gsw_enthalpy_diff_CT_exact.m

function enthalpy_diff_CT_exact = gsw_enthalpy_diff_CT_exact(SA,CT,p_shallow,p_deep)

% gsw_enthalpy_diff_CT_exact        difference of enthalpy at two pressures
%==========================================================================
%
% USAGE:
%  enthalpy_diff_CT_exact = gsw_enthalpy_diff_CT_exact(SA,CT,p_shallow,p_deep)
%
% DESCRIPTION:
%  Calculates the difference of the specific enthalpy of seawater between 
%  two different pressures, p_deep (the deeper pressure) and p_shallow
%  (the shallower pressure), at the same values of SA and CT.  The output
%  (enthalpy_diff_CT_exact) is the specific enthalpy evaluated at 
%  (SA,CT,p_deep) minus the specific enthalpy at (SA,CT,p_shallow). 
%
%  Note that this function uses the full Gibbs function.  There is an 
%  alternative to calling this function, namely gsw_enthalpy_diff(SA,CT,p),
%  which uses the computationally efficient 75-term expression for specific
%  volume in terms of SA, CT and p (Roquet et al., 2015).   
%
% INPUT:
%  SA        =  Absolute Salinity                                  [ g/kg ]
%  CT        =  Conservative Temperature (ITS-90)                 [ deg C ]
%  p_shallow =  upper sea pressure                                 [ dbar ]
%               ( i.e. shallower absolute pressure - 10.1325 dbar ) 
%  p_deep    =  lower sea pressure                                 [ dbar ]
%               ( i.e. deeper absolute pressure - 10.1325 dbar )
%
%  p_shallow and p_deep may have dimensions Mx1 or 1xN or MxN, 
%  where SA and CT are MxN.
%
% OUTPUT:
%  enthalpy_diff_CT_exact = difference of specific enthalpy        [ J/kg ]
%                           (deep minus shallow)
%
% AUTHOR: 
%  Trevor McDougall and Paul Barker                    [ 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. (3.32.2) of this TEOS-10 Manual. 
%
%  McDougall, T.J., 2003: Potential enthalpy: A conservative oceanic 
%   variable for evaluating heat content and heat fluxes. Journal of 
%   Physical Oceanography, 33, 945-963.  
%    See Eqns. (18) and (22)
%
%  Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate
%   polynomial expressions for the density and specifc volume of seawater
%   using the TEOS-10 standard. Ocean Modelling.
%
%  The software is available from http://www.TEOS-10.org
%
%==========================================================================

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

if ~(nargin == 4)
    error('gsw_enthalpy_diff_CT_exact: requires four inputs')
end

[ms,ns] = size(SA);
[mt,nt] = size(CT); 
[mpu,npu] = size(p_shallow);
[mpl,npl] = size(p_deep);

if (ms~=mt) | (ns~=nt)
    error('gsw_enthalpy_diff_CT_exact: SA & CT need to have the same dimensions')
end

if (mpu == 1) & (npu == 1)                          % p_shallow is a scalar
    p_shallow = p_shallow*ones(size(SA));
elseif (ns == npu) & (mpu == 1)                  % p_shallow is row vector,
    p_shallow = p_shallow(ones(1,ms), :);          % copy down each column.
elseif (ms == mpu) & (npu == 1)               % p_shallow is column vector,
    p_shallow = p_shallow(:,ones(1,ns));            % copy across each row.
elseif (ns == mpu) & (npu == 1)          % p_shallow is a transposed row vector,
    p_shallow = p_shallow.';                  % transposed then
    p_shallow = p_shallow(ones(1,ms), :);     % copy down each column.
elseif (ms == mpu) & (ns == npu)
    % ok
end

if (mpl == 1) & (npl == 1)               % p_deep is a scalar
    p_deep = p_deep*ones(size(SA));
elseif (ns == npl) & (mpl == 1)          % p_deep is row vector,
    p_deep = p_deep(ones(1,ms), :);      % copy down each column.
elseif (ms == mpl) & (npl == 1)          % p_deep is column vector,
    p_deep = p_deep(:,ones(1,ns));       % copy across each row.
elseif (ns == mpl) & (npl == 1)          % p_deep is a transposed row vector,
    p_deep = p_deep.';                    % transposed then
    p_deep = p_deep(ones(1,ms), :);      % copy down each column.
elseif (ms == mpl) & (ns == npl)
    % ok
else
    error('gsw_enthalpy_diff_CT_exact: Inputs array dimensions arguments do not agree')
end %if

if ms == 1
    SA = SA.';
    CT = CT.';
    p_shallow = p_shallow.';
    p_deep = p_deep.';
    transposed = 1;
else
    transposed = 0;
end

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

t_shallow = gsw_t_from_CT(SA,CT,p_shallow);
t_deep = gsw_t_from_CT(SA,CT,p_deep);
enthalpy_diff_CT_exact = gsw_enthalpy_t_exact(SA,t_deep,p_deep) - ...
                     gsw_enthalpy_t_exact(SA,t_shallow,p_shallow);

if transposed
    enthalpy_diff_CT_exact = enthalpy_diff_CT_exact.';
end

end