gsw_entropy_first_derivatives.m

function [eta_SA, eta_CT] = gsw_entropy_first_derivatives(SA,CT)

% gsw_entropy_first_derivatives                first derivatives of entropy
% =========================================================================
%
% USAGE:
%  [eta_SA, eta_CT] = gsw_eta_first_derivatives(SA,CT)
%
% DESCRIPTION:
%  Calculates the following two partial derivatives of specific entropy
%  (eta) 
%   (1) eta_SA, the derivative with respect to Absolute Salinity at 
%       constant Conservative Temperature, and
%   (2) eta_CT, the derivative with respect to Conservative Temperature at 
%       constant Absolute Salinity. 
%
% INPUT:
%  SA  =  Absolute Salinity                                        [ g/kg ]
%  CT  =  Conservative Temperature (ITS-90)                       [ deg C ]
%
%  SA & CT need to have the same dimensions.
%
% OUTPUT:
%  eta_SA =  The derivative of specific entropy with respect to 
%            Absolute Salinity (in units of g kg^-1) at constant  
%            Conservative Temperature.  
%            eta_SA has units of:         [ J/(kg K(g/kg))]  or [ J/(g K) ]
%  eta_CT =  The derivative of specific entropy with respect to 
%            Conservative Temperature at constant Absolute Salinity.
%            eta_CT has units of:                            [ J/(kg K^2) ]
%
% AUTHOR: 
%  Trevor McDougall.                                   [ help@teos-10.org ]
%      
% VERSION NUMBER: 3.05 (27th January 2015)
%
% 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.12.8) and (P.14a,c) of this TEOS-10 Manual.   
%
%  This software is available from http://www.TEOS-10.org
%
%==========================================================================

%--------------------------------------------------------------------------
% Check variables and resize if necessary
%--------------------------------------------------------------------------

if ~(nargin == 2)
   error('gsw_entropy_first_derivatives:  Requires two inputs')
end %if

if ~(nargout == 2)
   error('gsw_entropy_first_derivatives:  Requires two outputs')
end %if

[ms,ns] = size(SA);
[mt,nt] = size(CT);

if (mt ~= ms | nt ~= ns)
    error('gsw_entropy_first_derivatives: SA and CT must have same dimensions')
end
if ms == 1
    SA = SA.';
    CT = CT.';
    transposed = 1;
else
    transposed = 0;
end

%--------------------------------------------------------------------------
% Start of the calculation
%--------------------------------------------------------------------------

T0 = gsw_T0;
pr0 = zeros(size(SA)); 
pt = gsw_pt_from_CT(SA,CT);

eta_SA = -(gsw_gibbs(1,0,0,SA,pt,pr0))./(T0 + pt);

eta_CT = (gsw_cp0*ones(size(pt)))./(T0 + pt);

if transposed
    eta_SA = eta_SA.';
    eta_CT = eta_CT.';
end

end