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gsw_spiciness1.m
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function spiciness1 = gsw_spiciness1(SA,CT)
% gsw_spiciness1 spiciness at p = 1000 dbar
% (75-term equation)
%==========================================================================
%
% USAGE:
% spiciness1 = gsw_spiciness1(SA,CT,p)
%
% DESCRIPTION:
% Calculates spiciness from Absolute Salinity and Conservative
% Temperature at a pressure of 1000 dbar, as described by McDougall and
% Krzysik (2015). This routine is based on the computationally-efficient
% 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:
% SA = Absolute Salinity [ g/kg ]
% CT = Conservative Temperature (ITS-90) [ deg C ]
%
% SA & CT need to have the same dimensions.
%
% OUTPUT:
% spiciness1 = spiciness referenced to a pressure of 1000 dbar
% [ kg/m^3 ]
%
% AUTHOR:
% Oliver Krzysik and Trevor McDougall [ help@teos-10.org ]
%
% VERSION NUMBER: 3.05 (5th December, 2014)
%
% 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
%
% 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.
%
% McDougall, T.J., and O.A. Krzysik, 2015: Spiciness. Journal of Marine
% Research, 73, 141-152.
%
% Roquet, F., G. Madec, T.J. McDougall and 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
%--------------------------------------------------------------------------
if ~(nargin == 2)
error('gsw_spiciness1: Requires two inputs')
end
[ms,ns] = size(SA);
[mt,nt] = size(CT);
if (mt ~= ms | nt ~= ns)
error('gsw_spiciness1: 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
%--------------------------------------------------------------------------
% This line ensures that SA is non-negative.
SA(SA < 0) = 0;
%deltaS = 24;
sfac = 0.0248826675584615; % sfac = 1/(40*(35.16504/35)).
offset = 5.971840214030754e-1; % offset = deltaS*sfac.
x2 = sfac.*SA;
xs = sqrt(x2 + offset);
ys = CT.*0.025;
s01 = -9.19874584868912e1;
s02 = -1.33517268529408e1;
s03 = 2.18352211648107e1;
s04 = -2.01491744114173e1;
s05 = 3.70004204355132e1;
s06 = -3.78831543226261e1;
s07 = 1.76337834294554e1;
s08 = 2.87838842773396e2;
s09 = 2.14531420554522e1;
s10 = 3.14679705198796e1;
s11 = -4.04398864750692e1;
s12 = -7.70796428950487e1;
s13 = 1.36783833820955e2;
s14 = -7.36834317044850e1;
s15 = -6.41753415180701e2;
s16 = 1.33701981685590;
s17 = -1.75289327948412e2;
s18 = 2.42666160657536e2;
s19 = 3.17062400799114e1;
s20 = -2.28131490440865e2;
s21 = 1.39564245068468e2;
s22 = 8.27747934506435e2;
s23 = -3.50901590694775e1;
s24 = 2.87473907262029e2;
s25 = -4.00227341144928e2;
s26 = 6.48307189919433e1;
s27 = 2.16433334701578e2;
s28 = -1.48273032774305e2;
s29 = -5.74545648799754e2;
s30 = 4.50446431127421e1;
s31 = -2.30714981343772e2;
s32 = 3.15958389253065e2;
s33 = -8.60635313930106e1;
s34 = -1.22978455069097e2;
s35 = 9.18287282626261e1;
s36 = 2.12120473062203e2;
s37 = -2.21528216973820e1;
s38 = 9.19013417923270e1;
s39 = -1.24400776026014e2;
s40 = 4.08512871163839e1;
s41 = 3.91127352213516e1;
s42 = -3.10508021853093e1;
s43 = -3.24790035899152e1;
s44 = 3.91029016556786;
s45 = -1.45362719385412e1;
s46 = 1.96136194246355e1;
s47 = -7.06035474689088;
s48 = -5.36884688614009;
s49 = 4.43247303092448;
spiciness1 = s01 + ys.*(s02 + ys.*(s03 + ys.*(s04 + ys.*(s05 + ys.*(s06 + s07*ys))))) ...
+ xs.*(s08 + ys.*(s09 + ys.*(s10 + ys.*(s11 + ys.*(s12 + ys.*(s13 + s14*ys)))))...
+ xs.*(s15 + ys.*(s16 + ys.*(s17 + ys.*(s18 + ys.*(s19 + ys.*(s20 + s21*ys))))) ...
+ xs.*(s22 + ys.*(s23 + ys.*(s24 + ys.*(s25 + ys.*(s26 + ys.*(s27 + s28*ys))))) ...
+ xs.*(s29 + ys.*(s30 + ys.*(s31 + ys.*(s32 + ys.*(s33 + ys.*(s34 + s35*ys))))) ...
+ xs.*(s36 + ys.*(s37 + ys.*(s38 + ys.*(s39 + ys.*(s40 + ys.*(s41 + s42*ys))))) ...
+ xs.*(s43 + ys.*(s44 + ys.*(s45 + ys.*(s46 + ys.*(s47 + ys.*(s48 + s49*ys)))))))))));
if transposed
spiciness1 = spiciness1.';
end
end