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
161
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
192
193
194
195
196
197
198
199
200
MODULE dynspg_ts
!! Includes ROMS wd scheme with diagnostic outputs ; puu(:,:,:,Kmm) and puu(:,:,:,Krhs) updates are commented out !
!!======================================================================
!! *** MODULE dynspg_ts ***
!! Ocean dynamics: surface pressure gradient trend, split-explicit scheme
!!======================================================================
!! History : 1.0 ! 2004-12 (L. Bessieres, G. Madec) Original code
!! - ! 2005-11 (V. Garnier, G. Madec) optimization
!! - ! 2006-08 (S. Masson) distributed restart using iom
!! 2.0 ! 2007-07 (D. Storkey) calls to BDY routines
!! - ! 2008-01 (R. Benshila) change averaging method
!! 3.2 ! 2009-07 (R. Benshila, G. Madec) Complete revisit associated to vvl reactivation
!! 3.3 ! 2010-09 (D. Storkey, E. O'Dea) update for BDY for Shelf configurations
!! 3.3 ! 2011-03 (R. Benshila, R. Hordoir, P. Oddo) update calculation of ub_b
!! 3.5 ! 2013-07 (J. Chanut) Switch to Forward-backward time stepping
!! 3.6 ! 2013-11 (A. Coward) Update for z-tilde compatibility
!! 3.7 ! 2015-11 (J. Chanut) free surface simplification
!! - ! 2016-12 (G. Madec, E. Clementi) update for Stoke-Drift divergence
!! 4.0 ! 2017-05 (G. Madec) drag coef. defined at t-point (zdfdrg.F90)
!!---------------------------------------------------------------------
!!----------------------------------------------------------------------
!! dyn_spg_ts : compute surface pressure gradient trend using a time-splitting scheme
!! dyn_spg_ts_init: initialisation of the time-splitting scheme
!! ts_wgt : set time-splitting weights for temporal averaging (or not)
!! ts_rst : read/write time-splitting fields in restart file
!!----------------------------------------------------------------------
USE oce ! ocean dynamics and tracers
USE dom_oce ! ocean space and time domain
USE sbc_oce ! surface boundary condition: ocean
USE isf_oce ! ice shelf variable (fwfisf)
USE zdf_oce ! vertical physics: variables
USE zdfdrg ! vertical physics: top/bottom drag coef.
USE sbcapr ! surface boundary condition: atmospheric pressure
USE dynadv , ONLY: ln_dynadv_vec
USE dynvor ! vortivity scheme indicators
USE phycst ! physical constants
USE dynvor ! vorticity term
USE wet_dry ! wetting/drying flux limter
USE bdy_oce ! open boundary
USE bdyvol ! open boundary volume conservation
USE bdytides ! open boundary condition data
USE bdydyn2d ! open boundary conditions on barotropic variables
USE tide_mod !
USE sbcwave ! surface wave
#if defined key_agrif
USE agrif_oce_interp ! agrif
USE agrif_oce
#endif
#if defined key_asminc
USE asminc ! Assimilation increment
#endif
!
USE in_out_manager ! I/O manager
USE lib_mpp ! distributed memory computing library
USE lbclnk ! ocean lateral boundary conditions (or mpp link)
USE prtctl ! Print control
USE iom ! IOM library
USE restart ! only for lrst_oce
USE iom ! to remove
IMPLICIT NONE
PRIVATE
PUBLIC dyn_spg_ts ! called by dyn_spg
PUBLIC dyn_spg_ts_init ! - - dyn_spg_init
!! Time filtered arrays at baroclinic time step:
REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: un_adv , vn_adv !: Advection vel. at "now" barocl. step
!
INTEGER, SAVE :: icycle ! Number of barotropic sub-steps for each internal step nn_e <= 2.5 nn_e
REAL(wp),SAVE :: rDt_e ! Barotropic time step
!
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:) :: wgtbtp1, wgtbtp2 ! 1st & 2nd weights used in time filtering of barotropic fields
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: zwz ! ff_f/h at F points
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: ftnw, ftne ! triad of coriolis parameter
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: ftsw, ftse ! (only used with een vorticity scheme)
REAL(wp) :: r1_12 = 1._wp / 12._wp ! local ratios
REAL(wp) :: r1_8 = 0.125_wp !
REAL(wp) :: r1_4 = 0.25_wp !
REAL(wp) :: r1_2 = 0.5_wp !
!! * Substitutions
# include "do_loop_substitute.h90"
# include "domzgr_substitute.h90"
!!----------------------------------------------------------------------
!! NEMO/OCE 4.0 , NEMO Consortium (2018)
!! $Id: dynspg_ts.F90 15489 2021-11-10 09:18:39Z jchanut $
!! Software governed by the CeCILL license (see ./LICENSE)
!!----------------------------------------------------------------------
CONTAINS
INTEGER FUNCTION dyn_spg_ts_alloc()
!!----------------------------------------------------------------------
!! *** routine dyn_spg_ts_alloc ***
!!----------------------------------------------------------------------
INTEGER :: ierr(3)
!!----------------------------------------------------------------------
ierr(:) = 0
!
ALLOCATE( wgtbtp1(3*nn_e), wgtbtp2(3*nn_e), zwz(jpi,jpj), STAT=ierr(1) )
IF( ln_dynvor_een .OR. ln_dynvor_eeT ) &
& ALLOCATE( ftnw(jpi,jpj) , ftne(jpi,jpj) , ftsw(jpi,jpj) , ftse(jpi,jpj), STAT=ierr(2) )
!
ALLOCATE( un_adv(jpi,jpj), vn_adv(jpi,jpj) , STAT=ierr(3) )
!
dyn_spg_ts_alloc = MAXVAL( ierr(:) )
!
CALL mpp_sum( 'dynspg_ts', dyn_spg_ts_alloc )
IF( dyn_spg_ts_alloc /= 0 ) CALL ctl_stop( 'STOP', 'dyn_spg_ts_alloc: failed to allocate arrays' )
!
END FUNCTION dyn_spg_ts_alloc
SUBROUTINE dyn_spg_ts( kt, Kbb, Kmm, Krhs, puu, pvv, pssh, puu_b, pvv_b, Kaa, k_only_ADV )
!!----------------------------------------------------------------------
!!
!! ** Purpose : - Compute the now trend due to the explicit time stepping
!! of the quasi-linear barotropic system, and add it to the
!! general momentum trend.
!!
!! ** Method : - split-explicit schem (time splitting) :
!! Barotropic variables are advanced from internal time steps
!! "n" to "n+1" if ln_bt_fw=T
!! or from
!! "n-1" to "n+1" if ln_bt_fw=F
!! thanks to a generalized forward-backward time stepping (see ref. below).
!!
!! ** Action :
!! -Update the filtered free surface at step "n+1" : pssh(:,:,Kaa)
!! -Update filtered barotropic velocities at step "n+1" : puu_b(:,:,:,Kaa), vv_b(:,:,:,Kaa)
!! -Compute barotropic advective fluxes at step "n" : un_adv, vn_adv
!! These are used to advect tracers and are compliant with discrete
!! continuity equation taken at the baroclinic time steps. This
!! ensures tracers conservation.
!! - (puu(:,:,:,Krhs), pvv(:,:,:,Krhs)) momentum trend updated with barotropic component.
!!
!! References : Shchepetkin and McWilliams, Ocean Modelling, 2005.
!!---------------------------------------------------------------------
INTEGER , INTENT( in ) :: kt ! ocean time-step index
INTEGER , INTENT( in ) :: Kbb, Kmm, Krhs, Kaa ! ocean time level indices
REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
REAL(wp), DIMENSION(jpi,jpj,jpt) , INTENT(inout) :: pssh, puu_b, pvv_b ! SSH and barotropic velocities at main time levels
INTEGER , OPTIONAL , INTENT( in ) :: k_only_ADV ! only Advection in the RHS
!
INTEGER :: ji, jj, jk, jn ! dummy loop indices
LOGICAL :: ll_fw_start ! =T : forward integration
LOGICAL :: ll_init ! =T : special startup of 2d equations
INTEGER :: noffset ! local integers : time offset for bdy update
REAL(wp) :: r1_Dt_b, z1_hu, z1_hv ! local scalars
REAL(wp) :: za0, za1, za2, za3 ! - -
REAL(wp) :: zztmp, zldg ! - -
REAL(wp) :: zhu_bck, zhv_bck, zhdiv ! - -
REAL(wp) :: zun_save, zvn_save ! - -
REAL(wp), DIMENSION(jpi,jpj) :: zu_trd, zu_frc, zu_spg, zssh_frc
REAL(wp), DIMENSION(jpi,jpj) :: zv_trd, zv_frc, zv_spg
REAL(wp), DIMENSION(jpi,jpj) :: zsshu_a, zhup2_e, zhtp2_e
REAL(wp), DIMENSION(jpi,jpj) :: zsshv_a, zhvp2_e, zsshp2_e
REAL(wp), DIMENSION(jpi,jpj) :: zCdU_u, zCdU_v ! top/bottom stress at u- & v-points
REAL(wp), DIMENSION(jpi,jpj) :: zhU, zhV ! fluxes
!!st#if defined key_qco
!!st REAL(wp), DIMENSION(jpi, jpj, jpk) :: ze3u, ze3v
!!st#endif
!
REAL(wp) :: zwdramp ! local scalar - only used if ln_wd_dl = .True.
INTEGER :: iwdg, jwdg, kwdg ! short-hand values for the indices of the output point
REAL(wp) :: zepsilon, zgamma ! - -
REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zcpx, zcpy ! Wetting/Dying gravity filter coef.
REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: ztwdmask, zuwdmask, zvwdmask ! ROMS wetting and drying masks at t,u,v points
REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zuwdav2, zvwdav2 ! averages over the sub-steps of zuwdmask and zvwdmask
REAL(wp) :: zt0substep ! Time of day at the beginning of the time substep
!!----------------------------------------------------------------------
!
IF( ln_wd_il ) ALLOCATE( zcpx(jpi,jpj), zcpy(jpi,jpj) )
! !* Allocate temporary arrays
IF( ln_wd_dl ) ALLOCATE( ztwdmask(jpi,jpj), zuwdmask(jpi,jpj), zvwdmask(jpi,jpj), zuwdav2(jpi,jpj), zvwdav2(jpi,jpj))
!
zwdramp = r_rn_wdmin1 ! simplest ramp
! zwdramp = 1._wp / (rn_wdmin2 - rn_wdmin1) ! more general ramp
! ! inverse of baroclinic time step
r1_Dt_b = 1._wp / rDt
!
ll_init = ln_bt_av ! if no time averaging, then no specific restart
ll_fw_start = .FALSE.
! ! time offset in steps for bdy data update
IF( .NOT.ln_bt_fw ) THEN ; noffset = - nn_e
ELSE ; noffset = 0
ENDIF
!
IF( kt == nit000 ) THEN !* initialisation
!
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) 'dyn_spg_ts : surface pressure gradient trend'
IF(lwp) WRITE(numout,*) '~~~~~~~~~~ free surface with time splitting'
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
387
388
389
390
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
425
426
427
428
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
455
456
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
753
754
755
756
757
758
759
760
761
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
858
859
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
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
IF(lwp) WRITE(numout,*)
!
IF( l_1st_euler ) ll_init=.TRUE.
!
IF( ln_bt_fw .OR. l_1st_euler ) THEN
ll_fw_start =.TRUE.
noffset = 0
ELSE
ll_fw_start =.FALSE.
ENDIF
! ! Set averaging weights and cycle length:
CALL ts_wgt( ln_bt_av, ll_fw_start, icycle, wgtbtp1, wgtbtp2 )
!
ELSEIF( kt == nit000 + 1 ) THEN !* initialisation 2nd time-step
!
IF( .NOT.ln_bt_fw ) THEN
! If we did an Euler timestep on the first timestep we need to reset ll_fw_start
! and the averaging weights. We don't have an easy way of telling whether we did
! an Euler timestep on the first timestep (because l_1st_euler is reset to .false.
! at the end of the first timestep) so just do this in all cases.
ll_fw_start = .FALSE.
CALL ts_wgt( ln_bt_av, ll_fw_start, icycle, wgtbtp1, wgtbtp2 )
ENDIF
!
ENDIF
!
! -----------------------------------------------------------------------------
! Phase 1 : Coupling between general trend and barotropic estimates (1st step)
! -----------------------------------------------------------------------------
!
!
! != zu_frc = 1/H e3*d/dt(Ua) =! (Vertical mean of Ua, the 3D trends)
! ! --------------------------- !
#if defined key_qco
zu_frc(:,:) = SUM( e3u_0(:,:,: ) * puu(:,:,:,Krhs) * umask(:,:,:), DIM=3 ) * r1_hu_0(:,:)
zv_frc(:,:) = SUM( e3v_0(:,:,: ) * pvv(:,:,:,Krhs) * vmask(:,:,:), DIM=3 ) * r1_hv_0(:,:)
#else
zu_frc(:,:) = SUM( e3u(:,:,:,Kmm) * puu(:,:,:,Krhs) * umask(:,:,:), DIM=3 ) * r1_hu(:,:,Kmm)
zv_frc(:,:) = SUM( e3v(:,:,:,Kmm) * pvv(:,:,:,Krhs) * vmask(:,:,:), DIM=3 ) * r1_hv(:,:,Kmm)
#endif
!
!
! != U(Krhs) => baroclinic trend =! (remove its vertical mean)
DO jk = 1, jpkm1 ! ----------------------------- !
puu(:,:,jk,Krhs) = ( puu(:,:,jk,Krhs) - zu_frc(:,:) ) * umask(:,:,jk)
pvv(:,:,jk,Krhs) = ( pvv(:,:,jk,Krhs) - zv_frc(:,:) ) * vmask(:,:,jk)
END DO
!!gm Question here when removing the Vertically integrated trends, we remove the vertically integrated NL trends on momentum....
!!gm Is it correct to do so ? I think so...
! != remove 2D Coriolis trend =!
! ! -------------------------- !
!
IF( kt == nit000 .OR. .NOT. ln_linssh ) CALL dyn_cor_2D_init( Kmm ) ! Set zwz, the barotropic Coriolis force coefficient
! ! recompute zwz = f/depth at every time step for (.NOT.ln_linssh) as the water colomn height changes
!
IF( .NOT. PRESENT(k_only_ADV) ) THEN !* remove the 2D Coriolis trend
zhU(:,:) = puu_b(:,:,Kmm) * hu(:,:,Kmm) * e2u(:,:) ! now fluxes
zhV(:,:) = pvv_b(:,:,Kmm) * hv(:,:,Kmm) * e1v(:,:) ! NB: FULL domain : put a value in last row and column
!
CALL dyn_cor_2d( ht(:,:), hu(:,:,Kmm), hv(:,:,Kmm), puu_b(:,:,Kmm), pvv_b(:,:,Kmm), zhU, zhV, & ! <<== in
& zu_trd, zv_trd ) ! ==>> out
!
DO_2D( 0, 0, 0, 0 ) ! Remove coriolis term (and possibly spg) from barotropic trend
zu_frc(ji,jj) = zu_frc(ji,jj) - zu_trd(ji,jj) * ssumask(ji,jj)
zv_frc(ji,jj) = zv_frc(ji,jj) - zv_trd(ji,jj) * ssvmask(ji,jj)
END_2D
ENDIF
!
! != Add bottom stress contribution from baroclinic velocities =!
! ! ----------------------------------------------------------- !
IF( PRESENT(k_only_ADV) ) THEN !* only Advection in the RHS : provide the barotropic bottom drag coefficients
DO_2D( 0, 0, 0, 0 )
zCdU_u(ji,jj) = r1_2*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) )
zCdU_v(ji,jj) = r1_2*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) )
END_2D
ELSE !* remove baroclinic drag AND provide the barotropic drag coefficients
CALL dyn_drg_init( Kbb, Kmm, puu, pvv, puu_b, pvv_b, zu_frc, zv_frc, zCdU_u, zCdU_v )
ENDIF
!
! != Add atmospheric pressure forcing =!
! ! ---------------------------------- !
IF( ln_apr_dyn ) THEN
IF( ln_bt_fw ) THEN ! FORWARD integration: use kt+1/2 pressure (NOW+1/2)
DO_2D( 0, 0, 0, 0 )
zu_frc(ji,jj) = zu_frc(ji,jj) + grav * ( ssh_ib (ji+1,jj ) - ssh_ib (ji,jj) ) * r1_e1u(ji,jj)
zv_frc(ji,jj) = zv_frc(ji,jj) + grav * ( ssh_ib (ji ,jj+1) - ssh_ib (ji,jj) ) * r1_e2v(ji,jj)
END_2D
ELSE ! CENTRED integration: use kt-1/2 + kt+1/2 pressure (NOW)
zztmp = grav * r1_2
DO_2D( 0, 0, 0, 0 )
zu_frc(ji,jj) = zu_frc(ji,jj) + zztmp * ( ssh_ib (ji+1,jj ) - ssh_ib (ji,jj) &
& + ssh_ibb(ji+1,jj ) - ssh_ibb(ji,jj) ) * r1_e1u(ji,jj)
zv_frc(ji,jj) = zv_frc(ji,jj) + zztmp * ( ssh_ib (ji ,jj+1) - ssh_ib (ji,jj) &
& + ssh_ibb(ji ,jj+1) - ssh_ibb(ji,jj) ) * r1_e2v(ji,jj)
END_2D
ENDIF
ENDIF
!
! != Add wind forcing =!
! ! ------------------ !
IF( ln_bt_fw ) THEN
DO_2D( 0, 0, 0, 0 )
zu_frc(ji,jj) = zu_frc(ji,jj) + r1_rho0 * utau(ji,jj) * r1_hu(ji,jj,Kmm)
zv_frc(ji,jj) = zv_frc(ji,jj) + r1_rho0 * vtau(ji,jj) * r1_hv(ji,jj,Kmm)
END_2D
ELSE
zztmp = r1_rho0 * r1_2
DO_2D( 0, 0, 0, 0 )
zu_frc(ji,jj) = zu_frc(ji,jj) + zztmp * ( utau_b(ji,jj) + utau(ji,jj) ) * r1_hu(ji,jj,Kmm)
zv_frc(ji,jj) = zv_frc(ji,jj) + zztmp * ( vtau_b(ji,jj) + vtau(ji,jj) ) * r1_hv(ji,jj,Kmm)
END_2D
ENDIF
!
! !----------------!
! !== sssh_frc ==! Right-Hand-Side of the barotropic ssh equation (over the FULL domain)
! !----------------!
! != Net water flux forcing applied to a water column =!
! ! --------------------------------------------------- !
IF (ln_bt_fw) THEN ! FORWARD integration: use kt+1/2 fluxes (NOW+1/2)
zssh_frc(:,:) = r1_rho0 * ( emp(:,:) - rnf(:,:) - fwfisf_cav(:,:) - fwfisf_par(:,:) )
ELSE ! CENTRED integration: use kt-1/2 + kt+1/2 fluxes (NOW)
zztmp = r1_rho0 * r1_2
zssh_frc(:,:) = zztmp * ( emp(:,:) + emp_b(:,:) &
& - rnf(:,:) - rnf_b(:,:) &
& - fwfisf_cav(:,:) - fwfisf_cav_b(:,:) &
& - fwfisf_par(:,:) - fwfisf_par_b(:,:) )
ENDIF
! != Add Stokes drift divergence =! (if exist)
IF( ln_sdw ) THEN ! ----------------------------- !
zssh_frc(:,:) = zssh_frc(:,:) + div_sd(:,:)
ENDIF
!
! ! ice sheet coupling
IF ( ln_isf .AND. ln_isfcpl ) THEN
!
! ice sheet coupling
IF( ln_rstart .AND. kt == nit000 ) THEN
zssh_frc(:,:) = zssh_frc(:,:) + risfcpl_ssh(:,:)
END IF
!
! conservation option
IF( ln_isfcpl_cons ) THEN
zssh_frc(:,:) = zssh_frc(:,:) + risfcpl_cons_ssh(:,:)
END IF
!
END IF
!
#if defined key_asminc
! != Add the IAU weighted SSH increment =!
! ! ------------------------------------ !
IF( lk_asminc .AND. ln_sshinc .AND. ln_asmiau ) THEN
zssh_frc(:,:) = zssh_frc(:,:) - ssh_iau(:,:)
ENDIF
#endif
! != Fill boundary data arrays for AGRIF
! ! ------------------------------------
#if defined key_agrif
IF( .NOT.Agrif_Root() ) CALL agrif_dta_ts( kt )
#endif
!
! -----------------------------------------------------------------------
! Phase 2 : Integration of the barotropic equations
! -----------------------------------------------------------------------
!
! ! ==================== !
! ! Initialisations !
! ! ==================== !
! Initialize barotropic variables:
IF( ll_init )THEN
sshbb_e(:,:) = 0._wp
ubb_e (:,:) = 0._wp
vbb_e (:,:) = 0._wp
sshb_e (:,:) = 0._wp
ub_e (:,:) = 0._wp
vb_e (:,:) = 0._wp
ENDIF
!
IF( ln_linssh ) THEN ! mid-step ocean depth is fixed (hup2_e=hu_n=hu_0)
zhup2_e(:,:) = hu_0(:,:)
zhvp2_e(:,:) = hv_0(:,:)
zhtp2_e(:,:) = ht_0(:,:)
ENDIF
!
IF( ln_bt_fw ) THEN ! FORWARD integration: start from NOW fields
sshn_e(:,:) = pssh (:,:,Kmm)
un_e (:,:) = puu_b(:,:,Kmm)
vn_e (:,:) = pvv_b(:,:,Kmm)
!
hu_e (:,:) = hu(:,:,Kmm)
hv_e (:,:) = hv(:,:,Kmm)
hur_e (:,:) = r1_hu(:,:,Kmm)
hvr_e (:,:) = r1_hv(:,:,Kmm)
ELSE ! CENTRED integration: start from BEFORE fields
sshn_e(:,:) = pssh (:,:,Kbb)
un_e (:,:) = puu_b(:,:,Kbb)
vn_e (:,:) = pvv_b(:,:,Kbb)
!
hu_e (:,:) = hu(:,:,Kbb)
hv_e (:,:) = hv(:,:,Kbb)
hur_e (:,:) = r1_hu(:,:,Kbb)
hvr_e (:,:) = r1_hv(:,:,Kbb)
ENDIF
!
! Initialize sums:
puu_b (:,:,Kaa) = 0._wp ! After barotropic velocities (or transport if flux form)
pvv_b (:,:,Kaa) = 0._wp
pssh (:,:,Kaa) = 0._wp ! Sum for after averaged sea level
un_adv(:,:) = 0._wp ! Sum for now transport issued from ts loop
vn_adv(:,:) = 0._wp
!
IF( ln_wd_dl ) THEN
zuwdmask(:,:) = 0._wp ! set to zero for definiteness (not sure this is necessary)
zvwdmask(:,:) = 0._wp !
zuwdav2 (:,:) = 0._wp
zvwdav2 (:,:) = 0._wp
END IF
! ! ==================== !
DO jn = 1, icycle ! sub-time-step loop !
! ! ==================== !
!
l_full_nf_update = jn == icycle ! false: disable full North fold update (performances) for jn = 1 to icycle-1
!
! !== Update the forcing ==! (BDY and tides)
!
IF( ln_bdy .AND. ln_tide ) CALL bdy_dta_tides( kt, kit=jn, pt_offset= REAL(noffset+1,wp) )
! Update tide potential at the beginning of current time substep
IF( ln_tide_pot .AND. ln_tide ) THEN
zt0substep = REAL(nsec_day, wp) - 0.5_wp*rn_Dt + (jn + noffset - 1) * rn_Dt / REAL(nn_e, wp)
CALL upd_tide(zt0substep, Kmm)
END IF
!
! !== extrapolation at mid-step ==! (jn+1/2)
!
! !* Set extrapolation coefficients for predictor step:
IF ((jn<3).AND.ll_init) THEN ! Forward
za1 = 1._wp
za2 = 0._wp
za3 = 0._wp
ELSE ! AB3-AM4 Coefficients: bet=0.281105
za1 = 1.781105_wp ! za1 = 3/2 + bet
za2 = -1.06221_wp ! za2 = -(1/2 + 2*bet)
za3 = 0.281105_wp ! za3 = bet
ENDIF
!
! !* Extrapolate barotropic velocities at mid-step (jn+1/2)
!-- m+1/2 m m-1 m-2 --!
!-- u = (3/2+beta) u -(1/2+2beta) u + beta u --!
!-------------------------------------------------------------------------!
ua_e(:,:) = za1 * un_e(:,:) + za2 * ub_e(:,:) + za3 * ubb_e(:,:)
va_e(:,:) = za1 * vn_e(:,:) + za2 * vb_e(:,:) + za3 * vbb_e(:,:)
IF( .NOT.ln_linssh ) THEN !* Update ocean depth (variable volume case only)
! ! ------------------
! Extrapolate Sea Level at step jit+0.5:
!-- m+1/2 m m-1 m-2 --!
!-- ssh = (3/2+beta) ssh -(1/2+2beta) ssh + beta ssh --!
!--------------------------------------------------------------------------------!
zsshp2_e(:,:) = za1 * sshn_e(:,:) + za2 * sshb_e(:,:) + za3 * sshbb_e(:,:)
! set wetting & drying mask at tracer points for this barotropic mid-step
IF( ln_wd_dl ) CALL wad_tmsk( zsshp2_e, ztwdmask )
!
! ! ocean t-depth at mid-step
zhtp2_e(:,:) = ht_0(:,:) + zsshp2_e(:,:)
!
! ! ocean u- and v-depth at mid-step (separate DO-loops remove the need of a lbc_lnk)
#if defined key_qcoTest_FluxForm
! ! 'key_qcoTest_FluxForm' : simple ssh average
DO_2D( 1, 0, 1, 1 ) ! not jpi-column
zhup2_e(ji,jj) = hu_0(ji,jj) + r1_2 * ( zsshp2_e(ji,jj) + zsshp2_e(ji+1,jj ) ) * ssumask(ji,jj)
END_2D
DO_2D( 1, 1, 1, 0 )
zhvp2_e(ji,jj) = hv_0(ji,jj) + r1_2 * ( zsshp2_e(ji,jj) + zsshp2_e(ji ,jj+1) ) * ssvmask(ji,jj)
END_2D
#else
! ! no 'key_qcoTest_FluxForm' : surface weighted ssh average
DO_2D( 1, 0, 1, 1 ) ! not jpi-column
zhup2_e(ji,jj) = hu_0(ji,jj) + r1_2 * r1_e1e2u(ji,jj) &
& * ( e1e2t(ji ,jj) * zsshp2_e(ji ,jj) &
& + e1e2t(ji+1,jj) * zsshp2_e(ji+1,jj) ) * ssumask(ji,jj)
END_2D
DO_2D( 1, 1, 1, 0 ) ! not jpj-row
zhvp2_e(ji,jj) = hv_0(ji,jj) + r1_2 * r1_e1e2v(ji,jj) &
& * ( e1e2t(ji,jj ) * zsshp2_e(ji,jj ) &
& + e1e2t(ji,jj+1) * zsshp2_e(ji,jj+1) ) * ssvmask(ji,jj)
END_2D
#endif
!
ENDIF
!
! !== after SSH ==! (jn+1)
!
! ! update (ua_e,va_e) to enforce volume conservation at open boundaries
! ! values of zhup2_e and zhvp2_e on the halo are not needed in bdy_vol2d
IF( ln_bdy .AND. ln_vol ) CALL bdy_vol2d( kt, jn, ua_e, va_e, zhup2_e, zhvp2_e )
!
! ! resulting flux at mid-step (not over the full domain)
DO_2D( 1, 0, 1, 1 ) ! not jpi-column
zhU(ji,jj) = e2u(ji,jj) * ua_e(ji,jj) * zhup2_e(ji,jj)
END_2D
DO_2D( 1, 1, 1, 0 ) ! not jpj-row
zhV(ji,jj) = e1v(ji,jj) * va_e(ji,jj) * zhvp2_e(ji,jj)
END_2D
!
#if defined key_agrif
! Set fluxes during predictor step to ensure volume conservation
IF( .NOT.Agrif_Root() .AND. ln_bt_fw ) CALL agrif_dyn_ts_flux( jn, zhU, zhV )
#endif
IF( ln_wd_il ) CALL wad_lmt_bt(zhU, zhV, sshn_e, zssh_frc, rDt_e) !!gm wad_lmt_bt use of lbc_lnk on zhU, zhV
IF( ln_wd_dl ) THEN ! un_e and vn_e are set to zero at faces where
! ! the direction of the flow is from dry cells
CALL wad_Umsk( ztwdmask, zhU, zhV, un_e, vn_e, zuwdmask, zvwdmask ) ! not jpi colomn for U, not jpj row for V
!
ENDIF
!
!
! Compute Sea Level at step jit+1
!-- m+1 m m+1/2 --!
!-- ssh = ssh - delta_t' * [ frc + div( flux ) ] --!
!-------------------------------------------------------------------------!
DO_2D( 0, 0, 0, 0 )
zhdiv = ( zhU(ji,jj) - zhU(ji-1,jj) + zhV(ji,jj) - zhV(ji,jj-1) ) * r1_e1e2t(ji,jj)
ssha_e(ji,jj) = ( sshn_e(ji,jj) - rDt_e * ( zssh_frc(ji,jj) + zhdiv ) ) * ssmask(ji,jj)
END_2D
!
CALL lbc_lnk( 'dynspg_ts', ssha_e, 'T', 1._wp, zhU, 'U', -1._wp, zhV, 'V', -1._wp )
!
! Duplicate sea level across open boundaries (this is only cosmetic if linssh=T)
IF( ln_bdy ) CALL bdy_ssh( ssha_e )
#if defined key_agrif
IF( .NOT.Agrif_Root() ) CALL agrif_ssh_ts( jn )
#endif
!
! ! Sum over sub-time-steps to compute advective velocities
za2 = wgtbtp2(jn) ! zhU, zhV hold fluxes extrapolated at jn+0.5
un_adv(:,:) = un_adv(:,:) + za2 * zhU(:,:) * r1_e2u(:,:)
vn_adv(:,:) = vn_adv(:,:) + za2 * zhV(:,:) * r1_e1v(:,:)
! sum over sub-time-steps to decide which baroclinic velocities to set to zero (zuwdav2 is only used when ln_wd_dl_bc=True)
IF ( ln_wd_dl_bc ) THEN
DO_2D( 1, 0, 1, 1 ) ! not jpi-column
zuwdav2(ji,jj) = zuwdav2(ji,jj) + za2 * zuwdmask(ji,jj)
END_2D
DO_2D( 1, 1, 1, 0 ) ! not jpj-row
zvwdav2(ji,jj) = zvwdav2(ji,jj) + za2 * zvwdmask(ji,jj)
END_2D
END IF
!
!
! Sea Surface Height at u-,v-points (vvl case only)
IF( .NOT.ln_linssh ) THEN
#if defined key_qcoTest_FluxForm
! ! 'key_qcoTest_FluxForm' : simple ssh average
DO_2D( 1, 0, 1, 1 )
zsshu_a(ji,jj) = r1_2 * ( ssha_e(ji,jj) + ssha_e(ji+1,jj ) ) * ssumask(ji,jj)
END_2D
DO_2D( 1, 1, 1, 0 )
zsshv_a(ji,jj) = r1_2 * ( ssha_e(ji,jj) + ssha_e(ji ,jj+1) ) * ssvmask(ji,jj)
END_2D
#else
DO_2D( 0, 0, 0, 0 )
zsshu_a(ji,jj) = r1_2 * r1_e1e2u(ji,jj) * ( e1e2t(ji ,jj ) * ssha_e(ji ,jj ) &
& + e1e2t(ji+1,jj ) * ssha_e(ji+1,jj ) ) * ssumask(ji,jj)
zsshv_a(ji,jj) = r1_2 * r1_e1e2v(ji,jj) * ( e1e2t(ji ,jj ) * ssha_e(ji ,jj ) &
& + e1e2t(ji ,jj+1) * ssha_e(ji ,jj+1) ) * ssvmask(ji,jj)
END_2D
#endif
ENDIF
!
! Half-step back interpolation of SSH for surface pressure computation at step jit+1/2
!-- m+1/2 m+1 m m-1 m-2 --!
!-- ssh' = za0 * ssh + za1 * ssh + za2 * ssh + za3 * ssh --!
!------------------------------------------------------------------------------------------!
CALL ts_bck_interp( jn, ll_init, za0, za1, za2, za3 ) ! coeficients of the interpolation
zsshp2_e(:,:) = za0 * ssha_e(:,:) + za1 * sshn_e (:,:) &
& + za2 * sshb_e(:,:) + za3 * sshbb_e(:,:)
!
! ! Surface pressure gradient
zldg = ( 1._wp - rn_scal_load ) * grav ! local factor
DO_2D( 0, 0, 0, 0 )
zu_spg(ji,jj) = - zldg * ( zsshp2_e(ji+1,jj) - zsshp2_e(ji,jj) ) * r1_e1u(ji,jj)
zv_spg(ji,jj) = - zldg * ( zsshp2_e(ji,jj+1) - zsshp2_e(ji,jj) ) * r1_e2v(ji,jj)
END_2D
IF( ln_wd_il ) THEN ! W/D : gravity filters applied on pressure gradient
CALL wad_spg( zsshp2_e, zcpx, zcpy ) ! Calculating W/D gravity filters
DO_2D( 0, 0, 0, 0 )
zu_spg(ji,jj) = zu_spg(ji,jj) * zcpx(ji,jj)
zv_spg(ji,jj) = zv_spg(ji,jj) * zcpy(ji,jj)
END_2D
ENDIF
!
! Add Coriolis trend:
! zwz array below or triads normally depend on sea level with ln_linssh=F and should be updated
! at each time step. We however keep them constant here for optimization.
! Recall that zhU and zhV hold fluxes at jn+0.5 (extrapolated not backward interpolated)
CALL dyn_cor_2d( zhtp2_e, zhup2_e, zhvp2_e, ua_e, va_e, zhU, zhV, zu_trd, zv_trd )
!
! Add tidal astronomical forcing if defined
IF ( ln_tide .AND. ln_tide_pot ) THEN
DO_2D( 0, 0, 0, 0 )
zu_trd(ji,jj) = zu_trd(ji,jj) + grav * ( pot_astro(ji+1,jj) - pot_astro(ji,jj) ) * r1_e1u(ji,jj)
zv_trd(ji,jj) = zv_trd(ji,jj) + grav * ( pot_astro(ji,jj+1) - pot_astro(ji,jj) ) * r1_e2v(ji,jj)
END_2D
ENDIF
!
! Add bottom stresses:
!jth do implicitly instead
IF ( .NOT. ll_wd ) THEN ! Revert to explicit for bit comparison tests in non wad runs
DO_2D( 0, 0, 0, 0 )
zu_trd(ji,jj) = zu_trd(ji,jj) + zCdU_u(ji,jj) * un_e(ji,jj) * hur_e(ji,jj)
zv_trd(ji,jj) = zv_trd(ji,jj) + zCdU_v(ji,jj) * vn_e(ji,jj) * hvr_e(ji,jj)
END_2D
ENDIF
!
! Set next velocities:
! Compute barotropic speeds at step jit+1 (h : total height of the water colomn)
!-- VECTOR FORM
!-- m+1 m / m+1/2 \ --!
!-- u = u + delta_t' * \ (1-r)*g * grad_x( ssh') - f * k vect u + frc / --!
!-- --!
!-- FLUX FORM --!
!-- m+1 __1__ / m m / m+1/2 m+1/2 m+1/2 n \ \ --!
!-- u = m+1 | h * u + delta_t' * \ h * (1-r)*g * grad_x( ssh') - h * f * k vect u + h * frc / | --!
!-- h \ / --!
!------------------------------------------------------------------------------------------------------------------------!
IF( ln_dynadv_vec .OR. ln_linssh ) THEN !* Vector form
DO_2D( 0, 0, 0, 0 )
ua_e(ji,jj) = ( un_e(ji,jj) &
& + rDt_e * ( zu_spg(ji,jj) &
& + zu_trd(ji,jj) &
& + zu_frc(ji,jj) ) &
& ) * ssumask(ji,jj)
va_e(ji,jj) = ( vn_e(ji,jj) &
& + rDt_e * ( zv_spg(ji,jj) &
& + zv_trd(ji,jj) &
& + zv_frc(ji,jj) ) &
& ) * ssvmask(ji,jj)
END_2D
!
ELSE !* Flux form
DO_2D( 0, 0, 0, 0 )
! ! hu_e, hv_e hold depth at jn, zhup2_e, zhvp2_e hold extrapolated depth at jn+1/2
! ! backward interpolated depth used in spg terms at jn+1/2
#if defined key_qcoTest_FluxForm
! ! 'key_qcoTest_FluxForm' : simple ssh average
zhu_bck = hu_0(ji,jj) + r1_2 * ( zsshp2_e(ji,jj) + zsshp2_e(ji+1,jj ) ) * ssumask(ji,jj)
zhv_bck = hv_0(ji,jj) + r1_2 * ( zsshp2_e(ji,jj) + zsshp2_e(ji ,jj+1) ) * ssvmask(ji,jj)
#else
zhu_bck = hu_0(ji,jj) + r1_2*r1_e1e2u(ji,jj) * ( e1e2t(ji ,jj) * zsshp2_e(ji ,jj) &
& + e1e2t(ji+1,jj) * zsshp2_e(ji+1,jj) ) * ssumask(ji,jj)
zhv_bck = hv_0(ji,jj) + r1_2*r1_e1e2v(ji,jj) * ( e1e2t(ji,jj ) * zsshp2_e(ji,jj ) &
& + e1e2t(ji,jj+1) * zsshp2_e(ji,jj+1) ) * ssvmask(ji,jj)
#endif
! ! inverse depth at jn+1
z1_hu = ssumask(ji,jj) / ( hu_0(ji,jj) + zsshu_a(ji,jj) + 1._wp - ssumask(ji,jj) )
z1_hv = ssvmask(ji,jj) / ( hv_0(ji,jj) + zsshv_a(ji,jj) + 1._wp - ssvmask(ji,jj) )
!
ua_e(ji,jj) = ( hu_e (ji,jj) * un_e (ji,jj) &
& + rDt_e * ( zhu_bck * zu_spg (ji,jj) & !
& + zhup2_e(ji,jj) * zu_trd (ji,jj) & !
& + hu(ji,jj,Kmm) * zu_frc (ji,jj) ) ) * z1_hu
!
va_e(ji,jj) = ( hv_e (ji,jj) * vn_e (ji,jj) &
& + rDt_e * ( zhv_bck * zv_spg (ji,jj) & !
& + zhvp2_e(ji,jj) * zv_trd (ji,jj) & !
& + hv(ji,jj,Kmm) * zv_frc (ji,jj) ) ) * z1_hv
END_2D
ENDIF
!jth implicit bottom friction:
IF ( ll_wd ) THEN ! revert to explicit for bit comparison tests in non wad runs
DO_2D( 0, 0, 0, 0 )
ua_e(ji,jj) = ua_e(ji,jj) / ( 1._wp - rDt_e * zCdU_u(ji,jj) * hur_e(ji,jj) )
va_e(ji,jj) = va_e(ji,jj) / ( 1._wp - rDt_e * zCdU_v(ji,jj) * hvr_e(ji,jj) )
END_2D
ENDIF
IF( .NOT.ln_linssh ) THEN !* Update ocean depth (variable volume case only)
DO_2D( 0, 0, 0, 0 )
hu_e (ji,jj) = hu_0(ji,jj) + zsshu_a(ji,jj)
hur_e(ji,jj) = ssumask(ji,jj) / ( hu_e(ji,jj) + 1._wp - ssumask(ji,jj) )
hv_e (ji,jj) = hv_0(ji,jj) + zsshv_a(ji,jj)
hvr_e(ji,jj) = ssvmask(ji,jj) / ( hv_e(ji,jj) + 1._wp - ssvmask(ji,jj) )
END_2D
ENDIF
!
IF( .NOT.ln_linssh ) THEN !* Update ocean depth (variable volume case only)
CALL lbc_lnk( 'dynspg_ts', ua_e , 'U', -1._wp, va_e , 'V', -1._wp &
& , hu_e , 'U', 1._wp, hv_e , 'V', 1._wp &
& , hur_e, 'U', 1._wp, hvr_e, 'V', 1._wp )
ELSE
CALL lbc_lnk( 'dynspg_ts', ua_e , 'U', -1._wp, va_e , 'V', -1._wp )
ENDIF
! ! open boundaries
IF( ln_bdy ) CALL bdy_dyn2d( jn, ua_e, va_e, un_e, vn_e, hur_e, hvr_e, ssha_e )
#if defined key_agrif
IF( .NOT.Agrif_Root() ) CALL agrif_dyn_ts( jn ) ! Agrif
#endif
! !* Swap
! ! ----
ubb_e (:,:) = ub_e (:,:)
ub_e (:,:) = un_e (:,:)
un_e (:,:) = ua_e (:,:)
!
vbb_e (:,:) = vb_e (:,:)
vb_e (:,:) = vn_e (:,:)
vn_e (:,:) = va_e (:,:)
!
sshbb_e(:,:) = sshb_e(:,:)
sshb_e (:,:) = sshn_e(:,:)
sshn_e (:,:) = ssha_e(:,:)
! !* Sum over whole bt loop
! ! ----------------------
za1 = wgtbtp1(jn)
IF( ln_dynadv_vec .OR. ln_linssh ) THEN ! Sum velocities
puu_b (:,:,Kaa) = puu_b (:,:,Kaa) + za1 * ua_e (:,:)
pvv_b (:,:,Kaa) = pvv_b (:,:,Kaa) + za1 * va_e (:,:)
ELSE ! Sum transports
IF ( .NOT.ln_wd_dl ) THEN
puu_b (:,:,Kaa) = puu_b (:,:,Kaa) + za1 * ua_e (:,:) * hu_e (:,:)
pvv_b (:,:,Kaa) = pvv_b (:,:,Kaa) + za1 * va_e (:,:) * hv_e (:,:)
ELSE
puu_b (:,:,Kaa) = puu_b (:,:,Kaa) + za1 * ua_e (:,:) * hu_e (:,:) * zuwdmask(:,:)
pvv_b (:,:,Kaa) = pvv_b (:,:,Kaa) + za1 * va_e (:,:) * hv_e (:,:) * zvwdmask(:,:)
END IF
ENDIF
! ! Sum sea level
pssh(:,:,Kaa) = pssh(:,:,Kaa) + za1 * ssha_e(:,:)
! ! ==================== !
END DO ! end loop !
! ! ==================== !
! -----------------------------------------------------------------------------
! Phase 3. update the general trend with the barotropic trend
! -----------------------------------------------------------------------------
!
! Set advection velocity correction:
IF (ln_bt_fw) THEN
IF( .NOT.( kt == nit000 .AND. l_1st_euler ) ) THEN
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
zun_save = un_adv(ji,jj)
zvn_save = vn_adv(ji,jj)
! ! apply the previously computed correction
un_adv(ji,jj) = r1_2 * ( ub2_b(ji,jj) + zun_save - rn_atfp * un_bf(ji,jj) )
vn_adv(ji,jj) = r1_2 * ( vb2_b(ji,jj) + zvn_save - rn_atfp * vn_bf(ji,jj) )
! ! Update corrective fluxes for next time step
un_bf(ji,jj) = rn_atfp * un_bf(ji,jj) + ( zun_save - ub2_b(ji,jj) )
vn_bf(ji,jj) = rn_atfp * vn_bf(ji,jj) + ( zvn_save - vb2_b(ji,jj) )
! ! Save integrated transport for next computation
ub2_b(ji,jj) = zun_save
vb2_b(ji,jj) = zvn_save
END_2D
ELSE
un_bf(:,:) = 0._wp ! corrective fluxes for next time step set to zero
vn_bf(:,:) = 0._wp
ub2_b(:,:) = un_adv(:,:) ! Save integrated transport for next computation
vb2_b(:,:) = vn_adv(:,:)
END IF
ENDIF
!
! Update barotropic trend:
IF( ln_dynadv_vec .OR. ln_linssh ) THEN
DO jk=1,jpkm1
puu(:,:,jk,Krhs) = puu(:,:,jk,Krhs) + ( puu_b(:,:,Kaa) - puu_b(:,:,Kbb) ) * r1_Dt_b
pvv(:,:,jk,Krhs) = pvv(:,:,jk,Krhs) + ( pvv_b(:,:,Kaa) - pvv_b(:,:,Kbb) ) * r1_Dt_b
END DO
ELSE
! At this stage, pssh(:,:,:,Krhs) has been corrected: compute new depths at velocity points
#if defined key_qcoTest_FluxForm
! ! 'key_qcoTest_FluxForm' : simple ssh average
DO_2D( 1, 0, 1, 0 )
zsshu_a(ji,jj) = r1_2 * ( pssh(ji,jj,Kaa) + pssh(ji+1,jj ,Kaa) ) * ssumask(ji,jj)
zsshv_a(ji,jj) = r1_2 * ( pssh(ji,jj,Kaa) + pssh(ji ,jj+1,Kaa) ) * ssvmask(ji,jj)
END_2D
#else
DO_2D( 1, 0, 1, 0 )
zsshu_a(ji,jj) = r1_2 * r1_e1e2u(ji,jj) * ( e1e2t(ji ,jj) * pssh(ji ,jj,Kaa) &
& + e1e2t(ji+1,jj) * pssh(ji+1,jj,Kaa) ) * ssumask(ji,jj)
zsshv_a(ji,jj) = r1_2 * r1_e1e2v(ji,jj) * ( e1e2t(ji,jj ) * pssh(ji,jj ,Kaa) &
& + e1e2t(ji,jj+1) * pssh(ji,jj+1,Kaa) ) * ssvmask(ji,jj)
END_2D
#endif
CALL lbc_lnk( 'dynspg_ts', zsshu_a, 'U', 1._wp, zsshv_a, 'V', 1._wp ) ! Boundary conditions
!
DO jk=1,jpkm1
puu(:,:,jk,Krhs) = puu(:,:,jk,Krhs) + r1_hu(:,:,Kmm) &
& * ( puu_b(:,:,Kaa) - puu_b(:,:,Kbb) * hu(:,:,Kbb) ) * r1_Dt_b
pvv(:,:,jk,Krhs) = pvv(:,:,jk,Krhs) + r1_hv(:,:,Kmm) &
& * ( pvv_b(:,:,Kaa) - pvv_b(:,:,Kbb) * hv(:,:,Kbb) ) * r1_Dt_b
END DO
! Save barotropic velocities not transport:
puu_b(:,:,Kaa) = puu_b(:,:,Kaa) / ( hu_0(:,:) + zsshu_a(:,:) + 1._wp - ssumask(:,:) )
pvv_b(:,:,Kaa) = pvv_b(:,:,Kaa) / ( hv_0(:,:) + zsshv_a(:,:) + 1._wp - ssvmask(:,:) )
ENDIF
! Correct velocities so that the barotropic velocity equals (un_adv, vn_adv) (in all cases)
DO jk = 1, jpkm1
puu(:,:,jk,Kmm) = ( puu(:,:,jk,Kmm) + un_adv(:,:)*r1_hu(:,:,Kmm) - puu_b(:,:,Kmm) ) * umask(:,:,jk)
pvv(:,:,jk,Kmm) = ( pvv(:,:,jk,Kmm) + vn_adv(:,:)*r1_hv(:,:,Kmm) - pvv_b(:,:,Kmm) ) * vmask(:,:,jk)
END DO
IF ( ln_wd_dl .and. ln_wd_dl_bc) THEN
DO jk = 1, jpkm1
puu(:,:,jk,Kmm) = ( un_adv(:,:)*r1_hu(:,:,Kmm) &
& + zuwdav2(:,:)*(puu(:,:,jk,Kmm) - un_adv(:,:)*r1_hu(:,:,Kmm)) ) * umask(:,:,jk)
pvv(:,:,jk,Kmm) = ( vn_adv(:,:)*r1_hv(:,:,Kmm) &
& + zvwdav2(:,:)*(pvv(:,:,jk,Kmm) - vn_adv(:,:)*r1_hv(:,:,Kmm)) ) * vmask(:,:,jk)
END DO
END IF
CALL iom_put( "ubar", un_adv(:,:)*r1_hu(:,:,Kmm) ) ! barotropic i-current
CALL iom_put( "vbar", vn_adv(:,:)*r1_hv(:,:,Kmm) ) ! barotropic i-current
!
#if defined key_agrif
! Save time integrated fluxes during child grid integration
! (used to update coarse grid transports at next time step)
!
IF( .NOT.Agrif_Root() .AND. ln_bt_fw .AND. ln_agrif_2way ) THEN
IF( Agrif_NbStepint() == 0 ) THEN
ub2_i_b(:,:) = 0._wp
vb2_i_b(:,:) = 0._wp
END IF
!
za1 = 1._wp / REAL(Agrif_rhot(), wp)
ub2_i_b(:,:) = ub2_i_b(:,:) + za1 * ub2_b(:,:)
vb2_i_b(:,:) = vb2_i_b(:,:) + za1 * vb2_b(:,:)
ENDIF
#endif
! !* write time-spliting arrays in the restart
IF( lrst_oce .AND.ln_bt_fw ) CALL ts_rst( kt, 'WRITE' )
!
IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy )
IF( ln_wd_dl ) DEALLOCATE( ztwdmask, zuwdmask, zvwdmask, zuwdav2, zvwdav2 )
!
CALL iom_put( "baro_u" , puu_b(:,:,Kmm) ) ! Barotropic U Velocity
CALL iom_put( "baro_v" , pvv_b(:,:,Kmm) ) ! Barotropic V Velocity
!
END SUBROUTINE dyn_spg_ts
SUBROUTINE ts_wgt( ll_av, ll_fw, jpit, zwgt1, zwgt2)
!!---------------------------------------------------------------------
!! *** ROUTINE ts_wgt ***
!!
!! ** Purpose : Set time-splitting weights for temporal averaging (or not)
!!----------------------------------------------------------------------
LOGICAL, INTENT(in) :: ll_av ! temporal averaging=.true.
LOGICAL, INTENT(in) :: ll_fw ! forward time splitting =.true.
INTEGER, INTENT(inout) :: jpit ! cycle length
REAL(wp), DIMENSION(3*nn_e), INTENT(inout) :: zwgt1, & ! Primary weights
zwgt2 ! Secondary weights
INTEGER :: jic, jn, ji ! temporary integers
REAL(wp) :: za1, za2
!!----------------------------------------------------------------------
zwgt1(:) = 0._wp
zwgt2(:) = 0._wp
! Set time index when averaged value is requested
IF (ll_fw) THEN
jic = nn_e
ELSE
jic = 2 * nn_e
ENDIF
! Set primary weights:
IF (ll_av) THEN
! Define simple boxcar window for primary weights
! (width = nn_e, centered around jic)
SELECT CASE ( nn_bt_flt )
CASE( 0 ) ! No averaging
zwgt1(jic) = 1._wp
jpit = jic
CASE( 1 ) ! Boxcar, width = nn_e
DO jn = 1, 3*nn_e
za1 = ABS(float(jn-jic))/float(nn_e)
IF (za1 < 0.5_wp) THEN
zwgt1(jn) = 1._wp
jpit = jn
ENDIF
ENDDO
CASE( 2 ) ! Boxcar, width = 2 * nn_e
DO jn = 1, 3*nn_e
za1 = ABS(float(jn-jic))/float(nn_e)
IF (za1 < 1._wp) THEN
zwgt1(jn) = 1._wp
jpit = jn
ENDIF
ENDDO
CASE DEFAULT ; CALL ctl_stop( 'unrecognised value for nn_bt_flt' )
END SELECT
ELSE ! No time averaging
zwgt1(jic) = 1._wp
jpit = jic
ENDIF
! Set secondary weights
DO jn = 1, jpit
DO ji = jn, jpit
zwgt2(jn) = zwgt2(jn) + zwgt1(ji)
END DO
END DO
! Normalize weigths:
za1 = 1._wp / SUM(zwgt1(1:jpit))
za2 = 1._wp / SUM(zwgt2(1:jpit))
DO jn = 1, jpit
zwgt1(jn) = zwgt1(jn) * za1
zwgt2(jn) = zwgt2(jn) * za2
END DO
!
END SUBROUTINE ts_wgt
SUBROUTINE ts_rst( kt, cdrw )
!!---------------------------------------------------------------------
!! *** ROUTINE ts_rst ***
!!
!! ** Purpose : Read or write time-splitting arrays in restart file
!!----------------------------------------------------------------------
INTEGER , INTENT(in) :: kt ! ocean time-step
CHARACTER(len=*), INTENT(in) :: cdrw ! "READ"/"WRITE" flag
!!----------------------------------------------------------------------
!
IF( TRIM(cdrw) == 'READ' ) THEN ! Read/initialise
! ! ---------------
IF( ln_rstart .AND. ln_bt_fw .AND. .NOT.l_1st_euler ) THEN !* Read the restart file
CALL iom_get( numror, jpdom_auto, 'ub2_b' , ub2_b (:,:), cd_type = 'U', psgn = -1._wp )
CALL iom_get( numror, jpdom_auto, 'vb2_b' , vb2_b (:,:), cd_type = 'V', psgn = -1._wp )
CALL iom_get( numror, jpdom_auto, 'un_bf' , un_bf (:,:), cd_type = 'U', psgn = -1._wp )
CALL iom_get( numror, jpdom_auto, 'vn_bf' , vn_bf (:,:), cd_type = 'V', psgn = -1._wp )
IF( .NOT.ln_bt_av ) THEN
CALL iom_get( numror, jpdom_auto, 'sshbb_e' , sshbb_e(:,:), cd_type = 'T', psgn = 1._wp )
CALL iom_get( numror, jpdom_auto, 'ubb_e' , ubb_e(:,:), cd_type = 'U', psgn = -1._wp )
CALL iom_get( numror, jpdom_auto, 'vbb_e' , vbb_e(:,:), cd_type = 'V', psgn = -1._wp )
CALL iom_get( numror, jpdom_auto, 'sshb_e' , sshb_e(:,:), cd_type = 'T', psgn = 1._wp )
CALL iom_get( numror, jpdom_auto, 'ub_e' , ub_e(:,:), cd_type = 'U', psgn = -1._wp )
CALL iom_get( numror, jpdom_auto, 'vb_e' , vb_e(:,:), cd_type = 'V', psgn = -1._wp )
ENDIF
#if defined key_agrif
! Read time integrated fluxes
IF ( .NOT.Agrif_Root() ) THEN
CALL iom_get( numror, jpdom_auto, 'ub2_i_b' , ub2_i_b(:,:), cd_type = 'U', psgn = -1._wp )
CALL iom_get( numror, jpdom_auto, 'vb2_i_b' , vb2_i_b(:,:), cd_type = 'V', psgn = -1._wp )
ELSE
ub2_i_b(:,:) = 0._wp ; vb2_i_b(:,:) = 0._wp ! used in the 1st update of agrif
ENDIF
#endif
ELSE !* Start from rest
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) ' ==>>> start from rest: set barotropic values to 0'
ub2_b (:,:) = 0._wp ; vb2_b (:,:) = 0._wp ! used in the 1st interpol of agrif
un_adv (:,:) = 0._wp ; vn_adv (:,:) = 0._wp ! used in the 1st interpol of agrif
un_bf (:,:) = 0._wp ; vn_bf (:,:) = 0._wp ! used in the 1st update of agrif
#if defined key_agrif
ub2_i_b(:,:) = 0._wp ; vb2_i_b(:,:) = 0._wp ! used in the 1st update of agrif
#endif
ENDIF
!
ELSEIF( TRIM(cdrw) == 'WRITE' ) THEN ! Create restart file
! ! -------------------
IF(lwp) WRITE(numout,*) '---- ts_rst ----'
CALL iom_rstput( kt, nitrst, numrow, 'ub2_b' , ub2_b (:,:) )
CALL iom_rstput( kt, nitrst, numrow, 'vb2_b' , vb2_b (:,:) )
CALL iom_rstput( kt, nitrst, numrow, 'un_bf' , un_bf (:,:) )
CALL iom_rstput( kt, nitrst, numrow, 'vn_bf' , vn_bf (:,:) )
!
IF (.NOT.ln_bt_av) THEN
CALL iom_rstput( kt, nitrst, numrow, 'sshbb_e' , sshbb_e(:,:) )
CALL iom_rstput( kt, nitrst, numrow, 'ubb_e' , ubb_e(:,:) )
CALL iom_rstput( kt, nitrst, numrow, 'vbb_e' , vbb_e(:,:) )
CALL iom_rstput( kt, nitrst, numrow, 'sshb_e' , sshb_e(:,:) )
CALL iom_rstput( kt, nitrst, numrow, 'ub_e' , ub_e(:,:) )
CALL iom_rstput( kt, nitrst, numrow, 'vb_e' , vb_e(:,:) )
ENDIF
#if defined key_agrif
! Save time integrated fluxes
IF ( .NOT.Agrif_Root() ) THEN
CALL iom_rstput( kt, nitrst, numrow, 'ub2_i_b' , ub2_i_b(:,:) )
CALL iom_rstput( kt, nitrst, numrow, 'vb2_i_b' , vb2_i_b(:,:) )
ENDIF
#endif
ENDIF
!
END SUBROUTINE ts_rst
SUBROUTINE dyn_spg_ts_init
!!---------------------------------------------------------------------
!! *** ROUTINE dyn_spg_ts_init ***
!!
!! ** Purpose : Set time splitting options
!!----------------------------------------------------------------------
INTEGER :: ji ,jj ! dummy loop indices
REAL(wp) :: zxr2, zyr2, zcmax ! local scalar
REAL(wp), DIMENSION(jpi,jpj) :: zcu
!!----------------------------------------------------------------------
!
! Max courant number for ext. grav. waves
!
DO_2D( 0, 0, 0, 0 )
zxr2 = r1_e1t(ji,jj) * r1_e1t(ji,jj)
zyr2 = r1_e2t(ji,jj) * r1_e2t(ji,jj)
zcu(ji,jj) = SQRT( grav * MAX(ht_0(ji,jj),0._wp) * (zxr2 + zyr2) )
END_2D
!
zcmax = MAXVAL( zcu(Nis0:Nie0,Njs0:Nje0) )
CALL mpp_max( 'dynspg_ts', zcmax )
! Estimate number of iterations to satisfy a max courant number= rn_bt_cmax
IF( ln_bt_auto ) nn_e = CEILING( rn_Dt / rn_bt_cmax * zcmax)
rDt_e = rn_Dt / REAL( nn_e , wp )
zcmax = zcmax * rDt_e
! Print results
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) 'dyn_spg_ts_init : split-explicit free surface'
IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~~'
IF( ln_bt_auto ) THEN
IF(lwp) WRITE(numout,*) ' ln_ts_auto =.true. Automatically set nn_e '
IF(lwp) WRITE(numout,*) ' Max. courant number allowed: ', rn_bt_cmax
ELSE
IF(lwp) WRITE(numout,*) ' ln_ts_auto=.false.: Use nn_e in namelist nn_e = ', nn_e
ENDIF
IF(ln_bt_av) THEN
IF(lwp) WRITE(numout,*) ' ln_bt_av =.true. ==> Time averaging over nn_e time steps is on '
ELSE
IF(lwp) WRITE(numout,*) ' ln_bt_av =.false. => No time averaging of barotropic variables '
ENDIF
!
!
IF(ln_bt_fw) THEN
IF(lwp) WRITE(numout,*) ' ln_bt_fw=.true. => Forward integration of barotropic variables '
ELSE
IF(lwp) WRITE(numout,*) ' ln_bt_fw =.false.=> Centred integration of barotropic variables '
ENDIF
!
#if defined key_agrif
! Restrict the use of Agrif to the forward case only
IF( .NOT.ln_bt_fw .AND. .NOT.Agrif_Root() ) CALL ctl_stop( 'AGRIF not implemented if ln_bt_fw=.FALSE.' )
#endif
!
IF(lwp) WRITE(numout,*) ' Time filter choice, nn_bt_flt: ', nn_bt_flt
SELECT CASE ( nn_bt_flt )
CASE( 0 ) ; IF(lwp) WRITE(numout,*) ' Dirac'
CASE( 1 ) ; IF(lwp) WRITE(numout,*) ' Boxcar: width = nn_e'
CASE( 2 ) ; IF(lwp) WRITE(numout,*) ' Boxcar: width = 2*nn_e'
CASE DEFAULT ; CALL ctl_stop( 'unrecognised value for nn_bt_flt: should 0,1, or 2' )
END SELECT
!
IF(lwp) WRITE(numout,*) ' '
IF(lwp) WRITE(numout,*) ' nn_e = ', nn_e
IF(lwp) WRITE(numout,*) ' Barotropic time step [s] is :', rDt_e
IF(lwp) WRITE(numout,*) ' Maximum Courant number is :', zcmax
!
IF(lwp) WRITE(numout,*) ' Time diffusion parameter rn_bt_alpha: ', rn_bt_alpha
IF ((ln_bt_av.AND.nn_bt_flt/=0).AND.(rn_bt_alpha>0._wp)) THEN
CALL ctl_stop( 'dynspg_ts ERROR: if rn_bt_alpha > 0, remove temporal averaging' )
ENDIF
!
IF( .NOT.ln_bt_av .AND. .NOT.ln_bt_fw ) THEN
CALL ctl_stop( 'dynspg_ts ERROR: No time averaging => only forward integration is possible' )
ENDIF
IF( zcmax>0.9_wp ) THEN
CALL ctl_stop( 'dynspg_ts ERROR: Maximum Courant number is greater than 0.9: Inc. nn_e !' )
ENDIF
!
! ! Allocate time-splitting arrays
IF( dyn_spg_ts_alloc() /= 0 ) CALL ctl_stop('STOP', 'dyn_spg_init: failed to allocate dynspg_ts arrays' )
!
! ! read restart when needed
CALL ts_rst( nit000, 'READ' )
!
END SUBROUTINE dyn_spg_ts_init
SUBROUTINE dyn_cor_2D_init( Kmm )
!!---------------------------------------------------------------------
!! *** ROUTINE dyn_cor_2D_init ***
!!
!! ** Purpose : Set time splitting options
!! Set arrays to remove/compute coriolis trend.
!! Do it once during initialization if volume is fixed, else at each long time step.
!! Note that these arrays are also used during barotropic loop. These are however frozen
!! although they should be updated in the variable volume case. Not a big approximation.
!! To remove this approximation, copy lines below inside barotropic loop
!! and update depths at T- points (ht) at each barotropic time step
!!
!! Compute zwz = f / ( height of the water colomn )
!!----------------------------------------------------------------------
INTEGER, INTENT(in) :: Kmm ! Time index
INTEGER :: ji ,jj, jk ! dummy loop indices
REAL(wp) :: z1_ht
!!----------------------------------------------------------------------
!
SELECT CASE( nvor_scheme )
CASE( np_EEN, np_ENE, np_ENS , np_MIX ) != schemes using the same e3f definition
SELECT CASE( nn_e3f_typ ) !* ff_f/e3 at F-point
CASE ( 0 ) ! original formulation (masked averaging of e3t divided by 4)
DO_2D( 0, 0, 0, 0 )
zwz(ji,jj) = ( ht(ji,jj+1) + ht(ji+1,jj+1) &
& + ht(ji,jj ) + ht(ji+1,jj ) ) * 0.25_wp
IF( zwz(ji,jj) /= 0._wp ) zwz(ji,jj) = ff_f(ji,jj) / zwz(ji,jj)
END_2D
CASE ( 1 ) ! new formulation (masked averaging of e3t divided by the sum of mask)
DO_2D( 0, 0, 0, 0 )
zwz(ji,jj) = ( ht(ji,jj+1) + ht(ji+1,jj+1) &
& + ht(ji,jj ) + ht(ji+1,jj ) ) &
& / ( MAX(ssmask(ji,jj+1) + ssmask(ji+1,jj+1) &
& + ssmask(ji,jj ) + ssmask(ji+1,jj ) , 1._wp ) )
IF( zwz(ji,jj) /= 0._wp ) zwz(ji,jj) = ff_f(ji,jj) / zwz(ji,jj)
END_2D
END SELECT
CALL lbc_lnk( 'dynspg_ts', zwz, 'F', 1._wp )
END SELECT
!
SELECT CASE( nvor_scheme )
CASE( np_EEN )
!
ftne(1,:) = 0._wp ; ftnw(1,:) = 0._wp ; ftse(1,:) = 0._wp ; ftsw(1,:) = 0._wp
DO_2D( 0, 1, 0, 1 )
ftne(ji,jj) = zwz(ji-1,jj ) + zwz(ji ,jj ) + zwz(ji ,jj-1)
ftnw(ji,jj) = zwz(ji-1,jj-1) + zwz(ji-1,jj ) + zwz(ji ,jj )
ftse(ji,jj) = zwz(ji ,jj ) + zwz(ji ,jj-1) + zwz(ji-1,jj-1)
ftsw(ji,jj) = zwz(ji ,jj-1) + zwz(ji-1,jj-1) + zwz(ji-1,jj )
END_2D
!
CASE( np_EET ) != EEN scheme using e3t energy conserving scheme
ftne(1,:) = 0._wp ; ftnw(1,:) = 0._wp ; ftse(1,:) = 0._wp ; ftsw(1,:) = 0._wp
DO_2D( 0, 1, 0, 1 )
z1_ht = ssmask(ji,jj) / ( ht(ji,jj) + 1._wp - ssmask(ji,jj) )
ftne(ji,jj) = ( ff_f(ji-1,jj ) + ff_f(ji ,jj ) + ff_f(ji ,jj-1) ) * z1_ht
ftnw(ji,jj) = ( ff_f(ji-1,jj-1) + ff_f(ji-1,jj ) + ff_f(ji ,jj ) ) * z1_ht
ftse(ji,jj) = ( ff_f(ji ,jj ) + ff_f(ji ,jj-1) + ff_f(ji-1,jj-1) ) * z1_ht
ftsw(ji,jj) = ( ff_f(ji ,jj-1) + ff_f(ji-1,jj-1) + ff_f(ji-1,jj ) ) * z1_ht
END_2D
!
END SELECT
END SUBROUTINE dyn_cor_2d_init
SUBROUTINE dyn_cor_2d( pht, phu, phv, punb, pvnb, zhU, zhV, zu_trd, zv_trd )
!!---------------------------------------------------------------------
!! *** ROUTINE dyn_cor_2d ***
!!
!! ** Purpose : Compute u and v coriolis trends
!!----------------------------------------------------------------------
INTEGER :: ji ,jj ! dummy loop indices
REAL(wp) :: zx1, zx2, zy1, zy2, z1_hu, z1_hv ! - -
REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pht, phu, phv, punb, pvnb, zhU, zhV
REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: zu_trd, zv_trd
!!----------------------------------------------------------------------
SELECT CASE( nvor_scheme )
CASE( np_ENT ) ! enstrophy conserving scheme (f-point)
DO_2D( 0, 0, 0, 0 )
z1_hu = ssumask(ji,jj) / ( phu(ji,jj) + 1._wp - ssumask(ji,jj) )
z1_hv = ssvmask(ji,jj) / ( phv(ji,jj) + 1._wp - ssvmask(ji,jj) )
zu_trd(ji,jj) = + r1_4 * r1_e1e2u(ji,jj) * z1_hu &
& * ( e1e2t(ji+1,jj)*pht(ji+1,jj)*ff_t(ji+1,jj) * ( pvnb(ji+1,jj) + pvnb(ji+1,jj-1) ) &
& + e1e2t(ji ,jj)*pht(ji ,jj)*ff_t(ji ,jj) * ( pvnb(ji ,jj) + pvnb(ji ,jj-1) ) )
!
zv_trd(ji,jj) = - r1_4 * r1_e1e2v(ji,jj) * z1_hv &
& * ( e1e2t(ji,jj+1)*pht(ji,jj+1)*ff_t(ji,jj+1) * ( punb(ji,jj+1) + punb(ji-1,jj+1) ) &
& + e1e2t(ji,jj )*pht(ji,jj )*ff_t(ji,jj ) * ( punb(ji,jj ) + punb(ji-1,jj ) ) )
END_2D
!
CASE( np_ENE , np_MIX ) ! energy conserving scheme (t-point) ENE or MIX
DO_2D( 0, 0, 0, 0 )
zy1 = ( zhV(ji,jj-1) + zhV(ji+1,jj-1) ) * r1_e1u(ji,jj)
zy2 = ( zhV(ji,jj ) + zhV(ji+1,jj ) ) * r1_e1u(ji,jj)
zx1 = ( zhU(ji-1,jj) + zhU(ji-1,jj+1) ) * r1_e2v(ji,jj)
zx2 = ( zhU(ji ,jj) + zhU(ji ,jj+1) ) * r1_e2v(ji,jj)
! energy conserving formulation for planetary vorticity term
zu_trd(ji,jj) = r1_4 * ( zwz(ji ,jj-1) * zy1 + zwz(ji,jj) * zy2 )
zv_trd(ji,jj) = - r1_4 * ( zwz(ji-1,jj ) * zx1 + zwz(ji,jj) * zx2 )
END_2D
!
CASE( np_ENS ) ! enstrophy conserving scheme (f-point)
DO_2D( 0, 0, 0, 0 )
zy1 = r1_8 * ( zhV(ji ,jj-1) + zhV(ji+1,jj-1) &
& + zhV(ji ,jj ) + zhV(ji+1,jj ) ) * r1_e1u(ji,jj)
zx1 = - r1_8 * ( zhU(ji-1,jj ) + zhU(ji-1,jj+1) &
& + zhU(ji ,jj ) + zhU(ji ,jj+1) ) * r1_e2v(ji,jj)
zu_trd(ji,jj) = zy1 * ( zwz(ji ,jj-1) + zwz(ji,jj) )
zv_trd(ji,jj) = zx1 * ( zwz(ji-1,jj ) + zwz(ji,jj) )
END_2D
!
CASE( np_EET , np_EEN ) ! energy & enstrophy scheme (using e3t or e3f)
DO_2D( 0, 0, 0, 0 )
zu_trd(ji,jj) = + r1_12 * r1_e1u(ji,jj) * ( ftne(ji,jj ) * zhV(ji ,jj ) &
& + ftnw(ji+1,jj) * zhV(ji+1,jj ) &
& + ftse(ji,jj ) * zhV(ji ,jj-1) &
& + ftsw(ji+1,jj) * zhV(ji+1,jj-1) )
zv_trd(ji,jj) = - r1_12 * r1_e2v(ji,jj) * ( ftsw(ji,jj+1) * zhU(ji-1,jj+1) &
& + ftse(ji,jj+1) * zhU(ji ,jj+1) &
& + ftnw(ji,jj ) * zhU(ji-1,jj ) &
& + ftne(ji,jj ) * zhU(ji ,jj ) )
END_2D
!
END SELECT
!
END SUBROUTINE dyn_cor_2D
SUBROUTINE wad_tmsk( pssh, ptmsk )
!!----------------------------------------------------------------------
!! *** ROUTINE wad_lmt ***
!!
!! ** Purpose : set wetting & drying mask at tracer points
!! for the current barotropic sub-step
!!
!! ** Method : ???
!!
!! ** Action : ptmsk : wetting & drying t-mask
!!----------------------------------------------------------------------
REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pssh !
REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: ptmsk !
!
INTEGER :: ji, jj ! dummy loop indices
!!----------------------------------------------------------------------
!
IF( ln_wd_dl_rmp ) THEN
DO_2D( 1, 1, 1, 1 )
IF ( pssh(ji,jj) + ht_0(ji,jj) > 2._wp * rn_wdmin1 ) THEN
! IF ( pssh(ji,jj) + ht_0(ji,jj) > rn_wdmin2 ) THEN
ptmsk(ji,jj) = 1._wp
ELSEIF( pssh(ji,jj) + ht_0(ji,jj) > rn_wdmin1 ) THEN
ptmsk(ji,jj) = TANH( 50._wp*( ( pssh(ji,jj) + ht_0(ji,jj) - rn_wdmin1 )*r_rn_wdmin1) )
ELSE
ptmsk(ji,jj) = 0._wp
ENDIF
END_2D
ELSE
DO_2D( 1, 1, 1, 1 )
IF ( pssh(ji,jj) + ht_0(ji,jj) > rn_wdmin1 ) THEN ; ptmsk(ji,jj) = 1._wp
ELSE ; ptmsk(ji,jj) = 0._wp
ENDIF
END_2D
ENDIF
!
END SUBROUTINE wad_tmsk
SUBROUTINE wad_Umsk( pTmsk, phU, phV, pu, pv, pUmsk, pVmsk )
!!----------------------------------------------------------------------
!! *** ROUTINE wad_lmt ***
!!
!! ** Purpose : set wetting & drying mask at tracer points
!! for the current barotropic sub-step
!!
!! ** Method : ???
!!
!! ** Action : ptmsk : wetting & drying t-mask
!!----------------------------------------------------------------------
REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pTmsk ! W & D t-mask
REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: phU, phV, pu, pv ! ocean velocities and transports
REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: pUmsk, pVmsk ! W & D u- and v-mask
!
INTEGER :: ji, jj ! dummy loop indices
!!----------------------------------------------------------------------
!
DO_2D( 1, 0, 1, 1 ) ! not jpi-column
IF ( phU(ji,jj) > 0._wp ) THEN ; pUmsk(ji,jj) = pTmsk(ji ,jj)
ELSE ; pUmsk(ji,jj) = pTmsk(ji+1,jj)
ENDIF
phU(ji,jj) = pUmsk(ji,jj)*phU(ji,jj)
pu (ji,jj) = pUmsk(ji,jj)*pu (ji,jj)
END_2D
!
DO_2D( 1, 1, 1, 0 ) ! not jpj-row
IF ( phV(ji,jj) > 0._wp ) THEN ; pVmsk(ji,jj) = pTmsk(ji,jj )
ELSE ; pVmsk(ji,jj) = pTmsk(ji,jj+1)
ENDIF
phV(ji,jj) = pVmsk(ji,jj)*phV(ji,jj)
pv (ji,jj) = pVmsk(ji,jj)*pv (ji,jj)
END_2D
!
END SUBROUTINE wad_Umsk
SUBROUTINE wad_spg( pshn, zcpx, zcpy )
!!---------------------------------------------------------------------
!! *** ROUTINE wad_sp ***
!!
!! ** Purpose :
!!----------------------------------------------------------------------
INTEGER :: ji ,jj ! dummy loop indices
LOGICAL :: ll_tmp1, ll_tmp2
REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pshn
REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: zcpx, zcpy
!!----------------------------------------------------------------------
DO_2D( 0, 0, 0, 0 )
ll_tmp1 = MIN( pshn(ji,jj) , pshn(ji+1,jj) ) > &
& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
& MAX( pshn(ji,jj) + ht_0(ji,jj) , pshn(ji+1,jj) + ht_0(ji+1,jj) ) &
& > rn_wdmin1 + rn_wdmin2
ll_tmp2 = ( ABS( pshn(ji+1,jj) - pshn(ji ,jj)) > 1.E-12 ).AND.( &
& MAX( pshn(ji,jj) , pshn(ji+1,jj) ) > &
& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
IF(ll_tmp1) THEN
zcpx(ji,jj) = 1.0_wp
ELSEIF(ll_tmp2) THEN
! no worries about pshn(ji+1,jj) - pshn(ji ,jj) = 0, it won't happen ! here
zcpx(ji,jj) = ABS( (pshn(ji+1,jj) + ht_0(ji+1,jj) - pshn(ji,jj) - ht_0(ji,jj)) &
& / (pshn(ji+1,jj) - pshn(ji ,jj)) )
zcpx(ji,jj) = max(min( zcpx(ji,jj) , 1.0_wp),0.0_wp)
ELSE
zcpx(ji,jj) = 0._wp
ENDIF
!
ll_tmp1 = MIN( pshn(ji,jj) , pshn(ji,jj+1) ) > &
& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
& MAX( pshn(ji,jj) + ht_0(ji,jj) , pshn(ji,jj+1) + ht_0(ji,jj+1) ) &
& > rn_wdmin1 + rn_wdmin2
ll_tmp2 = ( ABS( pshn(ji,jj) - pshn(ji,jj+1)) > 1.E-12 ).AND.( &
& MAX( pshn(ji,jj) , pshn(ji,jj+1) ) > &
& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
IF(ll_tmp1) THEN
zcpy(ji,jj) = 1.0_wp
ELSE IF(ll_tmp2) THEN
! no worries about pshn(ji,jj+1) - pshn(ji,jj ) = 0, it won't happen ! here
zcpy(ji,jj) = ABS( (pshn(ji,jj+1) + ht_0(ji,jj+1) - pshn(ji,jj) - ht_0(ji,jj)) &
& / (pshn(ji,jj+1) - pshn(ji,jj )) )
zcpy(ji,jj) = MAX( 0._wp , MIN( zcpy(ji,jj) , 1.0_wp ) )
ELSE
zcpy(ji,jj) = 0._wp
ENDIF
END_2D
END SUBROUTINE wad_spg
SUBROUTINE dyn_drg_init( Kbb, Kmm, puu, pvv, puu_b ,pvv_b, pu_RHSi, pv_RHSi, pCdU_u, pCdU_v )
!!----------------------------------------------------------------------
!! *** ROUTINE dyn_drg_init ***
!!
!! ** Purpose : - add the baroclinic top/bottom drag contribution to
!! the baroclinic part of the barotropic RHS
!! - compute the barotropic drag coefficients
!!
!! ** Method : computation done over the INNER domain only
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: Kbb, Kmm ! ocean time level indices
REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(in ) :: puu, pvv ! ocean velocities and RHS of momentum equation
REAL(wp), DIMENSION(jpi,jpj,jpt) , INTENT(in ) :: puu_b, pvv_b ! barotropic velocities at main time levels
REAL(wp), DIMENSION(jpi,jpj) , INTENT(inout) :: pu_RHSi, pv_RHSi ! baroclinic part of the barotropic RHS
REAL(wp), DIMENSION(jpi,jpj) , INTENT( out) :: pCdU_u , pCdU_v ! barotropic drag coefficients
!
INTEGER :: ji, jj ! dummy loop indices
INTEGER :: ikbu, ikbv, iktu, iktv
REAL(wp) :: zztmp
REAL(wp), DIMENSION(jpi,jpj) :: zu_i, zv_i
!!----------------------------------------------------------------------
!
! !== Set the barotropic drag coef. ==!
!
IF( ln_isfcav.OR.ln_drgice_imp ) THEN ! top+bottom friction (ocean cavities)
DO_2D( 0, 0, 0, 0 )
pCdU_u(ji,jj) = r1_2*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) + rCdU_top(ji+1,jj)+rCdU_top(ji,jj) )
pCdU_v(ji,jj) = r1_2*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) + rCdU_top(ji,jj+1)+rCdU_top(ji,jj) )
END_2D
ELSE ! bottom friction only
DO_2D( 0, 0, 0, 0 )
pCdU_u(ji,jj) = r1_2*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) )
pCdU_v(ji,jj) = r1_2*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) )
END_2D
ENDIF
!
! !== BOTTOM stress contribution from baroclinic velocities ==!
!
IF( ln_bt_fw ) THEN ! FORWARD integration: use NOW bottom baroclinic velocities
DO_2D( 0, 0, 0, 0 )
ikbu = mbku(ji,jj)
ikbv = mbkv(ji,jj)
zu_i(ji,jj) = puu(ji,jj,ikbu,Kmm) - puu_b(ji,jj,Kmm)
zv_i(ji,jj) = pvv(ji,jj,ikbv,Kmm) - pvv_b(ji,jj,Kmm)
END_2D
ELSE ! CENTRED integration: use BEFORE bottom baroclinic velocities
DO_2D( 0, 0, 0, 0 )
ikbu = mbku(ji,jj)
ikbv = mbkv(ji,jj)
zu_i(ji,jj) = puu(ji,jj,ikbu,Kbb) - puu_b(ji,jj,Kbb)
zv_i(ji,jj) = pvv(ji,jj,ikbv,Kbb) - pvv_b(ji,jj,Kbb)
END_2D
ENDIF
!
IF( ln_wd_il ) THEN ! W/D : use the "clipped" bottom friction !!gm explain WHY, please !
zztmp = -1._wp / rDt_e
DO_2D( 0, 0, 0, 0 )
pu_RHSi(ji,jj) = pu_RHSi(ji,jj) + zu_i(ji,jj) * wdrampu(ji,jj) * MAX( &
& r1_hu(ji,jj,Kmm) * r1_2*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) , zztmp )
pv_RHSi(ji,jj) = pv_RHSi(ji,jj) + zv_i(ji,jj) * wdrampv(ji,jj) * MAX( &
& r1_hv(ji,jj,Kmm) * r1_2*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) , zztmp )
END_2D
ELSE ! use "unclipped" drag (even if explicit friction is used in 3D calculation)
DO_2D( 0, 0, 0, 0 )
pu_RHSi(ji,jj) = pu_RHSi(ji,jj) + r1_hu(ji,jj,Kmm) * r1_2*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) * zu_i(ji,jj)
pv_RHSi(ji,jj) = pv_RHSi(ji,jj) + r1_hv(ji,jj,Kmm) * r1_2*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) * zv_i(ji,jj)
END_2D
END IF
!
! !== TOP stress contribution from baroclinic velocities ==! (no W/D case)
!
IF( ln_isfcav.OR.ln_drgice_imp ) THEN
!
IF( ln_bt_fw ) THEN ! FORWARD integration: use NOW top baroclinic velocity
DO_2D( 0, 0, 0, 0 )
iktu = miku(ji,jj)
iktv = mikv(ji,jj)
zu_i(ji,jj) = puu(ji,jj,iktu,Kmm) - puu_b(ji,jj,Kmm)
zv_i(ji,jj) = pvv(ji,jj,iktv,Kmm) - pvv_b(ji,jj,Kmm)
END_2D
ELSE ! CENTRED integration: use BEFORE top baroclinic velocity
DO_2D( 0, 0, 0, 0 )
iktu = miku(ji,jj)
iktv = mikv(ji,jj)
zu_i(ji,jj) = puu(ji,jj,iktu,Kbb) - puu_b(ji,jj,Kbb)
zv_i(ji,jj) = pvv(ji,jj,iktv,Kbb) - pvv_b(ji,jj,Kbb)
END_2D
ENDIF
!
! ! use "unclipped" top drag (even if explicit friction is used in 3D calculation)
DO_2D( 0, 0, 0, 0 )
pu_RHSi(ji,jj) = pu_RHSi(ji,jj) + r1_hu(ji,jj,Kmm) * r1_2*( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) * zu_i(ji,jj)
pv_RHSi(ji,jj) = pv_RHSi(ji,jj) + r1_hv(ji,jj,Kmm) * r1_2*( rCdU_top(ji,jj+1)+rCdU_top(ji,jj) ) * zv_i(ji,jj)
END_2D
!
ENDIF
!
END SUBROUTINE dyn_drg_init
SUBROUTINE ts_bck_interp( jn, ll_init, & ! <== in
& za0, za1, za2, za3 ) ! ==> out
!!----------------------------------------------------------------------
INTEGER ,INTENT(in ) :: jn ! index of sub time step
LOGICAL ,INTENT(in ) :: ll_init !
REAL(wp),INTENT( out) :: za0, za1, za2, za3 ! Half-step back interpolation coefficient
!
REAL(wp) :: zepsilon, zgamma ! - -
!!----------------------------------------------------------------------
! ! set Half-step back interpolation coefficient
IF ( jn==1 .AND. ll_init ) THEN !* Forward-backward
za0 = 1._wp
za1 = 0._wp
za2 = 0._wp
za3 = 0._wp
ELSEIF( jn==2 .AND. ll_init ) THEN !* AB2-AM3 Coefficients; bet=0 ; gam=-1/6 ; eps=1/12
za0 = 1.0833333333333_wp ! za0 = 1-gam-eps
za1 =-0.1666666666666_wp ! za1 = gam
za2 = 0.0833333333333_wp ! za2 = eps
za3 = 0._wp
ELSE !* AB3-AM4 Coefficients; bet=0.281105 ; eps=0.013 ; gam=0.0880
IF( rn_bt_alpha == 0._wp ) THEN ! Time diffusion
za0 = 0.614_wp ! za0 = 1/2 + gam + 2*eps
za1 = 0.285_wp ! za1 = 1/2 - 2*gam - 3*eps
za2 = 0.088_wp ! za2 = gam
za3 = 0.013_wp ! za3 = eps
ELSE ! no time diffusion
zepsilon = 0.00976186_wp - 0.13451357_wp * rn_bt_alpha
zgamma = 0.08344500_wp - 0.51358400_wp * rn_bt_alpha
za0 = 0.5_wp + zgamma + 2._wp * rn_bt_alpha + 2._wp * zepsilon
za1 = 1._wp - za0 - zgamma - zepsilon
za2 = zgamma
za3 = zepsilon
ENDIF
ENDIF
END SUBROUTINE ts_bck_interp
!!======================================================================
END MODULE dynspg_ts