/[MITgcm]/MITgcm_contrib/ksnow/press_release/code_expt/shelfice_thermodynamics.F
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Revision 1.3 - (hide annotations) (download)
Wed Feb 1 12:45:49 2017 UTC (9 years, 7 months ago) by dgoldberg
Branch: MAIN
Changes since 1.2: +62 -45 lines 
reorganise files to minimize duplicate files from remeshing exp
1 dgoldberg 1.3 C $Header: /u/gcmpack/MITgcm_contrib/verification_other/shelfice_remeshing/code/shelfice_thermodynamics.F,v 1.21 2016/09/04 08:32:04 ksnow Exp $
2 ksnow 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 dgoldberg 1.3 #include "SURFACE.h"
42 ksnow 1.1 #ifdef ALLOW_AUTODIFF
43     # include "CTRL_SIZE.h"
44     # include "ctrl.h"
45     # include "ctrl_dummy.h"
46     #endif /* ALLOW_AUTODIFF */
47     #ifdef ALLOW_AUTODIFF_TAMC
48     # ifdef SHI_ALLOW_GAMMAFRICT
49     # include "tamc.h"
50     # include "tamc_keys.h"
51     # endif /* SHI_ALLOW_GAMMAFRICT */
52     #endif /* ALLOW_AUTODIFF_TAMC */
53     #ifdef ALLOW_STREAMICE
54     # include "STREAMICE.h"
55     #endif /* ALLOW_STREAMICE */
56    
57     C !INPUT/OUTPUT PARAMETERS:
58     C === Routine arguments ===
59     C myIter :: iteration counter for this thread
60     C myTime :: time counter for this thread
61     C myThid :: thread number for this instance of the routine.
62     _RL myTime
63     INTEGER myIter
64     INTEGER myThid
65    
66     #ifdef ALLOW_SHELFICE
67     C !LOCAL VARIABLES :
68     C === Local variables ===
69     C I,J,K,Kp1,bi,bj :: loop counters
70     C tLoc, sLoc, pLoc :: local in-situ temperature, salinity, pressure
71     C theta/saltFreeze :: temperature and salinity of water at the
72     C ice-ocean interface (at the freezing point)
73     C freshWaterFlux :: local variable for fresh water melt flux due
74     C to melting in kg/m^2/s
75     C (negative density x melt rate)
76     C convertFW2SaltLoc:: local copy of convertFW2Salt
77     C cFac :: 1 for conservative form, 0, otherwise
78     C rFac :: realFreshWaterFlux factor
79     C dFac :: 0 for diffusive heat flux (Holland and Jenkins, 1999,
80     C eq21)
81     C 1 for advective and diffusive heat flux (eq22, 26, 31)
82     C fwflxFac :: only effective for dFac=1, 1 if we expect a melting
83     C fresh water flux, 0 otherwise
84     C auxiliary variables and abbreviations:
85     C a0, a1, a2, b, c0
86     C eps1, eps2, eps3, eps3a, eps4, eps5, eps6, eps7, eps8
87     C aqe, bqe, cqe, discrim, recip_aqe
88     C drKp1, recip_drLoc
89     INTEGER I,J,K,Kp1
90     INTEGER bi,bj
91     _RL tLoc(1:sNx,1:sNy)
92     _RL sLoc(1:sNx,1:sNy)
93     _RL pLoc(1:sNx,1:sNy)
94     #ifndef SHI_USTAR_WETPOINT
95     _RL uLoc(1:sNx,1:sNy)
96     _RL vLoc(1:sNx,1:sNy)
97     #endif
98     #ifdef SHI_USTAR_TOPDR
99     _RL u_topdr(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
100     _RL v_topdr(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
101     #endif
102     _RL velSq(1:sNx,1:sNy)
103     _RL thetaFreeze, saltFreeze, recip_Cp
104     _RL freshWaterFlux, convertFW2SaltLoc
105     _RL a0, a1, a2, b, c0
106     _RL eps1, eps2, eps3, eps3a, eps4, eps5, eps6, eps7, eps8
107     _RL cFac, rFac, dFac, fwflxFac, realfwFac
108     _RL aqe, bqe, cqe, discrim, recip_aqe
109     _RL drKp1, recip_drLoc
110     _RL recip_latentHeat
111     _RL tmpFac
112     C _RL massMin, mass, DELZ
113     _RL mass, DELZ
114     _RL SHA,FACTOR1,FACTOR2,FACTOR3
115     _RL ETA,SEALEVEL,oce_density
116     C KS_dens, add massMin and EFFR, R_min, and remove above
117 ksnow 1.2 _RL EFFR(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
118 ksnow 1.1 _RL massMin(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
119     _RL R_min(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
120    
121     #ifdef SHI_ALLOW_GAMMAFRICT
122     _RL shiPr, shiSc, shiLo, recip_shiKarman, shiTwoThirds
123     _RL gammaTmoleT, gammaTmoleS, gammaTurb, gammaTurbConst
124     _RL ustar, ustarSq, etastar
125     PARAMETER ( shiTwoThirds = 0.66666666666666666666666666667D0 )
126     #ifdef ALLOW_DIAGNOSTICS
127     _RL uStarDiag(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
128     #endif /* ALLOW_DIAGNOSTICS */
129     #endif
130    
131     #ifndef ALLOW_OPENAD
132     _RL SW_TEMP
133     EXTERNAL SW_TEMP
134     #endif
135    
136     #ifdef ALLOW_SHIFWFLX_CONTROL
137     _RL xx_shifwflx_loc(1-olx:snx+olx,1-oly:sny+oly,nsx,nsy)
138     #endif
139    
140 dgoldberg 1.3 #ifdef ALLOW_SHELFICE_GROUNDED_ICE
141     LOGICAL massmin_truedens_temp
142     #endif
143    
144 ksnow 1.1 CEOP
145     C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
146    
147     #ifdef SHI_ALLOW_GAMMAFRICT
148     #ifdef ALLOW_AUTODIFF
149     C re-initialize here again, curtesy to TAF
150     DO bj = myByLo(myThid), myByHi(myThid)
151     DO bi = myBxLo(myThid), myBxHi(myThid)
152     DO J = 1-OLy,sNy+OLy
153     DO I = 1-OLx,sNx+OLx
154     shiTransCoeffT(i,j,bi,bj) = SHELFICEheatTransCoeff
155     shiTransCoeffS(i,j,bi,bj) = SHELFICEsaltTransCoeff
156     ENDDO
157     ENDDO
158     ENDDO
159     ENDDO
160     #endif /* ALLOW_AUTODIFF */
161     IF ( SHELFICEuseGammaFrict ) THEN
162     C Implement friction velocity-dependent transfer coefficient
163     C of Holland and Jenkins, JPO, 1999
164     recip_shiKarman= 1. _d 0 / 0.4 _d 0
165     shiLo = 0. _d 0
166     shiPr = shiPrandtl**shiTwoThirds
167     shiSc = shiSchmidt**shiTwoThirds
168     cph shiPr = (viscArNr(1)/diffKrNrT(1))**shiTwoThirds
169     cph shiSc = (viscArNr(1)/diffKrNrS(1))**shiTwoThirds
170     gammaTmoleT = 12.5 _d 0 * shiPr - 6. _d 0
171     gammaTmoleS = 12.5 _d 0 * shiSc - 6. _d 0
172     C instead of etastar = sqrt(1+zetaN*ustar./(f*Lo*Rc))
173     etastar = 1. _d 0
174     gammaTurbConst = 1. _d 0 / (2. _d 0 * shiZetaN*etastar)
175     & - recip_shiKarman
176     #ifdef ALLOW_AUTODIFF
177     DO bj = myByLo(myThid), myByHi(myThid)
178     DO bi = myBxLo(myThid), myBxHi(myThid)
179     DO J = 1-OLy,sNy+OLy
180     DO I = 1-OLx,sNx+OLx
181     shiTransCoeffT(i,j,bi,bj) = 0. _d 0
182     shiTransCoeffS(i,j,bi,bj) = 0. _d 0
183     ENDDO
184     ENDDO
185     ENDDO
186     ENDDO
187     #endif /* ALLOW_AUTODIFF */
188     ENDIF
189     #endif /* SHI_ALLOW_GAMMAFRICT */
190    
191     recip_latentHeat = 0. _d 0
192     IF ( SHELFICElatentHeat .NE. 0. _d 0 )
193     & recip_latentHeat = 1. _d 0/SHELFICElatentHeat
194     C are we doing the conservative form of Jenkins et al. (2001)?
195     recip_Cp = 1. _d 0 / HeatCapacity_Cp
196     cFac = 0. _d 0
197     IF ( SHELFICEconserve ) cFac = 1. _d 0
198     C with "real fresh water flux" (affecting ETAN),
199     C there is more to modify
200     rFac = 1. _d 0
201     IF ( SHELFICEconserve .AND. useRealFreshWaterFlux ) rFac = 0. _d 0
202     C heat flux into the ice shelf, default is diffusive flux
203     C (Holland and Jenkins, 1999, eq.21)
204     dFac = 0. _d 0
205     IF ( SHELFICEadvDiffHeatFlux ) dFac = 1. _d 0
206     fwflxFac = 0. _d 0
207     C if shelficeboundarylayer is used with real freshwater flux,
208     c the T/S used for surface fluxes must be the cell T/S
209     realFWfac = 0. _d 0
210     IF ( SHELFICErealFWflux ) realFWfac = 1. _d 0
211    
212     C linear dependence of freezing point on salinity
213     a0 = -0.0575 _d 0
214     a1 = 0.0 _d -0
215     a2 = 0.0 _d -0
216     c0 = 0.0901 _d 0
217     b = -7.61 _d -4
218     #ifdef ALLOW_ISOMIP_TD
219     IF ( useISOMIPTD ) THEN
220     C non-linear dependence of freezing point on salinity
221     a0 = -0.0575 _d 0
222     a1 = 1.710523 _d -3
223     a2 = -2.154996 _d -4
224     b = -7.53 _d -4
225     c0 = 0. _d 0
226     ENDIF
227     convertFW2SaltLoc = convertFW2Salt
228     C hardcoding this value here is OK because it only applies to ISOMIP
229     C where this value is part of the protocol
230     IF ( convertFW2SaltLoc .EQ. -1. ) convertFW2SaltLoc = 33.4 _d 0
231     #endif /* ALLOW_ISOMIP_TD */
232    
233     DO bj = myByLo(myThid), myByHi(myThid)
234     DO bi = myBxLo(myThid), myBxHi(myThid)
235     DO J = 1-OLy,sNy+OLy
236     DO I = 1-OLx,sNx+OLx
237     shelfIceHeatFlux (I,J,bi,bj) = 0. _d 0
238     shelfIceFreshWaterFlux(I,J,bi,bj) = 0. _d 0
239     shelficeForcingT (I,J,bi,bj) = 0. _d 0
240     shelficeForcingS (I,J,bi,bj) = 0. _d 0
241     #if (defined SHI_ALLOW_GAMMAFRICT && defined ALLOW_DIAGNOSTICS)
242     uStarDiag (I,J,bi,bj) = 0. _d 0
243     #endif /* SHI_ALLOW_GAMMAFRICT and ALLOW_DIAGNOSTICS */
244     ENDDO
245     ENDDO
246     ENDDO
247     ENDDO
248     #ifdef ALLOW_SHIFWFLX_CONTROL
249     DO bj = myByLo(myThid), myByHi(myThid)
250     DO bi = myBxLo(myThid), myBxHi(myThid)
251     DO J = 1-OLy,sNy+OLy
252     DO I = 1-OLx,sNx+OLx
253     xx_shifwflx_loc(I,J,bi,bj) = 0. _d 0
254     ENDDO
255     ENDDO
256     ENDDO
257     ENDDO
258     #ifdef ALLOW_CTRL
259     if (useCTRL) CALL CTRL_GET_GEN (
260     & xx_shifwflx_file, xx_shifwflxstartdate, xx_shifwflxperiod,
261     & maskSHI, xx_shifwflx_loc, xx_shifwflx0, xx_shifwflx1,
262     & xx_shifwflx_dummy,
263     & xx_shifwflx_remo_intercept, xx_shifwflx_remo_slope,
264     & wshifwflx,
265     & myTime, myIter, myThid )
266     #endif
267     #endif /* ALLOW_SHIFWFLX_CONTROL */
268 ksnow 1.2
269    
270 ksnow 1.1 #ifdef ALLOW_SHELFICE_GROUNDED_ICE
271    
272 dgoldberg 1.3 DO bj = myByLo(myThid), myByHi(myThid)
273     DO bi = myBxLo(myThid), myBxHi(myThid)
274     DO j = 1-OLy, sNy+OLy
275     DO i = 1-OLx, sNx+OLx
276     MASSMIN(i,j,bi,bj) = 0. _d 0
277     ENDDO
278     ENDDO
279     ENDDO
280     ENDDO
281 ksnow 1.1
282 dgoldberg 1.3 IF (myIter.eq.0) THEN
283     massmin_truedens_temp = shelfice_massmin_trueDens
284     shelfice_massmin_trueDens = .FALSE.
285     ENDIF
286     CALL SHELFICE_CALC_GRD_FAC( massMin, myThid )
287 ksnow 1.1
288 dgoldberg 1.3 IF (myIter.eq.0) THEN
289     shelfice_massmin_trueDens = massmin_truedens_temp
290     ENDIF
291 ksnow 1.1
292 dgoldberg 1.3 DO bj = myByLo(myThid), myByHi(myThid)
293     DO bi = myBxLo(myThid), myBxHi(myThid)
294     DO j = 1-OLy, sNy+OLy
295     DO i = 1-OLx, sNx+OLx
296 ksnow 1.1
297     mass = shelficemass(i,j,bi,bj)
298    
299 dgoldberg 1.3 ! GrdFactor(i,j,bi,bj) = tanh((massMin(i,j,bi,bj)
300     ! & - mass)*1. _d 5)
301 ksnow 1.1
302     SHA=massMin(i,j,bi,bj)/
303     & SQRT(.01+mass**2)
304     FACTOR1 = ((1-sha)/2.)
305     FACTOR2 = (1+sha)/2.
306    
307     EFFMASS(I,J,BI,BJ)=
308     & (FACTOR1*GrdFactor(i,j,bi,bj) + FACTOR2)*mass
309    
310     ENDDO
311 dgoldberg 1.3 ENDDO
312     ENDDO
313     ENDDO
314 ksnow 1.1 C KS_dens -----------------------------------------------
315    
316 ksnow 1.2
317 dgoldberg 1.3
318 ksnow 1.1 #endif
319     ! allow shelfice_grounded_ice
320 ksnow 1.2
321 dgoldberg 1.3 DO bj = myByLo(myThid), myByHi(myThid)
322     DO bi = myBxLo(myThid), myBxHi(myThid)
323    
324 ksnow 1.1 #ifdef SHI_USTAR_TOPDR
325     IF ( SHELFICEBoundaryLayer ) THEN
326     C-- average over boundary layer width
327     DO J = 1, sNy+1
328     DO I = 1, sNx+1
329     u_topdr(I,J,bi,bj) = 0.0
330     v_topdr(I,J,bi,bj) = 0.0
331     ENDDO
332     ENDDO
333     ENDIF
334     #endif
335    
336     #ifdef ALLOW_AUTODIFF_TAMC
337     # ifdef SHI_ALLOW_GAMMAFRICT
338     act1 = bi - myBxLo(myThid)
339     max1 = myBxHi(myThid) - myBxLo(myThid) + 1
340     act2 = bj - myByLo(myThid)
341     max2 = myByHi(myThid) - myByLo(myThid) + 1
342     act3 = myThid - 1
343     max3 = nTx*nTy
344     act4 = ikey_dynamics - 1
345     ikey = (act1 + 1) + act2*max1
346     & + act3*max1*max2
347     & + act4*max1*max2*max3
348     # endif /* SHI_ALLOW_GAMMAFRICT */
349     #endif /* ALLOW_AUTODIFF_TAMC */
350     DO J = 1, sNy
351     DO I = 1, sNx
352     C-- make local copies of temperature, salinity and depth (pressure in deci-bar)
353     C-- underneath the ice
354     K = MAX(1,kTopC(I,J,bi,bj))
355     pLoc(I,J) = ABS(R_shelfIce(I,J,bi,bj))
356     c pLoc(I,J) = shelficeMass(I,J,bi,bj)*gravity*1. _d -4
357     tLoc(I,J) = theta(I,J,K,bi,bj)
358     sLoc(I,J) = MAX(salt(I,J,K,bi,bj), zeroRL)
359     #ifdef SHI_USTAR_WETPOINT
360     velSq(I,J) = 0.
361     tmpFac = _hFacW(I, J,K,bi,bj) + _hFacW(I+1,J,K,bi,bj)
362     IF ( tmpFac.GT.0. _d 0 )
363     & velSq(I,J) = (
364     & uVel( I, J,K,bi,bj)*uVel( I, J,K,bi,bj)*_hFacW( I, J,K,bi,bj)
365     & + uVel(I+1,J,K,bi,bj)*uVel(I+1,J,K,bi,bj)*_hFacW(I+1,J,K,bi,bj)
366     & )/tmpFac
367     tmpFac = _hFacS(I,J, K,bi,bj) + _hFacS(I,J+1,K,bi,bj)
368     IF ( tmpFac.GT.0. _d 0 )
369     & velSq(I,J) = velSq(I,J) + (
370     & vVel(I, J, K,bi,bj)*vVel(I, J, K,bi,bj)*_hFacS(I, J, K,bi,bj)
371     & + vVel(I,J+1,K,bi,bj)*vVel(I,J+1,K,bi,bj)*_hFacS(I,J+1,K,bi,bj)
372     & )/tmpFac
373     #else /* SHI_USTAR_WETPOINT */
374     uLoc(I,J) = recip_hFacC(I,J,K,bi,bj) * halfRL *
375     & ( uVel(I, J,K,bi,bj) * _hFacW(I, J,K,bi,bj)
376     & + uVel(I+1,J,K,bi,bj) * _hFacW(I+1,J,K,bi,bj) )
377     vLoc(I,J) = recip_hFacC(I,J,K,bi,bj) * halfRL *
378     & ( vVel(I,J, K,bi,bj) * _hFacS(I,J, K,bi,bj)
379     & + vVel(I,J+1,K,bi,bj) * _hFacS(I,J+1,K,bi,bj) )
380     velSq(I,J) = uLoc(I,J)*uLoc(I,J)+vLoc(I,J)*vLoc(I,J)
381     #endif /* SHI_USTAR_WETPOINT */
382     ENDDO
383     ENDDO
384    
385     #ifdef SHI_USTAR_TOPDR
386     IF ( SHELFICEBoundaryLayer ) THEN
387     DO J = 1, sNy+1
388     DO I = 1, sNx+1
389     K = ksurfW(I,J,bi,bj)
390     Kp1 = K+1
391     IF (K.lt.Nr) then
392     drKp1 = drF(K)*(1. _d 0-_hFacW(I,J,K,bi,bj))
393 ksnow 1.2 drKp1 = MIN( drKp1, drF(Kp1)*_hFacW(I,J,Kp1,bi,bj))
394 ksnow 1.1 drKp1 = max (drKp1, 0. _d 0)
395     recip_drLoc = 1.0 /
396     & (drF(K)*_hFacW(I,J,K,bi,bj)+drKp1)
397     u_topdr(I,J,bi,bj) =
398     & (drF(K)*_hFacW(I,J,K,bi,bj)*uVel(I,J,K,bi,bj) +
399     & drKp1*uVel(I,J,Kp1,bi,bj))
400     & * recip_drLoc
401 ksnow 1.2 C zero out u_topdr under grounded ice as uLoc is average of u_topdr
402     C in adjacent cells.
403 dgoldberg 1.3 #ifdef ALLOW_SHELFICE_GROUNDED_ICE
404 ksnow 1.2 u_topdr(i,j,bi,bj) =
405     & u_topdr(i,j,bi,bj)*(GrdFactor(i,j,bi,bj)*0.5+0.5)
406 dgoldberg 1.3 #endif
407 ksnow 1.1 ELSE
408     u_topdr(I,J,bi,bj) = 0. _d 0
409     ENDIF
410    
411     K = ksurfS(I,J,bi,bj)
412     Kp1 = K+1
413     IF (K.lt.Nr) then
414     drKp1 = drF(K)*(1. _d 0-_hFacS(I,J,K,bi,bj))
415 ksnow 1.2 drKp1 = MIN( drKp1, drF(Kp1)*_hFacS(I,J,Kp1,bi,bj))
416 ksnow 1.1 drKp1 = max (drKp1, 0. _d 0)
417     recip_drLoc = 1.0 /
418     & (drF(K)*_hFacS(I,J,K,bi,bj)+drKp1)
419     v_topdr(I,J,bi,bj) =
420     & (drF(K)*_hFacS(I,J,K,bi,bj)*vVel(I,J,K,bi,bj) +
421     & drKp1*vVel(I,J,Kp1,bi,bj))
422     & * recip_drLoc
423 ksnow 1.2 C zero out v_topdr under grounded ice as uLoc is average of v_topdr
424     C in adjacent cells.
425 dgoldberg 1.3 #ifdef ALLOW_SHELFICE_GROUNDED_ICE
426 ksnow 1.2 v_topdr(i,j,bi,bj) =
427     & v_topdr(i,j,bi,bj)*(GrdFactor(i,j,bi,bj)*0.5+0.5)
428 dgoldberg 1.3 #endif
429 ksnow 1.1 ELSE
430     v_topdr(I,J,bi,bj) = 0. _d 0
431     ENDIF
432    
433     ENDDO
434     ENDDO
435     ENDIF
436     #endif
437    
438     IF ( SHELFICEBoundaryLayer ) THEN
439     C-- average over boundary layer width
440     DO J = 1, sNy
441     DO I = 1, sNx
442     K = kTopC(I,J,bi,bj)
443     IF ( K .NE. 0 .AND. K .LT. Nr ) THEN
444     Kp1 = MIN(Nr,K+1)
445     C-- overlap into lower cell
446     drKp1 = drF(K)*( 1. _d 0 - _hFacC(I,J,K,bi,bj) )
447     C-- lower cell may not be as thick as required
448     drKp1 = MIN( drKp1, drF(Kp1) * _hFacC(I,J,Kp1,bi,bj) )
449     drKp1 = MAX( drKp1, 0. _d 0 )
450     recip_drLoc = 1. _d 0 /
451     & ( drF(K)*_hFacC(I,J,K,bi,bj) + drKp1 )
452     tLoc(I,J) = ( tLoc(I,J) * drF(K)*_hFacC(I,J,K,bi,bj)
453     & + theta(I,J,Kp1,bi,bj) *drKp1 )
454     & * recip_drLoc
455     sLoc(I,J) = ( sLoc(I,J) * drF(K)*_hFacC(I,J,K,bi,bj)
456     & + MAX(salt(I,J,Kp1,bi,bj), zeroRL) * drKp1 )
457     & * recip_drLoc
458     #ifndef SHI_USTAR_WETPOINT
459     uLoc(I,J) = ( uLoc(I,J) * drF(K)*_hFacC(I,J,K,bi,bj)
460     & + drKp1 * recip_hFacC(I,J,Kp1,bi,bj) * halfRL *
461     & ( uVel(I, J,Kp1,bi,bj) * _hFacW(I, J,Kp1,bi,bj)
462     & + uVel(I+1,J,Kp1,bi,bj) * _hFacW(I+1,J,Kp1,bi,bj) )
463     & ) * recip_drLoc
464     vLoc(I,J) = ( vLoc(I,J) * drF(K)*_hFacC(I,J,K,bi,bj)
465     & + drKp1 * recip_hFacC(I,J,Kp1,bi,bj) * halfRL *
466     & ( vVel(I,J, Kp1,bi,bj) * _hFacS(I,J, Kp1,bi,bj)
467     & + vVel(I,J+1,Kp1,bi,bj) * _hFacS(I,J+1,Kp1,bi,bj) )
468     & ) * recip_drLoc
469     velSq(I,J) = uLoc(I,J)*uLoc(I,J)+vLoc(I,J)*vLoc(I,J)
470     #endif /* ndef SHI_USTAR_WETPOINT */
471     ENDIF
472     ENDDO
473     ENDDO
474     ENDIF
475    
476     #ifdef SHI_USTAR_TOPDR
477     IF ( SHELFICEBoundaryLayer ) THEN
478     DO J = 1, sNy
479     DO I = 1, sNx
480 dgoldberg 1.3 uLoc(I,J) =
481     C halfRL*
482 ksnow 1.2 & (u_topdr(I,J,bi,bj) + u_topdr(I+1,J,bi,bj))
483 dgoldberg 1.3 vLoc(I,J) =
484     C halfRL*
485 ksnow 1.2 & (v_topdr(I,J,bi,bj) + v_topdr(I,J+1,bi,bj))
486 ksnow 1.1 velSq(I,J) = uLoc(I,J)*uLoc(I,J)+vLoc(I,J)*vLoc(I,J)
487     ENDDO
488     ENDDO
489     ENDIF
490     #endif
491    
492    
493    
494     C-- turn potential temperature into in-situ temperature relative
495     C-- to the surface
496     DO J = 1, sNy
497     DO I = 1, sNx
498     #ifndef ALLOW_OPENAD
499     tLoc(I,J) = SW_TEMP(sLoc(I,J),tLoc(I,J),pLoc(I,J),zeroRL)
500     #else
501     CALL SW_TEMP(sLoc(I,J),tLoc(I,J),pLoc(I,J),zeroRL,tLoc(I,J))
502     #endif
503     ENDDO
504     ENDDO
505    
506     #ifdef SHI_ALLOW_GAMMAFRICT
507     IF ( SHELFICEuseGammaFrict ) THEN
508     DO J = 1, sNy
509     DO I = 1, sNx
510     K = kTopC(I,J,bi,bj)
511     IF ( K .NE. 0 .AND. pLoc(I,J) .GT. 0. _d 0 ) THEN
512     ustarSq = shiCdrag * MAX( 1.D-6, velSq(I,J) )
513     ustar = SQRT(ustarSq)
514     #ifdef ALLOW_DIAGNOSTICS
515     uStarDiag(I,J,bi,bj) = ustar
516     #endif /* ALLOW_DIAGNOSTICS */
517     C instead of etastar = sqrt(1+zetaN*ustar./(f*Lo*Rc))
518     C etastar = 1. _d 0
519     C gammaTurbConst = 1. _d 0 / (2. _d 0 * shiZetaN*etastar)
520     C & - recip_shiKarman
521     IF ( fCori(I,J,bi,bj) .NE. 0. _d 0 ) THEN
522     gammaTurb = LOG( ustarSq * shiZetaN * etastar**2
523     & / ABS(fCori(I,J,bi,bj) * 5.0 _d 0 * shiKinVisc))
524     & * recip_shiKarman
525     & + gammaTurbConst
526     C Do we need to catch the unlikely case of very small ustar
527     C that can lead to negative gammaTurb?
528     C gammaTurb = MAX(0.D0, gammaTurb)
529     ELSE
530     gammaTurb = gammaTurbConst
531     ENDIF
532     shiTransCoeffT(i,j,bi,bj) = MAX( zeroRL,
533 dgoldberg 1.3 & ustar/(gammaTurb + gammaTmoleT) )
534 ksnow 1.1 shiTransCoeffS(i,j,bi,bj) = MAX( zeroRL,
535 dgoldberg 1.3 & ustar/(gammaTurb + gammaTmoleS) )
536 ksnow 1.1 ENDIF
537     ENDDO
538     ENDDO
539     ENDIF
540     #endif /* SHI_ALLOW_GAMMAFRICT */
541    
542     #ifdef ALLOW_AUTODIFF_TAMC
543     # ifdef SHI_ALLOW_GAMMAFRICT
544     CADJ STORE shiTransCoeffS(:,:,bi,bj) = comlev1_bibj,
545     CADJ & key=ikey, byte=isbyte
546     CADJ STORE shiTransCoeffT(:,:,bi,bj) = comlev1_bibj,
547     CADJ & key=ikey, byte=isbyte
548     # endif /* SHI_ALLOW_GAMMAFRICT */
549     #endif /* ALLOW_AUTODIFF_TAMC */
550     #ifdef ALLOW_ISOMIP_TD
551     IF ( useISOMIPTD ) THEN
552     DO J = 1, sNy
553     DO I = 1, sNx
554     K = kTopC(I,J,bi,bj)
555     IF ( K .NE. 0 .AND. pLoc(I,J) .GT. 0. _d 0 ) THEN
556     C-- Calculate freezing temperature as a function of salinity and pressure
557     thetaFreeze =
558     & sLoc(I,J) * ( a0 + a1*sqrt(sLoc(I,J)) + a2*sLoc(I,J) )
559     & + b*pLoc(I,J) + c0
560     C-- Calculate the upward heat and fresh water fluxes
561     shelfIceHeatFlux(I,J,bi,bj) = maskC(I,J,K,bi,bj)
562     & * shiTransCoeffT(i,j,bi,bj)
563     & * ( tLoc(I,J) - thetaFreeze )
564     & * HeatCapacity_Cp*rUnit2mass
565     #ifdef ALLOW_SHIFWFLX_CONTROL
566     & - xx_shifwflx_loc(I,J,bi,bj)*SHELFICElatentHeat
567     #endif /* ALLOW_SHIFWFLX_CONTROL */
568     C upward heat flux into the shelf-ice implies basal melting,
569     C thus a downward (negative upward) fresh water flux (as a mass flux),
570     C and vice versa
571     shelfIceFreshWaterFlux(I,J,bi,bj) =
572     & - shelfIceHeatFlux(I,J,bi,bj)
573     & *recip_latentHeat
574     C-- compute surface tendencies
575     shelficeForcingT(i,j,bi,bj) =
576     & - shelfIceHeatFlux(I,J,bi,bj)
577     & *recip_Cp*mass2rUnit
578     & - cFac * shelfIceFreshWaterFlux(I,J,bi,bj)*mass2rUnit
579     & * ( thetaFreeze - tLoc(I,J) )
580     shelficeForcingS(i,j,bi,bj) =
581     & shelfIceFreshWaterFlux(I,J,bi,bj) * mass2rUnit
582     & * ( cFac*sLoc(I,J) + (1. _d 0-cFac)*convertFW2SaltLoc )
583     C-- stress at the ice/water interface is computed in separate
584     C routines that are called from mom_fluxform/mom_vecinv
585     ELSE
586     shelfIceHeatFlux (I,J,bi,bj) = 0. _d 0
587     shelfIceFreshWaterFlux(I,J,bi,bj) = 0. _d 0
588     shelficeForcingT (I,J,bi,bj) = 0. _d 0
589     shelficeForcingS (I,J,bi,bj) = 0. _d 0
590     ENDIF
591     ENDDO
592     ENDDO
593     ELSE
594     #else
595     IF ( .TRUE. ) THEN
596     #endif /* ALLOW_ISOMIP_TD */
597     C use BRIOS thermodynamics, following Hellmers PhD thesis:
598     C Hellmer, H., 1989, A two-dimensional model for the thermohaline
599     C circulation under an ice shelf, Reports on Polar Research, No. 60
600     C (in German).
601    
602     DO J = 1, sNy
603     DO I = 1, sNx
604     K = kTopC(I,J,bi,bj)
605     IF ( K .NE. 0 .AND. pLoc(I,J) .GT. 0. _d 0 ) THEN
606     C heat flux into the ice shelf, default is diffusive flux
607     C (Holland and Jenkins, 1999, eq.21)
608     thetaFreeze = a0*sLoc(I,J)+c0+b*pLoc(I,J)
609     fwflxFac = 0. _d 0
610     IF ( tLoc(I,J) .GT. thetaFreeze ) fwflxFac = dFac
611     C a few abbreviations
612     eps1 = rUnit2mass*HeatCapacity_Cp
613     & *shiTransCoeffT(i,j,bi,bj)
614     eps2 = rUnit2mass*SHELFICElatentHeat
615     & *shiTransCoeffS(i,j,bi,bj)
616     eps5 = rUnit2mass*HeatCapacity_Cp
617     & *shiTransCoeffS(i,j,bi,bj)
618    
619     C solve quadratic equation for salinity at shelfice-ocean interface
620     C note: this part of the code is not very intuitive as it involves
621     C many arbitrary abbreviations that were introduced to derive the
622     C correct form of the quadratic equation for salinity. The abbreviations
623     C only make sense in connection with my notes on this (M.Losch)
624     C
625     C eps3a was introduced as a constant variant of eps3 to avoid AD of
626     C code of typ (pLoc-const)/pLoc
627     eps3a = rhoShelfIce*SHELFICEheatCapacity_Cp
628     & * SHELFICEkappa * ( 1. _d 0 - dFac )
629     eps3 = eps3a/pLoc(I,J)
630     eps4 = b*pLoc(I,J) + c0
631     eps6 = eps4 - tLoc(I,J)
632     eps7 = eps4 - SHELFICEthetaSurface
633     eps8 = rUnit2mass*SHELFICEheatCapacity_Cp
634     & *shiTransCoeffS(i,j,bi,bj) * fwflxFac
635     aqe = a0 *(eps1+eps3-eps8)
636     recip_aqe = 0. _d 0
637     IF ( aqe .NE. 0. _d 0 ) recip_aqe = 0.5 _d 0/aqe
638     c bqe = eps1*eps6 + eps3*eps7 - eps2
639     bqe = eps1*eps6
640     & + eps3a*( b
641     & + ( c0 - SHELFICEthetaSurface )/pLoc(I,J) )
642     & - eps2
643     & + eps8*( a0*sLoc(I,J) - eps7 )
644     cqe = ( eps2 + eps8*eps7 )*sLoc(I,J)
645     discrim = bqe*bqe - 4. _d 0*aqe*cqe
646     #undef ALLOW_SHELFICE_DEBUG
647     #ifdef ALLOW_SHELFICE_DEBUG
648     IF ( discrim .LT. 0. _d 0 ) THEN
649     print *, 'ml-shelfice: discrim = ', discrim,aqe,bqe,cqe
650     print *, 'ml-shelfice: pLoc = ', pLoc(I,J)
651     print *, 'ml-shelfice: tLoc = ', tLoc(I,J)
652     print *, 'ml-shelfice: sLoc = ', sLoc(I,J)
653     print *, 'ml-shelfice: tsurface= ',
654     & SHELFICEthetaSurface
655     print *, 'ml-shelfice: eps1 = ', eps1
656     print *, 'ml-shelfice: eps2 = ', eps2
657     print *, 'ml-shelfice: eps3 = ', eps3
658     print *, 'ml-shelfice: eps4 = ', eps4
659     print *, 'ml-shelfice: eps5 = ', eps5
660     print *, 'ml-shelfice: eps6 = ', eps6
661     print *, 'ml-shelfice: eps7 = ', eps7
662     print *, 'ml-shelfice: eps8 = ', eps8
663     print *, 'ml-shelfice: rU2mass = ', rUnit2mass
664     print *, 'ml-shelfice: rhoIce = ', rhoShelfIce
665     print *, 'ml-shelfice: cFac = ', cFac
666     print *, 'ml-shelfice: Cp_W = ', HeatCapacity_Cp
667     print *, 'ml-shelfice: Cp_I = ',
668     & SHELFICEHeatCapacity_Cp
669     print *, 'ml-shelfice: gammaT = ',
670     & SHELFICEheatTransCoeff
671     print *, 'ml-shelfice: gammaS = ',
672     & SHELFICEsaltTransCoeff
673     print *, 'ml-shelfice: lat.heat= ',
674     & SHELFICElatentHeat
675     STOP 'ABNORMAL END in S/R SHELFICE_THERMODYNAMICS'
676     ENDIF
677     #endif /* ALLOW_SHELFICE_DEBUG */
678     saltFreeze = (- bqe - SQRT(discrim))*recip_aqe
679     IF ( saltFreeze .LT. 0. _d 0 )
680     & saltFreeze = (- bqe + SQRT(discrim))*recip_aqe
681     thetaFreeze = a0*saltFreeze + eps4
682     C-- upward fresh water flux due to melting (in kg/m^2/s)
683     cph change to identical form
684     cph freshWaterFlux = rUnit2mass
685     cph & * shiTransCoeffS(i,j,bi,bj)
686     cph & * ( saltFreeze - sLoc(I,J) ) / saltFreeze
687     freshWaterFlux = rUnit2mass
688     & * shiTransCoeffS(i,j,bi,bj)
689     & * ( 1. _d 0 - sLoc(I,J) / saltFreeze )
690     #ifdef ALLOW_SHIFWFLX_CONTROL
691     & + xx_shifwflx_loc(I,J,bi,bj)
692     #endif /* ALLOW_SHIFWFLX_CONTROL */
693    
694    
695     #ifdef ALLOW_SHELFICE_GROUNDED_ICE
696     freshWaterFlux =
697     & freshWaterFlux*(GrdFactor(i,j,bi,bj)*0.5+0.5)
698     #endif
699    
700     C-- Calculate the upward heat and fresh water fluxes;
701     C-- MITgcm sign conventions: downward (negative) fresh water flux
702     C-- implies melting and due to upward (positive) heat flux
703     shelfIceHeatFlux(I,J,bi,bj) =
704     & ( eps3
705     & - freshWaterFlux*SHELFICEheatCapacity_Cp*fwflxFac )
706     & * ( thetaFreeze - SHELFICEthetaSurface )
707     & - cFac*freshWaterFlux*( SHELFICElatentHeat
708     & - HeatCapacity_Cp*( thetaFreeze - rFac*tLoc(I,J) ) )
709     shelfIceFreshWaterFlux(I,J,bi,bj) = freshWaterFlux
710     C-- compute surface tendencies
711     shelficeForcingT(i,j,bi,bj) =
712     & ( shiTransCoeffT(i,j,bi,bj)
713     & - cFac*shelfIceFreshWaterFlux(I,J,bi,bj)*mass2rUnit )
714     & * ( thetaFreeze - tLoc(I,J) )
715     & - realFWfac*shelfIceFreshWaterFlux(I,J,bi,bj)*
716     & mass2rUnit*
717     & ( tLoc(I,J) - theta(I,J,K,bi,bj) )
718     shelficeForcingS(i,j,bi,bj) =
719     & ( shiTransCoeffS(i,j,bi,bj)
720     & - cFac*shelfIceFreshWaterFlux(I,J,bi,bj)*mass2rUnit )
721     & * ( saltFreeze - sLoc(I,J) )
722     & - realFWfac*shelfIceFreshWaterFlux(I,J,bi,bj)*
723     & mass2rUnit*
724     & ( sLoc(I,J) - salt(I,J,K,bi,bj) )
725 ksnow 1.2 #ifdef ALLOW_SHELFICE_GROUNDED_ICE
726     shelfIceHeatFlux(i,j,bi,bj) =
727     & shelfIceHeatFlux(i,j,bi,bj)*(GrdFactor(i,j,bi,bj)*0.5+0.5)
728     shelfIceForcingT(i,j,bi,bj) =
729     & shelfIceForcingT(i,j,bi,bj)*(GrdFactor(i,j,bi,bj)*0.5+0.5)
730     shelfIceForcingS(i,j,bi,bj) =
731     & shelfIceForcingS(i,j,bi,bj)*(GrdFactor(i,j,bi,bj)*0.5+0.5)
732     #endif
733 ksnow 1.1 ELSE
734     shelfIceHeatFlux (I,J,bi,bj) = 0. _d 0
735     shelfIceFreshWaterFlux(I,J,bi,bj) = 0. _d 0
736     shelficeForcingT (I,J,bi,bj) = 0. _d 0
737     shelficeForcingS (I,J,bi,bj) = 0. _d 0
738     ENDIF
739     ENDDO
740     ENDDO
741     ENDIF
742     C endif (not) useISOMIPTD
743     ENDDO
744     ENDDO
745    
746     IF (SHELFICEMassStepping) THEN
747     CALL SHELFICE_STEP_ICEMASS( myTime, myIter, myThid )
748     ENDIF
749    
750     C-- Calculate new loading anomaly (in case the ice-shelf mass was updated)
751     #ifndef ALLOW_AUTODIFF
752     c IF ( SHELFICEloadAnomalyFile .EQ. ' ' ) THEN
753     DO bj = myByLo(myThid), myByHi(myThid)
754     DO bi = myBxLo(myThid), myBxHi(myThid)
755     DO j = 1-OLy, sNy+OLy
756     DO i = 1-OLx, sNx+OLx
757     #ifndef ALLOW_SHELFICE_GROUNDED_ICE
758    
759     shelficeLoadAnomaly(i,j,bi,bj) = gravity
760     & *( shelficeMass(i,j,bi,bj) + rhoConst*Ro_surf(i,j,bi,bj) )
761    
762     #else
763    
764     shelficeLoadAnomaly(i,j,bi,bj) = gravity
765     & *( EFFMASS(I,J,BI,BJ) + rhoConst*Ro_surf(i,j,bi,bj) )
766    
767     #endif
768     ENDDO
769     ENDDO
770     ENDDO
771     ENDDO
772     c ENDIF
773     #endif /* ndef ALLOW_AUTODIFF */
774    
775    
776    
777     #ifdef ALLOW_DIAGNOSTICS
778     IF ( useDiagnostics ) THEN
779     CALL DIAGNOSTICS_FILL_RS(shelfIceFreshWaterFlux,'SHIfwFlx',
780     & 0,1,0,1,1,myThid)
781     CALL DIAGNOSTICS_FILL_RS(shelfIceHeatFlux, 'SHIhtFlx',
782     & 0,1,0,1,1,myThid)
783     C SHIForcT (Ice shelf forcing for theta [W/m2], >0 increases theta)
784     tmpFac = HeatCapacity_Cp*rUnit2mass
785     CALL DIAGNOSTICS_SCALE_FILL(shelficeForcingT,tmpFac,1,
786     & 'SHIForcT',0,1,0,1,1,myThid)
787     C SHIForcS (Ice shelf forcing for salt [g/m2/s], >0 increases salt)
788     tmpFac = rUnit2mass
789     CALL DIAGNOSTICS_SCALE_FILL(shelficeForcingS,tmpFac,1,
790     & 'SHIForcS',0,1,0,1,1,myThid)
791     C Transfer coefficients
792     CALL DIAGNOSTICS_FILL(shiTransCoeffT,'SHIgammT',
793     & 0,1,0,1,1,myThid)
794     CALL DIAGNOSTICS_FILL(shiTransCoeffS,'SHIgammS',
795     & 0,1,0,1,1,myThid)
796     C Friction velocity
797     #ifdef SHI_ALLOW_GAMMAFRICT
798     IF ( SHELFICEuseGammaFrict )
799     & CALL DIAGNOSTICS_FILL(uStarDiag,'SHIuStar',0,1,0,1,1,myThid)
800     #endif /* SHI_ALLOW_GAMMAFRICT */
801     #ifdef ALLOW_SHELFICE_REMESHING
802     CALL DIAGNOSTICS_FILL(R_shelfice,'SHIRshel',
803     & 0,1,0,1,1,myThid)
804     #endif
805     #ifdef ALLOW_SHELFICE_GROUNDED_ICE
806     CALL DIAGNOSTICS_FILL(EFFMASS,'SHI_MEff',
807     & 0,1,0,1,1,myThid)
808     #endif
809 dgoldberg 1.3 #ifdef ALLOW_SHELFICE_GROUNDED_ICE
810     CALL DIAGNOSTICS_FILL(EFFMASS,'SHI_MEff',
811     & 0,1,0,1,1,myThid)
812     CALL DIAGNOSTICS_FILL(Rmin_surf,'SHI_Rmin',
813     & 0,1,0,1,1,myThid)
814     #ifdef ALLOW_PRESSURE_RELEASE_CODE
815     CALL DIAGNOSTICS_FILL(pReleaseTransX,'pRelUflx',
816     & 0,1,0,1,1,myThid)
817     CALL DIAGNOSTICS_FILL(pReleaseTransY,'pRelVflx',
818     & 0,1,0,1,1,myThid)
819     CALL DIAGNOSTICS_FILL(depthcolw,'DEPTH_DX',
820     & 0,1,0,1,1,myThid)
821     CALL DIAGNOSTICS_FILL(depthcols,'DEPTH_DY',
822     & 0,1,0,1,1,myThid)
823     #endif
824     #endif
825 ksnow 1.1 ENDIF
826     #endif /* ALLOW_DIAGNOSTICS */
827    
828     #endif /* ALLOW_SHELFICE */
829     RETURN
830     END
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