Newer
Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
MODULE icedyn_rhg_evp
!!======================================================================
!! *** MODULE icedyn_rhg_evp ***
!! Sea-Ice dynamics : rheology Elasto-Viscous-Plastic
!!======================================================================
!! History : - ! 2007-03 (M.A. Morales Maqueda, S. Bouillon) Original code
!! 3.0 ! 2008-03 (M. Vancoppenolle) adaptation to new model
!! - ! 2008-11 (M. Vancoppenolle, S. Bouillon, Y. Aksenov) add surface tilt in ice rheolohy
!! 3.3 ! 2009-05 (G.Garric) addition of the evp case
!! 3.4 ! 2011-01 (A. Porter) dynamical allocation
!! 3.5 ! 2012-08 (R. Benshila) AGRIF
!! 3.6 ! 2016-06 (C. Rousset) Rewriting + landfast ice + mEVP (Bouillon 2013)
!! 3.7 ! 2017 (C. Rousset) add aEVP (Kimmritz 2016-2017)
!! 4.0 ! 2018 (many people) SI3 [aka Sea Ice cube]
!!----------------------------------------------------------------------
#if defined key_si3
!!----------------------------------------------------------------------
!! 'key_si3' SI3 sea-ice model
!!----------------------------------------------------------------------
!! ice_dyn_rhg_evp : computes ice velocities from EVP rheology
!! rhg_evp_rst : read/write EVP fields in ice restart
!!----------------------------------------------------------------------
USE phycst ! Physical constant
USE dom_oce ! Ocean domain
USE sbc_oce , ONLY : ln_ice_embd, nn_fsbc, ssh_m
USE sbc_ice , ONLY : utau_ice, vtau_ice, snwice_mass, snwice_mass_b
USE ice ! sea-ice: ice variables
USE icevar ! ice_var_sshdyn
USE icedyn_rdgrft ! sea-ice: ice strength
USE bdy_oce , ONLY : ln_bdy
USE bdyice
#if defined key_agrif
USE agrif_ice_interp
#endif
!
USE in_out_manager ! I/O manager
USE iom ! I/O manager library
USE lib_mpp ! MPP library
USE lib_fortran ! fortran utilities (glob_sum + no signed zero)
USE lbclnk ! lateral boundary conditions (or mpp links)
USE prtctl ! Print control
USE netcdf ! NetCDF library for convergence test
IMPLICIT NONE
PRIVATE
PUBLIC ice_dyn_rhg_evp ! called by icedyn_rhg.F90
PUBLIC rhg_evp_rst ! called by icedyn_rhg.F90
!! for convergence tests
INTEGER :: ncvgid ! netcdf file id
INTEGER :: nvarid ! netcdf variable id
REAL(wp), DIMENSION(:,:), ALLOCATABLE :: fimask ! mask at F points for the ice
!! * Substitutions
# include "do_loop_substitute.h90"
# include "domzgr_substitute.h90"
!!----------------------------------------------------------------------
!! NEMO/ICE 4.0 , NEMO Consortium (2018)
!! $Id: icedyn_rhg_evp.F90 15550 2021-11-28 20:02:31Z clem $
!! Software governed by the CeCILL license (see ./LICENSE)
!!----------------------------------------------------------------------
CONTAINS
SUBROUTINE ice_dyn_rhg_evp( kt, Kmm, pstress1_i, pstress2_i, pstress12_i, pshear_i, pdivu_i, pdelta_i )
!!-------------------------------------------------------------------
!! *** SUBROUTINE ice_dyn_rhg_evp ***
!! EVP-C-grid
!!
!! ** purpose : determines sea ice drift from wind stress, ice-ocean
!! stress and sea-surface slope. Ice-ice interaction is described by
!! a non-linear elasto-viscous-plastic (EVP) law including shear
!! strength and a bulk rheology (Hunke and Dukowicz, 2002).
!!
!! The points in the C-grid look like this, dear reader
!!
!! (ji,jj)
!! |
!! |
!! (ji-1,jj) | (ji,jj)
!! ---------
!! | |
!! | (ji,jj) |------(ji,jj)
!! | |
!! ---------
!! (ji-1,jj-1) (ji,jj-1)
!!
!! ** Inputs : - wind forcing (stress), oceanic currents
!! ice total volume (vt_i) per unit area
!! snow total volume (vt_s) per unit area
!!
!! ** Action : - compute u_ice, v_ice : the components of the
!! sea-ice velocity vector
!! - compute delta_i, shear_i, divu_i, which are inputs
!! of the ice thickness distribution
!!
!! ** Steps : 0) compute mask at F point
!! 1) Compute ice snow mass, ice strength
!! 2) Compute wind, oceanic stresses, mass terms and
!! coriolis terms of the momentum equation
!! 3) Solve the momentum equation (iterative procedure)
!! 4) Recompute delta, shear and divergence
!! (which are inputs of the ITD) & store stress
!! for the next time step
!! 5) Diagnostics including charge ellipse
!!
!! ** Notes : There is the possibility to use aEVP from the nice work of Kimmritz et al. (2016 & 2017)
!! by setting up ln_aEVP=T (i.e. changing alpha and beta parameters).
!! This is an upgraded version of mEVP from Bouillon et al. 2013
!! (i.e. more stable and better convergence)
!!
!! References : Hunke and Dukowicz, JPO97
!! Bouillon et al., Ocean Modelling 2009
!! Bouillon et al., Ocean Modelling 2013
!! Kimmritz et al., Ocean Modelling 2016 & 2017
!!-------------------------------------------------------------------
INTEGER , INTENT(in ) :: kt ! time step
INTEGER , INTENT(in ) :: Kmm ! ocean time level index
REAL(wp), DIMENSION(:,:), INTENT(inout) :: pstress1_i, pstress2_i, pstress12_i !
REAL(wp), DIMENSION(:,:), INTENT( out) :: pshear_i , pdivu_i , pdelta_i !
!!
INTEGER :: ji, jj ! dummy loop indices
INTEGER :: jter ! local integers
!
REAL(wp) :: zrhoco ! rho0 * rn_cio
REAL(wp) :: zdtevp, z1_dtevp ! time step for subcycling
REAL(wp) :: ecc2, z1_ecc2 ! square of yield ellipse eccenticity
REAL(wp) :: zalph1, z1_alph1, zalph2, z1_alph2 ! alpha coef from Bouillon 2009 or Kimmritz 2017
REAl(wp) :: zbetau, zbetav
REAL(wp) :: zm1, zm2, zm3, zmassU, zmassV, zvU, zvV ! ice/snow mass and volume
REAL(wp) :: zp_delf, zds2, zdt, zdt2, zdiv, zdiv2 ! temporary scalars
REAL(wp) :: zTauO, zTauB, zRHS, zvel ! temporary scalars
REAL(wp) :: zkt ! isotropic tensile strength for landfast ice
REAL(wp) :: zvCr ! critical ice volume above which ice is landfast
!
REAL(wp) :: zfac_x, zfac_y
!
REAL(wp), DIMENSION(jpi,jpj) :: zdelta, zp_delt ! delta and P/delta at T points
REAL(wp), DIMENSION(jpi,jpj) :: zbeta ! beta coef from Kimmritz 2017
!
REAL(wp), DIMENSION(jpi,jpj) :: zdt_m ! (dt / ice-snow_mass) on T points
REAL(wp), DIMENSION(jpi,jpj) :: zaU , zaV ! ice fraction on U/V points
REAL(wp), DIMENSION(jpi,jpj) :: zmU_t, zmV_t ! (ice-snow_mass / dt) on U/V points
REAL(wp), DIMENSION(jpi,jpj) :: zmf ! coriolis parameter at T points
REAL(wp), DIMENSION(jpi,jpj) :: v_oceU, u_oceV, v_iceU, u_iceV ! ocean/ice u/v component on V/U points
!
REAL(wp), DIMENSION(jpi,jpj) :: zds ! shear
REAL(wp), DIMENSION(jpi,jpj) :: zten_i ! tension
REAL(wp), DIMENSION(jpi,jpj) :: zs1, zs2, zs12 ! stress tensor components
REAL(wp), DIMENSION(jpi,jpj) :: zsshdyn ! array used for the calculation of ice surface slope:
! ! ocean surface (ssh_m) if ice is not embedded
! ! ice bottom surface if ice is embedded
REAL(wp), DIMENSION(jpi,jpj) :: zfU , zfV ! internal stresses
REAL(wp), DIMENSION(jpi,jpj) :: zspgU, zspgV ! surface pressure gradient at U/V points
REAL(wp), DIMENSION(jpi,jpj) :: zCorU, zCorV ! Coriolis stress array
REAL(wp), DIMENSION(jpi,jpj) :: ztaux_ai, ztauy_ai ! ice-atm. stress at U-V points
REAL(wp), DIMENSION(jpi,jpj) :: ztaux_oi, ztauy_oi ! ice-ocean stress at U-V points
REAL(wp), DIMENSION(jpi,jpj) :: ztaux_bi, ztauy_bi ! ice-OceanBottom stress at U-V points (landfast)
REAL(wp), DIMENSION(jpi,jpj) :: ztaux_base, ztauy_base ! ice-bottom stress at U-V points (landfast)
!
Clement Rousset
committed
REAL(wp), DIMENSION(jpi,jpj) :: zmsk, zmsk00, zmsk15
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
REAL(wp), DIMENSION(jpi,jpj) :: zmsk01x, zmsk01y ! dummy arrays
REAL(wp), DIMENSION(jpi,jpj) :: zmsk00x, zmsk00y ! mask for ice presence
REAL(wp), PARAMETER :: zepsi = 1.0e-20_wp ! tolerance parameter
REAL(wp), PARAMETER :: zmmin = 1._wp ! ice mass (kg/m2) below which ice velocity becomes very small
REAL(wp), PARAMETER :: zamin = 0.001_wp ! ice concentration below which ice velocity becomes very small
!! --- check convergence
REAL(wp), DIMENSION(jpi,jpj) :: zu_ice, zv_ice
!! --- diags
REAL(wp) :: zsig1, zsig2, zsig12, zfac, z1_strength
REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zsig_I, zsig_II, zsig1_p, zsig2_p
!! --- SIMIP diags
REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xmtrp_ice ! X-component of ice mass transport (kg/s)
REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_ymtrp_ice ! Y-component of ice mass transport (kg/s)
REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xmtrp_snw ! X-component of snow mass transport (kg/s)
REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_ymtrp_snw ! Y-component of snow mass transport (kg/s)
REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_xatrp ! X-component of area transport (m2/s)
REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zdiag_yatrp ! Y-component of area transport (m2/s)
!! -- advect fields at the rheology time step for the calculation of strength
!! it seems that convergence is worse when ll_advups=true. So it is not really a good idea
LOGICAL :: ll_advups = .FALSE.
REAL(wp) :: zdt_ups
REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: za_i_ups, zv_i_ups ! tracers advected upstream
!!-------------------------------------------------------------------
IF( kt == nit000 .AND. lwp ) WRITE(numout,*) '-- ice_dyn_rhg_evp: EVP sea-ice rheology'
!
! for diagnostics and convergence tests
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
zmsk00(ji,jj) = MAX( 0._wp , SIGN( 1._wp , at_i(ji,jj) - epsi06 ) ) ! 1 if ice , 0 if no ice
Clement Rousset
committed
zmsk (ji,jj) = MAX( 0._wp , SIGN( 1._wp , at_i(ji,jj) - epsi10 ) ) ! 1 if ice , 0 if no ice
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
END_2D
IF( nn_rhg_chkcvg > 0 ) THEN
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
zmsk15(ji,jj) = MAX( 0._wp , SIGN( 1._wp , at_i(ji,jj) - 0.15_wp ) ) ! 1 if 15% ice, 0 if less
END_2D
ENDIF
!
!------------------------------------------------------------------------------!
! 0) mask at F points for the ice
!------------------------------------------------------------------------------!
IF( kt == nit000 ) THEN
! ocean/land mask
ALLOCATE( fimask(jpi,jpj) )
IF( rn_ishlat == 0._wp ) THEN
DO_2D( 0, 0, 0, 0 )
fimask(ji,jj) = tmask(ji,jj,1) * tmask(ji+1,jj,1) * tmask(ji,jj+1,1) * tmask(ji+1,jj+1,1)
END_2D
ELSE
DO_2D( 0, 0, 0, 0 )
fimask(ji,jj) = tmask(ji,jj,1) * tmask(ji+1,jj,1) * tmask(ji,jj+1,1) * tmask(ji+1,jj+1,1)
! Lateral boundary conditions on velocity (modify fimask)
IF( fimask(ji,jj) == 0._wp ) THEN
fimask(ji,jj) = rn_ishlat * MIN( 1._wp , MAX( umask(ji,jj,1), umask(ji,jj+1,1), &
& vmask(ji,jj,1), vmask(ji+1,jj,1) ) )
ENDIF
END_2D
ENDIF
CALL lbc_lnk( 'icedyn_rhg_evp', fimask, 'F', 1._wp )
ENDIF
!------------------------------------------------------------------------------!
! 1) define some variables and initialize arrays
!------------------------------------------------------------------------------!
zrhoco = rho0 * rn_cio
! ecc2: square of yield ellipse eccenticrity
ecc2 = rn_ecc * rn_ecc
z1_ecc2 = 1._wp / ecc2
! alpha parameters (Bouillon 2009)
IF( .NOT. ln_aEVP ) THEN
zdtevp = rDt_ice / REAL( nn_nevp )
zalph1 = 2._wp * rn_relast * REAL( nn_nevp )
zalph2 = zalph1 * z1_ecc2
z1_alph1 = 1._wp / ( zalph1 + 1._wp )
z1_alph2 = 1._wp / ( zalph2 + 1._wp )
ELSE
zdtevp = rDt_ice
! zalpha parameters set later on adaptatively
ENDIF
z1_dtevp = 1._wp / zdtevp
! Initialise stress tensor
zs1 (:,:) = pstress1_i (:,:)
zs2 (:,:) = pstress2_i (:,:)
zs12(:,:) = pstress12_i(:,:)
! Ice strength
CALL ice_strength
! landfast param from Lemieux(2016): add isotropic tensile strength (following Konig Beatty and Holland, 2010)
IF( ln_landfast_L16 ) THEN ; zkt = rn_lf_tensile
ELSE ; zkt = 0._wp
ENDIF
!
!------------------------------------------------------------------------------!
! 2) Wind / ocean stress, mass terms, coriolis terms
!------------------------------------------------------------------------------!
! sea surface height
! embedded sea ice: compute representative ice top surface
! non-embedded sea ice: use ocean surface for slope calculation
zsshdyn(:,:) = ice_var_sshdyn( ssh_m, snwice_mass, snwice_mass_b)
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
zm1 = ( rhos * vt_s(ji,jj) + rhoi * vt_i(ji,jj) ) ! Ice/snow mass at U-V points
zmf (ji,jj) = zm1 * ff_t(ji,jj) ! Coriolis at T points (m*f)
zdt_m(ji,jj) = zdtevp / MAX( zm1, zmmin ) ! dt/m at T points (for alpha and beta coefficients)
END_2D
DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
! ice fraction at U-V points
zaU(ji,jj) = 0.5_wp * ( at_i(ji,jj) * e1e2t(ji,jj) + at_i(ji+1,jj) * e1e2t(ji+1,jj) ) * r1_e1e2u(ji,jj) * umask(ji,jj,1)
zaV(ji,jj) = 0.5_wp * ( at_i(ji,jj) * e1e2t(ji,jj) + at_i(ji,jj+1) * e1e2t(ji,jj+1) ) * r1_e1e2v(ji,jj) * vmask(ji,jj,1)
! Ice/snow mass at U-V points
zm1 = ( rhos * vt_s(ji ,jj ) + rhoi * vt_i(ji ,jj ) )
zm2 = ( rhos * vt_s(ji+1,jj ) + rhoi * vt_i(ji+1,jj ) )
zm3 = ( rhos * vt_s(ji ,jj+1) + rhoi * vt_i(ji ,jj+1) )
zmassU = 0.5_wp * ( zm1 * e1e2t(ji,jj) + zm2 * e1e2t(ji+1,jj) ) * r1_e1e2u(ji,jj) * umask(ji,jj,1)
zmassV = 0.5_wp * ( zm1 * e1e2t(ji,jj) + zm3 * e1e2t(ji,jj+1) ) * r1_e1e2v(ji,jj) * vmask(ji,jj,1)
! Ocean currents at U-V points
! (brackets added to fix the order of floating point operations for halo 1 - halo 2 compatibility)
v_oceU(ji,jj) = 0.25_wp * ( (v_oce(ji,jj) + v_oce(ji,jj-1)) + (v_oce(ji+1,jj) + v_oce(ji+1,jj-1)) ) * umask(ji,jj,1)
u_oceV(ji,jj) = 0.25_wp * ( (u_oce(ji,jj) + u_oce(ji-1,jj)) + (u_oce(ji,jj+1) + u_oce(ji-1,jj+1)) ) * vmask(ji,jj,1)
! m/dt
zmU_t(ji,jj) = zmassU * z1_dtevp
zmV_t(ji,jj) = zmassV * z1_dtevp
! Drag ice-atm.
ztaux_ai(ji,jj) = zaU(ji,jj) * utau_ice(ji,jj)
ztauy_ai(ji,jj) = zaV(ji,jj) * vtau_ice(ji,jj)
! Surface pressure gradient (- m*g*GRAD(ssh)) at U-V points
zspgU(ji,jj) = - zmassU * grav * ( zsshdyn(ji+1,jj) - zsshdyn(ji,jj) ) * r1_e1u(ji,jj)
zspgV(ji,jj) = - zmassV * grav * ( zsshdyn(ji,jj+1) - zsshdyn(ji,jj) ) * r1_e2v(ji,jj)
! masks
zmsk00x(ji,jj) = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zmassU ) ) ! 0 if no ice
zmsk00y(ji,jj) = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zmassV ) ) ! 0 if no ice
! switches
IF( zmassU <= zmmin .AND. zaU(ji,jj) <= zamin ) THEN ; zmsk01x(ji,jj) = 0._wp
ELSE ; zmsk01x(ji,jj) = 1._wp ; ENDIF
IF( zmassV <= zmmin .AND. zaV(ji,jj) <= zamin ) THEN ; zmsk01y(ji,jj) = 0._wp
ELSE ; zmsk01y(ji,jj) = 1._wp ; ENDIF
END_2D
!
! !== Landfast ice parameterization ==!
!
IF( ln_landfast_L16 ) THEN !-- Lemieux 2016
DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
! ice thickness at U-V points
zvU = 0.5_wp * ( vt_i(ji,jj) * e1e2t(ji,jj) + vt_i(ji+1,jj) * e1e2t(ji+1,jj) ) * r1_e1e2u(ji,jj) * umask(ji,jj,1)
zvV = 0.5_wp * ( vt_i(ji,jj) * e1e2t(ji,jj) + vt_i(ji,jj+1) * e1e2t(ji,jj+1) ) * r1_e1e2v(ji,jj) * vmask(ji,jj,1)
! ice-bottom stress at U points
zvCr = zaU(ji,jj) * rn_lf_depfra * hu(ji,jj,Kmm) * ( 1._wp - icb_mask(ji,jj) ) ! if grounded icebergs are read: ocean depth = 0
ztaux_base(ji,jj) = - rn_lf_bfr * MAX( 0._wp, zvU - zvCr ) * EXP( -rn_crhg * ( 1._wp - zaU(ji,jj) ) )
! ice-bottom stress at V points
zvCr = zaV(ji,jj) * rn_lf_depfra * hv(ji,jj,Kmm) * ( 1._wp - icb_mask(ji,jj) ) ! if grounded icebergs are read: ocean depth = 0
ztauy_base(ji,jj) = - rn_lf_bfr * MAX( 0._wp, zvV - zvCr ) * EXP( -rn_crhg * ( 1._wp - zaV(ji,jj) ) )
! ice_bottom stress at T points
zvCr = at_i(ji,jj) * rn_lf_depfra * ht(ji,jj) * ( 1._wp - icb_mask(ji,jj) ) ! if grounded icebergs are read: ocean depth = 0
tau_icebfr(ji,jj) = - rn_lf_bfr * MAX( 0._wp, vt_i(ji,jj) - zvCr ) * EXP( -rn_crhg * ( 1._wp - at_i(ji,jj) ) )
END_2D
CALL lbc_lnk( 'icedyn_rhg_evp', tau_icebfr(:,:), 'T', 1.0_wp )
!
ELSE !-- no landfast
DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
ztaux_base(ji,jj) = 0._wp
ztauy_base(ji,jj) = 0._wp
END_2D
ENDIF
!------------------------------------------------------------------------------!
! 3) Solution of the momentum equation, iterative procedure
!------------------------------------------------------------------------------!
!
! ! ==================== !
DO jter = 1 , nn_nevp ! loop over jter !
! ! ==================== !
l_full_nf_update = jter == nn_nevp ! false: disable full North fold update (performances) for iter = 1 to nn_nevp-1
!
! convergence test
IF( nn_rhg_chkcvg == 1 .OR. nn_rhg_chkcvg == 2 ) THEN
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
zu_ice(ji,jj) = u_ice(ji,jj) * umask(ji,jj,1) ! velocity at previous time step
zv_ice(ji,jj) = v_ice(ji,jj) * vmask(ji,jj,1)
END_2D
ENDIF
! --- divergence, tension & shear (Appendix B of Hunke & Dukowicz, 2002) --- !
DO_2D( nn_hls, nn_hls-1, nn_hls, nn_hls-1 )
! shear at F points
zds(ji,jj) = ( ( u_ice(ji,jj+1) * r1_e1u(ji,jj+1) - u_ice(ji,jj) * r1_e1u(ji,jj) ) * e1f(ji,jj) * e1f(ji,jj) &
& + ( v_ice(ji+1,jj) * r1_e2v(ji+1,jj) - v_ice(ji,jj) * r1_e2v(ji,jj) ) * e2f(ji,jj) * e2f(ji,jj) &
& ) * r1_e1e2f(ji,jj) * fimask(ji,jj)
END_2D
DO_2D( 0, 0, 0, 0 )
! shear**2 at T points (doc eq. A16)
zds2 = ( zds(ji,jj ) * zds(ji,jj ) * e1e2f(ji,jj ) + zds(ji-1,jj ) * zds(ji-1,jj ) * e1e2f(ji-1,jj ) &
& + zds(ji,jj-1) * zds(ji,jj-1) * e1e2f(ji,jj-1) + zds(ji-1,jj-1) * zds(ji-1,jj-1) * e1e2f(ji-1,jj-1) &
& ) * 0.25_wp * r1_e1e2t(ji,jj)
! divergence at T points
zdiv = ( e2u(ji,jj) * u_ice(ji,jj) - e2u(ji-1,jj) * u_ice(ji-1,jj) &
& + e1v(ji,jj) * v_ice(ji,jj) - e1v(ji,jj-1) * v_ice(ji,jj-1) &
& ) * r1_e1e2t(ji,jj)
zdiv2 = zdiv * zdiv
! tension at T points
zdt = ( ( u_ice(ji,jj) * r1_e2u(ji,jj) - u_ice(ji-1,jj) * r1_e2u(ji-1,jj) ) * e2t(ji,jj) * e2t(ji,jj) &
& - ( v_ice(ji,jj) * r1_e1v(ji,jj) - v_ice(ji,jj-1) * r1_e1v(ji,jj-1) ) * e1t(ji,jj) * e1t(ji,jj) &
& ) * r1_e1e2t(ji,jj)
zdt2 = zdt * zdt
! delta at T points
Clement Rousset
committed
zdelta(ji,jj) = SQRT( zdiv2 + ( zdt2 + zds2 ) * z1_ecc2 ) * zmsk(ji,jj) ! zmsk is for reducing cpu
Clement Rousset
committed
zp_delt(ji,jj) = strength(ji,jj) / ( zdelta(ji,jj) + rn_creepl ) * zmsk(ji,jj) ! zmsk is for reducing cpu
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
END_2D
CALL lbc_lnk( 'icedyn_rhg_evp', zdelta, 'T', 1.0_wp, zp_delt, 'T', 1.0_wp )
!
DO_2D( nn_hls-1, nn_hls, nn_hls-1, nn_hls ) ! loop ends at jpi,jpj so that no lbc_lnk are needed for zs1 and zs2
! divergence at T points (duplication to avoid communications)
! (brackets added to fix the order of floating point operations for halo 1 - halo 2 compatibility)
zdiv = ( (e2u(ji,jj) * u_ice(ji,jj) - e2u(ji-1,jj) * u_ice(ji-1,jj)) &
& + (e1v(ji,jj) * v_ice(ji,jj) - e1v(ji,jj-1) * v_ice(ji,jj-1)) &
& ) * r1_e1e2t(ji,jj)
! tension at T points (duplication to avoid communications)
zdt = ( ( u_ice(ji,jj) * r1_e2u(ji,jj) - u_ice(ji-1,jj) * r1_e2u(ji-1,jj) ) * e2t(ji,jj) * e2t(ji,jj) &
& - ( v_ice(ji,jj) * r1_e1v(ji,jj) - v_ice(ji,jj-1) * r1_e1v(ji,jj-1) ) * e1t(ji,jj) * e1t(ji,jj) &
& ) * r1_e1e2t(ji,jj)
! alpha for aEVP
! gamma = 0.5*P/(delta+creepl) * (c*pi)**2/Area * dt/m
! alpha = beta = sqrt(4*gamma)
IF( ln_aEVP ) THEN
zalph1 = MAX( 50._wp, rpi * SQRT( 0.5_wp * zp_delt(ji,jj) * r1_e1e2t(ji,jj) * zdt_m(ji,jj) ) )
z1_alph1 = 1._wp / ( zalph1 + 1._wp )
zalph2 = zalph1
z1_alph2 = z1_alph1
! explicit:
! z1_alph1 = 1._wp / zalph1
! z1_alph2 = 1._wp / zalph1
! zalph1 = zalph1 - 1._wp
! zalph2 = zalph1
ENDIF
! stress at T points (zkt/=0 if landfast)
Clement Rousset
committed
zs1(ji,jj) = ( zs1(ji,jj)*zalph1 + zp_delt(ji,jj) * ( zdiv*(1._wp + zkt) - zdelta(ji,jj)*(1._wp - zkt) ) ) &
& * z1_alph1 * zmsk(ji,jj) ! zmsk is for reducing cpu
zs2(ji,jj) = ( zs2(ji,jj)*zalph2 + zp_delt(ji,jj) * ( zdt * z1_ecc2 * (1._wp + zkt) ) ) &
& * z1_alph2 * zmsk(ji,jj) ! zmsk is for reducing cpu
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
END_2D
! Save beta at T-points for further computations
IF( ln_aEVP ) THEN
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
zbeta(ji,jj) = MAX( 50._wp, rpi * SQRT( 0.5_wp * zp_delt(ji,jj) * r1_e1e2t(ji,jj) * zdt_m(ji,jj) ) )
END_2D
ENDIF
DO_2D( nn_hls, nn_hls-1, nn_hls, nn_hls-1 )
! alpha for aEVP
IF( ln_aEVP ) THEN
zalph2 = MAX( zbeta(ji,jj), zbeta(ji+1,jj), zbeta(ji,jj+1), zbeta(ji+1,jj+1) )
z1_alph2 = 1._wp / ( zalph2 + 1._wp )
! explicit:
! z1_alph2 = 1._wp / zalph2
! zalph2 = zalph2 - 1._wp
ENDIF
! P/delta at F points
! (brackets added to fix the order of floating point operations for halo 1 - halo 2 compatibility)
zp_delf = 0.25_wp * ( (zp_delt(ji,jj) + zp_delt(ji+1,jj)) + (zp_delt(ji,jj+1) + zp_delt(ji+1,jj+1)) )
! stress at F points (zkt/=0 if landfast)
Clement Rousset
committed
zs12(ji,jj)= ( zs12(ji,jj) * zalph2 + zp_delf * ( zds(ji,jj) * z1_ecc2 * (1._wp + zkt) ) * 0.5_wp ) &
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
END_2D
! --- Ice internal stresses (Appendix C of Hunke and Dukowicz, 2002) --- !
! (brackets added to fix the order of floating point operations for halo 1 - halo 2 compatibility)
DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
! !--- U points
zfU(ji,jj) = 0.5_wp * ( (( zs1(ji+1,jj) - zs1(ji,jj) ) * e2u(ji,jj) &
& + ( zs2(ji+1,jj) * e2t(ji+1,jj) * e2t(ji+1,jj) - zs2(ji,jj) * e2t(ji,jj) * e2t(ji,jj) &
& ) * r1_e2u(ji,jj)) &
& + ( zs12(ji,jj) * e1f(ji,jj) * e1f(ji,jj) - zs12(ji,jj-1) * e1f(ji,jj-1) * e1f(ji,jj-1) &
& ) * 2._wp * r1_e1u(ji,jj) &
& ) * r1_e1e2u(ji,jj)
!
! !--- V points
zfV(ji,jj) = 0.5_wp * ( (( zs1(ji,jj+1) - zs1(ji,jj) ) * e1v(ji,jj) &
& - ( zs2(ji,jj+1) * e1t(ji,jj+1) * e1t(ji,jj+1) - zs2(ji,jj) * e1t(ji,jj) * e1t(ji,jj) &
& ) * r1_e1v(ji,jj)) &
& + ( zs12(ji,jj) * e2f(ji,jj) * e2f(ji,jj) - zs12(ji-1,jj) * e2f(ji-1,jj) * e2f(ji-1,jj) &
& ) * 2._wp * r1_e2v(ji,jj) &
& ) * r1_e1e2v(ji,jj)
!
! !--- ice currents at U-V point
v_iceU(ji,jj) = 0.25_wp * ( (v_ice(ji,jj) + v_ice(ji,jj-1)) + (v_ice(ji+1,jj) + v_ice(ji+1,jj-1)) ) * umask(ji,jj,1)
u_iceV(ji,jj) = 0.25_wp * ( (u_ice(ji,jj) + u_ice(ji-1,jj)) + (u_ice(ji,jj+1) + u_ice(ji-1,jj+1)) ) * vmask(ji,jj,1)
!
END_2D
!
! --- Computation of ice velocity --- !
! Bouillon et al. 2013 (eq 47-48) => unstable unless alpha, beta vary as in Kimmritz 2016 & 2017
! Bouillon et al. 2009 (eq 34-35) => stable
IF( MOD(jter,2) == 0 ) THEN ! even iterations
!
DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
! !--- tau_io/(v_oce - v_ice)
zTauO = zaV(ji,jj) * zrhoco * SQRT( ( v_ice (ji,jj) - v_oce (ji,jj) ) * ( v_ice (ji,jj) - v_oce (ji,jj) ) &
& + ( u_iceV(ji,jj) - u_oceV(ji,jj) ) * ( u_iceV(ji,jj) - u_oceV(ji,jj) ) )
! !--- Ocean-to-Ice stress
ztauy_oi(ji,jj) = zTauO * ( v_oce(ji,jj) - v_ice(ji,jj) )
!
! !--- tau_bottom/v_ice
zvel = 5.e-05_wp + SQRT( v_ice(ji,jj) * v_ice(ji,jj) + u_iceV(ji,jj) * u_iceV(ji,jj) )
zTauB = ztauy_base(ji,jj) / zvel
! !--- OceanBottom-to-Ice stress
ztauy_bi(ji,jj) = zTauB * v_ice(ji,jj)
!
! !--- Coriolis at V-points (energy conserving formulation)
zCorV(ji,jj) = - 0.25_wp * r1_e2v(ji,jj) * &
& ( zmf(ji,jj ) * ( e2u(ji,jj ) * u_ice(ji,jj ) + e2u(ji-1,jj ) * u_ice(ji-1,jj ) ) &
& + zmf(ji,jj+1) * ( e2u(ji,jj+1) * u_ice(ji,jj+1) + e2u(ji-1,jj+1) * u_ice(ji-1,jj+1) ) )
!
! !--- Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io
zRHS = zfV(ji,jj) + ztauy_ai(ji,jj) + zCorV(ji,jj) + zspgV(ji,jj) + ztauy_oi(ji,jj)
!
! !--- landfast switch => 0 = static friction : TauB > RHS & sign(TauB) /= sign(RHS)
! 1 = sliding friction : TauB < RHS
rswitch = 1._wp - MIN( 1._wp, ABS( SIGN( 1._wp, zRHS + ztauy_base(ji,jj) ) - SIGN( 1._wp, zRHS ) ) )
!
IF( ln_aEVP ) THEN !--- ice velocity using aEVP (Kimmritz et al 2016 & 2017)
zbetav = MAX( zbeta(ji,jj), zbeta(ji,jj+1) )
v_ice(ji,jj) = ( ( rswitch * ( zmV_t(ji,jj) * ( zbetav * v_ice(ji,jj) + v_ice_b(ji,jj) ) & ! previous velocity
& + zRHS + zTauO * v_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part)
& ) / MAX( zepsi, zmV_t(ji,jj) * ( zbetav + 1._wp ) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast
& + ( 1._wp - rswitch ) * ( v_ice_b(ji,jj) &
& + v_ice (ji,jj) * MAX( 0._wp, zbetav - zdtevp * rn_lf_relax ) & ! static friction => slow decrease to v=0
& ) / ( zbetav + 1._wp ) &
& ) * zmsk01y(ji,jj) + v_oce(ji,jj) * 0.01_wp * ( 1._wp - zmsk01y(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin
& ) * zmsk00y(ji,jj)
ELSE !--- ice velocity using EVP implicit formulation (cf Madec doc & Bouillon 2009)
v_ice(ji,jj) = ( ( rswitch * ( zmV_t(ji,jj) * v_ice(ji,jj) & ! previous velocity
& + zRHS + zTauO * v_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part)
& ) / MAX( zepsi, zmV_t(ji,jj) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast
& + ( 1._wp - rswitch ) * v_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lf_relax ) & ! static friction => slow decrease to v=0
& ) * zmsk01y(ji,jj) + v_oce(ji,jj) * 0.01_wp * ( 1._wp - zmsk01y(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin
& ) * zmsk00y(ji,jj)
ENDIF
END_2D
IF( nn_hls == 1 ) CALL lbc_lnk( 'icedyn_rhg_evp', v_ice, 'V', -1.0_wp )
!
DO_2D( 0, 0, 0, 0 )
! !--- tau_io/(u_oce - u_ice)
zTauO = zaU(ji,jj) * zrhoco * SQRT( ( u_ice (ji,jj) - u_oce (ji,jj) ) * ( u_ice (ji,jj) - u_oce (ji,jj) ) &
& + ( v_iceU(ji,jj) - v_oceU(ji,jj) ) * ( v_iceU(ji,jj) - v_oceU(ji,jj) ) )
! !--- Ocean-to-Ice stress
ztaux_oi(ji,jj) = zTauO * ( u_oce(ji,jj) - u_ice(ji,jj) )
!
! !--- tau_bottom/u_ice
zvel = 5.e-05_wp + SQRT( v_iceU(ji,jj) * v_iceU(ji,jj) + u_ice(ji,jj) * u_ice(ji,jj) )
zTauB = ztaux_base(ji,jj) / zvel
! !--- OceanBottom-to-Ice stress
ztaux_bi(ji,jj) = zTauB * u_ice(ji,jj)
!
! !--- Coriolis at U-points (energy conserving formulation)
zCorU(ji,jj) = 0.25_wp * r1_e1u(ji,jj) * &
& ( zmf(ji ,jj) * ( e1v(ji ,jj) * v_ice(ji ,jj) + e1v(ji ,jj-1) * v_ice(ji ,jj-1) ) &
& + zmf(ji+1,jj) * ( e1v(ji+1,jj) * v_ice(ji+1,jj) + e1v(ji+1,jj-1) * v_ice(ji+1,jj-1) ) )
!
! !--- Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io
zRHS = zfU(ji,jj) + ztaux_ai(ji,jj) + zCorU(ji,jj) + zspgU(ji,jj) + ztaux_oi(ji,jj)
!
! !--- landfast switch => 0 = static friction : TauB > RHS & sign(TauB) /= sign(RHS)
! 1 = sliding friction : TauB < RHS
rswitch = 1._wp - MIN( 1._wp, ABS( SIGN( 1._wp, zRHS + ztaux_base(ji,jj) ) - SIGN( 1._wp, zRHS ) ) )
!
IF( ln_aEVP ) THEN !--- ice velocity using aEVP (Kimmritz et al 2016 & 2017)
zbetau = MAX( zbeta(ji,jj), zbeta(ji+1,jj) )
u_ice(ji,jj) = ( ( rswitch * ( zmU_t(ji,jj) * ( zbetau * u_ice(ji,jj) + u_ice_b(ji,jj) ) & ! previous velocity
& + zRHS + zTauO * u_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part)
& ) / MAX( zepsi, zmU_t(ji,jj) * ( zbetau + 1._wp ) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast
& + ( 1._wp - rswitch ) * ( u_ice_b(ji,jj) &
& + u_ice (ji,jj) * MAX( 0._wp, zbetau - zdtevp * rn_lf_relax ) & ! static friction => slow decrease to v=0
& ) / ( zbetau + 1._wp ) &
& ) * zmsk01x(ji,jj) + u_oce(ji,jj) * 0.01_wp * ( 1._wp - zmsk01x(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin
& ) * zmsk00x(ji,jj)
ELSE !--- ice velocity using EVP implicit formulation (cf Madec doc & Bouillon 2009)
u_ice(ji,jj) = ( ( rswitch * ( zmU_t(ji,jj) * u_ice(ji,jj) & ! previous velocity
& + zRHS + zTauO * u_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part)
& ) / MAX( zepsi, zmU_t(ji,jj) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast
& + ( 1._wp - rswitch ) * u_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lf_relax ) & ! static friction => slow decrease to v=0
& ) * zmsk01x(ji,jj) + u_oce(ji,jj) * 0.01_wp * ( 1._wp - zmsk01x(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin
& ) * zmsk00x(ji,jj)
ENDIF
END_2D
IF( nn_hls == 1 ) THEN ; CALL lbc_lnk( 'icedyn_rhg_evp', u_ice, 'U', -1.0_wp )
ELSE ; CALL lbc_lnk( 'icedyn_rhg_evp', u_ice, 'U', -1.0_wp, v_ice, 'V', -1.0_wp )
ENDIF
!
ELSE ! odd iterations
!
DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
! !--- tau_io/(u_oce - u_ice)
zTauO = zaU(ji,jj) * zrhoco * SQRT( ( u_ice (ji,jj) - u_oce (ji,jj) ) * ( u_ice (ji,jj) - u_oce (ji,jj) ) &
& + ( v_iceU(ji,jj) - v_oceU(ji,jj) ) * ( v_iceU(ji,jj) - v_oceU(ji,jj) ) )
! !--- Ocean-to-Ice stress
ztaux_oi(ji,jj) = zTauO * ( u_oce(ji,jj) - u_ice(ji,jj) )
!
! !--- tau_bottom/u_ice
zvel = 5.e-05_wp + SQRT( v_iceU(ji,jj) * v_iceU(ji,jj) + u_ice(ji,jj) * u_ice(ji,jj) )
zTauB = ztaux_base(ji,jj) / zvel
! !--- OceanBottom-to-Ice stress
ztaux_bi(ji,jj) = zTauB * u_ice(ji,jj)
!
! !--- Coriolis at U-points (energy conserving formulation)
zCorU(ji,jj) = 0.25_wp * r1_e1u(ji,jj) * &
& ( zmf(ji ,jj) * ( e1v(ji ,jj) * v_ice(ji ,jj) + e1v(ji ,jj-1) * v_ice(ji ,jj-1) ) &
& + zmf(ji+1,jj) * ( e1v(ji+1,jj) * v_ice(ji+1,jj) + e1v(ji+1,jj-1) * v_ice(ji+1,jj-1) ) )
!
! !--- Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io
zRHS = zfU(ji,jj) + ztaux_ai(ji,jj) + zCorU(ji,jj) + zspgU(ji,jj) + ztaux_oi(ji,jj)
!
! !--- landfast switch => 0 = static friction : TauB > RHS & sign(TauB) /= sign(RHS)
! 1 = sliding friction : TauB < RHS
rswitch = 1._wp - MIN( 1._wp, ABS( SIGN( 1._wp, zRHS + ztaux_base(ji,jj) ) - SIGN( 1._wp, zRHS ) ) )
!
IF( ln_aEVP ) THEN !--- ice velocity using aEVP (Kimmritz et al 2016 & 2017)
zbetau = MAX( zbeta(ji,jj), zbeta(ji+1,jj) )
u_ice(ji,jj) = ( ( rswitch * ( zmU_t(ji,jj) * ( zbetau * u_ice(ji,jj) + u_ice_b(ji,jj) ) & ! previous velocity
& + zRHS + zTauO * u_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part)
& ) / MAX( zepsi, zmU_t(ji,jj) * ( zbetau + 1._wp ) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast
& + ( 1._wp - rswitch ) * ( u_ice_b(ji,jj) &
& + u_ice (ji,jj) * MAX( 0._wp, zbetau - zdtevp * rn_lf_relax ) & ! static friction => slow decrease to v=0
& ) / ( zbetau + 1._wp ) &
& ) * zmsk01x(ji,jj) + u_oce(ji,jj) * 0.01_wp * ( 1._wp - zmsk01x(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin
& ) * zmsk00x(ji,jj)
ELSE !--- ice velocity using EVP implicit formulation (cf Madec doc & Bouillon 2009)
u_ice(ji,jj) = ( ( rswitch * ( zmU_t(ji,jj) * u_ice(ji,jj) & ! previous velocity
& + zRHS + zTauO * u_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part)
& ) / MAX( zepsi, zmU_t(ji,jj) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast
& + ( 1._wp - rswitch ) * u_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lf_relax ) & ! static friction => slow decrease to v=0
& ) * zmsk01x(ji,jj) + u_oce(ji,jj) * 0.01_wp * ( 1._wp - zmsk01x(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin
& ) * zmsk00x(ji,jj)
ENDIF
END_2D
IF( nn_hls == 1 ) CALL lbc_lnk( 'icedyn_rhg_evp', u_ice, 'U', -1.0_wp )
!
DO_2D( 0, 0, 0, 0 )
! !--- tau_io/(v_oce - v_ice)
zTauO = zaV(ji,jj) * zrhoco * SQRT( ( v_ice (ji,jj) - v_oce (ji,jj) ) * ( v_ice (ji,jj) - v_oce (ji,jj) ) &
& + ( u_iceV(ji,jj) - u_oceV(ji,jj) ) * ( u_iceV(ji,jj) - u_oceV(ji,jj) ) )
! !--- Ocean-to-Ice stress
ztauy_oi(ji,jj) = zTauO * ( v_oce(ji,jj) - v_ice(ji,jj) )
!
! !--- tau_bottom/v_ice
zvel = 5.e-05_wp + SQRT( v_ice(ji,jj) * v_ice(ji,jj) + u_iceV(ji,jj) * u_iceV(ji,jj) )
zTauB = ztauy_base(ji,jj) / zvel
! !--- OceanBottom-to-Ice stress
ztauy_bi(ji,jj) = zTauB * v_ice(ji,jj)
!
! !--- Coriolis at v-points (energy conserving formulation)
zCorV(ji,jj) = - 0.25_wp * r1_e2v(ji,jj) * &
& ( zmf(ji,jj ) * ( e2u(ji,jj ) * u_ice(ji,jj ) + e2u(ji-1,jj ) * u_ice(ji-1,jj ) ) &
& + zmf(ji,jj+1) * ( e2u(ji,jj+1) * u_ice(ji,jj+1) + e2u(ji-1,jj+1) * u_ice(ji-1,jj+1) ) )
!
! !--- Sum of external forces (explicit solution) = F + tau_ia + Coriolis + spg + tau_io
zRHS = zfV(ji,jj) + ztauy_ai(ji,jj) + zCorV(ji,jj) + zspgV(ji,jj) + ztauy_oi(ji,jj)
!
! !--- landfast switch => 0 = static friction : TauB > RHS & sign(TauB) /= sign(RHS)
! 1 = sliding friction : TauB < RHS
rswitch = 1._wp - MIN( 1._wp, ABS( SIGN( 1._wp, zRHS + ztauy_base(ji,jj) ) - SIGN( 1._wp, zRHS ) ) )
!
IF( ln_aEVP ) THEN !--- ice velocity using aEVP (Kimmritz et al 2016 & 2017)
zbetav = MAX( zbeta(ji,jj), zbeta(ji,jj+1) )
v_ice(ji,jj) = ( ( rswitch * ( zmV_t(ji,jj) * ( zbetav * v_ice(ji,jj) + v_ice_b(ji,jj) ) & ! previous velocity
& + zRHS + zTauO * v_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part)
& ) / MAX( zepsi, zmV_t(ji,jj) * ( zbetav + 1._wp ) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast
& + ( 1._wp - rswitch ) * ( v_ice_b(ji,jj) &
& + v_ice (ji,jj) * MAX( 0._wp, zbetav - zdtevp * rn_lf_relax ) & ! static friction => slow decrease to v=0
& ) / ( zbetav + 1._wp ) &
& ) * zmsk01y(ji,jj) + v_oce(ji,jj) * 0.01_wp * ( 1._wp - zmsk01y(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin
& ) * zmsk00y(ji,jj)
ELSE !--- ice velocity using EVP implicit formulation (cf Madec doc & Bouillon 2009)
v_ice(ji,jj) = ( ( rswitch * ( zmV_t(ji,jj) * v_ice(ji,jj) & ! previous velocity
& + zRHS + zTauO * v_ice(ji,jj) & ! F + tau_ia + Coriolis + spg + tau_io(only ocean part)
& ) / MAX( zepsi, zmV_t(ji,jj) + zTauO - zTauB ) & ! m/dt + tau_io(only ice part) + landfast
& + ( 1._wp - rswitch ) * v_ice(ji,jj) * MAX( 0._wp, 1._wp - zdtevp * rn_lf_relax ) & ! static friction => slow decrease to v=0
& ) * zmsk01y(ji,jj) + v_oce(ji,jj) * 0.01_wp * ( 1._wp - zmsk01y(ji,jj) ) & ! v_ice = v_oce/100 if mass < zmmin & conc < zamin
& ) * zmsk00y(ji,jj)
ENDIF
END_2D
IF( nn_hls == 1 ) THEN ; CALL lbc_lnk( 'icedyn_rhg_evp', v_ice, 'V', -1.0_wp )
ELSE ; CALL lbc_lnk( 'icedyn_rhg_evp', u_ice, 'U', -1.0_wp, v_ice, 'V', -1.0_wp )
ENDIF
!
ENDIF
!
#if defined key_agrif
!! CALL agrif_interp_ice( 'U', jter, nn_nevp )
!! CALL agrif_interp_ice( 'V', jter, nn_nevp )
CALL agrif_interp_ice( 'U' )
CALL agrif_interp_ice( 'V' )
#endif
IF( ln_bdy ) CALL bdy_ice_dyn( 'U' )
IF( ln_bdy ) CALL bdy_ice_dyn( 'V' )
!
! convergence test
IF( nn_rhg_chkcvg == 2 ) CALL rhg_cvg( kt, jter, nn_nevp, u_ice, v_ice, zu_ice, zv_ice, zmsk15 )
!
!
! --- change strength according to advected a_i and v_i (upstream for now) --- !
IF( ll_advups .AND. ln_str_H79 ) THEN
!
IF( jter == 1 ) THEN ! init
ALLOCATE( za_i_ups(jpi,jpj,jpl), zv_i_ups(jpi,jpj,jpl) )
zdt_ups = rDt_ice / REAL( nn_nevp )
za_i_ups(:,:,:) = a_i(:,:,:)
zv_i_ups(:,:,:) = v_i(:,:,:)
ELSE
CALL lbc_lnk( 'icedyn_rhg_evp', za_i_ups, 'T', 1.0_wp, zv_i_ups, 'T', 1.0_wp )
ENDIF
!
CALL rhg_upstream( jter, zdt_ups, u_ice, v_ice, za_i_ups ) ! upstream advection: a_i
CALL rhg_upstream( jter, zdt_ups, u_ice, v_ice, zv_i_ups ) ! upstream advection: v_i
!
DO_2D( 0, 0, 0, 0 ) ! strength
strength(ji,jj) = rn_pstar * SUM( zv_i_ups(ji,jj,:) ) * EXP( -rn_crhg * ( 1._wp - SUM( za_i_ups(ji,jj,:) ) ) )
END_2D
!
IF( jter == nn_nevp ) THEN
DEALLOCATE( za_i_ups, zv_i_ups )
ENDIF
ENDIF
! ! ==================== !
END DO ! end loop over jter !
! ! ==================== !
IF( ln_aEVP ) CALL iom_put( 'beta_evp' , zbeta )
!
IF( ll_advups .AND. ln_str_H79 ) CALL lbc_lnk( 'icedyn_rhg_evp', strength, 'T', 1.0_wp )
!
!------------------------------------------------------------------------------!
! 4) Recompute delta, shear and div (inputs for mechanical redistribution)
!------------------------------------------------------------------------------!
DO_2D( nn_hls, nn_hls-1, nn_hls, nn_hls-1 )
! shear at F points
zds(ji,jj) = ( ( u_ice(ji,jj+1) * r1_e1u(ji,jj+1) - u_ice(ji,jj) * r1_e1u(ji,jj) ) * e1f(ji,jj) * e1f(ji,jj) &
& + ( v_ice(ji+1,jj) * r1_e2v(ji+1,jj) - v_ice(ji,jj) * r1_e2v(ji,jj) ) * e2f(ji,jj) * e2f(ji,jj) &
& ) * r1_e1e2f(ji,jj) * fimask(ji,jj)
END_2D
DO_2D( 0, 0, 0, 0 ) ! no vector loop
! tension**2 at T points
zdt = ( ( u_ice(ji,jj) * r1_e2u(ji,jj) - u_ice(ji-1,jj) * r1_e2u(ji-1,jj) ) * e2t(ji,jj) * e2t(ji,jj) &
& - ( v_ice(ji,jj) * r1_e1v(ji,jj) - v_ice(ji,jj-1) * r1_e1v(ji,jj-1) ) * e1t(ji,jj) * e1t(ji,jj) &
& ) * r1_e1e2t(ji,jj)
zdt2 = zdt * zdt
zten_i(ji,jj) = zdt
! shear**2 at T points (doc eq. A16)
zds2 = ( zds(ji,jj ) * zds(ji,jj ) * e1e2f(ji,jj ) + zds(ji-1,jj ) * zds(ji-1,jj ) * e1e2f(ji-1,jj ) &
& + zds(ji,jj-1) * zds(ji,jj-1) * e1e2f(ji,jj-1) + zds(ji-1,jj-1) * zds(ji-1,jj-1) * e1e2f(ji-1,jj-1) &
& ) * 0.25_wp * r1_e1e2t(ji,jj)
! shear at T points
Clement Rousset
committed
pshear_i(ji,jj) = SQRT( zdt2 + zds2 ) * zmsk(ji,jj)
! divergence at T points
pdivu_i(ji,jj) = ( e2u(ji,jj) * u_ice(ji,jj) - e2u(ji-1,jj) * u_ice(ji-1,jj) &
& + e1v(ji,jj) * v_ice(ji,jj) - e1v(ji,jj-1) * v_ice(ji,jj-1) &
Clement Rousset
committed
& ) * r1_e1e2t(ji,jj) * zmsk(ji,jj)
Clement Rousset
committed
zfac = SQRT( pdivu_i(ji,jj) * pdivu_i(ji,jj) + ( zdt2 + zds2 ) * z1_ecc2 ) * zmsk(ji,jj) ! delta
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
rswitch = 1._wp - MAX( 0._wp, SIGN( 1._wp, -zfac ) ) ! 0 if delta=0
pdelta_i(ji,jj) = zfac + rn_creepl * rswitch ! delta+creepl
END_2D
CALL lbc_lnk( 'icedyn_rhg_evp', pshear_i, 'T', 1._wp, pdivu_i, 'T', 1._wp, pdelta_i, 'T', 1._wp, zten_i, 'T', 1._wp, &
& zs1 , 'T', 1._wp, zs2 , 'T', 1._wp, zs12 , 'F', 1._wp )
! --- Store the stress tensor for the next time step --- !
pstress1_i (:,:) = zs1 (:,:)
pstress2_i (:,:) = zs2 (:,:)
pstress12_i(:,:) = zs12(:,:)
!
!------------------------------------------------------------------------------!
! 5) diagnostics
!------------------------------------------------------------------------------!
! --- ice-ocean, ice-atm. & ice-oceanbottom(landfast) stresses --- !
IF( iom_use('utau_oi') .OR. iom_use('vtau_oi') .OR. iom_use('utau_ai') .OR. iom_use('vtau_ai') .OR. &
& iom_use('utau_bi') .OR. iom_use('vtau_bi') ) THEN
!
CALL lbc_lnk( 'icedyn_rhg_evp', ztaux_oi, 'U', -1.0_wp, ztauy_oi, 'V', -1.0_wp, &
& ztaux_ai, 'U', -1.0_wp, ztauy_ai, 'V', -1.0_wp, &
& ztaux_bi, 'U', -1.0_wp, ztauy_bi, 'V', -1.0_wp )
!
CALL iom_put( 'utau_oi' , ztaux_oi * zmsk00 )
CALL iom_put( 'vtau_oi' , ztauy_oi * zmsk00 )
CALL iom_put( 'utau_ai' , ztaux_ai * zmsk00 )
CALL iom_put( 'vtau_ai' , ztauy_ai * zmsk00 )
CALL iom_put( 'utau_bi' , ztaux_bi * zmsk00 )
CALL iom_put( 'vtau_bi' , ztauy_bi * zmsk00 )
ENDIF
! --- divergence, shear and strength --- !
IF( iom_use('icediv') ) CALL iom_put( 'icediv' , pdivu_i * zmsk00 ) ! divergence
IF( iom_use('iceshe') ) CALL iom_put( 'iceshe' , pshear_i * zmsk00 ) ! shear
IF( iom_use('icestr') ) CALL iom_put( 'icestr' , strength * zmsk00 ) ! strength
IF( iom_use('icedlt') ) CALL iom_put( 'icedlt' , pdelta_i * zmsk00 ) ! delta
! --- Stress tensor invariants (SIMIP diags) --- !
IF( iom_use('normstr') .OR. iom_use('sheastr') ) THEN
!
ALLOCATE( zsig_I(jpi,jpj) , zsig_II(jpi,jpj) )
!
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
! Ice stresses
! sigma1, sigma2, sigma12 are some useful recombination of the stresses (Hunke and Dukowicz MWR 2002, Bouillon et al., OM2013)
! These are NOT stress tensor components, neither stress invariants, neither stress principal components
! I know, this can be confusing...
zfac = strength(ji,jj) / ( pdelta_i(ji,jj) + rn_creepl )
zsig1 = zfac * ( pdivu_i(ji,jj) - pdelta_i(ji,jj) )
zsig2 = zfac * z1_ecc2 * zten_i(ji,jj)
zsig12 = zfac * z1_ecc2 * pshear_i(ji,jj)
! Stress invariants (sigma_I, sigma_II, Coon 1974, Feltham 2008)
zsig_I (ji,jj) = zsig1 * 0.5_wp ! 1st stress invariant, aka average normal stress, aka negative pressure
zsig_II(ji,jj) = SQRT ( zsig2 * zsig2 * 0.25_wp + zsig12 * zsig12 ) ! 2nd '' '' , aka maximum shear stress
END_2D
!
! Stress tensor invariants (normal and shear stress N/m) - SIMIP diags - definitions following Coon (1974) and Feltham (2008)
IF( iom_use('normstr') ) CALL iom_put( 'normstr', zsig_I (:,:) * zmsk00(:,:) ) ! Normal stress
IF( iom_use('sheastr') ) CALL iom_put( 'sheastr', zsig_II(:,:) * zmsk00(:,:) ) ! Maximum shear stress
DEALLOCATE ( zsig_I, zsig_II )
ENDIF
! --- Normalized stress tensor principal components --- !
! This are used to plot the normalized yield curve, see Lemieux & Dupont, 2020
! Recommendation 1 : we use ice strength, not replacement pressure
! Recommendation 2 : need to use deformations at PREVIOUS iterate for viscosities
IF( iom_use('sig1_pnorm') .OR. iom_use('sig2_pnorm') ) THEN
!
ALLOCATE( zsig1_p(jpi,jpj) , zsig2_p(jpi,jpj) , zsig_I(jpi,jpj) , zsig_II(jpi,jpj) )
!
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
! Ice stresses computed with **viscosities** (delta, p/delta) at **previous** iterates
! and **deformations** at current iterates
! following Lemieux & Dupont (2020)
zfac = zp_delt(ji,jj)
zsig1 = zfac * ( pdivu_i(ji,jj) - ( zdelta(ji,jj) + rn_creepl ) )
zsig2 = zfac * z1_ecc2 * zten_i(ji,jj)
zsig12 = zfac * z1_ecc2 * pshear_i(ji,jj)
! Stress invariants (sigma_I, sigma_II, Coon 1974, Feltham 2008), T-point
zsig_I(ji,jj) = zsig1 * 0.5_wp ! 1st stress invariant, aka average normal stress, aka negative pressure
zsig_II(ji,jj) = SQRT ( zsig2 * zsig2 * 0.25_wp + zsig12 * zsig12 ) ! 2nd '' '' , aka maximum shear stress
! Normalized principal stresses (used to display the ellipse)
z1_strength = 1._wp / MAX( 1._wp, strength(ji,jj) )
zsig1_p(ji,jj) = ( zsig_I(ji,jj) + zsig_II(ji,jj) ) * z1_strength
zsig2_p(ji,jj) = ( zsig_I(ji,jj) - zsig_II(ji,jj) ) * z1_strength
END_2D
!
Clement Rousset
committed
CALL iom_put( 'sig1_pnorm' , zsig1_p * zmsk00 )
CALL iom_put( 'sig2_pnorm' , zsig2_p * zmsk00 )
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
DEALLOCATE( zsig1_p , zsig2_p , zsig_I, zsig_II )
ENDIF
! --- SIMIP --- !
IF( iom_use('dssh_dx') .OR. iom_use('dssh_dy') .OR. &
& iom_use('corstrx') .OR. iom_use('corstry') .OR. iom_use('intstrx') .OR. iom_use('intstry') ) THEN
!
CALL lbc_lnk( 'icedyn_rhg_evp', zspgU, 'U', -1.0_wp, zspgV, 'V', -1.0_wp, &
& zCorU, 'U', -1.0_wp, zCorV, 'V', -1.0_wp, zfU, 'U', -1.0_wp, zfV, 'V', -1.0_wp )
CALL iom_put( 'dssh_dx' , zspgU * zmsk00 ) ! Sea-surface tilt term in force balance (x)
CALL iom_put( 'dssh_dy' , zspgV * zmsk00 ) ! Sea-surface tilt term in force balance (y)
CALL iom_put( 'corstrx' , zCorU * zmsk00 ) ! Coriolis force term in force balance (x)
CALL iom_put( 'corstry' , zCorV * zmsk00 ) ! Coriolis force term in force balance (y)
CALL iom_put( 'intstrx' , zfU * zmsk00 ) ! Internal force term in force balance (x)
CALL iom_put( 'intstry' , zfV * zmsk00 ) ! Internal force term in force balance (y)
ENDIF
IF( iom_use('xmtrpice') .OR. iom_use('ymtrpice') .OR. &
& iom_use('xmtrpsnw') .OR. iom_use('ymtrpsnw') .OR. iom_use('xatrp') .OR. iom_use('yatrp') ) THEN
!
ALLOCATE( zdiag_xmtrp_ice(jpi,jpj) , zdiag_ymtrp_ice(jpi,jpj) , &
& zdiag_xmtrp_snw(jpi,jpj) , zdiag_ymtrp_snw(jpi,jpj) , zdiag_xatrp(jpi,jpj) , zdiag_yatrp(jpi,jpj) )
!
DO_2D( 0, 0, 0, 0 )
! 2D ice mass, snow mass, area transport arrays (X, Y)
zfac_x = 0.5 * u_ice(ji,jj) * e2u(ji,jj) * zmsk00(ji,jj)
zfac_y = 0.5 * v_ice(ji,jj) * e1v(ji,jj) * zmsk00(ji,jj)
zdiag_xmtrp_ice(ji,jj) = rhoi * zfac_x * ( vt_i(ji+1,jj) + vt_i(ji,jj) ) ! ice mass transport, X-component
zdiag_ymtrp_ice(ji,jj) = rhoi * zfac_y * ( vt_i(ji,jj+1) + vt_i(ji,jj) ) ! '' Y- ''
zdiag_xmtrp_snw(ji,jj) = rhos * zfac_x * ( vt_s(ji+1,jj) + vt_s(ji,jj) ) ! snow mass transport, X-component
zdiag_ymtrp_snw(ji,jj) = rhos * zfac_y * ( vt_s(ji,jj+1) + vt_s(ji,jj) ) ! '' Y- ''
zdiag_xatrp(ji,jj) = zfac_x * ( at_i(ji+1,jj) + at_i(ji,jj) ) ! area transport, X-component
zdiag_yatrp(ji,jj) = zfac_y * ( at_i(ji,jj+1) + at_i(ji,jj) ) ! '' Y- ''
END_2D
CALL lbc_lnk( 'icedyn_rhg_evp', zdiag_xmtrp_ice, 'U', -1.0_wp, zdiag_ymtrp_ice, 'V', -1.0_wp, &
& zdiag_xmtrp_snw, 'U', -1.0_wp, zdiag_ymtrp_snw, 'V', -1.0_wp, &
& zdiag_xatrp , 'U', -1.0_wp, zdiag_yatrp , 'V', -1.0_wp )
CALL iom_put( 'xmtrpice' , zdiag_xmtrp_ice ) ! X-component of sea-ice mass transport (kg/s)
CALL iom_put( 'ymtrpice' , zdiag_ymtrp_ice ) ! Y-component of sea-ice mass transport
CALL iom_put( 'xmtrpsnw' , zdiag_xmtrp_snw ) ! X-component of snow mass transport (kg/s)
CALL iom_put( 'ymtrpsnw' , zdiag_ymtrp_snw ) ! Y-component of snow mass transport
CALL iom_put( 'xatrp' , zdiag_xatrp ) ! X-component of ice area transport
CALL iom_put( 'yatrp' , zdiag_yatrp ) ! Y-component of ice area transport
DEALLOCATE( zdiag_xmtrp_ice , zdiag_ymtrp_ice , &
& zdiag_xmtrp_snw , zdiag_ymtrp_snw , zdiag_xatrp , zdiag_yatrp )
ENDIF
!
! --- convergence tests --- !
IF( nn_rhg_chkcvg == 1 .OR. nn_rhg_chkcvg == 2 ) THEN
IF( iom_use('uice_cvg') ) THEN
IF( ln_aEVP ) THEN ! output: beta * ( u(t=nn_nevp) - u(t=nn_nevp-1) )
CALL iom_put( 'uice_cvg', MAX( ABS( u_ice(:,:) - zu_ice(:,:) ) * zbeta(:,:) * umask(:,:,1) , &
& ABS( v_ice(:,:) - zv_ice(:,:) ) * zbeta(:,:) * vmask(:,:,1) ) * zmsk15(:,:) )
ELSE ! output: nn_nevp * ( u(t=nn_nevp) - u(t=nn_nevp-1) )
CALL iom_put( 'uice_cvg', REAL( nn_nevp ) * MAX( ABS( u_ice(:,:) - zu_ice(:,:) ) * umask(:,:,1) , &
& ABS( v_ice(:,:) - zv_ice(:,:) ) * vmask(:,:,1) ) * zmsk15(:,:) )
ENDIF
ENDIF
ENDIF
!
END SUBROUTINE ice_dyn_rhg_evp
SUBROUTINE rhg_cvg( kt, kiter, kitermax, pu, pv, pub, pvb, pmsk15 )
!!----------------------------------------------------------------------
!! *** ROUTINE rhg_cvg ***
!!
!! ** Purpose : check convergence of oce rheology
!!
!! ** Method : create a file ice_cvg.nc containing the convergence of ice velocity
!! during the sub timestepping of rheology so as:
!! uice_cvg = MAX( u(t+1) - u(t) , v(t+1) - v(t) )
!! This routine is called every sub-iteration, so it is cpu expensive
!!
!! ** Note : for the first sub-iteration, uice_cvg is set to 0 (too large otherwise)
!!----------------------------------------------------------------------
INTEGER , INTENT(in) :: kt, kiter, kitermax ! ocean time-step index
REAL(wp), DIMENSION(:,:), INTENT(in) :: pu, pv, pub, pvb ! now and before velocities
REAL(wp), DIMENSION(:,:), INTENT(in) :: pmsk15
!!
INTEGER :: it, idtime, istatus
INTEGER :: ji, jj ! dummy loop indices
REAL(wp) :: zresm ! local real
CHARACTER(len=20) :: clname
LOGICAL :: ll_maxcvg
REAL(wp), DIMENSION(jpi,jpj,2) :: zres
REAL(wp), DIMENSION(2) :: ztmp
!!----------------------------------------------------------------------
ll_maxcvg = .FALSE.
!
! create file
IF( kt == nit000 .AND. kiter == 1 ) THEN
!
IF( lwp ) THEN
WRITE(numout,*)
WRITE(numout,*) 'rhg_cvg : ice rheology convergence control'
WRITE(numout,*) '~~~~~~~'
ENDIF
!
IF( lwm ) THEN
clname = 'ice_cvg.nc'
IF( .NOT. Agrif_Root() ) clname = TRIM(Agrif_CFixed())//"_"//TRIM(clname)
istatus = NF90_CREATE( TRIM(clname), NF90_CLOBBER, ncvgid )
istatus = NF90_DEF_DIM( ncvgid, 'time' , NF90_UNLIMITED, idtime )
istatus = NF90_DEF_VAR( ncvgid, 'uice_cvg', NF90_DOUBLE , (/ idtime /), nvarid )
istatus = NF90_ENDDEF(ncvgid)
ENDIF
!
ENDIF
! time
it = ( kt - nit000 ) * kitermax + kiter
! convergence
IF( kiter == 1 ) THEN ! remove the first iteration for calculations of convergence (always very large)
zresm = 0._wp
ELSE
zresm = 0._wp
IF( ll_maxcvg ) THEN ! error max over the domain
DO_2D( 0, 0, 0, 0 )
zresm = MAX( zresm, MAX( ABS( pu(ji,jj) - pub(ji,jj) ) * umask(ji,jj,1), &
& ABS( pv(ji,jj) - pvb(ji,jj) ) * vmask(ji,jj,1) ) * pmsk15(ji,jj) )
END_2D
CALL mpp_max( 'icedyn_rhg_evp', zresm )
ELSE ! error averaged over the domain
DO_2D( 0, 0, 0, 0 )
zres(ji,jj,1) = MAX( ABS( pu(ji,jj) - pub(ji,jj) ) * umask(ji,jj,1), &
& ABS( pv(ji,jj) - pvb(ji,jj) ) * vmask(ji,jj,1) ) * pmsk15(ji,jj)
zres(ji,jj,2) = pmsk15(ji,jj)
END_2D