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densjmd95.m
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densjmd95.m
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function rho = densjmd95(s,t,p);
%
% DENSJMD95 Density of sea water
%=========================================================================
%
% USAGE: dens = densjmd95(S,Theta,P)
%
% DESCRIPTION:
% Density of Sea Water using Jackett and McDougall 1995 (JAOT 12)
% polynomial (modified UNESCO polynomial).
%
% INPUT: (all must have same dimensions)
% S = salinity [psu (PSS-78)]
% Theta = potential temperature [degree C (IPTS-68)]
% P = pressure [dbar]
% (P may have dims 1x1, mx1, 1xn or mxn for S(mxn) )
%
% OUTPUT:
% dens = density [kg/m^3]
%
% AUTHOR: Martin Losch 2002-08-09 (mlosch@mit.edu)
%
% check value
% S = 35.5 PSU
% Theta = 3 degC
% P = 3000 dbar
% rho = 1041.83267 kg/m^3
% Jackett and McDougall, 1995, JAOT 12(4), pp. 381-388
% created by mlosch on 2002-08-09
%----------------------
% CHECK INPUT ARGUMENTS
%----------------------
if nargin ~=3
error('densjmd95.m: Must pass 3 parameters')
end
if ndims(s) > 2
dims = size(s);
dimt = size(t);
dimp = size(p);
if length(dims) ~= length(dimt) | length(dims) ~= length(dimp) ...
length(dimt) ~= length(dimp)
error(['for more than two dimensions, S, Theta, and P must have the' ...
' same number of dimensions'])
else
for k=length(dims)
if dims(k)~=dimt(k) | dims(k)~=dimp(k) | dimt(k)~=dimp(k)
error(['for more than two dimensions, S, Theta, and P must have' ...
' the same dimensions'])
end
end
end
else
% CHECK S,T,P dimensions and verify consistent
[ms,ns] = size(s);
[mt,nt] = size(t);
[mp,np] = size(p);
% CHECK THAT S & T HAVE SAME SHAPE
if (ms~=mt) | (ns~=nt)
error('check_stp: S & T must have same dimensions')
end %if
% CHECK OPTIONAL SHAPES FOR P
if mp==1 & np==1 % P is a scalar. Fill to size of S
p = p(1)*ones(ms,ns);
elseif np==ns & mp==1 % P is row vector with same cols as S
p = p( ones(1,ms), : ); % Copy down each column.
elseif mp==ms & np==1 % P is column vector
p = p( :, ones(1,ns) ); % Copy across each row
elseif mp==ms & np==ns % P is a matrix size(S)
% shape ok
else
error('check_stp: P has wrong dimensions')
end %if
[mp,np] = size(p);
% IF ALL ROW VECTORS ARE PASSED THEN LET US PRESERVE SHAPE ON RETURN.
Transpose = 0;
if mp == 1 % row vector
p = p(:);
t = t(:);
s = s(:);
Transpose = 1;
end
%***check_stp
end
% convert pressure to bar
p = .1*p;
% coefficients nonlinear equation of state in pressure coordinates for
% 1. density of fresh water at p = 0
eosJMDCFw(1) = 999.842594;
eosJMDCFw(2) = 6.793952e-02;
eosJMDCFw(3) = - 9.095290e-03;
eosJMDCFw(4) = 1.001685e-04;
eosJMDCFw(5) = - 1.120083e-06;
eosJMDCFw(6) = 6.536332e-09;
% 2. density of sea water at p = 0
eosJMDCSw(1) = 8.244930e-01;
eosJMDCSw(2) = - 4.089900e-03;
eosJMDCSw(3) = 7.643800e-05 ;
eosJMDCSw(4) = - 8.246700e-07;
eosJMDCSw(5) = 5.387500e-09;
eosJMDCSw(6) = - 5.724660e-03;
eosJMDCSw(7) = 1.022700e-04;
eosJMDCSw(8) = - 1.654600e-06;
eosJMDCSw(9) = 4.831400e-04;
t2 = t.*t;
t3 = t2.*t;
t4 = t3.*t;
is = find(s(:) < 0 );
if ~isempty(is)
warning('found negative salinity values, reset them to NaN');
s(is) = NaN;
end
s3o2 = s.*sqrt(s);
% density of freshwater at the surface
rho = eosJMDCFw(1) ...
+ eosJMDCFw(2)*t ...
+ eosJMDCFw(3)*t2 ...
+ eosJMDCFw(4)*t3 ...
+ eosJMDCFw(5)*t4 ...
+ eosJMDCFw(6)*t4.*t;
% density of sea water at the surface
rho = rho ...
+ s.*( ...
eosJMDCSw(1) ...
+ eosJMDCSw(2)*t ...
+ eosJMDCSw(3)*t2 ...
+ eosJMDCSw(4)*t3 ...
+ eosJMDCSw(5)*t4 ...
) ...
+ s3o2.*( ...
eosJMDCSw(6) ...
+ eosJMDCSw(7)*t ...
+ eosJMDCSw(8)*t2 ...
) ...
+ eosJMDCSw(9)*s.*s;
rho = rho./(1 - p./bulkmodjmd95(s,t,p));
if ndims(s) < 3 & Transpose
rho = rho';
end %if
return
function bulkmod = bulkmodjmd95(s,t,p)
%function bulkmod = bulkmodjmd95(s,t,p)
dummy = 0;
% coefficients in pressure coordinates for
% 3. secant bulk modulus K of fresh water at p = 0
eosJMDCKFw(1) = 1.965933e+04;
eosJMDCKFw(2) = 1.444304e+02;
eosJMDCKFw(3) = - 1.706103e+00;
eosJMDCKFw(4) = 9.648704e-03;
eosJMDCKFw(5) = - 4.190253e-05;
% 4. secant bulk modulus K of sea water at p = 0
eosJMDCKSw(1) = 5.284855e+01;
eosJMDCKSw(2) = - 3.101089e-01;
eosJMDCKSw(3) = 6.283263e-03;
eosJMDCKSw(4) = - 5.084188e-05;
eosJMDCKSw(5) = 3.886640e-01;
eosJMDCKSw(6) = 9.085835e-03;
eosJMDCKSw(7) = - 4.619924e-04;
% 5. secant bulk modulus K of sea water at p
eosJMDCKP( 1) = 3.186519e+00;
eosJMDCKP( 2) = 2.212276e-02;
eosJMDCKP( 3) = - 2.984642e-04;
eosJMDCKP( 4) = 1.956415e-06;
eosJMDCKP( 5) = 6.704388e-03;
eosJMDCKP( 6) = - 1.847318e-04;
eosJMDCKP( 7) = 2.059331e-07;
eosJMDCKP( 8) = 1.480266e-04;
eosJMDCKP( 9) = 2.102898e-04;
eosJMDCKP(10) = - 1.202016e-05;
eosJMDCKP(11) = 1.394680e-07;
eosJMDCKP(12) = - 2.040237e-06;
eosJMDCKP(13) = 6.128773e-08;
eosJMDCKP(14) = 6.207323e-10;
t2 = t.*t;
t3 = t2.*t;
t4 = t3.*t;
is = find(s(:) < 0 );
if ~isempty(is)
warning('found negative salinity values, reset them to NaN');
s(is) = NaN;
end
s3o2 = s.*sqrt(s);
%p = pressure(i,j,k,bi,bj)*SItoBar
p2 = p.*p;
% secant bulk modulus of fresh water at the surface
bulkmod = eosJMDCKFw(1) ...
+ eosJMDCKFw(2)*t ...
+ eosJMDCKFw(3)*t2 ...
+ eosJMDCKFw(4)*t3 ...
+ eosJMDCKFw(5)*t4;
% secant bulk modulus of sea water at the surface
bulkmod = bulkmod ...
+ s.*( eosJMDCKSw(1) ...
+ eosJMDCKSw(2)*t ...
+ eosJMDCKSw(3)*t2 ...
+ eosJMDCKSw(4)*t3 ...
) ...
+ s3o2.*( eosJMDCKSw(5) ...
+ eosJMDCKSw(6)*t ...
+ eosJMDCKSw(7)*t2 ...
);
% secant bulk modulus of sea water at pressure p
bulkmod = bulkmod ...
+ p.*( eosJMDCKP(1) ...
+ eosJMDCKP(2)*t ...
+ eosJMDCKP(3)*t2 ...
+ eosJMDCKP(4)*t3 ...
) ...
+ p.*s.*( eosJMDCKP(5) ...
+ eosJMDCKP(6)*t ...
+ eosJMDCKP(7)*t2 ...
) ...
+ p.*s3o2*eosJMDCKP(8) ...
+ p2.*( eosJMDCKP(9) ...
+ eosJMDCKP(10)*t ...
+ eosJMDCKP(11)*t2 ...
) ...
+ p2.*s.*( eosJMDCKP(12) ...
+ eosJMDCKP(13)*t ...
+ eosJMDCKP(14)*t2 ...
);
return