model/src/seawater.F

C $Header: /u/gcmpack/MITgcm/model/src/seawater.F,v 1.4 2009/06/30 20:47:32 ce107 Exp $
C $Name:  $

#include "CPP_OPTIONS.h"

C--  File seawater.F: routines that compute quantities related to seawater.
C--   Contents
C--   o SW_PTMP: function to compute potential temperature
C--   o SW_TEMP: function to compute in-situ temperature from pot. temp.
C--   o SW_ADTG: function to compute adiabatic temperature gradient
C--              (used by both SW_PTMP & SW_TEMP)

C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|

CBOP
C     !ROUTINE: SW_PTMP
C     !INTERFACE:
      _RL FUNCTION SW_PTMP  (S,T,P,PR)

C     !DESCRIPTION: \bv
C     *=============================================================*
C     | S/R  SW_PTMP
C     | o compute potential temperature as per UNESCO 1983 report.
C     *=============================================================*
C
C     started:
C              Armin Koehl akoehl@ucsd.edu
C
C     ==================================================================
C     SUBROUTINE SW_PTMP
C     ==================================================================
C     S  :: salinity    [psu      (PSS-78) ]
C     T  :: temperature [degree C (IPTS-68)]
C     P  :: pressure    [db]
C     PR :: Reference pressure  [db]

C     !USES:
      IMPLICIT NONE

C     !INPUT/OUTPUT PARAMETERS:
      _RL S,T,P,PR

C     !FUNCTIONS:
      _RL sw_adtg
      EXTERNAL sw_adtg

C     !LOCAL VARIABLES
      _RL del_P ,del_th, th, q
      _RL onehalf, two, three
      PARAMETER ( onehalf = 0.5 _d 0, two = 2. _d 0, three = 3. _d 0 )
CEOP

C theta1
      del_P  = PR - P
      del_th = del_P*sw_adtg(S,T,P)
      th     = T + onehalf*del_th
      q      = del_th
C theta2
      del_th = del_P*sw_adtg(S,th,P+onehalf*del_P)

      th     = th + (1 - 1/sqrt(two))*(del_th - q)
      q      = (two-sqrt(two))*del_th + (-two+three/sqrt(two))*q

C theta3
      del_th = del_P*sw_adtg(S,th,P+onehalf*del_P)
      th     = th + (1 + 1/sqrt(two))*(del_th - q)
      q      = (two + sqrt(two))*del_th + (-two-three/sqrt(two))*q

C theta4
      del_th = del_P*sw_adtg(S,th,P+del_P)
      SW_PTMP     = th + (del_th - two*q)/(two*three)

      RETURN
      END

C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|

CBOP
C     !ROUTINE: SW_TEMP
C     !INTERFACE:
      _RL FUNCTION SW_TEMP( S, T, P, PR )
C     !DESCRIPTION: \bv
C     *=============================================================*
C     | S/R  SW_TEMP
C     | o compute in-situ temperature from potential temperature
C     *=============================================================*
C
C     REFERENCES:
C     Fofonoff, P. and Millard, R.C. Jr
C     Unesco 1983. Algorithms for computation of fundamental properties of
C     seawater, 1983. _Unesco Tech. Pap. in Mar. Sci._, No. 44, 53 pp.
C     Eqn.(31) p.39
C
C     Bryden, H. 1973.
C     "New Polynomials for thermal expansion, adiabatic temperature gradient
C     and potential temperature of sea water."
C     DEEP-SEA RES., 1973, Vol20,401-408.

C     !USES:
      IMPLICIT NONE
C     === Global variables ===

C     !INPUT/OUTPUT PARAMETERS:
C     === Routine arguments ===
C     S      :: salinity
C     T      :: potential temperature
C     P      :: pressure
C     PR     :: reference pressure
      _RL  S, T, P, PR
CEOP

C     !FUNCTIONS:
      _RL sw_adtg
      EXTERNAL sw_adtg

C     !LOCAL VARIABLES:
      _RL del_P ,del_th, th, q
      _RL onehalf, two, three
      PARAMETER ( onehalf = 0.5 _d 0, two = 2. _d 0, three = 3. _d 0 )

C theta1
C--   here we swap P and PR in order to get in-situ temperature
C     del_P  = PR - P ! to get potential from in-situ temperature
      del_P  = P - PR ! to get in-situ from potential temperature
      del_th = del_P*sw_adtg(S,T,P)
      th     = T + onehalf*del_th
      q      = del_th
C theta2
      del_th = del_P*sw_adtg(S,th,P+onehalf*del_P)

      th     = th + (1 - 1/sqrt(two))*(del_th - q)
      q      = (two-sqrt(two))*del_th + (-two+three/sqrt(two))*q

C theta3
      del_th = del_P*sw_adtg(S,th,P+onehalf*del_P)
      th     = th + (1 + 1/sqrt(two))*(del_th - q)
      q      = (two + sqrt(two))*del_th + (-two-three/sqrt(two))*q

C theta4
      del_th = del_P*sw_adtg(S,th,P+del_P)
      SW_temp= th + (del_th - two*q)/(two*three)

      RETURN
      END

C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|

CBOP
C     !ROUTINE: SW_ADTG
C     !INTERFACE:
      _RL FUNCTION SW_ADTG  (S,T,P)

C     !DESCRIPTION: \bv
C     *=============================================================*
C     | S/R  SW_ADTG
C     | o compute adiabatic temperature gradient as per UNESCO 1983 routines.
C     *=============================================================*
C
C     started:
C              Armin Koehl akoehl@ucsd.edu

C     !USES:
      IMPLICIT NONE

C     !INPUT/OUTPUT PARAMETERS:
      _RL S,T,P

C     !LOCAL VARIABLES:
      _RL a0,a1,a2,a3,b0,b1,c0,c1,c2,c3,d0,d1,e0,e1,e2
      _RL sref
CEOP

      sref = 35. _d 0
      a0 =  3.5803 _d -5
      a1 = +8.5258 _d -6
      a2 = -6.836 _d -8
      a3 =  6.6228 _d -10

      b0 = +1.8932 _d -6
      b1 = -4.2393 _d -8

      c0 = +1.8741 _d -8
      c1 = -6.7795 _d -10
      c2 = +8.733 _d -12
      c3 = -5.4481 _d -14

      d0 = -1.1351 _d -10
      d1 =  2.7759 _d -12

      e0 = -4.6206 _d -13
      e1 = +1.8676 _d -14
      e2 = -2.1687 _d -16

      SW_ADTG =      a0 + (a1 + (a2 + a3*T)*T)*T
     &     + (b0 + b1*T)*(S-sref)
     &     + ( (c0 + (c1 + (c2 + c3*T)*T)*T) + (d0 + d1*T)*(S-sref) )*P
     &     + (  e0 + (e1 + e2*T)*T )*P*P

      RETURN
      END
1	jmc	1.5	C $Header: /u/gcmpack/MITgcm/model/src/seawater.F,v 1.4 2009/06/30 20:47:32 ce107 Exp $
2	ce107	1.4	C $Name: $
3	mlosch	1.1
4			#include "CPP_OPTIONS.h"
5	jmc	1.2
6			C-- File seawater.F: routines that compute quantities related to seawater.
7			C-- Contents
8			C-- o SW_PTMP: function to compute potential temperature
9	jmc	1.5	C-- o SW_TEMP: function to compute in-situ temperature from pot. temp.
10			C-- o SW_ADTG: function to compute adiabatic temperature gradient
11			C-- (used by both SW_PTMP & SW_TEMP)
12
13			C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-\|--+----\|
14
15			CBOP
16			C !ROUTINE: SW_PTMP
17			C !INTERFACE:
18			_RL FUNCTION SW_PTMP (S,T,P,PR)
19	mlosch	1.1
20			C !DESCRIPTION: \bv
21	jmc	1.5	C =============================================================
22			C \| S/R SW_PTMP
23			C \| o compute potential temperature as per UNESCO 1983 report.
24			C =============================================================
25			C
26			C started:
27			C Armin Koehl akoehl@ucsd.edu
28			C
29			C ==================================================================
30			C SUBROUTINE SW_PTMP
31			C ==================================================================
32			C S :: salinity [psu (PSS-78) ]
33			C T :: temperature [degree C (IPTS-68)]
34			C P :: pressure [db]
35			C PR :: Reference pressure [db]
36	mlosch	1.1
37			C !USES:
38			IMPLICIT NONE
39
40			C !INPUT/OUTPUT PARAMETERS:
41	jmc	1.5	_RL S,T,P,PR
42	mlosch	1.1
43	jmc	1.5	C !FUNCTIONS:
44			_RL sw_adtg
45			EXTERNAL sw_adtg
46	mlosch	1.1
47	jmc	1.5	C !LOCAL VARIABLES
48	mlosch	1.1	_RL del_P ,del_th, th, q
49			_RL onehalf, two, three
50	jmc	1.5	PARAMETER ( onehalf = 0.5 _d 0, two = 2. _d 0, three = 3. _d 0 )
51			CEOP
52	mlosch	1.1
53	jmc	1.5	C theta1
54	mlosch	1.1	del_P = PR - P
55			del_th = del_P*sw_adtg(S,T,P)
56			th = T + onehalf*del_th
57			q = del_th
58	jmc	1.5	C theta2
59	mlosch	1.1	del_th = del_Psw_adtg(S,th,P+onehalfdel_P)
60
61			th = th + (1 - 1/sqrt(two))*(del_th - q)
62			q = (two-sqrt(two))del_th + (-two+three/sqrt(two))q
63
64	jmc	1.5	C theta3
65	mlosch	1.1	del_th = del_Psw_adtg(S,th,P+onehalfdel_P)
66			th = th + (1 + 1/sqrt(two))*(del_th - q)
67			q = (two + sqrt(two))del_th + (-two-three/sqrt(two))q
68
69	jmc	1.5	C theta4
70	mlosch	1.1	del_th = del_P*sw_adtg(S,th,P+del_P)
71			SW_PTMP = th + (del_th - twoq)/(twothree)
72
73	jmc	1.5	RETURN
74			END
75
76			C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-\|--+----\|
77	mlosch	1.1
78			CBOP
79			C !ROUTINE: SW_TEMP
80			C !INTERFACE:
81	jmc	1.5	_RL FUNCTION SW_TEMP( S, T, P, PR )
82	mlosch	1.1	C !DESCRIPTION: \bv
83			C =============================================================
84			C \| S/R SW_TEMP
85	jmc	1.2	C \| o compute in-situ temperature from potential temperature
86	mlosch	1.1	C =============================================================
87			C
88			C REFERENCES:
89			C Fofonoff, P. and Millard, R.C. Jr
90			C Unesco 1983. Algorithms for computation of fundamental properties of
91			C seawater, 1983. _Unesco Tech. Pap. in Mar. Sci._, No. 44, 53 pp.
92			C Eqn.(31) p.39
93	jmc	1.2	C
94	mlosch	1.1	C Bryden, H. 1973.
95			C "New Polynomials for thermal expansion, adiabatic temperature gradient
96			C and potential temperature of sea water."
97			C DEEP-SEA RES., 1973, Vol20,401-408.
98
99			C !USES:
100			IMPLICIT NONE
101			C === Global variables ===
102	jmc	1.2
103	mlosch	1.1	C !INPUT/OUTPUT PARAMETERS:
104			C === Routine arguments ===
105	jmc	1.5	C S :: salinity
106			C T :: potential temperature
107			C P :: pressure
108			C PR :: reference pressure
109			_RL S, T, P, PR
110	mlosch	1.1	CEOP
111
112	jmc	1.5	C !FUNCTIONS:
113			_RL sw_adtg
114			EXTERNAL sw_adtg
115
116			C !LOCAL VARIABLES:
117	mlosch	1.1	_RL del_P ,del_th, th, q
118			_RL onehalf, two, three
119			PARAMETER ( onehalf = 0.5 _d 0, two = 2. _d 0, three = 3. _d 0 )
120
121	jmc	1.5	C theta1
122	mlosch	1.1	C-- here we swap P and PR in order to get in-situ temperature
123			C del_P = PR - P ! to get potential from in-situ temperature
124			del_P = P - PR ! to get in-situ from potential temperature
125			del_th = del_P*sw_adtg(S,T,P)
126			th = T + onehalf*del_th
127			q = del_th
128	jmc	1.5	C theta2
129	mlosch	1.1	del_th = del_Psw_adtg(S,th,P+onehalfdel_P)
130
131			th = th + (1 - 1/sqrt(two))*(del_th - q)
132			q = (two-sqrt(two))del_th + (-two+three/sqrt(two))q
133
134	jmc	1.5	C theta3
135	mlosch	1.1	del_th = del_Psw_adtg(S,th,P+onehalfdel_P)
136			th = th + (1 + 1/sqrt(two))*(del_th - q)
137			q = (two + sqrt(two))del_th + (-two-three/sqrt(two))q
138
139	jmc	1.5	C theta4
140	mlosch	1.1	del_th = del_P*sw_adtg(S,th,P+del_P)
141			SW_temp= th + (del_th - twoq)/(twothree)
142
143			RETURN
144			END
145
146	jmc	1.5	C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-\|--+----\|
147	mlosch	1.1
148	jmc	1.5	CBOP
149			C !ROUTINE: SW_ADTG
150			C !INTERFACE:
151	jmc	1.2	_RL FUNCTION SW_ADTG (S,T,P)
152	mlosch	1.1
153	jmc	1.5	C !DESCRIPTION: \bv
154			C =============================================================
155			C \| S/R SW_ADTG
156			C \| o compute adiabatic temperature gradient as per UNESCO 1983 routines.
157			C =============================================================
158			C
159			C started:
160			C Armin Koehl akoehl@ucsd.edu
161
162			C !USES:
163			IMPLICIT NONE
164
165			C !INPUT/OUTPUT PARAMETERS:
166			_RL S,T,P
167	mlosch	1.1
168	jmc	1.5	C !LOCAL VARIABLES:
169	mlosch	1.1	_RL a0,a1,a2,a3,b0,b1,c0,c1,c2,c3,d0,d1,e0,e1,e2
170			_RL sref
171	jmc	1.5	CEOP
172	mlosch	1.1
173			sref = 35. _d 0
174			a0 = 3.5803 _d -5
175			a1 = +8.5258 _d -6
176			a2 = -6.836 _d -8
177			a3 = 6.6228 _d -10
178
179			b0 = +1.8932 _d -6
180			b1 = -4.2393 _d -8
181
182			c0 = +1.8741 _d -8
183			c1 = -6.7795 _d -10
184			c2 = +8.733 _d -12
185			c3 = -5.4481 _d -14
186
187			d0 = -1.1351 _d -10
188			d1 = 2.7759 _d -12
189
190			e0 = -4.6206 _d -13
191			e1 = +1.8676 _d -14
192			e2 = -2.1687 _d -16
193
194			SW_ADTG = a0 + (a1 + (a2 + a3T)T)*T
195			& + (b0 + b1T)(S-sref)
196			& + ( (c0 + (c1 + (c2 + c3T)T)T) + (d0 + d1T)(S-sref) )P
197			& + ( e0 + (e1 + e2T)T )PP
198	jmc	1.5
199			RETURN
200			END