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dynhpg.F90 @ 9120

Last change on this file since 9120 was 9120, checked in by clne, 6 years ago
Initial work on 2D surge configuration. Works for tide-only, no SBC yet
Property svn:keywords set to `Id`
File size: 75.2 KB

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1	MODULE dynhpg
2	!!======================================================================
3	!! * MODULE dynhpg *
4	!! Ocean dynamics: hydrostatic pressure gradient trend
5	!!======================================================================
6	!! History : OPA ! 1987-09 (P. Andrich, M.-A. Foujols) hpg_zco: Original code
7	!! 5.0 ! 1991-11 (G. Madec)
8	!! 7.0 ! 1996-01 (G. Madec) hpg_sco: Original code for s-coordinates
9	!! 8.0 ! 1997-05 (G. Madec) split dynber into dynkeg and dynhpg
10	!! 8.5 ! 2002-07 (G. Madec) F90: Free form and module
11	!! 8.5 ! 2002-08 (A. Bozec) hpg_zps: Original code
12	!! NEMO 1.0 ! 2005-10 (A. Beckmann, B.W. An) various s-coordinate options
13	!! ! Original code for hpg_ctl, hpg_hel hpg_wdj, hpg_djc, hpg_rot
14	!! - ! 2005-11 (G. Madec) style & small optimisation
15	!! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase
16	!! 3.4 ! 2011-11 (H. Liu) hpg_prj: Original code for s-coordinates
17	!! ! (A. Coward) suppression of hel, wdj and rot options
18	!! 3.6 ! 2014-11 (P. Mathiot) hpg_isf: original code for ice shelf cavity
19	!!----------------------------------------------------------------------
20
21	!!----------------------------------------------------------------------
22	!! dyn_hpg : update the momentum trend with the now horizontal
23	!! gradient of the hydrostatic pressure
24	!! dyn_hpg_init : initialisation and control of options
25	!! hpg_zco : z-coordinate scheme
26	!! hpg_zps : z-coordinate plus partial steps (interpolation)
27	!! hpg_sco : s-coordinate (standard jacobian formulation)
28	!! hpg_isf : s-coordinate (sco formulation) adapted to ice shelf
29	!! hpg_djc : s-coordinate (Density Jacobian with Cubic polynomial)
30	!! hpg_prj : s-coordinate (Pressure Jacobian with Cubic polynomial)
31	!!----------------------------------------------------------------------
32	USE oce ! ocean dynamics and tracers
33	USE sbc_oce ! surface variable (only for the flag with ice shelf)
34	USE dom_oce ! ocean space and time domain
35	USE wet_dry ! wetting and drying
36	USE phycst ! physical constants
37	USE trd_oce ! trends: ocean variables
38	USE trddyn ! trend manager: dynamics
39	!jc USE zpshde ! partial step: hor. derivative (zps_hde routine)
40	!
41	USE in_out_manager ! I/O manager
42	USE prtctl ! Print control
43	USE lbclnk ! lateral boundary condition
44	USE lib_mpp ! MPP library
45	USE eosbn2 ! compute density
46	USE wrk_nemo ! Memory Allocation
47	USE timing ! Timing
48	USE iom
49
50	IMPLICIT NONE
51	PRIVATE
52
53	PUBLIC dyn_hpg ! routine called by step module
54	PUBLIC dyn_hpg_init ! routine called by opa module
55
56	! !!* Namelist namdyn_hpg : hydrostatic pressure gradient
57	LOGICAL , PUBLIC :: ln_hpg_zco !: z-coordinate - full steps
58	LOGICAL , PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation)
59	LOGICAL , PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation)
60	LOGICAL , PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial)
61	LOGICAL , PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme)
62	LOGICAL , PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf
63
64	INTEGER , PUBLIC :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM)
65
66	!! * Substitutions
67	# include "vectopt_loop_substitute.h90"
68	!!----------------------------------------------------------------------
69	!! NEMO/OPA 3.3 , NEMO Consortium (2010)
70	!! $Id$
71	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
72	!!----------------------------------------------------------------------
73	CONTAINS
74
75	SUBROUTINE dyn_hpg( kt )
76	!!---------------------------------------------------------------------
77	!! * ROUTINE dyn_hpg *
78	!!
79	!! ** Method : Call the hydrostatic pressure gradient routine
80	!! using the scheme defined in the namelist
81	!!
82	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
83	!! - send trends to trd_dyn for futher diagnostics (l_trddyn=T)
84	!!----------------------------------------------------------------------
85	INTEGER, INTENT(in) :: kt ! ocean time-step index
86	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdu, ztrdv
87	!!----------------------------------------------------------------------
88	!
89	IF( nn_timing == 1 ) CALL timing_start('dyn_hpg')
90	!
91	IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn)
92	CALL wrk_alloc( jpi,jpj,jpk, ztrdu, ztrdv )
93	ztrdu(:,:,:) = ua(:,:,:)
94	ztrdv(:,:,:) = va(:,:,:)
95	ENDIF
96	!
97	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
98	CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate
99	CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation)
100	CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation)
101	CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial)
102	CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme)
103	CASE ( 5 ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf
104	END SELECT
105	!
106	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
107	ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:)
108	ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:)
109	CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt )
110	CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv )
111	ENDIF
112	!
113	IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, &
114	& tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
115	!
116	IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg')
117	!
118	END SUBROUTINE dyn_hpg
119
120
121	SUBROUTINE dyn_hpg_init
122	!!----------------------------------------------------------------------
123	!! * ROUTINE dyn_hpg_init *
124	!!
125	!! ** Purpose : initializations for the hydrostatic pressure gradient
126	!! computation and consistency control
127	!!
128	!! ** Action : Read the namelist namdyn_hpg and check the consistency
129	!! with the type of vertical coordinate used (zco, zps, sco)
130	!!----------------------------------------------------------------------
131	INTEGER :: ioptio = 0 ! temporary integer
132	INTEGER :: ios ! Local integer output status for namelist read
133	!!
134	INTEGER :: ji, jj, jk, ikt ! dummy loop indices ISF
135	REAL(wp) :: znad
136	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop, zrhd ! hypothesys on isf density
137	REAL(wp), POINTER, DIMENSION(:,:) :: zrhdtop_isf ! density at bottom of ISF
138	REAL(wp), POINTER, DIMENSION(:,:) :: ziceload ! density at bottom of ISF
139	!!
140	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
141	& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf
142	!!----------------------------------------------------------------------
143	!
144	REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient
145	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
146	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp )
147	!
148	REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient
149	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
150	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp )
151	IF(lwm) WRITE ( numond, namdyn_hpg )
152	!
153	IF(lwp) THEN ! Control print
154	WRITE(numout,*)
155	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
156	WRITE(numout,*) '~~~~~~~~~~~~'
157	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
158	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
159	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
160	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
161	WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf
162	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
163	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
164	ENDIF
165	!
166	IF( ln_hpg_djc ) &
167	& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method &
168	& currently disabled (bugs under investigation). Please select &
169	& either ln_hpg_sco or ln_hpg_prj instead')
170	!
171	IF( .NOT.ln_linssh .AND. .NOT.(ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) &
172	& CALL ctl_stop('dyn_hpg_init : non-linear free surface requires either ', &
173	& ' the standard jacobian formulation hpg_sco or ' , &
174	& ' the pressure jacobian formulation hpg_prj' )
175
176	IF( ln_hpg_isf .AND. .NOT. ln_isfcav ) &
177	& CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' )
178	IF( .NOT. ln_hpg_isf .AND. ln_isfcav ) &
179	& CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' )
180	!
181	! ! Set nhpg from ln_hpg_... flags
182	IF( ln_hpg_zco ) nhpg = 0
183	IF( ln_hpg_zps ) nhpg = 1
184	IF( ln_hpg_sco ) nhpg = 2
185	IF( ln_hpg_djc ) nhpg = 3
186	IF( ln_hpg_prj ) nhpg = 4
187	IF( ln_hpg_isf ) nhpg = 5
188	!
189	! ! Consistency check
190	ioptio = 0
191	IF( ln_hpg_zco ) ioptio = ioptio + 1
192	IF( ln_hpg_zps ) ioptio = ioptio + 1
193	IF( ln_hpg_sco ) ioptio = ioptio + 1
194	IF( ln_hpg_djc ) ioptio = ioptio + 1
195	IF( ln_hpg_prj ) ioptio = ioptio + 1
196	IF( ln_hpg_isf ) ioptio = ioptio + 1
197	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
198	!
199	! initialisation of ice shelf load
200	IF ( .NOT. ln_isfcav ) riceload(:,:)=0.0
201	IF ( ln_isfcav ) THEN
202	CALL wrk_alloc( jpi,jpj, 2, ztstop)
203	CALL wrk_alloc( jpi,jpj,jpk, zrhd )
204	CALL wrk_alloc( jpi,jpj, zrhdtop_isf, ziceload)
205	!
206	IF(lwp) WRITE(numout,*)
207	IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf'
208	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~'
209
210	! To use density and not density anomaly
211	znad=1._wp
212
213	! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude)
214	ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp
215
216	! compute density of the water displaced by the ice shelf
217	DO jk = 1, jpk
218	CALL eos(ztstop(:,:,:),gdept_n(:,:,jk),zrhd(:,:,jk))
219	END DO
220
221	! compute rhd at the ice/oce interface (ice shelf side)
222	CALL eos(ztstop,risfdep,zrhdtop_isf)
223
224	! Surface value + ice shelf gradient
225	! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v)
226	! divided by 2 later
227	ziceload = 0._wp
228	DO jj = 1, jpj
229	DO ji = 1, jpi
230	ikt=mikt(ji,jj)
231	ziceload(ji,jj) = ziceload(ji,jj) + (znad + zrhd(ji,jj,1) ) * e3w_n(ji,jj,1) * (1._wp - tmask(ji,jj,1))
232	DO jk=2,ikt-1
233	ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhd(ji,jj,jk-1) + zrhd(ji,jj,jk)) * e3w_n(ji,jj,jk) &
234	& * (1._wp - tmask(ji,jj,jk))
235	END DO
236	IF (ikt >= 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + zrhd(ji,jj,ikt-1)) &
237	& * ( risfdep(ji,jj) - gdept_1d(ikt-1) )
238	END DO
239	END DO
240	riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5
241
242	CALL wrk_dealloc( jpi,jpj, 2, ztstop)
243	CALL wrk_dealloc( jpi,jpj,jpk, zrhd )
244	CALL wrk_dealloc( jpi,jpj, zrhdtop_isf, ziceload)
245	END IF
246	!
247	END SUBROUTINE dyn_hpg_init
248
249
250	SUBROUTINE hpg_zco( kt )
251	!!---------------------------------------------------------------------
252	!! * ROUTINE hpg_zco *
253	!!
254	!! ** Method : z-coordinate case, levels are horizontal surfaces.
255	!! The now hydrostatic pressure gradient at a given level, jk,
256	!! is computed by taking the vertical integral of the in-situ
257	!! density gradient along the model level from the suface to that
258	!! level: zhpi = grav .....
259	!! zhpj = grav .....
260	!! add it to the general momentum trend (ua,va).
261	!! ua = ua - 1/e1u * zhpi
262	!! va = va - 1/e2v * zhpj
263	!!
264	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
265	!!----------------------------------------------------------------------
266	INTEGER, INTENT(in) :: kt ! ocean time-step index
267	!
268	INTEGER :: ji, jj, jk ! dummy loop indices
269	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
270	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
271	!!----------------------------------------------------------------------
272	!
273	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
274	!
275	IF( kt == nit000 ) THEN
276	IF(lwp) WRITE(numout,*)
277	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
278	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
279	ENDIF
280
281	zcoef0 = - grav * 0.5_wp ! Local constant initialization
282
283	! Surface value
284	DO jj = 2, jpjm1
285	DO ji = fs_2, fs_jpim1 ! vector opt.
286	zcoef1 = zcoef0 * e3w_n(ji,jj,1)
287	! hydrostatic pressure gradient
288	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
289	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
290	! add to the general momentum trend
291	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
292	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
293	END DO
294	END DO
295
296	!
297	! interior value (2=<jk=<jpkm1)
298	DO jk = 2, jpkm1
299	DO jj = 2, jpjm1
300	DO ji = fs_2, fs_jpim1 ! vector opt.
301	zcoef1 = zcoef0 * e3w_n(ji,jj,jk)
302	! hydrostatic pressure gradient
303	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
304	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
305	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
306
307	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
308	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
309	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
310	! add to the general momentum trend
311	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
312	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
313	END DO
314	END DO
315	END DO
316	!
317	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
318	!
319	END SUBROUTINE hpg_zco
320
321
322	SUBROUTINE hpg_zps( kt )
323	!!---------------------------------------------------------------------
324	!! * ROUTINE hpg_zps *
325	!!
326	!! ** Method : z-coordinate plus partial steps case. blahblah...
327	!!
328	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
329	!!----------------------------------------------------------------------
330	INTEGER, INTENT(in) :: kt ! ocean time-step index
331	!!
332	INTEGER :: ji, jj, jk ! dummy loop indices
333	INTEGER :: iku, ikv ! temporary integers
334	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
335	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
336	!!----------------------------------------------------------------------
337	!
338	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
339	!
340	IF( kt == nit000 ) THEN
341	IF(lwp) WRITE(numout,*)
342	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
343	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
344	ENDIF
345
346	! Partial steps: bottom before horizontal gradient of t, s, rd at the last ocean level
347	!jc CALL zps_hde ( kt, jpts, tsn, gtsu, gtsv, rhd, gru , grv )
348
349	! Local constant initialization
350	zcoef0 = - grav * 0.5_wp
351
352	! Surface value (also valid in partial step case)
353	DO jj = 2, jpjm1
354	DO ji = fs_2, fs_jpim1 ! vector opt.
355	zcoef1 = zcoef0 * e3w_n(ji,jj,1)
356	! hydrostatic pressure gradient
357	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
358	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
359	! add to the general momentum trend
360	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
361	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
362	END DO
363	END DO
364
365	! interior value (2=<jk=<jpkm1)
366	DO jk = 2, jpkm1
367	DO jj = 2, jpjm1
368	DO ji = fs_2, fs_jpim1 ! vector opt.
369	zcoef1 = zcoef0 * e3w_n(ji,jj,jk)
370	! hydrostatic pressure gradient
371	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
372	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
373	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
374
375	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
376	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
377	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
378	! add to the general momentum trend
379	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
380	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
381	END DO
382	END DO
383	END DO
384
385	! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
386	DO jj = 2, jpjm1
387	DO ji = 2, jpim1
388	iku = mbku(ji,jj)
389	ikv = mbkv(ji,jj)
390	zcoef2 = zcoef0 * MIN( e3w_n(ji,jj,iku), e3w_n(ji+1,jj ,iku) )
391	zcoef3 = zcoef0 * MIN( e3w_n(ji,jj,ikv), e3w_n(ji ,jj+1,ikv) )
392	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
393	ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value
394	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
395	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) * r1_e1u(ji,jj)
396	ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
397	ENDIF
398	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
399	va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value
400	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
401	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) * r1_e2v(ji,jj)
402	va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
403	ENDIF
404	END DO
405	END DO
406	!
407	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
408	!
409	END SUBROUTINE hpg_zps
410
411
412	SUBROUTINE hpg_sco( kt )
413	!!---------------------------------------------------------------------
414	!! * ROUTINE hpg_sco *
415	!!
416	!! ** Method : s-coordinate case. Jacobian scheme.
417	!! The now hydrostatic pressure gradient at a given level, jk,
418	!! is computed by taking the vertical integral of the in-situ
419	!! density gradient along the model level from the suface to that
420	!! level. s-coordinates (ln_sco): a corrective term is added
421	!! to the horizontal pressure gradient :
422	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
423	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
424	!! add it to the general momentum trend (ua,va).
425	!! ua = ua - 1/e1u * zhpi
426	!! va = va - 1/e2v * zhpj
427	!!
428	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
429	!!----------------------------------------------------------------------
430	INTEGER, INTENT(in) :: kt ! ocean time-step index
431	!!
432	INTEGER :: ji, jj, jk, jii, jjj ! dummy loop indices
433	REAL(wp) :: zcoef0, zuap, zvap, znad, ztmp ! temporary scalars
434	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
435	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
436	REAL(wp), POINTER, DIMENSION(:,:) :: zcpx, zcpy !W/D pressure filter
437	!!----------------------------------------------------------------------
438	!
439	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
440	IF( ln_wd ) CALL wrk_alloc( jpi,jpj, zcpx, zcpy )
441	!
442	IF( kt == nit000 ) THEN
443	IF(lwp) WRITE(numout,*)
444	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
445	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
446	ENDIF
447	!
448	zcoef0 = - grav * 0.5_wp
449	IF ( ln_linssh ) THEN ; znad = 0._wp ! Fixed volume: density anomaly
450	ELSE ; znad = 1._wp ! Variable volume: density
451	ENDIF
452	!
453	IF( ln_wd ) THEN
454	DO jj = 2, jpjm1
455	DO ji = 2, jpim1
456	ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji+1,jj) ) > &
457	& MAX( -ht_wd(ji,jj) , -ht_wd(ji+1,jj) ) .AND. &
458	& MAX( sshn(ji,jj) + ht_wd(ji,jj), sshn(ji+1,jj) + ht_wd(ji+1,jj) ) &
459	& > rn_wdmin1 + rn_wdmin2
460	ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji+1,jj) ) > 1.E-12 ) .AND. ( &
461	& MAX( sshn(ji,jj) , sshn(ji+1,jj) ) > &
462	& MAX( -ht_wd(ji,jj) , -ht_wd(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
463
464	IF(ll_tmp1) THEN
465	zcpx(ji,jj) = 1.0_wp
466	ELSE IF(ll_tmp2) THEN
467	! no worries about sshn(ji+1,jj) - sshn(ji ,jj) = 0, it won't happen ! here
468	zcpx(ji,jj) = ABS( (sshn(ji+1,jj) + ht_wd(ji+1,jj) - sshn(ji,jj) - ht_wd(ji,jj)) &
469	& / (sshn(ji+1,jj) - sshn(ji ,jj)) )
470	ELSE
471	zcpx(ji,jj) = 0._wp
472	END IF
473
474	ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji,jj+1) ) > &
475	& MAX( -ht_wd(ji,jj) , -ht_wd(ji,jj+1) ) .AND. &
476	& MAX( sshn(ji,jj) + ht_wd(ji,jj), sshn(ji,jj+1) + ht_wd(ji,jj+1) ) &
477	& > rn_wdmin1 + rn_wdmin2
478	ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji,jj+1) ) > 1.E-12 ) .AND. ( &
479	& MAX( sshn(ji,jj) , sshn(ji,jj+1) ) > &
480	& MAX( -ht_wd(ji,jj) , -ht_wd(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
481
482	IF(ll_tmp1) THEN
483	zcpy(ji,jj) = 1.0_wp
484	ELSE IF(ll_tmp2) THEN
485	! no worries about sshn(ji,jj+1) - sshn(ji,jj ) = 0, it won't happen ! here
486	zcpy(ji,jj) = ABS( (sshn(ji,jj+1) + ht_wd(ji,jj+1) - sshn(ji,jj) - ht_wd(ji,jj)) &
487	& / (sshn(ji,jj+1) - sshn(ji,jj )) )
488	ELSE
489	zcpy(ji,jj) = 0._wp
490	END IF
491	END DO
492	END DO
493	CALL lbc_lnk( zcpx, 'U', 1._wp ) ; CALL lbc_lnk( zcpy, 'V', 1._wp )
494	END IF
495
496	IF (ln_2d) THEN
497	! Surface value
498	DO jj = 2, jpjm1
499	DO ji = fs_2, fs_jpim1 ! vector opt.
500	! hydrostatic pressure gradient along s-surfaces
501	zhpi(ji,jj,1) = zcoef0 * ( e3w_n(ji+1,jj ,1) * znad &
502	& - e3w_n(ji ,jj ,1) * znad ) * r1_e1u(ji,jj)
503	zhpj(ji,jj,1) = zcoef0 * ( e3w_n(ji ,jj+1,1) * znad &
504	& - e3w_n(ji ,jj ,1) * znad ) * r1_e2v(ji,jj)
505	! s-coordinate pressure gradient correction
506	zuap = -zcoef0 * ( 2._wp * znad ) &
507	& * ( gde3w_n(ji+1,jj,1) - gde3w_n(ji,jj,1) ) * r1_e1u(ji,jj)
508	zvap = -zcoef0 * ( 2._wp * znad ) &
509	& * ( gde3w_n(ji,jj+1,1) - gde3w_n(ji,jj,1) ) * r1_e2v(ji,jj)
510
511
512	IF( ln_wd ) THEN
513
514	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
515	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
516	zuap = zuap * zcpx(ji,jj)
517	zvap = zvap * zcpy(ji,jj)
518	ENDIF
519
520	! add to the general momentum trend
521	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap * umask(ji,jj,1)
522	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap * vmask(ji,jj,1)
523	END DO
524	END DO
525
526	! interior value (2=<jk=<jpkm1)
527	DO jk = 2, jpkm1
528	DO jj = 2, jpjm1
529	DO ji = fs_2, fs_jpim1 ! vector opt.
530	! hydrostatic pressure gradient along s-surfaces
531	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 * r1_e1u(ji,jj) &
532	& * ( e3w_n(ji+1,jj,jk) * ( 2*znad ) &
533	& - e3w_n(ji ,jj,jk) * ( 2*znad ) )
534	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 * r1_e2v(ji,jj) &
535	& * ( e3w_n(ji,jj+1,jk) * ( 2*znad ) &
536	& - e3w_n(ji,jj ,jk) * ( 2*znad ) )
537	! s-coordinate pressure gradient correction
538	zuap = -zcoef0 * ( 2._wp * znad ) &
539	& * ( gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk) ) * r1_e1u(ji,jj)
540	zvap = -zcoef0 * ( 2._wp * znad ) &
541	& * ( gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk) ) * r1_e2v(ji,jj)
542
543	IF( ln_wd ) THEN
544	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
545	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
546	zuap = zuap * zcpx(ji,jj)
547	zvap = zvap * zcpy(ji,jj)
548	ENDIF
549
550	! add to the general momentum trend
551	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap * umask(ji,jj,1)
552	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap * vmask(ji,jj,1)
553	END DO
554	END DO
555	END DO
556
557	ELSE
558
559	! Surface value
560	DO jj = 2, jpjm1
561	DO ji = fs_2, fs_jpim1 ! vector opt.
562	! hydrostatic pressure gradient along s-surfaces
563	zhpi(ji,jj,1) = zcoef0 * ( e3w_n(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) &
564	& - e3w_n(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e1u(ji,jj)
565	zhpj(ji,jj,1) = zcoef0 * ( e3w_n(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) &
566	& - e3w_n(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e2v(ji,jj)
567	! s-coordinate pressure gradient correction
568	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
569	& * ( gde3w_n(ji+1,jj,1) - gde3w_n(ji,jj,1) ) * r1_e1u(ji,jj)
570	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
571	& * ( gde3w_n(ji,jj+1,1) - gde3w_n(ji,jj,1) ) * r1_e2v(ji,jj)
572
573
574	IF( ln_wd ) THEN
575
576	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
577	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
578	zuap = zuap * zcpx(ji,jj)
579	zvap = zvap * zcpy(ji,jj)
580	ENDIF
581
582	! add to the general momentum trend
583	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap
584	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap
585	END DO
586	END DO
587
588	! interior value (2=<jk=<jpkm1)
589	DO jk = 2, jpkm1
590	DO jj = 2, jpjm1
591	DO ji = fs_2, fs_jpim1 ! vector opt.
592	! hydrostatic pressure gradient along s-surfaces
593	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 * r1_e1u(ji,jj) &
594	& * ( e3w_n(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) &
595	& - e3w_n(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) )
596	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 * r1_e2v(ji,jj) &
597	& * ( e3w_n(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) &
598	& - e3w_n(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) )
599	! s-coordinate pressure gradient correction
600	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
601	& * ( gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk) ) * r1_e1u(ji,jj)
602	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
603	& * ( gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk) ) * r1_e2v(ji,jj)
604
605	IF( ln_wd ) THEN
606	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
607	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
608	zuap = zuap * zcpx(ji,jj)
609	zvap = zvap * zcpy(ji,jj)
610	ENDIF
611
612	! add to the general momentum trend
613	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap
614	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap
615	END DO
616	END DO
617	END DO
618	END IF ! if ln_2d
619
620	!
621	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
622	IF( ln_wd ) CALL wrk_dealloc( jpi,jpj, zcpx, zcpy )
623	!
624	END SUBROUTINE hpg_sco
625
626
627	SUBROUTINE hpg_isf( kt )
628	!!---------------------------------------------------------------------
629	!! * ROUTINE hpg_isf *
630	!!
631	!! ** Method : s-coordinate case. Jacobian scheme.
632	!! The now hydrostatic pressure gradient at a given level, jk,
633	!! is computed by taking the vertical integral of the in-situ
634	!! density gradient along the model level from the suface to that
635	!! level. s-coordinates (ln_sco): a corrective term is added
636	!! to the horizontal pressure gradient :
637	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
638	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
639	!! add it to the general momentum trend (ua,va).
640	!! ua = ua - 1/e1u * zhpi
641	!! va = va - 1/e2v * zhpj
642	!! iceload is added and partial cell case are added to the top and bottom
643	!!
644	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
645	!!----------------------------------------------------------------------
646	INTEGER, INTENT(in) :: kt ! ocean time-step index
647	!!
648	INTEGER :: ji, jj, jk, ikt, iktp1i, iktp1j ! dummy loop indices
649	REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars
650	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
651	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop
652	REAL(wp), POINTER, DIMENSION(:,:) :: zrhdtop_oce
653	!!----------------------------------------------------------------------
654	!
655	CALL wrk_alloc( jpi,jpj, 2, ztstop)
656	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj)
657	CALL wrk_alloc( jpi,jpj, zrhdtop_oce )
658	!
659	! Local constant initialization
660	zcoef0 = - grav * 0.5_wp
661
662	! To use density and not density anomaly
663	znad=1._wp
664
665	! iniitialised to 0. zhpi zhpi
666	zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp
667
668	! compute rhd at the ice/oce interface (ocean side)
669	! usefull to reduce residual current in the test case ISOMIP with no melting
670	DO ji=1,jpi
671	DO jj=1,jpj
672	ikt=mikt(ji,jj)
673	ztstop(ji,jj,1)=tsn(ji,jj,ikt,1)
674	ztstop(ji,jj,2)=tsn(ji,jj,ikt,2)
675	END DO
676	END DO
677	CALL eos( ztstop, risfdep, zrhdtop_oce )
678
679	!==================================================================================
680	!===== Compute surface value =====================================================
681	!==================================================================================
682	DO jj = 2, jpjm1
683	DO ji = fs_2, fs_jpim1 ! vector opt.
684	ikt = mikt(ji,jj)
685	iktp1i = mikt(ji+1,jj)
686	iktp1j = mikt(ji,jj+1)
687	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
688	! we assume ISF is in isostatic equilibrium
689	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * e3w_n(ji+1,jj,iktp1i) &
690	& * ( 2._wp * znad + rhd(ji+1,jj,iktp1i) + zrhdtop_oce(ji+1,jj) ) &
691	& - 0.5_wp * e3w_n(ji,jj,ikt) &
692	& * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) &
693	& + ( riceload(ji+1,jj) - riceload(ji,jj)) )
694	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * e3w_n(ji,jj+1,iktp1j) &
695	& * ( 2._wp * znad + rhd(ji,jj+1,iktp1j) + zrhdtop_oce(ji,jj+1) ) &
696	& - 0.5_wp * e3w_n(ji,jj,ikt) &
697	& * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) &
698	& + ( riceload(ji,jj+1) - riceload(ji,jj)) )
699	! s-coordinate pressure gradient correction (=0 if z coordinate)
700	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
701	& * ( gde3w_n(ji+1,jj,1) - gde3w_n(ji,jj,1) ) * r1_e1u(ji,jj)
702	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
703	& * ( gde3w_n(ji,jj+1,1) - gde3w_n(ji,jj,1) ) * r1_e2v(ji,jj)
704	! add to the general momentum trend
705	ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
706	va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
707	END DO
708	END DO
709	!==================================================================================
710	!===== Compute interior value =====================================================
711	!==================================================================================
712	! interior value (2=<jk=<jpkm1)
713	DO jk = 2, jpkm1
714	DO jj = 2, jpjm1
715	DO ji = fs_2, fs_jpim1 ! vector opt.
716	! hydrostatic pressure gradient along s-surfaces
717	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
718	& * ( e3w_n(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2znad ) wmask(ji+1,jj,jk) &
719	& - e3w_n(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2znad ) wmask(ji ,jj,jk) )
720	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
721	& * ( e3w_n(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2znad ) wmask(ji,jj+1,jk) &
722	& - e3w_n(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2znad ) wmask(ji,jj ,jk) )
723	! s-coordinate pressure gradient correction
724	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
725	& * ( gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk) ) / e1u(ji,jj)
726	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
727	& * ( gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk) ) / e2v(ji,jj)
728	! add to the general momentum trend
729	ua(ji,jj,jk) = ua(ji,jj,jk) + (zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
730	va(ji,jj,jk) = va(ji,jj,jk) + (zhpj(ji,jj,jk) + zvap) * vmask(ji,jj,jk)
731	END DO
732	END DO
733	END DO
734	!
735	CALL wrk_dealloc( jpi,jpj,2 , ztstop)
736	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj)
737	CALL wrk_dealloc( jpi,jpj , zrhdtop_oce )
738	!
739	END SUBROUTINE hpg_isf
740
741
742	SUBROUTINE hpg_djc( kt )
743	!!---------------------------------------------------------------------
744	!! * ROUTINE hpg_djc *
745	!!
746	!! ** Method : Density Jacobian with Cubic polynomial scheme
747	!!
748	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
749	!!----------------------------------------------------------------------
750	INTEGER, INTENT(in) :: kt ! ocean time-step index
751	!!
752	INTEGER :: ji, jj, jk ! dummy loop indices
753	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
754	REAL(wp) :: z1_10, cffu, cffx ! " "
755	REAL(wp) :: z1_12, cffv, cffy ! " "
756	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
757	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
758	REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw
759	REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow
760	REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k
761	REAL(wp), POINTER, DIMENSION(:,:) :: zcpx, zcpy !W/D pressure filter
762	!!----------------------------------------------------------------------
763	!
764	CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
765	CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
766	CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
767	IF( ln_wd ) CALL wrk_alloc( jpi,jpj, zcpx, zcpy )
768	!
769	!
770	IF( ln_wd ) THEN
771	DO jj = 2, jpjm1
772	DO ji = 2, jpim1
773	ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji+1,jj) ) > &
774	& MAX( -ht_wd(ji,jj) , -ht_wd(ji+1,jj) ) .AND. &
775	& MAX( sshn(ji,jj) + ht_wd(ji,jj), sshn(ji+1,jj) + ht_wd(ji+1,jj) ) &
776	& > rn_wdmin1 + rn_wdmin2
777	ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji+1,jj) ) > 1.E-12 ) .AND. ( &
778	& MAX( sshn(ji,jj) , sshn(ji+1,jj) ) > &
779	& MAX( -ht_wd(ji,jj) , -ht_wd(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
780
781	IF(ll_tmp1) THEN
782	zcpx(ji,jj) = 1.0_wp
783	ELSE IF(ll_tmp2) THEN
784	! no worries about sshn(ji+1,jj) - sshn(ji ,jj) = 0, it won't happen ! here
785	zcpx(ji,jj) = ABS( (sshn(ji+1,jj) + ht_wd(ji+1,jj) - sshn(ji,jj) - ht_wd(ji,jj)) &
786	& / (sshn(ji+1,jj) - sshn(ji ,jj)) )
787	ELSE
788	zcpx(ji,jj) = 0._wp
789	END IF
790
791	ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji,jj+1) ) > &
792	& MAX( -ht_wd(ji,jj) , -ht_wd(ji,jj+1) ) .AND. &
793	& MAX( sshn(ji,jj) + ht_wd(ji,jj), sshn(ji,jj+1) + ht_wd(ji,jj+1) ) &
794	& > rn_wdmin1 + rn_wdmin2
795	ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji,jj+1) ) > 1.E-12 ) .AND. ( &
796	& MAX( sshn(ji,jj) , sshn(ji,jj+1) ) > &
797	& MAX( -ht_wd(ji,jj) , -ht_wd(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
798
799	IF(ll_tmp1) THEN
800	zcpy(ji,jj) = 1.0_wp
801	ELSE IF(ll_tmp2) THEN
802	! no worries about sshn(ji,jj+1) - sshn(ji,jj ) = 0, it won't happen ! here
803	zcpy(ji,jj) = ABS( (sshn(ji,jj+1) + ht_wd(ji,jj+1) - sshn(ji,jj) - ht_wd(ji,jj)) &
804	& / (sshn(ji,jj+1) - sshn(ji,jj )) )
805	ELSE
806	zcpy(ji,jj) = 0._wp
807	END IF
808	END DO
809	END DO
810	CALL lbc_lnk( zcpx, 'U', 1._wp ) ; CALL lbc_lnk( zcpy, 'V', 1._wp )
811	END IF
812
813	IF( kt == nit000 ) THEN
814	IF(lwp) WRITE(numout,*)
815	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
816	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
817	ENDIF
818
819	! Local constant initialization
820	zcoef0 = - grav * 0.5_wp
821	z1_10 = 1._wp / 10._wp
822	z1_12 = 1._wp / 12._wp
823
824	!----------------------------------------------------------------------------------------
825	! compute and store in provisional arrays elementary vertical and horizontal differences
826	!----------------------------------------------------------------------------------------
827
828	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
829
830	DO jk = 2, jpkm1
831	DO jj = 2, jpjm1
832	DO ji = fs_2, fs_jpim1 ! vector opt.
833	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
834	dzz (ji,jj,jk) = gde3w_n(ji ,jj ,jk) - gde3w_n(ji,jj,jk-1)
835	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
836	dzx (ji,jj,jk) = gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk )
837	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
838	dzy (ji,jj,jk) = gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk )
839	END DO
840	END DO
841	END DO
842
843	!-------------------------------------------------------------------------
844	! compute harmonic averages using eq. 5.18
845	!-------------------------------------------------------------------------
846	zep = 1.e-15
847
848	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
849	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
850
851	DO jk = 2, jpkm1
852	DO jj = 2, jpjm1
853	DO ji = fs_2, fs_jpim1 ! vector opt.
854	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
855
856	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
857	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
858
859	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
860	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
861
862	IF( cffw > zep) THEN
863	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
864	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
865	ELSE
866	drhow(ji,jj,jk) = 0._wp
867	ENDIF
868
869	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
870	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
871
872	IF( cffu > zep ) THEN
873	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
874	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
875	ELSE
876	drhou(ji,jj,jk ) = 0._wp
877	ENDIF
878
879	IF( cffx > zep ) THEN
880	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
881	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
882	ELSE
883	dzu(ji,jj,jk) = 0._wp
884	ENDIF
885
886	IF( cffv > zep ) THEN
887	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
888	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
889	ELSE
890	drhov(ji,jj,jk) = 0._wp
891	ENDIF
892
893	IF( cffy > zep ) THEN
894	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
895	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
896	ELSE
897	dzv(ji,jj,jk) = 0._wp
898	ENDIF
899
900	END DO
901	END DO
902	END DO
903
904	!----------------------------------------------------------------------------------
905	! apply boundary conditions at top and bottom using 5.36-5.37
906	!----------------------------------------------------------------------------------
907	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
908	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
909	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
910
911	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
912	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
913	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
914
915
916	!--------------------------------------------------------------
917	! Upper half of top-most grid box, compute and store
918	!-------------------------------------------------------------
919
920	!!bug gm : e3w-gde3w = 0.5*e3w .... and gde3w(2)-gde3w(1)=e3w(2) .... to be verified
921	! true if gde3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
922
923	DO jj = 2, jpjm1
924	DO ji = fs_2, fs_jpim1 ! vector opt.
925	rho_k(ji,jj,1) = -grav * ( e3w_n(ji,jj,1) - gde3w_n(ji,jj,1) ) &
926	& * ( rhd(ji,jj,1) &
927	& + 0.5_wp * ( rhd (ji,jj,2) - rhd (ji,jj,1) ) &
928	& * ( e3w_n (ji,jj,1) - gde3w_n(ji,jj,1) ) &
929	& / ( gde3w_n(ji,jj,2) - gde3w_n(ji,jj,1) ) )
930	END DO
931	END DO
932
933	!!bug gm : here also, simplification is possible
934	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
935
936	DO jk = 2, jpkm1
937	DO jj = 2, jpjm1
938	DO ji = fs_2, fs_jpim1 ! vector opt.
939
940	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
941	& * ( gde3w_n(ji,jj,jk) - gde3w_n(ji,jj,jk-1) ) &
942	& - grav * z1_10 * ( &
943	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
944	& * ( gde3w_n(ji,jj,jk) - gde3w_n(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
945	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
946	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
947	& )
948
949	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
950	& * ( gde3w_n(ji+1,jj,jk) - gde3w_n(ji,jj,jk) ) &
951	& - grav* z1_10 * ( &
952	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
953	& * ( gde3w_n(ji+1,jj,jk) - gde3w_n(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
954	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
955	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
956	& )
957
958	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
959	& * ( gde3w_n(ji,jj+1,jk) - gde3w_n(ji,jj,jk) ) &
960	& - grav* z1_10 * ( &
961	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
962	& * ( gde3w_n(ji,jj+1,jk) - gde3w_n(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
963	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
964	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
965	& )
966
967	END DO
968	END DO
969	END DO
970	CALL lbc_lnk(rho_k,'W',1.)
971	CALL lbc_lnk(rho_i,'U',1.)
972	CALL lbc_lnk(rho_j,'V',1.)
973
974
975	! ---------------
976	! Surface value
977	! ---------------
978	DO jj = 2, jpjm1
979	DO ji = fs_2, fs_jpim1 ! vector opt.
980	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) * r1_e1u(ji,jj)
981	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) * r1_e2v(ji,jj)
982	IF( ln_wd ) THEN
983	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
984	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
985	ENDIF
986	! add to the general momentum trend
987	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
988	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
989	END DO
990	END DO
991
992	! ----------------
993	! interior value (2=<jk=<jpkm1)
994	! ----------------
995	DO jk = 2, jpkm1
996	DO jj = 2, jpjm1
997	DO ji = fs_2, fs_jpim1 ! vector opt.
998	! hydrostatic pressure gradient along s-surfaces
999	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
1000	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
1001	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) * r1_e1u(ji,jj)
1002	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
1003	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
1004	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) * r1_e2v(ji,jj)
1005	IF( ln_wd ) THEN
1006	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
1007	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
1008	ENDIF
1009	! add to the general momentum trend
1010	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
1011	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
1012	END DO
1013	END DO
1014	END DO
1015	!
1016	CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
1017	CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
1018	CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
1019	IF( ln_wd ) CALL wrk_dealloc( jpi,jpj, zcpx, zcpy )
1020	!
1021	END SUBROUTINE hpg_djc
1022
1023
1024	SUBROUTINE hpg_prj( kt )
1025	!!---------------------------------------------------------------------
1026	!! * ROUTINE hpg_prj *
1027	!!
1028	!! ** Method : s-coordinate case.
1029	!! A Pressure-Jacobian horizontal pressure gradient method
1030	!! based on the constrained cubic-spline interpolation for
1031	!! all vertical coordinate systems
1032	!!
1033	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
1034	!!----------------------------------------------------------------------
1035	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
1036	INTEGER, INTENT(in) :: kt ! ocean time-step index
1037	!!
1038	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
1039	REAL(wp) :: zcoef0, znad ! local scalars
1040	!
1041	!! The local variables for the correction term
1042	INTEGER :: jk1, jis, jid, jjs, jjd
1043	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
1044	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
1045	REAL(wp) :: zrhdt1
1046	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
1047	REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh
1048	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
1049	REAL(wp), POINTER, DIMENSION(:,:) :: zsshu_n, zsshv_n
1050	REAL(wp), POINTER, DIMENSION(:,:) :: zcpx, zcpy !W/D pressure filter
1051	!!----------------------------------------------------------------------
1052	!
1053	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
1054	CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh )
1055	CALL wrk_alloc( jpi,jpj, zsshu_n, zsshv_n )
1056	IF( ln_wd ) CALL wrk_alloc( jpi,jpj, zcpx, zcpy )
1057	!
1058	IF( kt == nit000 ) THEN
1059	IF(lwp) WRITE(numout,*)
1060	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
1061	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
1062	ENDIF
1063
1064	! Local constant initialization
1065	zcoef0 = - grav
1066	znad = 1._wp
1067	IF( ln_linssh ) znad = 0._wp
1068
1069	IF( ln_wd ) THEN
1070	DO jj = 2, jpjm1
1071	DO ji = 2, jpim1
1072	ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji+1,jj) ) > &
1073	& MAX( -ht_wd(ji,jj) , -ht_wd(ji+1,jj) ) .AND. &
1074	& MAX( sshn(ji,jj) + ht_wd(ji,jj), sshn(ji+1,jj) + ht_wd(ji+1,jj) ) &
1075	& > rn_wdmin1 + rn_wdmin2
1076	ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji+1,jj) ) > 1.E-12 ) .AND. ( &
1077	& MAX( sshn(ji,jj) , sshn(ji+1,jj) ) > &
1078	& MAX( -ht_wd(ji,jj) , -ht_wd(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
1079
1080	IF(ll_tmp1) THEN
1081	zcpx(ji,jj) = 1.0_wp
1082	ELSE IF(ll_tmp2) THEN
1083	! no worries about sshn(ji+1,jj) - sshn(ji ,jj) = 0, it won't happen ! here
1084	zcpx(ji,jj) = ABS( (sshn(ji+1,jj) + ht_wd(ji+1,jj) - sshn(ji,jj) - ht_wd(ji,jj)) &
1085	& / (sshn(ji+1,jj) - sshn(ji ,jj)) )
1086	ELSE
1087	zcpx(ji,jj) = 0._wp
1088	END IF
1089
1090	ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji,jj+1) ) > &
1091	& MAX( -ht_wd(ji,jj) , -ht_wd(ji,jj+1) ) .AND. &
1092	& MAX( sshn(ji,jj) + ht_wd(ji,jj), sshn(ji,jj+1) + ht_wd(ji,jj+1) ) &
1093	& > rn_wdmin1 + rn_wdmin2
1094	ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji,jj+1) ) > 1.E-12 ) .AND. ( &
1095	& MAX( sshn(ji,jj) , sshn(ji,jj+1) ) > &
1096	& MAX( -ht_wd(ji,jj) , -ht_wd(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
1097
1098	IF(ll_tmp1) THEN
1099	zcpy(ji,jj) = 1.0_wp
1100	ELSE IF(ll_tmp2) THEN
1101	! no worries about sshn(ji,jj+1) - sshn(ji,jj ) = 0, it won't happen ! here
1102	zcpy(ji,jj) = ABS( (sshn(ji,jj+1) + ht_wd(ji,jj+1) - sshn(ji,jj) - ht_wd(ji,jj)) &
1103	& / (sshn(ji,jj+1) - sshn(ji,jj )) )
1104	ELSE
1105	zcpy(ji,jj) = 0._wp
1106	END IF
1107	END DO
1108	END DO
1109	CALL lbc_lnk( zcpx, 'U', 1._wp ) ; CALL lbc_lnk( zcpy, 'V', 1._wp )
1110	END IF
1111
1112	! Clean 3-D work arrays
1113	zhpi(:,:,:) = 0._wp
1114	zrhh(:,:,:) = rhd(:,:,:)
1115
1116	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
1117	DO jj = 1, jpj
1118	DO ji = 1, jpi
1119	jk = mbkt(ji,jj)+1
1120	IF( jk <= 0 ) THEN ; zrhh(ji,jj, : ) = 0._wp
1121	ELSEIF( jk == 1 ) THEN ; zrhh(ji,jj,jk+1:jpk) = rhd(ji,jj,jk)
1122	ELSEIF( jk < jpkm1 ) THEN
1123	DO jkk = jk+1, jpk
1124	zrhh(ji,jj,jkk) = interp1(gde3w_n(ji,jj,jkk ), gde3w_n(ji,jj,jkk-1), &
1125	& gde3w_n(ji,jj,jkk-2), rhd (ji,jj,jkk-1), rhd(ji,jj,jkk-2))
1126	END DO
1127	ENDIF
1128	END DO
1129	END DO
1130
1131	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
1132	DO jj = 1, jpj
1133	DO ji = 1, jpi
1134	zdept(ji,jj,1) = 0.5_wp * e3w_n(ji,jj,1) - sshn(ji,jj) * znad
1135	END DO
1136	END DO
1137
1138	DO jk = 2, jpk
1139	DO jj = 1, jpj
1140	DO ji = 1, jpi
1141	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + e3w_n(ji,jj,jk)
1142	END DO
1143	END DO
1144	END DO
1145
1146	fsp(:,:,:) = zrhh (:,:,:)
1147	xsp(:,:,:) = zdept(:,:,:)
1148
1149	! Construct the vertical density profile with the
1150	! constrained cubic spline interpolation
1151	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
1152	CALL cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
1153
1154	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
1155	DO jj = 2, jpj
1156	DO ji = 2, jpi
1157	zrhdt1 = zrhh(ji,jj,1) - interp3( zdept(ji,jj,1), asp(ji,jj,1), bsp(ji,jj,1), &
1158	& csp(ji,jj,1), dsp(ji,jj,1) ) * 0.25_wp * e3w_n(ji,jj,1)
1159
1160	! assuming linear profile across the top half surface layer
1161	zhpi(ji,jj,1) = 0.5_wp * e3w_n(ji,jj,1) * zrhdt1
1162	END DO
1163	END DO
1164
1165	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
1166	DO jk = 2, jpkm1
1167	DO jj = 2, jpj
1168	DO ji = 2, jpi
1169	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
1170	& integ_spline( zdept(ji,jj,jk-1), zdept(ji,jj,jk), &
1171	& asp (ji,jj,jk-1), bsp (ji,jj,jk-1), &
1172	& csp (ji,jj,jk-1), dsp (ji,jj,jk-1) )
1173	END DO
1174	END DO
1175	END DO
1176
1177	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
1178
1179	! Prepare zsshu_n and zsshv_n
1180	DO jj = 2, jpjm1
1181	DO ji = 2, jpim1
1182	!!gm BUG ? if it is ssh at u- & v-point then it should be:
1183	! zsshu_n(ji,jj) = (e1e2t(ji,jj) * sshn(ji,jj) + e1e2t(ji+1,jj) * sshn(ji+1,jj)) * &
1184	! & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
1185	! zsshv_n(ji,jj) = (e1e2t(ji,jj) * sshn(ji,jj) + e1e2t(ji,jj+1) * sshn(ji,jj+1)) * &
1186	! & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
1187	!!gm not this:
1188	zsshu_n(ji,jj) = (e1e2u(ji,jj) * sshn(ji,jj) + e1e2u(ji+1, jj) * sshn(ji+1,jj)) * &
1189	& r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
1190	zsshv_n(ji,jj) = (e1e2v(ji,jj) * sshn(ji,jj) + e1e2v(ji+1, jj) * sshn(ji,jj+1)) * &
1191	& r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
1192	END DO
1193	END DO
1194
1195	CALL lbc_lnk (zsshu_n, 'U', 1.)
1196	CALL lbc_lnk (zsshv_n, 'V', 1.)
1197
1198	DO jj = 2, jpjm1
1199	DO ji = 2, jpim1
1200	zu(ji,jj,1) = - ( e3u_n(ji,jj,1) - zsshu_n(ji,jj) * znad)
1201	zv(ji,jj,1) = - ( e3v_n(ji,jj,1) - zsshv_n(ji,jj) * znad)
1202	END DO
1203	END DO
1204
1205	DO jk = 2, jpkm1
1206	DO jj = 2, jpjm1
1207	DO ji = 2, jpim1
1208	zu(ji,jj,jk) = zu(ji,jj,jk-1) - e3u_n(ji,jj,jk)
1209	zv(ji,jj,jk) = zv(ji,jj,jk-1) - e3v_n(ji,jj,jk)
1210	END DO
1211	END DO
1212	END DO
1213
1214	DO jk = 1, jpkm1
1215	DO jj = 2, jpjm1
1216	DO ji = 2, jpim1
1217	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * e3u_n(ji,jj,jk)
1218	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * e3v_n(ji,jj,jk)
1219	END DO
1220	END DO
1221	END DO
1222
1223	DO jk = 1, jpkm1
1224	DO jj = 2, jpjm1
1225	DO ji = 2, jpim1
1226	zu(ji,jj,jk) = MIN( zu(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
1227	zu(ji,jj,jk) = MAX( zu(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
1228	zv(ji,jj,jk) = MIN( zv(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
1229	zv(ji,jj,jk) = MAX( zv(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
1230	END DO
1231	END DO
1232	END DO
1233
1234
1235	DO jk = 1, jpkm1
1236	DO jj = 2, jpjm1
1237	DO ji = 2, jpim1
1238	zpwes = 0._wp; zpwed = 0._wp
1239	zpnss = 0._wp; zpnsd = 0._wp
1240	zuijk = zu(ji,jj,jk)
1241	zvijk = zv(ji,jj,jk)
1242
1243	!!!!! for u equation
1244	IF( jk <= mbku(ji,jj) ) THEN
1245	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
1246	jis = ji + 1; jid = ji
1247	ELSE
1248	jis = ji; jid = ji +1
1249	ENDIF
1250
1251	! integrate the pressure on the shallow side
1252	jk1 = jk
1253	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
1254	IF( jk1 == mbku(ji,jj) ) THEN
1255	zuijk = -zdept(jis,jj,jk1)
1256	EXIT
1257	ENDIF
1258	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
1259	zpwes = zpwes + &
1260	integ_spline(zdept(jis,jj,jk1), zdeps, &
1261	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
1262	csp(jis,jj,jk1), dsp(jis,jj,jk1))
1263	jk1 = jk1 + 1
1264	END DO
1265
1266	! integrate the pressure on the deep side
1267	jk1 = jk
1268	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
1269	IF( jk1 == 1 ) THEN
1270	zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad)
1271	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
1272	bsp(jid,jj,1), csp(jid,jj,1), &
1273	dsp(jid,jj,1)) * zdeps
1274	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
1275	EXIT
1276	ENDIF
1277	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
1278	zpwed = zpwed + &
1279	integ_spline(zdeps, zdept(jid,jj,jk1), &
1280	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
1281	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
1282	jk1 = jk1 - 1
1283	END DO
1284
1285	! update the momentum trends in u direction
1286
1287	zdpdx1 = zcoef0 * r1_e1u(ji,jj) * ( zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk) )
1288	IF( .NOT.ln_linssh ) THEN
1289	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * &
1290	& ( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) )
1291	ELSE
1292	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
1293	ENDIF
1294	IF( ln_wd ) THEN
1295	zdpdx1 = zdpdx1 * zcpx(ji,jj)
1296	zdpdx2 = zdpdx2 * zcpx(ji,jj)
1297	ENDIF
1298	ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * umask(ji,jj,jk)
1299	ENDIF
1300
1301	!!!!! for v equation
1302	IF( jk <= mbkv(ji,jj) ) THEN
1303	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
1304	jjs = jj + 1; jjd = jj
1305	ELSE
1306	jjs = jj ; jjd = jj + 1
1307	ENDIF
1308
1309	! integrate the pressure on the shallow side
1310	jk1 = jk
1311	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
1312	IF( jk1 == mbkv(ji,jj) ) THEN
1313	zvijk = -zdept(ji,jjs,jk1)
1314	EXIT
1315	ENDIF
1316	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
1317	zpnss = zpnss + &
1318	integ_spline(zdept(ji,jjs,jk1), zdeps, &
1319	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
1320	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
1321	jk1 = jk1 + 1
1322	END DO
1323
1324	! integrate the pressure on the deep side
1325	jk1 = jk
1326	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
1327	IF( jk1 == 1 ) THEN
1328	zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad)
1329	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
1330	bsp(ji,jjd,1), csp(ji,jjd,1), &
1331	dsp(ji,jjd,1) ) * zdeps
1332	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
1333	EXIT
1334	ENDIF
1335	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
1336	zpnsd = zpnsd + &
1337	integ_spline(zdeps, zdept(ji,jjd,jk1), &
1338	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
1339	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
1340	jk1 = jk1 - 1
1341	END DO
1342
1343
1344	! update the momentum trends in v direction
1345
1346	zdpdy1 = zcoef0 * r1_e2v(ji,jj) * ( zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk) )
1347	IF( .NOT.ln_linssh ) THEN
1348	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * &
1349	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) )
1350	ELSE
1351	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
1352	ENDIF
1353	IF( ln_wd ) THEN
1354	zdpdy1 = zdpdy1 * zcpy(ji,jj)
1355	zdpdy2 = zdpdy2 * zcpy(ji,jj)
1356	ENDIF
1357
1358	va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2) * vmask(ji,jj,jk)
1359	ENDIF
1360	!
1361	END DO
1362	END DO
1363	END DO
1364	!
1365	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
1366	CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh )
1367	CALL wrk_dealloc( jpi,jpj, zsshu_n, zsshv_n )
1368	IF( ln_wd ) CALL wrk_dealloc( jpi,jpj, zcpx, zcpy )
1369	!
1370	END SUBROUTINE hpg_prj
1371
1372
1373	SUBROUTINE cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
1374	!!----------------------------------------------------------------------
1375	!! * ROUTINE cspline *
1376	!!
1377	!! ** Purpose : constrained cubic spline interpolation
1378	!!
1379	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
1380	!!
1381	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
1382	!!----------------------------------------------------------------------
1383	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: fsp, xsp ! value and coordinate
1384	REAL(wp), DIMENSION(:,:,:), INTENT( out) :: asp, bsp, csp, dsp ! coefficients of the interpoated function
1385	INTEGER , INTENT(in ) :: polynomial_type ! 1: cubic spline ; 2: Linear
1386	!
1387	INTEGER :: ji, jj, jk ! dummy loop indices
1388	INTEGER :: jpi, jpj, jpkm1
1389	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
1390	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
1391	REAL(wp) :: zdf(size(fsp,3))
1392	!!----------------------------------------------------------------------
1393	!
1394	!!gm WHAT !!!!! THIS IS VERY DANGEROUS !!!!!
1395	jpi = size(fsp,1)
1396	jpj = size(fsp,2)
1397	jpkm1 = MAX( 1, size(fsp,3) - 1 )
1398	!
1399	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
1400	DO ji = 1, jpi
1401	DO jj = 1, jpj
1402	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
1403	! DO jk = 2, jpkm1-1
1404	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
1405	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1406	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
1407	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
1408	!
1409	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
1410	!
1411	! IF(zdf1 * zdf2 <= 0._wp) THEN
1412	! zdf(jk) = 0._wp
1413	! ELSE
1414	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
1415	! ENDIF
1416	! END DO
1417
1418	!!Simply geometric average
1419	DO jk = 2, jpkm1-1
1420	zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1))
1421	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk))
1422
1423	IF(zdf1 * zdf2 <= 0._wp) THEN
1424	zdf(jk) = 0._wp
1425	ELSE
1426	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
1427	ENDIF
1428	END DO
1429
1430	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
1431	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
1432	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
1433	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - 0.5_wp * zdf(jpkm1 - 1)
1434
1435	DO jk = 1, jpkm1 - 1
1436	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1437	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
1438	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
1439	zddf1 = -2._wp * ztmp1 + ztmp2
1440	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
1441	zddf2 = 2._wp * ztmp1 - ztmp2
1442
1443	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
1444	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
1445	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
1446	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
1447	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
1448	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
1449	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
1450	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
1451	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
1452	END DO
1453	END DO
1454	END DO
1455
1456	ELSEIF ( polynomial_type == 2 ) THEN ! Linear
1457	DO ji = 1, jpi
1458	DO jj = 1, jpj
1459	DO jk = 1, jpkm1-1
1460	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1461	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
1462
1463	dsp(ji,jj,jk) = 0._wp
1464	csp(ji,jj,jk) = 0._wp
1465	bsp(ji,jj,jk) = ztmp1 / zdxtmp
1466	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
1467	END DO
1468	END DO
1469	END DO
1470
1471	ELSE
1472	CALL ctl_stop( 'invalid polynomial type in cspline' )
1473	ENDIF
1474
1475	END SUBROUTINE cspline
1476
1477
1478	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
1479	!!----------------------------------------------------------------------
1480	!! * ROUTINE interp1 *
1481	!!
1482	!! ** Purpose : 1-d linear interpolation
1483	!!
1484	!! ** Method : interpolation is straight forward
1485	!! extrapolation is also permitted (no value limit)
1486	!!----------------------------------------------------------------------
1487	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
1488	REAL(wp) :: f ! result of the interpolation (extrapolation)
1489	REAL(wp) :: zdeltx
1490	!!----------------------------------------------------------------------
1491	!
1492	zdeltx = xr - xl
1493	IF( abs(zdeltx) <= 10._wp * EPSILON(x) ) THEN
1494	f = 0.5_wp * (fl + fr)
1495	ELSE
1496	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
1497	ENDIF
1498	!
1499	END FUNCTION interp1
1500
1501
1502	FUNCTION interp2( x, a, b, c, d ) RESULT(f)
1503	!!----------------------------------------------------------------------
1504	!! * ROUTINE interp1 *
1505	!!
1506	!! ** Purpose : 1-d constrained cubic spline interpolation
1507	!!
1508	!! ** Method : cubic spline interpolation
1509	!!
1510	!!----------------------------------------------------------------------
1511	REAL(wp), INTENT(in) :: x, a, b, c, d
1512	REAL(wp) :: f ! value from the interpolation
1513	!!----------------------------------------------------------------------
1514	!
1515	f = a + x* ( b + x * ( c + d * x ) )
1516	!
1517	END FUNCTION interp2
1518
1519
1520	FUNCTION interp3( x, a, b, c, d ) RESULT(f)
1521	!!----------------------------------------------------------------------
1522	!! * ROUTINE interp1 *
1523	!!
1524	!! ** Purpose : Calculate the first order of deriavtive of
1525	!! a cubic spline function y=a+bx+cx^2+d*x^3
1526	!!
1527	!! ** Method : f=dy/dx=b+2cx+3dx^2
1528	!!
1529	!!----------------------------------------------------------------------
1530	REAL(wp), INTENT(in) :: x, a, b, c, d
1531	REAL(wp) :: f ! value from the interpolation
1532	!!----------------------------------------------------------------------
1533	!
1534	f = b + x * ( 2._wp * c + 3._wp * d * x)
1535	!
1536	END FUNCTION interp3
1537
1538
1539	FUNCTION integ_spline( xl, xr, a, b, c, d ) RESULT(f)
1540	!!----------------------------------------------------------------------
1541	!! * ROUTINE interp1 *
1542	!!
1543	!! ** Purpose : 1-d constrained cubic spline integration
1544	!!
1545	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
1546	!!
1547	!!----------------------------------------------------------------------
1548	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
1549	REAL(wp) :: za1, za2, za3
1550	REAL(wp) :: f ! integration result
1551	!!----------------------------------------------------------------------
1552	!
1553	za1 = 0.5_wp * b
1554	za2 = c / 3.0_wp
1555	za3 = 0.25_wp * d
1556	!
1557	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
1558	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
1559	!
1560	END FUNCTION integ_spline
1561
1562	!!======================================================================
1563	END MODULE dynhpg
1564

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