function sigma1 = gsw_sigma1(SA,CT)

% gsw_sigma1 potential density anomaly with reference
% sea pressure of 1000 dbar (48-term equation)
%==========================================================================
%
% USAGE:
% sigma1 = gsw_sigma1(SA,CT)
%
% DESCRIPTION:
% Calculates potential density anomaly with reference pressure of 1000
% dbar, this being this particular potential density minus 1000 kg/m^3.
% This function has inputs of Absolute Salinity and Conservative
% Temperature.
%
% Note that the 48-term equation has been fitted in a restricted range of
% parameter space, and is most accurate inside the "oceanographic funnel"
% described in McDougall et al. (2011). The GSW library function
% "gsw_infunnel(SA,CT,p)" is avaialble to be used if one wants to test if
% some of one's data lies outside this "funnel".
%
% INPUT:
% SA = Absolute Salinity [ g/kg ]
% CT = Conservative Temperature (ITS-90) [ deg C ]
%
% SA & CT need to have the same dimensions.
%
% OUTPUT:
% sigma1 = potential density anomaly with [ kg/m^3 ]
% respect to a reference pressure of 1000 dbar,
% that is, this potential density - 1000 kg/m^3.
%
% AUTHOR:
% Paul Barker and Trevor McDougall [ help@teos-10.org ]
%
% VERSION NUMBER: 3.01 (24th March, 2011)
%
% 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. (A.30.1) of this TEOS-10 Manual.
%
% McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011: A
% computationally efficient 48-term expression for the density of
% seawater in terms of Conservative Temperature, and related properties
% of seawater. To be submitted to Ocean Science Discussions.
%
% The software is available from http://www.TEOS-10.org
%
%==========================================================================

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

if ~(nargin == 2)
error('gsw_sigma1: Requires two inputs')
end %if

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

if (mt ~= ms | nt ~= ns)
error('gsw_sigma1: 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
%--------------------------------------------------------------------------

pr1000 = 1000*ones(size(SA));

rho1 = gsw_rho(SA,CT,pr1000);

%--------------------------------------------------------------------------
% This function calculates rho using the computationally-efficient
% 48-term expression for density in terms of SA, CT and p. If one wanted
% to compute rho with the full TEOS-10 Gibbs function expression for
% density, the following lines of code will enable this.
%
% rho1 = gsw_rho_CT_exact(SA,CT,pr1000);
%
%---------------This is the end of the alternative code -------------------

sigma1 = rho1 - 1000;

if transposed
sigma1 = sigma1.';
end

% The output, being potential density anomaly, has units of kg/m^3 and is
% potential density with 1000 kg/m^3 subtracted from it.

end