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	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	%=========================================================================