/[MITgcm]/MITgcm_contrib/verification_other/shelfice_remeshing/code/shelfice_thermodynamics.F
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Revision 1.19 - (hide annotations) (download)
Wed Jul 6 18:03:40 2016 UTC (9 years ago) by dgoldberg
Branch: MAIN
CVS Tags: checkpoint65y
Changes since 1.18: +37 -8 lines 
new files for vertical remeshing test only
1 dgoldberg 1.19 C $Header: /u/gcmpack/MITgcm_contrib/verification_other/shelfice_remeshing/code/shelfice_thermodynamics.F,v 1.18 2016/05/26 11:31:34 ksnow Exp $
2 dgoldberg 1.1 C $Name: $
3    
4     #include "SHELFICE_OPTIONS.h"
5     #ifdef ALLOW_AUTODIFF
6     # include "AUTODIFF_OPTIONS.h"
7     #endif
8     #ifdef ALLOW_CTRL
9     # include "CTRL_OPTIONS.h"
10     #endif
11    
12     CBOP
13     C !ROUTINE: SHELFICE_THERMODYNAMICS
14     C !INTERFACE:
15     SUBROUTINE SHELFICE_THERMODYNAMICS(
16     I myTime, myIter, myThid )
17     C !DESCRIPTION: \bv
18     C *=============================================================*
19     C | S/R SHELFICE_THERMODYNAMICS
20     C | o shelf-ice main routine.
21     C | compute temperature and (virtual) salt flux at the
22     C | shelf-ice ocean interface
23     C |
24     C | stresses at the ice/water interface are computed in separate
25     C | routines that are called from mom_fluxform/mom_vecinv
26     C *=============================================================*
27     C \ev
28    
29     C !USES:
30     IMPLICIT NONE
31    
32     C === Global variables ===
33     #include "SIZE.h"
34     #include "EEPARAMS.h"
35     #include "PARAMS.h"
36     #include "GRID.h"
37     #include "DYNVARS.h"
38     #include "FFIELDS.h"
39     #include "SHELFICE.h"
40     #include "SHELFICE_COST.h"
41     #ifdef ALLOW_AUTODIFF
42     # include "CTRL_SIZE.h"
43     # include "ctrl.h"
44     # include "ctrl_dummy.h"
45     #endif /* ALLOW_AUTODIFF */
46     #ifdef ALLOW_AUTODIFF_TAMC
47     # ifdef SHI_ALLOW_GAMMAFRICT
48     # include "tamc.h"
49     # include "tamc_keys.h"
50     # endif /* SHI_ALLOW_GAMMAFRICT */
51     #endif /* ALLOW_AUTODIFF_TAMC */
52     #ifdef ALLOW_STREAMICE
53     # include "STREAMICE.h"
54     #endif /* ALLOW_STREAMICE */
55    
56     C !INPUT/OUTPUT PARAMETERS:
57     C === Routine arguments ===
58     C myIter :: iteration counter for this thread
59     C myTime :: time counter for this thread
60     C myThid :: thread number for this instance of the routine.
61     _RL myTime
62     INTEGER myIter
63     INTEGER myThid
64    
65     #ifdef ALLOW_SHELFICE
66     C !LOCAL VARIABLES :
67     C === Local variables ===
68     C I,J,K,Kp1,bi,bj :: loop counters
69     C tLoc, sLoc, pLoc :: local in-situ temperature, salinity, pressure
70     C theta/saltFreeze :: temperature and salinity of water at the
71     C ice-ocean interface (at the freezing point)
72     C freshWaterFlux :: local variable for fresh water melt flux due
73     C to melting in kg/m^2/s
74     C (negative density x melt rate)
75     C convertFW2SaltLoc:: local copy of convertFW2Salt
76     C cFac :: 1 for conservative form, 0, otherwise
77     C rFac :: realFreshWaterFlux factor
78     C dFac :: 0 for diffusive heat flux (Holland and Jenkins, 1999,
79     C eq21)
80     C 1 for advective and diffusive heat flux (eq22, 26, 31)
81     C fwflxFac :: only effective for dFac=1, 1 if we expect a melting
82     C fresh water flux, 0 otherwise
83     C auxiliary variables and abbreviations:
84     C a0, a1, a2, b, c0
85     C eps1, eps2, eps3, eps3a, eps4, eps5, eps6, eps7, eps8
86     C aqe, bqe, cqe, discrim, recip_aqe
87     C drKp1, recip_drLoc
88 dgoldberg 1.16 INTEGER I,J,K,Kp1
89 dgoldberg 1.1 INTEGER bi,bj
90     _RL tLoc(1:sNx,1:sNy)
91     _RL sLoc(1:sNx,1:sNy)
92     _RL pLoc(1:sNx,1:sNy)
93 dgoldberg 1.16 #ifndef SHI_USTAR_WETPOINT
94 dgoldberg 1.1 _RL uLoc(1:sNx,1:sNy)
95     _RL vLoc(1:sNx,1:sNy)
96 dgoldberg 1.16 #endif
97     #ifdef SHI_USTAR_TOPDR
98     _RL u_topdr(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
99 dgoldberg 1.1 _RL v_topdr(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
100 dgoldberg 1.16 #endif
101     _RL velSq(1:sNx,1:sNy)
102 dgoldberg 1.1 _RL thetaFreeze, saltFreeze, recip_Cp
103     _RL freshWaterFlux, convertFW2SaltLoc
104     _RL a0, a1, a2, b, c0
105     _RL eps1, eps2, eps3, eps3a, eps4, eps5, eps6, eps7, eps8
106     _RL cFac, rFac, dFac, fwflxFac, realfwFac
107     _RL aqe, bqe, cqe, discrim, recip_aqe
108 dgoldberg 1.16 _RL drKp1, recip_drLoc
109 dgoldberg 1.1 _RL recip_latentHeat
110     _RL tmpFac
111 ksnow 1.17 C _RL massMin, mass, DELZ
112     _RL mass, DELZ
113 dgoldberg 1.3 _RL SHA,FACTOR1,FACTOR2,FACTOR3
114 dgoldberg 1.16 _RL ETA,SEALEVEL,oce_density
115 ksnow 1.17 C KS_dens, add massMin and EFFR, R_min, and remove above
116     _RL EFFR(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
117     _RL massMin(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
118     _RL R_min(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
119 dgoldberg 1.16
120 dgoldberg 1.1 #ifdef SHI_ALLOW_GAMMAFRICT
121     _RL shiPr, shiSc, shiLo, recip_shiKarman, shiTwoThirds
122     _RL gammaTmoleT, gammaTmoleS, gammaTurb, gammaTurbConst
123 dgoldberg 1.16 _RL ustar, ustarSq, etastar
124 dgoldberg 1.1 PARAMETER ( shiTwoThirds = 0.66666666666666666666666666667D0 )
125     #ifdef ALLOW_DIAGNOSTICS
126     _RL uStarDiag(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
127     #endif /* ALLOW_DIAGNOSTICS */
128     #endif
129    
130 dgoldberg 1.16 #ifndef ALLOW_OPENAD
131 dgoldberg 1.1 _RL SW_TEMP
132     EXTERNAL SW_TEMP
133     #endif
134    
135     #ifdef ALLOW_SHIFWFLX_CONTROL
136     _RL xx_shifwflx_loc(1-olx:snx+olx,1-oly:sny+oly,nsx,nsy)
137     #endif
138 dgoldberg 1.15
139     #ifdef ALLOW_SHELFICE_REMESHING
140     _RL GrdFactor(1-olx:snx+olx,1-oly:sny+oly,nsx,nsy)
141     #endif
142 dgoldberg 1.1 CEOP
143     C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
144    
145     #ifdef SHI_ALLOW_GAMMAFRICT
146     #ifdef ALLOW_AUTODIFF
147     C re-initialize here again, curtesy to TAF
148     DO bj = myByLo(myThid), myByHi(myThid)
149     DO bi = myBxLo(myThid), myBxHi(myThid)
150     DO J = 1-OLy,sNy+OLy
151     DO I = 1-OLx,sNx+OLx
152     shiTransCoeffT(i,j,bi,bj) = SHELFICEheatTransCoeff
153     shiTransCoeffS(i,j,bi,bj) = SHELFICEsaltTransCoeff
154     ENDDO
155     ENDDO
156     ENDDO
157     ENDDO
158     #endif /* ALLOW_AUTODIFF */
159     IF ( SHELFICEuseGammaFrict ) THEN
160     C Implement friction velocity-dependent transfer coefficient
161     C of Holland and Jenkins, JPO, 1999
162     recip_shiKarman= 1. _d 0 / 0.4 _d 0
163     shiLo = 0. _d 0
164     shiPr = shiPrandtl**shiTwoThirds
165     shiSc = shiSchmidt**shiTwoThirds
166     cph shiPr = (viscArNr(1)/diffKrNrT(1))**shiTwoThirds
167     cph shiSc = (viscArNr(1)/diffKrNrS(1))**shiTwoThirds
168     gammaTmoleT = 12.5 _d 0 * shiPr - 6. _d 0
169     gammaTmoleS = 12.5 _d 0 * shiSc - 6. _d 0
170     C instead of etastar = sqrt(1+zetaN*ustar./(f*Lo*Rc))
171     etastar = 1. _d 0
172     gammaTurbConst = 1. _d 0 / (2. _d 0 * shiZetaN*etastar)
173     & - recip_shiKarman
174     #ifdef ALLOW_AUTODIFF
175     DO bj = myByLo(myThid), myByHi(myThid)
176     DO bi = myBxLo(myThid), myBxHi(myThid)
177     DO J = 1-OLy,sNy+OLy
178     DO I = 1-OLx,sNx+OLx
179     shiTransCoeffT(i,j,bi,bj) = 0. _d 0
180     shiTransCoeffS(i,j,bi,bj) = 0. _d 0
181     ENDDO
182     ENDDO
183     ENDDO
184     ENDDO
185     #endif /* ALLOW_AUTODIFF */
186     ENDIF
187     #endif /* SHI_ALLOW_GAMMAFRICT */
188    
189     recip_latentHeat = 0. _d 0
190     IF ( SHELFICElatentHeat .NE. 0. _d 0 )
191     & recip_latentHeat = 1. _d 0/SHELFICElatentHeat
192     C are we doing the conservative form of Jenkins et al. (2001)?
193     recip_Cp = 1. _d 0 / HeatCapacity_Cp
194     cFac = 0. _d 0
195     IF ( SHELFICEconserve ) cFac = 1. _d 0
196     C with "real fresh water flux" (affecting ETAN),
197     C there is more to modify
198     rFac = 1. _d 0
199     IF ( SHELFICEconserve .AND. useRealFreshWaterFlux ) rFac = 0. _d 0
200     C heat flux into the ice shelf, default is diffusive flux
201     C (Holland and Jenkins, 1999, eq.21)
202     dFac = 0. _d 0
203     IF ( SHELFICEadvDiffHeatFlux ) dFac = 1. _d 0
204     fwflxFac = 0. _d 0
205 dgoldberg 1.16 C if shelficeboundarylayer is used with real freshwater flux,
206     c the T/S used for surface fluxes must be the cell T/S
207     realFWfac = 0. _d 0
208     IF ( SHELFICErealFWflux ) realFWfac = 1. _d 0
209    
210 dgoldberg 1.1 C linear dependence of freezing point on salinity
211     a0 = -0.0575 _d 0
212     a1 = 0.0 _d -0
213     a2 = 0.0 _d -0
214     c0 = 0.0901 _d 0
215     b = -7.61 _d -4
216     #ifdef ALLOW_ISOMIP_TD
217     IF ( useISOMIPTD ) THEN
218     C non-linear dependence of freezing point on salinity
219     a0 = -0.0575 _d 0
220     a1 = 1.710523 _d -3
221     a2 = -2.154996 _d -4
222     b = -7.53 _d -4
223     c0 = 0. _d 0
224     ENDIF
225     convertFW2SaltLoc = convertFW2Salt
226     C hardcoding this value here is OK because it only applies to ISOMIP
227     C where this value is part of the protocol
228     IF ( convertFW2SaltLoc .EQ. -1. ) convertFW2SaltLoc = 33.4 _d 0
229     #endif /* ALLOW_ISOMIP_TD */
230    
231     DO bj = myByLo(myThid), myByHi(myThid)
232     DO bi = myBxLo(myThid), myBxHi(myThid)
233     DO J = 1-OLy,sNy+OLy
234     DO I = 1-OLx,sNx+OLx
235     shelfIceHeatFlux (I,J,bi,bj) = 0. _d 0
236     shelfIceFreshWaterFlux(I,J,bi,bj) = 0. _d 0
237     shelficeForcingT (I,J,bi,bj) = 0. _d 0
238     shelficeForcingS (I,J,bi,bj) = 0. _d 0
239     #if (defined SHI_ALLOW_GAMMAFRICT && defined ALLOW_DIAGNOSTICS)
240     uStarDiag (I,J,bi,bj) = 0. _d 0
241     #endif /* SHI_ALLOW_GAMMAFRICT and ALLOW_DIAGNOSTICS */
242     ENDDO
243     ENDDO
244     ENDDO
245     ENDDO
246     #ifdef ALLOW_SHIFWFLX_CONTROL
247     DO bj = myByLo(myThid), myByHi(myThid)
248     DO bi = myBxLo(myThid), myBxHi(myThid)
249     DO J = 1-OLy,sNy+OLy
250     DO I = 1-OLx,sNx+OLx
251     xx_shifwflx_loc(I,J,bi,bj) = 0. _d 0
252     ENDDO
253     ENDDO
254     ENDDO
255     ENDDO
256     #ifdef ALLOW_CTRL
257     if (useCTRL) CALL CTRL_GET_GEN (
258     & xx_shifwflx_file, xx_shifwflxstartdate, xx_shifwflxperiod,
259     & maskSHI, xx_shifwflx_loc, xx_shifwflx0, xx_shifwflx1,
260     & xx_shifwflx_dummy,
261     & xx_shifwflx_remo_intercept, xx_shifwflx_remo_slope,
262     & wshifwflx,
263     & myTime, myIter, myThid )
264     #endif
265     #endif /* ALLOW_SHIFWFLX_CONTROL */
266     DO bj = myByLo(myThid), myByHi(myThid)
267     DO bi = myBxLo(myThid), myBxHi(myThid)
268    
269 dgoldberg 1.15
270 dgoldberg 1.16 IF (.not.usestreamice) THEN
271 dgoldberg 1.15 oce_density = 1028.
272 dgoldberg 1.16 ELSE
273 dgoldberg 1.15 oce_density = streamice_density_ocean_avg
274 dgoldberg 1.16 ENDIF
275 dgoldberg 1.15
276 dgoldberg 1.19 #ifdef ALLOW_SHELFICE_GROUNDED_ICE
277 dgoldberg 1.15
278 dgoldberg 1.16 SEALEVEL = 0. _d 0
279     C KS16 ------ add ETA, initialize and in called S/R------
280     ETA = 0. _d 0
281     CALL SHELFICE_SEA_LEVEL_AVG( SEALEVEL, ETA, myThid )
282 dgoldberg 1.15
283 ksnow 1.17 C KS_dens
284 dgoldberg 1.19 IF (shelfice_massmin_trueDens) then
285     CALL SHELFICE_MASSMIN(R_min,massMin,bi,bj,myThid)
286     ELSE
287     DO j = 1-OLy, sNy+OLy
288     DO i = 1-OLx, sNx+OLx
289    
290     massMin(i,j,bi,bj) = oce_density *
291     & (SEALEVEL-(R_low(i,j,bi,bj)+R_MWCT(i,j,bi,bj)))
292    
293    
294     ENDDO
295     ENDDO
296     ENDIF
297    
298 ksnow 1.17
299 dgoldberg 1.15 DO j = 1-OLy, sNy+OLy
300     DO i = 1-OLx, sNx+OLx
301    
302     mass = shelficemass(i,j,bi,bj)
303    
304 ksnow 1.17 GrdFactor(i,j,bi,bj) = tanh((massMin(i,j,bi,bj)
305     & - mass)*1. _d 5)
306 dgoldberg 1.15
307 ksnow 1.18 SHA=massMin(i,j,bi,bj)/
308     & SQRT(.01+mass**2)
309     FACTOR1 = ((1-sha)/2.)
310     FACTOR2 = (1+sha)/2.
311    
312     EFFMASS(I,J,BI,BJ)=
313     & (FACTOR1*GrdFactor(i,j,bi,bj) + FACTOR2)*mass
314 dgoldberg 1.15
315 ksnow 1.17 ENDDO
316     ENDDO
317     C KS_dens -----------------------------------------------
318 dgoldberg 1.15
319    
320     #endif
321 dgoldberg 1.19 ! allow shelfice_grounded_ice
322 dgoldberg 1.15
323 dgoldberg 1.16 #ifdef SHI_USTAR_TOPDR
324 dgoldberg 1.1 IF ( SHELFICEBoundaryLayer ) THEN
325     C-- average over boundary layer width
326     DO J = 1, sNy+1
327     DO I = 1, sNx+1
328     u_topdr(I,J,bi,bj) = 0.0
329     v_topdr(I,J,bi,bj) = 0.0
330     ENDDO
331     ENDDO
332     ENDIF
333 dgoldberg 1.16 #endif
334 dgoldberg 1.1
335     #ifdef ALLOW_AUTODIFF_TAMC
336     # ifdef SHI_ALLOW_GAMMAFRICT
337     act1 = bi - myBxLo(myThid)
338     max1 = myBxHi(myThid) - myBxLo(myThid) + 1
339     act2 = bj - myByLo(myThid)
340     max2 = myByHi(myThid) - myByLo(myThid) + 1
341     act3 = myThid - 1
342     max3 = nTx*nTy
343     act4 = ikey_dynamics - 1
344     ikey = (act1 + 1) + act2*max1
345     & + act3*max1*max2
346     & + act4*max1*max2*max3
347     # endif /* SHI_ALLOW_GAMMAFRICT */
348     #endif /* ALLOW_AUTODIFF_TAMC */
349     DO J = 1, sNy
350     DO I = 1, sNx
351     C-- make local copies of temperature, salinity and depth (pressure in deci-bar)
352     C-- underneath the ice
353     K = MAX(1,kTopC(I,J,bi,bj))
354     pLoc(I,J) = ABS(R_shelfIce(I,J,bi,bj))
355     c pLoc(I,J) = shelficeMass(I,J,bi,bj)*gravity*1. _d -4
356     tLoc(I,J) = theta(I,J,K,bi,bj)
357     sLoc(I,J) = MAX(salt(I,J,K,bi,bj), zeroRL)
358 dgoldberg 1.16 #ifdef SHI_USTAR_WETPOINT
359     velSq(I,J) = 0.
360     tmpFac = _hFacW(I, J,K,bi,bj) + _hFacW(I+1,J,K,bi,bj)
361     IF ( tmpFac.GT.0. _d 0 )
362     & velSq(I,J) = (
363     & uVel( I, J,K,bi,bj)*uVel( I, J,K,bi,bj)*_hFacW( I, J,K,bi,bj)
364     & + uVel(I+1,J,K,bi,bj)*uVel(I+1,J,K,bi,bj)*_hFacW(I+1,J,K,bi,bj)
365     & )/tmpFac
366     tmpFac = _hFacS(I,J, K,bi,bj) + _hFacS(I,J+1,K,bi,bj)
367     IF ( tmpFac.GT.0. _d 0 )
368     & velSq(I,J) = velSq(I,J) + (
369     & vVel(I, J, K,bi,bj)*vVel(I, J, K,bi,bj)*_hFacS(I, J, K,bi,bj)
370     & + vVel(I,J+1,K,bi,bj)*vVel(I,J+1,K,bi,bj)*_hFacS(I,J+1,K,bi,bj)
371     & )/tmpFac
372     #else /* SHI_USTAR_WETPOINT */
373     uLoc(I,J) = recip_hFacC(I,J,K,bi,bj) * halfRL *
374 dgoldberg 1.1 & ( uVel(I, J,K,bi,bj) * _hFacW(I, J,K,bi,bj)
375     & + uVel(I+1,J,K,bi,bj) * _hFacW(I+1,J,K,bi,bj) )
376 dgoldberg 1.16 vLoc(I,J) = recip_hFacC(I,J,K,bi,bj) * halfRL *
377     & ( vVel(I,J, K,bi,bj) * _hFacS(I,J, K,bi,bj)
378 dgoldberg 1.1 & + vVel(I,J+1,K,bi,bj) * _hFacS(I,J+1,K,bi,bj) )
379 dgoldberg 1.16 velSq(I,J) = uLoc(I,J)*uLoc(I,J)+vLoc(I,J)*vLoc(I,J)
380     #endif /* SHI_USTAR_WETPOINT */
381 dgoldberg 1.1 ENDDO
382     ENDDO
383    
384 dgoldberg 1.16 #ifdef SHI_USTAR_TOPDR
385 dgoldberg 1.1 IF ( SHELFICEBoundaryLayer ) THEN
386     DO J = 1, sNy+1
387     DO I = 1, sNx+1
388     K = ksurfW(I,J,bi,bj)
389     Kp1 = K+1
390     IF (K.lt.Nr) then
391     drKp1 = drF(K)*(1. _d 0-_hFacW(I,J,K,bi,bj))
392     drKp1 = max (drKp1, 0. _d 0)
393     recip_drLoc = 1.0 /
394     & (drF(K)*_hFacW(I,J,K,bi,bj)+drKp1)
395     u_topdr(I,J,bi,bj) =
396     & (drF(K)*_hFacW(I,J,K,bi,bj)*uVel(I,J,K,bi,bj) +
397     & drKp1*uVel(I,J,Kp1,bi,bj))
398     & * recip_drLoc
399     ELSE
400     u_topdr(I,J,bi,bj) = 0. _d 0
401     ENDIF
402    
403     K = ksurfS(I,J,bi,bj)
404     Kp1 = K+1
405     IF (K.lt.Nr) then
406     drKp1 = drF(K)*(1. _d 0-_hFacS(I,J,K,bi,bj))
407     drKp1 = max (drKp1, 0. _d 0)
408     recip_drLoc = 1.0 /
409     & (drF(K)*_hFacS(I,J,K,bi,bj)+drKp1)
410     v_topdr(I,J,bi,bj) =
411     & (drF(K)*_hFacS(I,J,K,bi,bj)*vVel(I,J,K,bi,bj) +
412     & drKp1*vVel(I,J,Kp1,bi,bj))
413     & * recip_drLoc
414     ELSE
415     v_topdr(I,J,bi,bj) = 0. _d 0
416     ENDIF
417    
418     ENDDO
419     ENDDO
420     ENDIF
421 dgoldberg 1.16 #endif
422 dgoldberg 1.1
423     IF ( SHELFICEBoundaryLayer ) THEN
424     C-- average over boundary layer width
425     DO J = 1, sNy
426     DO I = 1, sNx
427     K = kTopC(I,J,bi,bj)
428     IF ( K .NE. 0 .AND. K .LT. Nr ) THEN
429     Kp1 = MIN(Nr,K+1)
430     C-- overlap into lower cell
431     drKp1 = drF(K)*( 1. _d 0 - _hFacC(I,J,K,bi,bj) )
432     C-- lower cell may not be as thick as required
433     drKp1 = MIN( drKp1, drF(Kp1) * _hFacC(I,J,Kp1,bi,bj) )
434 dgoldberg 1.16 drKp1 = MAX( drKp1, 0. _d 0 )
435 dgoldberg 1.1 recip_drLoc = 1. _d 0 /
436     & ( drF(K)*_hFacC(I,J,K,bi,bj) + drKp1 )
437     tLoc(I,J) = ( tLoc(I,J) * drF(K)*_hFacC(I,J,K,bi,bj)
438     & + theta(I,J,Kp1,bi,bj) *drKp1 )
439     & * recip_drLoc
440     sLoc(I,J) = ( sLoc(I,J) * drF(K)*_hFacC(I,J,K,bi,bj)
441     & + MAX(salt(I,J,Kp1,bi,bj), zeroRL) * drKp1 )
442     & * recip_drLoc
443 dgoldberg 1.16 #ifndef SHI_USTAR_WETPOINT
444     uLoc(I,J) = ( uLoc(I,J) * drF(K)*_hFacC(I,J,K,bi,bj)
445     & + drKp1 * recip_hFacC(I,J,Kp1,bi,bj) * halfRL *
446     & ( uVel(I, J,Kp1,bi,bj) * _hFacW(I, J,Kp1,bi,bj)
447     & + uVel(I+1,J,Kp1,bi,bj) * _hFacW(I+1,J,Kp1,bi,bj) )
448     & ) * recip_drLoc
449     vLoc(I,J) = ( vLoc(I,J) * drF(K)*_hFacC(I,J,K,bi,bj)
450     & + drKp1 * recip_hFacC(I,J,Kp1,bi,bj) * halfRL *
451     & ( vVel(I,J, Kp1,bi,bj) * _hFacS(I,J, Kp1,bi,bj)
452     & + vVel(I,J+1,Kp1,bi,bj) * _hFacS(I,J+1,Kp1,bi,bj) )
453     & ) * recip_drLoc
454     velSq(I,J) = uLoc(I,J)*uLoc(I,J)+vLoc(I,J)*vLoc(I,J)
455     #endif /* ndef SHI_USTAR_WETPOINT */
456 dgoldberg 1.1 ENDIF
457     ENDDO
458     ENDDO
459     ENDIF
460    
461 dgoldberg 1.19 #ifdef SHI_USTAR_TOPDR
462     IF ( SHELFICEBoundaryLayer ) THEN
463     DO J = 1, sNy
464     DO I = 1, sNx
465     uLoc(I,J) =
466     & u_topdr(I,J,bi,bj) + u_topdr(I+1,J,bi,bj)
467     vLoc(I,J) =
468     & v_topdr(I,J,bi,bj) + v_topdr(I,J+1,bi,bj)
469     velSq(I,J) = uLoc(I,J)*uLoc(I,J)+vLoc(I,J)*vLoc(I,J)
470     ENDDO
471     ENDDO
472     ENDIF
473     #endif
474    
475 dgoldberg 1.1
476    
477     C-- turn potential temperature into in-situ temperature relative
478     C-- to the surface
479     DO J = 1, sNy
480     DO I = 1, sNx
481     #ifndef ALLOW_OPENAD
482     tLoc(I,J) = SW_TEMP(sLoc(I,J),tLoc(I,J),pLoc(I,J),zeroRL)
483     #else
484     CALL SW_TEMP(sLoc(I,J),tLoc(I,J),pLoc(I,J),zeroRL,tLoc(I,J))
485     #endif
486     ENDDO
487     ENDDO
488    
489     #ifdef SHI_ALLOW_GAMMAFRICT
490     IF ( SHELFICEuseGammaFrict ) THEN
491     DO J = 1, sNy
492     DO I = 1, sNx
493     K = kTopC(I,J,bi,bj)
494     IF ( K .NE. 0 .AND. pLoc(I,J) .GT. 0. _d 0 ) THEN
495 dgoldberg 1.16 ustarSq = shiCdrag * MAX( 1.D-6, velSq(I,J) )
496 dgoldberg 1.1 ustar = SQRT(ustarSq)
497     #ifdef ALLOW_DIAGNOSTICS
498     uStarDiag(I,J,bi,bj) = ustar
499     #endif /* ALLOW_DIAGNOSTICS */
500     C instead of etastar = sqrt(1+zetaN*ustar./(f*Lo*Rc))
501     C etastar = 1. _d 0
502     C gammaTurbConst = 1. _d 0 / (2. _d 0 * shiZetaN*etastar)
503     C & - recip_shiKarman
504     IF ( fCori(I,J,bi,bj) .NE. 0. _d 0 ) THEN
505     gammaTurb = LOG( ustarSq * shiZetaN * etastar**2
506     & / ABS(fCori(I,J,bi,bj) * 5.0 _d 0 * shiKinVisc))
507     & * recip_shiKarman
508     & + gammaTurbConst
509     C Do we need to catch the unlikely case of very small ustar
510     C that can lead to negative gammaTurb?
511     C gammaTurb = MAX(0.D0, gammaTurb)
512     ELSE
513     gammaTurb = gammaTurbConst
514     ENDIF
515     shiTransCoeffT(i,j,bi,bj) = MAX( zeroRL,
516     & ustar/(gammaTurb + gammaTmoleT) )
517     shiTransCoeffS(i,j,bi,bj) = MAX( zeroRL,
518     & ustar/(gammaTurb + gammaTmoleS) )
519     ENDIF
520     ENDDO
521     ENDDO
522     ENDIF
523     #endif /* SHI_ALLOW_GAMMAFRICT */
524    
525     #ifdef ALLOW_AUTODIFF_TAMC
526     # ifdef SHI_ALLOW_GAMMAFRICT
527     CADJ STORE shiTransCoeffS(:,:,bi,bj) = comlev1_bibj,
528     CADJ & key=ikey, byte=isbyte
529     CADJ STORE shiTransCoeffT(:,:,bi,bj) = comlev1_bibj,
530     CADJ & key=ikey, byte=isbyte
531     # endif /* SHI_ALLOW_GAMMAFRICT */
532     #endif /* ALLOW_AUTODIFF_TAMC */
533     #ifdef ALLOW_ISOMIP_TD
534     IF ( useISOMIPTD ) THEN
535     DO J = 1, sNy
536     DO I = 1, sNx
537     K = kTopC(I,J,bi,bj)
538     IF ( K .NE. 0 .AND. pLoc(I,J) .GT. 0. _d 0 ) THEN
539     C-- Calculate freezing temperature as a function of salinity and pressure
540     thetaFreeze =
541     & sLoc(I,J) * ( a0 + a1*sqrt(sLoc(I,J)) + a2*sLoc(I,J) )
542     & + b*pLoc(I,J) + c0
543     C-- Calculate the upward heat and fresh water fluxes
544     shelfIceHeatFlux(I,J,bi,bj) = maskC(I,J,K,bi,bj)
545     & * shiTransCoeffT(i,j,bi,bj)
546     & * ( tLoc(I,J) - thetaFreeze )
547     & * HeatCapacity_Cp*rUnit2mass
548     #ifdef ALLOW_SHIFWFLX_CONTROL
549     & - xx_shifwflx_loc(I,J,bi,bj)*SHELFICElatentHeat
550     #endif /* ALLOW_SHIFWFLX_CONTROL */
551     C upward heat flux into the shelf-ice implies basal melting,
552     C thus a downward (negative upward) fresh water flux (as a mass flux),
553     C and vice versa
554     shelfIceFreshWaterFlux(I,J,bi,bj) =
555     & - shelfIceHeatFlux(I,J,bi,bj)
556     & *recip_latentHeat
557     C-- compute surface tendencies
558     shelficeForcingT(i,j,bi,bj) =
559     & - shelfIceHeatFlux(I,J,bi,bj)
560     & *recip_Cp*mass2rUnit
561     & - cFac * shelfIceFreshWaterFlux(I,J,bi,bj)*mass2rUnit
562     & * ( thetaFreeze - tLoc(I,J) )
563     shelficeForcingS(i,j,bi,bj) =
564     & shelfIceFreshWaterFlux(I,J,bi,bj) * mass2rUnit
565     & * ( cFac*sLoc(I,J) + (1. _d 0-cFac)*convertFW2SaltLoc )
566     C-- stress at the ice/water interface is computed in separate
567     C routines that are called from mom_fluxform/mom_vecinv
568     ELSE
569     shelfIceHeatFlux (I,J,bi,bj) = 0. _d 0
570     shelfIceFreshWaterFlux(I,J,bi,bj) = 0. _d 0
571     shelficeForcingT (I,J,bi,bj) = 0. _d 0
572     shelficeForcingS (I,J,bi,bj) = 0. _d 0
573     ENDIF
574     ENDDO
575     ENDDO
576     ELSE
577     #else
578     IF ( .TRUE. ) THEN
579     #endif /* ALLOW_ISOMIP_TD */
580     C use BRIOS thermodynamics, following Hellmers PhD thesis:
581     C Hellmer, H., 1989, A two-dimensional model for the thermohaline
582     C circulation under an ice shelf, Reports on Polar Research, No. 60
583     C (in German).
584    
585     DO J = 1, sNy
586     DO I = 1, sNx
587     K = kTopC(I,J,bi,bj)
588     IF ( K .NE. 0 .AND. pLoc(I,J) .GT. 0. _d 0 ) THEN
589     C heat flux into the ice shelf, default is diffusive flux
590     C (Holland and Jenkins, 1999, eq.21)
591     thetaFreeze = a0*sLoc(I,J)+c0+b*pLoc(I,J)
592     fwflxFac = 0. _d 0
593     IF ( tLoc(I,J) .GT. thetaFreeze ) fwflxFac = dFac
594     C a few abbreviations
595     eps1 = rUnit2mass*HeatCapacity_Cp
596     & *shiTransCoeffT(i,j,bi,bj)
597     eps2 = rUnit2mass*SHELFICElatentHeat
598     & *shiTransCoeffS(i,j,bi,bj)
599     eps5 = rUnit2mass*HeatCapacity_Cp
600     & *shiTransCoeffS(i,j,bi,bj)
601    
602     C solve quadratic equation for salinity at shelfice-ocean interface
603     C note: this part of the code is not very intuitive as it involves
604     C many arbitrary abbreviations that were introduced to derive the
605     C correct form of the quadratic equation for salinity. The abbreviations
606     C only make sense in connection with my notes on this (M.Losch)
607     C
608     C eps3a was introduced as a constant variant of eps3 to avoid AD of
609     C code of typ (pLoc-const)/pLoc
610     eps3a = rhoShelfIce*SHELFICEheatCapacity_Cp
611     & * SHELFICEkappa * ( 1. _d 0 - dFac )
612     eps3 = eps3a/pLoc(I,J)
613     eps4 = b*pLoc(I,J) + c0
614     eps6 = eps4 - tLoc(I,J)
615     eps7 = eps4 - SHELFICEthetaSurface
616     eps8 = rUnit2mass*SHELFICEheatCapacity_Cp
617     & *shiTransCoeffS(i,j,bi,bj) * fwflxFac
618     aqe = a0 *(eps1+eps3-eps8)
619     recip_aqe = 0. _d 0
620     IF ( aqe .NE. 0. _d 0 ) recip_aqe = 0.5 _d 0/aqe
621     c bqe = eps1*eps6 + eps3*eps7 - eps2
622     bqe = eps1*eps6
623     & + eps3a*( b
624     & + ( c0 - SHELFICEthetaSurface )/pLoc(I,J) )
625     & - eps2
626     & + eps8*( a0*sLoc(I,J) - eps7 )
627     cqe = ( eps2 + eps8*eps7 )*sLoc(I,J)
628     discrim = bqe*bqe - 4. _d 0*aqe*cqe
629     #undef ALLOW_SHELFICE_DEBUG
630     #ifdef ALLOW_SHELFICE_DEBUG
631     IF ( discrim .LT. 0. _d 0 ) THEN
632     print *, 'ml-shelfice: discrim = ', discrim,aqe,bqe,cqe
633     print *, 'ml-shelfice: pLoc = ', pLoc(I,J)
634     print *, 'ml-shelfice: tLoc = ', tLoc(I,J)
635     print *, 'ml-shelfice: sLoc = ', sLoc(I,J)
636     print *, 'ml-shelfice: tsurface= ',
637     & SHELFICEthetaSurface
638     print *, 'ml-shelfice: eps1 = ', eps1
639     print *, 'ml-shelfice: eps2 = ', eps2
640     print *, 'ml-shelfice: eps3 = ', eps3
641     print *, 'ml-shelfice: eps4 = ', eps4
642     print *, 'ml-shelfice: eps5 = ', eps5
643     print *, 'ml-shelfice: eps6 = ', eps6
644     print *, 'ml-shelfice: eps7 = ', eps7
645     print *, 'ml-shelfice: eps8 = ', eps8
646     print *, 'ml-shelfice: rU2mass = ', rUnit2mass
647     print *, 'ml-shelfice: rhoIce = ', rhoShelfIce
648     print *, 'ml-shelfice: cFac = ', cFac
649     print *, 'ml-shelfice: Cp_W = ', HeatCapacity_Cp
650     print *, 'ml-shelfice: Cp_I = ',
651     & SHELFICEHeatCapacity_Cp
652     print *, 'ml-shelfice: gammaT = ',
653     & SHELFICEheatTransCoeff
654     print *, 'ml-shelfice: gammaS = ',
655     & SHELFICEsaltTransCoeff
656     print *, 'ml-shelfice: lat.heat= ',
657     & SHELFICElatentHeat
658     STOP 'ABNORMAL END in S/R SHELFICE_THERMODYNAMICS'
659     ENDIF
660     #endif /* ALLOW_SHELFICE_DEBUG */
661     saltFreeze = (- bqe - SQRT(discrim))*recip_aqe
662     IF ( saltFreeze .LT. 0. _d 0 )
663     & saltFreeze = (- bqe + SQRT(discrim))*recip_aqe
664     thetaFreeze = a0*saltFreeze + eps4
665     C-- upward fresh water flux due to melting (in kg/m^2/s)
666     cph change to identical form
667     cph freshWaterFlux = rUnit2mass
668     cph & * shiTransCoeffS(i,j,bi,bj)
669     cph & * ( saltFreeze - sLoc(I,J) ) / saltFreeze
670     freshWaterFlux = rUnit2mass
671     & * shiTransCoeffS(i,j,bi,bj)
672     & * ( 1. _d 0 - sLoc(I,J) / saltFreeze )
673     #ifdef ALLOW_SHIFWFLX_CONTROL
674     & + xx_shifwflx_loc(I,J,bi,bj)
675     #endif /* ALLOW_SHIFWFLX_CONTROL */
676 dgoldberg 1.15
677    
678 dgoldberg 1.19 #ifdef ALLOW_SHELFICE_GROUNDED_ICE
679 dgoldberg 1.15 freshWaterFlux =
680     & freshWaterFlux*(GrdFactor(i,j,bi,bj)*0.5+0.5)
681     #endif
682    
683 dgoldberg 1.16 C-- Calculate the upward heat and fresh water fluxes;
684     C-- MITgcm sign conventions: downward (negative) fresh water flux
685     C-- implies melting and due to upward (positive) heat flux
686 dgoldberg 1.1 shelfIceHeatFlux(I,J,bi,bj) =
687     & ( eps3
688     & - freshWaterFlux*SHELFICEheatCapacity_Cp*fwflxFac )
689     & * ( thetaFreeze - SHELFICEthetaSurface )
690     & - cFac*freshWaterFlux*( SHELFICElatentHeat
691     & - HeatCapacity_Cp*( thetaFreeze - rFac*tLoc(I,J) ) )
692     shelfIceFreshWaterFlux(I,J,bi,bj) = freshWaterFlux
693     C-- compute surface tendencies
694     shelficeForcingT(i,j,bi,bj) =
695     & ( shiTransCoeffT(i,j,bi,bj)
696     & - cFac*shelfIceFreshWaterFlux(I,J,bi,bj)*mass2rUnit )
697     & * ( thetaFreeze - tLoc(I,J) )
698     & - realFWfac*shelfIceFreshWaterFlux(I,J,bi,bj)*
699     & mass2rUnit*
700     & ( tLoc(I,J) - theta(I,J,K,bi,bj) )
701     shelficeForcingS(i,j,bi,bj) =
702     & ( shiTransCoeffS(i,j,bi,bj)
703     & - cFac*shelfIceFreshWaterFlux(I,J,bi,bj)*mass2rUnit )
704     & * ( saltFreeze - sLoc(I,J) )
705     & - realFWfac*shelfIceFreshWaterFlux(I,J,bi,bj)*
706     & mass2rUnit*
707     & ( sLoc(I,J) - salt(I,J,K,bi,bj) )
708     ELSE
709     shelfIceHeatFlux (I,J,bi,bj) = 0. _d 0
710     shelfIceFreshWaterFlux(I,J,bi,bj) = 0. _d 0
711     shelficeForcingT (I,J,bi,bj) = 0. _d 0
712     shelficeForcingS (I,J,bi,bj) = 0. _d 0
713     ENDIF
714     ENDDO
715     ENDDO
716     ENDIF
717     C endif (not) useISOMIPTD
718     ENDDO
719     ENDDO
720    
721 dgoldberg 1.16 IF (SHELFICEMassStepping) THEN
722     CALL SHELFICE_STEP_ICEMASS( myTime, myIter, myThid )
723     ENDIF
724    
725     C-- Calculate new loading anomaly (in case the ice-shelf mass was updated)
726 dgoldberg 1.15 #ifndef ALLOW_AUTODIFF
727 dgoldberg 1.16 c IF ( SHELFICEloadAnomalyFile .EQ. ' ' ) THEN
728     DO bj = myByLo(myThid), myByHi(myThid)
729     DO bi = myBxLo(myThid), myBxHi(myThid)
730     DO j = 1-OLy, sNy+OLy
731     DO i = 1-OLx, sNx+OLx
732 dgoldberg 1.19 #ifndef ALLOW_SHELFICE_GROUNDED_ICE
733 dgoldberg 1.1
734 dgoldberg 1.15 shelficeLoadAnomaly(i,j,bi,bj) = gravity
735 dgoldberg 1.2 & *( shelficeMass(i,j,bi,bj) + rhoConst*Ro_surf(i,j,bi,bj) )
736 dgoldberg 1.1
737 dgoldberg 1.15 #else
738 dgoldberg 1.4
739 dgoldberg 1.15 shelficeLoadAnomaly(i,j,bi,bj) = gravity
740 ksnow 1.18 & *( EFFMASS(I,J,BI,BJ) + rhoConst*Ro_surf(i,j,bi,bj) )
741 dgoldberg 1.4
742 dgoldberg 1.15 #endif
743 dgoldberg 1.16 ENDDO
744 dgoldberg 1.3 ENDDO
745     ENDDO
746     ENDDO
747 dgoldberg 1.16 c ENDIF
748 dgoldberg 1.1 #endif /* ndef ALLOW_AUTODIFF */
749    
750 dgoldberg 1.19
751    
752 dgoldberg 1.1 #ifdef ALLOW_DIAGNOSTICS
753     IF ( useDiagnostics ) THEN
754     CALL DIAGNOSTICS_FILL_RS(shelfIceFreshWaterFlux,'SHIfwFlx',
755     & 0,1,0,1,1,myThid)
756     CALL DIAGNOSTICS_FILL_RS(shelfIceHeatFlux, 'SHIhtFlx',
757     & 0,1,0,1,1,myThid)
758     C SHIForcT (Ice shelf forcing for theta [W/m2], >0 increases theta)
759     tmpFac = HeatCapacity_Cp*rUnit2mass
760     CALL DIAGNOSTICS_SCALE_FILL(shelficeForcingT,tmpFac,1,
761     & 'SHIForcT',0,1,0,1,1,myThid)
762     C SHIForcS (Ice shelf forcing for salt [g/m2/s], >0 increases salt)
763     tmpFac = rUnit2mass
764     CALL DIAGNOSTICS_SCALE_FILL(shelficeForcingS,tmpFac,1,
765     & 'SHIForcS',0,1,0,1,1,myThid)
766     C Transfer coefficients
767     CALL DIAGNOSTICS_FILL(shiTransCoeffT,'SHIgammT',
768     & 0,1,0,1,1,myThid)
769     CALL DIAGNOSTICS_FILL(shiTransCoeffS,'SHIgammS',
770     & 0,1,0,1,1,myThid)
771     C Friction velocity
772     #ifdef SHI_ALLOW_GAMMAFRICT
773     IF ( SHELFICEuseGammaFrict )
774     & CALL DIAGNOSTICS_FILL(uStarDiag,'SHIuStar',0,1,0,1,1,myThid)
775     #endif /* SHI_ALLOW_GAMMAFRICT */
776 dgoldberg 1.16 #ifdef ALLOW_SHELFICE_REMESHING
777     CALL DIAGNOSTICS_FILL(R_shelfice,'SHIRshel',
778 dgoldberg 1.1 & 0,1,0,1,1,myThid)
779 dgoldberg 1.19 #endif
780     #ifdef ALLOW_SHELFICE_GROUNDED_ICE
781 dgoldberg 1.16 CALL DIAGNOSTICS_FILL(EFFMASS,'SHI_MEff',
782 dgoldberg 1.3 & 0,1,0,1,1,myThid)
783     #endif
784 dgoldberg 1.16 ENDIF
785     #endif /* ALLOW_DIAGNOSTICS */
786 dgoldberg 1.1
787     #endif /* ALLOW_SHELFICE */
788     RETURN
789     END
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