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dynspg_ts.F90 in NEMO/branches/2019/dev_r12072_MERGE_OPTION2_2019/src/OCE/DYN – NEMO

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source: NEMO/branches/2019/dev_r12072_MERGE_OPTION2_2019/src/OCE/DYN/dynspg_ts.F90 @ 12246

Last change on this file since 12246 was 12246, checked in by smasson, 4 years ago
rev12232_dev_r12072_MERGE_OPTION2_2019: add modifications from dev_r12114_ticket_2263, results unchanged except SPITZ12 as explained in #2263
Property svn:keywords set to `Id`
File size: 80.9 KB

Line
1	MODULE dynspg_ts
2
3	!! Includes ROMS wd scheme with diagnostic outputs ; un and ua updates are commented out !
4
5	!!======================================================================
6	!! * MODULE dynspg_ts *
7	!! Ocean dynamics: surface pressure gradient trend, split-explicit scheme
8	!!======================================================================
9	!! History : 1.0 ! 2004-12 (L. Bessieres, G. Madec) Original code
10	!! - ! 2005-11 (V. Garnier, G. Madec) optimization
11	!! - ! 2006-08 (S. Masson) distributed restart using iom
12	!! 2.0 ! 2007-07 (D. Storkey) calls to BDY routines
13	!! - ! 2008-01 (R. Benshila) change averaging method
14	!! 3.2 ! 2009-07 (R. Benshila, G. Madec) Complete revisit associated to vvl reactivation
15	!! 3.3 ! 2010-09 (D. Storkey, E. O'Dea) update for BDY for Shelf configurations
16	!! 3.3 ! 2011-03 (R. Benshila, R. Hordoir, P. Oddo) update calculation of ub_b
17	!! 3.5 ! 2013-07 (J. Chanut) Switch to Forward-backward time stepping
18	!! 3.6 ! 2013-11 (A. Coward) Update for z-tilde compatibility
19	!! 3.7 ! 2015-11 (J. Chanut) free surface simplification
20	!! - ! 2016-12 (G. Madec, E. Clementi) update for Stoke-Drift divergence
21	!! 4.0 ! 2017-05 (G. Madec) drag coef. defined at t-point (zdfdrg.F90)
22	!!---------------------------------------------------------------------
23
24	!!----------------------------------------------------------------------
25	!! dyn_spg_ts : compute surface pressure gradient trend using a time-splitting scheme
26	!! dyn_spg_ts_init: initialisation of the time-splitting scheme
27	!! ts_wgt : set time-splitting weights for temporal averaging (or not)
28	!! ts_rst : read/write time-splitting fields in restart file
29	!!----------------------------------------------------------------------
30	USE oce ! ocean dynamics and tracers
31	USE dom_oce ! ocean space and time domain
32	USE sbc_oce ! surface boundary condition: ocean
33	USE isf_oce ! ice shelf variable (fwfisf)
34	USE zdf_oce ! vertical physics: variables
35	USE zdfdrg ! vertical physics: top/bottom drag coef.
36	USE sbcapr ! surface boundary condition: atmospheric pressure
37	USE dynadv , ONLY: ln_dynadv_vec
38	USE dynvor ! vortivity scheme indicators
39	USE phycst ! physical constants
40	USE dynvor ! vorticity term
41	USE wet_dry ! wetting/drying flux limter
42	USE bdy_oce ! open boundary
43	USE bdyvol ! open boundary volume conservation
44	USE bdytides ! open boundary condition data
45	USE bdydyn2d ! open boundary conditions on barotropic variables
46	USE tide_mod !
47	USE sbcwave ! surface wave
48	USE diatmb ! Top,middle,bottom output
49	#if defined key_agrif
50	USE agrif_oce_interp ! agrif
51	USE agrif_oce
52	#endif
53	#if defined key_asminc
54	USE asminc ! Assimilation increment
55	#endif
56	!
57	USE in_out_manager ! I/O manager
58	USE lib_mpp ! distributed memory computing library
59	USE lbclnk ! ocean lateral boundary conditions (or mpp link)
60	USE prtctl ! Print control
61	USE iom ! IOM library
62	USE restart ! only for lrst_oce
63	USE diatmb ! Top,middle,bottom output
64
65	USE iom ! to remove
66
67	IMPLICIT NONE
68	PRIVATE
69
70	PUBLIC dyn_spg_ts ! called by dyn_spg
71	PUBLIC dyn_spg_ts_init ! - - dyn_spg_init
72
73	!! Time filtered arrays at baroclinic time step:
74	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: un_adv , vn_adv !: Advection vel. at "now" barocl. step
75	!
76	INTEGER, SAVE :: icycle ! Number of barotropic sub-steps for each internal step nn_baro <= 2.5 nn_baro
77	REAL(wp),SAVE :: rdtbt ! Barotropic time step
78	!
79	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:) :: wgtbtp1, wgtbtp2 ! 1st & 2nd weights used in time filtering of barotropic fields
80	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: zwz ! ff_f/h at F points
81	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: ftnw, ftne ! triad of coriolis parameter
82	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: ftsw, ftse ! (only used with een vorticity scheme)
83
84	REAL(wp) :: r1_12 = 1._wp / 12._wp ! local ratios
85	REAL(wp) :: r1_8 = 0.125_wp !
86	REAL(wp) :: r1_4 = 0.25_wp !
87	REAL(wp) :: r1_2 = 0.5_wp !
88
89	!! * Substitutions
90	# include "vectopt_loop_substitute.h90"
91	!!----------------------------------------------------------------------
92	!! NEMO/OCE 4.0 , NEMO Consortium (2018)
93	!! $Id$
94	!! Software governed by the CeCILL license (see ./LICENSE)
95	!!----------------------------------------------------------------------
96	CONTAINS
97
98	INTEGER FUNCTION dyn_spg_ts_alloc()
99	!!----------------------------------------------------------------------
100	!! * routine dyn_spg_ts_alloc *
101	!!----------------------------------------------------------------------
102	INTEGER :: ierr(3)
103	!!----------------------------------------------------------------------
104	ierr(:) = 0
105	!
106	ALLOCATE( wgtbtp1(3nn_baro), wgtbtp2(3nn_baro), zwz(jpi,jpj), STAT=ierr(1) )
107	IF( ln_dynvor_een .OR. ln_dynvor_eeT ) &
108	& ALLOCATE( ftnw(jpi,jpj) , ftne(jpi,jpj) , ftsw(jpi,jpj) , ftse(jpi,jpj), STAT=ierr(2) )
109	!
110	ALLOCATE( un_adv(jpi,jpj), vn_adv(jpi,jpj) , STAT=ierr(3) )
111	!
112	dyn_spg_ts_alloc = MAXVAL( ierr(:) )
113	!
114	CALL mpp_sum( 'dynspg_ts', dyn_spg_ts_alloc )
115	IF( dyn_spg_ts_alloc /= 0 ) CALL ctl_stop( 'STOP', 'dyn_spg_ts_alloc: failed to allocate arrays' )
116	!
117	END FUNCTION dyn_spg_ts_alloc
118
119
120	SUBROUTINE dyn_spg_ts( kt )
121	!!----------------------------------------------------------------------
122	!!
123	!! ** Purpose : - Compute the now trend due to the explicit time stepping
124	!! of the quasi-linear barotropic system, and add it to the
125	!! general momentum trend.
126	!!
127	!! ** Method : - split-explicit schem (time splitting) :
128	!! Barotropic variables are advanced from internal time steps
129	!! "n" to "n+1" if ln_bt_fw=T
130	!! or from
131	!! "n-1" to "n+1" if ln_bt_fw=F
132	!! thanks to a generalized forward-backward time stepping (see ref. below).
133	!!
134	!! ** Action :
135	!! -Update the filtered free surface at step "n+1" : ssha
136	!! -Update filtered barotropic velocities at step "n+1" : ua_b, va_b
137	!! -Compute barotropic advective fluxes at step "n" : un_adv, vn_adv
138	!! These are used to advect tracers and are compliant with discrete
139	!! continuity equation taken at the baroclinic time steps. This
140	!! ensures tracers conservation.
141	!! - (ua, va) momentum trend updated with barotropic component.
142	!!
143	!! References : Shchepetkin and McWilliams, Ocean Modelling, 2005.
144	!!---------------------------------------------------------------------
145	INTEGER, INTENT(in) :: kt ! ocean time-step index
146	!
147	INTEGER :: ji, jj, jk, jn ! dummy loop indices
148	LOGICAL :: ll_fw_start ! =T : forward integration
149	LOGICAL :: ll_init ! =T : special startup of 2d equations
150	INTEGER :: noffset ! local integers : time offset for bdy update
151	REAL(wp) :: r1_2dt_b, z1_hu, z1_hv ! local scalars
152	REAL(wp) :: za0, za1, za2, za3 ! - -
153	REAL(wp) :: zmdi, zztmp, zldg ! - -
154	REAL(wp) :: zhu_bck, zhv_bck, zhdiv ! - -
155	REAL(wp) :: zun_save, zvn_save ! - -
156	REAL(wp), DIMENSION(jpi,jpj) :: zu_trd, zu_frc, zu_spg, zssh_frc
157	REAL(wp), DIMENSION(jpi,jpj) :: zv_trd, zv_frc, zv_spg
158	REAL(wp), DIMENSION(jpi,jpj) :: zsshu_a, zhup2_e, zhtp2_e
159	REAL(wp), DIMENSION(jpi,jpj) :: zsshv_a, zhvp2_e, zsshp2_e
160	REAL(wp), DIMENSION(jpi,jpj) :: zCdU_u, zCdU_v ! top/bottom stress at u- & v-points
161	REAL(wp), DIMENSION(jpi,jpj) :: zhU, zhV ! fluxes
162	!
163	REAL(wp) :: zwdramp ! local scalar - only used if ln_wd_dl = .True.
164
165	INTEGER :: iwdg, jwdg, kwdg ! short-hand values for the indices of the output point
166
167	REAL(wp) :: zepsilon, zgamma ! - -
168	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zcpx, zcpy ! Wetting/Dying gravity filter coef.
169	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: ztwdmask, zuwdmask, zvwdmask ! ROMS wetting and drying masks at t,u,v points
170	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zuwdav2, zvwdav2 ! averages over the sub-steps of zuwdmask and zvwdmask
171	REAL(wp) :: zt0substep ! Time of day at the beginning of the time substep
172	!!----------------------------------------------------------------------
173	!
174	IF( ln_wd_il ) ALLOCATE( zcpx(jpi,jpj), zcpy(jpi,jpj) )
175	! !* Allocate temporary arrays
176	IF( ln_wd_dl ) ALLOCATE( ztwdmask(jpi,jpj), zuwdmask(jpi,jpj), zvwdmask(jpi,jpj), zuwdav2(jpi,jpj), zvwdav2(jpi,jpj))
177	!
178	zmdi=1.e+20 ! missing data indicator for masking
179	!
180	zwdramp = r_rn_wdmin1 ! simplest ramp
181	! zwdramp = 1._wp / (rn_wdmin2 - rn_wdmin1) ! more general ramp
182	! ! inverse of baroclinic time step
183	IF( kt == nit000 .AND. neuler == 0 ) THEN ; r1_2dt_b = 1._wp / ( rdt )
184	ELSE ; r1_2dt_b = 1._wp / ( 2._wp * rdt )
185	ENDIF
186	!
187	ll_init = ln_bt_av ! if no time averaging, then no specific restart
188	ll_fw_start = .FALSE.
189	! ! time offset in steps for bdy data update
190	IF( .NOT.ln_bt_fw ) THEN ; noffset = - nn_baro
191	ELSE ; noffset = 0
192	ENDIF
193	!
194	IF( kt == nit000 ) THEN !* initialisation
195	!
196	IF(lwp) WRITE(numout,*)
197	IF(lwp) WRITE(numout,*) 'dyn_spg_ts : surface pressure gradient trend'
198	IF(lwp) WRITE(numout,*) '~~~~~~~~~~ free surface with time splitting'
199	IF(lwp) WRITE(numout,*)
200	!
201	IF( neuler == 0 ) ll_init=.TRUE.
202	!
203	IF( ln_bt_fw .OR. neuler == 0 ) THEN
204	ll_fw_start =.TRUE.
205	noffset = 0
206	ELSE
207	ll_fw_start =.FALSE.
208	ENDIF
209	! ! Set averaging weights and cycle length:
210	CALL ts_wgt( ln_bt_av, ll_fw_start, icycle, wgtbtp1, wgtbtp2 )
211	!
212	ENDIF
213	!
214	! If forward start at previous time step, and centered integration,
215	! then update averaging weights:
216	IF (.NOT.ln_bt_fw .AND.( neuler==0 .AND. kt==nit000+1 ) ) THEN
217	ll_fw_start=.FALSE.
218	CALL ts_wgt( ln_bt_av, ll_fw_start, icycle, wgtbtp1, wgtbtp2 )
219	ENDIF
220	!
221
222	! -----------------------------------------------------------------------------
223	! Phase 1 : Coupling between general trend and barotropic estimates (1st step)
224	! -----------------------------------------------------------------------------
225	!
226	!
227	! != zu_frc = 1/H e3*d/dt(Ua) =! (Vertical mean of Ua, the 3D trends)
228	! ! --------------------------- !
229	zu_frc(:,:) = SUM( e3u_n(:,:,:) * ua(:,:,:) * umask(:,:,:) , DIM=3 ) * r1_hu_n(:,:)
230	zv_frc(:,:) = SUM( e3v_n(:,:,:) * va(:,:,:) * vmask(:,:,:) , DIM=3 ) * r1_hv_n(:,:)
231	!
232	!
233	! != Ua => baroclinic trend =! (remove its vertical mean)
234	DO jk = 1, jpkm1 ! ------------------------ !
235	ua(:,:,jk) = ( ua(:,:,jk) - zu_frc(:,:) ) * umask(:,:,jk)
236	va(:,:,jk) = ( va(:,:,jk) - zv_frc(:,:) ) * vmask(:,:,jk)
237	END DO
238
239	!!gm Question here when removing the Vertically integrated trends, we remove the vertically integrated NL trends on momentum....
240	!!gm Is it correct to do so ? I think so...
241
242	! != remove 2D Coriolis and pressure gradient trends =!
243	! ! ------------------------------------------------- !
244	!
245	IF( kt == nit000 .OR. .NOT. ln_linssh ) CALL dyn_cor_2D_init ! Set zwz, the barotropic Coriolis force coefficient
246	! ! recompute zwz = f/depth at every time step for (.NOT.ln_linssh) as the water colomn height changes
247	!
248	! !* 2D Coriolis trends
249	zhU(:,:) = un_b(:,:) * hu_n(:,:) * e2u(:,:) ! now fluxes
250	zhV(:,:) = vn_b(:,:) * hv_n(:,:) * e1v(:,:) ! NB: FULL domain : put a value in last row and column
251	!
252	CALL dyn_cor_2d( hu_n, hv_n, un_b, vn_b, zhU, zhV, & ! <<== in
253	& zu_trd, zv_trd ) ! ==>> out
254	!
255	IF( .NOT.ln_linssh ) THEN !* surface pressure gradient (variable volume only)
256	!
257	IF( ln_wd_il ) THEN ! W/D : limiter applied to spgspg
258	CALL wad_spg( sshn, zcpx, zcpy ) ! Calculating W/D gravity filters, zcpx and zcpy
259	DO jj = 2, jpjm1
260	DO ji = 2, jpim1 ! SPG with the application of W/D gravity filters
261	zu_trd(ji,jj) = zu_trd(ji,jj) - grav * ( sshn(ji+1,jj ) - sshn(ji ,jj ) ) &
262	& * r1_e1u(ji,jj) * zcpx(ji,jj) * wdrampu(ji,jj) !jth
263	zv_trd(ji,jj) = zv_trd(ji,jj) - grav * ( sshn(ji ,jj+1) - sshn(ji ,jj ) ) &
264	& * r1_e2v(ji,jj) * zcpy(ji,jj) * wdrampv(ji,jj) !jth
265	END DO
266	END DO
267	ELSE ! now suface pressure gradient
268	DO jj = 2, jpjm1
269	DO ji = fs_2, fs_jpim1 ! vector opt.
270	zu_trd(ji,jj) = zu_trd(ji,jj) - grav * ( sshn(ji+1,jj ) - sshn(ji ,jj ) ) * r1_e1u(ji,jj)
271	zv_trd(ji,jj) = zv_trd(ji,jj) - grav * ( sshn(ji ,jj+1) - sshn(ji ,jj ) ) * r1_e2v(ji,jj)
272	END DO
273	END DO
274	ENDIF
275	!
276	ENDIF
277	!
278	DO jj = 2, jpjm1 ! Remove coriolis term (and possibly spg) from barotropic trend
279	DO ji = fs_2, fs_jpim1
280	zu_frc(ji,jj) = zu_frc(ji,jj) - zu_trd(ji,jj) * ssumask(ji,jj)
281	zv_frc(ji,jj) = zv_frc(ji,jj) - zv_trd(ji,jj) * ssvmask(ji,jj)
282	END DO
283	END DO
284	!
285	! != Add bottom stress contribution from baroclinic velocities =!
286	! ! ----------------------------------------------------------- !
287	CALL dyn_drg_init( zu_frc, zv_frc, zCdU_u, zCdU_v ) ! also provide the barotropic drag coefficients
288	!
289	! != Add atmospheric pressure forcing =!
290	! ! ---------------------------------- !
291	IF( ln_apr_dyn ) THEN
292	IF( ln_bt_fw ) THEN ! FORWARD integration: use kt+1/2 pressure (NOW+1/2)
293	DO jj = 2, jpjm1
294	DO ji = fs_2, fs_jpim1 ! vector opt.
295	zu_frc(ji,jj) = zu_frc(ji,jj) + grav * ( ssh_ib (ji+1,jj ) - ssh_ib (ji,jj) ) * r1_e1u(ji,jj)
296	zv_frc(ji,jj) = zv_frc(ji,jj) + grav * ( ssh_ib (ji ,jj+1) - ssh_ib (ji,jj) ) * r1_e2v(ji,jj)
297	END DO
298	END DO
299	ELSE ! CENTRED integration: use kt-1/2 + kt+1/2 pressure (NOW)
300	zztmp = grav * r1_2
301	DO jj = 2, jpjm1
302	DO ji = fs_2, fs_jpim1 ! vector opt.
303	zu_frc(ji,jj) = zu_frc(ji,jj) + zztmp * ( ssh_ib (ji+1,jj ) - ssh_ib (ji,jj) &
304	& + ssh_ibb(ji+1,jj ) - ssh_ibb(ji,jj) ) * r1_e1u(ji,jj)
305	zv_frc(ji,jj) = zv_frc(ji,jj) + zztmp * ( ssh_ib (ji ,jj+1) - ssh_ib (ji,jj) &
306	& + ssh_ibb(ji ,jj+1) - ssh_ibb(ji,jj) ) * r1_e2v(ji,jj)
307	END DO
308	END DO
309	ENDIF
310	ENDIF
311	!
312	! != Add atmospheric pressure forcing =!
313	! ! ---------------------------------- !
314	IF( ln_bt_fw ) THEN ! Add wind forcing
315	DO jj = 2, jpjm1
316	DO ji = fs_2, fs_jpim1 ! vector opt.
317	zu_frc(ji,jj) = zu_frc(ji,jj) + r1_rau0 * utau(ji,jj) * r1_hu_n(ji,jj)
318	zv_frc(ji,jj) = zv_frc(ji,jj) + r1_rau0 * vtau(ji,jj) * r1_hv_n(ji,jj)
319	END DO
320	END DO
321	ELSE
322	zztmp = r1_rau0 * r1_2
323	DO jj = 2, jpjm1
324	DO ji = fs_2, fs_jpim1 ! vector opt.
325	zu_frc(ji,jj) = zu_frc(ji,jj) + zztmp * ( utau_b(ji,jj) + utau(ji,jj) ) * r1_hu_n(ji,jj)
326	zv_frc(ji,jj) = zv_frc(ji,jj) + zztmp * ( vtau_b(ji,jj) + vtau(ji,jj) ) * r1_hv_n(ji,jj)
327	END DO
328	END DO
329	ENDIF
330	!
331	! !----------------!
332	! !== sssh_frc ==! Right-Hand-Side of the barotropic ssh equation (over the FULL domain)
333	! !----------------!
334	! != Net water flux forcing applied to a water column =!
335	! ! --------------------------------------------------- !
336	IF (ln_bt_fw) THEN ! FORWARD integration: use kt+1/2 fluxes (NOW+1/2)
337	zssh_frc(:,:) = r1_rau0 * ( emp(:,:) - rnf(:,:) + fwfisf_cav(:,:) + fwfisf_par(:,:) )
338	ELSE ! CENTRED integration: use kt-1/2 + kt+1/2 fluxes (NOW)
339	zztmp = r1_rau0 * r1_2
340	zssh_frc(:,:) = zztmp * ( emp(:,:) + emp_b(:,:) &
341	& - rnf(:,:) - rnf_b(:,:) &
342	& + fwfisf_cav(:,:) + fwfisf_cav_b(:,:) &
343	& + fwfisf_par(:,:) + fwfisf_par_b(:,:) )
344	ENDIF
345	! != Add Stokes drift divergence =! (if exist)
346	IF( ln_sdw ) THEN ! ----------------------------- !
347	zssh_frc(:,:) = zssh_frc(:,:) + div_sd(:,:)
348	ENDIF
349	!
350	! ! ice sheet coupling
351	IF ( ln_isf .AND. ln_isfcpl ) THEN
352	!
353	! ice sheet coupling
354	IF( ln_rstart .AND. kt == nit000 ) THEN
355	zssh_frc(:,:) = zssh_frc(:,:) + risfcpl_ssh(:,:)
356	END IF
357	!
358	! conservation option
359	IF( ln_isfcpl_cons ) THEN
360	zssh_frc(:,:) = zssh_frc(:,:) + risfcpl_cons_ssh(:,:)
361	END IF
362	!
363	END IF
364	!
365	#if defined key_asminc
366	! != Add the IAU weighted SSH increment =!
367	! ! ------------------------------------ !
368	IF( lk_asminc .AND. ln_sshinc .AND. ln_asmiau ) THEN
369	zssh_frc(:,:) = zssh_frc(:,:) - ssh_iau(:,:)
370	ENDIF
371	#endif
372	! != Fill boundary data arrays for AGRIF
373	! ! ------------------------------------
374	#if defined key_agrif
375	IF( .NOT.Agrif_Root() ) CALL agrif_dta_ts( kt )
376	#endif
377	!
378	! -----------------------------------------------------------------------
379	! Phase 2 : Integration of the barotropic equations
380	! -----------------------------------------------------------------------
381	!
382	! ! ==================== !
383	! ! Initialisations !
384	! ! ==================== !
385	! Initialize barotropic variables:
386	IF( ll_init )THEN
387	sshbb_e(:,:) = 0._wp
388	ubb_e (:,:) = 0._wp
389	vbb_e (:,:) = 0._wp
390	sshb_e (:,:) = 0._wp
391	ub_e (:,:) = 0._wp
392	vb_e (:,:) = 0._wp
393	ENDIF
394	!
395	IF( ln_linssh ) THEN ! mid-step ocean depth is fixed (hup2_e=hu_n=hu_0)
396	zhup2_e(:,:) = hu_n(:,:)
397	zhvp2_e(:,:) = hv_n(:,:)
398	zhtp2_e(:,:) = ht_n(:,:)
399	ENDIF
400	!
401	IF (ln_bt_fw) THEN ! FORWARD integration: start from NOW fields
402	sshn_e(:,:) = sshn(:,:)
403	un_e (:,:) = un_b(:,:)
404	vn_e (:,:) = vn_b(:,:)
405	!
406	hu_e (:,:) = hu_n(:,:)
407	hv_e (:,:) = hv_n(:,:)
408	hur_e (:,:) = r1_hu_n(:,:)
409	hvr_e (:,:) = r1_hv_n(:,:)
410	ELSE ! CENTRED integration: start from BEFORE fields
411	sshn_e(:,:) = sshb(:,:)
412	un_e (:,:) = ub_b(:,:)
413	vn_e (:,:) = vb_b(:,:)
414	!
415	hu_e (:,:) = hu_b(:,:)
416	hv_e (:,:) = hv_b(:,:)
417	hur_e (:,:) = r1_hu_b(:,:)
418	hvr_e (:,:) = r1_hv_b(:,:)
419	ENDIF
420	!
421	! Initialize sums:
422	ua_b (:,:) = 0._wp ! After barotropic velocities (or transport if flux form)
423	va_b (:,:) = 0._wp
424	ssha (:,:) = 0._wp ! Sum for after averaged sea level
425	un_adv(:,:) = 0._wp ! Sum for now transport issued from ts loop
426	vn_adv(:,:) = 0._wp
427	!
428	IF( ln_wd_dl ) THEN
429	zuwdmask(:,:) = 0._wp ! set to zero for definiteness (not sure this is necessary)
430	zvwdmask(:,:) = 0._wp !
431	zuwdav2 (:,:) = 0._wp
432	zvwdav2 (:,:) = 0._wp
433	END IF
434
435	! ! ==================== !
436	DO jn = 1, icycle ! sub-time-step loop !
437	! ! ==================== !
438	!
439	l_full_nf_update = jn == icycle ! false: disable full North fold update (performances) for jn = 1 to icycle-1
440	!
441	! !== Update the forcing ==! (BDY and tides)
442	!
443	IF( ln_bdy .AND. ln_tide ) CALL bdy_dta_tides( kt, kit=jn, pt_offset= REAL(noffset+1,wp) )
444	! Update tide potential at the beginning of current time substep
445	IF( ln_tide_pot .AND. ln_tide ) THEN
446	zt0substep = REAL(nsec_day, wp) - 0.5_wprdt + (jn + noffset - 1) rdt / REAL(nn_baro, wp)
447	CALL upd_tide(zt0substep)
448	END IF
449	!
450	! !== extrapolation at mid-step ==! (jn+1/2)
451	!
452	! !* Set extrapolation coefficients for predictor step:
453	IF ((jn<3).AND.ll_init) THEN ! Forward
454	za1 = 1._wp
455	za2 = 0._wp
456	za3 = 0._wp
457	ELSE ! AB3-AM4 Coefficients: bet=0.281105
458	za1 = 1.781105_wp ! za1 = 3/2 + bet
459	za2 = -1.06221_wp ! za2 = -(1/2 + 2*bet)
460	za3 = 0.281105_wp ! za3 = bet
461	ENDIF
462	!
463	! !* Extrapolate barotropic velocities at mid-step (jn+1/2)
464	!-- m+1/2 m m-1 m-2 --!
465	!-- u = (3/2+beta) u -(1/2+2beta) u + beta u --!
466	!-------------------------------------------------------------------------!
467	ua_e(:,:) = za1 * un_e(:,:) + za2 * ub_e(:,:) + za3 * ubb_e(:,:)
468	va_e(:,:) = za1 * vn_e(:,:) + za2 * vb_e(:,:) + za3 * vbb_e(:,:)
469
470	IF( .NOT.ln_linssh ) THEN !* Update ocean depth (variable volume case only)
471	! ! ------------------
472	! Extrapolate Sea Level at step jit+0.5:
473	!-- m+1/2 m m-1 m-2 --!
474	!-- ssh = (3/2+beta) ssh -(1/2+2beta) ssh + beta ssh --!
475	!--------------------------------------------------------------------------------!
476	zsshp2_e(:,:) = za1 * sshn_e(:,:) + za2 * sshb_e(:,:) + za3 * sshbb_e(:,:)
477
478	! set wetting & drying mask at tracer points for this barotropic mid-step
479	IF( ln_wd_dl ) CALL wad_tmsk( zsshp2_e, ztwdmask )
480	!
481	! ! ocean t-depth at mid-step
482	zhtp2_e(:,:) = ht_0(:,:) + zsshp2_e(:,:)
483	!
484	! ! ocean u- and v-depth at mid-step (separate DO-loops remove the need of a lbc_lnk)
485	DO jj = 1, jpj
486	DO ji = 1, jpim1 ! not jpi-column
487	zhup2_e(ji,jj) = hu_0(ji,jj) + r1_2 * r1_e1e2u(ji,jj) &
488	& * ( e1e2t(ji ,jj) * zsshp2_e(ji ,jj) &
489	& + e1e2t(ji+1,jj) * zsshp2_e(ji+1,jj) ) * ssumask(ji,jj)
490	END DO
491	END DO
492	DO jj = 1, jpjm1 ! not jpj-row
493	DO ji = 1, jpi
494	zhvp2_e(ji,jj) = hv_0(ji,jj) + r1_2 * r1_e1e2v(ji,jj) &
495	& * ( e1e2t(ji,jj ) * zsshp2_e(ji,jj ) &
496	& + e1e2t(ji,jj+1) * zsshp2_e(ji,jj+1) ) * ssvmask(ji,jj)
497	END DO
498	END DO
499	!
500	ENDIF
501	!
502	! !== after SSH ==! (jn+1)
503	!
504	! ! update (ua_e,va_e) to enforce volume conservation at open boundaries
505	! ! values of zhup2_e and zhvp2_e on the halo are not needed in bdy_vol2d
506	IF( ln_bdy .AND. ln_vol ) CALL bdy_vol2d( kt, jn, ua_e, va_e, zhup2_e, zhvp2_e )
507	!
508	! ! resulting flux at mid-step (not over the full domain)
509	zhU(1:jpim1,1:jpj ) = e2u(1:jpim1,1:jpj ) * ua_e(1:jpim1,1:jpj ) * zhup2_e(1:jpim1,1:jpj ) ! not jpi-column
510	zhV(1:jpi ,1:jpjm1) = e1v(1:jpi ,1:jpjm1) * va_e(1:jpi ,1:jpjm1) * zhvp2_e(1:jpi ,1:jpjm1) ! not jpj-row
511	!
512	#if defined key_agrif
513	! Set fluxes during predictor step to ensure volume conservation
514	IF( .NOT.Agrif_Root() .AND. ln_bt_fw ) CALL agrif_dyn_ts_flux( jn, zhU, zhV )
515	#endif
516	IF( ln_wd_il ) CALL wad_lmt_bt(zhU, zhV, sshn_e, zssh_frc, rdtbt) !!gm wad_lmt_bt use of lbc_lnk on zhU, zhV
517
518	IF( ln_wd_dl ) THEN ! un_e and vn_e are set to zero at faces where
519	! ! the direction of the flow is from dry cells
520	CALL wad_Umsk( ztwdmask, zhU, zhV, un_e, vn_e, zuwdmask, zvwdmask ) ! not jpi colomn for U, not jpj row for V
521	!
522	ENDIF
523	!
524	!
525	! Compute Sea Level at step jit+1
526	!-- m+1 m m+1/2 --!
527	!-- ssh = ssh - delta_t' * [ frc + div( flux ) ] --!
528	!-------------------------------------------------------------------------!
529	DO jj = 2, jpjm1 ! INNER domain
530	DO ji = 2, jpim1
531	zhdiv = ( zhU(ji,jj) - zhU(ji-1,jj) + zhV(ji,jj) - zhV(ji,jj-1) ) * r1_e1e2t(ji,jj)
532	ssha_e(ji,jj) = ( sshn_e(ji,jj) - rdtbt * ( zssh_frc(ji,jj) + zhdiv ) ) * ssmask(ji,jj)
533	END DO
534	END DO
535	!
536	CALL lbc_lnk_multi( 'dynspg_ts', ssha_e, 'T', 1._wp, zhU, 'U', -1._wp, zhV, 'V', -1._wp )
537	!
538	! ! Sum over sub-time-steps to compute advective velocities
539	za2 = wgtbtp2(jn) ! zhU, zhV hold fluxes extrapolated at jn+0.5
540	un_adv(:,:) = un_adv(:,:) + za2 * zhU(:,:) * r1_e2u(:,:)
541	vn_adv(:,:) = vn_adv(:,:) + za2 * zhV(:,:) * r1_e1v(:,:)
542	! sum over sub-time-steps to decide which baroclinic velocities to set to zero (zuwdav2 is only used when ln_wd_dl_bc=True)
543	IF ( ln_wd_dl_bc ) THEN
544	zuwdav2(1:jpim1,1:jpj ) = zuwdav2(1:jpim1,1:jpj ) + za2 * zuwdmask(1:jpim1,1:jpj ) ! not jpi-column
545	zvwdav2(1:jpi ,1:jpjm1) = zvwdav2(1:jpi ,1:jpjm1) + za2 * zvwdmask(1:jpi ,1:jpjm1) ! not jpj-row
546	END IF
547	!
548	! Duplicate sea level across open boundaries (this is only cosmetic if linssh=T)
549	IF( ln_bdy ) CALL bdy_ssh( ssha_e )
550	#if defined key_agrif
551	IF( .NOT.Agrif_Root() ) CALL agrif_ssh_ts( jn )
552	#endif
553	!
554	! Sea Surface Height at u-,v-points (vvl case only)
555	IF( .NOT.ln_linssh ) THEN
556	DO jj = 2, jpjm1 ! INNER domain, will be extended to whole domain later
557	DO ji = 2, jpim1 ! NO Vector Opt.
558	zsshu_a(ji,jj) = r1_2 * ssumask(ji,jj) * r1_e1e2u(ji,jj) &
559	& * ( e1e2t(ji ,jj ) * ssha_e(ji ,jj ) &
560	& + e1e2t(ji+1,jj ) * ssha_e(ji+1,jj ) )
561	zsshv_a(ji,jj) = r1_2 * ssvmask(ji,jj) * r1_e1e2v(ji,jj) &
562	& * ( e1e2t(ji ,jj ) * ssha_e(ji ,jj ) &
563	& + e1e2t(ji ,jj+1) * ssha_e(ji ,jj+1) )
564	END DO
565	END DO
566	ENDIF
567	!
568	! Half-step back interpolation of SSH for surface pressure computation at step jit+1/2
569	!-- m+1/2 m+1 m m-1 m-2 --!
570	!-- ssh' = za0 * ssh + za1 * ssh + za2 * ssh + za3 * ssh --!
571	!------------------------------------------------------------------------------------------!
572	CALL ts_bck_interp( jn, ll_init, za0, za1, za2, za3 ) ! coeficients of the interpolation
573	zsshp2_e(:,:) = za0 * ssha_e(:,:) + za1 * sshn_e (:,:) &
574	& + za2 * sshb_e(:,:) + za3 * sshbb_e(:,:)
575	!
576	! ! Surface pressure gradient
577	zldg = ( 1._wp - rn_scal_load ) * grav ! local factor
578	DO jj = 2, jpjm1
579	DO ji = 2, jpim1
580	zu_spg(ji,jj) = - zldg * ( zsshp2_e(ji+1,jj) - zsshp2_e(ji,jj) ) * r1_e1u(ji,jj)
581	zv_spg(ji,jj) = - zldg * ( zsshp2_e(ji,jj+1) - zsshp2_e(ji,jj) ) * r1_e2v(ji,jj)
582	END DO
583	END DO
584	IF( ln_wd_il ) THEN ! W/D : gravity filters applied on pressure gradient
585	CALL wad_spg( zsshp2_e, zcpx, zcpy ) ! Calculating W/D gravity filters
586	zu_spg(2:jpim1,2:jpjm1) = zu_spg(2:jpim1,2:jpjm1) * zcpx(2:jpim1,2:jpjm1)
587	zv_spg(2:jpim1,2:jpjm1) = zv_spg(2:jpim1,2:jpjm1) * zcpy(2:jpim1,2:jpjm1)
588	ENDIF
589	!
590	! Add Coriolis trend:
591	! zwz array below or triads normally depend on sea level with ln_linssh=F and should be updated
592	! at each time step. We however keep them constant here for optimization.
593	! Recall that zhU and zhV hold fluxes at jn+0.5 (extrapolated not backward interpolated)
594	CALL dyn_cor_2d( zhup2_e, zhvp2_e, ua_e, va_e, zhU, zhV, zu_trd, zv_trd )
595	!
596	! Add tidal astronomical forcing if defined
597	IF ( ln_tide .AND. ln_tide_pot ) THEN
598	DO jj = 2, jpjm1
599	DO ji = fs_2, fs_jpim1 ! vector opt.
600	zu_trd(ji,jj) = zu_trd(ji,jj) + grav * ( pot_astro(ji+1,jj) - pot_astro(ji,jj) ) * r1_e1u(ji,jj)
601	zv_trd(ji,jj) = zv_trd(ji,jj) + grav * ( pot_astro(ji,jj+1) - pot_astro(ji,jj) ) * r1_e2v(ji,jj)
602	END DO
603	END DO
604	ENDIF
605	!
606	! Add bottom stresses:
607	!jth do implicitly instead
608	IF ( .NOT. ll_wd ) THEN ! Revert to explicit for bit comparison tests in non wad runs
609	DO jj = 2, jpjm1
610	DO ji = fs_2, fs_jpim1 ! vector opt.
611	zu_trd(ji,jj) = zu_trd(ji,jj) + zCdU_u(ji,jj) * un_e(ji,jj) * hur_e(ji,jj)
612	zv_trd(ji,jj) = zv_trd(ji,jj) + zCdU_v(ji,jj) * vn_e(ji,jj) * hvr_e(ji,jj)
613	END DO
614	END DO
615	ENDIF
616	!
617	! Set next velocities:
618	! Compute barotropic speeds at step jit+1 (h : total height of the water colomn)
619	!-- VECTOR FORM
620	!-- m+1 m / m+1/2 \ --!
621	!-- u = u + delta_t' * \ (1-r)g grad_x( ssh') - f * k vect u + frc / --!
622	!-- --!
623	!-- FLUX FORM --!
624	!-- m+1 __1__ / m m / m+1/2 m+1/2 m+1/2 n \ \ --!
625	!-- u = m+1 \| h * u + delta_t' * \ h * (1-r)g grad_x( ssh') - h * f * k vect u + h * frc / \| --!
626	!-- h \ / --!
627	!------------------------------------------------------------------------------------------------------------------------!
628	IF( ln_dynadv_vec .OR. ln_linssh ) THEN !* Vector form
629	DO jj = 2, jpjm1
630	DO ji = fs_2, fs_jpim1 ! vector opt.
631	ua_e(ji,jj) = ( un_e(ji,jj) &
632	& + rdtbt * ( zu_spg(ji,jj) &
633	& + zu_trd(ji,jj) &
634	& + zu_frc(ji,jj) ) &
635	& ) * ssumask(ji,jj)
636
637	va_e(ji,jj) = ( vn_e(ji,jj) &
638	& + rdtbt * ( zv_spg(ji,jj) &
639	& + zv_trd(ji,jj) &
640	& + zv_frc(ji,jj) ) &
641	& ) * ssvmask(ji,jj)
642	END DO
643	END DO
644	!
645	ELSE !* Flux form
646	DO jj = 2, jpjm1
647	DO ji = 2, jpim1
648	! ! hu_e, hv_e hold depth at jn, zhup2_e, zhvp2_e hold extrapolated depth at jn+1/2
649	! ! backward interpolated depth used in spg terms at jn+1/2
650	zhu_bck = hu_0(ji,jj) + r1_2r1_e1e2u(ji,jj) ( e1e2t(ji ,jj) * zsshp2_e(ji ,jj) &
651	& + e1e2t(ji+1,jj) * zsshp2_e(ji+1,jj) ) * ssumask(ji,jj)
652	zhv_bck = hv_0(ji,jj) + r1_2r1_e1e2v(ji,jj) ( e1e2t(ji,jj ) * zsshp2_e(ji,jj ) &
653	& + e1e2t(ji,jj+1) * zsshp2_e(ji,jj+1) ) * ssvmask(ji,jj)
654	! ! inverse depth at jn+1
655	z1_hu = ssumask(ji,jj) / ( hu_0(ji,jj) + zsshu_a(ji,jj) + 1._wp - ssumask(ji,jj) )
656	z1_hv = ssvmask(ji,jj) / ( hv_0(ji,jj) + zsshv_a(ji,jj) + 1._wp - ssvmask(ji,jj) )
657	!
658	ua_e(ji,jj) = ( hu_e (ji,jj) * un_e (ji,jj) &
659	& + rdtbt * ( zhu_bck * zu_spg (ji,jj) & !
660	& + zhup2_e(ji,jj) * zu_trd (ji,jj) & !
661	& + hu_n (ji,jj) * zu_frc (ji,jj) ) ) * z1_hu
662	!
663	va_e(ji,jj) = ( hv_e (ji,jj) * vn_e (ji,jj) &
664	& + rdtbt * ( zhv_bck * zv_spg (ji,jj) & !
665	& + zhvp2_e(ji,jj) * zv_trd (ji,jj) & !
666	& + hv_n (ji,jj) * zv_frc (ji,jj) ) ) * z1_hv
667	END DO
668	END DO
669	ENDIF
670	!jth implicit bottom friction:
671	IF ( ll_wd ) THEN ! revert to explicit for bit comparison tests in non wad runs
672	DO jj = 2, jpjm1
673	DO ji = fs_2, fs_jpim1 ! vector opt.
674	ua_e(ji,jj) = ua_e(ji,jj) /(1.0 - rdtbt * zCdU_u(ji,jj) * hur_e(ji,jj))
675	va_e(ji,jj) = va_e(ji,jj) /(1.0 - rdtbt * zCdU_v(ji,jj) * hvr_e(ji,jj))
676	END DO
677	END DO
678	ENDIF
679
680	IF( .NOT.ln_linssh ) THEN !* Update ocean depth (variable volume case only)
681	hu_e (2:jpim1,2:jpjm1) = hu_0(2:jpim1,2:jpjm1) + zsshu_a(2:jpim1,2:jpjm1)
682	hur_e(2:jpim1,2:jpjm1) = ssumask(2:jpim1,2:jpjm1) / ( hu_e(2:jpim1,2:jpjm1) + 1._wp - ssumask(2:jpim1,2:jpjm1) )
683	hv_e (2:jpim1,2:jpjm1) = hv_0(2:jpim1,2:jpjm1) + zsshv_a(2:jpim1,2:jpjm1)
684	hvr_e(2:jpim1,2:jpjm1) = ssvmask(2:jpim1,2:jpjm1) / ( hv_e(2:jpim1,2:jpjm1) + 1._wp - ssvmask(2:jpim1,2:jpjm1) )
685	CALL lbc_lnk_multi( 'dynspg_ts', ua_e , 'U', -1._wp, va_e , 'V', -1._wp &
686	& , hu_e , 'U', 1._wp, hv_e , 'V', 1._wp &
687	& , hur_e, 'U', 1._wp, hvr_e, 'V', 1._wp )
688	ELSE
689	CALL lbc_lnk_multi( 'dynspg_ts', ua_e , 'U', -1._wp, va_e , 'V', -1._wp )
690	ENDIF
691	!
692	!
693	! ! open boundaries
694	IF( ln_bdy ) CALL bdy_dyn2d( jn, ua_e, va_e, un_e, vn_e, hur_e, hvr_e, ssha_e )
695	#if defined key_agrif
696	IF( .NOT.Agrif_Root() ) CALL agrif_dyn_ts( jn ) ! Agrif
697	#endif
698	! !* Swap
699	! ! ----
700	ubb_e (:,:) = ub_e (:,:)
701	ub_e (:,:) = un_e (:,:)
702	un_e (:,:) = ua_e (:,:)
703	!
704	vbb_e (:,:) = vb_e (:,:)
705	vb_e (:,:) = vn_e (:,:)
706	vn_e (:,:) = va_e (:,:)
707	!
708	sshbb_e(:,:) = sshb_e(:,:)
709	sshb_e (:,:) = sshn_e(:,:)
710	sshn_e (:,:) = ssha_e(:,:)
711
712	! !* Sum over whole bt loop
713	! ! ----------------------
714	za1 = wgtbtp1(jn)
715	IF( ln_dynadv_vec .OR. ln_linssh ) THEN ! Sum velocities
716	ua_b (:,:) = ua_b (:,:) + za1 * ua_e (:,:)
717	va_b (:,:) = va_b (:,:) + za1 * va_e (:,:)
718	ELSE ! Sum transports
719	IF ( .NOT.ln_wd_dl ) THEN
720	ua_b (:,:) = ua_b (:,:) + za1 * ua_e (:,:) * hu_e (:,:)
721	va_b (:,:) = va_b (:,:) + za1 * va_e (:,:) * hv_e (:,:)
722	ELSE
723	ua_b (:,:) = ua_b (:,:) + za1 * ua_e (:,:) * hu_e (:,:) * zuwdmask(:,:)
724	va_b (:,:) = va_b (:,:) + za1 * va_e (:,:) * hv_e (:,:) * zvwdmask(:,:)
725	END IF
726	ENDIF
727	! ! Sum sea level
728	ssha(:,:) = ssha(:,:) + za1 * ssha_e(:,:)
729
730	! ! ==================== !
731	END DO ! end loop !
732	! ! ==================== !
733	! -----------------------------------------------------------------------------
734	! Phase 3. update the general trend with the barotropic trend
735	! -----------------------------------------------------------------------------
736	!
737	! Set advection velocity correction:
738	IF (ln_bt_fw) THEN
739	IF( .NOT.( kt == nit000 .AND. neuler==0 ) ) THEN
740	DO jj = 1, jpj
741	DO ji = 1, jpi
742	zun_save = un_adv(ji,jj)
743	zvn_save = vn_adv(ji,jj)
744	! ! apply the previously computed correction
745	un_adv(ji,jj) = r1_2 * ( ub2_b(ji,jj) + zun_save - atfp * un_bf(ji,jj) )
746	vn_adv(ji,jj) = r1_2 * ( vb2_b(ji,jj) + zvn_save - atfp * vn_bf(ji,jj) )
747	! ! Update corrective fluxes for next time step
748	un_bf(ji,jj) = atfp * un_bf(ji,jj) + ( zun_save - ub2_b(ji,jj) )
749	vn_bf(ji,jj) = atfp * vn_bf(ji,jj) + ( zvn_save - vb2_b(ji,jj) )
750	! ! Save integrated transport for next computation
751	ub2_b(ji,jj) = zun_save
752	vb2_b(ji,jj) = zvn_save
753	END DO
754	END DO
755	ELSE
756	un_bf(:,:) = 0._wp ! corrective fluxes for next time step set to zero
757	vn_bf(:,:) = 0._wp
758	ub2_b(:,:) = un_adv(:,:) ! Save integrated transport for next computation
759	vb2_b(:,:) = vn_adv(:,:)
760	END IF
761	ENDIF
762
763
764	!
765	! Update barotropic trend:
766	IF( ln_dynadv_vec .OR. ln_linssh ) THEN
767	DO jk=1,jpkm1
768	ua(:,:,jk) = ua(:,:,jk) + ( ua_b(:,:) - ub_b(:,:) ) * r1_2dt_b
769	va(:,:,jk) = va(:,:,jk) + ( va_b(:,:) - vb_b(:,:) ) * r1_2dt_b
770	END DO
771	ELSE
772	! At this stage, ssha has been corrected: compute new depths at velocity points
773	DO jj = 1, jpjm1
774	DO ji = 1, jpim1 ! NO Vector Opt.
775	zsshu_a(ji,jj) = r1_2 * ssumask(ji,jj) * r1_e1e2u(ji,jj) &
776	& * ( e1e2t(ji ,jj) * ssha(ji ,jj) &
777	& + e1e2t(ji+1,jj) * ssha(ji+1,jj) )
778	zsshv_a(ji,jj) = r1_2 * ssvmask(ji,jj) * r1_e1e2v(ji,jj) &
779	& * ( e1e2t(ji,jj ) * ssha(ji,jj ) &
780	& + e1e2t(ji,jj+1) * ssha(ji,jj+1) )
781	END DO
782	END DO
783	CALL lbc_lnk_multi( 'dynspg_ts', zsshu_a, 'U', 1._wp, zsshv_a, 'V', 1._wp ) ! Boundary conditions
784	!
785	DO jk=1,jpkm1
786	ua(:,:,jk) = ua(:,:,jk) + r1_hu_n(:,:) * ( ua_b(:,:) - ub_b(:,:) * hu_b(:,:) ) * r1_2dt_b
787	va(:,:,jk) = va(:,:,jk) + r1_hv_n(:,:) * ( va_b(:,:) - vb_b(:,:) * hv_b(:,:) ) * r1_2dt_b
788	END DO
789	! Save barotropic velocities not transport:
790	ua_b(:,:) = ua_b(:,:) / ( hu_0(:,:) + zsshu_a(:,:) + 1._wp - ssumask(:,:) )
791	va_b(:,:) = va_b(:,:) / ( hv_0(:,:) + zsshv_a(:,:) + 1._wp - ssvmask(:,:) )
792	ENDIF
793
794
795	! Correct velocities so that the barotropic velocity equals (un_adv, vn_adv) (in all cases)
796	DO jk = 1, jpkm1
797	un(:,:,jk) = ( un(:,:,jk) + un_adv(:,:)r1_hu_n(:,:) - un_b(:,:) ) umask(:,:,jk)
798	vn(:,:,jk) = ( vn(:,:,jk) + vn_adv(:,:)r1_hv_n(:,:) - vn_b(:,:) ) vmask(:,:,jk)
799	END DO
800
801	IF ( ln_wd_dl .and. ln_wd_dl_bc) THEN
802	! need to set lbc here because not done prior time averaging
803	CALL lbc_lnk_multi( 'dynspg_ts', zuwdav2, 'U', 1._wp, zvwdav2, 'V', 1._wp)
804	DO jk = 1, jpkm1
805	un(:,:,jk) = ( un_adv(:,:)*r1_hu_n(:,:) &
806	& + zuwdav2(:,:)(un(:,:,jk) - un_adv(:,:)r1_hu_n(:,:)) ) * umask(:,:,jk)
807	vn(:,:,jk) = ( vn_adv(:,:)*r1_hv_n(:,:) &
808	& + zvwdav2(:,:)(vn(:,:,jk) - vn_adv(:,:)r1_hv_n(:,:)) ) * vmask(:,:,jk)
809	END DO
810	END IF
811
812
813	CALL iom_put( "ubar", un_adv(:,:)*r1_hu_n(:,:) ) ! barotropic i-current
814	CALL iom_put( "vbar", vn_adv(:,:)*r1_hv_n(:,:) ) ! barotropic i-current
815	!
816	#if defined key_agrif
817	! Save time integrated fluxes during child grid integration
818	! (used to update coarse grid transports at next time step)
819	!
820	IF( .NOT.Agrif_Root() .AND. ln_bt_fw ) THEN
821	IF( Agrif_NbStepint() == 0 ) THEN
822	ub2_i_b(:,:) = 0._wp
823	vb2_i_b(:,:) = 0._wp
824	END IF
825	!
826	za1 = 1._wp / REAL(Agrif_rhot(), wp)
827	ub2_i_b(:,:) = ub2_i_b(:,:) + za1 * ub2_b(:,:)
828	vb2_i_b(:,:) = vb2_i_b(:,:) + za1 * vb2_b(:,:)
829	ENDIF
830	#endif
831	! !* write time-spliting arrays in the restart
832	IF( lrst_oce .AND.ln_bt_fw ) CALL ts_rst( kt, 'WRITE' )
833	!
834	IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy )
835	IF( ln_wd_dl ) DEALLOCATE( ztwdmask, zuwdmask, zvwdmask, zuwdav2, zvwdav2 )
836	!
837	IF( ln_diatmb ) THEN
838	CALL iom_put( "baro_u" , un_bssumask(:,:)+zmdi(1.-ssumask(:,:) ) ) ! Barotropic U Velocity
839	CALL iom_put( "baro_v" , vn_bssvmask(:,:)+zmdi(1.-ssvmask(:,:) ) ) ! Barotropic V Velocity
840	ENDIF
841	!
842	END SUBROUTINE dyn_spg_ts
843
844
845	SUBROUTINE ts_wgt( ll_av, ll_fw, jpit, zwgt1, zwgt2)
846	!!---------------------------------------------------------------------
847	!! * ROUTINE ts_wgt *
848	!!
849	!! ** Purpose : Set time-splitting weights for temporal averaging (or not)
850	!!----------------------------------------------------------------------
851	LOGICAL, INTENT(in) :: ll_av ! temporal averaging=.true.
852	LOGICAL, INTENT(in) :: ll_fw ! forward time splitting =.true.
853	INTEGER, INTENT(inout) :: jpit ! cycle length
854	REAL(wp), DIMENSION(3*nn_baro), INTENT(inout) :: zwgt1, & ! Primary weights
855	zwgt2 ! Secondary weights
856
857	INTEGER :: jic, jn, ji ! temporary integers
858	REAL(wp) :: za1, za2
859	!!----------------------------------------------------------------------
860
861	zwgt1(:) = 0._wp
862	zwgt2(:) = 0._wp
863
864	! Set time index when averaged value is requested
865	IF (ll_fw) THEN
866	jic = nn_baro
867	ELSE
868	jic = 2 * nn_baro
869	ENDIF
870
871	! Set primary weights:
872	IF (ll_av) THEN
873	! Define simple boxcar window for primary weights
874	! (width = nn_baro, centered around jic)
875	SELECT CASE ( nn_bt_flt )
876	CASE( 0 ) ! No averaging
877	zwgt1(jic) = 1._wp
878	jpit = jic
879
880	CASE( 1 ) ! Boxcar, width = nn_baro
881	DO jn = 1, 3*nn_baro
882	za1 = ABS(float(jn-jic))/float(nn_baro)
883	IF (za1 < 0.5_wp) THEN
884	zwgt1(jn) = 1._wp
885	jpit = jn
886	ENDIF
887	ENDDO
888
889	CASE( 2 ) ! Boxcar, width = 2 * nn_baro
890	DO jn = 1, 3*nn_baro
891	za1 = ABS(float(jn-jic))/float(nn_baro)
892	IF (za1 < 1._wp) THEN
893	zwgt1(jn) = 1._wp
894	jpit = jn
895	ENDIF
896	ENDDO
897	CASE DEFAULT ; CALL ctl_stop( 'unrecognised value for nn_bt_flt' )
898	END SELECT
899
900	ELSE ! No time averaging
901	zwgt1(jic) = 1._wp
902	jpit = jic
903	ENDIF
904
905	! Set secondary weights
906	DO jn = 1, jpit
907	DO ji = jn, jpit
908	zwgt2(jn) = zwgt2(jn) + zwgt1(ji)
909	END DO
910	END DO
911
912	! Normalize weigths:
913	za1 = 1._wp / SUM(zwgt1(1:jpit))
914	za2 = 1._wp / SUM(zwgt2(1:jpit))
915	DO jn = 1, jpit
916	zwgt1(jn) = zwgt1(jn) * za1
917	zwgt2(jn) = zwgt2(jn) * za2
918	END DO
919	!
920	END SUBROUTINE ts_wgt
921
922
923	SUBROUTINE ts_rst( kt, cdrw )
924	!!---------------------------------------------------------------------
925	!! * ROUTINE ts_rst *
926	!!
927	!! ** Purpose : Read or write time-splitting arrays in restart file
928	!!----------------------------------------------------------------------
929	INTEGER , INTENT(in) :: kt ! ocean time-step
930	CHARACTER(len=*), INTENT(in) :: cdrw ! "READ"/"WRITE" flag
931	!!----------------------------------------------------------------------
932	!
933	IF( TRIM(cdrw) == 'READ' ) THEN ! Read/initialise
934	! ! ---------------
935	IF( ln_rstart .AND. ln_bt_fw .AND. (neuler/=0) ) THEN !* Read the restart file
936	CALL iom_get( numror, jpdom_autoglo, 'ub2_b' , ub2_b (:,:), ldxios = lrxios )
937	CALL iom_get( numror, jpdom_autoglo, 'vb2_b' , vb2_b (:,:), ldxios = lrxios )
938	CALL iom_get( numror, jpdom_autoglo, 'un_bf' , un_bf (:,:), ldxios = lrxios )
939	CALL iom_get( numror, jpdom_autoglo, 'vn_bf' , vn_bf (:,:), ldxios = lrxios )
940	IF( .NOT.ln_bt_av ) THEN
941	CALL iom_get( numror, jpdom_autoglo, 'sshbb_e' , sshbb_e(:,:), ldxios = lrxios )
942	CALL iom_get( numror, jpdom_autoglo, 'ubb_e' , ubb_e(:,:), ldxios = lrxios )
943	CALL iom_get( numror, jpdom_autoglo, 'vbb_e' , vbb_e(:,:), ldxios = lrxios )
944	CALL iom_get( numror, jpdom_autoglo, 'sshb_e' , sshb_e(:,:), ldxios = lrxios )
945	CALL iom_get( numror, jpdom_autoglo, 'ub_e' , ub_e(:,:), ldxios = lrxios )
946	CALL iom_get( numror, jpdom_autoglo, 'vb_e' , vb_e(:,:), ldxios = lrxios )
947	ENDIF
948	#if defined key_agrif
949	! Read time integrated fluxes
950	IF ( .NOT.Agrif_Root() ) THEN
951	CALL iom_get( numror, jpdom_autoglo, 'ub2_i_b' , ub2_i_b(:,:), ldxios = lrxios )
952	CALL iom_get( numror, jpdom_autoglo, 'vb2_i_b' , vb2_i_b(:,:), ldxios = lrxios )
953	ENDIF
954	#endif
955	ELSE !* Start from rest
956	IF(lwp) WRITE(numout,*)
957	IF(lwp) WRITE(numout,*) ' ==>>> start from rest: set barotropic values to 0'
958	ub2_b (:,:) = 0._wp ; vb2_b (:,:) = 0._wp ! used in the 1st interpol of agrif
959	un_adv(:,:) = 0._wp ; vn_adv(:,:) = 0._wp ! used in the 1st interpol of agrif
960	un_bf (:,:) = 0._wp ; vn_bf (:,:) = 0._wp ! used in the 1st update of agrif
961	#if defined key_agrif
962	IF ( .NOT.Agrif_Root() ) THEN
963	ub2_i_b(:,:) = 0._wp ; vb2_i_b(:,:) = 0._wp ! used in the 1st update of agrif
964	ENDIF
965	#endif
966	ENDIF
967	!
968	ELSEIF( TRIM(cdrw) == 'WRITE' ) THEN ! Create restart file
969	! ! -------------------
970	IF(lwp) WRITE(numout,*) '---- ts_rst ----'
971	IF( lwxios ) CALL iom_swap( cwxios_context )
972	CALL iom_rstput( kt, nitrst, numrow, 'ub2_b' , ub2_b (:,:), ldxios = lwxios )
973	CALL iom_rstput( kt, nitrst, numrow, 'vb2_b' , vb2_b (:,:), ldxios = lwxios )
974	CALL iom_rstput( kt, nitrst, numrow, 'un_bf' , un_bf (:,:), ldxios = lwxios )
975	CALL iom_rstput( kt, nitrst, numrow, 'vn_bf' , vn_bf (:,:), ldxios = lwxios )
976	!
977	IF (.NOT.ln_bt_av) THEN
978	CALL iom_rstput( kt, nitrst, numrow, 'sshbb_e' , sshbb_e(:,:), ldxios = lwxios )
979	CALL iom_rstput( kt, nitrst, numrow, 'ubb_e' , ubb_e(:,:), ldxios = lwxios )
980	CALL iom_rstput( kt, nitrst, numrow, 'vbb_e' , vbb_e(:,:), ldxios = lwxios )
981	CALL iom_rstput( kt, nitrst, numrow, 'sshb_e' , sshb_e(:,:), ldxios = lwxios )
982	CALL iom_rstput( kt, nitrst, numrow, 'ub_e' , ub_e(:,:), ldxios = lwxios )
983	CALL iom_rstput( kt, nitrst, numrow, 'vb_e' , vb_e(:,:), ldxios = lwxios )
984	ENDIF
985	#if defined key_agrif
986	! Save time integrated fluxes
987	IF ( .NOT.Agrif_Root() ) THEN
988	CALL iom_rstput( kt, nitrst, numrow, 'ub2_i_b' , ub2_i_b(:,:), ldxios = lwxios )
989	CALL iom_rstput( kt, nitrst, numrow, 'vb2_i_b' , vb2_i_b(:,:), ldxios = lwxios )
990	ENDIF
991	#endif
992	IF( lwxios ) CALL iom_swap( cxios_context )
993	ENDIF
994	!
995	END SUBROUTINE ts_rst
996
997
998	SUBROUTINE dyn_spg_ts_init
999	!!---------------------------------------------------------------------
1000	!! * ROUTINE dyn_spg_ts_init *
1001	!!
1002	!! ** Purpose : Set time splitting options
1003	!!----------------------------------------------------------------------
1004	INTEGER :: ji ,jj ! dummy loop indices
1005	REAL(wp) :: zxr2, zyr2, zcmax ! local scalar
1006	REAL(wp), DIMENSION(jpi,jpj) :: zcu
1007	INTEGER :: inum
1008	!!----------------------------------------------------------------------
1009	!
1010	! Max courant number for ext. grav. waves
1011	!
1012	DO jj = 1, jpj
1013	DO ji =1, jpi
1014	zxr2 = r1_e1t(ji,jj) * r1_e1t(ji,jj)
1015	zyr2 = r1_e2t(ji,jj) * r1_e2t(ji,jj)
1016	zcu(ji,jj) = SQRT( grav * MAX(ht_0(ji,jj),0._wp) * (zxr2 + zyr2) )
1017	END DO
1018	END DO
1019	!
1020	zcmax = MAXVAL( zcu(:,:) )
1021	CALL mpp_max( 'dynspg_ts', zcmax )
1022
1023	! Estimate number of iterations to satisfy a max courant number= rn_bt_cmax
1024	IF( ln_bt_auto ) nn_baro = CEILING( rdt / rn_bt_cmax * zcmax)
1025
1026	rdtbt = rdt / REAL( nn_baro , wp )
1027	zcmax = zcmax * rdtbt
1028	! Print results
1029	IF(lwp) WRITE(numout,*)
1030	IF(lwp) WRITE(numout,*) 'dyn_spg_ts_init : split-explicit free surface'
1031	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~~'
1032	IF( ln_bt_auto ) THEN
1033	IF(lwp) WRITE(numout,*) ' ln_ts_auto =.true. Automatically set nn_baro '
1034	IF(lwp) WRITE(numout,*) ' Max. courant number allowed: ', rn_bt_cmax
1035	ELSE
1036	IF(lwp) WRITE(numout,*) ' ln_ts_auto=.false.: Use nn_baro in namelist nn_baro = ', nn_baro
1037	ENDIF
1038
1039	IF(ln_bt_av) THEN
1040	IF(lwp) WRITE(numout,*) ' ln_bt_av =.true. ==> Time averaging over nn_baro time steps is on '
1041	ELSE
1042	IF(lwp) WRITE(numout,*) ' ln_bt_av =.false. => No time averaging of barotropic variables '
1043	ENDIF
1044	!
1045	!
1046	IF(ln_bt_fw) THEN
1047	IF(lwp) WRITE(numout,*) ' ln_bt_fw=.true. => Forward integration of barotropic variables '
1048	ELSE
1049	IF(lwp) WRITE(numout,*) ' ln_bt_fw =.false.=> Centred integration of barotropic variables '
1050	ENDIF
1051	!
1052	#if defined key_agrif
1053	! Restrict the use of Agrif to the forward case only
1054	!!! IF( .NOT.ln_bt_fw .AND. .NOT.Agrif_Root() ) CALL ctl_stop( 'AGRIF not implemented if ln_bt_fw=.FALSE.' )
1055	#endif
1056	!
1057	IF(lwp) WRITE(numout,*) ' Time filter choice, nn_bt_flt: ', nn_bt_flt
1058	SELECT CASE ( nn_bt_flt )
1059	CASE( 0 ) ; IF(lwp) WRITE(numout,*) ' Dirac'
1060	CASE( 1 ) ; IF(lwp) WRITE(numout,*) ' Boxcar: width = nn_baro'
1061	CASE( 2 ) ; IF(lwp) WRITE(numout,) ' Boxcar: width = 2nn_baro'
1062	CASE DEFAULT ; CALL ctl_stop( 'unrecognised value for nn_bt_flt: should 0,1, or 2' )
1063	END SELECT
1064	!
1065	IF(lwp) WRITE(numout,*) ' '
1066	IF(lwp) WRITE(numout,*) ' nn_baro = ', nn_baro
1067	IF(lwp) WRITE(numout,*) ' Barotropic time step [s] is :', rdtbt
1068	IF(lwp) WRITE(numout,*) ' Maximum Courant number is :', zcmax
1069	!
1070	IF(lwp) WRITE(numout,*) ' Time diffusion parameter rn_bt_alpha: ', rn_bt_alpha
1071	IF ((ln_bt_av.AND.nn_bt_flt/=0).AND.(rn_bt_alpha>0._wp)) THEN
1072	CALL ctl_stop( 'dynspg_ts ERROR: if rn_bt_alpha > 0, remove temporal averaging' )
1073	ENDIF
1074	!
1075	IF( .NOT.ln_bt_av .AND. .NOT.ln_bt_fw ) THEN
1076	CALL ctl_stop( 'dynspg_ts ERROR: No time averaging => only forward integration is possible' )
1077	ENDIF
1078	IF( zcmax>0.9_wp ) THEN
1079	CALL ctl_stop( 'dynspg_ts ERROR: Maximum Courant number is greater than 0.9: Inc. nn_baro !' )
1080	ENDIF
1081	!
1082	! ! Allocate time-splitting arrays
1083	IF( dyn_spg_ts_alloc() /= 0 ) CALL ctl_stop('STOP', 'dyn_spg_init: failed to allocate dynspg_ts arrays' )
1084	!
1085	! ! read restart when needed
1086	CALL ts_rst( nit000, 'READ' )
1087	!
1088	IF( lwxios ) THEN
1089	! define variables in restart file when writing with XIOS
1090	CALL iom_set_rstw_var_active('ub2_b')
1091	CALL iom_set_rstw_var_active('vb2_b')
1092	CALL iom_set_rstw_var_active('un_bf')
1093	CALL iom_set_rstw_var_active('vn_bf')
1094	!
1095	IF (.NOT.ln_bt_av) THEN
1096	CALL iom_set_rstw_var_active('sshbb_e')
1097	CALL iom_set_rstw_var_active('ubb_e')
1098	CALL iom_set_rstw_var_active('vbb_e')
1099	CALL iom_set_rstw_var_active('sshb_e')
1100	CALL iom_set_rstw_var_active('ub_e')
1101	CALL iom_set_rstw_var_active('vb_e')
1102	ENDIF
1103	#if defined key_agrif
1104	! Save time integrated fluxes
1105	IF ( .NOT.Agrif_Root() ) THEN
1106	CALL iom_set_rstw_var_active('ub2_i_b')
1107	CALL iom_set_rstw_var_active('vb2_i_b')
1108	ENDIF
1109	#endif
1110	ENDIF
1111	!
1112	END SUBROUTINE dyn_spg_ts_init
1113
1114
1115	SUBROUTINE dyn_cor_2d_init
1116	!!---------------------------------------------------------------------
1117	!! * ROUTINE dyn_cor_2d_init *
1118	!!
1119	!! ** Purpose : Set time splitting options
1120	!! Set arrays to remove/compute coriolis trend.
1121	!! Do it once during initialization if volume is fixed, else at each long time step.
1122	!! Note that these arrays are also used during barotropic loop. These are however frozen
1123	!! although they should be updated in the variable volume case. Not a big approximation.
1124	!! To remove this approximation, copy lines below inside barotropic loop
1125	!! and update depths at T-F points (ht and zhf resp.) at each barotropic time step
1126	!!
1127	!! Compute zwz = f / ( height of the water colomn )
1128	!!----------------------------------------------------------------------
1129	INTEGER :: ji ,jj, jk ! dummy loop indices
1130	REAL(wp) :: z1_ht
1131	REAL(wp), DIMENSION(jpi,jpj) :: zhf
1132	!!----------------------------------------------------------------------
1133	!
1134	SELECT CASE( nvor_scheme )
1135	CASE( np_EEN ) != EEN scheme using e3f (energy & enstrophy scheme)
1136	SELECT CASE( nn_een_e3f ) !* ff_f/e3 at F-point
1137	CASE ( 0 ) ! original formulation (masked averaging of e3t divided by 4)
1138	DO jj = 1, jpjm1
1139	DO ji = 1, jpim1
1140	zwz(ji,jj) = ( ht_n(ji ,jj+1) + ht_n(ji+1,jj+1) + &
1141	& ht_n(ji ,jj ) + ht_n(ji+1,jj ) ) * 0.25_wp
1142	IF( zwz(ji,jj) /= 0._wp ) zwz(ji,jj) = ff_f(ji,jj) / zwz(ji,jj)
1143	END DO
1144	END DO
1145	CASE ( 1 ) ! new formulation (masked averaging of e3t divided by the sum of mask)
1146	DO jj = 1, jpjm1
1147	DO ji = 1, jpim1
1148	zwz(ji,jj) = ( ht_n (ji ,jj+1) + ht_n (ji+1,jj+1) &
1149	& + ht_n (ji ,jj ) + ht_n (ji+1,jj ) ) &
1150	& / ( MAX( 1._wp, ssmask(ji ,jj+1) + ssmask(ji+1,jj+1) &
1151	& + ssmask(ji ,jj ) + ssmask(ji+1,jj ) ) )
1152	IF( zwz(ji,jj) /= 0._wp ) zwz(ji,jj) = ff_f(ji,jj) / zwz(ji,jj)
1153	END DO
1154	END DO
1155	END SELECT
1156	CALL lbc_lnk( 'dynspg_ts', zwz, 'F', 1._wp )
1157	!
1158	ftne(1,:) = 0._wp ; ftnw(1,:) = 0._wp ; ftse(1,:) = 0._wp ; ftsw(1,:) = 0._wp
1159	DO jj = 2, jpj
1160	DO ji = 2, jpi
1161	ftne(ji,jj) = zwz(ji-1,jj ) + zwz(ji ,jj ) + zwz(ji ,jj-1)
1162	ftnw(ji,jj) = zwz(ji-1,jj-1) + zwz(ji-1,jj ) + zwz(ji ,jj )
1163	ftse(ji,jj) = zwz(ji ,jj ) + zwz(ji ,jj-1) + zwz(ji-1,jj-1)
1164	ftsw(ji,jj) = zwz(ji ,jj-1) + zwz(ji-1,jj-1) + zwz(ji-1,jj )
1165	END DO
1166	END DO
1167	!
1168	CASE( np_EET ) != EEN scheme using e3t (energy conserving scheme)
1169	ftne(1,:) = 0._wp ; ftnw(1,:) = 0._wp ; ftse(1,:) = 0._wp ; ftsw(1,:) = 0._wp
1170	DO jj = 2, jpj
1171	DO ji = 2, jpi
1172	z1_ht = ssmask(ji,jj) / ( ht_n(ji,jj) + 1._wp - ssmask(ji,jj) )
1173	ftne(ji,jj) = ( ff_f(ji-1,jj ) + ff_f(ji ,jj ) + ff_f(ji ,jj-1) ) * z1_ht
1174	ftnw(ji,jj) = ( ff_f(ji-1,jj-1) + ff_f(ji-1,jj ) + ff_f(ji ,jj ) ) * z1_ht
1175	ftse(ji,jj) = ( ff_f(ji ,jj ) + ff_f(ji ,jj-1) + ff_f(ji-1,jj-1) ) * z1_ht
1176	ftsw(ji,jj) = ( ff_f(ji ,jj-1) + ff_f(ji-1,jj-1) + ff_f(ji-1,jj ) ) * z1_ht
1177	END DO
1178	END DO
1179	!
1180	CASE( np_ENE, np_ENS , np_MIX ) != all other schemes (ENE, ENS, MIX) except ENT !
1181	!
1182	zwz(:,:) = 0._wp
1183	zhf(:,:) = 0._wp
1184
1185	!!gm assume 0 in both cases (which is almost surely WRONG ! ) as hvatf has been removed
1186	!!gm A priori a better value should be something like :
1187	!!gm zhf(i,j) = masked sum of ht(i,j) , ht(i+1,j) , ht(i,j+1) , (i+1,j+1)
1188	!!gm divided by the sum of the corresponding mask
1189	!!gm
1190	!!
1191	IF( .NOT.ln_sco ) THEN
1192
1193	!!gm agree the JC comment : this should be done in a much clear way
1194
1195	! JC: It not clear yet what should be the depth at f-points over land in z-coordinate case
1196	! Set it to zero for the time being
1197	! IF( rn_hmin < 0._wp ) THEN ; jk = - INT( rn_hmin ) ! from a nb of level
1198	! ELSE ; jk = MINLOC( gdepw_0, mask = gdepw_0 > rn_hmin, dim = 1 ) ! from a depth
1199	! ENDIF
1200	! zhf(:,:) = gdepw_0(:,:,jk+1)
1201	!
1202	ELSE
1203	!
1204	!zhf(:,:) = hbatf(:,:)
1205	DO jj = 1, jpjm1
1206	DO ji = 1, jpim1
1207	zhf(ji,jj) = ( ht_0 (ji,jj ) + ht_0 (ji+1,jj ) &
1208	& + ht_0 (ji,jj+1) + ht_0 (ji+1,jj+1) ) &
1209	& / MAX( ssmask(ji,jj ) + ssmask(ji+1,jj ) &
1210	& + ssmask(ji,jj+1) + ssmask(ji+1,jj+1) , 1._wp )
1211	END DO
1212	END DO
1213	ENDIF
1214	!
1215	DO jj = 1, jpjm1
1216	zhf(:,jj) = zhf(:,jj) * (1._wp- umask(:,jj,1) * umask(:,jj+1,1))
1217	END DO
1218	!
1219	DO jk = 1, jpkm1
1220	DO jj = 1, jpjm1
1221	zhf(:,jj) = zhf(:,jj) + e3f_n(:,jj,jk) * umask(:,jj,jk) * umask(:,jj+1,jk)
1222	END DO
1223	END DO
1224	CALL lbc_lnk( 'dynspg_ts', zhf, 'F', 1._wp )
1225	! JC: TBC. hf should be greater than 0
1226	DO jj = 1, jpj
1227	DO ji = 1, jpi
1228	IF( zhf(ji,jj) /= 0._wp ) zwz(ji,jj) = 1._wp / zhf(ji,jj)
1229	END DO
1230	END DO
1231	zwz(:,:) = ff_f(:,:) * zwz(:,:)
1232	END SELECT
1233
1234	END SUBROUTINE dyn_cor_2d_init
1235
1236
1237
1238	SUBROUTINE dyn_cor_2d( hu_n, hv_n, un_b, vn_b, zhU, zhV, zu_trd, zv_trd )
1239	!!---------------------------------------------------------------------
1240	!! * ROUTINE dyn_cor_2d *
1241	!!
1242	!! ** Purpose : Compute u and v coriolis trends
1243	!!----------------------------------------------------------------------
1244	INTEGER :: ji ,jj ! dummy loop indices
1245	REAL(wp) :: zx1, zx2, zy1, zy2, z1_hu, z1_hv ! - -
1246	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: hu_n, hv_n, un_b, vn_b, zhU, zhV
1247	REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: zu_trd, zv_trd
1248	!!----------------------------------------------------------------------
1249	SELECT CASE( nvor_scheme )
1250	CASE( np_ENT ) ! enstrophy conserving scheme (f-point)
1251	DO jj = 2, jpjm1
1252	DO ji = 2, jpim1
1253	z1_hu = ssumask(ji,jj) / ( hu_n(ji,jj) + 1._wp - ssumask(ji,jj) )
1254	z1_hv = ssvmask(ji,jj) / ( hv_n(ji,jj) + 1._wp - ssvmask(ji,jj) )
1255	zu_trd(ji,jj) = + r1_4 * r1_e1e2u(ji,jj) * z1_hu &
1256	& * ( e1e2t(ji+1,jj)ht_n(ji+1,jj)ff_t(ji+1,jj) * ( vn_b(ji+1,jj) + vn_b(ji+1,jj-1) ) &
1257	& + e1e2t(ji ,jj)ht_n(ji ,jj)ff_t(ji ,jj) * ( vn_b(ji ,jj) + vn_b(ji ,jj-1) ) )
1258	!
1259	zv_trd(ji,jj) = - r1_4 * r1_e1e2v(ji,jj) * z1_hv &
1260	& * ( e1e2t(ji,jj+1)ht_n(ji,jj+1)ff_t(ji,jj+1) * ( un_b(ji,jj+1) + un_b(ji-1,jj+1) ) &
1261	& + e1e2t(ji,jj )ht_n(ji,jj )ff_t(ji,jj ) * ( un_b(ji,jj ) + un_b(ji-1,jj ) ) )
1262	END DO
1263	END DO
1264	!
1265	CASE( np_ENE , np_MIX ) ! energy conserving scheme (t-point) ENE or MIX
1266	DO jj = 2, jpjm1
1267	DO ji = fs_2, fs_jpim1 ! vector opt.
1268	zy1 = ( zhV(ji,jj-1) + zhV(ji+1,jj-1) ) * r1_e1u(ji,jj)
1269	zy2 = ( zhV(ji,jj ) + zhV(ji+1,jj ) ) * r1_e1u(ji,jj)
1270	zx1 = ( zhU(ji-1,jj) + zhU(ji-1,jj+1) ) * r1_e2v(ji,jj)
1271	zx2 = ( zhU(ji ,jj) + zhU(ji ,jj+1) ) * r1_e2v(ji,jj)
1272	! energy conserving formulation for planetary vorticity term
1273	zu_trd(ji,jj) = r1_4 * ( zwz(ji ,jj-1) * zy1 + zwz(ji,jj) * zy2 )
1274	zv_trd(ji,jj) = - r1_4 * ( zwz(ji-1,jj ) * zx1 + zwz(ji,jj) * zx2 )
1275	END DO
1276	END DO
1277	!
1278	CASE( np_ENS ) ! enstrophy conserving scheme (f-point)
1279	DO jj = 2, jpjm1
1280	DO ji = fs_2, fs_jpim1 ! vector opt.
1281	zy1 = r1_8 * ( zhV(ji ,jj-1) + zhV(ji+1,jj-1) &
1282	& + zhV(ji ,jj ) + zhV(ji+1,jj ) ) * r1_e1u(ji,jj)
1283	zx1 = - r1_8 * ( zhU(ji-1,jj ) + zhU(ji-1,jj+1) &
1284	& + zhU(ji ,jj ) + zhU(ji ,jj+1) ) * r1_e2v(ji,jj)
1285	zu_trd(ji,jj) = zy1 * ( zwz(ji ,jj-1) + zwz(ji,jj) )
1286	zv_trd(ji,jj) = zx1 * ( zwz(ji-1,jj ) + zwz(ji,jj) )
1287	END DO
1288	END DO
1289	!
1290	CASE( np_EET , np_EEN ) ! energy & enstrophy scheme (using e3t or e3f)
1291	DO jj = 2, jpjm1
1292	DO ji = fs_2, fs_jpim1 ! vector opt.
1293	zu_trd(ji,jj) = + r1_12 * r1_e1u(ji,jj) * ( ftne(ji,jj ) * zhV(ji ,jj ) &
1294	& + ftnw(ji+1,jj) * zhV(ji+1,jj ) &
1295	& + ftse(ji,jj ) * zhV(ji ,jj-1) &
1296	& + ftsw(ji+1,jj) * zhV(ji+1,jj-1) )
1297	zv_trd(ji,jj) = - r1_12 * r1_e2v(ji,jj) * ( ftsw(ji,jj+1) * zhU(ji-1,jj+1) &
1298	& + ftse(ji,jj+1) * zhU(ji ,jj+1) &
1299	& + ftnw(ji,jj ) * zhU(ji-1,jj ) &
1300	& + ftne(ji,jj ) * zhU(ji ,jj ) )
1301	END DO
1302	END DO
1303	!
1304	END SELECT
1305	!
1306	END SUBROUTINE dyn_cor_2D
1307
1308
1309	SUBROUTINE wad_tmsk( pssh, ptmsk )
1310	!!----------------------------------------------------------------------
1311	!! * ROUTINE wad_lmt *
1312	!!
1313	!! ** Purpose : set wetting & drying mask at tracer points
1314	!! for the current barotropic sub-step
1315	!!
1316	!! ** Method : ???
1317	!!
1318	!! ** Action : ptmsk : wetting & drying t-mask
1319	!!----------------------------------------------------------------------
1320	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pssh !
1321	REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: ptmsk !
1322	!
1323	INTEGER :: ji, jj ! dummy loop indices
1324	!!----------------------------------------------------------------------
1325	!
1326	IF( ln_wd_dl_rmp ) THEN
1327	DO jj = 1, jpj
1328	DO ji = 1, jpi
1329	IF ( pssh(ji,jj) + ht_0(ji,jj) > 2._wp * rn_wdmin1 ) THEN
1330	! IF ( pssh(ji,jj) + ht_0(ji,jj) > rn_wdmin2 ) THEN
1331	ptmsk(ji,jj) = 1._wp
1332	ELSEIF( pssh(ji,jj) + ht_0(ji,jj) > rn_wdmin1 ) THEN
1333	ptmsk(ji,jj) = TANH( 50._wp( ( pssh(ji,jj) + ht_0(ji,jj) - rn_wdmin1 )r_rn_wdmin1) )
1334	ELSE
1335	ptmsk(ji,jj) = 0._wp
1336	ENDIF
1337	END DO
1338	END DO
1339	ELSE
1340	DO jj = 1, jpj
1341	DO ji = 1, jpi
1342	IF ( pssh(ji,jj) + ht_0(ji,jj) > rn_wdmin1 ) THEN ; ptmsk(ji,jj) = 1._wp
1343	ELSE ; ptmsk(ji,jj) = 0._wp
1344	ENDIF
1345	END DO
1346	END DO
1347	ENDIF
1348	!
1349	END SUBROUTINE wad_tmsk
1350
1351
1352	SUBROUTINE wad_Umsk( pTmsk, phU, phV, pu, pv, pUmsk, pVmsk )
1353	!!----------------------------------------------------------------------
1354	!! * ROUTINE wad_lmt *
1355	!!
1356	!! ** Purpose : set wetting & drying mask at tracer points
1357	!! for the current barotropic sub-step
1358	!!
1359	!! ** Method : ???
1360	!!
1361	!! ** Action : ptmsk : wetting & drying t-mask
1362	!!----------------------------------------------------------------------
1363	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pTmsk ! W & D t-mask
1364	REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: phU, phV, pu, pv ! ocean velocities and transports
1365	REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: pUmsk, pVmsk ! W & D u- and v-mask
1366	!
1367	INTEGER :: ji, jj ! dummy loop indices
1368	!!----------------------------------------------------------------------
1369	!
1370	DO jj = 1, jpj
1371	DO ji = 1, jpim1 ! not jpi-column
1372	IF ( phU(ji,jj) > 0._wp ) THEN ; pUmsk(ji,jj) = pTmsk(ji ,jj)
1373	ELSE ; pUmsk(ji,jj) = pTmsk(ji+1,jj)
1374	ENDIF
1375	phU(ji,jj) = pUmsk(ji,jj)*phU(ji,jj)
1376	pu (ji,jj) = pUmsk(ji,jj)*pu (ji,jj)
1377	END DO
1378	END DO
1379	!
1380	DO jj = 1, jpjm1 ! not jpj-row
1381	DO ji = 1, jpi
1382	IF ( phV(ji,jj) > 0._wp ) THEN ; pVmsk(ji,jj) = pTmsk(ji,jj )
1383	ELSE ; pVmsk(ji,jj) = pTmsk(ji,jj+1)
1384	ENDIF
1385	phV(ji,jj) = pVmsk(ji,jj)*phV(ji,jj)
1386	pv (ji,jj) = pVmsk(ji,jj)*pv (ji,jj)
1387	END DO
1388	END DO
1389	!
1390	END SUBROUTINE wad_Umsk
1391
1392
1393	SUBROUTINE wad_spg( sshn, zcpx, zcpy )
1394	!!---------------------------------------------------------------------
1395	!! * ROUTINE wad_sp *
1396	!!
1397	!! ** Purpose :
1398	!!----------------------------------------------------------------------
1399	INTEGER :: ji ,jj ! dummy loop indices
1400	LOGICAL :: ll_tmp1, ll_tmp2
1401	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: sshn
1402	REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: zcpx, zcpy
1403	!!----------------------------------------------------------------------
1404	DO jj = 2, jpjm1
1405	DO ji = 2, jpim1
1406	ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji+1,jj) ) > &
1407	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
1408	& MAX( sshn(ji,jj) + ht_0(ji,jj) , sshn(ji+1,jj) + ht_0(ji+1,jj) ) &
1409	& > rn_wdmin1 + rn_wdmin2
1410	ll_tmp2 = ( ABS( sshn(ji+1,jj) - sshn(ji ,jj)) > 1.E-12 ).AND.( &
1411	& MAX( sshn(ji,jj) , sshn(ji+1,jj) ) > &
1412	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
1413	IF(ll_tmp1) THEN
1414	zcpx(ji,jj) = 1.0_wp
1415	ELSEIF(ll_tmp2) THEN
1416	! no worries about sshn(ji+1,jj) - sshn(ji ,jj) = 0, it won't happen ! here
1417	zcpx(ji,jj) = ABS( (sshn(ji+1,jj) + ht_0(ji+1,jj) - sshn(ji,jj) - ht_0(ji,jj)) &
1418	& / (sshn(ji+1,jj) - sshn(ji ,jj)) )
1419	zcpx(ji,jj) = max(min( zcpx(ji,jj) , 1.0_wp),0.0_wp)
1420	ELSE
1421	zcpx(ji,jj) = 0._wp
1422	ENDIF
1423	!
1424	ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji,jj+1) ) > &
1425	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
1426	& MAX( sshn(ji,jj) + ht_0(ji,jj) , sshn(ji,jj+1) + ht_0(ji,jj+1) ) &
1427	& > rn_wdmin1 + rn_wdmin2
1428	ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji,jj+1)) > 1.E-12 ).AND.( &
1429	& MAX( sshn(ji,jj) , sshn(ji,jj+1) ) > &
1430	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
1431
1432	IF(ll_tmp1) THEN
1433	zcpy(ji,jj) = 1.0_wp
1434	ELSE IF(ll_tmp2) THEN
1435	! no worries about sshn(ji,jj+1) - sshn(ji,jj ) = 0, it won't happen ! here
1436	zcpy(ji,jj) = ABS( (sshn(ji,jj+1) + ht_0(ji,jj+1) - sshn(ji,jj) - ht_0(ji,jj)) &
1437	& / (sshn(ji,jj+1) - sshn(ji,jj )) )
1438	zcpy(ji,jj) = MAX( 0._wp , MIN( zcpy(ji,jj) , 1.0_wp ) )
1439	ELSE
1440	zcpy(ji,jj) = 0._wp
1441	ENDIF
1442	END DO
1443	END DO
1444
1445	END SUBROUTINE wad_spg
1446
1447
1448
1449	SUBROUTINE dyn_drg_init( pu_RHSi, pv_RHSi, pCdU_u, pCdU_v )
1450	!!----------------------------------------------------------------------
1451	!! * ROUTINE dyn_drg_init *
1452	!!
1453	!! ** Purpose : - add the baroclinic top/bottom drag contribution to
1454	!! the baroclinic part of the barotropic RHS
1455	!! - compute the barotropic drag coefficients
1456	!!
1457	!! ** Method : computation done over the INNER domain only
1458	!!----------------------------------------------------------------------
1459	REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: pu_RHSi, pv_RHSi ! baroclinic part of the barotropic RHS
1460	REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pCdU_u , pCdU_v ! barotropic drag coefficients
1461	!
1462	INTEGER :: ji, jj ! dummy loop indices
1463	INTEGER :: ikbu, ikbv, iktu, iktv
1464	REAL(wp) :: zztmp
1465	REAL(wp), DIMENSION(jpi,jpj) :: zu_i, zv_i
1466	!!----------------------------------------------------------------------
1467	!
1468	! !== Set the barotropic drag coef. ==!
1469	!
1470	IF( ln_isfcav ) THEN ! top+bottom friction (ocean cavities)
1471
1472	DO jj = 2, jpjm1
1473	DO ji = 2, jpim1 ! INNER domain
1474	pCdU_u(ji,jj) = r1_2*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) + rCdU_top(ji+1,jj)+rCdU_top(ji,jj) )
1475	pCdU_v(ji,jj) = r1_2*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) + rCdU_top(ji,jj+1)+rCdU_top(ji,jj) )
1476	END DO
1477	END DO
1478	ELSE ! bottom friction only
1479	DO jj = 2, jpjm1
1480	DO ji = 2, jpim1 ! INNER domain
1481	pCdU_u(ji,jj) = r1_2*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) )
1482	pCdU_v(ji,jj) = r1_2*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) )
1483	END DO
1484	END DO
1485	ENDIF
1486	!
1487	! !== BOTTOM stress contribution from baroclinic velocities ==!
1488	!
1489	IF( ln_bt_fw ) THEN ! FORWARD integration: use NOW bottom baroclinic velocities
1490
1491	DO jj = 2, jpjm1
1492	DO ji = 2, jpim1 ! INNER domain
1493	ikbu = mbku(ji,jj)
1494	ikbv = mbkv(ji,jj)
1495	zu_i(ji,jj) = un(ji,jj,ikbu) - un_b(ji,jj)
1496	zv_i(ji,jj) = vn(ji,jj,ikbv) - vn_b(ji,jj)
1497	END DO
1498	END DO
1499	ELSE ! CENTRED integration: use BEFORE bottom baroclinic velocities
1500
1501	DO jj = 2, jpjm1
1502	DO ji = 2, jpim1 ! INNER domain
1503	ikbu = mbku(ji,jj)
1504	ikbv = mbkv(ji,jj)
1505	zu_i(ji,jj) = ub(ji,jj,ikbu) - ub_b(ji,jj)
1506	zv_i(ji,jj) = vb(ji,jj,ikbv) - vb_b(ji,jj)
1507	END DO
1508	END DO
1509	ENDIF
1510	!
1511	IF( ln_wd_il ) THEN ! W/D : use the "clipped" bottom friction !!gm explain WHY, please !
1512	zztmp = -1._wp / rdtbt
1513	DO jj = 2, jpjm1
1514	DO ji = 2, jpim1 ! INNER domain
1515	pu_RHSi(ji,jj) = pu_RHSi(ji,jj) + zu_i(ji,jj) * wdrampu(ji,jj) * MAX( &
1516	& r1_hu_n(ji,jj) * r1_2*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) , zztmp )
1517	pv_RHSi(ji,jj) = pv_RHSi(ji,jj) + zv_i(ji,jj) * wdrampv(ji,jj) * MAX( &
1518	& r1_hv_n(ji,jj) * r1_2*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) , zztmp )
1519	END DO
1520	END DO
1521	ELSE ! use "unclipped" drag (even if explicit friction is used in 3D calculation)
1522
1523	DO jj = 2, jpjm1
1524	DO ji = 2, jpim1 ! INNER domain
1525	pu_RHSi(ji,jj) = pu_RHSi(ji,jj) + r1_hu_n(ji,jj) * r1_2( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) zu_i(ji,jj)
1526	pv_RHSi(ji,jj) = pv_RHSi(ji,jj) + r1_hv_n(ji,jj) * r1_2( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) zv_i(ji,jj)
1527	END DO
1528	END DO
1529	END IF
1530	!
1531	! !== TOP stress contribution from baroclinic velocities ==! (no W/D case)
1532	!
1533	IF( ln_isfcav ) THEN
1534	!
1535	IF( ln_bt_fw ) THEN ! FORWARD integration: use NOW top baroclinic velocity
1536
1537	DO jj = 2, jpjm1
1538	DO ji = 2, jpim1 ! INNER domain
1539	iktu = miku(ji,jj)
1540	iktv = mikv(ji,jj)
1541	zu_i(ji,jj) = un(ji,jj,iktu) - un_b(ji,jj)
1542	zv_i(ji,jj) = vn(ji,jj,iktv) - vn_b(ji,jj)
1543	END DO
1544	END DO
1545	ELSE ! CENTRED integration: use BEFORE top baroclinic velocity
1546
1547	DO jj = 2, jpjm1
1548	DO ji = 2, jpim1 ! INNER domain
1549	iktu = miku(ji,jj)
1550	iktv = mikv(ji,jj)
1551	zu_i(ji,jj) = ub(ji,jj,iktu) - ub_b(ji,jj)
1552	zv_i(ji,jj) = vb(ji,jj,iktv) - vb_b(ji,jj)
1553	END DO
1554	END DO
1555	ENDIF
1556	!
1557	! ! use "unclipped" top drag (even if explicit friction is used in 3D calculation)
1558
1559	DO jj = 2, jpjm1
1560	DO ji = 2, jpim1 ! INNER domain
1561	pu_RHSi(ji,jj) = pu_RHSi(ji,jj) + r1_hu_n(ji,jj) * r1_2( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) zu_i(ji,jj)
1562	pv_RHSi(ji,jj) = pv_RHSi(ji,jj) + r1_hv_n(ji,jj) * r1_2( rCdU_top(ji,jj+1)+rCdU_top(ji,jj) ) zv_i(ji,jj)
1563	END DO
1564	END DO
1565	!
1566	ENDIF
1567	!
1568	END SUBROUTINE dyn_drg_init
1569
1570	SUBROUTINE ts_bck_interp( jn, ll_init, & ! <== in
1571	& za0, za1, za2, za3 ) ! ==> out
1572	!!----------------------------------------------------------------------
1573	INTEGER ,INTENT(in ) :: jn ! index of sub time step
1574	LOGICAL ,INTENT(in ) :: ll_init !
1575	REAL(wp),INTENT( out) :: za0, za1, za2, za3 ! Half-step back interpolation coefficient
1576	!
1577	REAL(wp) :: zepsilon, zgamma ! - -
1578	!!----------------------------------------------------------------------
1579	! ! set Half-step back interpolation coefficient
1580	IF ( jn==1 .AND. ll_init ) THEN !* Forward-backward
1581	za0 = 1._wp
1582	za1 = 0._wp
1583	za2 = 0._wp
1584	za3 = 0._wp
1585	ELSEIF( jn==2 .AND. ll_init ) THEN !* AB2-AM3 Coefficients; bet=0 ; gam=-1/6 ; eps=1/12
1586	za0 = 1.0833333333333_wp ! za0 = 1-gam-eps
1587	za1 =-0.1666666666666_wp ! za1 = gam
1588	za2 = 0.0833333333333_wp ! za2 = eps
1589	za3 = 0._wp
1590	ELSE !* AB3-AM4 Coefficients; bet=0.281105 ; eps=0.013 ; gam=0.0880
1591	IF( rn_bt_alpha == 0._wp ) THEN ! Time diffusion
1592	za0 = 0.614_wp ! za0 = 1/2 + gam + 2*eps
1593	za1 = 0.285_wp ! za1 = 1/2 - 2gam - 3eps
1594	za2 = 0.088_wp ! za2 = gam
1595	za3 = 0.013_wp ! za3 = eps
1596	ELSE ! no time diffusion
1597	zepsilon = 0.00976186_wp - 0.13451357_wp * rn_bt_alpha
1598	zgamma = 0.08344500_wp - 0.51358400_wp * rn_bt_alpha
1599	za0 = 0.5_wp + zgamma + 2._wp * rn_bt_alpha + 2._wp * zepsilon
1600	za1 = 1._wp - za0 - zgamma - zepsilon
1601	za2 = zgamma
1602	za3 = zepsilon
1603	ENDIF
1604	ENDIF
1605	END SUBROUTINE ts_bck_interp
1606
1607
1608	!!======================================================================
1609	END MODULE dynspg_ts

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