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function R = sw_cndr(S,T,P)
% SW_CNDR Conductivity ratio R = C(S,T,P)/C(35,15,0)
%=========================================================================
% SW_CNDR $Revision: 1.3 $ $Date: 1994/10/10 04:36:58 $
% Copyright (C) CSIRO, Phil Morgan 1993.
%
% USAGE: cndr = sw_cndr(S,T,P)
%
% DESCRIPTION:
% Calculates conductivity ratio from S,T,P.
%
% INPUT: (all must have same dimensions)
% S = salinity [psu (PSS-78) ]
% T = temperature [degree C (IPTS-68)]
% P = pressure [db]
% (P may have dims 1x1, mx1, 1xn or mxn for S(mxn) )
%
% OUTPUT:
% cndr = Conductivity ratio R = C(S,T,P)/C(35,15,0) [no units]
%
% AUTHOR: Phil Morgan 93-04-21 (morgan@ml.csiro.au)
%
% DISCLAIMER:
% This software is provided "as is" without warranty of any kind.
% See the file sw_copy.m for conditions of use and licence.
%
% REFERENCES:
% Fofonoff, P. and Millard, R.C. Jr
% Unesco 1983. Algorithms for computation of fundamental properties of
% seawater, 1983. _Unesco Tech. Pap. in Mar. Sci._, No. 44, 53 pp.
%=========================================================================
% CALLER: general purpose
% CALLEE: sw_salds.m sw_sals.m sw_salrt.m
%--------------
% check inputs
%-------------
if nargin~=3
error('sw_cndr.m: must have 3 input arguments')
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
%-------
% BEGIN
%-------
del_T = T - 15;
for i = 1:ms
for j = 1:ns
%---------------------------------------------------------------------
% DO A NEWTON-RAPHSON ITERATION FOR INVERSE INTERPOLATION OF Rt FROM S.
%---------------------------------------------------------------------
S_loop = S(i,j); % S in the loop
T_loop = T(i,j); % T in the loop
Rx_loop = sqrt(S_loop/35.0); % first guess at Rx = sqrt(Rt)
SInc = sw_sals(Rx_loop.*Rx_loop,T_loop); % S INCrement (guess) from Rx
iloop = 0;
end_loop = 0;
while ~end_loop
Rx_loop = Rx_loop + (S_loop - SInc)./sw_salds(Rx_loop,del_T(i,j));
SInc = sw_sals(Rx_loop.*Rx_loop,T_loop);
iloop = iloop + 1;
dels = abs(SInc-S_loop);
if (dels>1.0e-4 & iloop<10)
end_loop = 0;
else
end_loop = 1;
end %if
end %while
Rx(i,j) = Rx_loop;
end %for j
end %for i
%------------------------------------------------------
% ONCE Rt FOUND, CORRESPONDING TO EACH (S,T) EVALUATE R
%------------------------------------------------------
% eqn(4) p.8 Unesco 1983
d1 = 3.426e-2;
d2 = 4.464e-4;
d3 = 4.215e-1;
d4 = -3.107e-3;
e1 = 2.070e-5;
e2 = -6.370e-10;
e3 = 3.989e-15;
A = (d3 + d4.*T);
B = 1 + d1.*T + d2.*T.^2;
C = P.*(e1 + e2.*P + e3.*P.^2);
% eqn(6) p.9 UNESCO 1983.
Rt = Rx.*Rx;
rt = sw_salrt(T);
Rtrt = rt.*Rt;
D = B - A.*rt.*Rt;
E = rt.*Rt.*A.*(B+C);
R = sqrt(abs(D.^2+4*E)) - D;
R = 0.5*R./A;
return
%-----------------------------------------------------------------------