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dynspg_ts.F90 in NEMO/branches/2019/dev_r11085_ASINTER-05_Brodeau_Advanced_Bulk/src/OCE/DYN – NEMO

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source: NEMO/branches/2019/dev_r11085_ASINTER-05_Brodeau_Advanced_Bulk/src/OCE/DYN/dynspg_ts.F90 @ 12061

Last change on this file since 12061 was 12061, checked in by laurent, 5 years ago
Catch up with r12055 of trunk...
Property svn:keywords set to `Id`
File size: 81.3 KB

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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 zdf_oce ! vertical physics: variables
34	USE zdfdrg ! vertical physics: top/bottom drag coef.
35	USE sbcisf ! ice shelf variable (fwfisf)
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 sbctide ! tides
47	USE updtide ! tide potential
48	USE sbcwave ! surface wave
49	USE diatmb ! Top,middle,bottom output
50	#if defined key_agrif
51	USE agrif_oce_interp ! agrif
52	USE agrif_oce
53	#endif
54	#if defined key_asminc
55	USE asminc ! Assimilation increment
56	#endif
57	!
58	USE in_out_manager ! I/O manager
59	USE lib_mpp ! distributed memory computing library
60	USE lbclnk ! ocean lateral boundary conditions (or mpp link)
61	USE prtctl ! Print control
62	USE iom ! IOM library
63	USE restart ! only for lrst_oce
64	USE diatmb ! Top,middle,bottom output
65
66	USE iom ! to remove
67
68	IMPLICIT NONE
69	PRIVATE
70
71	PUBLIC dyn_spg_ts ! called by dyn_spg
72	PUBLIC dyn_spg_ts_init ! - - dyn_spg_init
73
74	!! Time filtered arrays at baroclinic time step:
75	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) :: un_adv , vn_adv !: Advection vel. at "now" barocl. step
76	!
77	INTEGER, SAVE :: icycle ! Number of barotropic sub-steps for each internal step nn_baro <= 2.5 nn_baro
78	REAL(wp),SAVE :: rdtbt ! Barotropic time step
79	!
80	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:) :: wgtbtp1, wgtbtp2 ! 1st & 2nd weights used in time filtering of barotropic fields
81	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: zwz ! ff_f/h at F points
82	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: ftnw, ftne ! triad of coriolis parameter
83	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: ftsw, ftse ! (only used with een vorticity scheme)
84
85	REAL(wp) :: r1_12 = 1._wp / 12._wp ! local ratios
86	REAL(wp) :: r1_8 = 0.125_wp !
87	REAL(wp) :: r1_4 = 0.25_wp !
88	REAL(wp) :: r1_2 = 0.5_wp !
89
90	!! * Substitutions
91	# include "vectopt_loop_substitute.h90"
92	!!----------------------------------------------------------------------
93	!! NEMO/OCE 4.0 , NEMO Consortium (2018)
94	!! $Id$
95	!! Software governed by the CeCILL license (see ./LICENSE)
96	!!----------------------------------------------------------------------
97	CONTAINS
98
99	INTEGER FUNCTION dyn_spg_ts_alloc()
100	!!----------------------------------------------------------------------
101	!! * routine dyn_spg_ts_alloc *
102	!!----------------------------------------------------------------------
103	INTEGER :: ierr(3)
104	!!----------------------------------------------------------------------
105	ierr(:) = 0
106	!
107	ALLOCATE( wgtbtp1(3nn_baro), wgtbtp2(3nn_baro), zwz(jpi,jpj), STAT=ierr(1) )
108	IF( ln_dynvor_een .OR. ln_dynvor_eeT ) &
109	& ALLOCATE( ftnw(jpi,jpj) , ftne(jpi,jpj) , ftsw(jpi,jpj) , ftse(jpi,jpj), STAT=ierr(2) )
110	!
111	ALLOCATE( un_adv(jpi,jpj), vn_adv(jpi,jpj) , STAT=ierr(3) )
112	!
113	dyn_spg_ts_alloc = MAXVAL( ierr(:) )
114	!
115	CALL mpp_sum( 'dynspg_ts', dyn_spg_ts_alloc )
116	IF( dyn_spg_ts_alloc /= 0 ) CALL ctl_stop( 'STOP', 'dyn_spg_ts_alloc: failed to allocate arrays' )
117	!
118	END FUNCTION dyn_spg_ts_alloc
119
120
121	SUBROUTINE dyn_spg_ts( kt )
122	!!----------------------------------------------------------------------
123	!!
124	!! ** Purpose : - Compute the now trend due to the explicit time stepping
125	!! of the quasi-linear barotropic system, and add it to the
126	!! general momentum trend.
127	!!
128	!! ** Method : - split-explicit schem (time splitting) :
129	!! Barotropic variables are advanced from internal time steps
130	!! "n" to "n+1" if ln_bt_fw=T
131	!! or from
132	!! "n-1" to "n+1" if ln_bt_fw=F
133	!! thanks to a generalized forward-backward time stepping (see ref. below).
134	!!
135	!! ** Action :
136	!! -Update the filtered free surface at step "n+1" : ssha
137	!! -Update filtered barotropic velocities at step "n+1" : ua_b, va_b
138	!! -Compute barotropic advective fluxes at step "n" : un_adv, vn_adv
139	!! These are used to advect tracers and are compliant with discrete
140	!! continuity equation taken at the baroclinic time steps. This
141	!! ensures tracers conservation.
142	!! - (ua, va) momentum trend updated with barotropic component.
143	!!
144	!! References : Shchepetkin and McWilliams, Ocean Modelling, 2005.
145	!!---------------------------------------------------------------------
146	INTEGER, INTENT(in) :: kt ! ocean time-step index
147	!
148	INTEGER :: ji, jj, jk, jn ! dummy loop indices
149	LOGICAL :: ll_fw_start ! =T : forward integration
150	LOGICAL :: ll_init ! =T : special startup of 2d equations
151	INTEGER :: noffset ! local integers : time offset for bdy update
152	REAL(wp) :: r1_2dt_b, z1_hu, z1_hv ! local scalars
153	REAL(wp) :: za0, za1, za2, za3 ! - -
154	REAL(wp) :: zmdi, zztmp, zldg ! - -
155	REAL(wp) :: zhu_bck, zhv_bck, zhdiv ! - -
156	REAL(wp) :: zun_save, zvn_save ! - -
157	REAL(wp), DIMENSION(jpi,jpj) :: zu_trd, zu_frc, zu_spg, zssh_frc
158	REAL(wp), DIMENSION(jpi,jpj) :: zv_trd, zv_frc, zv_spg
159	REAL(wp), DIMENSION(jpi,jpj) :: zsshu_a, zhup2_e, zhtp2_e
160	REAL(wp), DIMENSION(jpi,jpj) :: zsshv_a, zhvp2_e, zsshp2_e
161	REAL(wp), DIMENSION(jpi,jpj) :: zCdU_u, zCdU_v ! top/bottom stress at u- & v-points
162	REAL(wp), DIMENSION(jpi,jpj) :: zhU, zhV ! fluxes
163	!
164	REAL(wp) :: zwdramp ! local scalar - only used if ln_wd_dl = .True.
165
166	INTEGER :: iwdg, jwdg, kwdg ! short-hand values for the indices of the output point
167
168	REAL(wp) :: zepsilon, zgamma ! - -
169	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zcpx, zcpy ! Wetting/Dying gravity filter coef.
170	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: ztwdmask, zuwdmask, zvwdmask ! ROMS wetting and drying masks at t,u,v points
171	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zuwdav2, zvwdav2 ! averages over the sub-steps of zuwdmask and zvwdmask
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(:,:) )
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(:,:) - rnf(:,:) - rnf_b(:,:) + fwfisf(:,:) + fwfisf_b(:,:) )
341	ENDIF
342	! != Add Stokes drift divergence =! (if exist)
343	IF( ln_sdw ) THEN ! ----------------------------- !
344	zssh_frc(:,:) = zssh_frc(:,:) + div_sd(:,:)
345	ENDIF
346	!
347	#if defined key_asminc
348	! != Add the IAU weighted SSH increment =!
349	! ! ------------------------------------ !
350	IF( lk_asminc .AND. ln_sshinc .AND. ln_asmiau ) THEN
351	zssh_frc(:,:) = zssh_frc(:,:) - ssh_iau(:,:)
352	ENDIF
353	#endif
354	! != Fill boundary data arrays for AGRIF
355	! ! ------------------------------------
356	#if defined key_agrif
357	IF( .NOT.Agrif_Root() ) CALL agrif_dta_ts( kt )
358	#endif
359	!
360	! -----------------------------------------------------------------------
361	! Phase 2 : Integration of the barotropic equations
362	! -----------------------------------------------------------------------
363	!
364	! ! ==================== !
365	! ! Initialisations !
366	! ! ==================== !
367	! Initialize barotropic variables:
368	IF( ll_init )THEN
369	sshbb_e(:,:) = 0._wp
370	ubb_e (:,:) = 0._wp
371	vbb_e (:,:) = 0._wp
372	sshb_e (:,:) = 0._wp
373	ub_e (:,:) = 0._wp
374	vb_e (:,:) = 0._wp
375	ENDIF
376	!
377	IF( ln_linssh ) THEN ! mid-step ocean depth is fixed (hup2_e=hu_n=hu_0)
378	zhup2_e(:,:) = hu_n(:,:)
379	zhvp2_e(:,:) = hv_n(:,:)
380	zhtp2_e(:,:) = ht_n(:,:)
381	ENDIF
382	!
383	IF (ln_bt_fw) THEN ! FORWARD integration: start from NOW fields
384	sshn_e(:,:) = sshn(:,:)
385	un_e (:,:) = un_b(:,:)
386	vn_e (:,:) = vn_b(:,:)
387	!
388	hu_e (:,:) = hu_n(:,:)
389	hv_e (:,:) = hv_n(:,:)
390	hur_e (:,:) = r1_hu_n(:,:)
391	hvr_e (:,:) = r1_hv_n(:,:)
392	ELSE ! CENTRED integration: start from BEFORE fields
393	sshn_e(:,:) = sshb(:,:)
394	un_e (:,:) = ub_b(:,:)
395	vn_e (:,:) = vb_b(:,:)
396	!
397	hu_e (:,:) = hu_b(:,:)
398	hv_e (:,:) = hv_b(:,:)
399	hur_e (:,:) = r1_hu_b(:,:)
400	hvr_e (:,:) = r1_hv_b(:,:)
401	ENDIF
402	!
403	! Initialize sums:
404	ua_b (:,:) = 0._wp ! After barotropic velocities (or transport if flux form)
405	va_b (:,:) = 0._wp
406	ssha (:,:) = 0._wp ! Sum for after averaged sea level
407	un_adv(:,:) = 0._wp ! Sum for now transport issued from ts loop
408	vn_adv(:,:) = 0._wp
409	!
410	IF( ln_wd_dl ) THEN
411	zuwdmask(:,:) = 0._wp ! set to zero for definiteness (not sure this is necessary)
412	zvwdmask(:,:) = 0._wp !
413	zuwdav2 (:,:) = 0._wp
414	zvwdav2 (:,:) = 0._wp
415	END IF
416
417	! ! ==================== !
418	DO jn = 1, icycle ! sub-time-step loop !
419	! ! ==================== !
420	!
421	l_full_nf_update = jn == icycle ! false: disable full North fold update (performances) for jn = 1 to icycle-1
422	!
423	! !== Update the forcing ==! (BDY and tides)
424	!
425	IF( ln_bdy .AND. ln_tide ) CALL bdy_dta_tides( kt, kit=jn, kt_offset= noffset+1 )
426	IF( ln_tide_pot .AND. ln_tide ) CALL upd_tide ( kt, kit=jn, kt_offset= noffset )
427	!
428	! !== extrapolation at mid-step ==! (jn+1/2)
429	!
430	! !* Set extrapolation coefficients for predictor step:
431	IF ((jn<3).AND.ll_init) THEN ! Forward
432	za1 = 1._wp
433	za2 = 0._wp
434	za3 = 0._wp
435	ELSE ! AB3-AM4 Coefficients: bet=0.281105
436	za1 = 1.781105_wp ! za1 = 3/2 + bet
437	za2 = -1.06221_wp ! za2 = -(1/2 + 2*bet)
438	za3 = 0.281105_wp ! za3 = bet
439	ENDIF
440	!
441	! !* Extrapolate barotropic velocities at mid-step (jn+1/2)
442	!-- m+1/2 m m-1 m-2 --!
443	!-- u = (3/2+beta) u -(1/2+2beta) u + beta u --!
444	!-------------------------------------------------------------------------!
445	ua_e(:,:) = za1 * un_e(:,:) + za2 * ub_e(:,:) + za3 * ubb_e(:,:)
446	va_e(:,:) = za1 * vn_e(:,:) + za2 * vb_e(:,:) + za3 * vbb_e(:,:)
447
448	IF( .NOT.ln_linssh ) THEN !* Update ocean depth (variable volume case only)
449	! ! ------------------
450	! Extrapolate Sea Level at step jit+0.5:
451	!-- m+1/2 m m-1 m-2 --!
452	!-- ssh = (3/2+beta) ssh -(1/2+2beta) ssh + beta ssh --!
453	!--------------------------------------------------------------------------------!
454	zsshp2_e(:,:) = za1 * sshn_e(:,:) + za2 * sshb_e(:,:) + za3 * sshbb_e(:,:)
455
456	! set wetting & drying mask at tracer points for this barotropic mid-step
457	IF( ln_wd_dl ) CALL wad_tmsk( zsshp2_e, ztwdmask )
458	!
459	! ! ocean t-depth at mid-step
460	zhtp2_e(:,:) = ht_0(:,:) + zsshp2_e(:,:)
461	!
462	! ! ocean u- and v-depth at mid-step (separate DO-loops remove the need of a lbc_lnk)
463	DO jj = 1, jpj
464	DO ji = 1, jpim1 ! not jpi-column
465	zhup2_e(ji,jj) = hu_0(ji,jj) + r1_2 * r1_e1e2u(ji,jj) &
466	& * ( e1e2t(ji ,jj) * zsshp2_e(ji ,jj) &
467	& + e1e2t(ji+1,jj) * zsshp2_e(ji+1,jj) ) * ssumask(ji,jj)
468	END DO
469	END DO
470	DO jj = 1, jpjm1 ! not jpj-row
471	DO ji = 1, jpi
472	zhvp2_e(ji,jj) = hv_0(ji,jj) + r1_2 * r1_e1e2v(ji,jj) &
473	& * ( e1e2t(ji,jj ) * zsshp2_e(ji,jj ) &
474	& + e1e2t(ji,jj+1) * zsshp2_e(ji,jj+1) ) * ssvmask(ji,jj)
475	END DO
476	END DO
477	!
478	ENDIF
479	!
480	! !== after SSH ==! (jn+1)
481	!
482	! ! update (ua_e,va_e) to enforce volume conservation at open boundaries
483	! ! values of zhup2_e and zhvp2_e on the halo are not needed in bdy_vol2d
484	IF( ln_bdy .AND. ln_vol ) CALL bdy_vol2d( kt, jn, ua_e, va_e, zhup2_e, zhvp2_e )
485	!
486	! ! resulting flux at mid-step (not over the full domain)
487	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
488	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
489	!
490	#if defined key_agrif
491	! Set fluxes during predictor step to ensure volume conservation
492	IF( .NOT.Agrif_Root() .AND. ln_bt_fw ) THEN
493	IF((nbondi == -1).OR.(nbondi == 2)) THEN
494	DO jj = 1, jpj
495	zhU(2:nbghostcells+1,jj) = ubdy_w(1:nbghostcells,jj) * e2u(2:nbghostcells+1,jj)
496	zhV(2:nbghostcells+1,jj) = vbdy_w(1:nbghostcells,jj) * e1v(2:nbghostcells+1,jj)
497	END DO
498	ENDIF
499	IF((nbondi == 1).OR.(nbondi == 2)) THEN
500	DO jj=1,jpj
501	zhU(nlci-nbghostcells-1:nlci-2,jj) = ubdy_e(1:nbghostcells,jj) * e2u(nlci-nbghostcells-1:nlci-2,jj)
502	zhV(nlci-nbghostcells :nlci-1,jj) = vbdy_e(1:nbghostcells,jj) * e1v(nlci-nbghostcells :nlci-1,jj)
503	END DO
504	ENDIF
505	IF((nbondj == -1).OR.(nbondj == 2)) THEN
506	DO ji=1,jpi
507	zhV(ji,2:nbghostcells+1) = vbdy_s(ji,1:nbghostcells) * e1v(ji,2:nbghostcells+1)
508	zhU(ji,2:nbghostcells+1) = ubdy_s(ji,1:nbghostcells) * e2u(ji,2:nbghostcells+1)
509	END DO
510	ENDIF
511	IF((nbondj == 1).OR.(nbondj == 2)) THEN
512	DO ji=1,jpi
513	zhV(ji,nlcj-nbghostcells-1:nlcj-2) = vbdy_n(ji,1:nbghostcells) * e1v(ji,nlcj-nbghostcells-1:nlcj-2)
514	zhU(ji,nlcj-nbghostcells :nlcj-1) = ubdy_n(ji,1:nbghostcells) * e2u(ji,nlcj-nbghostcells :nlcj-1)
515	END DO
516	ENDIF
517	ENDIF
518	#endif
519	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
520
521	IF( ln_wd_dl ) THEN ! un_e and vn_e are set to zero at faces where
522	! ! the direction of the flow is from dry cells
523	CALL wad_Umsk( ztwdmask, zhU, zhV, un_e, vn_e, zuwdmask, zvwdmask ) ! not jpi colomn for U, not jpj row for V
524	!
525	ENDIF
526	!
527	!
528	! Compute Sea Level at step jit+1
529	!-- m+1 m m+1/2 --!
530	!-- ssh = ssh - delta_t' * [ frc + div( flux ) ] --!
531	!-------------------------------------------------------------------------!
532	DO jj = 2, jpjm1 ! INNER domain
533	DO ji = 2, jpim1
534	zhdiv = ( zhU(ji,jj) - zhU(ji-1,jj) + zhV(ji,jj) - zhV(ji,jj-1) ) * r1_e1e2t(ji,jj)
535	ssha_e(ji,jj) = ( sshn_e(ji,jj) - rdtbt * ( zssh_frc(ji,jj) + zhdiv ) ) * ssmask(ji,jj)
536	END DO
537	END DO
538	!
539	CALL lbc_lnk_multi( 'dynspg_ts', ssha_e, 'T', 1._wp, zhU, 'U', -1._wp, zhV, 'V', -1._wp )
540	!
541	! ! Sum over sub-time-steps to compute advective velocities
542	za2 = wgtbtp2(jn) ! zhU, zhV hold fluxes extrapolated at jn+0.5
543	un_adv(:,:) = un_adv(:,:) + za2 * zhU(:,:) * r1_e2u(:,:)
544	vn_adv(:,:) = vn_adv(:,:) + za2 * zhV(:,:) * r1_e1v(:,:)
545	! sum over sub-time-steps to decide which baroclinic velocities to set to zero (zuwdav2 is only used when ln_wd_dl_bc=True)
546	IF ( ln_wd_dl_bc ) THEN
547	zuwdav2(1:jpim1,1:jpj ) = zuwdav2(1:jpim1,1:jpj ) + za2 * zuwdmask(1:jpim1,1:jpj ) ! not jpi-column
548	zvwdav2(1:jpi ,1:jpjm1) = zvwdav2(1:jpi ,1:jpjm1) + za2 * zvwdmask(1:jpi ,1:jpjm1) ! not jpj-row
549	END IF
550	!
551	! Duplicate sea level across open boundaries (this is only cosmetic if linssh=T)
552	IF( ln_bdy ) CALL bdy_ssh( ssha_e )
553	#if defined key_agrif
554	IF( .NOT.Agrif_Root() ) CALL agrif_ssh_ts( jn )
555	#endif
556	!
557	! Sea Surface Height at u-,v-points (vvl case only)
558	IF( .NOT.ln_linssh ) THEN
559	DO jj = 2, jpjm1 ! INNER domain, will be extended to whole domain later
560	DO ji = 2, jpim1 ! NO Vector Opt.
561	zsshu_a(ji,jj) = r1_2 * ssumask(ji,jj) * r1_e1e2u(ji,jj) &
562	& * ( e1e2t(ji ,jj ) * ssha_e(ji ,jj ) &
563	& + e1e2t(ji+1,jj ) * ssha_e(ji+1,jj ) )
564	zsshv_a(ji,jj) = r1_2 * ssvmask(ji,jj) * r1_e1e2v(ji,jj) &
565	& * ( e1e2t(ji ,jj ) * ssha_e(ji ,jj ) &
566	& + e1e2t(ji ,jj+1) * ssha_e(ji ,jj+1) )
567	END DO
568	END DO
569	ENDIF
570	!
571	! Half-step back interpolation of SSH for surface pressure computation at step jit+1/2
572	!-- m+1/2 m+1 m m-1 m-2 --!
573	!-- ssh' = za0 * ssh + za1 * ssh + za2 * ssh + za3 * ssh --!
574	!------------------------------------------------------------------------------------------!
575	CALL ts_bck_interp( jn, ll_init, za0, za1, za2, za3 ) ! coeficients of the interpolation
576	zsshp2_e(:,:) = za0 * ssha_e(:,:) + za1 * sshn_e (:,:) &
577	& + za2 * sshb_e(:,:) + za3 * sshbb_e(:,:)
578	!
579	! ! Surface pressure gradient
580	zldg = ( 1._wp - rn_scal_load ) * grav ! local factor
581	DO jj = 2, jpjm1
582	DO ji = 2, jpim1
583	zu_spg(ji,jj) = - zldg * ( zsshp2_e(ji+1,jj) - zsshp2_e(ji,jj) ) * r1_e1u(ji,jj)
584	zv_spg(ji,jj) = - zldg * ( zsshp2_e(ji,jj+1) - zsshp2_e(ji,jj) ) * r1_e2v(ji,jj)
585	END DO
586	END DO
587	IF( ln_wd_il ) THEN ! W/D : gravity filters applied on pressure gradient
588	CALL wad_spg( zsshp2_e, zcpx, zcpy ) ! Calculating W/D gravity filters
589	zu_spg(2:jpim1,2:jpjm1) = zu_spg(2:jpim1,2:jpjm1) * zcpx(2:jpim1,2:jpjm1)
590	zv_spg(2:jpim1,2:jpjm1) = zv_spg(2:jpim1,2:jpjm1) * zcpy(2:jpim1,2:jpjm1)
591	ENDIF
592	!
593	! Add Coriolis trend:
594	! zwz array below or triads normally depend on sea level with ln_linssh=F and should be updated
595	! at each time step. We however keep them constant here for optimization.
596	! Recall that zhU and zhV hold fluxes at jn+0.5 (extrapolated not backward interpolated)
597	CALL dyn_cor_2d( zhup2_e, zhvp2_e, ua_e, va_e, zhU, zhV, zu_trd, zv_trd )
598	!
599	! Add tidal astronomical forcing if defined
600	IF ( ln_tide .AND. ln_tide_pot ) THEN
601	DO jj = 2, jpjm1
602	DO ji = fs_2, fs_jpim1 ! vector opt.
603	zu_trd(ji,jj) = zu_trd(ji,jj) + grav * ( pot_astro(ji+1,jj) - pot_astro(ji,jj) ) * r1_e1u(ji,jj)
604	zv_trd(ji,jj) = zv_trd(ji,jj) + grav * ( pot_astro(ji,jj+1) - pot_astro(ji,jj) ) * r1_e2v(ji,jj)
605	END DO
606	END DO
607	ENDIF
608	!
609	! Add bottom stresses:
610	!jth do implicitly instead
611	IF ( .NOT. ll_wd ) THEN ! Revert to explicit for bit comparison tests in non wad runs
612	DO jj = 2, jpjm1
613	DO ji = fs_2, fs_jpim1 ! vector opt.
614	zu_trd(ji,jj) = zu_trd(ji,jj) + zCdU_u(ji,jj) * un_e(ji,jj) * hur_e(ji,jj)
615	zv_trd(ji,jj) = zv_trd(ji,jj) + zCdU_v(ji,jj) * vn_e(ji,jj) * hvr_e(ji,jj)
616	END DO
617	END DO
618	ENDIF
619	!
620	! Set next velocities:
621	! Compute barotropic speeds at step jit+1 (h : total height of the water colomn)
622	!-- VECTOR FORM
623	!-- m+1 m / m+1/2 \ --!
624	!-- u = u + delta_t' * \ (1-r)g grad_x( ssh') - f * k vect u + frc / --!
625	!-- --!
626	!-- FLUX FORM --!
627	!-- m+1 __1__ / m m / m+1/2 m+1/2 m+1/2 n \ \ --!
628	!-- u = m+1 \| h * u + delta_t' * \ h * (1-r)g grad_x( ssh') - h * f * k vect u + h * frc / \| --!
629	!-- h \ / --!
630	!------------------------------------------------------------------------------------------------------------------------!
631	IF( ln_dynadv_vec .OR. ln_linssh ) THEN !* Vector form
632	DO jj = 2, jpjm1
633	DO ji = fs_2, fs_jpim1 ! vector opt.
634	ua_e(ji,jj) = ( un_e(ji,jj) &
635	& + rdtbt * ( zu_spg(ji,jj) &
636	& + zu_trd(ji,jj) &
637	& + zu_frc(ji,jj) ) &
638	& ) * ssumask(ji,jj)
639
640	va_e(ji,jj) = ( vn_e(ji,jj) &
641	& + rdtbt * ( zv_spg(ji,jj) &
642	& + zv_trd(ji,jj) &
643	& + zv_frc(ji,jj) ) &
644	& ) * ssvmask(ji,jj)
645	END DO
646	END DO
647	!
648	ELSE !* Flux form
649	DO jj = 2, jpjm1
650	DO ji = 2, jpim1
651	! ! hu_e, hv_e hold depth at jn, zhup2_e, zhvp2_e hold extrapolated depth at jn+1/2
652	! ! backward interpolated depth used in spg terms at jn+1/2
653	zhu_bck = hu_0(ji,jj) + r1_2r1_e1e2u(ji,jj) ( e1e2t(ji ,jj) * zsshp2_e(ji ,jj) &
654	& + e1e2t(ji+1,jj) * zsshp2_e(ji+1,jj) ) * ssumask(ji,jj)
655	zhv_bck = hv_0(ji,jj) + r1_2r1_e1e2v(ji,jj) ( e1e2t(ji,jj ) * zsshp2_e(ji,jj ) &
656	& + e1e2t(ji,jj+1) * zsshp2_e(ji,jj+1) ) * ssvmask(ji,jj)
657	! ! inverse depth at jn+1
658	z1_hu = ssumask(ji,jj) / ( hu_0(ji,jj) + zsshu_a(ji,jj) + 1._wp - ssumask(ji,jj) )
659	z1_hv = ssvmask(ji,jj) / ( hv_0(ji,jj) + zsshv_a(ji,jj) + 1._wp - ssvmask(ji,jj) )
660	!
661	ua_e(ji,jj) = ( hu_e (ji,jj) * un_e (ji,jj) &
662	& + rdtbt * ( zhu_bck * zu_spg (ji,jj) & !
663	& + zhup2_e(ji,jj) * zu_trd (ji,jj) & !
664	& + hu_n (ji,jj) * zu_frc (ji,jj) ) ) * z1_hu
665	!
666	va_e(ji,jj) = ( hv_e (ji,jj) * vn_e (ji,jj) &
667	& + rdtbt * ( zhv_bck * zv_spg (ji,jj) & !
668	& + zhvp2_e(ji,jj) * zv_trd (ji,jj) & !
669	& + hv_n (ji,jj) * zv_frc (ji,jj) ) ) * z1_hv
670	END DO
671	END DO
672	ENDIF
673	!jth implicit bottom friction:
674	IF ( ll_wd ) THEN ! revert to explicit for bit comparison tests in non wad runs
675	DO jj = 2, jpjm1
676	DO ji = fs_2, fs_jpim1 ! vector opt.
677	ua_e(ji,jj) = ua_e(ji,jj) /(1.0 - rdtbt * zCdU_u(ji,jj) * hur_e(ji,jj))
678	va_e(ji,jj) = va_e(ji,jj) /(1.0 - rdtbt * zCdU_v(ji,jj) * hvr_e(ji,jj))
679	END DO
680	END DO
681	ENDIF
682
683	IF( .NOT.ln_linssh ) THEN !* Update ocean depth (variable volume case only)
684	hu_e (2:jpim1,2:jpjm1) = hu_0(2:jpim1,2:jpjm1) + zsshu_a(2:jpim1,2:jpjm1)
685	hur_e(2:jpim1,2:jpjm1) = ssumask(2:jpim1,2:jpjm1) / ( hu_e(2:jpim1,2:jpjm1) + 1._wp - ssumask(2:jpim1,2:jpjm1) )
686	hv_e (2:jpim1,2:jpjm1) = hv_0(2:jpim1,2:jpjm1) + zsshv_a(2:jpim1,2:jpjm1)
687	hvr_e(2:jpim1,2:jpjm1) = ssvmask(2:jpim1,2:jpjm1) / ( hv_e(2:jpim1,2:jpjm1) + 1._wp - ssvmask(2:jpim1,2:jpjm1) )
688	CALL lbc_lnk_multi( 'dynspg_ts', ua_e , 'U', -1._wp, va_e , 'V', -1._wp &
689	& , hu_e , 'U', -1._wp, hv_e , 'V', -1._wp &
690	& , hur_e, 'U', -1._wp, hvr_e, 'V', -1._wp )
691	ELSE
692	CALL lbc_lnk_multi( 'dynspg_ts', ua_e , 'U', -1._wp, va_e , 'V', -1._wp )
693	ENDIF
694	!
695	!
696	! ! open boundaries
697	IF( ln_bdy ) CALL bdy_dyn2d( jn, ua_e, va_e, un_e, vn_e, hur_e, hvr_e, ssha_e )
698	#if defined key_agrif
699	IF( .NOT.Agrif_Root() ) CALL agrif_dyn_ts( jn ) ! Agrif
700	#endif
701	! !* Swap
702	! ! ----
703	ubb_e (:,:) = ub_e (:,:)
704	ub_e (:,:) = un_e (:,:)
705	un_e (:,:) = ua_e (:,:)
706	!
707	vbb_e (:,:) = vb_e (:,:)
708	vb_e (:,:) = vn_e (:,:)
709	vn_e (:,:) = va_e (:,:)
710	!
711	sshbb_e(:,:) = sshb_e(:,:)
712	sshb_e (:,:) = sshn_e(:,:)
713	sshn_e (:,:) = ssha_e(:,:)
714
715	! !* Sum over whole bt loop
716	! ! ----------------------
717	za1 = wgtbtp1(jn)
718	IF( ln_dynadv_vec .OR. ln_linssh ) THEN ! Sum velocities
719	ua_b (:,:) = ua_b (:,:) + za1 * ua_e (:,:)
720	va_b (:,:) = va_b (:,:) + za1 * va_e (:,:)
721	ELSE ! Sum transports
722	IF ( .NOT.ln_wd_dl ) THEN
723	ua_b (:,:) = ua_b (:,:) + za1 * ua_e (:,:) * hu_e (:,:)
724	va_b (:,:) = va_b (:,:) + za1 * va_e (:,:) * hv_e (:,:)
725	ELSE
726	ua_b (:,:) = ua_b (:,:) + za1 * ua_e (:,:) * hu_e (:,:) * zuwdmask(:,:)
727	va_b (:,:) = va_b (:,:) + za1 * va_e (:,:) * hv_e (:,:) * zvwdmask(:,:)
728	END IF
729	ENDIF
730	! ! Sum sea level
731	ssha(:,:) = ssha(:,:) + za1 * ssha_e(:,:)
732
733	! ! ==================== !
734	END DO ! end loop !
735	! ! ==================== !
736	! -----------------------------------------------------------------------------
737	! Phase 3. update the general trend with the barotropic trend
738	! -----------------------------------------------------------------------------
739	!
740	! Set advection velocity correction:
741	IF (ln_bt_fw) THEN
742	IF( .NOT.( kt == nit000 .AND. neuler==0 ) ) THEN
743	DO jj = 1, jpj
744	DO ji = 1, jpi
745	zun_save = un_adv(ji,jj)
746	zvn_save = vn_adv(ji,jj)
747	! ! apply the previously computed correction
748	un_adv(ji,jj) = r1_2 * ( ub2_b(ji,jj) + zun_save - atfp * un_bf(ji,jj) )
749	vn_adv(ji,jj) = r1_2 * ( vb2_b(ji,jj) + zvn_save - atfp * vn_bf(ji,jj) )
750	! ! Update corrective fluxes for next time step
751	un_bf(ji,jj) = atfp * un_bf(ji,jj) + ( zun_save - ub2_b(ji,jj) )
752	vn_bf(ji,jj) = atfp * vn_bf(ji,jj) + ( zvn_save - vb2_b(ji,jj) )
753	! ! Save integrated transport for next computation
754	ub2_b(ji,jj) = zun_save
755	vb2_b(ji,jj) = zvn_save
756	END DO
757	END DO
758	ELSE
759	un_bf(:,:) = 0._wp ! corrective fluxes for next time step set to zero
760	vn_bf(:,:) = 0._wp
761	ub2_b(:,:) = un_adv(:,:) ! Save integrated transport for next computation
762	vb2_b(:,:) = vn_adv(:,:)
763	END IF
764	ENDIF
765
766
767	!
768	! Update barotropic trend:
769	IF( ln_dynadv_vec .OR. ln_linssh ) THEN
770	DO jk=1,jpkm1
771	ua(:,:,jk) = ua(:,:,jk) + ( ua_b(:,:) - ub_b(:,:) ) * r1_2dt_b
772	va(:,:,jk) = va(:,:,jk) + ( va_b(:,:) - vb_b(:,:) ) * r1_2dt_b
773	END DO
774	ELSE
775	! At this stage, ssha has been corrected: compute new depths at velocity points
776	DO jj = 1, jpjm1
777	DO ji = 1, jpim1 ! NO Vector Opt.
778	zsshu_a(ji,jj) = r1_2 * ssumask(ji,jj) * r1_e1e2u(ji,jj) &
779	& * ( e1e2t(ji ,jj) * ssha(ji ,jj) &
780	& + e1e2t(ji+1,jj) * ssha(ji+1,jj) )
781	zsshv_a(ji,jj) = r1_2 * ssvmask(ji,jj) * r1_e1e2v(ji,jj) &
782	& * ( e1e2t(ji,jj ) * ssha(ji,jj ) &
783	& + e1e2t(ji,jj+1) * ssha(ji,jj+1) )
784	END DO
785	END DO
786	CALL lbc_lnk_multi( 'dynspg_ts', zsshu_a, 'U', 1._wp, zsshv_a, 'V', 1._wp ) ! Boundary conditions
787	!
788	DO jk=1,jpkm1
789	ua(:,:,jk) = ua(:,:,jk) + r1_hu_n(:,:) * ( ua_b(:,:) - ub_b(:,:) * hu_b(:,:) ) * r1_2dt_b
790	va(:,:,jk) = va(:,:,jk) + r1_hv_n(:,:) * ( va_b(:,:) - vb_b(:,:) * hv_b(:,:) ) * r1_2dt_b
791	END DO
792	! Save barotropic velocities not transport:
793	ua_b(:,:) = ua_b(:,:) / ( hu_0(:,:) + zsshu_a(:,:) + 1._wp - ssumask(:,:) )
794	va_b(:,:) = va_b(:,:) / ( hv_0(:,:) + zsshv_a(:,:) + 1._wp - ssvmask(:,:) )
795	ENDIF
796
797
798	! Correct velocities so that the barotropic velocity equals (un_adv, vn_adv) (in all cases)
799	DO jk = 1, jpkm1
800	un(:,:,jk) = ( un(:,:,jk) + un_adv(:,:)r1_hu_n(:,:) - un_b(:,:) ) umask(:,:,jk)
801	vn(:,:,jk) = ( vn(:,:,jk) + vn_adv(:,:)r1_hv_n(:,:) - vn_b(:,:) ) vmask(:,:,jk)
802	END DO
803
804	IF ( ln_wd_dl .and. ln_wd_dl_bc) THEN
805	! need to set lbc here because not done prior time averaging
806	CALL lbc_lnk_multi( 'dynspg_ts', zuwdav2, 'U', 1._wp, zvwdav2, 'V', 1._wp)
807	DO jk = 1, jpkm1
808	un(:,:,jk) = ( un_adv(:,:)*r1_hu_n(:,:) &
809	& + zuwdav2(:,:)(un(:,:,jk) - un_adv(:,:)r1_hu_n(:,:)) ) * umask(:,:,jk)
810	vn(:,:,jk) = ( vn_adv(:,:)*r1_hv_n(:,:) &
811	& + zvwdav2(:,:)(vn(:,:,jk) - vn_adv(:,:)r1_hv_n(:,:)) ) * vmask(:,:,jk)
812	END DO
813	END IF
814
815
816	CALL iom_put( "ubar", un_adv(:,:)*r1_hu_n(:,:) ) ! barotropic i-current
817	CALL iom_put( "vbar", vn_adv(:,:)*r1_hv_n(:,:) ) ! barotropic i-current
818	!
819	#if defined key_agrif
820	! Save time integrated fluxes during child grid integration
821	! (used to update coarse grid transports at next time step)
822	!
823	IF( .NOT.Agrif_Root() .AND. ln_bt_fw ) THEN
824	IF( Agrif_NbStepint() == 0 ) THEN
825	ub2_i_b(:,:) = 0._wp
826	vb2_i_b(:,:) = 0._wp
827	END IF
828	!
829	za1 = 1._wp / REAL(Agrif_rhot(), wp)
830	ub2_i_b(:,:) = ub2_i_b(:,:) + za1 * ub2_b(:,:)
831	vb2_i_b(:,:) = vb2_i_b(:,:) + za1 * vb2_b(:,:)
832	ENDIF
833	#endif
834	! !* write time-spliting arrays in the restart
835	IF( lrst_oce .AND.ln_bt_fw ) CALL ts_rst( kt, 'WRITE' )
836	!
837	IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy )
838	IF( ln_wd_dl ) DEALLOCATE( ztwdmask, zuwdmask, zvwdmask, zuwdav2, zvwdav2 )
839	!
840	IF( ln_diatmb ) THEN
841	CALL iom_put( "baro_u" , un_bssumask(:,:)+zmdi(1.-ssumask(:,:) ) ) ! Barotropic U Velocity
842	CALL iom_put( "baro_v" , vn_bssvmask(:,:)+zmdi(1.-ssvmask(:,:) ) ) ! Barotropic V Velocity
843	ENDIF
844	!
845	END SUBROUTINE dyn_spg_ts
846
847
848	SUBROUTINE ts_wgt( ll_av, ll_fw, jpit, zwgt1, zwgt2)
849	!!---------------------------------------------------------------------
850	!! * ROUTINE ts_wgt *
851	!!
852	!! ** Purpose : Set time-splitting weights for temporal averaging (or not)
853	!!----------------------------------------------------------------------
854	LOGICAL, INTENT(in) :: ll_av ! temporal averaging=.true.
855	LOGICAL, INTENT(in) :: ll_fw ! forward time splitting =.true.
856	INTEGER, INTENT(inout) :: jpit ! cycle length
857	REAL(wp), DIMENSION(3*nn_baro), INTENT(inout) :: zwgt1, & ! Primary weights
858	zwgt2 ! Secondary weights
859
860	INTEGER :: jic, jn, ji ! temporary integers
861	REAL(wp) :: za1, za2
862	!!----------------------------------------------------------------------
863
864	zwgt1(:) = 0._wp
865	zwgt2(:) = 0._wp
866
867	! Set time index when averaged value is requested
868	IF (ll_fw) THEN
869	jic = nn_baro
870	ELSE
871	jic = 2 * nn_baro
872	ENDIF
873
874	! Set primary weights:
875	IF (ll_av) THEN
876	! Define simple boxcar window for primary weights
877	! (width = nn_baro, centered around jic)
878	SELECT CASE ( nn_bt_flt )
879	CASE( 0 ) ! No averaging
880	zwgt1(jic) = 1._wp
881	jpit = jic
882
883	CASE( 1 ) ! Boxcar, width = nn_baro
884	DO jn = 1, 3*nn_baro
885	za1 = ABS(float(jn-jic))/float(nn_baro)
886	IF (za1 < 0.5_wp) THEN
887	zwgt1(jn) = 1._wp
888	jpit = jn
889	ENDIF
890	ENDDO
891
892	CASE( 2 ) ! Boxcar, width = 2 * nn_baro
893	DO jn = 1, 3*nn_baro
894	za1 = ABS(float(jn-jic))/float(nn_baro)
895	IF (za1 < 1._wp) THEN
896	zwgt1(jn) = 1._wp
897	jpit = jn
898	ENDIF
899	ENDDO
900	CASE DEFAULT ; CALL ctl_stop( 'unrecognised value for nn_bt_flt' )
901	END SELECT
902
903	ELSE ! No time averaging
904	zwgt1(jic) = 1._wp
905	jpit = jic
906	ENDIF
907
908	! Set secondary weights
909	DO jn = 1, jpit
910	DO ji = jn, jpit
911	zwgt2(jn) = zwgt2(jn) + zwgt1(ji)
912	END DO
913	END DO
914
915	! Normalize weigths:
916	za1 = 1._wp / SUM(zwgt1(1:jpit))
917	za2 = 1._wp / SUM(zwgt2(1:jpit))
918	DO jn = 1, jpit
919	zwgt1(jn) = zwgt1(jn) * za1
920	zwgt2(jn) = zwgt2(jn) * za2
921	END DO
922	!
923	END SUBROUTINE ts_wgt
924
925
926	SUBROUTINE ts_rst( kt, cdrw )
927	!!---------------------------------------------------------------------
928	!! * ROUTINE ts_rst *
929	!!
930	!! ** Purpose : Read or write time-splitting arrays in restart file
931	!!----------------------------------------------------------------------
932	INTEGER , INTENT(in) :: kt ! ocean time-step
933	CHARACTER(len=*), INTENT(in) :: cdrw ! "READ"/"WRITE" flag
934	!!----------------------------------------------------------------------
935	!
936	IF( TRIM(cdrw) == 'READ' ) THEN ! Read/initialise
937	! ! ---------------
938	IF( ln_rstart .AND. ln_bt_fw .AND. (neuler/=0) ) THEN !* Read the restart file
939	CALL iom_get( numror, jpdom_autoglo, 'ub2_b' , ub2_b (:,:), ldxios = lrxios )
940	CALL iom_get( numror, jpdom_autoglo, 'vb2_b' , vb2_b (:,:), ldxios = lrxios )
941	CALL iom_get( numror, jpdom_autoglo, 'un_bf' , un_bf (:,:), ldxios = lrxios )
942	CALL iom_get( numror, jpdom_autoglo, 'vn_bf' , vn_bf (:,:), ldxios = lrxios )
943	IF( .NOT.ln_bt_av ) THEN
944	CALL iom_get( numror, jpdom_autoglo, 'sshbb_e' , sshbb_e(:,:), ldxios = lrxios )
945	CALL iom_get( numror, jpdom_autoglo, 'ubb_e' , ubb_e(:,:), ldxios = lrxios )
946	CALL iom_get( numror, jpdom_autoglo, 'vbb_e' , vbb_e(:,:), ldxios = lrxios )
947	CALL iom_get( numror, jpdom_autoglo, 'sshb_e' , sshb_e(:,:), ldxios = lrxios )
948	CALL iom_get( numror, jpdom_autoglo, 'ub_e' , ub_e(:,:), ldxios = lrxios )
949	CALL iom_get( numror, jpdom_autoglo, 'vb_e' , vb_e(:,:), ldxios = lrxios )
950	ENDIF
951	#if defined key_agrif
952	! Read time integrated fluxes
953	IF ( .NOT.Agrif_Root() ) THEN
954	CALL iom_get( numror, jpdom_autoglo, 'ub2_i_b' , ub2_i_b(:,:), ldxios = lrxios )
955	CALL iom_get( numror, jpdom_autoglo, 'vb2_i_b' , vb2_i_b(:,:), ldxios = lrxios )
956	ENDIF
957	#endif
958	ELSE !* Start from rest
959	IF(lwp) WRITE(numout,*)
960	IF(lwp) WRITE(numout,*) ' ==>>> start from rest: set barotropic values to 0'
961	ub2_b (:,:) = 0._wp ; vb2_b (:,:) = 0._wp ! used in the 1st interpol of agrif
962	un_adv(:,:) = 0._wp ; vn_adv(:,:) = 0._wp ! used in the 1st interpol of agrif
963	un_bf (:,:) = 0._wp ; vn_bf (:,:) = 0._wp ! used in the 1st update of agrif
964	#if defined key_agrif
965	IF ( .NOT.Agrif_Root() ) THEN
966	ub2_i_b(:,:) = 0._wp ; vb2_i_b(:,:) = 0._wp ! used in the 1st update of agrif
967	ENDIF
968	#endif
969	ENDIF
970	!
971	ELSEIF( TRIM(cdrw) == 'WRITE' ) THEN ! Create restart file
972	! ! -------------------
973	IF(lwp) WRITE(numout,*) '---- ts_rst ----'
974	IF( lwxios ) CALL iom_swap( cwxios_context )
975	CALL iom_rstput( kt, nitrst, numrow, 'ub2_b' , ub2_b (:,:), ldxios = lwxios )
976	CALL iom_rstput( kt, nitrst, numrow, 'vb2_b' , vb2_b (:,:), ldxios = lwxios )
977	CALL iom_rstput( kt, nitrst, numrow, 'un_bf' , un_bf (:,:), ldxios = lwxios )
978	CALL iom_rstput( kt, nitrst, numrow, 'vn_bf' , vn_bf (:,:), ldxios = lwxios )
979	!
980	IF (.NOT.ln_bt_av) THEN
981	CALL iom_rstput( kt, nitrst, numrow, 'sshbb_e' , sshbb_e(:,:), ldxios = lwxios )
982	CALL iom_rstput( kt, nitrst, numrow, 'ubb_e' , ubb_e(:,:), ldxios = lwxios )
983	CALL iom_rstput( kt, nitrst, numrow, 'vbb_e' , vbb_e(:,:), ldxios = lwxios )
984	CALL iom_rstput( kt, nitrst, numrow, 'sshb_e' , sshb_e(:,:), ldxios = lwxios )
985	CALL iom_rstput( kt, nitrst, numrow, 'ub_e' , ub_e(:,:), ldxios = lwxios )
986	CALL iom_rstput( kt, nitrst, numrow, 'vb_e' , vb_e(:,:), ldxios = lwxios )
987	ENDIF
988	#if defined key_agrif
989	! Save time integrated fluxes
990	IF ( .NOT.Agrif_Root() ) THEN
991	CALL iom_rstput( kt, nitrst, numrow, 'ub2_i_b' , ub2_i_b(:,:), ldxios = lwxios )
992	CALL iom_rstput( kt, nitrst, numrow, 'vb2_i_b' , vb2_i_b(:,:), ldxios = lwxios )
993	ENDIF
994	#endif
995	IF( lwxios ) CALL iom_swap( cxios_context )
996	ENDIF
997	!
998	END SUBROUTINE ts_rst
999
1000
1001	SUBROUTINE dyn_spg_ts_init
1002	!!---------------------------------------------------------------------
1003	!! * ROUTINE dyn_spg_ts_init *
1004	!!
1005	!! ** Purpose : Set time splitting options
1006	!!----------------------------------------------------------------------
1007	INTEGER :: ji ,jj ! dummy loop indices
1008	REAL(wp) :: zxr2, zyr2, zcmax ! local scalar
1009	REAL(wp), DIMENSION(jpi,jpj) :: zcu
1010	INTEGER :: inum
1011	!!----------------------------------------------------------------------
1012	!
1013	! Max courant number for ext. grav. waves
1014	!
1015	DO jj = 1, jpj
1016	DO ji =1, jpi
1017	zxr2 = r1_e1t(ji,jj) * r1_e1t(ji,jj)
1018	zyr2 = r1_e2t(ji,jj) * r1_e2t(ji,jj)
1019	zcu(ji,jj) = SQRT( grav * MAX(ht_0(ji,jj),0._wp) * (zxr2 + zyr2) )
1020	END DO
1021	END DO
1022	!
1023	zcmax = MAXVAL( zcu(:,:) )
1024	CALL mpp_max( 'dynspg_ts', zcmax )
1025
1026	! Estimate number of iterations to satisfy a max courant number= rn_bt_cmax
1027	IF( ln_bt_auto ) nn_baro = CEILING( rdt / rn_bt_cmax * zcmax)
1028
1029	rdtbt = rdt / REAL( nn_baro , wp )
1030	zcmax = zcmax * rdtbt
1031	! Print results
1032	IF(lwp) WRITE(numout,*)
1033	IF(lwp) WRITE(numout,*) 'dyn_spg_ts_init : split-explicit free surface'
1034	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~~'
1035	IF( ln_bt_auto ) THEN
1036	IF(lwp) WRITE(numout,*) ' ln_ts_auto =.true. Automatically set nn_baro '
1037	IF(lwp) WRITE(numout,*) ' Max. courant number allowed: ', rn_bt_cmax
1038	ELSE
1039	IF(lwp) WRITE(numout,*) ' ln_ts_auto=.false.: Use nn_baro in namelist nn_baro = ', nn_baro
1040	ENDIF
1041
1042	IF(ln_bt_av) THEN
1043	IF(lwp) WRITE(numout,*) ' ln_bt_av =.true. ==> Time averaging over nn_baro time steps is on '
1044	ELSE
1045	IF(lwp) WRITE(numout,*) ' ln_bt_av =.false. => No time averaging of barotropic variables '
1046	ENDIF
1047	!
1048	!
1049	IF(ln_bt_fw) THEN
1050	IF(lwp) WRITE(numout,*) ' ln_bt_fw=.true. => Forward integration of barotropic variables '
1051	ELSE
1052	IF(lwp) WRITE(numout,*) ' ln_bt_fw =.false.=> Centred integration of barotropic variables '
1053	ENDIF
1054	!
1055	#if defined key_agrif
1056	! Restrict the use of Agrif to the forward case only
1057	!!! IF( .NOT.ln_bt_fw .AND. .NOT.Agrif_Root() ) CALL ctl_stop( 'AGRIF not implemented if ln_bt_fw=.FALSE.' )
1058	#endif
1059	!
1060	IF(lwp) WRITE(numout,*) ' Time filter choice, nn_bt_flt: ', nn_bt_flt
1061	SELECT CASE ( nn_bt_flt )
1062	CASE( 0 ) ; IF(lwp) WRITE(numout,*) ' Dirac'
1063	CASE( 1 ) ; IF(lwp) WRITE(numout,*) ' Boxcar: width = nn_baro'
1064	CASE( 2 ) ; IF(lwp) WRITE(numout,) ' Boxcar: width = 2nn_baro'
1065	CASE DEFAULT ; CALL ctl_stop( 'unrecognised value for nn_bt_flt: should 0,1, or 2' )
1066	END SELECT
1067	!
1068	IF(lwp) WRITE(numout,*) ' '
1069	IF(lwp) WRITE(numout,*) ' nn_baro = ', nn_baro
1070	IF(lwp) WRITE(numout,*) ' Barotropic time step [s] is :', rdtbt
1071	IF(lwp) WRITE(numout,*) ' Maximum Courant number is :', zcmax
1072	!
1073	IF(lwp) WRITE(numout,*) ' Time diffusion parameter rn_bt_alpha: ', rn_bt_alpha
1074	IF ((ln_bt_av.AND.nn_bt_flt/=0).AND.(rn_bt_alpha>0._wp)) THEN
1075	CALL ctl_stop( 'dynspg_ts ERROR: if rn_bt_alpha > 0, remove temporal averaging' )
1076	ENDIF
1077	!
1078	IF( .NOT.ln_bt_av .AND. .NOT.ln_bt_fw ) THEN
1079	CALL ctl_stop( 'dynspg_ts ERROR: No time averaging => only forward integration is possible' )
1080	ENDIF
1081	IF( zcmax>0.9_wp ) THEN
1082	CALL ctl_stop( 'dynspg_ts ERROR: Maximum Courant number is greater than 0.9: Inc. nn_baro !' )
1083	ENDIF
1084	!
1085	! ! Allocate time-splitting arrays
1086	IF( dyn_spg_ts_alloc() /= 0 ) CALL ctl_stop('STOP', 'dyn_spg_init: failed to allocate dynspg_ts arrays' )
1087	!
1088	! ! read restart when needed
1089	CALL ts_rst( nit000, 'READ' )
1090	!
1091	IF( lwxios ) THEN
1092	! define variables in restart file when writing with XIOS
1093	CALL iom_set_rstw_var_active('ub2_b')
1094	CALL iom_set_rstw_var_active('vb2_b')
1095	CALL iom_set_rstw_var_active('un_bf')
1096	CALL iom_set_rstw_var_active('vn_bf')
1097	!
1098	IF (.NOT.ln_bt_av) THEN
1099	CALL iom_set_rstw_var_active('sshbb_e')
1100	CALL iom_set_rstw_var_active('ubb_e')
1101	CALL iom_set_rstw_var_active('vbb_e')
1102	CALL iom_set_rstw_var_active('sshb_e')
1103	CALL iom_set_rstw_var_active('ub_e')
1104	CALL iom_set_rstw_var_active('vb_e')
1105	ENDIF
1106	#if defined key_agrif
1107	! Save time integrated fluxes
1108	IF ( .NOT.Agrif_Root() ) THEN
1109	CALL iom_set_rstw_var_active('ub2_i_b')
1110	CALL iom_set_rstw_var_active('vb2_i_b')
1111	ENDIF
1112	#endif
1113	ENDIF
1114	!
1115	END SUBROUTINE dyn_spg_ts_init
1116
1117
1118	SUBROUTINE dyn_cor_2d_init
1119	!!---------------------------------------------------------------------
1120	!! * ROUTINE dyn_cor_2d_init *
1121	!!
1122	!! ** Purpose : Set time splitting options
1123	!! Set arrays to remove/compute coriolis trend.
1124	!! Do it once during initialization if volume is fixed, else at each long time step.
1125	!! Note that these arrays are also used during barotropic loop. These are however frozen
1126	!! although they should be updated in the variable volume case. Not a big approximation.
1127	!! To remove this approximation, copy lines below inside barotropic loop
1128	!! and update depths at T-F points (ht and zhf resp.) at each barotropic time step
1129	!!
1130	!! Compute zwz = f / ( height of the water colomn )
1131	!!----------------------------------------------------------------------
1132	INTEGER :: ji ,jj, jk ! dummy loop indices
1133	REAL(wp) :: z1_ht
1134	REAL(wp), DIMENSION(jpi,jpj) :: zhf
1135	!!----------------------------------------------------------------------
1136	!
1137	SELECT CASE( nvor_scheme )
1138	CASE( np_EEN ) != EEN scheme using e3f (energy & enstrophy scheme)
1139	SELECT CASE( nn_een_e3f ) !* ff_f/e3 at F-point
1140	CASE ( 0 ) ! original formulation (masked averaging of e3t divided by 4)
1141	DO jj = 1, jpjm1
1142	DO ji = 1, jpim1
1143	zwz(ji,jj) = ( ht_n(ji ,jj+1) + ht_n(ji+1,jj+1) + &
1144	& ht_n(ji ,jj ) + ht_n(ji+1,jj ) ) * 0.25_wp
1145	IF( zwz(ji,jj) /= 0._wp ) zwz(ji,jj) = ff_f(ji,jj) / zwz(ji,jj)
1146	END DO
1147	END DO
1148	CASE ( 1 ) ! new formulation (masked averaging of e3t divided by the sum of mask)
1149	DO jj = 1, jpjm1
1150	DO ji = 1, jpim1
1151	zwz(ji,jj) = ( ht_n (ji ,jj+1) + ht_n (ji+1,jj+1) &
1152	& + ht_n (ji ,jj ) + ht_n (ji+1,jj ) ) &
1153	& / ( MAX( 1._wp, ssmask(ji ,jj+1) + ssmask(ji+1,jj+1) &
1154	& + ssmask(ji ,jj ) + ssmask(ji+1,jj ) ) )
1155	IF( zwz(ji,jj) /= 0._wp ) zwz(ji,jj) = ff_f(ji,jj) / zwz(ji,jj)
1156	END DO
1157	END DO
1158	END SELECT
1159	CALL lbc_lnk( 'dynspg_ts', zwz, 'F', 1._wp )
1160	!
1161	ftne(1,:) = 0._wp ; ftnw(1,:) = 0._wp ; ftse(1,:) = 0._wp ; ftsw(1,:) = 0._wp
1162	DO jj = 2, jpj
1163	DO ji = 2, jpi
1164	ftne(ji,jj) = zwz(ji-1,jj ) + zwz(ji ,jj ) + zwz(ji ,jj-1)
1165	ftnw(ji,jj) = zwz(ji-1,jj-1) + zwz(ji-1,jj ) + zwz(ji ,jj )
1166	ftse(ji,jj) = zwz(ji ,jj ) + zwz(ji ,jj-1) + zwz(ji-1,jj-1)
1167	ftsw(ji,jj) = zwz(ji ,jj-1) + zwz(ji-1,jj-1) + zwz(ji-1,jj )
1168	END DO
1169	END DO
1170	!
1171	CASE( np_EET ) != EEN scheme using e3t (energy conserving scheme)
1172	ftne(1,:) = 0._wp ; ftnw(1,:) = 0._wp ; ftse(1,:) = 0._wp ; ftsw(1,:) = 0._wp
1173	DO jj = 2, jpj
1174	DO ji = 2, jpi
1175	z1_ht = ssmask(ji,jj) / ( ht_n(ji,jj) + 1._wp - ssmask(ji,jj) )
1176	ftne(ji,jj) = ( ff_f(ji-1,jj ) + ff_f(ji ,jj ) + ff_f(ji ,jj-1) ) * z1_ht
1177	ftnw(ji,jj) = ( ff_f(ji-1,jj-1) + ff_f(ji-1,jj ) + ff_f(ji ,jj ) ) * z1_ht
1178	ftse(ji,jj) = ( ff_f(ji ,jj ) + ff_f(ji ,jj-1) + ff_f(ji-1,jj-1) ) * z1_ht
1179	ftsw(ji,jj) = ( ff_f(ji ,jj-1) + ff_f(ji-1,jj-1) + ff_f(ji-1,jj ) ) * z1_ht
1180	END DO
1181	END DO
1182	!
1183	CASE( np_ENE, np_ENS , np_MIX ) != all other schemes (ENE, ENS, MIX) except ENT !
1184	!
1185	zwz(:,:) = 0._wp
1186	zhf(:,:) = 0._wp
1187
1188	!!gm assume 0 in both cases (which is almost surely WRONG ! ) as hvatf has been removed
1189	!!gm A priori a better value should be something like :
1190	!!gm zhf(i,j) = masked sum of ht(i,j) , ht(i+1,j) , ht(i,j+1) , (i+1,j+1)
1191	!!gm divided by the sum of the corresponding mask
1192	!!gm
1193	!!
1194	IF( .NOT.ln_sco ) THEN
1195
1196	!!gm agree the JC comment : this should be done in a much clear way
1197
1198	! JC: It not clear yet what should be the depth at f-points over land in z-coordinate case
1199	! Set it to zero for the time being
1200	! IF( rn_hmin < 0._wp ) THEN ; jk = - INT( rn_hmin ) ! from a nb of level
1201	! ELSE ; jk = MINLOC( gdepw_0, mask = gdepw_0 > rn_hmin, dim = 1 ) ! from a depth
1202	! ENDIF
1203	! zhf(:,:) = gdepw_0(:,:,jk+1)
1204	!
1205	ELSE
1206	!
1207	!zhf(:,:) = hbatf(:,:)
1208	DO jj = 1, jpjm1
1209	DO ji = 1, jpim1
1210	zhf(ji,jj) = ( ht_0 (ji,jj ) + ht_0 (ji+1,jj ) &
1211	& + ht_0 (ji,jj+1) + ht_0 (ji+1,jj+1) ) &
1212	& / MAX( ssmask(ji,jj ) + ssmask(ji+1,jj ) &
1213	& + ssmask(ji,jj+1) + ssmask(ji+1,jj+1) , 1._wp )
1214	END DO
1215	END DO
1216	ENDIF
1217	!
1218	DO jj = 1, jpjm1
1219	zhf(:,jj) = zhf(:,jj) * (1._wp- umask(:,jj,1) * umask(:,jj+1,1))
1220	END DO
1221	!
1222	DO jk = 1, jpkm1
1223	DO jj = 1, jpjm1
1224	zhf(:,jj) = zhf(:,jj) + e3f_n(:,jj,jk) * umask(:,jj,jk) * umask(:,jj+1,jk)
1225	END DO
1226	END DO
1227	CALL lbc_lnk( 'dynspg_ts', zhf, 'F', 1._wp )
1228	! JC: TBC. hf should be greater than 0
1229	DO jj = 1, jpj
1230	DO ji = 1, jpi
1231	IF( zhf(ji,jj) /= 0._wp ) zwz(ji,jj) = 1._wp / zhf(ji,jj)
1232	END DO
1233	END DO
1234	zwz(:,:) = ff_f(:,:) * zwz(:,:)
1235	END SELECT
1236
1237	END SUBROUTINE dyn_cor_2d_init
1238
1239
1240
1241	SUBROUTINE dyn_cor_2d( hu_n, hv_n, un_b, vn_b, zhU, zhV, zu_trd, zv_trd )
1242	!!---------------------------------------------------------------------
1243	!! * ROUTINE dyn_cor_2d *
1244	!!
1245	!! ** Purpose : Compute u and v coriolis trends
1246	!!----------------------------------------------------------------------
1247	INTEGER :: ji ,jj ! dummy loop indices
1248	REAL(wp) :: zx1, zx2, zy1, zy2, z1_hu, z1_hv ! - -
1249	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: hu_n, hv_n, un_b, vn_b, zhU, zhV
1250	REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: zu_trd, zv_trd
1251	!!----------------------------------------------------------------------
1252	SELECT CASE( nvor_scheme )
1253	CASE( np_ENT ) ! enstrophy conserving scheme (f-point)
1254	DO jj = 2, jpjm1
1255	DO ji = 2, jpim1
1256	z1_hu = ssumask(ji,jj) / ( hu_n(ji,jj) + 1._wp - ssumask(ji,jj) )
1257	z1_hv = ssvmask(ji,jj) / ( hv_n(ji,jj) + 1._wp - ssvmask(ji,jj) )
1258	zu_trd(ji,jj) = + r1_4 * r1_e1e2u(ji,jj) * z1_hu &
1259	& * ( 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) ) &
1260	& + e1e2t(ji ,jj)ht_n(ji ,jj)ff_t(ji ,jj) * ( vn_b(ji ,jj) + vn_b(ji ,jj-1) ) )
1261	!
1262	zv_trd(ji,jj) = - r1_4 * r1_e1e2v(ji,jj) * z1_hv &
1263	& * ( 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) ) &
1264	& + e1e2t(ji,jj )ht_n(ji,jj )ff_t(ji,jj ) * ( un_b(ji,jj ) + un_b(ji-1,jj ) ) )
1265	END DO
1266	END DO
1267	!
1268	CASE( np_ENE , np_MIX ) ! energy conserving scheme (t-point) ENE or MIX
1269	DO jj = 2, jpjm1
1270	DO ji = fs_2, fs_jpim1 ! vector opt.
1271	zy1 = ( zhV(ji,jj-1) + zhV(ji+1,jj-1) ) * r1_e1u(ji,jj)
1272	zy2 = ( zhV(ji,jj ) + zhV(ji+1,jj ) ) * r1_e1u(ji,jj)
1273	zx1 = ( zhU(ji-1,jj) + zhU(ji-1,jj+1) ) * r1_e2v(ji,jj)
1274	zx2 = ( zhU(ji ,jj) + zhU(ji ,jj+1) ) * r1_e2v(ji,jj)
1275	! energy conserving formulation for planetary vorticity term
1276	zu_trd(ji,jj) = r1_4 * ( zwz(ji ,jj-1) * zy1 + zwz(ji,jj) * zy2 )
1277	zv_trd(ji,jj) = - r1_4 * ( zwz(ji-1,jj ) * zx1 + zwz(ji,jj) * zx2 )
1278	END DO
1279	END DO
1280	!
1281	CASE( np_ENS ) ! enstrophy conserving scheme (f-point)
1282	DO jj = 2, jpjm1
1283	DO ji = fs_2, fs_jpim1 ! vector opt.
1284	zy1 = r1_8 * ( zhV(ji ,jj-1) + zhV(ji+1,jj-1) &
1285	& + zhV(ji ,jj ) + zhV(ji+1,jj ) ) * r1_e1u(ji,jj)
1286	zx1 = - r1_8 * ( zhU(ji-1,jj ) + zhU(ji-1,jj+1) &
1287	& + zhU(ji ,jj ) + zhU(ji ,jj+1) ) * r1_e2v(ji,jj)
1288	zu_trd(ji,jj) = zy1 * ( zwz(ji ,jj-1) + zwz(ji,jj) )
1289	zv_trd(ji,jj) = zx1 * ( zwz(ji-1,jj ) + zwz(ji,jj) )
1290	END DO
1291	END DO
1292	!
1293	CASE( np_EET , np_EEN ) ! energy & enstrophy scheme (using e3t or e3f)
1294	DO jj = 2, jpjm1
1295	DO ji = fs_2, fs_jpim1 ! vector opt.
1296	zu_trd(ji,jj) = + r1_12 * r1_e1u(ji,jj) * ( ftne(ji,jj ) * zhV(ji ,jj ) &
1297	& + ftnw(ji+1,jj) * zhV(ji+1,jj ) &
1298	& + ftse(ji,jj ) * zhV(ji ,jj-1) &
1299	& + ftsw(ji+1,jj) * zhV(ji+1,jj-1) )
1300	zv_trd(ji,jj) = - r1_12 * r1_e2v(ji,jj) * ( ftsw(ji,jj+1) * zhU(ji-1,jj+1) &
1301	& + ftse(ji,jj+1) * zhU(ji ,jj+1) &
1302	& + ftnw(ji,jj ) * zhU(ji-1,jj ) &
1303	& + ftne(ji,jj ) * zhU(ji ,jj ) )
1304	END DO
1305	END DO
1306	!
1307	END SELECT
1308	!
1309	END SUBROUTINE dyn_cor_2D
1310
1311
1312	SUBROUTINE wad_tmsk( pssh, ptmsk )
1313	!!----------------------------------------------------------------------
1314	!! * ROUTINE wad_lmt *
1315	!!
1316	!! ** Purpose : set wetting & drying mask at tracer points
1317	!! for the current barotropic sub-step
1318	!!
1319	!! ** Method : ???
1320	!!
1321	!! ** Action : ptmsk : wetting & drying t-mask
1322	!!----------------------------------------------------------------------
1323	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pssh !
1324	REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: ptmsk !
1325	!
1326	INTEGER :: ji, jj ! dummy loop indices
1327	!!----------------------------------------------------------------------
1328	!
1329	IF( ln_wd_dl_rmp ) THEN
1330	DO jj = 1, jpj
1331	DO ji = 1, jpi
1332	IF ( pssh(ji,jj) + ht_0(ji,jj) > 2._wp * rn_wdmin1 ) THEN
1333	! IF ( pssh(ji,jj) + ht_0(ji,jj) > rn_wdmin2 ) THEN
1334	ptmsk(ji,jj) = 1._wp
1335	ELSEIF( pssh(ji,jj) + ht_0(ji,jj) > rn_wdmin1 ) THEN
1336	ptmsk(ji,jj) = TANH( 50._wp( ( pssh(ji,jj) + ht_0(ji,jj) - rn_wdmin1 )r_rn_wdmin1) )
1337	ELSE
1338	ptmsk(ji,jj) = 0._wp
1339	ENDIF
1340	END DO
1341	END DO
1342	ELSE
1343	DO jj = 1, jpj
1344	DO ji = 1, jpi
1345	IF ( pssh(ji,jj) + ht_0(ji,jj) > rn_wdmin1 ) THEN ; ptmsk(ji,jj) = 1._wp
1346	ELSE ; ptmsk(ji,jj) = 0._wp
1347	ENDIF
1348	END DO
1349	END DO
1350	ENDIF
1351	!
1352	END SUBROUTINE wad_tmsk
1353
1354
1355	SUBROUTINE wad_Umsk( pTmsk, phU, phV, pu, pv, pUmsk, pVmsk )
1356	!!----------------------------------------------------------------------
1357	!! * ROUTINE wad_lmt *
1358	!!
1359	!! ** Purpose : set wetting & drying mask at tracer points
1360	!! for the current barotropic sub-step
1361	!!
1362	!! ** Method : ???
1363	!!
1364	!! ** Action : ptmsk : wetting & drying t-mask
1365	!!----------------------------------------------------------------------
1366	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pTmsk ! W & D t-mask
1367	REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: phU, phV, pu, pv ! ocean velocities and transports
1368	REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: pUmsk, pVmsk ! W & D u- and v-mask
1369	!
1370	INTEGER :: ji, jj ! dummy loop indices
1371	!!----------------------------------------------------------------------
1372	!
1373	DO jj = 1, jpj
1374	DO ji = 1, jpim1 ! not jpi-column
1375	IF ( phU(ji,jj) > 0._wp ) THEN ; pUmsk(ji,jj) = pTmsk(ji ,jj)
1376	ELSE ; pUmsk(ji,jj) = pTmsk(ji+1,jj)
1377	ENDIF
1378	phU(ji,jj) = pUmsk(ji,jj)*phU(ji,jj)
1379	pu (ji,jj) = pUmsk(ji,jj)*pu (ji,jj)
1380	END DO
1381	END DO
1382	!
1383	DO jj = 1, jpjm1 ! not jpj-row
1384	DO ji = 1, jpi
1385	IF ( phV(ji,jj) > 0._wp ) THEN ; pVmsk(ji,jj) = pTmsk(ji,jj )
1386	ELSE ; pVmsk(ji,jj) = pTmsk(ji,jj+1)
1387	ENDIF
1388	phV(ji,jj) = pVmsk(ji,jj)*phV(ji,jj)
1389	pv (ji,jj) = pVmsk(ji,jj)*pv (ji,jj)
1390	END DO
1391	END DO
1392	!
1393	END SUBROUTINE wad_Umsk
1394
1395
1396	SUBROUTINE wad_spg( sshn, zcpx, zcpy )
1397	!!---------------------------------------------------------------------
1398	!! * ROUTINE wad_sp *
1399	!!
1400	!! ** Purpose :
1401	!!----------------------------------------------------------------------
1402	INTEGER :: ji ,jj ! dummy loop indices
1403	LOGICAL :: ll_tmp1, ll_tmp2
1404	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: sshn
1405	REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: zcpx, zcpy
1406	!!----------------------------------------------------------------------
1407	DO jj = 2, jpjm1
1408	DO ji = 2, jpim1
1409	ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji+1,jj) ) > &
1410	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
1411	& MAX( sshn(ji,jj) + ht_0(ji,jj) , sshn(ji+1,jj) + ht_0(ji+1,jj) ) &
1412	& > rn_wdmin1 + rn_wdmin2
1413	ll_tmp2 = ( ABS( sshn(ji+1,jj) - sshn(ji ,jj)) > 1.E-12 ).AND.( &
1414	& MAX( sshn(ji,jj) , sshn(ji+1,jj) ) > &
1415	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
1416	IF(ll_tmp1) THEN
1417	zcpx(ji,jj) = 1.0_wp
1418	ELSEIF(ll_tmp2) THEN
1419	! no worries about sshn(ji+1,jj) - sshn(ji ,jj) = 0, it won't happen ! here
1420	zcpx(ji,jj) = ABS( (sshn(ji+1,jj) + ht_0(ji+1,jj) - sshn(ji,jj) - ht_0(ji,jj)) &
1421	& / (sshn(ji+1,jj) - sshn(ji ,jj)) )
1422	zcpx(ji,jj) = max(min( zcpx(ji,jj) , 1.0_wp),0.0_wp)
1423	ELSE
1424	zcpx(ji,jj) = 0._wp
1425	ENDIF
1426	!
1427	ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji,jj+1) ) > &
1428	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
1429	& MAX( sshn(ji,jj) + ht_0(ji,jj) , sshn(ji,jj+1) + ht_0(ji,jj+1) ) &
1430	& > rn_wdmin1 + rn_wdmin2
1431	ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji,jj+1)) > 1.E-12 ).AND.( &
1432	& MAX( sshn(ji,jj) , sshn(ji,jj+1) ) > &
1433	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
1434
1435	IF(ll_tmp1) THEN
1436	zcpy(ji,jj) = 1.0_wp
1437	ELSE IF(ll_tmp2) THEN
1438	! no worries about sshn(ji,jj+1) - sshn(ji,jj ) = 0, it won't happen ! here
1439	zcpy(ji,jj) = ABS( (sshn(ji,jj+1) + ht_0(ji,jj+1) - sshn(ji,jj) - ht_0(ji,jj)) &
1440	& / (sshn(ji,jj+1) - sshn(ji,jj )) )
1441	zcpy(ji,jj) = MAX( 0._wp , MIN( zcpy(ji,jj) , 1.0_wp ) )
1442	ELSE
1443	zcpy(ji,jj) = 0._wp
1444	ENDIF
1445	END DO
1446	END DO
1447
1448	END SUBROUTINE wad_spg
1449
1450
1451
1452	SUBROUTINE dyn_drg_init( pu_RHSi, pv_RHSi, pCdU_u, pCdU_v )
1453	!!----------------------------------------------------------------------
1454	!! * ROUTINE dyn_drg_init *
1455	!!
1456	!! ** Purpose : - add the baroclinic top/bottom drag contribution to
1457	!! the baroclinic part of the barotropic RHS
1458	!! - compute the barotropic drag coefficients
1459	!!
1460	!! ** Method : computation done over the INNER domain only
1461	!!----------------------------------------------------------------------
1462	REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: pu_RHSi, pv_RHSi ! baroclinic part of the barotropic RHS
1463	REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pCdU_u , pCdU_v ! barotropic drag coefficients
1464	!
1465	INTEGER :: ji, jj ! dummy loop indices
1466	INTEGER :: ikbu, ikbv, iktu, iktv
1467	REAL(wp) :: zztmp
1468	REAL(wp), DIMENSION(jpi,jpj) :: zu_i, zv_i
1469	!!----------------------------------------------------------------------
1470	!
1471	! !== Set the barotropic drag coef. ==!
1472	!
1473	IF( ln_isfcav ) THEN ! top+bottom friction (ocean cavities)
1474
1475	DO jj = 2, jpjm1
1476	DO ji = 2, jpim1 ! INNER domain
1477	pCdU_u(ji,jj) = r1_2*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) + rCdU_top(ji+1,jj)+rCdU_top(ji,jj) )
1478	pCdU_v(ji,jj) = r1_2*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) + rCdU_top(ji,jj+1)+rCdU_top(ji,jj) )
1479	END DO
1480	END DO
1481	ELSE ! bottom friction only
1482	DO jj = 2, jpjm1
1483	DO ji = 2, jpim1 ! INNER domain
1484	pCdU_u(ji,jj) = r1_2*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) )
1485	pCdU_v(ji,jj) = r1_2*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) )
1486	END DO
1487	END DO
1488	ENDIF
1489	!
1490	! !== BOTTOM stress contribution from baroclinic velocities ==!
1491	!
1492	IF( ln_bt_fw ) THEN ! FORWARD integration: use NOW bottom baroclinic velocities
1493
1494	DO jj = 2, jpjm1
1495	DO ji = 2, jpim1 ! INNER domain
1496	ikbu = mbku(ji,jj)
1497	ikbv = mbkv(ji,jj)
1498	zu_i(ji,jj) = un(ji,jj,ikbu) - un_b(ji,jj)
1499	zv_i(ji,jj) = vn(ji,jj,ikbv) - vn_b(ji,jj)
1500	END DO
1501	END DO
1502	ELSE ! CENTRED integration: use BEFORE bottom baroclinic velocities
1503
1504	DO jj = 2, jpjm1
1505	DO ji = 2, jpim1 ! INNER domain
1506	ikbu = mbku(ji,jj)
1507	ikbv = mbkv(ji,jj)
1508	zu_i(ji,jj) = ub(ji,jj,ikbu) - ub_b(ji,jj)
1509	zv_i(ji,jj) = vb(ji,jj,ikbv) - vb_b(ji,jj)
1510	END DO
1511	END DO
1512	ENDIF
1513	!
1514	IF( ln_wd_il ) THEN ! W/D : use the "clipped" bottom friction !!gm explain WHY, please !
1515	zztmp = -1._wp / rdtbt
1516	DO jj = 2, jpjm1
1517	DO ji = 2, jpim1 ! INNER domain
1518	pu_RHSi(ji,jj) = pu_RHSi(ji,jj) + zu_i(ji,jj) * wdrampu(ji,jj) * MAX( &
1519	& r1_hu_n(ji,jj) * r1_2*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) , zztmp )
1520	pv_RHSi(ji,jj) = pv_RHSi(ji,jj) + zv_i(ji,jj) * wdrampv(ji,jj) * MAX( &
1521	& r1_hv_n(ji,jj) * r1_2*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) , zztmp )
1522	END DO
1523	END DO
1524	ELSE ! use "unclipped" drag (even if explicit friction is used in 3D calculation)
1525
1526	DO jj = 2, jpjm1
1527	DO ji = 2, jpim1 ! INNER domain
1528	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)
1529	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)
1530	END DO
1531	END DO
1532	END IF
1533	!
1534	! !== TOP stress contribution from baroclinic velocities ==! (no W/D case)
1535	!
1536	IF( ln_isfcav ) THEN
1537	!
1538	IF( ln_bt_fw ) THEN ! FORWARD integration: use NOW top baroclinic velocity
1539
1540	DO jj = 2, jpjm1
1541	DO ji = 2, jpim1 ! INNER domain
1542	iktu = miku(ji,jj)
1543	iktv = mikv(ji,jj)
1544	zu_i(ji,jj) = un(ji,jj,iktu) - un_b(ji,jj)
1545	zv_i(ji,jj) = vn(ji,jj,iktv) - vn_b(ji,jj)
1546	END DO
1547	END DO
1548	ELSE ! CENTRED integration: use BEFORE top baroclinic velocity
1549
1550	DO jj = 2, jpjm1
1551	DO ji = 2, jpim1 ! INNER domain
1552	iktu = miku(ji,jj)
1553	iktv = mikv(ji,jj)
1554	zu_i(ji,jj) = ub(ji,jj,iktu) - ub_b(ji,jj)
1555	zv_i(ji,jj) = vb(ji,jj,iktv) - vb_b(ji,jj)
1556	END DO
1557	END DO
1558	ENDIF
1559	!
1560	! ! use "unclipped" top drag (even if explicit friction is used in 3D calculation)
1561
1562	DO jj = 2, jpjm1
1563	DO ji = 2, jpim1 ! INNER domain
1564	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)
1565	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)
1566	END DO
1567	END DO
1568	!
1569	ENDIF
1570	!
1571	END SUBROUTINE dyn_drg_init
1572
1573	SUBROUTINE ts_bck_interp( jn, ll_init, & ! <== in
1574	& za0, za1, za2, za3 ) ! ==> out
1575	!!----------------------------------------------------------------------
1576	INTEGER ,INTENT(in ) :: jn ! index of sub time step
1577	LOGICAL ,INTENT(in ) :: ll_init !
1578	REAL(wp),INTENT( out) :: za0, za1, za2, za3 ! Half-step back interpolation coefficient
1579	!
1580	REAL(wp) :: zepsilon, zgamma ! - -
1581	!!----------------------------------------------------------------------
1582	! ! set Half-step back interpolation coefficient
1583	IF ( jn==1 .AND. ll_init ) THEN !* Forward-backward
1584	za0 = 1._wp
1585	za1 = 0._wp
1586	za2 = 0._wp
1587	za3 = 0._wp
1588	ELSEIF( jn==2 .AND. ll_init ) THEN !* AB2-AM3 Coefficients; bet=0 ; gam=-1/6 ; eps=1/12
1589	za0 = 1.0833333333333_wp ! za0 = 1-gam-eps
1590	za1 =-0.1666666666666_wp ! za1 = gam
1591	za2 = 0.0833333333333_wp ! za2 = eps
1592	za3 = 0._wp
1593	ELSE !* AB3-AM4 Coefficients; bet=0.281105 ; eps=0.013 ; gam=0.0880
1594	IF( rn_bt_alpha == 0._wp ) THEN ! Time diffusion
1595	za0 = 0.614_wp ! za0 = 1/2 + gam + 2*eps
1596	za1 = 0.285_wp ! za1 = 1/2 - 2gam - 3eps
1597	za2 = 0.088_wp ! za2 = gam
1598	za3 = 0.013_wp ! za3 = eps
1599	ELSE ! no time diffusion
1600	zepsilon = 0.00976186_wp - 0.13451357_wp * rn_bt_alpha
1601	zgamma = 0.08344500_wp - 0.51358400_wp * rn_bt_alpha
1602	za0 = 0.5_wp + zgamma + 2._wp * rn_bt_alpha + 2._wp * zepsilon
1603	za1 = 1._wp - za0 - zgamma - zepsilon
1604	za2 = zgamma
1605	za3 = zepsilon
1606	ENDIF
1607	ENDIF
1608	END SUBROUTINE ts_bck_interp
1609
1610
1611	!!======================================================================
1612	END MODULE dynspg_ts

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