1 | MODULE limthd_lac |
---|
2 | !!---------------------------------------------------------------------- |
---|
3 | !! 'key_lim3' LIM3 sea-ice model |
---|
4 | !!---------------------------------------------------------------------- |
---|
5 | !!====================================================================== |
---|
6 | !! *** MODULE limthd_lac *** |
---|
7 | !! lateral thermodynamic growth of the ice |
---|
8 | !!====================================================================== |
---|
9 | #if defined key_lim3 |
---|
10 | !!---------------------------------------------------------------------- |
---|
11 | !! lim_lat_acr : lateral accretion of ice |
---|
12 | !! * Modules used |
---|
13 | USE par_oce ! ocean parameters |
---|
14 | USE dom_oce |
---|
15 | USE in_out_manager |
---|
16 | USE phycst |
---|
17 | USE sbc_oce ! Surface boundary condition: ocean fields |
---|
18 | USE sbc_ice ! Surface boundary condition: ice fields |
---|
19 | USE thd_ice |
---|
20 | USE dom_ice |
---|
21 | USE par_ice |
---|
22 | USE ice |
---|
23 | USE iceini |
---|
24 | USE limtab |
---|
25 | USE limcons |
---|
26 | |
---|
27 | IMPLICIT NONE |
---|
28 | PRIVATE |
---|
29 | |
---|
30 | !! * Routine accessibility |
---|
31 | PUBLIC lim_thd_lac ! called by lim_thd |
---|
32 | |
---|
33 | !! * Module variables |
---|
34 | REAL(wp) :: & ! constant values |
---|
35 | epsi20 = 1.e-20 , & |
---|
36 | epsi13 = 1.e-13 , & |
---|
37 | epsi11 = 1.e-13 , & |
---|
38 | epsi03 = 1.e-03 , & |
---|
39 | epsi06 = 1.e-06 , & |
---|
40 | zeps = 1.e-10 , & |
---|
41 | zzero = 0.e0 , & |
---|
42 | zone = 1.e0 |
---|
43 | |
---|
44 | !!---------------------------------------------------------------------- |
---|
45 | !! LIM 3.0, UCL-ASTR-LOCEAN-IPSL (2008) |
---|
46 | !! $Id$ |
---|
47 | !! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt) |
---|
48 | !!---------------------------------------------------------------------- |
---|
49 | |
---|
50 | CONTAINS |
---|
51 | |
---|
52 | SUBROUTINE lim_thd_lac |
---|
53 | !!------------------------------------------------------------------- |
---|
54 | !! *** ROUTINE lim_thd_lac *** |
---|
55 | !! |
---|
56 | !! ** Purpose : Computation of the evolution of the ice thickness and |
---|
57 | !! concentration as a function of the heat balance in the leads. |
---|
58 | !! It is only used for lateral accretion |
---|
59 | !! |
---|
60 | !! ** Method : Ice is formed in the open water when ocean lose heat |
---|
61 | !! (heat budget of open water Bl is negative) . |
---|
62 | !! Computation of the increase of 1-A (ice concentration) fol- |
---|
63 | !! lowing the law : |
---|
64 | !! (dA/dt)acc = F[ (1-A)/(1-a) ] * [ Bl / (Li*h0) ] |
---|
65 | !! where - h0 is the thickness of ice created in the lead |
---|
66 | !! - a is a minimum fraction for leads |
---|
67 | !! - F is a monotonic non-increasing function defined as: |
---|
68 | !! F(X)=( 1 - X**exld )**(1.0/exld) |
---|
69 | !! - exld is the exponent closure rate (=2 default val.) |
---|
70 | !! |
---|
71 | !! ** Action : - Adjustment of snow and ice thicknesses and heat |
---|
72 | !! content in brine pockets |
---|
73 | !! - Updating ice internal temperature |
---|
74 | !! - Computation of variation of ice volume and mass |
---|
75 | !! - Computation of frldb after lateral accretion and |
---|
76 | !! update ht_s_b, ht_i_b and tbif_1d(:,:) |
---|
77 | !! |
---|
78 | !! ** References : Not available yet |
---|
79 | !! |
---|
80 | !! History : |
---|
81 | !! 3.0 ! 12-05 (M. Vancoppenolle) Thorough rewrite of the routine |
---|
82 | !! Salinity variations in sea ice, |
---|
83 | !! Multi-layer code |
---|
84 | !! 3.1 ! 01-06 (M. Vancoppenolle) ITD |
---|
85 | !! 3.2 ! 04-07 (M. Vancoppenolle) Mass and energy conservation tested |
---|
86 | !!------------------------------------------------------------------------ |
---|
87 | !! * Arguments |
---|
88 | !! * Local variables |
---|
89 | INTEGER :: & |
---|
90 | ji,jj,jk,jl,jm , & !: dummy loop indices |
---|
91 | layer , & !: layer index |
---|
92 | nbpac !: nb of pts for lateral accretion |
---|
93 | |
---|
94 | INTEGER :: & |
---|
95 | zji , & !: ji of dummy test point |
---|
96 | zjj , & !: jj of dummy test point |
---|
97 | iter !: iteration for frazil ice computation |
---|
98 | |
---|
99 | INTEGER, DIMENSION(jpij) :: & |
---|
100 | zcatac , & !: indexes of categories where new ice grows |
---|
101 | zswinew !: switch for new ice or not |
---|
102 | |
---|
103 | REAL(wp), DIMENSION(jpij) :: & |
---|
104 | zv_newice , & !: volume of accreted ice |
---|
105 | za_newice , & !: fractional area of accreted ice |
---|
106 | zh_newice , & !: thickness of accreted ice |
---|
107 | ze_newice , & !: heat content of accreted ice |
---|
108 | zs_newice , & !: salinity of accreted ice |
---|
109 | zo_newice , & !: age of accreted ice |
---|
110 | zdv_res , & !: residual volume in case of excessive heat budget |
---|
111 | zda_res , & !: residual area in case of excessive heat budget |
---|
112 | zat_i_ac , & !: total ice fraction |
---|
113 | zat_i_lev , & !: total ice fraction for level ice only (type 1) |
---|
114 | zdh_frazb , & !: accretion of frazil ice at the ice bottom |
---|
115 | zvrel_ac !: relative ice / frazil velocity (1D vector) |
---|
116 | |
---|
117 | REAL(wp), DIMENSION(jpij,jpl) :: & |
---|
118 | zhice_old , & !: previous ice thickness |
---|
119 | zdummy , & !: dummy thickness of new ice |
---|
120 | zdhicbot , & !: thickness of new ice which is accreted vertically |
---|
121 | zv_old , & !: old volume of ice in category jl |
---|
122 | za_old , & !: old area of ice in category jl |
---|
123 | za_i_ac , & !: 1-D version of a_i |
---|
124 | zv_i_ac , & !: 1-D version of v_i |
---|
125 | zoa_i_ac , & !: 1-D version of oa_i |
---|
126 | zsmv_i_ac !: 1-D version of smv_i |
---|
127 | |
---|
128 | REAL(wp), DIMENSION(jpij,jkmax,jpl) :: & |
---|
129 | ze_i_ac !: 1-D version of e_i |
---|
130 | |
---|
131 | REAL(wp), DIMENSION(jpij) :: & |
---|
132 | zqbgow , & !: heat budget of the open water (negative) |
---|
133 | zdhex !: excessively thick accreted sea ice (hlead-hice) |
---|
134 | |
---|
135 | REAL(wp) :: & |
---|
136 | ztmelts , & !: melting point of an ice layer |
---|
137 | zdv , & !: increase in ice volume in each category |
---|
138 | zfrazb !: fraction of frazil ice accreted at the ice bottom |
---|
139 | |
---|
140 | ! Redistribution of energy after bottom accretion |
---|
141 | REAL(wp) :: & !: Energy redistribution |
---|
142 | zqold , & !: old ice enthalpy |
---|
143 | zweight , & !: weight of redistribution |
---|
144 | zeps6 , & !: epsilon value |
---|
145 | zalphai , & !: factor describing how old and new layers overlap each other [m] |
---|
146 | zindb |
---|
147 | |
---|
148 | REAL(wp), DIMENSION(jpij,jkmax+1,jpl) :: & |
---|
149 | zqm0 , & !: old layer-system heat content |
---|
150 | zthick0 !: old ice thickness |
---|
151 | |
---|
152 | ! Frazil ice collection thickness |
---|
153 | LOGICAL :: & !: iterate frazil ice collection thickness |
---|
154 | iterate_frazil |
---|
155 | |
---|
156 | REAL(wp), DIMENSION(jpi,jpj) :: & |
---|
157 | zvrel !: relative ice / frazil velocity |
---|
158 | |
---|
159 | REAL(wp) :: & |
---|
160 | zgamafr , & !: mult. coeff. between frazil vel. and wind speed |
---|
161 | ztenagm , & !: square root of wind stress |
---|
162 | zvfrx , & !: x-component of frazil velocity |
---|
163 | zvfry , & !: y-component of frazil velocity |
---|
164 | zvgx , & !: x-component of ice velocity |
---|
165 | zvgy , & !: y-component of ice velocity |
---|
166 | ztaux , & !: x-component of wind stress |
---|
167 | ztauy , & !: y-component of wind stress |
---|
168 | ztwogp , & !: dummy factor including reduced gravity |
---|
169 | zvrel2 , & !: square of the relative ice-frazil velocity |
---|
170 | zf , & !: F for Newton-Raphson procedure |
---|
171 | zfp , & !: dF for Newton-Raphson procedure |
---|
172 | zhicol_new , & !: updated collection thickness |
---|
173 | zsqcd , & !: 1 / square root of ( airdensity * drag ) |
---|
174 | zhicrit !: minimum thickness of frazil ice |
---|
175 | |
---|
176 | ! Variables for energy conservation |
---|
177 | REAL (wp), DIMENSION(jpi,jpj) :: & ! |
---|
178 | vt_i_init, vt_i_final, & ! ice volume summed over categories |
---|
179 | vt_s_init, vt_s_final, & ! snow volume summed over categories |
---|
180 | et_i_init, et_i_final, & ! ice energy summed over categories |
---|
181 | et_s_init ! snow energy summed over categories |
---|
182 | |
---|
183 | REAL(wp) :: & |
---|
184 | zde ! :increment of energy in category jl |
---|
185 | |
---|
186 | CHARACTER (len = 15) :: fieldid |
---|
187 | |
---|
188 | !!-----------------------------------------------------------------------! |
---|
189 | |
---|
190 | et_i_init(:,:) = 0.0 |
---|
191 | et_s_init(:,:) = 0.0 |
---|
192 | vt_i_init(:,:) = 0.0 |
---|
193 | vt_s_init(:,:) = 0.0 |
---|
194 | zeps6 = 1.0e-6 |
---|
195 | |
---|
196 | !------------------------------------------------------------------------------! |
---|
197 | ! 1) Conservation check and changes in each ice category |
---|
198 | !------------------------------------------------------------------------------! |
---|
199 | IF ( con_i ) THEN |
---|
200 | CALL lim_column_sum (jpl, v_i, vt_i_init) |
---|
201 | CALL lim_column_sum (jpl, v_s, vt_s_init) |
---|
202 | CALL lim_column_sum_energy (jpl, nlay_i, e_i, et_i_init) |
---|
203 | CALL lim_column_sum (jpl, e_s(:,:,1,:) , et_s_init) |
---|
204 | ENDIF |
---|
205 | |
---|
206 | !------------------------------------------------------------------------------| |
---|
207 | ! 2) Convert units for ice internal energy |
---|
208 | !------------------------------------------------------------------------------| |
---|
209 | DO jl = 1, jpl |
---|
210 | DO jk = 1, nlay_i |
---|
211 | DO jj = 1, jpj |
---|
212 | DO ji = 1, jpi |
---|
213 | !Energy of melting q(S,T) [J.m-3] |
---|
214 | e_i(ji,jj,jk,jl) = e_i(ji,jj,jk,jl) / & |
---|
215 | MAX( area(ji,jj) * v_i(ji,jj,jl) , zeps ) * & |
---|
216 | nlay_i |
---|
217 | zindb = 1.0-MAX(0.0,SIGN(1.0,-v_i(ji,jj,jl))) !0 if no ice and 1 if yes |
---|
218 | e_i(ji,jj,jk,jl) = e_i(ji,jj,jk,jl)*unit_fac*zindb |
---|
219 | END DO |
---|
220 | END DO |
---|
221 | END DO |
---|
222 | END DO |
---|
223 | |
---|
224 | !------------------------------------------------------------------------------! |
---|
225 | ! 3) Collection thickness of ice formed in leads and polynyas |
---|
226 | !------------------------------------------------------------------------------! |
---|
227 | ! hicol is the thickness of new ice formed in open water |
---|
228 | ! hicol can be either prescribed (frazswi = 0) |
---|
229 | ! or computed (frazswi = 1) |
---|
230 | ! Frazil ice forms in open water, is transported by wind |
---|
231 | ! accumulates at the edge of the consolidated ice edge |
---|
232 | ! where it forms aggregates of a specific thickness called |
---|
233 | ! collection thickness. |
---|
234 | |
---|
235 | ! Note : the following algorithm currently breaks vectorization |
---|
236 | ! |
---|
237 | |
---|
238 | zvrel(:,:) = 0.0 |
---|
239 | |
---|
240 | ! Default new ice thickness |
---|
241 | DO jj = 1, jpj |
---|
242 | DO ji = 1, jpi |
---|
243 | hicol(ji,jj) = hiccrit(1) |
---|
244 | END DO |
---|
245 | END DO |
---|
246 | |
---|
247 | IF (fraz_swi.eq.1.0) THEN |
---|
248 | |
---|
249 | !-------------------- |
---|
250 | ! Physical constants |
---|
251 | !-------------------- |
---|
252 | hicol(:,:) = 0.0 |
---|
253 | |
---|
254 | zhicrit = 0.04 ! frazil ice thickness |
---|
255 | ztwogp = 2. * rau0 / ( grav * 0.3 * ( rau0 - rhoic ) ) ! reduced grav |
---|
256 | zsqcd = 1.0 / SQRT( 1.3 * cai ) ! 1/SQRT(airdensity*drag) |
---|
257 | zgamafr = 0.03 |
---|
258 | |
---|
259 | DO jj = 1, jpj |
---|
260 | DO ji = 1, jpi |
---|
261 | |
---|
262 | IF ( tms(ji,jj) * ( qcmif(ji,jj) - qldif(ji,jj) ) > 0.e0 ) THEN |
---|
263 | !------------- |
---|
264 | ! Wind stress |
---|
265 | !------------- |
---|
266 | ! C-grid wind stress components |
---|
267 | ztaux = ( utau_ice(ji-1,jj ) * tmu(ji-1,jj ) & |
---|
268 | & + utau_ice(ji ,jj ) * tmu(ji ,jj ) ) / 2.0 |
---|
269 | ztauy = ( vtau_ice(ji ,jj-1) * tmv(ji ,jj-1) & |
---|
270 | & + vtau_ice(ji ,jj ) * tmv(ji ,jj ) ) / 2.0 |
---|
271 | ! Square root of wind stress |
---|
272 | ztenagm = SQRT( SQRT( ztaux * ztaux + ztauy * ztauy ) ) |
---|
273 | |
---|
274 | !--------------------- |
---|
275 | ! Frazil ice velocity |
---|
276 | !--------------------- |
---|
277 | zvfrx = zgamafr * zsqcd * ztaux / MAX(ztenagm,zeps) |
---|
278 | zvfry = zgamafr * zsqcd * ztauy / MAX(ztenagm,zeps) |
---|
279 | |
---|
280 | !------------------- |
---|
281 | ! Pack ice velocity |
---|
282 | !------------------- |
---|
283 | ! C-grid ice velocity |
---|
284 | zindb = MAX(0.0, SIGN(1.0, at_i(ji,jj) )) |
---|
285 | zvgx = zindb * ( u_ice(ji-1,jj ) * tmu(ji-1,jj ) & |
---|
286 | + u_ice(ji,jj ) * tmu(ji ,jj ) ) / 2.0 |
---|
287 | zvgy = zindb * ( v_ice(ji ,jj-1) * tmv(ji ,jj-1) & |
---|
288 | + v_ice(ji,jj ) * tmv(ji ,jj ) ) / 2.0 |
---|
289 | |
---|
290 | !----------------------------------- |
---|
291 | ! Relative frazil/pack ice velocity |
---|
292 | !----------------------------------- |
---|
293 | ! absolute relative velocity |
---|
294 | zvrel2 = MAX( ( zvfrx - zvgx ) * ( zvfrx - zvgx ) + & |
---|
295 | ( zvfry - zvgy ) * ( zvfry - zvgy ) & |
---|
296 | , 0.15 * 0.15 ) |
---|
297 | zvrel(ji,jj) = SQRT(zvrel2) |
---|
298 | |
---|
299 | !--------------------- |
---|
300 | ! Iterative procedure |
---|
301 | !--------------------- |
---|
302 | hicol(ji,jj) = zhicrit + 0.1 |
---|
303 | hicol(ji,jj) = zhicrit + hicol(ji,jj) / & |
---|
304 | ( hicol(ji,jj) * hicol(ji,jj) - & |
---|
305 | zhicrit * zhicrit ) * ztwogp * zvrel2 |
---|
306 | |
---|
307 | iter = 1 |
---|
308 | iterate_frazil = .true. |
---|
309 | |
---|
310 | DO WHILE ( iter .LT. 100 .AND. iterate_frazil ) |
---|
311 | zf = ( hicol(ji,jj) - zhicrit ) * ( hicol(ji,jj)**2 - zhicrit**2 ) & |
---|
312 | - hicol(ji,jj) * zhicrit * ztwogp * zvrel2 |
---|
313 | zfp = ( hicol(ji,jj) - zhicrit ) * ( 3.0*hicol(ji,jj) + zhicrit ) & |
---|
314 | - zhicrit * ztwogp * zvrel2 |
---|
315 | zhicol_new = hicol(ji,jj) - zf/zfp |
---|
316 | hicol(ji,jj) = zhicol_new |
---|
317 | |
---|
318 | iter = iter + 1 |
---|
319 | |
---|
320 | END DO ! do while |
---|
321 | |
---|
322 | ENDIF ! end of selection of pixels where ice forms |
---|
323 | |
---|
324 | END DO ! loop on ji ends |
---|
325 | END DO ! loop on jj ends |
---|
326 | |
---|
327 | ENDIF ! End of computation of frazil ice collection thickness |
---|
328 | |
---|
329 | !------------------------------------------------------------------------------! |
---|
330 | ! 4) Identify grid points where new ice forms |
---|
331 | !------------------------------------------------------------------------------! |
---|
332 | |
---|
333 | !------------------------------------- |
---|
334 | ! Select points for new ice formation |
---|
335 | !------------------------------------- |
---|
336 | ! This occurs if open water energy budget is negative |
---|
337 | nbpac = 0 |
---|
338 | DO jj = 1, jpj |
---|
339 | DO ji = 1, jpi |
---|
340 | IF ( tms(ji,jj) * ( qcmif(ji,jj) - qldif(ji,jj) ) > 0.e0 ) THEN |
---|
341 | nbpac = nbpac + 1 |
---|
342 | npac( nbpac ) = (jj - 1) * jpi + ji |
---|
343 | IF ( (ji.eq.jiindx).AND.(jj.eq.jjindx) ) THEN |
---|
344 | jiindex_1d = nbpac |
---|
345 | ENDIF |
---|
346 | ENDIF |
---|
347 | END DO |
---|
348 | END DO |
---|
349 | |
---|
350 | IF( ln_nicep ) THEN |
---|
351 | WRITE(numout,*) 'lim_thd_lac : nbpac = ', nbpac |
---|
352 | ENDIF |
---|
353 | |
---|
354 | !------------------------------ |
---|
355 | ! Move from 2-D to 1-D vectors |
---|
356 | !------------------------------ |
---|
357 | ! If ocean gains heat do nothing |
---|
358 | ! 0therwise compute new ice formation |
---|
359 | |
---|
360 | IF ( nbpac > 0 ) THEN |
---|
361 | |
---|
362 | CALL tab_2d_1d( nbpac, zat_i_ac (1:nbpac) , at_i , & |
---|
363 | jpi, jpj, npac(1:nbpac) ) |
---|
364 | DO jl = 1, jpl |
---|
365 | CALL tab_2d_1d( nbpac, za_i_ac(1:nbpac,jl) , a_i(:,:,jl) , & |
---|
366 | jpi, jpj, npac(1:nbpac) ) |
---|
367 | CALL tab_2d_1d( nbpac, zv_i_ac(1:nbpac,jl) , v_i(:,:,jl) , & |
---|
368 | jpi, jpj, npac(1:nbpac) ) |
---|
369 | CALL tab_2d_1d( nbpac, zoa_i_ac(1:nbpac,jl) , oa_i(:,:,jl) , & |
---|
370 | jpi, jpj, npac(1:nbpac) ) |
---|
371 | CALL tab_2d_1d( nbpac, zsmv_i_ac(1:nbpac,jl), smv_i(:,:,jl), & |
---|
372 | jpi, jpj, npac(1:nbpac) ) |
---|
373 | DO jk = 1, nlay_i |
---|
374 | CALL tab_2d_1d( nbpac, ze_i_ac(1:nbpac,jk,jl), e_i(:,:,jk,jl) , & |
---|
375 | jpi, jpj, npac(1:nbpac) ) |
---|
376 | END DO ! jk |
---|
377 | END DO ! jl |
---|
378 | |
---|
379 | CALL tab_2d_1d( nbpac, qldif_1d (1:nbpac) , qldif , & |
---|
380 | jpi, jpj, npac(1:nbpac) ) |
---|
381 | CALL tab_2d_1d( nbpac, qcmif_1d (1:nbpac) , qcmif , & |
---|
382 | jpi, jpj, npac(1:nbpac) ) |
---|
383 | CALL tab_2d_1d( nbpac, t_bo_b (1:nbpac) , t_bo , & |
---|
384 | jpi, jpj, npac(1:nbpac) ) |
---|
385 | CALL tab_2d_1d( nbpac, fseqv_1d (1:nbpac) , fseqv , & |
---|
386 | jpi, jpj, npac(1:nbpac) ) |
---|
387 | CALL tab_2d_1d( nbpac, hicol_b (1:nbpac) , hicol , & |
---|
388 | jpi, jpj, npac(1:nbpac) ) |
---|
389 | CALL tab_2d_1d( nbpac, zvrel_ac (1:nbpac) , zvrel , & |
---|
390 | jpi, jpj, npac(1:nbpac) ) |
---|
391 | |
---|
392 | !------------------------------------------------------------------------------! |
---|
393 | ! 5) Compute thickness, salinity, enthalpy, age, area and volume of new ice |
---|
394 | !------------------------------------------------------------------------------! |
---|
395 | |
---|
396 | !---------------------- |
---|
397 | ! Thickness of new ice |
---|
398 | !---------------------- |
---|
399 | DO ji = 1, nbpac |
---|
400 | zh_newice(ji) = hiccrit(1) |
---|
401 | END DO |
---|
402 | IF ( fraz_swi .EQ. 1.0 ) zh_newice(:) = hicol_b(:) |
---|
403 | |
---|
404 | !---------------------- |
---|
405 | ! Salinity of new ice |
---|
406 | !---------------------- |
---|
407 | |
---|
408 | IF ( num_sal .EQ. 1 ) THEN |
---|
409 | zs_newice(:) = bulk_sal |
---|
410 | ENDIF ! num_sal |
---|
411 | |
---|
412 | IF ( ( num_sal .EQ. 2 ) .OR. ( num_sal .EQ. 4 ) ) THEN |
---|
413 | |
---|
414 | DO ji = 1, nbpac |
---|
415 | zs_newice(ji) = MIN( 4.606 + 0.91 / zh_newice(ji) , s_i_max ) |
---|
416 | zji = MOD( npac(ji) - 1, jpi ) + 1 |
---|
417 | zjj = ( npac(ji) - 1 ) / jpi + 1 |
---|
418 | zs_newice(ji) = MIN( 0.5*sss_m(zji,zjj) , zs_newice(ji) ) |
---|
419 | END DO ! jl |
---|
420 | |
---|
421 | ENDIF ! num_sal |
---|
422 | |
---|
423 | IF ( num_sal .EQ. 3 ) THEN |
---|
424 | zs_newice(:) = 2.3 |
---|
425 | ENDIF ! num_sal |
---|
426 | |
---|
427 | !------------------------- |
---|
428 | ! Heat content of new ice |
---|
429 | !------------------------- |
---|
430 | ! We assume that new ice is formed at the seawater freezing point |
---|
431 | DO ji = 1, nbpac |
---|
432 | ztmelts = - tmut * zs_newice(ji) + rtt ! Melting point (K) |
---|
433 | ze_newice(ji) = rhoic * ( cpic * ( ztmelts - t_bo_b(ji) ) & |
---|
434 | + lfus * ( 1.0 - ( ztmelts - rtt ) & |
---|
435 | / ( t_bo_b(ji) - rtt ) ) & |
---|
436 | - rcp * ( ztmelts-rtt ) ) |
---|
437 | ze_newice(ji) = MAX( ze_newice(ji) , 0.0 ) + & |
---|
438 | MAX( 0.0 , SIGN( 1.0 , - ze_newice(ji) ) ) & |
---|
439 | * rhoic * lfus |
---|
440 | END DO ! ji |
---|
441 | !---------------- |
---|
442 | ! Age of new ice |
---|
443 | !---------------- |
---|
444 | DO ji = 1, nbpac |
---|
445 | zo_newice(ji) = 0.0 |
---|
446 | END DO ! ji |
---|
447 | |
---|
448 | !-------------------------- |
---|
449 | ! Open water energy budget |
---|
450 | !-------------------------- |
---|
451 | DO ji = 1, nbpac |
---|
452 | zqbgow(ji) = qldif_1d(ji) - qcmif_1d(ji) !<0 |
---|
453 | END DO ! ji |
---|
454 | |
---|
455 | !------------------- |
---|
456 | ! Volume of new ice |
---|
457 | !------------------- |
---|
458 | DO ji = 1, nbpac |
---|
459 | zv_newice(ji) = - zqbgow(ji) / ze_newice(ji) |
---|
460 | |
---|
461 | ! A fraction zfrazb of frazil ice is accreted at the ice bottom |
---|
462 | zfrazb = ( TANH ( Cfrazb * ( zvrel_ac(ji) - vfrazb ) ) & |
---|
463 | + 1.0 ) / 2.0 * maxfrazb |
---|
464 | zdh_frazb(ji) = zfrazb*zv_newice(ji) |
---|
465 | zv_newice(ji) = ( 1.0 - zfrazb ) * zv_newice(ji) |
---|
466 | END DO |
---|
467 | |
---|
468 | !--------------------------------- |
---|
469 | ! Salt flux due to new ice growth |
---|
470 | !--------------------------------- |
---|
471 | IF ( ( num_sal .EQ. 4 ) ) THEN |
---|
472 | DO ji = 1, nbpac |
---|
473 | zji = MOD( npac(ji) - 1, jpi ) + 1 |
---|
474 | zjj = ( npac(ji) - 1 ) / jpi + 1 |
---|
475 | fseqv_1d(ji) = fseqv_1d(ji) + & |
---|
476 | ( sss_m(zji,zjj) - bulk_sal ) * rhoic * & |
---|
477 | zv_newice(ji) / rdt_ice |
---|
478 | END DO |
---|
479 | ELSE |
---|
480 | DO ji = 1, nbpac |
---|
481 | zji = MOD( npac(ji) - 1, jpi ) + 1 |
---|
482 | zjj = ( npac(ji) - 1 ) / jpi + 1 |
---|
483 | fseqv_1d(ji) = fseqv_1d(ji) + & |
---|
484 | ( sss_m(zji,zjj) - zs_newice(ji) ) * rhoic * & |
---|
485 | zv_newice(ji) / rdt_ice |
---|
486 | END DO ! ji |
---|
487 | ENDIF |
---|
488 | |
---|
489 | !------------------------------------ |
---|
490 | ! Diags for energy conservation test |
---|
491 | !------------------------------------ |
---|
492 | DO ji = 1, nbpac |
---|
493 | ! Volume |
---|
494 | zji = MOD( npac(ji) - 1, jpi ) + 1 |
---|
495 | zjj = ( npac(ji) - 1 ) / jpi + 1 |
---|
496 | vt_i_init(zji,zjj) = vt_i_init(zji,zjj) + zv_newice(ji) |
---|
497 | ! Energy |
---|
498 | zde = ze_newice(ji) / unit_fac |
---|
499 | zde = zde * area(zji,zjj) * zv_newice(ji) |
---|
500 | et_i_init(zji,zjj) = et_i_init(zji,zjj) + zde |
---|
501 | END DO |
---|
502 | |
---|
503 | ! keep new ice volume in memory |
---|
504 | CALL tab_1d_2d( nbpac, v_newice , npac(1:nbpac), zv_newice(1:nbpac) , & |
---|
505 | jpi, jpj ) |
---|
506 | |
---|
507 | !----------------- |
---|
508 | ! Area of new ice |
---|
509 | !----------------- |
---|
510 | DO ji = 1, nbpac |
---|
511 | za_newice(ji) = zv_newice(ji) / zh_newice(ji) |
---|
512 | ! diagnostic |
---|
513 | zji = MOD( npac(ji) - 1, jpi ) + 1 |
---|
514 | zjj = ( npac(ji) - 1 ) / jpi + 1 |
---|
515 | diag_lat_gr(zji,zjj) = zv_newice(ji) / rdt_ice |
---|
516 | END DO !ji |
---|
517 | |
---|
518 | !------------------------------------------------------------------------------! |
---|
519 | ! 6) Redistribute new ice area and volume into ice categories ! |
---|
520 | !------------------------------------------------------------------------------! |
---|
521 | |
---|
522 | !----------------------------------------- |
---|
523 | ! Keep old ice areas and volume in memory |
---|
524 | !----------------------------------------- |
---|
525 | zv_old(:,:) = zv_i_ac(:,:) |
---|
526 | za_old(:,:) = za_i_ac(:,:) |
---|
527 | |
---|
528 | !------------------------------------------- |
---|
529 | ! Compute excessive new ice area and volume |
---|
530 | !------------------------------------------- |
---|
531 | ! If lateral ice growth gives an ice concentration gt 1, then |
---|
532 | ! we keep the excessive volume in memory and attribute it later |
---|
533 | ! to bottom accretion |
---|
534 | DO ji = 1, nbpac |
---|
535 | ! vectorize |
---|
536 | IF ( za_newice(ji) .GT. ( 1.0 - zat_i_ac(ji) ) ) THEN |
---|
537 | zda_res(ji) = za_newice(ji) - (1.0 - zat_i_ac(ji) ) |
---|
538 | zdv_res(ji) = zda_res(ji) * zh_newice(ji) |
---|
539 | za_newice(ji) = za_newice(ji) - zda_res(ji) |
---|
540 | zv_newice(ji) = zv_newice(ji) - zdv_res(ji) |
---|
541 | ELSE |
---|
542 | zda_res(ji) = 0.0 |
---|
543 | zdv_res(ji) = 0.0 |
---|
544 | ENDIF |
---|
545 | END DO ! ji |
---|
546 | |
---|
547 | !------------------------------------------------ |
---|
548 | ! Laterally redistribute new ice volume and area |
---|
549 | !------------------------------------------------ |
---|
550 | zat_i_ac(:) = 0.0 |
---|
551 | |
---|
552 | DO jl = 1, jpl |
---|
553 | DO ji = 1, nbpac |
---|
554 | ! vectorize |
---|
555 | IF ( ( hi_max(jl-1) .LT. zh_newice(ji) ) & |
---|
556 | .AND. ( zh_newice(ji) .LE. hi_max(jl) ) ) THEN |
---|
557 | za_i_ac(ji,jl) = za_i_ac(ji,jl) + za_newice(ji) |
---|
558 | zv_i_ac(ji,jl) = zv_i_ac(ji,jl) + zv_newice(ji) |
---|
559 | zat_i_ac(ji) = zat_i_ac(ji) + za_i_ac(ji,jl) |
---|
560 | zcatac(ji) = jl |
---|
561 | ENDIF |
---|
562 | END DO ! ji |
---|
563 | END DO ! jl |
---|
564 | |
---|
565 | !---------------------------------- |
---|
566 | ! Heat content - lateral accretion |
---|
567 | !---------------------------------- |
---|
568 | DO ji = 1, nbpac |
---|
569 | jl = zcatac(ji) ! categroy in which new ice is put |
---|
570 | ! zindb = 0 if no ice and 1 if yes |
---|
571 | zindb = 1.0 - MAX ( 0.0 , SIGN ( 1.0 , -za_old(ji,jl) ) ) |
---|
572 | ! old ice thickness |
---|
573 | zhice_old(ji,jl) = zv_old(ji,jl) & |
---|
574 | / MAX ( za_old(ji,jl) , zeps ) * zindb |
---|
575 | ! difference in thickness |
---|
576 | zdhex(ji) = MAX( 0.0, zh_newice(ji) - zhice_old(ji,jl) ) |
---|
577 | ! is ice totally new in category jl ? |
---|
578 | zswinew(ji) = MAX( 0.0, SIGN( 1.0 , - za_old(ji,jl) + epsi11 ) ) |
---|
579 | END DO |
---|
580 | |
---|
581 | DO jk = 1, nlay_i |
---|
582 | DO ji = 1, nbpac |
---|
583 | jl = zcatac(ji) |
---|
584 | zqold = ze_i_ac(ji,jk,jl) ! [ J.m-3 ] |
---|
585 | zalphai = MIN( zhice_old(ji,jl) * jk / nlay_i , & |
---|
586 | zh_newice(ji) ) & |
---|
587 | - MIN( zhice_old(ji,jl) * ( jk - 1 ) & |
---|
588 | / nlay_i , zh_newice(ji) ) |
---|
589 | ze_i_ac(ji,jk,jl) = & |
---|
590 | zswinew(ji) * ze_newice(ji) & |
---|
591 | + ( 1.0 - zswinew(ji) ) * & |
---|
592 | ( za_old(ji,jl) * zqold * zhice_old(ji,jl) / nlay_i & |
---|
593 | + za_newice(ji) * ze_newice(ji) * zalphai & |
---|
594 | + za_newice(ji) * ze_newice(ji) * zdhex(ji) / nlay_i ) / & |
---|
595 | ( ( zv_i_ac(ji,jl) ) / nlay_i ) |
---|
596 | |
---|
597 | END DO !ji |
---|
598 | END DO !jl |
---|
599 | |
---|
600 | !----------------------------------------------- |
---|
601 | ! Add excessive volume of new ice at the bottom |
---|
602 | !----------------------------------------------- |
---|
603 | ! If the ice concentration exceeds 1, the remaining volume of new ice |
---|
604 | ! is equally redistributed among all ice categories in which there is |
---|
605 | ! ice |
---|
606 | |
---|
607 | ! Fraction of level ice |
---|
608 | jm = 1 |
---|
609 | zat_i_lev(:) = 0.0 |
---|
610 | |
---|
611 | DO jl = ice_cat_bounds(jm,1), ice_cat_bounds(jm,2) |
---|
612 | DO ji = 1, nbpac |
---|
613 | zat_i_lev(ji) = zat_i_lev(ji) + za_i_ac(ji,jl) |
---|
614 | END DO |
---|
615 | END DO |
---|
616 | |
---|
617 | IF( ln_nicep ) WRITE(numout,*) ' zv_i_ac : ', zv_i_ac(jiindx, 1:jpl) |
---|
618 | DO jl = ice_cat_bounds(jm,1), ice_cat_bounds(jm,2) |
---|
619 | DO ji = 1, nbpac |
---|
620 | zindb = MAX( 0.0, SIGN( 1.0, zdv_res(ji) ) ) |
---|
621 | zv_i_ac(ji,jl) = zv_i_ac(ji,jl) + & |
---|
622 | zindb * zdv_res(ji) * za_i_ac(ji,jl) / & |
---|
623 | MAX( zat_i_lev(ji) , epsi06 ) |
---|
624 | END DO ! ji |
---|
625 | END DO ! jl |
---|
626 | IF( ln_nicep ) WRITE(numout,*) ' zv_i_ac : ', zv_i_ac(jiindx, 1:jpl) |
---|
627 | |
---|
628 | !--------------------------------- |
---|
629 | ! Heat content - bottom accretion |
---|
630 | !--------------------------------- |
---|
631 | jm = 1 |
---|
632 | DO jl = ice_cat_bounds(jm,1), ice_cat_bounds(jm,2) |
---|
633 | DO ji = 1, nbpac |
---|
634 | ! zindb = 0 if no ice and 1 if yes |
---|
635 | zindb = 1.0 - MAX( 0.0 , SIGN( 1.0 & |
---|
636 | , - za_i_ac(ji,jl ) ) ) |
---|
637 | zhice_old(ji,jl) = zv_i_ac(ji,jl) / & |
---|
638 | MAX( za_i_ac(ji,jl) , zeps ) * zindb |
---|
639 | zdhicbot(ji,jl) = zdv_res(ji) / MAX( za_i_ac(ji,jl) , zeps ) & |
---|
640 | * zindb & |
---|
641 | + zindb * zdh_frazb(ji) ! frazil ice |
---|
642 | ! may coalesce |
---|
643 | ! thickness of residual ice |
---|
644 | zdummy(ji,jl) = zv_i_ac(ji,jl)/MAX(za_i_ac(ji,jl),zeps)*zindb |
---|
645 | END DO !ji |
---|
646 | END DO !jl |
---|
647 | |
---|
648 | ! old layers thicknesses and enthalpies |
---|
649 | DO jl = ice_cat_bounds(jm,1), ice_cat_bounds(jm,2) |
---|
650 | DO jk = 1, nlay_i |
---|
651 | DO ji = 1, nbpac |
---|
652 | zthick0(ji,jk,jl)= zhice_old(ji,jl) / nlay_i |
---|
653 | zqm0 (ji,jk,jl)= ze_i_ac(ji,jk,jl) * zthick0(ji,jk,jl) |
---|
654 | END DO !ji |
---|
655 | END DO !jk |
---|
656 | END DO !jl |
---|
657 | |
---|
658 | DO jl = ice_cat_bounds(jm,1), ice_cat_bounds(jm,2) |
---|
659 | DO ji = 1, nbpac |
---|
660 | zthick0(ji,nlay_i+1,jl) = zdhicbot(ji,jl) |
---|
661 | zqm0 (ji,nlay_i+1,jl) = ze_newice(ji)*zdhicbot(ji,jl) |
---|
662 | END DO ! ji |
---|
663 | END DO ! jl |
---|
664 | |
---|
665 | ! Redistributing energy on the new grid |
---|
666 | ze_i_ac(:,:,:) = 0.0 |
---|
667 | DO jl = ice_cat_bounds(jm,1), ice_cat_bounds(jm,2) |
---|
668 | DO jk = 1, nlay_i |
---|
669 | DO layer = 1, nlay_i + 1 |
---|
670 | DO ji = 1, nbpac |
---|
671 | zindb = 1.0 - MAX( 0.0 , SIGN( 1.0 , & |
---|
672 | - za_i_ac(ji,jl ) ) ) |
---|
673 | ! Redistributing energy on the new grid |
---|
674 | zweight = MAX ( & |
---|
675 | MIN( zhice_old(ji,jl) * layer , zdummy(ji,jl) * jk ) - & |
---|
676 | MAX( zhice_old(ji,jl) * ( layer - 1 ) , zdummy(ji,jl) * & |
---|
677 | ( jk - 1 ) ) , 0.0 ) & |
---|
678 | / ( MAX(nlay_i * zthick0(ji,layer,jl),zeps) ) * zindb |
---|
679 | ze_i_ac(ji,jk,jl) = ze_i_ac(ji,jk,jl) + & |
---|
680 | zweight * zqm0(ji,layer,jl) |
---|
681 | END DO ! ji |
---|
682 | END DO ! layer |
---|
683 | END DO ! jk |
---|
684 | END DO ! jl |
---|
685 | |
---|
686 | DO jl = ice_cat_bounds(jm,1), ice_cat_bounds(jm,2) |
---|
687 | DO jk = 1, nlay_i |
---|
688 | DO ji = 1, nbpac |
---|
689 | zindb = 1.0 - MAX( 0.0 , SIGN( 1.0 & |
---|
690 | , - zv_i_ac(ji,jl) ) ) !0 if no ice |
---|
691 | ze_i_ac(ji,jk,jl) = ze_i_ac(ji,jk,jl) / & |
---|
692 | MAX( zv_i_ac(ji,jl) , zeps) & |
---|
693 | * za_i_ac(ji,jl) * nlay_i * zindb |
---|
694 | END DO |
---|
695 | END DO |
---|
696 | END DO |
---|
697 | |
---|
698 | !------------ |
---|
699 | ! Update age |
---|
700 | !------------ |
---|
701 | DO jl = 1, jpl |
---|
702 | DO ji = 1, nbpac |
---|
703 | !--ice age |
---|
704 | zindb = 1.0 - MAX( 0.0 , SIGN( 1.0 , - & |
---|
705 | za_i_ac(ji,jl) ) ) ! 0 if no ice and 1 if yes |
---|
706 | zoa_i_ac(ji,jl) = za_old(ji,jl) * zoa_i_ac(ji,jl) / & |
---|
707 | MAX( za_i_ac(ji,jl) , zeps ) * zindb |
---|
708 | END DO ! ji |
---|
709 | END DO ! jl |
---|
710 | |
---|
711 | !----------------- |
---|
712 | ! Update salinity |
---|
713 | !----------------- |
---|
714 | IF ( ( num_sal .EQ. 2 ) .OR. ( num_sal .EQ. 4 ) ) THEN |
---|
715 | |
---|
716 | DO jl = 1, jpl |
---|
717 | DO ji = 1, nbpac |
---|
718 | !zindb = 0 if no ice and 1 if yes |
---|
719 | zindb = 1.0 - MAX( 0.0 , SIGN( 1.0 , - & |
---|
720 | zv_i_ac(ji,jl) ) ) ! 0 if no ice and 1 if yes |
---|
721 | zdv = zv_i_ac(ji,jl) - zv_old(ji,jl) |
---|
722 | zsmv_i_ac(ji,jl) = ( zsmv_i_ac(ji,jl) + zdv * zs_newice(ji) ) * & |
---|
723 | zindb |
---|
724 | END DO ! ji |
---|
725 | END DO ! jl |
---|
726 | |
---|
727 | ENDIF ! num_sal |
---|
728 | |
---|
729 | |
---|
730 | !------------------------------------------------------------------------------! |
---|
731 | ! 8) Change 2D vectors to 1D vectors |
---|
732 | !------------------------------------------------------------------------------! |
---|
733 | |
---|
734 | DO jl = 1, jpl |
---|
735 | CALL tab_1d_2d( nbpac, a_i(:,:,jl) , npac(1:nbpac) , & |
---|
736 | za_i_ac(1:nbpac,jl) , jpi, jpj ) |
---|
737 | CALL tab_1d_2d( nbpac, v_i(:,:,jl) , npac(1:nbpac) , & |
---|
738 | zv_i_ac(1:nbpac,jl) , jpi, jpj ) |
---|
739 | CALL tab_1d_2d( nbpac, oa_i(:,:,jl), npac(1:nbpac) , & |
---|
740 | zoa_i_ac(1:nbpac,jl), jpi, jpj ) |
---|
741 | IF ( ( num_sal .EQ. 2 ) .OR. ( num_sal .EQ. 4 ) ) & |
---|
742 | CALL tab_1d_2d( nbpac, smv_i(:,:,jl) , npac(1:nbpac) , & |
---|
743 | zsmv_i_ac(1:nbpac,jl) , jpi, jpj ) |
---|
744 | DO jk = 1, nlay_i |
---|
745 | CALL tab_1d_2d( nbpac, e_i(:,:,jk,jl) , npac(1:nbpac), & |
---|
746 | ze_i_ac(1:nbpac,jk,jl), jpi, jpj ) |
---|
747 | END DO ! jk |
---|
748 | END DO !jl |
---|
749 | CALL tab_1d_2d( nbpac, fseqv , npac(1:nbpac), fseqv_1d (1:nbpac) , & |
---|
750 | jpi, jpj ) |
---|
751 | |
---|
752 | ENDIF ! nbpac > 0 |
---|
753 | |
---|
754 | !------------------------------------------------------------------------------! |
---|
755 | ! 9) Change units for e_i |
---|
756 | !------------------------------------------------------------------------------! |
---|
757 | |
---|
758 | DO jl = 1, jpl |
---|
759 | DO jk = 1, nlay_i |
---|
760 | DO jj = 1, jpj |
---|
761 | DO ji = 1, jpi |
---|
762 | ! Correct dimensions to avoid big values |
---|
763 | e_i(ji,jj,jk,jl) = e_i(ji,jj,jk,jl) / unit_fac |
---|
764 | |
---|
765 | ! Mutliply by ice volume, and divide by number |
---|
766 | ! of layers to get heat content in 10^9 Joules |
---|
767 | e_i(ji,jj,jk,jl) = e_i(ji,jj,jk,jl) * & |
---|
768 | area(ji,jj) * v_i(ji,jj,jl) / & |
---|
769 | nlay_i |
---|
770 | END DO |
---|
771 | END DO |
---|
772 | END DO |
---|
773 | END DO |
---|
774 | |
---|
775 | !------------------------------------------------------------------------------| |
---|
776 | ! 10) Conservation check and changes in each ice category |
---|
777 | !------------------------------------------------------------------------------| |
---|
778 | |
---|
779 | IF ( con_i ) THEN |
---|
780 | CALL lim_column_sum (jpl, v_i, vt_i_final) |
---|
781 | fieldid = 'v_i, limthd_lac' |
---|
782 | CALL lim_cons_check (vt_i_init, vt_i_final, 1.0e-6, fieldid) |
---|
783 | |
---|
784 | CALL lim_column_sum_energy(jpl, nlay_i, e_i, et_i_final) |
---|
785 | fieldid = 'e_i, limthd_lac' |
---|
786 | CALL lim_cons_check (et_i_final, et_i_final, 1.0e-3, fieldid) |
---|
787 | |
---|
788 | CALL lim_column_sum (jpl, v_s, vt_s_final) |
---|
789 | fieldid = 'v_s, limthd_lac' |
---|
790 | CALL lim_cons_check (vt_s_init, vt_s_final, 1.0e-6, fieldid) |
---|
791 | |
---|
792 | ! CALL lim_column_sum (jpl, e_s(:,:,1,:) , et_s_init) |
---|
793 | ! fieldid = 'e_s, limthd_lac' |
---|
794 | ! CALL lim_cons_check (et_s_init, et_s_final, 1.0e-3, fieldid) |
---|
795 | |
---|
796 | IF( ln_nicep ) THEN |
---|
797 | WRITE(numout,*) ' vt_i_init : ', vt_i_init(jiindx,jjindx) |
---|
798 | WRITE(numout,*) ' vt_i_final: ', vt_i_final(jiindx,jjindx) |
---|
799 | WRITE(numout,*) ' et_i_init : ', et_i_init(jiindx,jjindx) |
---|
800 | WRITE(numout,*) ' et_i_final: ', et_i_final(jiindx,jjindx) |
---|
801 | ENDIF |
---|
802 | |
---|
803 | ENDIF |
---|
804 | |
---|
805 | END SUBROUTINE lim_thd_lac |
---|
806 | |
---|
807 | #else |
---|
808 | !!====================================================================== |
---|
809 | !! *** MODULE limthd_lac *** |
---|
810 | !! no sea ice model |
---|
811 | !!====================================================================== |
---|
812 | CONTAINS |
---|
813 | SUBROUTINE lim_thd_lac ! Empty routine |
---|
814 | END SUBROUTINE lim_thd_lac |
---|
815 | #endif |
---|
816 | END MODULE limthd_lac |
---|