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limrhg_2.F90 @ 7910

Last change on this file since 7910 was 7910, checked in by timgraham, 7 years ago
All wrk_alloc removed
Property svn:keywords set to `Id`
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1	MODULE limrhg_2
2	!!======================================================================
3	!! * MODULE limrhg_2 *
4	!! Ice rheology : performs sea ice rheology
5	!!======================================================================
6	!! History : 0.0 ! 1993-12 (M.A. Morales Maqueda.) Original code
7	!! 1.0 ! 1994-12 (H. Goosse)
8	!! 2.0 ! 2003-12 (C. Ethe, G. Madec) F90, mpp
9	!! - ! 2006-08 (G. Madec) surface module, ice-stress at I-point
10	!! - ! 2009-09 (G. Madec) Huge verctor optimisation
11	!! 3.3 ! 2009-05 (G.Garric, C. Bricaud) addition of the lim2_evp case
12	!!----------------------------------------------------------------------
13	#if defined key_lim2 && defined key_lim2_vp
14	!!----------------------------------------------------------------------
15	!! 'key_lim2' AND LIM-2 sea-ice model
16	!! 'key_lim2_vp' VP ice rheology
17	!!----------------------------------------------------------------------
18	!! lim_rhg_2 : computes ice velocities
19	!!----------------------------------------------------------------------
20	USE par_oce ! ocean parameter
21	USE dom_oce ! ocean space and time domain
22	USE sbc_oce ! surface boundary condition: ocean variables
23	USE sbc_ice ! surface boundary condition: ice variables
24	USE dom_ice_2 ! LIM2: ice domain
25	USE phycst ! physical constant
26	USE ice_2 ! LIM2: ice variables
27	USE lbclnk ! lateral boundary condition - MPP exchanges
28	USE lib_mpp ! MPP library
29	USE in_out_manager ! I/O manager
30	USE prtctl ! Print control
31	USE oce , ONLY : snwice_mass, snwice_mass_b
32	USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined)
33	#if defined key_agrif
34	USE agrif_lim2_interp ! nesting
35	#endif
36
37	IMPLICIT NONE
38	PRIVATE
39
40	PUBLIC lim_rhg_2 ! routine called by lim_dyn
41
42	REAL(wp) :: rzero = 0._wp ! constant value: zero
43	REAL(wp) :: rone = 1._wp ! and one
44
45	!! * Substitutions
46	# include "vectopt_loop_substitute.h90"
47	!!----------------------------------------------------------------------
48	!! NEMO/LIM2 3.3 , UCL - NEMO Consortium (2010)
49	!! $Id$
50	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
51	!!----------------------------------------------------------------------
52	CONTAINS
53
54	SUBROUTINE lim_rhg_2( k_j1, k_jpj )
55	!!-------------------------------------------------------------------
56	!! * SUBROUTINR lim_rhg_2 *
57	!!
58	!! ** purpose : determines the velocity field of sea ice by using
59	!! atmospheric (wind stress) and oceanic (water stress and surface
60	!! tilt) forcings. Ice-ice interaction is described by a non-linear
61	!! viscous-plastic law including shear strength and a bulk rheology.
62	!!
63	!! ** Action : - compute u_ice, v_ice the sea-ice velocity defined
64	!! at I-point
65	!!-------------------------------------------------------------------
66	INTEGER, INTENT(in) :: k_j1 ! southern j-index for ice computation
67	INTEGER, INTENT(in) :: k_jpj ! northern j-index for ice computation
68	!!
69	INTEGER :: ji, jj ! dummy loop indices
70	INTEGER :: iter, jter ! temporary integers
71	CHARACTER (len=50) :: charout
72	REAL(wp) :: ze11 , ze12 , ze22 , ze21 ! local scalars
73	REAL(wp) :: zt11 , zt12 , zt21 , zt22 ! - -
74	REAL(wp) :: zvis11, zvis21, zvis12, zvis22 ! - -
75	REAL(wp) :: zgphsx, ztagnx, zgsshx, zunw, zur, zusw ! - -
76	REAL(wp) :: zgphsy, ztagny, zgsshy, zvnw, zvr ! - -
77	REAL(wp) :: zresm, za, zac, zmod
78	REAL(wp) :: zmpzas, zstms, zindu, zusdtp, zmassdt, zcorlal
79	REAL(wp) :: ztrace2, zdeter, zdelta, zmask, zdgp, zdgi, zdiag
80	REAL(wp) :: za1, zb1, zc1, zd1
81	REAL(wp) :: za2, zb2, zc2, zd2, zden
82	REAL(wp) :: zs11_11, zs11_12, zs11_21, zs11_22
83	REAL(wp) :: zs12_11, zs12_12, zs12_21, zs12_22
84	REAL(wp) :: zs21_11, zs21_12, zs21_21, zs21_22
85	REAL(wp) :: zs22_11, zs22_12, zs22_21, zs22_22
86	REAL(wp) :: zintb, zintn
87	REAL(wp), DIMENSION(jpi,jpj) :: zfrld, zmass, zcorl
88	REAL(wp), DIMENSION(jpi,jpj) :: za1ct, za2ct, zresr
89	REAL(wp), DIMENSION(jpi,jpj) :: zc1u, zc1v, zc2u, zc2v
90	REAL(wp), DIMENSION(jpi,jpj) :: zsang, zpice
91	REAL(wp), DIMENSION(jpi,0:jpj+1) :: zu0, zv0
92	REAL(wp), DIMENSION(jpi,0:jpj+1) :: zu_n, zv_n
93	REAL(wp), DIMENSION(jpi,0:jpj+1) :: zu_a, zv_a
94	REAL(wp), DIMENSION(jpi,0:jpj+1) :: zviszeta, zviseta
95	REAL(wp), DIMENSION(jpi,0:jpj+1) :: zzfrld, zztms
96	REAL(wp), DIMENSION(jpi,0:jpj+1) :: zi1, zi2, zmasst, zpresh
97	!!-------------------------------------------------------------------
98
99
100	! Store initial velocities
101	! ----------------
102	zztms(:,0 ) = 0._wp ; zzfrld(:,0 ) = 0._wp
103	zztms(:,jpj+1) = 0._wp ; zzfrld(:,jpj+1) = 0._wp
104	zu0 (:,0 ) = 0._wp ; zv0 (:,0 ) = 0._wp
105	zu0 (:,jpj+1) = 0._wp ; zv0 (:,jpj+1) = 0._wp
106	zztms(:,1:jpj) = tms (:,:) ; zzfrld(:,1:jpj) = frld (:,:)
107	zu0 (:,1:jpj) = u_ice(:,:) ; zv0 (:,1:jpj) = v_ice(:,:)
108	zu_a (:, : ) = zu0 (:,:) ; zv_a (:, : ) = zv0 (:,:)
109	zu_n (:, : ) = zu0 (:,:) ; zv_n (:, : ) = zv0 (:,:)
110
111	!i
112	zi1 (:,:) = 0._wp
113	zi2 (:,:) = 0._wp
114	zpresh(:,:) = 0._wp
115	zmasst(:,:) = 0._wp
116	!i
117	!!gm violant
118	zfrld(:,:) =0._wp
119	zcorl(:,:) =0._wp
120	zmass(:,:) =0._wp
121	za1ct(:,:) =0._wp
122	za2ct(:,:) =0._wp
123	!!gm end
124
125	zviszeta(:,:) = 0._wp
126	zviseta (:,:) = 0._wp
127
128	!i zviszeta(:,0 ) = 0._wp ; zviseta(:,0 ) = 0._wp
129	!i zviszeta(:,jpj ) = 0._wp ; zviseta(:,jpj ) = 0._wp
130	!i zviszeta(:,jpj+1) = 0._wp ; zviseta(:,jpj+1) = 0._wp
131
132	IF( nn_ice_embd == 2 ) THEN !== embedded sea ice: compute representative ice top surface ==!
133	!
134	! average interpolation coeff as used in dynspg = (1/nn_fsbc) * {SUM[n/nn_fsbc], n=0,nn_fsbc-1}
135	! = (1/nn_fsbc)^2 * {SUM[n], n=0,nn_fsbc-1}
136	zintn = REAL( nn_fsbc - 1 ) / REAL( nn_fsbc ) * 0.5_wp
137	!
138	! average interpolation coeff as used in dynspg = (1/nn_fsbc) * {SUM[1-n/nn_fsbc], n=0,nn_fsbc-1}
139	! = (1/nn_fsbc)^2 * (nn_fsbc^2 - {SUM[n], n=0,nn_fsbc-1})
140	zintb = REAL( nn_fsbc + 1 ) / REAL( nn_fsbc ) * 0.5_wp
141	!
142	zpice(:,:) = ssh_m(:,:) + ( zintn * snwice_mass(:,:) + zintb * snwice_mass_b(:,:) ) * r1_rau0
143	!
144	!
145	ELSE !== non-embedded sea ice: use ocean surface for slope calculation ==!
146	zpice(:,:) = ssh_m(:,:)
147	ENDIF
148	#if defined key_agrif
149	! load the boundary value of velocity in special array zuive and zvice
150	CALL agrif_rhg_lim2_load
151	#endif
152
153	! Ice mass, ice strength, and wind stress at the center \|
154	! of the grid squares. \|
155	!-------------------------------------------------------------------
156
157	DO jj = k_j1 , k_jpj-1
158	DO ji = 1 , jpi
159	! only the sinus changes its sign with the hemisphere
160	zsang(ji,jj) = SIGN( 1._wp, ff_t(ji,jj) ) * sangvg ! only the sinus changes its sign with the hemisphere
161	!
162	zmasst(ji,jj) = tms(ji,jj) * ( rhosn * hsnm(ji,jj) + rhoic * hicm(ji,jj) )
163	zpresh(ji,jj) = tms(ji,jj) * pstarh * hicm(ji,jj) * EXP( -c_rhg * frld(ji,jj) )
164	!!gm :: stress given at I-point (F-point for the ocean) only compute the ponderation with the ice fraction (1-frld)
165	zi1(ji,jj) = tms(ji,jj) * ( 1._wp - frld(ji,jj) )
166	zi2(ji,jj) = tms(ji,jj) * ( 1._wp - frld(ji,jj) )
167	END DO
168	END DO
169
170
171	!---------------------------------------------------------------------------
172	! Wind stress, coriolis and mass terms at the corners of the grid squares \|
173	! Gradient of ice strenght. \|
174	!---------------------------------------------------------------------------
175
176	DO jj = k_j1+1, k_jpj-1
177	DO ji = 2, jpi ! NO vector opt.
178	zstms = zztms(ji,jj ) * wght(ji,jj,2,2) + zztms(ji-1,jj ) * wght(ji,jj,1,2) &
179	& + zztms(ji,jj-1) * wght(ji,jj,2,1) + zztms(ji-1,jj-1) * wght(ji,jj,1,1)
180	zusw = 1._wp / MAX( zstms, epsd )
181
182	zt11 = zztms(ji ,jj ) * zzfrld(ji ,jj )
183	zt12 = zztms(ji-1,jj ) * zzfrld(ji-1,jj )
184	zt21 = zztms(ji ,jj-1) * zzfrld(ji ,jj-1)
185	zt22 = zztms(ji-1,jj-1) * zzfrld(ji-1,jj-1)
186
187	! Leads area.
188	zfrld(ji,jj) = ( zt11 * wght(ji,jj,2,2) + zt12 * wght(ji,jj,1,2) &
189	& + zt21 * wght(ji,jj,2,1) + zt22 * wght(ji,jj,1,1) ) * zusw
190
191	! Mass and coriolis coeff. at I-point
192	zmass(ji,jj) = ( zmasst(ji,jj ) * wght(ji,jj,2,2) + zmasst(ji-1,jj ) * wght(ji,jj,1,2) &
193	& + zmasst(ji,jj-1) * wght(ji,jj,2,1) + zmasst(ji-1,jj-1) * wght(ji,jj,1,1) ) * zusw
194	zcorl(ji,jj) = zmass(ji,jj) &
195	& ( ff_t(ji,jj ) wght(ji,jj,2,2) + ff_t(ji-1,jj )*wght(ji,jj,1,2) &
196	& + ff_t(ji,jj-1) * wght(ji,jj,2,1) + ff_t(ji-1,jj-1)wght(ji,jj,1,1) ) zusw
197
198	! Wind stress.
199	! always provide stress at I-point
200	ztagnx = ( zi1(ji,jj ) * wght(ji,jj,2,2) + zi1(ji-1,jj ) * wght(ji,jj,1,2) &
201	& + zi1(ji,jj-1) * wght(ji,jj,2,1) + zi1(ji-1,jj-1) * wght(ji,jj,1,1) ) * zusw * utau_ice(ji,jj)
202	ztagny = ( zi2(ji,jj ) * wght(ji,jj,2,2) + zi2(ji-1,jj ) * wght(ji,jj,1,2) &
203	& + zi2(ji,jj-1) * wght(ji,jj,2,1) + zi2(ji-1,jj-1) * wght(ji,jj,1,1) ) * zusw * vtau_ice(ji,jj)
204
205	! Gradient of ice strength
206	zgphsx = ( alambd(ji,jj,2,2,2,1) - alambd(ji,jj,2,1,2,1) ) * zpresh(ji ,jj-1) &
207	& + ( alambd(ji,jj,2,2,2,2) - alambd(ji,jj,2,1,2,2) ) * zpresh(ji ,jj ) &
208	& - ( alambd(ji,jj,2,2,1,1) + alambd(ji,jj,2,1,1,1) ) * zpresh(ji-1,jj-1) &
209	& - ( alambd(ji,jj,2,2,1,2) + alambd(ji,jj,2,1,1,2) ) * zpresh(ji-1,jj )
210
211	zgphsy = - ( alambd(ji,jj,1,1,2,1) + alambd(ji,jj,1,2,2,1) ) * zpresh(ji ,jj-1) &
212	& - ( alambd(ji,jj,1,1,1,1) + alambd(ji,jj,1,2,1,1) ) * zpresh(ji-1,jj-1) &
213	& + ( alambd(ji,jj,1,1,2,2) - alambd(ji,jj,1,2,2,2) ) * zpresh(ji ,jj ) &
214	& + ( alambd(ji,jj,1,1,1,2) - alambd(ji,jj,1,2,1,2) ) * zpresh(ji-1,jj )
215
216	! Gradient of the sea surface height
217	zgsshx = ( (zpice(ji ,jj ) - zpice(ji-1,jj ))/e1u(ji-1,jj ) &
218	& + (zpice(ji ,jj-1) - zpice(ji-1,jj-1))/e1u(ji-1,jj-1) ) * 0.5_wp
219	zgsshy = ( (zpice(ji ,jj ) - zpice(ji ,jj-1))/e2v(ji ,jj-1) &
220	& + (zpice(ji-1,jj ) - zpice(ji-1,jj-1))/e2v(ji-1,jj-1) ) * 0.5_wp
221
222	! Computation of the velocity field taking into account the ice-ice interaction.
223	! Terms that are independent of the ice velocity field.
224	za1ct(ji,jj) = ztagnx - zmass(ji,jj) * grav * zgsshx - zgphsx
225	za2ct(ji,jj) = ztagny - zmass(ji,jj) * grav * zgsshy - zgphsy
226	END DO
227	END DO
228
229
230	! SOLUTION OF THE MOMENTUM EQUATION.
231	!------------------------------------------
232	! ! ==================== !
233	DO iter = 1 , 2 * nbiter ! loop over iter !
234	! ! ==================== !
235	zindu = MOD( iter , 2 )
236	zusdtp = ( zindu * 2._wp + ( 1._wp - zindu ) * 1._wp ) * REAL( nbiter ) / rdt_ice
237
238	! Computation of free drift field for free slip boundary conditions.
239
240	DO jj = k_j1, k_jpj-1
241	DO ji = 1, fs_jpim1
242	!- Rate of strain tensor.
243	zt11 = akappa(ji,jj,1,1) * ( zu_a(ji+1,jj) + zu_a(ji+1,jj+1) - zu_a(ji,jj ) - zu_a(ji ,jj+1) ) &
244	& + akappa(ji,jj,1,2) * ( zv_a(ji+1,jj) + zv_a(ji+1,jj+1) + zv_a(ji,jj ) + zv_a(ji ,jj+1) )
245	zt12 = - akappa(ji,jj,2,2) * ( zu_a(ji ,jj) + zu_a(ji+1,jj ) - zu_a(ji,jj+1) - zu_a(ji+1,jj+1) ) &
246	& - akappa(ji,jj,2,1) * ( zv_a(ji ,jj) + zv_a(ji+1,jj ) + zv_a(ji,jj+1) + zv_a(ji+1,jj+1) )
247	zt22 = - akappa(ji,jj,2,2) * ( zv_a(ji ,jj) + zv_a(ji+1,jj ) - zv_a(ji,jj+1) - zv_a(ji+1,jj+1) ) &
248	& + akappa(ji,jj,2,1) * ( zu_a(ji ,jj) + zu_a(ji+1,jj ) + zu_a(ji,jj+1) + zu_a(ji+1,jj+1) )
249	zt21 = akappa(ji,jj,1,1) * ( zv_a(ji+1,jj) + zv_a(ji+1,jj+1) - zv_a(ji,jj ) - zv_a(ji ,jj+1) ) &
250	& - akappa(ji,jj,1,2) * ( zu_a(ji+1,jj) + zu_a(ji+1,jj+1) + zu_a(ji,jj ) + zu_a(ji ,jj+1) )
251
252	!- Rate of strain tensor.
253	zdgp = zt11 + zt22
254	zdgi = zt12 + zt21
255	ztrace2 = zdgp * zdgp
256	zdeter = zt11 * zt22 - 0.25_wp * zdgi * zdgi
257
258	! Creep limit depends on the size of the grid.
259	zdelta = MAX( SQRT( ztrace2 + ( ztrace2 - 4._wp * zdeter ) * usecc2 ), rn_creepl)
260
261	!- Computation of viscosities.
262	zviszeta(ji,jj) = MAX( zpresh(ji,jj) / zdelta, etamn )
263	zviseta (ji,jj) = zviszeta(ji,jj) * usecc2
264	END DO
265	END DO
266
267	!- Determination of zc1u, zc2u, zc1v and zc2v.
268	DO jj = k_j1+1, k_jpj-1
269	DO ji = 2, fs_jpim1 ! NO vector opt.
270	!* zc1u , zc2v
271	zvis11 = 2._wp * zviseta (ji-1,jj-1) + dm
272	zvis12 = zviseta (ji-1,jj-1) + dm
273	zvis21 = zviseta (ji-1,jj-1)
274	zvis22 = zviszeta(ji-1,jj-1) - zviseta(ji-1,jj-1)
275	zdiag = zvis22 * ( akappa(ji-1,jj-1,1,1) + akappa(ji-1,jj-1,2,1) )
276	zs11_11 = zvis11 * akappa(ji-1,jj-1,1,1) + zdiag
277	zs12_11 = zvis12 * akappa(ji-1,jj-1,2,2) - zvis21 * akappa(ji-1,jj-1,1,2)
278	zs21_11 = -zvis12 * akappa(ji-1,jj-1,1,2) + zvis21 * akappa(ji-1,jj-1,2,2)
279	zs22_11 = zvis11 * akappa(ji-1,jj-1,2,1) + zdiag
280
281	zvis11 = 2._wp * zviseta (ji,jj-1) + dm
282	zvis22 = zviszeta(ji,jj-1) - zviseta(ji,jj-1)
283	zvis12 = zviseta (ji,jj-1) + dm
284	zvis21 = zviseta (ji,jj-1)
285	zdiag = zvis22 * ( -akappa(ji,jj-1,1,1) + akappa(ji,jj-1,2,1) )
286	zs11_21 = -zvis11 * akappa(ji,jj-1,1,1) + zdiag
287	zs12_21 = zvis12 * akappa(ji,jj-1,2,2) - zvis21 * akappa(ji,jj-1,1,2)
288	zs22_21 = zvis11 * akappa(ji,jj-1,2,1) + zdiag
289	zs21_21 = -zvis12 * akappa(ji,jj-1,1,2) + zvis21 * akappa(ji,jj-1,2,2)
290
291	zvis11 = 2._wp * zviseta (ji-1,jj) + dm
292	zvis22 = zviszeta(ji-1,jj) - zviseta(ji-1,jj)
293	zvis12 = zviseta (ji-1,jj) + dm
294	zvis21 = zviseta (ji-1,jj)
295	zdiag = zvis22 * ( akappa(ji-1,jj,1,1) + akappa(ji-1,jj,2,1) )
296	zs11_12 = zvis11 * akappa(ji-1,jj,1,1) + zdiag
297	zs12_12 = -zvis12 * akappa(ji-1,jj,2,2) - zvis21 * akappa(ji-1,jj,1,2)
298	zs22_12 = zvis11 * akappa(ji-1,jj,2,1) + zdiag
299	zs21_12 = -zvis12 * akappa(ji-1,jj,1,2) - zvis21 * akappa(ji-1,jj,2,2)
300
301	zvis11 = 2._wp * zviseta (ji,jj) + dm
302	zvis22 = zviszeta(ji,jj) - zviseta(ji,jj)
303	zvis12 = zviseta (ji,jj) + dm
304	zvis21 = zviseta (ji,jj)
305	zdiag = zvis22 * ( -akappa(ji,jj,1,1) + akappa(ji,jj,2,1) )
306	zs11_22 = -zvis11 * akappa(ji,jj,1,1) + zdiag
307	zs12_22 = -zvis12 * akappa(ji,jj,2,2) - zvis21 * akappa(ji,jj,1,2)
308	zs22_22 = zvis11 * akappa(ji,jj,2,1) + zdiag
309	zs21_22 = -zvis12 * akappa(ji,jj,1,2) - zvis21 * akappa(ji,jj,2,2)
310
311	zc1u(ji,jj) = + alambd(ji,jj,2,2,2,1) * zs11_21 + alambd(ji,jj,2,2,2,2) * zs11_22 &
312	& - alambd(ji,jj,2,2,1,1) * zs11_11 - alambd(ji,jj,2,2,1,2) * zs11_12 &
313	& - alambd(ji,jj,1,1,2,1) * zs12_21 - alambd(ji,jj,1,1,1,1) * zs12_11 &
314	& + alambd(ji,jj,1,1,2,2) * zs12_22 + alambd(ji,jj,1,1,1,2) * zs12_12 &
315	& + alambd(ji,jj,1,2,1,1) * zs21_11 + alambd(ji,jj,1,2,2,1) * zs21_21 &
316	& + alambd(ji,jj,1,2,1,2) * zs21_12 + alambd(ji,jj,1,2,2,2) * zs21_22 &
317	& - alambd(ji,jj,2,1,1,1) * zs22_11 - alambd(ji,jj,2,1,2,1) * zs22_21 &
318	& - alambd(ji,jj,2,1,1,2) * zs22_12 - alambd(ji,jj,2,1,2,2) * zs22_22
319
320	zc2u(ji,jj) = + alambd(ji,jj,2,2,2,1) * zs21_21 + alambd(ji,jj,2,2,2,2) * zs21_22 &
321	& - alambd(ji,jj,2,2,1,1) * zs21_11 - alambd(ji,jj,2,2,1,2) * zs21_12 &
322	& - alambd(ji,jj,1,1,2,1) * zs22_21 - alambd(ji,jj,1,1,1,1) * zs22_11 &
323	& + alambd(ji,jj,1,1,2,2) * zs22_22 + alambd(ji,jj,1,1,1,2) * zs22_12 &
324	& - alambd(ji,jj,1,2,1,1) * zs11_11 - alambd(ji,jj,1,2,2,1) * zs11_21 &
325	& - alambd(ji,jj,1,2,1,2) * zs11_12 - alambd(ji,jj,1,2,2,2) * zs11_22 &
326	& + alambd(ji,jj,2,1,1,1) * zs12_11 + alambd(ji,jj,2,1,2,1) * zs12_21 &
327	& + alambd(ji,jj,2,1,1,2) * zs12_12 + alambd(ji,jj,2,1,2,2) * zs12_22
328
329	!* zc1v , zc2v.
330	zvis11 = 2._wp * zviseta (ji-1,jj-1) + dm
331	zvis22 = zviszeta(ji-1,jj-1) - zviseta(ji-1,jj-1)
332	zvis12 = zviseta (ji-1,jj-1) + dm
333	zvis21 = zviseta (ji-1,jj-1)
334	zdiag = zvis22 * ( akappa(ji-1,jj-1,1,2) + akappa(ji-1,jj-1,2,2) )
335	zs11_11 = zvis11 * akappa(ji-1,jj-1,1,2) + zdiag
336	zs12_11 = -zvis12 * akappa(ji-1,jj-1,2,1) + zvis21 * akappa(ji-1,jj-1,1,1)
337	zs22_11 = zvis11 * akappa(ji-1,jj-1,2,2) + zdiag
338	zs21_11 = zvis12 * akappa(ji-1,jj-1,1,1) - zvis21 * akappa(ji-1,jj-1,2,1)
339
340	zvis11 = 2._wp * zviseta (ji,jj-1) + dm
341	zvis22 = zviszeta(ji,jj-1) - zviseta(ji,jj-1)
342	zvis12 = zviseta (ji,jj-1) + dm
343	zvis21 = zviseta (ji,jj-1)
344	zdiag = zvis22 * ( akappa(ji,jj-1,1,2) + akappa(ji,jj-1,2,2) )
345	zs11_21 = zvis11 * akappa(ji,jj-1,1,2) + zdiag
346	zs12_21 = -zvis12 * akappa(ji,jj-1,2,1) - zvis21 * akappa(ji,jj-1,1,1)
347	zs22_21 = zvis11 * akappa(ji,jj-1,2,2) + zdiag
348	zs21_21 = -zvis12 * akappa(ji,jj-1,1,1) - zvis21 * akappa(ji,jj-1,2,1)
349
350	zvis11 = 2._wp * zviseta (ji-1,jj) + dm
351	zvis22 = zviszeta(ji-1,jj) - zviseta(ji-1,jj)
352	zvis12 = zviseta (ji-1,jj) + dm
353	zvis21 = zviseta (ji-1,jj)
354	zdiag = zvis22 * ( akappa(ji-1,jj,1,2) - akappa(ji-1,jj,2,2) )
355	zs11_12 = zvis11 * akappa(ji-1,jj,1,2) + zdiag
356	zs12_12 = -zvis12 * akappa(ji-1,jj,2,1) + zvis21 * akappa(ji-1,jj,1,1)
357	zs22_12 = -zvis11 * akappa(ji-1,jj,2,2) + zdiag
358	zs21_12 = zvis12 * akappa(ji-1,jj,1,1) - zvis21 * akappa(ji-1,jj,2,1)
359
360	zvis11 = 2._wp * zviseta (ji,jj) + dm
361	zvis22 = zviszeta(ji,jj) - zviseta(ji,jj)
362	zvis12 = zviseta (ji,jj) + dm
363	zvis21 = zviseta (ji,jj)
364	zdiag = zvis22 * ( akappa(ji,jj,1,2) - akappa(ji,jj,2,2) )
365	zs11_22 = zvis11 * akappa(ji,jj,1,2) + zdiag
366	zs12_22 = -zvis12 * akappa(ji,jj,2,1) - zvis21 * akappa(ji,jj,1,1)
367	zs22_22 = -zvis11 * akappa(ji,jj,2,2) + zdiag
368	zs21_22 = -zvis12 * akappa(ji,jj,1,1) - zvis21 * akappa(ji,jj,2,1)
369
370	zc1v(ji,jj) = + alambd(ji,jj,2,2,2,1) * zs11_21 + alambd(ji,jj,2,2,2,2) * zs11_22 &
371	& - alambd(ji,jj,2,2,1,1) * zs11_11 - alambd(ji,jj,2,2,1,2) * zs11_12 &
372	& - alambd(ji,jj,1,1,2,1) * zs12_21 - alambd(ji,jj,1,1,1,1) * zs12_11 &
373	& + alambd(ji,jj,1,1,2,2) * zs12_22 + alambd(ji,jj,1,1,1,2) * zs12_12 &
374	& + alambd(ji,jj,1,2,1,1) * zs21_11 + alambd(ji,jj,1,2,2,1) * zs21_21 &
375	& + alambd(ji,jj,1,2,1,2) * zs21_12 + alambd(ji,jj,1,2,2,2) * zs21_22 &
376	& - alambd(ji,jj,2,1,1,1) * zs22_11 - alambd(ji,jj,2,1,2,1) * zs22_21 &
377	& - alambd(ji,jj,2,1,1,2) * zs22_12 - alambd(ji,jj,2,1,2,2) * zs22_22
378
379	zc2v(ji,jj) = + alambd(ji,jj,2,2,2,1) * zs21_21 + alambd(ji,jj,2,2,2,2) * zs21_22 &
380	& - alambd(ji,jj,2,2,1,1) * zs21_11 - alambd(ji,jj,2,2,1,2) * zs21_12 &
381	& - alambd(ji,jj,1,1,2,1) * zs22_21 - alambd(ji,jj,1,1,1,1) * zs22_11 &
382	& + alambd(ji,jj,1,1,2,2) * zs22_22 + alambd(ji,jj,1,1,1,2) * zs22_12 &
383	& - alambd(ji,jj,1,2,1,1) * zs11_11 - alambd(ji,jj,1,2,2,1) * zs11_21 &
384	& - alambd(ji,jj,1,2,1,2) * zs11_12 - alambd(ji,jj,1,2,2,2) * zs11_22 &
385	& + alambd(ji,jj,2,1,1,1) * zs12_11 + alambd(ji,jj,2,1,2,1) * zs12_21 &
386	& + alambd(ji,jj,2,1,1,2) * zs12_12 + alambd(ji,jj,2,1,2,2) * zs12_22
387	END DO
388	END DO
389
390	! GAUSS-SEIDEL method
391	! ! ================ !
392	iflag: DO jter = 1 , nbitdr ! Relaxation !
393	! ! ================ !
394	DO jj = k_j1+1, k_jpj-1
395	DO ji = 2, fs_jpim1 ! NO vector opt.
396	!
397	ze11 = akappa(ji,jj-1,1,1) * zu_a(ji+1,jj) + akappa(ji,jj-1,1,2) * zv_a(ji+1,jj)
398	ze12 = + akappa(ji,jj-1,2,2) * zu_a(ji+1,jj) - akappa(ji,jj-1,2,1) * zv_a(ji+1,jj)
399	ze22 = + akappa(ji,jj-1,2,2) * zv_a(ji+1,jj) + akappa(ji,jj-1,2,1) * zu_a(ji+1,jj)
400	ze21 = akappa(ji,jj-1,1,1) * zv_a(ji+1,jj) - akappa(ji,jj-1,1,2) * zu_a(ji+1,jj)
401	zvis11 = 2._wp * zviseta (ji,jj-1) + dm
402	zvis22 = zviszeta(ji,jj-1) - zviseta(ji,jj-1)
403	zvis12 = zviseta (ji,jj-1) + dm
404	zvis21 = zviseta (ji,jj-1)
405	zdiag = zvis22 * ( ze11 + ze22 )
406	zs11_21 = zvis11 * ze11 + zdiag
407	zs12_21 = zvis12 * ze12 + zvis21 * ze21
408	zs22_21 = zvis11 * ze22 + zdiag
409	zs21_21 = zvis12 * ze21 + zvis21 * ze12
410
411	ze11 = akappa(ji-1,jj,1,1) * ( zu_a(ji ,jj+1) - zu_a(ji-1,jj+1) ) &
412	& + akappa(ji-1,jj,1,2) * ( zv_a(ji ,jj+1) + zv_a(ji-1,jj+1) )
413	ze12 = + akappa(ji-1,jj,2,2) * ( zu_a(ji-1,jj+1) + zu_a(ji ,jj+1) ) &
414	& - akappa(ji-1,jj,2,1) * ( zv_a(ji-1,jj+1) + zv_a(ji ,jj+1) )
415	ze22 = + akappa(ji-1,jj,2,2) * ( zv_a(ji-1,jj+1) + zv_a(ji ,jj+1) ) &
416	& + akappa(ji-1,jj,2,1) * ( zu_a(ji-1,jj+1) + zu_a(ji ,jj+1) )
417	ze21 = akappa(ji-1,jj,1,1) * ( zv_a(ji ,jj+1) - zv_a(ji-1,jj+1) ) &
418	& - akappa(ji-1,jj,1,2) * ( zu_a(ji ,jj+1) + zu_a(ji-1,jj+1) )
419	zvis11 = 2._wp * zviseta (ji-1,jj) + dm
420	zvis22 = zviszeta(ji-1,jj) - zviseta(ji-1,jj)
421	zvis12 = zviseta (ji-1,jj) + dm
422	zvis21 = zviseta (ji-1,jj)
423	zdiag = zvis22 * ( ze11 + ze22 )
424	zs11_12 = zvis11 * ze11 + zdiag
425	zs12_12 = zvis12 * ze12 + zvis21 * ze21
426	zs22_12 = zvis11 * ze22 + zdiag
427	zs21_12 = zvis12 * ze21 + zvis21 * ze12
428
429	ze11 = akappa(ji,jj,1,1) * ( zu_a(ji+1,jj) + zu_a(ji+1,jj+1) - zu_a(ji ,jj+1) ) &
430	& + akappa(ji,jj,1,2) * ( zv_a(ji+1,jj) + zv_a(ji+1,jj+1) + zv_a(ji ,jj+1) )
431	ze12 = - akappa(ji,jj,2,2) * ( zu_a(ji+1,jj) - zu_a(ji ,jj+1) - zu_a(ji+1,jj+1) ) &
432	& - akappa(ji,jj,2,1) * ( zv_a(ji+1,jj) + zv_a(ji ,jj+1) + zv_a(ji+1,jj+1) )
433	ze22 = - akappa(ji,jj,2,2) * ( zv_a(ji+1,jj) - zv_a(ji ,jj+1) - zv_a(ji+1,jj+1) ) &
434	& + akappa(ji,jj,2,1) * ( zu_a(ji+1,jj) + zu_a(ji ,jj+1) + zu_a(ji+1,jj+1) )
435	ze21 = akappa(ji,jj,1,1) * ( zv_a(ji+1,jj) + zv_a(ji+1,jj+1) - zv_a(ji ,jj+1) ) &
436	& - akappa(ji,jj,1,2) * ( zu_a(ji+1,jj) + zu_a(ji+1,jj+1) + zu_a(ji ,jj+1) )
437	zvis11 = 2._wp * zviseta (ji,jj) + dm
438	zvis22 = zviszeta(ji,jj) - zviseta(ji,jj)
439	zvis12 = zviseta (ji,jj) + dm
440	zvis21 = zviseta (ji,jj)
441	zdiag = zvis22 * ( ze11 + ze22 )
442	zs11_22 = zvis11 * ze11 + zdiag
443	zs12_22 = zvis12 * ze12 + zvis21 * ze21
444	zs22_22 = zvis11 * ze22 + zdiag
445	zs21_22 = zvis12 * ze21 + zvis21 * ze12
446
447	! 2nd part
448	ze11 = akappa(ji-1,jj-1,1,1) * ( zu_a(ji ,jj-1) - zu_a(ji-1,jj-1) - zu_a(ji-1,jj) ) &
449	& + akappa(ji-1,jj-1,1,2) * ( zv_a(ji ,jj-1) + zv_a(ji-1,jj-1) + zv_a(ji-1,jj) )
450	ze12 = - akappa(ji-1,jj-1,2,2) * ( zu_a(ji-1,jj-1) + zu_a(ji ,jj-1) - zu_a(ji-1,jj) ) &
451	& - akappa(ji-1,jj-1,2,1) * ( zv_a(ji-1,jj-1) + zv_a(ji ,jj-1) + zv_a(ji-1,jj) )
452	ze22 = - akappa(ji-1,jj-1,2,2) * ( zv_a(ji-1,jj-1) + zv_a(ji ,jj-1) - zv_a(ji-1,jj) ) &
453	& + akappa(ji-1,jj-1,2,1) * ( zu_a(ji-1,jj-1) + zu_a(ji ,jj-1) + zu_a(ji-1,jj) )
454	ze21 = akappa(ji-1,jj-1,1,1) * ( zv_a(ji ,jj-1) - zv_a(ji-1,jj-1) - zv_a(ji-1,jj) ) &
455	& - akappa(ji-1,jj-1,1,2) * ( zu_a(ji ,jj-1) + zu_a(ji-1,jj-1) + zu_a(ji-1,jj) )
456	zvis11 = 2._wp * zviseta (ji-1,jj-1) + dm
457	zvis22 = zviszeta(ji-1,jj-1) - zviseta(ji-1,jj-1)
458	zvis12 = zviseta (ji-1,jj-1) + dm
459	zvis21 = zviseta (ji-1,jj-1)
460	zdiag = zvis22 * ( ze11 + ze22 )
461	zs11_11 = zvis11 * ze11 + zdiag
462	zs12_11 = zvis12 * ze12 + zvis21 * ze21
463	zs22_11 = zvis11 * ze22 + zdiag
464	zs21_11 = zvis12 * ze21 + zvis21 * ze12
465
466	ze11 = akappa(ji,jj-1,1,1) * ( zu_a(ji+1,jj-1) - zu_a(ji ,jj-1) ) &
467	& + akappa(ji,jj-1,1,2) * ( zv_a(ji+1,jj-1) + zv_a(ji ,jj-1) )
468	ze12 = - akappa(ji,jj-1,2,2) * ( zu_a(ji ,jj-1) + zu_a(ji+1,jj-1) ) &
469	& - akappa(ji,jj-1,2,1) * ( zv_a(ji ,jj-1) + zv_a(ji+1,jj-1) )
470	ze22 = - akappa(ji,jj-1,2,2) * ( zv_a(ji ,jj-1) + zv_a(ji+1,jj-1) ) &
471	& + akappa(ji,jj-1,2,1) * ( zu_a(ji ,jj-1) + zu_a(ji+1,jj-1) )
472	ze21 = akappa(ji,jj-1,1,1) * ( zv_a(ji+1,jj-1) - zv_a(ji ,jj-1) ) &
473	& - akappa(ji,jj-1,1,2) * ( zu_a(ji+1,jj-1) + zu_a(ji ,jj-1) )
474	zvis11 = 2._wp * zviseta (ji,jj-1) + dm
475	zvis22 = zviszeta(ji,jj-1) - zviseta(ji,jj-1)
476	zvis12 = zviseta (ji,jj-1) + dm
477	zvis21 = zviseta (ji,jj-1)
478	zdiag = zvis22 * ( ze11 + ze22 )
479	zs11_21 = zs11_21 + zvis11 * ze11 + zdiag
480	zs12_21 = zs12_21 + zvis12 * ze12 + zvis21 * ze21
481	zs22_21 = zs22_21 + zvis11 * ze22 + zdiag
482	zs21_21 = zs21_21 + zvis12 * ze21 + zvis21 * ze12
483
484	ze11 = - akappa(ji-1,jj,1,1) * zu_a(ji-1,jj) + akappa(ji-1,jj,1,2) * zv_a(ji-1,jj)
485	ze12 = - akappa(ji-1,jj,2,2) * zu_a(ji-1,jj) - akappa(ji-1,jj,2,1) * zv_a(ji-1,jj)
486	ze22 = - akappa(ji-1,jj,2,2) * zv_a(ji-1,jj) + akappa(ji-1,jj,2,1) * zu_a(ji-1,jj)
487	ze21 = - akappa(ji-1,jj,1,1) * zv_a(ji-1,jj) - akappa(ji-1,jj,1,2) * zu_a(ji-1,jj)
488	zvis11 = 2._wp * zviseta (ji-1,jj) + dm
489	zvis22 = zviszeta(ji-1,jj) - zviseta(ji-1,jj)
490	zvis12 = zviseta (ji-1,jj) + dm
491	zvis21 = zviseta (ji-1,jj)
492	zdiag = zvis22 * ( ze11 + ze22 )
493	zs11_12 = zs11_12 + zvis11 * ze11 + zdiag
494	zs12_12 = zs12_12 + zvis12 * ze12 + zvis21 * ze21
495	zs22_12 = zs22_12 + zvis11 * ze22 + zdiag
496	zs21_12 = zs21_12 + zvis12 * ze21 + zvis21 * ze12
497
498	zd1 = + alambd(ji,jj,2,2,2,1) * zs11_21 + alambd(ji,jj,2,2,2,2) * zs11_22 &
499	& - alambd(ji,jj,2,2,1,1) * zs11_11 - alambd(ji,jj,2,2,1,2) * zs11_12 &
500	& - alambd(ji,jj,1,1,2,1) * zs12_21 - alambd(ji,jj,1,1,1,1) * zs12_11 &
501	& + alambd(ji,jj,1,1,2,2) * zs12_22 + alambd(ji,jj,1,1,1,2) * zs12_12 &
502	& + alambd(ji,jj,1,2,1,1) * zs21_11 + alambd(ji,jj,1,2,2,1) * zs21_21 &
503	& + alambd(ji,jj,1,2,1,2) * zs21_12 + alambd(ji,jj,1,2,2,2) * zs21_22 &
504	& - alambd(ji,jj,2,1,1,1) * zs22_11 - alambd(ji,jj,2,1,2,1) * zs22_21 &
505	& - alambd(ji,jj,2,1,1,2) * zs22_12 - alambd(ji,jj,2,1,2,2) * zs22_22
506
507	zd2 = + alambd(ji,jj,2,2,2,1) * zs21_21 + alambd(ji,jj,2,2,2,2) * zs21_22 &
508	& - alambd(ji,jj,2,2,1,1) * zs21_11 - alambd(ji,jj,2,2,1,2) * zs21_12 &
509	& - alambd(ji,jj,1,1,2,1) * zs22_21 - alambd(ji,jj,1,1,1,1) * zs22_11 &
510	& + alambd(ji,jj,1,1,2,2) * zs22_22 + alambd(ji,jj,1,1,1,2) * zs22_12 &
511	& - alambd(ji,jj,1,2,1,1) * zs11_11 - alambd(ji,jj,1,2,2,1) * zs11_21 &
512	& - alambd(ji,jj,1,2,1,2) * zs11_12 - alambd(ji,jj,1,2,2,2) * zs11_22 &
513	& + alambd(ji,jj,2,1,1,1) * zs12_11 + alambd(ji,jj,2,1,2,1) * zs12_21 &
514	& + alambd(ji,jj,2,1,1,2) * zs12_12 + alambd(ji,jj,2,1,2,2) * zs12_22
515
516	zur = zu_a(ji,jj) - u_oce(ji,jj)
517	zvr = zv_a(ji,jj) - v_oce(ji,jj)
518	!!!!
519	zmod = SQRT( zurzur + zvrzvr ) * ( 1._wp - zfrld(ji,jj) )
520	za = rhoco * zmod
521	!!!!
522	!!gm chg resul za = rhoco * SQRT( zurzur + zvrzvr ) * ( 1._wp - zfrld(ji,jj) )
523	zac = za * cangvg
524	zmpzas = alpha * zcorl(ji,jj) + za * zsang(ji,jj)
525	zmassdt = zusdtp * zmass(ji,jj)
526	zcorlal = ( 1._wp - alpha ) * zcorl(ji,jj)
527
528	za1 = zmassdt * zu0(ji,jj) + zcorlal * zv0(ji,jj) + za1ct(ji,jj) &
529	& + za * ( cangvg * u_oce(ji,jj) - zsang(ji,jj) * v_oce(ji,jj) )
530	za2 = zmassdt * zv0(ji,jj) - zcorlal * zu0(ji,jj) + za2ct(ji,jj) &
531	& + za * ( cangvg * v_oce(ji,jj) + zsang(ji,jj) * u_oce(ji,jj) )
532	zb1 = zmassdt + zac - zc1u(ji,jj)
533	zb2 = zmpzas - zc2u(ji,jj)
534	zc1 = zmpzas + zc1v(ji,jj)
535	zc2 = zmassdt + zac - zc2v(ji,jj)
536	zdeter = zc1 * zb2 + zc2 * zb1
537	zden = SIGN( rone, zdeter) / MAX( epsd , ABS( zdeter ) )
538	zunw = ( ( za1 + zd1 ) * zc2 + ( za2 + zd2 ) * zc1 ) * zden
539	zvnw = ( ( za2 + zd2 ) * zb1 - ( za1 + zd1 ) * zb2 ) * zden
540	zmask = ( 1._wp - MAX( rzero, SIGN( rone , 1._wp - zmass(ji,jj) ) ) ) * tmu(ji,jj)
541
542	zu_n(ji,jj) = ( zu_a(ji,jj) + om * ( zunw - zu_a(ji,jj) ) * tmu(ji,jj) ) * zmask
543	zv_n(ji,jj) = ( zv_a(ji,jj) + om * ( zvnw - zv_a(ji,jj) ) * tmu(ji,jj) ) * zmask
544	END DO
545	END DO
546
547	CALL lbc_lnk( zu_n(:,1:jpj), 'I', -1. )
548	CALL lbc_lnk( zv_n(:,1:jpj), 'I', -1. )
549
550	#if defined key_agrif
551	! copy the boundary value from u_ice_nst and v_ice_nst to u_ice and v_ice
552	! before next interations
553	CALL agrif_rhg_lim2(zu_n,zv_n)
554	#endif
555
556	! Test of Convergence
557	DO jj = k_j1+1 , k_jpj-1
558	zresr(:,jj) = MAX( ABS( zu_a(:,jj) - zu_n(:,jj) ) , ABS( zv_a(:,jj) - zv_n(:,jj) ) )
559	END DO
560	zresm = MAXVAL( zresr(1:jpi,k_j1+1:k_jpj-1) )
561	!!!! this should be faster on scalar processor
562	! zresm = MAXVAL( MAX( ABS( zu_a(1:jpi,k_j1+1:k_jpj-1) - zu_n(1:jpi,k_j1+1:k_jpj-1) ), &
563	! & ABS( zv_a(1:jpi,k_j1+1:k_jpj-1) - zv_n(1:jpi,k_j1+1:k_jpj-1) ) ) )
564	!!!!
565	IF( lk_mpp ) CALL mpp_max( zresm ) ! max over the global domain
566
567	DO jj = k_j1, k_jpj
568	zu_a(:,jj) = zu_n(:,jj)
569	zv_a(:,jj) = zv_n(:,jj)
570	END DO
571
572	IF( zresm <= resl ) EXIT iflag
573
574	! ! ================ !
575	END DO iflag ! end Relaxation !
576	! ! ================ !
577
578	IF( zindu == 0 ) THEN ! even iteration
579	DO jj = k_j1 , k_jpj-1
580	zu0(:,jj) = zu_a(:,jj)
581	zv0(:,jj) = zv_a(:,jj)
582	END DO
583	ENDIF
584	! ! ==================== !
585	END DO ! end loop over iter !
586	! ! ==================== !
587
588	u_ice(:,:) = zu_a(:,1:jpj)
589	v_ice(:,:) = zv_a(:,1:jpj)
590
591	IF(ln_ctl) THEN
592	WRITE(charout,FMT="('lim_rhg : res =',D23.16, ' iter =',I4)") zresm, jter
593	CALL prt_ctl_info(charout)
594	CALL prt_ctl(tab2d_1=u_ice, clinfo1=' lim_rhg : u_ice :', tab2d_2=v_ice, clinfo2=' v_ice :')
595	ENDIF
596
597
598	END SUBROUTINE lim_rhg_2
599
600	#else
601	!!----------------------------------------------------------------------
602	!! Default option Dummy module NO VP & LIM-2 sea-ice model
603	!!----------------------------------------------------------------------
604	CONTAINS
605	SUBROUTINE lim_rhg_2( k1 , k2 ) ! Dummy routine
606	WRITE(,) 'lim_rhg_2: You should not have seen this print! error?', k1, k2
607	END SUBROUTINE lim_rhg_2
608	#endif
609
610	!!==============================================================================
611	END MODULE limrhg_2

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source: branches/2017/dev_r7881_no_wrk_alloc/NEMOGCM/NEMO/LIM_SRC_2/limrhg_2.F90 @ 7910

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