/[MITgcm]/MITgcm/pkg/seaice/seaice_solve4temp.F
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Revision 1.24 - (hide annotations) (download)
Wed Feb 1 23:58:09 2012 UTC (12 years, 4 months ago) by jmc
Branch: MAIN
Changes since 1.23: +52 -41 lines
- remove from F_ia (and it's derivative dFiDTs1) the contribution of
  conductive heat flux F_c , which is added explicitly when updating tsurf
  as solution of: Fc = Fia + d/dT(Fia - Fc) *delta.tsurf
  so that now F_ia has a consistent meaning through the entire routine.
- add two 2-D arrays (dFia_dTs & dqh_dTs) in prep for next modif.

1 jmc 1.24 C $Header: /u/gcmpack/MITgcm/pkg/seaice/seaice_solve4temp.F,v 1.23 2012/01/31 15:57:17 jmc Exp $
2 jmc 1.1 C $Name: $
3    
4     #include "SEAICE_OPTIONS.h"
5 jmc 1.19 #ifdef ALLOW_EXF
6     # include "EXF_OPTIONS.h"
7     #endif
8 jmc 1.1
9     CBOP
10     C !ROUTINE: SEAICE_SOLVE4TEMP
11     C !INTERFACE:
12     SUBROUTINE SEAICE_SOLVE4TEMP(
13     I UG, HICE_ACTUAL, HSNOW_ACTUAL,
14 ifenty 1.16 #ifdef SEAICE_ADD_SUBLIMATION_TO_FWBUDGET
15     I F_lh_max,
16     #endif
17 jmc 1.1 U TSURF,
18 jmc 1.21 O F_ia, IcePenetSW,
19 mlosch 1.10 O FWsublim,
20 jmc 1.1 I bi, bj, myTime, myIter, myThid )
21    
22     C !DESCRIPTION: \bv
23     C *==========================================================*
24     C | SUBROUTINE SOLVE4TEMP
25     C | o Calculate ice growth rate, surface fluxes and
26     C | temperature of ice surface.
27     C | see Hibler, MWR, 108, 1943-1973, 1980
28     C *==========================================================*
29     C \ev
30    
31     C !USES:
32     IMPLICIT NONE
33     C === Global variables ===
34     #include "SIZE.h"
35     #include "GRID.h"
36     #include "EEPARAMS.h"
37 jmc 1.3 #include "PARAMS.h"
38 jmc 1.1 #include "FFIELDS.h"
39 heimbach 1.13 #include "SEAICE_SIZE.h"
40     #include "SEAICE_PARAMS.h"
41 jmc 1.1 #include "SEAICE.h"
42     #ifdef SEAICE_VARIABLE_FREEZING_POINT
43     #include "DYNVARS.h"
44     #endif /* SEAICE_VARIABLE_FREEZING_POINT */
45     #ifdef ALLOW_EXF
46     # include "EXF_FIELDS.h"
47     #endif
48 mlosch 1.8 #ifdef ALLOW_AUTODIFF_TAMC
49     # include "tamc.h"
50     #endif
51 jmc 1.1
52 jmc 1.21 C !INPUT PARAMETERS:
53     C UG :: atmospheric wind speed (m/s)
54 jmc 1.1 C HICE_ACTUAL :: actual ice thickness
55     C HSNOW_ACTUAL :: actual snow thickness
56 jmc 1.21 C TSURF :: surface temperature of ice/snow in Kelvin
57     C bi,bj :: tile indices
58     C myTime :: current time in simulation
59     C myIter :: iteration number in simulation
60     C myThid :: my Thread Id number
61     C !OUTPUT PARAMETERS:
62     C TSURF :: updated surface temperature of ice/snow in Kelvin
63     C F_ia :: upward seaice/snow surface heat flux to atmosphere (W/m^2)
64     C IcePenetSW :: short wave heat flux transmitted through ice (+=upward)
65     C FWsublim :: fresh water (mass) flux due to sublimation (+=up)(kg/m^2/s)
66 jmc 1.24 C---- Notes:
67     C 1) should add IcePenetSW to F_ia to get the net surface heat flux
68     C from the atmosphere (IcePenetSW not currently included in F_ia)
69     C 2) since zero ice/snow heat capacity is assumed, all the absorbed Short
70     C -Wave is used to warm the ice/snow surface (heating profile ignored).
71     C----------
72 jmc 1.21 _RL UG (1:sNx,1:sNy)
73     _RL HICE_ACTUAL (1:sNx,1:sNy)
74     _RL HSNOW_ACTUAL(1:sNx,1:sNy)
75 ifenty 1.16 #ifdef SEAICE_ADD_SUBLIMATION_TO_FWBUDGET
76 jmc 1.21 _RL F_lh_max (1:sNx,1:sNy)
77 ifenty 1.16 #endif
78 jmc 1.21 _RL TSURF (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
79     _RL F_ia (1:sNx,1:sNy)
80     _RL IcePenetSW (1:sNx,1:sNy)
81     _RL FWsublim (1:sNx,1:sNy)
82 jmc 1.1 INTEGER bi, bj
83     _RL myTime
84     INTEGER myIter, myThid
85 jmc 1.19 CEOP
86 jmc 1.1
87 jmc 1.19 #if defined(ALLOW_ATM_TEMP) && defined(ALLOW_DOWNWARD_RADIATION)
88 jmc 1.1 C !LOCAL VARIABLES:
89     C === Local variables ===
90 jmc 1.3 C i, j :: Loop counters
91     C kSrf :: vertical index of surface layer
92 jmc 1.1 INTEGER i, j
93 jmc 1.3 #ifdef SEAICE_VARIABLE_FREEZING_POINT
94     INTEGER kSrf
95     #endif /* SEAICE_VARIABLE_FREEZING_POINT */
96 jmc 1.1 INTEGER ITER
97 jmc 1.21 C TB :: ocean temperature in contact with ice (=seawater freezing point) (K)
98 mlosch 1.5 _RL TB (1:sNx,1:sNy)
99 mlosch 1.18 _RL D1, D1I
100     _RL D3(1:sNx,1:sNy)
101 mlosch 1.5 _RL TMELT, XKI, XKS, HCUT, XIO
102     _RL SurfMeltTemp
103 jmc 1.21 C effConduct :: effective conductivity of combined ice and snow
104 mlosch 1.5 _RL effConduct(1:sNx,1:sNy)
105 jmc 1.21 C lhSublim :: latent heat of sublimation (SEAICE_lhEvap + SEAICE_lhFusion)
106     _RL lhSublim
107     C t1,t2,t3,t4 :: powers of temperature
108     _RL t1, t2, t3, t4
109 jmc 1.1
110 jmc 1.24 C- Constants to calculate Saturation Vapor Pressure
111 jmc 1.6 #ifdef SEAICE_SOLVE4TEMP_LEGACY
112 jmc 1.24 C Maykut Polynomia Coeff. for Sat. Vapor Press
113 jmc 1.21 _RL C1, C2, C3, C4, C5, QS1
114 jmc 1.6 #else /* SEAICE_SOLVE4TEMP_LEGACY */
115 jmc 1.24 C Extended temp-range expon. relation Coeff. for Sat. Vapor Press
116 jmc 1.21 _RL lnTEN
117 jmc 1.1 _RL aa1,aa2,bb1,bb2,Ppascals,cc0,cc1,cc2,cc3t
118     C specific humidity at ice surface variables
119 jmc 1.21 _RL mm_pi,mm_log10pi
120 jmc 1.6 #endif /* SEAICE_SOLVE4TEMP_LEGACY */
121 jmc 1.1
122 jmc 1.22 C F_c :: conductive heat flux through seaice+snow (+=upward)
123 jmc 1.21 C F_lh :: latent heat flux (sublimation) (+=upward)
124 jmc 1.24 C qhice :: saturation vapor pressure of snow/ice surface
125     C dqh_dTs :: derivative of qhice w.r.t snow/ice surf. temp
126 jmc 1.21 #ifdef SEAICE_SOLVE4TEMP_LEGACY
127     C A1 :: part of atmos surface flux (+=downward) independent of tsurf
128     C A2 :: part of atmos surface flux (+=upward) which depends on tsurf
129 jmc 1.24 C A3 :: derivative of (A2-F_c) w.r.t tsurf
130 jmc 1.21 _RL A2 (1:sNx,1:sNy)
131     _RL A3 (1:sNx,1:sNy)
132     _RL A1 (1:sNx,1:sNy)
133     #else /* SEAICE_SOLVE4TEMP_LEGACY */
134 jmc 1.22 C F_lwu :: upward long-wave surface heat flux (+=upward)
135     C F_sens :: sensible surface heat flux (+=upward)
136 jmc 1.24 C dFia_dTs :: derivative of surf heat flux (F_ia) w.r.t surf. temp
137 jmc 1.21 _RL F_lwu (1:sNx,1:sNy)
138     _RL F_sens (1:sNx,1:sNy)
139 jmc 1.24 _RL dFia_dTs (1:sNx,1:sNy)
140 jmc 1.21 #endif /* SEAICE_SOLVE4TEMP_LEGACY */
141     _RL F_lh (1:sNx,1:sNy)
142     _RL F_c (1:sNx,1:sNy)
143     _RL qhice (1:sNx,1:sNy)
144 jmc 1.24 _RL dqh_dTs (1:sNx,1:sNy)
145 jmc 1.21 _RL absorbedSW (1:sNx,1:sNy)
146     _RL penetSWFrac
147    
148     C local copies of global variables
149     _RL tsurfLoc (1:sNx,1:sNy)
150     _RL atempLoc (1:sNx,1:sNy)
151     _RL lwdownLoc (1:sNx,1:sNy)
152     _RL ALB (1:sNx,1:sNy)
153     _RL ALB_ICE (1:sNx,1:sNy)
154     _RL ALB_SNOW (1:sNx,1:sNy)
155     C iceOrNot :: this is HICE_ACTUAL.GT.0.
156     LOGICAL iceOrNot(1:sNx,1:sNy)
157     #ifdef SEAICE_DEBUG
158     C F_io_net :: upward conductive heat flux through seaice+snow
159     C F_ia_net :: net heat flux divergence at the sea ice/snow surface:
160     C includes ice conductive fluxes and atmospheric fluxes (W/m^2)
161     _RL F_io_net (1:sNx,1:sNy)
162     _RL F_ia_net (1:sNx,1:sNy)
163     #endif /* SEAICE_DEBUG */
164 ifenty 1.14
165 jmc 1.21 C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
166 jmc 1.1
167 mlosch 1.8 #ifdef ALLOW_AUTODIFF_TAMC
168     CADJ INIT comlev1_solve4temp = COMMON, sNx*sNy*NMAX_TICE
169     #endif /* ALLOW_AUTODIFF_TAMC */
170    
171 jmc 1.6 #ifdef SEAICE_SOLVE4TEMP_LEGACY
172 jmc 1.24 C- MAYKUT CONSTANTS FOR SAT. VAP. PRESSURE TEMP. POLYNOMIAL
173 mlosch 1.5 C1= 2.7798202 _d -06
174     C2= -2.6913393 _d -03
175     C3= 0.97920849 _d +00
176     C4= -158.63779 _d +00
177     C5= 9653.1925 _d +00
178 jmc 1.1
179     QS1=0.622 _d +00/1013.0 _d +00
180 jmc 1.6 #else /* SEAICE_SOLVE4TEMP_LEGACY */
181 jmc 1.24 C- Extended temp-range expon. relation Coeff. for Sat. Vapor Press
182 jmc 1.21 lnTEN = LOG(10.0 _d 0)
183 jmc 1.1 aa1 = 2663.5 _d 0
184     aa2 = 12.537 _d 0
185     bb1 = 0.622 _d 0
186 mlosch 1.5 bb2 = 1.0 _d 0 - bb1
187 jmc 1.1 Ppascals = 100000. _d 0
188 mlosch 1.5 C cc0 = TEN ** aa2
189 jmc 1.21 cc0 = EXP(aa2*lnTEN)
190 mlosch 1.5 cc1 = cc0*aa1*bb1*Ppascals*lnTEN
191 jmc 1.1 cc2 = cc0*bb2
192 jmc 1.6 #endif /* SEAICE_SOLVE4TEMP_LEGACY */
193 jmc 1.1
194 jmc 1.4 #ifdef SEAICE_VARIABLE_FREEZING_POINT
195     kSrf = 1
196     #endif /* SEAICE_VARIABLE_FREEZING_POINT */
197 jmc 1.1
198     C SENSIBLE HEAT CONSTANT
199 mlosch 1.7 D1=SEAICE_dalton*SEAICE_cpAir*SEAICE_rhoAir
200 jmc 1.1
201     C ICE LATENT HEAT CONSTANT
202 ifenty 1.14 lhSublim = SEAICE_lhEvap + SEAICE_lhFusion
203     D1I=SEAICE_dalton*lhSublim*SEAICE_rhoAir
204 jmc 1.1
205     C MELTING TEMPERATURE OF ICE
206 mlosch 1.5 TMELT = celsius2K
207 jmc 1.1 SurfMeltTemp = TMELT
208    
209     C ICE CONDUCTIVITY
210     XKI=SEAICE_iceConduct
211    
212     C SNOW CONDUCTIVITY
213     XKS=SEAICE_snowConduct
214    
215     C CUTOFF SNOW THICKNESS
216 jmc 1.21 C Snow-Thickness above HCUT: SW optically thick snow (=> snow-albedo).
217     C Snow-Thickness below HCUT: linear transition to ice-albedo
218 jmc 1.24 HCUT = SEAICE_snowThick
219    
220     C PENETRATION SHORTWAVE RADIATION FACTOR
221     XIO=SEAICE_shortwave
222    
223     C-- until these become run-time params, set according to CPP OPTION:
224 jmc 1.21 #ifdef SEAICE_SOLVE4TEMP_LEGACY
225 jmc 1.24 C old SOLVE4TEMP_LEGACY setting, consistent with former celsius2K value:
226     c TMELT = 273.16 _d +00
227     c SurfMeltTemp = 273.159 _d +00
228     SurfMeltTemp = TMELT - 1. _d -3
229 jmc 1.21 #else /* SEAICE_SOLVE4TEMP_LEGACY */
230     HCUT = 0. _d 0
231     #endif /* SEAICE_SOLVE4TEMP_LEGACY */
232 jmc 1.1
233 jmc 1.3 C Initialize variables
234 jmc 1.1 DO J=1,sNy
235 mlosch 1.5 DO I=1,sNx
236     C HICE_ACTUAL is modified in this routine, but at the same time
237     C used to decided where there is ice, therefore we save this information
238     C here in a separate array
239 jmc 1.21 iceOrNot (I,J) = HICE_ACTUAL(I,J) .GT. 0. _d 0
240     IcePenetSW(I,J) = 0. _d 0
241     absorbedSW(I,J) = 0. _d 0
242 mlosch 1.5 qhice (I,J) = 0. _d 0
243 jmc 1.24 dqh_dTs (I,J) = 0. _d 0
244 mlosch 1.5 F_ia (I,J) = 0. _d 0
245 jmc 1.21 c F_io_net (I,J) = 0. _d 0
246     c F_ia_net (I,J) = 0. _d 0
247 mlosch 1.10 F_lh (I,J) = 0. _d 0
248    
249 mlosch 1.5 C Reset the snow/ice surface to TMELT and bound the atmospheric temperature
250 jmc 1.6 #ifdef SEAICE_SOLVE4TEMP_LEGACY
251 mlosch 1.5 A1(I,J) = 0.0 _d 0
252     A2(I,J) = 0.0 _d 0
253     A3(I,J) = 0.0 _d 0
254 jmc 1.23 tsurfLoc (I,J) = MIN( celsius2K+MAX_TICE, TSURF(I,J,bi,bj) )
255 jmc 1.21 lwdownLoc(I,J) = MAX( MIN_LWDOWN, LWDOWN(I,J,bi,bj) )
256 jmc 1.6 #else /* SEAICE_SOLVE4TEMP_LEGACY */
257 mlosch 1.5 F_lwu (I,J) = 0. _d 0
258     F_sens (I,J) = 0. _d 0
259     tsurfLoc (I,J) = TSURF(I,J,bi,bj)
260     lwdownLoc(I,J) = LWDOWN(I,J,bi,bj)
261 jmc 1.6 #endif /* SEAICE_SOLVE4TEMP_LEGACY */
262 jmc 1.24 atempLoc (I,J) = MAX( celsius2K+MIN_ATEMP, ATEMP(I,J,bi,bj) )
263 jmc 1.1
264 mlosch 1.5 C FREEZING TEMPERATURE OF SEAWATER
265     #ifdef SEAICE_VARIABLE_FREEZING_POINT
266     C Use a variable seawater freezing point
267     TB(I,J) = -0.0575 _d 0*salt(I,J,kSrf,bi,bj) + 0.0901 _d 0
268     & + celsius2K
269     #else
270     C Use a constant freezing temperature (SEAICE_VARIABLE_FREEZING_POINT undef)
271 jmc 1.23 C old SOLVE4TEMP_LEGACY setting (not consistent with seaice_growth value)
272     c TB(I,J) = 271.2 _d 0
273 mlosch 1.5 TB(I,J) = celsius2K + SEAICE_freeze
274     #endif /* SEAICE_VARIABLE_FREEZING_POINT */
275 mlosch 1.18 IF(HSNOW_ACTUAL(I,J).GT.0.0) THEN
276 jmc 1.21 C Stefan-Boltzmann constant times emissivity
277 mlosch 1.18 D3(I,J)=SEAICE_snow_emiss*SEAICE_boltzmann
278     #ifdef EXF_LWDOWN_WITH_EMISSIVITY
279     C This is now [(1-emiss)*lwdown - lwdown]
280     lwdownloc(I,J) = SEAICE_snow_emiss*lwdownloc(I,J)
281     #else /* use the old hard wired inconsistent value */
282     lwdownloc(I,J) = 0.97 _d 0*lwdownloc(I,J)
283     #endif /* EXF_LWDOWN_WITH_EMISSIVITY */
284     ELSE
285 jmc 1.21 C Stefan-Boltzmann constant times emissivity
286 mlosch 1.18 D3(I,J)=SEAICE_ice_emiss*SEAICE_boltzmann
287     #ifdef EXF_LWDOWN_WITH_EMISSIVITY
288     C This is now [(1-emiss)*lwdown - lwdown]
289     lwdownloc(I,J) = SEAICE_ice_emiss*lwdownloc(I,J)
290     #else /* use the old hard wired inconsistent value */
291     lwdownloc(I,J) = 0.97 _d 0*lwdownloc(I,J)
292     #endif /* EXF_LWDOWN_WITH_EMISSIVITY */
293     ENDIF
294 mlosch 1.5 ENDDO
295 jmc 1.1 ENDDO
296    
297     DO J=1,sNy
298 mlosch 1.5 DO I=1,sNx
299 jmc 1.1
300     C DECIDE ON ALBEDO
301 mlosch 1.5 IF ( iceOrNot(I,J) ) THEN
302 jmc 1.6
303 mlosch 1.5 IF ( YC(I,J,bi,bj) .LT. 0.0 _d 0 ) THEN
304     IF (tsurfLoc(I,J) .GE. SurfMeltTemp) THEN
305     ALB_ICE (I,J) = SEAICE_wetIceAlb_south
306     ALB_SNOW(I,J) = SEAICE_wetSnowAlb_south
307     ELSE ! no surface melting
308     ALB_ICE (I,J) = SEAICE_dryIceAlb_south
309     ALB_SNOW(I,J) = SEAICE_drySnowAlb_south
310     ENDIF
311     ELSE !/ Northern Hemisphere
312     IF (tsurfLoc(I,J) .GE. SurfMeltTemp) THEN
313     ALB_ICE (I,J) = SEAICE_wetIceAlb
314     ALB_SNOW(I,J) = SEAICE_wetSnowAlb
315     ELSE ! no surface melting
316     ALB_ICE (I,J) = SEAICE_dryIceAlb
317     ALB_SNOW(I,J) = SEAICE_drySnowAlb
318     ENDIF
319     ENDIF !/ Albedo for snow and ice
320    
321 jmc 1.21 C If actual snow thickness exceeds the cutoff thickness, use snow albedo
322 mlosch 1.5 IF (HSNOW_ACTUAL(I,J) .GT. HCUT) THEN
323     ALB(I,J) = ALB_SNOW(I,J)
324 jmc 1.21 ELSEIF ( HCUT.LE.ZERO ) THEN
325     ALB(I,J) = ALB_ICE(I,J)
326 mlosch 1.5 ELSE
327 jmc 1.21 C otherwise, use linear transition between ice and snow albedo
328     ALB(I,J) = MIN( ALB_ICE(I,J) + HSNOW_ACTUAL(I,J)/HCUT
329     & *(ALB_SNOW(I,J) -ALB_ICE(I,J))
330     & , ALB_SNOW(I,J) )
331 mlosch 1.5 ENDIF
332    
333 jmc 1.21 C Determine the fraction of shortwave radiative flux remaining
334     C at ocean interface after scattering through the snow and ice.
335     C If snow is present, no radiation penetrates through snow+ice
336 mlosch 1.5 IF (HSNOW_ACTUAL(I,J) .GT. 0.0 _d 0) THEN
337 jmc 1.21 penetSWFrac = 0.0 _d 0
338 mlosch 1.5 ELSE
339 jmc 1.21 penetSWFrac = XIO*EXP(-1.5 _d 0 * HICE_ACTUAL(I,J))
340 mlosch 1.5 ENDIF
341 jmc 1.21 C The shortwave radiative flux leaving ocean beneath ice (+=up).
342     IcePenetSW(I,J) = -(1.0 _d 0 - ALB(I,J))
343     & *penetSWFrac * SWDOWN(I,J,bi,bj)
344     C The shortwave radiative flux convergence in the seaice.
345     absorbedSW(I,J) = (1.0 _d 0 - ALB(I,J))
346     & *(1.0 _d 0 - penetSWFrac)* SWDOWN(I,J,bi,bj)
347 jmc 1.1
348 jmc 1.6 #ifdef SEAICE_SOLVE4TEMP_LEGACY
349 jmc 1.21 C Now determine fixed (relative to tsurf) forcing term in heat budget
350     A1(I,J) = absorbedSW(I,J) + lwdownLoc(I,J)
351 mlosch 1.5 & +D1*UG(I,J)*atempLoc(I,J)+D1I*UG(I,J)*AQH(I,J,bi,bj)
352 jmc 1.6 #endif /* SEAICE_SOLVE4TEMP_LEGACY */
353 jmc 1.1
354 jmc 1.24 C The effective conductivity of the two-layer snow/ice system.
355 jmc 1.6 #ifdef SEAICE_SOLVE4TEMP_LEGACY
356 mlosch 1.5 effConduct(I,J)=
357     & XKS/(HSNOW_ACTUAL(I,J)/HICE_ACTUAL(I,J) +
358     & XKS/XKI)/HICE_ACTUAL(I,J)
359 jmc 1.6 #else /* SEAICE_SOLVE4TEMP_LEGACY */
360 jmc 1.21 C Set a mininum sea ice thickness of 5 cm to bound
361     C the magnitude of conductive heat fluxes.
362     Cif * now taken care of by SEAICE_hice_reg in seaice_growth
363     c hice_tmp = max(HICE_ACTUAL(I,J),5. _d -2)
364 mlosch 1.5 effConduct(I,J) = XKI * XKS /
365 jmc 1.21 & (XKS * HICE_ACTUAL(I,J) + XKI * HSNOW_ACTUAL(I,J))
366 jmc 1.6 #endif /* SEAICE_SOLVE4TEMP_LEGACY */
367 jmc 1.1
368     #ifdef SEAICE_DEBUG
369 jmc 1.21 IF ( (I .EQ. SEAICE_debugPointI) .AND.
370 ifenty 1.16 & (J .EQ. SEAICE_debugPointJ) ) THEN
371 mlosch 1.5 print '(A,i6)','-----------------------------------'
372     print '(A,i6)','ibi merged initialization ', myIter
373     print '(A,i6,4(1x,D24.15))',
374     & 'ibi iter, TSL, TS ',myIter,
375     & tsurfLoc(I,J), TSURF(I,J,bi,bj)
376     print '(A,i6,4(1x,D24.15))',
377     & 'ibi iter, TMELT ',myIter,TMELT
378     print '(A,i6,4(1x,D24.15))',
379     & 'ibi iter, HIA, EFKCON ',myIter,
380     & HICE_ACTUAL(I,J), effConduct(I,J)
381     print '(A,i6,4(1x,D24.15))',
382     & 'ibi iter, HSNOW ',myIter,
383     & HSNOW_ACTUAL(I,J), ALB(I,J)
384     print '(A,i6)','-----------------------------------'
385     print '(A,i6)','ibi energy balance iterat ', myIter
386     ENDIF
387 jmc 1.2 #endif /* SEAICE_DEBUG */
388 jmc 1.6
389 mlosch 1.5 ENDIF !/* iceOrNot */
390     ENDDO !/* i */
391     ENDDO !/* j */
392 jmc 1.21
393     C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
394 mlosch 1.5 DO ITER=1,IMAX_TICE
395     DO J=1,sNy
396     DO I=1,sNx
397 mlosch 1.8 #ifdef ALLOW_AUTODIFF_TAMC
398     iicekey = I + sNx*(J-1) + (ITER-1)*sNx*sNy
399     CADJ STORE tsurfloc(i,j) = comlev1_solve4temp,
400     CADJ & key = iicekey, byte = isbyte
401     #endif /* ALLOW_AUTODIFF_TAMC */
402    
403 mlosch 1.5 IF ( iceOrNot(I,J) ) THEN
404 jmc 1.1
405 mlosch 1.5 t1 = tsurfLoc(I,J)
406     t2 = t1*t1
407     t3 = t2*t1
408     t4 = t2*t2
409 jmc 1.1
410 jmc 1.24 C-- Calculate the specific humidity in the BL above the snow/ice
411 jmc 1.6 #ifdef SEAICE_SOLVE4TEMP_LEGACY
412 jmc 1.24 C- Use the Maykut polynomial
413 mlosch 1.5 qhice(I,J)=QS1*(C1*t4+C2*t3 +C3*t2+C4*t1+C5)
414 jmc 1.24 dqh_dTs(I,J) = 0. _d 0
415 jmc 1.1
416 jmc 1.6 #else /* SEAICE_SOLVE4TEMP_LEGACY */
417 jmc 1.24 C- Use exponential relation approx., more accurate at low temperatures
418 mlosch 1.5 C log 10 of the sat vap pressure
419     mm_log10pi = -aa1 / t1 + aa2
420     C The saturation vapor pressure (SVP) in the surface
421     C boundary layer (BL) above the snow/ice.
422 jmc 1.24 c mm_pi = TEN **(mm_log10pi)
423 jmc 1.6 C The following form does the same, but is faster
424 jmc 1.21 mm_pi = EXP(mm_log10pi*lnTEN)
425 jmc 1.24 qhice(I,J) = bb1*mm_pi/( Ppascals -(1.0 _d 0 - bb1)*mm_pi )
426 jmc 1.21 C A constant for SVP derivative w.r.t TICE
427 jmc 1.24 c cc3t = TEN **(aa1 / t1)
428 jmc 1.21 C The following form does the same, but is faster
429     cc3t = EXP(aa1 / t1 * lnTEN)
430     C d(qh)/d(TICE)
431 jmc 1.24 dqh_dTs(I,J) = cc1*cc3t/((cc2-cc3t*Ppascals)**2 *t2)
432 jmc 1.6 #endif /* SEAICE_SOLVE4TEMP_LEGACY */
433 jmc 1.1
434 mlosch 1.10 C Calculate the flux terms based on the updated tsurfLoc
435 jmc 1.22 F_c(I,J) = effConduct(I,J)*(TB(I,J)-tsurfLoc(I,J))
436 mlosch 1.10 F_lh(I,J) = D1I*UG(I,J)*(qhice(I,J)-AQH(I,J,bi,bj))
437 jmc 1.6 #ifdef SEAICE_SOLVE4TEMP_LEGACY
438 jmc 1.21 A2(I,J) = D1*UG(I,J)*t1+D1I*UG(I,J)*qhice(I,J)+D3(I,J)*t4
439 mlosch 1.18 A3(I,J) = 4.0 _d 0*D3(I,J)*t3 + effConduct(I,J)+D1*UG(I,J)
440 jmc 1.24 & + D1I*UG(I,J)*dqh_dTs(I,J)
441 jmc 1.6 #else /* SEAICE_SOLVE4TEMP_LEGACY */
442 ifenty 1.16 #ifdef SEAICE_ADD_SUBLIMATION_TO_FWBUDGET
443 jmc 1.21 C if the latent heat flux implied by tsurfLoc exceeds
444     C F_lh_max, cap F_lh and decouple the flux magnitude from TICE
445     IF (F_lh(I,J) .GT. F_lh_max(I,J)) THEN
446 ifenty 1.16 F_lh(I,J) = F_lh_max(I,J)
447 jmc 1.24 dqh_dTs(I,J) = ZERO
448 jmc 1.21 ENDIF
449     #endif /* SEAICE_ADD_SUBLIMATION_TO_FWBUDGET */
450 ifenty 1.16
451 jmc 1.24 C d(F_ia)/d(Tsurf)
452     dFia_dTs(I,J) = 4.0 _d 0*D3(I,J)*t3 + D1*UG(I,J)
453     & + D1I*UG(I,J)*dqh_dTs(I,J)
454 mlosch 1.5
455 jmc 1.21 F_lwu(I,J) = t4 * D3(I,J)
456 mlosch 1.5 F_sens(I,J)= D1 * UG(I,J) * (t1 - atempLoc(I,J))
457 jmc 1.21 F_ia(I,J) = -lwdownLoc(I,J) -absorbedSW(I,J) + F_lwu(I,J)
458 jmc 1.24 & + F_sens(I,J) + F_lh(I,J)
459 jmc 1.6 #endif /* SEAICE_SOLVE4TEMP_LEGACY */
460 jmc 1.1
461     #ifdef SEAICE_DEBUG
462 jmc 1.21 IF ( (I .EQ. SEAICE_debugPointI) .AND.
463 ifenty 1.16 & (J .EQ. SEAICE_debugPointJ) ) THEN
464 mlosch 1.5 print '(A,i6,4(1x,D24.15))',
465     & 'ice-iter qhICE, ', ITER,qhIce(I,J)
466 jmc 1.6 #ifdef SEAICE_SOLVE4TEMP_LEGACY
467 mlosch 1.5 print '(A,i6,4(1x,D24.15))',
468 jmc 1.22 & 'ice-iter A1 A2 B ',ITER,A1(I,J),A2(I,J),F_c(I,J)
469 mlosch 1.5 print '(A,i6,4(1x,D24.15))',
470 jmc 1.21 & 'ice-iter A3 (-A1+A2) ',ITER,A3(I,J),-A1(I,J)+A2(I,J)
471 jmc 1.6 #else /* SEAICE_SOLVE4TEMP_LEGACY */
472 mlosch 1.5 print '(A,i6,4(1x,D24.15))',
473 jmc 1.24 & 'ice-iter dFiDTs1 F_ia ', ITER,
474     & dFia_dTs(I,J)+effConduct(I,J), F_ia(I,J)-F_c(I,J)
475 jmc 1.6 #endif /* SEAICE_SOLVE4TEMP_LEGACY */
476 mlosch 1.5 ENDIF
477 jmc 1.2 #endif /* SEAICE_DEBUG */
478 jmc 1.1
479 mlosch 1.5 C Update tsurfLoc
480 jmc 1.6 #ifdef SEAICE_SOLVE4TEMP_LEGACY
481 jmc 1.22 C update tsurf as solution of : Fc = A2 - A1 + A3 *delta.tsurf
482 mlosch 1.5 tsurfLoc(I,J)=tsurfLoc(I,J)
483 jmc 1.22 & +(A1(I,J)-A2(I,J)+F_c(I,J))/A3(I,J)
484 jmc 1.23 tsurfLoc(I,J) = MAX( celsius2K+MIN_TICE, tsurfLoc(I,J) )
485 jmc 1.6
486     #else /* SEAICE_SOLVE4TEMP_LEGACY */
487 jmc 1.24 C update tsurf as solution of : Fc = Fia + d/dT(Fia - Fc) *delta.tsurf
488     tsurfLoc(I,J) = tsurfLoc(I,J)
489     & + ( F_c(I,J)-F_ia(I,J) ) / ( effConduct(I,J)+dFia_dTs(I,J) )
490 jmc 1.1
491 jmc 1.21 C If the search leads to tsurfLoc < 50 Kelvin, restart the search
492     C at tsurfLoc = TMELT. Note that one solution to the energy balance problem
493     C is an extremely low temperature - a temperature far below realistic values.
494 mlosch 1.5 IF (tsurfLoc(I,J) .LT. 50.0 _d 0 ) THEN
495     tsurfLoc(I,J) = TMELT
496     ENDIF
497 jmc 1.6 #endif /* SEAICE_SOLVE4TEMP_LEGACY */
498 jmc 1.21 tsurfLoc(I,J) = MIN( tsurfLoc(I,J), TMELT )
499 jmc 1.1
500     #ifdef SEAICE_DEBUG
501 jmc 1.21 IF ( (I .EQ. SEAICE_debugPointI) .AND.
502 ifenty 1.16 & (J .EQ. SEAICE_debugPointJ) ) THEN
503 mlosch 1.5 print '(A,i6,4(1x,D24.15))',
504     & 'ice-iter tsurfLc,|dif|', ITER,
505     & tsurfLoc(I,J),
506 jmc 1.21 & LOG10(ABS(tsurfLoc(I,J) - t1))
507 mlosch 1.5 ENDIF
508 jmc 1.2 #endif /* SEAICE_DEBUG */
509 jmc 1.1
510 mlosch 1.5 ENDIF !/* iceOrNot */
511     ENDDO !/* i */
512     ENDDO !/* j */
513     ENDDO !/* Iterations */
514 jmc 1.21 C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
515    
516 mlosch 1.5 DO J=1,sNy
517     DO I=1,sNx
518     IF ( iceOrNot(I,J) ) THEN
519 jmc 1.1
520 jmc 1.21 C Save updated tsurf and finalize the flux terms
521     TSURF(I,J,bi,bj) = tsurfLoc(I,J)
522    
523 jmc 1.6 #ifdef SEAICE_SOLVE4TEMP_LEGACY
524 jmc 1.21 F_ia(I,J)=-A1(I,J)+A2(I,J)
525 jmc 1.6 #else /* SEAICE_SOLVE4TEMP_LEGACY */
526 mlosch 1.5 C Recalculate the fluxes based on the (possibly) adjusted TSURF
527     t1 = tsurfLoc(I,J)
528     t2 = t1*t1
529     t3 = t2*t1
530     t4 = t2*t2
531 jmc 1.1
532 mlosch 1.5 C log 10 of the sat vap pressure
533     mm_log10pi = -aa1 / t1 + aa2
534     C saturation vapor pressure
535 jmc 1.24 c mm_pi = TEN **(mm_log10pi)
536 jmc 1.6 C The following form does the same, but is faster
537 jmc 1.21 mm_pi = EXP(mm_log10pi*lnTEN)
538     C over ice specific humidity
539 jmc 1.24 qhice(I,J) = bb1*mm_pi/( Ppascals -(1.0 _d 0 - bb1)*mm_pi )
540 mlosch 1.5 F_lh(I,J) = D1I * UG(I,J)*(qhice(I,J)-AQH(I,J,bi,bj))
541 ifenty 1.16 #ifdef SEAICE_ADD_SUBLIMATION_TO_FWBUDGET
542 jmc 1.21 IF (F_lh(I,J) .GT. F_lh_max(I,J)) THEN
543 ifenty 1.16 F_lh(I,J) = F_lh_max(I,J)
544 jmc 1.21 ENDIF
545     #endif /* SEAICE_ADD_SUBLIMATION_TO_FWBUDGET */
546 ifenty 1.16
547 jmc 1.22 F_c(I,J) = effConduct(I,J) * (TB(I,J) - t1)
548 mlosch 1.18 F_lwu(I,J) = t4 * D3(I,J)
549 mlosch 1.5 F_sens(I,J) = D1 * UG(I,J) * (t1 - atempLoc(I,J))
550 jmc 1.1
551 jmc 1.21 C The flux between the ice/snow surface and the atmosphere.
552     F_ia(I,J) = -lwdownLoc(I,J) -absorbedSW(I,J) + F_lwu(I,J)
553     & + F_sens(I,J) + F_lh(I,J)
554 jmc 1.6 #endif /* SEAICE_SOLVE4TEMP_LEGACY */
555 jmc 1.1
556 gforget 1.9 #ifdef SEAICE_MODIFY_GROWTH_ADJ
557     Cgf no additional dependency through solver, snow, etc.
558 jmc 1.21 IF ( SEAICEadjMODE.GE.2 ) THEN
559 gforget 1.9 CALL ZERO_ADJ_1D( 1, TSURF(I,J,bi,bj), myThid)
560     t1 = TSURF(I,J,bi,bj)
561     t2 = t1*t1
562     t3 = t2*t1
563     t4 = t2*t2
564     qhice(I,J)=QS1*(C1*t4+C2*t3 +C3*t2+C4*t1+C5)
565    
566 mlosch 1.18 A1(I,J)=0.3 _d 0 *SWDOWN(I,J,bi,bj)+lwdownLoc(I,J)
567 gforget 1.9 & +D1*UG(I,J)*atempLoc(I,J)+D1I*UG(I,J)*AQH(I,J,bi,bj)
568 jmc 1.21 A2(I,J)= D1*UG(I,J)*t1+D1I*UG(I,J)*qhice(I,J)+D3(I,J)*t4
569 gforget 1.9
570 jmc 1.21 F_ia(I,J)=-A1(I,J)+A2(I,J)
571     IcePenetSW(I,J)= 0. _d 0
572     ENDIF
573     #endif /* SEAICE_MODIFY_GROWTH_ADJ */
574    
575     C Fresh water flux (kg/m^2/s) from latent heat of sublimation.
576     C F_lh is positive upward (sea ice looses heat) and FWsublim
577     C is also positive upward (atmosphere gains freshwater)
578     FWsublim(I,J) = F_lh(I,J)/lhSublim
579 gforget 1.9
580 jmc 1.21 #ifdef SEAICE_DEBUG
581 mlosch 1.5 C Caclulate the net ice-ocean and ice-atmosphere fluxes
582 jmc 1.22 IF (F_c(I,J) .GT. 0.0 _d 0) THEN
583     F_io_net(I,J) = F_c(I,J)
584 mlosch 1.5 F_ia_net(I,J) = 0.0 _d 0
585     ELSE
586     F_io_net(I,J) = 0.0 _d 0
587     F_ia_net(I,J) = F_ia(I,J)
588     ENDIF !/* conductive fluxes up or down */
589 jmc 1.1
590 jmc 1.21 IF ( (I .EQ. SEAICE_debugPointI) .AND.
591 ifenty 1.16 & (J .EQ. SEAICE_debugPointJ) ) THEN
592 mlosch 1.5 print '(A)','----------------------------------------'
593     print '(A,i6)','ibi complete ', myIter
594     print '(A,4(1x,D24.15))',
595     & 'ibi T(SURF, surfLoc,atmos) ',
596     & TSURF(I,J,bi,bj), tsurfLoc(I,J),atempLoc(I,J)
597     print '(A,4(1x,D24.15))',
598     & 'ibi LWL ', lwdownLoc(I,J)
599     print '(A,4(1x,D24.15))',
600     & 'ibi QSW(Total, Penetrating)',
601 jmc 1.21 & SWDOWN(I,J,bi,bj), IcePenetSW(I,J)
602 mlosch 1.5 print '(A,4(1x,D24.15))',
603     & 'ibi qh(ATM ICE) ',
604     & AQH(I,J,bi,bj),qhice(I,J)
605 ifenty 1.16 #ifndef SEAICE_SOLVE4TEMP_LEGACY
606     print '(A,4(1x,D24.15))',
607     & 'ibi F(lwd,swi,lwu) ',
608 jmc 1.21 & -lwdownLoc(I,J), -absorbedSW(I,J), F_lwu(I,J)
609 ifenty 1.16 print '(A,4(1x,D24.15))',
610     & 'ibi F(c,lh,sens) ',
611     & F_c(I,J), F_lh(I,J), F_sens(I,J)
612     #ifdef SEAICE_ADD_SUBLIMATION_TO_FWBUDGET
613     IF (F_lh_max(I,J) .GT. ZERO) THEN
614     print '(A,4(1x,D24.15))',
615     & 'ibi F_lh_max, F_lh/lhmax) ',
616     & F_lh_max(I,J), F_lh(I,J)/ F_lh_max(I,J)
617 jmc 1.19 ELSE
618 ifenty 1.16 print '(A,4(1x,D24.15))',
619     & 'ibi F_lh_max = ZERO! '
620     ENDIF
621     print '(A,4(1x,D24.15))',
622     & 'ibi FWsub, FWsubm*dT/rhoI ',
623     & FWsublim(I,J),
624     & FWsublim(I,J)*SEAICE_deltaTtherm/SEAICE_rhoICE
625 jmc 1.21 #endif /* SEAICE_ADD_SUBLIMATION_TO_FWBUDGET */
626     #endif /* SEAICE_SOLVE4TEMP_LEGACY */
627 mlosch 1.5 print '(A,4(1x,D24.15))',
628     & 'ibi F_ia, F_ia_net, F_c ',
629 jmc 1.6 #ifdef SEAICE_SOLVE4TEMP_LEGACY
630 jmc 1.22 & -A1(I,J)+A2(I,J), -A1(I,J)+A2(I,J)-F_c(I,J), F_c(I,J)
631 jmc 1.21 #else /* SEAICE_SOLVE4TEMP_LEGACY */
632     & F_ia(I,J), F_ia_net(I,J), F_c(I,J)
633 jmc 1.6 #endif /* SEAICE_SOLVE4TEMP_LEGACY */
634 mlosch 1.5 print '(A)','----------------------------------------'
635     ENDIF
636 jmc 1.2 #endif /* SEAICE_DEBUG */
637 jmc 1.6
638 mlosch 1.5 ENDIF !/* iceOrNot */
639     ENDDO !/* i */
640 jmc 1.1 ENDDO !/* j */
641    
642 jmc 1.19 #endif /* ALLOW_ATM_TEMP && ALLOW_DOWNWARD_RADIATION */
643     RETURN
644 jmc 1.1 END

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