/[MITgcm]/MITgcm/model/src/calc_gt.F
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Revision 1.22 - (hide annotations) (download)
Wed May 26 20:26:42 1999 UTC (25 years ago) by adcroft
Branch: MAIN
CVS Tags: checkpoint23, checkpoint24, checkpoint25
Changes since 1.21: +51 -15 lines
Added bi-harmonic diffusion to calc_gs (Salt) and calc_gt (Temperature).

1 adcroft 1.22 C $Header: /u/gcmpack/models/MITgcmUV/model/src/calc_gt.F,v 1.21 1999/05/24 14:24:24 adcroft Exp $
2 cnh 1.1
3 cnh 1.19 #include "CPP_OPTIONS.h"
4 cnh 1.1
5     CStartOfInterFace
6     SUBROUTINE CALC_GT(
7     I bi,bj,iMin,iMax,jMin,jMax,k,kM1,kUp,kDown,
8 cnh 1.14 I xA,yA,uTrans,vTrans,rTrans,maskup,maskC,
9     I K13,K23,KappaRT,KapGM,
10 cnh 1.1 U af,df,fZon,fMer,fVerT,
11 cnh 1.18 I myCurrentTime, myThid )
12 cnh 1.1 C /==========================================================\
13     C | SUBROUTINE CALC_GT |
14     C | o Calculate the temperature tendency terms. |
15     C |==========================================================|
16     C | A procedure called EXTERNAL_FORCING_T is called from |
17     C | here. These procedures can be used to add per problem |
18     C | heat flux source terms. |
19     C | Note: Although it is slightly counter-intuitive the |
20     C | EXTERNAL_FORCING routine is not the place to put |
21     C | file I/O. Instead files that are required to |
22     C | calculate the external source terms are generally |
23     C | read during the model main loop. This makes the |
24     C | logisitics of multi-processing simpler and also |
25     C | makes the adjoint generation simpler. It also |
26     C | allows for I/O to overlap computation where that |
27     C | is supported by hardware. |
28     C | Aside from the problem specific term the code here |
29     C | forms the tendency terms due to advection and mixing |
30     C | The baseline implementation here uses a centered |
31     C | difference form for the advection term and a tensorial |
32     C | divergence of a flux form for the diffusive term. The |
33     C | diffusive term is formulated so that isopycnal mixing and|
34     C | GM-style subgrid-scale terms can be incorporated b simply|
35     C | setting the diffusion tensor terms appropriately. |
36     C \==========================================================/
37     IMPLICIT NONE
38    
39     C == GLobal variables ==
40     #include "SIZE.h"
41     #include "DYNVARS.h"
42     #include "EEPARAMS.h"
43     #include "PARAMS.h"
44     #include "GRID.h"
45 cnh 1.11 #include "FFIELDS.h"
46 adcroft 1.20 #ifdef ALLOW_KPP
47     #include "KPPMIX.h"
48     #endif
49    
50 cnh 1.1
51     C == Routine arguments ==
52     C fZon - Work array for flux of temperature in the east-west
53     C direction at the west face of a cell.
54     C fMer - Work array for flux of temperature in the north-south
55     C direction at the south face of a cell.
56     C fVerT - Flux of temperature (T) in the vertical
57     C direction at the upper(U) and lower(D) faces of a cell.
58     C maskUp - Land mask used to denote base of the domain.
59 adcroft 1.13 C maskC - Land mask for theta cells (used in TOP_LAYER only)
60 cnh 1.1 C xA - Tracer cell face area normal to X
61     C yA - Tracer cell face area normal to X
62     C uTrans - Zonal volume transport through cell face
63     C vTrans - Meridional volume transport through cell face
64 cnh 1.14 C rTrans - Vertical volume transport through cell face
65 cnh 1.1 C af - Advective flux component work array
66     C df - Diffusive flux component work array
67     C bi, bj, iMin, iMax, jMin, jMax - Range of points for which calculation
68     C results will be set.
69     C myThid - Instance number for this innvocation of CALC_GT
70     _RL fZon (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
71     _RL fMer (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
72     _RL fVerT (1-OLx:sNx+OLx,1-OLy:sNy+OLy,2)
73     _RS xA (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
74     _RS yA (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
75     _RL uTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
76     _RL vTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
77 cnh 1.14 _RL rTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
78 cnh 1.1 _RS maskUp(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
79 adcroft 1.13 _RS maskC (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
80 cnh 1.16 _RL K13 (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
81     _RL K23 (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
82     _RL KappaRT(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
83 adcroft 1.3 _RL KapGM (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
84 cnh 1.1 _RL af (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
85     _RL df (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
86 adcroft 1.3 INTEGER k,kUp,kDown,kM1
87 cnh 1.1 INTEGER bi,bj,iMin,iMax,jMin,jMax
88     INTEGER myThid
89 cnh 1.18 _RL myCurrentTime
90 cnh 1.1 CEndOfInterface
91    
92     C == Local variables ==
93     C I, J, K - Loop counters
94 adcroft 1.3 INTEGER i,j
95 cnh 1.10 LOGICAL TOP_LAYER
96 adcroft 1.3 _RL afFacT, dfFacT
97     _RL dTdx(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
98     _RL dTdy(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
99 adcroft 1.22 _RL df4 (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
100 adcroft 1.20 #ifdef ALLOW_KPP
101 adcroft 1.21 _RS hbl (1-OLx:sNx+OLx,1-OLy:sNy+OLy) ! used by KPP mixing scheme
102     _RS frac (1-OLx:sNx+OLx,1-OLy:sNy+OLy) ! used by KPP mixing scheme
103     _RS negone ! used as argument to SWFRAC
104 adcroft 1.20 integer jwtype ! index for Jerlov water type
105     #endif
106 cnh 1.1
107     afFacT = 1. _d 0
108     dfFacT = 1. _d 0
109 cnh 1.10 TOP_LAYER = K .EQ. 1
110 cnh 1.1
111     C--- Calculate advective and diffusive fluxes between cells.
112    
113 adcroft 1.22 #ifdef INCLUDE_T_DIFFUSION_CODE
114     C o Zonal tracer gradient
115     DO j=1-Oly,sNy+Oly
116     DO i=1-Olx+1,sNx+Olx
117     dTdx(i,j) = _recip_dxC(i,j,bi,bj)*
118     & (theta(i,j,k,bi,bj)-theta(i-1,j,k,bi,bj))
119     ENDDO
120     ENDDO
121     C o Meridional tracer gradient
122     DO j=1-Oly+1,sNy+Oly
123     DO i=1-Olx,sNx+Olx
124     dTdy(i,j) = _recip_dyC(i,j,bi,bj)*
125     & (theta(i,j,k,bi,bj)-theta(i,j-1,k,bi,bj))
126     ENDDO
127     ENDDO
128    
129     C-- del^2 of T, needed for bi-harmonic (del^4) term
130     IF (diffK4T .NE. 0.) THEN
131     DO j=1-Oly+1,sNy+Oly-1
132     DO i=1-Olx+1,sNx+Olx-1
133     df4(i,j)= _recip_hFacC(i,j,k,bi,bj)
134     & *recip_drF(k)/_rA(i,j,bi,bj)
135     & *(
136     & +( xA(i+1,j)*dTdx(i+1,j)-xA(i,j)*dTdx(i,j) )
137     & +( yA(i,j+1)*dTdy(i,j+1)-yA(i,j)*dTdy(i,j) )
138     & )
139     ENDDO
140     ENDDO
141     ENDIF
142     #endif
143    
144 cnh 1.1 C-- Zonal flux (fZon is at west face of "theta" cell)
145 cnh 1.19 #ifdef INCLUDE_T_ADVECTION_CODE
146     C o Advective component of zonal flux
147 cnh 1.1 DO j=jMin,jMax
148     DO i=iMin,iMax
149     af(i,j) =
150     & uTrans(i,j)*(theta(i,j,k,bi,bj)+theta(i-1,j,k,bi,bj))*0.5 _d 0
151     ENDDO
152     ENDDO
153 cnh 1.19 #endif /* INCLUDE_T_ADVECTION_CODE */
154     #ifdef INCLUDE_T_DIFFUSION_CODE
155     C o Diffusive component of zonal flux
156 cnh 1.1 DO j=jMin,jMax
157     DO i=iMin,iMax
158 adcroft 1.3 df(i,j) = -(diffKhT+0.5*(KapGM(i,j)+KapGM(i-1,j)))*
159     & xA(i,j)*dTdx(i,j)
160 cnh 1.1 ENDDO
161     ENDDO
162 adcroft 1.22 C o Add the bi-harmonic contribution
163     IF (diffK4T .NE. 0.) THEN
164     DO j=jMin,jMax
165     DO i=iMin,iMax
166     df(i,j) = df(i,j) + xA(i,j)*
167     & diffK4T*(df4(i,j)-df4(i-1,j))*_recip_dxC(i,j,bi,bj)
168     ENDDO
169     ENDDO
170     ENDIF
171 cnh 1.19 #endif /* INCLUDE_T_DIFFUSION_CODE */
172     C o Net zonal flux
173 cnh 1.1 DO j=jMin,jMax
174     DO i=iMin,iMax
175 cnh 1.19 fZon(i,j) = 0.
176     _ADT(& + afFacT*af(i,j) )
177     _LPT(& + dfFacT*df(i,j) )
178 cnh 1.1 ENDDO
179     ENDDO
180    
181     C-- Meridional flux (fMer is at south face of "theta" cell)
182 cnh 1.19 #ifdef INCLUDE_T_ADVECTION_CODE
183     C o Advective component of meridional flux
184 cnh 1.1 DO j=jMin,jMax
185     DO i=iMin,iMax
186     af(i,j) =
187     & vTrans(i,j)*(theta(i,j,k,bi,bj)+theta(i,j-1,k,bi,bj))*0.5 _d 0
188     ENDDO
189     ENDDO
190 cnh 1.19 #endif /* INCLUDE_T_ADVECTION_CODE */
191     #ifdef INCLUDE_T_DIFFUSION_CODE
192     C o Diffusive component of meridional flux
193 cnh 1.1 DO j=jMin,jMax
194     DO i=iMin,iMax
195 adcroft 1.3 df(i,j) = -(diffKhT+0.5*(KapGM(i,j)+KapGM(i,j-1)))*
196     & yA(i,j)*dTdy(i,j)
197 cnh 1.1 ENDDO
198     ENDDO
199 adcroft 1.22 C o Add the bi-harmonic contribution
200     IF (diffK4T .NE. 0.) THEN
201     DO j=jMin,jMax
202     DO i=iMin,iMax
203     df(i,j) = df(i,j) + yA(i,j)*
204     & diffK4T*(df4(i,j)-df4(i,j-1))*_recip_dyC(i,j,bi,bj)
205     ENDDO
206     ENDDO
207     ENDIF
208 cnh 1.19 #endif /* INCLUDE_T_DIFFUSION_CODE */
209     C o Net meridional flux
210 cnh 1.1 DO j=jMin,jMax
211     DO i=iMin,iMax
212 cnh 1.19 fMer(i,j) = 0.
213     _ADT(& + afFacT*af(i,j) )
214     _LPT(& + dfFacT*df(i,j) )
215 cnh 1.1 ENDDO
216     ENDDO
217    
218 cnh 1.19 #ifdef INCLUDE_T_DIFFUSION_CODE
219     C-- Terms that diffusion tensor projects onto z
220 adcroft 1.3 DO j=jMin,jMax
221     DO i=iMin,iMax
222     dTdx(i,j) = 0.5*(
223 cnh 1.17 & +0.5*(_maskW(i+1,j,k,bi,bj)
224     & *_recip_dxC(i+1,j,bi,bj)*
225 adcroft 1.3 & (theta(i+1,j,k,bi,bj)-theta(i,j,k,bi,bj))
226 cnh 1.17 & +_maskW(i,j,k,bi,bj)
227     & *_recip_dxC(i,j,bi,bj)*
228 adcroft 1.3 & (theta(i,j,k,bi,bj)-theta(i-1,j,k,bi,bj)))
229 cnh 1.17 & +0.5*(_maskW(i+1,j,km1,bi,bj)
230     & *_recip_dxC(i+1,j,bi,bj)*
231 adcroft 1.3 & (theta(i+1,j,km1,bi,bj)-theta(i,j,km1,bi,bj))
232 cnh 1.17 & +_maskW(i,j,km1,bi,bj)
233     & *_recip_dxC(i,j,bi,bj)*
234 adcroft 1.3 & (theta(i,j,km1,bi,bj)-theta(i-1,j,km1,bi,bj)))
235     & )
236     ENDDO
237     ENDDO
238     DO j=jMin,jMax
239     DO i=iMin,iMax
240     dTdy(i,j) = 0.5*(
241 cnh 1.17 & +0.5*(_maskS(i,j,k,bi,bj)
242     & *_recip_dyC(i,j,bi,bj)*
243 adcroft 1.3 & (theta(i,j,k,bi,bj)-theta(i,j-1,k,bi,bj))
244 cnh 1.17 & +_maskS(i,j+1,k,bi,bj)
245     & *_recip_dyC(i,j+1,bi,bj)*
246 adcroft 1.3 & (theta(i,j+1,k,bi,bj)-theta(i,j,k,bi,bj)))
247 cnh 1.17 & +0.5*(_maskS(i,j,km1,bi,bj)
248     & *_recip_dyC(i,j,bi,bj)*
249 adcroft 1.3 & (theta(i,j,km1,bi,bj)-theta(i,j-1,km1,bi,bj))
250 cnh 1.17 & +_maskS(i,j+1,km1,bi,bj)
251     & *_recip_dyC(i,j+1,bi,bj)*
252 adcroft 1.3 & (theta(i,j+1,km1,bi,bj)-theta(i,j,km1,bi,bj)))
253     & )
254     ENDDO
255     ENDDO
256 cnh 1.19 #endif /* INCLUDE_T_DIFFUSION_CODE */
257 adcroft 1.3
258 cnh 1.19 C-- Vertical flux ( fVerT(,,kUp) is at upper face of "theta" cell )
259     #ifdef INCLUDE_T_ADVECTION_CODE
260     C o Advective component of vertical flux
261 adcroft 1.3 C Note: For K=1 then KM1=1 this gives a barZ(T) = T
262     C (this plays the role of the free-surface correction)
263 cnh 1.1 DO j=jMin,jMax
264     DO i=iMin,iMax
265     af(i,j) =
266 cnh 1.14 & rTrans(i,j)*(theta(i,j,k,bi,bj)+theta(i,j,kM1,bi,bj))*0.5 _d 0
267 cnh 1.1 ENDDO
268     ENDDO
269 cnh 1.19 #endif /* INCLUDE_T_ADVECTION_CODE */
270     #ifdef INCLUDE_T_DIFFUSION_CODE
271     C o Diffusive component of vertical flux
272     C Note: For K=1 then KM1=1 and this gives a dT/dr = 0 upper
273 adcroft 1.3 C boundary condition.
274 cnh 1.1 DO j=jMin,jMax
275     DO i=iMin,iMax
276 cnh 1.14 df(i,j) = _rA(i,j,bi,bj)*(
277 adcroft 1.3 & -KapGM(i,j)*K13(i,j,k)*dTdx(i,j)
278     & -KapGM(i,j)*K23(i,j,k)*dTdy(i,j)
279     & )
280 cnh 1.1 ENDDO
281     ENDDO
282 adcroft 1.9 IF (.NOT.implicitDiffusion) THEN
283     DO j=jMin,jMax
284     DO i=iMin,iMax
285 cnh 1.14 df(i,j) = df(i,j) + _rA(i,j,bi,bj)*(
286 cnh 1.16 & -KappaRT(i,j,k)*recip_drC(k)
287 cnh 1.15 & *(theta(i,j,kM1,bi,bj)-theta(i,j,k,bi,bj))*rkFac
288 adcroft 1.9 & )
289     ENDDO
290     ENDDO
291     ENDIF
292 cnh 1.19 #endif /* INCLUDE_T_DIFFUSION_CODE */
293 adcroft 1.20
294     #ifdef ALLOW_KPP
295     IF (usingKPPmixing) THEN
296     C-- Compute fraction of solar short-wave flux penetrating to
297     C the bottom of the mixing layer
298     DO j=jMin,jMax
299     DO i=iMin,iMax
300     hbl(i,j) = KPPhbl(i,j,bi,bj)
301     ENDDO
302     ENDDO
303     j=(sNx+2*OLx)*(sNy+2*OLy)
304     jwtype = 3
305 adcroft 1.21 negone = -1.
306 adcroft 1.20 CALL SWFRAC(
307 adcroft 1.21 I j, negone, hbl, jwtype,
308 adcroft 1.20 O frac )
309    
310     C Add non local transport coefficient (ghat term) to right-hand-side
311     C The nonlocal transport term is noNrero only for scalars in unstable
312     C (convective) forcing conditions.
313     C Note: -[Qnet * delZ(1) + Qsw * (1-frac) / KPPhbl] * 4000 * rho
314     C is the total heat flux
315     C penetrating the mixed layer from the surface in (deg C / s)
316     IF ( TOP_LAYER ) THEN
317     DO j=jMin,jMax
318     DO i=iMin,iMax
319     df(i,j) = df(i,j) + _rA(i,j,bi,bj) *
320     & ( Qnet(i,j,bi,bj) * delZ(1) +
321     & Qsw(i,j,bi,bj) * (1.-frac(i,j))
322     & / KPPhbl(i,j,bi,bj) ) *
323     & ( KappaRT(i,j,k) * KPPghat(i,j,k, bi,bj) )
324     ENDDO
325     ENDDO
326     ELSE
327     DO j=jMin,jMax
328     DO i=iMin,iMax
329     df(i,j) = df(i,j) + _rA(i,j,bi,bj) *
330     & ( Qnet(i,j,bi,bj) * delZ(1) +
331     & Qsw(i,j,bi,bj) * (1.-frac(i,j))
332     & / KPPhbl(i,j,bi,bj) ) *
333     & ( KappaRT(i,j,k) * KPPghat(i,j,k, bi,bj)
334     & - KappaRT(i,j,k-1) * KPPghat(i,j,k-1,bi,bj) )
335     ENDDO
336     ENDDO
337     ENDIF
338     ENDIF
339     #endif /* ALLOW_KPP */
340    
341 cnh 1.19 C o Net vertical flux
342 cnh 1.1 DO j=jMin,jMax
343     DO i=iMin,iMax
344 cnh 1.19 fVerT(i,j,kUp) = 0.
345     _ADT(& +afFacT*af(i,j)*maskUp(i,j) )
346     _LPT(& +dfFacT*df(i,j)*maskUp(i,j) )
347 cnh 1.1 ENDDO
348     ENDDO
349 cnh 1.19 #ifdef INCLUDE_T_ADVECTION_CODE
350 cnh 1.10 IF ( TOP_LAYER ) THEN
351     DO j=jMin,jMax
352     DO i=iMin,iMax
353     fVerT(i,j,kUp) = afFacT*af(i,j)*freeSurfFac
354     ENDDO
355     ENDDO
356     ENDIF
357 cnh 1.19 #endif /* INCLUDE_T_ADVECTION_CODE */
358 cnh 1.1
359     C-- Tendency is minus divergence of the fluxes.
360     C Note. Tendency terms will only be correct for range
361     C i=iMin+1:iMax-1, j=jMin+1:jMax-1. Edge points
362     C will contain valid floating point numbers but
363     C they are not algorithmically correct. These points
364     C are not used.
365     DO j=jMin,jMax
366     DO i=iMin,iMax
367 cnh 1.17 #define _recip_VolT1(i,j,k,bi,bj) _recip_hFacC(i,j,k,bi,bj)*recip_drF(k)
368     #define _recip_VolT2(i,j,k,bi,bj) /_rA(i,j,bi,bj)
369 cnh 1.1 gT(i,j,k,bi,bj)=
370 cnh 1.17 & -_recip_VolT1(i,j,k,bi,bj)
371     & _recip_VolT2(i,j,k,bi,bj)
372 cnh 1.1 & *(
373     & +( fZon(i+1,j)-fZon(i,j) )
374     & +( fMer(i,j+1)-fMer(i,j) )
375 cnh 1.14 & +( fVerT(i,j,kUp)-fVerT(i,j,kDown) )*rkFac
376 cnh 1.1 & )
377     ENDDO
378     ENDDO
379    
380 cnh 1.19 #ifdef INCLUDE_T_FORCING_CODE
381 cnh 1.1 C-- External thermal forcing term(s)
382 cnh 1.19 CALL EXTERNAL_FORCING_T(
383     I iMin,iMax,jMin,jMax,bi,bj,k,
384     I maskC,
385     I myCurrentTime,myThid)
386     #endif /* INCLUDE_T_FORCING_CODE */
387    
388     #ifdef INCLUDE_LAT_CIRC_FFT_FILTER_CODE
389     C-- Zonal FFT filter of tendency
390     CALL FILTER_LATCIRCS_FFT_APPLY(
391     U gT,
392     I 1, sNy, k, k, bi, bj, 1, myThid)
393     #endif /* INCLUDE_LAT_CIRC_FFT_FILTER_CODE */
394    
395 cnh 1.1
396     RETURN
397     END

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