gsw_specvol_anom_CT_exact.m

function specvol_anom_CT_exact = gsw_specvol_anom_CT_exact(SA,CT,p,SA_ref,CT_ref)

% gsw_specvol_anom_CT_exact                         specific volume anomaly
%==========================================================================
% 
% USAGE:  
%  specvol_anom_CT_exact = gsw_specvol_anom_CT_exact(SA,CT,p,SA_ref,CT_ref)
%
% DESCRIPTION:
%  Calculates specific volume anomaly from Absolute Salinity, Conservative 
%  Temperature and pressure.  If the Absolute Salinity and Conservative
%  Temperature reference value (SA_ref and CT_ref) are not defined then a
%  default reference value of Absolute Salinity is SSO and the reference 
%  value of Conservative Temperature is equal to 0 degress C.
%
%  Note that this function uses the full Gibbs function.  There is an 
%  alternative to calling this function, namely 
%  gsw_specvol_anom(SA,CT,p,SA_ref,CT_ref), 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   =  sea pressure                                             [ dbar ]
%         ( i.e. absolute pressure - 10.1325 dbar )
% Optional:
%  SA_ref =  reference Absolute Salinity                           [ g/kg ]
%  CT_ref =  reference Conservative Temperature (ITS-90)          [ deg C ]
%
%  SA & CT  need to have the same dimensions.
%  p may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA & CT are MxN.
%  SA_ref & CT_ref muct be scalars and have dimensions 1x1.
%
% OUTPUT:
%  specvol_anom_CT_exact  =  specific volume anomaly             [ m^3/kg ]
%
% AUTHOR: 
%  Trevor McDougall and Paul Barker                    [ help@teos-10.org ]
%
% VERSION NUMBER: 3.05 (17th 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 Eqn. (3.7.3) of this TEOS-10 Manual. 
%
%  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 == 3 | nargin == 5)
    error('gsw_specvol_anom_CT_exact: Requires three or five inputs')
end

if nargin == 5
    if ~(isscalar(CT_ref) | isscalar(SA_ref))
        error('gsw_specvol_anom_CT_exact: SA_ref and CT_ref must be scalars (single values)')
    end
end

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

if (mt ~= ms | nt ~= ns)
    error('gsw_specvol_anom_CT_exact: SA and CT must have same dimensions')
end

if (mp == 1) & (np == 1)              % p scalar - fill to size of SA
    p = p*ones(size(SA));
elseif (ns == np) & (mp == 1)         % p is row vector,
    p = p(ones(1,ms), :);              % copy down each column.
elseif (ms == mp) & (np == 1)         % p is column vector,
    p = p(:,ones(1,ns));               % copy across each row.
elseif (ns == mp) & (np == 1)          % p is a transposed row vector,
    p = p.';                              % transposed then
    p = p(ones(1,ms), :);                % copy down each column.
elseif (ms == mp) & (ns == np)
    % ok
else
    error('gsw_specvol_anom_CT_exact: Inputs array dimensions arguments do not agree')
end 

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

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

t = gsw_t_from_CT(SA,CT,p);

if nargin == 3
    specvol_anom_CT_exact = gsw_specvol_anom_standard_t_exact(SA,t,p);
else
    SA_ref_array = SA_ref.*ones(size(p));
    CT_ref_array = CT_ref.*ones(size(p));
    t_ref_array = gsw_t_from_CT(SA_ref_array,CT_ref_array,p);   
    specvol_anom_CT_exact = gsw_gibbs(0,0,1,SA,t,p) - gsw_gibbs(0,0,1,SA_ref_array,t_ref_array,p);
end

if transposed
    specvol_anom_CT_exact = specvol_anom_CT_exact.';
end

end