profilesMatlabProcessing/profiles_misc/sw_ptmp.m

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      
%=========================================================================
1	gforget	1.1	function PT = sw_ptmp(S,T,P,PR)
2
3			% SW_PTMP Potential temperature
4			%===========================================================================
5			% SW_PTMP $Revision: 1.3 $ $Date: 1994/10/10 05:45:13 $
6			% Copyright (C) CSIRO, Phil Morgan 1992.
7			%
8			% USAGE: ptmp = sw_ptmp(S,T,P,PR)
9			%
10			% DESCRIPTION:
11			% Calculates potential temperature as per UNESCO 1983 report.
12			%
13			% INPUT: (all must have same dimensions)
14			% S = salinity [psu (PSS-78) ]
15			% T = temperature [degree C (IPTS-68)]
16			% P = pressure [db]
17			% PR = Reference pressure [db]
18			% (P & PR may have dims 1x1, mx1, 1xn or mxn for S(mxn) )
19			%
20			% OUTPUT:
21			% ptmp = Potential temperature relative to PR [degree C (IPTS-68)]
22			%
23			% AUTHOR: Phil Morgan 92-04-06 (morgan@ml.csiro.au)
24			%
25			% DISCLAIMER:
26			% This software is provided "as is" without warranty of any kind.
27			% See the file sw_copy.m for conditions of use and licence.
28			%
29			% REFERENCES:
30			% Fofonoff, P. and Millard, R.C. Jr
31			% Unesco 1983. Algorithms for computation of fundamental properties of
32			% seawater, 1983. _Unesco Tech. Pap. in Mar. Sci._, No. 44, 53 pp.
33			% Eqn.(31) p.39
34			%
35			% Bryden, H. 1973.
36			% "New Polynomials for thermal expansion, adiabatic temperature gradient
37			% and potential temperature of sea water."
38			% DEEP-SEA RES., 1973, Vol20,401-408.
39			%=========================================================================
40
41			% CALLER: general purpose
42			% CALLEE: sw_adtg.m
43
44			%-------------
45			% CHECK INPUTS
46			%-------------
47			if nargin ~= 4
48			error('sw_ptmp.m: Must pass 4 parameters ')
49			end %if
50
51			% CHECK S,T,P dimensions and verify consistent
52			[ms,ns] = size(S);
53			[mt,nt] = size(T);
54			[mp,np] = size(P);
55
56			[mpr,npr] = size(PR);
57
58
59			% CHECK THAT S & T HAVE SAME SHAPE
60			if (ms~=mt) \| (ns~=nt)
61			error('check_stp: S & T must have same dimensions')
62			end %if
63
64			% CHECK OPTIONAL SHAPES FOR P
65			if mp==1 & np==1 % P is a scalar. Fill to size of S
66			P = P(1)*ones(ms,ns);
67			elseif np==ns & mp==1 % P is row vector with same cols as S
68			P = P( ones(1,ms), : ); % Copy down each column.
69			elseif mp==ms & np==1 % P is column vector
70			P = P( :, ones(1,ns) ); % Copy across each row
71			elseif mp==ms & np==ns % PR is a matrix size(S)
72			% shape ok
73			else
74			error('check_stp: P has wrong dimensions')
75			end %if
76			[mp,np] = size(P);
77
78
79			% CHECK OPTIONAL SHAPES FOR PR
80			if mpr==1 & npr==1 % PR is a scalar. Fill to size of S
81			PR = PR(1)*ones(ms,ns);
82			elseif npr==ns & mpr==1 % PR is row vector with same cols as S
83			PR = PR( ones(1,ms), : ); % Copy down each column.
84			elseif mpr==ms & npr==1 % P is column vector
85			PR = PR( :, ones(1,ns) ); % Copy across each row
86			elseif mpr==ms & npr==ns % PR is a matrix size(S)
87			% shape ok
88			else
89			error('check_stp: PR has wrong dimensions')
90			end %if
91			[mpr,npr] = size(PR);
92
93
94			% IF ALL ROW VECTORS ARE PASSED THEN LET US PRESERVE SHAPE ON RETURN.
95			Transpose = 0;
96			if mp == 1 % row vector
97			P = P(:);
98			T = T(:);
99			S = S(:);
100
101			PR = PR(:);
102
103			Transpose = 1;
104			end %if
105			%***check_stp
106
107			%------
108			% BEGIN
109			%------
110
111			% theta1
112			del_P = PR - P;
113			del_th = del_P.*sw_adtg(S,T,P);
114			th = T + 0.5*del_th;
115			q = del_th;
116
117			% theta2
118			del_th = del_P.sw_adtg(S,th,P+0.5del_P);
119			th = th + (1 - 1/sqrt(2))*(del_th - q);
120			q = (2-sqrt(2))del_th + (-2+3/sqrt(2))q;
121
122			% theta3
123			del_th = del_P.sw_adtg(S,th,P+0.5del_P);
124			th = th + (1 + 1/sqrt(2))*(del_th - q);
125			q = (2 + sqrt(2))del_th + (-2-3/sqrt(2))q;
126
127			% theta4
128			del_th = del_P.*sw_adtg(S,th,P+del_P);
129			PT = th + (del_th - 2*q)/6;
130
131			if Transpose
132			PT = PT';
133			end %if
134
135			return
136			%=========================================================================