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dynspg_ts.F90 in NEMO/branches/2020/test_12905_xios_restart/src/OCE/DYN – NEMO

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source: NEMO/branches/2020/test_12905_xios_restart/src/OCE/DYN/dynspg_ts.F90 @ 13751

Last change on this file since 13751 was 13751, checked in by andmirek, 4 years ago
Ticket #2462: Update test branch to the revision 13750 of the development branch
Property svn:keywords set to `Id`
File size: 78.9 KB

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1	MODULE dynspg_ts
2
3	!! Includes ROMS wd scheme with diagnostic outputs ; puu(:,:,:,Kmm) and puu(:,:,:,Krhs) 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	#if defined key_agrif
49	USE agrif_oce_interp ! agrif
50	USE agrif_oce
51	#endif
52	#if defined key_asminc
53	USE asminc ! Assimilation increment
54	#endif
55	!
56	USE in_out_manager ! I/O manager
57	USE lib_mpp ! distributed memory computing library
58	USE lbclnk ! ocean lateral boundary conditions (or mpp link)
59	USE prtctl ! Print control
60	USE iom ! IOM library
61	USE restart ! only for lrst_oce
62
63	USE iom ! to remove
64
65	IMPLICIT NONE
66	PRIVATE
67
68	PUBLIC dyn_spg_ts ! called by dyn_spg
69	PUBLIC dyn_spg_ts_init ! - - dyn_spg_init
70
71	!! Time filtered arrays at baroclinic time step:
72	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: un_adv , vn_adv !: Advection vel. at "now" barocl. step
73	!
74	INTEGER, SAVE :: icycle ! Number of barotropic sub-steps for each internal step nn_e <= 2.5 nn_e
75	REAL(wp),SAVE :: rDt_e ! Barotropic time step
76	!
77	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:) :: wgtbtp1, wgtbtp2 ! 1st & 2nd weights used in time filtering of barotropic fields
78	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: zwz ! ff_f/h at F points
79	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: ftnw, ftne ! triad of coriolis parameter
80	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: ftsw, ftse ! (only used with een vorticity scheme)
81
82	REAL(wp) :: r1_12 = 1._wp / 12._wp ! local ratios
83	REAL(wp) :: r1_8 = 0.125_wp !
84	REAL(wp) :: r1_4 = 0.25_wp !
85	REAL(wp) :: r1_2 = 0.5_wp !
86
87	!! * Substitutions
88	# include "do_loop_substitute.h90"
89	# include "domzgr_substitute.h90"
90	!!----------------------------------------------------------------------
91	!! NEMO/OCE 4.0 , NEMO Consortium (2018)
92	!! $Id$
93	!! Software governed by the CeCILL license (see ./LICENSE)
94	!!----------------------------------------------------------------------
95	CONTAINS
96
97	INTEGER FUNCTION dyn_spg_ts_alloc()
98	!!----------------------------------------------------------------------
99	!! * routine dyn_spg_ts_alloc *
100	!!----------------------------------------------------------------------
101	INTEGER :: ierr(3)
102	!!----------------------------------------------------------------------
103	ierr(:) = 0
104	!
105	ALLOCATE( wgtbtp1(3nn_e), wgtbtp2(3nn_e), zwz(jpi,jpj), STAT=ierr(1) )
106	IF( ln_dynvor_een .OR. ln_dynvor_eeT ) &
107	& ALLOCATE( ftnw(jpi,jpj) , ftne(jpi,jpj) , ftsw(jpi,jpj) , ftse(jpi,jpj), STAT=ierr(2) )
108	!
109	ALLOCATE( un_adv(jpi,jpj), vn_adv(jpi,jpj) , STAT=ierr(3) )
110	!
111	dyn_spg_ts_alloc = MAXVAL( ierr(:) )
112	!
113	CALL mpp_sum( 'dynspg_ts', dyn_spg_ts_alloc )
114	IF( dyn_spg_ts_alloc /= 0 ) CALL ctl_stop( 'STOP', 'dyn_spg_ts_alloc: failed to allocate arrays' )
115	!
116	END FUNCTION dyn_spg_ts_alloc
117
118
119	SUBROUTINE dyn_spg_ts( kt, Kbb, Kmm, Krhs, puu, pvv, pssh, puu_b, pvv_b, Kaa )
120	!!----------------------------------------------------------------------
121	!!
122	!! ** Purpose : - Compute the now trend due to the explicit time stepping
123	!! of the quasi-linear barotropic system, and add it to the
124	!! general momentum trend.
125	!!
126	!! ** Method : - split-explicit schem (time splitting) :
127	!! Barotropic variables are advanced from internal time steps
128	!! "n" to "n+1" if ln_bt_fw=T
129	!! or from
130	!! "n-1" to "n+1" if ln_bt_fw=F
131	!! thanks to a generalized forward-backward time stepping (see ref. below).
132	!!
133	!! ** Action :
134	!! -Update the filtered free surface at step "n+1" : pssh(:,:,Kaa)
135	!! -Update filtered barotropic velocities at step "n+1" : puu_b(:,:,:,Kaa), vv_b(:,:,:,Kaa)
136	!! -Compute barotropic advective fluxes at step "n" : un_adv, vn_adv
137	!! These are used to advect tracers and are compliant with discrete
138	!! continuity equation taken at the baroclinic time steps. This
139	!! ensures tracers conservation.
140	!! - (puu(:,:,:,Krhs), pvv(:,:,:,Krhs)) momentum trend updated with barotropic component.
141	!!
142	!! References : Shchepetkin and McWilliams, Ocean Modelling, 2005.
143	!!---------------------------------------------------------------------
144	INTEGER , INTENT( in ) :: kt ! ocean time-step index
145	INTEGER , INTENT( in ) :: Kbb, Kmm, Krhs, Kaa ! ocean time level indices
146	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
147	REAL(wp), DIMENSION(jpi,jpj,jpt) , INTENT(inout) :: pssh, puu_b, pvv_b ! SSH and barotropic velocities at main time levels
148	!
149	INTEGER :: ji, jj, jk, jn ! dummy loop indices
150	LOGICAL :: ll_fw_start ! =T : forward integration
151	LOGICAL :: ll_init ! =T : special startup of 2d equations
152	INTEGER :: noffset ! local integers : time offset for bdy update
153	REAL(wp) :: r1_Dt_b, z1_hu, z1_hv ! local scalars
154	REAL(wp) :: za0, za1, za2, za3 ! - -
155	REAL(wp) :: zztmp, zldg ! - -
156	REAL(wp) :: zhu_bck, zhv_bck, zhdiv ! - -
157	REAL(wp) :: zun_save, zvn_save ! - -
158	REAL(wp), DIMENSION(jpi,jpj) :: zu_trd, zu_frc, zu_spg, zssh_frc
159	REAL(wp), DIMENSION(jpi,jpj) :: zv_trd, zv_frc, zv_spg
160	REAL(wp), DIMENSION(jpi,jpj) :: zsshu_a, zhup2_e, zhtp2_e
161	REAL(wp), DIMENSION(jpi,jpj) :: zsshv_a, zhvp2_e, zsshp2_e
162	REAL(wp), DIMENSION(jpi,jpj) :: zCdU_u, zCdU_v ! top/bottom stress at u- & v-points
163	REAL(wp), DIMENSION(jpi,jpj) :: zhU, zhV ! fluxes
164	REAL(wp), DIMENSION(jpi, jpj, jpk) :: ze3u, ze3v
165	!
166	REAL(wp) :: zwdramp ! local scalar - only used if ln_wd_dl = .True.
167
168	INTEGER :: iwdg, jwdg, kwdg ! short-hand values for the indices of the output point
169
170	REAL(wp) :: zepsilon, zgamma ! - -
171	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zcpx, zcpy ! Wetting/Dying gravity filter coef.
172	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: ztwdmask, zuwdmask, zvwdmask ! ROMS wetting and drying masks at t,u,v points
173	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zuwdav2, zvwdav2 ! averages over the sub-steps of zuwdmask and zvwdmask
174	REAL(wp) :: zt0substep ! Time of day at the beginning of the time substep
175	!!----------------------------------------------------------------------
176	!
177	IF( ln_wd_il ) ALLOCATE( zcpx(jpi,jpj), zcpy(jpi,jpj) )
178	! !* Allocate temporary arrays
179	IF( ln_wd_dl ) ALLOCATE( ztwdmask(jpi,jpj), zuwdmask(jpi,jpj), zvwdmask(jpi,jpj), zuwdav2(jpi,jpj), zvwdav2(jpi,jpj))
180	!
181	zwdramp = r_rn_wdmin1 ! simplest ramp
182	! zwdramp = 1._wp / (rn_wdmin2 - rn_wdmin1) ! more general ramp
183	! ! inverse of baroclinic time step
184	r1_Dt_b = 1._wp / rDt
185	!
186	ll_init = ln_bt_av ! if no time averaging, then no specific restart
187	ll_fw_start = .FALSE.
188	! ! time offset in steps for bdy data update
189	IF( .NOT.ln_bt_fw ) THEN ; noffset = - nn_e
190	ELSE ; noffset = 0
191	ENDIF
192	!
193	IF( kt == nit000 ) THEN !* initialisation
194	!
195	IF(lwp) WRITE(numout,*)
196	IF(lwp) WRITE(numout,*) 'dyn_spg_ts : surface pressure gradient trend'
197	IF(lwp) WRITE(numout,*) '~~~~~~~~~~ free surface with time splitting'
198	IF(lwp) WRITE(numout,*)
199	!
200	IF( l_1st_euler ) ll_init=.TRUE.
201	!
202	IF( ln_bt_fw .OR. l_1st_euler ) THEN
203	ll_fw_start =.TRUE.
204	noffset = 0
205	ELSE
206	ll_fw_start =.FALSE.
207	ENDIF
208	! ! Set averaging weights and cycle length:
209	CALL ts_wgt( ln_bt_av, ll_fw_start, icycle, wgtbtp1, wgtbtp2 )
210	!
211	ELSEIF( kt == nit000 + 1 ) THEN !* initialisation 2nd time-step
212	!
213	IF( .NOT.ln_bt_fw ) THEN
214	! If we did an Euler timestep on the first timestep we need to reset ll_fw_start
215	! and the averaging weights. We don't have an easy way of telling whether we did
216	! an Euler timestep on the first timestep (because l_1st_euler is reset to .false.
217	! at the end of the first timestep) so just do this in all cases.
218	ll_fw_start = .FALSE.
219	CALL ts_wgt( ln_bt_av, ll_fw_start, icycle, wgtbtp1, wgtbtp2 )
220	ENDIF
221	!
222	ENDIF
223	!
224	! -----------------------------------------------------------------------------
225	! Phase 1 : Coupling between general trend and barotropic estimates (1st step)
226	! -----------------------------------------------------------------------------
227	!
228	!
229	! != zu_frc = 1/H e3*d/dt(Ua) =! (Vertical mean of Ua, the 3D trends)
230	! ! --------------------------- !
231	DO jk = 1 , jpk
232	ze3u(:,:,jk) = e3u(:,:,jk,Kmm)
233	ze3v(:,:,jk) = e3v(:,:,jk,Kmm)
234	END DO
235	!
236	zu_frc(:,:) = SUM( ze3u(:,:,:) * uu(:,:,:,Krhs) * umask(:,:,:) , DIM=3 ) * r1_hu(:,:,Kmm)
237	zv_frc(:,:) = SUM( ze3v(:,:,:) * vv(:,:,:,Krhs) * vmask(:,:,:) , DIM=3 ) * r1_hv(:,:,Kmm)
238	!
239	!
240	! != U(Krhs) => baroclinic trend =! (remove its vertical mean)
241	DO jk = 1, jpkm1 ! ----------------------------- !
242	uu(:,:,jk,Krhs) = ( uu(:,:,jk,Krhs) - zu_frc(:,:) ) * umask(:,:,jk)
243	vv(:,:,jk,Krhs) = ( vv(:,:,jk,Krhs) - zv_frc(:,:) ) * vmask(:,:,jk)
244	END DO
245
246	!!gm Question here when removing the Vertically integrated trends, we remove the vertically integrated NL trends on momentum....
247	!!gm Is it correct to do so ? I think so...
248
249	! != remove 2D Coriolis and pressure gradient trends =!
250	! ! ------------------------------------------------- !
251	!
252	IF( kt == nit000 .OR. .NOT. ln_linssh ) CALL dyn_cor_2D_init( Kmm ) ! Set zwz, the barotropic Coriolis force coefficient
253	! ! recompute zwz = f/depth at every time step for (.NOT.ln_linssh) as the water colomn height changes
254	!
255	! !* 2D Coriolis trends
256	zhU(:,:) = puu_b(:,:,Kmm) * hu(:,:,Kmm) * e2u(:,:) ! now fluxes
257	zhV(:,:) = pvv_b(:,:,Kmm) * hv(:,:,Kmm) * e1v(:,:) ! NB: FULL domain : put a value in last row and column
258	!
259	CALL dyn_cor_2d( ht(:,:), hu(:,:,Kmm), hv(:,:,Kmm), puu_b(:,:,Kmm), pvv_b(:,:,Kmm), zhU, zhV, & ! <<== in
260	& zu_trd, zv_trd ) ! ==>> out
261	!
262	IF( .NOT.ln_linssh ) THEN !* surface pressure gradient (variable volume only)
263	!
264	IF( ln_wd_il ) THEN ! W/D : limiter applied to spgspg
265	CALL wad_spg( pssh(:,:,Kmm), zcpx, zcpy ) ! Calculating W/D gravity filters, zcpx and zcpy
266	DO_2D( 0, 0, 0, 0 ) ! SPG with the application of W/D gravity filters
267	zu_trd(ji,jj) = zu_trd(ji,jj) - grav * ( pssh(ji+1,jj ,Kmm) - pssh(ji ,jj ,Kmm) ) &
268	& * r1_e1u(ji,jj) * zcpx(ji,jj) * wdrampu(ji,jj) !jth
269	zv_trd(ji,jj) = zv_trd(ji,jj) - grav * ( pssh(ji ,jj+1,Kmm) - pssh(ji ,jj ,Kmm) ) &
270	& * r1_e2v(ji,jj) * zcpy(ji,jj) * wdrampv(ji,jj) !jth
271	END_2D
272	ELSE ! now suface pressure gradient
273	DO_2D( 0, 0, 0, 0 )
274	zu_trd(ji,jj) = zu_trd(ji,jj) - grav * ( pssh(ji+1,jj ,Kmm) - pssh(ji ,jj ,Kmm) ) * r1_e1u(ji,jj)
275	zv_trd(ji,jj) = zv_trd(ji,jj) - grav * ( pssh(ji ,jj+1,Kmm) - pssh(ji ,jj ,Kmm) ) * r1_e2v(ji,jj)
276	END_2D
277	ENDIF
278	!
279	ENDIF
280	!
281	DO_2D( 0, 0, 0, 0 ) ! Remove coriolis term (and possibly spg) from barotropic trend
282	zu_frc(ji,jj) = zu_frc(ji,jj) - zu_trd(ji,jj) * ssumask(ji,jj)
283	zv_frc(ji,jj) = zv_frc(ji,jj) - zv_trd(ji,jj) * ssvmask(ji,jj)
284	END_2D
285	!
286	! != Add bottom stress contribution from baroclinic velocities =!
287	! ! ----------------------------------------------------------- !
288	CALL dyn_drg_init( Kbb, Kmm, puu, pvv, puu_b ,pvv_b, zu_frc, zv_frc, zCdU_u, zCdU_v ) ! also provide the barotropic drag coefficients
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_2D( 0, 0, 0, 0 )
294	zu_frc(ji,jj) = zu_frc(ji,jj) + grav * ( ssh_ib (ji+1,jj ) - ssh_ib (ji,jj) ) * r1_e1u(ji,jj)
295	zv_frc(ji,jj) = zv_frc(ji,jj) + grav * ( ssh_ib (ji ,jj+1) - ssh_ib (ji,jj) ) * r1_e2v(ji,jj)
296	END_2D
297	ELSE ! CENTRED integration: use kt-1/2 + kt+1/2 pressure (NOW)
298	zztmp = grav * r1_2
299	DO_2D( 0, 0, 0, 0 )
300	zu_frc(ji,jj) = zu_frc(ji,jj) + zztmp * ( ssh_ib (ji+1,jj ) - ssh_ib (ji,jj) &
301	& + ssh_ibb(ji+1,jj ) - ssh_ibb(ji,jj) ) * r1_e1u(ji,jj)
302	zv_frc(ji,jj) = zv_frc(ji,jj) + zztmp * ( ssh_ib (ji ,jj+1) - ssh_ib (ji,jj) &
303	& + ssh_ibb(ji ,jj+1) - ssh_ibb(ji,jj) ) * r1_e2v(ji,jj)
304	END_2D
305	ENDIF
306	ENDIF
307	!
308	! != Add atmospheric pressure forcing =!
309	! ! ---------------------------------- !
310	IF( ln_bt_fw ) THEN ! Add wind forcing
311	DO_2D( 0, 0, 0, 0 )
312	zu_frc(ji,jj) = zu_frc(ji,jj) + r1_rho0 * utau(ji,jj) * r1_hu(ji,jj,Kmm)
313	zv_frc(ji,jj) = zv_frc(ji,jj) + r1_rho0 * vtau(ji,jj) * r1_hv(ji,jj,Kmm)
314	END_2D
315	ELSE
316	zztmp = r1_rho0 * r1_2
317	DO_2D( 0, 0, 0, 0 )
318	zu_frc(ji,jj) = zu_frc(ji,jj) + zztmp * ( utau_b(ji,jj) + utau(ji,jj) ) * r1_hu(ji,jj,Kmm)
319	zv_frc(ji,jj) = zv_frc(ji,jj) + zztmp * ( vtau_b(ji,jj) + vtau(ji,jj) ) * r1_hv(ji,jj,Kmm)
320	END_2D
321	ENDIF
322	!
323	! !----------------!
324	! !== sssh_frc ==! Right-Hand-Side of the barotropic ssh equation (over the FULL domain)
325	! !----------------!
326	! != Net water flux forcing applied to a water column =!
327	! ! --------------------------------------------------- !
328	IF (ln_bt_fw) THEN ! FORWARD integration: use kt+1/2 fluxes (NOW+1/2)
329	zssh_frc(:,:) = r1_rho0 * ( emp(:,:) - rnf(:,:) + fwfisf_cav(:,:) + fwfisf_par(:,:) )
330	ELSE ! CENTRED integration: use kt-1/2 + kt+1/2 fluxes (NOW)
331	zztmp = r1_rho0 * r1_2
332	zssh_frc(:,:) = zztmp * ( emp(:,:) + emp_b(:,:) &
333	& - rnf(:,:) - rnf_b(:,:) &
334	& + fwfisf_cav(:,:) + fwfisf_cav_b(:,:) &
335	& + fwfisf_par(:,:) + fwfisf_par_b(:,:) )
336	ENDIF
337	! != Add Stokes drift divergence =! (if exist)
338	IF( ln_sdw ) THEN ! ----------------------------- !
339	zssh_frc(:,:) = zssh_frc(:,:) + div_sd(:,:)
340	ENDIF
341	!
342	! ! ice sheet coupling
343	IF ( ln_isf .AND. ln_isfcpl ) THEN
344	!
345	! ice sheet coupling
346	IF( ln_rstart .AND. kt == nit000 ) THEN
347	zssh_frc(:,:) = zssh_frc(:,:) + risfcpl_ssh(:,:)
348	END IF
349	!
350	! conservation option
351	IF( ln_isfcpl_cons ) THEN
352	zssh_frc(:,:) = zssh_frc(:,:) + risfcpl_cons_ssh(:,:)
353	END IF
354	!
355	END IF
356	!
357	#if defined key_asminc
358	! != Add the IAU weighted SSH increment =!
359	! ! ------------------------------------ !
360	IF( lk_asminc .AND. ln_sshinc .AND. ln_asmiau ) THEN
361	zssh_frc(:,:) = zssh_frc(:,:) - ssh_iau(:,:)
362	ENDIF
363	#endif
364	! != Fill boundary data arrays for AGRIF
365	! ! ------------------------------------
366	#if defined key_agrif
367	IF( .NOT.Agrif_Root() ) CALL agrif_dta_ts( kt )
368	#endif
369	!
370	! -----------------------------------------------------------------------
371	! Phase 2 : Integration of the barotropic equations
372	! -----------------------------------------------------------------------
373	!
374	! ! ==================== !
375	! ! Initialisations !
376	! ! ==================== !
377	! Initialize barotropic variables:
378	IF( ll_init )THEN
379	sshbb_e(:,:) = 0._wp
380	ubb_e (:,:) = 0._wp
381	vbb_e (:,:) = 0._wp
382	sshb_e (:,:) = 0._wp
383	ub_e (:,:) = 0._wp
384	vb_e (:,:) = 0._wp
385	ENDIF
386	!
387	IF( ln_linssh ) THEN ! mid-step ocean depth is fixed (hup2_e=hu_n=hu_0)
388	zhup2_e(:,:) = hu(:,:,Kmm)
389	zhvp2_e(:,:) = hv(:,:,Kmm)
390	zhtp2_e(:,:) = ht(:,:)
391	ENDIF
392	!
393	IF (ln_bt_fw) THEN ! FORWARD integration: start from NOW fields
394	sshn_e(:,:) = pssh(:,:,Kmm)
395	un_e (:,:) = puu_b(:,:,Kmm)
396	vn_e (:,:) = pvv_b(:,:,Kmm)
397	!
398	hu_e (:,:) = hu(:,:,Kmm)
399	hv_e (:,:) = hv(:,:,Kmm)
400	hur_e (:,:) = r1_hu(:,:,Kmm)
401	hvr_e (:,:) = r1_hv(:,:,Kmm)
402	ELSE ! CENTRED integration: start from BEFORE fields
403	sshn_e(:,:) = pssh(:,:,Kbb)
404	un_e (:,:) = puu_b(:,:,Kbb)
405	vn_e (:,:) = pvv_b(:,:,Kbb)
406	!
407	hu_e (:,:) = hu(:,:,Kbb)
408	hv_e (:,:) = hv(:,:,Kbb)
409	hur_e (:,:) = r1_hu(:,:,Kbb)
410	hvr_e (:,:) = r1_hv(:,:,Kbb)
411	ENDIF
412	!
413	! Initialize sums:
414	puu_b (:,:,Kaa) = 0._wp ! After barotropic velocities (or transport if flux form)
415	pvv_b (:,:,Kaa) = 0._wp
416	pssh (:,:,Kaa) = 0._wp ! Sum for after averaged sea level
417	un_adv(:,:) = 0._wp ! Sum for now transport issued from ts loop
418	vn_adv(:,:) = 0._wp
419	!
420	IF( ln_wd_dl ) THEN
421	zuwdmask(:,:) = 0._wp ! set to zero for definiteness (not sure this is necessary)
422	zvwdmask(:,:) = 0._wp !
423	zuwdav2 (:,:) = 0._wp
424	zvwdav2 (:,:) = 0._wp
425	END IF
426
427	! ! ==================== !
428	DO jn = 1, icycle ! sub-time-step loop !
429	! ! ==================== !
430	!
431	l_full_nf_update = jn == icycle ! false: disable full North fold update (performances) for jn = 1 to icycle-1
432	!
433	! !== Update the forcing ==! (BDY and tides)
434	!
435	IF( ln_bdy .AND. ln_tide ) CALL bdy_dta_tides( kt, kit=jn, pt_offset= REAL(noffset+1,wp) )
436	! Update tide potential at the beginning of current time substep
437	IF( ln_tide_pot .AND. ln_tide ) THEN
438	zt0substep = REAL(nsec_day, wp) - 0.5_wprn_Dt + (jn + noffset - 1) rn_Dt / REAL(nn_e, wp)
439	CALL upd_tide(zt0substep, Kmm)
440	END IF
441	!
442	! !== extrapolation at mid-step ==! (jn+1/2)
443	!
444	! !* Set extrapolation coefficients for predictor step:
445	IF ((jn<3).AND.ll_init) THEN ! Forward
446	za1 = 1._wp
447	za2 = 0._wp
448	za3 = 0._wp
449	ELSE ! AB3-AM4 Coefficients: bet=0.281105
450	za1 = 1.781105_wp ! za1 = 3/2 + bet
451	za2 = -1.06221_wp ! za2 = -(1/2 + 2*bet)
452	za3 = 0.281105_wp ! za3 = bet
453	ENDIF
454	!
455	! !* Extrapolate barotropic velocities at mid-step (jn+1/2)
456	!-- m+1/2 m m-1 m-2 --!
457	!-- u = (3/2+beta) u -(1/2+2beta) u + beta u --!
458	!-------------------------------------------------------------------------!
459	ua_e(:,:) = za1 * un_e(:,:) + za2 * ub_e(:,:) + za3 * ubb_e(:,:)
460	va_e(:,:) = za1 * vn_e(:,:) + za2 * vb_e(:,:) + za3 * vbb_e(:,:)
461
462	IF( .NOT.ln_linssh ) THEN !* Update ocean depth (variable volume case only)
463	! ! ------------------
464	! Extrapolate Sea Level at step jit+0.5:
465	!-- m+1/2 m m-1 m-2 --!
466	!-- ssh = (3/2+beta) ssh -(1/2+2beta) ssh + beta ssh --!
467	!--------------------------------------------------------------------------------!
468	zsshp2_e(:,:) = za1 * sshn_e(:,:) + za2 * sshb_e(:,:) + za3 * sshbb_e(:,:)
469
470	! set wetting & drying mask at tracer points for this barotropic mid-step
471	IF( ln_wd_dl ) CALL wad_tmsk( zsshp2_e, ztwdmask )
472	!
473	! ! ocean t-depth at mid-step
474	zhtp2_e(:,:) = ht_0(:,:) + zsshp2_e(:,:)
475	!
476	! ! ocean u- and v-depth at mid-step (separate DO-loops remove the need of a lbc_lnk)
477	DO_2D( 1, 1, 1, 0 ) ! not jpi-column
478	zhup2_e(ji,jj) = hu_0(ji,jj) + r1_2 * r1_e1e2u(ji,jj) &
479	& * ( e1e2t(ji ,jj) * zsshp2_e(ji ,jj) &
480	& + e1e2t(ji+1,jj) * zsshp2_e(ji+1,jj) ) * ssumask(ji,jj)
481	END_2D
482	DO_2D( 1, 0, 1, 1 ) ! not jpj-row
483	zhvp2_e(ji,jj) = hv_0(ji,jj) + r1_2 * r1_e1e2v(ji,jj) &
484	& * ( e1e2t(ji,jj ) * zsshp2_e(ji,jj ) &
485	& + e1e2t(ji,jj+1) * zsshp2_e(ji,jj+1) ) * ssvmask(ji,jj)
486	END_2D
487	!
488	ENDIF
489	!
490	! !== after SSH ==! (jn+1)
491	!
492	! ! update (ua_e,va_e) to enforce volume conservation at open boundaries
493	! ! values of zhup2_e and zhvp2_e on the halo are not needed in bdy_vol2d
494	IF( ln_bdy .AND. ln_vol ) CALL bdy_vol2d( kt, jn, ua_e, va_e, zhup2_e, zhvp2_e )
495	!
496	! ! resulting flux at mid-step (not over the full domain)
497	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
498	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
499	!
500	#if defined key_agrif
501	! Set fluxes during predictor step to ensure volume conservation
502	IF( .NOT.Agrif_Root() .AND. ln_bt_fw ) CALL agrif_dyn_ts_flux( jn, zhU, zhV )
503	#endif
504	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
505
506	IF( ln_wd_dl ) THEN ! un_e and vn_e are set to zero at faces where
507	! ! the direction of the flow is from dry cells
508	CALL wad_Umsk( ztwdmask, zhU, zhV, un_e, vn_e, zuwdmask, zvwdmask ) ! not jpi colomn for U, not jpj row for V
509	!
510	ENDIF
511	!
512	!
513	! Compute Sea Level at step jit+1
514	!-- m+1 m m+1/2 --!
515	!-- ssh = ssh - delta_t' * [ frc + div( flux ) ] --!
516	!-------------------------------------------------------------------------!
517	DO_2D( 0, 0, 0, 0 )
518	zhdiv = ( zhU(ji,jj) - zhU(ji-1,jj) + zhV(ji,jj) - zhV(ji,jj-1) ) * r1_e1e2t(ji,jj)
519	ssha_e(ji,jj) = ( sshn_e(ji,jj) - rDt_e * ( zssh_frc(ji,jj) + zhdiv ) ) * ssmask(ji,jj)
520	END_2D
521	!
522	CALL lbc_lnk_multi( 'dynspg_ts', ssha_e, 'T', 1._wp, zhU, 'U', -1._wp, zhV, 'V', -1._wp )
523	!
524	! Duplicate sea level across open boundaries (this is only cosmetic if linssh=T)
525	IF( ln_bdy ) CALL bdy_ssh( ssha_e )
526	#if defined key_agrif
527	IF( .NOT.Agrif_Root() ) CALL agrif_ssh_ts( jn )
528	#endif
529	!
530	! ! Sum over sub-time-steps to compute advective velocities
531	za2 = wgtbtp2(jn) ! zhU, zhV hold fluxes extrapolated at jn+0.5
532	un_adv(:,:) = un_adv(:,:) + za2 * zhU(:,:) * r1_e2u(:,:)
533	vn_adv(:,:) = vn_adv(:,:) + za2 * zhV(:,:) * r1_e1v(:,:)
534	! sum over sub-time-steps to decide which baroclinic velocities to set to zero (zuwdav2 is only used when ln_wd_dl_bc=True)
535	IF ( ln_wd_dl_bc ) THEN
536	zuwdav2(1:jpim1,1:jpj ) = zuwdav2(1:jpim1,1:jpj ) + za2 * zuwdmask(1:jpim1,1:jpj ) ! not jpi-column
537	zvwdav2(1:jpi ,1:jpjm1) = zvwdav2(1:jpi ,1:jpjm1) + za2 * zvwdmask(1:jpi ,1:jpjm1) ! not jpj-row
538	END IF
539	!
540	!
541	! Sea Surface Height at u-,v-points (vvl case only)
542	IF( .NOT.ln_linssh ) THEN
543	DO_2D( 0, 0, 0, 0 )
544	zsshu_a(ji,jj) = r1_2 * ssumask(ji,jj) * r1_e1e2u(ji,jj) &
545	& * ( e1e2t(ji ,jj ) * ssha_e(ji ,jj ) &
546	& + e1e2t(ji+1,jj ) * ssha_e(ji+1,jj ) )
547	zsshv_a(ji,jj) = r1_2 * ssvmask(ji,jj) * r1_e1e2v(ji,jj) &
548	& * ( e1e2t(ji ,jj ) * ssha_e(ji ,jj ) &
549	& + e1e2t(ji ,jj+1) * ssha_e(ji ,jj+1) )
550	END_2D
551	ENDIF
552	!
553	! Half-step back interpolation of SSH for surface pressure computation at step jit+1/2
554	!-- m+1/2 m+1 m m-1 m-2 --!
555	!-- ssh' = za0 * ssh + za1 * ssh + za2 * ssh + za3 * ssh --!
556	!------------------------------------------------------------------------------------------!
557	CALL ts_bck_interp( jn, ll_init, za0, za1, za2, za3 ) ! coeficients of the interpolation
558	zsshp2_e(:,:) = za0 * ssha_e(:,:) + za1 * sshn_e (:,:) &
559	& + za2 * sshb_e(:,:) + za3 * sshbb_e(:,:)
560	!
561	! ! Surface pressure gradient
562	zldg = ( 1._wp - rn_scal_load ) * grav ! local factor
563	DO_2D( 0, 0, 0, 0 )
564	zu_spg(ji,jj) = - zldg * ( zsshp2_e(ji+1,jj) - zsshp2_e(ji,jj) ) * r1_e1u(ji,jj)
565	zv_spg(ji,jj) = - zldg * ( zsshp2_e(ji,jj+1) - zsshp2_e(ji,jj) ) * r1_e2v(ji,jj)
566	END_2D
567	IF( ln_wd_il ) THEN ! W/D : gravity filters applied on pressure gradient
568	CALL wad_spg( zsshp2_e, zcpx, zcpy ) ! Calculating W/D gravity filters
569	zu_spg(2:jpim1,2:jpjm1) = zu_spg(2:jpim1,2:jpjm1) * zcpx(2:jpim1,2:jpjm1)
570	zv_spg(2:jpim1,2:jpjm1) = zv_spg(2:jpim1,2:jpjm1) * zcpy(2:jpim1,2:jpjm1)
571	ENDIF
572	!
573	! Add Coriolis trend:
574	! zwz array below or triads normally depend on sea level with ln_linssh=F and should be updated
575	! at each time step. We however keep them constant here for optimization.
576	! Recall that zhU and zhV hold fluxes at jn+0.5 (extrapolated not backward interpolated)
577	CALL dyn_cor_2d( zhtp2_e, zhup2_e, zhvp2_e, ua_e, va_e, zhU, zhV, zu_trd, zv_trd )
578	!
579	! Add tidal astronomical forcing if defined
580	IF ( ln_tide .AND. ln_tide_pot ) THEN
581	DO_2D( 0, 0, 0, 0 )
582	zu_trd(ji,jj) = zu_trd(ji,jj) + grav * ( pot_astro(ji+1,jj) - pot_astro(ji,jj) ) * r1_e1u(ji,jj)
583	zv_trd(ji,jj) = zv_trd(ji,jj) + grav * ( pot_astro(ji,jj+1) - pot_astro(ji,jj) ) * r1_e2v(ji,jj)
584	END_2D
585	ENDIF
586	!
587	! Add bottom stresses:
588	!jth do implicitly instead
589	IF ( .NOT. ll_wd ) THEN ! Revert to explicit for bit comparison tests in non wad runs
590	DO_2D( 0, 0, 0, 0 )
591	zu_trd(ji,jj) = zu_trd(ji,jj) + zCdU_u(ji,jj) * un_e(ji,jj) * hur_e(ji,jj)
592	zv_trd(ji,jj) = zv_trd(ji,jj) + zCdU_v(ji,jj) * vn_e(ji,jj) * hvr_e(ji,jj)
593	END_2D
594	ENDIF
595	!
596	! Set next velocities:
597	! Compute barotropic speeds at step jit+1 (h : total height of the water colomn)
598	!-- VECTOR FORM
599	!-- m+1 m / m+1/2 \ --!
600	!-- u = u + delta_t' * \ (1-r)g grad_x( ssh') - f * k vect u + frc / --!
601	!-- --!
602	!-- FLUX FORM --!
603	!-- m+1 __1__ / m m / m+1/2 m+1/2 m+1/2 n \ \ --!
604	!-- u = m+1 \| h * u + delta_t' * \ h * (1-r)g grad_x( ssh') - h * f * k vect u + h * frc / \| --!
605	!-- h \ / --!
606	!------------------------------------------------------------------------------------------------------------------------!
607	IF( ln_dynadv_vec .OR. ln_linssh ) THEN !* Vector form
608	DO_2D( 0, 0, 0, 0 )
609	ua_e(ji,jj) = ( un_e(ji,jj) &
610	& + rDt_e * ( zu_spg(ji,jj) &
611	& + zu_trd(ji,jj) &
612	& + zu_frc(ji,jj) ) &
613	& ) * ssumask(ji,jj)
614
615	va_e(ji,jj) = ( vn_e(ji,jj) &
616	& + rDt_e * ( zv_spg(ji,jj) &
617	& + zv_trd(ji,jj) &
618	& + zv_frc(ji,jj) ) &
619	& ) * ssvmask(ji,jj)
620	END_2D
621	!
622	ELSE !* Flux form
623	DO_2D( 0, 0, 0, 0 )
624	! ! hu_e, hv_e hold depth at jn, zhup2_e, zhvp2_e hold extrapolated depth at jn+1/2
625	! ! backward interpolated depth used in spg terms at jn+1/2
626	zhu_bck = hu_0(ji,jj) + r1_2r1_e1e2u(ji,jj) ( e1e2t(ji ,jj) * zsshp2_e(ji ,jj) &
627	& + e1e2t(ji+1,jj) * zsshp2_e(ji+1,jj) ) * ssumask(ji,jj)
628	zhv_bck = hv_0(ji,jj) + r1_2r1_e1e2v(ji,jj) ( e1e2t(ji,jj ) * zsshp2_e(ji,jj ) &
629	& + e1e2t(ji,jj+1) * zsshp2_e(ji,jj+1) ) * ssvmask(ji,jj)
630	! ! inverse depth at jn+1
631	z1_hu = ssumask(ji,jj) / ( hu_0(ji,jj) + zsshu_a(ji,jj) + 1._wp - ssumask(ji,jj) )
632	z1_hv = ssvmask(ji,jj) / ( hv_0(ji,jj) + zsshv_a(ji,jj) + 1._wp - ssvmask(ji,jj) )
633	!
634	ua_e(ji,jj) = ( hu_e (ji,jj) * un_e (ji,jj) &
635	& + rDt_e * ( zhu_bck * zu_spg (ji,jj) & !
636	& + zhup2_e(ji,jj) * zu_trd (ji,jj) & !
637	& + hu(ji,jj,Kmm) * zu_frc (ji,jj) ) ) * z1_hu
638	!
639	va_e(ji,jj) = ( hv_e (ji,jj) * vn_e (ji,jj) &
640	& + rDt_e * ( zhv_bck * zv_spg (ji,jj) & !
641	& + zhvp2_e(ji,jj) * zv_trd (ji,jj) & !
642	& + hv(ji,jj,Kmm) * zv_frc (ji,jj) ) ) * z1_hv
643	END_2D
644	ENDIF
645	!jth implicit bottom friction:
646	IF ( ll_wd ) THEN ! revert to explicit for bit comparison tests in non wad runs
647	DO_2D( 0, 0, 0, 0 )
648	ua_e(ji,jj) = ua_e(ji,jj) /(1.0 - rDt_e * zCdU_u(ji,jj) * hur_e(ji,jj))
649	va_e(ji,jj) = va_e(ji,jj) /(1.0 - rDt_e * zCdU_v(ji,jj) * hvr_e(ji,jj))
650	END_2D
651	ENDIF
652
653	IF( .NOT.ln_linssh ) THEN !* Update ocean depth (variable volume case only)
654	hu_e (2:jpim1,2:jpjm1) = hu_0(2:jpim1,2:jpjm1) + zsshu_a(2:jpim1,2:jpjm1)
655	hur_e(2:jpim1,2:jpjm1) = ssumask(2:jpim1,2:jpjm1) / ( hu_e(2:jpim1,2:jpjm1) + 1._wp - ssumask(2:jpim1,2:jpjm1) )
656	hv_e (2:jpim1,2:jpjm1) = hv_0(2:jpim1,2:jpjm1) + zsshv_a(2:jpim1,2:jpjm1)
657	hvr_e(2:jpim1,2:jpjm1) = ssvmask(2:jpim1,2:jpjm1) / ( hv_e(2:jpim1,2:jpjm1) + 1._wp - ssvmask(2:jpim1,2:jpjm1) )
658	ENDIF
659	!
660	IF( .NOT.ln_linssh ) THEN !* Update ocean depth (variable volume case only)
661	CALL lbc_lnk_multi( 'dynspg_ts', ua_e , 'U', -1._wp, va_e , 'V', -1._wp &
662	& , hu_e , 'U', 1._wp, hv_e , 'V', 1._wp &
663	& , hur_e, 'U', 1._wp, hvr_e, 'V', 1._wp )
664	ELSE
665	CALL lbc_lnk_multi( 'dynspg_ts', ua_e , 'U', -1._wp, va_e , 'V', -1._wp )
666	ENDIF
667	! ! open boundaries
668	IF( ln_bdy ) CALL bdy_dyn2d( jn, ua_e, va_e, un_e, vn_e, hur_e, hvr_e, ssha_e )
669	#if defined key_agrif
670	IF( .NOT.Agrif_Root() ) CALL agrif_dyn_ts( jn ) ! Agrif
671	#endif
672	! !* Swap
673	! ! ----
674	ubb_e (:,:) = ub_e (:,:)
675	ub_e (:,:) = un_e (:,:)
676	un_e (:,:) = ua_e (:,:)
677	!
678	vbb_e (:,:) = vb_e (:,:)
679	vb_e (:,:) = vn_e (:,:)
680	vn_e (:,:) = va_e (:,:)
681	!
682	sshbb_e(:,:) = sshb_e(:,:)
683	sshb_e (:,:) = sshn_e(:,:)
684	sshn_e (:,:) = ssha_e(:,:)
685
686	! !* Sum over whole bt loop
687	! ! ----------------------
688	za1 = wgtbtp1(jn)
689	IF( ln_dynadv_vec .OR. ln_linssh ) THEN ! Sum velocities
690	puu_b (:,:,Kaa) = puu_b (:,:,Kaa) + za1 * ua_e (:,:)
691	pvv_b (:,:,Kaa) = pvv_b (:,:,Kaa) + za1 * va_e (:,:)
692	ELSE ! Sum transports
693	IF ( .NOT.ln_wd_dl ) THEN
694	puu_b (:,:,Kaa) = puu_b (:,:,Kaa) + za1 * ua_e (:,:) * hu_e (:,:)
695	pvv_b (:,:,Kaa) = pvv_b (:,:,Kaa) + za1 * va_e (:,:) * hv_e (:,:)
696	ELSE
697	puu_b (:,:,Kaa) = puu_b (:,:,Kaa) + za1 * ua_e (:,:) * hu_e (:,:) * zuwdmask(:,:)
698	pvv_b (:,:,Kaa) = pvv_b (:,:,Kaa) + za1 * va_e (:,:) * hv_e (:,:) * zvwdmask(:,:)
699	END IF
700	ENDIF
701	! ! Sum sea level
702	pssh(:,:,Kaa) = pssh(:,:,Kaa) + za1 * ssha_e(:,:)
703
704	! ! ==================== !
705	END DO ! end loop !
706	! ! ==================== !
707	! -----------------------------------------------------------------------------
708	! Phase 3. update the general trend with the barotropic trend
709	! -----------------------------------------------------------------------------
710	!
711	! Set advection velocity correction:
712	IF (ln_bt_fw) THEN
713	IF( .NOT.( kt == nit000 .AND. l_1st_euler ) ) THEN
714	DO_2D( 1, 1, 1, 1 )
715	zun_save = un_adv(ji,jj)
716	zvn_save = vn_adv(ji,jj)
717	! ! apply the previously computed correction
718	un_adv(ji,jj) = r1_2 * ( ub2_b(ji,jj) + zun_save - rn_atfp * un_bf(ji,jj) )
719	vn_adv(ji,jj) = r1_2 * ( vb2_b(ji,jj) + zvn_save - rn_atfp * vn_bf(ji,jj) )
720	! ! Update corrective fluxes for next time step
721	un_bf(ji,jj) = rn_atfp * un_bf(ji,jj) + ( zun_save - ub2_b(ji,jj) )
722	vn_bf(ji,jj) = rn_atfp * vn_bf(ji,jj) + ( zvn_save - vb2_b(ji,jj) )
723	! ! Save integrated transport for next computation
724	ub2_b(ji,jj) = zun_save
725	vb2_b(ji,jj) = zvn_save
726	END_2D
727	ELSE
728	un_bf(:,:) = 0._wp ! corrective fluxes for next time step set to zero
729	vn_bf(:,:) = 0._wp
730	ub2_b(:,:) = un_adv(:,:) ! Save integrated transport for next computation
731	vb2_b(:,:) = vn_adv(:,:)
732	END IF
733	ENDIF
734
735
736	!
737	! Update barotropic trend:
738	IF( ln_dynadv_vec .OR. ln_linssh ) THEN
739	DO jk=1,jpkm1
740	puu(:,:,jk,Krhs) = puu(:,:,jk,Krhs) + ( puu_b(:,:,Kaa) - puu_b(:,:,Kbb) ) * r1_Dt_b
741	pvv(:,:,jk,Krhs) = pvv(:,:,jk,Krhs) + ( pvv_b(:,:,Kaa) - pvv_b(:,:,Kbb) ) * r1_Dt_b
742	END DO
743	ELSE
744	! At this stage, pssh(:,:,:,Krhs) has been corrected: compute new depths at velocity points
745	DO_2D( 1, 0, 1, 0 )
746	zsshu_a(ji,jj) = r1_2 * ssumask(ji,jj) * r1_e1e2u(ji,jj) &
747	& * ( e1e2t(ji ,jj) * pssh(ji ,jj,Kaa) &
748	& + e1e2t(ji+1,jj) * pssh(ji+1,jj,Kaa) )
749	zsshv_a(ji,jj) = r1_2 * ssvmask(ji,jj) * r1_e1e2v(ji,jj) &
750	& * ( e1e2t(ji,jj ) * pssh(ji,jj ,Kaa) &
751	& + e1e2t(ji,jj+1) * pssh(ji,jj+1,Kaa) )
752	END_2D
753	CALL lbc_lnk_multi( 'dynspg_ts', zsshu_a, 'U', 1._wp, zsshv_a, 'V', 1._wp ) ! Boundary conditions
754	!
755	DO jk=1,jpkm1
756	puu(:,:,jk,Krhs) = puu(:,:,jk,Krhs) + r1_hu(:,:,Kmm) * ( puu_b(:,:,Kaa) - puu_b(:,:,Kbb) * hu(:,:,Kbb) ) * r1_Dt_b
757	pvv(:,:,jk,Krhs) = pvv(:,:,jk,Krhs) + r1_hv(:,:,Kmm) * ( pvv_b(:,:,Kaa) - pvv_b(:,:,Kbb) * hv(:,:,Kbb) ) * r1_Dt_b
758	END DO
759	! Save barotropic velocities not transport:
760	puu_b(:,:,Kaa) = puu_b(:,:,Kaa) / ( hu_0(:,:) + zsshu_a(:,:) + 1._wp - ssumask(:,:) )
761	pvv_b(:,:,Kaa) = pvv_b(:,:,Kaa) / ( hv_0(:,:) + zsshv_a(:,:) + 1._wp - ssvmask(:,:) )
762	ENDIF
763
764
765	! Correct velocities so that the barotropic velocity equals (un_adv, vn_adv) (in all cases)
766	DO jk = 1, jpkm1
767	puu(:,:,jk,Kmm) = ( puu(:,:,jk,Kmm) + un_adv(:,:)r1_hu(:,:,Kmm) - puu_b(:,:,Kmm) ) umask(:,:,jk)
768	pvv(:,:,jk,Kmm) = ( pvv(:,:,jk,Kmm) + vn_adv(:,:)r1_hv(:,:,Kmm) - pvv_b(:,:,Kmm) ) vmask(:,:,jk)
769	END DO
770
771	IF ( ln_wd_dl .and. ln_wd_dl_bc) THEN
772	DO jk = 1, jpkm1
773	puu(:,:,jk,Kmm) = ( un_adv(:,:)*r1_hu(:,:,Kmm) &
774	& + zuwdav2(:,:)(puu(:,:,jk,Kmm) - un_adv(:,:)r1_hu(:,:,Kmm)) ) * umask(:,:,jk)
775	pvv(:,:,jk,Kmm) = ( vn_adv(:,:)*r1_hv(:,:,Kmm) &
776	& + zvwdav2(:,:)(pvv(:,:,jk,Kmm) - vn_adv(:,:)r1_hv(:,:,Kmm)) ) * vmask(:,:,jk)
777	END DO
778	END IF
779
780
781	CALL iom_put( "ubar", un_adv(:,:)*r1_hu(:,:,Kmm) ) ! barotropic i-current
782	CALL iom_put( "vbar", vn_adv(:,:)*r1_hv(:,:,Kmm) ) ! barotropic i-current
783	!
784	#if defined key_agrif
785	! Save time integrated fluxes during child grid integration
786	! (used to update coarse grid transports at next time step)
787	!
788	IF( .NOT.Agrif_Root() .AND. ln_bt_fw ) THEN
789	IF( Agrif_NbStepint() == 0 ) THEN
790	ub2_i_b(:,:) = 0._wp
791	vb2_i_b(:,:) = 0._wp
792	END IF
793	!
794	za1 = 1._wp / REAL(Agrif_rhot(), wp)
795	ub2_i_b(:,:) = ub2_i_b(:,:) + za1 * ub2_b(:,:)
796	vb2_i_b(:,:) = vb2_i_b(:,:) + za1 * vb2_b(:,:)
797	ENDIF
798	#endif
799	! !* write time-spliting arrays in the restart
800	IF( lrst_oce .AND.ln_bt_fw ) CALL ts_rst( kt, 'WRITE' )
801	!
802	IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy )
803	IF( ln_wd_dl ) DEALLOCATE( ztwdmask, zuwdmask, zvwdmask, zuwdav2, zvwdav2 )
804	!
805	CALL iom_put( "baro_u" , puu_b(:,:,Kmm) ) ! Barotropic U Velocity
806	CALL iom_put( "baro_v" , pvv_b(:,:,Kmm) ) ! Barotropic V Velocity
807	!
808	END SUBROUTINE dyn_spg_ts
809
810
811	SUBROUTINE ts_wgt( ll_av, ll_fw, jpit, zwgt1, zwgt2)
812	!!---------------------------------------------------------------------
813	!! * ROUTINE ts_wgt *
814	!!
815	!! ** Purpose : Set time-splitting weights for temporal averaging (or not)
816	!!----------------------------------------------------------------------
817	LOGICAL, INTENT(in) :: ll_av ! temporal averaging=.true.
818	LOGICAL, INTENT(in) :: ll_fw ! forward time splitting =.true.
819	INTEGER, INTENT(inout) :: jpit ! cycle length
820	REAL(wp), DIMENSION(3*nn_e), INTENT(inout) :: zwgt1, & ! Primary weights
821	zwgt2 ! Secondary weights
822
823	INTEGER :: jic, jn, ji ! temporary integers
824	REAL(wp) :: za1, za2
825	!!----------------------------------------------------------------------
826
827	zwgt1(:) = 0._wp
828	zwgt2(:) = 0._wp
829
830	! Set time index when averaged value is requested
831	IF (ll_fw) THEN
832	jic = nn_e
833	ELSE
834	jic = 2 * nn_e
835	ENDIF
836
837	! Set primary weights:
838	IF (ll_av) THEN
839	! Define simple boxcar window for primary weights
840	! (width = nn_e, centered around jic)
841	SELECT CASE ( nn_bt_flt )
842	CASE( 0 ) ! No averaging
843	zwgt1(jic) = 1._wp
844	jpit = jic
845
846	CASE( 1 ) ! Boxcar, width = nn_e
847	DO jn = 1, 3*nn_e
848	za1 = ABS(float(jn-jic))/float(nn_e)
849	IF (za1 < 0.5_wp) THEN
850	zwgt1(jn) = 1._wp
851	jpit = jn
852	ENDIF
853	ENDDO
854
855	CASE( 2 ) ! Boxcar, width = 2 * nn_e
856	DO jn = 1, 3*nn_e
857	za1 = ABS(float(jn-jic))/float(nn_e)
858	IF (za1 < 1._wp) THEN
859	zwgt1(jn) = 1._wp
860	jpit = jn
861	ENDIF
862	ENDDO
863	CASE DEFAULT ; CALL ctl_stop( 'unrecognised value for nn_bt_flt' )
864	END SELECT
865
866	ELSE ! No time averaging
867	zwgt1(jic) = 1._wp
868	jpit = jic
869	ENDIF
870
871	! Set secondary weights
872	DO jn = 1, jpit
873	DO ji = jn, jpit
874	zwgt2(jn) = zwgt2(jn) + zwgt1(ji)
875	END DO
876	END DO
877
878	! Normalize weigths:
879	za1 = 1._wp / SUM(zwgt1(1:jpit))
880	za2 = 1._wp / SUM(zwgt2(1:jpit))
881	DO jn = 1, jpit
882	zwgt1(jn) = zwgt1(jn) * za1
883	zwgt2(jn) = zwgt2(jn) * za2
884	END DO
885	!
886	END SUBROUTINE ts_wgt
887
888
889	SUBROUTINE ts_rst( kt, cdrw )
890	!!---------------------------------------------------------------------
891	!! * ROUTINE ts_rst *
892	!!
893	!! ** Purpose : Read or write time-splitting arrays in restart file
894	!!----------------------------------------------------------------------
895	INTEGER , INTENT(in) :: kt ! ocean time-step
896	CHARACTER(len=*), INTENT(in) :: cdrw ! "READ"/"WRITE" flag
897	!!----------------------------------------------------------------------
898	!
899	IF( TRIM(cdrw) == 'READ' ) THEN ! Read/initialise
900	! ! ---------------
901	IF( lroxios ) CALL iom_swap( TRIM(crxios_context) )
902	IF( ln_rstart .AND. ln_bt_fw .AND. (.NOT.l_1st_euler) ) THEN !* Read the restart file
903	CALL iom_get( numror, jpdom_auto, 'ub2_b' , ub2_b (:,:), cd_type = 'U', psgn = -1._wp, ldxios = lroxios )
904	CALL iom_get( numror, jpdom_auto, 'vb2_b' , vb2_b (:,:), cd_type = 'V', psgn = -1._wp, ldxios = lroxios )
905	CALL iom_get( numror, jpdom_auto, 'un_bf' , un_bf (:,:), cd_type = 'U', psgn = -1._wp, ldxios = lroxios )
906	CALL iom_get( numror, jpdom_auto, 'vn_bf' , vn_bf (:,:), cd_type = 'V', psgn = -1._wp, ldxios = lroxios )
907	IF( .NOT.ln_bt_av ) THEN
908	CALL iom_get( numror, jpdom_auto, 'sshbb_e' , sshbb_e(:,:), cd_type = 'T', psgn = 1._wp, ldxios = lroxios )
909	CALL iom_get( numror, jpdom_auto, 'ubb_e' , ubb_e(:,:), cd_type = 'U', psgn = -1._wp, ldxios = lroxios )
910	CALL iom_get( numror, jpdom_auto, 'vbb_e' , vbb_e(:,:), cd_type = 'V', psgn = -1._wp, ldxios = lroxios )
911	CALL iom_get( numror, jpdom_auto, 'sshb_e' , sshb_e(:,:), cd_type = 'T', psgn = 1._wp, ldxios = lroxios )
912	CALL iom_get( numror, jpdom_auto, 'ub_e' , ub_e(:,:), cd_type = 'U', psgn = -1._wp, ldxios = lroxios )
913	CALL iom_get( numror, jpdom_auto, 'vb_e' , vb_e(:,:), cd_type = 'V', psgn = -1._wp, ldxios = lroxios )
914	ENDIF
915	#if defined key_agrif
916	! Read time integrated fluxes
917	IF ( .NOT.Agrif_Root() ) THEN
918	CALL iom_get( numror, jpdom_auto, 'ub2_i_b' , ub2_i_b(:,:), cd_type = 'U', psgn = -1._wp, ldxios = lroxios )
919	CALL iom_get( numror, jpdom_auto, 'vb2_i_b' , vb2_i_b(:,:), cd_type = 'V', psgn = -1._wp, ldxios = lroxios )
920	ELSE
921	ub2_i_b(:,:) = 0._wp ; vb2_i_b(:,:) = 0._wp ! used in the 1st update of agrif
922	ENDIF
923	#endif
924	ELSE !* Start from rest
925	IF(lwp) WRITE(numout,*)
926	IF(lwp) WRITE(numout,*) ' ==>>> start from rest: set barotropic values to 0'
927	ub2_b (:,:) = 0._wp ; vb2_b (:,:) = 0._wp ! used in the 1st interpol of agrif
928	un_adv (:,:) = 0._wp ; vn_adv (:,:) = 0._wp ! used in the 1st interpol of agrif
929	un_bf (:,:) = 0._wp ; vn_bf (:,:) = 0._wp ! used in the 1st update of agrif
930	#if defined key_agrif
931	ub2_i_b(:,:) = 0._wp ; vb2_i_b(:,:) = 0._wp ! used in the 1st update of agrif
932	#endif
933	ENDIF
934	IF( lroxios ) CALL iom_swap( TRIM(cxios_context) )
935	!
936	ELSEIF( TRIM(cdrw) == 'WRITE' ) THEN ! Create restart file
937	! ! -------------------
938	IF(lwp) WRITE(numout,*) '---- ts_rst ----'
939	IF( lwxios ) CALL iom_swap( cwxios_context )
940	CALL iom_rstput( kt, nitrst, numrow, 'ub2_b' , ub2_b (:,:), ldxios = lwxios )
941	CALL iom_rstput( kt, nitrst, numrow, 'vb2_b' , vb2_b (:,:), ldxios = lwxios )
942	CALL iom_rstput( kt, nitrst, numrow, 'un_bf' , un_bf (:,:), ldxios = lwxios )
943	CALL iom_rstput( kt, nitrst, numrow, 'vn_bf' , vn_bf (:,:), ldxios = lwxios )
944	!
945	IF (.NOT.ln_bt_av) THEN
946	CALL iom_rstput( kt, nitrst, numrow, 'sshbb_e' , sshbb_e(:,:), ldxios = lwxios )
947	CALL iom_rstput( kt, nitrst, numrow, 'ubb_e' , ubb_e(:,:), ldxios = lwxios )
948	CALL iom_rstput( kt, nitrst, numrow, 'vbb_e' , vbb_e(:,:), ldxios = lwxios )
949	CALL iom_rstput( kt, nitrst, numrow, 'sshb_e' , sshb_e(:,:), ldxios = lwxios )
950	CALL iom_rstput( kt, nitrst, numrow, 'ub_e' , ub_e(:,:), ldxios = lwxios )
951	CALL iom_rstput( kt, nitrst, numrow, 'vb_e' , vb_e(:,:), ldxios = lwxios )
952	ENDIF
953	#if defined key_agrif
954	! Save time integrated fluxes
955	IF ( .NOT.Agrif_Root() ) THEN
956	CALL iom_rstput( kt, nitrst, numrow, 'ub2_i_b' , ub2_i_b(:,:), ldxios = lwxios )
957	CALL iom_rstput( kt, nitrst, numrow, 'vb2_i_b' , vb2_i_b(:,:), ldxios = lwxios )
958	ENDIF
959	#endif
960	IF( lwxios ) CALL iom_swap( cxios_context )
961	ENDIF
962	!
963	END SUBROUTINE ts_rst
964
965
966	SUBROUTINE dyn_spg_ts_init
967	!!---------------------------------------------------------------------
968	!! * ROUTINE dyn_spg_ts_init *
969	!!
970	!! ** Purpose : Set time splitting options
971	!!----------------------------------------------------------------------
972	INTEGER :: ji ,jj ! dummy loop indices
973	REAL(wp) :: zxr2, zyr2, zcmax ! local scalar
974	REAL(wp), DIMENSION(jpi,jpj) :: zcu
975	!!----------------------------------------------------------------------
976	!
977	! Max courant number for ext. grav. waves
978	!
979	DO_2D( 0, 0, 0, 0 )
980	zxr2 = r1_e1t(ji,jj) * r1_e1t(ji,jj)
981	zyr2 = r1_e2t(ji,jj) * r1_e2t(ji,jj)
982	zcu(ji,jj) = SQRT( grav * MAX(ht_0(ji,jj),0._wp) * (zxr2 + zyr2) )
983	END_2D
984	!
985	zcmax = MAXVAL( zcu(Nis0:Nie0,Njs0:Nje0) )
986	CALL mpp_max( 'dynspg_ts', zcmax )
987
988	! Estimate number of iterations to satisfy a max courant number= rn_bt_cmax
989	IF( ln_bt_auto ) nn_e = CEILING( rn_Dt / rn_bt_cmax * zcmax)
990
991	rDt_e = rn_Dt / REAL( nn_e , wp )
992	zcmax = zcmax * rDt_e
993	! Print results
994	IF(lwp) WRITE(numout,*)
995	IF(lwp) WRITE(numout,*) 'dyn_spg_ts_init : split-explicit free surface'
996	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~~'
997	IF( ln_bt_auto ) THEN
998	IF(lwp) WRITE(numout,*) ' ln_ts_auto =.true. Automatically set nn_e '
999	IF(lwp) WRITE(numout,*) ' Max. courant number allowed: ', rn_bt_cmax
1000	ELSE
1001	IF(lwp) WRITE(numout,*) ' ln_ts_auto=.false.: Use nn_e in namelist nn_e = ', nn_e
1002	ENDIF
1003
1004	IF(ln_bt_av) THEN
1005	IF(lwp) WRITE(numout,*) ' ln_bt_av =.true. ==> Time averaging over nn_e time steps is on '
1006	ELSE
1007	IF(lwp) WRITE(numout,*) ' ln_bt_av =.false. => No time averaging of barotropic variables '
1008	ENDIF
1009	!
1010	!
1011	IF(ln_bt_fw) THEN
1012	IF(lwp) WRITE(numout,*) ' ln_bt_fw=.true. => Forward integration of barotropic variables '
1013	ELSE
1014	IF(lwp) WRITE(numout,*) ' ln_bt_fw =.false.=> Centred integration of barotropic variables '
1015	ENDIF
1016	!
1017	#if defined key_agrif
1018	! Restrict the use of Agrif to the forward case only
1019	!!! IF( .NOT.ln_bt_fw .AND. .NOT.Agrif_Root() ) CALL ctl_stop( 'AGRIF not implemented if ln_bt_fw=.FALSE.' )
1020	#endif
1021	!
1022	IF(lwp) WRITE(numout,*) ' Time filter choice, nn_bt_flt: ', nn_bt_flt
1023	SELECT CASE ( nn_bt_flt )
1024	CASE( 0 ) ; IF(lwp) WRITE(numout,*) ' Dirac'
1025	CASE( 1 ) ; IF(lwp) WRITE(numout,*) ' Boxcar: width = nn_e'
1026	CASE( 2 ) ; IF(lwp) WRITE(numout,) ' Boxcar: width = 2nn_e'
1027	CASE DEFAULT ; CALL ctl_stop( 'unrecognised value for nn_bt_flt: should 0,1, or 2' )
1028	END SELECT
1029	!
1030	IF(lwp) WRITE(numout,*) ' '
1031	IF(lwp) WRITE(numout,*) ' nn_e = ', nn_e
1032	IF(lwp) WRITE(numout,*) ' Barotropic time step [s] is :', rDt_e
1033	IF(lwp) WRITE(numout,*) ' Maximum Courant number is :', zcmax
1034	!
1035	IF(lwp) WRITE(numout,*) ' Time diffusion parameter rn_bt_alpha: ', rn_bt_alpha
1036	IF ((ln_bt_av.AND.nn_bt_flt/=0).AND.(rn_bt_alpha>0._wp)) THEN
1037	CALL ctl_stop( 'dynspg_ts ERROR: if rn_bt_alpha > 0, remove temporal averaging' )
1038	ENDIF
1039	!
1040	IF( .NOT.ln_bt_av .AND. .NOT.ln_bt_fw ) THEN
1041	CALL ctl_stop( 'dynspg_ts ERROR: No time averaging => only forward integration is possible' )
1042	ENDIF
1043	IF( zcmax>0.9_wp ) THEN
1044	CALL ctl_stop( 'dynspg_ts ERROR: Maximum Courant number is greater than 0.9: Inc. nn_e !' )
1045	ENDIF
1046	!
1047	! ! Allocate time-splitting arrays
1048	IF( dyn_spg_ts_alloc() /= 0 ) CALL ctl_stop('STOP', 'dyn_spg_init: failed to allocate dynspg_ts arrays' )
1049	!
1050	! ! read restart when needed
1051	CALL ts_rst( nit000, 'READ' )
1052	!
1053	END SUBROUTINE dyn_spg_ts_init
1054
1055
1056	SUBROUTINE dyn_cor_2D_init( Kmm )
1057	!!---------------------------------------------------------------------
1058	!! * ROUTINE dyn_cor_2D_init *
1059	!!
1060	!! ** Purpose : Set time splitting options
1061	!! Set arrays to remove/compute coriolis trend.
1062	!! Do it once during initialization if volume is fixed, else at each long time step.
1063	!! Note that these arrays are also used during barotropic loop. These are however frozen
1064	!! although they should be updated in the variable volume case. Not a big approximation.
1065	!! To remove this approximation, copy lines below inside barotropic loop
1066	!! and update depths at T-F points (ht and zhf resp.) at each barotropic time step
1067	!!
1068	!! Compute zwz = f / ( height of the water colomn )
1069	!!----------------------------------------------------------------------
1070	INTEGER, INTENT(in) :: Kmm ! Time index
1071	INTEGER :: ji ,jj, jk ! dummy loop indices
1072	REAL(wp) :: z1_ht
1073	REAL(wp), DIMENSION(jpi,jpj) :: zhf
1074	!!----------------------------------------------------------------------
1075	!
1076	SELECT CASE( nvor_scheme )
1077	CASE( np_EEN ) != EEN scheme using e3f energy & enstrophy scheme
1078	SELECT CASE( nn_een_e3f ) !* ff_f/e3 at F-point
1079	CASE ( 0 ) ! original formulation (masked averaging of e3t divided by 4)
1080	DO_2D( 1, 0, 1, 0 )
1081	zwz(ji,jj) = ( ht(ji ,jj+1) + ht(ji+1,jj+1) + &
1082	& ht(ji ,jj ) + ht(ji+1,jj ) ) * 0.25_wp
1083	IF( zwz(ji,jj) /= 0._wp ) zwz(ji,jj) = ff_f(ji,jj) / zwz(ji,jj)
1084	END_2D
1085	CASE ( 1 ) ! new formulation (masked averaging of e3t divided by the sum of mask)
1086	DO_2D( 1, 0, 1, 0 )
1087	zwz(ji,jj) = ( ht (ji ,jj+1) + ht (ji+1,jj+1) &
1088	& + ht (ji ,jj ) + ht (ji+1,jj ) ) &
1089	& / ( MAX( 1._wp, ssmask(ji ,jj+1) + ssmask(ji+1,jj+1) &
1090	& + ssmask(ji ,jj ) + ssmask(ji+1,jj ) ) )
1091	IF( zwz(ji,jj) /= 0._wp ) zwz(ji,jj) = ff_f(ji,jj) / zwz(ji,jj)
1092	END_2D
1093	END SELECT
1094	CALL lbc_lnk( 'dynspg_ts', zwz, 'F', 1._wp )
1095	!
1096	ftne(1,:) = 0._wp ; ftnw(1,:) = 0._wp ; ftse(1,:) = 0._wp ; ftsw(1,:) = 0._wp
1097	DO_2D( 0, 1, 0, 1 )
1098	ftne(ji,jj) = zwz(ji-1,jj ) + zwz(ji ,jj ) + zwz(ji ,jj-1)
1099	ftnw(ji,jj) = zwz(ji-1,jj-1) + zwz(ji-1,jj ) + zwz(ji ,jj )
1100	ftse(ji,jj) = zwz(ji ,jj ) + zwz(ji ,jj-1) + zwz(ji-1,jj-1)
1101	ftsw(ji,jj) = zwz(ji ,jj-1) + zwz(ji-1,jj-1) + zwz(ji-1,jj )
1102	END_2D
1103	!
1104	CASE( np_EET ) != EEN scheme using e3t energy conserving scheme
1105	ftne(1,:) = 0._wp ; ftnw(1,:) = 0._wp ; ftse(1,:) = 0._wp ; ftsw(1,:) = 0._wp
1106	DO_2D( 0, 1, 0, 1 )
1107	z1_ht = ssmask(ji,jj) / ( ht(ji,jj) + 1._wp - ssmask(ji,jj) )
1108	ftne(ji,jj) = ( ff_f(ji-1,jj ) + ff_f(ji ,jj ) + ff_f(ji ,jj-1) ) * z1_ht
1109	ftnw(ji,jj) = ( ff_f(ji-1,jj-1) + ff_f(ji-1,jj ) + ff_f(ji ,jj ) ) * z1_ht
1110	ftse(ji,jj) = ( ff_f(ji ,jj ) + ff_f(ji ,jj-1) + ff_f(ji-1,jj-1) ) * z1_ht
1111	ftsw(ji,jj) = ( ff_f(ji ,jj-1) + ff_f(ji-1,jj-1) + ff_f(ji-1,jj ) ) * z1_ht
1112	END_2D
1113	!
1114	CASE( np_ENE, np_ENS , np_MIX ) != all other schemes (ENE, ENS, MIX) except ENT !
1115	!
1116	zwz(:,:) = 0._wp
1117	zhf(:,:) = 0._wp
1118
1119	!!gm assume 0 in both cases (which is almost surely WRONG ! ) as hvatf has been removed
1120	!!gm A priori a better value should be something like :
1121	!!gm zhf(i,j) = masked sum of ht(i,j) , ht(i+1,j) , ht(i,j+1) , (i+1,j+1)
1122	!!gm divided by the sum of the corresponding mask
1123	!!gm
1124	!!
1125	IF( .NOT.ln_sco ) THEN
1126
1127	!!gm agree the JC comment : this should be done in a much clear way
1128
1129	! JC: It not clear yet what should be the depth at f-points over land in z-coordinate case
1130	! Set it to zero for the time being
1131	! IF( rn_hmin < 0._wp ) THEN ; jk = - INT( rn_hmin ) ! from a nb of level
1132	! ELSE ; jk = MINLOC( gdepw_0, mask = gdepw_0 > rn_hmin, dim = 1 ) ! from a depth
1133	! ENDIF
1134	! zhf(:,:) = gdepw_0(:,:,jk+1)
1135	!
1136	ELSE
1137	!
1138	!zhf(:,:) = hbatf(:,:)
1139	DO_2D( 1, 0, 1, 0 )
1140	zhf(ji,jj) = ( ht_0 (ji,jj ) + ht_0 (ji+1,jj ) &
1141	& + ht_0 (ji,jj+1) + ht_0 (ji+1,jj+1) ) &
1142	& / MAX( ssmask(ji,jj ) + ssmask(ji+1,jj ) &
1143	& + ssmask(ji,jj+1) + ssmask(ji+1,jj+1) , 1._wp )
1144	END_2D
1145	ENDIF
1146	!
1147	DO jj = 1, jpjm1
1148	zhf(:,jj) = zhf(:,jj) * (1._wp- umask(:,jj,1) * umask(:,jj+1,1))
1149	END DO
1150	!
1151	DO jk = 1, jpkm1
1152	DO jj = 1, jpjm1
1153	zhf(:,jj) = zhf(:,jj) + e3f(:,jj,jk) * umask(:,jj,jk) * umask(:,jj+1,jk)
1154	END DO
1155	END DO
1156	CALL lbc_lnk( 'dynspg_ts', zhf, 'F', 1._wp )
1157	! JC: TBC. hf should be greater than 0
1158	DO_2D( 1, 1, 1, 1 )
1159	IF( zhf(ji,jj) /= 0._wp ) zwz(ji,jj) = 1._wp / zhf(ji,jj)
1160	END_2D
1161	zwz(:,:) = ff_f(:,:) * zwz(:,:)
1162	END SELECT
1163
1164	END SUBROUTINE dyn_cor_2d_init
1165
1166
1167
1168	SUBROUTINE dyn_cor_2d( pht, phu, phv, punb, pvnb, zhU, zhV, zu_trd, zv_trd )
1169	!!---------------------------------------------------------------------
1170	!! * ROUTINE dyn_cor_2d *
1171	!!
1172	!! ** Purpose : Compute u and v coriolis trends
1173	!!----------------------------------------------------------------------
1174	INTEGER :: ji ,jj ! dummy loop indices
1175	REAL(wp) :: zx1, zx2, zy1, zy2, z1_hu, z1_hv ! - -
1176	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pht, phu, phv, punb, pvnb, zhU, zhV
1177	REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: zu_trd, zv_trd
1178	!!----------------------------------------------------------------------
1179	SELECT CASE( nvor_scheme )
1180	CASE( np_ENT ) ! enstrophy conserving scheme (f-point)
1181	DO_2D( 0, 0, 0, 0 )
1182	z1_hu = ssumask(ji,jj) / ( phu(ji,jj) + 1._wp - ssumask(ji,jj) )
1183	z1_hv = ssvmask(ji,jj) / ( phv(ji,jj) + 1._wp - ssvmask(ji,jj) )
1184	zu_trd(ji,jj) = + r1_4 * r1_e1e2u(ji,jj) * z1_hu &
1185	& * ( e1e2t(ji+1,jj)pht(ji+1,jj)ff_t(ji+1,jj) * ( pvnb(ji+1,jj) + pvnb(ji+1,jj-1) ) &
1186	& + e1e2t(ji ,jj)pht(ji ,jj)ff_t(ji ,jj) * ( pvnb(ji ,jj) + pvnb(ji ,jj-1) ) )
1187	!
1188	zv_trd(ji,jj) = - r1_4 * r1_e1e2v(ji,jj) * z1_hv &
1189	& * ( e1e2t(ji,jj+1)pht(ji,jj+1)ff_t(ji,jj+1) * ( punb(ji,jj+1) + punb(ji-1,jj+1) ) &
1190	& + e1e2t(ji,jj )pht(ji,jj )ff_t(ji,jj ) * ( punb(ji,jj ) + punb(ji-1,jj ) ) )
1191	END_2D
1192	!
1193	CASE( np_ENE , np_MIX ) ! energy conserving scheme (t-point) ENE or MIX
1194	DO_2D( 0, 0, 0, 0 )
1195	zy1 = ( zhV(ji,jj-1) + zhV(ji+1,jj-1) ) * r1_e1u(ji,jj)
1196	zy2 = ( zhV(ji,jj ) + zhV(ji+1,jj ) ) * r1_e1u(ji,jj)
1197	zx1 = ( zhU(ji-1,jj) + zhU(ji-1,jj+1) ) * r1_e2v(ji,jj)
1198	zx2 = ( zhU(ji ,jj) + zhU(ji ,jj+1) ) * r1_e2v(ji,jj)
1199	! energy conserving formulation for planetary vorticity term
1200	zu_trd(ji,jj) = r1_4 * ( zwz(ji ,jj-1) * zy1 + zwz(ji,jj) * zy2 )
1201	zv_trd(ji,jj) = - r1_4 * ( zwz(ji-1,jj ) * zx1 + zwz(ji,jj) * zx2 )
1202	END_2D
1203	!
1204	CASE( np_ENS ) ! enstrophy conserving scheme (f-point)
1205	DO_2D( 0, 0, 0, 0 )
1206	zy1 = r1_8 * ( zhV(ji ,jj-1) + zhV(ji+1,jj-1) &
1207	& + zhV(ji ,jj ) + zhV(ji+1,jj ) ) * r1_e1u(ji,jj)
1208	zx1 = - r1_8 * ( zhU(ji-1,jj ) + zhU(ji-1,jj+1) &
1209	& + zhU(ji ,jj ) + zhU(ji ,jj+1) ) * r1_e2v(ji,jj)
1210	zu_trd(ji,jj) = zy1 * ( zwz(ji ,jj-1) + zwz(ji,jj) )
1211	zv_trd(ji,jj) = zx1 * ( zwz(ji-1,jj ) + zwz(ji,jj) )
1212	END_2D
1213	!
1214	CASE( np_EET , np_EEN ) ! energy & enstrophy scheme (using e3t or e3f)
1215	DO_2D( 0, 0, 0, 0 )
1216	zu_trd(ji,jj) = + r1_12 * r1_e1u(ji,jj) * ( ftne(ji,jj ) * zhV(ji ,jj ) &
1217	& + ftnw(ji+1,jj) * zhV(ji+1,jj ) &
1218	& + ftse(ji,jj ) * zhV(ji ,jj-1) &
1219	& + ftsw(ji+1,jj) * zhV(ji+1,jj-1) )
1220	zv_trd(ji,jj) = - r1_12 * r1_e2v(ji,jj) * ( ftsw(ji,jj+1) * zhU(ji-1,jj+1) &
1221	& + ftse(ji,jj+1) * zhU(ji ,jj+1) &
1222	& + ftnw(ji,jj ) * zhU(ji-1,jj ) &
1223	& + ftne(ji,jj ) * zhU(ji ,jj ) )
1224	END_2D
1225	!
1226	END SELECT
1227	!
1228	END SUBROUTINE dyn_cor_2D
1229
1230
1231	SUBROUTINE wad_tmsk( pssh, ptmsk )
1232	!!----------------------------------------------------------------------
1233	!! * ROUTINE wad_lmt *
1234	!!
1235	!! ** Purpose : set wetting & drying mask at tracer points
1236	!! for the current barotropic sub-step
1237	!!
1238	!! ** Method : ???
1239	!!
1240	!! ** Action : ptmsk : wetting & drying t-mask
1241	!!----------------------------------------------------------------------
1242	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pssh !
1243	REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: ptmsk !
1244	!
1245	INTEGER :: ji, jj ! dummy loop indices
1246	!!----------------------------------------------------------------------
1247	!
1248	IF( ln_wd_dl_rmp ) THEN
1249	DO_2D( 1, 1, 1, 1 )
1250	IF ( pssh(ji,jj) + ht_0(ji,jj) > 2._wp * rn_wdmin1 ) THEN
1251	! IF ( pssh(ji,jj) + ht_0(ji,jj) > rn_wdmin2 ) THEN
1252	ptmsk(ji,jj) = 1._wp
1253	ELSEIF( pssh(ji,jj) + ht_0(ji,jj) > rn_wdmin1 ) THEN
1254	ptmsk(ji,jj) = TANH( 50._wp( ( pssh(ji,jj) + ht_0(ji,jj) - rn_wdmin1 )r_rn_wdmin1) )
1255	ELSE
1256	ptmsk(ji,jj) = 0._wp
1257	ENDIF
1258	END_2D
1259	ELSE
1260	DO_2D( 1, 1, 1, 1 )
1261	IF ( pssh(ji,jj) + ht_0(ji,jj) > rn_wdmin1 ) THEN ; ptmsk(ji,jj) = 1._wp
1262	ELSE ; ptmsk(ji,jj) = 0._wp
1263	ENDIF
1264	END_2D
1265	ENDIF
1266	!
1267	END SUBROUTINE wad_tmsk
1268
1269
1270	SUBROUTINE wad_Umsk( pTmsk, phU, phV, pu, pv, pUmsk, pVmsk )
1271	!!----------------------------------------------------------------------
1272	!! * ROUTINE wad_lmt *
1273	!!
1274	!! ** Purpose : set wetting & drying mask at tracer points
1275	!! for the current barotropic sub-step
1276	!!
1277	!! ** Method : ???
1278	!!
1279	!! ** Action : ptmsk : wetting & drying t-mask
1280	!!----------------------------------------------------------------------
1281	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pTmsk ! W & D t-mask
1282	REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: phU, phV, pu, pv ! ocean velocities and transports
1283	REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: pUmsk, pVmsk ! W & D u- and v-mask
1284	!
1285	INTEGER :: ji, jj ! dummy loop indices
1286	!!----------------------------------------------------------------------
1287	!
1288	DO_2D( 1, 1, 1, 0 ) ! not jpi-column
1289	IF ( phU(ji,jj) > 0._wp ) THEN ; pUmsk(ji,jj) = pTmsk(ji ,jj)
1290	ELSE ; pUmsk(ji,jj) = pTmsk(ji+1,jj)
1291	ENDIF
1292	phU(ji,jj) = pUmsk(ji,jj)*phU(ji,jj)
1293	pu (ji,jj) = pUmsk(ji,jj)*pu (ji,jj)
1294	END_2D
1295	!
1296	DO_2D( 1, 0, 1, 1 ) ! not jpj-row
1297	IF ( phV(ji,jj) > 0._wp ) THEN ; pVmsk(ji,jj) = pTmsk(ji,jj )
1298	ELSE ; pVmsk(ji,jj) = pTmsk(ji,jj+1)
1299	ENDIF
1300	phV(ji,jj) = pVmsk(ji,jj)*phV(ji,jj)
1301	pv (ji,jj) = pVmsk(ji,jj)*pv (ji,jj)
1302	END_2D
1303	!
1304	END SUBROUTINE wad_Umsk
1305
1306
1307	SUBROUTINE wad_spg( pshn, zcpx, zcpy )
1308	!!---------------------------------------------------------------------
1309	!! * ROUTINE wad_sp *
1310	!!
1311	!! ** Purpose :
1312	!!----------------------------------------------------------------------
1313	INTEGER :: ji ,jj ! dummy loop indices
1314	LOGICAL :: ll_tmp1, ll_tmp2
1315	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pshn
1316	REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: zcpx, zcpy
1317	!!----------------------------------------------------------------------
1318	DO_2D( 0, 0, 0, 0 )
1319	ll_tmp1 = MIN( pshn(ji,jj) , pshn(ji+1,jj) ) > &
1320	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
1321	& MAX( pshn(ji,jj) + ht_0(ji,jj) , pshn(ji+1,jj) + ht_0(ji+1,jj) ) &
1322	& > rn_wdmin1 + rn_wdmin2
1323	ll_tmp2 = ( ABS( pshn(ji+1,jj) - pshn(ji ,jj)) > 1.E-12 ).AND.( &
1324	& MAX( pshn(ji,jj) , pshn(ji+1,jj) ) > &
1325	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
1326	IF(ll_tmp1) THEN
1327	zcpx(ji,jj) = 1.0_wp
1328	ELSEIF(ll_tmp2) THEN
1329	! no worries about pshn(ji+1,jj) - pshn(ji ,jj) = 0, it won't happen ! here
1330	zcpx(ji,jj) = ABS( (pshn(ji+1,jj) + ht_0(ji+1,jj) - pshn(ji,jj) - ht_0(ji,jj)) &
1331	& / (pshn(ji+1,jj) - pshn(ji ,jj)) )
1332	zcpx(ji,jj) = max(min( zcpx(ji,jj) , 1.0_wp),0.0_wp)
1333	ELSE
1334	zcpx(ji,jj) = 0._wp
1335	ENDIF
1336	!
1337	ll_tmp1 = MIN( pshn(ji,jj) , pshn(ji,jj+1) ) > &
1338	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
1339	& MAX( pshn(ji,jj) + ht_0(ji,jj) , pshn(ji,jj+1) + ht_0(ji,jj+1) ) &
1340	& > rn_wdmin1 + rn_wdmin2
1341	ll_tmp2 = ( ABS( pshn(ji,jj) - pshn(ji,jj+1)) > 1.E-12 ).AND.( &
1342	& MAX( pshn(ji,jj) , pshn(ji,jj+1) ) > &
1343	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
1344
1345	IF(ll_tmp1) THEN
1346	zcpy(ji,jj) = 1.0_wp
1347	ELSE IF(ll_tmp2) THEN
1348	! no worries about pshn(ji,jj+1) - pshn(ji,jj ) = 0, it won't happen ! here
1349	zcpy(ji,jj) = ABS( (pshn(ji,jj+1) + ht_0(ji,jj+1) - pshn(ji,jj) - ht_0(ji,jj)) &
1350	& / (pshn(ji,jj+1) - pshn(ji,jj )) )
1351	zcpy(ji,jj) = MAX( 0._wp , MIN( zcpy(ji,jj) , 1.0_wp ) )
1352	ELSE
1353	zcpy(ji,jj) = 0._wp
1354	ENDIF
1355	END_2D
1356
1357	END SUBROUTINE wad_spg
1358
1359
1360
1361	SUBROUTINE dyn_drg_init( Kbb, Kmm, puu, pvv, puu_b ,pvv_b, pu_RHSi, pv_RHSi, pCdU_u, pCdU_v )
1362	!!----------------------------------------------------------------------
1363	!! * ROUTINE dyn_drg_init *
1364	!!
1365	!! ** Purpose : - add the baroclinic top/bottom drag contribution to
1366	!! the baroclinic part of the barotropic RHS
1367	!! - compute the barotropic drag coefficients
1368	!!
1369	!! ** Method : computation done over the INNER domain only
1370	!!----------------------------------------------------------------------
1371	INTEGER , INTENT(in ) :: Kbb, Kmm ! ocean time level indices
1372	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(in ) :: puu, pvv ! ocean velocities and RHS of momentum equation
1373	REAL(wp), DIMENSION(jpi,jpj,jpt) , INTENT(in ) :: puu_b, pvv_b ! barotropic velocities at main time levels
1374	REAL(wp), DIMENSION(jpi,jpj) , INTENT(inout) :: pu_RHSi, pv_RHSi ! baroclinic part of the barotropic RHS
1375	REAL(wp), DIMENSION(jpi,jpj) , INTENT( out) :: pCdU_u , pCdU_v ! barotropic drag coefficients
1376	!
1377	INTEGER :: ji, jj ! dummy loop indices
1378	INTEGER :: ikbu, ikbv, iktu, iktv
1379	REAL(wp) :: zztmp
1380	REAL(wp), DIMENSION(jpi,jpj) :: zu_i, zv_i
1381	!!----------------------------------------------------------------------
1382	!
1383	! !== Set the barotropic drag coef. ==!
1384	!
1385	IF( ln_isfcav.OR.ln_drgice_imp ) THEN ! top+bottom friction (ocean cavities)
1386
1387	DO_2D( 0, 0, 0, 0 )
1388	pCdU_u(ji,jj) = r1_2*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) + rCdU_top(ji+1,jj)+rCdU_top(ji,jj) )
1389	pCdU_v(ji,jj) = r1_2*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) + rCdU_top(ji,jj+1)+rCdU_top(ji,jj) )
1390	END_2D
1391	ELSE ! bottom friction only
1392	DO_2D( 0, 0, 0, 0 )
1393	pCdU_u(ji,jj) = r1_2*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) )
1394	pCdU_v(ji,jj) = r1_2*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) )
1395	END_2D
1396	ENDIF
1397	!
1398	! !== BOTTOM stress contribution from baroclinic velocities ==!
1399	!
1400	IF( ln_bt_fw ) THEN ! FORWARD integration: use NOW bottom baroclinic velocities
1401
1402	DO_2D( 0, 0, 0, 0 )
1403	ikbu = mbku(ji,jj)
1404	ikbv = mbkv(ji,jj)
1405	zu_i(ji,jj) = puu(ji,jj,ikbu,Kmm) - puu_b(ji,jj,Kmm)
1406	zv_i(ji,jj) = pvv(ji,jj,ikbv,Kmm) - pvv_b(ji,jj,Kmm)
1407	END_2D
1408	ELSE ! CENTRED integration: use BEFORE bottom baroclinic velocities
1409
1410	DO_2D( 0, 0, 0, 0 )
1411	ikbu = mbku(ji,jj)
1412	ikbv = mbkv(ji,jj)
1413	zu_i(ji,jj) = puu(ji,jj,ikbu,Kbb) - puu_b(ji,jj,Kbb)
1414	zv_i(ji,jj) = pvv(ji,jj,ikbv,Kbb) - pvv_b(ji,jj,Kbb)
1415	END_2D
1416	ENDIF
1417	!
1418	IF( ln_wd_il ) THEN ! W/D : use the "clipped" bottom friction !!gm explain WHY, please !
1419	zztmp = -1._wp / rDt_e
1420	DO_2D( 0, 0, 0, 0 )
1421	pu_RHSi(ji,jj) = pu_RHSi(ji,jj) + zu_i(ji,jj) * wdrampu(ji,jj) * MAX( &
1422	& r1_hu(ji,jj,Kmm) * r1_2*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) , zztmp )
1423	pv_RHSi(ji,jj) = pv_RHSi(ji,jj) + zv_i(ji,jj) * wdrampv(ji,jj) * MAX( &
1424	& r1_hv(ji,jj,Kmm) * r1_2*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) , zztmp )
1425	END_2D
1426	ELSE ! use "unclipped" drag (even if explicit friction is used in 3D calculation)
1427
1428	DO_2D( 0, 0, 0, 0 )
1429	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)
1430	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)
1431	END_2D
1432	END IF
1433	!
1434	! !== TOP stress contribution from baroclinic velocities ==! (no W/D case)
1435	!
1436	IF( ln_isfcav.OR.ln_drgice_imp ) THEN
1437	!
1438	IF( ln_bt_fw ) THEN ! FORWARD integration: use NOW top baroclinic velocity
1439
1440	DO_2D( 0, 0, 0, 0 )
1441	iktu = miku(ji,jj)
1442	iktv = mikv(ji,jj)
1443	zu_i(ji,jj) = puu(ji,jj,iktu,Kmm) - puu_b(ji,jj,Kmm)
1444	zv_i(ji,jj) = pvv(ji,jj,iktv,Kmm) - pvv_b(ji,jj,Kmm)
1445	END_2D
1446	ELSE ! CENTRED integration: use BEFORE top baroclinic velocity
1447
1448	DO_2D( 0, 0, 0, 0 )
1449	iktu = miku(ji,jj)
1450	iktv = mikv(ji,jj)
1451	zu_i(ji,jj) = puu(ji,jj,iktu,Kbb) - puu_b(ji,jj,Kbb)
1452	zv_i(ji,jj) = pvv(ji,jj,iktv,Kbb) - pvv_b(ji,jj,Kbb)
1453	END_2D
1454	ENDIF
1455	!
1456	! ! use "unclipped" top drag (even if explicit friction is used in 3D calculation)
1457
1458	DO_2D( 0, 0, 0, 0 )
1459	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)
1460	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)
1461	END_2D
1462	!
1463	ENDIF
1464	!
1465	END SUBROUTINE dyn_drg_init
1466
1467	SUBROUTINE ts_bck_interp( jn, ll_init, & ! <== in
1468	& za0, za1, za2, za3 ) ! ==> out
1469	!!----------------------------------------------------------------------
1470	INTEGER ,INTENT(in ) :: jn ! index of sub time step
1471	LOGICAL ,INTENT(in ) :: ll_init !
1472	REAL(wp),INTENT( out) :: za0, za1, za2, za3 ! Half-step back interpolation coefficient
1473	!
1474	REAL(wp) :: zepsilon, zgamma ! - -
1475	!!----------------------------------------------------------------------
1476	! ! set Half-step back interpolation coefficient
1477	IF ( jn==1 .AND. ll_init ) THEN !* Forward-backward
1478	za0 = 1._wp
1479	za1 = 0._wp
1480	za2 = 0._wp
1481	za3 = 0._wp
1482	ELSEIF( jn==2 .AND. ll_init ) THEN !* AB2-AM3 Coefficients; bet=0 ; gam=-1/6 ; eps=1/12
1483	za0 = 1.0833333333333_wp ! za0 = 1-gam-eps
1484	za1 =-0.1666666666666_wp ! za1 = gam
1485	za2 = 0.0833333333333_wp ! za2 = eps
1486	za3 = 0._wp
1487	ELSE !* AB3-AM4 Coefficients; bet=0.281105 ; eps=0.013 ; gam=0.0880
1488	IF( rn_bt_alpha == 0._wp ) THEN ! Time diffusion
1489	za0 = 0.614_wp ! za0 = 1/2 + gam + 2*eps
1490	za1 = 0.285_wp ! za1 = 1/2 - 2gam - 3eps
1491	za2 = 0.088_wp ! za2 = gam
1492	za3 = 0.013_wp ! za3 = eps
1493	ELSE ! no time diffusion
1494	zepsilon = 0.00976186_wp - 0.13451357_wp * rn_bt_alpha
1495	zgamma = 0.08344500_wp - 0.51358400_wp * rn_bt_alpha
1496	za0 = 0.5_wp + zgamma + 2._wp * rn_bt_alpha + 2._wp * zepsilon
1497	za1 = 1._wp - za0 - zgamma - zepsilon
1498	za2 = zgamma
1499	za3 = zepsilon
1500	ENDIF
1501	ENDIF
1502	END SUBROUTINE ts_bck_interp
1503
1504
1505	!!======================================================================
1506	END MODULE dynspg_ts

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