/[MITgcm]/MITgcm_contrib/verification_other/shelfice_remeshing/code/shelfice_thermodynamics.F
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Revision 1.21 - (hide annotations) (download)
Sun Sep 4 08:32:04 2016 UTC (8 years, 10 months ago) by ksnow
Branch: MAIN
CVS Tags: checkpoint66g, checkpoint66f, checkpoint66e, checkpoint66d, checkpoint66c, checkpoint66b, checkpoint66a, checkpoint66j, checkpoint66i, checkpoint66h, checkpoint65z
Changes since 1.20: +9 -3 lines 
Fix missed CPP ifdef option
1 ksnow 1.21 C $Header: /u/gcmpack/MITgcm_contrib/verification_other/shelfice_remeshing/code/shelfice_thermodynamics.F,v 1.20 2016/09/02 08:19:49 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 ksnow 1.20 drKp1 = MIN( drKp1, drF(Kp1)*_hFacW(I,J,Kp1,bi,bj))
393 dgoldberg 1.1 drKp1 = max (drKp1, 0. _d 0)
394     recip_drLoc = 1.0 /
395     & (drF(K)*_hFacW(I,J,K,bi,bj)+drKp1)
396     u_topdr(I,J,bi,bj) =
397     & (drF(K)*_hFacW(I,J,K,bi,bj)*uVel(I,J,K,bi,bj) +
398     & drKp1*uVel(I,J,Kp1,bi,bj))
399     & * recip_drLoc
400 ksnow 1.20 C zero out u_topdr under grounded ice as uLoc is average of u_topdr
401     C in adjacent cells.
402 ksnow 1.21 #ifdef ALLOW_SHELFICE_GROUNDED_ICE
403 ksnow 1.20 u_topdr(i,j,bi,bj) =
404     & u_topdr(i,j,bi,bj)*(GrdFactor(i,j,bi,bj)*0.5+0.5)
405 ksnow 1.21 #endif
406 dgoldberg 1.1 ELSE
407     u_topdr(I,J,bi,bj) = 0. _d 0
408     ENDIF
409    
410     K = ksurfS(I,J,bi,bj)
411     Kp1 = K+1
412     IF (K.lt.Nr) then
413     drKp1 = drF(K)*(1. _d 0-_hFacS(I,J,K,bi,bj))
414 ksnow 1.20 drKp1 = MIN( drKp1, drF(Kp1)*_hFacS(I,J,Kp1,bi,bj))
415 dgoldberg 1.1 drKp1 = max (drKp1, 0. _d 0)
416     recip_drLoc = 1.0 /
417     & (drF(K)*_hFacS(I,J,K,bi,bj)+drKp1)
418     v_topdr(I,J,bi,bj) =
419     & (drF(K)*_hFacS(I,J,K,bi,bj)*vVel(I,J,K,bi,bj) +
420     & drKp1*vVel(I,J,Kp1,bi,bj))
421     & * recip_drLoc
422 ksnow 1.20 C zero out v_topdr under grounded ice as uLoc is average of v_topdr
423     C in adjacent cells.
424 ksnow 1.21 #ifdef ALLOW_SHELFICE_GROUNDED_ICE
425 ksnow 1.20 v_topdr(i,j,bi,bj) =
426     & v_topdr(i,j,bi,bj)*(GrdFactor(i,j,bi,bj)*0.5+0.5)
427 ksnow 1.21 #endif
428 dgoldberg 1.1 ELSE
429     v_topdr(I,J,bi,bj) = 0. _d 0
430     ENDIF
431    
432     ENDDO
433     ENDDO
434     ENDIF
435 dgoldberg 1.16 #endif
436 dgoldberg 1.1
437     IF ( SHELFICEBoundaryLayer ) THEN
438     C-- average over boundary layer width
439     DO J = 1, sNy
440     DO I = 1, sNx
441     K = kTopC(I,J,bi,bj)
442     IF ( K .NE. 0 .AND. K .LT. Nr ) THEN
443     Kp1 = MIN(Nr,K+1)
444     C-- overlap into lower cell
445     drKp1 = drF(K)*( 1. _d 0 - _hFacC(I,J,K,bi,bj) )
446     C-- lower cell may not be as thick as required
447     drKp1 = MIN( drKp1, drF(Kp1) * _hFacC(I,J,Kp1,bi,bj) )
448 dgoldberg 1.16 drKp1 = MAX( drKp1, 0. _d 0 )
449 dgoldberg 1.1 recip_drLoc = 1. _d 0 /
450     & ( drF(K)*_hFacC(I,J,K,bi,bj) + drKp1 )
451     tLoc(I,J) = ( tLoc(I,J) * drF(K)*_hFacC(I,J,K,bi,bj)
452     & + theta(I,J,Kp1,bi,bj) *drKp1 )
453     & * recip_drLoc
454     sLoc(I,J) = ( sLoc(I,J) * drF(K)*_hFacC(I,J,K,bi,bj)
455     & + MAX(salt(I,J,Kp1,bi,bj), zeroRL) * drKp1 )
456     & * recip_drLoc
457 dgoldberg 1.16 #ifndef SHI_USTAR_WETPOINT
458     uLoc(I,J) = ( uLoc(I,J) * drF(K)*_hFacC(I,J,K,bi,bj)
459     & + drKp1 * recip_hFacC(I,J,Kp1,bi,bj) * halfRL *
460     & ( uVel(I, J,Kp1,bi,bj) * _hFacW(I, J,Kp1,bi,bj)
461     & + uVel(I+1,J,Kp1,bi,bj) * _hFacW(I+1,J,Kp1,bi,bj) )
462     & ) * recip_drLoc
463     vLoc(I,J) = ( vLoc(I,J) * drF(K)*_hFacC(I,J,K,bi,bj)
464     & + drKp1 * recip_hFacC(I,J,Kp1,bi,bj) * halfRL *
465     & ( vVel(I,J, Kp1,bi,bj) * _hFacS(I,J, Kp1,bi,bj)
466     & + vVel(I,J+1,Kp1,bi,bj) * _hFacS(I,J+1,Kp1,bi,bj) )
467     & ) * recip_drLoc
468     velSq(I,J) = uLoc(I,J)*uLoc(I,J)+vLoc(I,J)*vLoc(I,J)
469     #endif /* ndef SHI_USTAR_WETPOINT */
470 dgoldberg 1.1 ENDIF
471     ENDDO
472     ENDDO
473     ENDIF
474    
475 dgoldberg 1.19 #ifdef SHI_USTAR_TOPDR
476     IF ( SHELFICEBoundaryLayer ) THEN
477     DO J = 1, sNy
478     DO I = 1, sNx
479 ksnow 1.21 uLoc(I,J) =
480     C halfRL*
481 ksnow 1.20 & (u_topdr(I,J,bi,bj) + u_topdr(I+1,J,bi,bj))
482 ksnow 1.21 vLoc(I,J) =
483     C halfRL*
484 ksnow 1.20 & (v_topdr(I,J,bi,bj) + v_topdr(I,J+1,bi,bj))
485 dgoldberg 1.19 velSq(I,J) = uLoc(I,J)*uLoc(I,J)+vLoc(I,J)*vLoc(I,J)
486     ENDDO
487     ENDDO
488     ENDIF
489     #endif
490    
491 dgoldberg 1.1
492    
493     C-- turn potential temperature into in-situ temperature relative
494     C-- to the surface
495     DO J = 1, sNy
496     DO I = 1, sNx
497     #ifndef ALLOW_OPENAD
498     tLoc(I,J) = SW_TEMP(sLoc(I,J),tLoc(I,J),pLoc(I,J),zeroRL)
499     #else
500     CALL SW_TEMP(sLoc(I,J),tLoc(I,J),pLoc(I,J),zeroRL,tLoc(I,J))
501     #endif
502     ENDDO
503     ENDDO
504    
505     #ifdef SHI_ALLOW_GAMMAFRICT
506     IF ( SHELFICEuseGammaFrict ) THEN
507     DO J = 1, sNy
508     DO I = 1, sNx
509     K = kTopC(I,J,bi,bj)
510     IF ( K .NE. 0 .AND. pLoc(I,J) .GT. 0. _d 0 ) THEN
511 dgoldberg 1.16 ustarSq = shiCdrag * MAX( 1.D-6, velSq(I,J) )
512 dgoldberg 1.1 ustar = SQRT(ustarSq)
513     #ifdef ALLOW_DIAGNOSTICS
514     uStarDiag(I,J,bi,bj) = ustar
515     #endif /* ALLOW_DIAGNOSTICS */
516     C instead of etastar = sqrt(1+zetaN*ustar./(f*Lo*Rc))
517     C etastar = 1. _d 0
518     C gammaTurbConst = 1. _d 0 / (2. _d 0 * shiZetaN*etastar)
519     C & - recip_shiKarman
520     IF ( fCori(I,J,bi,bj) .NE. 0. _d 0 ) THEN
521     gammaTurb = LOG( ustarSq * shiZetaN * etastar**2
522     & / ABS(fCori(I,J,bi,bj) * 5.0 _d 0 * shiKinVisc))
523     & * recip_shiKarman
524     & + gammaTurbConst
525     C Do we need to catch the unlikely case of very small ustar
526     C that can lead to negative gammaTurb?
527     C gammaTurb = MAX(0.D0, gammaTurb)
528     ELSE
529     gammaTurb = gammaTurbConst
530     ENDIF
531     shiTransCoeffT(i,j,bi,bj) = MAX( zeroRL,
532     & ustar/(gammaTurb + gammaTmoleT) )
533     shiTransCoeffS(i,j,bi,bj) = MAX( zeroRL,
534     & ustar/(gammaTurb + gammaTmoleS) )
535     ENDIF
536     ENDDO
537     ENDDO
538     ENDIF
539     #endif /* SHI_ALLOW_GAMMAFRICT */
540    
541     #ifdef ALLOW_AUTODIFF_TAMC
542     # ifdef SHI_ALLOW_GAMMAFRICT
543     CADJ STORE shiTransCoeffS(:,:,bi,bj) = comlev1_bibj,
544     CADJ & key=ikey, byte=isbyte
545     CADJ STORE shiTransCoeffT(:,:,bi,bj) = comlev1_bibj,
546     CADJ & key=ikey, byte=isbyte
547     # endif /* SHI_ALLOW_GAMMAFRICT */
548     #endif /* ALLOW_AUTODIFF_TAMC */
549     #ifdef ALLOW_ISOMIP_TD
550     IF ( useISOMIPTD ) THEN
551     DO J = 1, sNy
552     DO I = 1, sNx
553     K = kTopC(I,J,bi,bj)
554     IF ( K .NE. 0 .AND. pLoc(I,J) .GT. 0. _d 0 ) THEN
555     C-- Calculate freezing temperature as a function of salinity and pressure
556     thetaFreeze =
557     & sLoc(I,J) * ( a0 + a1*sqrt(sLoc(I,J)) + a2*sLoc(I,J) )
558     & + b*pLoc(I,J) + c0
559     C-- Calculate the upward heat and fresh water fluxes
560     shelfIceHeatFlux(I,J,bi,bj) = maskC(I,J,K,bi,bj)
561     & * shiTransCoeffT(i,j,bi,bj)
562     & * ( tLoc(I,J) - thetaFreeze )
563     & * HeatCapacity_Cp*rUnit2mass
564     #ifdef ALLOW_SHIFWFLX_CONTROL
565     & - xx_shifwflx_loc(I,J,bi,bj)*SHELFICElatentHeat
566     #endif /* ALLOW_SHIFWFLX_CONTROL */
567     C upward heat flux into the shelf-ice implies basal melting,
568     C thus a downward (negative upward) fresh water flux (as a mass flux),
569     C and vice versa
570     shelfIceFreshWaterFlux(I,J,bi,bj) =
571     & - shelfIceHeatFlux(I,J,bi,bj)
572     & *recip_latentHeat
573     C-- compute surface tendencies
574     shelficeForcingT(i,j,bi,bj) =
575     & - shelfIceHeatFlux(I,J,bi,bj)
576     & *recip_Cp*mass2rUnit
577     & - cFac * shelfIceFreshWaterFlux(I,J,bi,bj)*mass2rUnit
578     & * ( thetaFreeze - tLoc(I,J) )
579     shelficeForcingS(i,j,bi,bj) =
580     & shelfIceFreshWaterFlux(I,J,bi,bj) * mass2rUnit
581     & * ( cFac*sLoc(I,J) + (1. _d 0-cFac)*convertFW2SaltLoc )
582     C-- stress at the ice/water interface is computed in separate
583     C routines that are called from mom_fluxform/mom_vecinv
584     ELSE
585     shelfIceHeatFlux (I,J,bi,bj) = 0. _d 0
586     shelfIceFreshWaterFlux(I,J,bi,bj) = 0. _d 0
587     shelficeForcingT (I,J,bi,bj) = 0. _d 0
588     shelficeForcingS (I,J,bi,bj) = 0. _d 0
589     ENDIF
590     ENDDO
591     ENDDO
592     ELSE
593     #else
594     IF ( .TRUE. ) THEN
595     #endif /* ALLOW_ISOMIP_TD */
596     C use BRIOS thermodynamics, following Hellmers PhD thesis:
597     C Hellmer, H., 1989, A two-dimensional model for the thermohaline
598     C circulation under an ice shelf, Reports on Polar Research, No. 60
599     C (in German).
600    
601     DO J = 1, sNy
602     DO I = 1, sNx
603     K = kTopC(I,J,bi,bj)
604     IF ( K .NE. 0 .AND. pLoc(I,J) .GT. 0. _d 0 ) THEN
605     C heat flux into the ice shelf, default is diffusive flux
606     C (Holland and Jenkins, 1999, eq.21)
607     thetaFreeze = a0*sLoc(I,J)+c0+b*pLoc(I,J)
608     fwflxFac = 0. _d 0
609     IF ( tLoc(I,J) .GT. thetaFreeze ) fwflxFac = dFac
610     C a few abbreviations
611     eps1 = rUnit2mass*HeatCapacity_Cp
612     & *shiTransCoeffT(i,j,bi,bj)
613     eps2 = rUnit2mass*SHELFICElatentHeat
614     & *shiTransCoeffS(i,j,bi,bj)
615     eps5 = rUnit2mass*HeatCapacity_Cp
616     & *shiTransCoeffS(i,j,bi,bj)
617    
618     C solve quadratic equation for salinity at shelfice-ocean interface
619     C note: this part of the code is not very intuitive as it involves
620     C many arbitrary abbreviations that were introduced to derive the
621     C correct form of the quadratic equation for salinity. The abbreviations
622     C only make sense in connection with my notes on this (M.Losch)
623     C
624     C eps3a was introduced as a constant variant of eps3 to avoid AD of
625     C code of typ (pLoc-const)/pLoc
626     eps3a = rhoShelfIce*SHELFICEheatCapacity_Cp
627     & * SHELFICEkappa * ( 1. _d 0 - dFac )
628     eps3 = eps3a/pLoc(I,J)
629     eps4 = b*pLoc(I,J) + c0
630     eps6 = eps4 - tLoc(I,J)
631     eps7 = eps4 - SHELFICEthetaSurface
632     eps8 = rUnit2mass*SHELFICEheatCapacity_Cp
633     & *shiTransCoeffS(i,j,bi,bj) * fwflxFac
634     aqe = a0 *(eps1+eps3-eps8)
635     recip_aqe = 0. _d 0
636     IF ( aqe .NE. 0. _d 0 ) recip_aqe = 0.5 _d 0/aqe
637     c bqe = eps1*eps6 + eps3*eps7 - eps2
638     bqe = eps1*eps6
639     & + eps3a*( b
640     & + ( c0 - SHELFICEthetaSurface )/pLoc(I,J) )
641     & - eps2
642     & + eps8*( a0*sLoc(I,J) - eps7 )
643     cqe = ( eps2 + eps8*eps7 )*sLoc(I,J)
644     discrim = bqe*bqe - 4. _d 0*aqe*cqe
645     #undef ALLOW_SHELFICE_DEBUG
646     #ifdef ALLOW_SHELFICE_DEBUG
647     IF ( discrim .LT. 0. _d 0 ) THEN
648     print *, 'ml-shelfice: discrim = ', discrim,aqe,bqe,cqe
649     print *, 'ml-shelfice: pLoc = ', pLoc(I,J)
650     print *, 'ml-shelfice: tLoc = ', tLoc(I,J)
651     print *, 'ml-shelfice: sLoc = ', sLoc(I,J)
652     print *, 'ml-shelfice: tsurface= ',
653     & SHELFICEthetaSurface
654     print *, 'ml-shelfice: eps1 = ', eps1
655     print *, 'ml-shelfice: eps2 = ', eps2
656     print *, 'ml-shelfice: eps3 = ', eps3
657     print *, 'ml-shelfice: eps4 = ', eps4
658     print *, 'ml-shelfice: eps5 = ', eps5
659     print *, 'ml-shelfice: eps6 = ', eps6
660     print *, 'ml-shelfice: eps7 = ', eps7
661     print *, 'ml-shelfice: eps8 = ', eps8
662     print *, 'ml-shelfice: rU2mass = ', rUnit2mass
663     print *, 'ml-shelfice: rhoIce = ', rhoShelfIce
664     print *, 'ml-shelfice: cFac = ', cFac
665     print *, 'ml-shelfice: Cp_W = ', HeatCapacity_Cp
666     print *, 'ml-shelfice: Cp_I = ',
667     & SHELFICEHeatCapacity_Cp
668     print *, 'ml-shelfice: gammaT = ',
669     & SHELFICEheatTransCoeff
670     print *, 'ml-shelfice: gammaS = ',
671     & SHELFICEsaltTransCoeff
672     print *, 'ml-shelfice: lat.heat= ',
673     & SHELFICElatentHeat
674     STOP 'ABNORMAL END in S/R SHELFICE_THERMODYNAMICS'
675     ENDIF
676     #endif /* ALLOW_SHELFICE_DEBUG */
677     saltFreeze = (- bqe - SQRT(discrim))*recip_aqe
678     IF ( saltFreeze .LT. 0. _d 0 )
679     & saltFreeze = (- bqe + SQRT(discrim))*recip_aqe
680     thetaFreeze = a0*saltFreeze + eps4
681     C-- upward fresh water flux due to melting (in kg/m^2/s)
682     cph change to identical form
683     cph freshWaterFlux = rUnit2mass
684     cph & * shiTransCoeffS(i,j,bi,bj)
685     cph & * ( saltFreeze - sLoc(I,J) ) / saltFreeze
686     freshWaterFlux = rUnit2mass
687     & * shiTransCoeffS(i,j,bi,bj)
688     & * ( 1. _d 0 - sLoc(I,J) / saltFreeze )
689     #ifdef ALLOW_SHIFWFLX_CONTROL
690     & + xx_shifwflx_loc(I,J,bi,bj)
691     #endif /* ALLOW_SHIFWFLX_CONTROL */
692 dgoldberg 1.15
693    
694 dgoldberg 1.19 #ifdef ALLOW_SHELFICE_GROUNDED_ICE
695 dgoldberg 1.15 freshWaterFlux =
696     & freshWaterFlux*(GrdFactor(i,j,bi,bj)*0.5+0.5)
697     #endif
698    
699 dgoldberg 1.16 C-- Calculate the upward heat and fresh water fluxes;
700     C-- MITgcm sign conventions: downward (negative) fresh water flux
701     C-- implies melting and due to upward (positive) heat flux
702 dgoldberg 1.1 shelfIceHeatFlux(I,J,bi,bj) =
703     & ( eps3
704     & - freshWaterFlux*SHELFICEheatCapacity_Cp*fwflxFac )
705     & * ( thetaFreeze - SHELFICEthetaSurface )
706     & - cFac*freshWaterFlux*( SHELFICElatentHeat
707     & - HeatCapacity_Cp*( thetaFreeze - rFac*tLoc(I,J) ) )
708     shelfIceFreshWaterFlux(I,J,bi,bj) = freshWaterFlux
709     C-- compute surface tendencies
710     shelficeForcingT(i,j,bi,bj) =
711     & ( shiTransCoeffT(i,j,bi,bj)
712     & - cFac*shelfIceFreshWaterFlux(I,J,bi,bj)*mass2rUnit )
713     & * ( thetaFreeze - tLoc(I,J) )
714     & - realFWfac*shelfIceFreshWaterFlux(I,J,bi,bj)*
715     & mass2rUnit*
716     & ( tLoc(I,J) - theta(I,J,K,bi,bj) )
717     shelficeForcingS(i,j,bi,bj) =
718     & ( shiTransCoeffS(i,j,bi,bj)
719     & - cFac*shelfIceFreshWaterFlux(I,J,bi,bj)*mass2rUnit )
720     & * ( saltFreeze - sLoc(I,J) )
721     & - realFWfac*shelfIceFreshWaterFlux(I,J,bi,bj)*
722     & mass2rUnit*
723     & ( sLoc(I,J) - salt(I,J,K,bi,bj) )
724 ksnow 1.20 #ifdef ALLOW_SHELFICE_GROUNDED_ICE
725     shelfIceHeatFlux(i,j,bi,bj) =
726     & shelfIceHeatFlux(i,j,bi,bj)*(GrdFactor(i,j,bi,bj)*0.5+0.5)
727     shelfIceForcingT(i,j,bi,bj) =
728     & shelfIceForcingT(i,j,bi,bj)*(GrdFactor(i,j,bi,bj)*0.5+0.5)
729     shelfIceForcingS(i,j,bi,bj) =
730     & shelfIceForcingS(i,j,bi,bj)*(GrdFactor(i,j,bi,bj)*0.5+0.5)
731     #endif
732 dgoldberg 1.1 ELSE
733     shelfIceHeatFlux (I,J,bi,bj) = 0. _d 0
734     shelfIceFreshWaterFlux(I,J,bi,bj) = 0. _d 0
735     shelficeForcingT (I,J,bi,bj) = 0. _d 0
736     shelficeForcingS (I,J,bi,bj) = 0. _d 0
737     ENDIF
738     ENDDO
739     ENDDO
740     ENDIF
741     C endif (not) useISOMIPTD
742     ENDDO
743     ENDDO
744    
745 dgoldberg 1.16 IF (SHELFICEMassStepping) THEN
746     CALL SHELFICE_STEP_ICEMASS( myTime, myIter, myThid )
747     ENDIF
748    
749     C-- Calculate new loading anomaly (in case the ice-shelf mass was updated)
750 dgoldberg 1.15 #ifndef ALLOW_AUTODIFF
751 dgoldberg 1.16 c IF ( SHELFICEloadAnomalyFile .EQ. ' ' ) THEN
752     DO bj = myByLo(myThid), myByHi(myThid)
753     DO bi = myBxLo(myThid), myBxHi(myThid)
754     DO j = 1-OLy, sNy+OLy
755     DO i = 1-OLx, sNx+OLx
756 dgoldberg 1.19 #ifndef ALLOW_SHELFICE_GROUNDED_ICE
757 dgoldberg 1.1
758 dgoldberg 1.15 shelficeLoadAnomaly(i,j,bi,bj) = gravity
759 dgoldberg 1.2 & *( shelficeMass(i,j,bi,bj) + rhoConst*Ro_surf(i,j,bi,bj) )
760 dgoldberg 1.1
761 dgoldberg 1.15 #else
762 dgoldberg 1.4
763 dgoldberg 1.15 shelficeLoadAnomaly(i,j,bi,bj) = gravity
764 ksnow 1.18 & *( EFFMASS(I,J,BI,BJ) + rhoConst*Ro_surf(i,j,bi,bj) )
765 dgoldberg 1.4
766 dgoldberg 1.15 #endif
767 dgoldberg 1.16 ENDDO
768 dgoldberg 1.3 ENDDO
769     ENDDO
770     ENDDO
771 dgoldberg 1.16 c ENDIF
772 dgoldberg 1.1 #endif /* ndef ALLOW_AUTODIFF */
773    
774 dgoldberg 1.19
775    
776 dgoldberg 1.1 #ifdef ALLOW_DIAGNOSTICS
777     IF ( useDiagnostics ) THEN
778     CALL DIAGNOSTICS_FILL_RS(shelfIceFreshWaterFlux,'SHIfwFlx',
779     & 0,1,0,1,1,myThid)
780     CALL DIAGNOSTICS_FILL_RS(shelfIceHeatFlux, 'SHIhtFlx',
781     & 0,1,0,1,1,myThid)
782     C SHIForcT (Ice shelf forcing for theta [W/m2], >0 increases theta)
783     tmpFac = HeatCapacity_Cp*rUnit2mass
784     CALL DIAGNOSTICS_SCALE_FILL(shelficeForcingT,tmpFac,1,
785     & 'SHIForcT',0,1,0,1,1,myThid)
786     C SHIForcS (Ice shelf forcing for salt [g/m2/s], >0 increases salt)
787     tmpFac = rUnit2mass
788     CALL DIAGNOSTICS_SCALE_FILL(shelficeForcingS,tmpFac,1,
789     & 'SHIForcS',0,1,0,1,1,myThid)
790     C Transfer coefficients
791     CALL DIAGNOSTICS_FILL(shiTransCoeffT,'SHIgammT',
792     & 0,1,0,1,1,myThid)
793     CALL DIAGNOSTICS_FILL(shiTransCoeffS,'SHIgammS',
794     & 0,1,0,1,1,myThid)
795     C Friction velocity
796     #ifdef SHI_ALLOW_GAMMAFRICT
797     IF ( SHELFICEuseGammaFrict )
798     & CALL DIAGNOSTICS_FILL(uStarDiag,'SHIuStar',0,1,0,1,1,myThid)
799     #endif /* SHI_ALLOW_GAMMAFRICT */
800 dgoldberg 1.16 #ifdef ALLOW_SHELFICE_REMESHING
801     CALL DIAGNOSTICS_FILL(R_shelfice,'SHIRshel',
802 dgoldberg 1.1 & 0,1,0,1,1,myThid)
803 dgoldberg 1.19 #endif
804     #ifdef ALLOW_SHELFICE_GROUNDED_ICE
805 dgoldberg 1.16 CALL DIAGNOSTICS_FILL(EFFMASS,'SHI_MEff',
806 dgoldberg 1.3 & 0,1,0,1,1,myThid)
807     #endif
808 dgoldberg 1.16 ENDIF
809     #endif /* ALLOW_DIAGNOSTICS */
810 dgoldberg 1.1
811     #endif /* ALLOW_SHELFICE */
812     RETURN
813     END
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