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gsw_SA_from_rho.m
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function SA = gsw_SA_from_rho(rho,CT,p)
% gsw_SA_from_rho Absolute Salinity from density
% (75-term equation)
% =========================================================================
%
% USAGE:
% SA = gsw_SA_from_rho(rho,CT,p)
%
% DESCRIPTION:
% Calculates the Absolute Salinity of a seawater sample, for given values
% of its density, Conservative Temperature and sea pressure (in dbar).
% This function uses the computationally-efficient 75-term expression for
% specific volume in terms of SA, CT and p (Roquet et al., 2015).
%
% Note that this 75-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. (2003). 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:
% rho = density of a seawater sample (e.g. 1026 kg/m^3). [ kg/m^3 ]
% Note. This input has not had 1000 kg/m^3 subtracted from it.
% That is, it is 'density', not 'density anomaly'.
% CT = Conservative Temperature (ITS-90) [ deg C ]
% p = sea pressure [ dbar ]
% ( i.e. absolute pressure - 10.1325 dbar )
%
% rho & CT need to have the same dimensions.
% p may have dimensions 1x1 or Mx1 or 1xN or MxN, where rho & CT are MxN.
%
% OUTPUT:
% SA = Absolute Salinity. [ g/kg ]
% Note. This is expressed on the Reference-Composition Salinity
% Scale of Millero et al. (2008).
%
% AUTHOR:
% Trevor McDougall & Paul Barker [ [email protected] ]
%
% 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 section 2.5 of this TEOS-10 Manual.
%
% McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003:
% Accurate and computationally efficient algorithms for potential
% temperature and density of seawater. J. Atmosph. Ocean. Tech., 20,
% pp. 730-741.
%
% Millero, F.J., R. Feistel, D.G. Wright, and T.J. McDougall, 2008:
% The composition of Standard Seawater and the definition of the
% Reference-Composition Salinity Scale. Deep-Sea Res. I, 55, 50-72.
%
% 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)
error('gsw_SA_from_rho: Requires three inputs')
end %if
[md,nd] = size(rho);
[mt,nt] = size(CT);
[mp,np] = size(p);
if (mt ~= md | nt ~= nd)
error('gsw_SA_from_rho: rho and CT must have same dimensions')
end
if (mp == 1) & (np == 1) % p scalar - fill to size of rho
p = p*ones(size(rho));
elseif (nd == np) & (mp == 1) % p is row vector,
p = p(ones(1,md), :); % copy down each column.
elseif (md == mp) & (np == 1) % p is column vector,
p = p(:,ones(1,nd)); % copy across each row.
elseif (nd == mp) & (np == 1) % p is a transposed row vector,
p = p.'; % transposed then
p = p(ones(1,md), :); % copy down each column.
elseif (md == mp) & (nd == np)
% ok
else
error('gsw_SA_from_rho: Inputs array dimensions arguments do not agree')
end %if
if md == 1
rho = rho.';
CT = CT.';
p = p.';
transposed = 1;
else
transposed = 0;
end
%--------------------------------------------------------------------------
% Start of the calculation
%--------------------------------------------------------------------------
v_lab = ones(size(rho))./rho;
v_0 = gsw_specvol(zeros(size(rho)),CT,p);
v_50 = gsw_specvol(50*ones(size(rho)),CT,p);
SA = 50*(v_lab - v_0)./(v_50 - v_0); % initial estimate of SA.
SA(SA < 0 | SA > 50) = NaN;
v_SA = (v_50 - v_0)./50; %initial estimate of v_SA, the SA derivative of v
%--------------------------------------------------------------------------
% Begin the modified Newton-Raphson iterative procedure
%--------------------------------------------------------------------------
for Number_of_iterations = 1:2
SA_old = SA;
delta_v = gsw_specvol(SA_old,CT,p) - v_lab;
SA = SA_old - delta_v./v_SA ; % this is half way through the modified N-R method (McDougall and Wotherspoon, 2012)
SA_mean = 0.5*(SA + SA_old);
[v_SA, dummy, dummy] = gsw_specvol_first_derivatives(SA_mean,CT,p);
SA = SA_old - delta_v./v_SA;
SA(SA < 0 | SA > 50) = NaN;
end
% After two iterations of this modified Newton-Raphson iteration,
% the error in SA is no larger than 8x10^-13 g/kg, which
% is machine precision for this calculation.
if transposed
SA = SA.';
end
end