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function [BETA] = sw_beta(S, T, P, keyword)
% SW_BETA Saline contraction coefficient (beta)
%========================================================================
% SW_BETA $Revision: 1.4 $ $Date: 1994/11/15 04:10:05 $
% % Copyright (C) CSIRO, Nathan Bindoff 1993.
%
% USAGE: [BETA] = sw_beta(S, T, P, {keyword} )
%
% [BETA] = sw_beta(S, T, P, 'temp') %default
% [BETA] = sw_beta(S, PTMP, P, 'ptmp')
%
% DESCRIPTION
% The saline contraction coefficient as defined by T.J. McDougall.
%
% INPUT: (all must have same dimensions)
% S = salinity [psu (PSS-78) ]
% * PTMP = potential temperature [degree C (IPTS-68)]
% * T = temperature [degree C (IPTS-68)]
% P = pressure [db]
% (P may have dims 1x1, mx1, 1xn or mxn for S(mxn) )
%
% keyword = optional string to identify if temp or ptmp passed.
% = No argument defaults to 'temp'
% = 'temp' assumes (S,T,P) passed. Will execute slower
% as ptmp will be calculated internally.
% = 'ptmp' assumes (S,PTMP,P) passed. Will execute faster.
%
% OUTPUT
% BETA = Saline Contraction Coefficient [psu.^-1]
%
% AUTHOR: N.L. Bindoff 1993
%
% DISCLAIMER:
% This software is provided "as is" without warranty of any kind.
% See the file sw_copy.m for conditions of use and licence.
%
% REFERENCE:
% McDougall, T.J. 1987. "Neutral Surfaces"
% Journal of Physical Oceanography vol 17 pages 1950-1964,
%
% CHECK VALUE:
% beta=0.72088e-3 psu.^-1 at S=40.0 psu, ptmp = 10.0 C, p=4000 db
%========================================================================
% Modifications
% 93-04-22. Phil Morgan, Help display modified to suit library
% 93-04-23. Phil Morgan, Input argument checking
% 94-10-15. Phil Morgan, Pass S,T,P and keyword for 'ptmp'
% CHECK INPUT ARGUMENTS
if ~(nargin==3 | nargin==4)
error('sw_beta.m: requires 3 or 4 input arguments')
end %if
if nargin == 3
keyword = 'temp';
end %if
% 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 % PR 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 %if
%***check_stp
% ENSURE WE USE PTMP IN CALCULATIONS
if strcmp(lower(keyword),'ptmp')
% already have ptmp
else
T = sw_ptmp(S,T,P,0); % now have ptmp
end %if
% BEGIN
c1=fliplr([ 0.785567e-3, -0.301985e-5 ...
0.555579e-7, -0.415613e-9]);
c2=fliplr([ -0.356603e-6, 0.788212e-8]);
c3=fliplr([0.0 0.408195e-10, -0.602281e-15]);
c4=[0.515032e-8];
c5=fliplr([-0.121555e-7, 0.192867e-9, -0.213127e-11]);
c6=fliplr([0.176621e-12 -0.175379e-14]);
c7=[0.121551e-17];
%
% Now calaculate the thermal expansion saline contraction ratio adb
%
[m,n] = size(S);
sm35 = S-35*ones(m,n);
BETA = polyval(c1,T) + sm35.*(polyval(c2,T) + ...
polyval(c3,P)) + c4*(sm35.^2) + ...
P.*polyval(c5,T) + (P.^2).*polyval(c6,T) ...
+c7*( P.^3);
return
%------------------------------------------------------------------------