s41561-022-00920-7.\n\n\nWalker, Wayne S., Seth R. Gorelik, Susan C. Cook-Patton, Alessandro Baccini, Mary K. Farina, Kylen K. Solvik, Peter W. Ellis, et al. 2022. “The Global Potential for Increased Storage of Carbon on Land.” Proceedings of the National Academy of Sciences 119 (23): e2111312119. https://doi.org/10.1073/pnas.2111312119." + "text": "1.2 Why we study the land\nThe examples given above illustrate the key role of the terrestrial biosphere in the Earth system and the importance of understanding the risks and mitigation options in the context of anthropogenic climate change. With climate change and its impacts moving into the centre of public attention and becoming an increasingly important boundary condition for policymaking, it is crucial to have a solid understanding of the Earth system and how the terrestrial biosphere works. That’s why we study Land in the Earth System.\n\n\n\n\nAhlström, Anders, Michael R. Raupach, Guy Schurgers, Benjamin Smith, Almut Arneth, Martin Jung, Markus Reichstein, et al. 2015. “The Dominant Role of Semi-Arid Ecosystems in the Trend and Variability of the Land CO2 Sink.” Science 348 (6237): 895–99.\n\n\nAnderegg, William R. L., Anna T. Trugman, Grayson Badgley, Christa M. Anderson, Ann Bartuska, Philippe Ciais, Danny Cullenward, et al. 2020. “Climate-Driven Risks to the Climate Mitigation Potential of Forests.” Science 368 (6497): eaaz7005. https://doi.org/10.1126/science.aaz7005.\n\n\nArias, P. A., N. Bellouin, E. Coppola, R. G. Jones, G. Krinner, J. Marotzke, V. Naik, et al. 2021. “Technical Summary.” Book Section. In Climate Change 2021: The Physical Science Basis. Contribution of Working Group i to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, edited by V. Masson-Delmotte, P. Zhai, A. Pirani, S. L. Connors, C. Péan, S. Berger, N. Caud, et al. Cambridge, UK; New York, NY, USA: Cambridge University Press. https://doi.org/10.1017/9781009157896.002.\n\n\nArmstrong McKay, David I., Arie Staal, Jesse F. Abrams, Ricarda Winkelmann, Boris Sakschewski, Sina Loriani, Ingo Fetzer, Sarah E. Cornell, Johan Rockström, and Timothy M. Lenton. 2022. “Exceeding 1.5°C Global Warming Could Trigger Multiple Climate Tipping Points.” Science 377 (6611): eabn7950. https://doi.org/10.1126/science.abn7950.\n\n\nArneth, A., S. P. Harrison, S. Zaehle, K. Tsigaridis, S. Menon, P. J. Bartlein, J. Feichter, et al. 2010. “Terrestrial Biogeochemical Feedbacks in the Climate System.” Nature Geoscience 3 (8): 525–32. https://doi.org/10.1038/ngeo905.\n\n\nBala, G., K. Caldeira, M. Wickett, T. J. Phillips, D. B. Lobell, C. Delire, and A. Mirin. 2007. “Combined Climate and Carbon-Cycle Effects of Large-Scale Deforestation.” Proceedings of the National Academy of Sciences 104 (16): 6550–55. https://doi.org/10.1073/pnas.0608998104.\n\n\nDansgaard, W., S. J. Johnsen, H. B. Clausen, D. Dahl-Jensen, N. S. Gundestrup, C. U. Hammer, C. S. Hvidberg, et al. 1993. “Evidence for General Instability of Past Climate from a 250-Kyr Ice-Core Record.” Nature 364 (6434): 218–20. https://doi.org/10.1038/364218a0.\n\n\nDeprez, Alexandra, Paul Leadley, Kate Dooley, Phil Williamson, Wolfgang Cramer, Jean-Pierre Gattuso, Aleksandar Rankovic, Eliot L. Carlson, and Felix Creutzig. 2024. “Sustainability Limits Needed for CO2 Removal.” Science 383 (6682): 484–86. https://doi.org/10.1126/science.adj6171.\n\n\nFalkowski, P., R. J. Scholes, E. Boyle, J. Canadell, D. Canfield, J. Elser, N. Gruber, et al. 2000. “The Global Carbon Cycle: A Test of Our Knowledge of Earth as a System.” Science 290 (5490): 291–96. https://doi.org/10.1126/science.290.5490.291.\n\n\nFriedlingstein, P., M. O’Sullivan, M. W. Jones, R. M. Andrew, D. C. E. Bakker, J. Hauck, P. Landschützer, et al. 2023. “Global Carbon Budget 2023.” Earth System Science Data 15 (12): 5301–69. https://doi.org/10.5194/essd-15-5301-2023.\n\n\nHumphrey, Vincent, Jakob Zscheischler, Philippe Ciais, Lukas Gudmundsson, Stephen Sitch, and Sonia I. Seneviratne. 2018. “Sensitivity of Atmospheric CO2 Growth Rate to Observed Changes in Terrestrial Water Storage.” Nature 560 (7720): 628–31. https://doi.org/10.1038/s41586-018-0424-4.\n\n\nIPCC. 2022. Climate Change 2022: Mitigation of Climate Change. Contribution of Working Group III to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change. Book. Edited by P. R. Shukla, J. Skea, R. Slade, A. Al Khourdajie, R. van Diemen, D. McCollum, M. Pathak, et al. Cambridge, UK; New York, NY, USA: Cambridge University Press. https://doi.org/10.1017/9781009157926.\n\n\nMo, Lidong, Constantin M. Zohner, Peter B. Reich, Jingjing Liang, Sergio de Miguel, Gert-Jan Nabuurs, Susanne S. Renner, et al. 2023. “Integrated Global Assessment of the Natural Forest Carbon Potential.” Nature, November, 1–10. https://doi.org/10.1038/s41586-023-06723-z.\n\n\nOeschger, H., J. Beer, U. Siegenthaler, B. Stauffer, W. Dansgaard, and C. C. Langway. 1984. “Late Glacial Climate History from Ice Cores.” Climate Processes and Climate Sensitivity, 299–306. https://doi.org/10.1029/gm029p0299.\n\n\nStocker, Thomas F., and Sigfùs J. Johnsen. 2003. “A Minimum Thermodynamic Model for the Bipolar Seesaw.” Paleoceanography 18 (4). https://doi.org/10.1029/2003PA000920.\n\n\nVettoretti, Guido, Peter Ditlevsen, Markus Jochum, and Sune Olander Rasmussen. 2022. “Atmospheric CO2 Control of Spontaneous Millennial-Scale Ice Age Climate Oscillations.” Nature Geoscience 15 (4): 300–306. https://doi.org/10.1038/s41561-022-00920-7.\n\n\nWalker, Wayne S., Seth R. Gorelik, Susan C. Cook-Patton, Alessandro Baccini, Mary K. Farina, Kylen K. Solvik, Peter W. Ellis, et al. 2022. “The Global Potential for Increased Storage of Carbon on Land.” Proceedings of the National Academy of Sciences 119 (23): e2111312119. https://doi.org/10.1073/pnas.2111312119." }, { "objectID": "part1.html", @@ -46,35 +46,35 @@ "href": "biogeography.html#a-global-view-of-vegetation", "title": "2  Biogeography", "section": "2.1 A global view of vegetation", - "text": "2.1 A global view of vegetation\nWe start with the observation that the global distribution of plants and characteristic assemblies of different plant species is not random, but relates to climate. Around the beginning of the 19th century, Alexander von Humboldt pursued expeditions to different places on Earth and connected the multitude of his local observations into a global view of biogeography. He was the first to realize that vegetation zones along elevational gradients were shifted across different mountain ranges on different continents and located on different latitudes, and that the elevational and latitudinal patterns in vegetation were related to climate - in much the same way across the earth. This finding is visualised by the schematic scientific drawing in Figure 2.1. The figure illustrates, for example, that the treeline increases from the high northern latitudes of Lapland at 68\\(^\\circ\\)N to the Alps and Pyrenees at 42-46\\(^\\circ\\)N and to the Himalaya at 29-32\\(^\\circ\\)N. Or that the elevation at which Betula alba (birch) grows varies from 1000-2000 ft in Lapland, to 4000-5000 ft in the Alps, and about 15,000 ft in the Himalaya. Figure 2.1 also illustrates that the treeline doesn’t increase monotonically with decreasing latitude. Although not spelled out in the figure, this is a hint at the importance of water, along with temperature, for controlling vegetation. We’ll revisit this observation later in this book. Humboldt’s integration of globally distributed observations into his global view of climate as a driver of vegetation was pioneering and forms the basis of our modern approach to understanding and modelling global vegetation patterns and how they are influenced by climate change.\n\n\n\n\n\nFigure 2.1: Vegetation zones along elevation and latitude. Source: Wikimedia." + "text": "2.1 A global view of vegetation\nWe start with the observation that the global distribution of plants and characteristic assemblies of different plant species is not random, but relates to climate. Around the beginning of the 19th century, Alexander von Humboldt pursued expeditions to different places on Earth and connected the multitude of his local observations into a global view of biogeography. He was the first to realize that vegetation zones along elevational gradients were shifted across different mountain ranges on different continents and located at different latitudes, and that the elevational and latitudinal patterns in vegetation were related to climate - in much the same way across the Earth. This finding is visualised by the schematic scientific drawing in Figure 2.1. The figure illustrates, for example, that the treeline increases from the high northern latitudes of Lapland at 68\\(^\\circ\\)N to the Alps and Pyrenees at 42-46\\(^\\circ\\)N and to the Himalaya at 29-32\\(^\\circ\\)N. Or that the elevation at which Betula alba (birch) grows varies from 1000-2000 ft in Lapland, to 4000-5000 ft in the Alps, and about 15,000 ft in the Himalaya. Figure 2.1 also illustrates that the treeline doesn’t increase monotonically with decreasing latitude. Although not spelled out in the figure, this is a hint at the importance of water, along with temperature, for controlling vegetation. We’ll revisit this observation later in this book. Humboldt’s integration of globally distributed observations into his global view of climate as a driver of vegetation was pioneering and forms the basis of our modern approach to understanding and modelling global vegetation patterns and how they are influenced by climate change.\n\n\n\n\n\nFigure 2.1: Vegetation zones along elevation and latitude. Source: Wikimedia." }, { "objectID": "biogeography.html#sec-biomes", "href": "biogeography.html#sec-biomes", "title": "2  Biogeography", "section": "2.2 Biomes", - "text": "2.2 Biomes\nToday’s geodata provides information on climate and vegetation properties with global coverage. This enables a global mapping of vegetation, filling in the blank spots between the local observations made by Alexander von Humboldt 200 years ago. Global patterns in the distribution of vegetation become apparent when grouping plants and plant functional types (see Section 2.3) into biomes or broad vegetation classes. A global map of biomes following the definition and global delineation by Olson et al. (2001) is given in Figure 2.2. The exact delineation and naming of biomes varies between different sources, but the main distinctions are shared among all of them.\n\n\n\n\n\nFigure 2.2: Fourteen biomes and the locations of sites representative for each biome (used below).\n\n\n\n\nEach biome is characterised by the types of dominant plants (plant functional types), their characteristics (traits), ecosystem structural and functional properties, and landscape processes (e.g., fire). Underlying all of this is the characteristic climate. The following biome classification (based on Bonan (2015) and slightly deviating from Olson et al. (2001)) can be made.\n\n\n\n\n\n\nNote\n\n\n\nClick on the biome names below to open a tab that lists some key characteristics and provides a Walter-Lieth climate diagram for a representative site, located in that biome. The sites are locations where ecoystem water and carbon fluxes, along with meteorological variables, are measured. We will revisit data from these same sites in later chapters, then with a focus on water and carbon fluxes and the phenology. The locations of the sites are indicated on the map in Figure 2.2.\nWalter-Lieth climate diagrams show monthly climatologies of average temperature and precipitation on the same axis and scaled such that months where the blue curve (precipitation, mm month-1) is above the red curve (temperature, \\(^\\circ\\)C) indicates humid periods and the opposite relative curve positions indicates dry periods. Dry periods are roughly indicating when potential evapotranspiration is higher than precipitation (see Chapter 7). Blue bars along the x-axis indicate months with likely frost. Annotations on the top of the graph indicate the observation period (left), the mean annual temperature (center), and the mean annual precipitation (right). The average temperatures of the warmest and coldest months are given to the left of the temperature axis.\n\n\n\nTropical moist broadleaved (evergreen) forestTropical deciduous forest (xeric woodland)Tropical savannahGrasslandsShrublands and desertsTemperate forestsMediterranean forestsBoreal forestsTundra\n\n\n\nwarm year-round\nno or little precipitation seasonality\ntall vegetation height, high productivity, high total leaf area per unit ground area (leaf area index, LAI), fast decomposition\nlarge, thin leaves\n\n\n\n\n\n\n\nFigure 2.3: Climate diagram of the site BR-Sa3, located in the ropical moist broadleaved (evergreen) forest biome.\n\n\n\n\n\n\n\nwarm year-round\ndry season\nleaves are (partly) shed during the dry season as a water saving strategy\nshorter stature and lower LAI than tropical moist broadleaved (evergreen) forests\nsmall, thick leaves\n\n\n\n\n\n\n\nFigure 2.4: Climate diagram of the site ZM-Mon, located in the Tropical deciduous forest biome.\n\n\n\n\n\n\n\nwarm year-round\npronounced dry season\nwidely spaced trees, mixed with grasses\nlow plant biomass, deep roots\nregular fires\n\n\n\n\n\n\nFigure 2.5: Climate diagram of the site AU-How, located in the Tropical savannah biome.\n\n\n\n\n\n\n\ntropical and temperate dry climates\nC3 and C4 grasses (see below), distribution governed by temperature\ntemperate grasslands in dry, seasonally hot, semiarid climates with annual precipitation less than about 1000 mm\ntransitional between forests and desert\n\n\n\n\n\n\nFigure 2.6: Climate diagram of the site US-Tw1, located in the Grasslands biome.\n\n\n\n\n\n\n\nless than 250 mm annual precipitation\nshort, widely spaced desert scrub and shrubland\ngermination after intense rain, leaf shedding during dry period\ncacti and succulents store water and use the CAM photosnthetic pathway to minimize water loss during photosynthesis\n\n\n\n\n\n\nFigure 2.7: Climate diagram of the site US-SRM, located in the Shrublands and deserts biome.\n\n\n\n\n\n\n\nmore than 1000 mm annual precipitation\ndeciduous and evergreen trees, sometimes mixed\nlow winter light and temperature limits productivity\ntall trees\n\n\n\n\n\n\nFigure 2.8: Climate diagram of the site DE-Hai, located in the Temperate forests biome.\n\n\n\n\n\n\n\nadditional productivity limitation in summer due to water limitation\nless limited productivity by temperature and light in winter than temperate forests\nmild and moist winters\nshort stature trees, dense shrubs\nthick, waxy leaves\n\n\n\n\n\n\nFigure 2.9: Climate diagram of the site FR-Pue, located in the Mediterranean forests biome.\n\n\n\n\n\n\n\n\nvery cold winters, cool summers\nwinter light and temperature limits productivity\nmostly needle-leaved evergreen\nshorter and more open than temperate forests\nin Siberia: extreme winter low temperatures favour deciduousness of larch (larix decidua)\n\n\n\n\n\n\nFigure 2.10: Climate diagram of the site FI-Hyy, located in the Boreal forests biome.\n\n\n\n\n\n\n\ntree-less, grass-like sedges, dwarf shrubs, lichens, and mosses\nvery short vegetation period\nfrozen ground, seasonal thawing of top ~50 cm (permafrost)\n\n\n\n\n\n\nFigure 2.11: Climate diagram of the site US-ICh, located in the Tundra biome.\n\n\n\n\n\n\n\n\n2.2.1 Biomes in climate space\nFigure 2.2 shows biomes in geographical space - as a global map. Acknowledging their intricate relationship with climate, biomes can also be delineated in climate space - in a diagram defined by mean annual temperature (MAT) along one axis and mean annual precipitation (MAP) along the other axis. This yields a plot following Whittaker (1975). Note that the biome definition shown in Figure 2.12 does not exactly match the definition of biomes given above as it is mainly aimed at separating with respect to MAT and MAP. For example, Mediterranean forests are not separated in the “Whittaker-plot”. This is because their characteristic climate is not distinguished by annual means, but by the seasonality of temperature, solar radiation, and precipitation.\n\n\nCode\n# library(ggplot2)\n# library(devtools)\n# devtools::install_github(\"valentinitnelav/plotbiomes\")\n# library(plotbiomes)\n# plotbiomes::whittaker_base_plot() +\n# theme_classic()\n# ggsave(here::here(\"book/images/biomes_whittaker.png\"), width = 7, height = 4)\n\nknitr::include_graphics(\"images/biomes_whittaker.png\")\n\n\n\n\n\nFigure 2.12: Biomes in climate space, defined by mean annual temperature and precipitation, following Whittaker (1975)." + "text": "2.2 Biomes\nToday’s geodata provides information on climate and vegetation properties with global coverage. This enables a global mapping of vegetation, filling in the blank spots between the local observations made by Alexander von Humboldt 200 years ago. Global patterns in the distribution of vegetation become apparent when grouping plants and plant functional types (see Section 2.3) into biomes or broad vegetation classes. A global map of biomes following the definition and global delineation by Olson et al. (2001) is given in Figure 2.2. The exact delineation and naming of biomes varies between different sources, but the main distinctions are shared among all of them.\n\n\n\n\n\nFigure 2.2: Fourteen biomes and the locations of sites representative for each biome (used below).\n\n\n\n\nEach biome is characterised by the types of dominant plants (plant functional types), their characteristics (traits), ecosystem structural and functional properties, and landscape processes (e.g., fire). Underlying all of this is the characteristic climate. The following biome classification (based on Bonan (2015) and slightly deviating from Olson et al. (2001)) can be made.\n\n\n\n\n\n\nNote\n\n\n\nClick on the biome names below to open a tab that lists some key characteristics and provides a Walter-Lieth climate diagram for a representative site, located in that biome. The sites are locations where ecosystem water and carbon fluxes, along with meteorological variables, are measured. We will revisit data from these same sites in later chapters, then with a focus on water and carbon fluxes and the phenology. The locations of the sites are indicated on the map in Figure 2.2.\nWalter-Lieth climate diagrams show monthly climatologies of average temperature and precipitation on the same axis and scaled such that months where the blue curve (precipitation, mm month-1) is above the red curve (temperature, \\(^\\circ\\)C) indicates humid periods, while the opposite relative curve position indicates dry periods. Dry periods are roughly characterized by a potential evapotranspiration higher than precipitation (see Chapter 7). Blue bars along the x-axis indicate months with likely frost. Annotations on the top of the graph indicate the observation period (left), the mean annual temperature (center), and the mean annual precipitation (right). The average temperatures of the warmest and coldest months are given to the left of the temperature axis.\n\n\n\nTropical moist broadleaved (evergreen) forestTropical deciduous forest (xeric woodland)Tropical savannahGrasslandsShrublands and desertsTemperate forestsMediterranean forestsBoreal forestsTundra\n\n\n\nwarm year-round\nno or little precipitation seasonality\ntall vegetation height, high productivity, high total leaf area per unit ground area (leaf area index, LAI), fast decomposition\nlarge, thin leaves\n\n\n\n\n\n\n\nFigure 2.3: Climate diagram of the site BR-Sa3, located in the ropical moist broadleaved (evergreen) forest biome.\n\n\n\n\n\n\n\nwarm year-round\ndry season\nleaves are (partly) shed during the dry season as a water saving strategy\nshorter stature and lower LAI than tropical moist broadleaved (evergreen) forests\nsmall, thick leaves\n\n\n\n\n\n\n\nFigure 2.4: Climate diagram of the site ZM-Mon, located in the Tropical deciduous forest biome.\n\n\n\n\n\n\n\nwarm year-round\npronounced dry season\nwidely spaced trees, mixed with grasses\nlow plant biomass, deep roots\nregular fires\n\n\n\n\n\n\nFigure 2.5: Climate diagram of the site AU-How, located in the Tropical savannah biome.\n\n\n\n\n\n\n\ntropical and temperate dry climates\nC3 and C4 grasses (see below), distribution governed by temperature\ntemperate grasslands in dry, seasonally hot, semiarid climates with annual precipitation less than about 1000 mm\ntransitional between forests and desert\n\n\n\n\n\n\nFigure 2.6: Climate diagram of the site US-Tw1, located in the Grasslands biome.\n\n\n\n\n\n\n\nless than 250 mm annual precipitation\nshort, widely spaced desert scrub and shrubland\ngermination after intense rain, leaf shedding during dry period\ncacti and succulents store water and use the CAM photosynthetic pathway to minimize water loss during photosynthesis\n\n\n\n\n\n\nFigure 2.7: Climate diagram of the site US-SRM, located in the Shrublands and deserts biome.\n\n\n\n\n\n\n\nmore than 1000 mm annual precipitation\ndeciduous and evergreen trees, sometimes mixed\nlow winter light and temperature limits productivity\ntall trees\n\n\n\n\n\n\nFigure 2.8: Climate diagram of the site DE-Hai, located in the Temperate forests biome.\n\n\n\n\n\n\n\nadditional productivity limitation in summer due to water limitation\nless limited productivity by temperature and light in winter than temperate forests\nmild and moist winters\nshort stature trees, dense shrubs\nthick, waxy leaves\n\n\n\n\n\n\nFigure 2.9: Climate diagram of the site FR-Pue, located in the Mediterranean forests biome.\n\n\n\n\n\n\n\n\nvery cold winters, cool summers\nwinter light and temperature limits productivity\nmostly needle-leaved evergreen\nshorter and more open than temperate forests\nin Siberia: extreme winter low temperatures favour deciduousness of larch (larix decidua)\n\n\n\n\n\n\nFigure 2.10: Climate diagram of the site FI-Hyy, located in the Boreal forests biome.\n\n\n\n\n\n\n\ntree-less, grass-like sedges, dwarf shrubs, lichens, and mosses\nvery short vegetation period\nfrozen ground, seasonal thawing of top ~50 cm (permafrost)\n\n\n\n\n\n\nFigure 2.11: Climate diagram of the site US-ICh, located in the Tundra biome.\n\n\n\n\n\n\n\n\n2.2.1 Biomes in climate space\nFigure 2.2 shows biomes in geographical space - as a global map. Acknowledging their intricate relationship with climate, biomes can also be delineated in climate space - in a diagram defined by mean annual temperature (MAT) along one axis and mean annual precipitation (MAP) along the other axis. This yields a plot following Whittaker (1975). Note that the biome definition shown in Figure 2.12 does not exactly match the definition of biomes given above as it is mainly aimed at separating with respect to MAT and MAP. For example, Mediterranean forests are not separated in the “Whittaker-plot”. This is because their characteristic climate is not distinguished by annual means, but by the seasonality of temperature, solar radiation, and precipitation.\n\n\nCode\n# library(ggplot2)\n# library(devtools)\n# devtools::install_github(\"valentinitnelav/plotbiomes\")\n# library(plotbiomes)\n# plotbiomes::whittaker_base_plot() +\n# theme_classic()\n# ggsave(here::here(\"book/images/biomes_whittaker.png\"), width = 7, height = 4)\n\nknitr::include_graphics(\"images/biomes_whittaker.png\")\n\n\n\n\n\nFigure 2.12: Biomes in climate space, defined by mean annual temperature and precipitation, following Whittaker (1975)." }, { "objectID": "biogeography.html#sec-pfts", "href": "biogeography.html#sec-pfts", "title": "2  Biogeography", "section": "2.3 Plant functional types", - "text": "2.3 Plant functional types\nEach biome is characterised by a typical assembly of plant functional types (PFT, Figure 2.13). PFTs are a grouping of plant species based on their key physiological, morphological, and life history characteristics. That is, we can distinguish between annual (mostly grasses and herbs) and perennial (mostly trees and shrubs) plants, between needle-leaved and broadleaved trees, and between deciduous and evergreen trees. A key physiological distinction can further be made between grasses following the C3 vs. the C4 photosynthetic pathway (see Chapter 4). Thereby, the bewildering diversity of the plant kingdom can be reduced to a small set of PFT. A common categorization distinguishes the following PFTs:\n\nneedle-leaved evergreen trees\nbroadleaved evergreen trees\nneedle-leaved deciduous trees\nbroadleaved deciduous trees\nbroadleaved annuals (herbs)\nC3 grasses\nC4 grasses\n\nGlobal vegetation models use PFTs as their basic unit for distinguishing plants. The exact delineation of PFTs implemented in such models may vary from the list given above. Further distinctions may be made and are relevant in a global vegetation and carbon cycle modelling context. For example, only a relatively small subset of plants are known to associate with symbiotic nitrogen (N)-fixing bacteria that live in root nodules of the host plant (“N-fixing plants”, see also Chapter 11). This association is highly relevant for the N economy of the plant and its productivity and competitiveness under different levels of N availability.\nPlants can also be distinguished into the botanical classification of angiosperms (flowering plants) and gymnnosperms (seed-producing plants that include conifers, cycads, and Ginkgo). The distinction between angiosperms and gymnosperms largely aligns with the distinction between needle-leaved and broadleaved plants (but see Ginkgo). The two groups are not only distinguished by their phylogenetic heritage, but also by essential characteristics that relate to the efficiency by which they photosynthesise and transpire water. Angiosperm leaves typically exhibit higher photosynthesis and transpiration rates and are thinner and shorter-lived than leaves of gymnosperms. These differences relate to differences in how the water transport system (plant hydraulics) is built. A larger number and a wider diameter of water transport organs in angiosperms enable a higher water conductivity - essential for sustaining higher photosynthetic rates than in gymnosperms.\n\n\n\n\n\nFigure 2.13: Assembly of plant functional types as a basis for biome classification" + "text": "2.3 Plant functional types\nEach biome is characterised by a typical assembly of plant functional types (PFT, Figure 2.13). PFTs are a grouping of plant species based on their key physiological, morphological, and life history characteristics. That is, we can distinguish between annual (mostly grasses and herbs) and perennial (mostly trees and shrubs) plants, between needle-leaved and broadleaved trees, and between deciduous and evergreen trees. A key physiological distinction can further be made between grasses following the C3 vs. the C4 photosynthetic pathway (see Chapter 4). Thereby, the bewildering diversity of the plant kingdom can be reduced to a small set of PFT. A common categorization distinguishes the following PFTs:\n\nneedle-leaved evergreen trees\nbroadleaved evergreen trees\nneedle-leaved deciduous trees\nbroadleaved deciduous trees\nbroadleaved annuals (herbs)\nC3 grasses\nC4 grasses\n\nGlobal vegetation models use PFTs as their basic unit for distinguishing plants. The exact delineation of PFTs implemented in such models may vary from the list given above. Further distinctions may be made and are relevant in a global vegetation and carbon cycle modelling context. For example, only a relatively small subset of plants is known to associate with symbiotic nitrogen (N)-fixing bacteria that live in root nodules of the host plant (“N-fixing plants”, see also Chapter 11). This association is highly relevant for the N economy of the plant and its productivity and competitiveness under different levels of N availability.\nPlants can also be distinguished into the botanical classification of angiosperms (flowering plants) and gymnosperms (seed-producing plants that include conifers, cycads, and Ginkgo). The distinction between angiosperms and gymnosperms largely aligns with the distinction between needle-leaved and broadleaved plants (but see Ginkgo). The two groups are not only distinguished by their phylogenetic heritage, but also by essential characteristics that relate to the efficiency by which they photosynthesise and transpire water. Angiosperm leaves typically exhibit higher photosynthesis and transpiration rates and are thinner and shorter-lived than leaves of gymnosperms. These differences relate to differences in how the water transport system (plant hydraulics) is built. A larger number and a wider diameter of water transport organs in angiosperms enable a higher water conductivity - essential for sustaining higher photosynthetic rates than in gymnosperms.\n\n\n\n\n\nFigure 2.13: Assembly of plant functional types as a basis for biome classification" }, { "objectID": "biogeography.html#sec-traits", "href": "biogeography.html#sec-traits", "title": "2  Biogeography", "section": "2.4 Traits", - "text": "2.4 Traits\n\nThe physiological, morphological, and life history characteristics of different plants determine their productivity and competitiveness in a given climate. Such characteristics are referred to as plant functional traits, or often just traits. Plant species can be described by a set of traits and a subset of certain traits yields the distinction into PFTs described above: leaf habit (deciduous vs. evergreen), leaf form (needle-leaved vs. broadleaved), and the life history strategy distinguising annual vs. perennial. A range of additional traits are commonly described and investigated scientifically. Here, we will not consider additional ones. The concept of a plant functional trait is that it describes a largely immutable characteristic of a plant species that determines metabolic rates (photosynthesis, respiration) and their relationship to the abiotic environment (e.g., temperature), nutrient and water demand, and ultimately its demographic rates (growth, fecundity, mortality) and thus competitiveness.\nToday’s global distribution of species and biomes (assuming no intervention by human land use and forest management) is the outcome of competition and thus reflects the combination of plant functional traits that optimises competitiveness of a species under the present-day climate. The distribution of biomes and PFTs is thus a direct reflection of the climate.\nFor example, whether a region is dominated by deciduous or by evergreen trees and forests is determined by the benefits and costs for a plant of maintaining leaves year-round. Evergreen trees benefit from the ability to photosynthesise and gain carbon around the year. For example, in Mediterranean regions, although light levels are lower in winter than in summer, ample moisture and non-negligible light enables evergreen trees to assimilate carbon also during winter months. However, leaves and needles of evergreen plants have to be built for lasting several years. Such leaves are typically much thicker than those of deciduous trees and thus require more carbon per unit leaf area for their construction. The leaf mass per unit leaf area is commonly referred to as the leaf mass per area, LMA, and is an important additional plant trait as it is directly linked to a plant’s carbon balance. Over the leaf lifespan, the initial high construction costs of high-LMA leaves are outweighed by the additional carbon assimilation during periods when deciduous trees shed their leaves.\nLeaf-shedding of deciduous trees, in contrast, is a strategy to avoid having to build costly long-lasting leaves and maintaining them year-round (which also incurs an additional respiration cost, also in the form of carbon). Leaves are shed during periods when the climate is unfavourable for photosynthesis - during cold and dark winter months, or during excessively dry periods.\nNote that plant functional traits are often not entirely immutable. Instead, traits may vary also within a species and these variations are often driven by the environment. This is called acclimation. Such variations can even arise over the course of a season. For example, photosynthetic traits can rapidly acclimate to the large changes in light availability over the course of a year. Some traits are more plastic than others. For example, a tree is either needle-leaved or broadleaved. There is no continuum between the two leaf forms. In contrast, the nitrogen content per unit leaf mass is relatively plastic within a species.\nA changing environment changes the competitiveness of a given species, i.e., of a given trait combination. As a result, some traits may acclimate to some extent within a weeks to years. Over longer time scales, the altered demographic rates in a new climate affect the competitiveness of a species (even after some of its traits may have acclimated to a new climate) and ultimately shift demographic rates and the community composition. In grasslands, where the demographic cycle is short, such community composition changes may unfold over time scales of a few years. In forests, the longevity of an individual tree is on the order of decades to centuries and community composition changes unfold on correspondingly long time scale." + "text": "2.4 Traits\n\nThe physiological, morphological, and life history characteristics of different plants determine their productivity and competitiveness in a given climate. Such characteristics are referred to as plant functional traits, or often just traits. Plant species can be described by a set of traits and a subset of certain traits yields the distinction into PFTs described above: leaf habit (deciduous vs. evergreen), leaf form (needle-leaved vs. broadleaved), and the life history strategy distinguishing annual vs. perennial. A range of additional traits are commonly described and investigated scientifically. Here, we will not consider additional ones. The concept of a plant functional trait is that it describes a largely immutable characteristic of a plant species that determines metabolic rates (photosynthesis, respiration) and their relationship to the abiotic environment (e.g., temperature), nutrient and water demand, and ultimately its demographic rates (growth, fecundity, mortality) and thus competitiveness.\nToday’s global distribution of species and biomes (assuming no intervention by human land use and forest management) is the outcome of competition and thus reflects the combination of plant functional traits that optimises competitiveness of a species under the present-day climate. The distribution of biomes and PFTs is thus a direct reflection of the climate.\nFor example, whether a region is dominated by deciduous or by evergreen trees and forests is determined by the benefits and costs for a plant of maintaining leaves year-round. Evergreen trees benefit from the ability to photosynthesise and gain carbon around the year. For example, in Mediterranean regions, although light levels are lower in winter than in summer, ample moisture and non-negligible light enables evergreen trees to assimilate carbon also during winter months. However, leaves and needles of evergreen plants have to be built for lasting several years. Such leaves are typically much thicker than those of deciduous trees and thus require more carbon per unit leaf area for their construction. The leaf mass per unit leaf area is commonly referred to as the leaf mass per area, LMA, and is an important additional plant trait as it is directly linked to a plant’s carbon balance. Over the leaf lifespan, the initial high construction costs of high-LMA leaves are outweighed by the additional carbon assimilation during periods when deciduous trees shed their leaves.\nLeaf-shedding of deciduous trees, in contrast, is a strategy to avoid having to build costly long-lasting leaves and maintaining them year-round (which also incurs an additional respiration cost, also in the form of carbon). Leaves are shed during periods when the climate is unfavourable for photosynthesis - during cold and dark winter months, or during excessively dry periods.\nNote that plant functional traits are often not entirely immutable. Instead, traits may vary also within a species, and these variations are often driven by the environment. This is called acclimation. Such variations can even arise over the course of a season. For example, photosynthetic traits can rapidly acclimate to the large changes in light availability over the course of a year. Some traits are more plastic than others. For example, a tree is either needle-leaved or broadleaved. There is no continuum between the two leaf forms. In contrast, the nitrogen content per unit leaf mass is relatively plastic within a species.\nA changing environment changes the competitiveness of a given species, i.e., of a given trait combination. As a result, some traits may acclimate to some extent within weeks to years. Over longer time scales, the altered demographic rates in a new climate affect the competitiveness of a species (even after some of its traits may have acclimated to a new climate) and ultimately shift demographic rates and the community composition. In grasslands, where the demographic cycle is short, such community composition changes may unfold over time scales of a few years. In forests, the longevity of an individual tree is on the order of decades to centuries and community composition changes unfold on a correspondingly long time scale." }, { "objectID": "biogeography.html#sec-global-veg-patterns", "href": "biogeography.html#sec-global-veg-patterns", "title": "2  Biogeography", "section": "2.5 Global vegetation patterns", - "text": "2.5 Global vegetation patterns\nThe biome classification is a way to discretize vegetation based on several characteristics (e.g., tree cover fraction). However, many of these characteristics describe observable variables that vary more or less gradually across environmental gradients and each of these variables can be mapped across the globe thanks to Earth observation data. These global patterns of different observable variables reflect how the climate influences vegetation structure and functioning across the globe (independent of a classification into biomes). In much of the remainder of this course, we will investigate these vegetation-climate relationships without considering the biome classification. These relationships are informative for understanding how different processes of terrestrial ecology, plant physiology, the carbon cycle, and land-climate interactions are driven by the environment and vary across the globe.\n\nVegetation heightLeaf area indexBiomassTree cover fraction\n\n\n\n\n\n\n\nFigure 2.14: The global distribution of vegetation height from Simard et al. (2011).\n\n\n\n\n\n\n\n\n\nFigure 2.15: Distribution of vegetation height by biome. Data from Simard et al. (2011). Note that the vegetation height data has gaps in areas with sparse or generally short-statured vegetation cover (deserts, grasslands, Tundra, see Figure 2.14). Therefore, the pixels for which data is used for visualising the vegetation height per biome is biased towards particularly tall vegetation in these areas. Consequently, the distribution of vegetation heights in the biome ‘Tundra’ appears implausibly high.\n\n\n\n\n\n\n\n\n\n\n\nFigure 2.16: Annual maximum leaf area index, averaged over years 2000-2008. Data from the MODIS MOD15A2 (C006) product.\n\n\n\n\n\n\n\n\n\nFigure 2.17: Multi-year average of the annual maximum leaf area index by biome.\n\n\n\n\n\n\n\n\n\n\n\nFigure 2.18: Aboveground biomass carbon, mean over years 1993-2012. Data from Liu et al. (2015).\n\n\n\n\n\n\n\n\n\nFigure 2.19: Aboveground biomass carbon by biome. Data from Liu et al. (2015).\n\n\n\n\n\n\n\n\n\n\n\nFigure 2.20: Tree cover fraction. Data from the MODIS MOD44B (v061) product.\n\n\n\n\n\n\n\n\n\nFigure 2.21: Tree cover fraction by biome.\n\n\n\n\n\n\n\nNote that the global vegetation patterns shown above are based on Earth observation data from satellite remote sensing. These reflect the actual state of the land surface and thus the influence of human land use and land use change. In contrast, biomes are defined for a potential natural vegetation. Therefore, you see, for example, that the tree cover fraction has very wide distributions, particularly in the biome “Temperate broadleaved and mixed forests” (Figure 2.21)." + "text": "2.5 Global vegetation patterns\nThe biome classification is a way to discretize vegetation based on several characteristics (e.g., tree cover fraction). However, many of these characteristics describe observable variables that vary more or less gradually across environmental gradients, and each of these variables can be mapped across the globe thanks to Earth observation data. These global patterns of different observable variables reflect how the climate influences vegetation structure and functioning across the globe (independent of a classification into biomes). In much of the remainder of this course, we will investigate these vegetation-climate relationships without considering the biome classification. These relationships are informative for understanding how different processes of terrestrial ecology, plant physiology, the carbon cycle, and land-climate interactions are driven by the environment and vary across the globe.\n\nVegetation heightLeaf area indexBiomassTree cover fraction\n\n\n\n\n\n\n\nFigure 2.14: The global distribution of vegetation height from Simard et al. (2011).\n\n\n\n\n\n\n\n\n\nFigure 2.15: Distribution of vegetation height by biome. Data from Simard et al. (2011). Note that the vegetation height data has gaps in areas with sparse or generally short-statured vegetation cover (deserts, grasslands, Tundra, see Figure 2.14). Therefore, the pixels for which data is used for visualising the vegetation height per biome is biased towards particularly tall vegetation in these areas. Consequently, the distribution of vegetation heights in the biome ‘Tundra’ appears implausibly high.\n\n\n\n\n\n\n\n\n\n\n\nFigure 2.16: Annual maximum leaf area index, averaged over years 2000-2008. Data from the MODIS MOD15A2 (C006) product.\n\n\n\n\n\n\n\n\n\nFigure 2.17: Multi-year average of the annual maximum leaf area index by biome.\n\n\n\n\n\n\n\n\n\n\n\nFigure 2.18: Aboveground biomass carbon, mean over years 1993-2012. Data from Liu et al. (2015).\n\n\n\n\n\n\n\n\n\nFigure 2.19: Aboveground biomass carbon by biome. Data from Liu et al. (2015).\n\n\n\n\n\n\n\n\n\n\n\nFigure 2.20: Tree cover fraction. Data from the MODIS MOD44B (v061) product.\n\n\n\n\n\n\n\n\n\nFigure 2.21: Tree cover fraction by biome.\n\n\n\n\n\n\n\nNote that the global vegetation patterns shown above are based on Earth observation data from satellite remote sensing. These reflect the actual state of the land surface and thus the influence of human land use and land use change. In contrast, biomes are defined for a potential natural vegetation. Therefore, you see, for example, that the tree cover fraction has very wide distributions, particularly in the biome “Temperate broadleaved and mixed forests” (Figure 2.21)." }, { "objectID": "biogeography.html#vegetation-types", @@ -95,21 +95,21 @@ "href": "biogeography.html#hillslope-scale-heterogeneity", "title": "2  Biogeography", "section": "2.8 Hillslope-scale heterogeneity", - "text": "2.8 Hillslope-scale heterogeneity\nTopography shapes microclimates and drives small-scale variations in hydrology. In mountain regions, vegetation may thus vary strongly along small spatial scales - on the order of 10-103 m. This scale - from the river channel to the ridge - is referred to as the hillslope scale. In much the same way as climate drives vegetation across biomes, so it does across the hillslope scale. The incident solar radiation and - as a consequence of that - near-surface air temperatures are affected by the local slope, aspect, and shading by the surrounding topography. Soil moisture and the groundwater table depth are affected by lateral subsurface flow of water, driven by gradients in water potentials along topographical gradients. Subsurface water flow converges in depressions and concave terrain (e.g., in valley bottoms) and diverges in convex terrain. (e.g., on ridges and hilltops). As a consequence, the water table is shallow in valley bottoms and deep under ridges. Radiation and hydrology thus create microclimates and plant water availability conditions that are shaped by topography and variations in vegetation that are shaped by the microclimates and hydrological conditions.\nThese hillslope-scale variations “intersect” with the the background climate (average climate across larger spatial scales, on the order of 104-105 m). A shallow groundwater table and moist soils in valley bottoms can promote plant productivity in arid regions and seasons. In contrast, in a humid climate, a very shallow water table in valley bottoms inhibits plant productivity due to anaerobic conditions in waterlogged soils and the inability of roots to penetrate into permanently water-saturated soil. Similarly, the influence of radiation in promoting versus inhibiting plant productivity depends on the background climate. In cold climates of the high northern latitudes, the solar zenith angle is relatively also, even in mid-summer. This creates a strong influence of the local slope and aspect. In the northern hemisphere, south-facing slopes receive more radiation - a difference to north-facing slopes that can be critical for sustaining tree growth in high northern regions. In contrast, elevated incident solar radiation in south-facing slopes can aggravate water limitation and suppress vegetation productivity in more arid climates of the subtropics and mid-latitudes of the northern hemisphere.\n\n\n\n\n\nFigure 2.24: Hillslope effects on vegetation in different background climate zones. Top-left: Hydrology promoting vegetation in valley bottoms in a semi-arid climate in Arizona, USA (Source: wikipedia.org). Top-right: Hydrology inhibiting vegetation in topographic depressions in a humid climate due to seasonal waterlogging in the Pantanal region (Source: wikimapia.org). Bottom-left: Radiation inhibiting vegetation on south-facing (sun-exposed) slopes in Texas, USA (Source: thecommonmilkweed.blogspot.com). Bottom-right: Radiation promoting vegetation on south-facing (sun-exposed) slopes in southwest Yukon, Canada (Source: photo by Ryan Danby, Queen’s University, Canada). Figure extracted from Fan et al. (2019).\n\n\n\n\nClimate also varies along elevation due to thermodynamics and radiative transfer in the atmosphere - independent of the slope and aspect of the local terrain. Temperatures decline following the lapse rate in the troposphere, leading to a shift of vegetation zones along large elevational gradients. This phenomenon is depicted also in Humboldt’s drawings (Figure 2.1). Radiation levels are elevated at high altitudes due to a shorter path length of solar radiation travelling across the atmosphere and, consequently, a reduced attenuation of the radiation intensity. Atmospheric pressure and thus the partial pressure of oxygen declines with elevation. This implies reduced respiration and an increased efficiency of photosynthesis.\nSmall-scale variations in vegetation may also be driven my variations in soil characteristics and bedrock lithology which influences drainage and soil chemistry (pH, nutrient availability). Where the ground is seasonally snow-covered, very small-scale terrain features (100-102) and dominant wind directions drive snow accumulation and dispersion, leading to substantial small-scale variations in maximum snow depth and the duration of seasonal snow cover - with implications for plants (Körner and Hiltbrunner 2021)." + "text": "2.8 Hillslope-scale heterogeneity\nTopography shapes microclimates and drives small-scale variations in hydrology. In mountain regions, vegetation may thus vary strongly along small spatial scales - on the order of 10-103 m. This scale - from the river channel to the ridge - is referred to as the hillslope scale. In much the same way that climate drives vegetation across biomes, so it does across the hillslope scale. The incident solar radiation and - as a consequence of that - near-surface air temperatures are affected by the local slope, aspect, and shading by the surrounding topography. Soil moisture and the groundwater table depth are affected by lateral subsurface flow of water, driven by gradients in water potentials along topographical gradients. Subsurface water flow converges in depressions and concave terrain (e.g., in valley bottoms) and diverges in convex terrain. (e.g., on ridges and hilltops). As a consequence, the water table is shallow in valley bottoms and deep under ridges. Radiation and hydrology thus create microclimates and plant water availability conditions that are shaped by topography, from which result variations in vegetation.\nThese hillslope-scale variations “intersect” with the background climate (average climate across larger spatial scales, on the order of 104-105 m). A shallow groundwater table and moist soils in valley bottoms can promote plant productivity in arid regions and seasons. In contrast, in a humid climate, a very shallow water table in valley bottoms inhibits plant productivity due to anaerobic conditions in waterlogged soils and the inability of roots to penetrate into permanently water-saturated soil. Similarly, the influence of radiation in promoting versus inhibiting plant productivity depends on the background climate. In cold climates of the high northern latitudes, the solar zenith angle is relatively also, even in mid-summer. This creates a strong influence of the local slope and aspect. In the northern hemisphere, south-facing slopes receive more radiation - a difference to north-facing slopes that can be critical for sustaining tree growth in high northern regions. In contrast, elevated incident solar radiation in south-facing slopes can aggravate water limitation and suppress vegetation productivity in more arid climates of the subtropics and mid-latitudes of the northern hemisphere.\n\n\n\n\n\nFigure 2.24: Hillslope effects on vegetation in different background climate zones. Top-left: Hydrology promoting vegetation in valley bottoms in a semi-arid climate in Arizona, USA (Source: wikipedia.org). Top-right: Hydrology inhibiting vegetation in topographic depressions in a humid climate due to seasonal waterlogging in the Pantanal region (Source: wikimapia.org). Bottom-left: Radiation inhibiting vegetation on south-facing (sun-exposed) slopes in Texas, USA (Source: thecommonmilkweed.blogspot.com). Bottom-right: Radiation promoting vegetation on south-facing (sun-exposed) slopes in southwest Yukon, Canada (Source: photo by Ryan Danby, Queen’s University, Canada). Figure extracted from Fan et al. (2019).\n\n\n\n\nClimate also varies along elevation due to thermodynamics and radiative transfer in the atmosphere - independent of the slope and aspect of the local terrain. Temperatures decline following the lapse rate in the troposphere, leading to a shift of vegetation zones along large elevational gradients. This phenomenon is depicted also in Humboldt’s drawings (Figure 2.1). Radiation levels are elevated at high altitudes due to a shorter path length of solar radiation travelling across the atmosphere and, consequently, a reduced attenuation of the radiation intensity. Atmospheric pressure and thus the partial pressure of oxygen declines with elevation. This implies reduced respiration and an increased efficiency of photosynthesis.\nSmall-scale variations in vegetation may also be driven my variations in soil characteristics and bedrock lithology which influences drainage and soil chemistry (pH, nutrient availability). Where the ground is seasonally snow-covered, very small-scale terrain features (100-102 m) and dominant wind directions drive snow accumulation and dispersion, leading to substantial small-scale variations in maximum snow depth and the duration of seasonal snow cover - with implications for plants (Körner and Hiltbrunner 2021)." }, { "objectID": "biogeography.html#species-distribution-modelling-and-ecological-niche", "href": "biogeography.html#species-distribution-modelling-and-ecological-niche", "title": "2  Biogeography", "section": "2.9 Species distribution modelling and ecological niche", - "text": "2.9 Species distribution modelling and ecological niche\nThe notion that climate drives vegetation and the distribution of plant species enables a prediction and mapping of the species occurrence across geographical space. Data on species presence and absence can be associated with multiple variables characterizing the abiotic environment (mostly climate) recorded for the same location. The resulting empirical patterns can be used for spatial modelling and predicting whether a species is likely to occur at a new location or even a novel climate Figure 2.25.\n\n\n\n\n\nFigure 2.25: Methodological approach to species distribution modelling and predicting to a novel climate. Figure from Svenning et al. (2011).\n\n\n\n\nThe approach to species distribution modelling is fundamentally rooted in the ecological niche concept. As formulated by Hutchinson (1957; Araújo and Guisan 2006), each species has a fundamental niche that can be conceived as a domain in a multi-dimensional space defined by the environmental conditions. Environmental filtering yields the fundamental niche which is generally a subset of the Earth’s climate space (Figure 2.26). The actual, or realized niche is smaller as it is additionally constrained by biotic interactions with other species. Natural selection yields the realized niche. Several challenges for species distribution modelling exist (Zimmermann et al. 2010). For example, the species distribution is hardly ever in equilibrium with the environment, given that climate has been constantly changing (although not as rapidly as today for millions of years); topographic heterogeneity, climatic history, and ecological refugia affect the species distribution and how it varies under climate change; genetic adaptation can lead to populations within species that exhibit different responses to the environment; and niche stability over long time scales may be undermined not only by genetic adaptation, but also by physiological effects of CO2 which fundamentally alters photosynthesis and transpiration and will therefore shift water availability-related niche limits observed today.\n\n\n\n\n\nFigure 2.26: Environmental filtering yields the fundamental niche. Biotic interactions yield the realized niche." + "text": "2.9 Species distribution modelling and ecological niche\nThe notion that climate drives vegetation and the distribution of plant species enables a prediction and mapping of the species occurrence across geographical space. Data on species presence and absence can be associated with multiple variables characterizing the abiotic environment (mostly climate) recorded for the same location. The resulting empirical patterns can be used for spatial modelling and predicting whether a species is likely to occur at a new location or even a novel climate Figure 2.25.\n\n\n\n\n\nFigure 2.25: Methodological approach to species distribution modelling and predicting to a novel climate. Figure from Svenning et al. (2011).\n\n\n\n\nThe approach to species distribution modelling is fundamentally rooted in the ecological niche concept. As formulated by Hutchinson (1957; Araújo and Guisan 2006), each species has a fundamental niche that can be conceived as a domain in a multidimensional space defined by the environmental conditions. Environmental filtering yields the fundamental niche which is generally a subset of the Earth’s climate space (Figure 2.26). The actual, or realized niche is smaller as it is additionally constrained by biotic interactions with other species. Natural selection yields the realized niche. Several challenges for species distribution modelling exist (Zimmermann et al. 2010). For example, the species distribution is hardly ever in equilibrium with the environment, given that climate has been constantly changing (although not as rapidly as today for millions of years); topographic heterogeneity, climatic history, and ecological refugia affect the species distribution and how it varies under climate change; genetic adaptation can lead to populations within species that exhibit different responses to the environment; and niche stability over long time scales may be undermined not only by genetic adaptation, but also by physiological effects of CO2 which fundamentally alters photosynthesis and transpiration and will therefore shift water availability-related niche limits observed today.\n\n\n\n\n\nFigure 2.26: Environmental filtering yields the fundamental niche. Biotic interactions yield the realized niche." }, { "objectID": "biogeography.html#temporal-variations-of-vegetation", "href": "biogeography.html#temporal-variations-of-vegetation", "title": "2  Biogeography", "section": "2.10 Temporal variations of vegetation", - "text": "2.10 Temporal variations of vegetation\nSpatial patterns in vegetation are influenced by how climate varies across different areas. Similarly, changes in vegetation are influenced by how climate changes over time. Vegetation change at temporal scales of thousands of years is recorded, for example, by pollen deposited in layered sediments. Given that they are preserved and that the sediment layers can be dated, the vegetation composition over time can be reconstructed. An example is given for the Moossee, near Bern in Figure 2.27. The pollen diagram documents how vegetation on the Swiss Plateau unterwent several major changes since the last Glacial. At around 19 kyr BP, a steppe tundra established, replaced around 16 kyr BP by a shrub tundra. At around 15 kyr BP, a boreal forest established before it was replaced by a temperate mixed oak forest at the beginning of the Holocene - the current warm period at 11,600 yr BP. A beech-dominated temperate forest, as it is common for this region today, established around 8200 yr BP. Figure 2.27 also shows that these biome replacements coincided with rapid climatic shifts and that the vegetation change was largely instantaneous. This instantaneous response of species composition is interpreted as a reflection of the importance of glacial refugia from which a species may rapidly expand upon climate change (Rey et al. 2020).\n\n\n\n\n\nFigure 2.27: Pollen diagram from the Moossee, Switzerland. The diagram shows the percentage of pollen recorded over time (green areas). Cultural indicators and charcoal influx indicate the presence of humans in the region. Parallel variations observed from other data sources are also shown for interpretation: Millennial-scale variations in solar radiation, lake levels, and temperature reconstructions. Figure from Rey et al. (2020).\n\n\n\n\nMultiple vegetation reconstructions for the Last Glacial Maximum (LGM) obtained from globally distributed locations provide a picture of how biomes were distributed across the Earth around 20 ka BP (Figure 2.29, bottom panel). The difference in climate and CO2 (global mean temperatures were around 6°C lower than at present; CO2 was at around 180 ppm, today it’s at over 420 ppm) caused forest biomes to recede and grasslands to expand across most of the globe. The upper panel of Figure 2.29 shows the simulated biome distribution. These simulation results are not based on a species distribution model, but on a Dynamic Global Vegetation Model that accounts for both climate and CO2 effects and simulates the distribution of PFTs from which biomes were derived here. The simulation of vegetation distribution at the level of PFTs instead of species is less affected by biotic interactions that are hard to simulate at global scale.\n\n\n\n\n\nFigure 2.28: The global distribution of biomes at the Mid-Holocene (6000 kyr BP). Figure from I. Colin Prentice, Jolly, and Participants (2000)\n\n\n\n\n\n\n\n\n\nFigure 2.29: The global distribution of biomes at the Last Glacial Maximum from a model simulation (top) and from a biome reconstruction based on pollen records. Figure from I. C. Prentice, Harrison, and Bartlein (2011).\n\n\n\n\nThe mapping of vegetation for past climates is enabled by the biomization of paleo-ecological records (I. Prentice et al. 1996). Classifying vegetation into biomes is useful for distilling ecological information beyond the anthropogenic impact. Biomes reflect a potential natural vegetation. The use of biomes is therefore important for designing conservation efforts suited for a specific climate (Olson et al. 2001), and is instructive for understanding environmental controls on ecosystem types as reflected by the agreement of biomes and climate zones (Section 2.7). Yet, to understand principles and mechanisms of how plant physiology, biogeochemical cycling, and land-climate interactions are shaped by the environment, we often don’t need to rely on a classification of vegetation. As we will learn in later chapters, the abiotic environment drives vegetation functioning in much the same way (bar some exceptions) through generally applicable physical laws across the whole terrestrial biosphere.\n\n\n\n\n\n\nExercise\n\n\n\n\nExplain the difference between biomes, as defined for example by Olson et al. (2001), and the IGBP vegetation classes.\nGive a good reason for why precipitation and temperature are plotted both along the y-axis in the Walter-Lieth climate diagrams. What is the meaning of the blue hashed area and the red dotted area?\nCompare the seasonality of temperature and precipitation of the example site given for the Mediterranean forest biome (FR-Pue) and the boreal forest biome (FI-Hyy). Which site do you expect to have a stronger seasonal variation in runoff?\nFor the seven biomes for which climate diagrams are shown above, establish a ranking with respect to the growing season length.\nConsider an ecosystem that is characterised with a fractional plant cover of trees of 10% and a fractional plant cover of grasses of 90%. What biome does it belong to?\nIn a changing climate, where do you expect vegetation composition shifts to unfold faster: in a large plain or in a mountainous landscape?\n\n\n\n\n\n\n\nAraújo, Miguel B., and Antoine Guisan. 2006. “Five (or so) Challenges for Species Distribution Modelling.” Journal of Biogeography 33 (10): 1677–88. https://doi.org/10.1111/j.1365-2699.2006.01584.x.\n\n\nBeck, Hylke E., Niklaus E. Zimmermann, Tim R. McVicar, Noemi Vergopolan, Alexis Berg, and Eric F. Wood. 2018. “Present and Future Köppen-Geiger Climate Classification Maps at 1-Km Resolution.” Scientific Data 5 (1): 180214. https://doi.org/10.1038/sdata.2018.214.\n\n\nBonan, Gordon. 2015. Ecological Climatology: Concepts and Applications. 3rd ed. Cambridge University Press.\n\n\nFan, Y., M. Clark, D. M. Lawrence, S. Swenson, L. E. Band, S. L. Brantley, P. D. Brooks, et al. 2019. “Hillslope Hydrology in Global Change Research and Earth System Modeling.” Water Resources Research 55 (2): 1737–72. https://doi.org/https://doi.org/10.1029/2018WR023903.\n\n\nHutchinson, G. Evelyn. 1957. “Concluding Remarks.” Cold Spring Harbor Symposia on Quantitative Biology 22 (January): 415–27. https://doi.org/10.1101/SQB.1957.022.01.039.\n\n\nKöppen, Wladimir. 1884. “Die Wärmezonen Der Erde, Nach Der Dauer Der Heissen, Gemässigten Und Kalten Zeit Und Nach Der Wirkung Der Wärme Auf Die Organische Welt Betrachtet (the Thermal Zones of the Earth According to the Duration of Hot, Moderate and Cold Periods and to the Impact of Heat on the Organic World).” Meteorologische Zeitschrift 20 (3): 351–60. https://doi.org/10.1127/0941-2948/2011/105.\n\n\nKörner, Christian, and Erika Hiltbrunner. 2021. “Why Is the Alpine Flora Comparatively Robust Against Climatic Warming?” Diversity 13 (8): 383. https://doi.org/10.3390/d13080383.\n\n\nLiu, Yi Y., Albert I. J. M. van Dijk, Richard A. M. de Jeu, Josep G. Canadell, Matthew F. McCabe, Jason P. Evans, and Guojie Wang. 2015. “Recent Reversal in Loss of Global Terrestrial Biomass.” Nature Climate Change 5 (5): 470–74. https://doi.org/10.1038/nclimate2581.\n\n\nOlson, David M., Eric Dinerstein, Eric D. Wikramanayake, Neil D. Burgess, George V. N. Powell, Emma C. Underwood, Jennifer A. D’amico, et al. 2001. “Terrestrial Ecoregions of the World: A New Map of Life on Earth: A New Global Map of Terrestrial Ecoregions Provides an Innovative Tool for Conserving Biodiversity.” BioScience 51 (11): 933–38. https://doi.org/10.1641/0006-3568(2001)051[0933:TEOTWA]2.0.CO;2.\n\n\nPeel, M. C., B. L. Finlayson, and T. A. McMahon. 2007. “Updated World Map of the Köppen-Geiger Climate Classification.” Hydrology and Earth System Sciences 11 (5): 1633–44. https://doi.org/10.5194/hess-11-1633-2007.\n\n\nPrentice, I Colin, D. Jolly, and BIOME 6000 Participants. 2000. “Mid-Holocene and Glacial-Maximum Vegetation Geography of the Northern Continents and Africa.” Journal of Biogeography 27 (3): 507–19. http://www.jstor.org/stable/2656208.\n\n\nPrentice, I. C., S. P. Harrison, and P. J. Bartlein. 2011. “Global Vegetation and Terrestrial Carbon Cycle Changes After the Last Ice Age.” New Phytologist 189 (4): 988–98. https://doi.org/10.1111/j.1469-8137.2010.03620.x.\n\n\nPrentice, Iain, Guiot Joel, Brian Huntley, Jolly D., and Rachid Cheddadi. 1996. “Reconstructing Biomes from Palaeoecological Data: A General Method and Its Application to European Pollen Data at 0 and 6 Ka.” Cd 12 (February): 185. https://doi.org/10.1007/s003820050102.\n\n\nRey, Fabian, Erika Gobet, Christoph Schwörer, Albert Hafner, Sönke Szidat, and Willy Tinner. 2020. “Climate Impacts on Vegetation and Fire Dynamics Since the Last Deglaciation at Moossee (Switzerland).” Climate of the Past 16 (4): 1347–67. https://doi.org/10.5194/cp-16-1347-2020.\n\n\nSimard, Marc, Naiara Pinto, Joshua B. Fisher, and Alessandro Baccini. 2011. “Mapping Forest Canopy Height Globally with Spaceborne Lidar.” Journal of Geophysical Research: Biogeosciences 116 (G4). https://doi.org/10.1029/2011JG001708.\n\n\nSvenning, Jens-Christian, Camilla Fløjgaard, Katharine A. Marske, David Nógues-Bravo, and Signe Normand. 2011. “Applications of Species Distribution Modeling to Paleobiology.” Quaternary Science Reviews 30 (21): 2930–47. https://doi.org/10.1016/j.quascirev.2011.06.012.\n\n\nWhittaker, Robert Harding. 1975. Communities and Ecosystems. 3rd ed. Macmillan.\n\n\nZimmermann, Niklaus E., Thomas C. Edwards Jr, Catherine H. Graham, Peter B. Pearman, and Jens-Christian Svenning. 2010. “New Trends in Species Distribution Modelling.” Ecography 33 (6): 985–89. https://doi.org/10.1111/j.1600-0587.2010.06953.x." + "text": "2.10 Temporal variations of vegetation\nSpatial patterns in vegetation are influenced by how climate varies across different areas. Similarly, changes in vegetation are influenced by how climate changes over time. Vegetation change at temporal scales of thousands of years is recorded, for example, by pollen deposited in layered sediments. Given that they are preserved and that the sediment layers can be dated, the vegetation composition over time can be reconstructed. An example is given for the Moossee, near Bern in Figure 2.27. The pollen diagram documents how vegetation on the Swiss Plateau underwent several major changes since the last Glacial. At around 19 kyr BP, a steppe tundra established, replaced around 16 kyr BP by a shrub tundra. At around 15 kyr BP, a boreal forest established before it was replaced by a temperate mixed oak forest at the beginning of the Holocene - the current warm period at 11,600 yr BP. A beech-dominated temperate forest, as it is common for this region today, established around 8200 yr BP. Figure 2.27 also shows that these biome replacements coincided with rapid climatic shifts and that the vegetation change was largely instantaneous. This instantaneous response of species composition is interpreted as a reflection of the importance of glacial refugia from which a species may rapidly expand upon climate change (Rey et al. 2020).\n\n\n\n\n\nFigure 2.27: Pollen diagram from the Moossee, Switzerland. The diagram shows the percentage of pollen recorded over time (green areas). Cultural indicators and charcoal influx indicate the presence of humans in the region. Parallel variations observed from other data sources are also shown for interpretation: Millennial-scale variations in solar radiation, lake levels, and temperature reconstructions. Figure from Rey et al. (2020).\n\n\n\n\nMultiple vegetation reconstructions for the Last Glacial Maximum (LGM) obtained from globally distributed locations provide a picture of how biomes were distributed across the Earth around 20 ka BP (Figure 2.29, bottom panel). The difference in climate and CO2 (global mean temperatures were around 6°C lower than at present; CO2 was at around 180 ppm, today it’s at over 420 ppm) caused forest biomes to recede and grasslands to expand across most of the globe. The upper panel of Figure 2.29 shows the simulated biome distribution. These simulation results are not based on a species distribution model, but on a Dynamic Global Vegetation Model that accounts for both climate and CO2 effects and simulates the distribution of PFTs from which biomes were derived here. The simulation of vegetation distribution at the level of PFTs instead of species is less affected by biotic interactions that are hard to simulate at global scale.\n\n\n\n\n\n\nFigure 2.28: The global distribution of biomes at the Mid-Holocene (6000 kyr BP). Figure from I. Colin Prentice, Jolly, and Participants (2000)\n\n\n\n\n\n\n\n\n\nFigure 2.29: The global distribution of biomes at the Last Glacial Maximum from a model simulation (top) and from a biome reconstruction based on pollen records. Figure from I. C. Prentice, Harrison, and Bartlein (2011).\n\n\n\n\nThe mapping of vegetation for past climates is enabled by the biomization of paleo-ecological records (I. Prentice et al. 1996). Classifying vegetation into biomes is useful for distilling ecological information beyond the anthropogenic impact. Biomes reflect a potential natural vegetation. The use of biomes is therefore important for designing conservation efforts suited for a specific climate (Olson et al. 2001), and is instructive for understanding environmental controls on ecosystem types as reflected by the agreement of biomes and climate zones (Section 2.7). Yet, to understand principles and mechanisms of how plant physiology, biogeochemical cycling, and land-climate interactions are shaped by the environment, we often don’t need to rely on a classification of vegetation. As we will learn in later chapters, the abiotic environment drives vegetation functioning in much the same way (bar some exceptions) through generally applicable physical laws across the whole terrestrial biosphere.\n\n\n\n\n\n\nExercise\n\n\n\n\nExplain the difference between biomes, as defined for example by Olson et al. (2001), and the IGBP vegetation classes.\nGive a good reason for why precipitation and temperature are plotted both along the y-axis in the Walter-Lieth climate diagrams. What is the meaning of the blue hashed area and the red dotted area?\nCompare the seasonality of temperature and precipitation of the example site given for the Mediterranean forest biome (FR-Pue) and the boreal forest biome (FI-Hyy). Which site do you expect to have a stronger seasonal variation in runoff?\nFor the seven biomes for which climate diagrams are shown above, establish a ranking with respect to the growing season length.\nConsider an ecosystem that is characterised with a fractional plant cover of trees of 10% and a fractional plant cover of grasses of 90%. What biome does it belong to?\nIn a changing climate, where do you expect vegetation composition shifts to unfold faster: in a large plain or in a mountainous landscape?\n\n\n\n\n\n\n\nAraújo, Miguel B., and Antoine Guisan. 2006. “Five (or so) Challenges for Species Distribution Modelling.” Journal of Biogeography 33 (10): 1677–88. https://doi.org/10.1111/j.1365-2699.2006.01584.x.\n\n\nBeck, Hylke E., Niklaus E. Zimmermann, Tim R. McVicar, Noemi Vergopolan, Alexis Berg, and Eric F. Wood. 2018. “Present and Future Köppen-Geiger Climate Classification Maps at 1-Km Resolution.” Scientific Data 5 (1): 180214. https://doi.org/10.1038/sdata.2018.214.\n\n\nBonan, Gordon. 2015. Ecological Climatology: Concepts and Applications. 3rd ed. Cambridge University Press.\n\n\nFan, Y., M. Clark, D. M. Lawrence, S. Swenson, L. E. Band, S. L. Brantley, P. D. Brooks, et al. 2019. “Hillslope Hydrology in Global Change Research and Earth System Modeling.” Water Resources Research 55 (2): 1737–72. https://doi.org/https://doi.org/10.1029/2018WR023903.\n\n\nHutchinson, G. Evelyn. 1957. “Concluding Remarks.” Cold Spring Harbor Symposia on Quantitative Biology 22 (January): 415–27. https://doi.org/10.1101/SQB.1957.022.01.039.\n\n\nKöppen, Wladimir. 1884. “Die Wärmezonen Der Erde, Nach Der Dauer Der Heissen, Gemässigten Und Kalten Zeit Und Nach Der Wirkung Der Wärme Auf Die Organische Welt Betrachtet (the Thermal Zones of the Earth According to the Duration of Hot, Moderate and Cold Periods and to the Impact of Heat on the Organic World).” Meteorologische Zeitschrift 20 (3): 351–60. https://doi.org/10.1127/0941-2948/2011/105.\n\n\nKörner, Christian, and Erika Hiltbrunner. 2021. “Why Is the Alpine Flora Comparatively Robust Against Climatic Warming?” Diversity 13 (8): 383. https://doi.org/10.3390/d13080383.\n\n\nLiu, Yi Y., Albert I. J. M. van Dijk, Richard A. M. de Jeu, Josep G. Canadell, Matthew F. McCabe, Jason P. Evans, and Guojie Wang. 2015. “Recent Reversal in Loss of Global Terrestrial Biomass.” Nature Climate Change 5 (5): 470–74. https://doi.org/10.1038/nclimate2581.\n\n\nOlson, David M., Eric Dinerstein, Eric D. Wikramanayake, Neil D. Burgess, George V. N. Powell, Emma C. Underwood, Jennifer A. D’amico, et al. 2001. “Terrestrial Ecoregions of the World: A New Map of Life on Earth: A New Global Map of Terrestrial Ecoregions Provides an Innovative Tool for Conserving Biodiversity.” BioScience 51 (11): 933–38. https://doi.org/10.1641/0006-3568(2001)051[0933:TEOTWA]2.0.CO;2.\n\n\nPeel, M. C., B. L. Finlayson, and T. A. McMahon. 2007. “Updated World Map of the Köppen-Geiger Climate Classification.” Hydrology and Earth System Sciences 11 (5): 1633–44. https://doi.org/10.5194/hess-11-1633-2007.\n\n\nPrentice, I Colin, D. Jolly, and BIOME 6000 Participants. 2000. “Mid-Holocene and Glacial-Maximum Vegetation Geography of the Northern Continents and Africa.” Journal of Biogeography 27 (3): 507–19. http://www.jstor.org/stable/2656208.\n\n\nPrentice, I. C., S. P. Harrison, and P. J. Bartlein. 2011. “Global Vegetation and Terrestrial Carbon Cycle Changes After the Last Ice Age.” New Phytologist 189 (4): 988–98. https://doi.org/10.1111/j.1469-8137.2010.03620.x.\n\n\nPrentice, Iain, Guiot Joel, Brian Huntley, Jolly D., and Rachid Cheddadi. 1996. “Reconstructing Biomes from Palaeoecological Data: A General Method and Its Application to European Pollen Data at 0 and 6 Ka.” Cd 12 (February): 185. https://doi.org/10.1007/s003820050102.\n\n\nRey, Fabian, Erika Gobet, Christoph Schwörer, Albert Hafner, Sönke Szidat, and Willy Tinner. 2020. “Climate Impacts on Vegetation and Fire Dynamics Since the Last Deglaciation at Moossee (Switzerland).” Climate of the Past 16 (4): 1347–67. https://doi.org/10.5194/cp-16-1347-2020.\n\n\nSimard, Marc, Naiara Pinto, Joshua B. Fisher, and Alessandro Baccini. 2011. “Mapping Forest Canopy Height Globally with Spaceborne Lidar.” Journal of Geophysical Research: Biogeosciences 116 (G4). https://doi.org/10.1029/2011JG001708.\n\n\nSvenning, Jens-Christian, Camilla Fløjgaard, Katharine A. Marske, David Nógues-Bravo, and Signe Normand. 2011. “Applications of Species Distribution Modeling to Paleobiology.” Quaternary Science Reviews 30 (21): 2930–47. https://doi.org/10.1016/j.quascirev.2011.06.012.\n\n\nWhittaker, Robert Harding. 1975. Communities and Ecosystems. 3rd ed. Macmillan.\n\n\nZimmermann, Niklaus E., Thomas C. Edwards Jr, Catherine H. Graham, Peter B. Pearman, and Jens-Christian Svenning. 2010. “New Trends in Species Distribution Modelling.” Ecography 33 (6): 985–89. https://doi.org/10.1111/j.1600-0587.2010.06953.x." }, { "objectID": "globalcarbonbudget.html#sec-preindustrialcarboncycle", @@ -123,21 +123,21 @@ "href": "globalcarbonbudget.html#sec-cpooldynamics", "title": "3  The global carbon budget", "section": "3.2 Carbon pool dynamics", - "text": "3.2 Carbon pool dynamics\n\n\n\n\n\n\nThe 1st-order decay model\n\n\n\nThe concept of pools and fluxes is central for describing and modelling the carbon cycle and other biogeochemical cycles in the environment. The dynamics of a pool \\(C(t)\\) is given by the balance of the flux of C into that pool \\(I(t)\\) and the flux \\(O(t)\\) leaving the pool - over time \\(t\\). In general terms, we can write the temporal change of the pool size as\n\\[\n\\frac{\\mathrm{d}C(t)}{\\mathrm{d}t} = I(t) - O(t) \\;.\n\\tag{3.1}\\]\nTo simplify the expressions, we will omit \\((t)\\) below. But remember, that the fluxes and pools vary with time. The assumption that the out-flux \\(O\\) scales linearly with the size of the pool \\(C\\) is a good simplifying description (i.e., a model) for many processes in the environment. For example, the amount of CO2 produced by the decomposition (decay) of organic matter in the soil scales roughly linearly with the amount of organic matter that is being respired. This leads to the 1st-order decay model of pool dynamics:\n\\[\n\\frac{\\mathrm{d}C}{\\mathrm{d}t} = I - kC \\;.\n\\tag{3.2}\\] Here, \\(k\\) is a decay constant and is in units of the inverse of time. In other words, it specifies the fraction of \\(C\\) decaying per unit time (e.g,. seconds, or years). The higher \\(k\\), the more rapidly the pool decays. For the case of \\(I=0\\), we get \\(\\mathrm{d}C/\\mathrm{d}t = -kC\\). This is a differential equation and can be understood as: What is the function that yields itself, multiplied by \\(-k\\), when taking its derivative with respect to time? The solution is:\n\\[\nC(t) = C_0 \\; e^{-kt} \\;.\n\\] For example, following this model, the pool of C in soil organic matter would decay exponentially if inputs (litterfall) were zero. The decay constant \\(k\\) determines how long it takes for it to be reduced by a certain factor. A commonly used factor is 0.5. We can calculate a half-life - the time \\(t\\) at which \\(C(t) = 0.5\\;C_0\\).\nIn a dynamic equilibrium the change in the pool size \\(C\\) is by definition zero. \\[\n\\frac{\\mathrm{d}C}{\\mathrm{d}t} = 0 \\;.\n\\tag{3.3}\\] Combining Equation 3.2 and Equation 3.3 and re-arranging terms leads to the steady-state pool size as a function of the in-flux and the decay constant \\(k\\). \\[\nC^\\ast = I/k\n\\tag{3.4}\\] Here, the asterisk denotes that \\(C\\) is at steady-state. This solution indicates two aspects. First, the size of the steady-state pool is proportional to the input flux. Note that we assumed that the input flux itself has no dependency on \\(C\\). Second, the size of the steady-state pool is inversely proportional to the decay constant. That is, the faster the decay, the smaller the steady state pool.\nEquation 3.2 can also be expressed in terms of an average lifetime or turnover time \\(\\tau\\), instead of \\(k\\): \\[\n\\frac{\\mathrm{d}C}{\\mathrm{d}t} = I - C/\\tau \\;.\n\\tag{3.5}\\]\n\n\n\n\n\n\n\n\nExercise\n\n\n\n\nConsider the C pool of the intermediate and deep sea (37,100 PgC) in Figure 3.1 (bottom right). What is the turnover time of C in that pool?\nExpress the steady-state pool size \\(C^\\ast\\) as a function of the in-flux and the turnover time \\(\\tau\\).\nExpress the half-life constant as a function of \\(k\\).\nDo you know about other processes in nature that can be described by the 1st-order decay model?\n\n\n\nWith the information in Figure 3.1 about pool sizes and steady-state gross fluxes (parallel input and output fluxes), and our model of pool dynamics, we get an insight about how fast C is cycling in and out of different pools. \\(k=I/C^\\ast\\) is a measure of this cycling rate. Or expressed in terms of its inverse, the turnover time \\(\\tau\\) measures how long a C atom resides in that pool. Table 3.1 documents the turnover times for major pools of the global carbon cycle. The small C burial fluxes into sediments on land and on the ocean floor are the supply of what is eventually converted into the very large pool of C in carbonate rock (limestone). A small fraction of the C burial flux is in the form of organic matter, including dead plants, algae, and other microorganisms. Under high heat and pressure, a fraction of it contributes to the formation of hydrocarbons such as oil and gas - fossil fuels. The discrepancy in turnover times between the lithosphere C pool and the other pools indicates that C cycles on vastly different time scales and the slow geological C cycle is largely disconnected from “fast” C cycle between the atmosphere, ocean, and biosphere. Reflecting this discrepancy in time scales, the geological C cycle is not depicted in Figure 3.1 and C in fossil fuel reservoirs is treated as an external input to the fast C cycle.\n\n\nTable 3.1: Pre-industrial pool sizes, input fluxes, and turnover times of major pools of the global carbon cycle. The preindustrial input flux into the atmosphere is calculated as the sum of fluxes from volcanism, total respiration and fire, freshwater, and ocean-atmosphere gas exchange from Figure 3.1. The input flux into the surface ocean is the sum of ocean-atmosphere gas exchange and the flux from intermediate and deep sea. The flux from marine biota is not additional to the ocean-atmosphere exchange flux. The pool size of the biosphere is taken as the sum of vegetation and soils. The permafrost C pool is relatively inert. The size of the lithosphere C pool includes C in the form of sedimentary (carbonate) rocks and kerogens (solid, insoluble organic matter in sedimentary rocks). Its estimate is based on Falkowski et al. (2000). The input flux into the lithosphere is calculated as the sum of burial on land, rock weathering, and ocean floor sedimentation\n\n\n\n\n\n\n\n\nPool\nPool size (PgC)\nInput flux (PgC yr-1)\nTurnover time (yr)\n\n\n\n\nAtmosphere\n591\n167.3\n3.5\n\n\nSurface ocean\n900\n329\n2.7\n\n\nDeep ocean\n37,000\n(see exercise 3.1)\n(see exercise 3.1)\n\n\nBiosphere\n2150\n113\n19\n\n\nLithosphere\n75,000,000\n0.7\n108\n\n\n\n\nIt should be noted that the turnover time \\(\\tau\\) describes the average time that an atom of C resides in the respective pool. This is a simplification. In the C pool ‘terrestrial biosphere’, not every C atom has the same probability of being oxidized and respired as CO2. Hence, in reality, \\(\\tau\\) is a wide distribution, ranging from seconds to years for non-structural carbon derived from photosynthesis, decades to centuries for C in woody biomass, and to millennia for a small fraction of soil organic matter, especially if the C is protected from oxidation, for example in water-logged soils. The turnover time should therefore be understood as a diagnostic, useful for describing the average systems dynamics in a simplified way, and subsuming multiple processes that operate at different time scales, contributing to different portions of C conversion to CO2.\nThe range of turnover times (e.g., within the terrestrial biosphere) arise because C is transferred between multiple pools within the biosphere and the ocean. Going to the next more detailed level of abstraction (model representation), multiple C pools in terrestrial ecosystems can be distinguished (e.g., non-structural C, leaves, roots, wood, litter, soil organic matter, microbes). Some C “cascades” through multiple pools, some is quickly respired back into the atmosphere. The interpretation that \\(k\\) equals the inverse of the turnover time \\(\\tau\\), and that the turnover time equals the mean age of all C atoms in that pool, and that the mean transit time (the time it takes between an atom of C entering a pool until it exits that pool again) equals \\(\\tau\\) is only valid for certain cases, and not for “C cascades” with fluxes between multiple pools. Requirements are that we’re dealing with a single well-mixed pool, that this pool is at steady-state, that it has been so for an infinitely long time, that \\(I\\) and \\(k\\) are constant over time, and the flux leaving the pool is a linear function of the pool size (\\(O=kC\\)) (Sierra et al. 2017). The transit time is the same as residence time - a term used more commonly in hydrology." + "text": "3.2 Carbon pool dynamics\n\n\n\n\n\n\nThe 1st-order decay model\n\n\n\nThe concept of pools and fluxes is central to describing and modelling the carbon cycle and other biogeochemical cycles in the environment. The dynamics of a pool \\(C(t)\\) is given by the balance of the flux of C into that pool \\(I(t)\\) and the flux \\(O(t)\\) leaving the pool - over time \\(t\\). In general terms, we can write the temporal change of the pool size as\n\\[\n\\frac{\\mathrm{d}C(t)}{\\mathrm{d}t} = I(t) - O(t) \\;.\n\\tag{3.1}\\]\nTo simplify the expressions, we will omit \\((t)\\) below. But remember that the fluxes and pools vary with time. The assumption that the out-flux \\(O\\) scales linearly with the size of the pool \\(C\\) is a good simplifying description (i.e., a model) for many processes in the environment. For example, the amount of CO2 produced by the decomposition (decay) of organic matter in the soil scales roughly linearly with the amount of organic matter that is being respired. This leads to the 1st-order decay model of pool dynamics:\n\\[\n\\frac{\\mathrm{d}C}{\\mathrm{d}t} = I - kC \\;.\n\\tag{3.2}\\] Here, \\(k\\) is a decay constant and is in units of the inverse of time. In other words, it specifies the fraction of \\(C\\) decaying per unit time (e.g,. seconds, or years). The higher \\(k\\), the more rapidly the pool decays. For the case of \\(I=0\\), we get \\(\\mathrm{d}C/\\mathrm{d}t = -kC\\). This is a differential equation and can be understood as: What is the function that yields itself, multiplied by \\(-k\\), when taking its derivative with respect to time? The solution is:\n\\[\nC(t) = C_0 \\; e^{-kt} \\;.\n\\] For example, following this model, the pool of C in soil organic matter would decay exponentially if inputs (litterfall) were zero. The decay constant \\(k\\) determines how long it takes for it to be reduced by a certain factor. A commonly used factor is 0.5. We can calculate a half-life - the time \\(t\\) at which \\(C(t) = 0.5\\;C_0\\).\nIn a dynamic equilibrium, the change in the pool size \\(C\\) is by definition zero. \\[\n\\frac{\\mathrm{d}C}{\\mathrm{d}t} = 0 \\;.\n\\tag{3.3}\\] Combining Equation 3.2 and Equation 3.3 and re-arranging terms leads to the steady-state pool size as a function of the in-flux and the decay constant \\(k\\). \\[\nC^\\ast = I/k\n\\tag{3.4}\\] Here, the asterisk denotes that \\(C\\) is at steady-state. This solution indicates two aspects. First, the size of the steady-state pool is proportional to the input flux. Note that we assumed that the input flux itself has no dependency on \\(C\\). Second, the size of the steady-state pool is inversely proportional to the decay constant. That is, the faster the decay, the smaller the steady state pool.\nEquation 3.2 can also be expressed in terms of an average lifetime or turnover time \\(\\tau\\), instead of \\(k\\): \\[\n\\frac{\\mathrm{d}C}{\\mathrm{d}t} = I - C/\\tau \\;.\n\\tag{3.5}\\]\n\n\n\n\n\n\n\n\nExercise\n\n\n\n\n\nConsider the C pool of the intermediate and deep sea (37,100 PgC) in Figure 3.1 (bottom right). What is the turnover time of C in that pool?\nExpress the steady-state pool size \\(C^\\ast\\) as a function of the in-flux and the turnover time \\(\\tau\\).\nExpress the half-life constant as a function of \\(k\\).\nDo you know about other processes in nature that can be described by the 1st-order decay model?\n\n\n\nWith the information in Figure 3.1 about pool sizes and steady-state gross fluxes (parallel input and output fluxes), and our model of pool dynamics, we get an insight about how fast C is cycling in and out of different pools. \\(k=I/C^\\ast\\) is a measure of this cycling rate. Expressed in terms of its inverse, the turnover time \\(\\tau\\) measures how long a C atom resides in that pool on average. Table 3.1 documents the turnover times for major pools of the global carbon cycle. The small C burial fluxes into sediments on land and on the ocean floor are the supply of what is eventually converted into the very large pool of C in carbonate rock (limestone). A small fraction of the C burial flux is in the form of organic matter, including dead plants, algae, and other microorganisms. Under high heat and pressure, a fraction of it contributes to the formation of hydrocarbons such as oil and gas - fossil fuels. The discrepancy in turnover times between the lithosphere C pool and the other pools indicates C cycles operating on vastly different time scales. The slow geological C cycle is largely disconnected from “fast” C cycle between the atmosphere, ocean, and biosphere. Reflecting this discrepancy in time scales, the geological C cycle is not depicted in Figure 3.1 and C in fossil fuel reservoirs is treated as an external input to the fast C cycle.\n\n\nTable 3.1: Pre-industrial pool sizes, input fluxes, and turnover times of major pools of the global carbon cycle. The pre-industrial input flux into the atmosphere is calculated as the sum of fluxes from volcanism, total respiration and fire, freshwater, and ocean-atmosphere gas exchange from Figure 3.1. The input flux into the surface ocean is the sum of ocean-atmosphere gas exchange and the flux from intermediate and deep sea. The flux from marine biota is not additional to the ocean-atmosphere exchange flux. The pool size of the biosphere is taken as the sum of vegetation and soils. The permafrost C pool is relatively inert. The size of the lithosphere C pool includes C in the form of sedimentary (carbonate) rocks and kerogens (solid, insoluble organic matter in sedimentary rocks). Its estimate is based on Falkowski et al. (2000). The input flux into the lithosphere is calculated as the sum of burial on land, rock weathering, and ocean floor sedimentation.\n\n\n\n\n\n\n\n\nPool\nPool size (PgC)\nInput flux (PgC yr-1)\nTurnover time (yr)\n\n\n\n\nAtmosphere\n591\n167.3\n3.5\n\n\nSurface ocean\n900\n329\n2.7\n\n\nDeep ocean\n37,000\n(see exercise 3.1)\n(see exercise 3.1)\n\n\nBiosphere\n2150\n113\n19\n\n\nLithosphere\n75,000,000\n0.7\n108\n\n\n\n\nIt should be noted that the turnover time \\(\\tau\\) describes the average time that an atom of C resides in the respective pool. This is a simplification. In the C pool ‘terrestrial biosphere’, not every C atom has the same probability of being oxidized and respired as CO2. Hence, in reality, the residency time of each C atom follows a wide distribution, ranging from seconds to years for non-structural carbon derived from photosynthesis, decades to centuries for C in woody biomass, and to millennia for a small fraction of soil organic matter, especially if the C is protected from oxidation, for example in water-logged soils. The turnover time should therefore be understood as a diagnostic, useful for describing the average systems dynamics in a simplified way, and subsuming multiple processes that operate at different time scales, contributing to different portions of C conversion to CO2.\nThe range of turnover times (e.g., within the terrestrial biosphere) arises because C is transferred between multiple pools within the biosphere and the ocean. Going to the next more detailed level of abstraction (model representation), multiple C pools in terrestrial ecosystems can be distinguished (e.g., non-structural C, leaves, roots, wood, litter, soil organic matter, microbes). Some C “cascades” through multiple pools, while some is quickly respired back into the atmosphere. The interpretation that \\(k\\) equals the inverse of the turnover time \\(\\tau\\), and that the turnover time equals the mean age of all C atoms in that pool, and that the mean transit time (the time it takes between an atom of C entering a pool until it exits that pool again) equals \\(\\tau\\) is only valid for certain cases, and not for “C cascades” with fluxes between multiple pools. Requirements are that we’re dealing with a single well-mixed pool, that this pool is at steady-state, that it has been so for an infinitely long time, that \\(I\\) and \\(k\\) are constant over time, and the flux leaving the pool is a linear function of the pool size (\\(O=kC\\)) (Sierra et al. 2017). The transit time is the same as residence time - a term used more commonly in hydrology." }, { "objectID": "globalcarbonbudget.html#sec-gcb", "href": "globalcarbonbudget.html#sec-gcb", "title": "3  The global carbon budget", "section": "3.3 The anthropogenic perturbation", - "text": "3.3 The anthropogenic perturbation\nAlthough fossil fuels are formed by natural processes of the C cycle, their combustion can be regarded as an external input of C into the (modern) global C cycle. This is because the time scale at which the reservoir of fossil fuels is depleted (102 yr) stands in stark contrast to the time scale at which it was formed (108 yr, see turnover time of C in the lithosphere in Table 3.1). The C is added in the form of CO2 to the atmosphere from where it is taken up by the ocean through diffusion and equilibration of the ocean surface water’s CO2 partial pressure with the atmosphere’s CO2 partial pressure, and by the terrestrial biosphere through photosynthesis. It is important to note that CO2 in the atmosphere does not decay through physical or chemical processes, nor are there C sinks on land or in the ocean that remove C away from the “fast” C cycle - except the burial into sediments (see Figure 3.1 and Table 3.1). However the magnitude of the burial fluxes are dwarfed by the magnitude of C inputs through the combustion of fossil fuels and deforestation. Hence, the present-day C emissions drive an accumulation of the total amount of C cycling in the “fast” C cycle and the added C gets redistributed between the spheres. The net fluxes from the atmosphere into land ecosystems and the ocean arise because the total terrestrial and oceanic C pools are increasing as CO2 is emitted into the atmosphere and the atmospheric CO2 concentration is rising. In subsequent chapters (Chapter 4 and Chapter 14), we will learn about the processes driving the CO2 uptake by land and ocean and the dynamics of the C redistribution in the Earth system. In this chapter, we will look at the global C budget - how much C has been emitted by the combustion of fossil fuels and deforestation and how much of this C has accumulated in the atmosphere and how much has been taken up by the ocean and the terrestrial biosphere?\nThe global C budget can be defined for globally aggregated fluxes as the balance between emissions from fossil fuels \\(E_\\mathrm{FF}\\) and land use change \\(E_\\mathrm{LUC}\\) on the left side of the equation and the redistribution of C among the atmosphere, land and ocean. \\(G_\\mathrm{atm}\\) is the atmospheric growth rate, \\(S_\\mathrm{ocean}\\) is the net ocean C uptake (also referred to as the ocean sink) and \\(S_\\mathrm{land}\\) is the net land C uptake (or land sink). A net flux from the atmosphere into the ocean or into land C storage is positive.\n\\[\nE_\\mathrm{FF} + E_\\mathrm{LUC} = G_\\mathrm{atm} + S_\\mathrm{ocean} + S_\\mathrm{land}\n\\tag{3.6}\\]\nThis terminology is adopted from the Global Carbon Budget (Friedlingstein et al. 2023) and is expressed as global annual total fluxes. The separation of \\(E_\\mathrm{LUC}\\) and \\(S_\\mathrm{land}\\) is not straight-forward, but can be understood in a simplified fashion as spatially separated fluxes, whereby the land sink occurs only on areas that are not affected by land use change (LUC). In reality, LUC affects the land sink which complicates a separation of the two components. This is further resolved in Chapter 10.\nThe values of the global carbon budget components are given in Figure 3.1 for an average across years 2010-2019, where \\(S_\\mathrm{ocean}\\) corresponds to the ‘net ocean flux’ and \\(S_\\mathrm{land}\\) corresponds to the the ‘net land flux’ in Figure 3.1. \\(E_\\mathrm{LUC}\\) corresponds to ‘net land-use change’. The ‘net’ indicates that \\(E_\\mathrm{LUC}\\) is the net effect between CO2 emissions from deforestation and C uptake by re-growing forests and afforestations. Note that the annual atmospheric growth rate is not resolved in Figure 3.1. The most recent update of the global carbon budget from Friedlingstein et al. (2023) is given in Table 3.2 as 10-year averages of annual fluxes for years 2013-2022 and cumulative fluxes for the industrial era - years 1750-2022.\n\n\n\nTable 3.2: Global carbon budget (in PgC and PgC yr-1) from the 2023 update by Friedlingstein et al. (2023)\n\n\nComponent\nCumulative 1750-2022\nAnnual 2013-2022\n\n\n\n\n\\(E_\\mathrm{FF}\\)\n480 \\(\\pm\\) 25\n9.6 \\(\\pm\\) 0.5\n\n\n\\(E_\\mathrm{LUC}\\)\n250 \\(\\pm\\) 75\n1.3 \\(\\pm\\) 0.7\n\n\n\\(G_\\mathrm{atm}\\)\n300 \\(\\pm\\) 5\n5.2 \\(\\pm\\) 0.02\n\n\n\\(S_\\mathrm{ocean}\\)\n190 \\(\\pm\\) 40\n2.8 \\(\\pm\\) 0.4\n\n\n\\(S_\\mathrm{land}\\)\n245 \\(\\pm\\) 60\n3.3 \\(\\pm\\) 0.8\n\n\n\n\nEstimates of each global carbon budget compenent are largely independent from each other and rely on different types of observations, data, and methods. \\(E_\\mathrm{FF}\\) estimates are based on energy statistics and cement production data. Values reported by Friedlingstein et al. (2023) include the cement carbonation sink. Without that sink, the value of \\(E_\\mathrm{FF}\\) for 2022 would be about 0.2 PgC yr-1 higher. \\(E_\\mathrm{LUC}\\) estimates are based on land-use and land-use change data from national statistics and forest carbon “bookkeeping models”. These models use information about vegetation C stocks, forest C re-growth curves, and the fate of C after deforestation and harvesting (e.g., wood products lifetime). Atmospheric CO2 concentration, and hence the accumulation of C in the atmosphere, is measured directly and bears the least uncertainty among all carbon budget components. The ocean sink is estimated from global ocean CO2 uptake models and observation-based products. In Friedlingstein et al. (2023), the land sink is estimated from dynamic global vegetation models.\nAdvances in observations and modelling in recent years now enable the land and ocean sink to be estimated in a “bottom-up fashion” - using models of land and ocean C uptake. Since every component of the global carbon budget is thereby estimated independently, a budget imbalance term \\(B_\\mathrm{IM}\\) can be defined. A value of zero indicates that models of the land and ocean C uptake exactly match the (better known) emission terms minus the atmospheric growth rate. \\[\nB_\\mathrm{IM} = E_\\mathrm{FF} + E_\\mathrm{LUC} - (G_\\mathrm{atm} + S_\\mathrm{ocean} + S_\\mathrm{land})\n\\tag{3.7}\\]\nToday, the global carbon budget is well specified thanks to reliable estimates of its individual components. The budget imbalance is only a fraction of the total emissions. Until recently, “bottom-up” estimates of \\(S_\\mathrm{land}\\) by land C cycle models were deemed insufficient for providing reliable estimates. Instead, \\(S_\\mathrm{land}\\) was estimated as the budget residual by neglecting \\(B_\\mathrm{IM}\\) and rearranging terms in Equation 3.7 to solve for \\(S_\\mathrm{land}\\). In fact, when the IPCC First Assessment Report was published in 1990, the existence of C sink on land was not known and it was treated as the budget imbalance and referred to as the ‘missing sink’. It was stated that “there are possible processes on land which could account for the missing CO2 (but it has not been possible to verify them)”.\nIt was only later that the existence of a terrestrial C sink could be more firmly established and quantified thanks to parallel measurements of the atmospheric O2 and CO2 concentrations (Keeling, Piper, and Heimann 1996). (In fact, the ratio O2/N2 is measured to avoid the much larger measurement uncertainty in absolute O2 measurements). The ratios of O2:CO2 are known from the stoichiometric molecular formulae for photosynthesis (O2:CO2 = 1.1), fossil fuel combustion (O2:CO2 = 1.4) and ocean uptake (O2:CO2 = 0). An ocean O2 source from marine organisms has to be factored in. Given the total C emissions from fossil fuel combustion, the net land C balance can thus be calculated and the calculation visualized geometrically (Figure 3.2). Note that net emissions from land use change are not considered and the what is termed the “Sland” in Figure 3.2 is actually the net \\((S_\\mathrm{land} - E_\\mathrm{LUC})\\) in Equation 3.6.\n\n\n\n\n\nFigure 3.2: Global land and ocean carbon sinks deduced from changes in atmospheric CO2 and O2 concentrations. The figure is an updated version of Fig. 2 from Keeling, Piper, and Heimann (1996), taken from a recent update of the atmospheric carbon and oxygen budget by Li et al. (2022). In this figure, what is termed ‘Sland’ corresponds to (Sland - ELUC) as defined in Equation 3.6.\n\n\n\n\nIn a mathematical sense, the constraint from atmospheric oxygen can be understood as a second equation, necessary for solving for two unknowns \\(S_\\mathrm{land}\\) and \\(S_\\mathrm{ocean}\\). Their sum must equal (well-known) emissions \\(E_\\mathrm{FF} + E_\\mathrm{LUC}\\) minus the atmospheric growth rate \\(G_\\mathrm{atm}\\). This yields only one equation - that for the C budget (Equation 3.6). The oxygen budget provides a second equation and thus enables solving for two unknowns. In a similar fashion, the isotopic composition of C (the ratio of 13C:12C) also provides a second equation (Joos and Bruno 1998). The history of 13C can be measured on ice cores and \\((S_\\mathrm{land} - E_\\mathrm{LUC})\\) can thus be reconstructed for the past (Figure 3.3). Note that in order to separate \\(S_\\mathrm{land}\\) from the budget, independent estimates of \\(E_\\mathrm{LUC}\\) are required.\n\n\n\n\n\nFigure 3.3: Top panel: Cumulative C uptake by the land biosphere over the past 11 kyr. The grey shaded area indicates uncertainty from ice core measurements. Bottom panel: Atmospheric CO2 concentration (grey squares and modelled atmospheric CO2 based on scenarios of drivers of past millennial-scale C cycle changes (green: land biosphere is the only driver, black: land biopshere, combined with effects by oceanic carbonate chemistry due to Holocene land C uptake, red: land biosphere, combined with effects by oceanic carbonate chemistry due to Holocene and pre-Holocene land C uptake). Figure from Elsig et al. (2009).\n\n\n\n\nWe can adopt the perspective of C cycle science stated in earlier publications. Falkowski et al. (2000) wrote: “Direct determination of changes in terrestrial carbon storage has proven extremely difficult. Rather, the contribution of terrestrial ecosystems to carbon storage is inferred from changes in the concentrations of atmospheric gases, especially CO2 and O2 […].” In that sense, let’s consider the land sink to be the budget residual and assume that the ocean sink estimate is accurate (indeed, its uncertainty is only about half the uncertainty in bottom-up land sink estimates, Table 3.2). Visually contrasting emissions and their redistribution reveals an interesting pattern (Figure 3.4). The substantial year-to-year (interannual) variations in the land sink are almost exclusively responsible for interannual variations in the atmospheric growth rate. Total emissions and the ocean sink exhibit little interannual variation. By definition, the sum of the atmospheric growth rate, land and ocean sink is equal to the sum of emissions from fossil fuels and land use change.\n\n\n\n\n\n\nExercise\n\n\n\n\nUse Equation 3.7 to express the land sink as the budget residual (assuming \\(B_\\mathrm{IM} = 0\\)).\n\n\n\n\n\nCode\nlibrary(readr)\nlibrary(here)\nlibrary(dplyr)\nlibrary(tidyr)\nlibrary(ggplot2)\n\n# Data from Friedlingstein et al. 2023. Downloaded excel file 'Global \n# Carbon Budget v2023' from\n# https://globalcarbonbudgetdata.org/latest-data.html\n# Saved tab Global Carbon Budget as a CSV file. \n# Reading this CSV here.\ndf <- read_csv(here(\"data/Global_Carbon_Budget_2023v1.0_tabGlobalCarbonBudget.csv\"))\n\n# (Re-) definitions\ndf <- df |> \n \n # Include the carbonation sink in the fossil fuel emissions\n mutate(e_ff = e_ff - s_cement) |> \n \n # Land sink defined as the budget residual\n mutate(s_res = e_ff + e_luc - g_atm - s_ocean)\n\n# Create the budget plot\ndf |> \n ggplot() +\n geom_ribbon(\n aes(\n x = year, \n ymax = e_ff + e_luc, \n ymin = e_luc, \n fill = \"ff\"), \n alpha = 0.8\n ) +\n geom_ribbon(\n aes(\n x = year, \n ymax = e_luc, \n ymin = 0, \n fill = \"luc\"), \n alpha = 0.8\n ) +\n geom_ribbon(\n aes(\n x = year, \n ymax = 0, \n ymin = -s_ocean, \n fill = \"ocean\"), \n alpha = 0.8\n ) +\n geom_ribbon(\n aes(\n x = year, \n ymax = -s_ocean, \n ymin = -(s_ocean + s_res), \n fill = \"land\"), \n alpha = 0.8\n ) +\n geom_ribbon(\n aes(\n x = year, \n ymax = -(s_ocean + s_res), \n ymin = -(s_ocean + s_res + g_atm), \n fill = \"atm\"), \n alpha = 0.8) +\n geom_line(\n aes(\n x = year, \n y = 0), \n linetype = \"dotted\") +\n geom_line(\n aes(\n x = year, \n y = e_ff + e_luc)\n ) +\n geom_line(\n aes(\n x = year, \n y = -(s_ocean + s_res + g_atm)\n )\n ) +\n geom_line(\n aes(\n x = year, \n y = imbalance, \n color = \"imbalance\"), \n linewidth = 0.2\n ) +\n labs(x = \"Year\",\n y = expression(paste(\"CO\"[2], \" flux (PgC yr\"^-1, \")\")),\n title = \"Annual carbon emissions (positive) \\nand their redistribution (negative)\"\n ) +\n scale_fill_manual(\n name = \"\",\n breaks = c(\"ff\", \"luc\", \"ocean\", \"land\", \"atm\"),\n values = c(\"ff\" = \"lightslategrey\",\n \"luc\" = \"chocolate1\",\n \"ocean\" = \"lightseagreen\",\n \"land\" = \"yellowgreen\",\n \"atm\" = \"deepskyblue1\"\n ),\n labels = c(\"Fossil fuel \\nemissions\", \n \"Net land-use \\nchange emissions\", \n \"Ocean \\nsink\", \n \"Land \\nsink\", \n \"Atmospheric \\ngrowth\"\n )\n ) +\n scale_color_manual(\n name = \"\", \n breaks = \"imbalance\", \n values = c(\"imbalance\" = \"grey40\"),\n labels = \"Budget imbalance\"\n ) +\n theme_minimal() +\n theme(\n legend.position=\"bottom\", \n legend.box = \"vertical\"\n )\n\nggsave(here::here(\"book/images/globalcarbonbudget.png\"), width = 6, height = 6)\n\n\n\n\n\nFigure 3.4: Annual carbon emissions (positive) and their redistribution between the ocean, land, and atmosphere (negative). The black line in the positive domain represents total emissions and is mirrored by the black line in the negative domain which represents the total of the land sink, ocean sink, and atmospheric growth. Design and data are based on the Global Carbon Budget. In contrast to Friedlingstein et al. (2023), the land sink is defined here as the carbon budget residual. The budget imbalance term - the difference between Sland calculated as the budget residual vs. bottom-up using land C cycle models - is shown by the separate fine grey line." + "text": "3.3 The anthropogenic perturbation\nAlthough fossil fuels are formed by natural processes of the C cycle, their combustion can be regarded as an external input of C into the (modern) global C cycle. This is because the time scale at which the reservoir of fossil fuels is depleted (102 yr) stands in stark contrast to the time scale at which it was formed (108 yr, see turnover time of C in the lithosphere in Table 3.1). The C is added in the form of CO2 to the atmosphere from where it is taken up by the ocean through diffusion and equilibration of the ocean surface water’s CO2 partial pressure with the atmosphere’s CO2 partial pressure, and by the terrestrial biosphere through photosynthesis. It is important to note that CO2 in the atmosphere does not decay through physical or chemical processes, nor are there C sinks on land or in the ocean that remove C away from the “fast” C cycle - except the burial into sediments (see Figure 3.1 and Table 3.1). However, the magnitude of the burial fluxes is dwarfed by the magnitude of C inputs through the combustion of fossil fuels and deforestation. Hence, the present-day C emissions drive an accumulation of the total amount of C cycling in the “fast” C cycle and the added C gets redistributed between the spheres. The net fluxes from the atmosphere into land ecosystems and the ocean arise because the total terrestrial and oceanic C pools are increasing as CO2 is emitted into the atmosphere and the atmospheric CO2 concentration is rising. In subsequent chapters (Chapter 4 and Chapter 14), we will learn about the processes driving the CO2 uptake by land and ocean and the dynamics of the C redistribution in the Earth system. In this chapter, we will look at the global C budget - how much C has been emitted by the combustion of fossil fuels and deforestation, how much of this C has accumulated in the atmosphere, and how much has been taken up by the ocean and the terrestrial biosphere.\nThe global C budget can be defined for globally aggregated fluxes as the balance between emissions from fossil fuels \\(E_\\mathrm{FF}\\) and land use change \\(E_\\mathrm{LUC}\\) on the left side of the equation and the redistribution of C among the atmosphere, land and ocean. \\(G_\\mathrm{atm}\\) is the atmospheric growth rate, \\(S_\\mathrm{ocean}\\) is the net ocean C uptake (also referred to as the ocean sink) and \\(S_\\mathrm{land}\\) is the net land C uptake (or land sink). A net flux from the atmosphere into the ocean or into land C storage is positive.\n\\[\nE_\\mathrm{FF} + E_\\mathrm{LUC} = G_\\mathrm{atm} + S_\\mathrm{ocean} + S_\\mathrm{land}\n\\tag{3.6}\\]\nThis terminology is adopted from the Global Carbon Budget (Friedlingstein et al. 2023) and is expressed as global annual total fluxes. The separation of \\(E_\\mathrm{LUC}\\) and \\(S_\\mathrm{land}\\) is not straight-forward, but can be understood in a simplified fashion as spatially separated fluxes, whereby the land sink occurs only on areas that are not affected by land use change (LUC). In reality, LUC affects the land sink which complicates a separation of the two components. This is further resolved in Chapter 10.\nThe values of the global carbon budget components are given in Figure 3.1 for an average across years 2010-2019, where \\(S_\\mathrm{ocean}\\) corresponds to the ‘net ocean flux’ and \\(S_\\mathrm{land}\\) corresponds to the ‘net land flux’ in Figure 3.1. \\(E_\\mathrm{LUC}\\) corresponds to ‘net land-use change’. The ‘net’ indicates that \\(E_\\mathrm{LUC}\\) is the net effect between CO2 emissions from deforestation and C uptake by re-growing forests and afforestation. Note that the annual atmospheric growth rate is not resolved in Figure 3.1. The most recent update of the global carbon budget from Friedlingstein et al. (2023) is given in Table 3.2 as 10-year averages of annual fluxes for years 2013-2022 and cumulative fluxes for the industrial era - years 1750-2022.\n\n\n\nTable 3.2: Global carbon budget (in PgC and PgC yr-1) from the 2023 update by Friedlingstein et al. (2023)\n\n\nComponent\nCumulative 1750-2022\nAnnual 2013-2022\n\n\n\n\n\\(E_\\mathrm{FF}\\)\n480 \\(\\pm\\) 25\n9.6 \\(\\pm\\) 0.5\n\n\n\\(E_\\mathrm{LUC}\\)\n250 \\(\\pm\\) 75\n1.3 \\(\\pm\\) 0.7\n\n\n\\(G_\\mathrm{atm}\\)\n300 \\(\\pm\\) 5\n5.2 \\(\\pm\\) 0.02\n\n\n\\(S_\\mathrm{ocean}\\)\n190 \\(\\pm\\) 40\n2.8 \\(\\pm\\) 0.4\n\n\n\\(S_\\mathrm{land}\\)\n245 \\(\\pm\\) 60\n3.3 \\(\\pm\\) 0.8\n\n\n\n\nEstimates of each global carbon budget compenent are largely independent from each other and rely on different types of observations, data, and methods. \\(E_\\mathrm{FF}\\) estimates are based on energy statistics and cement production data. Values reported by Friedlingstein et al. (2023) include the cement carbonation sink. Without that sink, the value of \\(E_\\mathrm{FF}\\) for 2022 would be about 0.2 PgC yr-1 higher. \\(E_\\mathrm{LUC}\\) estimates are based on land-use and land-use change data from national statistics and forest carbon “bookkeeping models”. These models use information about vegetation C stocks, forest C re-growth curves, and the fate of C after deforestation and harvesting (e.g., wood products lifetime). Atmospheric CO2 concentration, and hence the accumulation of C in the atmosphere, is measured directly and bears the least uncertainty among all carbon budget components. The ocean sink is estimated from global ocean CO2 uptake models and observation-based products. In Friedlingstein et al. (2023), the land sink is estimated from dynamic global vegetation models.\nAdvances in observations and modelling in recent years now enable the land and ocean sink to be estimated in a “bottom-up fashion” - using models of land and ocean C uptake. Since every component of the global carbon budget is thereby estimated independently, a budget imbalance term \\(B_\\mathrm{IM}\\) can be defined. A value of zero indicates that models of the land and ocean C uptake exactly match the (better known) emission terms minus the atmospheric growth rate. \\[\nB_\\mathrm{IM} = E_\\mathrm{FF} + E_\\mathrm{LUC} - (G_\\mathrm{atm} + S_\\mathrm{ocean} + S_\\mathrm{land})\n\\tag{3.7}\\]\nToday, the global carbon budget is well specified thanks to reliable estimates of its individual components. The budget imbalance is only a fraction of the total emissions. Until recently, “bottom-up” estimates of \\(S_\\mathrm{land}\\) by land C cycle models were deemed insufficient for providing reliable estimates. Instead, \\(S_\\mathrm{land}\\) was estimated as the budget residual by neglecting \\(B_\\mathrm{IM}\\) and rearranging terms in Equation 3.7 to solve for \\(S_\\mathrm{land}\\). In fact, when the IPCC First Assessment Report was published in 1990, the existence of C sink on land was not known, and it was treated as the budget imbalance and referred to as the ‘missing sink’. It was stated that “there are possible processes on land which could account for the missing CO2 (but it has not been possible to verify them)”.\nIt was only later that the existence of a terrestrial C sink could be more firmly established and quantified thanks to parallel measurements of the atmospheric O2 and CO2 concentrations (Keeling, Piper, and Heimann 1996). (In fact, the ratio O2/N2 is measured to avoid the much larger measurement uncertainty in absolute O2 measurements). The ratios of O2:CO2 are known from the stoichiometric molecular formulae for photosynthesis (O2:CO2 = 1.1), fossil fuel combustion (O2:CO2 = 1.4) and ocean uptake (O2:CO2 = 0). An ocean O2 source from marine organisms has to be factored in. Given the total C emissions from fossil fuel combustion, the net land C balance can thus be calculated and the calculation visualized geometrically (Figure 3.2). Note that net emissions from land use change are not considered and what is termed the “Sland” in Figure 3.2 is actually the net \\((S_\\mathrm{land} - E_\\mathrm{LUC})\\) in Equation 3.6.\n\n\n\n\n\nFigure 3.2: Global land and ocean carbon sinks deduced from changes in atmospheric CO2 and O2 concentrations. The figure is an updated version of Fig. 2 from Keeling, Piper, and Heimann (1996), taken from a recent update of the atmospheric carbon and oxygen budget by Li et al. (2022). In this figure, what is termed ‘Sland’ corresponds to (Sland - ELUC) as defined in Equation 3.6.\n\n\n\n\nIn a mathematical sense, the constraint from atmospheric oxygen can be understood as a second equation, necessary for solving for two unknowns \\(S_\\mathrm{land}\\) and \\(S_\\mathrm{ocean}\\). Their sum must equal (well-known) emissions \\(E_\\mathrm{FF} + E_\\mathrm{LUC}\\) minus the atmospheric growth rate \\(G_\\mathrm{atm}\\). This yields only one equation - that for the C budget (Equation 3.6). The oxygen budget provides a second equation and thus enables solving for two unknowns. In a similar fashion, the isotopic composition of C (the ratio of 13C:12C) also provides a second equation (Joos and Bruno 1998). The history of 13C can be measured on ice cores and \\((S_\\mathrm{land} - E_\\mathrm{LUC})\\) can thus be reconstructed for the past (Figure 3.3). Note that in order to separate \\(S_\\mathrm{land}\\) from the budget, independent estimates of \\(E_\\mathrm{LUC}\\) are required.\n\n\n\n\n\nFigure 3.3: Top panel: Cumulative C uptake by the land biosphere over the past 11 kyr. The grey shaded area indicates uncertainty from ice core measurements. Bottom panel: Atmospheric CO2 concentration (grey squares and modelled atmospheric CO2 based on scenarios of drivers of past millennial-scale C cycle changes (green: land biosphere is the only driver, black: land biopshere, combined with effects by oceanic carbonate chemistry due to Holocene land C uptake, red: land biosphere, combined with effects by oceanic carbonate chemistry due to Holocene and pre-Holocene land C uptake). Figure from Elsig et al. (2009).\n\n\n\n\nWe can adopt the perspective of C cycle science stated in earlier publications. Falkowski et al. (2000) wrote: “Direct determination of changes in terrestrial carbon storage has proven extremely difficult. Rather, the contribution of terrestrial ecosystems to carbon storage is inferred from changes in the concentrations of atmospheric gases, especially CO2 and O2 […].” In that sense, let’s consider the land sink to be the budget residual and assume that the ocean sink estimate is accurate (indeed, its uncertainty is only about half the uncertainty in bottom-up land sink estimates, Table 3.2). Visually contrasting emissions and their redistribution reveals an interesting pattern (Figure 3.4). The substantial year-to-year (interannual) variations in the land sink are almost exclusively responsible for interannual variations in the atmospheric growth rate. Total emissions and the ocean sink exhibit little interannual variation. By definition, the sum of the atmospheric growth rate, land and ocean sink is equal to the sum of emissions from fossil fuels and land use change.\n\n\n\n\n\n\nExercise\n\n\n\n\nUse Equation 3.7 to express the land sink as the budget residual (assuming \\(B_\\mathrm{IM} = 0\\)).\n\n\n\n\n\nCode\nlibrary(readr)\nlibrary(here)\nlibrary(dplyr)\nlibrary(tidyr)\nlibrary(ggplot2)\n\n# Data from Friedlingstein et al. 2023. Downloaded excel file 'Global \n# Carbon Budget v2023' from\n# https://globalcarbonbudgetdata.org/latest-data.html\n# Saved tab Global Carbon Budget as a CSV file. \n# Reading this CSV here.\ndf <- read_csv(here(\"data/Global_Carbon_Budget_2023v1.0_tabGlobalCarbonBudget.csv\"))\n\n# (Re-) definitions\ndf <- df |> \n \n # Include the carbonation sink in the fossil fuel emissions\n mutate(e_ff = e_ff - s_cement) |> \n \n # Land sink defined as the budget residual\n mutate(s_res = e_ff + e_luc - g_atm - s_ocean)\n\n# Create the budget plot\ndf |> \n ggplot() +\n geom_ribbon(\n aes(\n x = year, \n ymax = e_ff + e_luc, \n ymin = e_luc, \n fill = \"ff\"), \n alpha = 0.8\n ) +\n geom_ribbon(\n aes(\n x = year, \n ymax = e_luc, \n ymin = 0, \n fill = \"luc\"), \n alpha = 0.8\n ) +\n geom_ribbon(\n aes(\n x = year, \n ymax = 0, \n ymin = -s_ocean, \n fill = \"ocean\"), \n alpha = 0.8\n ) +\n geom_ribbon(\n aes(\n x = year, \n ymax = -s_ocean, \n ymin = -(s_ocean + s_res), \n fill = \"land\"), \n alpha = 0.8\n ) +\n geom_ribbon(\n aes(\n x = year, \n ymax = -(s_ocean + s_res), \n ymin = -(s_ocean + s_res + g_atm), \n fill = \"atm\"), \n alpha = 0.8) +\n geom_line(\n aes(\n x = year, \n y = 0), \n linetype = \"dotted\") +\n geom_line(\n aes(\n x = year, \n y = e_ff + e_luc)\n ) +\n geom_line(\n aes(\n x = year, \n y = -(s_ocean + s_res + g_atm)\n )\n ) +\n geom_line(\n aes(\n x = year, \n y = imbalance, \n color = \"imbalance\"), \n linewidth = 0.2\n ) +\n labs(x = \"Year\",\n y = expression(paste(\"CO\"[2], \" flux (PgC yr\"^-1, \")\")),\n title = \"Annual carbon emissions (positive) \\nand their redistribution (negative)\"\n ) +\n scale_fill_manual(\n name = \"\",\n breaks = c(\"ff\", \"luc\", \"ocean\", \"land\", \"atm\"),\n values = c(\"ff\" = \"lightslategrey\",\n \"luc\" = \"chocolate1\",\n \"ocean\" = \"lightseagreen\",\n \"land\" = \"yellowgreen\",\n \"atm\" = \"deepskyblue1\"\n ),\n labels = c(\"Fossil fuel \\nemissions\", \n \"Net land-use \\nchange emissions\", \n \"Ocean \\nsink\", \n \"Land \\nsink\", \n \"Atmospheric \\ngrowth\"\n )\n ) +\n scale_color_manual(\n name = \"\", \n breaks = \"imbalance\", \n values = c(\"imbalance\" = \"grey40\"),\n labels = \"Budget imbalance\"\n ) +\n theme_minimal() +\n theme(\n legend.position=\"bottom\", \n legend.box = \"vertical\"\n )\n\nggsave(here::here(\"book/images/globalcarbonbudget.png\"), width = 6, height = 6)\n\n\n\n\n\nFigure 3.4: Annual carbon emissions (positive) and their redistribution between the ocean, land, and atmosphere (negative). The black line in the positive domain represents total emissions and is mirrored by the black line in the negative domain which represents the total of the land sink, ocean sink, and atmospheric growth. Design and data are based on the Global Carbon Budget. In contrast to Friedlingstein et al. (2023), the land sink is defined here as the carbon budget residual. The budget imbalance term - the difference between Sland calculated as the budget residual vs. bottom-up using land C cycle models - is shown by the separate fine grey line." }, { "objectID": "globalcarbonbudget.html#sec-sink", "href": "globalcarbonbudget.html#sec-sink", "title": "3  The global carbon budget", "section": "3.4 Understanding the land C sink", - "text": "3.4 Understanding the land C sink\n\n3.4.1 Processes\nAs challenging as it was to locate the “missing C sink” in the terrestrial biosphere in the 1990s (see above), it remains a great challenge to locate the C sink within the terrestrial biosphere and attribute it to processes. Three processes are considered to be particularly influential for the terrestrial C balance, and they each affect ecosystems’ C balances in different regions across the globe - land use change, the relief of temperature limitations on photosynthesis and growth, and the CO2 fertilization effect.\nThe land C balance from land use change is the net of a flux to the atmosphere due to deforestation and a flux from the atmosphere to the land biosphere due to regrowth after deforestation. Land use change trends are very different across regions globally. While large C losses due to land use change are currently occurring in the tropics, northern extra-tropical regions generally gain C as forests are recovering from more intense wood harvesting in the past - prior the the mid-20th century. Chapter 10 delves deeper into the role of land use change on the carbon cycle and climate. The net C flux from land use change is accounted for in the global carbon budget by the term \\(E_\\mathrm{LUC}\\) (Equation 3.6) and should reflect also effects by C accumulation in recovering forests. However, past land use changes are uncertain and the impact of pre-1950 wood harvesting in temperate regions may be underestimated by models that supply estimates for \\(E_\\mathrm{LUC}\\). \\(S_\\mathrm{land}\\), when defined as the budget residual, may thus be driven by the C sink in recovering forests. A recent estimate suggests that about a quarter of the land sink, or 1.3 PgC yr-1, is due to recovery from past forest disturbances (fire, wind, and wood harvesting) (Pugh et al. 2019).\nWarming trends due to anthropogenic climate change are relieving temperature limitations on photosynthesis and tree growth, enabling an extension of the growing season (Ruehr et al. 2023), and an expansion of forest areas and vegetation greenness in high northern latitudes - as sensed from space (T. F. Keenan and Riley 2018). The associated land C sink, as the one driven by forest recovery from past land use change, is located in the northern extra-tropics.\nRising atmospheric CO2 stimulates leaf-level photosynthetic rates. The additional C assimilated likely drives increases in ecosystem C storage. However, a multitude of processes and ecosystem feedbacks are involved and affect the link between the leaf-level CO2-fertilization of photosynthesis and ecosystem-level C storage (nutrient limitation, tree longevity reduction due to accelerated growth, soil organic C loss due to plant-soil interactions). Free-Air-CO2-Experiments, where plots of outdoor growing vegetation are exposed to elevated CO2 during multiple years indicate a stimulation of photosynthesis and growth, but evidence for gains in biomass and soil C stocks is mixed. Yet, C gains in mature forest growth, biomass, and ecosystem C stocks are documented and, particularly in the tropics, CO2-fertilization appears to be the main driver of this trend. This is consistent with Dynamic Global Vegetation Models that attribute about 60-85% of the total land sink to CO2-fertilization (Schimel, Stephens, and Fisher 2015; Trevor F. Keenan et al. 2016). Published review studies (Ruehr et al. 2023; Walker et al. 2021) provide a more detailed account of the complex role of CO2-fertilization in driving the land C sink.\nTheory suggests that the CO2 effect on photosynthesis should be higher under warm than under cold temperatures. Therefore, a CO2-driven land sink should be strongest in the tropics. As mentioned above, a C sink that is driven predominantly by either growing season extensions and cold limitation reliefs or by recovery from past land use change would be located mainly in the northern extra-tropics. How to discriminate between these drivers and their associated C sink regions? Once more, atmospheric CO2 measurements provide a constraint. While the total terrestrial C sink is relatively well-constrained through the global carbon budget, contributions from the tropics (and southern hemisphere) vs. the northern extra-tropics requires an additional constraint. Atmospheric CO2 measurements, in combination with known CO2 sources and their location and with atmospheric transport fields (atmospheric inversions) enable a split of the global land C sink into contribution from the two regions, while their sum is constrained by the global carbon budget. This approach is visualized in Figure 3.5. The combination of the two constraints indicates that model simulations where the CO2-fertilization effect was “turned off” tend to be outside the range of plausible combinations of tropical and northern-extratropical land C sinks. This indicates the importance of a strong CO2-fertilization-driven C sink in the tropics. Hence, the hypothesis that the land C sink is driven exclusively by forest recovery from past land use and the extension of the growing season in cold-limited regions of the northern extra-tropics is not compatible with the C budget and the inter-hemispheric split of land C uptake inferred from atmospheric inversions.\n\n\n\n\n\nFigure 3.5: The anti-correlation of the northern extra-tropical and the tropical-plus-southern land C sink. Atmospheric inversions from different sources (red and purple points and squares) indicate an anti-correlation of the regional sinks, constrained by the C mass balance from the global carbon budget: The sum of regional land C sinks must equal the total terrestrial C sink from the global carbon budget. Several Dynamic Global Vegetation Models (DGVMs) without the CO2-fertilisation effect (white triangles) lie outside the range constrained by the global C mass balance, while DGVMs with the CO2-fertilisation effect considered are better compatible with the budget. Figure from Schimel, Stephens, and Fisher (2015).\n\n\n\n\nThe processes for understanding the oceanic C sink will be introduced in Chapter 14.\n\n\n3.4.2 Interannual variability\nAs highlighted above, pointing to Figure 3.4, the magnitude of the land C sink varies strongly between years. Semi-arid regions, where dry conditions during a substantial part of the year limit photosynthesis and where drought-related disturbances strongly influence ecosystem C balances, are contributing most strongly to the signal apparent from the global C budget (Ahlström et al. 2015). Semi-arid regions largely align with temperate and tropical grasslands, savannahs, and shrubland biomes (Figure 2.2). Years with a small land sink and a high atmospheric CO2 growth rate are dry years, associated with low global-scale terrestrial water storage (Humphrey et al. 2018), and are associated with warm temperature anomalies in the tropics (Cox et al. 2013). This indicates two important points. First, C storage in the terrestrial biosphere is highly susceptible to climate variations. Second, water availability has a strong control on the terrestrial carbon cycle. We will learn more about how the water and the carbon cycles are coupled in Chapter 7 and how the influence of water availability on vegetation varies across the globe in Chapter 8.\n\n\n\n\n\nFigure 3.6: Interannual variability of the atmospheric CO2 growth rate (CGR) and terrestrial water storage (TWS). (a) Monthly de-seasonalized and de-trended CGR, TWS from gravimetric satellite observations (GRACE mission) and TWS from a statistical model that reconstructs the TWS based on climate data (GRACE-REC). The vertical axis is inverted for CGR so that positive (downwards) CGR anomalies indicate a weaker land carbon sink. A 6-month moving average was applied to GRACE data for readability. (b) Yearly CGR versus GRACE TWS anomalies. Figure and caption text from Humphrey et al. (2018).\n\n\n\n\n\n\n\n\n\n\nCO2 trajectories and the land C cycle response\n\n\n\nEquation 3.2 describes the dynamics of land C storage based on a 1-box model. Let’s apply this model for understanding the link between changes in \\(I\\) and the land C balance (\\(\\mathrm{d}C/\\mathrm{d}t\\)). We explore different future trajectories of atmospheric CO2, branching off from its observed history, and simulate the resulting total terrestrial photosynthetic CO2 uptake (also referred to as the gross primary productivity, see also Chapter 4), the terrestrial C pool, and the land sink (i.e., the temporal change in the terrestrial C pool).\nWe make the (strong) assumption that the land C balance dynamics are exclusively driven by the CO2-fertilization effect on photosynthetic C uptake, represented by \\(I\\), while the turnover rate (\\(\\tau\\)) remains constant. The CO2-fertilization effect on a variable \\(x\\) is commonly measured as the sensitivity factor \\(\\beta\\): \\[\n\\beta = \\frac{\\ln (x/x_0)}{\\ln (c_a/c_{a,0})}\n\\tag{3.8}\\] Here, \\(c_a\\) is the atmospheric CO2 concentration (ambient CO2). For ratios of \\(x/x_0\\) and \\(c_a/c_{a,0}\\) approaching 1, Equation 3.8 is equivalent to the ratio of the relative change in \\(x\\) over the relative change in CO2. \\[\n\\beta \\approx \\frac{\\Delta x/x}{\\Delta c_a/c_a}\\;,\n\\tag{3.9}\\] where \\(\\Delta x = x - x_0\\). The sensitivity of the total terrestrial photosynthetic CO2 uptake to atmospheric CO2 has been estimated by T. F. Keenan et al. (2023) as \\(\\beta = 0.59 \\pm 0.16\\). With this, we can model \\(I\\) as a function of \\(c_a\\) using Equation 3.9.\nThe 1-box model can be implemented numerically by discretization in time (i.e., considering time steps \\(\\Delta t\\)). To simulate the terrestrial C pool over time (\\(C(t)\\)), Equation 3.2 can thus be written as \\[\nC(t+\\Delta t) = C(t) + I(t) - \\tau^{-1}C(t)\n\\]\nWe further assume that \\(C(t)\\) was at steady-state in year 1850 - the first year of the CO2 time series used here. \\(\\tau\\) could be estimated by using values of terrestrial C pools (sum of vegetation C and soil C) and the gross photosynthesis flux from Figure 3.1 (\\(\\tau = (450\\; \\mathrm{GtC} + 1700\\; \\mathrm{GtC})/113\\; \\mathrm{GtC\\;yr}^{-1} = 19.0 \\; \\mathrm{yr}\\)). However, the resulting land C sink would be strongly overestimated when compared to the residual sink \\(S_\\mathrm{land}\\) from the Global Carbon Budget. When choosing \\(\\tau = 9 \\; \\mathrm{yr}\\), a better fit between the 1-box model-derived land sink and the observed land sink emerges. This could indicate that CO2-fertilization drives additional C storage that is more short lived than on average in vegetation and soil biomass. It probably also indicates that not all of the C assimilated by photosynthesis stays in the system for more than a few minutes to weeks. A substantial fraction of that C is respired by plants (autotrophic respiration, see also Chapter 4) before it is synthesized into longer-lived plant tissue biomass. The resulting evolution(s) of the land C cycle are illustrated in Figure 3.7.\n\n\n\n\n\nFigure 3.7: Evolution of the land C cycle in response to alternative (schematic) trajectories of future CO2. The green line in panels of the bottom row indicates the observed land sink, derived as the residual of the Global Carbon Budget.\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nExercise\n\n\n\n\nExpress \\(I\\) as a function of \\(c_a\\), using the definition of \\(\\beta\\) from Equation 3.9, and using \\(c_{a,0}\\) and \\(I_0\\).\nCalculate \\(I(c_a)\\) for \\(c_a = 400\\) ppm and \\(I_0\\) as the pre-industrial value of total terrestrial gross photosynthesis from Figure 3.1 and using the value of \\(\\beta\\) (mean) from T. F. Keenan et al. (2023).\nIt is important to note that the land C sink trajectories are strongly dependent on whether the dominating process driving it is CO2 fertilization or forest recovery from past disturbance (or other drivers). The temporal course of ecosystem C pools after a disturbance is schematically illustrated in Figure 3.8. Sketch the resulting land C sink for the different CO2 trajectories of Figure 3.7 if the sink was exclusively driven by forest recovery.\n\n\n\n\n\n\nFigure 3.8: Schematic illustration of the recovery of the ecosystem C pool (relative magnitude) after a disturbance in time step 10.\n\n\n\n\n\n\n\n\n\n\nAhlström, Anders, Michael R. Raupach, Guy Schurgers, Benjamin Smith, Almut Arneth, Martin Jung, Markus Reichstein, et al. 2015. “The Dominant Role of Semi-Arid Ecosystems in the Trend and Variability of the Land CO2 Sink.” Science 348 (6237): 895–99. https://doi.org/10.1126/science.aaa1668.\n\n\nBallantyne, A. P., C. B. Alden, J. B. Miller, P. P. Tans, and J. W. C. White. 2012. “Increase in Observed Net Carbon Dioxide Uptake by Land and Oceans During the Past 50 Years.” Nature 488 (7409): 70–72. https://doi.org/10.1038/nature11299.\n\n\nCanadell, J. G., P. M. S. Monteiro, M. H. Costa, L. Cotrim da Cunha, P. M. Cox, A. V. Eliseev, S. Henson, et al. 2021. “Global Carbon and Other Biogeochemical Cycles and Feedbacks.” Book Section. In Climate Change 2021: The Physical Science Basis. Contribution of Working Group i to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, edited by V. Masson-Delmotte, P. Zhai, A. Pirani, S. L. Connors, C. Péan, S. Berger, N. Caud, et al., 673–816. Cambridge, United Kingdom; New York, NY, USA: Cambridge University Press. https://doi.org/10.1017/9781009157896.007.\n\n\nCox, Peter M., David Pearson, Ben B. Booth, Pierre Friedlingstein, Chris Huntingford, Chris D. Jones, and Catherine M. Luke. 2013. “Sensitivity of Tropical Carbon to Climate Change Constrained by Carbon Dioxide Variability.” Nature 494 (7437): 341–44. https://doi.org/10.1038/nature11882.\n\n\nElsig, Joachim, Jochen Schmitt, Daiana Leuenberger, Robert Schneider, Marc Eyer, Markus Leuenberger, Fortunat Joos, Hubertus Fischer, and Thomas F Stocker. 2009. “Stable Isotope Constraints on Holocene Carbon Cycle Changes from an Antarctic Ice Core.” Nature 461 (7263): 507–10. https://doi.org/10.1038/nature08393.\n\n\nFalkowski, P., R. J. Scholes, E. Boyle, J. Canadell, D. Canfield, J. Elser, N. Gruber, et al. 2000. “The Global Carbon Cycle: A Test of Our Knowledge of Earth as a System.” Science 290 (5490): 291–96. https://doi.org/10.1126/science.290.5490.291.\n\n\nFriedlingstein, P., M. O’Sullivan, M. W. Jones, R. M. Andrew, D. C. E. Bakker, J. Hauck, P. Landschützer, et al. 2023. “Global Carbon Budget 2023.” Earth System Science Data 15 (12): 5301–69. https://doi.org/10.5194/essd-15-5301-2023.\n\n\nHumphrey, Vincent, Jakob Zscheischler, Philippe Ciais, Lukas Gudmundsson, Stephen Sitch, and Sonia I. Seneviratne. 2018. “Sensitivity of Atmospheric CO2 Growth Rate to Observed Changes in Terrestrial Water Storage.” Nature 560 (7720): 628–31. https://doi.org/10.1038/s41586-018-0424-4.\n\n\nJoos, Fortunat, and Michele Bruno. 1998. “Long-Term Variability of the Terrestrial and Oceanic Carbon Sinks and the Budgets of the Carbon Isotopes 13C and 14C.” Global Biogeochemical Cycles 12 (2): 277–95. https://doi.org/10.1029/98GB00746.\n\n\nKeeling, Ralph F., Stephen C. Piper, and Martin Heimann. 1996. “Global and Hemispheric CO2 Sinks Deduced from Changes in Atmospheric O2 Concentration.” Nature 381 (6579): 218–21. https://doi.org/10.1038/381218a0.\n\n\nKeenan, T. F., X. Luo, B. D. Stocker, M. G. De Kauwe, B. E. Medlyn, I. C. Prentice, N. G. Smith, et al. 2023. “A Constraint on Historic Growth in Global Photosynthesis Due to Rising CO2.” Nature Climate Change, November, 1–6. https://doi.org/10.1038/s41558-023-01867-2.\n\n\nKeenan, T. F., and W. J. Riley. 2018. “Greening of the Land Surface in the World’s Cold Regions Consistent with Recent Warming.” Nature Climate Change 8 (9): 825–28. https://doi.org/10.1038/s41558-018-0258-y.\n\n\nKeenan, Trevor F., I. Colin Prentice, Josep G. Canadell, Christopher A. Williams, Han Wang, Michael Raupach, and G. James Collatz. 2016. “Recent Pause in the Growth Rate of Atmospheric CO2 Due to Enhanced Terrestrial Carbon Uptake.” Nature Communications 7 (1): 13428. https://doi.org/10.1038/ncomms13428.\n\n\nLi, Changyu, Jianping Huang, Lei Ding, Yu Ren, Linli An, Xiaoyue Liu, and Jiping Huang. 2022. “The Variability of Air-Sea O2 Flux in CMIP6: Implications for Estimating Terrestrial and Oceanic Carbon Sinks.” Advances in Atmospheric Sciences 39 (8): 1271–84. https://doi.org/10.1007/s00376-021-1273-x.\n\n\nPugh, Thomas A. M., Mats Lindeskog, Benjamin Smith, Benjamin Poulter, Almut Arneth, Vanessa Haverd, and Leonardo Calle. 2019. “Role of Forest Regrowth in Global Carbon Sink Dynamics.” Proceedings of the National Academy of Sciences 116 (10): 4382–87. https://doi.org/10.1073/pnas.1810512116.\n\n\nRuehr, Sophie, Trevor F. Keenan, Christopher Williams, Yu Zhou, Xinchen Lu, Ana Bastos, Josep G. Canadell, Iain Colin Prentice, Stephen Sitch, and César Terrer. 2023. “Evidence and Attribution of the Enhanced Land Carbon Sink.” Nature Reviews Earth & Environment 4 (8): 518–34. https://doi.org/10.1038/s43017-023-00456-3.\n\n\nSchimel, David, Britton B. Stephens, and Joshua B. Fisher. 2015. “Effect of Increasing CO2 on the Terrestrial Carbon Cycle.” Proceedings of the National Academy of Sciences 112 (2): 436–41. https://doi.org/10.1073/pnas.1407302112.\n\n\nShanahan, Timothy M., Nicholas P. McKay, Konrad A. Hughen, Jonathan T. Overpeck, Bette Otto-Bliesner, Clifford W. Heil, John King, Christopher A. Scholz, and John Peck. 2015. “The Time-Transgressive Termination of the African Humid Period.” Nature Geoscience 8 (2): 140–44. https://doi.org/10.1038/ngeo2329.\n\n\nSierra, Carlos A., Markus Müller, Holger Metzler, Stefano Manzoni, and Susan E. Trumbore. 2017. “The Muddle of Ages, Turnover, Transit, and Residence Times in the Carbon Cycle.” Global Change Biology 23 (5): 1763–73. https://doi.org/10.1111/gcb.13556.\n\n\nWalker, Anthony P., Martin G. De Kauwe, Ana Bastos, Soumaya Belmecheri, Katerina Georgiou, Ralph F. Keeling, Sean M. McMahon, et al. 2021. “Integrating the Evidence for a Terrestrial Carbon Sink Caused by Increasing Atmospheric CO \\(_{\\textrm{2}}\\).” New Phytologist 229 (5): 2413–45. https://doi.org/10.1111/nph.16866." + "text": "3.4 Understanding the land C sink\n\n3.4.1 Processes\nAs challenging as it was to locate the “missing C sink” in the terrestrial biosphere in the 1990s (see above), it remains a great challenge to locate the C sink within the terrestrial biosphere and attribute it to processes. Three processes are considered to be particularly influential for the terrestrial C balance, and they each affect ecosystems’ C balances in different regions across the globe - land use change, the relief of temperature limitations on photosynthesis and growth, and the CO2 fertilization effect.\nThe land C balance from land use change is the net sum of a flux to the atmosphere due to deforestation and a flux from the atmosphere to the land biosphere due to regrowth after deforestation. Land use change trends are very different across regions globally. While large C losses due to land use change are currently occurring in the tropics, northern extra-tropical regions generally gain C as forests are recovering from more intense wood harvesting in the past - prior the mid-20th century. Chapter 10 delves deeper into the role of land use change on the carbon cycle and climate. The net C flux from land use change is accounted for in the global carbon budget by the term \\(E_\\mathrm{LUC}\\) (Equation 3.6) and should reflect also effects by C accumulation in recovering forests. However, past land use changes are uncertain and the impact of pre-1950 wood harvesting in temperate regions may be underestimated by models that supply estimates for \\(E_\\mathrm{LUC}\\). \\(S_\\mathrm{land}\\), when defined as the budget residual, may thus be driven by the C sink in recovering forests. A recent estimate suggests that about a quarter of the land sink, or 1.3 PgC yr-1, is due to recovery from past forest disturbances (fire, wind, and wood harvesting) (Pugh et al. 2019).\nWarming trends due to anthropogenic climate change are relieving temperature limitations on photosynthesis and tree growth, enabling an extension of the growing season (Ruehr et al. 2023), and an expansion of forest areas and vegetation greenness in high northern latitudes - as sensed from space (T. F. Keenan and Riley 2018). The associated land C sink, as the one driven by forest recovery from past land use change, is located in the northern extra-tropics.\nRising atmospheric CO2 stimulates leaf-level photosynthetic rates. The additional C assimilated likely drives increases in ecosystem C storage. However, a multitude of processes and ecosystem feedbacks are involved and affect the link between the leaf-level CO2-fertilization of photosynthesis and ecosystem-level C storage (nutrient limitation, tree longevity reduction due to accelerated growth, soil organic C loss due to plant-soil interactions). Free-Air-CO2-Experiments, where plots of outdoor growing vegetation are exposed to elevated CO2 during multiple years, indicate a stimulation of photosynthesis and growth, but evidence for gains in biomass and soil C stocks is mixed. Yet, C gains in mature forest growth, biomass, and ecosystem C stocks are documented and, particularly in the tropics, CO2-fertilization appears to be the main driver of this trend. This is consistent with Dynamic Global Vegetation Models that attribute about 60-85% of the total land sink to CO2-fertilization (Schimel, Stephens, and Fisher 2015; Trevor F. Keenan et al. 2016). Published review studies (Ruehr et al. 2023; Walker et al. 2021) provide a more detailed account of the complex role of CO2-fertilization in driving the land C sink.\nTheory suggests that the CO2 effect on photosynthesis should be higher under warm than under cold temperatures. Therefore, a CO2-driven land sink should be strongest in the tropics. As mentioned above, a C sink that is driven predominantly by either growing season extensions and cold limitation reliefs or by recovery from past land use change would be located mainly in the northern extra-tropics. How to discriminate between these drivers and their associated C sink regions? Once more, atmospheric CO2 measurements provide a constraint. While the total terrestrial C sink is relatively well-constrained through the global carbon budget, contributions from the tropics (and southern hemisphere) vs. the northern extra-tropics requires an additional constraint. Atmospheric CO2 measurements, in combination with known CO2 sources and their location and with atmospheric transport fields (atmospheric inversions) enable a split of the global land C sink into contribution from the two regions, while their sum is constrained by the global carbon budget. This approach is visualized in Figure 3.5. The combination of the two constraints indicates that model simulations where the CO2-fertilization effect was “turned off” tend to be outside the range of plausible combinations of tropical and northern-extratropical land C sinks. This indicates the importance of a strong CO2-fertilization-driven C sink in the tropics. Hence, the hypothesis that the land C sink is driven exclusively by forest recovery from past land use and the extension of the growing season in cold-limited regions of the northern extra-tropics is not compatible with the C budget and the inter-hemispheric split of land C uptake inferred from atmospheric inversions.\n\n\n\n\n\nFigure 3.5: The anti-correlation of the northern extra-tropical and the tropical-plus-southern land C sink. Atmospheric inversions from different sources (red and purple points and squares) indicate an anti-correlation of the regional sinks, constrained by the C mass balance from the global carbon budget: The sum of regional land C sinks must equal the total terrestrial C sink from the global carbon budget. Several Dynamic Global Vegetation Models (DGVMs) without the CO2-fertilisation effect (white triangles) lie outside the range constrained by the global C mass balance, while DGVMs with the CO2-fertilisation effect considered are better compatible with the budget. Figure from Schimel, Stephens, and Fisher (2015).\n\n\n\n\nThe processes for understanding the oceanic C sink will be introduced in Chapter 14.\n\n\n3.4.2 Interannual variability\nAs highlighted above, pointing to Figure 3.4, the magnitude of the land C sink varies strongly between years. Semi-arid regions, where dry conditions during a substantial part of the year limit photosynthesis and where drought-related disturbances strongly influence ecosystem C balances, are contributing most strongly to the signal apparent from the global C budget (Ahlström et al. 2015). Semi-arid regions largely align with temperate and tropical grasslands, savannahs, and shrubland biomes (Figure 2.2). Years with a small land sink and a high atmospheric CO2 growth rate are dry years, associated with low global-scale terrestrial water storage (Humphrey et al. 2018), and are associated with warm temperature anomalies in the tropics (Cox et al. 2013). This indicates two important points. First, C storage in the terrestrial biosphere is highly susceptible to climate variations. Second, water availability has a strong control on the terrestrial carbon cycle. We will learn more about how the water and the carbon cycles are coupled in Chapter 7 and how the influence of water availability on vegetation varies across the globe in Chapter 8.\n\n\n\n\n\nFigure 3.6: Interannual variability of the atmospheric CO2 growth rate (CGR) and terrestrial water storage (TWS). (a) Monthly de-seasonalized and de-trended CGR, TWS from gravimetric satellite observations (GRACE mission) and TWS from a statistical model that reconstructs the TWS based on climate data (GRACE-REC). The vertical axis is inverted for CGR so that positive (downwards) CGR anomalies indicate a weaker land carbon sink. A 6-month moving average was applied to GRACE data for readability. (b) Yearly CGR versus GRACE TWS anomalies. Figure and caption text from Humphrey et al. (2018).\n\n\n\n\n\n\n\n\n\n\nCO2 trajectories and the land C cycle response\n\n\n\nEquation 3.2 describes the dynamics of land C storage based on a 1-box model. Let’s apply this model for understanding the link between changes in \\(I\\) and the land C balance (\\(\\mathrm{d}C/\\mathrm{d}t\\)). We explore different future trajectories of atmospheric CO2, branching off from its observed history, and simulate the resulting total terrestrial photosynthetic CO2 uptake (also referred to as the gross primary productivity, see also Chapter 4), the terrestrial C pool, and the land sink (i.e., the temporal change in the terrestrial C pool).\nWe make the (strong) assumption that the land C balance dynamics are exclusively driven by the CO2-fertilization effect on photosynthetic C uptake, represented by \\(I\\), while the turnover rate (\\(\\tau\\)) remains constant. The CO2-fertilization effect on a variable \\(x\\) is commonly measured as the sensitivity factor \\(\\beta\\): \\[\n\\beta = \\frac{\\ln (x/x_0)}{\\ln (c_a/c_{a,0})}\n\\tag{3.8}\\] Here, \\(c_a\\) is the atmospheric CO2 concentration (ambient CO2). For ratios of \\(x/x_0\\) and \\(c_a/c_{a,0}\\) approaching 1, Equation 3.8 is equivalent to the ratio of the relative change in \\(x\\) over the relative change in CO2. \\[\n\\beta \\approx \\frac{\\Delta x/x}{\\Delta c_a/c_a}\\;,\n\\tag{3.9}\\] where \\(\\Delta x = x - x_0\\). The sensitivity of the total terrestrial photosynthetic CO2 uptake to atmospheric CO2 has been estimated by T. F. Keenan et al. (2023) as \\(\\beta = 0.59 \\pm 0.16\\). With this, we can model \\(I\\) as a function of \\(c_a\\) using Equation 3.9.\nThe 1-box model can be implemented numerically by discretization in time (i.e., considering time steps \\(\\Delta t\\)). To simulate the terrestrial C pool over time (\\(C(t)\\)), Equation 3.2 can thus be written as \\[\nC(t+\\Delta t) = C(t) + (I(t) - \\tau^{-1}C(t)) * \\Delta t\n\\]\nWe further assume that \\(C(t)\\) was at steady-state in year 1850 - the first year of the CO2 time series used here. \\(\\tau\\) could be estimated by using values of terrestrial C pools (sum of vegetation C and soil C) and the gross photosynthesis flux from Figure 3.1 (\\(\\tau = (450\\; \\mathrm{GtC} + 1700\\; \\mathrm{GtC})/113\\; \\mathrm{GtC\\;yr}^{-1} = 19.0 \\; \\mathrm{yr}\\)). However, the resulting land C sink would be strongly overestimated when compared to the residual sink \\(S_\\mathrm{land}\\) from the Global Carbon Budget. When choosing \\(\\tau = 9 \\; \\mathrm{yr}\\), a better fit between the 1-box model-derived land sink and the observed land sink emerges. This could indicate that CO2-fertilization drives additional C storage that is more short-lived than on average in vegetation and soil biomass. It probably also indicates that not all of the C assimilated by photosynthesis stays in the system for more than a few minutes to weeks. A substantial fraction of that C is respired by plants (autotrophic respiration, see also Chapter 4) before it is synthesized into longer-lived plant tissue biomass. The resulting evolution(s) of the land C cycle are illustrated in Figure 3.7.\n\n\n\n\n\nFigure 3.7: Evolution of the land C cycle in response to alternative (schematic) trajectories of future CO2. The green line in panels of the bottom row indicates the observed land sink, derived as the residual of the Global Carbon Budget.\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nExercise\n\n\n\n\nExpress \\(I\\) as a function of \\(c_a\\), using the definition of \\(\\beta\\) from Equation 3.9, and using \\(c_{a,0}\\) and \\(I_0\\).\nCalculate \\(I(c_a)\\) for \\(c_a = 400\\) ppm and \\(I_0\\) as the pre-industrial value of total terrestrial gross photosynthesis from Figure 3.1 and using the value of \\(\\beta\\) (mean) from T. F. Keenan et al. (2023).\nIt is important to note that the land C sink trajectories are strongly dependent on whether the dominating process driving it is CO2 fertilization or forest recovery from past disturbance (or other drivers). The temporal course of ecosystem C pools after a disturbance is schematically illustrated in Figure 3.8. Sketch the resulting land C sink for the different CO2 trajectories of Figure 3.7 if the sink was exclusively driven by forest recovery.\n\n\n\n\n\n\nFigure 3.8: Schematic illustration of the recovery of the ecosystem C pool (relative magnitude) after a disturbance in time step 10.\n\n\n\n\n\n\n\n\n\n\nAhlström, Anders, Michael R. Raupach, Guy Schurgers, Benjamin Smith, Almut Arneth, Martin Jung, Markus Reichstein, et al. 2015. “The Dominant Role of Semi-Arid Ecosystems in the Trend and Variability of the Land CO2 Sink.” Science 348 (6237): 895–99. https://doi.org/10.1126/science.aaa1668.\n\n\nBallantyne, A. P., C. B. Alden, J. B. Miller, P. P. Tans, and J. W. C. White. 2012. “Increase in Observed Net Carbon Dioxide Uptake by Land and Oceans During the Past 50 Years.” Nature 488 (7409): 70–72. https://doi.org/10.1038/nature11299.\n\n\nCanadell, J. G., P. M. S. Monteiro, M. H. Costa, L. Cotrim da Cunha, P. M. Cox, A. V. Eliseev, S. Henson, et al. 2021. “Global Carbon and Other Biogeochemical Cycles and Feedbacks.” Book Section. In Climate Change 2021: The Physical Science Basis. Contribution of Working Group i to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, edited by V. Masson-Delmotte, P. Zhai, A. Pirani, S. L. Connors, C. Péan, S. Berger, N. Caud, et al., 673–816. Cambridge, United Kingdom; New York, NY, USA: Cambridge University Press. https://doi.org/10.1017/9781009157896.007.\n\n\nCox, Peter M., David Pearson, Ben B. Booth, Pierre Friedlingstein, Chris Huntingford, Chris D. Jones, and Catherine M. Luke. 2013. “Sensitivity of Tropical Carbon to Climate Change Constrained by Carbon Dioxide Variability.” Nature 494 (7437): 341–44. https://doi.org/10.1038/nature11882.\n\n\nElsig, Joachim, Jochen Schmitt, Daiana Leuenberger, Robert Schneider, Marc Eyer, Markus Leuenberger, Fortunat Joos, Hubertus Fischer, and Thomas F Stocker. 2009. “Stable Isotope Constraints on Holocene Carbon Cycle Changes from an Antarctic Ice Core.” Nature 461 (7263): 507–10. https://doi.org/10.1038/nature08393.\n\n\nFalkowski, P., R. J. Scholes, E. Boyle, J. Canadell, D. Canfield, J. Elser, N. Gruber, et al. 2000. “The Global Carbon Cycle: A Test of Our Knowledge of Earth as a System.” Science 290 (5490): 291–96. https://doi.org/10.1126/science.290.5490.291.\n\n\nFriedlingstein, P., M. O’Sullivan, M. W. Jones, R. M. Andrew, D. C. E. Bakker, J. Hauck, P. Landschützer, et al. 2023. “Global Carbon Budget 2023.” Earth System Science Data 15 (12): 5301–69. https://doi.org/10.5194/essd-15-5301-2023.\n\n\nHumphrey, Vincent, Jakob Zscheischler, Philippe Ciais, Lukas Gudmundsson, Stephen Sitch, and Sonia I. Seneviratne. 2018. “Sensitivity of Atmospheric CO2 Growth Rate to Observed Changes in Terrestrial Water Storage.” Nature 560 (7720): 628–31. https://doi.org/10.1038/s41586-018-0424-4.\n\n\nJoos, Fortunat, and Michele Bruno. 1998. “Long-Term Variability of the Terrestrial and Oceanic Carbon Sinks and the Budgets of the Carbon Isotopes 13C and 14C.” Global Biogeochemical Cycles 12 (2): 277–95. https://doi.org/10.1029/98GB00746.\n\n\nKeeling, Ralph F., Stephen C. Piper, and Martin Heimann. 1996. “Global and Hemispheric CO2 Sinks Deduced from Changes in Atmospheric O2 Concentration.” Nature 381 (6579): 218–21. https://doi.org/10.1038/381218a0.\n\n\nKeenan, T. F., X. Luo, B. D. Stocker, M. G. De Kauwe, B. E. Medlyn, I. C. Prentice, N. G. Smith, et al. 2023. “A Constraint on Historic Growth in Global Photosynthesis Due to Rising CO2.” Nature Climate Change, November, 1–6. https://doi.org/10.1038/s41558-023-01867-2.\n\n\nKeenan, T. F., and W. J. Riley. 2018. “Greening of the Land Surface in the World’s Cold Regions Consistent with Recent Warming.” Nature Climate Change 8 (9): 825–28. https://doi.org/10.1038/s41558-018-0258-y.\n\n\nKeenan, Trevor F., I. Colin Prentice, Josep G. Canadell, Christopher A. Williams, Han Wang, Michael Raupach, and G. James Collatz. 2016. “Recent Pause in the Growth Rate of Atmospheric CO2 Due to Enhanced Terrestrial Carbon Uptake.” Nature Communications 7 (1): 13428. https://doi.org/10.1038/ncomms13428.\n\n\nLi, Changyu, Jianping Huang, Lei Ding, Yu Ren, Linli An, Xiaoyue Liu, and Jiping Huang. 2022. “The Variability of Air-Sea O2 Flux in CMIP6: Implications for Estimating Terrestrial and Oceanic Carbon Sinks.” Advances in Atmospheric Sciences 39 (8): 1271–84. https://doi.org/10.1007/s00376-021-1273-x.\n\n\nPugh, Thomas A. M., Mats Lindeskog, Benjamin Smith, Benjamin Poulter, Almut Arneth, Vanessa Haverd, and Leonardo Calle. 2019. “Role of Forest Regrowth in Global Carbon Sink Dynamics.” Proceedings of the National Academy of Sciences 116 (10): 4382–87. https://doi.org/10.1073/pnas.1810512116.\n\n\nRuehr, Sophie, Trevor F. Keenan, Christopher Williams, Yu Zhou, Xinchen Lu, Ana Bastos, Josep G. Canadell, Iain Colin Prentice, Stephen Sitch, and César Terrer. 2023. “Evidence and Attribution of the Enhanced Land Carbon Sink.” Nature Reviews Earth & Environment 4 (8): 518–34. https://doi.org/10.1038/s43017-023-00456-3.\n\n\nSchimel, David, Britton B. Stephens, and Joshua B. Fisher. 2015. “Effect of Increasing CO2 on the Terrestrial Carbon Cycle.” Proceedings of the National Academy of Sciences 112 (2): 436–41. https://doi.org/10.1073/pnas.1407302112.\n\n\nShanahan, Timothy M., Nicholas P. McKay, Konrad A. Hughen, Jonathan T. Overpeck, Bette Otto-Bliesner, Clifford W. Heil, John King, Christopher A. Scholz, and John Peck. 2015. “The Time-Transgressive Termination of the African Humid Period.” Nature Geoscience 8 (2): 140–44. https://doi.org/10.1038/ngeo2329.\n\n\nSierra, Carlos A., Markus Müller, Holger Metzler, Stefano Manzoni, and Susan E. Trumbore. 2017. “The Muddle of Ages, Turnover, Transit, and Residence Times in the Carbon Cycle.” Global Change Biology 23 (5): 1763–73. https://doi.org/10.1111/gcb.13556.\n\n\nWalker, Anthony P., Martin G. De Kauwe, Ana Bastos, Soumaya Belmecheri, Katerina Georgiou, Ralph F. Keeling, Sean M. McMahon, et al. 2021. “Integrating the Evidence for a Terrestrial Carbon Sink Caused by Increasing Atmospheric CO \\(_{\\textrm{2}}\\).” New Phytologist 229 (5): 2413–45. https://doi.org/10.1111/nph.16866." }, { "objectID": "gpp.html#light-use-efficiency-model", @@ -151,21 +151,21 @@ "href": "gpp.html#sec-light-absorption", "title": "4  Gross primary production and photosynthesis", "section": "4.2 Canopy light absorption", - "text": "4.2 Canopy light absorption\nPhotosynthetic CO2 uptake only operates if active (green) leaves are out. The relationship between the amount of leaves and GPP is introduced here. Active leaf area varies across the seasons and space in response to the seasonality of temperature, light and water availability. The seasonal fluctuation of leaf area, most visible for deciduous trees, is referred to as (leaf) phenology. The drivers of temporal and spatial variations of phenology and leaf area are introduced in Section 6.2.\nThe fraction of absorbed photosynthetically active radiation (fAPAR) increases with the projected (one-sided) surface area of leaves per unit ground area (the leaf area index, LAI). The total surface area of leaves is roughly twice the projected surface area. The LAI is an ecosystem-level variable and reflects the leaf area density of the whole canopy. The canopy may be composed of multiple species and organised in multiple canopy layers (Figure 4.1). While temperate and boreal forests commonly form a single understorey and attain LAI values of 4-6 m2 m-1, tropical moist forests may have multiple canopy layers and an LAI of over 6 m2 m-1 (Figure 2.16).\n\n\n\n\n\nFigure 4.1: Vertical profile of the leaf area index (LAI) and light absorption the canopy for a typical oak forest, where most leaves are located in a dense canopy without an understorey. Figure from Bonan (2015).\n\n\n\n\nWhile the intensity of shortwave (solar) radiation is highest at the top of the canopy, it is progressively attenuated as it penetrates into the canopy. Radiation gets reflected, absorbed and transmitted by individual leaves. The penetration of radiation into a canopy is referred to as canopy radiative transfer. Each of the processes - reflection, absorption, and transmittance - affects light differently in different wavelengths, depends on the solar zenith angle, on the three-dimensional arrangement of leaves in the canopy (angles, “clumping”), and on the pigments on the leaf surfaces that are responsible for light absorption. Pigments change across species and may vary in response to stress (e.g., by frost, heat, or water limitation).\nIn brief, canopy radiative transfer is complex. A simple model for how (solar) radiation (light) is attenuated as it penetrates into the canopy is given by the Beer-Lambert law. To apply it for canopy radiative transfer, we assume that a leaf only absorbs light, but does not reflect or transmit it. Following this model, the light intensity \\(I\\) at the bottom of the canopy (\\(z_0\\)) is an exponential function of LAI (\\(L\\)). The rate of decline of the light intensity is given by the light extinction coefficient \\(k\\). A typical value of \\(k\\) in the visible (photosynthetically active) wavelength spectrum is 0.5. \\[\nI(z_0) = I_0 \\; e^{-kL}\n\\] We have assumed that no light is reflected. Therefore the reduction of light levels at the bottom of the canopy tells us how much light was absorbed by the canopy (and used for photosynthesis). The fraction of absorbed (photosynthetically active) radiation therefore is \\[\n\\begin{align}\n\\mathrm{fAPAR} &= 1 - I(z_0)/I_0 \\\\\n &= 1 - e^{-kL}\\;.\n\\end{align}\n\\]\nThe shape of this function is illuatrated in Figure 4.2 (a). This implies a dependency of light levels on canopy depth \\(z\\), as illustrated in Figure 4.2 (b) - consistent with the observation shown in Figure 4.1 (b).\n\n\nCode\nlibrary(ggplot2)\nlibrary(dplyr)\n\ncalc_fapar <- function(lai, k_beer){\n 1 - exp(-k_beer * lai)\n}\n\ngg_fapar <- ggplot() +\n geom_function(\n fun = calc_fapar, \n args = list(k_beer = 0.5),\n linewidth = 0.75\n ) +\n xlim(0, 10) +\n labs(x = expression(paste(\"LAI (m\"^2, \" m\"^-2, \")\")),\n y = \"fAPAR (unitless)\") +\n theme_classic()\n\ncalc_cumlai <- function(z){\n ifelse(z <= 3.5, z*4.6/3.5, 4.6)\n}\n\ncalc_light_rel <- function(z, k_beer){\n exp(-k_beer * calc_cumlai(z))\n}\n\ndf <- tibble(z = seq(0, 7, by = 0.01)) |> \n mutate(\n light_rel = calc_light_rel(z, k_beer = 0.5)\n )\n\ngg_canopydepth <- ggplot() +\n geom_rect(\n aes(\n xmin = 0, xmax = 1,\n ymin = 0, ymax = 3.5\n ),\n fill = \"#009E73\",\n alpha = 0.5\n ) +\n geom_rect(\n aes(\n xmin = 0.45, xmax = 0.55,\n ymin = 3.5, ymax = 7\n ),\n fill = \"sienna\",\n alpha = 0.5\n ) +\n geom_line(\n data = df,\n aes(\n y = z,\n x = light_rel),\n linewidth = 1,\n color = \"#E69F00\"\n ) +\n labs(y = \"Canopy depth (m)\",\n x = \"Light level (relative)\") +\n theme_classic() +\n scale_y_reverse()\n\ncowplot::plot_grid(\n gg_fapar,\n gg_canopydepth,\n nrow = 1,\n labels = c(\"a\", \"b\"),\n rel_widths = c(1, 0.6)\n)\n\n\n\n\n\nFigure 4.2: The fraction of absorbed photosynthetically active radiation (fAPAR) as a function of LAI (a) and relative light (or photosynthetically active radiation) levels as a function of canopy depth (z) following the Beer-Lambert law. The arrangement of the canopy versus depth (z = 0 at the top of the canopy) is shown by the green rectangle in (b), within which leaves are assumed to be evenly distributed. The yellow line in (b) represents the light levels, relative to the top of the canopy. The brown rectangle represents a stem, indicating that this part is below the canopy - without light-absorbing leaves.\n\n\n\n\n\n\n\n\n\n\nBasis of the Beer-Lambert law for canopy light extinction\n\n\n\n\n\nFollowing the Beer-Lambert law model, the light extinction at canopy depth \\(z\\) (measuring from the top) is proportional to the light intensity at that depth and an “optical density” \\(\\mu\\). \\[\n\\frac{\\mathrm{d}I}{\\mathrm{d}z} = -\\mu\\;I(z)\n\\tag{4.2}\\] Therefore, the light intensity declines exponentially with \\(z\\). \\[\nI(z) = I_0 \\exp(-\\mu z)\n\\tag{4.3}\\] How does the dependency on \\(z\\) relate to the dependency on LAI (\\(L\\))?\nFor applying the Beer Lambert law, it is further assumed that the canopy is a homogenous turbid medium. In other words, we assume that leaves are uniformly distributed across the canopy and that the optical density is given by the leaf area index \\(L\\) divided by the total canopy depth \\(z_0\\): \\[\n\\mu = k \\frac{L}{z_0}\n\\tag{4.4}\\] \\(k\\) is the leaf area-specific optical density, or light extinction coefficient. Using Equation 4.3 and Equation 4.4, we can thus express the light level at the bottom of the canopy (\\(z_0\\)) as a function of \\(L\\) as \\[\nI(z_0) = I_0 \\; e^{-kL}\n\\] and the fraction of absorbed (photosynthetically active) radiation is \\[\n\\mathrm{fAPAR} = 1 - e^{-kL}\\;.\n\\]\n\n\n\nThe radiation \\(I\\) consists of direct radiation from the sun and diffuse radiation from the sky and from radiation scattered within the canopy. This distinction is relevant for understanding radiation absorption by the canopy and canopy-level photosynthesis. Two important implications are the following. First, diffuse radiation is more effectively absorbed by canopies, particularly at low LAI. The reduction of GPP under cloudy conditions is therefore less than what would be expected from considering only changes in \\(I_0\\) (the effective \\(k\\) is higher for diffuse radiation than for direct radiation).\nSecond, the energy flux of direct radiation is much higher than that of diffuse radiation. Although at greater canopy depths, leaves are more frequently exposed to diffuse than to direct radiation, the latter provides potentially valuable energy for photosynthesis, but occurs very rarely (sunflecks). Leaves have to balance the rare high-intensity light levels and the frequent low-intensity levels for adjusting photosynthetic capacities." + "text": "4.2 Canopy light absorption\nPhotosynthetic CO2 uptake only operates if active (green) leaves are out. The relationship between the amount of leaves and GPP is introduced here. Active leaf area varies across the seasons and space in response to the seasonality of temperature, light and water availability. The seasonal fluctuation of leaf area, most visible for deciduous trees, is referred to as (leaf) phenology. The drivers of temporal and spatial variations of phenology and leaf area are introduced in Section 6.2.\nThe fraction of absorbed photosynthetically active radiation (fAPAR) increases with the projected (one-sided) surface area of leaves per unit ground area (the leaf area index, LAI). The total surface area of leaves is roughly twice the projected surface area. The LAI is an ecosystem-level variable and reflects the leaf area density of the whole canopy. The canopy may be composed of multiple species and organised in multiple canopy layers (Figure 4.1). While temperate and boreal forests commonly form a single understorey and attain LAI values of 4-6 m2 m-2, tropical moist forests may have multiple canopy layers and an LAI of over 6 m2 m-2 (Figure 2.16).\n\n\n\n\n\nFigure 4.1: Vertical profile of the leaf area index (LAI) and light absorption the canopy for a typical oak forest, where most leaves are located in a dense canopy without an understorey. Figure from Bonan (2015).\n\n\n\n\nWhile the intensity of shortwave (solar) radiation is highest at the top of the canopy, it is progressively attenuated as it penetrates into the canopy. Radiation gets reflected, absorbed and transmitted by individual leaves. The penetration of radiation into a canopy is referred to as canopy radiative transfer. Each of the processes - reflection, absorption, and transmittance - affects light differently in different wavelengths, depends on the solar zenith angle, on the three-dimensional arrangement of leaves in the canopy (angles, “clumping”), and on the pigments on the leaf surfaces that are responsible for light absorption. Pigments change across species and may vary in response to stress (e.g., by frost, heat, or water limitation).\nIn brief, canopy radiative transfer is complex. A simple model for how (solar) radiation (light) is attenuated as it penetrates into the canopy is given by the Beer-Lambert law. To apply it for canopy radiative transfer, we assume that a leaf only absorbs light, but does not reflect or transmit it. Following this model, the light intensity \\(I\\) at the bottom of the canopy (\\(z_0\\)) is an exponential function of LAI (\\(L\\)). The rate of decline of the light intensity is given by the light extinction coefficient \\(k\\). A typical value of \\(k\\) in the visible (photosynthetically active) wavelength spectrum is 0.5. \\[\nI(z_0) = I_0 \\; e^{-kL}\n\\] We have assumed that no light is reflected. Therefore, the reduction of light levels at the bottom of the canopy tells us how much light was absorbed by the canopy (and used for photosynthesis). The fraction of absorbed (photosynthetically active) radiation therefore is \\[\n\\begin{align}\n\\mathrm{fAPAR} &= 1 - I(z_0)/I_0 \\\\\n &= 1 - e^{-kL}\\;.\n\\end{align}\n\\]\nThe shape of this function is illustrated in Figure 4.2 (a). This implies a dependency of light levels on canopy depth \\(z\\), as illustrated in Figure 4.2 (b) - consistent with the observation shown in Figure 4.1 (b).\n\n\nCode\nlibrary(ggplot2)\nlibrary(dplyr)\n\ncalc_fapar <- function(lai, k_beer){\n 1 - exp(-k_beer * lai)\n}\n\ngg_fapar <- ggplot() +\n geom_function(\n fun = calc_fapar, \n args = list(k_beer = 0.5),\n linewidth = 0.75\n ) +\n xlim(0, 10) +\n labs(x = expression(paste(\"LAI (m\"^2, \" m\"^-2, \")\")),\n y = \"fAPAR (unitless)\") +\n theme_classic()\n\ncalc_cumlai <- function(z){\n ifelse(z <= 3.5, z*4.6/3.5, 4.6)\n}\n\ncalc_light_rel <- function(z, k_beer){\n exp(-k_beer * calc_cumlai(z))\n}\n\ndf <- tibble(z = seq(0, 7, by = 0.01)) |> \n mutate(\n light_rel = calc_light_rel(z, k_beer = 0.5)\n )\n\ngg_canopydepth <- ggplot() +\n geom_rect(\n aes(\n xmin = 0, xmax = 1,\n ymin = 0, ymax = 3.5\n ),\n fill = \"#009E73\",\n alpha = 0.5\n ) +\n geom_rect(\n aes(\n xmin = 0.45, xmax = 0.55,\n ymin = 3.5, ymax = 7\n ),\n fill = \"sienna\",\n alpha = 0.5\n ) +\n geom_line(\n data = df,\n aes(\n y = z,\n x = light_rel),\n linewidth = 1,\n color = \"#E69F00\"\n ) +\n labs(y = \"Canopy depth (m)\",\n x = \"Light level (relative)\") +\n theme_classic() +\n scale_y_reverse()\n\ncowplot::plot_grid(\n gg_fapar,\n gg_canopydepth,\n nrow = 1,\n labels = c(\"a\", \"b\"),\n rel_widths = c(1, 0.6)\n)\n\n\n\n\n\nFigure 4.2: The fraction of absorbed photosynthetically active radiation (fAPAR) as a function of LAI (a) and relative light (or photosynthetically active radiation) levels as a function of canopy depth (z) following the Beer-Lambert law. The arrangement of the canopy versus depth (z = 0 at the top of the canopy) is shown by the green rectangle in (b), within which leaves are assumed to be evenly distributed. The yellow line in (b) represents the light levels, relative to the top of the canopy. The brown rectangle represents a stem, indicating that this part is below the canopy - without light-absorbing leaves.\n\n\n\n\n\n\n\n\n\n\nBasis of the Beer-Lambert law for canopy light extinction\n\n\n\n\n\nFollowing the Beer-Lambert law model, the light extinction at canopy depth \\(z\\) (measuring from the top) is proportional to the light intensity at that depth and an “optical density” \\(\\mu\\). \\[\n\\frac{\\mathrm{d}I}{\\mathrm{d}z} = -\\mu\\;I(z)\n\\tag{4.2}\\] Therefore, the light intensity declines exponentially with \\(z\\). \\[\nI(z) = I_0 \\exp(-\\mu z)\n\\tag{4.3}\\] How does the dependency on \\(z\\) relate to the dependency on LAI (\\(L\\))?\nFor applying the Beer Lambert law, it is further assumed that the canopy is a homogenous turbid medium. In other words, we assume that leaves are uniformly distributed across the canopy and that the optical density is given by the leaf area index \\(L\\) divided by the total canopy depth \\(z_0\\): \\[\n\\mu = k \\frac{L}{z_0}\n\\tag{4.4}\\] \\(k\\) is the leaf area-specific optical density, or light extinction coefficient. Using Equation 4.3 and Equation 4.4, we can thus express the light level at the bottom of the canopy (\\(z_0\\)) as a function of \\(L\\) as \\[\nI(z_0) = I_0 \\; e^{-kL}\n\\] and the fraction of absorbed (photosynthetically active) radiation is \\[\n\\mathrm{fAPAR} = 1 - e^{-kL}\\;.\n\\]\n\n\n\nThe radiation \\(I\\) consists of direct radiation from the sun and diffuse radiation from the sky and from radiation scattered within the canopy. This distinction is relevant for understanding radiation absorption by the canopy and canopy-level photosynthesis. Two important implications are the following. First, diffuse radiation is more effectively absorbed by canopies, particularly at low LAI. The reduction of GPP under cloudy conditions is therefore less than what would be expected from considering only changes in \\(I_0\\) (the effective \\(k\\) is higher for diffuse radiation than for direct radiation).\nSecond, the energy flux of direct radiation is much higher than that of diffuse radiation. Although at greater canopy depths, leaves are more frequently exposed to diffuse than to direct radiation, the latter provides potentially valuable energy for photosynthesis, but occurs very rarely (sunflecks). Leaves have to balance the rare high-intensity light levels and the frequent low-intensity levels for adjusting photosynthetic capacities." }, { "objectID": "gpp.html#sec-photosynthesis", "href": "gpp.html#sec-photosynthesis", "title": "4  Gross primary production and photosynthesis", "section": "4.3 Photosynthesis", - "text": "4.3 Photosynthesis\nLight use efficiency (LUE, Equation 4.1) measures the efficiency at which absorbed photons (radiation) are converted into C in the form of sugars. LUE is an ecosystem-level quantity and reflects the collective photosynthetic CO2 uptake efficiency of all leaves in the canopy. This efficiency is determined by the leaf physiology and the activity of the photosynthetic machinery. In this subsection, we dive very deep into the physiology of photosynthesis.\n\nCO2 uptake by the leaf happens by diffusion through pores at the leaf surface (stomata, Figure 4.3). The opening of stomata is dynamically regulated in response to environmental conditions (light, CO2, temperature, atmospheric humidity) and controls the conductance to CO2 diffusion. The CO2 uptake flux by diffusive transport through stomata can thus be described by Fick’s law which states that the flux is proportional to the concentration difference of CO2 inside and outside the leaf. \\[\nA = g_s(c_a - c_i)\n\\tag{4.5}\\] \\(c_a\\) is the ambient CO2 concentration (outside the leaf), and \\(c_i\\) is the CO2 concentration inside the leaf - at the chloroplast. \\(g_s\\) is the stomatal conductance. Note that we use the variable name \\(A\\) here for CO2 assimilation by photosynthesis. In constrast to the ecosystem-level variable GPP, \\(A\\) refers to the leaf-level flux.\n\n\n\n\n\nFigure 4.3: CO2 diffuses into the leaf through stomata, while water vapour diffuses out of the leaf. The water vapour diffusion out of the leaves (transpiration) is introduced in Chapter 7.\n\n\n\n\n\n\nOnce inside the leaf, CO2 diffuses across mesophyll cells to the chloroplasts - the site of photosynthetic reactions. The conductance to this diffusion step - mesophyll conductance - is often ignored for modelling photosynthesis. Reflecting this, we are referring to “leaf-internal” CO2 concentration, \\(c_i\\)” here, instead of a more correct CO2 concentration at the chloroplast.\nPhotosynthesis can be considered as a sequence of three processes that are serially connected - the three processes run one after the other and the rate of the slowest of the three processes determines the overall process rate of photosynthesis. The following is a condensed description, based on Lambers, Chapin, and Pons (2008) and Bonan (2015).\n\n\n\n\n\nFigure 4.4: Overview of photosynthesis, distinguishing the light reactions and the Calvin cycle. Image taken https://bookdown.org/jcog196013/BS2003/photosynthesis.html.\n\n\n\n\n\n4.3.1 Light absorption at the cellular level\nLight (photons) in the photosynthetically active wavelength spectrum (400-700 nm) is absorbed by pigments - mainly chlorophyll. The absorbed energy is transported in the form of excited chlorophyll to the reaction centers of photosystem I (PSI) and photosystem II (PSII). Relevant for photosynthesis is the number of photons in the photosynthetically active spectrum, not their total energy. That’s why Equation 4.1 is expressed in units of photons, not energy (Watts). (A photon in the blue wavelength has the same effect on CO2 assimilation as a photon in the red wavelength, although it carries a higher energy). The excess energy is dissipated as heat or through other pathways.\n\n\n4.3.2 Light reactions\nIn the reaction centers, the excitation energy of the chlorophyll is used for splitting electrons from water molecules, producing oxygen (O2) as a “side-product”. The electrons are transported along the electron transport chain and are used to produce NADPH and ATP. These are called the light reactions of photosynthesis. Up to here, radiation energy has been converted into chemical energy in the form of ATP. The production of ATP consumes inorganic phosphate.\n\n\n4.3.3 Calvin cycle\nNADPH and ATP are then used for reducing CO2 (the energy-demanding reversal of oxidation) in the Calvin cycle. This step forms C3 compounds (triose-phosphates) and occurs independently of light. It is therefore commonly referred to as the “dark reactions” of photosynthesis. Rubisco (ribulose-1,5-bisphosphate carboxylase/oxygenase) is the principal enzyme involved in the Calvin cycle and the amount of Rubisco determines the capacity for the carboxylation of RuBP (Ribulose-1,5-bisphosphate). Rubisco also catalyzes the oxygenation of RuBP which consumes O2 and produces CO2 as part of photorespiration. This respiration scales with photosynthetic activity and reduces the net photosynthetic CO2 by 30-50%, depending on the relative concentrations of CO2 and O2. At very low CO2 levels, at around 30-50 ppm, the photorespiratory compensation point (\\(\\Gamma^\\ast\\)) is reached and net photosynthesis is zero. In contrast to photorespiration, dark respiration (\\(R_d\\)), which also produces CO2, arises from the decarboxylation of Rubisco and is independent of light, but proportional to the amount of Rubisco.\nReduced C in the form of sucrose or (after an additional step) starch is either consumed in the leaf during the night, or exported through the phloem and used for synthesising biomass or supplying plant-internal C storage as non-structural C (see Chapter 5).\n\n\n4.3.4 Summary\nThe chemical summary equation of photosynthesis is: \\[\nn\\mathrm{CO}_2 + 2n\\mathrm{H}_2\\mathrm{O} \\rightarrow (\\mathrm{CH}_2\\mathrm{O})_n + n\\mathrm{O}_2 + n\\mathrm{H}_2\\mathrm{O}\n\\tag{4.6}\\] A total of eight photons is consumed to assimilate one molecule of CO2. For each molecule of CO2, one molecule of O2 is produced. And for each molecule of CO2, one molecule of H2O is consumed (net). Note however, that this water consumption is not the primary reason for why plants use water. A much larger amount of water is consumed by the diffusion of water vapour from the water-saturated air inside the leaves out of the stomata. This transpiration flux is further explained in Chapter 7.\n\n\n4.3.5 Response to light and CO2\nThe three steps described above operate in series and each step is potentially rate-limiting and responds differently to the environment. The rates of the processes are coordinated such that they are roughly equal and co-limiting for average environmental conditions to which a leaf is exposed during a day. An imbalance of rates can lead to an excess production of electrons and can cause damage to the photosynthetic apparatus. This happens for example when leaves are exposed to very cold temperatures and high light during a frost event, or when you move your indoor plant that has been sitting in a dark corner for years suddenly into full sunlight outdoors.\nThe response of photosynthetic CO2 assimilation (\\(A\\)) to light (PPFD) and leaf-internal CO2 (\\(c_i\\)) reflects the serial nature of how the light and dark reactions are connected. \\(A\\) saturates both in response to increasing PPFD as well as to increasing \\(c_i\\). When a leaf is exposed to increasing PPFD, \\(A\\) initially increases and eventually saturates (Figure 4.5). The slope of the initial linear increase reflects the efficiency at which photons are used for CO2 assimilation in the light reactions (the quantum yield \\(\\varphi_0\\)). Under these conditions, light, i.e. the rate of the light reactions, is limiting, not CO2 inside the leaf. Under conditions of very high light, the dark reactions of the Calvin cycle become limiting. The assimilation rate attained under saturating light is commonly referred to as \\(A_\\mathrm{sat}\\).\nThe level at which the light response of \\(A\\) saturates (\\(A_\\mathrm{sat}\\)) varies within a species and across different plant species. Variations within species arise through the acclimation of the light reaction capacities to the typical light intensities to which a leaf is exposed. Acclimation of photosynthesis evolves over time scales of weeks to months. (Thus, your indoor plant suffers because the change to high-light conditions happened to fast.) \\(A_\\mathrm{sat}\\) also varies across species, reflecting the adaptation through evolution of different plant species to the environment in which they commonly grow. A typical light adaptation to different light levels is expressed by plants that commonly grow in the shady understorey versus plants that grow in the sun-exposed upper canopy.\n\n\n\n\n\nFigure 4.5: Response of leaf photosynthesis to light and how it varies within species through acclimation to different growth environments (A) and across species through evolutionary adaptation (B). Figure from Lambers, Chapin, and Pons (2008).\n\n\n\n\nIn a similar fashion, the response of \\(A\\) to \\(c_i\\) initially increase and saturates at high \\(c_i\\). This is reflected by the so-called “A-ci curve” (Figure 4.6). Commonly, net assimilation \\(A_n = A - R_d\\) is considered when analysing A-ci curves. \\(A_n\\) is initially negative until the photorespiratory compensation point (\\(\\Gamma^\\ast\\)) is reached. Then, \\(A_n\\) increases steeply with \\(c_i\\) as it is limited by the rate of RuBP carboxylation by Rubisco. This Rubisco carboxylation-limited functional response of assimilation is commonly denoted \\(A_C\\).\nAs \\(c_i\\) increases further, \\(A\\) is no longer limited by RuBP carboxylation, but by the rate at which RuBP becomes available. This, in turn, is governed by the rate at which ATP and NADPH are produced and thus by the rate of electron transport \\(J\\). This functional response of assimilation is commonly denoted \\(A_J\\). A limiting electron transport rate may be due to limiting light or a limiting capacity of electron transport (\\(J_\\mathrm{max}\\)). A slower further increase of \\(A\\) with \\(c_i\\) in the electron transport-limited range is due to the suppression of RuBP oxygenation at high concentrations of CO2 (relative to O2). The effective assimilation rate across the full range of \\(c_i\\) is the minimum of the electron transport-limited and the RuBP carboxylation-limited rate: \\[\nA_n = \\min(A_C, A_J) - R_d\n\\tag{4.7}\\]\nThe A-ci curve (Figure 4.6) can be measured in the field and reveals the rates and efficiencies of the individual processes of the photosynthesis “chain” (light and dark reactions). These quantities are key for quantitatively describing and modeling leaf photosynthesis (see Box Farquhar-von Caemmerer-Berry model below).\n\n\n\n\n\n\nFigure 4.6: The A-ci curve. Net assimilation (An = A - Rd) is measured for different levels of leaf-internal CO2 concentrations (black dots). The functional forms of AC and AJ are fitted to the data points. The grey point indicates the co-limitation point. Figure from Duursma (2015).\n\n\n\n\n\n\n\n\n\n\nFarquhar-von Caemmerer-Berry model\n\n\n\nFollowing the Farquhar-von Caemmerer-Berry (FvCB) model for C3 photosynthesis (Farquhar, Caemmerer, and Berry 1980), the RuBP carboxylation-limited assimilation rate \\(A_C\\) can be described as \\[\nA_C = V_\\mathrm{cmax} \\frac{c_i - \\Gamma^\\ast}{c_i + K} \\;,\n\\tag{4.8}\\] where \\(K\\) is the effective Michaelis-Menten coefficient for \\(A_C\\), considering the balance of carboxylation and oxygenation by Rubisco. It depends on the partial pressure of oxygen (\\(p\\mathrm{O}_2\\)). \\[\nK = K_c \\left(1 + \\frac{p\\mathrm{O}_2}{K_o} \\right)\n\\] \\(V_\\mathrm{cmax}\\), \\(K_c\\), \\(K_o\\), and \\(\\Gamma^\\ast\\) all have a temperature dependency. In addition, \\(\\Gamma^\\ast\\) is proportional to atmospheric pressure. These dependencies are shown in Section 4.3.6 and are described in full detail in Stocker et al. (2020).\nThe electron transport-limited assimilation rate \\(A_J\\) can be described as \\[\nA_J = \\frac{J}{4} \\cdot \\frac{c_i - \\Gamma^\\ast}{c_i + 2 \\Gamma^\\ast}\\;.\n\\tag{4.9}\\] The electron transport rate \\(J\\) is described by a saturating function that increases with absorbed light \\(I_\\mathrm{abs}\\) up to a maximum rate \\(J_\\mathrm{max}\\) \\[\nJ = \\frac{4\\varphi_0 I_\\mathrm{abs}}{\\sqrt{1+\\left(\\frac{4\\varphi_0 I_\\mathrm{abs}}{J_\\mathrm{max}}\\right)^2}}\n\\tag{4.10}\\]\nTogether, Equation 4.8 and Equation 4.9 describe the combined effect of \\(c_i\\), (leaf) temperature, the absorbed photon flux density, and atmospheric pressure on leaf-level CO2 assimilation.\nWith the mathematical description of \\(A_C\\) and \\(A_J\\) and their dependency on light and CO2 following the FvCB model, A-ci and the A vs. PPFD curves, as shown for measurements in Figure 4.5 and Figure 4.6, can thereby be modeled.\n\n\nCode\nlibrary(rpmodel)\nlibrary(dplyr)\nlibrary(tidyr)\nlibrary(ggplot2)\n\n# modified seq() function to get a logarithmically spaced sequence\nlseq <- function(from=1, to=100000, length.out=6) {\n exp(seq(log(from), log(to), length.out = length.out))\n}\n\n# Set model parameters (constants)\n# see Stocker et al., 2020 GMD for a description\nbeta <- 146 # unit cost ratio a/b\nc_cost <- 0.41 # marginal cost of Jmax\ngamma <- 0.105 # unit cost ratio c/b\nkphio <- 0.085 # quantum yield efficiency\nc_molmass <- 12.0107 # molar mass, g / mol\n\n# Define environmental conditions\ntc <- 15 # temperature, deg C\nppfd <- 500 # micro-mol/m2/s\nvpd <- 300 # Pa\nco2 <- 400 # ppm\nelv <- 0 # m.a.s.l.\nfapar <- 1 # fraction\npatm <- 101325 # Pa\n\n# get photosynthesis parameters gammastar, vcmax, jmax from p-model\n# this assumes vcmax and jmax to be optimally acclimated/adapted to\n# the specified environmental conditions and considers the temperature\n# and atmospheric-pressure dependence of all parameters.\nout_pmodel <- rpmodel(\n tc = tc,\n vpd = vpd,\n co2 = co2,\n elv = elv,\n kphio = kphio,\n beta = beta,\n fapar = fapar,\n ppfd = ppfd,\n method_optci = \"prentice14\",\n method_jmaxlim = \"wang17\",\n do_ftemp_kphio = FALSE\n )\n\n# electron transport-limited assimilation rate as a function of CO2 partial pressure\ncalc_aj <- function(ci, gammastar, kphio, ppfd, jmax){\n kphio * ppfd * (ci - gammastar)/(ci + 2 * gammastar) * 1/sqrt(1+((4 * kphio * ppfd)/jmax)^2)\n}\n\n# RuBP carboxylation-limited assimilation rate as a function of CO2 partial pressure\ncalc_ac <- function(ci, gammastar, kmm, vcmax){\n vcmax * (ci - gammastar)/(ci + kmm)\n}\n\n# assimilation rate given stomatal conductance and leaf-internal \n# CO2 partial pressure\ncalc_a_gs <- function(ci, gs, ca){\n gs * (ca - ci)\n}\n\n# conversion of CO2 concentration in ppm to partial pressure in Pa\nco2_to_ca <- function( co2, patm ){\n ( 1.0e-6 ) * co2 * patm\n}\n\ndf_ci <- tibble(\n ci = seq(0, 1000, length.out = 100)) |> \n rowwise() |> \n mutate(ci_pa = co2_to_ca(ci, patm = patm)) |> \n mutate(a_j = calc_aj(ci_pa, \n out_pmodel$gammastar, \n kphio = kphio, \n ppfd = ppfd, \n jmax = out_pmodel$jmax)) |> \n mutate(a_c = calc_ac(ci_pa, \n out_pmodel$gammastar, \n out_pmodel$kmm, \n vcmax = out_pmodel$vcmax)) |>\n mutate(a_act = min(a_j, a_c)) |> \n mutate(a_gs = calc_a_gs(ci_pa, \n gs = out_pmodel$gs, \n ca = out_pmodel$ca))\n \ndf_ci |> \n pivot_longer(cols = c(\n a_j, \n a_c\n # a_gs\n ), \n names_to = \"Rate\", \n values_to = \"a_\") |>\n ggplot(aes(x = ci)) +\n geom_line(aes(y = a_, color = Rate)) +\n geom_line(aes(y = a_act)) +\n xlim(00, 1000) + \n # ylim(-20, 80) +\n geom_hline(yintercept = 0, linetype = \"dotted\") +\n geom_vline(xintercept = 0, linetype = \"dotted\") +\n geom_vline(xintercept = (out_pmodel$gammastar/(1.0e-6 * patm)), linetype = \"dotted\") +\n labs(x = expression(paste(italic(\"c\")[i], \" (ppm)\")), \n y = expression(paste(italic(\"A\"), \" (\", mu, \"mol m\" ^{-2},\" s\" ^{-1}, \")\"))) +\n scale_color_manual(\n name = \"\",\n breaks = c(\n # \"a_gs\",\n \"a_j\",\n \"a_c\"\n ),\n labels = c(\n # expression(paste(italic(\"A\")[gs])),\n expression(paste(italic(\"A\")[J])),\n expression(paste(italic(\"A\")[C]))\n ),\n values = c( \n # \"#009E73\", \n \"#56B4E9\", \n \"#E69F00\"\n )) +\n theme_classic()\n\n\n\n\n\nFigure 4.7: The A-ci curve as simulated by the FvCB model. Ags is shown here as the dependency of A on stomatal conductance following Equation 4.5 for a given gs. The fact that AC, AJ, and Ags intersect in one point does not follow from the FvCB model, but is simulated here based on a model of eco-evolutionary optimality (P-model Stocker et al. (2020), implemented by the {rpmodel} R package) which predicts that photosynthetic capacities are acclimated such that a leaf operates close to the intersection point of AC and and AJ. The point at which curves intersect with the x-axis (y = 0) is the photorespiratory compensation point. The environmental conditions used as forcing for the simulation displayed here can be seen by unfolding code.\n\n\n\n\nFigure 4.8 shows the light response curve of \\(A_J - R_d\\) following the FvCB model. The response is shown for leaves acclimated to different levels of light, thus having different values for \\(J_\\mathrm{max}\\). Because acclimation to light also involves a change in the Rubisco content of leaves and thus \\(V_\\mathrm{cmax}\\), “high-light leaves” also have higher dark respiration rates. Therefore, under low light conditions, leaves acclimated to low light have higher net assimilation rates than leaves acclimated to high light. This is illustrated by Figure 4.8 a.\n\n\nCode\nlibrary(rpmodel)\nlibrary(dplyr)\nlibrary(tidyr)\nlibrary(ggplot2)\n\n# modified seq() function to get a logarithmically spaced sequence\nlseq <- function(from=1, to=100000, length.out=6) {\n exp(seq(log(from), log(to), length.out = length.out))\n}\n\n# Set model parameters (constants)\n# see Stocker et al., 2020 GMD for a description\nbeta <- 146 # unit cost ratio a/b\nc_cost <- 0.41 # marginal cost of Jmax\ngamma <- 0.105 # unit cost ratio c/b\nkphio <- 0.085 # quantum yield efficiency\nc_molmass <- 12.0107 # molar mass, g / mol\n\n# Define environmental conditions\ntc <- 15 # temperature, deg C\nppfd <- 500 # micro-mol/m2/s\nvpd <- 300 # Pa\nco2 <- 400 # ppm\nelv <- 0 # m.a.s.l.\nfapar <- 1 # fraction\npatm <- 101325 # Pa\n\n# get photosynthesis parameters gammastar, vcmax, jmax from p-model\n# this assumes vcmax and jmax to be optimally acclimated/adapted to\n# the specified environmental conditions and considers the temperature\n# and atmospheric-pressure dependence of all parameters.\n\n# first for low light\nout_pmodel_lo <- rpmodel(\n tc = tc,\n vpd = vpd,\n co2 = co2,\n elv = elv,\n kphio = kphio,\n beta = beta,\n fapar = fapar,\n ppfd = ppfd*0.5,\n method_optci = \"prentice14\",\n method_jmaxlim = \"wang17\",\n do_ftemp_kphio = FALSE\n )\n\n# medium light\nout_pmodel_me <- rpmodel(\n tc = tc,\n vpd = vpd,\n co2 = co2,\n elv = elv,\n kphio = kphio,\n beta = beta,\n fapar = fapar,\n ppfd = ppfd,\n method_optci = \"prentice14\",\n method_jmaxlim = \"wang17\",\n do_ftemp_kphio = FALSE\n )\n\n# high light\nout_pmodel_hi <- rpmodel(\n tc = tc,\n vpd = vpd,\n co2 = co2,\n elv = elv,\n kphio = kphio,\n beta = beta,\n fapar = fapar,\n ppfd = ppfd*2,\n method_optci = \"prentice14\",\n method_jmaxlim = \"wang17\",\n do_ftemp_kphio = FALSE\n )\n\n# electron transport-limited assimilation rate as a function of CO2 partial pressure\ncalc_aj <- function(ci, gammastar, kphio, ppfd, jmax){\n kphio * ppfd * (ci - gammastar)/(ci + 2 * gammastar) * 1/sqrt(1+((4 * kphio * ppfd)/jmax)^2)\n}\n\n# RuBP carboxylation-limited assimilation rate as a function of CO2 partial pressure\ncalc_ac <- function(ci, gammastar, kmm, vcmax){\n vcmax * (ci - gammastar)/(ci + kmm)\n}\n\n# assimilation rate given stomatal conductance and leaf-internal \n# CO2 partial pressure\ncalc_a_gs <- function(ci, gs, ca){\n gs * (ca - ci)\n}\n\n# conversion of CO2 concentration in ppm to partial pressure in Pa\nco2_to_ca <- function( co2, patm ){\n ( 1.0e-6 ) * co2 * patm\n}\n\ndf_ppfd <- tibble(\n ppfd = seq(0, 2000, length.out = 100)) |> \n rowwise() |> \n mutate(a_j_lo = calc_aj(co2_to_ca(400, patm = patm), \n out_pmodel_lo$gammastar, \n kphio = kphio, \n ppfd = ppfd, \n jmax = out_pmodel_lo$jmax * 0.5) - \n out_pmodel_lo$rd) |> \n mutate(a_j_me = calc_aj(co2_to_ca(400, patm = patm), \n out_pmodel_me$gammastar, \n kphio = kphio, \n ppfd = ppfd, \n jmax = out_pmodel_me$jmax) - \n out_pmodel_me$rd) |> \n mutate(a_j_hi = calc_aj(co2_to_ca(400, patm = patm), \n out_pmodel_hi$gammastar, \n kphio = kphio, \n ppfd = ppfd, \n jmax = out_pmodel_hi$jmax * 2) - \n out_pmodel_hi$rd)\n\ngg <- df_ppfd |> \n pivot_longer(cols = c(a_j_lo, a_j_me, a_j_hi), \n names_to = \"Rate\", \n values_to = \"a_\") |>\n ggplot(aes(x = ppfd)) +\n geom_line(aes(y = a_, color = Rate)) +\n geom_hline(yintercept = 0, linetype = \"dotted\") +\n labs(x = expression(paste(\"PPFD (\", mu, \"mol m\"^{-2}, \"s\"^{-1}, \")\")), \n y = expression(paste(italic(\"A\")[J] - italic(R)[d], \" (\", mu, \"mol m\" ^{-2},\" s\" ^{-1}, \")\"))) +\n scale_color_manual(\n name = \"\",\n breaks = c(\"a_j_lo\",\n \"a_j_me\",\n \"a_j_hi\"\n ),\n labels = c(expression(paste(\"Low light\")),\n expression(paste(\"Medium light\")),\n expression(paste(\"High light\"))),\n values = c( \"#009E73\", \"#56B4E9\", \"#E69F00\")) +\n theme_classic()\n\ngg1 <- gg +\n xlim(0, 250) +\n ylim(NA, 20)\n\ngg2 <- gg +\n xlim(0, 2000)\n\ncowplot::plot_grid(gg1, gg2, \n nrow = 2,\n labels = c(\"a\", \"b\"))\n\n\n\n\n\nFigure 4.8: The light response curve of the electron transport-limited net assimilation rate AJ - Rd as simulated by the FvCB model using simulated acclimated Jmax values for different light levels from the P-model (implemented by the {rpmodel} R package) . The environmental conditions used as forcing for the simulation displayed here can be seen by unfolding code.\n\n\n\n\nNote that the FvCB model, on its own, does not allow us to model the LUE term in Equation 4.1. An important additional ingredient is the stomatal conductance (\\(g_s\\)) which is relevant for determining the ratio of ambient to leaf-internal CO2 concentrations. It is described in Section 4.4.\n\n\n\n\n4.3.6 Response to temperature\nAll processes involved in photosynthesis are strongly affected by temperature. Enzymatic rates, like Rubisco carboxylation, have a temperature at which reaction rates have a maximum. As a consequence, assimilation rates also attain a maximum at a certain temperature - the temperature optimum (Topt). In contrast, dark respiration (\\(R_d\\)) monotonically increases with temperature. That is, it continues to rise as temperatures go up - without attaining a maximum. As a consequence, the decline of net assimilation rates is even faster at towards high temperatures than that of gross assimilation rates.\nThe temperature dependency of leaf CO2 assimilation rates can be measured in the field by exposing a leaf to a range of temperatures (within a relatively short period of time) and measuring assimilation rates for each temperature. When looking at such measurements, a temperature optimum of net photosynthesis is evident.\nThe Farquhar-von Caemmerer Berry model for C3 photosynthesis (see Box ‘Farquhar von Caemmerer Berry model’) and the mathematical description of temperature dependencies of factors therein (\\(V_\\mathrm{cmax}\\), \\(J_\\mathrm{max}\\), \\(K_c\\), \\(K_o\\), and \\(\\Gamma^\\ast\\), temperature dependencies not shown here) provide a basis for modelling the temperature dependency of assimilation rates. Such modelled temperature dependencies are shown in Figure 4.9.\n\n\nCode\ndf_temp <- tibble(\n temp = seq(0, 40, length.out = 100)) |> \n rowwise() |> \n mutate(gammastar = gammastar(temp, patm = 101325),\n kmm = kmm(temp, patm = 101325),\n vcmax = out_pmodel$vcmax25 * ftemp_inst_vcmax(temp, tcgrowth = 15),\n jmax = 1.7 * out_pmodel$vcmax25 * ftemp_inst_jmax(temp, tcgrowth = 15),\n rd = 0.05 * out_pmodel$vcmax25 * ftemp_inst_rd(temp)\n ) |> \n mutate(a_j = calc_aj(ci = 28.14209, \n gammastar, \n kphio = kphio, \n ppfd = ppfd, \n jmax = jmax)) |> \n mutate(a_c = calc_ac(ci = 28.14209, \n gammastar, \n kmm, \n vcmax = vcmax)) |> \n mutate(a_cr = a_c - rd, \n a_jr = a_j - rd) |> \n mutate(assim = min(a_jr, a_cr))\n\ngg1 <- df_temp |> \n pivot_longer(cols = c(gammastar, kmm), \n names_to = \"Rate\", \n values_to = \"value\") |>\n ggplot(aes(x = temp)) +\n geom_line(aes(y = value, color = Rate)) +\n geom_hline(yintercept = 0, linetype = \"dotted\") +\n labs(x = expression(paste(\"Temperature (°C)\")), \n y = expression(paste(\"Value (Pa)\"))) +\n khroma::scale_color_okabeito(\n name = \"\", \n breaks = c(\"gammastar\", \n \"kmm\"),\n labels = c(expression(paste(italic(Gamma)^\"*\")), \n expression(italic(K)))\n ) +\n theme_classic()\n\ngg2 <- df_temp |> \n pivot_longer(cols = c(vcmax, jmax, rd), \n names_to = \"Rate\", \n values_to = \"value\") |>\n ggplot(aes(x = temp)) +\n geom_line(aes(y = value, color = Rate)) +\n geom_hline(yintercept = 0, linetype = \"dotted\") +\n labs(x = expression(paste(\"Temperature (°C)\")), \n y = expression(paste(\"Rate (\", mu, \"mol m\" ^{-2},\" s\" ^{-1}, \")\"))) +\n khroma::scale_color_okabeito(\n name = \"\", \n breaks = c(\"vcmax\", \n \"jmax\", \n \"rd\"),\n labels = c(expression(paste(italic(\"V\")[cmax])), \n expression(paste(italic(\"J\")[max])), \n expression(paste(italic(\"R\")[d])))\n ) +\n theme_classic()\n\ndf_net_plot <- df_temp |> \n mutate(a_cr = a_c - rd,\n a_jr = a_j - rd) |> \n pivot_longer(cols = c(rd, a_cr, a_jr, assim), \n names_to = \"Rate\", \n values_to = \"value\")\n\ndf_gross_plot <- df_temp |> \n pivot_longer(cols = c(a_c, a_j), \n names_to = \"Rate\", \n values_to = \"value\")\n\ngg3 <- ggplot() +\n geom_line(aes(x = temp, y = value, color = Rate),\n data = df_gross_plot,\n linetype = \"dashed\") +\n geom_line(aes(x = temp, y = value, color = Rate),\n data = df_net_plot) +\n geom_hline(yintercept = 0, linetype = \"dotted\") +\n scale_color_manual(\n name = \"\",\n breaks = c(\"rd\",\n \"a_c\",\n \"a_j\",\n \"a_cr\",\n \"a_jr\",\n \"assim\"\n ),\n labels = c(expression(paste(italic(\"R\")[d])),\n expression(paste(italic(\"A\")[C])),\n expression(paste(italic(\"A\")[J])),\n expression(paste(italic(\"A\")[C] ~ - ~ italic(\"R\")[d])),\n expression(paste(italic(\"A\")[J] ~ - ~ italic(\"R\")[d])),\n expression(paste(italic(\"A\")[n]))),\n values = c(\"#CC79A7\", \"#E69F00\", \"#56B4E9\", \"#E69F00\", \"#56B4E9\", \"black\")\n ) +\n labs(x = expression(paste(\"Temperature (°C)\")), \n y = expression(paste(italic(\"A\"), \"(\", mu, \"mol m\" ^{-2},\" s\" ^{-1}, \")\")),\n color = \"Rate\",\n linetype = \"Rate\") +\n theme_classic()\n\ncowplot::plot_grid(gg1, gg2, gg3, ncol = 1)\n\n\n\n\n\nFigure 4.9: Temperature dependencies of quantities in the FvCB model. The dashed lines in the bottom panel are the gross assimilation rates AC and AJ.\n\n\n\n\n\n\n4.3.7 Adptation and acclimation of Topt\nThe temperature dependencies shown in Figure 4.9 are instantaneous responses. That is, they represent the responses to changes in temperature that evolve over short time scales - minutes to hours. Over longer time scales, the shapes of the instantaneous temperature responses change. The temperature optimum of photosynthesis (Topt) tends to be higher for plant species that grow in warm climates than for plants that can be found in cold climates (Figure 4.10 a). Such variations of Topt across different plant species reflects species’ adaptation to their growth environment which makes them perform well and compete effectively under certain environmental conditions and is related to their genes and is thus passed on from generation to generation. Topt can be considered as a plant trait (see Section 2.4).\nTopt not only varies between species growing in different climates, but can also vary within a given species and even within a given plant when it is exposed to different temperatures for a longer period (Kumarathunge et al. 2019). Given enough time, the instantaneous temperature response and Topt will shift to higher temperatures as a result of persistent exposure to warmer temperatures. Such variations in a plant trait (here Topt) within species and an individual plant is referred to as acclimation. Figure 4.10 b shows how Topt varies within different species (distinguished by color) over the course of the seasons - a demonstration of acclimation.\n\n\n\n\n\nFigure 4.10: Temperature optimum of leaf net photosynthesis at an intercellular CO2 concentration of 275 micro-mol mol-1 (ToptA275) of mature plants growing in their native environments (d), species in the field (grown at ambient growth temperatures) measured in at least two or more seasons (e). Tgrowth is the mean air temperature of the preceding 30 d. Different colours depict plant functional types: orange, tropical evergreen angiosperms (EA-Tr); light blue, arctic tundra; red, temperate deciduous angiosperms (DA-Te); blue, temperate evergreen angiosperms (EA-Te); green, boreal evergreen gymnosperms (EG-Br); purple, temperate evergreen gymnosperms (EG-Te); those in (b,c,e,f) depict different datasets. The thick black lines are: (in d) least-squares linear regression fits and linear mixed-effect model fits (in e) with random intercepts for each dataset. Error bars represent +/-1 standard error. Figure and caption text from Kumarathunge et al. (2019).\n\n\n\n\nAcclimation is relatively common to observe also for other physiological traits than Topt. For example, photosynthetic capacities (the maximum rate of Rubisco carboxylation - \\(V_\\mathrm{cmax}\\) in the FvCB model - or the maximum rate of electron transport - \\(J_\\mathrm{max}\\)) acclimate over the course of seasons (Jiang et al. 2020). Other plant traits are less plastic or not plastic at all. For example phenological strategies (e.g., deciduousness) does not acclimate. The acclimation of physiological traits is important for understanding vegetation and land carbon cycle responses to long-term trends in climate. While it may be exected that plants have a certain capacity for acclimation to a new climate, limits to acclimation must be better understood.\n\n\n\n4.3.8 C4 photosynthesis\nComing soon." + "text": "4.3 Photosynthesis\nLight use efficiency (LUE, Equation 4.1) measures the efficiency at which absorbed photons (radiation) are converted into C in the form of sugars. LUE is an ecosystem-level quantity and reflects the collective photosynthetic CO2 uptake efficiency of all leaves in the canopy. This efficiency is determined by the leaf physiology and the activity of the photosynthetic machinery. In this subsection, we dive very deep into the physiology of photosynthesis.\n\nCO2 uptake by the leaf happens by diffusion through pores at the leaf surface (stomata, Figure 4.3). The opening of stomata is dynamically regulated in response to environmental conditions (light, CO2, temperature, atmospheric humidity) and controls the conductance to CO2 diffusion. The CO2 uptake flux by diffusive transport through stomata can thus be described by Fick’s law which states that the flux is proportional to the concentration difference of CO2 inside and outside the leaf. \\[\nA = g_s(c_a - c_i)\n\\tag{4.5}\\] \\(c_a\\) is the ambient CO2 concentration (outside the leaf), and \\(c_i\\) is the CO2 concentration inside the leaf - at the chloroplast. \\(g_s\\) is the stomatal conductance. Note that we use the variable name \\(A\\) here for CO2 assimilation by photosynthesis. In constrast to the ecosystem-level variable GPP, \\(A\\) refers to the leaf-level flux.\n\n\n\n\n\nFigure 4.3: CO2 diffuses into the leaf through stomata, while water vapor diffuses out of the leaf. The water vapor diffusion out of the leaves (transpiration) is introduced in Chapter 7.\n\n\n\n\n\n\nOnce inside the leaf, CO2 diffuses across mesophyll cells to the chloroplasts - the site of photosynthetic reactions. The conductance to this diffusion step - mesophyll conductance - is often ignored for modelling photosynthesis. Reflecting this, we are referring to “leaf-internal” CO2 concentration, \\(c_i\\)” here, instead of a more correct CO2 concentration at the chloroplast.\nPhotosynthesis can be considered as a sequence of three processes that are serially connected - the three processes run one after the other, and the rate of the slowest of the three processes determines the overall process rate of photosynthesis. The following is a condensed description, based on Lambers, Chapin, and Pons (2008) and Bonan (2015).\n\n\n\n\n\nFigure 4.4: Overview of photosynthesis, distinguishing the light reactions and the Calvin cycle. Image taken https://bookdown.org/jcog196013/BS2003/photosynthesis.html.\n\n\n\n\n\n4.3.1 Light absorption at the cellular level\nLight (photons) in the photosynthetically active wavelength spectrum (400-700 nm) is absorbed by pigments - mainly chlorophyll. The absorbed energy is transported in the form of excited chlorophyll to the reaction centers of photosystem I (PSI) and photosystem II (PSII). Relevant for photosynthesis is the number of photons in the photosynthetically active spectrum, not their total energy. That’s why Equation 4.1 is expressed in units of photons, not energy (Watts). (A photon in the blue wavelength has the same effect on CO2 assimilation as a photon in the red wavelength, although it carries a higher energy). The excess energy is dissipated as heat or through other pathways.\n\n\n4.3.2 Light reactions\nIn the reaction centers, the excitation energy of the chlorophyll is used for splitting electrons from water molecules, producing oxygen (O2) as a “side-product”. The electrons are transported along the electron transport chain and are used to produce NADPH and ATP. These are called the light reactions of photosynthesis. Up to here, radiation energy has been converted into chemical energy in the form of ATP. The production of ATP consumes inorganic phosphate.\n\n\n4.3.3 Calvin cycle\nNADPH and ATP are then used for reducing CO2 (the energy-demanding reversal of oxidation) in the Calvin cycle. This step forms C3 compounds (triose-phosphates) and occurs independently of light. It is therefore commonly referred to as the “dark reactions” of photosynthesis. Rubisco (ribulose-1,5-bisphosphate carboxylase/oxygenase) is the principal enzyme involved in the Calvin cycle and the amount of Rubisco determines the capacity for the carboxylation of RuBP (Ribulose-1,5-bisphosphate). Rubisco also catalyzes the oxygenation of RuBP which consumes O2 and produces CO2 as part of photorespiration. This respiration scales with photosynthetic activity and reduces the net photosynthetic CO2 by 30-50%, depending on the relative concentrations of CO2 and O2. At very low CO2 levels, at around 30-50 ppm, the photorespiratory compensation point (\\(\\Gamma^\\ast\\)) is reached and net photosynthesis is zero. In contrast to photorespiration, dark respiration (\\(R_d\\)), which also produces CO2, arises from the decarboxylation of Rubisco and is independent of light, but proportional to the amount of Rubisco.\nReduced C in the form of sucrose or (after an additional step) starch is either consumed in the leaf during the night, or exported through the phloem and used for synthesising biomass or supplying plant-internal C storage as non-structural C (see Chapter 5).\n\n\n4.3.4 Summary\nThe chemical summary equation of photosynthesis is: \\[\nn\\mathrm{CO}_2 + 2n\\mathrm{H}_2\\mathrm{O} \\rightarrow (\\mathrm{CH}_2\\mathrm{O})_n + n\\mathrm{O}_2 + n\\mathrm{H}_2\\mathrm{O}\n\\tag{4.6}\\] A total of eight photons is consumed to assimilate one molecule of CO2. For each molecule of CO2, one molecule of O2 is produced. And for each molecule of CO2, one molecule of H2O is consumed (net). Note however, that this water consumption is not the primary reason for why plants use water. A much larger amount of water is consumed by the diffusion of water vapor from the water-saturated air inside the leaves out of the stomata. This transpiration flux is further explained in Chapter 7.\n\n\n4.3.5 Response to light and CO2\nThe three steps described above operate in series, and each step is potentially rate-limiting and responds differently to the environment. The rates of the processes are coordinated such that they are roughly equal and co-limiting for average environmental conditions to which a leaf is exposed during a day. An imbalance of rates can lead to an excess production of electrons and can cause damage to the photosynthetic apparatus. This happens, for example, when leaves are exposed to very cold temperatures and high light during a frost event, or when you move your indoor plant that has been sitting in a dark corner for years suddenly into full sunlight outdoors.\nThe response of photosynthetic CO2 assimilation (\\(A\\)) to light (PPFD) and leaf-internal CO2 (\\(c_i\\)) reflects the serial nature of how the light and dark reactions are connected. \\(A\\) saturates both in response to increasing PPFD as well as to increasing \\(c_i\\). When a leaf is exposed to increasing PPFD, \\(A\\) initially increases and eventually saturates (Figure 4.5). The slope of the initial linear increase reflects the efficiency at which photons are used for CO2 assimilation in the light reactions (the quantum yield \\(\\varphi_0\\)). Under these conditions, light, i.e. the rate of the light reactions, is limiting, not CO2 inside the leaf. Under conditions of very high light, the dark reactions of the Calvin cycle become limiting. The assimilation rate attained under saturating light is commonly referred to as \\(A_\\mathrm{sat}\\).\nThe level at which the light response of \\(A\\) saturates (\\(A_\\mathrm{sat}\\)) varies within a species and across different plant species. Variations within species arise through the acclimation of the light reaction capacities to the typical light intensities to which a leaf is exposed. Acclimation of photosynthesis evolves over time scales of weeks to months. (Thus, your indoor plant suffers because the change to high-light conditions happened to fast.) \\(A_\\mathrm{sat}\\) also varies across species, reflecting the adaptation through evolution of different plant species to the environment in which they commonly grow. A typical light adaptation to different light levels is expressed by plants that commonly grow in the shady understorey versus plants that grow in the sun-exposed upper canopy.\n\n\n\n\n\nFigure 4.5: Response of leaf photosynthesis to light and how it varies within species through acclimation to different growth environments (A) and across species through evolutionary adaptation (B). Figure from Lambers, Chapin, and Pons (2008).\n\n\n\n\nIn a similar fashion, the response of \\(A\\) to \\(c_i\\) initially increases and saturates at high \\(c_i\\). This is reflected by the so-called “A-ci curve” (Figure 4.6). Commonly, net assimilation \\(A_n = A - R_d\\) is considered when analysing A-ci curves. \\(A_n\\) is initially negative until the photorespiratory compensation point (\\(\\Gamma^\\ast\\)) is reached. Then, \\(A_n\\) increases steeply with \\(c_i\\) as it is limited by the rate of RuBP carboxylation by Rubisco. This Rubisco carboxylation-limited functional response of assimilation is commonly denoted \\(A_C\\).\nAs \\(c_i\\) increases further, \\(A\\) is no longer limited by RuBP carboxylation, but by the rate at which RuBP becomes available. This, in turn, is governed by the rate at which ATP and NADPH are produced and thus by the rate of electron transport \\(J\\). This functional response of assimilation is commonly denoted \\(A_J\\). A limiting electron transport rate may be due to limiting light or a limiting capacity of electron transport (\\(J_\\mathrm{max}\\)). A slower further increase of \\(A\\) with \\(c_i\\) in the electron transport-limited range is due to the suppression of RuBP oxygenation at high concentrations of CO2 (relative to O2). The effective assimilation rate across the full range of \\(c_i\\) is the minimum of the electron transport-limited and the RuBP carboxylation-limited rate: \\[\nA_n = \\min(A_C, A_J) - R_d\n\\tag{4.7}\\]\nThe A-ci curve (Figure 4.6) can be measured in the field and reveals the rates and efficiencies of the individual processes of the photosynthesis “chain” (light and dark reactions). These quantities are key for quantitatively describing and modeling leaf photosynthesis (see Box Farquhar-von Caemmerer-Berry model below).\n\n\n\n\n\n\nFigure 4.6: The A-ci curve. Net assimilation (An = A - Rd) is measured for different levels of leaf-internal CO2 concentrations (black dots). The functional forms of AC and AJ are fitted to the data points. The grey point indicates the co-limitation point. Figure from Duursma (2015).\n\n\n\n\n\n\n\n\n\n\nFarquhar-von Caemmerer-Berry model\n\n\n\nFollowing the Farquhar-von Caemmerer-Berry (FvCB) model for C3 photosynthesis (Farquhar, Caemmerer, and Berry 1980), the RuBP carboxylation-limited assimilation rate \\(A_C\\) can be described as \\[\nA_C = V_\\mathrm{cmax} \\frac{c_i - \\Gamma^\\ast}{c_i + K} \\;,\n\\tag{4.8}\\] where \\(K\\) is the effective Michaelis-Menten coefficient for \\(A_C\\), considering the balance of carboxylation and oxygenation by Rubisco. It depends on the partial pressure of oxygen (\\(p\\mathrm{O}_2\\)). \\[\nK = K_c \\left(1 + \\frac{p\\mathrm{O}_2}{K_o} \\right)\n\\] \\(V_\\mathrm{cmax}\\), \\(K_c\\), \\(K_o\\), and \\(\\Gamma^\\ast\\) all have a temperature dependency. In addition, \\(\\Gamma^\\ast\\) is proportional to atmospheric pressure. These dependencies are shown in Section 4.3.6 and are described in full detail in Stocker et al. (2020).\nThe electron transport-limited assimilation rate \\(A_J\\) can be described as \\[\nA_J = \\frac{J}{4} \\cdot \\frac{c_i - \\Gamma^\\ast}{c_i + 2 \\Gamma^\\ast}\\;.\n\\tag{4.9}\\] The electron transport rate \\(J\\) is described by a saturating function that increases with absorbed light \\(I_\\mathrm{abs}\\) up to a maximum rate \\(J_\\mathrm{max}\\) \\[\nJ = \\frac{4\\varphi_0 I_\\mathrm{abs}}{\\sqrt{1+\\left(\\frac{4\\varphi_0 I_\\mathrm{abs}}{J_\\mathrm{max}}\\right)^2}}\n\\tag{4.10}\\]\nTogether, Equation 4.8 and Equation 4.9 describe the combined effect of \\(c_i\\), (leaf) temperature, the absorbed photon flux density, and atmospheric pressure on leaf-level CO2 assimilation.\nWith the mathematical description of \\(A_C\\) and \\(A_J\\) and their dependency on light and CO2 following the FvCB model, A-ci and the A vs. PPFD curves, as shown for measurements in Figure 4.5 and Figure 4.6, can thereby be modeled.\n\n\nCode\nlibrary(rpmodel)\nlibrary(dplyr)\nlibrary(tidyr)\nlibrary(ggplot2)\n\n# modified seq() function to get a logarithmically spaced sequence\nlseq <- function(from=1, to=100000, length.out=6) {\n exp(seq(log(from), log(to), length.out = length.out))\n}\n\n# Set model parameters (constants)\n# see Stocker et al., 2020 GMD for a description\nbeta <- 146 # unit cost ratio a/b\nc_cost <- 0.41 # marginal cost of Jmax\ngamma <- 0.105 # unit cost ratio c/b\nkphio <- 0.085 # quantum yield efficiency\nc_molmass <- 12.0107 # molar mass, g / mol\n\n# Define environmental conditions\ntc <- 15 # temperature, deg C\nppfd <- 500 # micro-mol/m2/s\nvpd <- 300 # Pa\nco2 <- 400 # ppm\nelv <- 0 # m.a.s.l.\nfapar <- 1 # fraction\npatm <- 101325 # Pa\n\n# get photosynthesis parameters gammastar, vcmax, jmax from p-model\n# this assumes vcmax and jmax to be optimally acclimated/adapted to\n# the specified environmental conditions and considers the temperature\n# and atmospheric-pressure dependence of all parameters.\nout_pmodel <- rpmodel(\n tc = tc,\n vpd = vpd,\n co2 = co2,\n elv = elv,\n kphio = kphio,\n beta = beta,\n fapar = fapar,\n ppfd = ppfd,\n method_optci = \"prentice14\",\n method_jmaxlim = \"wang17\",\n do_ftemp_kphio = FALSE\n )\n\n# electron transport-limited assimilation rate as a function of CO2 partial pressure\ncalc_aj <- function(ci, gammastar, kphio, ppfd, jmax){\n kphio * ppfd * (ci - gammastar)/(ci + 2 * gammastar) * 1/sqrt(1+((4 * kphio * ppfd)/jmax)^2)\n}\n\n# RuBP carboxylation-limited assimilation rate as a function of CO2 partial pressure\ncalc_ac <- function(ci, gammastar, kmm, vcmax){\n vcmax * (ci - gammastar)/(ci + kmm)\n}\n\n# assimilation rate given stomatal conductance and leaf-internal \n# CO2 partial pressure\ncalc_a_gs <- function(ci, gs, ca){\n gs * (ca - ci)\n}\n\n# conversion of CO2 concentration in ppm to partial pressure in Pa\nco2_to_ca <- function( co2, patm ){\n ( 1.0e-6 ) * co2 * patm\n}\n\ndf_ci <- tibble(\n ci = seq(0, 1000, length.out = 100)) |> \n rowwise() |> \n mutate(ci_pa = co2_to_ca(ci, patm = patm)) |> \n mutate(a_j = calc_aj(ci_pa, \n out_pmodel$gammastar, \n kphio = kphio, \n ppfd = ppfd, \n jmax = out_pmodel$jmax)) |> \n mutate(a_c = calc_ac(ci_pa, \n out_pmodel$gammastar, \n out_pmodel$kmm, \n vcmax = out_pmodel$vcmax)) |>\n mutate(a_act = min(a_j, a_c)) |> \n mutate(a_gs = calc_a_gs(ci_pa, \n gs = out_pmodel$gs, \n ca = out_pmodel$ca))\n \ndf_ci |> \n pivot_longer(cols = c(\n a_j, \n a_c\n # a_gs\n ), \n names_to = \"Rate\", \n values_to = \"a_\") |>\n ggplot(aes(x = ci)) +\n geom_line(aes(y = a_, color = Rate)) +\n geom_line(aes(y = a_act)) +\n xlim(00, 1000) + \n # ylim(-20, 80) +\n geom_hline(yintercept = 0, linetype = \"dotted\") +\n geom_vline(xintercept = 0, linetype = \"dotted\") +\n geom_vline(xintercept = (out_pmodel$gammastar/(1.0e-6 * patm)), linetype = \"dotted\") +\n labs(x = expression(paste(italic(\"c\")[i], \" (ppm)\")), \n y = expression(paste(italic(\"A\"), \" (\", mu, \"mol m\" ^{-2},\" s\" ^{-1}, \")\"))) +\n scale_color_manual(\n name = \"\",\n breaks = c(\n # \"a_gs\",\n \"a_j\",\n \"a_c\"\n ),\n labels = c(\n # expression(paste(italic(\"A\")[gs])),\n expression(paste(italic(\"A\")[J])),\n expression(paste(italic(\"A\")[C]))\n ),\n values = c( \n # \"#009E73\", \n \"#56B4E9\", \n \"#E69F00\"\n )) +\n theme_classic()\n\n\n\n\n\nFigure 4.7: The A-ci curve as simulated by the FvCB model. Ags is shown here as the dependency of A on stomatal conductance following Equation 4.5 for a given gs. The fact that AC, AJ, and Ags intersect in one point does not follow from the FvCB model, but is simulated here based on a model of eco-evolutionary optimality (P-model Stocker et al. (2020), implemented by the {rpmodel} R package) which predicts that photosynthetic capacities are acclimated such that a leaf operates close to the intersection point of AC and and AJ. The point at which curves intersect with the x-axis (y = 0) is the photorespiratory compensation point. The environmental conditions used as forcing for the simulation displayed here can be seen by unfolding code.\n\n\n\n\nFigure 4.8 shows the light response curve of \\(A_J - R_d\\) following the FvCB model. The response is shown for leaves acclimated to different levels of light, thus having different values for \\(J_\\mathrm{max}\\). Because acclimation to light also involves a change in the Rubisco content of leaves and thus \\(V_\\mathrm{cmax}\\), “high-light leaves” also have higher dark respiration rates. Therefore, under low light conditions, leaves acclimated to low light have higher net assimilation rates than leaves acclimated to high light. This is illustrated by Figure 4.8 a.\n\n\nCode\nlibrary(rpmodel)\nlibrary(dplyr)\nlibrary(tidyr)\nlibrary(ggplot2)\n\n# modified seq() function to get a logarithmically spaced sequence\nlseq <- function(from=1, to=100000, length.out=6) {\n exp(seq(log(from), log(to), length.out = length.out))\n}\n\n# Set model parameters (constants)\n# see Stocker et al., 2020 GMD for a description\nbeta <- 146 # unit cost ratio a/b\nc_cost <- 0.41 # marginal cost of Jmax\ngamma <- 0.105 # unit cost ratio c/b\nkphio <- 0.085 # quantum yield efficiency\nc_molmass <- 12.0107 # molar mass, g / mol\n\n# Define environmental conditions\ntc <- 15 # temperature, deg C\nppfd <- 500 # micro-mol/m2/s\nvpd <- 300 # Pa\nco2 <- 400 # ppm\nelv <- 0 # m.a.s.l.\nfapar <- 1 # fraction\npatm <- 101325 # Pa\n\n# get photosynthesis parameters gammastar, vcmax, jmax from p-model\n# this assumes vcmax and jmax to be optimally acclimated/adapted to\n# the specified environmental conditions and considers the temperature\n# and atmospheric-pressure dependence of all parameters.\n\n# first for low light\nout_pmodel_lo <- rpmodel(\n tc = tc,\n vpd = vpd,\n co2 = co2,\n elv = elv,\n kphio = kphio,\n beta = beta,\n fapar = fapar,\n ppfd = ppfd*0.5,\n method_optci = \"prentice14\",\n method_jmaxlim = \"wang17\",\n do_ftemp_kphio = FALSE\n )\n\n# medium light\nout_pmodel_me <- rpmodel(\n tc = tc,\n vpd = vpd,\n co2 = co2,\n elv = elv,\n kphio = kphio,\n beta = beta,\n fapar = fapar,\n ppfd = ppfd,\n method_optci = \"prentice14\",\n method_jmaxlim = \"wang17\",\n do_ftemp_kphio = FALSE\n )\n\n# high light\nout_pmodel_hi <- rpmodel(\n tc = tc,\n vpd = vpd,\n co2 = co2,\n elv = elv,\n kphio = kphio,\n beta = beta,\n fapar = fapar,\n ppfd = ppfd*2,\n method_optci = \"prentice14\",\n method_jmaxlim = \"wang17\",\n do_ftemp_kphio = FALSE\n )\n\n# electron transport-limited assimilation rate as a function of CO2 partial pressure\ncalc_aj <- function(ci, gammastar, kphio, ppfd, jmax){\n kphio * ppfd * (ci - gammastar)/(ci + 2 * gammastar) * 1/sqrt(1+((4 * kphio * ppfd)/jmax)^2)\n}\n\n# RuBP carboxylation-limited assimilation rate as a function of CO2 partial pressure\ncalc_ac <- function(ci, gammastar, kmm, vcmax){\n vcmax * (ci - gammastar)/(ci + kmm)\n}\n\n# assimilation rate given stomatal conductance and leaf-internal \n# CO2 partial pressure\ncalc_a_gs <- function(ci, gs, ca){\n gs * (ca - ci)\n}\n\n# conversion of CO2 concentration in ppm to partial pressure in Pa\nco2_to_ca <- function( co2, patm ){\n ( 1.0e-6 ) * co2 * patm\n}\n\ndf_ppfd <- tibble(\n ppfd = seq(0, 2000, length.out = 100)) |> \n rowwise() |> \n mutate(a_j_lo = calc_aj(co2_to_ca(400, patm = patm), \n out_pmodel_lo$gammastar, \n kphio = kphio, \n ppfd = ppfd, \n jmax = out_pmodel_lo$jmax * 0.5) - \n out_pmodel_lo$rd) |> \n mutate(a_j_me = calc_aj(co2_to_ca(400, patm = patm), \n out_pmodel_me$gammastar, \n kphio = kphio, \n ppfd = ppfd, \n jmax = out_pmodel_me$jmax) - \n out_pmodel_me$rd) |> \n mutate(a_j_hi = calc_aj(co2_to_ca(400, patm = patm), \n out_pmodel_hi$gammastar, \n kphio = kphio, \n ppfd = ppfd, \n jmax = out_pmodel_hi$jmax * 2) - \n out_pmodel_hi$rd)\n\ngg <- df_ppfd |> \n pivot_longer(cols = c(a_j_lo, a_j_me, a_j_hi), \n names_to = \"Rate\", \n values_to = \"a_\") |>\n ggplot(aes(x = ppfd)) +\n geom_line(aes(y = a_, color = Rate)) +\n geom_hline(yintercept = 0, linetype = \"dotted\") +\n labs(x = expression(paste(\"PPFD (\", mu, \"mol m\"^{-2}, \"s\"^{-1}, \")\")), \n y = expression(paste(italic(\"A\")[J] - italic(R)[d], \" (\", mu, \"mol m\" ^{-2},\" s\" ^{-1}, \")\"))) +\n scale_color_manual(\n name = \"\",\n breaks = c(\"a_j_lo\",\n \"a_j_me\",\n \"a_j_hi\"\n ),\n labels = c(expression(paste(\"Low light\")),\n expression(paste(\"Medium light\")),\n expression(paste(\"High light\"))),\n values = c( \"#009E73\", \"#56B4E9\", \"#E69F00\")) +\n theme_classic()\n\ngg1 <- gg +\n xlim(0, 250) +\n ylim(NA, 20)\n\ngg2 <- gg +\n xlim(0, 2000)\n\ncowplot::plot_grid(gg1, gg2, \n nrow = 2,\n labels = c(\"a\", \"b\"))\n\n\n\n\n\nFigure 4.8: The light response curve of the electron transport-limited net assimilation rate AJ - Rd as simulated by the FvCB model using simulated acclimated Jmax values for different light levels from the P-model (implemented by the {rpmodel} R package) . The environmental conditions used as forcing for the simulation displayed here can be seen by unfolding code.\n\n\n\n\nNote that the FvCB model, on its own, does not allow us to model the LUE term in Equation 4.1. An important additional ingredient is the stomatal conductance (\\(g_s\\)) which is relevant for determining the ratio of ambient to leaf-internal CO2 concentrations. It is described in Section 4.4.\n\n\n\n\n4.3.6 Response to temperature\nAll processes involved in photosynthesis are strongly affected by temperature. Enzymatic rates, like Rubisco carboxylation, have a temperature at which reaction rates have a maximum. As a consequence, assimilation rates also attain a maximum at a certain temperature - the temperature optimum (Topt). In contrast, dark respiration (\\(R_d\\)) monotonically increases with temperature. That is, it continues to rise as temperatures go up - without attaining a maximum. As a consequence, the decline of net assimilation rates is even faster towards high temperatures than that of gross assimilation rates.\nThe temperature dependency of leaf CO2 assimilation rates can be measured in the field by exposing a leaf to a range of temperatures (within a relatively short period of time) and measuring assimilation rates for each temperature. When looking at such measurements, a temperature optimum of net photosynthesis is evident.\nThe Farquhar-von Caemmerer Berry model for C3 photosynthesis (see Box ‘Farquhar von Caemmerer Berry model’) and the mathematical description of temperature dependencies of factors therein (\\(V_\\mathrm{cmax}\\), \\(J_\\mathrm{max}\\), \\(K_c\\), \\(K_o\\), and \\(\\Gamma^\\ast\\), temperature dependencies not shown here) provide a basis for modelling the temperature dependency of assimilation rates. Such modelled temperature dependencies are shown in Figure 4.9. \n\n\nCode\ndf_temp <- tibble(\n temp = seq(0, 40, length.out = 100)) |> \n rowwise() |> \n mutate(gammastar = gammastar(temp, patm = 101325),\n kmm = kmm(temp, patm = 101325),\n vcmax = out_pmodel$vcmax25 * ftemp_inst_vcmax(temp, tcgrowth = 15),\n jmax = 1.7 * out_pmodel$vcmax25 * ftemp_inst_jmax(temp, tcgrowth = 15),\n rd = 0.05 * out_pmodel$vcmax25 * ftemp_inst_rd(temp)\n ) |> \n mutate(a_j = calc_aj(ci = 28.14209, \n gammastar, \n kphio = kphio, \n ppfd = ppfd, \n jmax = jmax)) |> \n mutate(a_c = calc_ac(ci = 28.14209, \n gammastar, \n kmm, \n vcmax = vcmax)) |> \n mutate(a_cr = a_c - rd, \n a_jr = a_j - rd) |> \n mutate(assim = min(a_jr, a_cr))\n\ngg1 <- df_temp |> \n pivot_longer(cols = c(gammastar, kmm), \n names_to = \"Rate\", \n values_to = \"value\") |>\n ggplot(aes(x = temp)) +\n geom_line(aes(y = value, color = Rate)) +\n geom_hline(yintercept = 0, linetype = \"dotted\") +\n labs(x = expression(paste(\"Temperature (°C)\")), \n y = expression(paste(\"Value (Pa)\"))) +\n khroma::scale_color_okabeito(\n name = \"\", \n breaks = c(\"gammastar\", \n \"kmm\"),\n labels = c(expression(paste(italic(Gamma)^\"*\")), \n expression(italic(K)))\n ) +\n theme_classic()\n\ngg2 <- df_temp |> \n pivot_longer(cols = c(vcmax, jmax, rd), \n names_to = \"Rate\", \n values_to = \"value\") |>\n ggplot(aes(x = temp)) +\n geom_line(aes(y = value, color = Rate)) +\n geom_hline(yintercept = 0, linetype = \"dotted\") +\n labs(x = expression(paste(\"Temperature (°C)\")), \n y = expression(paste(\"Rate (\", mu, \"mol m\" ^{-2},\" s\" ^{-1}, \")\"))) +\n khroma::scale_color_okabeito(\n name = \"\", \n breaks = c(\"vcmax\", \n \"jmax\", \n \"rd\"),\n labels = c(expression(paste(italic(\"V\")[cmax])), \n expression(paste(italic(\"J\")[max])), \n expression(paste(italic(\"R\")[d])))\n ) +\n theme_classic()\n\ndf_net_plot <- df_temp |> \n mutate(a_cr = a_c - rd,\n a_jr = a_j - rd) |> \n pivot_longer(cols = c(rd, a_cr, a_jr, assim), \n names_to = \"Rate\", \n values_to = \"value\")\n\ndf_gross_plot <- df_temp |> \n pivot_longer(cols = c(a_c, a_j), \n names_to = \"Rate\", \n values_to = \"value\")\n\ngg3 <- ggplot() +\n geom_line(aes(x = temp, y = value, color = Rate),\n data = df_gross_plot,\n linetype = \"dashed\") +\n geom_line(aes(x = temp, y = value, color = Rate),\n data = df_net_plot) +\n geom_hline(yintercept = 0, linetype = \"dotted\") +\n scale_color_manual(\n name = \"\",\n breaks = c(\"rd\",\n \"a_c\",\n \"a_j\",\n \"a_cr\",\n \"a_jr\",\n \"assim\"\n ),\n labels = c(expression(paste(italic(\"R\")[d])),\n expression(paste(italic(\"A\")[C])),\n expression(paste(italic(\"A\")[J])),\n expression(paste(italic(\"A\")[C] ~ - ~ italic(\"R\")[d])),\n expression(paste(italic(\"A\")[J] ~ - ~ italic(\"R\")[d])),\n expression(paste(italic(\"A\")[n]))),\n values = c(\"#CC79A7\", \"#E69F00\", \"#56B4E9\", \"#E69F00\", \"#56B4E9\", \"black\")\n ) +\n labs(x = expression(paste(\"Temperature (°C)\")), \n y = expression(paste(italic(\"A\"), \"(\", mu, \"mol m\" ^{-2},\" s\" ^{-1}, \")\")),\n color = \"Rate\",\n linetype = \"Rate\") +\n theme_classic()\n\ncowplot::plot_grid(gg1, gg2, gg3, ncol = 1)\n\n\n\n\n\nFigure 4.9: Temperature dependencies of quantities in the FvCB model. The dashed lines in the bottom panel are the gross assimilation rates AC and AJ.\n\n\n\n\n\n\n4.3.7 Adaptation and acclimation of Topt\nThe temperature dependencies shown in Figure 4.9 are instantaneous responses. That is, they represent the responses to changes in temperature that evolve over short time scales - minutes to hours. Over longer time scales, the shapes of the instantaneous temperature responses change. The temperature optimum of photosynthesis (Topt) tends to be higher for plant species that grow in warm climates than for plants that can be found in cold climates (Figure 4.10 a). Such variations of Topt across different plant species reflect species’ adaptation to their growth environment which makes them perform well and compete effectively under certain environmental conditions and is related to their genes and is thus passed on from generation to generation. Topt can be considered as a plant trait (see Section 2.4).\nTopt not only varies between species growing in different climates, but can also vary within a given species and even within a given plant when it is exposed to different temperatures for a longer period (Kumarathunge et al. 2019). Given enough time, the instantaneous temperature response and Topt will shift to higher temperatures as a result of persistent exposure to warmer temperatures. Such variations in a plant trait (here Topt) within species and an individual plant is referred to as acclimation. Figure 4.10 b shows how Topt varies within different species (distinguished by color) over the course of the seasons - a demonstration of acclimation.\n\n\n\n\n\nFigure 4.10: Temperature optimum of leaf net photosynthesis at an intercellular CO2 concentration of 275 micro-mol mol-1 (ToptA275) of mature plants growing in their native environments (d), species in the field (grown at ambient growth temperatures) measured in at least two or more seasons (e). Tgrowth is the mean air temperature of the preceding 30 d. Different colours depict plant functional types: orange, tropical evergreen angiosperms (EA-Tr); light blue, arctic tundra; red, temperate deciduous angiosperms (DA-Te); blue, temperate evergreen angiosperms (EA-Te); green, boreal evergreen gymnosperms (EG-Br); purple, temperate evergreen gymnosperms (EG-Te); those in (b,c,e,f) depict different datasets. The thick black lines are: (in d) least-squares linear regression fits and linear mixed-effect model fits (in e) with random intercepts for each dataset. Error bars represent +/-1 standard error. Figure and caption text from Kumarathunge et al. (2019).\n\n\n\n\nAcclimation is relatively common to observe also for other physiological traits than Topt. For example, photosynthetic capacities (the maximum rate of Rubisco carboxylation - \\(V_\\mathrm{cmax}\\) in the FvCB model - or the maximum rate of electron transport - \\(J_\\mathrm{max}\\)) acclimate over the course of seasons (Jiang et al. 2020). Other plant traits are less plastic or not plastic at all. For example, phenological strategies (e.g., deciduousness) do not acclimate. The acclimation of physiological traits is important for understanding vegetation and land carbon cycle responses to long-term trends in climate. While it may be expected that plants have a certain capacity for acclimation to a new climate, limits to acclimation must be better understood.\n\n\n\n4.3.8 C4 photosynthesis\nComing soon." }, { "objectID": "gpp.html#sec-transpiration", "href": "gpp.html#sec-transpiration", "title": "4  Gross primary production and photosynthesis", "section": "4.4 Transpiration and leaf water-carbon coupling", - "text": "4.4 Transpiration and leaf water-carbon coupling\nThe opening of stomata is highly sensitive to environmental factors and the CO2 assimilation rate feeds back to stomatal opening. By opening and closing stomata, plants regulate the conductance to CO2 diffusion from the ambient air into the leaves and to the photosynthesis reaction sites. Simultaneously, when stomata are open, water vapour diffuses out of the leaf - transpiration. This link between CO2 and water loss is at the core of stomatal regulation to balance C uptake and desiccation.\nThe diffusive supply of CO2 to the photosynthetic reaction sites is determined by a series of conductances. The description of the diffusive CO2 uptake in Equation 4.5 resolves this as a single conductance. However, stomatal conductance is only one chain in this series. More realistically, the leaf boundary layer conductance and the mesophyll conductance are treated separately from the stomatal conductance. However, because the leaf boundary layer conductance is much larger than the stomatal conductance, it is not limiting. Furthermore, actively regulated plant physiological responses to the environment arise through the stomatal conductance \\(g_s\\). As described in Section 4.3, mesophyll conductance is often ignored due to practical limitations for separating it from stomatal conductance in measurements and due to very poorly known dependencies to the environment. Hence, we focus on \\(g_s\\) here and describe the diffusive CO2 supply to photosynthesis by Equation 4.5.\nThe diffusive water vapour flux out of the leaf - transpiration - is driven by the difference of water vapour pressure in the leaf-interior air spaces (\\(e_i\\)) and the the water vapour pressure at the leaf surface (\\(e_s\\)). Their difference is commonly referred to as the vapour pressure deficit (VPD), here denoted as \\(D = e_s - e_i\\). Leaf-interior air spaces are water vapour-saturated, while the surrounding air is not. Fick’s law predicts that a diffusive flux occurs in presence of a concentration difference, hence transpiration can be described as \\[\nE = 1.6 \\; g_s \\; D\n\\tag{4.11}\\] The factor 1.6 arises due to the lower diffusivity of CO2 compared with H2O. Hence, \\(g_s\\) has to be understood as a conductance to CO2 diffusion (mol CO2 m-2 s-1). Note that \\(g_s\\) regulates both transpiration (Equation 4.11) and assimilation (Equation 4.5) at the leaf-level. A tight coupling between water and carbon fluxes at the leaf-level follows from the physical principle of diffusion.\nWater loss through transpiration poses risks and incurs costs for a plant. The diffusive water vapour flux through stomata has to be maintained by root water uptake from the soil and transport along the xylem in the plant. When the water content in the rooting zone declines, it becomes increasingly hard for plants to extract water from the soil - they have to “suck” out the water with a increasingly negative water potential - a negative pressure. The hydraulic relationships of water transport along the soil-plant-atmosphere continuum will be introduced later. What matters here is that such negative water potentials along the water transport pathway are dangerous for the plant and can lead to lethal desiccation of cells, leaves, branches, or entire plants.\nAvoidance of dangerous desiccation is enabled by responses at the level of leaves and the plant which operate at a range of time scales. At time scales of seconds to minutes and at the level of a leaf, stomatal conductance is reduced in response to dry air and dry soil conditions. At time scales of weeks to months, or even years, the the leaf area of a plant may decline under dry conditions. At even longer time scales (albeit this time scale is subject to large unknowns and active research), plants are genetically adapted (or may acclimate within their lifetime) to dry conditions by resistant water transport (resistant xylem) and effective water uptake organs (deeper roots).\nObviously, such adaptations and the largely instantaneous stomatal response incurs a cost - the opportunity cost of reduced CO2 assimilation when stomatal conductance is reduced and the construction cost of building water-stress adapted organs. Hence, plants always have to balance carbon uptake and water loss and a tight carbon-water coupling at the level of plants, and ecosystems arises from these leaf-level processes.\n\n4.4.1 Water use efficiency\nThe trade-off between transpiration and assimilation can be measured by considering their ratio by combining Equation 4.5 and Equation 4.11 to define the instantaneous water-use efficiency: \\[\n\\frac{A_n}{E} = \\frac{c_a(1 - \\chi)}{1.6\\;D}\\;,\n\\tag{4.12}\\] where \\(\\chi = c_i/c_a\\). The instantaneous water-use efficiency is proportional to \\(D^{-1}\\). In other words, the drier the air, the more transpiration per unit net CO2 assimilation a leaf “suffers”. This demonstrates the strong effect of atmospheric dryness on the water-carbon trade-off. To remove the effect of vapour pressure deficit (\\(D\\)) on transpiration and focus on the biological component of the water-carbon trade-off, the intrinsic water-use efficiency (iWUE) is defined by relating net assimilation to stomatal conductance: \\[\n\\frac{A_n}{g_s} = \\frac{c_a}{1.6}(1 - \\chi)\n\\tag{4.13}\\] Note that Equation 4.12 and Equation 4.13 are written as being proportional to \\(c_a(1-\\chi)\\). Of course, this term is mathematically equivalent to \\((c_a - c_i)\\). However, there is a reason for expressing it this way. First, it reflects the direct influence of \\(c_a\\) ambient (atmospheric) CO2 concentration on the water-carbon trade-off - less water is lost for a given amount of C assimilation under elevated CO2. Second, observations suggest that \\(\\chi\\) is regulated by plants to remain relatively constant under a wide range of CO2 levels (Ainsworth and Long 2005) and Figure 4.11. The near constancy of \\(\\chi\\) is also reflected by the observation that \\(A_n\\) and \\(g_s\\) vary in near proportion across a wide range of light levels (Bonan 2015).\n\n\n\n\n\nFigure 4.11: Constancy of leaf-internal to ambient CO2. (a) Relationship between net photosynthesis (An) and stomatal conductance (gs) of one species (Jack pine) over a range of light conditions. A linear relationship is reflective of a constant ci:ca. Figure from Bonan (2015). (b) Response of multiple photosynthesis-related variables to elevated CO2 from free-air carbon dioxide enrichment experiments. Figure from Ainsworth and Long (2005). ci:ca\n\n\n\n\n\n\n4.4.2 Isotopic fractionation\nComing soon.\n\n\n4.4.3 Stomatal regulation\nThe closing of stomates and the reduction of stomatal conductance \\(g_s\\) under dry conditions prevents plants from dangerous desiccation. However, a reduced \\(g_s\\) also leads to a reduction in CO2 diffusion into leaves and thus a reduction of photosynthetic CO2 assimilation. Hence, plants have to balance a trade-off between carbon gain and the risk of desiccation. A complete stomatal closure under moderately dry conditions (low soil moisture, high VPD) may be safe in terms of desiccation avoidance but comes at an excessive cost in terms of foregone CO2 uptake (and similarly vice-versa). An optimal strategy must lie somewhere in between these extreme strategies.\nObservations of leaf and ecosystem fluxes CO2 and water vapour fluxes document how stomatal conductance responds to increasing VPD and decreasing soil moisture. Figure 4.12 shows this for measurements taken at the ecosystem-level, quantifying the canopy stomatal conductance (denoted by an uppercase \\(G_s\\)), representative for the collective behaviour of all leaves in the canopy. Three important aspects of this relationship stand out. First, \\(G_s\\) declines in response to VPD in a non-linear fashion (high sensitivity to VPD at low VPD, lower sensitivity towards higher VPD). Second, there is an interaction between the effect of VPD and soil moisture. Under conditions of dry soils, \\(G_s\\) is reduced compared to wet soils, given the same VPD. Third, at the most moist site (Figure 4.12 a), \\(G_s\\) under moist conditions (moist soils, low VPD) is highest but declines most rapidly with VPD.\n\n\n\n\n\nFigure 4.12: Response of canopy conductance (ecosystem-level aggregate stomatal conductance) to soil and air drying at four different sites (a-d) that differ in average aridity. Soil moisture levels are represented by colors of circles. DI in each panel’s title is the site’s dryness index calculated as the ratio of potential evapotranspiration over precipitation. Figure from Novick et al. (2016).\n\n\n\n\nA simple empirical model for the \\(G_s\\) response to VPD (Oren et al. 2001) is given by \\[\nG_s = G_{s,\\mathrm{ref}} \\left(1 - m \\ln D \\right)\\;.\n\\] Here, \\(G_{s,\\mathrm{ref}}\\) is a reference canopy conductance, \\(D\\) is VPD, and \\(m\\) is a stomatal sensitivity parameter. The data shown in Figure 4.12 indicate that the sensitivity parameter \\(m\\) is not a constant, but decreases with drying soils and tends to be lower at dry sites than at moist sites investigated by Novick et al. (2016).\n\n\n\n\n\n\nStomatal optimization models\n\n\n\n\n\nThe aspect that plants regulate stomatal conductance to balance the trade-off between carbon gain and water loss lends itself to modelling the stomatal response considering optimality principles. Indeed, there is empirical evidence that optimality models are a good representation of how stomata are regulated. Following this notion, it can be assumed that stomatal conductance is optimised such that the net between the carbon gain by increasing stomatal conductance and the carbon cost by the resulting increased transpiration and is maximized.\n\\[\nA - aE - bV_\\mathrm{cmax} = \\arg \\max\n\\tag{4.14}\\]\nOver time scales of days to weeks, \\(V_\\mathrm{cmax}\\) in the FvCB model (see box above) is coordinated with stomatal conductance (Joshi et al. 2022). The simultaneous effects of \\(V_\\mathrm{cmax}\\) and \\(g_s\\) are reflected by \\(\\chi\\). Therefore, Equation 4.14 can be expressed with respect to optimising \\(\\chi\\). Maximising a function is equivalent to finding the point where its first derivative (here with respect to \\(\\chi\\)) is zero. (Prentice et al. 2014) formulated such a similar (but not strictly equivalent) optimality criterion as \\[\n\\frac{\\partial (E/A)}{\\partial \\chi} + \\beta \\frac{\\partial (V_\\mathrm{cmax}/A)}{\\partial \\chi} = 0 \\;.\n\\] \\(E/A\\) is the unit cost of transpiration. \\(V_\\mathrm{cmax}/A\\) is the unit cost of carboxylation. Their sum is minimized here with respect to \\(\\chi\\). \\(\\beta\\) is the unit cost ratio. From this, the response of the stomatal conductance to \\(D\\) and \\(A\\) can be derived (not shown here, but in Stocker et al. (2020)) as \\[\ng_s = \\left( 1 + \\frac{g_1}{\\sqrt{D}} \\right) \\frac{A}{c_a - \\Gamma^\\ast}\n\\] \\(g_1\\) is a stomatal sensitivity parameter. Similar results are obtained with a related but not identical optimality criterion (Medlyn et al. 2011)." + "text": "4.4 Transpiration and leaf water-carbon coupling\nThe opening of stomata is highly sensitive to environmental factors, and the CO2 assimilation rate feeds back to stomatal opening. By opening and closing stomata, plants regulate the conductance to CO2 diffusion from the ambient air into the leaves and to the photosynthesis reaction sites. Simultaneously, when stomata are open, water vapor diffuses out of the leaf - transpiration. This link between CO2 and water loss is at the core of stomatal regulation to balance C uptake and desiccation.\nThe diffusive supply of CO2 to the photosynthetic reaction sites is determined by a series of conductances. The description of the diffusive CO2 uptake in Equation 4.5 resolves this as a single conductance. However, stomatal conductance is only one chain in this series. More realistically, the leaf boundary layer conductance and the mesophyll conductance are treated separately from the stomatal conductance. However, because the leaf boundary layer conductance is much larger than the stomatal conductance, it is not limiting. Furthermore, actively regulated plant physiological responses to the environment arise through the stomatal conductance \\(g_s\\). As described in Section 4.3, mesophyll conductance is often ignored due to practical limitations for separating it from stomatal conductance in measurements and due to very poorly known dependencies to the environment. Hence, we focus on \\(g_s\\) here and describe the diffusive CO2 supply to photosynthesis by Equation 4.5.\nThe diffusive water vapor flux out of the leaf - transpiration - is driven by the difference of water vapor pressure in the leaf-interior air spaces (\\(e_i\\)) and the the water vapor pressure at the leaf surface (\\(e_s\\)). Their difference is commonly referred to as the vapor pressure deficit (VPD), here denoted as \\(D = e_s - e_i\\). Leaf-interior air spaces are water vapor-saturated, while the surrounding air is not. Fick’s law predicts that a diffusive flux occurs in presence of a concentration difference, hence transpiration can be described as \\[\nE = 1.6 \\; g_s \\; D\n\\tag{4.11}\\] The factor 1.6 arises due to the lower diffusivity of CO2 compared with H2O. Hence, \\(g_s\\) has to be understood as a conductance to CO2 diffusion (mol CO2 m-2 s-1). Note that \\(g_s\\) regulates both transpiration (Equation 4.11) and assimilation (Equation 4.5) at the leaf-level. A tight coupling between water and carbon fluxes at the leaf-level follows from the physical principle of diffusion.\nWater loss through transpiration poses risks and incurs costs for a plant. The diffusive water vapor flux through stomata has to be maintained by root water uptake from the soil and transport along the xylem in the plant. When the water content in the rooting zone declines, it becomes increasingly hard for plants to extract water from the soil - they have to “suck” out the water with a increasingly negative water potential - a negative pressure. The hydraulic relationships of water transport along the soil-plant-atmosphere continuum will be introduced later. What matters here is that such negative water potentials along the water transport pathway are dangerous for the plant and can lead to lethal desiccation of cells, leaves, branches, or entire plants.\nAvoidance of dangerous desiccation is enabled by responses at the level of leaves and the plant which operate at a range of time scales. At time scales of seconds to minutes and at the level of a leaf, stomatal conductance is reduced in response to dry air and dry soil conditions. At time scales of weeks to months, or even years, the leaf area of a plant may decline under dry conditions. At even longer time scales (albeit this time scale is subject to large unknowns and active research), plants are genetically adapted (or may acclimate within their lifetime) to dry conditions by resistant water transport (resistant xylem) and effective water uptake organs (deeper roots).\nObviously, such adaptations and the largely instantaneous stomatal response incurs a cost - the opportunity cost of reduced CO2 assimilation when stomatal conductance is reduced and the construction cost of building water-stress adapted organs. Hence, plants always have to balance carbon uptake and water loss and a tight carbon-water coupling at the level of plants, and ecosystems arises from these leaf-level processes.\n\n4.4.1 Water use efficiency\nThe trade-off between transpiration and assimilation can be measured by considering their ratio by combining Equation 4.5 and Equation 4.11 to define the instantaneous water-use efficiency: \\[\n\\frac{A_n}{E} = \\frac{c_a(1 - \\chi)}{1.6\\;D}\\;,\n\\tag{4.12}\\] where \\(\\chi = c_i/c_a\\). The instantaneous water-use efficiency is proportional to \\(D^{-1}\\). In other words, the drier the air, the more transpiration per unit net CO2 assimilation a leaf “suffers”. This demonstrates the strong effect of atmospheric dryness on the water-carbon trade-off. To remove the effect of vapor pressure deficit (\\(D\\)) on transpiration and focus on the biological component of the water-carbon trade-off, the intrinsic water-use efficiency (iWUE) is defined by relating net assimilation to stomatal conductance: \\[\n\\frac{A_n}{g_s} = \\frac{c_a}{1.6}(1 - \\chi)\n\\tag{4.13}\\] Note that Equation 4.12 and Equation 4.13 are written as being proportional to \\(c_a(1-\\chi)\\). Of course, this term is mathematically equivalent to \\((c_a - c_i)\\). However, there is a reason for expressing it this way. First, it reflects the direct influence of \\(c_a\\) ambient (atmospheric) CO2 concentration on the water-carbon trade-off - less water is lost for a given amount of C assimilation under elevated CO2. Second, observations suggest that \\(\\chi\\) is regulated by plants to remain relatively constant under a wide range of CO2 levels (Ainsworth and Long 2005) and Figure 4.11. The near constancy of \\(\\chi\\) is also reflected by the observation that \\(A_n\\) and \\(g_s\\) vary in near proportion across a wide range of light levels (Bonan 2015).\n\n\n\n\n\nFigure 4.11: Constancy of leaf-internal to ambient CO2. (a) Relationship between net photosynthesis (An) and stomatal conductance (gs) of one species (Jack pine) over a range of light conditions. A linear relationship is reflective of a constant ci:ca. Figure from Bonan (2015). (b) Response of multiple photosynthesis-related variables to elevated CO2 from free-air carbon dioxide enrichment experiments. Figure from Ainsworth and Long (2005).\n\n\n\n\n\n\n4.4.2 Isotopic fractionation\nComing soon.\n\n\n4.4.3 Stomatal regulation\nThe closing of stomates and the reduction of stomatal conductance \\(g_s\\) under dry conditions prevents plants from dangerous desiccation. However, a reduced \\(g_s\\) also leads to a reduction in CO2 diffusion into leaves and thus a reduction of photosynthetic CO2 assimilation. Hence, plants have to balance a trade-off between carbon gain and the risk of desiccation. A complete stomatal closure under moderately dry conditions (low soil moisture, high VPD) may be safe in terms of desiccation avoidance but comes at an excessive cost in terms of foregone CO2 uptake (and similarly vice-versa). An optimal strategy must lie somewhere in between these extreme strategies.\nObservations of leaf and ecosystem fluxes CO2 and water vapor fluxes document how stomatal conductance responds to increasing VPD and decreasing soil moisture. Figure 4.12 shows this for measurements taken at the ecosystem-level, quantifying the canopy stomatal conductance (denoted by an uppercase \\(G_s\\)), representative for the collective behaviour of all leaves in the canopy. Three important aspects of this relationship stand out. First, \\(G_s\\) declines in response to VPD in a non-linear fashion (high sensitivity to VPD at low VPD, lower sensitivity towards higher VPD). Second, there is an interaction between the effect of VPD and soil moisture. Under conditions of dry soils, \\(G_s\\) is reduced compared to wet soils, given the same VPD. Third, at the moistest site (Figure 4.12 a), \\(G_s\\) under moist conditions (moist soils, low VPD) is highest but declines most rapidly with VPD.\n\n\n\n\n\nFigure 4.12: Response of canopy conductance (ecosystem-level aggregate stomatal conductance) to soil and air drying at four different sites (a-d) that differ in average aridity. Soil moisture levels are represented by colors of circles. DI in each panel’s title is the site’s dryness index calculated as the ratio of potential evapotranspiration over precipitation. Figure from Novick et al. (2016).\n\n\n\n\nA simple empirical model for the \\(G_s\\) response to VPD (Oren et al. 2001) is given by \\[\nG_s = G_{s,\\mathrm{ref}} \\left(1 - m \\ln D \\right)\\;.\n\\] Here, \\(G_{s,\\mathrm{ref}}\\) is a reference canopy conductance, \\(D\\) is VPD, and \\(m\\) is a stomatal sensitivity parameter. The data shown in Figure 4.12 indicate that the sensitivity parameter \\(m\\) is not a constant, but decreases with drying soils and tends to be lower at dry sites than at moist sites investigated by Novick et al. (2016).\n\n\n\n\n\n\nStomatal optimization models\n\n\n\n\n\nThe aspect that plants regulate stomatal conductance to balance the trade-off between carbon gain and water loss lends itself to modelling the stomatal response considering optimality principles. Indeed, there is empirical evidence that optimality models are a good representation of how stomata are regulated. Following this notion, it can be assumed that stomatal conductance is optimised such that the net between the carbon gain by increasing stomatal conductance and the carbon cost by the resulting increased transpiration is maximized.\n\\[\nA - aE - bV_\\mathrm{cmax} = \\arg \\max\n\\tag{4.14}\\]\nOver time scales of days to weeks, \\(V_\\mathrm{cmax}\\) in the FvCB model (see box above) is coordinated with stomatal conductance (Joshi et al. 2022). The simultaneous effects of \\(V_\\mathrm{cmax}\\) and \\(g_s\\) are reflected by \\(\\chi\\). Therefore, Equation 4.14 can be expressed with respect to optimising \\(\\chi\\). Maximising a function is equivalent to finding the point where its first derivative (here with respect to \\(\\chi\\)) is zero. (Prentice et al. 2014) formulated such a similar (but not strictly equivalent) optimality criterion as \\[\n\\frac{\\partial (E/A)}{\\partial \\chi} + \\beta \\frac{\\partial (V_\\mathrm{cmax}/A)}{\\partial \\chi} = 0 \\;.\n\\] \\(E/A\\) is the unit cost of transpiration. \\(V_\\mathrm{cmax}/A\\) is the unit cost of carboxylation. Their sum is minimized here with respect to \\(\\chi\\). \\(\\beta\\) is the unit cost ratio. From this, the response of the stomatal conductance to \\(D\\) and \\(A\\) can be derived (not shown here, but in Stocker et al. (2020)) as \\[\ng_s = \\left( 1 + \\frac{g_1}{\\sqrt{D}} \\right) \\frac{A}{c_a - \\Gamma^\\ast}\n\\] \\(g_1\\) is a stomatal sensitivity parameter. Similar results are obtained with a related but not identical optimality criterion (Medlyn et al. 2011)." }, { "objectID": "gpp.html#sec-constlue", @@ -179,14 +179,14 @@ "href": "ecosystemcarbon.html#ecosystem-carbon-flows-and-pools", "title": "5  Ecosystem carbon dynamics", "section": "5.1 Ecosystem carbon flows and pools", - "text": "5.1 Ecosystem carbon flows and pools\nAt the ecosystem-level, C dynamics can be described as the flows (fluxes) between carbon pools that represent C in non-structural forms, leaves (foliage), (stem) wood, fine roots, litter, and soil (Figure 5.1). C is respired by plants (autotrophic respiration) and by soil microbes (heterotrophic respiration). C in live vegetation biomass is turned over to produce litter (litterfall) as trees shed their leaves and lose branches (over years) and as they die (over decades to centuries). Plant mortality is related to the size and age of a tree and may be driven by disturbances (fire, pests, extreme drought and heat). Within years, litter is respired or transformed into soil organic C where it may be stabilized for centuries and more. Heterotrophic respiration originates from litter and soil C decomposition by microbes (fungi and bacteria).\n\n\n\n\n\nFigure 5.1: An illustrative (a) and schematic (b) representation of arbon fluxes and pools in land ecosystems. Major fluxes in (b) are introduced in this chapter below. Rh is heterotrophic respiration. CWD is coarse woody debris. SOM is soil organic matter. PS-products is photosynthetic products. The width of arrows is representative of flux magnitudes. Panel (a) is from Bonan (2008). Panel (b) is from Schulze et al. (2019).\n\n\n\n\n\n5.1.1 Non-structural carbon and autotrophic respiration\nC assimilated by photosynthesis is initially present as non-structural C (NSC) in the form of hydrocarbons (sugars). Some of the assimilated C is stored internally in the form of starch to fuel the reserves pool. Some of the assimilated carbon is consumed by autotrophic respiration (\\(R_a\\)) which subsumes different processes, including maintaining vital functions of the plant (maintenance respiration), inevitable losses during photosynthesis (leaf dark respiration, \\(R_d\\), see Section 4.3.5), and energetic costs for biomass synthesis (growth respiration, \\(R_g\\)). Growth respiration produces CO2 as new biomass is formed, scales with the rate of new biomass formation (BP, see below), and is typically taken to be independent of temperature in vegetation models. Symbols used in this chapter are listed in Table 5.2.\nMaintenance respiration depends on plant size and temperature. It is commonly modelled as being proportional to the pool size of live biomass (sapwood, fine roots). Hence, the respiratory costs is higher for larger plants than for small plants. In vegetation models, \\(R_a\\) is often assumed to depend on the C:N ratio (mass ratio of C to nitrogen in biomass), with lower C:N ratios associated with higher respiration rates. Temperature drives a strong instantaneous response in \\(R_a\\), but respiration rates acclimate to average growth temperatures such that the relationship between \\(R_a\\) and temperature is less steep when considering longer time scales or variations across different climates.\n\n\n\n\n\n\nTemperature dependency of respiration\n\n\n\n\n\nA typical temperature dependency of respiration, used in the LPJ vegetation model (Lloyd and Taylor 1994; Sitch et al. 2003), is given by Equation 5.1 and visualised in Figure 5.2. \\[\n\\begin{align}\nR_{m,i} &= r_i C_i f(T) \\\\\nf(T) &= \\exp \\left( E_0 \\left( \\frac{1}{56.02} - \\frac{1}{T+46.02} \\right) \\right)\n\\end{align}\n\\tag{5.1}\\] \\(r_i\\) is a specific respiration rate for a given plant compartment \\(i\\) and at standard temperature, typically taken to be 10°C. \\(C_i\\) is the biomass C pool size and \\(f(T)\\) is a factor that accounts for the temperature dependency of maintenance respiration. \\(E_0\\) is an activation energy, set to 308.56 J.\n\n\nCode\nlibrary(ggplot2)\n\ncalc_ft_arrhenius <- function(temp){\n exp(308.56 * (1/56.02 - 1/(temp + 46.02)))\n}\n\nggplot() +\n geom_function(fun = calc_ft_arrhenius) +\n xlim(0, 35) +\n geom_vline(xintercept = 10, linetype = \"dotted\") +\n geom_hline(yintercept = 1, linetype = \"dotted\") +\n labs(x = \"Temperature (°C)\",\n y = expression(paste(\"Respiration factor \", italic(f), \"(\", italic(T), \")\"))) + \n theme_classic()\n\n\n\n\n\nFigure 5.2: Temperature dependency of maintenance respiration, modelled based on a modified Arrhenius equation (Lloyd and Taylor 1994; Sitch et al. 2003).\n\n\n\n\n\n\n\n\n\n5.1.2 Net primary productivity\nAt the plant-level, C used for growth is supplied by NSC. The availability of NSC for growth depends on the balance of C assimilation and autotrophic respiration, is influenced by abiotic conditions (temperature, plant desiccation), and varies over the seasons. For example, when leaves are flushed in deciduous plants, the required C is drawn from the NSC pool. Wood is produced not evenly over the seasons, but in a limited period during the growing season which varies strongly between species. Grasses switch from a vegetative growth phase, producing leaves, in the early season to a seed-producing phase later.\nThe amount of C invested into growth of new biomass in leaves (\\(\\Delta C_\\mathrm{leaves}\\)), fine roots (\\(\\Delta C_\\mathrm{roots}\\)), and wood (\\(\\Delta C_\\mathrm{wood}\\)) plus the production organic compounds released through leaves (volatile organic compounds, \\(C_\\mathrm{VOC}\\)) and roots (exudates, \\(C_\\mathrm{exu}\\)), plus the change in NSC storage (\\(\\Delta C_\\mathrm{NSC}\\)) is equal to the gross primary productivity (GPP) minus autotrophic respiration (\\(R_a\\)). This is the definition of the ecosystem-level vegetation C mass balance. The sum of biomass production in different plant compartments plus \\((C_\\mathrm{VOC} + C_\\mathrm{exu})\\) is referred to as the net primary productivity (NPP) and is commonly expressed for annual total fluxes. Over longer (\\(\\sim\\)annual) time scales, the change in NSC storage can be neglected \\((\\Delta C_\\mathrm{NSC} = 0)\\) and the following applies: \\[\n\\begin{aligned}\n\\mathrm{NPP} &= \\mathrm{GPP} - R_a \\\\\n &= \\Delta C_\\mathrm{leaves} + \\Delta C_\\mathrm{roots} + \\Delta C_\\mathrm{wood} + C_\\mathrm{VOC} + C_\\mathrm{exu}\n\\end{aligned}\n\\tag{5.2}\\] These two terms \\(C_\\mathrm{VOC}\\) and \\(C_\\mathrm{exu}\\) are difficult to measure in the field and tend to be smaller than the other terms. Therefore, the biomass productivity is more commonly quantified from observations. \\[\n\\mathrm{BP} = \\Delta C_\\mathrm{leaves} + \\Delta C_\\mathrm{roots} + \\Delta C_\\mathrm{wood}\n\\tag{5.3}\\] Note that there is often some ambiguity in definitions of in the literature and ‘NPP’ is used instead of ‘BP’. BP is expressed as a flux of C per unit square meter (for example gC m-2 yr-1). It measures the amount of biomass C produced per unit ground area and time. NPP is expressed in the same units and additionally includes C produced and released as volatie organic compounds and exudates. These do not contribute to biomass of the plant itself and are relatively short-lived. However, they are not in the form of oxidized C (as is \\(R_a\\)) and therefore are counted towards NPP.\nThe ratio of NPP:GPP is commonly referred to as the ecosystem carbon use efficiency (CUE), and BP:GPP as the biomass production efficiency (BPE).\n\\[\n\\begin{aligned}\n\\mathrm{CUE} &= \\mathrm{NPP} / \\mathrm{GPP} \\\\\n\\mathrm{BPE} &= \\mathrm{BP} / \\mathrm{GPP}\n\\end{aligned}\n\\tag{5.4}\\]\nAs shown in Figure 5.3, BP is linearly related to GPP across ecosystems, indicating that BP can be assumed to be a constant fraction of GPP - albeit with substantial uncertainty.\n\n\n\n\n\nFigure 5.3: BP and BPE. (a) relationship of biomass productivity (BP) versus gross primary productivity (GPP) across 231 sites. (b) Distribution of the biomass production efficiency (BPE) across 231 sites. Data from Peng et al. (n.d.).\n\n\n\n\n\n\n\n\n\n\nExercise\n\n\n\n\nWhat is a typical magnitude of \\(R_a\\), expressed as a fraction of GPP?\n\n\n\n\n\n\n5.1.3 Allocation and growth\nThe partitioning of available NSC to growth in different plant compartments, to VOC, exudates, or respiration is referred to as allocation. Quantitatively, allocation to a given compartment can be expressed as the ratio of BP of that compartment (leaves, roots, wood) over the total NPP. \\[\n\\alpha_i = \\Delta C_i / \\mathrm{NPP}\n\\tag{5.5}\\] Since C allocated to exudates and volatile organic compounds are rarely measured, BP is commonly used instead of NPP in Equation 5.5.\n\n\n\n\n\nFigure 5.4: Allocation. (a) Relationship of leaf biomass production vs. total biomass production. (b) Distribution of the fractional allocation to leaves. (c) Relationship of woody biomass production vs. total biomass production. ‘Wood’ contains stem, branches, and coarse roots. ‘Roots’ is fine roots only. (d) Distribution of the fractional allocation to woody biomass. (e) Relationship of fine root biomass production vs. total biomass production. (b) Distribution of the fractional allocation to fine roots. Data from Peng et al. (n.d.).\n\n\n\n\nThe absence of woody biomass and C allocation to wood production in grasses and herbs as opposed to woody plants (trees and shrubs) is a major difference of allocation across different vegetation types and biomes. While in forests, about half of the total BP is in woody biomass, in grasslands, this is zero. In grasslands, the fractional allocation to leaves and fine roots is about twice as high as in forests (Table 5.1).\n\n\n\n\nTable 5.1: Carbon allocation fractions in forests and grasslands. Wood contains stem, branches, and coarse roots. ‘Roots’ is fine roots only. Data from Peng et al. (n.d.).\n\n\nVegetation\nLeaves\nWood\nRoots\n\n\n\n\nForest\n0.28\n0.47\n0.27\n\n\nGrassland\n0.47\n0.00\n0.53\n\n\n\n\n\n\nThe fractional belowground C allocation is under a strong influence by environmental conditions (nutrient availability, water availability, and CO2). The fraction of C allocated to fine root growth tends to increase under poor soil nutrient availability, under elevated CO2 (as seen in experiments), and under dry conditions. This can be understood as a response to the balance of above vs. belowground resource availabilities (light and CO2 vs. nutrients and water).\nBecause C in leaves and fine roots has a much shorter turnover time than in wood, allocation is a key quantity that controls the effective ecosystem C turnover time and ecosystem C dynamics. Thus, a changing environment affects ecosystem C dynamics, i.a., through its influence on allocation.\n\n\n5.1.4 Biomass turnover and litterfall\nTurnover of different plant compartments is driven by different processes. The leaf turnover in grasses and deciduous trees is linked to the seasons. In evergreen trees, the leaf turnover time (or leaf longevity) is commonly longer than one year and is related to the leaf mass per unit leaf area (LMA - thicker leaves live longer). Leaves may also be damaged and shed after severe water stress and exposure to desiccation. Fine roots turn over at time scales of months to years. Woody biomass is much more long-lived than fine roots and leaf biomass. Its turnover is governed by tree mortality (Section 5.4) and ecosystem disturbances (Section 5.5) or the mortality of individual branches of a tree.\n\n\n\n5.1.5 Soil and litter C dynamics\nSenesced leaves are shed and, together with deadwood, form the litter pool on the ground surface. Litter is decomposed by soil microorganisms - heterotrophic organisms - that gain energy from consuming the organic matter. Litter also gets mixed into the topsoil by bioturbation (mixing by the soil fauna). C in the litter pool has a turnover time on the order of months to years for the fast-decomposing litter of dead leaves and fine roots (Figure 5.5), to 101-102 years for deadwood. Litter can have an important role as fuel for fire and as an insulation layer between soil and air.\nThe rate of litter decomposition is strongly affected by temperature and moisture. The warmer, the more rapid the decomposition. The moisture-dependency is a peaked relationship. Below the peak, decomposition increases with moisture. Above the peak, it declines due to a lack of oxygen. The decomposition rate is also influenced by the chemical composition. As a consequence of this environment-dependency, the time scale of litter decomposition varies across biomes (Figure 5.5). Lignified (woody) biomass decomposes more slowly than, e.g., fine roots and leaves.\n\n\n\n\n\nFigure 5.5: Litter decomposition in different biomes. Shown is the average mass remaining as a function of time for leaf (n = 5 to 6 species) and root (n = 3 species) litters decomposed in 21 sites. (A) Leaf litter decomposed in forest and tundra biomes; (B) root litter decomposed in forest and tundra biomes; (C) leaf litter decomposed in humid and arid grasslands; (D) root litter decomposed in humid and arid grasslands. Each species and litter type was decomposed in replicate bags and collected at multiple time points. Results show that leaf and root litter decomposition rates generally increase as the climatic decomposition index (CDI) increases (Table 1). In arid grasslands, leaf litter decomposed more rapidly than expected (based on the CDI), possibly due to photodegradation. The CDI is incorporates seasonality in temperature and moisture. Figure and caption text from Parton et al. (2007)\n\n\n\n\nSoil organic matter (SOM) refers to the organic mass fraction in soils. It consists of litter at advanced stages of decomposition and of microbial biomass and necromass. The decomposition rate of organic matter in soil can be strongly reduced compared to the decomposition rate of litter. This is due to stabilisation processes. Stabilisation of SOM arises from the chemical transformation through soil micro and macro-fauna and through physical protection in the soil matrix (association to minerals, occlusion in soil aggregates). Yet, the decomposition of SOM is rarely fully suppressed (except under fully anoxic conditions).\nSOM exposed to decomposition is consumed by microbes (fungi and bacteria) and fuels their growth. As they consume organic matter - like humans - they use the chemical energy “stored” in organic matter and oxidise the carbohydrates to CO2. The CO2 is respired away in gaseous form and leaves the soil volume and is referred to as heterotrophic respiration (\\(R_h\\)). The rate of microbial activity and hence \\(R_h\\) increases with temperature in a similar way as the temperature dependency of \\(R_a\\). \\(R_h\\) also depends on soil moisture and has a peaked relationship. It initially increases with increasing soil moisture until a point where the oxygen availability in the soil probihits activity by heterotrophic microorganisms. At this point, \\(R_h\\) drops sharply. Under water-logged soil conditions, SOM decomposition and \\(R_h\\) are suppressed. The temperature dependency of \\(R_h\\), implemented in the LPJ vegetation model is the same as described for \\(R_m\\) by Equation 5.1.\nSOM plays important roles for global biogeochemical cycles and for land-climate interactions. SOM is a vast store of C (~1700 PgC, see Figure 3.1). The soil organic matter content is an important measure for nutrient availability, and strongly influences the water holding capacity of the soil (Chapter 7). C in soil organic matter (SOM) has a turnover time on the order of years to centuries. Under anoxic conditions, the turnover time of SOM can attain millennia. As for litter decomposition, the rate of SOM decomposition (\\(k\\) in Equation 5.6) is controlled by the soil temperature and moisture.\n\n\n\n\n\n\n1st-order decay model for litter and SOM\n\n\n\nSoil and litter C dynamics can be conceived as a 1-st order decay model, consisting of multiple pools, characterized by distinct turnover rates, and supplied with biomass turnover from different plant compartments. The dynamics of an individual pool can be described following 1st-order dynamics (Box in Section 3.2). \\[\n\\frac{\\mathrm{d}C}{\\mathrm{d}t} = I - k(T,\\theta) \\;C \\;.\n\\tag{5.6}\\] Terrestrial biosphere models commonly treat the decay rate \\(k\\) as a function of temperature and moisture, as indicated in Equation 5.6 (\\(T\\) is temperature, \\(\\theta\\) is soil moisture). Some models also use the pH of the soil solution and the oxygen content in the soil for modifying \\(k\\). \\(k\\) at a standard temperature varies for different pools, ranging from 1/3-1 years-1 for litter, to 50-500 years-1 for SOM.\nExperiments of litter decomposition in the field, where a specified initial mass of litter is tracked over time (Figure 5.5), reveal a general pattern that is consistent with the 1st-order decay model. The solution of Equation 5.6 with \\(I=0\\) yields: \\[\nC(t) = C_0\\; e^{-k t}\\;,\n\\] where \\(t\\) is time. Indeed, the litter mass shown in Figure 5.5 exhibits an exponential decline over time.\nAlso SOM decay can be represented following Equation 5.6. In words, the amount of SOM C that gets decomposed in a given amount of time is proportional to the SOM C pool size. The input into that pool is independent of the pool itself.\nLitter and SOM pools in terrestrial biosphere models are most commonly represented by an array of pools that are characterized by different turnover times and that are connected following a specific structure. The litter pools receive inputs from biomass turnover. Decomposed litter is diverted to SOM pools. Fast-decomposing litter is diverted too a SOM pool with a short turnover time (high \\(k\\)), slow-decomposing litter is diverted to a SOM pool with a long turnover time. C is respired away as CO2 during litter and SOM decomposition. The microbial carbon use efficiency (\\(e\\)) determines the ratio of the decomposed C contributing to microbial biomass growth. \\((1-e)\\) is respired as CO2.\n\n\n\n\n\nFigure 5.6: Model for litter and SOM C pools and fluxes. Decomposition of fast and slow litter and SOM pools are modelled using Equation 5.6 with a relatively high and low k respectively. The input term I for each pool is depicted by straight arrows. e is the carbon use efficiency of litter decomposition. ffast is the fraction of litter decomposition diverted to the fast decomposing SOM pool. Rh is the heterotrophic respiration of C, leaving the system as CO2. This shows a simplified version of the litter and SOM model structure implemented in the LPJ terrestrial biosphere model (Sitch et al. 2003). ‘Fast’ and ‘slow’ litter pools are also commonly referred to as ‘metabolic’ and ‘structural’ litter, respectively. ‘Fast’ and ‘slow’ SOM pools are also commonly referred to as ‘active’ and ‘passive’, respectively - although the structure of how they are connected through mass transfers may differ.\n\n\n\n\n\n\n\n\n\n5.1.6 Net ecosystem productivity\nThe net of gross primary productivity (GPP), autotrophic respiration by plants (\\(R_a\\)), and heterotrophic microorganisms (\\(R_h\\)) is referred to as the net ecosystem productivity, NEP. It is expressed in units of a flux of C mass per unit ground area and time, e.g., gC m-2 yr-1. It measures how much C accumulates in an ecosystem in the form of live biomass, litter, and soil (plus VOC and exudates). Since GPP and respiration terms typically have a strong seasonality and diurnal cycle and are not (perfectly) synchronized, NEP has a strong seasonality and diurnal cycle, too (see also Chapter 6). However, integrated over a year, the NEP is small - much smaller than the absolute of its components GPP, \\(R_a\\), and \\(R_h\\).\n\\[\n\\begin{align}\n\\mathrm{NEP} &= \\mathrm{GPP} - R_a - R_h \\\\\n &= \\mathrm{NPP} - R_h\n\\end{align}\n\\tag{5.7}\\] NEP can be measured by eddy covariance flux measurement technique. The net CO2 exchange (NEE) between the canopy and the atmosphere is measured. It is termed NEE (and not NEP) because the processes and components are not directly identified by the measurement. For example, chemically dissolved C in the soil solution and particulate organic matter may be laterally transported off-site and is not reflected in the measurements. NEE is defined such that negative values indicate an net C gain by the ecosystem - opposite from the definition of NEP.\nThe classical model of ecological succession and an ecosystem’s carbon balance is that it reaches a steady state at time scales of forest stand maturity (shorter for grasslands), where, under constant environmental conditions, the NEP approaches zero. Respiration balances photosynthetic C uptake, biomass turnover balances biomass accumulation, and ecosystems become “C neutral” (Odum 1969).\n\n\n\n\n\nFigure 5.7: Classical model of ecosystem an ecosystem’s carbon fluxes and balance. PG corresponds to GPP, PN to NPP, and R to Ra. The concept can be extended such that B is not only (live) biomass, but includes also litter and soil organic matter. Then, PN corresponds to NEP, and R is (Ra + Rh). Figure from (Odum 1969).\n\n\n\n\nHowever, field data of biomass stocks in mature forests seem to Odum’s steady state (and zero NEP) model (Luyssaert et al. 2008). Biometric data (forest inventories) and eddy covariance flux measurements from forests do not show a clear decline of NEP towards zero with increasing stand age, but rather show a sustained positive NEP over several decades to centuries since forest stand development.\nWill forests accumulate C infinitely? Tracking soil C stocks over millennia is per se not possible but clear patterns of a positive influence of soil age on SOM content would have to be evident in data - but are not. Biomass C stocks do not increase indefinitely, either. Individual trees in maturing forest stands continue accumulating biomass but the lifetime of a tree is limited due to hydraulic, mechanical, or C balance constraints whereby increasing respiratory costs pose limits to further growth and may trigger mortality. Self-thinning drives the exclusion of individual trees based on the competition for limited resources and leads to a negative relationship between the number and the average size of trees in a maturing forest stand (see Section 5.4). Therefore, although individual trees may accumulate C in the form of biomass for centuries, the biomass C accumulation at the stand level is much lower due to the declining tree number and the associated mortality, turnover, and decomposition of affected trees.\nVery old stands are dominated by few very large individual trees that contribute strongly to the total ecosystem biomass. However, also these individuals are inevitably affected by mortality. Once they fall, the ecosystem C stock rapidly declines (NEP is negative) and they create a forest gap that enables younger and smaller individuals to benefit from increased light levels. Smaller individuals around the newly formed gap accelerate growth, reach the canopy, and eventually fill the gap.\nThese dynamics imply that the NEP is rarely zero, but is positive for most of the time, except when affected by rare mortality events of large individuals. The spatial extent of a forest gap is on the order of 100-101 m and the maximum tree longevity is on the centuries (and the probability of a tree dying in a given year is its inverse - on the order of 10-2). This implies that the probability of observing a gap formation within a given areal extent is a function of the size of the areal extent. The larger the areal extent, the larger the probability that the influence of gap formation on NEP is captured and the large negative NEP of the gap is balanced by the small positive NEP of the remaining forest area. With an increasing size of the areal extent, the mean NEP should therefore tend to zero.\nForest monitoring plots are usually on the order of 20-50 m in radius. Hence, such data is sensitive to whether the observed plots are a representative sample of forest dynamics and forest gap formation across the landscape.\n\n\n5.1.7 Net biome productivity\n\nNet biome productivity (NBP, expressed in a mass carbon per unit ground area and time, for example gC m-2 yr-1) is the net of NEP and C loss by disturbances \\(\\Delta C_\\mathrm{dist}\\). The NBP is defined for large spatial domains - large enough to contain a representative sample of stochastically occurring disturbances. Across an entire biome, this is given. \\[\n\\begin{align}\n\\mathrm{NBP} &= \\mathrm{GPP} - R_a - R_h - \\Delta C_\\mathrm{dist} \\\\\n &= \\mathrm{NEP} - \\Delta C_\\mathrm{dist}\n\\end{align}\n\\tag{5.8}\\] Disturbances are commonly referred to as stand-replacing events that drive mortality in a large portion of individual plants of an ecosystem. Causes for disturbances include fire, pests, windthrow, or wood harvesting. A disturbance can be conceived as a re-setting of the “Odum-type” ecosystem succession. In contrast to the forest gap dynamics (Section 5.1.6), which play out at the level of individual trees, disturbances affect larger spatial extents (ecosystem or forest patches, Figure 5.8). However, the same aspects of stochasticity across the landscape applies.\n\n\n\n\n\n\nFigure 5.8: Scale in ecological investigations. The C balance of a forest patch is measured by the net ecosystem production. The C balance of a cluster or mosaic of multiple forest patches - each affected by a different land use history - is measured by the net biome production. Figure from Encyclopedia Britannica.\n\n\n\n\nAt the landscape-level, a forest can be conceived as a mosaic of forest patches, characterized by different times since the last stand-replacing disturbance. The first years after a disturbance, ecosystems tend to lose C (negative NEP). This is because the respiration from decomposing litter outweighs the biomass production of regrowth. After a few years, this balance reverses and the ecosystem total C stock increases. Although individual patches tend to have a positive NEP, a small portion of young patches will have a strongly negative NEP. When considering a large number of patches in absence of environmental change (driving trends in GPP, \\(R_a\\), \\(R_h\\) or the disturbance probability), the mean NEP across patches - this is the NBP - tends to zero.\nThe terrestrial carbon balance can be understood of the global total NBP." + "text": "5.1 Ecosystem carbon flows and pools\nAt the ecosystem-level, C dynamics can be described as the flows (fluxes) between carbon pools that represent C in non-structural forms, leaves (foliage), (stem) wood, fine roots, litter, and soil (Figure 5.1). C is respired by plants (autotrophic respiration) and by soil microbes (heterotrophic respiration). C in live vegetation biomass is turned over to produce litter (litterfall) as trees shed their leaves and lose branches (over years) and as they die (over decades to centuries). Plant mortality is related to the size and age of a tree and may be driven by disturbances (fire, pests, extreme drought and heat). Within years, litter is respired or transformed into soil organic C where it may be stabilized for centuries and more. Heterotrophic respiration originates from litter and soil C decomposition by microbes (fungi and bacteria).\n\n\n\n\n\nFigure 5.1: An illustrative (a) and schematic (b) representation of arbon fluxes and pools in land ecosystems. Major fluxes in (b) are introduced in this chapter below. Rh is heterotrophic respiration. CWD is coarse woody debris. SOM is soil organic matter. PS-products is photosynthetic products. The width of arrows is representative of flux magnitudes. Panel (a) is from Bonan (2008). Panel (b) is from Schulze et al. (2019).\n\n\n\n\n\n5.1.1 Non-structural carbon and autotrophic respiration\nC assimilated by photosynthesis is initially present as non-structural C (NSC) in the form of hydrocarbons (sugars). Some of the assimilated C is stored internally in the form of starch to fuel the reserves pool. Some of the assimilated carbon is consumed by autotrophic respiration (\\(R_a\\)) which subsumes different processes, including maintaining vital functions of the plant (maintenance respiration), inevitable losses during photosynthesis (leaf dark respiration, \\(R_d\\), see Section 4.3.5), and energetic costs for biomass synthesis (growth respiration, \\(R_g\\)). Growth respiration produces CO2 as new biomass is formed, scales with the rate of new biomass formation (BP, see below), and is typically taken to be independent of temperature in vegetation models. Symbols used in this chapter are listed in Table 5.2.\nMaintenance respiration depends on plant size and temperature. It is commonly modelled as being proportional to the pool size of live biomass (sapwood, fine roots). Hence, the respiratory costs is higher for larger plants than for small plants. In vegetation models, \\(R_a\\) is often assumed to depend on the C:N ratio (mass ratio of C to nitrogen in biomass), with lower C:N ratios associated with higher respiration rates. Temperature drives a strong instantaneous response in \\(R_a\\), but respiration rates acclimate to average growth temperatures such that the relationship between \\(R_a\\) and temperature is less steep when considering longer time scales or variations across different climates.\n\n\n\n\n\n\nTemperature dependency of respiration\n\n\n\n\n\nA typical temperature dependency of respiration, used in the LPJ vegetation model (Lloyd and Taylor 1994; Sitch et al. 2003), is given by Equation 5.1 and visualised in Figure 5.2. \\[\n\\begin{align}\nR_{m,i} &= r_i C_i f(T) \\\\\nf(T) &= \\exp \\left( E_0 \\left( \\frac{1}{56.02} - \\frac{1}{T+46.02} \\right) \\right)\n\\end{align}\n\\tag{5.1}\\] \\(r_i\\) is a specific respiration rate for a given plant compartment \\(i\\) and at standard temperature, typically taken to be 10°C. \\(C_i\\) is the biomass C pool size and \\(f(T)\\) is a factor that accounts for the temperature dependency of maintenance respiration. \\(E_0\\) is an activation energy, set to 308.56 J.\n\n\nCode\nlibrary(ggplot2)\n\ncalc_ft_arrhenius <- function(temp){\n exp(308.56 * (1/56.02 - 1/(temp + 46.02)))\n}\n\nggplot() +\n geom_function(fun = calc_ft_arrhenius) +\n xlim(0, 35) +\n geom_vline(xintercept = 10, linetype = \"dotted\") +\n geom_hline(yintercept = 1, linetype = \"dotted\") +\n labs(x = \"Temperature (°C)\",\n y = expression(paste(\"Respiration factor \", italic(f), \"(\", italic(T), \")\"))) + \n theme_classic()\n\n\n\n\n\nFigure 5.2: Temperature dependency of maintenance respiration, modelled based on a modified Arrhenius equation (Lloyd and Taylor 1994; Sitch et al. 2003).\n\n\n\n\n\n\n\n\n\n5.1.2 Net primary productivity\nAt the plant-level, C used for growth is supplied by NSC. The availability of NSC for growth depends on the balance of C assimilation and autotrophic respiration, is influenced by abiotic conditions (temperature, plant desiccation), and varies over the seasons. For example, when leaves are flushed in deciduous plants, the required C is drawn from the NSC pool. Wood is produced not evenly over the seasons, but in a limited period during the growing season which varies strongly between species. Grasses switch from a vegetative growth phase, producing leaves, in the early season to a seed-producing phase later.\nThe amount of C invested into growth of new biomass in leaves (\\(\\Delta C_\\mathrm{leaves}\\)), fine roots (\\(\\Delta C_\\mathrm{roots}\\)), and wood (\\(\\Delta C_\\mathrm{wood}\\)) plus the production organic compounds released through leaves (volatile organic compounds, \\(C_\\mathrm{VOC}\\)) and roots (exudates, \\(C_\\mathrm{exu}\\)), plus the change in NSC storage (\\(\\Delta C_\\mathrm{NSC}\\)) is equal to the gross primary productivity (GPP) minus autotrophic respiration (\\(R_a\\)). This is the definition of the ecosystem-level vegetation C mass balance. The sum of biomass production in different plant compartments plus \\((C_\\mathrm{VOC} + C_\\mathrm{exu})\\) is referred to as the net primary productivity (NPP) and is commonly expressed for annual total fluxes. Over longer (\\(\\sim\\)annual) time scales, the change in NSC storage can be neglected \\((\\Delta C_\\mathrm{NSC} = 0)\\) and the following applies: \\[\n\\begin{aligned}\n\\mathrm{NPP} &= \\mathrm{GPP} - R_a \\\\\n &= \\Delta C_\\mathrm{leaves} + \\Delta C_\\mathrm{roots} + \\Delta C_\\mathrm{wood} + C_\\mathrm{VOC} + C_\\mathrm{exu}\n\\end{aligned}\n\\tag{5.2}\\] These two terms \\(C_\\mathrm{VOC}\\) and \\(C_\\mathrm{exu}\\) are difficult to measure in the field and tend to be smaller than the other terms. Therefore, the biomass productivity is more commonly quantified from observations. \\[\n\\mathrm{BP} = \\Delta C_\\mathrm{leaves} + \\Delta C_\\mathrm{roots} + \\Delta C_\\mathrm{wood}\n\\tag{5.3}\\] Note that there is often some ambiguity in definitions in the literature and ‘NPP’ is often used instead of ‘BP’. BP is expressed as a flux of C per unit square meter (for example gC m-2 yr-1). It measures the amount of biomass C produced per unit ground area and time. NPP is expressed in the same units and additionally includes C produced and released as volatile organic compounds and exudates. These do not contribute to the biomass of the plant itself and are relatively short-lived. However, they are not in the form of oxidized C (as is \\(R_a\\)) and therefore are counted towards NPP.\nThe ratio of NPP:GPP is commonly referred to as the ecosystem carbon use efficiency (CUE), and BP:GPP as the biomass production efficiency (BPE).\n\\[\n\\begin{aligned}\n\\mathrm{CUE} &= \\mathrm{NPP} / \\mathrm{GPP} \\\\\n\\mathrm{BPE} &= \\mathrm{BP} / \\mathrm{GPP}\n\\end{aligned}\n\\tag{5.4}\\]\nAs shown in Figure 5.3, BP is linearly related to GPP across ecosystems, indicating that BP can be assumed to be a constant fraction of GPP - albeit with substantial uncertainty.\n\n\n\n\n\nFigure 5.3: BP and BPE. (a) relationship of biomass productivity (BP) versus gross primary productivity (GPP) across 231 sites. (b) Distribution of the biomass production efficiency (BPE) across 231 sites. Data from Peng et al. (n.d.).\n\n\n\n\n\n\n\n\n\n\nExercise\n\n\n\n\nWhat is a typical magnitude of \\(R_a\\), expressed as a fraction of GPP?\n\n\n\n\n\n\n5.1.3 Allocation and growth\nThe partitioning of available NSC to growth in different plant compartments, to VOC, exudates, or respiration is referred to as allocation. Quantitatively, allocation to a given compartment can be expressed as the ratio of BP of that compartment (leaves, roots, wood) over the total NPP. \\[\n\\alpha_i = \\Delta C_i / \\mathrm{NPP}\n\\tag{5.5}\\] Since C allocated to exudates and volatile organic compounds are rarely measured, BP is commonly used instead of NPP in Equation 5.5.\n\n\n\n\n\nFigure 5.4: Allocation. (a) Relationship of leaf biomass production vs. total biomass production. (b) Distribution of the fractional allocation to leaves. (c) Relationship of woody biomass production vs. total biomass production. ‘Wood’ contains stem, branches, and coarse roots. ‘Roots’ is fine roots only. (d) Distribution of the fractional allocation to woody biomass. (e) Relationship of fine root biomass production vs. total biomass production. (b) Distribution of the fractional allocation to fine roots. Data from Peng et al. (n.d.).\n\n\n\n\nThe absence of woody biomass and C allocation to wood production in grasses and herbs as opposed to woody plants (trees and shrubs) is a major difference of allocation across different vegetation types and biomes. While in forests, about half of the total BP is in woody biomass, in grasslands, this is zero. In grasslands, the fractional allocation to leaves and fine roots is about twice as high as in forests (Table 5.1).\n\n\n\n\nTable 5.1: Carbon allocation fractions in forests and grasslands. Wood contains stem, branches, and coarse roots. ‘Roots’ is fine roots only. Data from Peng et al. (n.d.).\n\n\nVegetation\nLeaves\nWood\nRoots\n\n\n\n\nForest\n0.28\n0.47\n0.27\n\n\nGrassland\n0.47\n0.00\n0.53\n\n\n\n\n\n\nThe fractional belowground C allocation is under a strong influence by environmental conditions (nutrient availability, water availability, and CO2). The fraction of C allocated to fine root growth tends to increase under poor soil nutrient availability, under elevated CO2 (as seen in experiments), and under dry conditions. This can be understood as a response to the balance of above vs. belowground resource availabilities (light and CO2 vs. nutrients and water).\nBecause C in leaves and fine roots has a much shorter turnover time than in wood, allocation is a key quantity that controls the effective ecosystem C turnover time and ecosystem C dynamics. Thus, a changing environment affects ecosystem C dynamics, i.a., through its influence on allocation.\n\n\n5.1.4 Biomass turnover and litterfall\nTurnover of different plant compartments is driven by different processes. The leaf turnover in grasses and deciduous trees is linked to the seasons. In evergreen trees, the leaf turnover time (or leaf longevity) is commonly longer than one year and is related to the leaf mass per unit leaf area (LMA - thicker leaves live longer). Leaves may also be damaged and shed after severe water stress and exposure to desiccation. Fine roots turn over at time scales of months to years. Woody biomass is much more long-lived than fine roots and leaf biomass. Its turnover is governed by tree mortality (Section 5.4) and ecosystem disturbances (Section 5.5) or the mortality of individual branches of a tree.\n\n\n\n5.1.5 Soil and litter C dynamics\nSenesced leaves are shed and, together with deadwood, form the litter pool on the ground surface. Litter is decomposed by soil microorganisms - heterotrophic organisms - that gain energy from consuming the organic matter. Litter also gets mixed into the topsoil by bioturbation (mixing by the soil fauna). C in the litter pool has a turnover time on the order of months to years for the fast-decomposing litter of dead leaves and fine roots (Figure 5.5), to 101-102 years for deadwood. Litter can have an important role as fuel for fire and as an insulation layer between soil and air.\nThe rate of litter decomposition is strongly affected by temperature and moisture. The warmer, the more rapid the decomposition. The moisture-dependency is a peaked relationship. Below the peak, decomposition increases with moisture. Above the peak, it declines due to a lack of oxygen. The decomposition rate is also influenced by the chemical composition. As a consequence of this environment-dependency, the time scale of litter decomposition varies across biomes (Figure 5.5). Lignified (woody) biomass decomposes more slowly than, e.g., fine roots and leaves.\n\n\n\n\n\nFigure 5.5: Litter decomposition in different biomes. Shown is the average mass remaining as a function of time for leaf (n = 5 to 6 species) and root (n = 3 species) litters decomposed in 21 sites. (A) Leaf litter decomposed in forest and tundra biomes; (B) root litter decomposed in forest and tundra biomes; (C) leaf litter decomposed in humid and arid grasslands; (D) root litter decomposed in humid and arid grasslands. Each species and litter type was decomposed in replicate bags and collected at multiple time points. Results show that leaf and root litter decomposition rates generally increase as the climatic decomposition index (CDI) increases (Table 1). In arid grasslands, leaf litter decomposed more rapidly than expected (based on the CDI), possibly due to photodegradation. The CDI is incorporates seasonality in temperature and moisture. Figure and caption text from Parton et al. (2007)\n\n\n\n\nSoil organic matter (SOM) refers to the organic mass fraction in soils. It consists of litter at advanced stages of decomposition and of microbial biomass and necromass. The decomposition rate of organic matter in soil can be strongly reduced compared to the decomposition rate of litter. This is due to stabilisation processes. Stabilisation of SOM arises from the chemical transformation through soil micro and macro-fauna and through physical protection in the soil matrix (association to minerals, occlusion in soil aggregates). Yet, the decomposition of SOM is rarely fully suppressed (except under fully anoxic conditions).\nSOM exposed to decomposition is consumed by microbes (fungi and bacteria) and fuels their growth. As they consume organic matter - like humans - they use the chemical energy “stored” in organic matter and oxidise the carbohydrates to CO2. The CO2 is respired away in gaseous form and leaves the soil volume and is referred to as heterotrophic respiration (\\(R_h\\)). The rate of microbial activity and hence \\(R_h\\) increases with temperature in a similar way as the temperature dependency of \\(R_a\\). \\(R_h\\) also depends on soil moisture and has a peaked relationship. It initially increases with increasing soil moisture until a point where the oxygen availability in the soil prohibits activity by heterotrophic microorganisms. At this point, \\(R_h\\) drops sharply. Under water-logged soil conditions, SOM decomposition and \\(R_h\\) are suppressed. The temperature dependency of \\(R_h\\), implemented in the LPJ vegetation model is the same as described for \\(R_m\\) by Equation 5.1.\nSOM plays important roles for global biogeochemical cycles and for land-climate interactions. SOM is a vast store of C (~1700 PgC, see Figure 3.1). The soil organic matter content is an important measure for nutrient availability, and strongly influences the water holding capacity of the soil (Chapter 7). C in soil organic matter (SOM) has a turnover time on the order of years to centuries. Under anoxic conditions, the turnover time of SOM can attain millennia. As for litter decomposition, the rate of SOM decomposition (\\(k\\) in Equation 5.6) is controlled by the soil temperature and moisture.\n\n\n\n\n\n\n1st-order decay model for litter and SOM\n\n\n\nSoil and litter C dynamics can be conceived as a 1-st order decay model, consisting of multiple pools, characterized by distinct turnover rates, and supplied with biomass turnover from different plant compartments. The dynamics of an individual pool can be described following 1st-order dynamics (Box in Section 3.2). \\[\n\\frac{\\mathrm{d}C}{\\mathrm{d}t} = I - k(T,\\theta) \\;C \\;.\n\\tag{5.6}\\] Terrestrial biosphere models commonly treat the decay rate \\(k\\) as a function of temperature and moisture, as indicated in Equation 5.6 (\\(T\\) is temperature, \\(\\theta\\) is soil moisture). Some models also use the pH of the soil solution and the oxygen content in the soil for modifying \\(k\\). \\(k\\) at a standard temperature varies for different pools, ranging from 1/3-1 years-1 for litter, to 50-500 years-1 for SOM.\nExperiments of litter decomposition in the field, where a specified initial mass of litter is tracked over time (Figure 5.5), reveal a general pattern that is consistent with the 1st-order decay model. The solution of Equation 5.6 with \\(I=0\\) yields: \\[\nC(t) = C_0\\; e^{-k t}\\;,\n\\] where \\(t\\) is time. Indeed, the litter mass shown in Figure 5.5 exhibits an exponential decline over time.\nAlso SOM decay can be represented following Equation 5.6. In words, the amount of SOM C that gets decomposed in a given amount of time is proportional to the SOM C pool size. The input into that pool is independent of the pool itself.\nLitter and SOM pools in terrestrial biosphere models are most commonly represented by an array of pools that are characterized by different turnover times and that are connected following a specific structure. The litter pools receive inputs from biomass turnover. Decomposed litter is diverted to SOM pools. Fast-decomposing litter is diverted to a SOM pool with a short turnover time (high \\(k\\)), slow-decomposing litter is diverted to a SOM pool with a long turnover time. C is respired away as CO2 during litter and SOM decomposition. The microbial carbon use efficiency (\\(e\\)) determines the ratio of the decomposed C contributing to microbial biomass growth. \\((1-e)\\) is respired as CO2.\n\n\n\n\n\nFigure 5.6: Model for litter and SOM C pools and fluxes. Decomposition of fast and slow litter and SOM pools are modelled using Equation 5.6 with a relatively high and low k respectively. The input term I for each pool is depicted by straight arrows. e is the carbon use efficiency of litter decomposition. ffast is the fraction of litter decomposition diverted to the fast decomposing SOM pool. Rh is the heterotrophic respiration of C, leaving the system as CO2. This shows a simplified version of the litter and SOM model structure implemented in the LPJ terrestrial biosphere model (Sitch et al. 2003). ‘Fast’ and ‘slow’ litter pools are also commonly referred to as ‘metabolic’ and ‘structural’ litter, respectively. ‘Fast’ and ‘slow’ SOM pools are also commonly referred to as ‘active’ and ‘passive’, respectively - although the structure of how they are connected through mass transfers may differ.\n\n\n\n\n\n\n\n\n\n5.1.6 Net ecosystem productivity\nThe net of gross primary productivity (GPP), autotrophic respiration by plants (\\(R_a\\)), and heterotrophic microorganisms (\\(R_h\\)) is referred to as the net ecosystem productivity, NEP. It is expressed in units of a flux of C mass per unit ground area and time, e.g., gC m-2 yr-1. It measures how much C accumulates in an ecosystem in the form of live biomass, litter, and soil (plus VOC and exudates). Since GPP and respiration terms typically have a strong seasonality and diurnal cycle and are not (perfectly) synchronized, NEP has a strong seasonality and diurnal cycle, too (see also Chapter 6). However, integrated over a year, the NEP is small - much smaller than the absolute of its components GPP, \\(R_a\\), and \\(R_h\\).\n\\[\n\\begin{align}\n\\mathrm{NEP} &= \\mathrm{GPP} - R_a - R_h \\\\\n &= \\mathrm{NPP} - R_h\n\\end{align}\n\\tag{5.7}\\] NEP can be measured by eddy covariance flux measurement technique. The net CO2 exchange (NEE) between the canopy and the atmosphere is measured. It is termed NEE (and not NEP) because the processes and components are not directly identified by the measurement. For example, chemically dissolved C in the soil solution and particulate organic matter may be laterally transported off-site and is not reflected in the measurements. NEE is defined such that negative values indicate a net C gain by the ecosystem - opposite to the definition of NEP.\nThe classical model of ecological succession and an ecosystem’s carbon balance is that it reaches a steady state at time scales of forest stand maturity (shorter for grasslands), where, under constant environmental conditions, the NEP approaches zero. Respiration balances photosynthetic C uptake, biomass turnover balances biomass accumulation, and ecosystems become “C neutral” (Odum 1969).\n\n\n\n\n\nFigure 5.7: Classical model of ecosystem an ecosystem’s carbon fluxes and balance. PG corresponds to GPP, PN to NPP, and R to Ra. The concept can be extended such that B is not only (live) biomass, but includes also litter and soil organic matter. Then, PN corresponds to NEP, and R is (Ra + Rh). Figure from (Odum 1969).\n\n\n\n\nHowever, field data of biomass stocks in mature forests seem to contradict Odum’s steady state (and zero NEP) model (Luyssaert et al. 2008). Biometric data (forest inventories) and eddy covariance flux measurements from forests do not show a clear decline of NEP towards zero with increasing stand age, but rather show a sustained positive NEP over several decades to centuries since forest stand development.\nWill forests accumulate C indefinitely? Tracking soil C stocks over millennia is per se not possible but clear patterns of a positive influence of soil age on SOM content would have to be evident in data - but are not. Biomass C stocks do not increase indefinitely, either. Individual trees in maturing forest stands continue accumulating biomass but the lifetime of a tree is limited due to hydraulic, mechanical, or C balance constraints whereby increasing respiratory costs pose limits to further growth and may trigger mortality. Self-thinning drives the exclusion of individual trees based on the competition for limited resources and leads to a negative relationship between the number and the average size of trees in a maturing forest stand (see Section 5.4). Therefore, although individual trees may accumulate C in the form of biomass for centuries, the biomass C accumulation at the stand level is much lower due to the declining tree number and the associated mortality, turnover, and decomposition of affected trees.\nVery old stands are dominated by few very large individual trees that contribute strongly to the total ecosystem biomass. However, also these individuals are inevitably affected by mortality. Once they fall, the ecosystem C stock rapidly declines (NEP is negative) and they create a forest gap that enables younger and smaller individuals to benefit from increased light levels. Smaller individuals around the newly formed gap accelerate growth, reach the canopy, and eventually fill the gap.\nThese dynamics imply that the NEP is rarely zero, but is positive for most of the time, except when affected by rare mortality events of large individuals. The spatial extent of a forest gap is on the order of 100-101 m and the maximum tree longevity is on the centuries (and the probability of a tree dying in a given year is its inverse - on the order of 10-2). This implies that the probability of observing a gap formation within a given areal extent is a function of the size of the areal extent. The larger the areal extent, the larger the probability that the influence of gap formation on NEP is captured and the large negative NEP of the gap is balanced by the small positive NEP of the remaining forest area. With an increasing size of the areal extent, the mean NEP should therefore tend to zero.\nForest monitoring plots are usually on the order of 20-50 m in radius. Hence, such data is sensitive to whether the observed plots are a representative sample of forest dynamics and forest gap formation across the landscape.\n\n\n5.1.7 Net biome productivity\n\nNet biome productivity (NBP, expressed in a mass carbon per unit ground area and time, for example gC m-2 yr-1) is the net of NEP and C loss by disturbances \\(\\Delta C_\\mathrm{dist}\\). The NBP is defined for large spatial domains - large enough to contain a representative sample of stochastically occurring disturbances. Across an entire biome, this is given. \\[\n\\begin{align}\n\\mathrm{NBP} &= \\mathrm{GPP} - R_a - R_h - \\Delta C_\\mathrm{dist} \\\\\n &= \\mathrm{NEP} - \\Delta C_\\mathrm{dist}\n\\end{align}\n\\tag{5.8}\\] Disturbances are commonly referred to as stand-replacing events that drive mortality in a large portion of individual plants of an ecosystem. Causes for disturbances include fire, pests, windthrow, or wood harvesting. A disturbance can be conceived as a re-setting of the “Odum-type” ecosystem succession. In contrast to the forest gap dynamics (Section 5.1.6), which play out at the level of individual trees, disturbances affect larger spatial extents (ecosystem or forest patches, Figure 5.8). However, the same aspects of stochasticity across the landscape applies.\n\n\n\n\n\n\nFigure 5.8: Scale in ecological investigations. The C balance of a forest patch is measured by the net ecosystem production. The C balance of a cluster or mosaic of multiple forest patches - each affected by a different land use history - is measured by the net biome production. Figure from Encyclopedia Britannica.\n\n\n\n\nAt the landscape-level, a forest can be conceived as a mosaic of forest patches, characterized by different times since the last stand-replacing disturbance. The first years after a disturbance, ecosystems tend to lose C (negative NEP). This is because the respiration from decomposing litter outweighs the biomass production of regrowth. After a few years, this balance reverses and the ecosystem total C stock increases. Although individual patches tend to have a positive NEP, a small portion of young patches will have a strongly negative NEP. When considering a large number of patches in absence of environmental change (driving trends in GPP, \\(R_a\\), \\(R_h\\) or the disturbance probability), the mean NEP across patches - this is the NBP - tends to zero.\nThe terrestrial carbon balance can be understood of the global total NBP." }, { "objectID": "ecosystemcarbon.html#sec-ccascade", "href": "ecosystemcarbon.html#sec-ccascade", "title": "5  Ecosystem carbon dynamics", "section": "5.2 The C cascade model", - "text": "5.2 The C cascade model\nThe C cascade model (Figure 5.9) integrates the information about ecosystem carbon pools and fluxes, provided above in this Chapter. A key insight is that C only enters ecosystems through photosynthesis, measured at the ecosystem-level by GPP. Once in the system, it fuels a “cascade” of pools. They can be conceived as a cascade because biomass pools receive C inputs only through GPP (minus \\(R_a\\)), litter pools only receive C inputs through biomass turnover, and SOM pools only receive C inputs through litter decomposition. Along this cascade, autotrophic and heterotrophic respiration incurs an ecosystem C loss. The rate at which C cascades through this system depends on the turnover rates of the individual pools and on the relative partitioning (allocation and partitioning to different litter and SOM pools) into the “downstream” pools. A schematic of the C cascade can be drawn by extending Figure 5.6.\n\n\n\n\n\nFigure 5.9: The carbon cascade in terrestrial ecosystems. Boxes indicate pools, arrows (including ‘pointed boxes’ for GPP and BP) indicate C fluxes. BPE is the biomass production efficiency. α is the fractional allocation, kl, kr, and kw are the decay constants of the leaf, root, and wood pool. e is the carbon use efficiency of litter decomposition. ffast is the fraction of litter decomposition diverted to the fast decomposing SOM pool. Rh is the heterotrophic respiration of C, leaving the system as CO2. Ra is autotrophic respiration.\n\n\n\n\nFigure 5.9 illustrates the pivotal role of BPE in determining how much C enters more long-lived storage as biomass vs. its largely immediate loss through respiration, of allocation in diverting C streams along cascades of very different turnover times (e.g., leaf vs. wood allocation), of microbial carbon use efficiency, and of processes determining the partitioning of C into (protected) slowly decomposing SOM pools and more rapidly decomposing SOM pools.\nIn Chapter 3, we simulated the response of terrestrial C storage to an increased GPP using a 1-box model and 1st-order decay. In this Chapter, we have “unboxed” C storage in terrestrial ecosystems, distinguishing a suite of pools and fluxes, arranged in a cascading order. When considering the response of this system to a change in GPP, how does the more complex representation affect the dynamics?\nA key characteristic of the 1st order decay model is that the steady-state C pool size \\(C^\\ast\\) is proportional to (is linearly dependent on) the input flux (Equation 3.4). Hence, with an change in the input flux of \\(x = I/I_0\\), the steady-state pools size changes also by \\(x = C^\\ast/C^\\ast_0\\).\nIt can be demonstrated (see Box ‘Simulating the C cascade’ below) that when considering the following properties for the C cascade model:\n\n1st-order decay dynamics of all pools\nconstant \\(\\alpha\\), \\(k_i\\), \\(e\\), and \\(f_\\mathrm{fast}\\)\n\n…, the same linear dependency of the total system C storage \\(\\sum_i C_i^\\ast\\) emerges: \\[\n\\frac{I}{I_0} = \\frac{\\sum_i C_i^\\ast}{\\sum_i C_{i,0}^\\ast} = \\frac{C_i^\\ast}{C_{i,0}^\\ast}, \\; \\forall i\n\\] The symbol \\(\\forall\\) means ‘for all’. However, whether a model with constant \\(\\alpha\\), \\(k_i\\), \\(e\\), and \\(f_\\mathrm{fast}\\) is a good representation of real ecosystems’ responses to environmental change is questionable. It is well established, for example, that \\(\\alpha\\) is very sensitive altered soil nutrient availability and changes in CO2 experiments (Poorter et al. 2012). The turnover rate of biomass in forests (or tree longevity) may be affected by accelerated self-thinning if environmental change positively influences tree-level growth (e.g., through CO2 fertilization or an extension of the growing season) (Marqués et al. 2023). This implies a departure from the linear systems behavior of the C cascade model described by the two points above.\n\n\n\n\n\n\nSimulating the C cascade\n\n\n\n\n\nThe two points (see above) are implemented in a multi-box model:\n\n1st-order decay dynamics of all pools\nconstant \\(\\alpha\\), \\(k_i\\), \\(e\\), and \\(f_\\mathrm{fast}\\)\n\nThe following parameters are set:\n\n\nCode\nlibrary(dplyr)\nsource(here::here(\"R/ccascade.R\"))\ngetpar() |> \n as_tibble() |> \n knitr::kable()\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nbpe\nfleaf\nfroot\nfwood\nkleaf\nkwood\nkroot\nkflitt\nkslitt\nkfsoil\nkssoil\neff\nffast\n\n\n\n\n0.4\n0.3\n3\n0.4\n0.5\n0.02\n0.5\n0.5\n0.1\n0.1\n0.003\n0.6\n0.95\n\n\n\nFigure 5.10: Parameters of the C cascade model. ‘bpe’ is the biomass production efficiency (unitless). ‘fleaf’, ‘froot’, and ‘fwood’ are the fractional allocation factors to leaves, roots, and wood (unitless). ‘kleaf’, ‘kwood’, and ‘kroot’ are the decay constants of the leaf, wood, and root pool, respectively (in yr-1). ‘kflitt’ and ‘kslitt’ are the decay constants of the fast and slow litter pools, respectively (in yr-1). ‘kfsoil’ and ‘kssoil’ are the decay constants of the fast and slow soil pools, respectively (in yr-1). ‘eff’ is the carbon use efficiency of litter decomposition. ‘ffast’ is the fraction of litter decomposition diverted to the fast-turnover soil pool\n\n\n\nThe model is “spun-up” to a steady state for 3000 simulation years. The turnover time of the slowest pool (here the slow soil pool, kssoil = 0.003, corresponding to 333 years) is indicative of how long the model has to be spun-up.\nThe GPP is then increased from 100 PgC yr-1 during the first 3000 simulation years to 120 PgC yr-1 for the subsequent 3000 simulation years.\n\n\nCode\n# specify GPP for each simulation year as a vector\ngpp <- c(rep(100, 3000), rep(120, 3000))\n\n# run the model, it returns a data frame\ndf <- ccascade(gpp)\n\nlibrary(ggplot2)\ndf |> \n ggplot() +\n geom_line(aes(year, cleaf, color = \"Leaf C\")) +\n geom_line(aes(year, cwood, color = \"Wood C\")) +\n geom_line(aes(year, croot, color = \"Root C\")) +\n geom_line(aes(year, flitt, color = \"Fast litter C\")) +\n geom_line(aes(year, slitt, color = \"Slow litter C\")) +\n geom_line(aes(year, fsoil, color = \"Fast soil C\")) +\n geom_line(aes(year, ssoil, color = \"Slow soil C\")) +\n geom_vline(xintercept = 2500, linetype = \"dotted\") +\n geom_vline(xintercept = 5500, linetype = \"dotted\") +\n xlim(2000, 6000) +\n khroma::scale_color_okabeito(name = \"\") +\n theme_classic() +\n labs(x = \"Simulation year\", y = \"Pool size (PgC)\")\n\n\n\n\n\nFigure 5.11: Time series of the pool sizes in the C cascade model, forced with an increase of GPP from 100 to 120 PgC yr-1. The first 2000 simulation years are not shown as they are used for model spin-up. The years used for quantifying relative changes below are indicated by the vertical dotted lines.\n\n\n\n\nThe relative change in each pool can be quantified by comparing the pool sizes, e.g., in simulation year 2500, with the pool sizes in simulation year 5500.\n\n\nCode\nlibrary(tidyr)\ndf_plot <- df |> \n filter(year == 2500) |> \n pivot_longer(2:10, names_to = \"variable\", values_to = \"value_2500\") |> \n select(-year) |> \n left_join(\n df |> \n filter(year == 5500) |> \n pivot_longer(2:10, names_to = \"variable\", values_to = \"value_5500\") |> \n select(-year),\n by = \"variable\"\n ) |> \n mutate(rel_change = value_5500 / value_2500)\n\ndf_plot |> \n filter(!(variable %in% c(\"ra\", \"rh\"))) |> \n ggplot(aes(value_2500, value_5500, color = variable)) +\n geom_abline(slope = 1, linetype = \"dotted\") +\n geom_abline(slope = 1.2, color = \"grey\") +\n geom_point(size = 3) +\n khroma::scale_color_okabeito(name = \"\") +\n theme_classic() +\n labs(x = \"Pool size in year 2500 (PgC)\", \n y = \"Pool size in year 5500 (PgC)\")\n\n\n\n\n\nFigure 5.12: Initial pool size (after spin-up and before step-change in GPP) along the x-axis and final pool size along the y-axis (in PgC). The 1:1 line (slope = 1, intercept = 0) is shown by the dotted line. The grey line has a slope of 1.2 (intercept = 0).\n\n\n\n\nThis illustrates that the relative change in the size of each pool in the C cascade is identical and corresponds to the relative change in GPP. In other words, the C cascade with constant allocation, turnover rates, and efficiencies exhibits a linear systems dynamics.\n\n\n\n\n\n\n\n\n\nWhat is the C balance effect of planting a forest?\n\n\n\nPlanting a forest on land that was previously a grassland, if well attended to and not affected by disturbances (e.g., drought-induced tree mortality, pests, or fire), may lead an increase in the biomass C stock over the course of several decades. Ignoring effects on the soil C stock, this implies that planting a forest sequesters C.\nHow does this relate to the C cascade description of ecosystem C dynamics in this chapter? A notable aspect is that photosynthesis rates and GPP are similar in grasslands and forests. If the same amount of C enters the ecosystem, why is the C storage larger in a forest than in a grassland?\nOf course, C in woody biomass has a much longer turnover time than C in leaves and fine roots. Therefore, following the logic of the box modelling and 1st-order decay, the steady-state C stock in biomass is larger in a forest than in a grassland despite GPP being similar.\nHow effective are forest plantations for compensating CO2 emissions? Again, let’s turn to the box model. We may assume that GPP is 1500 gC m-2 yr-1 and that a forest is planted in simulation year 10 - implemented in the model by increasing the allocation fraction to wood from zero initially (in a grassland) to 0.5 from year 10 onwards. The turnover time of leaves and fine roots is 2 years and 50 years for woody biomass.\nThe model simulation below shows the accumulation of vegetation biomass (leaf, root, and wood C) over time and the net ecosystem productivity - measuring the C balance of the ecosystem.\n\n\nCode\nlibrary(dplyr)\nlibrary(ggplot2)\nlibrary(cowplot)\nsource(here::here(\"R/ccascade.R\"))\n\n# first spin up the C cascade model representing a grassland\n# modify default parameters for allocation\npar <- getpar()\npar$fwood <- 0\npar$fleaf <- 0.5\npar$froot <- 0.5\n\n# specify GPP (gC m-2 yr-1) for each simulation year as a vector\ngpp <- rep(1500, 3000)\n\n# run the model, it returns a data frame\ndf_spinup <- ccascade(gpp, par = par)\n\n# save state and fluxes after spinup\nstate <- df_spinup |> \n tail(1) |> \n select(cleaf, cwood, croot, flitt, slitt, fsoil, ssoil) |> \n as.list()\n\nfluxes <- df_spinup |> \n tail(1) |> \n select(ra, rh) |> \n as.list()\n\n# run model forward (300 years), converting to forest in year 10 (changing allocation)\n# GPP as forcing\ngpp <- rep(1500, 300)\n\nlen <- length(gpp)\n\n# output the state and fluxes in one data frame\ndf <- dplyr::tibble()\n\n# integrate over each time step (this is an implementation of the differential equation)\nfor (yr in seq(len)){\n \n if (yr == 10){\n par$fwood <- 0.5\n par$fleaf <- 0.3\n par$froot <- 0.2\n }\n\n # update states and fluxes\n out <- ccascade_onestep(\n gpp[yr], \n state, \n par, \n fluxes\n )\n \n state <- out$state\n fluxes <- out$fluxes\n\n # record for output\n df <- dplyr::bind_rows(\n df,\n dplyr::bind_cols( \n dplyr::tibble(year = yr),\n dplyr::as_tibble(state), \n dplyr::as_tibble(fluxes))\n )\n}\n\n\ngg1 <- df |> \n ggplot() +\n geom_line(aes(year, (cleaf + cwood + croot)/1000)) +\n geom_vline(xintercept = 10, linetype = \"dotted\") +\n theme_classic() +\n labs(\n x = \"Simulation year\", \n y = expression(paste(\"Biomass C (kgC m\"^-2, \")\"))\n )\n\ngg2 <- df |> \n mutate(nep = gpp - ra - rh) |> \n ggplot() +\n geom_line(aes(year, nep)) +\n geom_vline(xintercept = 10, linetype = \"dotted\") +\n theme_classic() +\n labs(\n x = \"Simulation year\", \n y = expression(paste(\"NEP (gC m\"^-2, \"yr\"^-1, \")\"))\n )\n\nplot_grid(gg1, gg2, ncol = 1)\n\n\n\n\n\nFigure 5.13: Simulated biomass C and the ecosystem C balance (measured by NEP) in response to planting a forest.\n\n\n\n\nThis illustrates that a forest is only a net C sink during its establishment. Once a new steady state is reached, biomass C no longer increases and NEP declines to zero. Forest plantations do not provide sustained CO2 removal. A mature forests tends towards becoming “C-neutral”.\n\n\n\n\n\n\n\n\nExercise\n\n\n\n\nWhich pool in the C cascade model (Figure 5.9) has the slowest C turnover? What is its turnover time \\(\\tau\\), considering model parameter values given in Figure 5.10?\nConsider the visualisation of litter decomposition in different biomes (Figure 5.5), and the 1st-order decay model. Establish the order of each biome’s decay constant \\(k\\) (e.g., \\(k_\\mathrm{biome1} < k_\\mathrm{biome2} < ...\\)).\nConsider two ecosystems (\\(a, b\\)) that differ with respect to their photosynthetic rates (\\(\\mathrm{GPP}_a < \\mathrm{GPP}_b\\)), but have identical (constant) carbon pool turnover times \\(k_i\\), identical (constant) allocation fractions \\(\\alpha\\), and identical (constant) soil organic matter dynamics (identical \\(f_\\mathrm{fast}\\) in the C cascade model). Which of the two has a higher steady-state total ecosystem C storage, considering the C cascade model and 1-st order decay in each C pool?\nConsider the same setup as in (3.), but now you have more information about the relative magnitudes of \\(\\mathrm{GPP}_a\\) and \\(\\mathrm{GPP}_b\\): \\[\n\\mathrm{GPP}_b / \\mathrm{GPP}_a = 1.2\n\\] What is the ratio of steady-state ecosystem C storage in the two ecosystems?\nDiscuss whether the C cascade model and the result obtained for (4.) is an accurate model for the real world. Do you expect the ratio of steady-state C storage in response to a 20% increase in GPP to be higher or lower than 20%? Do you expect BPE, allocation fractions \\(\\alpha_i\\), and decay constants \\(k_i\\) to change in response to increases in GPP?\nWhat quantity do you consider for measuring the annual C balance of an ecosystem? 7, What quantity do you consider for measuring the annual C balance of forests, grasslands, and agricultural lands in Switzerland?" + "text": "5.2 The C cascade model\nThe C cascade model (Figure 5.9) integrates the information about ecosystem carbon pools and fluxes, provided above in this Chapter. A key insight is that C only enters ecosystems through photosynthesis, measured at the ecosystem-level by GPP. Once in the system, it fuels a “cascade” of pools. They can be conceived as a cascade because biomass pools receive C inputs only through GPP (minus \\(R_a\\)), litter pools only receive C inputs through biomass turnover, and SOM pools only receive C inputs through litter decomposition. Along this cascade, autotrophic and heterotrophic respiration incurs an ecosystem C loss. The rate at which C cascades through this system depends on the turnover rates of the individual pools and on the relative partitioning (allocation and partitioning to different litter and SOM pools) into the “downstream” pools. A schematic of the C cascade can be drawn by extending Figure 5.6.\n\n\n\n\n\nFigure 5.9: The carbon cascade in terrestrial ecosystems. Boxes indicate pools, arrows (including ‘pointed boxes’ for GPP and BP) indicate C fluxes. BPE is the biomass production efficiency. α is the fractional allocation, kl, kr, and kw are the decay constants of the leaf, root, and wood pool. e is the carbon use efficiency of litter decomposition. ffast is the fraction of litter decomposition diverted to the fast decomposing SOM pool. Rh is the heterotrophic respiration of C, leaving the system as CO2. Ra is autotrophic respiration.\n\n\n\n\nFigure 5.9 illustrates the pivotal role of BPE in determining how much C enters more long-lived storage as biomass vs. its largely immediate loss through respiration, of allocation in diverting C streams along cascades of very different turnover times (e.g., leaf vs. wood allocation), of microbial carbon use efficiency, and of processes determining the partitioning of C into (protected) slowly decomposing SOM pools and more rapidly decomposing SOM pools.\nIn Chapter 3, we simulated the response of terrestrial C storage to an increased GPP using a 1-box model and 1st-order decay. In this Chapter, we have “unboxed” C storage in terrestrial ecosystems, distinguishing a suite of pools and fluxes, arranged in a cascading order. When considering the response of this system to a change in GPP, how does the more complex representation affect the dynamics?\nA key characteristic of the 1st order decay model is that the steady-state C pool size \\(C^\\ast\\) is proportional to (is linearly dependent on) the input flux (Equation 3.4). Hence, with a change in the input flux of \\(x = I/I_0\\), the steady-state pools size changes also by \\(x = C^\\ast/C^\\ast_0\\).\nIt can be demonstrated (see Box ‘Simulating the C cascade’ below) that when considering the following properties for the C cascade model:\n\n1st-order decay dynamics of all pools\nconstant \\(\\alpha\\), \\(k_i\\), \\(e\\), and \\(f_\\mathrm{fast}\\)\n\n…, the same linear dependency of the total system C storage \\(\\sum_i C_i^\\ast\\) emerges: \\[\n\\frac{I}{I_0} = \\frac{\\sum_i C_i^\\ast}{\\sum_i C_{i,0}^\\ast} = \\frac{C_i^\\ast}{C_{i,0}^\\ast}, \\; \\forall i\n\\] The symbol \\(\\forall\\) means ‘for all’. However, whether a model with constant \\(\\alpha\\), \\(k_i\\), \\(e\\), and \\(f_\\mathrm{fast}\\) is a good representation of real ecosystems’ responses to environmental change is questionable. It is well established, for example, that \\(\\alpha\\) is very sensitive to altered soil nutrient availability and changes in CO2 experiments (Poorter et al. 2012). The turnover rate of biomass in forests (or tree longevity) may be affected by accelerated self-thinning if environmental change positively influences tree-level growth (e.g., through CO2 fertilization or an extension of the growing season) (Marqués et al. 2023). This implies a departure from the linear systems behavior of the C cascade model described by the two points above.\n\n\n\n\n\n\nSimulating the C cascade\n\n\n\n\n\nThe two points (see above) are implemented in a multi-box model:\n\n1st-order decay dynamics of all pools\nconstant \\(\\alpha\\), \\(k_i\\), \\(e\\), and \\(f_\\mathrm{fast}\\)\n\nThe following parameters are set:\n\n\nCode\nlibrary(dplyr)\nsource(here::here(\"R/ccascade.R\"))\ngetpar() |> \n as_tibble() |> \n knitr::kable()\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nbpe\nfleaf\nfroot\nfwood\nkleaf\nkwood\nkroot\nkflitt\nkslitt\nkfsoil\nkssoil\neff\nffast\n\n\n\n\n0.4\n0.3\n3\n0.4\n0.5\n0.02\n0.5\n0.5\n0.1\n0.1\n0.003\n0.6\n0.95\n\n\n\nFigure 5.10: Parameters of the C cascade model. ‘bpe’ is the biomass production efficiency (unitless). ‘fleaf’, ‘froot’, and ‘fwood’ are the fractional allocation factors to leaves, roots, and wood (unitless). ‘kleaf’, ‘kwood’, and ‘kroot’ are the decay constants of the leaf, wood, and root pool, respectively (in yr-1). ‘kflitt’ and ‘kslitt’ are the decay constants of the fast and slow litter pools, respectively (in yr-1). ‘kfsoil’ and ‘kssoil’ are the decay constants of the fast and slow soil pools, respectively (in yr-1). ‘eff’ is the carbon use efficiency of litter decomposition. ‘ffast’ is the fraction of litter decomposition diverted to the fast-turnover soil pool\n\n\n\nThe model is “spun-up” to a steady state for 3000 simulation years. The turnover time of the slowest pool (here the slow soil pool, kssoil = 0.003, corresponding to 333 years) is indicative of how long the model has to be spun-up.\nThe GPP is then increased from 100 PgC yr-1 during the first 3000 simulation years to 120 PgC yr-1 for the subsequent 3000 simulation years.\n\n\nCode\n# specify GPP for each simulation year as a vector\ngpp <- c(rep(100, 3000), rep(120, 3000))\n\n# run the model, it returns a data frame\ndf <- ccascade(gpp)\n\nlibrary(ggplot2)\ndf |> \n ggplot() +\n geom_line(aes(year, cleaf, color = \"Leaf C\")) +\n geom_line(aes(year, cwood, color = \"Wood C\")) +\n geom_line(aes(year, croot, color = \"Root C\")) +\n geom_line(aes(year, flitt, color = \"Fast litter C\")) +\n geom_line(aes(year, slitt, color = \"Slow litter C\")) +\n geom_line(aes(year, fsoil, color = \"Fast soil C\")) +\n geom_line(aes(year, ssoil, color = \"Slow soil C\")) +\n geom_vline(xintercept = 2500, linetype = \"dotted\") +\n geom_vline(xintercept = 5500, linetype = \"dotted\") +\n xlim(2000, 6000) +\n khroma::scale_color_okabeito(name = \"\") +\n theme_classic() +\n labs(x = \"Simulation year\", y = \"Pool size (PgC)\")\n\n\n\n\n\nFigure 5.11: Time series of the pool sizes in the C cascade model, forced with an increase of GPP from 100 to 120 PgC yr-1. The first 2000 simulation years are not shown as they are used for model spin-up. The years used for quantifying relative changes below are indicated by the vertical dotted lines.\n\n\n\n\nThe relative change in each pool can be quantified by comparing the pool sizes, e.g., in simulation year 2500, with the pool sizes in simulation year 5500.\n\n\nCode\nlibrary(tidyr)\ndf_plot <- df |> \n filter(year == 2500) |> \n pivot_longer(2:10, names_to = \"variable\", values_to = \"value_2500\") |> \n select(-year) |> \n left_join(\n df |> \n filter(year == 5500) |> \n pivot_longer(2:10, names_to = \"variable\", values_to = \"value_5500\") |> \n select(-year),\n by = \"variable\"\n ) |> \n mutate(rel_change = value_5500 / value_2500)\n\ndf_plot |> \n filter(!(variable %in% c(\"ra\", \"rh\"))) |> \n ggplot(aes(value_2500, value_5500, color = variable)) +\n geom_abline(slope = 1, linetype = \"dotted\") +\n geom_abline(slope = 1.2, color = \"grey\") +\n geom_point(size = 3) +\n khroma::scale_color_okabeito(name = \"\") +\n theme_classic() +\n labs(x = \"Pool size in year 2500 (PgC)\", \n y = \"Pool size in year 5500 (PgC)\")\n\n\n\n\n\nFigure 5.12: Initial pool size (after spin-up and before step-change in GPP) along the x-axis and final pool size along the y-axis (in PgC). The 1:1 line (slope = 1, intercept = 0) is shown by the dotted line. The grey line has a slope of 1.2 (intercept = 0).\n\n\n\n\nThis illustrates that the relative change in the size of each pool in the C cascade is identical and corresponds to the relative change in GPP. In other words, the C cascade with constant allocation, turnover rates, and efficiencies exhibits a linear systems dynamics.\n\n\n\n\n\n\n\n\n\nWhat is the C balance effect of planting a forest?\n\n\n\nPlanting a forest on land that was previously a grassland, if well attended to and not affected by disturbances (e.g., drought-induced tree mortality, pests, or fire), may lead an increase in the biomass C stock over the course of several decades. Ignoring effects on the soil C stock, this implies that planting a forest sequesters C.\nHow does this relate to the C cascade description of ecosystem C dynamics in this chapter? A notable aspect is that photosynthesis rates and GPP are similar in grasslands and forests. If the same amount of C enters the ecosystem, why is the C storage larger in a forest than in a grassland?\nOf course, C in woody biomass has a much longer turnover time than C in leaves and fine roots. Therefore, following the logic of the box modelling and 1st-order decay, the steady-state C stock in biomass is larger in a forest than in a grassland despite GPP being similar.\nHow effective are forest plantations for compensating CO2 emissions? Again, let’s turn to the box model. We may assume that GPP is 1500 gC m-2 yr-1 and that a forest is planted in simulation year 10 - implemented in the model by increasing the allocation fraction to wood from zero initially (in a grassland) to 0.5 from year 10 onwards. The turnover time of leaves and fine roots is 2 years and 50 years for woody biomass.\nThe model simulation below shows the accumulation of vegetation biomass (leaf, root, and wood C) over time and the net ecosystem productivity - measuring the C balance of the ecosystem.\n\n\nCode\nlibrary(dplyr)\nlibrary(ggplot2)\nlibrary(cowplot)\nsource(here::here(\"R/ccascade.R\"))\n\n# first spin up the C cascade model representing a grassland\n# modify default parameters for allocation\npar <- getpar()\npar$fwood <- 0\npar$fleaf <- 0.5\npar$froot <- 0.5\n\n# specify GPP (gC m-2 yr-1) for each simulation year as a vector\ngpp <- rep(1500, 3000)\n\n# run the model, it returns a data frame\ndf_spinup <- ccascade(gpp, par = par)\n\n# save state and fluxes after spinup\nstate <- df_spinup |> \n tail(1) |> \n select(cleaf, cwood, croot, flitt, slitt, fsoil, ssoil) |> \n as.list()\n\nfluxes <- df_spinup |> \n tail(1) |> \n select(ra, rh) |> \n as.list()\n\n# run model forward (300 years), converting to forest in year 10 (changing allocation)\n# GPP as forcing\ngpp <- rep(1500, 300)\n\nlen <- length(gpp)\n\n# output the state and fluxes in one data frame\ndf <- dplyr::tibble()\n\n# integrate over each time step (this is an implementation of the differential equation)\nfor (yr in seq(len)){\n \n if (yr == 10){\n par$fwood <- 0.5\n par$fleaf <- 0.3\n par$froot <- 0.2\n }\n\n # update states and fluxes\n out <- ccascade_onestep(\n gpp[yr], \n state, \n par, \n fluxes\n )\n \n state <- out$state\n fluxes <- out$fluxes\n\n # record for output\n df <- dplyr::bind_rows(\n df,\n dplyr::bind_cols( \n dplyr::tibble(year = yr),\n dplyr::as_tibble(state), \n dplyr::as_tibble(fluxes))\n )\n}\n\n\ngg1 <- df |> \n ggplot() +\n geom_line(aes(year, (cleaf + cwood + croot)/1000)) +\n geom_vline(xintercept = 10, linetype = \"dotted\") +\n theme_classic() +\n labs(\n x = \"Simulation year\", \n y = expression(paste(\"Biomass C (kgC m\"^-2, \")\"))\n )\n\ngg2 <- df |> \n mutate(nep = gpp - ra - rh) |> \n ggplot() +\n geom_line(aes(year, nep)) +\n geom_vline(xintercept = 10, linetype = \"dotted\") +\n theme_classic() +\n labs(\n x = \"Simulation year\", \n y = expression(paste(\"NEP (gC m\"^-2, \"yr\"^-1, \")\"))\n )\n\nplot_grid(gg1, gg2, ncol = 1)\n\n\n\n\n\nFigure 5.13: Simulated biomass C and the ecosystem C balance (measured by NEP) in response to planting a forest.\n\n\n\n\nThis illustrates that a forest is only a net C sink during its establishment. Once a new steady state is reached, biomass C no longer increases and NEP declines to zero. Forest plantations do not provide sustained CO2 removal. A mature forests tends towards becoming “C-neutral”.\n\n\n\n\n\n\n\n\nExercise\n\n\n\n\nWhich pool in the C cascade model (Figure 5.9) has the slowest C turnover? What is its turnover time \\(\\tau\\), considering model parameter values given in Figure 5.10?\nConsider the visualisation of litter decomposition in different biomes (Figure 5.5), and the 1st-order decay model. Establish the order of each biome’s decay constant \\(k\\) (e.g., \\(k_\\mathrm{biome1} < k_\\mathrm{biome2} < ...\\)).\nConsider two ecosystems (\\(a, b\\)) that differ with respect to their photosynthetic rates (\\(\\mathrm{GPP}_a < \\mathrm{GPP}_b\\)), but have identical (constant) carbon pool turnover times \\(k_i\\), identical (constant) allocation fractions \\(\\alpha\\), and identical (constant) soil organic matter dynamics (identical \\(f_\\mathrm{fast}\\) in the C cascade model). Which of the two has a higher steady-state total ecosystem C storage, considering the C cascade model and 1-st order decay in each C pool?\nConsider the same setup as in (3.), but now you have more information about the relative magnitudes of \\(\\mathrm{GPP}_a\\) and \\(\\mathrm{GPP}_b\\): \\[\n\\mathrm{GPP}_b / \\mathrm{GPP}_a = 1.2\n\\] What is the ratio of steady-state ecosystem C storage in the two ecosystems?\nDiscuss whether the C cascade model and the result obtained for (4.) is an accurate model for the real world. Do you expect the ratio of steady-state C storage in response to a 20% increase in GPP to be higher or lower than 20%? Do you expect BPE, allocation fractions \\(\\alpha_i\\), and decay constants \\(k_i\\) to change in response to increases in GPP?\nWhat quantity do you consider for measuring the annual C balance of an ecosystem? 7, What quantity do you consider for measuring the annual C balance of forests, grasslands, and agricultural lands in Switzerland?" }, { "objectID": "ecosystemcarbon.html#tree-growth-and-allometry", @@ -214,77 +214,77 @@ "href": "globalcarbonpatterns.html#sec-solar-radiation", "title": "6  Spatial and temporal patterns of the terrestrial carbon cycle", "section": "6.1 Solar radiation", - "text": "6.1 Solar radiation\nPPFD is a fraction of the solar radiation at the top of the atmosphere (\\(I_\\mathrm{TOA}\\)). This fraction depends on the planetary albedo for visible light (\\(\\alpha_v\\), unitless), an atmospheric attenuation factor (\\(\\tau\\), unitless) that accounts for the elevation (\\(z\\))-dependent path length of a light ray travelling through the atmosphere and a factor that accounts for cloud cover \\(f_c\\). A further reduction by about 50% arises because photosynthesis uses only a range of the spectrum of wavelengths of solar radiation, corresponding to the visible light spectrum. The factor \\(f_{p}\\) accounts for this and for the conversion of \\(I_\\mathrm{TOA}\\), expressed as an energy flux in W m-2, to a flux of photons in mol s-1 m-2. \\[\n\\mathrm{PPFD} = (1-\\alpha_{v})\\; \\tau(z, f_c) \\; f_{p} \\; I_\\mathrm{TOA}\n\\tag{6.1}\\]\nSolar radiation across the full short-wave spectrum emitted by the sun and incident at the land surface (top-of-canopy, \\(I_\\mathrm{0}\\)) is similarly related to \\(I_\\mathrm{TOA}\\). A different albedo applies for total short-wave radiation vs. the radiation in the photosynthetically active (and visible) spectrum. \\(I_\\mathrm{0}\\) is commonly expressed in energy units (W m-2). \\[\nI_\\mathrm{0} = (1-\\alpha_\\mathrm{sw})\\; \\tau(z, f_c) \\; I_\\mathrm{TOA}\n\\tag{6.2}\\]\n\n\n\n\n\n\nFigure 6.1: Map of solar radiation incident at the Earth surface, averaged over 1981-2010, based on Brun et al. (2022). Figure from https://en.wikipedia.org/wiki/Solar_irradiance#/media/File:RSDS_wiki.png.\n\n\n\n\n\n6.1.1 Solar geometry\nLet’s first step outside the atmosphere and focus on the solar geometry to understand \\(I_\\mathrm{TOA}\\). Solar geometry describes the cyclical movement of the Earth around the sun and how the resulting cyclically varying amount of solar energy that reaches the Earth. The top-of-the atmosphere perspective is relevant to separate atmospheric effects from planetary effects.\n\\(I_\\mathrm{TOA}\\) scales in proportion with the solar constant \\(I_S\\) (1360.8 W m-2) and is inversely proportional to the square of the distance between the Earth and the sun (\\(r_E\\)). \\[\nI_\\mathrm{TOA} = I_S r_E^{-2} \\cos \\theta_z\n\\tag{6.3}\\] \\(\\theta_z\\) is the solar zenith angle. The term \\(\\cos \\theta_z\\) accounts for the dependence of the solar radiation on the angle at which the sun’s rays reach the Earth surface (no terrain considered). It varies cyclically over the course of a day (with hour-of-day) and over the course of a year (with day-of-year). The zenith angle is zero when the sun is directly above the observer - in the zenith (Figure 6.2). At this point, the intensity of the solar radiation is at its maximum.\n\nNote that \\(r_E\\) is not constant over the course of a year as the Earth rotates around the sun not following a perfect circle but an ellipse.\n\n\n\n\n\nFigure 6.2: Illustration of solar geometry, including the zenith angle, the solar altitude angle, and the azimuth angle. Figure from Bonan (2015).\n\n\n\n\nThe dependence of the solar zenith angle on the hour-of-day, day-of-year, and the latitude is described by \\[\n\\cos \\theta_z = \\sin \\varphi \\sin \\delta +\\cos \\varphi \\cos \\delta \\cos h\n\\tag{6.4}\\]\n\n\\(\\varphi\\) is the local latitude in radians (0 at the equator, \\(\\pi/2\\) at the poles)\n\\(\\delta\\) is the solar declination angle. It accounts for the tilt of the Earth relative to the plane in which it moves around the sun. It varies with the day-of-year (\\(23.5^\\circ \\pi/180\\) on the northern-hemispheric summer solstice, June 21, and \\(-23.5^\\circ \\pi/180\\) on the northern-hemispheric winter solstice, December 21)\n\\(h\\) is the solar hour angle. It varies with the hour-of-day (0 at solar noon, \\(\\pi\\) at “solar midnight”, \\(\\pi/12\\) at 1 hour after solar noon).\n\nA derivation of Equation 6.4 is given on Wikipedia.\n\n\n6.1.2 Sloped surfaces\nComing soon.\n\n\n6.1.3 Variations in solar radiation\nVariations in the solar zenith angle, as expressed through Equation 6.4, are shown for different latitudes and a mid-summer diurnal cycle in Figure 6.3.\n\n\nCode\nlibrary(ggplot2)\nlibrary(cowplot)\nlibrary(dplyr)\nlibrary(tidyr)\n\ncalc_cos_zenith_angle <- function(\n lat, # latitude in degrees\n doy, # day of year (1-365)\n hod # hour of day (0-24, 12 is solar noon)\n){\n doy_summer_solstice <- 173 # day-of-year of summer solstice (21 Jun)\n decl <- 23.5 * cos((doy - doy_summer_solstice) / 365 * 2 * pi) * pi/180\n phi <- lat * pi / 180 # latitude in radians\n hour_angle <- (hod - 12) / 24 * 2 * pi\n cos_zenith_angle <- sin(phi) * sin(decl) + cos(phi) * cos(decl) * cos(hour_angle)\n\n # limit to zero - sun disappears behind the horizon\n cos_zenith_angle <- ifelse(cos_zenith_angle < 0, 0, cos_zenith_angle)\n return(cos_zenith_angle)\n}\n\n# Solar azimuth -------\n# at NH summer solstice (doy = 173)\nggplot() +\n # at equator\n geom_function(\n aes(color = \"Equator\"),\n fun = calc_cos_zenith_angle,\n args = list(\n lat = 0,\n doy = 173\n )) +\n # at tropic (lat = 23.5)\n geom_function(\n aes(color = \"23.5° N\"),\n fun = calc_cos_zenith_angle,\n args = list(\n lat = 23.5,\n doy = 173\n )) +\n # at polar (lat = 66.5)\n geom_function(\n aes(color = \"66.5° N\"),\n fun = calc_cos_zenith_angle,\n args = list(\n lat = 66.5,\n doy = 173\n )) +\n # at north pole\n geom_function(\n aes(color = \"North pole\"),\n fun = calc_cos_zenith_angle,\n args = list(\n lat = 90,\n doy = 173\n )) +\n xlim(0, 24) +\n geom_vline(xintercept = 12, linetype = \"dotted\") +\n scale_color_viridis_d(\n breaks = c(\"Equator\", \"23.5° N\", \"66.5° N\", \"North pole\"),\n name = \"\"\n ) +\n labs(title = \"Cosine of solar zenith angle\",\n subtitle = \"Summer solstice (21 June)\",\n x = \"Hour of day\",\n y = \"\") +\n theme_classic()\n\n\n\n\n\nFigure 6.3: Cosine of the solar zenith angle at the solar noon and at the northern hemispheric summer solstice for different latitudes. The solar noon (here at 12.00) is indicated by the dotted line.\n\n\n\n\nThe areas under the curves in Figure 6.3 are proportional to the daily total solar radiation. Calculating daily totals involves a few integrals. The derivation is not shown here, but is explained in Davis et al. (2017). Daily totals and their variation over the seasons are shown below in Figure 6.4 and Figure 6.5.\n\n\nCode\n# use function calc_daily_solar() from Davis et al., 2017 GMD\nsource(here::here(\"R/solar.R\"))\n\n# Daily total and daytime-average S_TOA ---------------------\n# for 4 different latitudes\ndf <- tibble(doy = seq(365)) |>\n rowwise() |>\n mutate(s_toa = calc_daily_solar(0, doy)$ra_j.m2,\n dayl = calc_daily_solar(0, doy)$hs_deg * 24.0 * 60 * 60 / 180,\n lat = 0\n ) |>\n bind_rows(\n tibble(doy = seq(365)) |>\n rowwise() |>\n mutate(s_toa = calc_daily_solar(23.5, doy)$ra_j.m2,\n dayl = calc_daily_solar(23.5, doy)$hs_deg * 24.0 * 60 * 60 / 180,\n lat = 23.5\n )\n ) |>\n bind_rows(\n tibble(doy = seq(365)) |>\n rowwise() |>\n mutate(s_toa = calc_daily_solar(66.5, doy)$ra_j.m2,\n dayl = calc_daily_solar(66.5, doy)$hs_deg * 24.0 * 60 * 60 / 180,\n lat = 66.5\n )\n ) |>\n bind_rows(\n tibble(doy = seq(365)) |>\n rowwise() |>\n mutate(s_toa = calc_daily_solar(90, doy)$ra_j.m2,\n dayl = calc_daily_solar(90, doy)$hs_deg * 24.0 * 60 * 60 / 180,\n lat = 90\n )\n ) |>\n mutate(s_toa_daily_avg = s_toa / dayl)\n\ndf |>\n rename(`Daily total` = s_toa, `Daytime mean` = s_toa_daily_avg) |>\n pivot_longer(c(\"Daily total\", \"Daytime mean\"), values_to = \"s_\", names_to = \"var\") |>\n ggplot(aes(doy, s_, color = as.factor(lat))) +\n geom_line() +\n geom_vline(xintercept = 173, linetype = \"dotted\") +\n scale_color_viridis_d(\n labels = c(\"Equator\", \"23.5° N\", \"66.5° N\", \"North pole\"),\n name = \"\"\n ) +\n labs(title = \"Top-of-atmosphere solar radiation\",\n x = \"Day of year\",\n y = expression(paste(\"Radiative energy flux (J m\"^-2, \")\"))) +\n theme_classic() +\n facet_wrap(vars(var),\n scales = \"free\") +\n theme(\n strip.background = element_rect(fill = \"grey\", color = NA),\n strip.text = element_text(color = \"black\", size = 10, hjust = 0)\n )\n\n\n\n\n\nFigure 6.4: Daily total top-of-atmosphere solar radiation in J m-2. The summer solstice (21 June) is indicated by the dotted line. Note that the curves are not perfectly symmetrical with respect to the summer solstice line. This is because the Earth moves around the sun on an ellipse and hence the distance between the Earth and the sun varies over the year. The distance is at its minimum near the southern-hemispheric summer solstice. Therefore, the mid-summer maximum solar radiation at the southern tropic (23.5° S) is slightly higher than the mid-summer maximum solar radiation at the northern tropic (23.5° N).\n\n\n\n\n\n\nCode\n# all combinations of day-of-year and latitude\ndf <- expand.grid(\n doy = seq(1, 365, by = 2),\n lat = seq(-90, 90, by = 2)\n ) |>\n rowwise() |>\n mutate(s_toa = calc_daily_solar(lat, doy)$ra_j.m2)\n\ndf |>\n ggplot(aes(x = doy,\n y = lat,\n fill = s_toa)) +\n\n geom_raster() +\n scale_fill_viridis_c(option = \"magma\") +\n coord_fixed(ratio = 1.2) +\n labs(title = \"Top-of-atmosphere solar radiation\",\n subtitle = \"Daily total, year 2000\",\n x = \"Day of year\",\n y = \"Latitude (°N)\",\n fill = expression(paste(\"J m\"^-2))) +\n scale_x_continuous(expand = c(0,0)) +\n scale_y_continuous(expand = c(0,0))\n\n\n\n\n\nFigure 6.5: Daily total top-of-atmosphere solar radiation in J m-2 by latitude and day-of-year.\n\n\n\n\nThe diurnal (over the course of a day) and seasonal patterns in top-of-atmosphere solar radiation, following from solar geometry and expressed through Equation 6.4, have direct consequences for CO2 uptake patterns, as expressed through Equation 4.1, Equation 6.1, and Equation 6.3 and described further in Chapter 6.\nSome features are particularly noteworthy about the patterns in \\(I_\\mathrm{TOA}\\):\n\nThe diurnal variation of the instantaneous flux is largest in the tropics.\nThe seasonal variation of the daily total flux is largest at the north pole.\nAt the summer solstice, the daily total solar radiation is largest at the north pole, …\n… but the daily maximum instantaneous and the daytime mean radiation flux are lower at the north pole than at the equator at the summer solstice.\n\nThe biology of plants is attuned to the solar radiation patterns across different latitudes. The photosynthetic apparatus is constructed to make best use of the light, even during the hours of peak light intensity at mid-day. The phenological phases of plant growth reflect the light distribution over the seasons - evergreen plants dominate in the moist tropics to make use of the light year-round, while deciduous leaf strategies and annual life history strategies dominate in the northern latitudes where the seasonal fluctuation of light is large.\n\n\n\n\n6.1.4 Long-term variations in solar radiation\nSolar irradiance\nThe solar constant \\(I_S\\) isn’t actually constant but varies on the order of 0.1% of the course of a solar cycle. One cycle is approximately 11 years. The cyclic behavior is related to the periodic flip of the sun’s magnetic field and the number of sunspots. The radiation emitted from the sun and the number of sunspots are at their minimum after a magnetic flip. There is also a small long-term trend in the solar radiation, having increased by <0.1% since the Maunder Minimum (1645–1715). Solar irradiance is measured at high altitude to minimize the influence of the atmosphere (\\(\\tau\\) in Eq. Equation 6.1) and get information about how \\(I_S\\) varies. Reconstructions of solar irradiance changes for the pre-instrumental period are based on the relationship between \\(I_S\\) and the (easily observable) sunspot number. Variations in \\(I_S\\) are small and do not have a dominant effect on climate and the carbon cycle that would override other forcings, especially for the industrial period (IPCC 2021).\nVolcanic activity\nVolcanic eruptions can influence the solar radiation at the Earth surface. Events that reduce solar radiation by more than 1 W m-2 occur approximately every 35-40 years (Gulev et al. 2021) and affect climate and the carbon cycle for up to a few years after very large eruptions. The increased aerosol load in the atmosphere reduces the total radiative energy flux (reducing \\(\\tau\\) in Eq. Equation 6.1). However, through the strong positive effect of the aerosol load on the share of diffuse versus direct radiation, volcanic aerosols can affect the terrestrial carbon cycle, (somehow surprisingly) leading to a greater land C sink following years of large volcanic eruptions (Section 4.2).\nOrbital parameters\nThe largest changes in \\(I_\\mathrm{TOA}\\) arise over millennial time scales and are related to variations in Earth’s orbit around the sun. These Milankovic cycles are the trigger for the large climate swings between ice ages and warm periods over the course of ~100,000 years. Variations in the orbital parameters affect the latitudinal and seasonal distribution of \\(I_\\mathrm{TOA}\\). Orbital parameters that vary periodically are:\n\nThe eccentricity of the Earth’s elliptical orbit which affects the distance between the Earth and the sun, affecting \\(I_\\mathrm{TOA}\\) via \\(r_E\\) in Equation 6.3. It varies with a period of approximately 100,000 years.\nThe obliquity - the tilt of the axis of the Earth’s own rotation relative to the plane in which the Earth rotates around the sun. A greater obliquity amplifies seasonal variations in \\(I_\\mathrm{TOA}\\). The obliquity is currently at 23.44°. At its minimum, it’s at 21.1°. Obliquity varies over 41,000 years.\nThe precession is the rotation of the Earth’s own rotation axis itself. The effect of precession, in combination with the fact that the Earth’s orbit is elliptical, is that the variation of the sun-Earth distance shifts over the seasons. It varies with a period of about 25,700 years.\n\nThe point of minimal distance coinciding with the summer solstice leads to the largest mid-summer radiation maximum. As a result, the incident solar radiation over the northern-hemispheric summer at 65°N varied by about 83 W m-2 during the past million years. These changes are much larger than the ones driven by solar irradiance and volcanic activity.\nAbout 6000 years ago, during the Mid-Holocene Warm Period, a summer maximum insolation for the northern hemisphere was reached (Figure 6.6). During this period, temperatures and solar irradiance during the growing season were elevated relative to the pre-industrial period and precipitation patterns shifted. This had profound effects on vegetation and the carbon cycle. Testimony to this change are reconstructions that document a “Green Sahara” and a northward shift temperate and boreal forest biomes (MacDonald et al. 2000; Prentice, Jolly, and Participants 2000) during this period.\n\n\nCode\n# test:\n# tmp <- purrr::map(seq(from = -300000, to = 2000, by = 500),\n# ~calc_daily_solar(65, 173, year = .)) |>\n# purrr::map_dbl(\"ra_j.m2\")\n\n# all combinations of day-of-year and latitude\ndf_holo <- expand.grid(\n doy = seq(1, 365, by = 2),\n lat = seq(-90, 90, by = 2)\n ) |>\n rowwise() |>\n mutate(s_toa_holo = calc_daily_solar(lat, doy, year = -4000)$ra_j.m2) |>\n left_join(\n df,\n by = c(\"doy\", \"lat\")\n ) |>\n mutate(diff = (s_toa_holo - s_toa))\n\ndf_holo |>\n ggplot(aes(x = doy,\n y = lat,\n fill = diff)) +\n geom_raster() +\n khroma::scale_fill_roma(reverse = TRUE) +\n geom_vline(xintercept = 173, linetype = \"dotted\") +\n coord_fixed(ratio = 1.2) +\n labs(title = \"Mid-Holocene top-of-atmosphere solar radiation anomaly\",\n subtitle = expression(paste(\"Daily total, \", italic(I)[TOA], \"(6 kyr BP) - \", italic(I)[TOA], \"(present)\" )),\n x = \"Day of year\",\n y = \"Latitude (°N)\",\n fill = expression(paste(\"J m\"^-2))) +\n scale_x_continuous(expand = c(0,0)) +\n scale_y_continuous(expand = c(0,0))\n\n\n\n\n\nFigure 6.6: Mid-Holocene solar radiation anomaly, calculated as the difference in the daily total top-of-atmosphere solar radiation at 6 kyr BP minus present-day (year 2000).\n\n\n\n\n\n\n\n\n\n\nExercise\n\n\n\n\nHigh solar radiation during summer drives monsoonal patterns in the tropics and sub-tropics. Considering Figure 6.6, how do you expect monsoonal precipitation intensity in the northern part of the African continent to have changed around 6 kyr BP, compared to today." + "text": "6.1 Solar radiation\nPPFD is a fraction of the solar radiation at the top of the atmosphere (\\(I_\\mathrm{TOA}\\)). This fraction depends on the planetary albedo for visible light (\\(\\alpha_v\\), unitless), an atmospheric attenuation factor (\\(\\tau\\), unitless) that accounts for the elevation (\\(z\\))-dependent path length of a light ray travelling through the atmosphere and a factor that accounts for cloud cover \\(f_c\\). A further reduction by about 50% arises because photosynthesis uses only a range of the spectrum of wavelengths of solar radiation, corresponding to the visible light spectrum. The factor \\(f_{p}\\) accounts for this and for the conversion of \\(I_\\mathrm{TOA}\\), expressed as an energy flux in W m-2, to a flux of photons in mol s-1 m-2. \\[\n\\mathrm{PPFD} = (1-\\alpha_{v})\\; \\tau(z, f_c) \\; f_{p} \\; I_\\mathrm{TOA}\n\\tag{6.1}\\]\nSolar radiation across the full short-wave spectrum emitted by the sun and incident at the land surface (top-of-canopy, \\(I_\\mathrm{0}\\)) is similarly related to \\(I_\\mathrm{TOA}\\). A different albedo applies for total short-wave radiation vs. the radiation in the photosynthetically active (and visible) spectrum. \\(I_\\mathrm{0}\\) is commonly expressed in energy units (W m-2). \\[\nI_\\mathrm{0} = (1-\\alpha_\\mathrm{sw})\\; \\tau(z, f_c) \\; I_\\mathrm{TOA}\n\\tag{6.2}\\]\n\n\n\n\n\n\nFigure 6.1: Map of solar radiation incident at the Earth surface, averaged over 1981-2010, based on Brun et al. (2022). Figure from https://en.wikipedia.org/wiki/Solar_irradiance#/media/File:RSDS_wiki.png.\n\n\n\n\n\n6.1.1 Solar geometry\nLet’s first step outside the atmosphere and focus on the solar geometry to understand \\(I_\\mathrm{TOA}\\). Solar geometry describes the cyclical movement of the Earth around the sun and how the resulting cyclically varying amount of solar energy that reaches the Earth. The top-of-the atmosphere perspective is relevant to separate atmospheric effects from planetary effects.\n\\(I_\\mathrm{TOA}\\) scales in proportion to the solar constant \\(I_S\\) (1360.8 W m-2) and is inversely proportional to the square of the distance between the Earth and the sun (\\(r_E\\)). \\[\nI_\\mathrm{TOA} = I_S r_E^{-2} \\cos \\theta_z\n\\tag{6.3}\\] \\(\\theta_z\\) is the solar zenith angle. The term \\(\\cos \\theta_z\\) accounts for the dependence of the solar radiation on the angle at which the sun’s rays reach the Earth surface (no terrain considered). It varies cyclically over the course of a day (with hour-of-day) and over the course of a year (with day-of-year). The zenith angle is zero when the sun is directly above the observer - in the zenith (Figure 6.2). At this point, the intensity of the solar radiation is at its maximum.\n\nNote that \\(r_E\\) is not constant over the course of a year as the Earth rotates around the sun not following a perfect circle but an ellipse.\n\n\n\n\n\nFigure 6.2: Illustration of solar geometry, including the zenith angle, the solar altitude angle, and the azimuth angle. Figure from Bonan (2015).\n\n\n\n\nThe dependence of the solar zenith angle on the hour-of-day, day-of-year, and the latitude is described by \\[\n\\cos \\theta_z = \\sin \\varphi \\sin \\delta +\\cos \\varphi \\cos \\delta \\cos h\n\\tag{6.4}\\]\n\n\\(\\varphi\\) is the local latitude in radians (0 at the equator, \\(\\pi/2\\) at the poles)\n\\(\\delta\\) is the solar declination angle. It accounts for the tilt of the Earth relative to the plane in which it moves around the sun. It varies with the day-of-year (\\(23.5^\\circ \\pi/180\\) on the northern-hemispheric summer solstice, June 21, and \\(-23.5^\\circ \\pi/180\\) on the northern-hemispheric winter solstice, December 21)\n\\(h\\) is the solar hour angle. It varies with the hour-of-day (0 at solar noon, \\(\\pi\\) at “solar midnight”, \\(\\pi/12\\) at 1 hour after solar noon).\n\nA derivation of Equation 6.4 is given on Wikipedia.\n\n\n6.1.2 Sloped surfaces\nComing soon.\n\n\n6.1.3 Variations in solar radiation\nVariations in the solar zenith angle, as expressed through Equation 6.4, are shown for different latitudes and a mid-summer diurnal cycle in Figure 6.3.\n\n\nCode\nlibrary(ggplot2)\nlibrary(cowplot)\nlibrary(dplyr)\nlibrary(tidyr)\n\ncalc_cos_zenith_angle <- function(\n lat, # latitude in degrees\n doy, # day of year (1-365)\n hod # hour of day (0-24, 12 is solar noon)\n){\n doy_summer_solstice <- 173 # day-of-year of summer solstice (21 Jun)\n decl <- 23.5 * cos((doy - doy_summer_solstice) / 365 * 2 * pi) * pi/180\n phi <- lat * pi / 180 # latitude in radians\n hour_angle <- (hod - 12) / 24 * 2 * pi\n cos_zenith_angle <- sin(phi) * sin(decl) + cos(phi) * cos(decl) * cos(hour_angle)\n\n # limit to zero - sun disappears behind the horizon\n cos_zenith_angle <- ifelse(cos_zenith_angle < 0, 0, cos_zenith_angle)\n return(cos_zenith_angle)\n}\n\n# Solar azimuth -------\n# at NH summer solstice (doy = 173)\nggplot() +\n # at equator\n geom_function(\n aes(color = \"Equator\"),\n fun = calc_cos_zenith_angle,\n args = list(\n lat = 0,\n doy = 173\n )) +\n # at tropic (lat = 23.5)\n geom_function(\n aes(color = \"23.5° N\"),\n fun = calc_cos_zenith_angle,\n args = list(\n lat = 23.5,\n doy = 173\n )) +\n # at polar (lat = 66.5)\n geom_function(\n aes(color = \"66.5° N\"),\n fun = calc_cos_zenith_angle,\n args = list(\n lat = 66.5,\n doy = 173\n )) +\n # at north pole\n geom_function(\n aes(color = \"North pole\"),\n fun = calc_cos_zenith_angle,\n args = list(\n lat = 90,\n doy = 173\n )) +\n xlim(0, 24) +\n geom_vline(xintercept = 12, linetype = \"dotted\") +\n scale_color_viridis_d(\n breaks = c(\"Equator\", \"23.5° N\", \"66.5° N\", \"North pole\"),\n name = \"\"\n ) +\n labs(title = \"Cosine of solar zenith angle\",\n subtitle = \"Summer solstice (21 June)\",\n x = \"Hour of day\",\n y = \"\") +\n theme_classic()\n\n\n\n\n\nFigure 6.3: Cosine of the solar zenith angle at the solar noon and at the northern hemispheric summer solstice for different latitudes. The solar noon (here at 12.00) is indicated by the dotted line.\n\n\n\n\nThe areas under the curves in Figure 6.3 are proportional to the daily total solar radiation. Calculating daily totals involves a few integrals. The derivation is not shown here, but is explained in Davis et al. (2017). Daily totals and their variation over the seasons are shown below in Figure 6.4 and Figure 6.5.\n\n\nCode\n# use function calc_daily_solar() from Davis et al., 2017 GMD\nsource(here::here(\"R/solar.R\"))\n\n# Daily total and daytime-average S_TOA ---------------------\n# for 4 different latitudes\ndf <- tibble(doy = seq(365)) |>\n rowwise() |>\n mutate(s_toa = calc_daily_solar(0, doy)$ra_j.m2,\n dayl = calc_daily_solar(0, doy)$hs_deg * 24.0 * 60 * 60 / 180,\n lat = 0\n ) |>\n bind_rows(\n tibble(doy = seq(365)) |>\n rowwise() |>\n mutate(s_toa = calc_daily_solar(23.5, doy)$ra_j.m2,\n dayl = calc_daily_solar(23.5, doy)$hs_deg * 24.0 * 60 * 60 / 180,\n lat = 23.5\n )\n ) |>\n bind_rows(\n tibble(doy = seq(365)) |>\n rowwise() |>\n mutate(s_toa = calc_daily_solar(66.5, doy)$ra_j.m2,\n dayl = calc_daily_solar(66.5, doy)$hs_deg * 24.0 * 60 * 60 / 180,\n lat = 66.5\n )\n ) |>\n bind_rows(\n tibble(doy = seq(365)) |>\n rowwise() |>\n mutate(s_toa = calc_daily_solar(90, doy)$ra_j.m2,\n dayl = calc_daily_solar(90, doy)$hs_deg * 24.0 * 60 * 60 / 180,\n lat = 90\n )\n ) |>\n mutate(s_toa_daily_avg = s_toa / dayl)\n\ndf |>\n rename(`Daily total` = s_toa, `Daytime mean` = s_toa_daily_avg) |>\n pivot_longer(c(\"Daily total\", \"Daytime mean\"), values_to = \"s_\", names_to = \"var\") |>\n ggplot(aes(doy, s_, color = as.factor(lat))) +\n geom_line() +\n geom_vline(xintercept = 173, linetype = \"dotted\") +\n scale_color_viridis_d(\n labels = c(\"Equator\", \"23.5° N\", \"66.5° N\", \"North pole\"),\n name = \"\"\n ) +\n labs(title = \"Top-of-atmosphere solar radiation\",\n x = \"Day of year\",\n y = expression(paste(\"Radiative energy flux (J m\"^-2, \")\"))) +\n theme_classic() +\n facet_wrap(vars(var),\n scales = \"free\") +\n theme(\n strip.background = element_rect(fill = \"grey\", color = NA),\n strip.text = element_text(color = \"black\", size = 10, hjust = 0)\n )\n\n\n\n\n\nFigure 6.4: Daily total top-of-atmosphere solar radiation in J m-2. The summer solstice (21 June) is indicated by the dotted line. Note that the curves are not perfectly symmetrical with respect to the summer solstice line. This is because the Earth moves around the sun on an ellipse and hence the distance between the Earth and the sun varies over the year. The distance is at its minimum near the southern-hemispheric summer solstice. Therefore, the mid-summer maximum solar radiation at the southern tropic (23.5° S) is slightly higher than the mid-summer maximum solar radiation at the northern tropic (23.5° N).\n\n\n\n\n\n\nCode\n# all combinations of day-of-year and latitude\ndf <- expand.grid(\n doy = seq(1, 365, by = 2),\n lat = seq(-90, 90, by = 2)\n ) |>\n rowwise() |>\n mutate(s_toa = calc_daily_solar(lat, doy)$ra_j.m2)\n\ndf |>\n ggplot(aes(x = doy,\n y = lat,\n fill = s_toa)) +\n\n geom_raster() +\n scale_fill_viridis_c(option = \"magma\") +\n coord_fixed(ratio = 1.2) +\n labs(title = \"Top-of-atmosphere solar radiation\",\n subtitle = \"Daily total, year 2000\",\n x = \"Day of year\",\n y = \"Latitude (°N)\",\n fill = expression(paste(\"J m\"^-2))) +\n scale_x_continuous(expand = c(0,0)) +\n scale_y_continuous(expand = c(0,0))\n\n\n\n\n\nFigure 6.5: Daily total top-of-atmosphere solar radiation in J m-2 by latitude and day-of-year.\n\n\n\n\nThe diurnal (over the course of a day) and seasonal patterns in top-of-atmosphere solar radiation, following from solar geometry and expressed through Equation 6.4, have direct consequences for CO2 uptake patterns, as expressed through Equation 4.1, Equation 6.1, and Equation 6.3 and described further in Chapter 6.\nSome features are particularly noteworthy about the patterns in \\(I_\\mathrm{TOA}\\):\n\nThe diurnal variation of the instantaneous flux is largest in the tropics.\nThe seasonal variation of the daily total flux is largest at the North Pole.\nAt the summer solstice, the daily total solar radiation is largest at the North Pole, …\n… but the daily maximum instantaneous and the daytime mean radiation flux are lower at the North Pole than at the equator at the summer solstice.\n\nThe biology of plants is attuned to the solar radiation patterns across different latitudes. The photosynthetic apparatus is constructed to make best use of the light, even during the hours of peak light intensity at mid-day. The phenological phases of plant growth reflect the light distribution over the seasons - evergreen plants dominate in the moist tropics to make use of the light year-round, while deciduous leaf strategies and annual life history strategies dominate in the northern latitudes where the seasonal fluctuation of light is large.\n\n\n\n\n6.1.4 Long-term variations in solar radiation\nSolar irradiance\nThe solar constant \\(I_S\\) isn’t actually constant but varies on the order of 0.1% of the course of a solar cycle. One cycle is approximately 11 years. The cyclic behavior is related to the periodic flip of the sun’s magnetic field and the number of sunspots. The radiation emitted from the sun and the number of sunspots are at their minimum after a magnetic flip. There is also a small long-term trend in the solar radiation, having increased by <0.1% since the Maunder Minimum (1645–1715). Solar irradiance is measured at high altitude to minimize the influence of the atmosphere (\\(\\tau\\) in Eq. Equation 6.1) and get information about how \\(I_S\\) varies. Reconstructions of solar irradiance changes for the pre-instrumental period are based on the relationship between \\(I_S\\) and the (easily observable) sunspot number. Variations in \\(I_S\\) are small and do not have a dominant effect on climate and the carbon cycle that would override other forcings, especially for the industrial period (IPCC 2021).\nVolcanic activity\nVolcanic eruptions can influence the solar radiation at the Earth’s surface. Events that reduce solar radiation by more than 1 W m-2 occur approximately every 35-40 years (Gulev et al. 2021) and affect climate and the carbon cycle for up to a few years after very large eruptions. The increased aerosol load in the atmosphere reduces the total radiative energy flux (reducing \\(\\tau\\) in Eq. Equation 6.1). However, through the strong positive effect of the aerosol load on the share of diffuse versus direct radiation, volcanic aerosols can affect the terrestrial carbon cycle, (somehow surprisingly) leading to a greater land C sink following years of large volcanic eruptions (Section 4.2).\nOrbital parameters\nThe largest changes in \\(I_\\mathrm{TOA}\\) arise over millennial time scales and are related to variations in Earth’s orbit around the sun. These Milankovic cycles are the trigger for the large climate swings between ice ages and warm periods over the course of ~100,000 years. Variations in the orbital parameters affect the latitudinal and seasonal distribution of \\(I_\\mathrm{TOA}\\). Orbital parameters that vary periodically are:\n\nThe eccentricity of the Earth’s elliptical orbit which affects the distance between the Earth and the sun, affecting \\(I_\\mathrm{TOA}\\) via \\(r_E\\) in Equation 6.3. It varies with a period of approximately 100,000 years.\nThe obliquity - the tilt of the axis of the Earth’s own rotation relative to the plane in which the Earth rotates around the sun. A greater obliquity amplifies seasonal variations in \\(I_\\mathrm{TOA}\\). The obliquity is currently at 23.44°. At its minimum, it’s at 21.1°. Obliquity varies over 41,000 years.\nThe precession is the rotation of the Earth’s own rotation axis itself. The effect of precession, in combination with the fact that the Earth’s orbit is elliptical, is that the variation of the sun-Earth distance shifts over the seasons. It varies with a period of about 25,700 years.\n\nThe point of minimal distance coinciding with the summer solstice leads to the largest mid-summer radiation maximum. As a result, the incident solar radiation over the northern-hemispheric summer at 65°N varied by about 83 W m-2 during the past million years. These changes are much larger than the ones driven by solar irradiance and volcanic activity.\nAbout 6000 years ago, during the Mid-Holocene Warm Period, a summer maximum insolation for the northern hemisphere was reached (Figure 6.6). During this period, temperatures and solar irradiance during the growing season were elevated relative to the pre-industrial period and precipitation patterns shifted. This had profound effects on vegetation and the carbon cycle. Testimonies to this change are reconstructions that document a “Green Sahara” and a northward shift temperate and boreal forest biomes (MacDonald et al. 2000; Prentice, Jolly, and Participants 2000) during this period.\n\n\nCode\n# test:\n# tmp <- purrr::map(seq(from = -300000, to = 2000, by = 500),\n# ~calc_daily_solar(65, 173, year = .)) |>\n# purrr::map_dbl(\"ra_j.m2\")\n\n# all combinations of day-of-year and latitude\ndf_holo <- expand.grid(\n doy = seq(1, 365, by = 2),\n lat = seq(-90, 90, by = 2)\n ) |>\n rowwise() |>\n mutate(s_toa_holo = calc_daily_solar(lat, doy, year = -4000)$ra_j.m2) |>\n left_join(\n df,\n by = c(\"doy\", \"lat\")\n ) |>\n mutate(diff = (s_toa_holo - s_toa))\n\ndf_holo |>\n ggplot(aes(x = doy,\n y = lat,\n fill = diff)) +\n geom_raster() +\n khroma::scale_fill_roma(reverse = TRUE) +\n geom_vline(xintercept = 173, linetype = \"dotted\") +\n coord_fixed(ratio = 1.2) +\n labs(title = \"Mid-Holocene top-of-atmosphere solar radiation anomaly\",\n subtitle = expression(paste(\"Daily total, \", italic(I)[TOA], \"(6 kyr BP) - \", italic(I)[TOA], \"(present)\" )),\n x = \"Day of year\",\n y = \"Latitude (°N)\",\n fill = expression(paste(\"J m\"^-2))) +\n scale_x_continuous(expand = c(0,0)) +\n scale_y_continuous(expand = c(0,0))\n\n\n\n\n\nFigure 6.6: Mid-Holocene solar radiation anomaly, calculated as the difference in the daily total top-of-atmosphere solar radiation at 6 kyr BP minus present-day (year 2000).\n\n\n\n\n\n\n\n\n\n\nExercise\n\n\n\n\nHigh solar radiation during summer drives monsoonal patterns in the tropics and sub-tropics. Considering Figure 6.6, how do you expect monsoonal precipitation intensity in the northern part of the African continent to have changed around 6 kyr BP, compared to today." }, { "objectID": "globalcarbonpatterns.html#sec-phenology", "href": "globalcarbonpatterns.html#sec-phenology", "title": "6  Spatial and temporal patterns of the terrestrial carbon cycle", "section": "6.2 Phenology", - "text": "6.2 Phenology\nIn general, phenology refers to the study of periodic events of biological activity. In most cases, such periodic events are linked the seasonal variations of the climate. In the context of terrestrial photosynthesis and land-climate interactions, the most important phenological event is the leaf unfolding and leaf senescence and shedding in response to seasonal variations in temperature, radiation, and water availability. The presence (or absence) of active green leaves has major implications for CO2, water vapour, and energy exchange between the land surface and the atmosphere.\nThe presence of green leaves is recorded by optical satellite remote sensing and documents the Earth’s greenness dynamics that follows the seasons - differently across the globe, as the video below illustrates.\n\n\n\n\n\n\n\nExercise\n\n\n\n\nWhy does the “green belt” in Africa move north and south over the seasons?\n\n\n\nLeaf phenology is either controlled by temperatures and light availability in temperate, boreal, and tundra ecosystems, or by water availability in warm, seasonally dry climates elsewhere. The water control on vegetation and leaf phenology will be discussed in Chapter 8.\nIn winter-cold climates (temperate, boreal, and tundra climate zones C, D, and E, see Figure 2.22), leaf phenology of deciduous plants is driven by the seasonal fluctuations of temperature and radiation. Leaves are shed before winter to avoid damage by cold temperatures and because the limited gains by C assimulation during dark and cold winter months does not outweigh the costs for maintenance of vital functions. In seasonally dry climates (mainly climate zones Am, Aw, see Figure 2.22), leaves are shed to avoid water loss and avoid dangerous desiccation of the plant. Leaf area also varies more gradually in response to seasonal variations in climate. LAI can have a seasonal cycle also in evergreen forests and shrublands. In grasslands, LAI typically has a strong seasonal cycle, with rapid foliage development and senescence during the typically relatively short vegetation period - but without the typical budbreak, leaf unfolding, and leaf shedding as in deciduous trees.\nPhotosynthesis and the exchange of CO2 between the land surface and the atmosphere are very directly affected by the amount of active green leaves - as measured by fAPAR (Equation 4.1). Coupled to this exchange is the exchange of water vapour and the surface energy balance. Therefore, leaf phenology is a primary control on land-climate interactions and the carbon cycle. Leaf phenology is not only a driver of land-climate interactions, but is also driven by climate. Different controls act on the leaf unfolding and leaf senescence dates.\n\n6.2.1 Leaf unfolding\nIn winter-cold (temperate and boreal) deciduous forests, the timing of leaf unfolding (bud-burst) is sensitive to temperatures prior to the leaf unfolding date. Warm temperatures in early spring accelerate leaf unfolding and can lead to a shift of spring phenology dates by several days or even weeks. Phenology models commonly use the concept of growing degree days (GDD) (Basler 2016) and consider a critical GDD (GDD*) for predicting leaf unfolding. Growing degree days on day \\(j\\) is defined as the cumulative sum of temperatures above a specified threshold (\\(T_0\\), most commonly \\(T_0 = 5^\\circ\\)C), counting from a given start date \\(M\\).\n\\[\n\\text{GDD}_{T_0,j}=\\sum_{i=M}^j \\max(T_i-T_0, 0)\n\\] The leaf unfolding date is then modeled as the day at which GDD* is reached. In other words, the leaf unfolding is triggered by the accumulated “warmth”. The GDD concept is also commonly used for modelling crop development stages in crop models (distinguishing vegetative growth, seed filling, etc.). GDD* is assumed to be a constant in space and time but may be distinguished by tree species (some trees require a higher GDD - more “warmth” - to start leaf unfolding than others.)\nMore complex models consider also abiotic factors leading up to the phase (endodormancy, state of inactivity mediated by factor inside the bud, (Basler 2016)) where an increasing GDD drives bud development and leaf unfolding. For example, some models consider the requirement of a chilling phase - a period of cool, but non-freezing temperatures in the range of 2–7°C (Basler 2016) - and photoperiod (measuring the seasonal variation of daylength). However, complex models do not generally yield better predictive power than simple GDD-based models (Basler 2016). It should also be noted that models relying purely on temperature for modelling leaf unfolding may have limited applicability for simulating responses to long-term climatic trends. Plant-specific, biotic factors responding to photoperiod impose bounds on the sensitivity of phenology to temperature (Christian Körner and David Basler 2010).\n\n\n\n\n\nFigure 6.7: Mean seasonal cycle of air temperature (a), growing degree days (GDD, b), and leaf area index (LAI, c) at a deciduous temperate forest site in Germany (DE-Hai FLUXNET site). LAI data is from MODIS remote sensing. 5°C is indicated by the dotted line in (a). GDD is calculated with respect to a 5°C base temperature.\n\n\n\n\nHere in Switzerland, most trees start leaf unfolding in the second half of April. Why are leaves of winter-cold deciduous trees not unfolding earlier in the year (given that there is light available for photosynthesis)? Leaf shedding is a protection of plants against frost. At temperatures below freezing, costly cell protection measures against frozen water and excessive photosynthetic light harvesting are required to avoiding damage. Delayed leaf unfolding is a strategy to avoid such damage.\n\n\n\n\n\n\nNote\n\n\n\nCheck out our tutorial here to learn more about phenology modelling and fitting the GDD model to remotely sensed phenology data\n\n\n\n\n6.2.2 Leaf senescence\nLeaf senescence in temperate and boreal deciduous forests is - similarly as leaf unfolding - a strategy to avoid stress and damage by low temperatures in winter. Before leaf abscission (leaf shedding), the leaf nutrients are resorbed and photosynthetic activity starts declining. Leaves are rich in nutrients. A large fraction of nutrients contained in leaf biomass, in particular nitrogen (N), are linked to photosynthesis - mostly Rubisco. These nutrients are re-mobilised before leaf abscission and resorbed into plant-internal storage compartments. Thereby, the loss of “costly” nutrients can be avoided. A side effect of the nutrient resorption is the change of the leaf color to yellow, reddish, or brown.\nEnvironmental controls on leaf senescence are not the same as for leaf unfolding and vary between tree species. Model predictability for leaf senescence dates is generally lower than for leaf unfolding dates, observed global trends are less clear (Piao et al. 2019), and drivers less well understood (Richardson et al. 2013) than for spring phenology. Photoperiod and temperature are considered important abiotic controls on leaf senescence dates. While photoperiod sets the induction of the end-of-season phenology, temperature modulates its progression with cold temperatures accelerating leaf senescence (Christian Körner and David Basler 2010). Also the timing of leaf unfolding can appears to affect the timing of leaf senescence [Keenan and Richardson (2015); marques23natee]. An earlier leaf unfolding in spring appears to induce an earlier leaf senescence in autumn. Processes driving this pattern may be related to cell aging and a conserved leaf longevity, but may also be related to the ecosystem water balance and premature defoliation as a response to dry soil conditions (after vegetation has started consuming water earlier in spring).\n\n\n6.2.3 Phenology trends and spatial patterns\nSince leaf unfolding and senescence phenology is sensitive to climate, patterns in spring phenology emerge across climatic gradients and over the course of long-term climate change. Phenology is very evident for an observer without technical instruments and the timing of phenological dates can be relatively well determined. This has enabled the recording of phenological dates since centuries and long-term phenological records now impressively document the unprecedented current warming in the context of the last few centuries Figure 6.8.\n\n\n\n\n\nFigure 6.8: Phenological indicators of changes in growing season. (a) Cherry blossom peak bloom in Kyoto, Japan; (b) grape harvest in Beaune, France; (c) spring phenology index in eastern China; (d) full flower of Piedmont species in Philadelphia, USA; (e) grape harvest in Central Victoria, Australia; (f) start of growing season in Tibetan Plateau, China. Red lines depict the 25-year moving average (top row) or the nine-year moving average (middle and bottom rows). Figure and caption taken from Gulev et al. (2021).\n\n\n\n\nVariations in leaf unfolding dates are also evident across space, i.e., across climatic gradients in space. In mountainous regions, climatic gradients are steep and variations in the timing of leaf unfolding can be observed by eye - or from space across a larger region (Figure 6.9).\n\n\n\n\n\nFigure 6.9: Spring phenology patterns along elevation in Switzerland. (a) Remotely sensed spring greenup date (day of year, DOY) in 2012 from the MODIS MCD12Q2 product. (b) Relationship of the spring greenup with elevation, derived from the map shown in (a). Figure created based on https://geco-bern.github.io/handfull_of_pixels/.\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nExercise\n\n\n\n\nWith rising temperature under anthropogenic climate change, how do you expect the risk of frost events causing damage on unfolded leaves to change?" + "text": "6.2 Phenology\nIn general, phenology refers to the study of periodic events of biological activity. In most cases, such periodic events are linked to the seasonal variations of the climate. In the context of terrestrial photosynthesis and land-climate interactions, the most important phenological event is the leaf unfolding and leaf senescence and shedding in response to seasonal variations in temperature, radiation, and water availability. The presence (or absence) of active green leaves has major implications for CO2, water vapor, and energy exchange between the land surface and the atmosphere.\nThe presence of green leaves is recorded by optical satellite remote sensing and documents the Earth’s greenness dynamics that follows the seasons - differently across the globe, as the video below illustrates.\n\n\n\n\n\n\n\nExercise\n\n\n\n\nWhy does the “green belt” in Africa move north and south over the seasons?\n\n\n\nLeaf phenology is either controlled by temperatures and light availability in temperate, boreal, and tundra ecosystems, or by water availability in warm, seasonally dry climates elsewhere. The water control on vegetation and leaf phenology will be discussed in Chapter 8.\nIn winter-cold climates (temperate, boreal, and tundra climate zones C, D, and E, see Figure 2.22), leaf phenology of deciduous plants is driven by the seasonal fluctuations of temperature and radiation. Leaves are shed before winter to avoid damage by cold temperatures and because the limited gains by C assimilation during dark and cold winter months does not outweigh the costs for maintenance of vital functions. In seasonally dry climates (mainly climate zones Am, Aw, see Figure 2.22), leaves are shed to avoid water loss and avoid dangerous desiccation of the plant. Leaf area also varies more gradually in response to seasonal variations in climate. LAI can have a seasonal cycle also in evergreen forests and shrublands. In grasslands, LAI typically has a strong seasonal cycle, with rapid foliage development and senescence during the typically relatively short vegetation period - but without the typical budbreak, leaf unfolding, and leaf shedding as in deciduous trees.\nPhotosynthesis and the exchange of CO2 between the land surface and the atmosphere are very directly affected by the amount of active green leaves - as measured by fAPAR (Equation 4.1). Coupled to this exchange is the exchange of water vapor and the surface energy balance. Therefore, leaf phenology is a primary control on land-climate interactions and the carbon cycle. Leaf phenology is not only a driver of land-climate interactions, but is also driven by climate. Different controls act on the leaf unfolding and leaf senescence dates.\n\n6.2.1 Leaf unfolding\nIn winter-cold (temperate and boreal) deciduous forests, the timing of leaf unfolding (bud-burst) is sensitive to temperatures prior to the leaf unfolding date. Warm temperatures in early spring accelerate leaf unfolding and can lead to a shift of spring phenology dates by several days or even weeks. Phenology models commonly use the concept of growing degree days (GDD) (Basler 2016) and consider a critical GDD (GDD*) for predicting leaf unfolding. Growing degree days on day \\(j\\) is defined as the cumulative sum of temperatures above a specified threshold (\\(T_0\\), most commonly \\(T_0 = 5^\\circ\\)C), counting from a given start date \\(M\\).\n\\[\n\\text{GDD}_{T_0,j}=\\sum_{i=M}^j \\max(T_i-T_0, 0)\n\\] The leaf unfolding date is then modeled as the day at which GDD* is reached. In other words, the leaf unfolding is triggered by the accumulated “warmth”. The GDD concept is also commonly used for modelling crop development stages in crop models (distinguishing vegetative growth, seed filling, etc.). GDD* is assumed to be a constant in space and time but may be distinguished by tree species (some trees require a higher GDD - more “warmth” - to start leaf unfolding than others.)\nMore complex models consider also abiotic factors leading up to the phase (endodormancy, state of inactivity mediated by factor inside the bud, (Basler 2016)) where an increasing GDD drives bud development and leaf unfolding. For example, some models consider the requirement of a chilling phase - a period of cool, but non-freezing temperatures in the range of 2–7°C (Basler 2016) - and photoperiod (measuring the seasonal variation of daylength). However, complex models do not generally yield better predictive power than simple GDD-based models (Basler 2016). It should also be noted that models relying purely on temperature for modelling leaf unfolding may have limited applicability for simulating responses to long-term climatic trends. Plant-specific, biotic factors responding to photoperiod impose bounds on the sensitivity of phenology to temperature (Christian Körner and David Basler 2010).\n\n\n\n\n\nFigure 6.7: Mean seasonal cycle of air temperature (a), growing degree days (GDD, b), and leaf area index (LAI, c) at a deciduous temperate forest site in Germany (DE-Hai FLUXNET site). LAI data is from MODIS remote sensing. 5°C is indicated by the dotted line in (a). GDD is calculated with respect to a 5°C base temperature.\n\n\n\n\nHere in Switzerland, most trees start leaf unfolding in the second half of April. Why are leaves of winter-cold deciduous trees not unfolding earlier in the year (given that there is light available for photosynthesis)? Leaf shedding is a protection of plants against frost. At temperatures below freezing, costly cell protection measures against frozen water and excessive photosynthetic light harvesting are required to avoid damage. Delayed leaf unfolding is a strategy to avoid such damage.\n\n\n\n\n\n\nNote\n\n\n\nCheck out our tutorial here to learn more about phenology modelling and fitting the GDD model to remotely sensed phenology data\n\n\n\n\n6.2.2 Leaf senescence\nLeaf senescence in temperate and boreal deciduous forests is - similarly as leaf unfolding - a strategy to avoid stress and damage by low temperatures in winter. Before leaf abscission (leaf shedding), the leaf nutrients are resorbed and photosynthetic activity starts declining. Leaves are rich in nutrients. A large fraction of nutrients contained in leaf biomass, in particular nitrogen (N), is linked to photosynthesis - mostly Rubisco. These nutrients are re-mobilised before leaf abscission and resorbed into plant-internal storage compartments. Thereby, the loss of “costly” nutrients can be avoided. A side effect of the nutrient resorption is the change of the leaf color to yellow, reddish, or brown.\nEnvironmental controls on leaf senescence are not the same as for leaf unfolding and vary between tree species. Model predictability for leaf senescence dates is generally lower than for leaf unfolding dates, observed global trends are less clear (Piao et al. 2019), and drivers less well understood (Richardson et al. 2013) than for spring phenology. Photoperiod and temperature are considered important abiotic controls on leaf senescence dates. While photoperiod sets the induction of the end-of-season phenology, temperature modulates its progression with cold temperatures accelerating leaf senescence (Christian Körner and David Basler 2010). Also, the timing of leaf unfolding can appear to affect the timing of leaf senescence [Keenan and Richardson (2015); marques23natee]. An earlier leaf unfolding in spring appears to induce an earlier leaf senescence in autumn. Processes driving this pattern may be related to cell aging and a conserved leaf longevity, but may also be related to the ecosystem water balance and premature defoliation as a response to dry soil conditions (after vegetation has started consuming water earlier in spring).\n\n\n6.2.3 Phenology trends and spatial patterns\nSince leaf unfolding and senescence phenology is sensitive to climate, patterns in spring phenology emerge across climatic gradients and over the course of long-term climate change. Phenology is very evident for an observer without technical instruments, and the timing of phenological dates can be relatively well determined. This has enabled the recording of phenological dates since centuries, and long-term phenological records now impressively document the unprecedented current warming in the context of the last few centuries Figure 6.8.\n\n\n\n\n\nFigure 6.8: Phenological indicators of changes in growing season. (a) Cherry blossom peak bloom in Kyoto, Japan; (b) grape harvest in Beaune, France; (c) spring phenology index in eastern China; (d) full flower of Piedmont species in Philadelphia, USA; (e) grape harvest in Central Victoria, Australia; (f) start of growing season in Tibetan Plateau, China. Red lines depict the 25-year moving average (top row) or the nine-year moving average (middle and bottom rows). Figure and caption taken from Gulev et al. (2021).\n\n\n\n\nVariations in leaf unfolding dates are also evident across space, i.e., across climatic gradients in space. In mountainous regions, climatic gradients are steep and variations in the timing of leaf unfolding can be observed by eye - or from space across a larger region (Figure 6.9).\n\n\n\n\n\nFigure 6.9: Spring phenology patterns along elevation in Switzerland. (a) Remotely sensed spring greenup date (day of year, DOY) in 2012 from the MODIS MCD12Q2 product. (b) Relationship of the spring greenup with elevation, derived from the map shown in (a). Figure created based on https://geco-bern.github.io/handfull_of_pixels/.\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nExercise\n\n\n\n\nWith rising temperature under anthropogenic climate change, how do you expect the risk of frost events causing damage on unfolded leaves to change?" }, { "objectID": "globalcarbonpatterns.html#sec-flux-variability", "href": "globalcarbonpatterns.html#sec-flux-variability", "title": "6  Spatial and temporal patterns of the terrestrial carbon cycle", "section": "6.3 Temporal variations of ecosystem C fluxes", - "text": "6.3 Temporal variations of ecosystem C fluxes\nSolar radiation is the “engine” of photosynthesis and thus of the terrestrial carbon cycle. This is expressed by the light use efficiency model of GPP (Equation 4.1). The temporal and spatial patterns of photosynthetic CO2 uptake are therefore driven by the temporal and spatial patterns in solar radiation. The Earth’s revolution around its own axis within a day, and its revolution around the sun within a year give rise to diurnal and seasonal variations in solar radiation, climate, C fluxes, and biological activity in all its forms. (It’s a fascinating thought that even physiological and psychological circadian rhythms like wake and sleep patterns are a consequence of solar geometry.) The variations of solar radiation over the course of a day and a year are expressed very differently along different latitudinal positions.\nNote that both spatial and temporal variations in the photosynthetic CO2 uptake are driven not only by solar radiation, but are constrained also by water availability. The ecosystems for which fluxes are shown below (BR-Sa3, DE-Hai, FI-Hyy, and US-ICh, site locations are shown in Figure 2.2 and climate diagrams in Section 2.2) are all relatively moist and fluxes are rarely limited by water availability. An exception is the tropical forest site BR-Sa3 where months from August to October are relatively dry (Figure 2.3).\n\n6.3.1 Diurnal cycle\nFigure 6.3 showed the diurnal cycle of the cosine of the solar zenith angle (\\(\\cos \\theta_z\\)) for different latitudes around summer solstice (21 June). \\(\\cos \\theta_z\\) is relevant because it linearly scales the top-of-atmosphere solar radiation, as described by Equation 6.3. The solar radiation incident at the Earth surface (\\(I_0\\)), that is at the top of the canopy, is shown for four different example sites in Figure 6.10. The same general pattern becomes evident:\n\nThe sites at high northern latitudes (US-ICh, a tundra heathland in Alaska, and FI-Hyy, a boreal coniferous forest in Finland) have the smallest diurnal cycle amplitude in \\(I_0\\), but the longest daylight period (\\(I_0 > 0\\)).\nThe low-latitude site in the tropics (BR-Sa3, a moist tropical forest) has the shortest duration of daylight (\\(I_0 > 0\\)), but reaches the highest mid-day solar radiation intensity. (Note that for \\(I_\\mathrm{TOA}\\), a site at 23.5°N was shown in Figure 6.3 and has an even higher mid-day peak.)\nThe temperate site (DE-Hai, a beech forest in Germany) is intermediate in terms of amplitude, peak value, and daylight duration.\n\nThe diurnal cycle in GPP (Figure 6.10 b) reflects the diurnal cycle in \\(I_0\\), but with some notable deviations:\n\nThe mid-day peak for the tundra site US-ICh is much lower in relation to the mid-day peak of other sites for GPP than for \\(I_0\\). This is likely due to sparse vegetation cover (low LAI ad fAPAR) and temperature effects on photosynthesis.\nThe shapes of the diurnal cycles in \\(I_0\\) and GPP are notably different for BR-Sa3. This may be an indication of water limitation on photosynthesis.\n\nIn absence of disturbances influencing ecosystem C fluxes, the net ecosystem exchange (NEE) is largely equivalent to the negative of NEP as defined in Section 5.1.6. NEE is what the atmosphere “sees” - it is the net C flux between the atmosphere and the land surface (here a forest vegetation). A negative NEE value indicates a net CO2 uptake by vegetation. Some notable patterns in the diurnal cycle of NEE are:\n\nThe diurnal cycle in NEE (Figure 6.10 d) is almost identical to the negative of the diurnal cycle in GPP. This reflects that variations in the net C balance of an ecosystem over the course of a day are strongly driven by photosynthetic CO2 uptake. Ecosystem respiration (Reco, the sum of autotrophic and heterotrophic respiration) varies less over the course of a day.\nSites with a strong mid-day CO2 uptake have a higher night-time respiration.\nDuring nighttime hours, NEE is relatively stable. During that time, GPP is zero. Hence, Reco is relatively stable during the night.\nThe daily total NEE (Figure 6.10 c) is smaller than daily totals in GPP and Reco. At the tropical site, NEE is very small in comparison to GPP and Reco. This indicates that over the course of one day, the tropical forest site is nearly C neutral. A substantial net C uptake is evident for DE-Hai. This is the C balance for a day in mid July. In general, during summer, temperate, boreal, and tundra ecosystems are a net C sink, and a net C source during winter (see Section 6.3.2).\n\n\n\n\n\n\nFigure 6.10: Mean diurnal (daily) cycle at northern hemispheric mid-summer (15 July) of (a) incident (top-of-canopy) shortwave radiation, (b) gross primary production, and (d) net ecosystem exchange for four different sites - a temperate deciduous forest (DE-Hai), a boreal needle-leaved forest (FI-Hyy), an arctic heathland in the tundra (US-ICh), and an evergreen moist tropical forest (BR-Sa3). Panel (c) shows the daily total GPP, Reco, and net ecosystem exchange (NEE). NEE is largely equivalent to the negative of NEP as defined in Section 5.1.6. Site locations are shown in Figure 2.2.\n\n\n\n\n\n\n6.3.2 Seasonal cycle\nFigure 6.4 shows the seasonal cycle of top-of-atmosphere solar radiation (\\(I_\\mathrm{TOA}\\)) for different latitudes. The daily totals exhibits the same general seasonal pattern as measured incident top-of-canopy solar radiation means, measured at four different sites along different latitudes (Figure 6.11):\n\nThe seasonal cycle amplitude is smallest at low latitudes (at Equator for \\(I_\\mathrm{TOA}\\) and site BR-Sa3 for \\(I_0\\)) and highest at high latitudes. Daily solar radiation drops to zero in the Arctic during winter north of the Arctic circle at 66.5°N. (FI-Hyy is located at 61.8°N, US-ICh is located at 68.6°N).\nMid-summer peak daily solar radiation is highest at high northern latitudes (at the North Pole for \\(I_\\mathrm{TOA}\\) and at site US-ICh for \\(I_0\\)).\nThe small seasonal variation in \\(I_\\mathrm{TOA}\\) at the Equator does not translate into congruent seasonal variation in \\(I_0\\).\n\nA similar overall pattern is visible for the seasonal variation in GPP, but with some notable exceptions:\n\nThe highest seasonal peak daily GPP values are recorded at the temperate site DE-Hai. This is despite LAI being mostly higher at the tropical (BR-Sa3) than at the temperate site and indicates an very high mid-summer LUE of ecosystem photosynthetic CO2 uptake at the temperate site.\nThe mid-summer peak daily GPP is (by far) lowest at the tundra site US-ICh. This reflects the very low LAI at this site.\nThe (deciduous) temperate forest site DE-Hai - a beech forest in Germany - exhibits the largest seasonal variation in LAI. Beech is a deciduous tree and forms forests that are strongly dominated by beech alone with little understorey vegetation. The simultaneous leaf phenology of the dominating tree species drives the rapid and large spring increase and autumn decrease in LAI.\nFI-Hyy is a needle-leaved forest, dominated by pine trees (Pinus sylvestris and Picea abies). Although these tree species are evergreen, a seasonal variation in LAI is recorded by the satellite remote sensing-derived observations shown in Figure 6.11 (b). This likely reflects three aspects: (i) the small but not absent actual seasonal variation in leaf area also in evergreens, (ii) the influence of the deciduous understorey vegetation on ecosystem-level greenness, (iii) the snow cover during winter months affecting the remotely sensed signal in surface reflectance which is interpreted by the algorithm for estimating LAI.\n\nAs for the diurnal cycle, also for the seasonal cycle, the pattern in NEE strongly resembles the negative of the pattern in GPP. Some notable aspects are:\n\nThe tundra (US-ICh) and boreal (FI-Hyy) sites are small sources of CO2 during winter and moderate sinks in summer.\nThe temperate site DE-Hai is a substantial sink in summer and a moderate source in winter. The peak of the source is attained in the shoulder seasons (April and November) - when temperatures are still above freezing and drive respiration, while leaves are already shed or not yet unfolded.\nThe annual total NEE is small for all sites and nearly zero for the tropical and the tundra sites (BR-Sa3 and US-ICh, respectively). The small NEE is the net of the two much larger opposing fluxes GPP and Reco.\n\n\n\n\n\n\nFigure 6.11: Mean seasonal cycle of (a) incident (top-of-canopy) shortwave radiation, (b) leaf area index, (c) gross primary production, and (d) net ecosystem exchange (NEE) for four different sites - a temperate deciduous forest (DE-Hai), a boreal needle-leaved forest (FI-Hyy), an arctic heathland in the tundra (US-ICh), and an evergreen moist tropical forest (BR-Sa3). Panel (e) shows the annual total GPP, Reco, and net ecosystem exchange (NEE). NEE is largely equivalent to the negative of NEP as defined in Section 5.1.6. Site locations are shown in Figure 2.2.\n\n\n\n\n\n\n\n\n\n\nExercise\n\n\n\n\nAt what latitude do you expect the largest diurnal cycle amplitude in top-of-atmosphere solar radiation?\nAt what latitude do you expect the largest seasonal amplitude in top-of-atmosphere solar radiation?\nWhere do you expect the smallest seasonal variation in the daily net ecosystem productivity.\nConsider mature forest ecosystems (sensu Odum (1969), Figure 5.7) in a moist tropical, temperate and boreal region. Where do you expect the largest annual NEP? Where do you expect the largest daily NEP during the peak growing season?\n\n\n\n\n\n6.3.2.1 The breathing of the Earth\nThe NEE (equivalent to the negative of NBP, introduced in Section 5.1.6) recorded at the four example sites shown above is representative for similar patterns across all vegetated land of the Earth. Seasonal variations in solar radiation are the underlying driver of the carbon flux variations and similarly affect all photosynthesizing organisms across the planet.\nCO2 is relatively well-mixed in the atmosphere due to its long lifetime. However the mixing time scale is on the order of a couple years. Hence, more rapid variations in net CO2 fluxes between the atmosphere and the Earth surface (over the ocean and over the land) are expressed in corresponding variations of the atmospheric CO2 concentration. As introduced in Section 1.1.1, the atmospheric CO2 concentration, measured at Mauna Loa (Hawaii) exhibits not only a steady increase since the 1950s, but also a seasonal cycle with lowest value at the end of the northern hemisphere summer. Atmospheric CO2 is continuously measured at a range of sites along different latitudes. At Point Barrow, the northernmost point of the US in Alaska, the CO2 seasonal amplitude is even larger than at Mauna Loa (Figure 6.12). This is the result of the collective net CO2 uptake in northern ecosystems during summer.\nFigure 6.12 shows the seasonal variation in atmospheric CO2 after the mean and long-term trend are removed from the time series (corresponding to the red curve minus the black curve in Figure 1.1). The shape of this seasonal variation is very similar to the shape of the seasonal NEE variation at northern sites (e.g., DE-Hai) - above average during winter months when ecosystem respiration prevails and a rapid draw-down starting in spring to attain a minimum during summer. This shows how the patterns in net ecosystem CO2 exchange directly affect variations in atmospheric CO2 over the course of a year.\n\n\n\n\n\nFigure 6.12: Seasonal CO2 cycles observed at Barrow (C) and Mauna Loa (D) for the 1961-63 or 1958-63 and 2009-11 time periods. The first six months of the year are repeated. Figure from Graven et al. (2013).\n\n\n\n\nFigure 6.12 also shows that the CO2 seasonal amplitude has been increasing since measurements started in the early sixties of the 20th century. This increase reflects changes in the terrestrial C cycle (Graven et al. 2013) and is likely driven by the warming climate and the extension of the growing season in northern ecosystems, increasing the photosynthetic CO2 uptake as a result of the fertilizing effect of rising CO2, and seasonal shifts in GPP and Reco and their relative timing.\nThe video below shows an animation of the modeled spatial and temporal variations of atmospheric CO2 over the course of one year. CO2 sources from fossil fuel combustion by industry, households, and traffic are combined with the modeled terrestrial and oceanic net CO2 exchange between the Earth surface and the atmosphere. An atmospheric transport model is then used for simulating variations in CO2 concentrations." + "text": "6.3 Temporal variations of ecosystem C fluxes\nSolar radiation is the “engine” of photosynthesis and thus of the terrestrial carbon cycle. This is expressed by the light use efficiency model of GPP (Equation 4.1). The temporal and spatial patterns of photosynthetic CO2 uptake are therefore driven by the temporal and spatial patterns in solar radiation. The Earth’s revolution around its own axis within a day, and its revolution around the sun within a year give rise to diurnal and seasonal variations in solar radiation, climate, C fluxes, and biological activity in all its forms. (It’s a fascinating thought that even physiological and psychological circadian rhythms like wake and sleep patterns are a consequence of solar geometry.) The variations of solar radiation over the course of a day and a year are expressed very differently along different latitudinal positions.\nNote that both spatial and temporal variations in the photosynthetic CO2 uptake are driven not only by solar radiation, but are constrained also by water availability. The ecosystems for which fluxes are shown below (BR-Sa3, DE-Hai, FI-Hyy, and US-ICh, site locations are shown in Figure 2.2 and climate diagrams in Section 2.2) are all relatively moist and fluxes are rarely limited by water availability. An exception is the tropical forest site BR-Sa3 where months from August to October are relatively dry (Figure 2.3).\n\n6.3.1 Diurnal cycle\nFigure 6.3 showed the diurnal cycle of the cosine of the solar zenith angle (\\(\\cos \\theta_z\\)) for different latitudes around summer solstice (21 June). \\(\\cos \\theta_z\\) is relevant because it linearly scales the top-of-atmosphere solar radiation, as described by Equation 6.3. The solar radiation incident at the Earth’s surface (\\(I_0\\)), that is at the top of the canopy, is shown for four different example sites in Figure 6.10. The same general pattern becomes evident:\n\nThe sites at high northern latitudes (US-ICh, a tundra heathland in Alaska, and FI-Hyy, a boreal coniferous forest in Finland) have the smallest diurnal cycle amplitude in \\(I_0\\), but the longest daylight period (\\(I_0 > 0\\)).\nThe low-latitude site in the tropics (BR-Sa3, a moist tropical forest) has the shortest duration of daylight (\\(I_0 > 0\\)), but reaches the highest mid-day solar radiation intensity. (Note that for \\(I_\\mathrm{TOA}\\), a site at 23.5°N was shown in Figure 6.3 and has an even higher mid-day peak.)\nThe temperate site (DE-Hai, a beech forest in Germany) is intermediate in terms of amplitude, peak value, and daylight duration.\n\nThe diurnal cycle in GPP (Figure 6.10 b) reflects the diurnal cycle in \\(I_0\\), but with some notable deviations:\n\nThe mid-day peak for the tundra site US-ICh is much lower in relation to the mid-day peak of other sites for GPP than for \\(I_0\\). This is likely due to sparse vegetation cover (low LAI ad fAPAR) and temperature effects on photosynthesis.\nThe shapes of the diurnal cycles in \\(I_0\\) and GPP are notably different for BR-Sa3. This may be an indication of water limitation on photosynthesis.\n\nIn the absence of disturbances influencing ecosystem C fluxes, the net ecosystem exchange (NEE) is largely equivalent to the negative of NEP as defined in Section 5.1.6. NEE is what the atmosphere “sees” - it is the net C flux between the atmosphere and the land surface (here a forest vegetation). A negative NEE value indicates a net CO2 uptake by vegetation. Some notable patterns in the diurnal cycle of NEE are:\n\nThe diurnal cycle in NEE (Figure 6.10 d) is almost identical to the negative of the diurnal cycle in GPP. This reflects that variations in the net C balance of an ecosystem over the course of a day are strongly driven by photosynthetic CO2 uptake. Ecosystem respiration (Reco, the sum of autotrophic and heterotrophic respiration) varies less over the course of a day.\nSites with a strong mid-day CO2 uptake have a higher night-time respiration.\nDuring nighttime hours, NEE is relatively stable. During that time, GPP is zero. Hence, Reco is relatively stable during the night.\nThe daily total NEE (Figure 6.10 c) is smaller than daily totals in GPP and Reco. At the tropical site, NEE is very small in comparison to GPP and Reco. This indicates that over the course of one day, the tropical forest site is nearly C neutral. A substantial net C uptake is evident for DE-Hai. This is the C balance for a day in mid July. In general, during summer, temperate, boreal, and tundra ecosystems are a net C sink, and a net C source during winter (see Section 6.3.2).\n\n\n\n\n\n\nFigure 6.10: Mean diurnal (daily) cycle at northern hemispheric mid-summer (15 July) of (a) incident (top-of-canopy) shortwave radiation, (b) gross primary production, and (d) net ecosystem exchange for four different sites - a temperate deciduous forest (DE-Hai), a boreal needle-leaved forest (FI-Hyy), an arctic heathland in the tundra (US-ICh), and an evergreen moist tropical forest (BR-Sa3). Panel (c) shows the daily total GPP, Reco, and net ecosystem exchange (NEE). NEE is largely equivalent to the negative of NEP as defined in Section 5.1.6. Site locations are shown in Figure 2.2.\n\n\n\n\n\n\n6.3.2 Seasonal cycle\nFigure 6.4 shows the seasonal cycle of top-of-atmosphere solar radiation (\\(I_\\mathrm{TOA}\\)) for different latitudes. The daily totals exhibit the same general seasonal pattern as measured incident top-of-canopy solar radiation means, measured at four different sites along different latitudes (Figure 6.11):\n\nThe seasonal cycle amplitude is smallest at low latitudes (at the Equator for \\(I_\\mathrm{TOA}\\) and site BR-Sa3 for \\(I_0\\)) and highest at high latitudes. Daily solar radiation drops to zero in the Arctic during winter north of the Arctic circle at 66.5°N. (FI-Hyy is located at 61.8°N, US-ICh is located at 68.6°N).\nMid-summer peak daily solar radiation is highest at high northern latitudes (at the North Pole for \\(I_\\mathrm{TOA}\\) and at site US-ICh for \\(I_0\\)).\nThe small seasonal variation in \\(I_\\mathrm{TOA}\\) at the Equator does not translate into congruent seasonal variation in \\(I_0\\).\n\nA similar overall pattern is visible for the seasonal variation in GPP, but with some notable exceptions:\n\nThe highest seasonal peak daily GPP values are recorded at the temperate site DE-Hai. This is despite LAI being mostly higher at the tropical (BR-Sa3) than at the temperate site and indicates a very high mid-summer LUE of ecosystem photosynthetic CO2 uptake at the temperate site.\nThe mid-summer peak daily GPP is (by far) lowest at the tundra site US-ICh. This reflects the very low LAI at this site.\nThe (deciduous) temperate forest site DE-Hai - a beech forest in Germany - exhibits the largest seasonal variation in LAI. Beech is a deciduous tree and forms forests that are strongly dominated by beech alone with little understorey vegetation. The simultaneous leaf phenology of the dominating tree species drives the rapid and large spring increase and autumn decrease in LAI.\nFI-Hyy is a needle-leaved forest, dominated by pine trees (Pinus sylvestris and Picea abies). Although these tree species are evergreen, a seasonal variation in LAI is recorded by the satellite remote sensing-derived observations shown in Figure 6.11 (b). This likely reflects three aspects: (i) the small but not absent actual seasonal variation in leaf area also in evergreens, (ii) the influence of the deciduous understorey vegetation on ecosystem-level greenness, (iii) the snow cover during winter months affecting the remotely sensed signal in surface reflectance which is interpreted by the algorithm for estimating LAI.\n\nAs for the diurnal cycle, also for the seasonal cycle, the pattern in NEE strongly resembles the negative of the pattern in GPP. Some notable aspects are:\n\nThe tundra (US-ICh) and boreal (FI-Hyy) sites are small sources of CO2 during winter and moderate sinks in summer.\nThe temperate site DE-Hai is a substantial sink in summer and a moderate source in winter. The peak of the source is attained in the shoulder seasons (April and November) - when temperatures are still above freezing and drive respiration, while leaves are already shed or not yet unfolded.\nThe annual total NEE is small for all sites and nearly zero for the tropical and the tundra sites (BR-Sa3 and US-ICh, respectively). The small NEE is the net of the two much larger opposing fluxes GPP and Reco.\n\n\n\n\n\n\nFigure 6.11: Mean seasonal cycle of (a) incident (top-of-canopy) shortwave radiation, (b) leaf area index, (c) gross primary production, and (d) net ecosystem exchange (NEE) for four different sites - a temperate deciduous forest (DE-Hai), a boreal needle-leaved forest (FI-Hyy), an arctic heathland in the tundra (US-ICh), and an evergreen moist tropical forest (BR-Sa3). Panel (e) shows the annual total GPP, Reco, and net ecosystem exchange (NEE). NEE is largely equivalent to the negative of NEP as defined in Section 5.1.6. Site locations are shown in Figure 2.2.\n\n\n\n\n\n\n\n\n\n\nExercise\n\n\n\n\nAt what latitude do you expect the largest diurnal cycle amplitude in top-of-atmosphere solar radiation?\nAt what latitude do you expect the largest seasonal amplitude in top-of-atmosphere solar radiation?\nWhere do you expect the smallest seasonal variation in the daily net ecosystem productivity?\nConsider mature forest ecosystems (sensu Odum (1969), Figure 5.7) in a moist tropical, temperate and boreal region. Where do you expect the largest annual NEP? Where do you expect the largest daily NEP during the peak growing season?\n\n\n\n\n\n6.3.2.1 The breathing of the Earth\nThe NEE (equivalent to the negative of NBP, introduced in Section 5.1.6) recorded at the four example sites shown above is representative for similar patterns across all vegetated land of the Earth. Seasonal variations in solar radiation are the underlying driver of the carbon flux variations and similarly affect all photosynthesizing organisms across the planet.\nCO2 is relatively well-mixed in the atmosphere due to its long lifetime. However, the mixing time scale is on the order of a couple of years. Hence, more rapid variations in net CO2 fluxes between the atmosphere and the Earth surface (over the ocean and over the land) are expressed in corresponding variations of the atmospheric CO2 concentration. As introduced in Section 1.1.1, the atmospheric CO2 concentration, measured at Mauna Loa (Hawaii) exhibits not only a steady increase since the 1950s, but also a seasonal cycle with the lowest value at the end of the northern hemisphere summer. Atmospheric CO2 is continuously measured at a range of sites along different latitudes. At Point Barrow, the northernmost point of the US in Alaska, the CO2 seasonal amplitude is even larger than at Mauna Loa (Figure 6.12). This is the result of the collective net CO2 uptake in northern ecosystems during summer.\nFigure 6.12 shows the seasonal variation in atmospheric CO2 after the mean and long-term trend are removed from the time series (corresponding to the red curve minus the black curve in Figure 1.1). The shape of this seasonal variation is very similar to the shape of the seasonal NEE variation at northern sites (e.g., DE-Hai) - above average during winter months when ecosystem respiration prevails and a rapid draw-down starting in spring to attain a minimum during summer. This shows how the patterns in net ecosystem CO2 exchange directly affect variations in atmospheric CO2 over the course of a year.\n\n\n\n\n\nFigure 6.12: Seasonal CO2 cycles observed at Barrow (C) and Mauna Loa (D) for the 1961-63 or 1958-63 and 2009-11 time periods. The first six months of the year are repeated. Figure from Graven et al. (2013).\n\n\n\n\nFigure 6.12 also shows that the CO2 seasonal amplitude has been increasing since measurements started in the early sixties of the 20th century. This increase reflects changes in the terrestrial C cycle (Graven et al. 2013) and is likely driven by the warming climate and the extension of the growing season in northern ecosystems, increasing the photosynthetic CO2 uptake as a result of the fertilizing effect of rising CO2, and seasonal shifts in GPP and Reco and their relative timing.\nThe video below shows an animation of the modeled spatial and temporal variations of atmospheric CO2 over the course of one year. CO2 sources from fossil fuel combustion by industry, households, and traffic are combined with the modeled terrestrial and oceanic net CO2 exchange between the Earth’s surface and the atmosphere. An atmospheric transport model is then used for simulating variations in CO2 concentrations." }, { "objectID": "globalcarbonpatterns.html#sec-fluxepools-spatial", "href": "globalcarbonpatterns.html#sec-fluxepools-spatial", "title": "6  Spatial and temporal patterns of the terrestrial carbon cycle", "section": "6.4 Spatial variations of ecosystem C fluxes and stocks", - "text": "6.4 Spatial variations of ecosystem C fluxes and stocks\nC fluxes between the a land ecosystem and the atmosphere vary over the course of a day and over the course of a year, as described above in Section 6.3. Annual totals vary relatively little between years (not shown). However, annual total C uptake and release fluxes vary very strongly across different geographical locations, climates and types of ecosystems. As much as solar radiation is the driver of temporal variations in photosynthetic CO2 uptake, it is also a strong driver of its spatial variations across the globe.\n\n6.4.1 Terrestrial primary productivity patterns\nOnce more, the light use efficiency model (Equation 4.1) serves as a guide for understanding the drivers of spatial patterns in terrestrial GPP. In this subsection, we follow the study by Wang, Prentice, and Davis (2014) and estimate the magnitude and global distribution of GPP by successively considering physical and physiological constraints on CO2 assimilation.\nWe start by adopting the hypothetical perspective from the top of the atmosphere (TOA). We estimate the geographic pattern of terrestrial photosynthesis if the full energy of solar radiation received at the TOA was used for photosynthetic CO2 assimilation (Figure 6.13 a). In this case, GPP is equal to the product of the quantum yield (\\(\\varphi_0\\)), a factor \\(\\tilde{a}\\) that accounts for the incomplete utilization of absorbed light by the light reactions, and the photosynthetically active radiation received at the top of the atmosphere (PARTOA in Figure 6.13, corresponds to ITOA in Equation 6.1). In this (hypothetical) case, the global distribution of GPP varies along latitudes, but not along longitudes and is estimated by Wang, Prentice, and Davis (2014) at 2960 PgC yr-1.\nNext, we consider the attenuation of solar radiation by the atmosphere, considering cloud cover and the elevation of the land surface. This considers Equation 6.2 and reflects the geographic pattern of distribution of solar radiation, incident at the land surface (Figure 6.1). Note that \\(\\varphi_0\\) and \\(\\tilde{a}\\) are considered here to be global constants. Atmospheric attenuation of photysnthetically active solar radiation reduces terrestrial GPP by over 50% (from 2960 to 1442 PgC yr-1, Wang, Prentice, and Davis (2014)).\nNot all solar radiation that reaches the land surface is absorbed by active green vegetation. The highest radiation intensities coincide with sparsely vegetated land, including major desert regions. The effect of reduced vegetation cover on GPP is quantified by the factor fAPAR which accounts for the fraction of absorbed photosynthetically active radiation (Section 4.2). Limited vegetation cover and light absorption reduces terrestrial GPP further by over 75% (from 1442 to 322 PgC yr-1, Wang, Prentice, and Davis (2014)).\nAt the global scale, temperature has a relatively weak effect on GPP. Considering that photosynthesis is inhibited by freezing temperatures (below 0°C) does not substantially reduce total terrestrial GPP (from 322 to 300 PgC yr-1, corresponding to a 7% reduction, Wang, Prentice, and Davis (2014)). This is because low temperatures coincide with low PAR (or \\(I_0\\)) and . Situations of high light and low temperatures are relatively rare.\nFinally, physiological effects of CO2, temperature, vapour pressure deficit, and the atmospheric pressure are considered. Note that the effect of temperatures below freezing is treated separately by the step described above. The potential maximum rate of the conversion of absorbed photosynthetically active radiation is reduced by the limited diffusion rate of CO2 through stomatal openings (thus reducing \\(c_i\\) relative to \\(c_a\\), Figure 6.13 e) and is further reduced by the effects of photorespiration as accounted for by the factor \\((c_i - \\Gamma^\\ast)/(c_i + 2\\Gamma^\\ast)\\). This represents the effect of leaf-internal CO2 concentration on the electron transport-limited assimilation rate \\(A_J\\) in the FvCB model (Equation 4.9). These physiological effects reduce terrestrial GPP from 300 to 211 PgC yr-1, corresponding to a 30% reduction (Wang, Prentice, and Davis 2014). Note that the range of published total annual terrestrial GPP estimates is lower - between 110 and 140 PgC yr-1 (Benjamin D. Stocker et al. 2019).\n\n\n\n\n\nFigure 6.13: Patterns of modelled global annual GPP (gC m-2 yr-1) controlled by PAR at the top of atmosphere (a), and modified by a sequence of effects: atmospheric transmissivity and cloud cover (b), vegetation cover (c), low-temperature inhibition (d) and physiological effects of CO2 (e). PARTOA corresponds to ITOA in Equation 6.1. Figure from Wang, Prentice, and Davis (2014).\n\n\n\n\n\n\n\n\n\n\nExercise\n\n\n\n\nWhich of the factors described above implies the strongest reduction in GPP? What resource limitation may be responsible for this large unrealised C assimilation?\n\n\n\n\n\n6.4.2 Global distribution of biomass carbon\nAs explained in Chapter 5, photosynthesis is the ultimate source of all C cycling in ecosystems and accumulating in different pools along the C cascade - from live vegetation to litter and soil organic matter. Variations in GPP thus affect all “downstream” fluxes and pools along the C cascade. A reflection of this is the similarity in the global patterns of GPP and aboveground biomass C (Figure 6.14). In Chapter 5, we considered the C cascade and simulated the dynamics of all pools and fluxes in response to a change in GPP. We showed that, assuming that allocation, SOM partitioning factors, and pool-specific turnover times are constant, GPP linearly scales all downstream fluxes and pools. We also noted that in reality, allocation, SOM partitioning, and turnover times cannot be assumed constant over time. When considering variations across space - across different climates, soils, and ecosystem types - constancy in these factors is probably an even less justified assumption.\nWhile Figure 6.14 shows an overall similarity between the patterns of GPP and aboveground carbon, it’s also instructive to consider the deviations. Aboveground biomass is by far largest in tropical forest regions. While temperate forest regions attain annual GPP of a similar magnitude as tropical forests (Figure 6.13 e), their aboveground biomass is substantially lower. Even more discrepant are differences between forest versus savannah and grassland regions. While the extent of the tropical forest biome in Africa is clearly reflected by the distribution of aboveground biomass and shows a sharp transition to much lower values at its margins, such a sharp transition is not visible for GPP (Figure 6.13 e). This indicates that grasslands and savannahs can be highly productive, but if assimilated C is not used for wood production, then their high productivity is not translated into high biomass stocks. This aspect is also explained in Section 5.1.3 where the difference in C allocation between forest and grasslands is described and quantified (Table 5.1).\n\n\n\n\n\nFigure 6.14: Aboveground biomass carbon, mean over years 1993-2012. Data from Liu et al. (2015). This is the same figure as Figure 2.18.\n\n\n\n\nWhile the global biomass map in Figure 6.14 shows the overall pattern of highest aboveground biomass C being located in tropical forests, it hides “pockets” of exceptionally high biomass in temperate forests. Some of the worlds highest biomass densities (average biomass per unit ground area in a forest plot) are found in cool and moist temperate forests, including Eucalyptus regnans-dominated forests in southeast Australia, Sequoia-dominated forests in coastal California, Oregon and Chile, and Agathis australis-dominated forests in New Zealand (Keith, Mackey, and Lindenmayer 2009).\n\n\n6.4.3 Global distribution of soil carbon\nIn Section 5.1.5, we conceived soil C dynamics as a first-order decay process. This assumes that the soil C stock scales linearly with the C inputs. C inputs are determined by litter production which, at long enough time scales, is equal to biomass production which, in turn, is correlated with GPP (Figure 5.3). In summary, a first-order decay model for SOM would predict that soil C stocks scale with GPP and the global distribution of soil C would be similar to the global distribution of GPP (Figure 6.13 e).\nHowever, Figure 6.15 shows that the pattern of the global soil C distribution is markedly different from the global pattern of GPP. This suggests that C inputs alone are not a good predictor of soil C stocks. Other factors play important roles, as described below. Note however that in unproductive desert regions, also soil C is low.\n\n\n\n\n\nFigure 6.15: Estimated soil organic carbon (SOC) stocks to a depth of 2 m based on data in the WISE30sec dataset (Batjes 2016). Figure and caption text from Jackson et al. (2017).\n\n\n\n\n\nControls on soil C stocks\nAllocation Root inputs are approximately five times more likely than an equivalent mass of aboveground litter to be stabilized as soil organic matter (SOM) (Jackson et al. 2017). Thus, allocation and plant growth in different tissues is an important factor determining the link between vegetation productivity, litter production, and soil C. In grasslands and shurblands, a much larger fraction of C is allocated to roots than in forests. Thus, soil C stocks are often higher in natural grasslands and shrublands than in forests. This is also visible in Figure 6.15 which indicates high soil C stocks in the Earth’s grassland and shrubland-dominated regions.\nClimate The activity of soil organic matter-decomposing microbes (fungi and bacteria) is strongly controlled by abiotic factors in the soil. Under low temperatures, their activity is reduced and soil and litter decomposition rates are slowed (see also Section 5.1.5). This is reflected in Figure 6.15 by the generally high soil organic C stocks in the cold climates of the high northern latitudes - despite the generally low productivity of vegetation in these regions.\nStabilisation and saturation of soil organic C depends on the mineralogy of the soil. This suggests that not (only) the C inputs determine stocks, but also the capacity of soil mineral surfaces to sorb organic matter.\nPlant-soil interactions via fungi and bacteria strongly influence C and nutrient cycling in soils. Inputs of fresh litter and labile C through root exudates can stimulate the decomposition (priming) of stable C in the soil. These relationships are complex and implications for the global distribution of soil C is not clear, but can undermine a positive and linear relationship between vegetation productivity, litter inputs, and soil C stocks.\n\n\nGlobal soil C stocks\nThe total C stock in soils up to 2 m is estimated 2273 PgC by Jackson et al. (2017) - higher than the number provided in the IPCC AR6 (Canadell et al. 2021) and Figure 3.1. Global soil C estimates are based on soil organic C content measurements which are available mostly from the top soil and are thus sensitive to assumptions regarding the soil C distribution across the soil profile. In general, the organic matter and thus soil C content declines with depth but the rate of decline depends on vegetation and the distribution of roots. The global soil C stock of 0-3 m is even higher and estimated by Jackson et al. (2017) at 2800 PgC. The soil depth-to-bedrock puts a constraint on soil C storage at depth in many places, is very uncertain, and may lead to a substantial reduction of the total 0-2 and 0-3 m soil C estimates.\nThe high soil C density in high northern latitudes (Figure 6.15) reflects also the particular functioning and soil C dynamics dynamics and stabilization under conditions where temperatures are below freezing for a large part of the year (in permafrost regions) and under permanently water-logged soil conditions (in peatlands). Contributions of soil C stocks in peatland and permafrost regions are substantial (see Section 6.4.4 and Section 6.4.5).\n\n\n6.4.3.1 Link to biomass C distribution\nTaken together, the global distribution of soil C deviates strongly from the distribution of GPP and biomass C. The parallel trends of average biomass and soil C along latitudes is shown in Figure 6.16 and illustrates the divergence of their latitudinal patterns. It should be noted that grasslands are typically very soil C rich due to the high allocation to fine root production as discussed above. Yet, aboveground biomass is low in grasslands compared to forests. This largely explains the pattern in Figure 6.16.\n\n\n\n\n\nFigure 6.16: The latitudinal patterns of terrestrial carbon stocks, both aboveground plant biomass (green) and soil carbon stocks (brown). Figure and caption text from Crowther et al. (2019).\n\n\n\n\n\n\n\n6.4.4 Peatlands\nUnder well-drained soil conditions, the organic carbon content of soil tends to stabilise during soil development. At this stage, on average over long time scales, decomposition of organic matter equals litter inputs. A steady-state is reached. However, decomposition by heterotrophic organisms requires oxygen. Under frequent flooding and water-logged soil conditions, oxygen availability becomes limiting for heterotrophic activity and decomposition is strongly reduced. If a long-term imbalance of vegetation productivity and litter inputs vs. decomposition persists, undecomposed litter C can accumulate. Peat and organic soils (histosols) form. Such conditions are given in very particular locations across the globe (Figure 6.17).\nPeatlands are extremely C-rich, containing 500-700 PgC on only 3% of the Earth’s land surface (Page and Baird 2016; Yu et al. 2010). Collectively, peatlands across the globe are also a persistent C sink. Due to their special role in the C cycle, we afford a small excursion into the special world of peatlands.\n\n\n\n\n\n\nDefinitions\n\n\n\n\nPeat is the material that constitutes soils in peatlands.\nPeatland is a type of wetland where peat is present.\nBog is a nutrient-poor type of peatlands.\nRaised bog (ombrotrophic bog, German: Hochmoor) is a bog in which organic matter has accumulated vertically to a degree such that plants with their roots are disconnected from the water table and receive nutrient inputs solely from atmospheric wet and dry deposition. Raised bogs are extremely nutrient-poor, acidic, and are dominated by mosses (sphagnum).\nFen is a more nutrient-enriched type of peatland, is more alkaline, and dominated by sedges and grasses, but can also host shrubs and sparse trees. Plants growing in fens have access to water that has been in touch with mineral soils and bedrock and contains dissolved minerals. Hence, fens are referred to as minerotrophic.\n\n\n\n\nPeatland distribution\nIn view of the frequent flooding and wet soil conditions, peatlands are considered a type of wetland. They occur in a wide range of biomes. In the tropics, decomposition rates - even under water logging - are much higher than in the Arctic. Yet, vegetation productivity is much higher, too, and can lead to an imbalance of organic matter inputs and decomposition and a long-term accumulation.\nToday, major peatlands are located in the Hudson Bay Lowland (Canada) and in the West Siberian Lowland (Russia). In the tropics, major peatlands are located in Southeast Asia (Indonesia, Malaysia, Papua New Guinea, and Brunei) (Page and Baird 2016) and in the Congo Basin (Dargie et al. 2017). Peatland vegetation is very different in boreal and temperate versus tropical peatlands. The latter occur in forested, often palm-dominated swamps and in coastal mangroves (Page and Baird 2016). Boreal and temperate peatlands are dominated by sedges or mosses (see box above).\n\n\n\n\n\nFigure 6.17: Global peatland distribution derived from PEATMAP. The colour classes indicate percentage peatland cover in Canada, where the source data were provided as grid cells rather than shape files; and regions where peatland cover was estimated from histosols of HWSD v1.2. Elsewhere, where shapefiles are freely available, individual peatlands and peat complexes are shown in solid black. Figure and caption text from Xu et al. (2018).\n\n\n\n\n\n\nPeatland establishment\nThe particular pattern of the global distribution of peatlands (Figure 6.17) reflects the environmental constraints on their development. This can be understood as a sequence of criteria that need to be fulfilled for the establishment of a peatland (B. D. Stocker, Spahni, and Joos 2014):\n\nHydroclimate: The balance of mean annual precipitation (MAP) should be higher than the mean annual potential evapotranspiration (PET, see Chapter 8). PET measures how much radiation is available for evaporating water. A positive ratio of MAP/PET indicates a wet hydroclimate and is a primary prerequisite for the establishment of a peatland.\nC balance: Under water-logged conditions, vegetation productivity and litter inputs must outpace soil organic matter decomposition and a long-term C accumulation is necessary to form peat.\nTopography and soil drainage: Water-logged soil conditions and a shallow groundwater table depth are present in the landscape where subsurface water flow converges and where drainage is hindered either due to the topographic situation or due to impermeable soil layers or bedrock. Frequent conditions with the groundwater table near the surface or above (inundation) thus occur in low-lying depressions or in poorly drained plains, but less in convex terrain (e.g, ridges).\n\n\n\nPeat growth\nPeat is undecomposed plant material. Most of this material accumulates at the surface. In sphagnum-dominated bogs, all of this material accumulates at the surface since sphagnum forms no roots. Hence, peat grows vertically. Eventually, peat domes form and the peatland transitions to becoming a raised bog (see box above).\nPeat layers form in each year by added litter, are subsequently covered by the next layer, and slowly decay over time, losing mass and volume. The oldest peat is found at its base, the youngest at the top. Due to the age-depth relation, peat soils also serve as a paleo archive.\n\n\nPeatland history\nDue to the very slow decay, oldest peat present at a peat dome’s base may date back millennia. Indeed, dated carbon in peatlands across the globe indicate a peak in the initiation of northern peatlands in the early Holocene around 11-9 kyr BP and of tropical peatlands even before - around 20 kyr BP (Yu et al. 2010; MacDonald et al. 2006) and. The timing of the rapid initiation of northern peatlands coincides with the retreat of the major ice sheets after the Last Glacial Maximum and with a peak in summer insolation (Figure 6.6 and Figure 6.18) and climate seasonality with warm summers in the northern hemisphere, supporting vegetation growth. As new peatlands formed in the early Holocene, old ones that established in the glacial climate, disappeared due to climatic change (Müller and Joos 2020) and were lost to rising sea levels during the melting of the ice sheets (Dommain et al. 2014).\n\n\n\n\n\nFigure 6.18: Timing of circumarctic peatland establishment compared with June insolation at 60°N, Greenland Ice Sheet Project 2 (GISP2) temperature reconstruction, atmospheric CO2 and CH4 concentrations, and estimates of Northern Hemisphere CH4 emissions derived from the InterPolar CH4 Gradient (IPG). Atmospheric CO2 and CH4 concentrations show ice-core data from European Project for Ice Coring in Antarctica (EPICA) Dome C (red for CO2 and blue for CH4)and GISP2 [green triangles show CH4]. Dome C data are shown on the original EPICA Dome C 1 time scale from 0 to 10 ka before present (circles) and on the GISP2 time scale with CH4 synchronization from 10 to 18 kyr before present (diamonds). Dome C error bars indicate 1sd uncertainty. (A) The occurrence frequency of 1516 radiocarbon dates of basal peat deposits (14) shows the number of calibrated age ranges that occur in any year (black curve). (B) Cumulative curve of 1516 dates (red curve). (C) The oldest basal peat dates within each 2° by 2° grid (gray bars). Figure and caption from MacDonald et al. (2006)\n\n\n\n\n\n\nPeatlands and the global carbon cycle\nAs mentioned above, peatlands store 500-700 PgC (more than all biomass C globally) on only 3% of the Earth’s land surface (Page and Baird 2016; Yu et al. 2010). Since the majority of the peat present today has accumulated over the course of the Holocene, an average C sink of >5 PgC (100 yr)-1 has persisted over the same duration (Yu et al. 2010). This is much smaller than the global fluxes of the anthropogenic C cycle perturbation, as quantified by the global carbon budget in Chapter 3. Yet, its persistent nature and the magnitude of long-term C accumulation has had implications for millennial-scale terrestrial carbon storage changes and atmospheric CO2 (Benjamin David Stocker et al. 2017). Due to their susceptibility to hydro-climatic conditions, peatland extent, global distribution, and C storage will likely undergo changes in a future climate. However, current research and model projections indicate unclear trends (Qiu et al. 2022).\nPeatlands, as all wetlands, are also a major source of methane (CH4). Under anoxic soil conditions, CH4 is produced, rather than C being oxidized and CO2 released (Chapter 12).\n\n\n\n\n\n\nExercise\n\n\n\n\nWater table variations affect the C balance of a peatland. If it falls, how do you expect NPP, Reco, and NEP of a peatland, and the turnover time of C in soil organic matter to change?\nWhat other greenhouse gas may be influenced by a declining water table in a peatland? In what direction would its emission change?\nWhy are soils dark in the Seeland of the Canton of Bern?\nWhy are wooden artefacts of the Bronze age preserved in some places but not in others? Do you know any such wooden artefacts?\n\n\n\n\n\n\n6.4.5 Permafrost\nAbout 24% of the northern hemisphere’s exposed land surface contains ground that remains frozen for at least two consecutive years - the definition of permafrost (Schuur and Mack 2018). The global distriution of permafrost in the northern hemisphere is shown in Figure 6.19. Organic matter in frozen soils is protected from decomposition - as long as the ground remains frozen. The total amount of C stored in permafrost soils (0-3 m depth) is estimated at 1,035 ± 150 PgC (Tarnocai et al. 2009; Hugelius et al. 2014) and substantial additional C (400-500 PgC) is stored at greater depth in particular locations (river sediments) (Schuur and Mack 2018). This amount of C adds another 50-100% to the total amount of C stored in soils (Figure 3.1) and suggests that the distribution of permafrost is an important determinant for the global distribution of soil C (Figure 6.15).\n\n\n\n\n\nFigure 6.19: Permafrost zone regions shown in shades of blue with percent of ground underlain by permafrost in parentheses. Generalized biome area for tundra and boreal regions shows intersection with permafrost across most, but not all, of these regions. Map created by Chris DeRolph, Oak Ridge National Laboratory, using data from various sources. Figure and caption from Schuur and Mack (2018).\n\n\n\n\nPermafrost occurs (roughly) where the mean annual temperature is below freezing. During summer, the upper soil layers, the active layer, thaw. However, the seasonal fluctuation of soil temperature is attenuated deeper in the soil due to constraints on the rate of thermal diffusion across the soil. At a certain depth, the seasonal cycle of soil temperature disappears and the soil temperature is largely constant and equal to the mean annual air temperature on the ground (\\(Z^\\ast\\) in Figure 6.20). Towards greater depth, the temperature increases again due to the geothermal heat flux. Permafrost is zone where temperatures never rise beyond 0°C.\n\n\n\n\n\nFigure 6.20: Thermal regime of permafrost. Schematic showing the maximum (red line) and minimum ground temperature (blue line) during the year, and their convergence to give the mean annual ground temperature T at the depth of zero annual amplitude Z*. Black dots show the schematic mean temperature for permafrost soils. Figure and caption from Biskaborn et al. (2019)\n\n\n\n\nThe presence of permafrost constrains the volume available for plant rooting, vegetation access to water and nutrients, and the heterotrophic activity if microbes. 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Evans, and Guojie Wang. 2015. “Recent Reversal in Loss of Global Terrestrial Biomass.” Nature Climate Change 5 (5): 470–74. https://doi.org/10.1038/nclimate2581.\n\n\nMacDonald, Glen M., David W. Beilman, Konstantine V. Kremenetski, Yongwei Sheng, Laurence C. Smith, and Andrei A. Velichko. 2006. “Rapid Early Development of Circumarctic Peatlands and Atmospheric CH4 and CO2 Variations.” Science 314 (5797): 285–88. https://doi.org/10.1126/science.1131722.\n\n\nMacDonald, Glen M., Andrei A. Velichko, Constantine V. Kremenetski, Olga K. Borisova, Aleksandra A. Goleva, Andrei A. Andreev, Les C. Cwynar, et al. 2000. “Holocene Treeline History and Climate Change Across Northern Eurasia.” Quaternary Research 53 (3): 302–11. https://doi.org/10.1006/qres.1999.2123.\n\n\nMüller, Jurek, and Fortunat Joos. 2020. “Global Peatland Area and Carbon Dynamics from the Last Glacial Maximum to the Present – a Process-Based Model Investigation.” Biogeosciences 17 (21): 5285–5308. https://doi.org/10.5194/bg-17-5285-2020.\n\n\nOdum, Eugene P. 1969. “The Strategy of Ecosystem Development.” Science 164 (3877): 262–70. https://doi.org/10.1126/science.164.3877.262.\n\n\nPage, S. E., and A. J. Baird. 2016. “Peatlands and Global Change: Response and Resilience.” Annual Review of Environment and Resources 41 (Volume 41, 2016): 35–57. https://doi.org/10.1146/annurev-environ-110615-085520.\n\n\nPiao, Shilong, Qiang Liu, Anping Chen, Ivan A. Janssens, Yongshuo Fu, Junhu Dai, Lingli Liu, Xu Lian, Miaogen Shen, and Xiaolin Zhu. 2019. “Plant Phenology and Global Climate Change: Current Progresses and Challenges.” Global Change Biology 25 (6): 1922–40. https://doi.org/10.1111/gcb.14619.\n\n\nPrentice, I Colin, D. Jolly, and BIOME 6000 Participants. 2000. “Mid-Holocene and Glacial-Maximum Vegetation Geography of the Northern Continents and Africa.” Journal of Biogeography 27 (3): 507–19. http://www.jstor.org/stable/2656208.\n\n\nQiu, Chunjing, Philippe Ciais, Dan Zhu, Bertrand Guenet, Jinfeng Chang, Nitin Chaudhary, Thomas Kleinen, et al. 2022. “A Strong Mitigation Scenario Maintains Climate Neutrality of Northern Peatlands.” One Earth, January. https://doi.org/10.1016/j.oneear.2021.12.008.\n\n\nRichardson, Andrew D., Trevor F. Keenan, Mirco Migliavacca, Youngryel Ryu, Oliver Sonnentag, and Michael Toomey. 2013. “Climate Change, Phenology, and Phenological Control of Vegetation Feedbacks to the Climate System.” Agricultural and Forest Meteorology 169 (February): 156–73. https://doi.org/10.1016/j.agrformet.2012.09.012.\n\n\nSchuur, Edward A. G., and Michelle C. Mack. 2018. “Ecological Response to Permafrost Thaw and Consequences for Local and Global Ecosystem Services.” Annual Review of Ecology, Evolution, and Systematics 49 (Volume 49, 2018): 279–301. https://doi.org/10.1146/annurev-ecolsys-121415-032349.\n\n\nStocker, B. D., R. Spahni, and F. Joos. 2014. “DYPTOP: A Cost-Efficient TOPMODEL Implementation to Simulate Sub-Grid Spatio-Temporal Dynamics of Global Wetlands and Peatlands.” Geoscientific Model Development 7 (6): 3089–3110. https://doi.org/10.5194/gmd-7-3089-2014.\n\n\nStocker, Benjamin David, Zicheng Yu, Charly Massa, and Fortunat Joos. 2017. “Holocene Peatland and Ice-Core Data Constraints on the Timing and Magnitude of CO2 Emissions from Past Land Use.” Proceedings of the National Academy of Sciences 114 (7): 1492–97. https://doi.org/10.1073/pnas.1613889114.\n\n\nStocker, Benjamin D., Jakob Zscheischler, Trevor F. Keenan, I. Colin Prentice, Sonia I. Seneviratne, and Josep Peñuelas. 2019. “Drought Impacts on Terrestrial Primary Production Underestimated by Satellite Monitoring.” Nature Geoscience 12 (4): 264–70. https://doi.org/10.1038/s41561-019-0318-6.\n\n\nTarnocai, C., J. G. Canadell, E. a. G. Schuur, P. Kuhry, G. Mazhitova, and S. Zimov. 2009. “Soil Organic Carbon Pools in the Northern Circumpolar Permafrost Region.” Global Biogeochemical Cycles 23 (2). https://doi.org/10.1029/2008GB003327.\n\n\nWang, H., I. C. Prentice, and T. W. Davis. 2014. “Biophsyical Constraints on Gross Primary Production by the Terrestrial Biosphere.” Biogeosciences 11 (20): 5987–6001. https://doi.org/10.5194/bg-11-5987-2014.\n\n\nXu, Jiren, Paul J. Morris, Junguo Liu, and Joseph Holden. 2018. “PEATMAP: Refining Estimates of Global Peatland Distribution Based on a Meta-Analysis.” CATENA 160 (January): 134–40. https://doi.org/10.1016/j.catena.2017.09.010.\n\n\nYu, Zicheng, Julie Loisel, Daniel P. Brosseau, David W. Beilman, and Stephanie J. Hunt. 2010. “Global Peatland Dynamics Since the Last Glacial Maximum.” Geophysical Research Letters 37 (13). https://doi.org/10.1029/2010GL043584." + "text": "6.4 Spatial variations of ecosystem C fluxes and stocks\nC fluxes between the a land ecosystem and the atmosphere vary over the course of a day and over the course of a year, as described above in Section 6.3. Annual totals vary relatively little between years (not shown). However, annual total C uptake and release fluxes vary very strongly across different geographical locations, climates and types of ecosystems. As much as solar radiation is the driver of temporal variations in photosynthetic CO2 uptake, it is also a strong driver of its spatial variations across the globe.\n\n6.4.1 Terrestrial primary productivity patterns\nOnce more, the light use efficiency model (Equation 4.1) serves as a guide for understanding the drivers of spatial patterns in terrestrial GPP. In this subsection, we follow the study by Wang, Prentice, and Davis (2014) and estimate the magnitude and global distribution of GPP by successively considering physical and physiological constraints on CO2 assimilation.\nWe start by adopting the hypothetical perspective from the top of the atmosphere (TOA). We estimate the geographic pattern of terrestrial photosynthesis if the full energy of solar radiation received at the TOA was used for photosynthetic CO2 assimilation (Figure 6.13 a). In this case, GPP is equal to the product of the quantum yield (\\(\\varphi_0\\)), a factor \\(\\tilde{a}\\) that accounts for the incomplete utilization of absorbed light by the light reactions, and the photosynthetically active radiation received at the top of the atmosphere (PARTOA in Figure 6.13, corresponds to ITOA in Equation 6.1). In this (hypothetical) case, the global distribution of GPP varies along latitudes, but not along longitudes and is estimated by Wang, Prentice, and Davis (2014) at 2960 PgC yr-1.\nNext, we consider the attenuation of solar radiation by the atmosphere, considering cloud cover and the elevation of the land surface. This considers Equation 6.2 and reflects the geographic pattern of distribution of solar radiation, incident at the land surface (Figure 6.1). Note that \\(\\varphi_0\\) and \\(\\tilde{a}\\) are considered here to be global constants. Atmospheric attenuation of photysnthetically active solar radiation reduces terrestrial GPP by over 50% (from 2960 to 1442 PgC yr-1, Wang, Prentice, and Davis (2014)).\nNot all solar radiation that reaches the land surface is absorbed by active green vegetation. The highest radiation intensities coincide with sparsely vegetated land, including major desert regions. The effect of reduced vegetation cover on GPP is quantified by the factor fAPAR which accounts for the fraction of absorbed photosynthetically active radiation (Section 4.2). Limited vegetation cover and light absorption reduces terrestrial GPP further by over 75% (from 1442 to 322 PgC yr-1, Wang, Prentice, and Davis (2014)).\nAt the global scale, temperature has a relatively weak effect on GPP. Considering that photosynthesis is inhibited by freezing temperatures (below 0°C) does not substantially reduce total terrestrial GPP (from 322 to 300 PgC yr-1, corresponding to a 7% reduction, Wang, Prentice, and Davis (2014)). This is because low temperatures coincide with low PAR (or \\(I_0\\)). Situations of high light and low temperatures are relatively rare.\nFinally, physiological effects of CO2, temperature, vapor pressure deficit, and the atmospheric pressure are considered. Note that the effect of temperatures below freezing is treated separately by the step described above. The potential maximum rate of the conversion of absorbed photosynthetically active radiation is reduced by the limited diffusion rate of CO2 through stomatal openings (thus reducing \\(c_i\\) relative to \\(c_a\\), Figure 6.13 e) and is further reduced by the effects of photorespiration as accounted for by the factor \\((c_i - \\Gamma^\\ast)/(c_i + 2\\Gamma^\\ast)\\). This represents the effect of leaf-internal CO2 concentration on the electron transport-limited assimilation rate \\(A_J\\) in the FvCB model (Equation 4.9). These physiological effects reduce terrestrial GPP from 300 to 211 PgC yr-1, corresponding to a 30% reduction (Wang, Prentice, and Davis 2014). Note that the range of published total annual terrestrial GPP estimates is lower - between 110 and 140 PgC yr-1 (Benjamin D. Stocker et al. 2019).\n\n\n\n\n\nFigure 6.13: Patterns of modelled global annual GPP (gC m-2 yr-1) controlled by PAR at the top of atmosphere (a), and modified by a sequence of effects: atmospheric transmissivity and cloud cover (b), vegetation cover (c), low-temperature inhibition (d) and physiological effects of CO2 (e). PARTOA corresponds to ITOA in Equation 6.1. Figure from Wang, Prentice, and Davis (2014).\n\n\n\n\n\n\n\n\n\n\nExercise\n\n\n\n\nWhich of the factors described above implies the strongest reduction in GPP? What resource limitation may be responsible for this large unrealised C assimilation?\n\n\n\n\n\n6.4.2 Global distribution of biomass carbon\nAs explained in Chapter 5, photosynthesis is the ultimate source of all C cycling in ecosystems and accumulating in different pools along the C cascade - from live vegetation to litter and soil organic matter. Variations in GPP thus affect all “downstream” fluxes and pools along the C cascade. A reflection of this is the similarity in the global patterns of GPP and aboveground biomass C (Figure 6.14). In Chapter 5, we considered the C cascade and simulated the dynamics of all pools and fluxes in response to a change in GPP. We showed that, assuming that allocation, SOM partitioning factors, and pool-specific turnover times are constant, GPP linearly scales all downstream fluxes and pools. We also noted that in reality, allocation, SOM partitioning, and turnover times cannot be assumed constant over time. When considering variations across space - across different climates, soils, and ecosystem types - constancy in these factors is probably an even less justified assumption.\nWhile Figure 6.14 shows an overall similarity between the patterns of GPP and aboveground carbon, it’s also instructive to consider the deviations. Aboveground biomass is by far largest in tropical forest regions. While temperate forest regions attain annual GPP of a similar magnitude as tropical forests (Figure 6.13 e), their aboveground biomass is substantially lower. Even more discrepant are differences between forest versus savannah and grassland regions. While the extent of the tropical forest biome in Africa is clearly reflected by the distribution of aboveground biomass and shows a sharp transition to much lower values at its margins, such a sharp transition is not visible for GPP (Figure 6.13 e). This indicates that grasslands and savannahs can be highly productive, but if assimilated C is not used for wood production, then their high productivity is not translated into high biomass stocks. This aspect is also explained in Section 5.1.3 where the difference in C allocation between forest and grasslands is described and quantified (Table 5.1).\n\n\n\n\n\nFigure 6.14: Aboveground biomass carbon, mean over years 1993-2012. Data from Liu et al. (2015). This is the same figure as Figure 2.18.\n\n\n\n\nWhile the global biomass map in Figure 6.14 shows the overall pattern of highest aboveground biomass C being located in tropical forests, it hides “pockets” of exceptionally high biomass in temperate forests. Some of the world’s highest biomass densities (average biomass per unit ground area in a forest plot) are found in cool and moist temperate forests, including Eucalyptus regnans-dominated forests in southeast Australia, Sequoia-dominated forests in coastal California, Oregon and Chile, and Agathis australis-dominated forests in New Zealand (Keith, Mackey, and Lindenmayer 2009).\n\n\n6.4.3 Global distribution of soil carbon\nIn Section 5.1.5, we conceived soil C dynamics as a first-order decay process. This assumes that the soil C stock scales linearly with the C inputs. C inputs are determined by litter production which, at long enough time scales, is equal to biomass production which, in turn, is correlated with GPP (Figure 5.3). In summary, a first-order decay model for SOM would predict that soil C stocks scale with GPP and the global distribution of soil C would be similar to the global distribution of GPP (Figure 6.13 e).\nHowever, Figure 6.15 shows that the pattern of the global soil C distribution is markedly different from the global pattern of GPP. This suggests that C inputs alone are not a good predictor of soil C stocks. Other factors play important roles, as described below. Note however that in unproductive desert regions, also soil C is low.\n\n\n\n\n\nFigure 6.15: Estimated soil organic carbon (SOC) stocks to a depth of 2 m based on data in the WISE30sec dataset (Batjes 2016). Figure and caption text from Jackson et al. (2017).\n\n\n\n\n\nControls on soil C stocks\nAllocation Root inputs are approximately five times more likely than an equivalent mass of aboveground litter to be stabilized as soil organic matter (SOM) (Jackson et al. 2017). Thus, allocation and plant growth in different tissues is an important factor determining the link between vegetation productivity, litter production, and soil C. In grasslands and shurblands, a much larger fraction of C is allocated to roots than in forests. Thus, soil C stocks are often higher in natural grasslands and shrublands than in forests. This is also visible in Figure 6.15 which indicates high soil C stocks in the Earth’s grassland and shrubland-dominated regions.\nClimate The activity of soil organic matter-decomposing microbes (fungi and bacteria) is strongly controlled by abiotic factors in the soil. Under low temperatures, their activity is reduced, and soil and litter decomposition rates are slowed (see also Section 5.1.5). This is reflected in Figure 6.15 by the generally high soil organic C stocks in the cold climates of the high northern latitudes - despite the generally low productivity of vegetation in these regions.\nSoil mineral composition Stabilisation and saturation of soil organic C depends on the mineralogy of the soil. This suggests that not (only) the C inputs determine stocks, but also the capacity of soil mineral surfaces to adsorb organic matter.\nPlant-soil interactions Plant-soil interactions via fungi and bacteria strongly influence C and nutrient cycling in soils. Inputs of fresh litter and labile C through root exudates can stimulate the decomposition (priming) of stable C in the soil. These relationships are complex and implications for the global distribution of soil C is not clear, but can undermine a positive and linear relationship between vegetation productivity, litter inputs, and soil C stocks.\n\n\n\nGlobal soil C stocks\nThe total C stock in soils up to 2 m is estimated 2273 PgC by Jackson et al. (2017) - higher than the number provided in the IPCC AR6 (Canadell et al. 2021) and Figure 3.1. Global soil C estimates are based on soil organic C content measurements which are available mostly from the top soil and are thus sensitive to assumptions regarding the soil C distribution across the soil profile. In general, the organic matter and thus soil C content declines with depth but the rate of decline depends on vegetation and the distribution of roots. The global soil C stock of 0-3 m is even higher and estimated by Jackson et al. (2017) at 2800 PgC. The soil depth-to-bedrock puts a constraint on soil C storage at depth in many places, which is very uncertain, and may lead to a substantial reduction of the total 0-2 and 0-3 m soil C estimates.\nThe high soil C density in high northern latitudes (Figure 6.15) reflects also the particular functioning and soil C dynamics and stabilization under conditions where temperatures are below freezing for a large part of the year (in permafrost regions) and under permanently water-logged soil conditions (in peatlands). Contributions of soil C stocks in peatland and permafrost regions are substantial (see Section 6.4.4 and Section 6.4.5).\n\n\n6.4.3.1 Link to biomass C distribution\nTaken together, the global distribution of soil C deviates strongly from the distribution of GPP and biomass C. The parallel trends of average biomass and soil C along latitudes is shown in Figure 6.16 and illustrates the divergence of their latitudinal patterns. It should be noted that grasslands are typically very soil C rich due to the high allocation to fine root production as discussed above. Yet, aboveground biomass is low in grasslands compared to forests. This largely explains the pattern in Figure 6.16.\n\n\n\n\n\nFigure 6.16: The latitudinal patterns of terrestrial carbon stocks, both aboveground plant biomass (green) and soil carbon stocks (brown). Figure and caption text from Crowther et al. (2019).\n\n\n\n\n\n\n\n6.4.4 Peatlands\nUnder well-drained soil conditions, the organic carbon content of soil tends to stabilise during soil development. At this stage, on average over long time scales, decomposition of organic matter equals litter inputs. A steady-state is reached. However, decomposition by heterotrophic organisms requires oxygen. Under frequent flooding and water-logged soil conditions, oxygen availability becomes limiting for heterotrophic activity and decomposition is strongly reduced. If a long-term imbalance of vegetation productivity and litter inputs vs. decomposition persists, undecomposed litter C can accumulate. Peat and organic soils (histosols) form. Such conditions are given in very particular locations across the globe (Figure 6.17).\nPeatlands are extremely C-rich, containing 500-700 PgC on only 3% of the Earth’s land surface (Page and Baird 2016; Yu et al. 2010). Collectively, peatlands across the globe are also a persistent C sink. Due to their special role in the C cycle, we afford a small excursion into the special world of peatlands.\n\n\n\n\n\n\nDefinitions\n\n\n\n\nPeat is the material that constitutes soils in peatlands.\nPeatland is a type of wetland where peat is present.\nBog is a nutrient-poor type of peatlands.\nRaised bog (ombrotrophic bog, German: Hochmoor) is a bog in which organic matter has accumulated vertically to a degree such that plants with their roots are disconnected from the water table and receive nutrient inputs solely from atmospheric wet and dry deposition. Raised bogs are extremely nutrient-poor, acidic, and are dominated by mosses (sphagnum).\nFen is a more nutrient-enriched type of peatland, is more alkaline, and dominated by sedges and grasses, but can also host shrubs and sparse trees. Plants growing in fens have access to water that has been in touch with mineral soils and bedrock and contains dissolved minerals. Hence, fens are referred to as minerotrophic.\n\n\n\n\nPeatland distribution\nIn view of the frequent flooding and wet soil conditions, peatlands are considered a type of wetland. They occur in a wide range of biomes. In the tropics, decomposition rates - even under water logging - are much higher than in the Arctic. Yet, vegetation productivity is much higher, too, and can lead to an imbalance of organic matter inputs and decomposition and a long-term accumulation.\nToday, major peatlands are located in the Hudson Bay Lowland (Canada) and in the West Siberian Lowland (Russia). In the tropics, major peatlands are located in Southeast Asia (Indonesia, Malaysia, Papua New Guinea, and Brunei) (Page and Baird 2016) and in the Congo Basin (Dargie et al. 2017). Peatland vegetation is very different in boreal and temperate versus tropical peatlands. The latter occurs in forested, often palm-dominated swamps and in coastal mangroves (Page and Baird 2016). Boreal and temperate peatlands are dominated by sedges or mosses (see box above).\n\n\n\n\n\nFigure 6.17: Global peatland distribution derived from PEATMAP. The colour classes indicate percentage peatland cover in Canada, where the source data were provided as grid cells rather than shape files; and regions where peatland cover was estimated from histosols of HWSD v1.2. Elsewhere, where shapefiles are freely available, individual peatlands and peat complexes are shown in solid black. Figure and caption text from Xu et al. (2018).\n\n\n\n\n\n\nPeatland establishment\nThe particular pattern of the global distribution of peatlands (Figure 6.17) reflects the environmental constraints on their development. This can be understood as a sequence of criteria that need to be fulfilled for the establishment of a peatland (B. D. Stocker, Spahni, and Joos 2014):\n\nHydroclimate: The balance of mean annual precipitation (MAP) should be higher than the mean annual potential evapotranspiration (PET, see Chapter 8). PET measures how much radiation is available for evaporating water. A positive ratio of MAP/PET indicates a wet hydroclimate and is a primary prerequisite for the establishment of a peatland.\nC balance: Under water-logged conditions, vegetation productivity and litter inputs must outpace soil organic matter decomposition and a long-term C accumulation is necessary to form peat.\nTopography and soil drainage: Water-logged soil conditions and a shallow groundwater table depth are present in the landscape where subsurface water flow converges and where drainage is hindered either due to the topographic situation or due to impermeable soil layers or bedrock. Frequent conditions with the groundwater table near the surface or above (inundation) thus occur in low-lying depressions or in poorly drained plains, but less in convex terrain (e.g, ridges).\n\n\n\nPeat growth\nPeat is undecomposed plant material. Most of this material accumulates at the surface. In sphagnum-dominated bogs, all of this material accumulates at the surface since sphagnum forms no roots. Hence, peat grows vertically. Eventually, peat domes form and the peatland transitions to becoming a raised bog (see box above).\nPeat layers form in each year by added litter, are subsequently covered by the next layer, and slowly decay over time, losing mass and volume. The oldest peat is found at its base, the youngest at the top. Due to the age-depth relation, peat soils also serve as a paleo archive.\n\n\nPeatland history\nDue to the very slow decay, the oldest peat present at a peat dome’s base may date back millennia. Indeed, dated carbon in peatlands across the globe indicates a peak in the initiation of northern peatlands in the early Holocene around 11-9 kyr BP and of tropical peatlands even before - around 20 kyr BP (Yu et al. 2010; MacDonald et al. 2006). The timing of the rapid initiation of northern peatlands coincides with the retreat of the major ice sheets after the Last Glacial Maximum and with a peak in summer insolation (Figure 6.6 and Figure 6.18) and climate seasonality with warm summers in the northern hemisphere, supporting vegetation growth. As new peatlands formed in the early Holocene, old ones that established in the glacial climate disappeared due to climatic change (Müller and Joos 2020) and were lost to rising sea levels during the melting of the ice sheets (Dommain et al. 2014).\n\n\n\n\n\nFigure 6.18: Timing of circumarctic peatland establishment compared with June insolation at 60°N, Greenland Ice Sheet Project 2 (GISP2) temperature reconstruction, atmospheric CO2 and CH4 concentrations, and estimates of Northern Hemisphere CH4 emissions derived from the InterPolar CH4 Gradient (IPG). Atmospheric CO2 and CH4 concentrations show ice-core data from European Project for Ice Coring in Antarctica (EPICA) Dome C (red for CO2 and blue for CH4)and GISP2 [green triangles show CH4]. Dome C data are shown on the original EPICA Dome C 1 time scale from 0 to 10 ka before present (circles) and on the GISP2 time scale with CH4 synchronization from 10 to 18 kyr before present (diamonds). Dome C error bars indicate 1sd uncertainty. (A) The occurrence frequency of 1516 radiocarbon dates of basal peat deposits (14) shows the number of calibrated age ranges that occur in any year (black curve). (B) Cumulative curve of 1516 dates (red curve). (C) The oldest basal peat dates within each 2° by 2° grid (gray bars). Figure and caption from MacDonald et al. (2006)\n\n\n\n\n\n\nPeatlands and the global carbon cycle\nAs mentioned above, peatlands store 500-700 PgC (more than all biomass C globally) on only 3% of the Earth’s land surface (Page and Baird 2016; Yu et al. 2010). Since the majority of the peat present today has accumulated over the course of the Holocene, an average C sink of >5 PgC (100 yr)-1 has persisted over the same duration (Yu et al. 2010). This is much smaller than the global fluxes of the anthropogenic C cycle perturbation, as quantified by the global carbon budget in Chapter 3. Yet, its persistent nature and the magnitude of long-term C accumulation has had implications for millennial-scale terrestrial carbon storage changes and atmospheric CO2 (Benjamin David Stocker et al. 2017). Due to their susceptibility to hydro-climatic conditions, peatland extent, global distribution, and C storage will likely undergo changes in a future climate. However, current research and model projections indicate unclear trends (Qiu et al. 2022).\nPeatlands, as all wetlands, are also a major source of methane (CH4). Under anoxic soil conditions, CH4 is produced, rather than C being oxidized and CO2 released (Chapter 12).\n\n\n\n\n\n\nExercise\n\n\n\n\nWater table variations affect the C balance of a peatland. If it falls, how do you expect NPP, Reco, and NEP of a peatland, and the turnover time of C in soil organic matter to change?\nWhat other greenhouse gas may be influenced by a declining water table in a peatland? In what direction would its emission change?\nWhy are soils dark in the Seeland of the Canton of Bern?\nWhy are wooden artefacts of the Bronze age preserved in some places but not in others? Do you know any such wooden artefacts?\n\n\n\n\n\n\n6.4.5 Permafrost\nAbout 24% of the northern hemisphere’s exposed land surface contains ground that remains frozen for at least two consecutive years - the definition of permafrost (Schuur and Mack 2018). The global distribution of permafrost in the northern hemisphere is shown in Figure 6.19. Organic matter in frozen soils is protected from decomposition - as long as the ground remains frozen. The total amount of C stored in permafrost soils (0-3 m depth) is estimated at 1,035 ± 150 PgC (Tarnocai et al. 2009; Hugelius et al. 2014) and substantial additional C (400-500 PgC) is stored at greater depth in particular locations (river sediments) (Schuur and Mack 2018). This amount of C adds another 50-100% to the total amount of C stored in soils (Figure 3.1) and suggests that the distribution of permafrost is an important determinant for the global distribution of soil C (Figure 6.15).\n\n\n\n\n\nFigure 6.19: Permafrost zone regions shown in shades of blue with percent of ground underlain by permafrost in parentheses. Generalized biome area for tundra and boreal regions shows intersection with permafrost across most, but not all, of these regions. Map created by Chris DeRolph, Oak Ridge National Laboratory, using data from various sources. Figure and caption from Schuur and Mack (2018).\n\n\n\n\nPermafrost occurs (roughly) where the mean annual temperature is below freezing. During summer, the upper soil layers, the active layer, thaw. However, the seasonal fluctuation of soil temperature is attenuated deeper in the soil due to constraints on the rate of thermal diffusion across the soil. At a certain depth, the seasonal cycle of soil temperature disappears, and the soil temperature is largely constant and equal to the mean annual air temperature on the ground (\\(Z^\\ast\\) in Figure 6.20). Towards greater depth, the temperature increases again due to the geothermal heat flux. Permafrost is the zone where temperatures never rise beyond 0°C.\n\n\n\n\n\nFigure 6.20: Thermal regime of permafrost. Schematic showing the maximum (red line) and minimum ground temperature (blue line) during the year, and their convergence to give the mean annual ground temperature T at the depth of zero annual amplitude Z*. Black dots show the schematic mean temperature for permafrost soils. Figure and caption from Biskaborn et al. (2019)\n\n\n\n\nThe presence of permafrost constrains the volume available for plant rooting, vegetation access to water and nutrients, and the heterotrophic activity if microbes. It also prohibits the infiltration of water into deeper layers which can lead to a perched water table, water-logging, and anoxic conditions in the soil.\nWith rapid warming in northern high latitudes, permafrost temperatures are rising throughout the Arctic (Biskaborn et al. 2019). Implications of permafrost melting for greenhouse gases (CO2 and CH4) and the climate-land Earth system feedback are discussed in later chapters.\n\n\n\n\n\n\nExercise\n\n\n\n\nWhy does the melting of permafrost affect methane emissions?\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nBasler, David. 2016. “Evaluating Phenological Models for the Prediction of Leaf-Out Dates in Six Temperate Tree Species Across Central Europe.” Agricultural and Forest Meteorology 217 (February): 10–21. https://doi.org/10.1016/j.agrformet.2015.11.007.\n\n\nBatjes, N. H. 2016. “Harmonized Soil Property Values for Broad-Scale Modelling (WISE30sec) with Estimates of Global Soil Carbon Stocks.” Geoderma 269 (May): 61–68. https://doi.org/10.1016/j.geoderma.2016.01.034.\n\n\nBiskaborn, Boris K., Sharon L. Smith, Jeannette Noetzli, Heidrun Matthes, Gonçalo Vieira, Dmitry A. Streletskiy, Philippe Schoeneich, et al. 2019. “Permafrost Is Warming at a Global Scale.” Nature Communications 10 (1): 264. https://doi.org/10.1038/s41467-018-08240-4.\n\n\nBonan, Gordon. 2015. Ecological Climatology: Concepts and Applications. 3rd ed. Cambridge University Press.\n\n\nBrun, Philipp, Niklaus E. Zimmermann, Chantal Hari, Loïc Pellissier, and Dirk Nikolaus Karger. 2022. “CHELSA-BIOCLIM+ a Novel Set of Global Climate-Related Predictors at Kilometre-Resolution.” EnviDat. https://doi.org/http://dx.doi.org/10.16904/envidat.332.\n\n\nCanadell, J. G., P. M. S. Monteiro, M. H. Costa, L. Cotrim da Cunha, P. M. Cox, A. V. Eliseev, S. Henson, et al. 2021. “Global Carbon and Other Biogeochemical Cycles and Feedbacks.” Book Section. In Climate Change 2021: The Physical Science Basis. Contribution of Working Group i to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, edited by V. Masson-Delmotte, P. Zhai, A. Pirani, S. L. Connors, C. Péan, S. Berger, N. Caud, et al., 673–816. Cambridge, United Kingdom; New York, NY, USA: Cambridge University Press. https://doi.org/10.1017/9781009157896.007.\n\n\nChristian Körner, and David Basler. 2010. “Phenology Under Global Warming Science” 327: 1461–62. https://doi.org/10.1126/science.1186473.\n\n\nCrowther, T. W., J. van den Hoogen, J. Wan, M. A. Mayes, A. D. Keiser, L. Mo, C. Averill, and D. S. Maynard. 2019. “The Global Soil Community and Its Influence on Biogeochemistry.” Science 365 (6455): eaav0550. https://doi.org/10.1126/science.aav0550.\n\n\nDargie, Greta C., Simon L. Lewis, Ian T. Lawson, Edward T. A. Mitchard, Susan E. Page, Yannick E. Bocko, and Suspense A. Ifo. 2017. “Age, Extent and Carbon Storage of the Central Congo Basin Peatland Complex.” Nature 542 (7639): 86–90. https://doi.org/10.1038/nature21048.\n\n\nDavis, T. W., I. C. Prentice, B. D. Stocker, R. T. Thomas, R. J. Whitley, H. Wang, B. J. Evans, A. V. Gallego-Sala, M. T. Sykes, and W. Cramer. 2017. “Simple Process-Led Algorithms for Simulating Habitats (SPLASH v.1.0): Robust Indices of Radiation, Evapotranspiration and Plant-Available Moisture.” Geoscientific Model Development 10 (2): 689–708. https://doi.org/10.5194/gmd-10-689-2017.\n\n\nDommain, René, John Couwenberg, Paul H. Glaser, Hans Joosten, and I. Nyoman N. Suryadiputra. 2014. “Carbon Storage and Release in Indonesian Peatlands Since the Last Deglaciation.” Quaternary Science Reviews 97 (August): 1–32. https://doi.org/10.1016/j.quascirev.2014.05.002.\n\n\nGraven, H. D., R. F. Keeling, S. C. Piper, P. K. Patra, B. B. Stephens, S. C. Wofsy, L. R. Welp, et al. 2013. “Enhanced Seasonal Exchange of CO2 by Northern Ecosystems Since 1960.” Science 341 (6150): 1085–89. https://doi.org/10.1126/science.1239207.\n\n\nGulev, S. K., P. W. Thorne, J. Ahn, F. J. Dentener, C. M. Domingues, S. Gerland, D. Gong, et al. 2021. “Changing State of the Climate System.” Book Section. In Climate Change 2021: The Physical Science Basis. Contribution of Working Group i to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, edited by V. Masson-Delmotte, P. Zhai, A. Pirani, S. L. Connors, C. Péan, S. Berger, N. Caud, et al. Cambridge, UK; New York, NY, USA: Cambridge University Press. https://doi.org/10.1017/9781009157896.004.\n\n\nHugelius, G., J. Strauss, S. Zubrzycki, J. W. Harden, E. a. G. Schuur, C.-L. Ping, L. Schirrmeister, et al. 2014. “Estimated Stocks of Circumpolar Permafrost Carbon with Quantified Uncertainty Ranges and Identified Data Gaps.” Biogeosciences 11 (23): 6573–93. https://doi.org/10.5194/bg-11-6573-2014.\n\n\nIPCC. 2021. “Summary for Policymakers.” Book Section. In Climate Change 2021: The Physical Science Basis. Contribution of Working Group i to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, edited by V. Masson-Delmotte, P. Zhai, A. Pirani, S. L. Connors, C. Péan, S. Berger, N. Caud, et al. Cambridge, UK; New York, NY, USA: Cambridge University Press. https://doi.org/10.1017/9781009157896.001.\n\n\nJackson, Robert B., Kate Lajtha, Susan E. Crow, Gustaf Hugelius, Marc G. Kramer, and Gervasio Piñeiro. 2017. “The Ecology of Soil Carbon: Pools, Vulnerabilities, and Biotic and Abiotic Controls.” Annual Review of Ecology, Evolution, and Systematics 48 (1): 419–45. https://doi.org/10.1146/annurev-ecolsys-112414-054234.\n\n\nKeenan, Trevor F., and Andrew D. Richardson. 2015. “The Timing of Autumn Senescence Is Affected by the Timing of Spring Phenology: Implications for Predictive Models.” Global Change Biology 21 (7): 2634–41. https://doi.org/10.1111/gcb.12890.\n\n\nKeith, Heather, Brendan G. Mackey, and David B. Lindenmayer. 2009. “Re-Evaluation of Forest Biomass Carbon Stocks and Lessons from the World’s Most Carbon-Dense Forests.” Proceedings of the National Academy of Sciences 106 (28): 11635–40. https://doi.org/10.1073/pnas.0901970106.\n\n\nLiu, Yi Y., Albert I. J. M. van Dijk, Richard A. M. de Jeu, Josep G. Canadell, Matthew F. McCabe, Jason P. Evans, and Guojie Wang. 2015. “Recent Reversal in Loss of Global Terrestrial Biomass.” Nature Climate Change 5 (5): 470–74. https://doi.org/10.1038/nclimate2581.\n\n\nMacDonald, Glen M., David W. Beilman, Konstantine V. Kremenetski, Yongwei Sheng, Laurence C. Smith, and Andrei A. Velichko. 2006. “Rapid Early Development of Circumarctic Peatlands and Atmospheric CH4 and CO2 Variations.” Science 314 (5797): 285–88. https://doi.org/10.1126/science.1131722.\n\n\nMacDonald, Glen M., Andrei A. Velichko, Constantine V. Kremenetski, Olga K. Borisova, Aleksandra A. Goleva, Andrei A. Andreev, Les C. Cwynar, et al. 2000. “Holocene Treeline History and Climate Change Across Northern Eurasia.” Quaternary Research 53 (3): 302–11. https://doi.org/10.1006/qres.1999.2123.\n\n\nMüller, Jurek, and Fortunat Joos. 2020. “Global Peatland Area and Carbon Dynamics from the Last Glacial Maximum to the Present – a Process-Based Model Investigation.” Biogeosciences 17 (21): 5285–5308. https://doi.org/10.5194/bg-17-5285-2020.\n\n\nOdum, Eugene P. 1969. “The Strategy of Ecosystem Development.” Science 164 (3877): 262–70. https://doi.org/10.1126/science.164.3877.262.\n\n\nPage, S. E., and A. J. Baird. 2016. “Peatlands and Global Change: Response and Resilience.” Annual Review of Environment and Resources 41 (Volume 41, 2016): 35–57. https://doi.org/10.1146/annurev-environ-110615-085520.\n\n\nPiao, Shilong, Qiang Liu, Anping Chen, Ivan A. Janssens, Yongshuo Fu, Junhu Dai, Lingli Liu, Xu Lian, Miaogen Shen, and Xiaolin Zhu. 2019. “Plant Phenology and Global Climate Change: Current Progresses and Challenges.” Global Change Biology 25 (6): 1922–40. https://doi.org/10.1111/gcb.14619.\n\n\nPrentice, I Colin, D. Jolly, and BIOME 6000 Participants. 2000. “Mid-Holocene and Glacial-Maximum Vegetation Geography of the Northern Continents and Africa.” Journal of Biogeography 27 (3): 507–19. http://www.jstor.org/stable/2656208.\n\n\nQiu, Chunjing, Philippe Ciais, Dan Zhu, Bertrand Guenet, Jinfeng Chang, Nitin Chaudhary, Thomas Kleinen, et al. 2022. “A Strong Mitigation Scenario Maintains Climate Neutrality of Northern Peatlands.” One Earth, January. https://doi.org/10.1016/j.oneear.2021.12.008.\n\n\nRichardson, Andrew D., Trevor F. Keenan, Mirco Migliavacca, Youngryel Ryu, Oliver Sonnentag, and Michael Toomey. 2013. “Climate Change, Phenology, and Phenological Control of Vegetation Feedbacks to the Climate System.” Agricultural and Forest Meteorology 169 (February): 156–73. https://doi.org/10.1016/j.agrformet.2012.09.012.\n\n\nSchuur, Edward A. G., and Michelle C. Mack. 2018. “Ecological Response to Permafrost Thaw and Consequences for Local and Global Ecosystem Services.” Annual Review of Ecology, Evolution, and Systematics 49 (Volume 49, 2018): 279–301. https://doi.org/10.1146/annurev-ecolsys-121415-032349.\n\n\nStocker, B. D., R. Spahni, and F. Joos. 2014. “DYPTOP: A Cost-Efficient TOPMODEL Implementation to Simulate Sub-Grid Spatio-Temporal Dynamics of Global Wetlands and Peatlands.” Geoscientific Model Development 7 (6): 3089–3110. https://doi.org/10.5194/gmd-7-3089-2014.\n\n\nStocker, Benjamin David, Zicheng Yu, Charly Massa, and Fortunat Joos. 2017. “Holocene Peatland and Ice-Core Data Constraints on the Timing and Magnitude of CO2 Emissions from Past Land Use.” Proceedings of the National Academy of Sciences 114 (7): 1492–97. https://doi.org/10.1073/pnas.1613889114.\n\n\nStocker, Benjamin D., Jakob Zscheischler, Trevor F. Keenan, I. Colin Prentice, Sonia I. Seneviratne, and Josep Peñuelas. 2019. “Drought Impacts on Terrestrial Primary Production Underestimated by Satellite Monitoring.” Nature Geoscience 12 (4): 264–70. https://doi.org/10.1038/s41561-019-0318-6.\n\n\nTarnocai, C., J. G. Canadell, E. a. G. Schuur, P. Kuhry, G. Mazhitova, and S. Zimov. 2009. “Soil Organic Carbon Pools in the Northern Circumpolar Permafrost Region.” Global Biogeochemical Cycles 23 (2). https://doi.org/10.1029/2008GB003327.\n\n\nWang, H., I. C. Prentice, and T. W. Davis. 2014. “Biophsyical Constraints on Gross Primary Production by the Terrestrial Biosphere.” Biogeosciences 11 (20): 5987–6001. https://doi.org/10.5194/bg-11-5987-2014.\n\n\nXu, Jiren, Paul J. Morris, Junguo Liu, and Joseph Holden. 2018. “PEATMAP: Refining Estimates of Global Peatland Distribution Based on a Meta-Analysis.” CATENA 160 (January): 134–40. https://doi.org/10.1016/j.catena.2017.09.010.\n\n\nYu, Zicheng, Julie Loisel, Daniel P. Brosseau, David W. Beilman, and Stephanie J. Hunt. 2010. “Global Peatland Dynamics Since the Last Glacial Maximum.” Geophysical Research Letters 37 (13). https://doi.org/10.1029/2010GL043584." }, { "objectID": "landclimate.html#components-of-surface-radiation", "href": "landclimate.html#components-of-surface-radiation", "title": "7  Land-climate interactions", "section": "7.1 Components of surface radiation", - "text": "7.1 Components of surface radiation\nAnalogous to solar radiation being the “engine” of biogeochemical processes through its control on photosynthesis, net radiation is the engine of energy and water vapour fluxes between the atmosphere and the land surface. Net radiation (\\(R_n\\)) is the net of incoming (or incident) shortwave radiation (\\(S\\downarrow\\)) minus outgoing shortwave (solar) radiation (\\(S\\uparrow\\)) and longwave radiation (\\(L\\downarrow\\) and \\(L\\uparrow\\)) at the land surface (Figure 7.1 a). \\[\nR_n = S\\downarrow - S\\uparrow + L\\downarrow - L\\uparrow\n\\tag{7.1}\\]\n\n\n\n\n\nFigure 7.1: Land surface energy partitioning. (a) Components of net radiation. (b) Energy balance of the land surface.\n\n\n\n\n\n7.1.1 Incident shortwave radiation\nIncident shortwave (solar) radiation \\(S\\downarrow\\) was referred to in Chapter 6 as \\(I_\\mathrm{0}\\). (Nomenclature will be homogenized across chapters in future issues this book.) It varies over the course of a day and a year, and is affected by the presence of clouds and the altitude of the land surface above sea level, as described in Chapter 6. As shown in Figure 7.2, the presence of clouds is a strong determinant of the incoming solar radiation energy flux, when considering global means (including the sea surface) under actual conditions and under cloud-free conditions (160 vs. 214 W-2).\n\n\n\n\n\nFigure 7.2: Schematic representation of the global mean energy budget of the Earth (upper panel), and its equivalent without considerations of cloud effects (lower panel). Numbers indicate best estimates for the magnitudes of the globally averaged energy balance components in W-2 together with their uncertainty ranges in parentheses (5–95% confidence range), representing climate conditions at the beginning of the 21st century. Note that the cloud-free energy budget shown in the lower panel is not the one that Earth would achieve in equilibrium when no clouds could form. It rather represents the global mean fluxes as determined solely by removing the clouds but otherwise retaining the entire atmospheric structure. This enables the quantification of the effects of clouds on the Earth energy budget and corresponds to the way clear-sky fluxes are calculated in climate models. Thus, the cloud-free energy budget is not closed and therefore the sensible and latent heat fluxes are not quantified in the lower panel. Figure and caption from Forster et al. (2021).\n\n\n\n\n\n\n7.1.2 Outgoing shortwave radiation and albedo\nOutgoing shortwave radiation at the land surface (\\(S\\uparrow\\)) is determined by the albedo (\\(\\alpha\\)) - the fraction of the incident radiation that gets reflected. \\[\nS\\uparrow = \\alpha S\\downarrow\n\\tag{7.2}\\] The albedo varies across different vegetation and other types of Earth surface covers. Values range from 0.8-0.95 for fresh snow, to 0.2-0.45 for a desert surface, 0.05–0.40 for bare soil, 0.05-0.26 for vegetation, and 0.03–0.10 for water (Oke 1987). Variations across different vegetation types are substantial as shown also in Figure 7.3. This indicates that the amount of outgoing shortwave radiation, and with it net radiation, is strongly affected by vegetation types.\n\n\nCode\nlibrary(dplyr)\nlibrary(readr)\nlibrary(ggplot2)\n\ndf <- read_csv(here::here(\"data-raw/albedo_cescatti.csv\"))\n\ndf |> \n ggplot(aes(\n x = reorder(vegtype, albedo_insitu, decreasing = TRUE), \n y = albedo_insitu\n )) +\n geom_boxplot(fill = \"grey70\") +\n geom_jitter(width = 0.15) +\n theme_classic() +\n labs(\n x = \"Vegetation type\",\n y = \"Albedo\"\n )\n\n\n\n\n\nFigure 7.3: Albedo values for different vegetation types. Each point represents a site where surface radiation fluxes were measured. Vegetation types are described in Table 2.1. Data from Cescatti et al. (2012).\n\n\n\n\nThe diurnal variation of albedo is U-shaped - high at sunrise and sunset, and lower in between. Over the seasons, land surface albedo is affected by variations in LAI and by the presence of snow. During winter and in the presence of snow, the albedo of a grassland or a cropland can reach very high values - determined by the albedo of snow. In contrast, the albedo of a forest, even in the presence of snow, remains. much lower (0.2-0.4, Zhao and Jackson (2014)). This is because trees are not fully “submerged” in the snow pack, as opposed to grasses, and the exposed canopy absorbs a substantial fraction of the incident radiation. This effect of forest vs. non-forest covers on the surface energy balance during winter is referred to as the snow masking effect. Climate model simulations suggest that the low surface albedo during winter warms climate compared compared to a snow-covered grassland. Thus, deforestation/afforestation of boreal forest has the greatest biogeophysical effect of all biomes on temperatures (G. B. Bonan 2008).\n\n\n\n\n\nFigure 7.4: Snow-free vs. snow-covered surface albedo for different vegetation types. Figure from G. B. Bonan (2008).\n\n\n\n\nNote that albedo also depends on the wavelength of the radiation, on the solar zenith angle (lower at noon), and on whether the solar radiation is diffuse or direct. Thus, albedo varies over time, \\(\\alpha\\) in Equation 7.2 represents the albedo for shortwave radiation, and values shown in Figure 7.3 are averages across the seasons.\n\n\n7.1.3 Longwave radiation\nEvery material body with a temperature above the absolute zero (0 K \\(= -\\) 273.15°C) emits radiative energy. The total radiative energy flux (integrated across wavelengths) and the wavelengths at which radiation is emitted depend on the temperature of the body and its emissivity. The surface of the sun is about 6000 K and emits radiation in the shorwave spectrum which is visible to the human eye. The Earth surface is on average 288 K and emits radiation in the longwave spectrum which is not visible to the eye.\n\n\nCode\nlibrary(ggplot2)\nlibrary(cowplot)\n\n# Formula for Planck's Law\ncalc_planck <- function(lambda, temp){\n h <- 6.626e-34 # Planck’s constant\n c <- 3e8 # speed of light\n k <- 1.38e-23 # Stefan Boltzmann constant\n out <- (2*pi*h*c^2) / (lambda^5*(exp(h*c/(k*lambda*temp)) - 1))\n return(out)\n}\n\ngg1 <- ggplot() +\n geom_function(\n fun = calc_planck,\n args = list(\n temp = 6000\n )\n ) +\n xlim(0, 0.4e-5) +\n theme_classic() +\n labs(\n title = \"Sun\",\n subtitle = \"6000 K\",\n x = \"Wavelength (m)\",\n y = expression(paste(\"Emittance (W m\"^-2, \" m\"^-1, \")\"))\n )\n\ngg2 <- ggplot() +\n geom_function(\n fun = calc_planck,\n args = list(\n temp = 288\n )\n ) +\n xlim(0, 1e-4) +\n theme_classic() +\n labs(\n title = \"Earth\",\n subtitle = \"288 K\",\n x = \"Wavelength (m)\",\n y = expression(paste(\"Emittance (W m\"^-2, \" m\"^-1, \")\"))\n )\n\nplot_grid(\n gg1,\n gg2,\n labels = c(\"a\", \"b\")\n)\n\n\n\n\n\nFigure 7.5: Spectral distribution of the radiative energy flux (a) for a body of 6000 K (the sun) and (b) a body of 288 K (the earth), assuming an emissivity of 1. Emittance (the y-axis) is the density of the radiative energy flux per unit wavelength spectrum. Note the different magnitudes of the emittances and wavelengths for the two bodies. Example following G. Bonan (2015).\n\n\n\n\nAccording to the Stefan-Boltzmann law, the total radiative energy flux scales with the temperature of the body \\(T\\) and an emissivity \\(\\varepsilon\\): \\[\nR = \\varepsilon \\sigma T^4\n\\tag{7.3}\\] \\(\\sigma\\) is the Stefan Boltzmann constant and has a value of \\(5.670\\times 10^{-8}\\) W m-2 K-4. Here, \\(T\\) is expressed in Kelvin. \\(R\\) is the integral under the curve in Figure 7.5. \\(R\\) stands for either longwave or shortwave radiation, as referred to as \\(L\\) and \\(S\\) in Equation 7.1.\nThe longwave radiation components are a substantial fraction of net radiation. In Figure 7.2, they are referred to as “thermal”. The outgoing longwave radiation \\(L\\uparrow\\) is on average 398 W m-2 and is a function of the Earth’s surface temperature and emissivity, following the Stefan-Boltzmann law (Equation 7.3), plus the incident longwave radiation reflected (not absorbed) by the surface: \\[\nL\\uparrow = \\varepsilon \\sigma T^4 + (1-\\varepsilon) L\\downarrow\n\\tag{7.4}\\] Note that \\(\\varepsilon\\) is used in Equation 7.4 as the absorbtivity and in Equation 7.3 as the emissivity. This is because the two are equal.\nClouds absorb radiation emitted by the earth surface and re-emit a large fraction of it. In absence of clouds, much less radiation is absorbed and re-emitted by the atmosphere. Therefore, the incoming longwave radiation depends strongly on the presence of clouds.\n\n\n\n\n\n\nNet radiation\n\n\n\nUsing Equation 7.2 and Equation 7.4, the net radiation at the earth surface (Equation 7.1) can be expressed as \\[\nR_n = (1-\\alpha) S\\downarrow + \\varepsilon L\\downarrow - \\varepsilon \\sigma T^4\n\\]\n\n\n\n\n\n\n\n\nExercise\n\n\n\n\nCalculate the albedo from ‘all sky’ conditions in Figure 7.2." + "text": "7.1 Components of surface radiation\nAnalogous to solar radiation being the “engine” of biogeochemical processes through its control on photosynthesis, net radiation is the engine of energy and water vapor fluxes between the atmosphere and the land surface. Net radiation (\\(R_n\\)) is the net of incoming (or incident) shortwave radiation (\\(S\\downarrow\\)) minus outgoing shortwave (solar) radiation (\\(S\\uparrow\\)) and longwave radiation (\\(L\\downarrow\\) and \\(L\\uparrow\\)) at the land surface (Figure 7.1 a). \\[\nR_n = S\\downarrow - S\\uparrow + L\\downarrow - L\\uparrow\n\\tag{7.1}\\]\n\n\n\n\n\nFigure 7.1: Land surface energy partitioning. (a) Components of net radiation. (b) Energy balance of the land surface.\n\n\n\n\n\n\n7.1.1 Incident shortwave radiation\nIncident shortwave (solar) radiation \\(S\\downarrow\\) was referred to in Chapter 6 as \\(I_\\mathrm{0}\\). (Nomenclature will be homogenized across chapters in future issues of this book.) It varies over the course of a day and a year, and is affected by the presence of clouds and the altitude of the land surface above sea level, as described in Chapter 6. As shown in Figure 7.2, the presence of clouds is a strong determinant of the incoming solar radiation energy flux, when considering global means (including the sea surface) under actual conditions and under cloud-free conditions (160 vs. 214 W-2).\n\n\n\n\n\nFigure 7.2: Schematic representation of the global mean energy budget of the Earth (upper panel), and its equivalent without considerations of cloud effects (lower panel). Numbers indicate best estimates for the magnitudes of the globally averaged energy balance components in W-2 together with their uncertainty ranges in parentheses (5–95% confidence range), representing climate conditions at the beginning of the 21st century. Note that the cloud-free energy budget shown in the lower panel is not the one that Earth would achieve in equilibrium when no clouds could form. It rather represents the global mean fluxes as determined solely by removing the clouds but otherwise retaining the entire atmospheric structure. This enables the quantification of the effects of clouds on the Earth energy budget and corresponds to the way clear-sky fluxes are calculated in climate models. Thus, the cloud-free energy budget is not closed and therefore the sensible and latent heat fluxes are not quantified in the lower panel. Figure and caption from Forster et al. (2021).\n\n\n\n\n\n\n\n7.1.2 Outgoing shortwave radiation and albedo\nOutgoing shortwave radiation at the land surface (\\(S\\uparrow\\)) is determined by the albedo (\\(\\alpha\\)) - the fraction of the incident radiation that gets reflected. \\[\nS\\uparrow = \\alpha S\\downarrow\n\\tag{7.2}\\] The albedo varies across different vegetation and other types of Earth surface covers. Values range from 0.8-0.95 for fresh snow, to 0.2-0.45 for a desert surface, 0.05–0.40 for bare soil, 0.05-0.26 for vegetation, and 0.03–0.10 for water (Oke 1987). Variations across different vegetation types are substantial as shown also in Figure 7.3. This indicates that the amount of outgoing shortwave radiation, and with it, net radiation, is strongly affected by vegetation types.\n\n\nCode\nlibrary(dplyr)\nlibrary(readr)\nlibrary(ggplot2)\n\ndf <- read_csv(here::here(\"data-raw/albedo_cescatti.csv\"))\n\ndf |> \n ggplot(aes(\n x = reorder(vegtype, albedo_insitu, decreasing = TRUE), \n y = albedo_insitu\n )) +\n geom_boxplot(fill = \"grey70\") +\n geom_jitter(width = 0.15) +\n theme_classic() +\n labs(\n x = \"Vegetation type\",\n y = \"Albedo\"\n )\n\n\n\n\n\nFigure 7.3: Albedo values for different vegetation types. Each point represents a site where surface radiation fluxes were measured. Vegetation types are described in Table 2.1. Data from Cescatti et al. (2012).\n\n\n\n\n\nOver the seasons, land surface albedo is affected by variations in LAI and by the presence of snow. During winter and in the presence of snow, the albedo of a grassland or a cropland can reach very high values - determined by the albedo of snow. In contrast, the albedo of a forest, even in the presence of snow, remains much lower (0.2-0.4, Zhao and Jackson (2014)). This is because trees are not fully “submerged” in the snow pack, as opposed to grasses, and the exposed canopy absorbs a substantial fraction of the incident radiation. This effect of forest vs. non-forest covers on the surface energy balance during winter is referred to as the snow masking effect. Climate model simulations suggest that the low surface albedo during winter warms climate compared to a snow-covered grassland. Thus, deforestation/afforestation of boreal forest has the greatest biogeophysical effect of all biomes on temperatures (G. B. Bonan 2008).\n\n\n\n\n\nFigure 7.4: Snow-free vs. snow-covered surface albedo for different vegetation types. Figure from G. B. Bonan (2008).\n\n\n\n\nNote that albedo also depends on the wavelength of the radiation, on the solar zenith angle (lower at noon), and on whether the solar radiation is diffuse or direct. Thus, albedo varies over time following a U-shaped diurnal variation - high at sunrise and sunset, and lower in between. \\(\\alpha\\) in Equation 7.2 represents the albedo for shortwave radiation, and values shown in Figure 7.3 are averages across the seasons.\n\n\n7.1.3 Longwave radiation\nEvery material body with a temperature above the absolute zero (0 K \\(= -\\) 273.15°C) emits radiative energy. The total radiative energy flux (integrated across wavelengths) and the wavelengths at which radiation is emitted depend on the temperature of the body and its emissivity. The surface of the sun is about 6000 K and emits radiation in the shorwave spectrum which is visible to the human eye. The Earth’s surface is on average 288 K and emits radiation in the longwave spectrum which is not visible to the eye.\n\n\nCode\nlibrary(ggplot2)\nlibrary(cowplot)\n\n# Formula for Planck's Law\ncalc_planck <- function(lambda, temp){\n h <- 6.626e-34 # Planck’s constant\n c <- 3e8 # speed of light\n k <- 1.38e-23 # Stefan Boltzmann constant\n out <- (2*pi*h*c^2) / (lambda^5*(exp(h*c/(k*lambda*temp)) - 1))\n return(out)\n}\n\ngg1 <- ggplot() +\n geom_function(\n fun = calc_planck,\n args = list(\n temp = 6000\n )\n ) +\n xlim(0, 0.4e-5) +\n theme_classic() +\n labs(\n title = \"Sun\",\n subtitle = \"6000 K\",\n x = \"Wavelength (m)\",\n y = expression(paste(\"Emittance (W m\"^-2, \" m\"^-1, \")\"))\n )\n\ngg2 <- ggplot() +\n geom_function(\n fun = calc_planck,\n args = list(\n temp = 288\n )\n ) +\n xlim(0, 1e-4) +\n theme_classic() +\n labs(\n title = \"Earth\",\n subtitle = \"288 K\",\n x = \"Wavelength (m)\",\n y = expression(paste(\"Emittance (W m\"^-2, \" m\"^-1, \")\"))\n )\n\nplot_grid(\n gg1,\n gg2,\n labels = c(\"a\", \"b\")\n)\n\n\n\n\n\nFigure 7.5: Spectral distribution of the radiative energy flux (a) for a body of 6000 K (the sun) and (b) a body of 288 K (the Earth), assuming an emissivity of 1. Emittance (the y-axis) is the density of the radiative energy flux per unit wavelength spectrum. Note the different magnitudes of the emittances and wavelengths for the two bodies. Example following G. Bonan (2015).\n\n\n\n\nAccording to the Stefan-Boltzmann law, the total radiative energy flux scales with the temperature of the body \\(T\\) and an emissivity \\(\\varepsilon\\): \\[\nR = \\varepsilon \\sigma T^4\n\\tag{7.3}\\] \\(\\sigma\\) is the Stefan Boltzmann constant and has a value of \\(5.670\\times 10^{-8}\\) W m-2 K-4. Here, \\(T\\) is expressed in Kelvin. \\(R\\) is the integral under the curve in Figure 7.5. \\(R\\) stands for either longwave or shortwave radiation, as referred to as \\(L\\) and \\(S\\) in Equation 7.1.\nThe longwave radiation components are a substantial fraction of net radiation. In Figure 7.2, they are referred to as “thermal”. The outgoing longwave radiation \\(L\\uparrow\\) is on average 398 W m-2 and is a function of the Earth’s surface temperature and emissivity, following the Stefan-Boltzmann law (Equation 7.3), plus the incident longwave radiation reflected (not absorbed) by the surface: \\[\nL\\uparrow = \\varepsilon \\sigma T^4 + (1-\\varepsilon) L\\downarrow\n\\tag{7.4}\\] Note that \\(\\varepsilon\\) is used in Equation 7.4 as the absorbtivity and in Equation 7.3 as the emissivity. This is because the two are equal.\nClouds absorb radiation emitted by the Earth’s surface and re-emit a large fraction of it. In the absence of clouds, much less radiation is absorbed and re-emitted by the atmosphere. Therefore, the incoming longwave radiation depends strongly on the presence of clouds.\n\n\n\n\n\n\nNet radiation\n\n\n\nUsing Equation 7.2 and Equation 7.4, the net radiation at the Earth surface (Equation 7.1) can be expressed as \\[\nR_n = (1-\\alpha) S\\downarrow + \\varepsilon L\\downarrow - \\varepsilon \\sigma T^4\n\\]\n\n\n\n\n\n\n\n\nExercise\n\n\n\n\nCalculate the albedo from ‘all sky’ conditions in Figure 7.2." }, { "objectID": "landclimate.html#sec-energybalance", "href": "landclimate.html#sec-energybalance", "title": "7  Land-climate interactions", "section": "7.2 Surface energy balance and partitioning", - "text": "7.2 Surface energy balance and partitioning\nThe energy available from radiative fluxes is converted into a sensible heat flux (\\(H\\)), a latent heat flux (\\(\\lambda E\\)), and a ground heat flux (\\(G\\), Figure 7.1 b). Following energy conservation, net radiation is equal to the sum of these three heat fluxes. \\[\nR_n = H + \\lambda E + G\n\\tag{7.5}\\]\nThe components of the surface energy balance (Equation 7.5) are commonly expressed in energy units (W m-2). Sensible heat is determined by the temperature of air. Latent heat is the energy contained by evaporated water. The latent heat flux (\\(\\lambda E\\)) can also be expressed as a mass flux of water vapour (\\(E\\)). \\(E\\) is the mass flux of water vapor, e.g., expressed in units of g m-2 s-1. \\(\\lambda\\) is the latent heat of vaporization and converts the mass units into energy units. It measures how much energy (Joules, J) is needed vapourize 1 g of water at constant temperature. \\(\\lambda\\) is 2.466 MJ kg-1 at 15°C and has a slight dependence on temperature, decreasing linearly by about 3% from an air temperature of 0°C to 30°C.\n\n\n\nCode\nlibrary(ggplot2)\n\n# Function adopted from function bigleaf::latent.heat.vaporization\n# Returns latent heat of vaporization (J g-1)\n# References:\n# Stull, B., 1988: An Introduction to Boundary Layer Meteorology (p.641) Kluwer Academic Publishers, Dordrecht, Netherlands\n# Foken, T, 2008: Micrometeorology. Springer, Berlin, Germany.\ncalc_lambda <- function(temp){\n k1 <- 2.501\n k2 <- 0.00237\n lambda <- (k1 - k2 * temp) * 1e+03\n return(lambda)\n}\n\nggplot() +\n geom_function(fun = calc_lambda) +\n xlim(0, 35) +\n labs(x = \"Temperature (°C)\",\n y = expression(paste(\"Latent heat of vaporization (J g\"^-1, \")\"))) + \n theme_classic()\n\n\n\n\n\nFigure 7.6: Latent heat of vaporization as a function of air temperature.\n\n\n\n\n\n\nThe sensible and latent heat fluxes are transported vertically, away from or to the land surface through convective transport. That is, through turbulences that mix the air and lead to a net vertical transport of heat and water vapor. Whether net fluxes are pointed upwards or downwards depends on the sign of the net radiation (see Figure 7.11 and Figure 7.12) and typically changes between night and daytime. Note that the latent heat flux can be negative, leading to a net flux of water vapor towards the surface. The respective water mass condensates at the surface (of leaves) and can be a considerable fraction of the ecosystem water balance. The ground heat flux \\(G\\) buffers variations of net radiation, absorbing energy and removing heat from the surface during the day and summer and releasing heat during night and winter.\n\n\n7.2.1 Potential evapotranspiration\nPhysical and biological properties of the land surface determine not only the net radiation through (mainly) effects of the albedo, but also strongly influence the partitioning of net radiation into sensible and latent heat fluxes in Equation 7.5. In particular, the availability of water for evaporation from the land surface through transpiration or directly from wet surfaces, is decisive for the partitioning of net radiation into \\(H\\) and \\(\\lambda E\\).\nA useful quantity for understanding the surface energy partitioning and the influence of limiting factors (e.g., water limitation) is the potential evapotranspiration (PET). Evapotranspiration is equivalent to the latent heat flux, but expressed in water vapour mass units. (You will learn more about evapotranspiration in Chapter 8). PET can be understood as the maximum possible \\(E\\), attained under conditions where water supply to evaporation is not limiting. Different methods are available for estimating PET. A physically based and widely used method is the one by Priestley and Taylor (1972) which relates PET to net radiation, considering that net radiation is consumed by the water vapor flux from a water-saturated surface into an air parcel at constant temperature and pressure. \\[\n\\mathrm{PET} = \\alpha \\frac{s}{s + \\gamma} \\frac{R_n}{\\lambda}\n\\tag{7.6}\\] Here, \\(s\\) (Pa K-2) is the slope the change in saturation vapor pressure with respect to temperature. \\(\\gamma\\) is the psychrometric constant (a representative value is 66.5 Pa K–1). The coefficient \\(\\alpha\\) is an empirically determined value and is taken to be 1.26 for a wet surface. However, for vegetated surfaces, it is substantially lower, even if the plants are not water-limited. It ranges between 0.82 for tropical and temperate broadleaf forests and 0.55 for boreal conifer forests (G. Bonan 2015).\n\n\n7.2.2 Metrics of energy partitioning\nDifferent metrics are used for quantifying the partitioning of net radiation into \\(H\\) and \\(\\lambda E\\). When considering totals over longer periods of time (over at least one annual cycle), the ground heat flux \\(G\\) can be neglected since the ground doesn’t gradually heat up over time. Hence, the sum of the latent and sensible heat fluxes add up to match net radiation. The evaporative fraction quantifies the fraction of available energy from net radiation goes into the latent heat flux. \\[\n\\mathrm{EF} = \\lambda E/R_n\n\\] The remainder goes into the sensible heat flux. The Bowen ratio expresses the same relation and is defined as \\[\nB = H/\\lambda E\n\\] The ratio of actual over potential evapotranspiration (\\(E/\\mathrm{PET}\\), also referred to as ‘AET/PET’) is often used, but measurements of actual evapotranspiration are scarce and model-based estimates are subject to strong assumptions.\nQuantifications of EF, \\(B\\), and \\(E/\\mathrm{PET}\\) give important and readily interpretable insights. Variations of these quantities across space and time reflect water limitation to \\(E\\), biophysical surface properties and vegetation activity. For example, in forests, the evaporative fraction is typically lower compared to certain crops, and it’s even lower in conifer forests than in deciduous broadleaf forests (Figure 7.8). The evaporative fraction declines as water becomes more limiting during dry (rain-free) periods. An example for the application of \\(E/\\mathrm{PET}\\) is the Evaporative Stress Index product (Figure 7.7), generated by the ECOSTRESS satellite mission (Fisher et al. 2020).\n\n\n\n\n\nFigure 7.7: ECOSTRESS evaporative stress index for the Guanacaste region of Costa Rica (in red on inset map, left) a few months after the onset of a major Central American drought. Red indicates high plant water stress, yellow is moderate stress and greens/blues are low stress. Light gray is cloud cover. The index measures how much water plants are using relative to how much they would use under optimal conditions; low numbers correlate with high stress. Figure from https://www.jpl.nasa.gov/images/pia22839-ecostress-focuses-on-costa-rican-drought.\n\n\n\n\n\n\n7.2.3 Combining energy, atmospheric, and biophysical controls on \\(\\lambda E\\)\nNot only the availability of water for evaporation, but also the atmospheric condition (specifically, the vapour pressure deficit) and biophysical surface properties determine the latent heat flux and the surface energy partitioning. The key biophysical surface properties are the aerodynamic conductance to heat transfer (\\(G_\\mathrm{ah}\\)) and the surface conductance to water vapor transport (\\(G_\\mathrm{sw}\\)). How energy, atmospheric, and biophysical controls drive the latent heat flux \\(\\lambda E\\) is described by the Penman-Monteith equation (Equation 7.7), as shown in the box below and Figure 7.9. The aerodynamic conductance depends on the roughness of the surface and on wind speed. Taller vegetation has a higher roughness and a higher aerodynamic conductance. Roughness also increases with LAI.\nOn vegetated surfaces, the surface conductance to water vapor transport is strongly influenced by the stomatal conductance (\\(g_s\\), Equation 4.5 and Equation 4.11) and by the LAI. Water evaporation from rock, soil, leaf, or branch surfaces contributes to surface conductance and occurs also from non-vegetated surfaces. In a closed canopy, surface conductance is dominated by the signal by stomatal conductance. When leaves are active and photosynthesizing (high light), and when water stress is low (high soil moisture, low VPD), stomatal conductance is high. How water availability and vegetation regulate stomatal conductance and thus the latent heat flux and energy partitioning at the land surface is introduced in Chapter 8.\n\n\n\n\n\nFigure 7.8: Surface resistance and normalized latent heat flux for different vegetation types. Normalization removes effects of different net radiation on latent heat fluxes. Canopy resistance is equivalent to the inverse of surface conductance described in this chapter. Figure from G. B. Bonan (2008).\n\n\n\n\nTaken together, the spatial distribution of vegetation and other land cover types, and the response of plants to temporal changes in the environment (and thus on LAI and stomatal conductance) influence the energy partitioning at the land surface and near-surface atmospheric conditions. In other words, we have to understand vegetation and its response to the environment in order to understand land-climate interactions and near-surface climate.\n\n\n\n\n\n\nDependency of energy partitioning on conductances\n\n\n\n\n\nGiven the atmospheric condition (net radiation \\(R_n\\) and the vapor pressure deficit of the ambient air \\(D_a\\)), the latent heat flux can be modelled following the Penman-Monteith equation: \\[\n\\lambda E = \\frac{s(R_n - G) + \\rho c_p D_a G_\\mathrm{ah}}{s + \\gamma (1 + G_\\mathrm{ah}/G_\\mathrm{sw})}\n\\tag{7.7}\\]\n\n\\(s\\) is the slope of the saturation vapor pressure versus temperature curve (kPa K−1)\n\\(\\rho\\) is the density of air (kg m-3)\n\\(c_p\\) is the heat capacity of dry air (J K−1 kg−1)\n\\(\\gamma\\) is the psychrometric constant (kPa K−1)\n\nA derivation of the Penman-Monteith equation is given by G. Bonan (2015), Ch. 12.7.\nWith this, and given the atmospheric condition, we can visualise the dependency of the latent heat flux on the aerodynamic and the surface conductances. Let’s assume \\(R_n =\\) 400 W m-1.\n\n\nCode\nlibrary(dplyr)\nlibrary(ggplot2)\nlibrary(bigleaf)\nlibrary(cowplot)\n\n# calculate latent heat flux using penman monteith\ncalc_le_pm <- function(netrad, vpd, temp, g_ah, g_sw){\n # ARGUMENTS\n # netrad: net radiation\n # vpd: vapour pressure deficit\n # temp: ambient air temperature\n # patm: atmospheric pressure (kPa)\n # aerodynamic conductance to heat transport, in mass units (m s-1)\n # surface conductance to water vapor transport, in mass units (m s-1)\n \n # using standard atmospheric pressure\n patm <- bigleaf.constants()$pressure0 * 1e-3\n \n # slope of the saturation vapor pressure, using \"Sonntag_1990\" in Bigleaf\n s <- Esat.slope(temp)$Delta\n \n # density of air\n rho <- air.density(temp, patm)\n \n # heat capacity of dry air\n cp <- bigleaf.constants()$cp\n \n # psychrometric constant\n gamma <- psychrometric.constant(temp, patm)\n \n # assuming G = 0; conductances are in mass units\n out <- (s * netrad + rho * cp * vpd * g_ah) / (s + gamma * (1 + g_ah / g_sw))\n \n return(out)\n}\n\n# from SPLASH (Davis et al. 2017)\ncalc_enthalpy_vap <- function(tc){\n 1.91846e6*((tc + 273.15)/(tc + 273.15 - 33.91))**2\n}\n# calc_enthalpy_vap(15)\n# \n# # bigleaf built-in function\n# latent.heat.vaporization(15)\n# \n# # ratio\n# calc_enthalpy_vap(15) / latent.heat.vaporization(15)\n\n# # test our function\n# calc_le_pm(\n# netrad = 100,\n# vpd = 1,\n# temp = 15,\n# g_ah = 0.1, # mass units (m s-1)\n# g_sw = mol.to.ms(0.6, Tair = 15, pressure = bigleaf.constants()$pressure0 * 1e-3, constants = bigleaf.constants()) # convert molar units (mol m-2 s-1) to mass units\n# )\n\n# # test bigleaf built-in function\n# potential.ET(\n# Gs_pot = 0.6, # molar units (mol m-2 s-1)\n# Tair = 15,\n# pressure = bigleaf.constants()$pressure0 * 1e-3,\n# VPD = 1,\n# Ga = 0.1, # mass units\n# Rn = 100,\n# approach = \"Penman-Monteith\"\n# )[,\"LE_pot\"]\n\n# plot vs aerodynamic conductance\ndf <- expand.grid(\n g_ah = seq(0, 0.3, by = 0.01),\n vpd = seq(0, 5, by = 0.5)\n) |> \n as_tibble() |> \n mutate(\n le = purrr::map2_dbl(\n g_ah,\n vpd,\n ~calc_le_pm(\n netrad = 400, \n vpd = .y, \n temp = 15, \n g_ah = .x, \n g_sw = mol.to.ms(\n 0.6, \n Tair = 15, \n pressure = bigleaf.constants()$pressure0 * 1e-3, \n constants = bigleaf.constants()\n ))\n )\n )\n\ngg1 <- df |> \n ggplot() +\n geom_line(aes(g_ah, le, color = vpd, group = vpd)) +\n scale_color_viridis_c(name = \"VPD (kPa)\") +\n geom_hline(yintercept = 0, linetype = \"dotted\") +\n theme_classic() +\n labs(\n x = expression(paste(\"Aerodynamic conductance (m s\"^-1, \")\")),\n y = expression(paste(lambda, italic(\"E\"), \" (W m\"^-2, \")\"))\n ) + \n theme(legend.position=\"none\")\n\n# plot vs surface conductance\ndf <- expand.grid(\n g_sw = seq(0, 0.2, by = 0.01),\n vpd = seq(0, 5, by = 0.5)\n) |> \n as_tibble() |> \n mutate(\n le = purrr::map2_dbl(\n g_sw,\n vpd,\n ~calc_le_pm(\n netrad = 400, \n vpd = .y, \n temp = 15, \n g_ah = 0.1, \n g_sw = .x)\n )\n )\n\ngg2 <- df |> \n ggplot() +\n geom_line(aes(g_sw, le, color = vpd, group = vpd)) +\n scale_color_viridis_c(name = \"VPD (kPa)\") +\n theme_classic() +\n labs(\n x = expression(paste(\"Surface conductance (m s\"^-1, \")\")),\n y = expression(paste(lambda, italic(\"E\"), \" (W m\"^-2, \")\"))\n )\n\nplot_grid(\n gg1,\n gg2,\n labels = c(\"a\", \"b\"),\n rel_widths = c(0.77, 1)\n)\n\n\n\n\n\nFigure 7.9: Dependency of the latent heat flux on (a) the aerodynamic conductance and (b) the surface conductance following the Penman-Monteith equation (Equation 7.7).\n\n\n\n\nFigure 7.9 shows an interesting interactive effect of aerodynamic conductance and the VPD of ambient air. At low VPD, plant transpiration is reduced, thus limiting the latent heat flux (\\(\\lambda E\\)). Under such conditions, the \\(\\lambda E\\) declines with increasing aerodynamic conductance. This is because \\(H\\) rises faster than \\(\\lambda E\\) with increasing aerodynamic conductance and consumes a larger share of the net radiation. Under moderate-to-high VPD (above $$1 kPa in this example), \\(\\lambda E\\) rises with increasing aerodynamic conductance.\nUnder conditions of very low aerodynamic conductance (e.g., in a short-statured grassland that has a low surface roughness and under stable atmospheric conditions, e.g., during an inversion), the latent heat flux does not approach zero. This is because as long as there is positive net radiation (here 400 W m-2), the surface (skin temperature) heats up relative to the ambient air and creates a positive VPD at the leaf surface (even if VPD of ambient air is zero). These aspects drive a continued positive \\(H\\) and \\(\\lambda E\\) and the rise of the surface boundary layer." + "text": "7.2 Surface energy balance and partitioning\nThe energy available from radiative fluxes is converted into a sensible heat flux (\\(H\\)), a latent heat flux (\\(\\lambda E\\)), and a ground heat flux (\\(G\\), Figure 7.1 b). Following energy conservation, net radiation is equal to the sum of these three heat fluxes. \\[\nR_n = H + \\lambda E + G\n\\tag{7.5}\\]\nThe components of the surface energy balance (Equation 7.5) are commonly expressed in energy units (W m-2). Sensible heat is determined by the temperature of air. Latent heat is the energy contained by evaporated water. The latent heat flux (\\(\\lambda E\\)) is the product of the mass flux of water vapor (\\(E\\)), expressed in units of g m-2 s-1, and the latent heat of vaporization (\\(\\lambda\\)), converting the mass units back into energy units. \\(\\lambda\\) measures how much energy (Joules, J) is needed to vaporize 1 g of water at constant temperature. \\(\\lambda\\) is 2.466 MJ kg-1 at 15°C and has a slight dependence on temperature, decreasing linearly by about 3% from an air temperature of 0°C to 30°C.\n\n\n\nCode\nlibrary(ggplot2)\n\n# Function adopted from function bigleaf::latent.heat.vaporization\n# Returns latent heat of vaporization (J g-1)\n# References:\n# Stull, B., 1988: An Introduction to Boundary Layer Meteorology (p.641) Kluwer Academic Publishers, Dordrecht, Netherlands\n# Foken, T, 2008: Micrometeorology. Springer, Berlin, Germany.\ncalc_lambda <- function(temp){\n k1 <- 2.501\n k2 <- 0.00237\n lambda <- (k1 - k2 * temp) * 1e+03\n return(lambda)\n}\n\nggplot() +\n geom_function(fun = calc_lambda) +\n xlim(0, 35) +\n labs(x = \"Temperature (°C)\",\n y = expression(paste(\"Latent heat of vaporization (J g\"^-1, \")\"))) + \n theme_classic()\n\n\n\n\n\nFigure 7.6: Latent heat of vaporization as a function of air temperature.\n\n\n\n\n\n\nThe sensible and latent heat fluxes are transported vertically, away from or to the land surface through convective transport. That is, through turbulences that mix the air and lead to a net vertical transport of heat and water vapor. Whether net fluxes are pointed upwards or downwards depends on the sign of the net radiation (see Figure 7.11 and Figure 7.12) and typically changes between night and daytime. Note that the latent heat flux can be negative, leading to a net flux of water vapor towards the surface. The respective water mass condensates at the surface (of leaves) and can be a considerable fraction of the ecosystem water balance.\nFinally, the ground heat flux \\(G\\) buffers variations of net radiation, absorbing energy and removing heat from the surface during the day and summer and releasing heat during night and winter.\n\n\n7.2.1 Potential evapotranspiration\nPhysical and biological properties of the land surface determine not only the net radiation through (mainly) effects of the albedo, but also strongly influence the partitioning of net radiation into sensible and latent heat fluxes in Equation 7.5. In particular, the availability of water for evaporation from the land surface through transpiration, or directly from wet surfaces, is decisive for the partitioning of net radiation into \\(H\\) and \\(\\lambda E\\).\nA useful quantity for understanding the surface energy partitioning and the influence of limiting factors (e.g., water limitation) is the potential evapotranspiration (PET). Evapotranspiration is equivalent to the latent heat flux, but expressed in water vapor mass units. (You will learn more about evapotranspiration in Chapter 8). PET can be understood as the maximum possible \\(E\\), attained under conditions where water supply to evaporation is not limiting. Different methods are available for estimating PET. A physically based and widely used method is the one by Priestley and Taylor (1972) which relates PET to net radiation, considering that net radiation is consumed by the water vapor flux from a water-saturated surface into an air parcel at constant temperature and pressure. \\[\n\\mathrm{PET} = \\alpha \\frac{s}{s + \\gamma} \\frac{R_n}{\\lambda}\n\\tag{7.6}\\] Here, \\(s\\) (Pa K-2) is the slope of the change in saturation vapor pressure with respect to temperature. \\(\\gamma\\) is the psychrometric constant (a representative value is 66.5 Pa K–1). The coefficient \\(\\alpha\\) is an empirically determined value and is taken to be 1.26 for a wet surface. However, for vegetated surfaces, it is substantially lower, even if the plants are not water-limited. It ranges between 0.82 for tropical and temperate broadleaf forests and 0.55 for boreal conifer forests (G. Bonan 2015).\n\n\n7.2.2 Metrics of energy partitioning\nDifferent metrics are used for quantifying the partitioning of net radiation into \\(H\\) and \\(\\lambda E\\). When considering totals over longer periods of time (over at least one annual cycle), the ground heat flux \\(G\\) can be neglected since the ground doesn’t gradually heat up over time. Hence, the sum of the latent and sensible heat fluxes add up to match net radiation. The evaporative fraction quantifies the fraction of available energy from net radiation goes into the latent heat flux. \\[\n\\mathrm{EF} = \\lambda E/R_n\n\\] The remainder goes into the sensible heat flux. The Bowen ratio expresses the same relation and is defined as \\[\nB = H/\\lambda E\n\\] The ratio of actual over potential evapotranspiration (\\(E/\\mathrm{PET}\\), also referred to as ‘AET/PET’) is often used, but measurements of actual evapotranspiration are scarce and model-based estimates are subject to strong assumptions.\nQuantifications of EF, \\(B\\), and \\(E/\\mathrm{PET}\\) give important and readily interpretable insights. Variations of these quantities across space and time reflect water limitation to \\(E\\), biophysical surface properties and vegetation activity. For example, in forests, the evaporative fraction is typically lower compared to certain crops, and it’s even lower in conifer forests than in deciduous broadleaf forests (Figure 7.8). The evaporative fraction declines as water becomes more limiting during dry (rain-free) periods. An example for the application of \\(E/\\mathrm{PET}\\) is the Evaporative Stress Index product (Figure 7.7), generated by the ECOSTRESS satellite mission (Fisher et al. 2020).\n\n\n\n\n\nFigure 7.7: ECOSTRESS evaporative stress index for the Guanacaste region of Costa Rica (in red on inset map, left) a few months after the onset of a major Central American drought. Red indicates high plant water stress, yellow is moderate stress and greens/blues are low stress. Light gray is cloud cover. The index measures how much water plants are using relative to how much they would use under optimal conditions; low numbers correlate with high stress. Figure from https://www.jpl.nasa.gov/images/pia22839-ecostress-focuses-on-costa-rican-drought.\n\n\n\n\n\n\n7.2.3 Combining energy, atmospheric, and biophysical controls on \\(\\lambda E\\)\nNot only the availability of water for evaporation, but also the atmospheric condition (specifically, the vapor pressure deficit) and biophysical surface properties determine the latent heat flux and the surface energy partitioning. The key biophysical surface properties are the aerodynamic conductance to heat transfer (\\(G_\\mathrm{ah}\\)) and the surface conductance to water vapor transport (\\(G_\\mathrm{sw}\\)). How energy, atmospheric, and biophysical controls drive the latent heat flux \\(\\lambda E\\) is described by the Penman-Monteith equation (Equation 7.7), as shown in the box below and Figure 7.9. The aerodynamic conductance depends on the roughness of the surface and on wind speed. Taller vegetation has a higher roughness and a higher aerodynamic conductance. Roughness also increases with LAI.\nOn vegetated surfaces, the surface conductance to water vapor transport is strongly influenced by the stomatal conductance (\\(g_s\\), Equation 4.5 and Equation 4.11) and by the LAI. Water evaporation from rock, soil, leaf, or branch surfaces contributes to surface conductance and occurs also from non-vegetated surfaces. In a closed canopy, surface conductance is dominated by the signal by stomatal conductance. When leaves are active and photosynthesizing (high light), and when water stress is low (high soil moisture, low VPD), stomatal conductance is high. How water availability and vegetation regulate stomatal conductance, and thus the latent heat flux and energy partitioning at the land surface is introduced in Chapter 8.\n\n\n\n\n\nFigure 7.8: Surface resistance and normalized latent heat flux for different vegetation types. Normalization removes effects of different net radiation on latent heat fluxes. Canopy resistance is equivalent to the inverse of surface conductance described in this chapter. Figure from G. B. Bonan (2008).\n\n\n\n\nTaken together, the spatial distribution of vegetation and other land cover types, and the response of plants to temporal changes in the environment (and thus on LAI and stomatal conductance) influence the energy partitioning at the land surface and near-surface atmospheric conditions. In other words, we have to understand vegetation and its response to the environment in order to understand land-climate interactions and near-surface climate.\n\n\n\n\n\n\nDependency of energy partitioning on conductances\n\n\n\n\n\nGiven the atmospheric condition (net radiation \\(R_n\\) and the vapor pressure deficit of the ambient air \\(D_a\\)), the latent heat flux can be modelled following the Penman-Monteith equation: \\[\n\\lambda E = \\frac{s(R_n - G) + \\rho c_p D_a G_\\mathrm{ah}}{s + \\gamma (1 + G_\\mathrm{ah}/G_\\mathrm{sw})}\n\\tag{7.7}\\]\n\n\\(s\\) is the slope of the saturation vapor pressure versus temperature curve (kPa K−1)\n\\(\\rho\\) is the density of air (kg m-3)\n\\(c_p\\) is the heat capacity of dry air (J K−1 kg−1)\n\\(\\gamma\\) is the psychrometric constant (kPa K−1)\n\nA derivation of the Penman-Monteith equation is given by G. Bonan (2015), Ch. 12.7.\nWith this, and given the atmospheric condition, we can visualise the dependency of the latent heat flux on the aerodynamic and the surface conductances. Let’s assume \\(R_n =\\) 400 W m-1.\n\n\nCode\nlibrary(dplyr)\nlibrary(ggplot2)\nlibrary(bigleaf)\nlibrary(cowplot)\n\n# calculate latent heat flux using penman monteith\ncalc_le_pm <- function(netrad, vpd, temp, g_ah, g_sw){\n # ARGUMENTS\n # netrad: net radiation\n # vpd: vapor pressure deficit\n # temp: ambient air temperature\n # patm: atmospheric pressure (kPa)\n # aerodynamic conductance to heat transport, in mass units (m s-1)\n # surface conductance to water vapor transport, in mass units (m s-1)\n \n # using standard atmospheric pressure\n patm <- bigleaf.constants()$pressure0 * 1e-3\n \n # slope of the saturation vapor pressure, using \"Sonntag_1990\" in Bigleaf\n s <- Esat.slope(temp)$Delta\n \n # density of air\n rho <- air.density(temp, patm)\n \n # heat capacity of dry air\n cp <- bigleaf.constants()$cp\n \n # psychrometric constant\n gamma <- psychrometric.constant(temp, patm)\n \n # assuming G = 0; conductances are in mass units\n out <- (s * netrad + rho * cp * vpd * g_ah) / (s + gamma * (1 + g_ah / g_sw))\n \n return(out)\n}\n\n# from SPLASH (Davis et al. 2017)\ncalc_enthalpy_vap <- function(tc){\n 1.91846e6*((tc + 273.15)/(tc + 273.15 - 33.91))**2\n}\n# calc_enthalpy_vap(15)\n# \n# # bigleaf built-in function\n# latent.heat.vaporization(15)\n# \n# # ratio\n# calc_enthalpy_vap(15) / latent.heat.vaporization(15)\n\n# # test our function\n# calc_le_pm(\n# netrad = 100,\n# vpd = 1,\n# temp = 15,\n# g_ah = 0.1, # mass units (m s-1)\n# g_sw = mol.to.ms(0.6, Tair = 15, pressure = bigleaf.constants()$pressure0 * 1e-3, constants = bigleaf.constants()) # convert molar units (mol m-2 s-1) to mass units\n# )\n\n# # test bigleaf built-in function\n# potential.ET(\n# Gs_pot = 0.6, # molar units (mol m-2 s-1)\n# Tair = 15,\n# pressure = bigleaf.constants()$pressure0 * 1e-3,\n# VPD = 1,\n# Ga = 0.1, # mass units\n# Rn = 100,\n# approach = \"Penman-Monteith\"\n# )[,\"LE_pot\"]\n\n# plot vs aerodynamic conductance\ndf <- expand.grid(\n g_ah = seq(0, 0.3, by = 0.01),\n vpd = seq(0, 5, by = 0.5)\n) |> \n as_tibble() |> \n mutate(\n le = purrr::map2_dbl(\n g_ah,\n vpd,\n ~calc_le_pm(\n netrad = 400, \n vpd = .y, \n temp = 15, \n g_ah = .x, \n g_sw = mol.to.ms(\n 0.6, \n Tair = 15, \n pressure = bigleaf.constants()$pressure0 * 1e-3, \n constants = bigleaf.constants()\n ))\n )\n )\n\ngg1 <- df |> \n ggplot() +\n geom_line(aes(g_ah, le, color = vpd, group = vpd)) +\n scale_color_viridis_c(name = \"VPD (kPa)\") +\n geom_hline(yintercept = 0, linetype = \"dotted\") +\n theme_classic() +\n labs(\n x = expression(paste(\"Aerodynamic conductance (m s\"^-1, \")\")),\n y = expression(paste(lambda, italic(\"E\"), \" (W m\"^-2, \")\"))\n ) + \n theme(legend.position=\"none\")\n\n# plot vs surface conductance\ndf <- expand.grid(\n g_sw = seq(0, 0.2, by = 0.01),\n vpd = seq(0, 5, by = 0.5)\n) |> \n as_tibble() |> \n mutate(\n le = purrr::map2_dbl(\n g_sw,\n vpd,\n ~calc_le_pm(\n netrad = 400, \n vpd = .y, \n temp = 15, \n g_ah = 0.1, \n g_sw = .x)\n )\n )\n\ngg2 <- df |> \n ggplot() +\n geom_line(aes(g_sw, le, color = vpd, group = vpd)) +\n scale_color_viridis_c(name = \"VPD (kPa)\") +\n theme_classic() +\n labs(\n x = expression(paste(\"Surface conductance (m s\"^-1, \")\")),\n y = expression(paste(lambda, italic(\"E\"), \" (W m\"^-2, \")\"))\n )\n\nplot_grid(\n gg1,\n gg2,\n labels = c(\"a\", \"b\"),\n rel_widths = c(0.77, 1)\n)\n\n\n\n\n\nFigure 7.9: Dependency of the latent heat flux on (a) the aerodynamic conductance and (b) the surface conductance following the Penman-Monteith equation (Equation 7.7).\n\n\n\n\nFigure 7.9 shows an interesting interactive effect of aerodynamic conductance and the VPD of ambient air. At low VPD, plant transpiration is reduced, thus limiting the latent heat flux (\\(\\lambda E\\)). Under such conditions, the \\(\\lambda E\\) declines with increasing aerodynamic conductance. This is because \\(H\\) rises faster than \\(\\lambda E\\) with increasing aerodynamic conductance and consumes a larger share of the net radiation. Under moderate-to-high VPD (above ~1 kPa in this example), \\(\\lambda E\\) rises with increasing aerodynamic conductance. \nUnder conditions of very low aerodynamic conductance (e.g., in a short-statured grassland that has a low surface roughness and under stable atmospheric conditions, e.g., during an inversion), the latent heat flux does not approach zero. This is because as long as there is positive net radiation (here 400 W m-2), the surface (skin temperature) heats up relative to the ambient air and creates a positive VPD at the leaf surface (even if VPD of ambient air is zero). These aspects drive a continued positive \\(H\\) and \\(\\lambda E\\) and the rise of the surface boundary layer." }, { "objectID": "landclimate.html#energy-fluxes-across-biomes", "href": "landclimate.html#energy-fluxes-across-biomes", "title": "7  Land-climate interactions", "section": "7.3 Energy fluxes across biomes", - "text": "7.3 Energy fluxes across biomes\nAs for C fluxes in Chapter 6, we turn to investigating diurnal and seasonal patterns in fluxes - this time the energy fluxes. The patterns observed at the same sites as used before illustrate general differences across biomes and how different characteristics of the vegetation cover affect the surface energy balance and flux partitioning. In addition to the temperate broadleaved forest site (Hainich Forest, DE-Hai), we consider a coniferous forest (DE-Tha) and a grassland site (DE-Gri) that are located closeby (and thus experience largely identical meterological conditions, ignoring feedbacks from vegetation-atmosphere fluxes that affect near-surface climate).\n\n\nCode\ndf_sites <- read_csv(here::here(\"data/fdk_site_info.csv\"))\n\n# chose representative sites\nuse_sites <- c(\n \"FI-Hyy\", # Boreal Forests/Taiga\n \"DE-Hai\", # Temperate Broadleaf & Mixed Forests\n \"DE-Tha\", # Temperate Coniferous\n \"DE-Gri\", # Grassland just next to DE-Tha\n \"BR-Sa3\", # Tropical\n \"US-ICh\" # Tundra\n)\n\n# subset data\ndf_sites |> \n filter(sitename %in% use_sites) |> \n mutate(\n lon = format(lon, digits = 3), \n lat = format(lat, digits = 3), \n elv = format(elv, digits = 3)\n ) |> \n select(\n Site = sitename, \n Longitude = lon, \n Latitude = lat, \n Elevation = elv, \n `Vegetation type` = igbp_land_use,\n `Climate zone` = koeppen_code\n ) |> \n knitr::kable()\n\n\n\n\n\n\nSite\nLongitude\nLatitude\nElevation\nVegetation type\nClimate zone\n\n\n\n\nBR-Sa3\n-55.0\n-3.02\n100\nEBF\nAm\n\n\nDE-Gri\n13.5\n50.95\n385\nGRA\nCfb\n\n\nDE-Hai\n10.5\n51.08\n439\nDBF\nCfb\n\n\nDE-Tha\n13.6\n50.96\n380\nENF\nCfb\n\n\nFI-Hyy\n24.3\n61.85\n181\nENF\nDfc\n\n\nUS-ICh\n-149.3\n68.61\n940\nOSH\nET\n\n\n\nFigure 7.10: Site meta information. Vegetation types are described in Table 2.1. Climate zones are described in Figure 2.22.\n\n\n\n\n7.3.1 Diurnal variations\n\n\n\n\n\n\nFigure 7.11: Diurnal variations of energy fluxes at sites representing different biomes, taken as the average for each half-hour of a day in July.\n\n\n\n\n\n\n\n\n\n\nExercise\n\n\n\nThe diurnal course of energy fluxes is considered for an average day in July for each site. Describe key patterns and differences between sites and relate them to your knowledge about radiation, energy partitioning, and land surface and vegetation properties.\n\nHow does net radiation compare across sites in the top row of Figure 7.11? What component of the net radiation (Figure 7.1 a) do you think is responsible for the observed differences? What surface property may contribute to the differences in net radiation and does it explain why the tropical site has a higher mid-day net radiation peak than the boreal site?\nHow does net radiation compare across the three sites in the temperate biome? Can vegetation properties that affect the reflectance explain why the mid-day peak net radiation is lower for DE-Gri han for DE-Tha?\nDuring night-time, net radiation is negative at all sites. Which of the four components of net radiation is largest during nighttime?\nIs the land surface losing or gaining energy during the night? What flux drives this gain/loss (\\(H\\) or \\(\\lambda E\\))?\nAt what site is the nighttime energy gain/loss highest? What surface property may be responsible for this?\nChararcterise the Bowen ratio at mid-day for all sites (greater than, close to, or smaller than 1).\nWhat site has the highest mid-day Bowen ratio? What site has the lowest mid-day Bowen ratio?\nAssuming all sites had the same aerodynamic and surface conductances, which site may have the highest mid-day VPD? Is this a valid assumption? If not, how do you expect conductances to differ among sites?\nThe temperate coniferous forest site (which one?) has the higher mid-day net radiation than the temperate broadleaved fores site (which one?). Yet, its latent heat flux is lower than for the latter. Assuming they had the same VPD and aerodynamic conductance, what other surface property may explain this difference?\nThe temperate grassland has a higher latent heat flux than the two temperate forest sites. Can the difference in vegetation height explain the difference in the latent heat flux?\nWhat site has the highest sensible heat flux? If you were a paraglider, over which site do you expect to find the strongest up-lift to take you to your next destination?\n\n\n\n\n\n\n\n\n\n\n7.3.2 Seasonal variations\n\n\n\n\n\nFigure 7.12: Seasonal variations of energy fluxes at sites representing different biomes.\n\n\n\n\n\n\n\n\n\n\nExercise\n\n\n\n\nWhich site has the highest net radiation around May? What surface property may this be related to?\nWhich site has the lowest summertime net radiation? How does this compare to differences in summertime solar radiation among these sites? What other components of net radiation do you expect to explain the low summertime net radiation at this site?\nWhat could explain the different seasonal course of the latent and sensible heat flux at DE-Hai, while they vary in parallel at DE-Tha?\nWhat may be the cause of the delayed springtime increase of \\(\\lambda E\\), compared to \\(H\\) at FI-Hyy?\nWhat site loses the largest amount of water on an annual basis?\nDo you find other interesting patterns and interpretable differences between sites?\n\n\n\n\n\n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nBonan, Gordon. 2015. Ecological Climatology: Concepts and Applications. 3rd ed. Cambridge University Press.\n\n\nBonan, Gordon B. 2008. “Forests and Climate Change: Forcings, Feedbacks, and the Climate Benefits of Forests.” Science 320 (5882): 1444–49. https://doi.org/10.1126/science.1155121.\n\n\nCescatti, Alessandro, Barbara Marcolla, Suresh K. Santhana Vannan, Jerry Yun Pan, Miguel O. Román, Xiaoyuan Yang, Philippe Ciais, et al. 2012. “Intercomparison of MODIS Albedo Retrievals and in Situ Measurements Across the Global FLUXNET Network.” Remote Sensing of Environment 121 (June): 323–34. https://doi.org/10.1016/j.rse.2012.02.019.\n\n\nFisher, Joshua B., Brian Lee, Adam J. Purdy, Gregory H. Halverson, Matthew B. Dohlen, Kerry Cawse‐Nicholson, Audrey Wang, et al. 2020. “ECOSTRESS: NASA’s Next Generation Mission to Measure Evapotranspiration From the International Space Station.” Water Resources Research 56 (4). https://doi.org/10.1029/2019WR026058.\n\n\nForster, P., T. Storelvmo, K. Armour, W. Collins, J.-L. Dufresne, D. Frame, D. J. Lunt, et al. 2021. “The Earth’s Energy Budget, Climate Feedbacks, and Climate Sensitivity.” Book Section. In Climate Change 2021: The Physical Science Basis. Contribution of Working Group i to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, edited by V. Masson-Delmotte, P. Zhai, A. Pirani, S. L. Connors, C. Péan, S. Berger, N. Caud, et al., 923–1054. Cambridge, UK; New York, NY, USA: Cambridge University Press. https://doi.org/10.1017/9781009157896.009.\n\n\nOke, T. R. 1987. Boundary Layer Climates. 2nd ed. London: Routledge. https://doi.org/10.4324/9780203407219.\n\n\nPriestley, C. H. B., and R. J. Taylor. 1972. “On the Assessment of Surface Heat Flux and Evaporation Using Large-Scale Parameters.” Monthly Weather Review 100 (2): 81–92. https://doi.org/10.1175/1520-0493(1972)100<0081:OTAOSH>2.3.CO;2.\n\n\nZhao, Kaiguang, and Robert B. Jackson. 2014. “Biophysical Forcings of Land-Use Changes from Potential Forestry Activities in North America.” Ecological Monographs 84 (2): 329–53. https://www.jstor.org/stable/43187893." + "text": "7.3 Energy fluxes across biomes\nAs for C fluxes in Chapter 6, we turn to investigating diurnal and seasonal patterns in fluxes - this time the energy fluxes. The patterns observed at the same sites as used before illustrate general differences across biomes and how different characteristics of the vegetation cover affect the surface energy balance and flux partitioning. In addition to the temperate broadleaved forest site (Hainich Forest, DE-Hai), we consider a coniferous forest (DE-Tha) and a grassland site (DE-Gri) that are located close by (and thus experience largely identical meteorological conditions, ignoring feedbacks from vegetation-atmosphere fluxes that affect near-surface climate).\n\n\nCode\ndf_sites <- read_csv(here::here(\"data/fdk_site_info.csv\"))\n\n# chose representative sites\nuse_sites <- c(\n \"FI-Hyy\", # Boreal Forests/Taiga\n \"DE-Hai\", # Temperate Broadleaf & Mixed Forests\n \"DE-Tha\", # Temperate Coniferous\n \"DE-Gri\", # Grassland just next to DE-Tha\n \"BR-Sa3\", # Tropical\n \"US-ICh\" # Tundra\n)\n\n# subset data\ndf_sites |> \n filter(sitename %in% use_sites) |> \n mutate(\n lon = format(lon, digits = 3), \n lat = format(lat, digits = 3), \n elv = format(elv, digits = 3)\n ) |> \n select(\n Site = sitename, \n Longitude = lon, \n Latitude = lat, \n Elevation = elv, \n `Vegetation type` = igbp_land_use,\n `Climate zone` = koeppen_code\n ) |> \n knitr::kable()\n\n\n\n\n\n\nSite\nLongitude\nLatitude\nElevation\nVegetation type\nClimate zone\n\n\n\n\nBR-Sa3\n-55.0\n-3.02\n100\nEBF\nAm\n\n\nDE-Gri\n13.5\n50.95\n385\nGRA\nCfb\n\n\nDE-Hai\n10.5\n51.08\n439\nDBF\nCfb\n\n\nDE-Tha\n13.6\n50.96\n380\nENF\nCfb\n\n\nFI-Hyy\n24.3\n61.85\n181\nENF\nDfc\n\n\nUS-ICh\n-149.3\n68.61\n940\nOSH\nET\n\n\n\nFigure 7.10: Site meta information. Vegetation types are described in Table 2.1. Climate zones are described in Figure 2.22.\n\n\n\n\n7.3.1 Diurnal variations\n\n\n\n\n\n\nFigure 7.11: Diurnal variations of energy fluxes at sites representing different biomes, taken as the average for each half-hour of a day in July.\n\n\n\n\n\n\n\n\n\n\nExercise\n\n\n\nThe diurnal course of energy fluxes is considered for an average day in July for each site. Describe key patterns and differences between sites and relate them to your knowledge about radiation, energy partitioning, and land surface and vegetation properties.\n\nHow does net radiation compare across sites in the top row of Figure 7.11? What component of the net radiation (Figure 7.1 a) do you think is responsible for the observed differences? What surface property may contribute to the differences in net radiation, and does it explain why the tropical site has a higher mid-day net radiation peak than the boreal site?\nHow does net radiation compare across the three sites in the temperate biome? Can vegetation properties that affect the reflectance explain why the mid-day peak net radiation is lower for DE-Gri han for DE-Tha?\nDuring night-time, net radiation is negative at all sites. Which of the four components of net radiation is largest during nighttime?\nIs the land surface losing or gaining energy during the night? What flux drives this gain/loss (\\(H\\) or \\(\\lambda E\\))?\nAt what site is the nighttime energy gain/loss highest? What surface property may be responsible for this?\nChararcterise the Bowen ratio at mid-day for all sites (greater than, close to, or smaller than 1).\nWhat site has the highest mid-day Bowen ratio? What site has the lowest mid-day Bowen ratio?\nAssuming all sites had the same aerodynamic and surface conductances, which site may have the highest mid-day VPD? Is this a valid assumption? If not, how do you expect conductances to differ among sites?\nThe temperate coniferous forest site (which one?) has the higher mid-day net radiation than the temperate broadleaved fores site (which one?). Yet, its latent heat flux is lower than for the latter. Assuming they had the same VPD and aerodynamic conductance, what other surface property may explain this difference?\nThe temperate grassland has a higher latent heat flux than the two temperate forest sites. Can the difference in vegetation height explain the difference in the latent heat flux?\nWhat site has the highest sensible heat flux? If you were a paraglider, over which site do you expect to find the strongest uplift to take you to your next destination?\n\n\n\n\n\n\n\n\n\n\n7.3.2 Seasonal variations\n\n\n\n\n\nFigure 7.12: Seasonal variations of energy fluxes at sites representing different biomes.\n\n\n\n\n\n\n\n\n\n\nExercise\n\n\n\n\nWhich site has the highest net radiation around May? What surface property may this be related to?\nWhich site has the lowest summertime net radiation? How does this compare to differences in summertime solar radiation among these sites? What other components of net radiation do you expect to explain the low summertime net radiation at this site?\nWhat could explain the different seasonal course of the latent and sensible heat flux at DE-Hai, while they vary in parallel at DE-Tha?\nWhat may be the cause of the delayed springtime increase of \\(\\lambda E\\), compared to \\(H\\) at FI-Hyy?\nWhat site loses the largest amount of water on an annual basis?\nDo you find other interesting patterns and interpretable differences between sites?\n\n\n\n\n\n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nBonan, Gordon. 2015. Ecological Climatology: Concepts and Applications. 3rd ed. Cambridge University Press.\n\n\nBonan, Gordon B. 2008. “Forests and Climate Change: Forcings, Feedbacks, and the Climate Benefits of Forests.” Science 320 (5882): 1444–49. https://doi.org/10.1126/science.1155121.\n\n\nCescatti, Alessandro, Barbara Marcolla, Suresh K. Santhana Vannan, Jerry Yun Pan, Miguel O. Román, Xiaoyuan Yang, Philippe Ciais, et al. 2012. “Intercomparison of MODIS Albedo Retrievals and in Situ Measurements Across the Global FLUXNET Network.” Remote Sensing of Environment 121 (June): 323–34. https://doi.org/10.1016/j.rse.2012.02.019.\n\n\nFisher, Joshua B., Brian Lee, Adam J. Purdy, Gregory H. Halverson, Matthew B. Dohlen, Kerry Cawse‐Nicholson, Audrey Wang, et al. 2020. “ECOSTRESS: NASA’s Next Generation Mission to Measure Evapotranspiration From the International Space Station.” Water Resources Research 56 (4). https://doi.org/10.1029/2019WR026058.\n\n\nForster, P., T. Storelvmo, K. Armour, W. Collins, J.-L. Dufresne, D. Frame, D. J. Lunt, et al. 2021. “The Earth’s Energy Budget, Climate Feedbacks, and Climate Sensitivity.” Book Section. In Climate Change 2021: The Physical Science Basis. Contribution of Working Group i to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, edited by V. Masson-Delmotte, P. Zhai, A. Pirani, S. L. Connors, C. Péan, S. Berger, N. Caud, et al., 923–1054. Cambridge, UK; New York, NY, USA: Cambridge University Press. https://doi.org/10.1017/9781009157896.009.\n\n\nOke, T. R. 1987. Boundary Layer Climates. 2nd ed. London: Routledge. https://doi.org/10.4324/9780203407219.\n\n\nPriestley, C. H. B., and R. J. Taylor. 1972. “On the Assessment of Surface Heat Flux and Evaporation Using Large-Scale Parameters.” Monthly Weather Review 100 (2): 81–92. https://doi.org/10.1175/1520-0493(1972)100<0081:OTAOSH>2.3.CO;2.\n\n\nZhao, Kaiguang, and Robert B. Jackson. 2014. “Biophysical Forcings of Land-Use Changes from Potential Forestry Activities in North America.” Ecological Monographs 84 (2): 329–53. https://www.jstor.org/stable/43187893." }, { "objectID": "ecohydrology.html#global-water-cycle", "href": "ecohydrology.html#global-water-cycle", "title": "8  Ecohydrology", "section": "8.1 Global water cycle", - "text": "8.1 Global water cycle\n\n\n\n\nWater cycles in the Earth system between the atmosphere, the ocean, the land biosphere and the cryosphere. The evaporation of water (H2O) from its liquid form to (gaseous) water vapour consumes energy (Section 7.2) and its condensation releases the same amount of energy in the form of heat again. Hence, the global water cycle is coupled to large energy transfers. For the Earth as a whole and as an annual average, 80 W m–2 are consumed for evaporation – more than three-quarters of the 98 W m–2 net radiation at the surface (Bonan 2015).\nThe vast majority (ca. 98%) of water on Earth is saline and is stored in the Oceans, inland seas, and saline groundwater (Figure 8.1 a). Among the total amount of freshwater, the vast majority is stored as ice. Only a small fraction of water on Earth cycles between the atmosphere, the ocean and land. However, this cycling is relatively rapid (see Exercise below).\nOceans dominate in total evaporation (470 km3 yr-1, vs. 74 km3 yr-1 from land, Figure 8.1 b) and the majority of precipitation falls over oceans. However, since precipitation over oceans is smaller than evaporation from oceans (424 km3 yr-1 vs. 470 km3 yr-1), a net transfer of water from oceans to land exists. Almost all of the surplus of the land’s water balance runs off as river discharge back into the ocean. A small fraction is discharged into the ocean through groundwater.\n\n\n\n\n\nFigure 8.1: Depiction of the present-day water cycle. In the atmosphere, which accounts for only 0.001% of all water on Earth, water primarily occurs as a gas (water vapour), but it is also present as ice and liquid water within clouds. The ocean is the primary water reservoir on Earth: it comprises mostly liquid water across much of the globe but also includes areas covered by ice in polar regions. Liquid freshwater on land forms surface water (lakes, rivers) and, together with soil moisture and mostly unusable groundwater stores, accounts for less than 2% of global water. Solid terrestrial water that occurs as ice sheets, glaciers, snow and ice on the surface, and permafrost currently represents nearly 2% of the planet’s water. Water that falls as snow in winter provides soil moisture and streamflow after melting, which are essential for human activities and ecosystem functioning. Note that these best estimates do not lead to a perfectly closed global water budget and that this budget has no reason to be closed given the ongoing human influence through both climate change (e.g., melting of ice sheets and glaciers, see Chapter 9) and water use (e.g., groundwater depletion through pumping into fossil aquifers, see Figure 8.10). Figure and caption from Douville et al. (2021).\n\n\n\n\nEvaporation from land is a smaller component than evaporation from oceans, and soils store less than 1% of the unfrozen freshwater on Earth. Yet, land processes are a key regulator of global water cycling and energy fluxes. This is because the majority of evaporation over land occurs through transpiration and is thus affected by the vegetation structure and ecophysiological relations - through effects of LAI (Section 4.2), surface conductance (Section 7.2.2) and stomatal conductance (Section 4.4). Another aspect is the fact that, while the amount of water stored in the rooting zone of vegetation is small, it supplies all transpiration. In many climates, the root zone moisture gets substantially depleted during episodic dry spells or regularly recurring dry seasons. The ensuing plant water stress leads to a reduction of transpiration and evaporation, and thus to an alteration also of the surface energy partitioning. This chapter introduces the quantities and mechanisms for understanding how water regulates vegetation and how vegetation shapes the cycling of water and land surface energy partitioning across the globe.\n\n\n\n\n\n\nExercise\n\n\n\n\nCalculate the total freshwater stored as ice as a fraction of total freshwater.\nCalculate the turnover time of water in the atmosphere.\nCalculate the turnover time of water in soils (soil moisture).\n\n\n\n\n\n\n\n\n\nAtmospheric humidity\n\n\n\n\n\n\nWe have encountered the vapour pressure deficit (VPD) and its control on transpiration in Section 4.4 and on evapotranspiration in Section 7.2.2. VPD is a measure of atmospheric humidity. This box is to explain how VPD relates to other metrics of atmospheric humidity and to the physics of moist air.\nThe total pressure of a gas can be expressed as the sum of partial pressures of different components of a gas mixture. For moist air, we can distinguish the partial pressures of water vapor (\\(e_a\\)) and dry air (\\(P_d\\)) and write the total pressure of moist air as \\[\nP = P_d + e_a \\;.\n\\] Both, the dry air and water vapour follow the ideal gas law. Expressed in molar form, it is \\[\nP_d = \\rho_d \\frac{RT}{M_d} \\\\\ne_a = \\rho_v \\frac{RT}{M_v} = \\rho_v \\frac{RT}{0.622 M_d}\n\\tag{8.1}\\] Here, \\(\\rho_d\\) is the density of dry air; \\(\\rho_v\\) is the density of water vapor, \\(R\\) is the universal gas constant (8.314 J K-1 mol-1); \\(T\\) is temperature (in K). The factor 0.622 relates the molecular mass of water ($M_v = $ 18.02 g mol–1) to that of dry air ($M_d = $28.97 g mol–1).\nThe specific humidity \\(q\\) can be derived from Equation 8.1 as \\[\nq = \\frac{\\rho_v}{\\rho_v + \\rho_d} = \\frac{0.622 e_a}{P-(1-0.622)e_a}\n\\] The vapour pressure deficit (\\(D\\)) is the difference between the actual vapour pressure \\(e_a\\) and the vapour pressure at saturation \\(e_s(T)\\) (where water condensates). \\[\nD = e_s - e_a\n\\] The saturation vapour pressure is a function of air temperature (\\(T\\) in °C). This relationship is related to the Clausius-Clapeyron relation of the temperature dependence of vapor pressure. A relatively accurate, yet simple empirical equation for this relationship is the following. \\[\ne_s(T) = 611.0 \\; \\exp \\left( \\frac{17.27 \\; T}{T + 237.3} \\right)\n\\] This equation calculates the the saturation vapour pressure \\(e_s(T)\\) in units of Pa.\n\n\nCode\nlibrary(ggplot2)\n\ncalc_e_sat <- function(temp){\n 611.0 * exp( (17.27 * temp)/(temp + 237.3) )\n}\n\nggplot() +\n geom_function(fun = calc_e_sat) +\n xlim(0, 35) +\n labs(x = \"Temperature (°C)\",\n y = \"Saturation vapour pressure (Pa)\") + \n theme_classic()\n\n\n\n\n\nFigure 8.2: Saturation vapour pressure as a function of air temperature.\n\n\n\n\nThe relative humidity (RH) also relates \\(e_a\\) to \\(e_s\\), but as its ratio and not the difference. \\[\n\\mathrm{RH} = 100 \\% \\; \\frac{e_a}{e_s(T)}\n\\]" + "text": "8.1 Global water cycle\n\n\n\n\nWater cycles in the Earth system between the atmosphere, the ocean, the land biosphere and the cryosphere. The evaporation of water (H2O) from its liquid form to (gaseous) water vapor consumes energy (Section 7.2) and its condensation releases the same amount of energy in the form of heat again. Hence, the global water cycle is coupled to large energy transfers. For the Earth as a whole and as an annual average, 80 W m–2 are consumed for evaporation – more than three-quarters of the 98 W m–2 net radiation at the surface (Bonan 2015).\nThe vast majority (ca. 98%) of water on Earth is saline and is stored in the Oceans, inland seas, and saline groundwater (Figure 8.1 a). Among the total amount of freshwater, the vast majority is stored as ice. Only a small fraction of water on Earth cycles between the atmosphere, the ocean and land. However, this cycling is relatively rapid (see Exercise below).\nOceans dominate in total evaporation (470 km3 yr-1, vs. 74 km3 yr-1 from land, Figure 8.1 b) and the majority of precipitation falls over oceans. However, since precipitation over oceans is smaller than evaporation from oceans (424 km3 yr-1 vs. 470 km3 yr-1), a net transfer of water from oceans to land exists. Almost all the surplus of the land’s water balance runs off as river discharge back into the ocean. A small fraction is discharged into the ocean through groundwater.\n\n\n\n\n\nFigure 8.1: Depiction of the present-day water cycle. In the atmosphere, which accounts for only 0.001% of all water on Earth, water primarily occurs as a gas (water vapor), but it is also present as ice and liquid water within clouds. The ocean is the primary water reservoir on Earth: it comprises mostly liquid water across much of the globe but also includes areas covered by ice in polar regions. Liquid freshwater on land forms surface water (lakes, rivers) and, together with soil moisture and mostly unusable groundwater stores, accounts for less than 2% of global water. Solid terrestrial water that occurs as ice sheets, glaciers, snow and ice on the surface, and permafrost currently represents nearly 2% of the planet’s water. Water that falls as snow in winter provides soil moisture and streamflow after melting, which are essential for human activities and ecosystem functioning. Note that these best estimates do not lead to a perfectly closed global water budget and that this budget has no reason to be closed given the ongoing human influence through both climate change (e.g., melting of ice sheets and glaciers, see Chapter 9) and water use (e.g., groundwater depletion through pumping into fossil aquifers, see Figure 8.10). Figure and caption from Douville et al. (2021).\n\n\n\n\nEvaporation from land is a smaller component than evaporation from oceans, and soils store less than 1% of the unfrozen freshwater on Earth. Yet, land processes are a key regulator of global water cycling and energy fluxes. This is because the majority of evaporation over land occurs through transpiration and is thus affected by the vegetation structure and ecophysiological relations - through effects of LAI (Section 4.2), surface conductance (Section 7.2.2) and stomatal conductance (Section 4.4). Another aspect is the fact that, while the amount of water stored in the rooting zone of vegetation is small, it supplies all transpiration. In many climates, the root zone moisture gets substantially depleted during episodic dry spells or regularly recurring dry seasons. The ensuing plant water stress leads to a reduction of transpiration and evaporation, and thus to an alteration also of the surface energy partitioning. This chapter introduces the quantities and mechanisms for understanding how water regulates vegetation and how vegetation shapes the cycling of water and land surface energy partitioning across the globe.\n\n\n\n\n\n\nExercise\n\n\n\n\nCalculate the total freshwater stored as ice as a fraction of total freshwater.\nCalculate the turnover time of water in the atmosphere.\nCalculate the turnover time of water in soils (soil moisture).\n\n\n\n\n\n\n\n\n\nAtmospheric humidity\n\n\n\n\n\n\nWe have encountered the vapor pressure deficit (VPD) and its control on transpiration in Section 4.4 and on evapotranspiration in Section 7.2.2. VPD is a measure of atmospheric humidity. This box is to explain how VPD relates to other metrics of atmospheric humidity and to the physics of moist air.\nThe total pressure of a gas can be expressed as the sum of partial pressures of different components of a gas mixture. For moist air, we can distinguish the partial pressures of water vapor (\\(e_a\\)) and dry air (\\(P_d\\)) and write the total pressure of moist air as \\[\nP = P_d + e_a \\;.\n\\] Both, the dry air and water vapor follow the ideal gas law. Expressed in molar form, they are \\[\nP_d = \\rho_d \\frac{RT}{M_d} \\\\\n\\text{ and } \\\\\ne_a = \\rho_v \\frac{RT}{M_v} = \\rho_v \\frac{RT}{0.622 M_d}\n\\tag{8.1}\\] \nHere, \\(\\rho_d\\) is the density of dry air; \\(\\rho_v\\) is the density of water vapor, \\(R\\) is the universal gas constant (8.314 J K-1 mol-1); \\(T\\) is temperature (in K). The factor 0.622 relates the molecular mass of water (\\(M_v = 18.02\\) g mol–1) to that of dry air (\\(M_d = 28.97\\) g mol–1). \nThe specific humidity \\(q\\) can be derived from Equation 8.1 as \\[\nq = \\frac{\\rho_v}{\\rho_v + \\rho_d} = \\frac{0.622 e_a}{P-(1-0.622)e_a}\n\\] The vapor pressure deficit (\\(D\\)) is the difference between the actual vapor pressure \\(e_a\\) and the vapor pressure at saturation \\(e_s(T)\\) (where water condensates). \\[\nD = e_s - e_a\n\\] The saturation vapor pressure is a function of air temperature (\\(T\\) in °C). This relationship is related to the Clausius-Clapeyron relation of the temperature dependence of vapor pressure. A relatively accurate, yet simple empirical equation for this relationship is the following. \\[\ne_s(T) = 611.0 \\; \\exp \\left( \\frac{17.27 \\; T}{T + 237.3} \\right)\n\\] This equation calculates the the saturation vapor pressure \\(e_s(T)\\) in units of Pa.\n\n\nCode\nlibrary(ggplot2)\n\ncalc_e_sat <- function(temp){\n 611.0 * exp( (17.27 * temp)/(temp + 237.3) )\n}\n\nggplot() +\n geom_function(fun = calc_e_sat) +\n xlim(0, 35) +\n labs(x = \"Temperature (°C)\",\n y = \"Saturation vapor pressure (Pa)\") +\n theme_classic()\n\n\n\n\n\nFigure 8.2: Saturation vapor pressure as a function of air temperature.\n\n\n\n\nThe relative humidity (RH) also relates \\(e_a\\) to \\(e_s\\), but as its ratio and not the difference. \\[\n\\mathrm{RH} = 100 \\% \\; \\frac{e_a}{e_s(T)}\n\\]" }, { "objectID": "ecohydrology.html#ecosystem-water-balance", "href": "ecohydrology.html#ecosystem-water-balance", "title": "8  Ecohydrology", "section": "8.2 Ecosystem water balance", - "text": "8.2 Ecosystem water balance\nFrom the conservation of water mass, it follows that the amount of water inputs into an ecosystem through precipitation must equal its outputs plus a change in ecosystem water storage. Outputs are either evaporation or runoff. The ecosystem water balance can thus be expressed as \\[\nP = E + R + \\Delta S \\;,\n\\tag{8.2}\\] where \\(P\\) is precipitation, \\(E\\) is evaporation, which includes different contributions (see below), \\(R\\) is runoff, and \\(\\Delta S\\) is the change in water storage, mostly in the form of groundwater. Lateral subsurface flow is accounted for by \\(R\\). Equation 8.2 applies to any system and scale. When considering totals or means of these fluxes over longer periods of time, \\(\\Delta S\\) tends to be small and may be neglected. At the scale of a river catchment, \\(R\\) is always zero or positive. At smaller scales, horizontal subsurface water flow convergence could make \\(R\\) negative (“run-on” instead of run-off). \\(E\\) is the same quantity as the \\(E\\) in Equation 7.5, but here expressed as a mass flux. (Remember, \\(\\lambda E\\) is the latent heat flux expressed in energy units).\n\n\n\n\n\n\nNote\n\n\n\nMost commonly, the components of Equation 8.2 are expressed as a mass per unit ground area and time. That is, for example in kg m-2 yr-1. With the density of water \\(\\rho_w = 1000\\) kg m-3, 1 kg m-2 is equivalent to 1 mm.\n\n\nWith \\(R \\geq 0\\) and \\(\\Delta S = 0\\), it follows that \\(P \\geq E\\). On a global average over land, \\(E/P = 0.65\\). However, \\(E/P\\) varies between about 0.2 and 1 across different ecosystems, catchments, and biomes. The pattern of how this ratio varies across the globe is described and explained in Section 8.7.\n\\(E\\) in Equation 8.2 includes contributions from multiples sources and processes (Figure 8.3). Below, we will refer to it as evapotranspiration, or short, ET. ET is the sum of transpiration by leaves (\\(T\\), corresponding to what is referred to as \\(E\\) in Section 4.4), evaporation from soil (\\(E_S\\)), evaporation from intercepted water on leaf and branch surfaces (\\(E_I\\)), and sublimation (\\(S\\), the phase change from solid water in the form of snow and ice directly to the gaseous phase). \\[\nE = T + E_S + E_I + S\n\\tag{8.3}\\]\nThe water balance of the rooting zone has to account for the fact that a portion of precipitation is intercepted and evaporates again as \\(E_I\\). Only the remainder reaches the ground as throughfall. Infiltration is referred to as the moisture flux that reaches a certain depth in the soil. On annual and longer time scales, snow water mass does not accumulate and snow melt equals the amount of precipitation that falls as snow minus sublimation (\\(S\\)). Snow accumulation and melt is therefore not reflected in Equation 8.2. However, at sub-seasonal time scales, snow accumulation and melting can substantially affect the water root zone water balance (see below).\n\n\n\n\n\nFigure 8.3: Ecosystem water balance components. The ground in the brown background color indicates the vadose (unsaturated) zone. The ground in the blue background color indicates the aquifer (groundwater). Figure adopted from Zhang et al. (2024).\n\n\n\n\nThe relative contributions of the different components of ET in Equation 8.3 are difficult to estimate. Model-based estimates for global averages are 48% for transpiration, 36% for soil evaporation, and 16% for canopy evaporation (Dirmeyer et al. 2006). A more recent estimate suggests a higher contribution by \\(T\\) (Wei et al. 2017). The partitioning depends on ecosystem characteristics, primarily LAI. A high LAI is associated with high \\(T\\) and \\(E_I\\). The higher LAI, the lower the radiation reaching the soil surface (Section 4.2) and thus the lower \\(E_S\\) (noting that energy is required for driving evaporation).\nThe different components to ET draw water from separate stores - from moisture in the root zone of vegetation for \\(T\\), from moisture in the top few centimeters of soil for \\(E_S\\), and from moisture adsorbed on canopy surfaces. Therefore, their evolution over time during dry (rain-free) phases is very different. While \\(E_I\\) drops to zero within 1-3 days as canopy surfaces become dry, \\(E_S\\) declines more slowly since the top soil takes longer to dry out to a degree where \\(E_S\\) becomes zero. In contrast, \\(T\\) takes much longer to decline as plants may draw moisture from much larger belowground stores - from water stored in the soil and sub-soil across the entire rooting zone.\n\n8.2.1 Cumulative water deficits\nThe latent heat flux and precipitation have clear seasonal variations in most biomes. As described above, for annual totals, \\(P \\geq E\\). However, over shorter periods of time, ET may exceed precipitation (\\(E > P\\)). Of course, on a rain-free day \\(P=0\\), while \\(E>0\\). In some climates, \\(E > P\\) may also be sustained over several weeks to months. For example, in Mediterranean or Monsoonal climates the asynchroneity of precipitation and solar radiation (and thus net radiation) can create a seasonal imbalance of water and energy availability and thus of water inputs and losses. As an example, Figure 8.4 a shows the multi-year average monthly total precipitation (\\(P\\)) and ET (the same as \\(E\\)) for an ecosystem in a Mediterranean climate - a woody savannah in California (eddy covariance measurement site US-Ton). It shows that \\(E>P\\) on average for May-Sep each year. The difference in monthly totals is relatively small - on the order of 10 mm or less. However, considering the cumuluative sum of daily \\(E-P\\) during the dry summer months for calculating the cumulative water deficit (Figure 8.4 b) shows that the maximum attained seasonal water deficit is 40-80 mm for this site (and varies between years). This is a substantial amount. Where does this water come from? Of course, it’s drawn by plants through their roots from the rooting zone, including the soil and potentially also the sub-soil or even the groundwater. How much water can be stored in the soil is the topic of the next section.\n\n\n\n\n\nFigure 8.4: (a) Mean monthly evapotranspiration (ET) and precipitation (P) for the site US-Ton, a woody savannah in a Mediterranean climate in California. (b) Time series of the cumulative water deficit (CWD) for the same site. The CWD is calculated as the cumulative sum of ET - P. It is terminated each year when P after the dry season has compensated the previously accumuated water deficit. Events of consecutive days with negative water balances and increasing cumulative water deficits are indicated by the grey bands in (b). No negative values of CWD are considered by design. The method of CWD calculation is based on Stocker et al. (2023)." + "text": "8.2 Ecosystem water balance\nFrom the conservation of water mass, it follows that the amount of water inputs into an ecosystem through precipitation must equal its outputs plus a change in ecosystem water storage. Outputs are either evaporation or runoff. The ecosystem water balance can thus be expressed as \\[\nP = E + R + \\Delta S \\;,\n\\tag{8.2}\\] where \\(P\\) is precipitation, \\(E\\) is evaporation, which includes different contributions (see below), \\(R\\) is runoff, and \\(\\Delta S\\) is the change in water storage, mostly in the form of groundwater. Lateral subsurface flow is accounted for by \\(R\\). Equation 8.2 applies to any system and scale. When considering totals or means of these fluxes over longer periods of time, \\(\\Delta S\\) tends to be small and may be neglected. At the scale of a river catchment, \\(R\\) is always zero or positive. At smaller scales, horizontal subsurface water flow convergence could make \\(R\\) negative (“run-on” instead of run-off). \\(E\\) is the same quantity as the \\(E\\) in Equation 7.5, but here expressed as a mass flux. (Remember, \\(\\lambda E\\) is the latent heat flux expressed in energy units).\n\n\n\n\n\n\nNote\n\n\n\nMost commonly, the components of Equation 8.2 are expressed as a mass per unit ground area and time. That is, for example in kg m-2 yr-1. With the density of water \\(\\rho_w = 1000\\) kg m-3, 1 kg m-2 is equivalent to 1 mm.\n\n\nWith \\(R \\geq 0\\) and \\(\\Delta S = 0\\), it follows that \\(P \\geq E\\). On a global average over land, \\(E/P = 0.65\\). However, \\(E/P\\) varies between about 0.2 and 1 across different ecosystems, catchments, and biomes. The pattern of how this ratio varies across the globe is described and explained in Section 8.7.\n\\(E\\) in Equation 8.2 includes contributions from multiples sources and processes (Figure 8.3). Below, we will refer to it as evapotranspiration, or short, ET. ET is the sum of transpiration by leaves (\\(T\\), corresponding to what is referred to as \\(E\\) in Section 4.4), evaporation from soil (\\(E_S\\)), evaporation from intercepted water on leaf and branch surfaces (\\(E_I\\)), and sublimation (\\(S\\), the phase change from solid water in the form of snow and ice directly to the gaseous phase). \\[\nE = T + E_S + E_I + S\n\\tag{8.3}\\]\nThe water balance of the rooting zone has to account for the fact that a portion of precipitation is intercepted and evaporates again as \\(E_I\\). Only the remainder reaches the ground as throughfall. Infiltration is referred to as the moisture flux that reaches a certain depth in the soil. On annual and longer time scales, snow water mass does not accumulate and snow melt equals the amount of precipitation that falls as snow minus sublimation (\\(S\\)). Snow accumulation and melt is therefore not reflected in Equation 8.2. However, at sub-seasonal time scales, snow accumulation and melting can substantially affect the water root zone water balance (see below).\n\n\n\n\n\nFigure 8.3: Ecosystem water balance components. The ground in the brown background color indicates the vadose (unsaturated) zone. The ground in the blue background color indicates the aquifer (groundwater). Figure adopted from Zhang et al. (2024).\n\n\n\n\nThe relative contributions of the different components of ET in Equation 8.3 are difficult to estimate. Model-based estimates for global averages are 48% for transpiration, 36% for soil evaporation, and 16% for canopy evaporation (Dirmeyer et al. 2006). A more recent estimate suggests a higher contribution by \\(T\\) (Wei et al. 2017). The partitioning depends on ecosystem characteristics, primarily LAI. A high LAI is associated with high \\(T\\) and \\(E_I\\). The higher LAI, the lower the radiation reaching the soil surface (Section 4.2) and thus the lower \\(E_S\\) (noting that energy is required for driving evaporation).\nThe different components to ET draw water from separate stores - from moisture in the root zone of vegetation for \\(T\\), from moisture in the top few centimeters of soil for \\(E_S\\), and from moisture adsorbed on canopy surfaces. Therefore, their evolution over time during dry (rain-free) phases is very different. While \\(E_I\\) drops to zero within 1-3 days as canopy surfaces become dry, \\(E_S\\) declines more slowly since the top soil takes longer to dry out to a degree where \\(E_S\\) becomes zero. In contrast, \\(T\\) takes much longer to decline as plants may draw moisture from much larger belowground stores - from water stored in the soil and sub-soil across the entire rooting zone.\n\n8.2.1 Cumulative water deficits\nThe latent heat flux and precipitation have clear seasonal variations in most biomes. As described above, for annual totals, \\(P \\geq E\\). However, over shorter periods of time, ET may exceed precipitation (\\(E > P\\)). Of course, on a rain-free day \\(P=0\\), while \\(E>0\\). In some climates, \\(E > P\\) may also be sustained over several weeks to months. For example, in Mediterranean or Monsoonal climates, the asynchroneity of precipitation and solar radiation (and thus net radiation) can create a seasonal imbalance of water and energy availability and thus of water inputs and losses. As an example, Figure 8.4 a shows the multi-year average monthly total precipitation (\\(P\\)) and ET (the same as \\(E\\)) for an ecosystem in a Mediterranean climate - a woody savannah in California (eddy covariance measurement site US-Ton). It shows that \\(E>P\\) on average for May-Sep each year. The difference in monthly totals is relatively small - on the order of 10 mm or less. However, considering the cumulative sum of daily \\(E-P\\) during the dry summer months for calculating the cumulative water deficit (Figure 8.4 b) shows that the maximum attained seasonal water deficit is 40-80 mm for this site (and varies between years). This is a substantial amount. Where does this water come from? Of course, it’s drawn by plants through their roots from the rooting zone, including the soil and potentially also the sub-soil or even the groundwater. How much water can be stored in the soil is the topic of the next section.\n\n\n\n\n\nFigure 8.4: (a) Mean monthly evapotranspiration (ET) and precipitation (P) for the site US-Ton, a woody savannah in a Mediterranean climate in California. (b) Time series of the cumulative water deficit (CWD) for the same site. The CWD is calculated as the cumulative sum of ET - P. It is terminated each year when P after the dry season has compensated the previously accumuated water deficit. Events of consecutive days with negative water balances and increasing cumulative water deficits are indicated by the grey bands in (b). No negative values of CWD are considered by design. The method of CWD calculation is based on Stocker et al. (2023)." }, { "objectID": "ecohydrology.html#sec-soilwater", "href": "ecohydrology.html#sec-soilwater", "title": "8  Ecohydrology", "section": "8.3 Soil water", - "text": "8.3 Soil water\nSoils are an important storage component of water. Soil water (or soil moisture) supplies water for plant transpiration and soil evaporation during dry periods. How much soil moisture is accessible to plants determines how rapidly plants experience water stress during dry periods and affects the surface energy partitioning, near-surface air heating and heat extremes. Soil moisture also acts to buffer the asynchroneity of precipitation and radiation (and thus potential evapotranspiration) and introduces an important memory element in the Earth system (Seneviratne et al. 2010). For example, an anomalously dry spring may aggravate water stress later in the season because soil moisture stores that have re-filled during the wet winter (and may still be relatively moist in spring) get depleted gradually and may reach a critically low moisture level earlier than after a wet spring. The strength of this memory effect and the time it takes for plants to experience water stress during dry periods depends (i.a.) on the capacity for plant-accessible water storage in the rooting zone of vegetation.\nAn important determinant for how much water can be stored in a given volume of soil is its texture. The size of soil particles determines their surface area. Water is adsorbed to the surfaces of the soil matrix and it takes work to remove it. Therefore, the size distribution of soil particles determines how much water the soil can bound. Soil particles are distinguished by size into sand (2-0.05 mm), silt (0.05-0.002 mm), and clay (<0.002 mm). A soil is a mixture of size classes and depending on this mixture, it can be classified into a soil texture class (Figure 8.5).\n\n\nCode\nlibrary(dplyr)\nlibrary(ggplot2)\nlibrary(ggtern)\nlibrary(grid)\n\n# Load the Data. (Available in ggtern 1.0.3.0 next version)\ndata(USDA)\n\n# Put tile labels at the midpoint of each tile based on https://stackoverflow.com/questions/29136168/add-texture-classes-to-soil-classification-triangle-via-ggplot2\nUSDA.LAB <- USDA |> \n group_by(Label) |> \n dplyr::summarise(across(where(is.numeric), mean))\n\n# Tweak\nUSDA.LAB$Angle = 0\nUSDA.LAB$Angle[which(USDA.LAB$Label == 'Loamy Sand')] = -35\n\n# Construct the plot.\nggplot(data = USDA, aes(y = Clay, x = Sand, z = Silt)) +\n coord_tern(L=\"x\", T=\"y\", R=\"z\") +\n geom_polygon(alpha = 0.75, size = 0.5, color = 'black', aes(color = Label, fill = Label)) +\n geom_text(data = USDA.LAB,\n aes(label = Label, angle = Angle),\n color = 'black',\n size = 3.5) +\n theme_rgbw() +\n theme_showsecondary() +\n theme_showarrows() +\n custom_percent(\"(%)\") +\n theme(legend.position=\"none\") +\n labs(fill = '',\n color = '')\n\n\n\n\n\nFigure 8.5: USDA soil texture classes.\n\n\n\n\nIn a common soil (not compacted, not an organic - peatland - soil), about 55% of the volume is comprised of solid material. The rest is air and water. The fraction of the soil that is not solid material is referred to as the porosity. When all pores are filled with water, the soil volumetric water content is at saturation (\\(\\theta_\\text{SAT}\\)). Soil texture classes vary relatively little with respect to porosity, but differ strongly in the strength at which the water is adsorbed to the soil matrix (Figure 8.7). Water movement in soil is driven by two distinct forces. The gravitational potential “pushes” water through soil under the influence of gravity. The soil matric potential \\(\\psi_s\\) arises from the adsorption of water to soil particles. It takes work to remove water from their adsorption to the soil matrix.\n\n\n\n\n\n\nSoil water content and matric potential relationship\n\n\n\nThe matric potential is commonly expressed in units of mm or Pa. It can also be expressed as the suction head which is the negative of the matric potential.\nImagine you stick a straw into the soil and try to suck out the water. When the soil is wet, you initially don’t have to suck hard to withdraw water. The suction head has a small positive value. The matric potential has a small negative value. After you have sucked out some amount water from the soil, you have to start sucking “harder” to extract the same amount again as the soil dries out. That’s because the matric potential declines to more negative numbers (and the suction head increases to larger positive numbers) for drier soils. Staying with the straw analogue, -1 mm matric potential (or 1 mm suction head) is equivalent sucking from your straw such that that 1 mm of water doesn’t drain out of the straw (ignoring capillary forces).\nThe same can also be expressed as a pressure - the gravitational force per unit area: \\[\np = \\frac{F_G}{A} = \\frac{mg}{A}\n\\] 1 mm corresponds to 1 kg m-2 and \\(g =\\) 9.81 m s-2. Therefore \\[\n1 \\; \\text{mm} = 9.81 \\; \\text{kg m}^{-1} \\text{s}^{-2} = 9.81 \\; \\text{Pa}\n\\]\nThe soil matric potential \\(\\psi_s\\) is related to the soil volumentric water content \\(\\theta\\) in a highly non-linear fashion. It stays near zero for a wide range \\(\\theta\\) and drops off sharply as \\(\\theta\\) falls below a certain range. Reflecting the large variation in how strongly water is bound to the soil matric across different soil texture classes, the relationship \\(\\psi_s(\\theta)\\) varies strongly across soil types. An empirical equation for this relationship is given by Clapp and Hornberger (1978) as: \\[\n\\psi_s = \\psi_\\text{SAT} \\left( \\frac{\\theta}{\\theta_\\text{SAT}} \\right)^{-b}\n\\tag{8.4}\\] Here, \\(\\psi_\\text{SAT}\\) is the soil matric potential at saturation, that is when \\(\\theta = \\theta_\\text{SAT}\\). The exponent \\(b\\) determines how rapidly the matric potential declines towards low \\(\\theta\\). These parameters have different values depending on the soil texture class, resulting in different functional forms of the relationship between volumetric water content and the matric potential.\n\n\nCode\nlibrary(dplyr)\nlibrary(readr)\nlibrary(ggplot2)\nlibrary(cowplot)\n\n# get table of soil parameters by texture class, adopted from Bonan 2015, Table 9.2\ndf_soilpar <- read_csv(here::here(\"data/df_soilpar.csv\")) |> \n mutate(\n fc_abs = fc * porosity,\n wp_abs = wp * porosity,\n solid = 1 - porosity\n ) |> \n mutate(\n unavailable = wp_abs,\n available = fc_abs - wp_abs,\n gravitational = porosity - fc_abs\n )\n\ncalc_psi <- function(swc, soilclass, df_soilpar){\n df_soilpar <- df_soilpar |> \n dplyr::filter(soiltext == soilclass)\n psi <- df_soilpar$psi_sat * (swc / df_soilpar$porosity)^(-df_soilpar$exponent)\n return(psi)\n}\n\ndrop_by_porosity <- function(swc, psi, soilclass, df_soilpar){\n df_soilpar <- df_soilpar |> \n filter(soiltext == soilclass)\n psi <- ifelse(swc > df_soilpar$porosity, NA, psi)\n}\n\ncreate_df_swc_bysoil <- function(soilclass, df_soilpar){\n tibble(swc = seq(0.01, 1, 0.001)) |> \n mutate(\n soilclass = soilclass\n ) |> \n rowwise() |> \n mutate(\n psi = calc_psi(swc, soilclass, df_soilpar)\n ) |> \n mutate(\n psi = drop_by_porosity(swc, psi, soilclass, df_soilpar)\n )\n}\n\ndf_swc <- purrr::map_dfr(\n df_soilpar$soiltext,\n ~create_df_swc_bysoil(., df_soilpar)\n)\n\ngg1 <- df_swc |> \n ggplot(aes(swc, psi, color = soilclass)) +\n geom_line() +\n geom_hline(yintercept = c(-1000, -150000), linetype = \"dotted\") +\n khroma::scale_color_okabeito() +\n labs(\n x = \"Volumetric soil water content\",\n y = expression(paste(\"Soil matric potential (mm)\"))\n ) +\n theme_classic() +\n ylim(-0.5e6, 0) + \n xlim(0, 0.5) + \n theme(legend.position=\"none\")\n\n# # extra plot\n# df_swc |> \n# filter(soilclass %in% c(\"Sand\", \"Loam\", \"Clay\")) |> \n# ggplot(aes(swc, psi, color = soilclass)) +\n# geom_line() +\n# geom_hline(yintercept = c(-1000, -150000), linetype = \"dotted\") +\n# khroma::scale_color_okabeito() +\n# labs(\n# x = \"Volumetric soil water content\",\n# y = expression(paste(\"Soil matric potential (mm)\"))\n# ) +\n# theme_classic() +\n# ylim(-0.5e6, 0) + \n# xlim(0, 0.5) + \n# theme(legend.position=\"none\")\n# \n# ggsave(here::here(\"fig/soil_matric_potential_vs_swc.png\"), width = 4, height = 3)\n\ngg2 <- df_swc |> \n ggplot(aes(swc, -psi, color = soilclass)) +\n geom_line() +\n geom_hline(yintercept = c(1000, 150000), linetype = \"dotted\") +\n scale_y_log10() +\n khroma::scale_color_okabeito(name = \"Soil texture\") +\n labs(\n x = \"Volumetric soil water content\",\n y = expression(paste(\"Suction head (mm)\"))\n ) +\n theme_classic() + \n xlim(0, 0.5)\n\nplot_grid(\n gg1,\n gg2,\n labels = c(\"a\", \"b\"),\n rel_widths = c(0.77, 1)\n)\n\n\n\n\n\nFigure 8.6: Soil (a) matric potential and (b) suction head as a function of volumetric water content, based on Equation 8.4 and soil texture class-specific parameters from Clapp and Hornberger (1978), adopted from Bonan (2015). Both panels show the same relationship but the y-axis in (b) is logarithmic. Horizontal dotted lines indicate the the field capacity and the permanent wilting point, which are defined here based on a soil matric potential of -1000 Pa and -150,000 mm.\n\n\n\n\n\n\nIn sandy soils, the size of particles and hence the size of soil pores is large, water is only loosely bound to the soil matrix, and can drain rapidly. The field capacity (\\(\\theta_\\text{FC}\\)) is the volumetric water content that is bound to the soil matrix and does not drain due to the gravitational force. Because the matric potential is comparatively low for a given amount of soil water in sandy soils, more water drains due to the gravitational force compared to other soil texture classes. Therefore, \\(\\theta_\\text{FC}\\) is lower in sandy soils than in other soils. The higher the field capacity, the more water is retained in the soil and prevented from drainage. However, not all of this water is available for uptake by plants. Depending on the soil texture a certain amount of water is too strongly adsorbed to the soil matrix for plants to “remove” it and mobilise it for uptake through their roots. The permanent wilting point \\(\\theta_\\text{PWP}\\) measures the volumetric soil water content that is bound to the soil at a matric potential of -150,000 mm which is taken to be too strongly negative for plants to access. Actually, plants start to respond to water stress by closing their stomates and suffering from damage to their transport vessels already earlier. \\(\\theta_\\text{PWP}\\) varies strongly between soil texture classes. It is high for clay soils, meaning that a relatively large amount of soil water remains inaccessible for plant uptake.\n\n\nCode\nlibrary(readr)\nlibrary(dplyr)\nlibrary(tidyr)\nlibrary(ggplot2)\n\ndf_soilpar <- read_csv(here::here(\"data/df_soilpar.csv\")) |> \n mutate(\n fc_abs = fc * porosity,\n wp_abs = wp * porosity,\n solid = 1 - porosity\n ) |> \n mutate(\n unavailable = wp_abs,\n available = fc_abs - wp_abs,\n gravitational = porosity - fc_abs\n )\n\n# Volume fractions\ndf_soilpar |> \n pivot_longer(cols = c(unavailable, available, gravitational, solid)) |> \n mutate(\n name = factor(name, levels = rev(c(\"unavailable\", \"available\", \"gravitational\", \"solid\"))),\n soiltext = factor(soiltext, levels = c(\"Clay\", \"Clay loam\", \"Loam\", \"Sandy loam\", \"Sand\"))\n ) |> \n ggplot(aes(soiltext, value, fill = name)) + \n geom_bar(position = \"stack\", stat = \"identity\") +\n scale_fill_manual(\n name = \"\",\n values = c(\n \"unavailable\" = \"#E69F00\",\n \"available\" = \"#0072B2\",\n \"gravitational\" = \"#56B4E9\",\n \"solid\" = \"#CC79A7\"\n )\n ) +\n scale_y_continuous(expand = c(0, 0)) +\n theme_classic() +\n labs(\n x = \"Soil texture class\",\n y = \"Volume fraction\"\n )\n\n\n\n\n\nFigure 8.7: Soil volume fractions of available and unavailable moisture by texture classes. Data from Clapp and Hornberger (1978), adopted from Bonan (2015).\n\n\n\n\nThe plant-available soil water holding capacity (WHC) is the difference between the field capacity and permanent wilting point. \\[\n\\text{WHC} = \\theta_\\text{FC} - \\theta_\\text{PWP}\n\\] Soil water storage above \\(\\theta_\\text{FC}\\) eventually drains and is thus inaccessible for plant uptake and soil water storage water below \\(\\theta_\\text{PWP}\\) is too strongly bound to the soil matrix and is therefore inaccessible for plant uptake. WHC is an important measure of suitability of soils for supporting vegetation. A low WHC means that a small amount of water can be stored per soil volume and made available for plant uptake during dry periods. However, the WHC varies only relatively little between soil texture classes as shown in Figure 8.7. This is because \\(\\theta_\\text{PWP}\\) and \\(\\theta_\\text{FC}\\) are correlated across soil texture classes. Soils with a high \\(\\theta_\\text{FC}\\) (clay soils) also tend to have a high \\(\\theta_\\text{PWP}\\) and vice versa. However, WHC may vary across different locations also due to other constraints. For example, a large share of gravel (rocks with diameters greater than sand) reduces the WHC.\nIn view of the relative constancy of WHC, but large variance of \\(\\theta_\\text{PWP}\\) and \\(\\theta_\\text{FC}\\) across soil texture classes, soil moisture is often expressed as a fraction of available water. The soil water index (also often referred to as the soil water scalar) is commonly defined as \\[\nW = \\frac{\\theta - \\theta_\\text{PWP}}{\\theta_\\text{FC} - \\theta_\\text{PWP}}\n\\] Another common expression of soil moisture is in percent saturation (\\(100\\% \\cdot \\theta / \\theta_\\text{SAT}\\)).\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nExercise\n\n\n\n\nLabel \\(\\theta_\\text{SAT}\\), \\(\\theta_\\text{FC}\\), \\(\\theta_\\text{WP}\\), porosity, and WHC in Figure 8.7.\n\n\n\n\n8.3.1 Rooting-zone water-storage capacity\nAll metrics and relationships described above are expressed with a unit soil volume as a reference. For example, the WHC is the amount of water, a given volume of soil can hold. The total amount of water that vegetation has access to - the rooting-zone water-storage capacity \\(S_0\\) - is determined not only by the soil texture across the rooting zone, but also to rooting depth \\(z_r\\). It can be conceived as the integral of the WHC across the rooting profile. Assuming a constant WHC across the rooting depth, this is simply \\[\nS_0 = z_r \\cdot \\text{WHC}\\;.\n\\tag{8.5}\\] The rooting depth \\(z_r\\) is measured in units of length (for example in m), while the WHC is a volume fraction (for example m3 m-3). Hence, \\(S_0\\) is in units of length. While the WHC varies relatively little across soil texture classes and across different locations globally, rooting depth \\(z_r\\) varies strongly between species, and plant functional types (Figure 8.8). It tends to be smaller for grasses and forbs than for trees and shrubs.\n\n\n\n\n\n\nExercise\n\n\n\n\nLook up species names shown in Figure 8.8 on the internet. Do you know these plants? Do you find patterns that relate to differences between PFTs shown in Figure 8.8 a, and in how the rooting depth relates to the biomes and climate zones in which these species grow?\n\n\n\n\n\n\n\n\n\nFigure 8.8: Distribution of plant rooting depth (a) across different plant functional types, and (b, c) across different selected species. Note the distinct ranges of the x-axis in the three panels. Curves in (a) represent the density distribution of individual plant-level observations, represented as tick marks along the bottom of each curve. Boxplots in (b) and (c) cover the inter-quartile range with boxes and 1.5 times the inter-quartile range extended above and below the quartiles with the whiskers. Individual plant-level observations are shown by points. Data from Tumber-Dávila et al. (2022).\n\n\n\n\nThe variations in rooting depth have implications for the rooting-zone water-storage capacity (a consequence of Equation 8.5). This, in turn, variations in \\(S_0\\) are linked to how sensitive different vegetation types and species respond to dry periods - with consequences for surface energy partitioning is altered as the rooting zone dries out. Variations in rooting depth are related not only to species and PFTs, but also to large-scale climate variations and differences in vegetation cover in the different biomes across the globe (Figure 8.9). As a consequence of the large variations in \\(z_r\\), the \\(S_0\\) exhibits a large variation across the globe and its variation is largely disconnected to WHC. In other words, variations in \\(S_0\\) are primarily driven by \\(z_r\\), rather than by WHC.\n\n\n\n\n\nFigure 8.9: (a) Total water holding capacity of the top 1 m of soil. (b) Rooting-zone water-storage capacity estimated from the annual maximum cumulative water deficits. Data and methods from Stocker et al. (2023)." + "text": "8.3 Soil water\nSoils are an important storage component of water. Soil water (or soil moisture) supplies water for plant transpiration and soil evaporation during dry periods. How much soil moisture is accessible to plants determines how rapidly plants experience water stress during dry periods and affects the surface energy partitioning, near-surface air heating and heat extremes. Soil moisture also acts to buffer the asynchroneity of precipitation and radiation (and thus potential evapotranspiration) and introduces an important memory element in the Earth system (Seneviratne et al. 2010). For example, an anomalously dry spring may aggravate water stress later in the season because soil moisture stores that have re-filled during the wet winter (and may still be relatively moist in spring) get depleted gradually and may reach a critically low moisture level earlier than after a wet spring. The strength of this memory effect and the time it takes for plants to experience water stress during dry periods depends (i.a.) on the capacity for plant-accessible water storage in the rooting zone of vegetation.\nAn important determinant for how much water can be stored in a given volume of soil is its texture. The size of soil particles determines their surface area. Water is adsorbed to the surfaces of the soil matrix and it takes work to remove it. Therefore, the size distribution of soil particles determines how much water the soil can bound. Soil particles are distinguished by size into sand (2-0.05 mm), silt (0.05-0.002 mm), and clay (<0.002 mm). A soil is a mixture of size classes and depending on this mixture, it can be classified into a soil texture class (Figure 8.5).\n\n\nCode\nlibrary(dplyr)\nlibrary(ggplot2)\nlibrary(ggtern)\nlibrary(grid)\n\n# Load the Data. (Available in ggtern 1.0.3.0 next version)\ndata(USDA)\n\n# Put tile labels at the midpoint of each tile based on https://stackoverflow.com/questions/29136168/add-texture-classes-to-soil-classification-triangle-via-ggplot2\nUSDA.LAB <- USDA |> \n group_by(Label) |> \n dplyr::summarise(across(where(is.numeric), mean))\n\n# Tweak\nUSDA.LAB$Angle = 0\nUSDA.LAB$Angle[which(USDA.LAB$Label == 'Loamy Sand')] = -35\n\n# Construct the plot.\nggplot(data = USDA, aes(y = Clay, x = Sand, z = Silt)) +\n coord_tern(L=\"x\", T=\"y\", R=\"z\") +\n geom_polygon(alpha = 0.75, size = 0.5, color = 'black', aes(color = Label, fill = Label)) +\n geom_text(data = USDA.LAB,\n aes(label = Label, angle = Angle),\n color = 'black',\n size = 3.5) +\n theme_rgbw() +\n theme_showsecondary() +\n theme_showarrows() +\n custom_percent(\"(%)\") +\n theme(legend.position=\"none\") +\n labs(fill = '',\n color = '')\n\n\n\n\n\nFigure 8.5: USDA soil texture classes.\n\n\n\n\nIn a common soil (not compacted, not an organic - peatland - soil), about 55% of the volume is comprised of solid material. The rest is air and water. The fraction of the soil that is not solid material is referred to as the porosity. When all pores are filled with water, the soil volumetric water content is at saturation (\\(\\theta_\\text{SAT}\\)). Soil texture classes vary relatively little with respect to porosity, but differ strongly in the strength at which the water is adsorbed to the soil matrix (Figure 8.7). Water movement in soil is driven by two distinct forces. The gravitational potential “pushes” water through soil under the influence of gravity. The soil matric potential \\(\\psi_s\\) arises from the adsorption of water to soil particles. It takes work to remove water from their adsorption to the soil matrix.\n\n\n\n\n\n\nSoil water content and matric potential relationship\n\n\n\nThe matric potential is commonly expressed in units of mm or Pa. It can also be expressed as the suction head which is the negative of the matric potential.\nImagine you stick a straw into the soil and try to suck out the water. When the soil is wet, you initially don’t have to suck hard to withdraw water. The suction head has a small positive value. The matric potential has a small negative value. After you have sucked out some amount water from the soil, you have to start sucking “harder” to extract the same amount again as the soil dries out. That’s because the matric potential declines to more negative numbers (and the suction head increases to larger positive numbers) for drier soils. Staying with the straw analogue, -1 mm matric potential (or 1 mm suction head) is equivalent sucking from your straw such that 1 mm of water doesn’t drain out of the straw (ignoring capillary forces).\nThe same can also be expressed as a pressure - the gravitational force per unit area: \\[\np = \\frac{F_G}{A} = \\frac{mg}{A}\n\\] 1 mm corresponds to 1 kg m-2 and \\(g =\\) 9.81 m s-2. Therefore, \\[\n1 \\; \\text{mm} = 9.81 \\; \\text{kg m}^{-1} \\text{s}^{-2} = 9.81 \\; \\text{Pa}\n\\]\nThe soil matric potential \\(\\psi_s\\) is related to the soil volumetric water content \\(\\theta\\) in a highly non-linear fashion. It stays near zero for a wide range \\(\\theta\\) and drops off sharply as \\(\\theta\\) falls below a certain range. Reflecting the large variation in how strongly water is bound to the soil matric across different soil texture classes, the relationship \\(\\psi_s(\\theta)\\) varies strongly across soil types. An empirical equation for this relationship is given by Clapp and Hornberger (1978) as: \\[\n\\psi_s = \\psi_\\text{SAT} \\left( \\frac{\\theta}{\\theta_\\text{SAT}} \\right)^{-b}\n\\tag{8.4}\\] Here, \\(\\psi_\\text{SAT}\\) is the soil matric potential at saturation, that is when \\(\\theta = \\theta_\\text{SAT}\\). The exponent \\(b\\) determines how rapidly the matric potential declines towards low \\(\\theta\\). These parameters have different values depending on the soil texture class, resulting in different functional forms of the relationship between volumetric water content and the matric potential.\n\n\nCode\nlibrary(dplyr)\nlibrary(readr)\nlibrary(ggplot2)\nlibrary(cowplot)\n\n# get table of soil parameters by texture class, adopted from Bonan 2015, Table 9.2\ndf_soilpar <- read_csv(here::here(\"data/df_soilpar.csv\")) |> \n mutate(\n fc_abs = fc * porosity,\n wp_abs = wp * porosity,\n solid = 1 - porosity\n ) |> \n mutate(\n unavailable = wp_abs,\n available = fc_abs - wp_abs,\n gravitational = porosity - fc_abs\n )\n\ncalc_psi <- function(swc, soilclass, df_soilpar){\n df_soilpar <- df_soilpar |> \n dplyr::filter(soiltext == soilclass)\n psi <- df_soilpar$psi_sat * (swc / df_soilpar$porosity)^(-df_soilpar$exponent)\n return(psi)\n}\n\ndrop_by_porosity <- function(swc, psi, soilclass, df_soilpar){\n df_soilpar <- df_soilpar |> \n filter(soiltext == soilclass)\n psi <- ifelse(swc > df_soilpar$porosity, NA, psi)\n}\n\ncreate_df_swc_bysoil <- function(soilclass, df_soilpar){\n tibble(swc = seq(0.01, 1, 0.001)) |> \n mutate(\n soilclass = soilclass\n ) |> \n rowwise() |> \n mutate(\n psi = calc_psi(swc, soilclass, df_soilpar)\n ) |> \n mutate(\n psi = drop_by_porosity(swc, psi, soilclass, df_soilpar)\n )\n}\n\ndf_swc <- purrr::map_dfr(\n df_soilpar$soiltext,\n ~create_df_swc_bysoil(., df_soilpar)\n)\n\ngg1 <- df_swc |> \n ggplot(aes(swc, psi, color = soilclass)) +\n geom_line() +\n geom_hline(yintercept = c(-1000, -150000), linetype = \"dotted\") +\n khroma::scale_color_okabeito() +\n labs(\n x = \"Volumetric soil water content\",\n y = expression(paste(\"Soil matric potential (mm)\"))\n ) +\n theme_classic() +\n ylim(-0.5e6, 0) + \n xlim(0, 0.5) + \n theme(legend.position=\"none\")\n\n# # extra plot\n# df_swc |> \n# filter(soilclass %in% c(\"Sand\", \"Loam\", \"Clay\")) |> \n# ggplot(aes(swc, psi, color = soilclass)) +\n# geom_line() +\n# geom_hline(yintercept = c(-1000, -150000), linetype = \"dotted\") +\n# khroma::scale_color_okabeito() +\n# labs(\n# x = \"Volumetric soil water content\",\n# y = expression(paste(\"Soil matric potential (mm)\"))\n# ) +\n# theme_classic() +\n# ylim(-0.5e6, 0) + \n# xlim(0, 0.5) + \n# theme(legend.position=\"none\")\n# \n# ggsave(here::here(\"fig/soil_matric_potential_vs_swc.png\"), width = 4, height = 3)\n\ngg2 <- df_swc |> \n ggplot(aes(swc, -psi, color = soilclass)) +\n geom_line() +\n geom_hline(yintercept = c(1000, 150000), linetype = \"dotted\") +\n scale_y_log10() +\n khroma::scale_color_okabeito(name = \"Soil texture\") +\n labs(\n x = \"Volumetric soil water content\",\n y = expression(paste(\"Suction head (mm)\"))\n ) +\n theme_classic() + \n xlim(0, 0.5)\n\nplot_grid(\n gg1,\n gg2,\n labels = c(\"a\", \"b\"),\n rel_widths = c(0.77, 1)\n)\n\n\n\n\n\nFigure 8.6: Soil (a) matric potential and (b) suction head as a function of volumetric water content, based on Equation 8.4 and soil texture class-specific parameters from Clapp and Hornberger (1978), adopted from Bonan (2015). Both panels show the same relationship but the y-axis in (b) is logarithmic. Horizontal dotted lines indicate the the field capacity and the permanent wilting point, which are defined here based on a soil matric potential of -1000 Pa and -150,000 mm.\n\n\n\n\n\n\nIn sandy soils, the size of particles and hence the size of soil pores is large, water is only loosely bound to the soil matrix, and can drain rapidly. The field capacity (\\(\\theta_\\text{FC}\\)) is the volumetric water content that is bound to the soil matrix and does not drain due to the gravitational force. Because the matric potential is comparatively low for a given amount of soil water in sandy soils, more water drains due to the gravitational force compared to other soil texture classes. Therefore, \\(\\theta_\\text{FC}\\) is lower in sandy soils than in other soils. The higher the field capacity, the more water is retained in the soil and prevented from drainage. However, not all of this water is available for uptake by plants. Depending on the soil texture a certain amount of water is too strongly adsorbed to the soil matrix for plants to “remove” it and mobilise it for uptake through their roots. The permanent wilting point \\(\\theta_\\text{PWP}\\) measures the volumetric soil water content that is bound to the soil at a matric potential of -150,000 mm which is taken to be too strongly negative for plants to access. Actually, plants start to respond to water stress by closing their stomates and suffering from damage to their transport vessels already earlier. \\(\\theta_\\text{PWP}\\) varies strongly between soil texture classes. It is high for clay soils, meaning that a relatively large amount of soil water remains inaccessible for plant uptake.\n\n\nCode\nlibrary(readr)\nlibrary(dplyr)\nlibrary(tidyr)\nlibrary(ggplot2)\n\ndf_soilpar <- read_csv(here::here(\"data/df_soilpar.csv\")) |> \n mutate(\n fc_abs = fc * porosity,\n wp_abs = wp * porosity,\n solid = 1 - porosity\n ) |> \n mutate(\n unavailable = wp_abs,\n available = fc_abs - wp_abs,\n gravitational = porosity - fc_abs\n )\n\n# Volume fractions\ndf_soilpar |> \n pivot_longer(cols = c(unavailable, available, gravitational, solid)) |> \n mutate(\n name = factor(name, levels = rev(c(\"unavailable\", \"available\", \"gravitational\", \"solid\"))),\n soiltext = factor(soiltext, levels = c(\"Clay\", \"Clay loam\", \"Loam\", \"Sandy loam\", \"Sand\"))\n ) |> \n ggplot(aes(soiltext, value, fill = name)) + \n geom_bar(position = \"stack\", stat = \"identity\") +\n scale_fill_manual(\n name = \"\",\n values = c(\n \"unavailable\" = \"#E69F00\",\n \"available\" = \"#0072B2\",\n \"gravitational\" = \"#56B4E9\",\n \"solid\" = \"#CC79A7\"\n )\n ) +\n scale_y_continuous(expand = c(0, 0)) +\n theme_classic() +\n labs(\n x = \"Soil texture class\",\n y = \"Volume fraction\"\n )\n\n\n\n\n\nFigure 8.7: Soil volume fractions of available and unavailable moisture by texture classes. Data from Clapp and Hornberger (1978), adopted from Bonan (2015).\n\n\n\n\nThe plant-available soil water holding capacity (WHC) is the difference between the field capacity and permanent wilting point. \\[\n\\text{WHC} = \\theta_\\text{FC} - \\theta_\\text{PWP}\n\\] Soil water storage above \\(\\theta_\\text{FC}\\) eventually drains and is thus inaccessible for plant uptake and soil water storage water below \\(\\theta_\\text{PWP}\\) is too strongly bound to the soil matrix and is therefore inaccessible for plant uptake. WHC is an important measure of suitability of soils for supporting vegetation. A low WHC means that a small amount of water can be stored per soil volume and made available for plant uptake during dry periods. However, the WHC varies only relatively little between soil texture classes as shown in Figure 8.7. This is because \\(\\theta_\\text{PWP}\\) and \\(\\theta_\\text{FC}\\) are correlated across soil texture classes. Soils with a high \\(\\theta_\\text{FC}\\) (clay soils) also tend to have a high \\(\\theta_\\text{PWP}\\) and vice versa. However, WHC may vary across different locations also due to other constraints. For example, a large share of gravel (rocks with diameters greater than sand) reduces the WHC.\nIn view of the relative constancy of WHC, but large variance of \\(\\theta_\\text{PWP}\\) and \\(\\theta_\\text{FC}\\) across soil texture classes, soil moisture is often expressed as a fraction of available water. The soil water index (also often referred to as the soil water scalar) is commonly defined as \\[\nW = \\frac{\\theta - \\theta_\\text{PWP}}{\\theta_\\text{FC} - \\theta_\\text{PWP}}\n\\] Another common expression of soil moisture is in percent saturation (\\(100\\% \\cdot \\theta / \\theta_\\text{SAT}\\)).\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nExercise\n\n\n\n\nLabel \\(\\theta_\\text{SAT}\\), \\(\\theta_\\text{FC}\\), \\(\\theta_\\text{WP}\\), porosity, and WHC in Figure 8.7.\n\n\n\n\n8.3.1 Rooting-zone water-storage capacity\nAll metrics and relationships described above are expressed with a unit soil volume as a reference. For example, the WHC is the amount of water, a given volume of soil can hold. The total amount of water that vegetation has access to - the rooting-zone water-storage capacity \\(S_0\\) - is determined not only by the soil texture across the rooting zone, but also to rooting depth \\(z_r\\). It can be conceived as the integral of the WHC across the rooting profile. Assuming a constant WHC across the rooting depth, this is simply \\[\nS_0 = z_r \\cdot \\text{WHC}\\;.\n\\tag{8.5}\\] The rooting depth \\(z_r\\) is measured in units of length (for example in m), while the WHC is a volume fraction (for example m3 m-3). Hence, \\(S_0\\) is in units of length. While the WHC varies relatively little across soil texture classes and across different locations globally, rooting depth \\(z_r\\) varies strongly between species, and plant functional types (Figure 8.8). It tends to be smaller for grasses and forbs than for trees and shrubs.\n\n\n\n\n\n\nExercise\n\n\n\n\nLook up species names shown in Figure 8.8 on the internet. Do you know these plants? Do you find patterns that relate to differences between PFTs shown in Figure 8.8 a, and in how the rooting depth relates to the biomes and climate zones in which these species grow?\n\n\n\n\n\n\n\n\n\nFigure 8.8: Distribution of plant rooting depth (a) across different plant functional types, and (b, c) across different selected species. Note the distinct ranges of the x-axis in the three panels. Curves in (a) represent the density distribution of individual plant-level observations, represented as tick marks along the bottom of each curve. Boxplots in (b) and (c) cover the inter-quartile range with boxes and 1.5 times the inter-quartile range extended above and below the quartiles with the whiskers. Individual plant-level observations are shown by points. Data from Tumber-Dávila et al. (2022).\n\n\n\n\nThe variations in rooting depth have implications for the rooting-zone water-storage capacity (a consequence of Equation 8.5). This, in turn, variations in \\(S_0\\) are linked to how sensitive different vegetation types and species respond to dry periods - with consequences for surface energy partitioning is altered as the rooting zone dries out. Variations in rooting depth are related not only to species and PFTs, but also to large-scale climate variations and differences in vegetation cover in the different biomes across the globe (Figure 8.9). As a consequence of the large variations in \\(z_r\\), the \\(S_0\\) exhibits a large variation across the globe and its variation is largely disconnected to WHC. In other words, variations in \\(S_0\\) are primarily driven by \\(z_r\\), rather than by WHC.\n\n\n\n\n\nFigure 8.9: (a) Total water holding capacity of the top 1 m of soil. (b) Rooting-zone water-storage capacity estimated from the annual maximum cumulative water deficits. Data and methods from Stocker et al. (2023)." }, { "objectID": "ecohydrology.html#sec-hydraulics", "href": "ecohydrology.html#sec-hydraulics", "title": "8  Ecohydrology", "section": "8.4 Plant hydraulics", - "text": "8.4 Plant hydraulics\nWater is transported from the soil, across the soil-root interface, and then inside the plant from the fine roots up and along inside the xylem (the water transport vessels) to the leaves. Water evaporates and diffuses through the stomates (Section 4.4). This water transport along the soil-plant-atmosphere (SPA) continuum is a passive process. That is, the plant does not invest energy directly in the process of transporting the water. The water evaporation through leaves is rather an unavoidable “burden” that is traded off against CO2 uptake for photosynthesis (Section 4.4.3).\nHave you thought about how water is transported up tall trees? It’s a fascinating aspect of how biology has evolved ways to deal with physics.\n\nThe driving force of water transport is the negative pressure that the vapor pressure deficit of the surrounding air creates. This force acts against a resistances and the gravitational force. To move the water up the plant, the water at the level of the leaves is under a strong negative pressure. The taller the plant and the higher the resistance along the soil-plant-atmosphere continuum, the more negative the pressure at the leaf-level to sustain a given water flux (transpiration). This negative water pressure at the level of the leaves is the leaf water potential (\\(\\psi_l\\)). It’s in the same units as the soil matric potential (\\(\\psi_s\\), Equation 8.4) and it is related to the soil water potential via a the transpiration stream \\(T\\) and an effective whole-plant hydraulic conductance \\(G_p\\) that considers resistance elements in series - from the soil to the leaf. Remember that a conductance is the inverse of a resistance. In simplified terms, this can be written as. \\[\nT = -G_p (\\psi_l - \\psi_s + \\rho g h)\n\\tag{8.6}\\] \\(\\rho\\) is the density of water (kg m-3), \\(g\\) is the gravitational constant (9.81 m s-2), and \\(h\\) is the height of the tree (m), measured from the average depth of the roots to the average height of the leaves. With the units of \\(\\psi_l\\) and \\(\\psi_s\\) in Pa and \\(T\\) in units of (kg m-2 s-1), \\(G_p\\) is in units of (s m-1). Equation 8.6 expresses the “supply” of water from the soil. From Equation 4.11, we know how the “demand” for water is determined by the vapor pressure deficit \\(D\\) and the stomatal conductance \\(g_s\\). The \\(T\\) in Equation 8.6 thus has to be equal to the \\(T\\) from Equation 4.11 (where it was called \\(E\\)): \\[\nT = 1.6 \\; g_s \\; D\n\\tag{8.7}\\] These equations illustrate some important points. First, a positive (upward) transpiration stream \\(T\\) that satisfies the demand from the atmosphere (Equation 8.7) can only be maintained if the leaf water potential is more negative than the soil water potential. Second, as the soil water potential becomes more negative, the leaf water potential also has to become more negative to transport the amount of water that is “demanded” by the atmosphere and determined by \\(D\\) and \\(g_s\\). Third, tall trees have to sustain more negative leaf water potentials than short for a given soil dryness and transpiration rate. By setting the two equations for \\(T\\) equal and solving for the leaf water potential \\(\\psi_l\\) also illustrates how soil moisture (\\(\\psi_s\\)) and VPD (\\(D\\)) have an interactive effect on \\(\\psi_l\\).\nResponses of plants to water stress are physiologically triggered through the sensing of leaf water potentials. In other words, \\(\\psi_l\\) is the central quantity that drives water stress responses of plants. Understanding how \\(\\psi_l\\) responds to environmental factors is thus key to understanding how water stress (stomatal closure, damaging drought stress) is a function of soil and air dryness, modified by plant hydraulic traits determining \\(G_p\\).\n\n\n\n\n\n\nNote\n\n\n\nEquation 8.6 is a simplification because the whole-plant hydraulic conductance \\(G_p\\) is a non-linear function of the water potential which drops along the transport pathway from \\(\\psi_s\\) to \\(\\psi_l\\). As a consequence, the interactive effect of VPD and soil moisture is non-linear. To account for the conductance drop with negative water potential, a more realistic form of Equation 8.6 can be written as \\[\nT = -G_{p,0} \\int_{\\psi_s}^{\\psi_l - \\rho g h} P(\\psi) \\; \\text{d}\\psi \\;,\n\\tag{8.8}\\] where \\(G_{p,0}\\) is a “base” conductance at zero water potential and \\(P(\\psi)\\) is a vulnerability function of the plant conductance. The latter declines towards more negative water potentials. A commonly used functional form is \\[\nP(\\psi) = 0.5^{(\\psi/P_{50})^b} \\;,\n\\tag{8.9}\\] where \\(P_\\text{50}\\) is the water potential at which \\(P\\) has dropped to 0.5.\n\n\nCode\nlibrary(ggplot2)\n\nvulnerability_curve <- function(psi, p50, b){\n 0.5 ^ ((psi/p50)^b)\n}\n\nggplot() +\n geom_function(fun = function(x) vulnerability_curve(x, -2000, 3)) +\n xlim(-4000, 0) +\n geom_vline(xintercept = c(-2000, 0), linetype = \"dotted\") +\n labs(x = expression(paste(psi, \" (Pa)\")),\n y = expression(paste(italic(P(psi))))) + \n theme_classic()\n\n\n\n\n\nFigure 8.10: Example plant hydraulic vulnerability curve. The water potential at which P has dropped to 0.5 is commonly referred to as P50 and is marked by the vertical dotted line at -2000 Pa (as an example). The abruptness of the drop in P is described by a shape parameter (b in Equation 8.9).\n\n\n\n\nEquation 8.8 can be regarded as the hydraulic supply function for transpiration (Sperry and Love 2015) and Equation 8.9 is commonly referred to as the hydraulic vulnerability curve (Tyree and Sperry 1989). The non-linearity arising from the latter implies that transpiration initially increases with an increasingly negative leaf water potential, but reaches a maximum beyond which transpiration does not further increase despite increasingly negative leaf water potentials. Reaching this point is risky for plants as it bears the danger of potentially lethal hydraulic failure (see below). Stomatal regulation acts to limit leaf water potentials reaching this point, while maximally exploiting soil water that is available for plant uptake without a substantial flattening of the \\(T(\\psi_l)\\) curve. What exactly “substantial” means, depends on plant strategies that vary between species.\n\n\nCode\nlibrary(dplyr)\n\nhydraulic_supply <- function(psi_leaf, psi_soil, g_plant, p50, b){\n transpiration <- -g_plant * \n integrate(\n f = vulnerability_curve, \n lower = psi_soil, \n upper = psi_leaf,\n p50 = p50, # argument for f\n b = b # argument for f\n )$value\n return(transpiration)\n}\n\ntmp <- expand.grid(\n psi_leaf = seq(-4000, 0, by = 50),\n psi_soil = seq(-2000, 0, by = 100)\n) |> \n as_tibble() |> \n rowwise() |> \n mutate(\n transp = hydraulic_supply(\n psi_leaf = psi_leaf, \n psi_soil = psi_soil, \n g_plant = 1e-6, \n p50 = -2000, \n b = 3\n )\n )\n\ntmp |> \n ggplot(aes(x = -psi_leaf, y = transp, color = psi_soil, group = psi_soil)) +\n geom_line() +\n scale_color_viridis_c(\n name = expression(paste(psi[soil], \" (Pa)\")),\n option = \"cividis\", \n direction = -1\n ) +\n labs(x = expression(paste(-psi[leaf], \" (Pa)\")),\n y = expression(paste(italic(T), \" (mm s\"^-1, \")\"))) + \n ylim(0, NA) +\n theme_classic()\n\n\n\n\n\nFigure 8.11: Hydraulic supply function. Transpiration as a function of an increasingly negative leaf water potential for different soil water potential levels. Water potentials are negative values. The x-axis shows the negative of the negative leaf water potential values (thus positive values). The visualisation shows that the leaf water potential is at least as strongly negative as the soil water potential and transpiration only exceeds zero if the leaf water potential becomes even more negative than the soil water potential. It also shows the strong sensitivity of the maximum transpiration rate as a function of the soil water potential. ‘Soil water potential’ represents the average water potential across the entire rooting zone. Here, the gravitational effect on water potentials is ignored by setting the tree height (h in Equation 8.8) to zero and the whole-plant base conductance Gp,0 is set to 10-6 s m-1.\n\n\n\n\n\n\nSustaining very negative water potentials along the transport pathway can be dangerous for the plant. As described in the box above, the whole-plant conductance declines with increasingly negative negative water potentials. This is because the very negative water potentials can only be sustained if no air is in contact with the water inside the xylem. As pressures become very negative, air may seep in and create embolisms. If the conductance was to drop towards zero, transpiration would collapse and embolisms would be excessive - creating potentially irreversible damage and triggering branch and eventually tree mortality due to hydraulic failure.\nPlants can avoid such water stress and hydraulic failure through stomatal regulation (see also Section 4.4.3). To avoid embolisms, stomata close (stomatal conductance is reduced) when the soil water potential declines to increasingly negative values. As a consequence transpiration, and also CO2 assimilation, are decline. Once soil moisture across the rooting zone is depleted and the soil water potential reach very negative values, vegetation activity (transpiration and assimilation) comes to a halt. However, this rarely happens since water loss cannot be fully avoided even if stomata are fully closed and plants have evolved adaptations and are adjusted through plasticity in various traits to avoid a complete depletion of moisture stores across the rooting zone and to limit water losses. Variations in rooting depth are an expression of this adaptation and acclimation. Leaf properties with thick, waxy leaves that prevent water loss, or a drought-deciduous strategy are other examples.\nDifferent plant species respond differently to water stress (variations in soil water potential) and are characterised with different hydraulic traits that determine the stomatal response to soil and leaf water potentials. Two examples are shown in Figure 8.12\n\n\n\n\n\nFigure 8.12: Response of (a) CO2 assimilation and (b) stomatal conductance to a declining soil water potential for two contrasting species - the drought-adapted Eucalyptus populnea and Eucalyptus pilularis, which is adapted to more moist climates. The lines represent predictions of the model by Joshi et al. (2022) where an optimal response of stomata in trading off CO2 assimilation and the risks associated with negative leaf water potentials is assumed.\n\n\n\n\n\n\n\n\n\n\n\n\nExercise\n\n\n\n\nConsider a soil dry down as in Figure 8.12. Sketch qualitatively how the following variables change as a function of the soil water potential (while all other meteorological variables remain constant):\n\n\nSoil water content\nLatent heat flux\nSensible heat flux\nBowen ratio\nEvaporative fraction\nGPP\nReco\nNEE\nTree mortality due to hydraulic failure" + "text": "8.4 Plant hydraulics\nWater is transported from the soil, across the soil-root interface, and then inside the plant from the fine roots up and along inside the xylem (the water transport vessels) to the leaves. Water evaporates and diffuses through the stomates (Section 4.4). This water transport along the soil-plant-atmosphere (SPA) continuum is a passive process. That is, the plant does not invest energy directly in the process of transporting the water. The water evaporation through leaves is rather an unavoidable “burden” that is traded off against CO2 uptake for photosynthesis (Section 4.4.3).\nHave you thought about how water is transported up tall trees? It’s a fascinating aspect of how biology has evolved ways to deal with physics.\n\nThe driving force of water transport is the negative pressure that the vapor pressure deficit of the surrounding air creates. This force acts against a resistances and the gravitational force. To move the water up the plant, the water at the level of the leaves is under a strong negative pressure. The taller the plant and the higher the resistance along the soil-plant-atmosphere continuum, the more negative the pressure at the leaf-level to sustain a given water flux (transpiration). This negative water pressure at the level of the leaves is the leaf water potential (\\(\\psi_l\\)). It’s in the same units as the soil matric potential (\\(\\psi_s\\), Equation 8.4) and it is related to the soil water potential via a the transpiration stream \\(T\\) and an effective whole-plant hydraulic conductance \\(G_p\\) that considers resistance elements in series - from the soil to the leaf. Remember that a conductance is the inverse of a resistance. In simplified terms, this can be written as. \\[\nT = -G_p (\\psi_l - \\psi_s + \\rho g h)\n\\tag{8.6}\\] \\(\\rho\\) is the density of water (kg m-3), \\(g\\) is the gravitational constant (9.81 m s-2), and \\(h\\) is the height of the tree (m), measured from the average depth of the roots to the average height of the leaves. With the units of \\(\\psi_l\\) and \\(\\psi_s\\) in Pa and \\(T\\) in units of (kg m-2 s-1), \\(G_p\\) is in units of (s m-1). Equation 8.6 expresses the “supply” of water from the soil. From Equation 4.11, we know how the “demand” for water is determined by the vapor pressure deficit \\(D\\) and the stomatal conductance \\(g_s\\). The \\(T\\) in Equation 8.6 thus has to be equal to the \\(T\\) from Equation 4.11 (where it was called \\(E\\)): \\[\nT = 1.6 \\; g_s \\; D\n\\tag{8.7}\\] These equations illustrate some important points. First, a positive (upward) transpiration stream \\(T\\) that satisfies the demand from the atmosphere (Equation 8.7) can only be maintained if the leaf water potential is more negative than the soil water potential. Second, as the soil water potential becomes more negative, the leaf water potential also has to become more negative to transport the amount of water that is “demanded” by the atmosphere and determined by \\(D\\) and \\(g_s\\). Third, tall trees have to sustain more negative leaf water potentials than short ones for a given soil dryness and transpiration rate. By setting the two equations for \\(T\\) equal and solving for the leaf water potential \\(\\psi_l\\) also illustrates how soil moisture (\\(\\psi_s\\)) and VPD (\\(D\\)) have an interactive effect on \\(\\psi_l\\).\nResponses of plants to water stress are physiologically triggered through the sensing of leaf water potentials. In other words, \\(\\psi_l\\) is the central quantity that drives water stress responses of plants. Understanding how \\(\\psi_l\\) responds to environmental factors is thus key to understanding how water stress (stomatal closure, damaging drought stress) is a function of soil and air dryness, modified by plant hydraulic traits determining \\(G_p\\).\n\n\n\n\n\n\nNote\n\n\n\nEquation 8.6 is a simplification because the whole-plant hydraulic conductance \\(G_p\\) is a non-linear function of the water potential which drops along the transport pathway from \\(\\psi_s\\) to \\(\\psi_l\\). As a consequence, the interactive effect of VPD and soil moisture is non-linear. To account for the conductance drop with negative water potential, a more realistic form of Equation 8.6 can be written as \\[\nT = -G_{p,0} \\int_{\\psi_s}^{\\psi_l - \\rho g h} P(\\psi) \\; \\text{d}\\psi \\;,\n\\tag{8.8}\\] where \\(G_{p,0}\\) is a “base” conductance at zero water potential and \\(P(\\psi)\\) is a vulnerability function of the plant conductance. The latter declines towards more negative water potentials. A commonly used functional form is \\[\nP(\\psi) = 0.5^{(\\psi/P_{50})^b} \\;,\n\\tag{8.9}\\] where \\(P_\\text{50}\\) is the water potential at which \\(P\\) has dropped to 0.5.\n\n\nCode\nlibrary(ggplot2)\n\nvulnerability_curve <- function(psi, p50, b){\n 0.5 ^ ((psi/p50)^b)\n}\n\nggplot() +\n geom_function(fun = function(x) vulnerability_curve(x, -2000, 3)) +\n xlim(-4000, 0) +\n geom_vline(xintercept = c(-2000, 0), linetype = \"dotted\") +\n labs(x = expression(paste(psi, \" (Pa)\")),\n y = expression(paste(italic(P(psi))))) + \n theme_classic()\n\n\n\n\n\nFigure 8.10: Example plant hydraulic vulnerability curve. The water potential at which P has dropped to 0.5 is commonly referred to as P50 and is marked by the vertical dotted line at -2000 Pa (as an example). The abruptness of the drop in P is described by a shape parameter (b in Equation 8.9).\n\n\n\n\nEquation 8.8 can be regarded as the hydraulic supply function for transpiration (Sperry and Love 2015) and Equation 8.9 is commonly referred to as the hydraulic vulnerability curve (Tyree and Sperry 1989). The non-linearity arising from the latter implies that transpiration initially increases with an increasingly negative leaf water potential, but reaches a maximum beyond which transpiration does not further increase despite increasingly negative leaf water potentials. Reaching this point is risky for plants as it bears the danger of potentially lethal hydraulic failure (see below). Stomatal regulation acts to limit leaf water potentials reaching this point, while maximally exploiting soil water that is available for plant uptake without a substantial flattening of the \\(T(\\psi_l)\\) curve. What exactly “substantial” means, depends on plant strategies that vary between species.\n\n\nCode\nlibrary(dplyr)\n\nhydraulic_supply <- function(psi_leaf, psi_soil, g_plant, p50, b){\n transpiration <- -g_plant * \n integrate(\n f = vulnerability_curve, \n lower = psi_soil, \n upper = psi_leaf,\n p50 = p50, # argument for f\n b = b # argument for f\n )$value\n return(transpiration)\n}\n\ntmp <- expand.grid(\n psi_leaf = seq(-4000, 0, by = 50),\n psi_soil = seq(-2000, 0, by = 100)\n) |> \n as_tibble() |> \n rowwise() |> \n mutate(\n transp = hydraulic_supply(\n psi_leaf = psi_leaf, \n psi_soil = psi_soil, \n g_plant = 1e-6, \n p50 = -2000, \n b = 3\n )\n )\n\ntmp |> \n ggplot(aes(x = -psi_leaf, y = transp, color = psi_soil, group = psi_soil)) +\n geom_line() +\n scale_color_viridis_c(\n name = expression(paste(psi[soil], \" (Pa)\")),\n option = \"cividis\", \n direction = -1\n ) +\n labs(x = expression(paste(-psi[leaf], \" (Pa)\")),\n y = expression(paste(italic(T), \" (mm s\"^-1, \")\"))) + \n ylim(0, NA) +\n theme_classic()\n\n\n\n\n\nFigure 8.11: Hydraulic supply function. Transpiration as a function of an increasingly negative leaf water potential for different soil water potential levels. Water potentials are negative values. The x-axis shows the negative of the negative leaf water potential values (thus positive values). The visualisation shows that the leaf water potential is at least as strongly negative as the soil water potential and transpiration only exceeds zero if the leaf water potential becomes even more negative than the soil water potential. It also shows the strong sensitivity of the maximum transpiration rate as a function of the soil water potential. ‘Soil water potential’ represents the average water potential across the entire rooting zone. Here, the gravitational effect on water potentials is ignored by setting the tree height (h in Equation 8.8) to zero and the whole-plant base conductance Gp,0 is set to 10-6 s m-1.\n\n\n\n\n\n\nSustaining very negative water potentials along the transport pathway can be dangerous for the plant. As described in the box above, the whole-plant conductance declines with increasingly negative water potentials. This is because the very negative water potentials can only be sustained if no air is in contact with the water inside the xylem. As pressures become very negative, air may seep in and create embolisms. If the conductance was to drop towards zero, transpiration would collapse and embolisms would be excessive - creating potentially irreversible damage and triggering branch and eventually tree mortality due to hydraulic failure.\nPlants can avoid such water stress and hydraulic failure through stomatal regulation (see also Section 4.4.3). To avoid embolisms, stomata close (stomatal conductance is reduced) when the soil water potential declines to increasingly negative values. As a consequence, transpiration, as well as CO2 assimilation, decline. Once soil moisture across the rooting zone is depleted and the soil water potential reach very negative values, vegetation activity (transpiration and assimilation) comes to a halt. However, this rarely happens since water loss cannot be fully avoided even if stomata are fully closed and plants have evolved adaptations and are adjusted through plasticity in various traits to avoid a complete depletion of moisture stores across the rooting zone and to limit water losses. Variations in rooting depth are an expression of this adaptation and acclimation. Leaf properties with thick, waxy leaves that prevent water loss, or a drought-deciduous strategy are other examples.\nDifferent plant species respond differently to water stress (variations in soil water potential) and are characterised with different hydraulic traits that determine the stomatal response to soil and leaf water potentials. Two examples are shown in Figure 8.12\n\n\n\n\n\nFigure 8.12: Response of (a) CO2 assimilation and (b) stomatal conductance to a declining soil water potential for two contrasting species - the drought-adapted Eucalyptus populnea and Eucalyptus pilularis, which is adapted to more moist climates. The lines represent predictions of the model by Joshi et al. (2022) where an optimal response of stomata in trading off CO2 assimilation and the risks associated with negative leaf water potentials is assumed.\n\n\n\n\n\n\n\n\n\n\n\n\nExercise\n\n\n\n\nConsider a soil dry down as in Figure 8.12. Sketch qualitatively how the following variables change as a function of the soil water potential (while all other meteorological variables remain constant):\n\n\nSoil water content\nLatent heat flux\nSensible heat flux\nBowen ratio\nEvaporative fraction\nGPP\nReco\nNEE\nTree mortality due to hydraulic failure" }, { "objectID": "ecohydrology.html#sec-waterbucket-relations", @@ -305,7 +305,7 @@ "href": "ecohydrology.html#sec-budyko", "title": "8  Ecohydrology", "section": "8.7 Energy and water limitation across the globe", - "text": "8.7 Energy and water limitation across the globe\nEcosystems are commonly distinguished into energy-limited and water-limited systems. This notion relates to the dominant limiting resource and to the relations described in Section 8.5. When the bucket is full, the system is energy-limited. When it gets depleted, the system becomes water-limited. Of course, this is a simplification. The relations described in Section 8.5 really refer to a spectrum, rather than a binary classification.\nFurthermore, water-limited conditions may be temporally limited and interspersed by energy-limited periods. Also, the water bucket model, as formulated above, suggests that water-limitation sets in at the point when soil moisture falls below the field capacity. However, as long as the net radiation and the atmospheric vapour pressure deficit are not “excessive”, the demand for transpiration (Equation 8.7) may be met by the supply (Equation 8.8) without substantial stomatal closure during the daytime.\nA common classification of ecosystems into aridity classes is given in Table 8.1 based on Middleton and Thomas (1992). This considers the moisture index as defined by P/PET.\n\n\nTable 8.1: Aridity classes after Middleton and Thomas (1992).\n\n\nMoisture index value\nAridity class\n\n\n\n\n<0.03\nHyper arid\n\n\n0.03-0.2\nArid\n\n\n0.2-0.5\nSemi-arid\n\n\n0.5-0.65\nDry sub-humid\n\n\n>0.65\nHumid\n\n\n\n\nThe global distribution of the moisture index (Figure 8.22) resembles global distributions of vegetation patterns (Section 2.5). In regions where radiation (and temperature) does not limit vegetation, it may additionally be limited by water, as reflected by the moisture index and its low values across the worlds drylands.\n\n\n\n\n\nFigure 8.22: Moisture index defined as P/PET. This is also commonly referred to as the aridity index (but note: high values mean moist conditions). Data from Zomer, Xu, and Trabucco (2022).\n\n\n\n\nWhen combining the data for the satellite remote-sensing based fAPAR and the moisture index, a similar pattern emerges as described in Section 8.5. The green vegetation cover, measured by fAPAR, initially increases linearly with increasing P/PET for low values of the latter. Beyond a certain value, fAPAR no longer shows a relationship with P/PET (Figure 8.23).\nThe slope of the initial linear increase of fAPAR vs. P/PET reflects the water-carbon coupling. The amount of active green and transpiring foliage area is limited by water availability. research has shown that the relationship shown in Figure 8.23 is shifting such that the slope of the initial increase tends to steepen over time (Donohue et al. 2013; Ukkola et al. 2016). This is related to the fact that under rising CO2, stomatal conductance tends to be reduced (Figure 4.11) and the water use efficiency is enhanced (Section 4.4.1). In other words, a larger area of green leaves per unit ground area can be sustained for a given level of aridity.\n\n\n\n\n\nFigure 8.23: Vegetation greenness (measured by the fraction of absorbed photosynthetically active radiation, fAPAR) versus the moisture index (measured by the ratio of precipitation over potential evapotranspiration, P/PET). Data for fAPAR is from the MODIS MOD15A2 C006 product and taken as the annual maximum of mean monthly values. The color of hexagons shows the density of points (count per bin). A Data for the moisture index is from Zomer, Xu, and Trabucco (2022).\n\n\n\n\nRelated patterns emerge from the annual sums of ecosystem water fluxes (AET, PET, and P) measured from surface-atmosphere exchange (eddy covariance technique, Figure 8.24). However, at the scale at which ecosystem fluxes are measured (~1 km2), AET is sometimes larger than precipitation, as suggested by Figure 8.24 (b). This may be related to errors in precipitation and latent heat flux estimates, or due to vegetation having access to the groundwater and/or being supplied moisture through lateral subsurface flow.\n\n\n\n\n\nFigure 8.24: (a) Ecosystems in the AET vs. PET space. (b) Ecosystems in the Bukyko space (AET/P vs. PET/P). Each point represents a site from which flux measurements are available. A selection of sites from which data were used in this and previous chapters are highlighted. AET, PET, and P are multi-year means of annual sums." + "text": "8.7 Energy and water limitation across the globe\nEcosystems are commonly distinguished into energy-limited and water-limited systems. This notion relates to the dominant limiting resource and to the relations described in Section 8.5. When the bucket is full, the system is energy-limited. When it gets depleted, the system becomes water-limited. Of course, this is a simplification. The relations described in Section 8.5 really refer to a spectrum, rather than a binary classification.\nFurthermore, water-limited conditions may be temporally limited and interspersed by energy-limited periods. Also, the water bucket model, as formulated above, suggests that water-limitation sets in at the point when soil moisture falls below the field capacity. However, as long as the net radiation and the atmospheric vapor pressure deficit are not “excessive”, the demand for transpiration (Equation 8.7) may be met by the supply (Equation 8.8) without substantial stomatal closure during the daytime.\nA common classification of ecosystems into aridity classes is given in Table 8.1 based on Middleton and Thomas (1992). This considers the moisture index as defined by P/PET.\n\n\nTable 8.1: Aridity classes after Middleton and Thomas (1992).\n\n\nMoisture index value\nAridity class\n\n\n\n\n<0.03\nHyper arid\n\n\n0.03-0.2\nArid\n\n\n0.2-0.5\nSemi-arid\n\n\n0.5-0.65\nDry sub-humid\n\n\n>0.65\nHumid\n\n\n\n\nThe global distribution of the moisture index (Figure 8.22) resembles global distributions of vegetation patterns (Section 2.5). In regions where radiation (and temperature) does not limit vegetation, it may additionally be limited by water, as reflected by the moisture index and its low values across the worlds drylands.\n\n\n\n\n\nFigure 8.22: Moisture index defined as P/PET. This is also commonly referred to as the aridity index (but note: high values mean moist conditions). Data from Zomer, Xu, and Trabucco (2022).\n\n\n\n\nWhen combining the data for the satellite remote-sensing based fAPAR and the moisture index, a similar pattern emerges as described in Section 8.5. The green vegetation cover, measured by fAPAR, initially increases linearly with increasing P/PET for low values of the latter. Beyond a certain value, fAPAR no longer shows a relationship with P/PET (Figure 8.23).\nThe slope of the initial linear increase of fAPAR vs. P/PET reflects the water-carbon coupling. The amount of active green and transpiring foliage area is limited by water availability. research has shown that the relationship shown in Figure 8.23 is shifting such that the slope of the initial increase tends to steepen over time (Donohue et al. 2013; Ukkola et al. 2016). This is related to the fact that under rising CO2, stomatal conductance tends to increase (Figure 4.11) and the water use efficiency is enhanced (Section 4.4.1). In other words, a larger area of green leaves per unit ground area can be sustained for a given level of aridity. \n\n\n\n\n\nFigure 8.23: Vegetation greenness (measured by the fraction of absorbed photosynthetically active radiation, fAPAR) versus the moisture index (measured by the ratio of precipitation over potential evapotranspiration, P/PET). Data for fAPAR is from the MODIS MOD15A2 C006 product and taken as the annual maximum of mean monthly values. The color of hexagons shows the density of points (count per bin). A Data for the moisture index is from Zomer, Xu, and Trabucco (2022).\n\n\n\n\nRelated patterns emerge from the annual sums of ecosystem water fluxes (AET, PET, and P) measured from surface-atmosphere exchange (eddy covariance technique, Figure 8.24). However, at the scale at which ecosystem fluxes are measured (~1 km2), AET is sometimes larger than precipitation, as suggested by Figure 8.24 (b). This may be related to errors in precipitation and latent heat flux estimates, or due to vegetation having access to the groundwater and/or being supplied moisture through lateral subsurface flow.\n\n\n\n\n\nFigure 8.24: (a) Ecosystems in the AET vs. PET space. (b) Ecosystems in the Bukyko space (AET/P vs. PET/P). Each point represents a site from which flux measurements are available. A selection of sites from which data were used in this and previous chapters are highlighted. AET, PET, and P are multi-year means of annual sums." }, { "objectID": "ecohydrology.html#landscape-scale-heterogeneity", @@ -326,21 +326,21 @@ "href": "feedbacks.html#land-as-an-element-in-the-earth-system", "title": "9  Earth system feedbacks", "section": "9.1 Land as an element in the Earth system", - "text": "9.1 Land as an element in the Earth system\nThe Earth system can be regarded as a coupled system in which its elements (atmosphere, ocean, cryosphere, biosphere, lithosphere) interact on various time scales. A primary goal of Earth System research is to understand the interactions occurring on time scales that are relevant for society in the context of anthropogenic climate change. It is now established with overwhelming evidence that anthropogenic CO2 emissions from the combustion of fossil fuels have caused a rise in atmospheric concentrations beyond levels reached over the past 800,000 years, and that this concentration increase is the dominant driver of climate change as observed over the last decades (Arias et al. 2021).\nAny prediction of climate change in the coming decades, centuries and millennia relies on an understanding of the processes that are key to the following questions:\n\nHow fast will anthropogenic CO2 emissions and other greenhouse gases accumulate in the atmosphere?\nHow does the anthropogenic modification of the biosphere through land use change affect greenhouse gas emissions by land ecosystems, land-climate interactions, and the carbon cycle?\nWhat is the climate response to changes in atmospheric CO2 and other drivers?\nWhat mechanisms does the rise in CO2 and the change in climate set in motion and how do they feed back to climate change?\n\nThe land carbon cycle, emissions of several greenhouse gases, and various land surface properties respond to a changing climate and atmospheric CO2. The processes responsible for the climate and CO2 effect on land ecosystems were introduced in Part I of this book. For example, rising CO2 has a fertilising effect on photosynthesis (Section 4.3.5). Rising temperatures accelerate respiration by autotrophs (e.g, plants) and heterotrophs (e.g., microbes and fungi) (Chapter 5) and may shift photosynthesis beyond its temperature optimum (Section 4.3.6). Increasing temperatures drive water loss through evapotranspiration and, potentially aggravated by reduced precipitation, can reduce root zone water availability and induce hydraulic stress in plants (Section 8.4), reduced CO2 uptake by photosynthesis (Section 4.4), and can trigger tree mortality.\n\n\n\n\n\nFigure 9.1: Interactions of terrestrial ecosystems (here, in particular forests) with the climate system via surface energy exchange (A), the water cycle (B), and the carbon cycle (C). Diffuse and direct solar radiation is partially reflected or absorbed, as determined by the surface albedo. Energy absorbed from shortwave and longwave radiation, in combination with water available for transpiration and evaporation determines fluxes of heat into the soil, sensible, and latent heat fluxes. Available water is determined by the soil water balance of inputs (infiltrating precipitation and snow melt) and outputs (evaporation, transpiration, surface runoff, drainage, and submilmation). Available water limits the rate of photosynthesis, which acts as the fixation of atmospheric CO2 and provides C used for the synthesis of foliage, stem, or root biomass, exudates (not shown) or is directly respired (autotrophic respiration). Assimilated biomass turns over as litterfall, feeds the soil carbon pool, and is remineralized by microbial activity, mobilising nutrients essential for the assimilation of new tissue. The processes and quantities shown in this figure are covered in Part I of this book. Figure from Bonan (2008).\n\n\n\n\nThe climate and CO2-driven responses of land ecosystems and land surface processes affect the C balance of the terrestrial biosphere (its net biome productivity, Section 5.1.7) and, through altered surface properties, land-climate interactions, e.g., through altered albedo and conductances to land-atmosphere water vapour fluxes (Chapter 7). While Part I of this book introduced the processes by which climate and CO2 affect the terrestrial biosphere, the land carbon cycle and land-climate interactions, Part II looks at how this affects the climate system. In addition to the focus on C, energy, and water, Part II extends the scope to the nitrogen (N) cycle, how it affects the C cycle and how emissions of the important greenhouse-gas N2O are controlled. Methane (CH4), an even stronger contributor to climate change than N2O, also has major sources in land ecosystems. Wetlands and fire are natural sources of CH4 and respond sensitively to climate change. Because greenhouse gases and land surface properties affect climate and are affected by it, feedbacks arise.\n\n\n\n\n\n\nNote\n\n\n\nA feedback arises when the output to a process triggers an amplification (positive feedback) or an attenuation (negative feedback) of the initial input.\n\n\n\n\n\nFigure 9.2: A feedback loop where an output of a process (P) adds as a causal input to that process. Figure and caption taken from Wikimedia (2024).\n\n\n\n\n\n\nGreenhouse gas emissions from land ecosystems and modifications of land-climate interactions are also the response of a direct anthropogenic forcing that would arise also in absence of changes in climate and CO2. For example, deforestation leads to a loss of C stored in biomass (and respective CO2 emissions) and to a modification of the surface radiation balance (Bala et al. 2007), nitrogen fertiliser inputs drive enhanced nitrous oxide (N2O) emissions (Galloway et al. 2004), and wetland drainage leads to C loss from soils and associated CO2 emissions, but also reduces CH4 emissions (Fluet-Chouinard et al. 2023). To complicate things, human alterations of the land surface and ecosystems also modify the feedbacks between terrestrial systems and climate. For example, deforestation reduces the capacity of the terrestrial biosphere to act as a C sink for anthropogenic CO2 emissions. These myriad interactions make the land an intricately coupled element of the earth system and call for a conceptual framework and formalism for separating feedbacks and forcings and measuring their strengths.\n\n\n\n\n\nFigure 9.3: Schematic of forcings and feedbacks related with terrestrial greenhouse gas emissions and biogeophysical changes. External forcings to this system are given in yellow, and act either on the terrestrial biosphere directly (land use and land use change, LU and LUC ; reactive N deposition (Nr -deposition); air pollution (O3tropos, sulphate deposition, etc.) or modify the atmospheric composition (direct anthropogenic emissions). Land biogeochemical emissions and biogeophysical changes are affected by external forcings acting on the land, as well as by the feedback drivers (atmospheric CO2 and climate). ‘Biogeochemical emissions’ include not only greenhouse-gases, but also several reactive gases that affect aerosols, atmospheric chemistry, and the atmospheric lifetime of CH2. BVOC are biogenic volatile organic compounds. Changes induced by these drivers imply feedbacks because drivers are mediated by the Earth system response to external forcings." + "text": "9.1 Land as an element in the Earth system\nThe Earth system can be regarded as a coupled system in which its elements (atmosphere, ocean, cryosphere, biosphere, lithosphere) interact on various time scales. A primary goal of Earth System research is to understand the interactions occurring on time scales that are relevant for society in the context of anthropogenic climate change. It is now established with overwhelming evidence that anthropogenic CO2 emissions from the combustion of fossil fuels have caused a rise in atmospheric concentrations beyond levels reached over the past 800,000 years, and that this concentration increase is the dominant driver of climate change as observed over the last decades (Arias et al. 2021).\nAny prediction of climate change in the coming decades, centuries and millennia relies on an understanding of the processes that are key to the following questions:\n\nHow fast will anthropogenic CO2 emissions and other greenhouse gases accumulate in the atmosphere?\nHow does the anthropogenic modification of the biosphere through land use change affect greenhouse gas emissions by land ecosystems, land-climate interactions, and the carbon cycle?\nWhat is the climate response to changes in atmospheric CO2 and other drivers?\nWhat mechanisms does the rise in CO2 and the change in climate set in motion and how do they feed back to climate change?\n\nThe land carbon cycle, emissions of several greenhouse gases, and various land surface properties respond to a changing climate and atmospheric CO2. The processes responsible for the climate and CO2 effect on land ecosystems were introduced in Part I of this book. For example, rising CO2 has a fertilising effect on photosynthesis (Section 4.3.5). Rising temperatures accelerate respiration by autotrophs (e.g, plants) and heterotrophs (e.g., microbes and fungi) (Chapter 5) and may shift photosynthesis beyond its temperature optimum (Section 4.3.6). Increasing temperatures drive water loss through evapotranspiration and, potentially aggravated by reduced precipitation, can reduce root zone water availability and induce hydraulic stress in plants (Section 8.4), reduced CO2 uptake by photosynthesis (Section 4.4), and can trigger tree mortality.\n\n\n\n\n\nFigure 9.1: Interactions of terrestrial ecosystems (here, in particular forests) with the climate system via surface energy exchange (A), the water cycle (B), and the carbon cycle (C). Diffuse and direct solar radiation is partially reflected or absorbed, as determined by the surface albedo. Energy absorbed from shortwave and longwave radiation, in combination with water available for transpiration and evaporation determines fluxes of heat into the soil, sensible, and latent heat fluxes. Available water is determined by the soil water balance of inputs (infiltrating precipitation and snow melt) and outputs (evaporation, transpiration, surface runoff, drainage, and submilmation). Available water limits the rate of photosynthesis, which acts as the fixation of atmospheric CO2 and provides C used for the synthesis of foliage, stem, or root biomass, exudates (not shown) or is directly respired (autotrophic respiration). Assimilated biomass turns over as litterfall, feeds the soil carbon pool, and is remineralized by microbial activity, mobilising nutrients essential for the assimilation of new tissue. The processes and quantities shown in this figure are covered in Part I of this book. Figure from Bonan (2008).\n\n\n\n\nThe climate and CO2-driven responses of land ecosystems and land surface processes affect the C balance of the terrestrial biosphere (its net biome productivity, Section 5.1.7) and, through altered surface properties, land-climate interactions, e.g., through altered albedo and conductance to land-atmosphere water vapor fluxes (Chapter 7). While Part I of this book introduced the processes by which climate and CO2 affect the terrestrial biosphere, the land carbon cycle and land-climate interactions, Part II looks at how this affects the climate system. In addition to the focus on C, energy, and water, Part II extends the scope to the nitrogen (N) cycle, how it affects the C cycle and how emissions of the important greenhouse-gas N2O are controlled. Methane (CH4), an even stronger contributor to climate change than N2O, also has major sources in land ecosystems. Wetlands and fire are natural sources of CH4 and respond sensitively to climate change. Because greenhouse gases and land surface properties affect climate and are affected by it, feedbacks arise.\n\n\n\n\n\n\nNote\n\n\n\nA feedback arises when the output to a process triggers an amplification (positive feedback) or an attenuation (negative feedback) of the initial input.\n\n\n\n\n\nFigure 9.2: A feedback loop where an output of a process (P) adds as a causal input to that process. Figure and caption taken from Wikimedia (2024).\n\n\n\n\n\n\nGreenhouse gas emissions from land ecosystems and modifications of land-climate interactions are also the response of a direct anthropogenic forcing that would arise also in absence of changes in climate and CO2. For example, deforestation leads to a loss of C stored in biomass (and respective CO2 emissions) and to a modification of the surface radiation balance (Bala et al. 2007), nitrogen fertiliser inputs drive enhanced nitrous oxide (N2O) emissions (Galloway et al. 2004), and wetland drainage leads to C loss from soils and associated CO2 emissions, but also reduces CH4 emissions (Fluet-Chouinard et al. 2023). To complicate things, human alterations of the land surface and ecosystems also modify the feedbacks between terrestrial systems and climate. For example, deforestation reduces the capacity of the terrestrial biosphere to act as a C sink for anthropogenic CO2 emissions. These myriad interactions make the land an intricately coupled element of the Earth system and call for a conceptual framework and formalism for separating feedbacks and forcings and measuring their strengths.\n\n\n\n\n\nFigure 9.3: Schematic of forcings and feedbacks related with terrestrial greenhouse gas emissions and biogeophysical changes. External forcings to this system are given in yellow, and act either on the terrestrial biosphere directly (land use and land use change, LU and LUC ; reactive N deposition (Nr -deposition); air pollution (O3tropos, sulphate deposition, etc.) or modify the atmospheric composition (direct anthropogenic emissions). Land biogeochemical emissions and biogeophysical changes are affected by external forcings acting on the land, as well as by the feedback drivers (atmospheric CO2 and climate). ‘Biogeochemical emissions’ include not only greenhouse-gases, but also several reactive gases that affect aerosols, atmospheric chemistry, and the atmospheric lifetime of CH2. BVOC are biogenic volatile organic compounds. Changes induced by these drivers imply feedbacks because drivers are mediated by the Earth system response to external forcings." }, { "objectID": "feedbacks.html#the-terrestrial-biosphere-in-equilibrium", "href": "feedbacks.html#the-terrestrial-biosphere-in-equilibrium", "title": "9  Earth system feedbacks", "section": "9.2 The terrestrial biosphere in equilibrium", - "text": "9.2 The terrestrial biosphere in equilibrium\nA useful staring point is to consider the terrestrial biosphere and the Earth system being in a dynamic equilibrium (Section 3.1). The terrestrial biosphere being in equilibrium with climate and atmospheric CO2 is an approximative concept often used as a description for its pre-industrial state. It is motivated by the finding that atmospheric CO2 (Siegenthaler et al. 2005; MacFarling Meure et al. 2006) and climate were remarkably stable during the pre-industrial Holocene (ca. 11 ka BP – 1750 AD) and that the terrestrial carbon (C) and nutrient balances and other ecosystem properties (greenhouse-gas emissions, surface energy and water exchange, see Figure 9.1) adjust to perturbations and re-equilibrate on time scales of decades to millennia. These time scales are determined by vegetation dynamics and related shifts in carbon and nutrient cycling (decades to centuries), and the relatively slow turnover times of soil organic matter pools (centuries to millennia). We learned about the dynamics of carbon cycling in ecosystems in Chapter 5.\nThe equilibrium concept implies that no net C fluxes occur between the terrestrial biosphere, the ocean and the atmosphere, and that all other properties remain constant. The relatively balanced state of the C cycle during the pre-industrial Holocene is remarkable in the view of the vast C reservoirs on land and the large gross exchange fluxes (Chapter 3). Globally, ca. 130 PgC yr-1 are assimilated by terrestrial photosynthesis (gross primary production, GPP), and ca. 60 PgC yr-1 are retained to assimilate vegetation biomass (net primary production, NPP). The vegetation C stock amounts to ca. 450 PgC and is turned over on time scales of years (grass, leaves) to decades (wood). Decomposed litter feeds soil C stocks (ca. 1700 PgC), where it is retained for centuries to millennia, and is ultimately respired back to the atmosphere as CO2 through heterotrophic respiration (Rh). Peatland C stocks (ca. 600 PgC, Yu et al. (2010)) have even longer lifetimes due to anaerobic soil conditions inhibiting decomposition. The turnover time (lifetime) of a given C reservoir determines its time scale of response to a perturbation (Section 5.2). Large C stocks are contained in permafrost soils (ca. 1200 PgC, including yedoma and deltaic deposits, Tarnocai et al. (2009)) where C is practically locked away from the C cycle but can be re-mobilised upon thawing. Figure 3.1 provides an schematic overview of these global C pools and fluxes.\nNote that on millennial time scales, the C cycle has only very minor long-term sinks (e.g., oceanic sediment burial, peat buildup), and that any perturbation of the equilibrium induces a redistribution of C within the different reservoirs. Until equilibration, net fluxes between reservoirs occur mostly in the form of gaseous CO2. In contrast, other greenhouse-gases (e.g., N2O , CH4) have considerable sinks in the atmosphere and, to a lesser degree, in soils. Thus, net land-to-atmosphere and ocean-to-atmosphere fluxes persist also in a C cycle equilibrium and maintain atmospheric concentrations.\nThe concept of a land C cycle equilibrium during the pre-industrial Holocene is approximate because (i) climate and CO2 conditions were not perfectly stable but responded to volcanic activity, changes in solar radiation, and slow changes in orbital configurations Wanner et al. (2008), (ii) anthropogenic land use change has had profound impacts on local ecosystem functioning since the emergence of agriculture at the turn of the Neolithicum and caused significant global impacts on the carbon cycle and climate probably as early as ca. 1000 BC (B. D. Stocker et al. 2017), (iii) a small net C sink in peatlands has persisted even millennia after their establishment at the end of the Last Deglaciation due to the extremely slow turnover rates of soil organic matter under anaerobic conditions (Yu et al. 2010), (iv) dynamics of permafrost buildup are likely to evolve on multi-millennial time scales as well, implying long-term disequilibrium fluxes, and (v) a small burial flux of terrigenous organic matter in inland lakes and coastal zones causes a continuous sink of C." + "text": "9.2 The terrestrial biosphere in equilibrium\nA useful staring point is to consider the terrestrial biosphere and the Earth system being in a dynamic equilibrium (Section 3.1). The terrestrial biosphere being in equilibrium with climate and atmospheric CO2 is an approximative concept often used as a description for its pre-industrial state. It is motivated by the finding that atmospheric CO2 (Siegenthaler et al. 2005; MacFarling Meure et al. 2006) and climate were remarkably stable during the pre-industrial Holocene (ca. 11 ka BP – 1750 AD) and that the terrestrial carbon (C) and nutrient balances and other ecosystem properties (greenhouse-gas emissions, surface energy and water exchange, see Figure 9.1) adjust to perturbations and re-equilibrate on time scales of decades to millennia. These time scales are determined by vegetation dynamics and related shifts in carbon and nutrient cycling (decades to centuries), and the relatively slow turnover times of soil organic matter pools (centuries to millennia). We learned about the dynamics of carbon cycling in ecosystems in Chapter 5.\nThe equilibrium concept implies that no net C fluxes occur between the terrestrial biosphere, the ocean and the atmosphere, and that all other properties remain constant. The relatively balanced state of the C cycle during the pre-industrial Holocene is remarkable in the view of the vast C reservoirs on land and the large gross exchange fluxes (Chapter 3). Globally, ca. 130 PgC yr-1 are assimilated by terrestrial photosynthesis (gross primary production, GPP), and ca. 60 PgC yr-1 are retained to assimilate vegetation biomass (net primary production, NPP). The vegetation C stock amounts to ca. 450 PgC and is turned over on time scales of years (grass, leaves) to decades (wood). Decomposed litter feeds soil C stocks (ca. 1700 PgC), where it is retained for centuries to millennia, and is ultimately respired back to the atmosphere as CO2 through heterotrophic respiration (Rh). Peatland C stocks (ca. 600 PgC, Yu et al. (2010)) have even longer lifetimes due to anaerobic soil conditions inhibiting decomposition. The turnover time (lifetime) of a given C reservoir determines its time scale of response to a perturbation (Section 5.2). Large C stocks are contained in permafrost soils (ca. 1200 PgC, including yedoma and deltaic deposits, Tarnocai et al. (2009)) where C is practically locked away from the C cycle but can be re-mobilised upon thawing. Figure 3.1 provides a schematic overview of these global C pools and fluxes.\nNote that on millennial time scales, the C cycle has only very minor long-term sinks (e.g., oceanic sediment burial, peat buildup), and that any perturbation of the equilibrium induces a redistribution of C within the different reservoirs. Until equilibration, net fluxes between reservoirs occur mostly in the form of gaseous CO2. In contrast, other greenhouse-gases (e.g., N2O , CH4) have considerable sinks in the atmosphere and, to a lesser degree, in soils. Thus, net land-to-atmosphere and ocean-to-atmosphere fluxes persist also in a C cycle equilibrium and maintain atmospheric concentrations.\nThe concept of a land C cycle equilibrium during the pre-industrial Holocene is approximate because (i) climate and CO2 conditions were not perfectly stable but responded to volcanic activity, changes in solar radiation, and slow changes in orbital configurations Wanner et al. (2008), (ii) anthropogenic land use change has had profound impacts on local ecosystem functioning since the emergence of agriculture at the turn of the Neolithic and caused significant global impacts on the carbon cycle and climate probably as early as ca. 1000 BC (B. D. Stocker et al. 2017), (iii) a small net C sink in peatlands has persisted even millennia after their establishment at the end of the Last Deglaciation due to the extremely slow turnover rates of soil organic matter under anaerobic conditions (Yu et al. 2010), (iv) dynamics of permafrost buildup are likely to evolve on multi-millennial time scales as well, implying long-term disequilibrium fluxes, and (v) a small burial flux of terrigenous organic matter in inland lakes and coastal zones causes a continuous sink of C." }, { "objectID": "feedbacks.html#the-terrestrial-response-to-the-anthropogenic-perturbation", "href": "feedbacks.html#the-terrestrial-response-to-the-anthropogenic-perturbation", "title": "9  Earth system feedbacks", "section": "9.3 The terrestrial response to the anthropogenic perturbation", - "text": "9.3 The terrestrial response to the anthropogenic perturbation\nThe pre-industrial “equilibrium” has been dramatically perturbed since fossil energy sources have been used and have enabled the rapid rise of the global economy and industrial production. The CO2 emitted from the combustion of fossil fuels has accumulated in different reservoirs of the land and ocean carbon cycle (Figure 3.1) and has wide ranging consequences for climate, ocean acidification, primary productivity of the biosphere, and the cycling of nutrients. The industrialisation has been accompanied by an increase in global population, a shift in consumption patterns and a growing demand for food. The associated expansion of agricultural land has transformed ca. 30% of the land surface (Ramankutty et al. 2008) and ca. 24% of the total terrestrial net primary production is appropriated by human uses (Vitousek et al. 1986; Haberl et al. 2007). The production of mineral fertilisers, necessary to support today’s agricultural output, has fundamentally disrupted the natural nutrient cycles and has amplified soil N2O emissions (Galloway et al. 2004). This has led to the accumulation of an array of radiatively active substances in the atmosphere and has contributed to anthropogenic climate change, eutrophication of ecosystems, loss of biodiversity, and impacts on human health.\nThe human-caused accumulation of greenhouse gases in the atmosphere and the increase in other forcing agents is measured by the additional energy input into the climate system as the effective radiative forcing (ERF, Figure 9.4). The ERF is measured as an energy flux in W m-2 and reflects the atmospheric concentration of greenhouse gases and their effectiveness in heating the atmosphere over a given time period - here 1750-2019. The influence of forcing agents on the Earth’s energy balance, e.g., the albedo change caused by land use change, can similarly be measured in terms of its ERF. Figure 9.4 provides an overview of the ERF of different forcing agents since 1750. Among these, CO2, CH4, N2O, and albedo are tightly linked to land processes. The effect of greenhouse gases plays out through their absorption of longwave radiation that would otherwise radiate back into space. Instead, the radiative energy is absorbed and the trapped energy contributes to heating air. The radiative effect of albedo changes play out through the energy balance of the Earth surface (Chapter 7).\n\n\n\n\n\nFigure 9.4: Change in effective radiative forcing (ERF) from 1750 to 2019 by contributing forcing agents (carbon dioxide, other well-mixed greenhouse gases, ozone, stratospheric water vapour, surface albedo, contrails and aviation-induced cirrus, aerosols, anthropogenic total, and solar). Solid bars represent best estimates, and very likely (5–95%) ranges are given by error bars. Non-CO2 well-mixed greenhouse gases are further broken down into contributions from methane (CH4), nitrous oxide (N2O) and halogenated compounds. Surface albedo is broken down into land-use changes and light-absorbing particles on snow and ice. Aerosols are broken down into contributions from aerosol–cloud interactions and aerosol–radiation interactions. For aerosols and solar, the 2019 single-year values are given (Table 7.8). Volcanic forcing is not shown due to the episodic nature of volcanic eruptions. Further details on data sources and processing are available in the chapter data table (Table 7.SM.14). Figure from Forster et al. (2021)." + "text": "9.3 The terrestrial response to the anthropogenic perturbation\nThe pre-industrial “equilibrium” has been dramatically perturbed since fossil energy sources have been used and have enabled the rapid rise of the global economy and industrial production. The CO2 emitted from the combustion of fossil fuels has accumulated in different reservoirs of the land and ocean carbon cycle (Figure 3.1) and has wide-ranging consequences for climate, ocean acidification, primary productivity of the biosphere, and the cycling of nutrients. The industrialization has been accompanied by an increase in global population, a shift in consumption patterns and a growing demand for food. The associated expansion of agricultural land has transformed ca. 30% of the land surface (Ramankutty et al. 2008) and ca. 24% of the total terrestrial net primary production is appropriated by human uses (Vitousek et al. 1986; Haberl et al. 2007). The production of mineral fertilisers, necessary to support today’s agricultural output, has fundamentally disrupted the natural nutrient cycles and has amplified soil N2O emissions (Galloway et al. 2004). This has led to the accumulation of an array of radiatively active substances in the atmosphere and has contributed to anthropogenic climate change, eutrophication of ecosystems, loss of biodiversity, and impacts on human health.\nThe human-caused accumulation of greenhouse gases in the atmosphere and the increase in other forcing agents is measured by the additional energy input into the climate system as the effective radiative forcing (ERF, Figure 9.4). The ERF is measured as an energy flux in W m-2 and reflects the atmospheric concentration of greenhouse gases and their effectiveness in heating the atmosphere over a given time period - here 1750-2019. The influence of forcing agents on the Earth’s energy balance, e.g., the albedo change caused by land use change, can similarly be measured in terms of its ERF. Figure 9.4 provides an overview of the ERF of different forcing agents since 1750. Among these, CO2, CH4, N2O, and albedo are tightly linked to land processes. The effect of greenhouse gases plays out through their absorption of longwave radiation that would otherwise radiate back into space. Instead, the radiative energy is absorbed and the trapped energy contributes to heating air. The radiative effect of albedo changes play out through the energy balance of the Earth surface (Chapter 7).\n\n\n\n\n\nFigure 9.4: Change in effective radiative forcing (ERF) from 1750 to 2019 by contributing forcing agents (carbon dioxide, other well-mixed greenhouse gases, ozone, stratospheric water vapor, surface albedo, contrails and aviation-induced cirrus, aerosols, anthropogenic total, and solar). Solid bars represent best estimates, and very likely (5–95%) ranges are given by error bars. Non-CO2 well-mixed greenhouse gases are further broken down into contributions from methane (CH4), nitrous oxide (N2O) and halogenated compounds. Surface albedo is broken down into land-use changes and light-absorbing particles on snow and ice. Aerosols are broken down into contributions from aerosol–cloud interactions and aerosol–radiation interactions. For aerosols and solar, the 2019 single-year values are given (Table 7.8). Volcanic forcing is not shown due to the episodic nature of volcanic eruptions. Further details on data sources and processing are available in the chapter data table (Table 7.SM.14). Figure from Forster et al. (2021)." }, { "objectID": "feedbacks.html#sec-terrforc", @@ -354,14 +354,14 @@ "href": "feedbacks.html#sec-terrfb", "title": "9  Earth system feedbacks", "section": "9.5 Feedbacks from the terrestrial biosphere", - "text": "9.5 Feedbacks from the terrestrial biosphere\nEmissions drive atmospheric concentrations and atmospheric concentrations determine the radiative forcing and thus climate. Land-climate feedback loops arise via the atmospheric concentration of CO2 - which affects photosynthesis and thus the carbon balance of terrestrial ecosystems - and via climate - which affects land processes and thereby the emissions of greenhouse gases and albedo (Figure 9.3). The change in climate and CO2 caused by the external forcings drive an additional response of land-mediated biogeochemical and biogeophysical forcing agents and the final change in climate is the combined outcome of the initial external forcing and the feedbacks.\n\n\n\n\n\n\nQuantifying feedbacks with an Earth System Model\n\n\n\nIn the context of Earth system modeling, the “forcing part” of land-mediated changes can be assessed by considering the radiative forcing and climate change (global mean surface temperature change, \\(\\Delta T^\\text{ctrl}\\) in Figure 9.5) in a simulation setup where changes in climate and CO2 are not communicated to the land model component. In contrast, a feedback is triggered by the perturbation of climate and CO2, feeding back to modify land-mediated forcing agents. The final climate change considering forcings and feedbacks is measured by the global mean temperature change in the respective simulation (\\(\\Delta T^\\text{CT}\\) in Figure 9.5). Including the feedbacks requires a coupled Earth system model setup where the land module “sees” changes in climate and CO2. The “feedback part” is then captured by the difference of the coupled and un-coupled simulations.\n\n\n\n\n\nFigure 9.5: Schematic illutstration of two Earth system model setups used for quantifying land-mediated forcings and feedbacks, arising through changes in terrestrial C storage (ΔT), N~O, and CH4 emissions, and albedo changes, and triggered by external forcings, including land use, N-deposition, N-fertiliser inputs, and direct emissions of greenhouse gases to the atmosphere (eEXT). Feedbacks arising through atmospheric CO2 are denoted with a ‘C’ and feedbacks arising through climate change are denoted with a ‘T’. Figure from B. Stocker et al. (2013).\n\n\n\n\n\n\nClimate-land feedbacks are a subset among a larger number of climate feedbacks that operate also in the atmosphere, ocean, and the cryosphere. A climate feedback is commonly defined as a process that drives a change of the energy balance of the climate system as a function the global mean temperature. A positive climate feedback drives an additional energy input, while a negative climate feedback drives an additional energy loss. A discrete set of such climate feedbacks are commonly distinguished Figure 9.6.\n\n9.5.1 The most important physical climate feedbacks\nPlanck response The energy emitted by the Earth (or any material body) through longwave radiation scales with \\(T^4\\) - with the fourth power of the temperature of the emitting body. Therefore, as the Earth’s atmosphere heats up, its loss of radiative energy increases rapidly. The Planck response is therefore a negative feedback and, reflecting the fourth power, it is a particularly strong negative feedback.\nWater vapour plus lapse rate More water vapour can be contained in warmer air, following the Clausius-Clapeyron relationship. Greater vapour content leads to more longwave and shortwave radiation to be absorbed, and this effect is greatest in the upper troposphere (over the tropics). Hence, the additional atmospheric warming reduces the lapse rate and increases the radiation of the warmed troposphere into space. The water vapour feedback alone is positive and strong, while the lapse rate feedback alone is negative and less strong. Since they act in combination, they are commonly quantified as a single feedback. Their combined effect is still a strong positive feedback.\nSurface albedo Increasing temperatures reduce sea ice and seasonal snow cover - on land and on sea ice. This reduces the albedo (Section 7.1.2) and thus increases the absorption of solar radiation at the surface and decreases its reflection into space. Hence, the surface albedo is a positive feedback.\nClouds Different types of clouds exhibit different responses to warming and lead to different effects on the Earth’s energy balance. The uncertainty of this feedback is particularly high.\n\n\n\n\n\nFigure 9.6: An overview of physical and biogeochemical feedbacks in the climate system. (a) Synthesis of physical, biogeophysical and non-carbon dioxide (CO2) biogeochemical feedbacks that are included in the definition of equilibrium climate sensitivity (ECS) assessed in this Technical Summary. These feedbacks have been assessed using multiple lines of evidence including observations, models and theory. The net feedback is the sum of the Planck response, water vapour and lapse rate, surface albedo, cloud, and biogeophysical and non-CO2 biogeochemical feedbacks. Bars denote the mean feedback values, and uncertainties representvery likely ranges; (b) Estimated values of individual biogeophysical and non-CO2 biogeochemical feedbacks. The atmospheric methane (CH4) lifetime and other non-CO2 biogeochemical feedbacks have been calculated using global Earth system model simulations from AerChemMIP, while the CH4 and nitrous oxide (N2O) source responses to climate have been assessed for the year 2100 using a range of modelling approaches using simplified radiative forcing equations. The estimates represent the mean and 5–95% range. The level of confidence in these estimates is lowowing to the large model spread. (c) Carbon-cycle feedbacks as simulated by models participating in the C4MIP of the Coupled Model Intercomparison Project Phase 6 (CMIP6). An independent estimate of the additional positive carbon-cycle climate feedbacks from permafrost thaw, which is not considered in most C4MIP models, is added. Note that the scale of the x-axis in (b) is much smaller than the scale of the other panels. Figure and caption text from the IPCC Assessment Report 6, Technical Summary, Figure TS.17 (Arias et al. 2021).\n\n\n\n\n\n\n9.5.2 Biogeochemical climate feedbacks\nThe land and ocean carbon responses to climate and to CO2 are commonly distinguished. The responses to CO2 induce relatively strong negative feedbacks, but their uncertaintly is large, particularly for the land carbon response to CO2. This uncertainty reflects open questions regarding the CO2 fertilisation effect on terrestrial carbon storage (Section 3.4). Increasing atmospheric CO2 also drives CO2 uptake by the ocean (Chapter 14), leading to a negative feedback. The response to climate induce positive feedbacks - a relatively weakly positive one through the ocean response, and a stronger positive but highly uncertain one through the land response. The positive feedback of ocean carbon to climate arises due to the reduced solubility of CO2 in warmed ocean water and reduced ocean mixing in a warm climate. The positive feedback of land carbon to climate arises due to a multitude of processes acting on plant physiology (Section 4.3.6), hydraulic stress through increased vapour pressure deficit of a warmer atmosphere (Section 8.4), tree mortality, enhanced autotrophic and heterotrophic respiration (Chapter 5), and the loss of permafrost (Section 6.4.5). Some land carbon responses to climate also induce negative feedbacks, e.g., the temperature-driven northward expansion of the boreal treeline and associated arctic greening (Keenan and Riley 2018).\nWeaker feedbacks arise through additional biogeochemical processes, most importantly through emissions of CH4 and N2O (B. Stocker et al. 2013), but also through reactive gases that affect the lifetime of CH4 in the atmopshere (Arneth et al. 2010). Chapter Chapter 12 will focus on these non-CO2 greenhouse gases.\nThe strengths of the feedbacks depend on the state of Earth and on the dominant radiative forcing agents that drive the temperature change. For example, if there was no terrestrial biosphere, the positive feedback of land carbon to climate and the negative feedback to CO2 would both be zero. If ecosystems that are currently responsible for the CO2 fertilisation effect were lost, then the respective negative feedback would be reduced. In other words, protecting ecosystems that are particularly valuable in the context of mitigating the anthropogenic CO2 rise, serves to maintain the strong negative feedback of the land carbon cycle to CO2. It should also be noted that the quantification of the land and ocean carbon cycle to CO2 feedback strength shown in Figure 9.6 refers to changes in the context of anthropogenic climate change, where the rise in CO2 is the dominant driver. For a change in global mean temperature induced by non-CO2 forcing agents, the respective negative feedbacks would be accordingly smaller. However, due to the tight coupling of climate and atmospheric CO2 also over glacial-interglacial cycles, the negative feedbacks to CO2 were at play also in in other climate change contexts.\nIn view of the large C stocks in permafrost and the potential large-scale soil waterlogging and associated CH4 emissions in regions of melting permafrost, the respective climate feedback is potentially strong. However, uncertainties are large (as shown in Figure 9.6) and effects of different processes induce both positive and negative feedbacks. For example, the melting of permafrost can cause additional - previously frozen - soil organic matter to be decomposed. This leads to additional CO2 emissions and a positive feedback to climate. Melting permafrost also enables the northward expansion of the boreal forest biome which leads to increasing C storage in woody biomass and thus to a negative feedback via the carbon balance, but potentially to an additional positive feedback via the associated albedo change. An increase in CH4 emissions from waterlogged soils in permafrost regions causes a positive feedback to climate. The permafrost feedback has received also popular attention as an example of a positive climate feedback (Yaffa 2022) and a separate box was devoted for it in Chapter 5 of the IPCC AR6 (Box 5.1, Canadell et al. (2021)). The example of the permafrost climate feedback illustrates the complexity of the land response to climate where a plethora of different processes induce opposing radiative effects, to a varying degree in different regions across the globe." + "text": "9.5 Feedbacks from the terrestrial biosphere\nEmissions drive atmospheric concentrations and atmospheric concentrations determine the radiative forcing and thus climate. Land-climate feedback loops arise via the atmospheric concentration of CO2 - which affects photosynthesis and thus the carbon balance of terrestrial ecosystems - and via climate - which affects land processes and thereby the emissions of greenhouse gases and albedo (Figure 9.3). The change in climate and CO2 caused by the external forcings drive an additional response of land-mediated biogeochemical and biogeophysical forcing agents and the final change in climate is the combined outcome of the initial external forcing and the feedbacks.\n\n\n\n\n\n\nQuantifying feedbacks with an Earth System Model\n\n\n\nIn the context of Earth system modeling, the “forcing part” of land-mediated changes can be assessed by considering the radiative forcing and climate change (global mean surface temperature change, \\(\\Delta T^\\text{ctrl}\\) in Figure 9.5) in a simulation setup where changes in climate and CO2 are not communicated to the land model component. In contrast, a feedback is triggered by the perturbation of climate and CO2, feeding back to modify land-mediated forcing agents. The final climate change considering forcings and feedbacks is measured by the global mean temperature change in the respective simulation (\\(\\Delta T^\\text{CT}\\) in Figure 9.5). Including the feedbacks requires a coupled Earth system model setup where the land module “sees” changes in climate and CO2. The “feedback part” is then captured by the difference of the coupled and uncoupled simulations.\n\n\n\n\n\nFigure 9.5: Schematic illutstration of two Earth system model setups used for quantifying land-mediated forcings and feedbacks, arising through changes in terrestrial C storage (ΔT), N~O, and CH4 emissions, and albedo changes, and triggered by external forcings, including land use, N-deposition, N-fertiliser inputs, and direct emissions of greenhouse gases to the atmosphere (eEXT). Feedbacks arising through atmospheric CO2 are denoted with a ‘C’ and feedbacks arising through climate change are denoted with a ‘T’. Figure from B. Stocker et al. (2013).\n\n\n\n\n\n\nClimate-land feedbacks are a subset among a larger number of climate feedbacks that operate also in the atmosphere, ocean, and the cryosphere. A climate feedback is commonly defined as a process that drives a change in the energy balance of the climate system as a function the global mean temperature. A positive climate feedback drives an additional energy input, while a negative climate feedback drives an additional energy loss. A discrete set of such climate feedbacks are commonly distinguished Figure 9.6.\n\n9.5.1 The most important physical climate feedbacks\nPlanck response The energy emitted by the Earth (or any material body) through longwave radiation scales with \\(T^4\\) - with the fourth power of the temperature of the emitting body. Therefore, as the Earth’s atmosphere heats up, its loss of radiative energy increases rapidly. The Planck response is therefore a negative feedback and, reflecting the fourth power, it is a particularly strong negative feedback.\nWater vapor plus lapse rate More water vapor can be contained in warmer air, following the Clausius-Clapeyron relationship. Greater vapor content leads to more longwave and shortwave radiation to be absorbed, and this effect is greatest in the upper troposphere (over the tropics). Hence, the additional atmospheric warming reduces the lapse rate (rate at which temperature changes with height in the Atmosphere) and increases the radiation of the warmed troposphere into space. The water vapor feedback alone is positive and strong, while the lapse rate feedback alone is negative and less strong. Since they act in combination, they are commonly quantified as a single feedback. Their combined effect is still a strong positive feedback.\nSurface albedo Increasing temperatures reduce sea ice and seasonal snow cover - on land and on sea ice. This reduces the albedo (Section 7.1.2) and thus increases the absorption of solar radiation at the surface and decreases its reflection into space. Hence, the surface albedo is a positive feedback.\nClouds Different types of clouds exhibit different responses to warming and lead to different effects on the Earth’s energy balance. The uncertainty of this feedback is particularly high.\n\n\n\n\n\nFigure 9.6: An overview of physical and biogeochemical feedbacks in the climate system. (a) Synthesis of physical, biogeophysical and non-carbon dioxide (CO2) biogeochemical feedbacks that are included in the definition of equilibrium climate sensitivity (ECS) assessed in this Technical Summary. These feedbacks have been assessed using multiple lines of evidence including observations, models and theory. The net feedback is the sum of the Planck response, water vapor and lapse rate, surface albedo, cloud, and biogeophysical and non-CO2 biogeochemical feedbacks. Bars denote the mean feedback values, and uncertainties representvery likely ranges; (b) Estimated values of individual biogeophysical and non-CO2 biogeochemical feedbacks. The atmospheric methane (CH4) lifetime and other non-CO2 biogeochemical feedbacks have been calculated using global Earth system model simulations from AerChemMIP, while the CH4 and nitrous oxide (N2O) source responses to climate have been assessed for the year 2100 using a range of modelling approaches using simplified radiative forcing equations. The estimates represent the mean and 5–95% range. The level of confidence in these estimates is lowowing to the large model spread. (c) Carbon-cycle feedbacks as simulated by models participating in the C4MIP of the Coupled Model Intercomparison Project Phase 6 (CMIP6). An independent estimate of the additional positive carbon-cycle climate feedbacks from permafrost thaw, which is not considered in most C4MIP models, is added. Note that the scale of the x-axis in (b) is much smaller than the scale of the other panels. Figure and caption text from the IPCC Assessment Report 6, Technical Summary, Figure TS.17 (Arias et al. 2021).\n\n\n\n\n\n\n9.5.2 Biogeochemical climate feedbacks\nThe land and ocean carbon responses to climate and to CO2 are commonly distinguished. The responses to CO2 induce relatively strong negative feedbacks, but their uncertainty is large, particularly for the land carbon response to CO2. This uncertainty reflects open questions regarding the CO2 fertilisation effect on terrestrial carbon storage (Section 3.4). Increasing atmospheric CO2 also drives CO2 uptake by the ocean (Chapter 14), leading to a negative feedback. The response to climate induce positive feedbacks - a relatively weakly positive one through the ocean response, and a stronger positive but highly uncertain one through the land response. The positive feedback of ocean carbon to climate arises due to the reduced solubility of CO2 in warmed ocean water and reduced ocean mixing in a warm climate. The positive feedback of land carbon to climate arises due to a multitude of processes acting on plant physiology (Section 4.3.6), hydraulic stress through increased vapor pressure deficit of a warmer atmosphere (Section 8.4), tree mortality, enhanced autotrophic and heterotrophic respiration (Chapter 5), and the loss of permafrost (Section 6.4.5). Some land carbon responses to climate also induce negative feedbacks, e.g., the temperature-driven northward expansion of the boreal treeline and associated arctic greening (Keenan and Riley 2018).\nWeaker feedbacks arise through additional biogeochemical processes, most importantly through emissions of CH4 and N2O (B. Stocker et al. 2013), but also through reactive gases that affect the lifetime of CH4 in the atmosphere (Arneth et al. 2010). Chapter Chapter 12 will focus on these non-CO2 greenhouse gases.\nThe strengths of the feedbacks depend on the state of Earth and on the dominant radiative forcing agents that drive the temperature change. For example, if there was no terrestrial biosphere, the positive feedback of land carbon to climate and the negative feedback to CO2 would both be zero. If ecosystems that are currently responsible for the CO2 fertilization effect were lost, then the respective negative feedback would be reduced. In other words, protecting ecosystems that are particularly valuable in the context of mitigating the anthropogenic CO2 rise, serves to maintain the strong negative feedback of the land carbon cycle to CO2. It should also be noted that the quantification of the land and ocean carbon cycle to CO2 feedback strength shown in Figure 9.6 refers to changes in the context of anthropogenic climate change, where the rise in CO2 is the dominant driver. For a change in global mean temperature induced by non-CO2 forcing agents, the respective negative feedbacks would be accordingly smaller. However, due to the tight coupling of climate and atmospheric CO2 also over glacial-interglacial cycles, the negative feedbacks to CO2 were at play also in other climate change contexts.\nIn view of the large C stocks in permafrost and the potential large-scale soil waterlogging and associated CH4 emissions in regions of melting permafrost, the respective climate feedback is potentially strong. However, uncertainties are large (as shown in Figure 9.6) and effects of different processes induce both positive and negative feedbacks. For example, the melting of permafrost can cause additional - previously frozen - soil organic matter to be decomposed. This leads to additional CO2 emissions and a positive feedback to climate. Melting permafrost also enables the northward expansion of the boreal forest biome which leads to increasing C storage in woody biomass and thus to a negative feedback via the carbon balance, but potentially to an additional positive feedback via the associated albedo change. An increase in CH4 emissions from waterlogged soils in permafrost regions causes a positive feedback to climate. The permafrost feedback has received also popular attention as an example of a positive climate feedback (Yaffa 2022) and a separate box was devoted to it in Chapter 5 of the IPCC AR6 (Box 5.1, Canadell et al. (2021)). The example of the permafrost climate feedback illustrates the complexity of the land response to climate where a plethora of different processes induce opposing radiative effects, to a varying degree in different regions across the globe." }, { "objectID": "feedbacks.html#forcings-vs.-feedbacks", "href": "feedbacks.html#forcings-vs.-feedbacks", "title": "9  Earth system feedbacks", "section": "9.6 Forcings vs. feedbacks", - "text": "9.6 Forcings vs. feedbacks\nThe mathematical formalism explained in the blue box below provides a conceptual distinction between forcings and feedbacks. It is often not straight-forward to separate them, especially in an observational setting. In a Earth system model simulation, they can be separated either by uncoupling model components (see Figure 9.5), or by regressing the Earth’s top-of-atmosphere energy flux against the global mean surface temperature. In the example illustrated by Figure 9.7, the atmospheric CO2 concentration is doubled instantaneously. Through the greenhouse effect of CO2, this induces an energy imbalance of the Earth, leading to a net radiative energy flux at the top-of-atmosphere. Over time, the combined effect of all feedbacks in the Earth system lead to a re-equilibration of the energy balance (zero energy imbalance) and to an adjustment of the global mean surface temperature. The points in Figure 9.7 illustrate the trajectory of this re-equilibration. Their regression line can be used to determine the climate sensitivity to a doubling of CO2 (the x-axis intercept), the effective radiative forcing of a doubling of CO2 (the y-axis intercept), and the climate feedback parameter (the slope), representing the sum of all feedbacks operating in the Earth system.\n\n\n\n\n\nFigure 9.7: Schematics of the forcing–feedback framework adopted within the assessment, following Equation 7.1. The figure illustrates how the Earth’s top-of-atmosphere (TOA) net energy flux might evolve for a hypothetical doubling of atmospheric CO2 concentration above pre-industrial levels, where an initial positive energy imbalance (energy entering the Earth system, shown on the y-axis) is gradually restored towards equilibrium as the surface temperature warms (shown on the x-axis). (a) illustrates the definitions of effective radiative forcing (ERF) for the special case of a doubling of atmospheric CO2 concentration, the feedback parameter and the equilibrium climate sensitivity (ECS). (b) illustrates how approximate estimates of these metrics are made within the chapter (IPCC AR6 WG1, Chapter 7) and how these approximations might relate to the exact definitions adopted in panel (a). Figure and caption from Forster et al. (2021).\n\n\n\n\n\n\n\n\n\n\nFeedback formalism\n\n\n\nIt is often challenging to disentangle the energy input by the radiative forcing from the change in the energy input through the feedbacks. In an Earth system modeling context, this separation can be achieved by coupling and de-coupling model components (see Box above). This section introduces a framework for the quantification of climate feedbacks, based the published literature (Friedlingstein et al. 2006; Gregory et al. 2009; Roe 2009) and by the IPCC AR6 in Chapter 7 (Forster et al. 2021).\nConsider the Earth’s climate to be a system responding to a radiative forcing \\(F\\) with a radiative response \\(H\\), so that in equilibrium, the net energy flux into the system \\(N\\) is zero and no warming or cooling occurs. \\[\nN = F - H\\;,\\; N = 0 \\; \\Rightarrow \\; F = H\n\\]\nObservations confirm that \\(H\\) can be linearized with respect to the temperature change \\(\\Delta T\\) (Gregory et al. 2009), so that\n\\[\nF = \\lambda \\cdot \\Delta T %\\; \\Rightarrow \\; \\lambda = \\frac{F}{\\Delta T}\n\\tag{9.1}\\]\n\\(\\lambda\\) is the climate feedback factor given in W m-2 K-1 and is equal to the inverse of the climate sensitivity factor. \\(\\lambda\\) is thus the basic quantity to describe the temperature change of the climate system in response to a given radiative forcing. However, \\(\\lambda\\) summarizes all feedbacks that operate in the Earth system. To quantify an individual feedback, we define a reference system, in which the feedback of interest is not operating. The most basic reference system is to consider the Earth as a Black Body. Figure 9.5 illustrates the case where the reference system considers no feedbacks from the terrestrial biosphere in which the radiative forcing \\(F\\) leads to a temperature change \\(\\Delta T^{\\text{ctrl}}\\) (“ctrl” refers to ‘control’).\n\\[\nF = \\lambda_0 \\cdot \\Delta T^{\\text{ctrl}}\n\\tag{9.2}\\]\nHere, \\(\\lambda_0\\) is the sum of all climate feedbacks that that operate in the reference system. In our case, these are the feedbacks that are not mediated through land processes, including feedbacks from the Black Body response or Planck feedback (BB), water vapor (WV), albedo (\\(\\alpha\\)), lapse rate (LR), cloud (C), ocean carbon (OC), etc.\n\\[\n\\lambda_0 = \\lambda_{\\text{BB}} + \\lambda_{\\text{WV}} + \\lambda_\\alpha + \\lambda_{\\text{LR}} + \\lambda_{\\text{C}} + \\lambda_{\\text{OC}} + \\; ...\n\\]\nNote that in our reference system, the terrestrial biosphere is still affected by external forcings (land use, Nr inputs), which leads to terrestrial greenhouse-gas (GHG) emissions and albedo change, eventually affecting \\(\\Delta T^{\\text{ctrl}}\\).\nWhen a feedback is included, the system adjusts to a different temperature \\(\\Delta T\\) because it now “sees” an additional energy input triggered by the feedback. E.g. a warmer climate stimulates terrestrial N2O emissions which increase its atmospheric concentration and lead to additionally absorbed energy due to its greenhouse effect. In the framework of climate feedbacks, this additional energy input (or loss) is always expressed as being proportional to the global mean surface temperature (\\(\\Delta T\\)). Note however that in reality, the energy gain/loss is not necessarily linear with respect to \\(\\Delta T\\). For example, the energy loss through the Planck response scales with \\(T^4\\). However, considering temperature variations in the context of anthropogenic climate change, this response can be linearised and expressed as a linear function of \\(\\Delta T\\) - as is done for all climate feedbacks.\nLet us now look at “land” as a feedback element in the climate system, interacting via a multitude of feedbacks. We summarize these as \\(r_{\\text{land}}\\). The additional energy loss/gain (\\(\\Delta F\\)) through all land-mediated feedbacks combined are expressed as a linear function of \\(\\Delta T\\): \\[\n\\Delta F = r_{\\text{land}} \\cdot \\Delta T\n\\] \\(r_{\\text{land}}\\) is the strength of all land feedbacks combined, is expressed in W m-2 K-1 - consistent with the values shown in Figure 9.6. It is positive for positive feedbacks. This additional energy gain/loss is considered separately and in addition to the initial radiative forcing \\(F\\) in Equation 9.2. When included, it yields \\(\\Delta T\\) (instead of \\(\\Delta T^\\text{ctrl}\\) when not considering land feedbacks)\n\\[\nF + r_{\\text{land}} \\cdot \\Delta T = \\lambda_0 \\cdot \\Delta T\n\\tag{9.3}\\]\nIt is common to use the negative of \\(r\\) (\\(\\lambda = -r\\)) for expressing the climate feedback factor as the sum of its components. Accordingly: \\[\nF = ( \\lambda_0 + \\lambda_{\\text{land}}) \\; \\Delta T \\;.\n\\tag{9.4}\\]\nEquation 9.3 can be rewritten as \\[\n\\Delta T = \\frac{F}{\\lambda_0} + \\frac{r}{\\lambda_0}\\;\\Delta T\\;,\n\\]\nThis illustrates mathematically that the feedback arises because a fraction \\(f=\\frac{r}{\\lambda_0}\\) of the system output \\(\\Delta T\\) is fed back into the input.\nWe can take a different perspective and characterise the effect of a feedback with the gain factor \\(G=\\frac{\\Delta T}{\\Delta T^{\\text{ctrl}}}\\). By combining Equations Equation 9.2 and Equation 9.3, the gain factor becomes\n\\[\nG=\\frac{\\Delta T}{\\Delta T^{\\text{ctrl}}} = \\frac{\\frac{F}{\\lambda_0-\\lambda_0f}}{\\frac{F}{\\lambda_0}} = \\frac{\\lambda_0}{\\lambda_0-\\lambda_0f} = \\frac{1}{1-f}\n\\]\nNote that \\(f=\\frac{r}{\\lambda_0}\\) is sometimes referred to as the ‘feedback factor’, but not here, where the feedback factor is \\(r = -\\lambda\\). The advantage of the formulation of Equation Equation 9.3 and Equation 9.4 is that individual feedbacks can be added to derive their combined effect.\n\\[\nF = ( \\lambda_0 + \\sum_i \\lambda_{\\text{i}} ) \\; \\Delta T\\;.\n\\]\nNote that \\(f=\\frac{1}{\\lambda_0}\\sum_i r_{\\text{i}}\\) and that \\(G\\neq\\sum_i G_{\\text{i}}\\).\n\n\n\n\n\n\n\n\nFeedbacks versus sensitivities\n\n\n\n\n\nThe strength of feedbacks as quantified by the feedback factor \\(r\\) is determined by the vigour of the cause-and-response chain depicted in Figure 9.5. Feedback factors can be derived as the product of the sensitivity of greenhouse-gas emissions to temperature (\\(\\partial e\\text{GHG}/\\partial T\\)), the sensitivity of atmospheric concentrations to emissions (\\(\\partial c\\text{GHG}/\\partial e\\text{GHG}\\)), and the sensitivity of the radiative forcing to a change in atmospheric concentrations (\\(\\partial F/\\partial c\\text{GHG}\\)).\n\\[\nr = \\frac{\\partial e\\text{GHG}}{\\partial T} \\times \\frac{\\partial c\\text{GHG}}{\\partial e\\text{GHG}} \\times \\frac{\\partial F}{\\partial c\\text{GHG}}\n\\tag{9.5}\\]\nThis is a simplification because it neglects that concentrations are also a function of the sinks (not only emissions), which in turn depend on other factors (e.g., \\(\\Delta T\\) in the case of CH4 ). Furthermore, the \\(r\\) quantified from observations and model simulations in the context of anthropogenic climate change implies that GHG emissions not only reflect the response to changes in climate (\\(\\Delta T\\)) but also to changes in atmospheric CO2 concentrations (cCO2), and that \\(\\Delta T\\) is a function of cCO2 and other forcing agents. To account for the CO2-driven (negative) feedbacks, the sensitivity of GHG emissions to cCO2 (\\(\\partial e\\text{GHG}/\\partial c\\text{CO}_2\\)) has to be included:\n\\[\nr = (\\frac{\\partial e\\text{GHG}}{\\partial T} + \\frac{\\partial e\\text{GHG}}{\\partial c\\text{CO}_2} \\times \\frac{\\partial c\\text{CO}_2}{\\partial T} )\\times \\frac{\\partial c\\text{GHG}}{\\partial e\\text{GHG}} \\times \\frac{\\partial F}{\\partial c\\text{GHG}}\\;\\,\n\\tag{9.6}\\]\nwhere \\(\\partial c\\text{CO}_2/\\partial T\\) is determined by the share of the non-CO2 forcing in the climate change scenario from which \\(r\\) is derived.\nIn the literature (Friedlingstein et al. 2006; Gregory et al. 2009; Roe 2009), sensitivities of terrestrial C storage (\\(\\Delta\\)C) to cCO2 and climate are often referred to as \\(\\beta\\) and \\(\\gamma\\) and are directly linked to feedback factors that would arise if the carbon cycle would respond only to atmospheric CO2 (\\(r_{\\Delta\\text{C}}^{\\text{C}}\\)) and the feedback factor that would arise if the carbon cycle would respond only to climate (\\(r_{\\Delta\\text{C}}^{\\text{T}}\\)).\n\\[\n \\beta_{\\Delta\\text{C}} = \\frac{\\Delta \\text{C}}{\\Delta c\\text{CO}_2} \\sim r_{\\Delta\\text{C}}^{\\text{C}}\n\\]\n\\[\n \\gamma_{\\Delta\\text{C}} = \\frac{\\Delta \\text{C}}{\\Delta T} \\sim r_{\\Delta\\text{C}}^{\\text{T}}\n\\]\nSuch \\(\\beta\\) and \\(\\gamma\\) sensitivities can be quantified also for other forcing agents and can be derived from offline (land-only) simulations by regressing C storage and other GHG emission changes to prescribed temperature or atmospheric cCO2. Thus, more generally:\n\\[\n \\beta = \\frac{\\partial e\\text{GHG}}{\\partial c\\text{CO}_2} \\sim r^{\\text{C}}\n\\] \\[\n \\gamma = \\frac{\\partial e\\text{GHG}}{\\partial T} \\sim r^{\\text{T}}\n\\]\nEstimates for \\(\\beta\\) and \\(\\gamma\\) can then be used to calculate feedback factors \\(r^{\\text{CT}}\\) without having to rely on coupled land-climate models. However, assumptions have to be made.:\n\nFor the conversion of an emission change to a change in concentrations (\\(\\partial c\\text{GHG}/\\partial e\\text{GHG}\\)), equilibrium of atmospheric concentration after the perturbation of emissions is usually assumed. For greenhouse-gases with a long atmospheric lifetime (e.g., N2O ), such an equilibrium is only reached on time scales of centuries after a stabilisation of emissions. Feedback factors are often quantified from transient siemulations where no equilibrium is reached yet, and thus represent transient feedbacks. For \\(\\Delta\\)C and associated terrestrial CO2 emissions, no such equilibrium can be defined as the airborne fraction of a perturbation \\(\\Delta c\\text{CO}_2/\\Delta e\\text{CO}_2\\) depends on the time scale of interest.\nRelatively simple functions can be applied for \\(\\partial F/\\partial c\\text{GHG}\\) to convert a concentration change into a radiative forcing (Joos et al. 2001). However, the non-linearity of these functions implies that the background (initial) concentration has to be defined. In other words, the radiative forcing of a unit greenhouse gas concentration declines at high concentrations and thus reduces the respective feedback factor.\nFeedback factors \\(r\\) are expressed with respect to \\(\\Delta T\\), while values are often derived from observational records where cCO2 co-varied with \\(\\Delta T\\) (Torn and Harte 2006). Thus, derived values for \\(r\\) are subject to the share of CO2 versus non-CO2 forcings (scenario dependence), as expressed by \\(\\partial c\\text{CO}_2/\\partial T\\) in Equation 9.6.\nAtmospheric sink processes of greenhouse gases may depend on climate. This inhibits a linear and constant relationship between emissions and concentrations.\n\nFeedback factors \\(r\\) have the advantage that the feedback strengths of different forcing agents to different drivers (climate and cCO2 ) have the same units (Wm\\(^{-2}\\)K\\(^{-1}\\)) and can be compared. However, Earth system state-dependency and the contribution of CO2 to the radiative forcing complicates the comparison of values derived from different simulations and observations. \\(\\beta\\)- and \\(\\gamma\\)-sensitivities are more robust in that respect as they are normalised to the change in temperature and cCO2 individually, but their different units prevent a comparison of their relative importance in the coupled Earth system.\n\n\n\n\n\n\n\n\n\n\nArias, P. A., N. Bellouin, E. Coppola, R. G. Jones, G. Krinner, J. Marotzke, V. Naik, et al. 2021. “Technical Summary.” Book Section. In Climate Change 2021: The Physical Science Basis. Contribution of Working Group i to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, edited by V. Masson-Delmotte, P. Zhai, A. Pirani, S. L. Connors, C. Péan, S. Berger, N. Caud, et al. Cambridge, UK; New York, NY, USA: Cambridge University Press. https://doi.org/10.1017/9781009157896.002.\n\n\nArneth, A., S. P. Harrison, S. Zaehle, K. Tsigaridis, S. Menon, P. J. Bartlein, J. Feichter, et al. 2010. “Terrestrial Biogeochemical Feedbacks in the Climate System.” Nature Geoscience 3 (8): 525–32. https://doi.org/10.1038/ngeo905.\n\n\nBala, G., K. Caldeira, M. Wickett, T. J. Phillips, D. B. Lobell, C. Delire, and A. Mirin. 2007. “Combined Climate and Carbon-Cycle Effects of Large-Scale Deforestation.” Proceedings of the National Academy of Sciences 104 (16): 6550–55. https://doi.org/10.1073/pnas.0608998104.\n\n\nBonan, Gordon B. 2008. “Forests and Climate Change: Forcings, Feedbacks, and the Climate Benefits of Forests.” Science 320 (5882): 1444–49. https://doi.org/10.1126/science.1155121.\n\n\nCanadell, J. G., P. M. S. Monteiro, M. H. Costa, L. Cotrim da Cunha, P. M. Cox, A. V. Eliseev, S. Henson, et al. 2021. “Global Carbon and Other Biogeochemical Cycles and Feedbacks.” Book Section. In Climate Change 2021: The Physical Science Basis. Contribution of Working Group i to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, edited by V. Masson-Delmotte, P. Zhai, A. Pirani, S. L. Connors, C. Péan, S. Berger, N. Caud, et al., 673–815. Cambridge, UK; New York, NY, USA: Cambridge University Press. https://doi.org/10.1017/9781009157896.007.\n\n\nFluet-Chouinard, Etienne, Benjamin D. Stocker, Zhen Zhang, Avni Malhotra, Joe R. Melton, Benjamin Poulter, Jed O. Kaplan, et al. 2023. “Extensive Global Wetland Loss over the Past Three Centuries.” Nature 614 (7947): 281–86. https://doi.org/10.1038/s41586-022-05572-6.\n\n\nForster, P., T. Storelvmo, K. Armour, W. Collins, J.-L. Dufresne, D. Frame, D. J. Lunt, et al. 2021. “The Earth’s Energy Budget, Climate Feedbacks, and Climate Sensitivity.” Book Section. In Climate Change 2021: The Physical Science Basis. Contribution of Working Group i to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, edited by V. Masson-Delmotte, P. 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Heinz Erb, Fridolin Krausmann, Veronika Gaube, Alberte Bondeau, Christoph Plutzar, Simone Gingrich, Wolfgang Lucht, and Marina Fischer-Kowalski. 2007. “Quantifying and Mapping the Human Appropriation of Net Primary Production in Earth’s Terrestrial Ecosystems.” Proceedings of the National Academy of Sciences 104 (31): 12942–47. https://doi.org/10.1073/pnas.0704243104.\n\n\nJoos, Fortunat, I. Colin Prentice, Stephen Sitch, Robert Meyer, Georg Hooss, Gian-Kasper Plattner, Stefan Gerber, and Klaus Hasselmann. 2001. “Global Warming Feedbacks on Terrestrial Carbon Uptake Under the Intergovernmental Panel on Climate Change (IPCC) Emission Scenarios.” Global Biogeochemical Cycles 15 (4): 891–907. https://doi.org/10.1029/2000GB001375.\n\n\nKeenan, T. F., and W. J. Riley. 2018. “Greening of the Land Surface in the World’s Cold Regions Consistent with Recent Warming.” Nature Climate Change 8 (9): 825–28. https://doi.org/10.1038/s41558-018-0258-y.\n\n\nMacFarling Meure, C., D. Etheridge, C. Trudinger, P. Steele, R. Langenfelds, T. van Ommen, A. Smith, and J. Elkins. 2006. “Law Dome CO2, CH4 and N2O Ice Core Records Extended to 2000 Years BP.” Geophysical Research Letters 33 (14). https://doi.org/10.1029/2006GL026152.\n\n\nRamankutty, Navin, Amato T. Evan, Chad Monfreda, and Jonathan A. Foley. 2008. “Farming the Planet: 1. Geographic Distribution of Global Agricultural Lands in the Year 2000.” Global Biogeochemical Cycles 22 (1). https://doi.org/10.1029/2007GB002952.\n\n\nRoe, Gerard. 2009. “Feedbacks, Timescales, and Seeing Red.” Annual Review of Earth and Planetary Sciences 37 (1): 93–115. https://doi.org/10.1146/annurev.earth.061008.134734.\n\n\nSiegenthaler, Urs, Eric Monnin, Kenji Kawamura, Renato Spahni, Jakob Schwander, Bernhard Stauffer, Thomas F. Stocker, Jean-Marc Barnola, and Hubertus Fischer. 2005. “Supporting Evidence from the EPICA Dronning Maud Land Ice Core for Atmospheric CO2 Changes During the Past Millennium.” Tellus B 57 (1): 51–57. https://doi.org/10.1111/j.1600-0889.2005.00131.x.\n\n\nSitch, S., P. M. Cox, W. J. Collins, and C. Huntingford. 2007. “Indirect Radiative Forcing of Climate Change Through Ozone Effects on the Land-Carbon Sink.” Nature 448 (7155): 791–94. https://doi.org/10.1038/nature06059.\n\n\nStocker, Benjamin David, Zicheng Yu, Charly Massa, and Fortunat Joos. 2017. “Holocene Peatland and Ice-Core Data Constraints on the Timing and Magnitude of CO2 Emissions from Past Land Use.” Proceedings of the National Academy of Sciences 114 (7): 1492–97. https://doi.org/10.1073/pnas.1613889114.\n\n\nStocker, Benjamin, Raphael Roth, Fortunat Joos, Renato Spahni, Marco Steinacher, Soenke Zaehle, Lex Bouwman, Xu-Ri, and Iain Colin Prentice. 2013. “Multiple Greenhouse-Gas Feedbacks from the Land Biosphere Under Future Climate Change Scenarios.” Nature Climate Change 3 (7): 666–72. https://doi.org/10.1038/nclimate1864.\n\n\nTarnocai, C., J. G. Canadell, E. a. G. Schuur, P. Kuhry, G. Mazhitova, and S. Zimov. 2009. “Soil Organic Carbon Pools in the Northern Circumpolar Permafrost Region.” Global Biogeochemical Cycles 23 (2). https://doi.org/10.1029/2008GB003327.\n\n\nTorn, Margaret S., and John Harte. 2006. “Missing Feedbacks, Asymmetric Uncertainties, and the Underestimation of Future Warming.” Geophysical Research Letters 33 (10). https://doi.org/10.1029/2005GL025540.\n\n\nVitousek, Peter M., Paul R. Ehrlich, Anne H. Ehrlich, and Pamela A. Matson. 1986. “Human Appropriation of the Products of Photosynthesis.” BioScience 36 (6): 368–73. https://doi.org/10.2307/1310258.\n\n\nWanner, Heinz, Jürg Beer, Jonathan Bütikofer, Thomas J. Crowley, Ulrich Cubasch, Jacqueline Flückiger, Hugues Goosse, et al. 2008. “Mid- to Late Holocene Climate Change: An Overview.” Quaternary Science Reviews 27 (19): 1791–1828. https://doi.org/10.1016/j.quascirev.2008.06.013.\n\n\nWikimedia. 2024. “Feedback.” Wikipedia. https://en.wikipedia.org/w/index.php?title=Feedback&oldid=1238858215.\n\n\nYaffa, Joshua. 2022. “The Great Siberian Thaw.” The New Yorker, January. https://www.newyorker.com/magazine/2022/01/17/the-great-siberian-thaw.\n\n\nYu, Zicheng, Julie Loisel, Daniel P. Brosseau, David W. Beilman, and Stephanie J. Hunt. 2010. “Global Peatland Dynamics Since the Last Glacial Maximum.” Geophysical Research Letters 37 (13). https://doi.org/10.1029/2010GL043584." + "text": "9.6 Forcings vs. feedbacks\nThe mathematical formalism explained in the blue box below provides a conceptual distinction between forcings and feedbacks. It is often not straight-forward to separate them, especially in an observational setting. In an Earth system model simulation, they can be separated either by uncoupling model components (see Figure 9.5), or by regressing the Earth’s top-of-atmosphere energy flux against the global mean surface temperature. In the example illustrated by Figure 9.7, the atmospheric CO2 concentration is doubled instantaneously. Through the greenhouse effect of CO2, this induces an energy imbalance of the Earth, leading to a net radiative energy flux at the top-of-atmosphere. Over time, the combined effects of all feedbacks in the Earth system lead to a re-equilibration of the energy balance (zero energy imbalance) and to an adjustment of the global mean surface temperature. The points in Figure 9.7 illustrate the trajectory of this re-equilibration. Their regression line can be used to determine the climate sensitivity to a doubling of CO2 (the x-axis intercept), the effective radiative forcing of a doubling of CO2 (the y-axis intercept), and the climate feedback parameter (the slope), representing the sum of all feedbacks operating in the Earth system.\n\n\n\n\n\nFigure 9.7: Schematics of the forcing–feedback framework adopted within the assessment, following Equation 7.1. The figure illustrates how the Earth’s top-of-atmosphere (TOA) net energy flux might evolve for a hypothetical doubling of atmospheric CO2 concentration above pre-industrial levels, where an initial positive energy imbalance (energy entering the Earth system, shown on the y-axis) is gradually restored towards equilibrium as the surface temperature warms (shown on the x-axis). (a) illustrates the definitions of effective radiative forcing (ERF) for the special case of a doubling of atmospheric CO2 concentration, the feedback parameter and the equilibrium climate sensitivity (ECS). (b) illustrates how approximate estimates of these metrics are made within the chapter (IPCC AR6 WG1, Chapter 7) and how these approximations might relate to the exact definitions adopted in panel (a). Figure and caption from Forster et al. (2021).\n\n\n\n\n\n\n\n\n\n\nFeedback formalism\n\n\n\nIt is often challenging to disentangle the energy input by the radiative forcing from the change in the energy input through the feedbacks. In an Earth system modeling context, this separation can be achieved by coupling and decoupling model components (see Box above). This section introduces a framework for the quantification of climate feedbacks, based on the published literature (Friedlingstein et al. 2006; Gregory et al. 2009; Roe 2009) and by the IPCC AR6 in Chapter 7 (Forster et al. 2021).\nConsider the Earth’s climate to be a system responding to a radiative forcing \\(F\\) with a radiative response \\(H\\), so that in equilibrium, the net energy flux into the system \\(N\\) is zero and no warming or cooling occurs. \\[\nN = F - H\\;,\\; N = 0 \\; \\Rightarrow \\; F = H\n\\]\nObservations confirm that \\(H\\) can be linearized with respect to the temperature change \\(\\Delta T\\) (Gregory et al. 2009), so that\n\\[\nF = \\lambda \\cdot \\Delta T %\\; \\Rightarrow \\; \\lambda = \\frac{F}{\\Delta T}\n\\tag{9.1}\\]\n\\(\\lambda\\) is the climate feedback factor given in W m-2 K-1 and is equal to the inverse of the climate sensitivity factor. \\(\\lambda\\) is thus the basic quantity to describe the temperature change of the climate system in response to a given radiative forcing. However, \\(\\lambda\\) summarizes all feedbacks that operate in the Earth system. To quantify an individual feedback, we define a reference system, in which the feedback of interest is not operating. The most basic reference system is to consider the Earth as a Black Body. Figure 9.5 illustrates the case where the reference system considers no feedbacks from the terrestrial biosphere in which the radiative forcing \\(F\\) leads to a temperature change \\(\\Delta T^{\\text{ctrl}}\\) (“ctrl” refers to ‘control’).\n\\[\nF = \\lambda_0 \\cdot \\Delta T^{\\text{ctrl}}\n\\tag{9.2}\\]\nHere, \\(\\lambda_0\\) is the sum of all climate feedbacks that operate in the reference system. In our case, these are the feedbacks that are not mediated through land processes, including feedbacks from the Black Body response or Planck feedback (BB), water vapor (WV), albedo (\\(\\alpha\\)), lapse rate (LR), cloud (C), ocean carbon (OC), etc.\n\\[\n\\lambda_0 = \\lambda_{\\text{BB}} + \\lambda_{\\text{WV}} + \\lambda_\\alpha + \\lambda_{\\text{LR}} + \\lambda_{\\text{C}} + \\lambda_{\\text{OC}} + \\; ...\n\\]\nNote that in our reference system, the terrestrial biosphere is still affected by external forcings (land use, Nr inputs), which leads to terrestrial greenhouse-gas (GHG) emissions and albedo change, eventually affecting \\(\\Delta T^{\\text{ctrl}}\\).\nWhen a feedback is included, the system adjusts to a different temperature \\(\\Delta T\\) because it now “sees” an additional energy input triggered by the feedback. E.g. a warmer climate stimulates terrestrial N2O emissions which increase its atmospheric concentration and lead to additionally absorbed energy due to its greenhouse effect. In the framework of climate feedbacks, this additional energy input (or loss) is always expressed as being proportional to the global mean surface temperature (\\(\\Delta T\\)). Note however that in reality, the energy gain/loss is not necessarily linear with respect to \\(\\Delta T\\). For example, the energy loss through the Planck response scales with \\(T^4\\). However, considering temperature variations in the context of anthropogenic climate change, this response can be linearised and expressed as a linear function of \\(\\Delta T\\) - as is done for all climate feedbacks.\nLet us now look at “land” as a feedback element in the climate system, interacting via a multitude of feedbacks. We summarize these as \\(r_{\\text{land}}\\). The additional energy loss/gain (\\(\\Delta F\\)) through all land-mediated feedbacks combined are expressed as a linear function of \\(\\Delta T\\): \\[\n\\Delta F = r_{\\text{land}} \\cdot \\Delta T\n\\] \\(r_{\\text{land}}\\) is the strength of all land feedbacks combined, is expressed in W m-2 K-1 - consistent with the values shown in Figure 9.6. It is positive for positive feedbacks. This additional energy gain/loss is considered separately and in addition to the initial radiative forcing \\(F\\) in Equation 9.2. When included, it yields \\(\\Delta T\\) (instead of \\(\\Delta T^\\text{ctrl}\\) when not considering land feedbacks)\n\\[\nF + r_{\\text{land}} \\cdot \\Delta T = \\lambda_0 \\cdot \\Delta T\n\\tag{9.3}\\]\nIt is common to use the negative of \\(r\\) (\\(\\lambda = -r\\)) for expressing the climate feedback factor as the sum of its components. Accordingly: \\[\nF = ( \\lambda_0 + \\lambda_{\\text{land}}) \\; \\Delta T \\;.\n\\tag{9.4}\\]\nEquation 9.3 can be rewritten as \\[\n\\Delta T = \\frac{F}{\\lambda_0} + \\frac{r}{\\lambda_0}\\;\\Delta T\\;,\n\\]\nThis illustrates mathematically that the feedback arises because a fraction \\(f=\\frac{r}{\\lambda_0}\\) of the system output \\(\\Delta T\\) is fed back into the input.\nWe can take a different perspective and characterise the effect of a feedback with the gain factor \\(G=\\frac{\\Delta T}{\\Delta T^{\\text{ctrl}}}\\). By combining Equations Equation 9.2 and Equation 9.3, the gain factor becomes\n\\[\nG=\\frac{\\Delta T}{\\Delta T^{\\text{ctrl}}} = \\frac{\\frac{F}{\\lambda_0-\\lambda_0f}}{\\frac{F}{\\lambda_0}} = \\frac{\\lambda_0}{\\lambda_0-\\lambda_0f} = \\frac{1}{1-f}\n\\]\nNote that \\(f=\\frac{r}{\\lambda_0}\\) is sometimes referred to as the ‘feedback factor’, but not here, where the feedback factor is \\(r = -\\lambda\\). The advantage of the formulation of Equation Equation 9.3 and Equation 9.4 is that individual feedbacks can be added to derive their combined effect.\n\\[\nF = ( \\lambda_0 + \\sum_i \\lambda_{\\text{i}} ) \\; \\Delta T\\;.\n\\]\nNote that \\(f=\\frac{1}{\\lambda_0}\\sum_i r_{\\text{i}}\\) and that \\(G\\neq\\sum_i G_{\\text{i}}\\).\n\n\n\n\n\n\n\n\nFeedbacks versus sensitivities\n\n\n\n\n\nThe strength of feedbacks as quantified by the feedback factor \\(r\\) is determined by the vigour of the cause-and-response chain depicted in Figure 9.5. Feedback factors can be derived as the product of the sensitivity of greenhouse-gas emissions to temperature (\\(\\partial e\\text{GHG}/\\partial T\\)), the sensitivity of atmospheric concentrations to emissions (\\(\\partial c\\text{GHG}/\\partial e\\text{GHG}\\)), and the sensitivity of the radiative forcing to a change in atmospheric concentrations (\\(\\partial F/\\partial c\\text{GHG}\\)).\n\\[\nr = \\frac{\\partial e\\text{GHG}}{\\partial T} \\times \\frac{\\partial c\\text{GHG}}{\\partial e\\text{GHG}} \\times \\frac{\\partial F}{\\partial c\\text{GHG}}\n\\tag{9.5}\\]\nThis is a simplification because it neglects that concentrations are also a function of the sinks (not only emissions), which in turn depend on other factors (e.g., \\(\\Delta T\\) in the case of CH4 ). Furthermore, the \\(r\\) quantified from observations and model simulations in the context of anthropogenic climate change implies that GHG emissions not only reflect the response to changes in climate (\\(\\Delta T\\)) but also to changes in atmospheric CO2 concentrations (cCO2), and that \\(\\Delta T\\) is a function of cCO2 and other forcing agents. To account for the CO2-driven (negative) feedbacks, the sensitivity of GHG emissions to cCO2 (\\(\\partial e\\text{GHG}/\\partial c\\text{CO}_2\\)) has to be included:\n\\[\nr = (\\frac{\\partial e\\text{GHG}}{\\partial T} + \\frac{\\partial e\\text{GHG}}{\\partial c\\text{CO}_2} \\times \\frac{\\partial c\\text{CO}_2}{\\partial T} )\\times \\frac{\\partial c\\text{GHG}}{\\partial e\\text{GHG}} \\times \\frac{\\partial F}{\\partial c\\text{GHG}}\\;\\,\n\\tag{9.6}\\]\nwhere \\(\\partial c\\text{CO}_2/\\partial T\\) is determined by the share of the non-CO2 forcing in the climate change scenario from which \\(r\\) is derived.\nIn the literature (Friedlingstein et al. 2006; Gregory et al. 2009; Roe 2009), sensitivities of terrestrial C storage (\\(\\Delta\\)C) to cCO2 and climate are often referred to as \\(\\beta\\) and \\(\\gamma\\) and are directly linked to feedback factors that would arise if the carbon cycle would respond only to atmospheric CO2 (\\(r_{\\Delta\\text{C}}^{\\text{C}}\\)) and the feedback factor that would arise if the carbon cycle would respond only to climate (\\(r_{\\Delta\\text{C}}^{\\text{T}}\\)).\n\\[\n \\beta_{\\Delta\\text{C}} = \\frac{\\Delta \\text{C}}{\\Delta c\\text{CO}_2} \\sim r_{\\Delta\\text{C}}^{\\text{C}}\n\\]\n\\[\n \\gamma_{\\Delta\\text{C}} = \\frac{\\Delta \\text{C}}{\\Delta T} \\sim r_{\\Delta\\text{C}}^{\\text{T}}\n\\]\nSuch \\(\\beta\\) and \\(\\gamma\\) sensitivities can be quantified also for other forcing agents and can be derived from offline (land-only) simulations by regressing C storage and other GHG emission changes to prescribed temperature or atmospheric cCO2. Thus, more generally:\n\\[\n \\beta = \\frac{\\partial e\\text{GHG}}{\\partial c\\text{CO}_2} \\sim r^{\\text{C}}\n\\] \\[\n \\gamma = \\frac{\\partial e\\text{GHG}}{\\partial T} \\sim r^{\\text{T}}\n\\]\nEstimates for \\(\\beta\\) and \\(\\gamma\\) can then be used to calculate feedback factors \\(r^{\\text{CT}}\\) without having to rely on coupled land-climate models. However, assumptions have to be made.:\n\nFor the conversion of an emission change to a change in concentrations (\\(\\partial c\\text{GHG}/\\partial e\\text{GHG}\\)), equilibrium of atmospheric concentration after the perturbation of emissions is usually assumed. For greenhouse-gases with a long atmospheric lifetime (e.g., N2O ), such an equilibrium is only reached on time scales of centuries after stabilization of emissions. Feedback factors are often quantified from transient simulations where no equilibrium is reached yet, and thus represent transient feedbacks. For \\(\\Delta\\)C and associated terrestrial CO2 emissions, no such equilibrium can be defined as the airborne fraction of a perturbation \\(\\Delta c\\text{CO}_2/\\Delta e\\text{CO}_2\\) depends on the time scale of interest.\nRelatively simple functions can be applied for \\(\\partial F/\\partial c\\text{GHG}\\) to convert a concentration change into a radiative forcing (Joos et al. 2001). However, the non-linearity of these functions implies that the background (initial) concentration has to be defined. In other words, the radiative forcing of a unit greenhouse gas concentration declines at high concentrations and thus reduces the respective feedback factor.\nFeedback factors \\(r\\) are expressed with respect to \\(\\Delta T\\), while values are often derived from observational records where cCO2 co-varied with \\(\\Delta T\\) (Torn and Harte 2006). Thus, derived values for \\(r\\) are subject to the share of CO2 versus non-CO2 forcings (scenario dependence), as expressed by \\(\\partial c\\text{CO}_2/\\partial T\\) in Equation 9.6.\nAtmospheric sink processes of greenhouse gases may depend on climate. This inhibits a linear and constant relationship between emissions and concentrations.\n\nFeedback factors \\(r\\) have the advantage that the feedback strengths of different forcing agents to different drivers (climate and cCO2 ) have the same units (Wm\\(^{-2}\\)K\\(^{-1}\\)) and can be compared. 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