/[MITgcm]/MITgcm_contrib/verification_other/shelfice_remeshing/code/shelfice_thermodynamics.F
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Revision 1.17 - (hide annotations) (download)
Tue May 24 08:22:45 2016 UTC (9 years, 1 month ago) by ksnow
Branch: MAIN
Changes since 1.16: +29 -26 lines 
Update calcultion of massmin with time dependent pload
1 ksnow 1.17 C $Header: /u/gcmpack/MITgcm_contrib/verification_other/shelfice_remeshing/code/shelfice_thermodynamics.F,v 1.16 2016/05/05 18:16:04 dgoldberg 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     #ifdef ALLOW_SHELFICE_REMESHING
277    
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     #ifdef ALLOW_STREAMICE
285     CALL SHELFICE_MASSMIN(R_min,massMin, myThid)
286    
287 dgoldberg 1.15 DO j = 1-OLy, sNy+OLy
288     DO i = 1-OLx, sNx+OLx
289    
290     mass = shelficemass(i,j,bi,bj)
291    
292 ksnow 1.17 GrdFactor(i,j,bi,bj) = tanh((massMin(i,j,bi,bj)
293     & - mass)*1. _d 5)
294 dgoldberg 1.15
295 ksnow 1.17 IF (GrdFactor(i,j,bi,bj) .GT. 0. _d 0) THEN
296     EFFMASS(i,j,bi,bj) = mass
297     EFFR(i,j,bi,bj) = Ro_surf(i,j,bi,bj)
298     ELSE
299     EFFMASS(i,j,bi,bj) = massMin(i,j,bi,bj)
300     EFFR(i,j,bi,bj) = R_min(i,j,bi,bj)
301     ENDIF
302 dgoldberg 1.15
303 ksnow 1.17 ENDDO
304     ENDDO
305     #endif /* ALLOW_STREAMICE */
306     C KS_dens -----------------------------------------------
307 dgoldberg 1.15
308    
309     #endif
310     ! allow shelfice_remeshing
311    
312 dgoldberg 1.16 #ifdef SHI_USTAR_TOPDR
313 dgoldberg 1.1 IF ( SHELFICEBoundaryLayer ) THEN
314     C-- average over boundary layer width
315     DO J = 1, sNy+1
316     DO I = 1, sNx+1
317     u_topdr(I,J,bi,bj) = 0.0
318     v_topdr(I,J,bi,bj) = 0.0
319     ENDDO
320     ENDDO
321     ENDIF
322 dgoldberg 1.16 #endif
323 dgoldberg 1.1
324     #ifdef ALLOW_AUTODIFF_TAMC
325     # ifdef SHI_ALLOW_GAMMAFRICT
326     act1 = bi - myBxLo(myThid)
327     max1 = myBxHi(myThid) - myBxLo(myThid) + 1
328     act2 = bj - myByLo(myThid)
329     max2 = myByHi(myThid) - myByLo(myThid) + 1
330     act3 = myThid - 1
331     max3 = nTx*nTy
332     act4 = ikey_dynamics - 1
333     ikey = (act1 + 1) + act2*max1
334     & + act3*max1*max2
335     & + act4*max1*max2*max3
336     # endif /* SHI_ALLOW_GAMMAFRICT */
337     #endif /* ALLOW_AUTODIFF_TAMC */
338     DO J = 1, sNy
339     DO I = 1, sNx
340     C-- make local copies of temperature, salinity and depth (pressure in deci-bar)
341     C-- underneath the ice
342     K = MAX(1,kTopC(I,J,bi,bj))
343     pLoc(I,J) = ABS(R_shelfIce(I,J,bi,bj))
344     c pLoc(I,J) = shelficeMass(I,J,bi,bj)*gravity*1. _d -4
345     tLoc(I,J) = theta(I,J,K,bi,bj)
346     sLoc(I,J) = MAX(salt(I,J,K,bi,bj), zeroRL)
347 dgoldberg 1.16 #ifdef SHI_USTAR_WETPOINT
348     velSq(I,J) = 0.
349     tmpFac = _hFacW(I, J,K,bi,bj) + _hFacW(I+1,J,K,bi,bj)
350     IF ( tmpFac.GT.0. _d 0 )
351     & velSq(I,J) = (
352     & uVel( I, J,K,bi,bj)*uVel( I, J,K,bi,bj)*_hFacW( I, J,K,bi,bj)
353     & + uVel(I+1,J,K,bi,bj)*uVel(I+1,J,K,bi,bj)*_hFacW(I+1,J,K,bi,bj)
354     & )/tmpFac
355     tmpFac = _hFacS(I,J, K,bi,bj) + _hFacS(I,J+1,K,bi,bj)
356     IF ( tmpFac.GT.0. _d 0 )
357     & velSq(I,J) = velSq(I,J) + (
358     & vVel(I, J, K,bi,bj)*vVel(I, J, K,bi,bj)*_hFacS(I, J, K,bi,bj)
359     & + vVel(I,J+1,K,bi,bj)*vVel(I,J+1,K,bi,bj)*_hFacS(I,J+1,K,bi,bj)
360     & )/tmpFac
361     #else /* SHI_USTAR_WETPOINT */
362     uLoc(I,J) = recip_hFacC(I,J,K,bi,bj) * halfRL *
363 dgoldberg 1.1 & ( uVel(I, J,K,bi,bj) * _hFacW(I, J,K,bi,bj)
364     & + uVel(I+1,J,K,bi,bj) * _hFacW(I+1,J,K,bi,bj) )
365 dgoldberg 1.16 vLoc(I,J) = recip_hFacC(I,J,K,bi,bj) * halfRL *
366     & ( vVel(I,J, K,bi,bj) * _hFacS(I,J, K,bi,bj)
367 dgoldberg 1.1 & + vVel(I,J+1,K,bi,bj) * _hFacS(I,J+1,K,bi,bj) )
368 dgoldberg 1.16 velSq(I,J) = uLoc(I,J)*uLoc(I,J)+vLoc(I,J)*vLoc(I,J)
369     #endif /* SHI_USTAR_WETPOINT */
370 dgoldberg 1.1 ENDDO
371     ENDDO
372    
373 dgoldberg 1.16 #ifdef SHI_USTAR_TOPDR
374 dgoldberg 1.1 IF ( SHELFICEBoundaryLayer ) THEN
375     DO J = 1, sNy+1
376     DO I = 1, sNx+1
377     K = ksurfW(I,J,bi,bj)
378     Kp1 = K+1
379     IF (K.lt.Nr) then
380     drKp1 = drF(K)*(1. _d 0-_hFacW(I,J,K,bi,bj))
381     drKp1 = max (drKp1, 0. _d 0)
382     recip_drLoc = 1.0 /
383     & (drF(K)*_hFacW(I,J,K,bi,bj)+drKp1)
384     u_topdr(I,J,bi,bj) =
385     & (drF(K)*_hFacW(I,J,K,bi,bj)*uVel(I,J,K,bi,bj) +
386     & drKp1*uVel(I,J,Kp1,bi,bj))
387     & * recip_drLoc
388     ELSE
389     u_topdr(I,J,bi,bj) = 0. _d 0
390     ENDIF
391    
392     K = ksurfS(I,J,bi,bj)
393     Kp1 = K+1
394     IF (K.lt.Nr) then
395     drKp1 = drF(K)*(1. _d 0-_hFacS(I,J,K,bi,bj))
396     drKp1 = max (drKp1, 0. _d 0)
397     recip_drLoc = 1.0 /
398     & (drF(K)*_hFacS(I,J,K,bi,bj)+drKp1)
399     v_topdr(I,J,bi,bj) =
400     & (drF(K)*_hFacS(I,J,K,bi,bj)*vVel(I,J,K,bi,bj) +
401     & drKp1*vVel(I,J,Kp1,bi,bj))
402     & * recip_drLoc
403     ELSE
404     v_topdr(I,J,bi,bj) = 0. _d 0
405     ENDIF
406    
407     ENDDO
408     ENDDO
409     ENDIF
410 dgoldberg 1.16 #endif
411 dgoldberg 1.1
412     IF ( SHELFICEBoundaryLayer ) THEN
413     C-- average over boundary layer width
414     DO J = 1, sNy
415     DO I = 1, sNx
416     K = kTopC(I,J,bi,bj)
417     IF ( K .NE. 0 .AND. K .LT. Nr ) THEN
418     Kp1 = MIN(Nr,K+1)
419     C-- overlap into lower cell
420     drKp1 = drF(K)*( 1. _d 0 - _hFacC(I,J,K,bi,bj) )
421     C-- lower cell may not be as thick as required
422     drKp1 = MIN( drKp1, drF(Kp1) * _hFacC(I,J,Kp1,bi,bj) )
423 dgoldberg 1.16 drKp1 = MAX( drKp1, 0. _d 0 )
424 dgoldberg 1.1 recip_drLoc = 1. _d 0 /
425     & ( drF(K)*_hFacC(I,J,K,bi,bj) + drKp1 )
426     tLoc(I,J) = ( tLoc(I,J) * drF(K)*_hFacC(I,J,K,bi,bj)
427     & + theta(I,J,Kp1,bi,bj) *drKp1 )
428     & * recip_drLoc
429     sLoc(I,J) = ( sLoc(I,J) * drF(K)*_hFacC(I,J,K,bi,bj)
430     & + MAX(salt(I,J,Kp1,bi,bj), zeroRL) * drKp1 )
431     & * recip_drLoc
432 dgoldberg 1.16 #ifndef SHI_USTAR_WETPOINT
433     uLoc(I,J) = ( uLoc(I,J) * drF(K)*_hFacC(I,J,K,bi,bj)
434     & + drKp1 * recip_hFacC(I,J,Kp1,bi,bj) * halfRL *
435     & ( uVel(I, J,Kp1,bi,bj) * _hFacW(I, J,Kp1,bi,bj)
436     & + uVel(I+1,J,Kp1,bi,bj) * _hFacW(I+1,J,Kp1,bi,bj) )
437     & ) * recip_drLoc
438     vLoc(I,J) = ( vLoc(I,J) * drF(K)*_hFacC(I,J,K,bi,bj)
439     & + drKp1 * recip_hFacC(I,J,Kp1,bi,bj) * halfRL *
440     & ( vVel(I,J, Kp1,bi,bj) * _hFacS(I,J, Kp1,bi,bj)
441     & + vVel(I,J+1,Kp1,bi,bj) * _hFacS(I,J+1,Kp1,bi,bj) )
442     & ) * recip_drLoc
443     velSq(I,J) = uLoc(I,J)*uLoc(I,J)+vLoc(I,J)*vLoc(I,J)
444     #endif /* ndef SHI_USTAR_WETPOINT */
445 dgoldberg 1.1 ENDIF
446     ENDDO
447     ENDDO
448     ENDIF
449    
450    
451    
452     C-- turn potential temperature into in-situ temperature relative
453     C-- to the surface
454     DO J = 1, sNy
455     DO I = 1, sNx
456     #ifndef ALLOW_OPENAD
457     tLoc(I,J) = SW_TEMP(sLoc(I,J),tLoc(I,J),pLoc(I,J),zeroRL)
458     #else
459     CALL SW_TEMP(sLoc(I,J),tLoc(I,J),pLoc(I,J),zeroRL,tLoc(I,J))
460     #endif
461     ENDDO
462     ENDDO
463    
464     #ifdef SHI_ALLOW_GAMMAFRICT
465     IF ( SHELFICEuseGammaFrict ) THEN
466     DO J = 1, sNy
467     DO I = 1, sNx
468     K = kTopC(I,J,bi,bj)
469     IF ( K .NE. 0 .AND. pLoc(I,J) .GT. 0. _d 0 ) THEN
470 dgoldberg 1.16 ustarSq = shiCdrag * MAX( 1.D-6, velSq(I,J) )
471 dgoldberg 1.1 ustar = SQRT(ustarSq)
472     #ifdef ALLOW_DIAGNOSTICS
473     uStarDiag(I,J,bi,bj) = ustar
474     #endif /* ALLOW_DIAGNOSTICS */
475     C instead of etastar = sqrt(1+zetaN*ustar./(f*Lo*Rc))
476     C etastar = 1. _d 0
477     C gammaTurbConst = 1. _d 0 / (2. _d 0 * shiZetaN*etastar)
478     C & - recip_shiKarman
479     IF ( fCori(I,J,bi,bj) .NE. 0. _d 0 ) THEN
480     gammaTurb = LOG( ustarSq * shiZetaN * etastar**2
481     & / ABS(fCori(I,J,bi,bj) * 5.0 _d 0 * shiKinVisc))
482     & * recip_shiKarman
483     & + gammaTurbConst
484     C Do we need to catch the unlikely case of very small ustar
485     C that can lead to negative gammaTurb?
486     C gammaTurb = MAX(0.D0, gammaTurb)
487     ELSE
488     gammaTurb = gammaTurbConst
489     ENDIF
490     shiTransCoeffT(i,j,bi,bj) = MAX( zeroRL,
491     & ustar/(gammaTurb + gammaTmoleT) )
492     shiTransCoeffS(i,j,bi,bj) = MAX( zeroRL,
493     & ustar/(gammaTurb + gammaTmoleS) )
494     ENDIF
495     ENDDO
496     ENDDO
497     ENDIF
498     #endif /* SHI_ALLOW_GAMMAFRICT */
499    
500     #ifdef ALLOW_AUTODIFF_TAMC
501     # ifdef SHI_ALLOW_GAMMAFRICT
502     CADJ STORE shiTransCoeffS(:,:,bi,bj) = comlev1_bibj,
503     CADJ & key=ikey, byte=isbyte
504     CADJ STORE shiTransCoeffT(:,:,bi,bj) = comlev1_bibj,
505     CADJ & key=ikey, byte=isbyte
506     # endif /* SHI_ALLOW_GAMMAFRICT */
507     #endif /* ALLOW_AUTODIFF_TAMC */
508     #ifdef ALLOW_ISOMIP_TD
509     IF ( useISOMIPTD ) THEN
510     DO J = 1, sNy
511     DO I = 1, sNx
512     K = kTopC(I,J,bi,bj)
513     IF ( K .NE. 0 .AND. pLoc(I,J) .GT. 0. _d 0 ) THEN
514     C-- Calculate freezing temperature as a function of salinity and pressure
515     thetaFreeze =
516     & sLoc(I,J) * ( a0 + a1*sqrt(sLoc(I,J)) + a2*sLoc(I,J) )
517     & + b*pLoc(I,J) + c0
518     C-- Calculate the upward heat and fresh water fluxes
519     shelfIceHeatFlux(I,J,bi,bj) = maskC(I,J,K,bi,bj)
520     & * shiTransCoeffT(i,j,bi,bj)
521     & * ( tLoc(I,J) - thetaFreeze )
522     & * HeatCapacity_Cp*rUnit2mass
523     #ifdef ALLOW_SHIFWFLX_CONTROL
524     & - xx_shifwflx_loc(I,J,bi,bj)*SHELFICElatentHeat
525     #endif /* ALLOW_SHIFWFLX_CONTROL */
526     C upward heat flux into the shelf-ice implies basal melting,
527     C thus a downward (negative upward) fresh water flux (as a mass flux),
528     C and vice versa
529     shelfIceFreshWaterFlux(I,J,bi,bj) =
530     & - shelfIceHeatFlux(I,J,bi,bj)
531     & *recip_latentHeat
532     C-- compute surface tendencies
533     shelficeForcingT(i,j,bi,bj) =
534     & - shelfIceHeatFlux(I,J,bi,bj)
535     & *recip_Cp*mass2rUnit
536     & - cFac * shelfIceFreshWaterFlux(I,J,bi,bj)*mass2rUnit
537     & * ( thetaFreeze - tLoc(I,J) )
538     shelficeForcingS(i,j,bi,bj) =
539     & shelfIceFreshWaterFlux(I,J,bi,bj) * mass2rUnit
540     & * ( cFac*sLoc(I,J) + (1. _d 0-cFac)*convertFW2SaltLoc )
541     C-- stress at the ice/water interface is computed in separate
542     C routines that are called from mom_fluxform/mom_vecinv
543     ELSE
544     shelfIceHeatFlux (I,J,bi,bj) = 0. _d 0
545     shelfIceFreshWaterFlux(I,J,bi,bj) = 0. _d 0
546     shelficeForcingT (I,J,bi,bj) = 0. _d 0
547     shelficeForcingS (I,J,bi,bj) = 0. _d 0
548     ENDIF
549     ENDDO
550     ENDDO
551     ELSE
552     #else
553     IF ( .TRUE. ) THEN
554     #endif /* ALLOW_ISOMIP_TD */
555     C use BRIOS thermodynamics, following Hellmers PhD thesis:
556     C Hellmer, H., 1989, A two-dimensional model for the thermohaline
557     C circulation under an ice shelf, Reports on Polar Research, No. 60
558     C (in German).
559    
560     DO J = 1, sNy
561     DO I = 1, sNx
562     K = kTopC(I,J,bi,bj)
563     IF ( K .NE. 0 .AND. pLoc(I,J) .GT. 0. _d 0 ) THEN
564     C heat flux into the ice shelf, default is diffusive flux
565     C (Holland and Jenkins, 1999, eq.21)
566     thetaFreeze = a0*sLoc(I,J)+c0+b*pLoc(I,J)
567     fwflxFac = 0. _d 0
568     IF ( tLoc(I,J) .GT. thetaFreeze ) fwflxFac = dFac
569     C a few abbreviations
570     eps1 = rUnit2mass*HeatCapacity_Cp
571     & *shiTransCoeffT(i,j,bi,bj)
572     eps2 = rUnit2mass*SHELFICElatentHeat
573     & *shiTransCoeffS(i,j,bi,bj)
574     eps5 = rUnit2mass*HeatCapacity_Cp
575     & *shiTransCoeffS(i,j,bi,bj)
576    
577     C solve quadratic equation for salinity at shelfice-ocean interface
578     C note: this part of the code is not very intuitive as it involves
579     C many arbitrary abbreviations that were introduced to derive the
580     C correct form of the quadratic equation for salinity. The abbreviations
581     C only make sense in connection with my notes on this (M.Losch)
582     C
583     C eps3a was introduced as a constant variant of eps3 to avoid AD of
584     C code of typ (pLoc-const)/pLoc
585     eps3a = rhoShelfIce*SHELFICEheatCapacity_Cp
586     & * SHELFICEkappa * ( 1. _d 0 - dFac )
587     eps3 = eps3a/pLoc(I,J)
588     eps4 = b*pLoc(I,J) + c0
589     eps6 = eps4 - tLoc(I,J)
590     eps7 = eps4 - SHELFICEthetaSurface
591     eps8 = rUnit2mass*SHELFICEheatCapacity_Cp
592     & *shiTransCoeffS(i,j,bi,bj) * fwflxFac
593     aqe = a0 *(eps1+eps3-eps8)
594     recip_aqe = 0. _d 0
595     IF ( aqe .NE. 0. _d 0 ) recip_aqe = 0.5 _d 0/aqe
596     c bqe = eps1*eps6 + eps3*eps7 - eps2
597     bqe = eps1*eps6
598     & + eps3a*( b
599     & + ( c0 - SHELFICEthetaSurface )/pLoc(I,J) )
600     & - eps2
601     & + eps8*( a0*sLoc(I,J) - eps7 )
602     cqe = ( eps2 + eps8*eps7 )*sLoc(I,J)
603     discrim = bqe*bqe - 4. _d 0*aqe*cqe
604     #undef ALLOW_SHELFICE_DEBUG
605     #ifdef ALLOW_SHELFICE_DEBUG
606     IF ( discrim .LT. 0. _d 0 ) THEN
607     print *, 'ml-shelfice: discrim = ', discrim,aqe,bqe,cqe
608     print *, 'ml-shelfice: pLoc = ', pLoc(I,J)
609     print *, 'ml-shelfice: tLoc = ', tLoc(I,J)
610     print *, 'ml-shelfice: sLoc = ', sLoc(I,J)
611     print *, 'ml-shelfice: tsurface= ',
612     & SHELFICEthetaSurface
613     print *, 'ml-shelfice: eps1 = ', eps1
614     print *, 'ml-shelfice: eps2 = ', eps2
615     print *, 'ml-shelfice: eps3 = ', eps3
616     print *, 'ml-shelfice: eps4 = ', eps4
617     print *, 'ml-shelfice: eps5 = ', eps5
618     print *, 'ml-shelfice: eps6 = ', eps6
619     print *, 'ml-shelfice: eps7 = ', eps7
620     print *, 'ml-shelfice: eps8 = ', eps8
621     print *, 'ml-shelfice: rU2mass = ', rUnit2mass
622     print *, 'ml-shelfice: rhoIce = ', rhoShelfIce
623     print *, 'ml-shelfice: cFac = ', cFac
624     print *, 'ml-shelfice: Cp_W = ', HeatCapacity_Cp
625     print *, 'ml-shelfice: Cp_I = ',
626     & SHELFICEHeatCapacity_Cp
627     print *, 'ml-shelfice: gammaT = ',
628     & SHELFICEheatTransCoeff
629     print *, 'ml-shelfice: gammaS = ',
630     & SHELFICEsaltTransCoeff
631     print *, 'ml-shelfice: lat.heat= ',
632     & SHELFICElatentHeat
633     STOP 'ABNORMAL END in S/R SHELFICE_THERMODYNAMICS'
634     ENDIF
635     #endif /* ALLOW_SHELFICE_DEBUG */
636     saltFreeze = (- bqe - SQRT(discrim))*recip_aqe
637     IF ( saltFreeze .LT. 0. _d 0 )
638     & saltFreeze = (- bqe + SQRT(discrim))*recip_aqe
639     thetaFreeze = a0*saltFreeze + eps4
640     C-- upward fresh water flux due to melting (in kg/m^2/s)
641     cph change to identical form
642     cph freshWaterFlux = rUnit2mass
643     cph & * shiTransCoeffS(i,j,bi,bj)
644     cph & * ( saltFreeze - sLoc(I,J) ) / saltFreeze
645     freshWaterFlux = rUnit2mass
646     & * shiTransCoeffS(i,j,bi,bj)
647     & * ( 1. _d 0 - sLoc(I,J) / saltFreeze )
648     #ifdef ALLOW_SHIFWFLX_CONTROL
649     & + xx_shifwflx_loc(I,J,bi,bj)
650     #endif /* ALLOW_SHIFWFLX_CONTROL */
651 dgoldberg 1.15
652    
653     #ifdef ALLOW_SHELFICE_REMESHING
654     freshWaterFlux =
655     & freshWaterFlux*(GrdFactor(i,j,bi,bj)*0.5+0.5)
656     #endif
657    
658 dgoldberg 1.16 C-- Calculate the upward heat and fresh water fluxes;
659     C-- MITgcm sign conventions: downward (negative) fresh water flux
660     C-- implies melting and due to upward (positive) heat flux
661 dgoldberg 1.1 shelfIceHeatFlux(I,J,bi,bj) =
662     & ( eps3
663     & - freshWaterFlux*SHELFICEheatCapacity_Cp*fwflxFac )
664     & * ( thetaFreeze - SHELFICEthetaSurface )
665     & - cFac*freshWaterFlux*( SHELFICElatentHeat
666     & - HeatCapacity_Cp*( thetaFreeze - rFac*tLoc(I,J) ) )
667     shelfIceFreshWaterFlux(I,J,bi,bj) = freshWaterFlux
668     C-- compute surface tendencies
669     shelficeForcingT(i,j,bi,bj) =
670     & ( shiTransCoeffT(i,j,bi,bj)
671     & - cFac*shelfIceFreshWaterFlux(I,J,bi,bj)*mass2rUnit )
672     & * ( thetaFreeze - tLoc(I,J) )
673     & - realFWfac*shelfIceFreshWaterFlux(I,J,bi,bj)*
674     & mass2rUnit*
675     & ( tLoc(I,J) - theta(I,J,K,bi,bj) )
676     shelficeForcingS(i,j,bi,bj) =
677     & ( shiTransCoeffS(i,j,bi,bj)
678     & - cFac*shelfIceFreshWaterFlux(I,J,bi,bj)*mass2rUnit )
679     & * ( saltFreeze - sLoc(I,J) )
680     & - realFWfac*shelfIceFreshWaterFlux(I,J,bi,bj)*
681     & mass2rUnit*
682     & ( sLoc(I,J) - salt(I,J,K,bi,bj) )
683     ELSE
684     shelfIceHeatFlux (I,J,bi,bj) = 0. _d 0
685     shelfIceFreshWaterFlux(I,J,bi,bj) = 0. _d 0
686     shelficeForcingT (I,J,bi,bj) = 0. _d 0
687     shelficeForcingS (I,J,bi,bj) = 0. _d 0
688     ENDIF
689     ENDDO
690     ENDDO
691     ENDIF
692     C endif (not) useISOMIPTD
693     ENDDO
694     ENDDO
695    
696 dgoldberg 1.16 IF (SHELFICEMassStepping) THEN
697     CALL SHELFICE_STEP_ICEMASS( myTime, myIter, myThid )
698     ENDIF
699    
700     C-- Calculate new loading anomaly (in case the ice-shelf mass was updated)
701 dgoldberg 1.15 #ifndef ALLOW_AUTODIFF
702 dgoldberg 1.16 c IF ( SHELFICEloadAnomalyFile .EQ. ' ' ) THEN
703     DO bj = myByLo(myThid), myByHi(myThid)
704     DO bi = myBxLo(myThid), myBxHi(myThid)
705     DO j = 1-OLy, sNy+OLy
706     DO i = 1-OLx, sNx+OLx
707 dgoldberg 1.15 #ifndef ALLOW_SHELFICE_REMESHING
708 dgoldberg 1.1
709 dgoldberg 1.15 shelficeLoadAnomaly(i,j,bi,bj) = gravity
710 dgoldberg 1.2 & *( shelficeMass(i,j,bi,bj) + rhoConst*Ro_surf(i,j,bi,bj) )
711 dgoldberg 1.1
712 dgoldberg 1.15 #else
713 dgoldberg 1.4
714 ksnow 1.17 C KS_dens
715 dgoldberg 1.15 shelficeLoadAnomaly(i,j,bi,bj) = gravity
716 ksnow 1.17 & *( EFFMASS(I,J,BI,BJ) + rhoConst*EFFR(i,j,bi,bj) )
717    
718     C shelficeLoadAnomaly(i,j,bi,bj) = gravity
719     C & *( EFFMASS(I,J,BI,BJ) + rhoConst*Ro_surf(i,j,bi,bj) )
720 dgoldberg 1.4
721 dgoldberg 1.15 #endif
722 dgoldberg 1.16 ENDDO
723 dgoldberg 1.3 ENDDO
724     ENDDO
725     ENDDO
726 dgoldberg 1.16 c ENDIF
727 dgoldberg 1.1 #endif /* ndef ALLOW_AUTODIFF */
728    
729     #ifdef ALLOW_DIAGNOSTICS
730     IF ( useDiagnostics ) THEN
731     CALL DIAGNOSTICS_FILL_RS(shelfIceFreshWaterFlux,'SHIfwFlx',
732     & 0,1,0,1,1,myThid)
733     CALL DIAGNOSTICS_FILL_RS(shelfIceHeatFlux, 'SHIhtFlx',
734     & 0,1,0,1,1,myThid)
735     C SHIForcT (Ice shelf forcing for theta [W/m2], >0 increases theta)
736     tmpFac = HeatCapacity_Cp*rUnit2mass
737     CALL DIAGNOSTICS_SCALE_FILL(shelficeForcingT,tmpFac,1,
738     & 'SHIForcT',0,1,0,1,1,myThid)
739     C SHIForcS (Ice shelf forcing for salt [g/m2/s], >0 increases salt)
740     tmpFac = rUnit2mass
741     CALL DIAGNOSTICS_SCALE_FILL(shelficeForcingS,tmpFac,1,
742     & 'SHIForcS',0,1,0,1,1,myThid)
743     C Transfer coefficients
744     CALL DIAGNOSTICS_FILL(shiTransCoeffT,'SHIgammT',
745     & 0,1,0,1,1,myThid)
746     CALL DIAGNOSTICS_FILL(shiTransCoeffS,'SHIgammS',
747     & 0,1,0,1,1,myThid)
748     C Friction velocity
749     #ifdef SHI_ALLOW_GAMMAFRICT
750     IF ( SHELFICEuseGammaFrict )
751     & CALL DIAGNOSTICS_FILL(uStarDiag,'SHIuStar',0,1,0,1,1,myThid)
752     #endif /* SHI_ALLOW_GAMMAFRICT */
753 dgoldberg 1.16 #ifdef ALLOW_SHELFICE_REMESHING
754     CALL DIAGNOSTICS_FILL(R_shelfice,'SHIRshel',
755 dgoldberg 1.1 & 0,1,0,1,1,myThid)
756 dgoldberg 1.16 CALL DIAGNOSTICS_FILL(EFFMASS,'SHI_MEff',
757 dgoldberg 1.3 & 0,1,0,1,1,myThid)
758     #endif
759 dgoldberg 1.16 ENDIF
760     #endif /* ALLOW_DIAGNOSTICS */
761 dgoldberg 1.1
762     #endif /* ALLOW_SHELFICE */
763     RETURN
764     END
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