Version 2

Absolute Salinity Anomaly extended to cover all areas of the ocean

Toolbox/gsw_CT_first_derivatives.m

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+function [CT_SA, CT_pt] = gsw_CT_first_derivatives(SA,pt)
+
+% gsw_CT_first_derivatives    first derivatives of Conservative Temperature
+%==========================================================================
+%
+% USAGE:
+%  [CT_SA, CT_pt] = gsw_CT_first_derivatives(SA,pt)
+%
+% DESCRIPTION:
+%  Calculates the following two derivatives of Conservative Temperature
+%  (1) CT_SA, the derivative with respect to Absolute Salinity at 
+%      constant potential temperature (with pr = 0 dbar), and
+%   2) CT_pt, the derivative with respect to potential temperature
+%      (the regular potential temperature which is referenced to 0 dbar)
+%      at constant Absolute Salinity.
+%
+% INPUT:
+%  SA  =  Absolute Salinity                                        [ g/kg ]
+%  pt  =  potential temperature (ITS-90)                          [ deg C ]   
+%         (whose reference pressure is 0 dbar)
+%
+%  SA & pt need to have the same dimensions.
+%
+% OUTPUT:
+%  CT_SA  =  The derivative of Conservative Temperature with respect to 
+%            Absolute Salinity at constant potential temperature 
+%            (the regular potential temperature which has reference 
+%            sea pressure of 0 dbar). The CT_SA output has units of:   
+%                                                               [ K/(g/kg)]
+%  CT_pt  =  The derivative of Conservative Temperature with respect to 
+%            potential temperature (the regular one with pr = 0 dbar)
+%            at constant SA. CT_pt is dimensionless.           [ unitless ]
+%
+% AUTHOR: 
+%  Trevor McDougall and Paul Barker   [ [email protected] ]
+%
+% VERSION NUMBER: 2.0 (26th August, 2010)
+%
+% REFERENCES:
+%  IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of 
+%   seawater - 2010: Calculation and use of thermodynamic properties.  
+%   Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
+%   UNESCO (English), 196 pp.  Available from http://www.TEOS-10.org.  
+%    See Eqns. (A.12.3) and (A.12.9a,b) of this TEOS-10 Manual.   
+%
+% McDougall T. J., D. R. Jackett, P. M. Barker, C. Roberts-Thomson, R.
+%  Feistel and R. W. Hallberg, 2010:  A computationally efficient 25-term 
+%  expression for the density of seawater in terms of Conservative 
+%  Temperature, and related properties of seawater.  To be submitted 
+%  to Ocean Science Discussions. 
+%
+%  This software is available from http://www.TEOS-10.org
+%
+%==========================================================================
+
+%--------------------------------------------------------------------------
+% Check variables and resize if necessary
+%--------------------------------------------------------------------------
+
+if ~(nargin == 2)
+   error('gsw_CT_first_derivatives:  Requires two inputs')
+end %if
+
+if ~(nargout == 2)
+   error('gsw_CT_first_derivatives:  Requires two outputs')
+end %if
+
+[ms,ns] = size(SA);
+[mt,nt] = size(pt);
+
+if (mt ~= ms | nt ~= ns)
+    error('gsw_CT_first_derivatives: SA and t must have same dimensions')
+end
+
+if ms == 1
+    SA = SA';
+    pt = pt';
+    transposed = 1;
+else
+    transposed = 0;
+end
+
+%--------------------------------------------------------------------------
+% Start of the calculation
+%--------------------------------------------------------------------------
+
+cp0 = 3991.86795711963;             % from Eqn. 3.3.3 of IOC et al. (2010).
+n0 = 0; 
+n1 = 1;
+n2 = 2;
+pr0 = zeros(size(SA));
+abs_pt = 273.15 + pt; 
+
+CT_SA = (gsw_gibbs(n1,n0,n0,SA,pt,pr0) -...
+               abs_pt.*gsw_gibbs(n1,n1,n0,SA,pt,pr0))./cp0;
+
+CT_pt = - (abs_pt.*gsw_gibbs(n0,n2,n0,SA,pt,pr0))./cp0;
+
+if transposed
+    CT_SA = CT_SA';
+    CT_pt = CT_pt';
+end
+
+end

Toolbox/gsw_CT_from_entropy.m

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+function CT = gsw_CT_from_entropy(SA,entropy)
+
+% gsw_CT_from_entropy                         Conservative Temperature with
+%                                                          entropy as input
+% =========================================================================
+%
+% USAGE:
+%   CT = gsw_CT_from_entropy(SA,entropy)
+%
+% DESCRIPTION:
+%  Calculates Conservative Temperature with entropy as an input variable.  
+%
+% INPUT:
+%  SA       =   Absolute Salinity                                  [ g/kg ]
+%  entropy  =   specific entropy                                  [ deg C ]
+%
+%  SA & entropy need to have the same dimensions.
+%
+% OUTPUT:
+%  CT   =  Conservative Temperature                               [ deg C ]
+%
+% AUTHOR:  
+%  Trevor McDougall and Paul Barker.       [ [email protected] ]
+%
+% VERSION NUMBER: 2.0 (13th October, 2010)
+%
+% REFERENCES:
+%  IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of
+%   seawater - 2010: Calculation and use of thermodynamic properties.
+%   Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
+%   UNESCO (English), 196 pp.  Available from http://www.TEOS-10.org
+%    See appendix  A.10 of this TEOS-10 Manual. 
+%
+%  The software is available from http://www.TEOS-10.org
+%
+%==========================================================================
+
+%--------------------------------------------------------------------------
+% Check variables and resize if necessary
+%--------------------------------------------------------------------------
+
+if ~(nargin == 2)
+    error('gsw_pt_from_entropy: Requires 2 inputs - Absolute Salinity and entropy')
+end %if
+
+[ms,ns] = size(SA);
+[me,ne] = size(entropy);
+
+if (ms ~= me | ns ~= ne )
+    error('gsw_pt_from_entropy: Input arguments do not have the same dimensions')
+end %if
+
+if ms == 1
+    SA = SA';
+    entropy = entropy';
+    transposed = 1;
+else
+    transposed = 0;
+end
+
+%--------------------------------------------------------------------------
+% Start of the calculation
+%--------------------------------------------------------------------------
+
+% These few lines ensure that SA is non-negative.
+[I_neg_SA] = find(SA < 0);
+if ~isempty(I_neg_SA)
+    SA(I_neg_SA) = 0;
+end
+
+pt = gsw_pt_from_entropy(SA,entropy);
+CT = gsw_CT_from_pt(SA,pt);
+
+if transposed
+    CT = CT';
+end
+
+end