/[MITgcm]/MITgcm_contrib/ecco_darwin/v4_llc270/code_darwin/ggl90_calc.F
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Revision 1.1 - (hide annotations) (download)
Thu Aug 15 23:38:50 2019 UTC (7 years ago) by dcarroll
Branch: MAIN
check in of revised CO2 flux budget code (development in progress)

1 dcarroll 1.1 C $Header: /u/gcmpack/MITgcm/pkg/ggl90/ggl90_calc.F,v 1.35 2016/10/26 00:49:04 jmc Exp $
2     C $Name: $
3    
4     #include "GGL90_OPTIONS.h"
5    
6     CBOP
7     C !ROUTINE: GGL90_CALC
8    
9     C !INTERFACE: ======================================================
10     SUBROUTINE GGL90_CALC(
11     I bi, bj, sigmaR, myTime, myIter, myThid )
12    
13     C !DESCRIPTION: \bv
14     C *==========================================================*
15     C | SUBROUTINE GGL90_CALC |
16     C | o Compute all GGL90 fields defined in GGL90.h |
17     C *==========================================================*
18     C | Equation numbers refer to |
19     C | Gaspar et al. (1990), JGR 95 (C9), pp 16,179 |
20     C | Some parts of the implementation follow Blanke and |
21     C | Delecuse (1993), JPO, and OPA code, in particular the |
22     C | computation of the |
23     C | mixing length = max(min(lk,depth),lkmin) |
24     C *==========================================================*
25    
26     C global parameters updated by ggl90_calc
27     C GGL90TKE :: sub-grid turbulent kinetic energy (m^2/s^2)
28     C GGL90viscAz :: GGL90 eddy viscosity coefficient (m^2/s)
29     C GGL90diffKzT :: GGL90 diffusion coefficient for temperature (m^2/s)
30     C \ev
31    
32     C !USES: ============================================================
33     IMPLICIT NONE
34     #include "SIZE.h"
35     #include "EEPARAMS.h"
36     #include "PARAMS.h"
37     #include "DYNVARS.h"
38     #include "FFIELDS.h"
39     #include "GRID.h"
40     #include "GGL90.h"
41    
42     C !INPUT PARAMETERS: ===================================================
43     C Routine arguments
44     C bi, bj :: Current tile indices
45     C sigmaR :: Vertical gradient of iso-neutral density
46     C myTime :: Current time in simulation
47     C myIter :: Current time-step number
48     C myThid :: My Thread Id number
49     INTEGER bi, bj
50     _RL sigmaR(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
51     _RL myTime
52     INTEGER myIter
53     INTEGER myThid
54    
55     #ifdef ALLOW_GGL90
56    
57     C !LOCAL VARIABLES: ====================================================
58     C Local constants
59     C iMin,iMax,jMin,jMax :: index boundaries of computation domain
60     C i, j, k, kp1,km1 :: array computation indices
61     C kSurf, kBottom :: vertical indices of domain boundaries
62     C hFac/hFacI :: fractional thickness of W-cell
63     C explDissFac :: explicit Dissipation Factor (in [0-1])
64     C implDissFac :: implicit Dissipation Factor (in [0-1])
65     C uStarSquare :: square of friction velocity
66     C verticalShear :: (squared) vertical shear of horizontal velocity
67     C Nsquare :: squared buoyancy freqency
68     C RiNumber :: local Richardson number
69     C KappaM :: (local) viscosity parameter (eq.10)
70     C KappaH :: (local) diffusivity parameter for temperature (eq.11)
71     C KappaE :: (local) diffusivity parameter for TKE (eq.15)
72     C TKEdissipation :: dissipation of TKE
73     C GGL90mixingLength:: mixing length of scheme following Banke+Delecuse
74     C rMixingLength:: inverse of mixing length
75     C totalDepth :: thickness of water column (inverse of recip_Rcol)
76     C TKEPrandtlNumber :: here, an empirical function of the Richardson number
77     INTEGER iMin ,iMax ,jMin ,jMax
78     INTEGER i, j, k, kp1, km1, kSurf, kBottom
79     _RL explDissFac, implDissFac
80     _RL uStarSquare
81     _RL verticalShear(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
82     _RL KappaM(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
83     _RL KappaH
84     c _RL Nsquare
85     _RL Nsquare(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
86     _RL deltaTggl90
87     c _RL SQRTTKE
88     _RL SQRTTKE(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
89     _RL RiNumber
90     #ifdef ALLOW_GGL90_IDEMIX
91     _RL IDEMIX_RiNumber
92     #endif
93     _RL TKEdissipation
94     _RL tempU, tempUp, tempV, tempVp, prTemp
95     _RL MaxLength, tmpmlx, tmpVisc
96     _RL TKEPrandtlNumber (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
97     _RL GGL90mixingLength(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
98     _RL rMixingLength (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
99     _RL mxLength_Dn (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
100     _RL KappaE (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
101     _RL totalDepth (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
102     _RL GGL90visctmp (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
103     #ifdef ALLOW_DIAGNOSTICS
104     _RL surf_flx_tke (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
105     #endif /* ALLOW_DIAGNOSTICS */
106     C hFac(I) :: fractional thickness of W-cell
107     _RL hFac
108     #ifdef ALLOW_GGL90_IDEMIX
109     _RL hFacI(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
110     #endif /* ALLOW_GGL90_IDEMIX */
111     _RL recip_hFacI(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
112     C- tri-diagonal matrix
113     _RL a3d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
114     _RL b3d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
115     _RL c3d(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
116     INTEGER errCode
117     #ifdef ALLOW_GGL90_HORIZDIFF
118     C xA, yA :: area of lateral faces
119     C dfx, dfy :: diffusive flux across lateral faces
120     C gTKE :: right hand side of diffusion equation
121     _RL xA (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
122     _RL yA (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
123     _RL dfx(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
124     _RL dfy(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
125     _RL gTKE(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
126     #endif /* ALLOW_GGL90_HORIZDIFF */
127     #ifdef ALLOW_GGL90_SMOOTH
128     _RL p4, p8, p16
129     #endif
130     CEOP
131    
132     PARAMETER( iMin = 2-OLx, iMax = sNx+OLx-1 )
133     PARAMETER( jMin = 2-OLy, jMax = sNy+OLy-1 )
134     #ifdef ALLOW_GGL90_SMOOTH
135     p4 = 0.25 _d 0
136     p8 = 0.125 _d 0
137     p16 = 0.0625 _d 0
138     #endif
139    
140     C set separate time step (should be deltaTtracer)
141     deltaTggl90 = dTtracerLev(1)
142    
143     kSurf = 1
144     C explicit/implicit timestepping weights for dissipation
145     explDissFac = 0. _d 0
146     implDissFac = 1. _d 0 - explDissFac
147    
148     C For nonlinear free surface and especially with r*-coordinates, the
149     C hFacs change every timestep, so we need to update them here in the
150     C case of using IDEMIX.
151     DO K=1,Nr
152     Km1 = MAX(K-1,1)
153     DO j=1-OLy,sNy+OLy
154     DO i=1-OLx,sNx+OLx
155     hFac =
156     & MIN(.5 _d 0,_hFacC(i,j,km1,bi,bj) ) +
157     & MIN(.5 _d 0,_hFacC(i,j,k ,bi,bj) )
158     recip_hFacI(I,J,K)=0. _d 0
159     IF ( hFac .NE. 0. _d 0 )
160     & recip_hFacI(I,J,K)=1. _d 0/hFac
161     #ifdef ALLOW_GGL90_IDEMIX
162     hFacI(i,j,k) = hFac
163     #endif /* ALLOW_GGL90_IDEMIX */
164     ENDDO
165     ENDDO
166     ENDDO
167    
168     C Initialize local fields
169     DO k = 1, Nr
170     DO j=1-OLy,sNy+OLy
171     DO i=1-OLx,sNx+OLx
172     rMixingLength(i,j,k) = 0. _d 0
173     mxLength_Dn(i,j,k) = 0. _d 0
174     GGL90visctmp(i,j,k) = 0. _d 0
175     KappaE(i,j,k) = 0. _d 0
176     TKEPrandtlNumber(i,j,k) = 1. _d 0
177     GGL90mixingLength(i,j,k) = GGL90mixingLengthMin
178     GGL90visctmp(i,j,k) = 0. _d 0
179     #ifndef SOLVE_DIAGONAL_LOWMEMORY
180     a3d(i,j,k) = 0. _d 0
181     b3d(i,j,k) = 1. _d 0
182     c3d(i,j,k) = 0. _d 0
183     #endif
184     Nsquare(i,j,k) = 0. _d 0
185     SQRTTKE(i,j,k) = 0. _d 0
186     ENDDO
187     ENDDO
188     ENDDO
189     DO j=1-OLy,sNy+OLy
190     DO i=1-OLx,sNx+OLx
191     KappaM(i,j) = 0. _d 0
192     verticalShear(i,j) = 0. _d 0
193     totalDepth(i,j) = Ro_surf(i,j,bi,bj) - R_low(i,j,bi,bj)
194     rMixingLength(i,j,1) = 0. _d 0
195     mxLength_Dn(i,j,1) = GGL90mixingLengthMin
196     SQRTTKE(i,j,1) = SQRT( GGL90TKE(i,j,1,bi,bj) )
197     #ifdef ALLOW_GGL90_HORIZDIFF
198     xA(i,j) = 0. _d 0
199     yA(i,j) = 0. _d 0
200     dfx(i,j) = 0. _d 0
201     dfy(i,j) = 0. _d 0
202     gTKE(i,j) = 0. _d 0
203     #endif /* ALLOW_GGL90_HORIZDIFF */
204     ENDDO
205     ENDDO
206    
207     #ifdef ALLOW_GGL90_IDEMIX
208     IF ( useIDEMIX) CALL GGL90_IDEMIX(
209     & bi, bj, hFacI, recip_hFacI, sigmaR, myTime, myIter, myThid )
210     #endif /* ALLOW_GGL90_IDEMIX */
211    
212     DO k = 2, Nr
213     DO j=jMin,jMax
214     DO i=iMin,iMax
215     SQRTTKE(i,j,k)=SQRT( GGL90TKE(i,j,k,bi,bj) )
216    
217     C buoyancy frequency
218     Nsquare(i,j,k) = gravity*gravitySign*recip_rhoConst
219     & * sigmaR(i,j,k)
220     C vertical shear term (dU/dz)^2+(dV/dz)^2 is computed later
221     C to save some memory
222     C mixing length
223     GGL90mixingLength(i,j,k) = SQRTTWO *
224     & SQRTTKE(i,j,k)/SQRT( MAX(Nsquare(i,j,k),GGL90eps) )
225     ENDDO
226     ENDDO
227     ENDDO
228    
229     C- ensure mixing between first and second level
230     IF (mxlSurfFlag) THEN
231     DO j=jMin,jMax
232     DO i=iMin,iMax
233     GGL90mixingLength(i,j,2)=drF(1)
234     ENDDO
235     ENDDO
236     ENDIF
237    
238     C-- Impose upper and lower bound for mixing length
239     C-- Impose minimum mixing length to avoid division by zero
240     IF ( mxlMaxFlag .EQ. 0 ) THEN
241    
242     DO k=2,Nr
243     DO j=jMin,jMax
244     DO i=iMin,iMax
245     MaxLength=totalDepth(i,j)
246     GGL90mixingLength(i,j,k) = MIN(GGL90mixingLength(i,j,k),
247     & MaxLength)
248     ENDDO
249     ENDDO
250     ENDDO
251    
252     DO k=2,Nr
253     DO j=jMin,jMax
254     DO i=iMin,iMax
255     GGL90mixingLength(i,j,k) = MAX(GGL90mixingLength(i,j,k),
256     & GGL90mixingLengthMin)
257     rMixingLength(i,j,k) = 1. _d 0 / GGL90mixingLength(i,j,k)
258     ENDDO
259     ENDDO
260     ENDDO
261    
262     ELSEIF ( mxlMaxFlag .EQ. 1 ) THEN
263    
264     DO k=2,Nr
265     DO j=jMin,jMax
266     DO i=iMin,iMax
267     MaxLength=MIN(Ro_surf(i,j,bi,bj)-rF(k),rF(k)-R_low(i,j,bi,bj))
268     c MaxLength=MAX(MaxLength,20. _d 0)
269     GGL90mixingLength(i,j,k) = MIN(GGL90mixingLength(i,j,k),
270     & MaxLength)
271     ENDDO
272     ENDDO
273     ENDDO
274    
275     DO k=2,Nr
276     DO j=jMin,jMax
277     DO i=iMin,iMax
278     GGL90mixingLength(i,j,k) = MAX(GGL90mixingLength(i,j,k),
279     & GGL90mixingLengthMin)
280     rMixingLength(i,j,k) = 1. _d 0 / GGL90mixingLength(i,j,k)
281     ENDDO
282     ENDDO
283     ENDDO
284    
285     ELSEIF ( mxlMaxFlag .EQ. 2 ) THEN
286    
287     DO k=2,Nr
288     DO j=jMin,jMax
289     DO i=iMin,iMax
290     GGL90mixingLength(i,j,k) = MIN(GGL90mixingLength(i,j,k),
291     & GGL90mixingLength(i,j,k-1)+drF(k-1))
292     ENDDO
293     ENDDO
294     ENDDO
295     DO j=jMin,jMax
296     DO i=iMin,iMax
297     GGL90mixingLength(i,j,Nr) = MIN(GGL90mixingLength(i,j,Nr),
298     & GGL90mixingLengthMin+drF(Nr))
299     ENDDO
300     ENDDO
301     DO k=Nr-1,2,-1
302     DO j=jMin,jMax
303     DO i=iMin,iMax
304     GGL90mixingLength(i,j,k) = MIN(GGL90mixingLength(i,j,k),
305     & GGL90mixingLength(i,j,k+1)+drF(k))
306     ENDDO
307     ENDDO
308     ENDDO
309    
310     DO k=2,Nr
311     DO j=jMin,jMax
312     DO i=iMin,iMax
313     GGL90mixingLength(i,j,k) = MAX(GGL90mixingLength(i,j,k),
314     & GGL90mixingLengthMin)
315     rMixingLength(i,j,k) = 1. _d 0 / GGL90mixingLength(i,j,k)
316     ENDDO
317     ENDDO
318     ENDDO
319    
320     ELSEIF ( mxlMaxFlag .EQ. 3 ) THEN
321    
322     DO k=2,Nr
323     DO j=jMin,jMax
324     DO i=iMin,iMax
325     mxLength_Dn(i,j,k) = MIN(GGL90mixingLength(i,j,k),
326     & mxLength_Dn(i,j,k-1)+drF(k-1))
327     ENDDO
328     ENDDO
329     ENDDO
330     DO j=jMin,jMax
331     DO i=iMin,iMax
332     GGL90mixingLength(i,j,Nr) = MIN(GGL90mixingLength(i,j,Nr),
333     & GGL90mixingLengthMin+drF(Nr))
334     ENDDO
335     ENDDO
336     DO k=Nr-1,2,-1
337     DO j=jMin,jMax
338     DO i=iMin,iMax
339     GGL90mixingLength(i,j,k) = MIN(GGL90mixingLength(i,j,k),
340     & GGL90mixingLength(i,j,k+1)+drF(k))
341     ENDDO
342     ENDDO
343     ENDDO
344    
345     DO k=2,Nr
346     DO j=jMin,jMax
347     DO i=iMin,iMax
348     GGL90mixingLength(i,j,k) = MIN(GGL90mixingLength(i,j,k),
349     & mxLength_Dn(i,j,k))
350     tmpmlx = SQRT( GGL90mixingLength(i,j,k)*mxLength_Dn(i,j,k) )
351     tmpmlx = MAX( tmpmlx, GGL90mixingLengthMin)
352     rMixingLength(i,j,k) = 1. _d 0 / tmpmlx
353     ENDDO
354     ENDDO
355     ENDDO
356    
357     ELSE
358     STOP 'GGL90_CALC: Wrong mxlMaxFlag (mixing length limit)'
359     ENDIF
360    
361     C start "proper" k-loop (the code above was moved out and up to
362     C implemement various mixing parameters efficiently)
363     DO k=2,Nr
364     km1 = k-1
365    
366     #ifdef ALLOW_GGL90_HORIZDIFF
367     IF ( GGL90diffTKEh .GT. 0. _d 0 ) THEN
368     C horizontal diffusion of TKE (requires an exchange in
369     C do_fields_blocking_exchanges)
370     C common factors
371     DO j=1-OLy,sNy+OLy
372     DO i=1-OLx,sNx+OLx
373     xA(i,j) = _dyG(i,j,bi,bj)*drC(k)*
374     & (min(.5 _d 0,_hFacW(i,j,k-1,bi,bj) ) +
375     & min(.5 _d 0,_hFacW(i,j,k ,bi,bj) ) )
376     yA(i,j) = _dxG(i,j,bi,bj)*drC(k)*
377     & (min(.5 _d 0,_hFacS(i,j,k-1,bi,bj) ) +
378     & min(.5 _d 0,_hFacS(i,j,k ,bi,bj) ) )
379     ENDDO
380     ENDDO
381     C Compute diffusive fluxes
382     C ... across x-faces
383     DO j=1-OLy,sNy+OLy
384     dfx(1-OLx,j)=0. _d 0
385     DO i=1-OLx+1,sNx+OLx
386     dfx(i,j) = -GGL90diffTKEh*xA(i,j)
387     & *_recip_dxC(i,j,bi,bj)
388     & *(GGL90TKE(i,j,k,bi,bj)-GGL90TKE(i-1,j,k,bi,bj))
389     #ifdef ISOTROPIC_COS_SCALING
390     & *CosFacU(j,bi,bj)
391     #endif /* ISOTROPIC_COS_SCALING */
392     ENDDO
393     ENDDO
394     C ... across y-faces
395     DO i=1-OLx,sNx+OLx
396     dfy(i,1-OLy)=0. _d 0
397     ENDDO
398     DO j=1-OLy+1,sNy+OLy
399     DO i=1-OLx,sNx+OLx
400     dfy(i,j) = -GGL90diffTKEh*yA(i,j)
401     & *_recip_dyC(i,j,bi,bj)
402     & *(GGL90TKE(i,j,k,bi,bj)-GGL90TKE(i,j-1,k,bi,bj))
403     #ifdef ISOTROPIC_COS_SCALING
404     & *CosFacV(j,bi,bj)
405     #endif /* ISOTROPIC_COS_SCALING */
406     ENDDO
407     ENDDO
408     C Compute divergence of fluxes
409     DO j=1-OLy,sNy+OLy-1
410     DO i=1-OLx,sNx+OLx-1
411     gTKE(i,j) = -recip_drC(k)*recip_rA(i,j,bi,bj)
412     & *recip_hFacI(i,j,k)
413     & *((dfx(i+1,j)-dfx(i,j))
414     & + (dfy(i,j+1)-dfy(i,j)) )
415     ENDDO
416     ENDDO
417     C end if GGL90diffTKEh .eq. 0.
418     ENDIF
419     #endif /* ALLOW_GGL90_HORIZDIFF */
420    
421     C viscosity and diffusivity
422     DO j=jMin,jMax
423     DO i=iMin,iMax
424     KappaM(i,j) = GGL90ck*GGL90mixingLength(i,j,k)*SQRTTKE(i,j,k)
425     GGL90visctmp(i,j,k) = MAX(KappaM(i,j),diffKrNrS(k))
426     & * maskC(i,j,k,bi,bj)
427     C note: storing GGL90visctmp like this, and using it later to compute
428     C GGL9rdiffKr etc. is robust in case of smoothing (e.g. see OPA)
429     KappaM(i,j) = MAX(KappaM(i,j),viscArNr(k)) * maskC(i,j,k,bi,bj)
430     ENDDO
431     ENDDO
432    
433     C compute vertical shear (dU/dz)^2+(dV/dz)^2
434     IF ( calcMeanVertShear ) THEN
435     C by averaging (@ grid-cell center) the 4 vertical shear compon @ U,V pos.
436     DO j=jMin,jMax
437     DO i=iMin,iMax
438     tempU = ( uVel( i ,j,km1,bi,bj) - uVel( i ,j,k,bi,bj) )
439     tempUp = ( uVel(i+1,j,km1,bi,bj) - uVel(i+1,j,k,bi,bj) )
440     tempV = ( vVel(i, j ,km1,bi,bj) - vVel(i, j ,k,bi,bj) )
441     tempVp = ( vVel(i,j+1,km1,bi,bj) - vVel(i,j+1,k,bi,bj) )
442     verticalShear(i,j) = (
443     & ( tempU*tempU + tempUp*tempUp )*halfRL
444     & + ( tempV*tempV + tempVp*tempVp )*halfRL
445     & )*recip_drC(k)*recip_drC(k)
446     ENDDO
447     ENDDO
448     ELSE
449     C from the averaged flow at grid-cell center (2 compon x 2 pos.)
450     DO j=jMin,jMax
451     DO i=iMin,iMax
452     tempU = ( ( uVel(i,j,km1,bi,bj) + uVel(i+1,j,km1,bi,bj) )
453     & -( uVel(i,j,k ,bi,bj) + uVel(i+1,j,k ,bi,bj) )
454     & )*halfRL*recip_drC(k)
455     tempV = ( ( vVel(i,j,km1,bi,bj) + vVel(i,j+1,km1,bi,bj) )
456     & -( vVel(i,j,k ,bi,bj) + vVel(i,j+1,k ,bi,bj) )
457     & )*halfRL*recip_drC(k)
458     verticalShear(i,j) = tempU*tempU + tempV*tempV
459     ENDDO
460     ENDDO
461     ENDIF
462    
463     C compute Prandtl number (always greater than 0)
464     #ifdef ALLOW_GGL90_IDEMIX
465     IF ( useIDEMIX ) THEN
466     DO j=jMin,jMax
467     DO i=iMin,iMax
468     C account for partical cell factor in vertical shear:
469     verticalShear(i,j) = verticalShear(i,j)
470     & * recip_hFacI(i,j,k)*recip_hFacI(i,j,k)
471     RiNumber = MAX(Nsquare(i,j,k),0. _d 0)
472     & /(verticalShear(i,j)+GGL90eps)
473     CML IDEMIX_RiNumber = 1./GGL90eps
474     IDEMIX_RiNumber = MAX( KappaM(i,j)*Nsquare(i,j,k), 0. _d 0)/
475     & (GGL90eps+IDEMIX_tau_d(i,j,k,bi,bj)*IDEMIX_E(i,j,k,bi,bj)**2)
476     prTemp = MIN(5.*RiNumber, 6.6 _d 0*IDEMIX_RiNumber)
477     TKEPrandtlNumber(i,j,k) = MIN(10. _d 0,prTemp)
478     TKEPrandtlNumber(i,j,k) = MAX( 1. _d 0,TKEPrandtlNumber(i,j,k))
479     ENDDO
480     ENDDO
481     ELSE
482     #else /* ndef ALLOW_GGL90_IDEMIX */
483     IF (.TRUE.) THEN
484     #endif /* ALLOW_GGL90_IDEMIX */
485     DO j=jMin,jMax
486     DO i=iMin,iMax
487     RiNumber = MAX(Nsquare(i,j,k),0. _d 0)
488     & /(verticalShear(i,j)+GGL90eps)
489     prTemp = 1. _d 0
490     IF ( RiNumber .GE. 0.2 _d 0 ) prTemp = 5. _d 0 * RiNumber
491     TKEPrandtlNumber(i,j,k) = MIN(10. _d 0,prTemp)
492     ENDDO
493     ENDDO
494     ENDIF
495    
496     DO j=jMin,jMax
497     DO i=iMin,iMax
498     C diffusivity
499     KappaH = KappaM(i,j)/TKEPrandtlNumber(i,j,k)
500     KappaE(i,j,k) = GGL90alpha * KappaM(i,j) * maskC(i,j,k,bi,bj)
501    
502     C dissipation term
503     TKEdissipation = explDissFac*GGL90ceps
504     & *SQRTTKE(i,j,k)*rMixingLength(i,j,k)
505     & *GGL90TKE(i,j,k,bi,bj)
506     C partial update with sum of explicit contributions
507     GGL90TKE(i,j,k,bi,bj) = GGL90TKE(i,j,k,bi,bj)
508     & + deltaTggl90*(
509     & + KappaM(i,j)*verticalShear(i,j)
510     & - KappaH*Nsquare(i,j,k)
511     & - TKEdissipation
512     & )
513     ENDDO
514     ENDDO
515    
516     #ifdef ALLOW_GGL90_IDEMIX
517     IF ( useIDEMIX ) THEN
518     C add IDEMIX contribution to the turbulent kinetic energy
519     DO j=jMin,jMax
520     DO i=iMin,iMax
521     GGL90TKE(i,j,k,bi,bj) = GGL90TKE(i,j,k,bi,bj)
522     & + deltaTggl90*(
523     & + IDEMIX_tau_d(i,j,k,bi,bj)*IDEMIX_E(i,j,k,bi,bj)**2
524     & )
525     ENDDO
526     ENDDO
527     ENDIF
528     #endif /* ALLOW_GGL90_IDEMIX */
529    
530     #ifdef ALLOW_GGL90_HORIZDIFF
531     IF ( GGL90diffTKEh .GT. 0. _d 0 ) THEN
532     C-- Add horiz. diffusion tendency
533     DO j=jMin,jMax
534     DO i=iMin,iMax
535     GGL90TKE(i,j,k,bi,bj) = GGL90TKE(i,j,k,bi,bj)
536     & + gTKE(i,j)*deltaTggl90
537     ENDDO
538     ENDDO
539     ENDIF
540     #endif /* ALLOW_GGL90_HORIZDIFF */
541    
542     C-- end of k loop
543     ENDDO
544    
545     C ============================================
546     C Implicit time step to update TKE for k=1,Nr;
547     C TKE(Nr+1)=0 by default
548     C ============================================
549     C set up matrix
550     C-- Lower diagonal
551     DO j=jMin,jMax
552     DO i=iMin,iMax
553     a3d(i,j,1) = 0. _d 0
554     ENDDO
555     ENDDO
556     DO k=2,Nr
557     km1=MAX(2,k-1)
558     DO j=jMin,jMax
559     DO i=iMin,iMax
560     C- We keep recip_hFacC in the diffusive flux calculation,
561     C- but no hFacC in TKE volume control
562     C- No need for maskC(k-1) with recip_hFacC(k-1)
563     a3d(i,j,k) = -deltaTggl90
564     & *recip_drF(k-1)*recip_hFacC(i,j,k-1,bi,bj)
565     & *.5 _d 0*(KappaE(i,j, k )+KappaE(i,j,km1))
566     & *recip_drC(k)*maskC(i,j,k,bi,bj)
567     ENDDO
568     ENDDO
569     ENDDO
570     C-- Upper diagonal
571     DO j=jMin,jMax
572     DO i=iMin,iMax
573     c3d(i,j,1) = 0. _d 0
574     ENDDO
575     ENDDO
576     DO k=2,Nr
577     DO j=jMin,jMax
578     DO i=iMin,iMax
579     kp1=MAX(1,MIN(klowC(i,j,bi,bj),k+1))
580     C- We keep recip_hFacC in the diffusive flux calculation,
581     C- but no hFacC in TKE volume control
582     C- No need for maskC(k) with recip_hFacC(k)
583     c3d(i,j,k) = -deltaTggl90
584     & *recip_drF( k ) * recip_hFacC(i,j,k,bi,bj)
585     & *.5 _d 0*(KappaE(i,j,k)+KappaE(i,j,kp1))
586     & *recip_drC(k)*maskC(i,j,k-1,bi,bj)
587     ENDDO
588     ENDDO
589     ENDDO
590    
591     #ifdef ALLOW_GGL90_IDEMIX
592     IF ( useIDEMIX ) THEN
593     DO k=2,Nr
594     DO j=jMin,jMax
595     DO i=iMin,iMax
596     a3d(i,j,k) = a3d(i,j,k)*recip_hFacI(i,j,k)
597     c3d(i,j,k) = c3d(i,j,k)*recip_hFacI(i,j,k)
598     ENDDO
599     ENDDO
600     ENDDO
601     ENDIF
602     #endif /* ALLOW_GGL90_IDEMIX */
603    
604     IF (.NOT.GGL90_dirichlet) THEN
605     C Neumann bottom boundary condition for TKE: no flux from bottom
606     DO j=jMin,jMax
607     DO i=iMin,iMax
608     kBottom = MAX(kLowC(i,j,bi,bj),1)
609     c3d(i,j,kBottom) = 0. _d 0
610     ENDDO
611     ENDDO
612     ENDIF
613    
614     C-- Center diagonal
615     DO k=1,Nr
616     km1 = MAX(k-1,1)
617     DO j=jMin,jMax
618     DO i=iMin,iMax
619     b3d(i,j,k) = 1. _d 0 - c3d(i,j,k) - a3d(i,j,k)
620     & + implDissFac*deltaTggl90*GGL90ceps*SQRTTKE(i,j,k)
621     & * rMixingLength(i,j,k)
622     & * maskC(i,j,k,bi,bj)*maskC(i,j,km1,bi,bj)
623     ENDDO
624     ENDDO
625     ENDDO
626     C end set up matrix
627    
628     C Apply boundary condition
629     kp1 = MIN(Nr,kSurf+1)
630     DO j=jMin,jMax
631     DO i=iMin,iMax
632     C estimate friction velocity uStar from surface forcing
633     uStarSquare = SQRT(
634     & ( .5 _d 0*( surfaceForcingU(i, j, bi,bj)
635     & + surfaceForcingU(i+1,j, bi,bj) ) )**2
636     & + ( .5 _d 0*( surfaceForcingV(i, j, bi,bj)
637     & + surfaceForcingV(i, j+1,bi,bj) ) )**2
638     & )
639     C Dirichlet surface boundary condition for TKE
640     GGL90TKE(i,j,kSurf,bi,bj) = maskC(i,j,kSurf,bi,bj)
641     & *MAX(GGL90TKEsurfMin,GGL90m2*uStarSquare)
642     GGL90TKE(i,j,kp1,bi,bj) = GGL90TKE(i,j,kp1,bi,bj)
643     & - a3d(i,j,kp1)*GGL90TKE(i,j,kSurf,bi,bj)
644     a3d(i,j,kp1) = 0. _d 0
645     ENDDO
646     ENDDO
647    
648     IF (GGL90_dirichlet) THEN
649     C Dirichlet bottom boundary condition for TKE = GGL90TKEbottom
650     DO j=jMin,jMax
651     DO i=iMin,iMax
652     kBottom = MAX(kLowC(i,j,bi,bj),1)
653     GGL90TKE(i,j,kBottom,bi,bj) = GGL90TKE(i,j,kBottom,bi,bj)
654     & - GGL90TKEbottom*c3d(i,j,kBottom)
655     c3d(i,j,kBottom) = 0. _d 0
656     ENDDO
657     ENDDO
658     ENDIF
659    
660     C solve tri-diagonal system
661     errCode = -1
662     CALL SOLVE_TRIDIAGONAL( iMin,iMax, jMin,jMax,
663     I a3d, b3d, c3d,
664     U GGL90TKE(1-OLx,1-OLy,1,bi,bj),
665     O errCode,
666     I bi, bj, myThid )
667    
668     DO k=1,Nr
669     DO j=jMin,jMax
670     DO i=iMin,iMax
671     C impose minimum TKE to avoid numerical undershoots below zero
672     GGL90TKE(i,j,k,bi,bj) = maskC(i,j,k,bi,bj)
673     & *MAX( GGL90TKE(i,j,k,bi,bj), GGL90TKEmin )
674     ENDDO
675     ENDDO
676     ENDDO
677    
678     C end of time step
679     C ===============================
680    
681     DO k=2,Nr
682     DO j=1,sNy
683     DO i=1,sNx
684     #ifdef ALLOW_GGL90_SMOOTH
685     tmpVisc = (
686     & p4 * GGL90visctmp(i ,j ,k)*mskCor(i ,j ,bi,bj)
687     & +p8 *( ( GGL90visctmp(i-1,j ,k)*mskCor(i-1,j ,bi,bj)
688     & + GGL90visctmp(i+1,j ,k)*mskCor(i+1,j ,bi,bj) )
689     & + ( GGL90visctmp(i ,j-1,k)*mskCor(i ,j-1,bi,bj)
690     & + GGL90visctmp(i ,j+1,k)*mskCor(i ,j+1,bi,bj) ) )
691     & +p16*( ( GGL90visctmp(i+1,j+1,k)*mskCor(i+1,j+1,bi,bj)
692     & + GGL90visctmp(i-1,j-1,k)*mskCor(i-1,j-1,bi,bj) )
693     & + ( GGL90visctmp(i+1,j-1,k)*mskCor(i+1,j-1,bi,bj)
694     & + GGL90visctmp(i-1,j+1,k)*mskCor(i-1,j+1,bi,bj) ) )
695     & )/(
696     & p4
697     & +p8 *( ( maskC(i-1,j ,k,bi,bj)*mskCor(i-1,j ,bi,bj)
698     & + maskC(i+1,j ,k,bi,bj)*mskCor(i+1,j ,bi,bj) )
699     & + ( maskC(i ,j-1,k,bi,bj)*mskCor(i ,j-1,bi,bj)
700     & + maskC(i ,j+1,k,bi,bj)*mskCor(i ,j+1,bi,bj) ) )
701     & +p16*( ( maskC(i+1,j+1,k,bi,bj)* mskCor(i+1,j+1,bi,bj)
702     & + maskC(i-1,j-1,k,bi,bj)*mskCor(i-1,j-1,bi,bj) )
703     & + ( maskC(i+1,j-1,k,bi,bj)*mskCor(i+1,j-1,bi,bj)
704     & + maskC(i-1,j+1,k,bi,bj)*mskCor(i-1,j+1,bi,bj) ) )
705     & )*maskC(i,j,k,bi,bj)*mskCor(i,j,bi,bj)
706     #else
707     tmpVisc = GGL90visctmp(i,j,k)
708     #endif
709     tmpVisc = MIN(tmpVisc/TKEPrandtlNumber(i,j,k),GGL90diffMax)
710     GGL90diffKr(i,j,k,bi,bj)= MAX( tmpVisc , diffKrNrS(k) )
711     ENDDO
712     ENDDO
713     ENDDO
714    
715     DO k=2,Nr
716     DO j=1,sNy
717     DO i=1,sNx+1
718     #ifdef ALLOW_GGL90_SMOOTH
719     tmpVisc = (
720     & p4 *( GGL90visctmp(i-1,j ,k)*mskCor(i-1,j ,bi,bj)
721     & + GGL90visctmp(i ,j ,k)*mskCor(i ,j ,bi,bj) )
722     & +p8 *( ( GGL90visctmp(i-1,j-1,k)*mskCor(i-1,j-1,bi,bj)
723     & + GGL90visctmp(i ,j-1,k)*mskCor(i ,j-1,bi,bj) )
724     & + ( GGL90visctmp(i-1,j+1,k)*mskCor(i-1,j+1,bi,bj)
725     & + GGL90visctmp(i ,j+1,k)*mskCor(i ,j+1,bi,bj) ) )
726     & )/(
727     & p4 * 2. _d 0
728     & +p8 *( ( maskC(i-1,j-1,k,bi,bj)*mskCor(i-1,j-1,bi,bj)
729     & + maskC(i ,j-1,k,bi,bj)*mskCor(i ,j-1,bi,bj) )
730     & + ( maskC(i-1,j+1,k,bi,bj)*mskCor(i-1,j+1,bi,bj)
731     & + maskC(i ,j+1,k,bi,bj)*mskCor(i ,j+1,bi,bj) ) )
732     & )*maskC(i-1,j,k,bi,bj)*mskCor(i-1,j,bi,bj)
733     & *maskC(i ,j,k,bi,bj)*mskCor(i ,j,bi,bj)
734     #else
735     tmpVisc = _maskW(i,j,k,bi,bj) * halfRL
736     & *( GGL90visctmp(i-1,j,k)
737     & + GGL90visctmp(i,j,k) )
738     #endif
739     tmpVisc = MIN( tmpVisc , GGL90viscMax )
740     GGL90viscArU(i,j,k,bi,bj) = MAX( tmpVisc, viscArNr(k) )
741     ENDDO
742     ENDDO
743     ENDDO
744    
745     DO k=2,Nr
746     DO j=1,sNy+1
747     DO i=1,sNx
748     #ifdef ALLOW_GGL90_SMOOTH
749     tmpVisc = (
750     & p4 *( GGL90visctmp(i ,j-1,k)*mskCor(i ,j-1,bi,bj)
751     & + GGL90visctmp(i ,j ,k)*mskCor(i ,j ,bi,bj) )
752     & +p8 *( ( GGL90visctmp(i-1,j-1,k)*mskCor(i-1,j-1,bi,bj)
753     & + GGL90visctmp(i-1,j ,k)*mskCor(i-1,j ,bi,bj) )
754     & + ( GGL90visctmp(i+1,j-1,k)*mskCor(i+1,j-1,bi,bj)
755     & + GGL90visctmp(i+1,j ,k)*mskCor(i+1,j ,bi,bj) ) )
756     & )/(
757     & p4 * 2. _d 0
758     & +p8 *( ( maskC(i-1,j-1,k,bi,bj)*mskCor(i-1,j-1,bi,bj)
759     & + maskC(i-1,j ,k,bi,bj)*mskCor(i-1,j ,bi,bj) )
760     & + ( maskC(i+1,j-1,k,bi,bj)*mskCor(i+1,j-1,bi,bj)
761     & + maskC(i+1,j ,k,bi,bj)*mskCor(i+1,j ,bi,bj) ) )
762     & )*maskC(i,j-1,k,bi,bj)*mskCor(i,j-1,bi,bj)
763     & *maskC(i,j ,k,bi,bj)*mskCor(i,j ,bi,bj)
764     #else
765     tmpVisc = _maskS(i,j,k,bi,bj) * halfRL
766     & *( GGL90visctmp(i,j-1,k)
767     & + GGL90visctmp(i,j,k) )
768     #endif
769     tmpVisc = MIN( tmpVisc , GGL90viscMax )
770     GGL90viscArV(i,j,k,bi,bj) = MAX( tmpVisc, viscArNr(k) )
771     ENDDO
772     ENDDO
773     ENDDO
774    
775     #ifdef ALLOW_DIAGNOSTICS
776     IF ( useDiagnostics ) THEN
777     CALL DIAGNOSTICS_FILL( GGL90TKE ,'GGL90TKE',
778     & 0,Nr, 1, bi, bj, myThid )
779     CALL DIAGNOSTICS_FILL( GGL90viscArU,'GGL90ArU',
780     & 0,Nr, 1, bi, bj, myThid )
781     CALL DIAGNOSTICS_FILL( GGL90viscArV,'GGL90ArV',
782     & 0,Nr, 1, bi, bj, myThid )
783     CALL DIAGNOSTICS_FILL( GGL90diffKr,'GGL90Kr ',
784     & 0,Nr, 1, bi, bj, myThid )
785     CALL DIAGNOSTICS_FILL( TKEPrandtlNumber ,'GGL90Prl',
786     & 0,Nr, 2, bi, bj, myThid )
787     CALL DIAGNOSTICS_FILL( GGL90mixingLength,'GGL90Lmx',
788     & 0,Nr, 2, bi, bj, myThid )
789    
790     kp1 = MIN(Nr,kSurf+1)
791     DO j=jMin,jMax
792     DO i=iMin,iMax
793     C diagnose surface flux of TKE
794     surf_flx_tke(i,j) =(GGL90TKE(i,j,kSurf,bi,bj)-
795     & GGL90TKE(i,j,kp1,bi,bj))
796     & *recip_drF(kSurf)*recip_hFacC(i,j,kSurf,bi,bj)
797     & *KappaE(i,j,kp1)
798     ENDDO
799     ENDDO
800     CALL DIAGNOSTICS_FILL( surf_flx_tke,'GGL90flx',
801     & 0, 1, 2, bi, bj, myThid )
802    
803     k=kSurf
804     DO j=jMin,jMax
805     DO i=iMin,iMax
806     C diagnose work done by the wind
807     surf_flx_tke(i,j) =
808     & halfRL*( surfaceForcingU(i, j,bi,bj)*uVel(i ,j,k,bi,bj)
809     & +surfaceForcingU(i+1,j,bi,bj)*uVel(i+1,j,k,bi,bj))
810     & + halfRL*( surfaceForcingV(i,j, bi,bj)*vVel(i,j ,k,bi,bj)
811     & +surfaceForcingV(i,j+1,bi,bj)*vVel(i,j+1,k,bi,bj))
812     ENDDO
813     ENDDO
814     CALL DIAGNOSTICS_FILL( surf_flx_tke,'GGL90tau',
815     & 0, 1, 2, bi, bj, myThid )
816    
817     ENDIF
818     #endif /* ALLOW_DIAGNOSTICS */
819    
820     #endif /* ALLOW_GGL90 */
821    
822     RETURN
823     END

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