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function PT = sw_ptmp(S,T,P,PR)
% SW_PTMP Potential temperature
%===========================================================================
% SW_PTMP $Revision: 1.3 $ $Date: 1994/10/10 05:45:13 $
% Copyright (C) CSIRO, Phil Morgan 1992.
%
% USAGE: ptmp = sw_ptmp(S,T,P,PR)
%
% DESCRIPTION:
% Calculates potential temperature as per UNESCO 1983 report.
%
% INPUT: (all must have same dimensions)
% S = salinity [psu (PSS-78) ]
% T = temperature [degree C (IPTS-68)]
% P = pressure [db]
% PR = Reference pressure [db]
% (P & PR may have dims 1x1, mx1, 1xn or mxn for S(mxn) )
%
% OUTPUT:
% ptmp = Potential temperature relative to PR [degree C (IPTS-68)]
%
% AUTHOR: Phil Morgan 92-04-06 (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.
% Eqn.(31) p.39
%
% Bryden, H. 1973.
% "New Polynomials for thermal expansion, adiabatic temperature gradient
% and potential temperature of sea water."
% DEEP-SEA RES., 1973, Vol20,401-408.
%=========================================================================
% CALLER: general purpose
% CALLEE: sw_adtg.m
%-------------
% CHECK INPUTS
%-------------
if nargin ~= 4
error('sw_ptmp.m: Must pass 4 parameters ')
end %if
% CHECK S,T,P dimensions and verify consistent
[ms,ns] = size(S);
[mt,nt] = size(T);
[mp,np] = size(P);
[mpr,npr] = size(PR);
% 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);
% CHECK OPTIONAL SHAPES FOR PR
if mpr==1 & npr==1 % PR is a scalar. Fill to size of S
PR = PR(1)*ones(ms,ns);
elseif npr==ns & mpr==1 % PR is row vector with same cols as S
PR = PR( ones(1,ms), : ); % Copy down each column.
elseif mpr==ms & npr==1 % P is column vector
PR = PR( :, ones(1,ns) ); % Copy across each row
elseif mpr==ms & npr==ns % PR is a matrix size(S)
% shape ok
else
error('check_stp: PR has wrong dimensions')
end %if
[mpr,npr] = size(PR);
% 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(:);
PR = PR(:);
Transpose = 1;
end %if
%***check_stp
%------
% BEGIN
%------
% theta1
del_P = PR - P;
del_th = del_P.*sw_adtg(S,T,P);
th = T + 0.5*del_th;
q = del_th;
% theta2
del_th = del_P.*sw_adtg(S,th,P+0.5*del_P);
th = th + (1 - 1/sqrt(2))*(del_th - q);
q = (2-sqrt(2))*del_th + (-2+3/sqrt(2))*q;
% theta3
del_th = del_P.*sw_adtg(S,th,P+0.5*del_P);
th = th + (1 + 1/sqrt(2))*(del_th - q);
q = (2 + sqrt(2))*del_th + (-2-3/sqrt(2))*q;
% theta4
del_th = del_P.*sw_adtg(S,th,P+del_P);
PT = th + (del_th - 2*q)/6;
if Transpose
PT = PT';
end %if
return
%=========================================================================