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dynhpg.F90 in branches/UKMO/dev_r5518_pcbias_ipc/NEMOGCM/NEMO/OPA_SRC/DYN – NEMO

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source: branches/UKMO/dev_r5518_pcbias_ipc/NEMOGCM/NEMO/OPA_SRC/DYN/dynhpg.F90 @ 7652

Last change on this file since 7652 was 7652, checked in by isabella, 8 years ago
adding output messages to understand what model does
File size: 71.0 KB

Line
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 phycst ! physical constants
36	USE trd_oce ! trends: ocean variables
37	USE trddyn ! trend manager: dynamics
38	!
39	USE in_out_manager ! I/O manager
40	USE prtctl ! Print control
41	USE lbclnk ! lateral boundary condition
42	USE lib_mpp ! MPP library
43	USE eosbn2 ! compute density
44	USE wrk_nemo ! Memory Allocation
45	USE timing ! Timing
46	USE biaspar ! bias correction variables
47
48	IMPLICIT NONE
49	PRIVATE
50
51	PUBLIC dyn_hpg ! routine called by step module
52	PUBLIC dyn_hpg_init ! routine called by opa module
53
54	! !!* Namelist namdyn_hpg : hydrostatic pressure gradient
55	LOGICAL , PUBLIC :: ln_hpg_zco !: z-coordinate - full steps
56	LOGICAL , PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation)
57	LOGICAL , PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation)
58	LOGICAL , PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial)
59	LOGICAL , PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme)
60	LOGICAL , PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf
61	LOGICAL , PUBLIC :: ln_dynhpg_imp !: semi-implicite hpg flag
62
63	INTEGER , PUBLIC :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM)
64
65	!! * Substitutions
66	# include "domzgr_substitute.h90"
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	REAL(wp), DIMENSION(jpi,jpj,jpk) :: z_rhd_st ! tmp density storage for pressure corr
88	REAL(wp), DIMENSION(jpi,jpj) :: z_gru_st ! tmp ua trends storage for pressure corr
89	REAL(wp), DIMENSION(jpi,jpj) :: z_grv_st ! tmp va trends storage for pressure corr
90	!!----------------------------------------------------------------------
91	!
92	IF( nn_timing == 1 ) CALL timing_start('dyn_hpg')
93	!
94	IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn)
95	CALL wrk_alloc( jpi,jpj,jpk, ztrdu, ztrdv )
96	ztrdu(:,:,:) = ua(:,:,:)
97	ztrdv(:,:,:) = va(:,:,:)
98	ENDIF
99	!
100	IF ( ln_bias .AND. ln_bias_pc_app ) THEN
101	IF(lwp) THEN
102	WRITE(numout,*) " ! store orig density, use pressure corrected density"
103	ENDIF
104	z_rhd_st(:,:,:) = rhd(:,:,:) ! store orig density
105	rhd(:,:,:) = rhd_pc(:,:,:) ! use pressure corrected density
106	z_gru_st(:,:) = gru(:,:)
107	gru(:,:) = gru_pc(:,:)
108	z_grv_st(:,:) = grv(:,:)
109	grv(:,:) = grv_pc(:,:)
110	ENDIF
111	!
112	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
113	CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate
114	CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation)
115	CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation)
116	CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial)
117	CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme)
118	CASE ( 5 ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf
119	END SELECT
120	!
121	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
122	ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:)
123	ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:)
124	CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt )
125	CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv )
126	ENDIF
127	!
128	IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, &
129	& tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
130	!
131	IF ( ln_bias .AND. ln_bias_pc_app ) THEN
132	IF(lwp) THEN
133	WRITE(numout,*) " ! restore original density"
134	ENDIF
135	rhd(:,:,:) = z_rhd_st(:,:,:) ! restore original density
136	gru(:,:) = z_gru_st(:,:)
137	grv(:,:) = z_grv_st(:,:)
138	ENDIF
139	!
140	IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg')
141	!
142	END SUBROUTINE dyn_hpg
143
144
145	SUBROUTINE dyn_hpg_init
146	!!----------------------------------------------------------------------
147	!! * ROUTINE dyn_hpg_init *
148	!!
149	!! ** Purpose : initializations for the hydrostatic pressure gradient
150	!! computation and consistency control
151	!!
152	!! ** Action : Read the namelist namdyn_hpg and check the consistency
153	!! with the type of vertical coordinate used (zco, zps, sco)
154	!!----------------------------------------------------------------------
155	INTEGER :: ioptio = 0 ! temporary integer
156	INTEGER :: ios ! Local integer output status for namelist read
157	!!
158	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
159	& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf, ln_dynhpg_imp
160	!!----------------------------------------------------------------------
161	!
162	REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient
163	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
164	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp )
165
166	REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient
167	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
168	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp )
169	IF(lwm) WRITE ( numond, namdyn_hpg )
170	!
171	IF(lwp) THEN ! Control print
172	WRITE(numout,*)
173	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
174	WRITE(numout,*) '~~~~~~~~~~~~'
175	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
176	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
177	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
178	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
179	WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf
180	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
181	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
182	WRITE(numout,*) ' time stepping: centered (F) or semi-implicit (T) ln_dynhpg_imp = ', ln_dynhpg_imp
183	ENDIF
184	!
185	IF( ln_hpg_djc ) &
186	& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method &
187	& currently disabled (bugs under investigation). Please select &
188	& either ln_hpg_sco or ln_hpg_prj instead')
189	!
190	IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) &
191	& CALL ctl_stop('dyn_hpg_init : variable volume key_vvl requires:&
192	& the standard jacobian formulation hpg_sco or &
193	& the pressure jacobian formulation hpg_prj')
194
195	IF( ln_hpg_isf .AND. .NOT. ln_isfcav ) &
196	& CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' )
197	IF( .NOT. ln_hpg_isf .AND. ln_isfcav ) &
198	& CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' )
199	!
200	! ! Set nhpg from ln_hpg_... flags
201	IF( ln_hpg_zco ) nhpg = 0
202	IF( ln_hpg_zps ) nhpg = 1
203	IF( ln_hpg_sco ) nhpg = 2
204	IF( ln_hpg_djc ) nhpg = 3
205	IF( ln_hpg_prj ) nhpg = 4
206	IF( ln_hpg_isf ) nhpg = 5
207	!
208	! ! Consistency check
209	ioptio = 0
210	IF( ln_hpg_zco ) ioptio = ioptio + 1
211	IF( ln_hpg_zps ) ioptio = ioptio + 1
212	IF( ln_hpg_sco ) ioptio = ioptio + 1
213	IF( ln_hpg_djc ) ioptio = ioptio + 1
214	IF( ln_hpg_prj ) ioptio = ioptio + 1
215	IF( ln_hpg_isf ) ioptio = ioptio + 1
216	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
217	!
218	! initialisation of ice load
219	riceload(:,:)=0.0
220	!
221	END SUBROUTINE dyn_hpg_init
222
223
224	SUBROUTINE hpg_zco( kt )
225	!!---------------------------------------------------------------------
226	!! * ROUTINE hpg_zco *
227	!!
228	!! ** Method : z-coordinate case, levels are horizontal surfaces.
229	!! The now hydrostatic pressure gradient at a given level, jk,
230	!! is computed by taking the vertical integral of the in-situ
231	!! density gradient along the model level from the suface to that
232	!! level: zhpi = grav .....
233	!! zhpj = grav .....
234	!! add it to the general momentum trend (ua,va).
235	!! ua = ua - 1/e1u * zhpi
236	!! va = va - 1/e2v * zhpj
237	!!
238	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
239	!!----------------------------------------------------------------------
240	INTEGER, INTENT(in) :: kt ! ocean time-step index
241	!!
242	INTEGER :: ji, jj, jk ! dummy loop indices
243	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
244	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
245	!!----------------------------------------------------------------------
246	!
247	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
248	!
249	IF( kt == nit000 ) THEN
250	IF(lwp) WRITE(numout,*)
251	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
252	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
253	ENDIF
254
255	zcoef0 = - grav * 0.5_wp ! Local constant initialization
256
257	! Surface value
258	DO jj = 2, jpjm1
259	DO ji = fs_2, fs_jpim1 ! vector opt.
260	zcoef1 = zcoef0 * fse3w(ji,jj,1)
261	! hydrostatic pressure gradient
262	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
263	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
264	! add to the general momentum trend
265	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
266	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
267	END DO
268	END DO
269
270	!
271	! interior value (2=<jk=<jpkm1)
272	DO jk = 2, jpkm1
273	DO jj = 2, jpjm1
274	DO ji = fs_2, fs_jpim1 ! vector opt.
275	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
276	! hydrostatic pressure gradient
277	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
278	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
279	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
280
281	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
282	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
283	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
284	! add to the general momentum trend
285	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
286	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
287	END DO
288	END DO
289	END DO
290	!
291	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
292	!
293	END SUBROUTINE hpg_zco
294
295
296	SUBROUTINE hpg_zps( kt )
297	!!---------------------------------------------------------------------
298	!! * ROUTINE hpg_zps *
299	!!
300	!! ** Method : z-coordinate plus partial steps case. blahblah...
301	!!
302	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
303	!!----------------------------------------------------------------------
304	INTEGER, INTENT(in) :: kt ! ocean time-step index
305	!!
306	INTEGER :: ji, jj, jk ! dummy loop indices
307	INTEGER :: iku, ikv ! temporary integers
308	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
309	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
310	!!----------------------------------------------------------------------
311	!
312	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
313	!
314	IF( kt == nit000 ) THEN
315	IF(lwp) WRITE(numout,*)
316	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
317	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
318	ENDIF
319
320
321	! Local constant initialization
322	zcoef0 = - grav * 0.5_wp
323
324	! Surface value (also valid in partial step case)
325	DO jj = 2, jpjm1
326	DO ji = fs_2, fs_jpim1 ! vector opt.
327	zcoef1 = zcoef0 * fse3w(ji,jj,1)
328	! hydrostatic pressure gradient
329	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
330	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
331	! add to the general momentum trend
332	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
333	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
334	END DO
335	END DO
336
337
338	! interior value (2=<jk=<jpkm1)
339	DO jk = 2, jpkm1
340	DO jj = 2, jpjm1
341	DO ji = fs_2, fs_jpim1 ! vector opt.
342	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
343	! hydrostatic pressure gradient
344	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
345	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
346	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
347
348	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
349	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
350	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
351	! add to the general momentum trend
352	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
353	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
354	END DO
355	END DO
356	END DO
357
358
359	! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
360	DO jj = 2, jpjm1
361	DO ji = 2, jpim1
362	iku = mbku(ji,jj)
363	ikv = mbkv(ji,jj)
364	zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) )
365	zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) )
366	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
367	ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value
368	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
369	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj)
370	ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
371	ENDIF
372	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
373	va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value
374	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
375	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj)
376	va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
377	ENDIF
378	END DO
379	END DO
380	!
381	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
382	!
383	END SUBROUTINE hpg_zps
384
385	SUBROUTINE hpg_sco( kt )
386	!!---------------------------------------------------------------------
387	!! * ROUTINE hpg_sco *
388	!!
389	!! ** Method : s-coordinate case. Jacobian scheme.
390	!! The now hydrostatic pressure gradient at a given level, jk,
391	!! is computed by taking the vertical integral of the in-situ
392	!! density gradient along the model level from the suface to that
393	!! level. s-coordinates (ln_sco): a corrective term is added
394	!! to the horizontal pressure gradient :
395	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
396	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
397	!! add it to the general momentum trend (ua,va).
398	!! ua = ua - 1/e1u * zhpi
399	!! va = va - 1/e2v * zhpj
400	!!
401	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
402	!!----------------------------------------------------------------------
403	INTEGER, INTENT(in) :: kt ! ocean time-step index
404	!!
405	INTEGER :: ji, jj, jk ! dummy loop indices
406	REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars
407	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
408	!!----------------------------------------------------------------------
409	!
410	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
411	!
412	IF( kt == nit000 ) THEN
413	IF(lwp) WRITE(numout,*)
414	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
415	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
416	ENDIF
417
418	! Local constant initialization
419	zcoef0 = - grav * 0.5_wp
420	! To use density and not density anomaly
421	IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
422	ELSE ; znad = 0._wp ! Fixed volume
423	ENDIF
424
425	! Surface value
426	DO jj = 2, jpjm1
427	DO ji = fs_2, fs_jpim1 ! vector opt.
428	! hydrostatic pressure gradient along s-surfaces
429	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) &
430	& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
431	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) &
432	& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
433	! s-coordinate pressure gradient correction
434	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
435	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
436	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
437	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
438	! add to the general momentum trend
439	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap
440	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap
441	END DO
442	END DO
443
444	! interior value (2=<jk=<jpkm1)
445	DO jk = 2, jpkm1
446	DO jj = 2, jpjm1
447	DO ji = fs_2, fs_jpim1 ! vector opt.
448	! hydrostatic pressure gradient along s-surfaces
449	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
450	& * ( fse3w(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) &
451	& - fse3w(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) )
452	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
453	& * ( fse3w(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) &
454	& - fse3w(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) )
455	! s-coordinate pressure gradient correction
456	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
457	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj)
458	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
459	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj)
460	! add to the general momentum trend
461	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap
462	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap
463	END DO
464	END DO
465	END DO
466	!
467	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
468	!
469	END SUBROUTINE hpg_sco
470
471	SUBROUTINE hpg_isf( kt )
472	!!---------------------------------------------------------------------
473	!! * ROUTINE hpg_sco *
474	!!
475	!! ** Method : s-coordinate case. Jacobian scheme.
476	!! The now hydrostatic pressure gradient at a given level, jk,
477	!! is computed by taking the vertical integral of the in-situ
478	!! density gradient along the model level from the suface to that
479	!! level. s-coordinates (ln_sco): a corrective term is added
480	!! to the horizontal pressure gradient :
481	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
482	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
483	!! add it to the general momentum trend (ua,va).
484	!! ua = ua - 1/e1u * zhpi
485	!! va = va - 1/e2v * zhpj
486	!! iceload is added and partial cell case are added to the top and bottom
487	!!
488	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
489	!!----------------------------------------------------------------------
490	INTEGER, INTENT(in) :: kt ! ocean time-step index
491	!!
492	INTEGER :: ji, jj, jk, iku, ikv, ikt, iktp1i, iktp1j ! dummy loop indices
493	REAL(wp) :: zcoef0, zuap, zvap, znad, ze3wu, ze3wv, zuapint, zvapint, zhpjint, zhpiint, zdzwt, zdzwtjp1, zdzwtip1 ! temporary scalars
494	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj, zrhd
495	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop
496	REAL(wp), POINTER, DIMENSION(:,:) :: ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj
497	!!----------------------------------------------------------------------
498	!
499	CALL wrk_alloc( jpi,jpj, 2, ztstop)
500	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
501	CALL wrk_alloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
502	!
503	IF( kt == nit000 ) THEN
504	IF(lwp) WRITE(numout,*)
505	IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf'
506	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
507	ENDIF
508
509	! Local constant initialization
510	zcoef0 = - grav * 0.5_wp
511	! To use density and not density anomaly
512	! IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
513	! ELSE ; znad = 0._wp ! Fixed volume
514	! ENDIF
515	znad=1._wp
516	! iniitialised to 0. zhpi zhpi
517	zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp
518
519	!==================================================================================
520	!=====Compute iceload and contribution of the half first wet layer =================
521	!===================================================================================
522
523	! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude)
524	ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp
525
526	! compute density of the water displaced by the ice shelf
527	zrhd = rhd ! save rhd
528	DO jk = 1, jpk
529	zdept(:,:)=gdept_1d(jk)
530	CALL eos(ztstop(:,:,:),zdept(:,:),rhd(:,:,jk))
531	END DO
532	WHERE ( tmask(:,:,:) == 1._wp)
533	rhd(:,:,:) = zrhd(:,:,:) ! replace wet cell by the saved rhd
534	END WHERE
535
536	! compute rhd at the ice/oce interface (ice shelf side)
537	CALL eos(ztstop,risfdep,zrhdtop_isf)
538
539	! compute rhd at the ice/oce interface (ocean side)
540	DO ji=1,jpi
541	DO jj=1,jpj
542	ikt=mikt(ji,jj)
543	ztstop(ji,jj,1)=tsn(ji,jj,ikt,1)
544	ztstop(ji,jj,2)=tsn(ji,jj,ikt,2)
545	END DO
546	END DO
547	CALL eos(ztstop,risfdep,zrhdtop_oce)
548	!
549	! Surface value + ice shelf gradient
550	! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v)
551	ziceload = 0._wp
552	DO jj = 1, jpj
553	DO ji = 1, jpi ! vector opt.
554	ikt=mikt(ji,jj)
555	ziceload(ji,jj) = ziceload(ji,jj) + (znad + rhd(ji,jj,1) ) * fse3w(ji,jj,1) * (1._wp - tmask(ji,jj,1))
556	DO jk=2,ikt-1
557	ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + rhd(ji,jj,jk-1) + rhd(ji,jj,jk)) * fse3w(ji,jj,jk) &
558	& * (1._wp - tmask(ji,jj,jk))
559	END DO
560	IF (ikt .GE. 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + rhd(ji,jj,ikt-1)) &
561	& * ( risfdep(ji,jj) - gdept_1d(ikt-1) )
562	END DO
563	END DO
564	riceload(:,:) = 0.0_wp ; riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5
565	! compute zp from z=0 to first T wet point (correction due to zps not yet applied)
566	DO jj = 2, jpjm1
567	DO ji = fs_2, fs_jpim1 ! vector opt.
568	ikt=mikt(ji,jj) ; iktp1i=mikt(ji+1,jj); iktp1j=mikt(ji,jj+1)
569	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
570	! we assume ISF is in isostatic equilibrium
571	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * fse3w(ji+1,jj ,iktp1i) &
572	& * ( 2._wp * znad + rhd(ji+1,jj ,iktp1i) + zrhdtop_oce(ji+1,jj ) ) &
573	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
574	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
575	& + ( ziceload(ji+1,jj) - ziceload(ji,jj)) )
576	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * fse3w(ji ,jj+1,iktp1j) &
577	& * ( 2._wp * znad + rhd(ji ,jj+1,iktp1j) + zrhdtop_oce(ji ,jj+1) ) &
578	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
579	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
580	& + ( ziceload(ji,jj+1) - ziceload(ji,jj) ) )
581	! s-coordinate pressure gradient correction (=0 if z coordinate)
582	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
583	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
584	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
585	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
586	! add to the general momentum trend
587	ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
588	va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
589	END DO
590	END DO
591	!==================================================================================
592	!===== Compute partial cell contribution for the top cell =========================
593	!==================================================================================
594	DO jj = 2, jpjm1
595	DO ji = fs_2, fs_jpim1 ! vector opt.
596	iku = miku(ji,jj) ;
597	zpshpi(ji,jj)=0.0_wp ; zpshpj(ji,jj)=0.0_wp
598	ze3wu = (gdepw_0(ji+1,jj,iku+1) - gdept_0(ji+1,jj,iku)) - (gdepw_0(ji,jj,iku+1) - gdept_0(ji,jj,iku))
599	! u direction
600	IF ( iku .GT. 1 ) THEN
601	! case iku
602	zhpi(ji,jj,iku) = zcoef0 / e1u(ji,jj) * ze3wu &
603	& * ( rhd (ji+1,jj,iku) + rhd (ji,jj,iku) &
604	& + SIGN(1._wp,ze3wu) * grui(ji,jj) + 2._wp * znad )
605	! corrective term ( = 0 if z coordinate )
606	zuap = -zcoef0 * ( arui(ji,jj) + 2._wp * znad ) * gzui(ji,jj) / e1u(ji,jj)
607	! zhpi will be added in interior loop
608	ua(ji,jj,iku) = ua(ji,jj,iku) + zuap
609	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
610	IF (mbku(ji,jj) == iku + 1) zpshpi(ji,jj) = zhpi(ji,jj,iku)
611
612	! case iku + 1 (remove the zphi term added in the interior loop and compute the one corrected for zps)
613	zhpiint = zcoef0 / e1u(ji,jj) &
614	& * ( fse3w(ji+1,jj ,iku+1) * ( (rhd(ji+1,jj,iku+1) + znad) &
615	& + (rhd(ji+1,jj,iku ) + znad) ) * tmask(ji+1,jj,iku) &
616	& - fse3w(ji ,jj ,iku+1) * ( (rhd(ji ,jj,iku+1) + znad) &
617	& + (rhd(ji ,jj,iku ) + znad) ) * tmask(ji ,jj,iku) )
618	zhpi(ji,jj,iku+1) = zcoef0 / e1u(ji,jj) * ge3rui(ji,jj) - zhpiint
619	END IF
620
621	! v direction
622	ikv = mikv(ji,jj)
623	ze3wv = (gdepw_0(ji,jj+1,ikv+1) - gdept_0(ji,jj+1,ikv)) - (gdepw_0(ji,jj,ikv+1) - gdept_0(ji,jj,ikv))
624	IF ( ikv .GT. 1 ) THEN
625	! case ikv
626	zhpj(ji,jj,ikv) = zcoef0 / e2v(ji,jj) * ze3wv &
627	& * ( rhd(ji,jj+1,ikv) + rhd (ji,jj,ikv) &
628	& + SIGN(1._wp,ze3wv) * grvi(ji,jj) + 2._wp * znad )
629	! corrective term ( = 0 if z coordinate )
630	zvap = -zcoef0 * ( arvi(ji,jj) + 2._wp * znad ) * gzvi(ji,jj) / e2v(ji,jj)
631	! zhpi will be added in interior loop
632	va(ji,jj,ikv) = va(ji,jj,ikv) + zvap
633	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
634	IF (mbkv(ji,jj) == ikv + 1) zpshpj(ji,jj) = zhpj(ji,jj,ikv)
635
636	! case ikv + 1 (remove the zphj term added in the interior loop and compute the one corrected for zps)
637	zhpjint = zcoef0 / e2v(ji,jj) &
638	& * ( fse3w(ji ,jj+1,ikv+1) * ( (rhd(ji,jj+1,ikv+1) + znad) &
639	& + (rhd(ji,jj+1,ikv ) + znad) ) * tmask(ji,jj+1,ikv) &
640	& - fse3w(ji ,jj ,ikv+1) * ( (rhd(ji,jj ,ikv+1) + znad) &
641	& + (rhd(ji,jj ,ikv ) + znad) ) * tmask(ji,jj ,ikv) )
642	zhpj(ji,jj,ikv+1) = zcoef0 / e2v(ji,jj) * ge3rvi(ji,jj) - zhpjint
643	END IF
644	END DO
645	END DO
646
647	!==================================================================================
648	!===== Compute interior value =====================================================
649	!==================================================================================
650
651	DO jj = 2, jpjm1
652	DO ji = fs_2, fs_jpim1 ! vector opt.
653	iku=miku(ji,jj); ikv=mikv(ji,jj)
654	DO jk = 2, jpkm1
655	! hydrostatic pressure gradient along s-surfaces
656	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
657	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) + zhpi(ji,jj,jk-1) &
658	& + zcoef0 / e1u(ji,jj) &
659	& * ( fse3w(ji+1,jj ,jk) * ( (rhd(ji+1,jj,jk ) + znad) &
660	& + (rhd(ji+1,jj,jk-1) + znad) ) * tmask(ji+1,jj,jk-1) &
661	& - fse3w(ji ,jj ,jk) * ( (rhd(ji ,jj,jk ) + znad) &
662	& + (rhd(ji ,jj,jk-1) + znad) ) * tmask(ji ,jj,jk-1) )
663	! s-coordinate pressure gradient correction
664	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
665	zuap = - zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
666	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) * umask(ji,jj,jk-1)
667	ua(ji,jj,jk) = ua(ji,jj,jk) + ( zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
668
669	! hydrostatic pressure gradient along s-surfaces
670	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
671	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) + zhpj(ji,jj,jk-1) &
672	& + zcoef0 / e2v(ji,jj) &
673	& * ( fse3w(ji ,jj+1,jk) * ( (rhd(ji,jj+1,jk ) + znad) &
674	& + (rhd(ji,jj+1,jk-1) + znad) ) * tmask(ji,jj+1,jk-1) &
675	& - fse3w(ji ,jj ,jk) * ( (rhd(ji,jj ,jk ) + znad) &
676	& + (rhd(ji,jj ,jk-1) + znad) ) * tmask(ji,jj ,jk-1) )
677	! s-coordinate pressure gradient correction
678	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
679	zvap = - zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
680	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) * vmask(ji,jj,jk-1)
681	! add to the general momentum trend
682	va(ji,jj,jk) = va(ji,jj,jk) + ( zhpj(ji,jj,jk) + zvap ) * vmask(ji,jj,jk)
683	END DO
684	END DO
685	END DO
686
687	!==================================================================================
688	!===== Compute bottom cell contribution (partial cell) ============================
689	!==================================================================================
690
691	DO jj = 2, jpjm1
692	DO ji = 2, jpim1
693	iku = mbku(ji,jj)
694	ikv = mbkv(ji,jj)
695
696	IF (iku .GT. 1) THEN
697	! remove old value (interior case)
698	zuap = -zcoef0 * ( rhd (ji+1,jj ,iku) + rhd (ji,jj,iku) + 2._wp * znad ) &
699	& * ( fsde3w(ji+1,jj ,iku) - fsde3w(ji,jj,iku) ) / e1u(ji,jj)
700	ua(ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) - zuap
701	! put new value
702	! -zpshpi to avoid double contribution of the partial step in the top layer
703	zuap = -zcoef0 * ( aru(ji,jj) + 2._wp * znad ) * gzu(ji,jj) / e1u(ji,jj)
704	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) + zcoef0 / e1u(ji,jj) * ge3ru(ji,jj) - zpshpi(ji,jj)
705	ua(ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) + zuap
706	END IF
707	! v direction
708	IF (ikv .GT. 1) THEN
709	! remove old value (interior case)
710	zvap = -zcoef0 * ( rhd (ji ,jj+1,ikv) + rhd (ji,jj,ikv) + 2._wp * znad ) &
711	& * ( fsde3w(ji ,jj+1,ikv) - fsde3w(ji,jj,ikv) ) / e2v(ji,jj)
712	va(ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) - zvap
713	! put new value
714	! -zpshpj to avoid double contribution of the partial step in the top layer
715	zvap = -zcoef0 * ( arv(ji,jj) + 2._wp * znad ) * gzv(ji,jj) / e2v(ji,jj)
716	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) + zcoef0 / e2v(ji,jj) * ge3rv(ji,jj) - zpshpj(ji,jj)
717	va(ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) + zvap
718	END IF
719	END DO
720	END DO
721
722	! set back to original density value into the ice shelf cell (maybe useless because it is masked)
723	rhd = zrhd
724	!
725	CALL wrk_dealloc( jpi,jpj,2, ztstop)
726	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
727	CALL wrk_dealloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
728	!
729	END SUBROUTINE hpg_isf
730
731
732	SUBROUTINE hpg_djc( kt )
733	!!---------------------------------------------------------------------
734	!! * ROUTINE hpg_djc *
735	!!
736	!! ** Method : Density Jacobian with Cubic polynomial scheme
737	!!
738	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
739	!!----------------------------------------------------------------------
740	INTEGER, INTENT(in) :: kt ! ocean time-step index
741	!!
742	INTEGER :: ji, jj, jk ! dummy loop indices
743	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
744	REAL(wp) :: z1_10, cffu, cffx ! " "
745	REAL(wp) :: z1_12, cffv, cffy ! " "
746	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
747	REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw
748	REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow
749	REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k
750	!!----------------------------------------------------------------------
751	!
752	CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
753	CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
754	CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
755	!
756
757	IF( kt == nit000 ) THEN
758	IF(lwp) WRITE(numout,*)
759	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
760	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
761	ENDIF
762
763	! Local constant initialization
764	zcoef0 = - grav * 0.5_wp
765	z1_10 = 1._wp / 10._wp
766	z1_12 = 1._wp / 12._wp
767
768	!----------------------------------------------------------------------------------------
769	! compute and store in provisional arrays elementary vertical and horizontal differences
770	!----------------------------------------------------------------------------------------
771
772	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
773
774	DO jk = 2, jpkm1
775	DO jj = 2, jpjm1
776	DO ji = fs_2, fs_jpim1 ! vector opt.
777	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
778	dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1)
779	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
780	dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk )
781	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
782	dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk )
783	END DO
784	END DO
785	END DO
786
787	!-------------------------------------------------------------------------
788	! compute harmonic averages using eq. 5.18
789	!-------------------------------------------------------------------------
790	zep = 1.e-15
791
792	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
793	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
794
795	DO jk = 2, jpkm1
796	DO jj = 2, jpjm1
797	DO ji = fs_2, fs_jpim1 ! vector opt.
798	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
799
800	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
801	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
802
803	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
804	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
805
806	IF( cffw > zep) THEN
807	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
808	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
809	ELSE
810	drhow(ji,jj,jk) = 0._wp
811	ENDIF
812
813	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
814	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
815
816	IF( cffu > zep ) THEN
817	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
818	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
819	ELSE
820	drhou(ji,jj,jk ) = 0._wp
821	ENDIF
822
823	IF( cffx > zep ) THEN
824	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
825	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
826	ELSE
827	dzu(ji,jj,jk) = 0._wp
828	ENDIF
829
830	IF( cffv > zep ) THEN
831	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
832	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
833	ELSE
834	drhov(ji,jj,jk) = 0._wp
835	ENDIF
836
837	IF( cffy > zep ) THEN
838	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
839	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
840	ELSE
841	dzv(ji,jj,jk) = 0._wp
842	ENDIF
843
844	END DO
845	END DO
846	END DO
847
848	!----------------------------------------------------------------------------------
849	! apply boundary conditions at top and bottom using 5.36-5.37
850	!----------------------------------------------------------------------------------
851	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
852	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
853	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
854
855	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
856	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
857	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
858
859
860	!--------------------------------------------------------------
861	! Upper half of top-most grid box, compute and store
862	!-------------------------------------------------------------
863
864	!!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified
865	! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
866
867	DO jj = 2, jpjm1
868	DO ji = fs_2, fs_jpim1 ! vector opt.
869	rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) &
870	& * ( rhd(ji,jj,1) &
871	& + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) &
872	& * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) &
873	& / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) )
874	END DO
875	END DO
876
877	!!bug gm : here also, simplification is possible
878	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
879
880	DO jk = 2, jpkm1
881	DO jj = 2, jpjm1
882	DO ji = fs_2, fs_jpim1 ! vector opt.
883
884	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
885	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) &
886	& - grav * z1_10 * ( &
887	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
888	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
889	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
890	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
891	& )
892
893	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
894	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) &
895	& - grav* z1_10 * ( &
896	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
897	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
898	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
899	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
900	& )
901
902	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
903	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) &
904	& - grav* z1_10 * ( &
905	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
906	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
907	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
908	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
909	& )
910
911	END DO
912	END DO
913	END DO
914	CALL lbc_lnk(rho_k,'W',1.)
915	CALL lbc_lnk(rho_i,'U',1.)
916	CALL lbc_lnk(rho_j,'V',1.)
917
918
919	! ---------------
920	! Surface value
921	! ---------------
922	DO jj = 2, jpjm1
923	DO ji = fs_2, fs_jpim1 ! vector opt.
924	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj)
925	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj)
926	! add to the general momentum trend
927	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
928	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
929	END DO
930	END DO
931
932	! ----------------
933	! interior value (2=<jk=<jpkm1)
934	! ----------------
935	DO jk = 2, jpkm1
936	DO jj = 2, jpjm1
937	DO ji = fs_2, fs_jpim1 ! vector opt.
938	! hydrostatic pressure gradient along s-surfaces
939	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
940	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
941	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj)
942	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
943	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
944	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj)
945	! add to the general momentum trend
946	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
947	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
948	END DO
949	END DO
950	END DO
951	!
952	CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
953	CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
954	CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
955	!
956	END SUBROUTINE hpg_djc
957
958
959	SUBROUTINE hpg_prj( kt )
960	!!---------------------------------------------------------------------
961	!! * ROUTINE hpg_prj *
962	!!
963	!! ** Method : s-coordinate case.
964	!! A Pressure-Jacobian horizontal pressure gradient method
965	!! based on the constrained cubic-spline interpolation for
966	!! all vertical coordinate systems
967	!!
968	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
969	!!----------------------------------------------------------------------
970	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
971	INTEGER, INTENT(in) :: kt ! ocean time-step index
972	!!
973	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
974	REAL(wp) :: zcoef0, znad ! temporary scalars
975	!!
976	!! The local variables for the correction term
977	INTEGER :: jk1, jis, jid, jjs, jjd
978	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
979	REAL(wp) :: zrhdt1
980	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
981	REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh
982	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
983	REAL(wp), POINTER, DIMENSION(:,:) :: zsshu_n, zsshv_n
984	!!----------------------------------------------------------------------
985	!
986	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
987	CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh )
988	CALL wrk_alloc( jpi,jpj, zsshu_n, zsshv_n )
989	!
990	IF( kt == nit000 ) THEN
991	IF(lwp) WRITE(numout,*)
992	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
993	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
994	ENDIF
995
996	!!----------------------------------------------------------------------
997	! Local constant initialization
998	zcoef0 = - grav
999	znad = 0.0_wp
1000	IF( lk_vvl ) znad = 1._wp
1001
1002	! Clean 3-D work arrays
1003	zhpi(:,:,:) = 0._wp
1004	zrhh(:,:,:) = rhd(:,:,:)
1005
1006	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
1007	DO jj = 1, jpj
1008	DO ji = 1, jpi
1009	jk = mbathy(ji,jj)
1010	IF( jk <= 0 ) THEN; zrhh(ji,jj,:) = 0._wp
1011	ELSE IF(jk == 1) THEN; zrhh(ji,jj, jk+1:jpk) = rhd(ji,jj,jk)
1012	ELSE IF(jk < jpkm1) THEN
1013	DO jkk = jk+1, jpk
1014	zrhh(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1), &
1015	fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2))
1016	END DO
1017	ENDIF
1018	END DO
1019	END DO
1020
1021	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
1022	DO jj = 1, jpj
1023	DO ji = 1, jpi
1024	zdept(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) - sshn(ji,jj) * znad
1025	END DO
1026	END DO
1027
1028	DO jk = 2, jpk
1029	DO jj = 1, jpj
1030	DO ji = 1, jpi
1031	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + fse3w(ji,jj,jk)
1032	END DO
1033	END DO
1034	END DO
1035
1036	fsp(:,:,:) = zrhh (:,:,:)
1037	xsp(:,:,:) = zdept(:,:,:)
1038
1039	! Construct the vertical density profile with the
1040	! constrained cubic spline interpolation
1041	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
1042	CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type)
1043
1044	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
1045	DO jj = 2, jpj
1046	DO ji = 2, jpi
1047	zrhdt1 = zrhh(ji,jj,1) - interp3(zdept(ji,jj,1),asp(ji,jj,1), &
1048	bsp(ji,jj,1), csp(ji,jj,1), &
1049	dsp(ji,jj,1) ) * 0.25_wp * fse3w(ji,jj,1)
1050
1051	! assuming linear profile across the top half surface layer
1052	zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * zrhdt1
1053	END DO
1054	END DO
1055
1056	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
1057	DO jk = 2, jpkm1
1058	DO jj = 2, jpj
1059	DO ji = 2, jpi
1060	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
1061	integ_spline(zdept(ji,jj,jk-1), zdept(ji,jj,jk),&
1062	asp(ji,jj,jk-1), bsp(ji,jj,jk-1), &
1063	csp(ji,jj,jk-1), dsp(ji,jj,jk-1))
1064	END DO
1065	END DO
1066	END DO
1067
1068	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
1069
1070	! Prepare zsshu_n and zsshv_n
1071	DO jj = 2, jpjm1
1072	DO ji = 2, jpim1
1073	zsshu_n(ji,jj) = (e12u(ji,jj) * sshn(ji,jj) + e12u(ji+1, jj) * sshn(ji+1,jj)) * &
1074	& r1_e12u(ji,jj) * umask(ji,jj,1) * 0.5_wp
1075	zsshv_n(ji,jj) = (e12v(ji,jj) * sshn(ji,jj) + e12v(ji+1, jj) * sshn(ji,jj+1)) * &
1076	& r1_e12v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
1077	END DO
1078	END DO
1079
1080	DO jj = 2, jpjm1
1081	DO ji = 2, jpim1
1082	zu(ji,jj,1) = - ( fse3u(ji,jj,1) - zsshu_n(ji,jj) * znad)
1083	zv(ji,jj,1) = - ( fse3v(ji,jj,1) - zsshv_n(ji,jj) * znad)
1084	END DO
1085	END DO
1086
1087	DO jk = 2, jpkm1
1088	DO jj = 2, jpjm1
1089	DO ji = 2, jpim1
1090	zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk)
1091	zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk)
1092	END DO
1093	END DO
1094	END DO
1095
1096	DO jk = 1, jpkm1
1097	DO jj = 2, jpjm1
1098	DO ji = 2, jpim1
1099	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk)
1100	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk)
1101	END DO
1102	END DO
1103	END DO
1104
1105	DO jk = 1, jpkm1
1106	DO jj = 2, jpjm1
1107	DO ji = 2, jpim1
1108	zu(ji,jj,jk) = min(zu(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
1109	zu(ji,jj,jk) = max(zu(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
1110	zv(ji,jj,jk) = min(zv(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
1111	zv(ji,jj,jk) = max(zv(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
1112	END DO
1113	END DO
1114	END DO
1115
1116
1117	DO jk = 1, jpkm1
1118	DO jj = 2, jpjm1
1119	DO ji = 2, jpim1
1120	zpwes = 0._wp; zpwed = 0._wp
1121	zpnss = 0._wp; zpnsd = 0._wp
1122	zuijk = zu(ji,jj,jk)
1123	zvijk = zv(ji,jj,jk)
1124
1125	!!!!! for u equation
1126	IF( jk <= mbku(ji,jj) ) THEN
1127	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
1128	jis = ji + 1; jid = ji
1129	ELSE
1130	jis = ji; jid = ji +1
1131	ENDIF
1132
1133	! integrate the pressure on the shallow side
1134	jk1 = jk
1135	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
1136	IF( jk1 == mbku(ji,jj) ) THEN
1137	zuijk = -zdept(jis,jj,jk1)
1138	EXIT
1139	ENDIF
1140	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
1141	zpwes = zpwes + &
1142	integ_spline(zdept(jis,jj,jk1), zdeps, &
1143	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
1144	csp(jis,jj,jk1), dsp(jis,jj,jk1))
1145	jk1 = jk1 + 1
1146	END DO
1147
1148	! integrate the pressure on the deep side
1149	jk1 = jk
1150	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
1151	IF( jk1 == 1 ) THEN
1152	zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad)
1153	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
1154	bsp(jid,jj,1), csp(jid,jj,1), &
1155	dsp(jid,jj,1)) * zdeps
1156	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
1157	EXIT
1158	ENDIF
1159	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
1160	zpwed = zpwed + &
1161	integ_spline(zdeps, zdept(jid,jj,jk1), &
1162	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
1163	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
1164	jk1 = jk1 - 1
1165	END DO
1166
1167	! update the momentum trends in u direction
1168
1169	zdpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk))
1170	IF( lk_vvl ) THEN
1171	zdpdx2 = zcoef0 / e1u(ji,jj) * &
1172	( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) )
1173	ELSE
1174	zdpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
1175	ENDIF
1176
1177	ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * &
1178	& umask(ji,jj,jk) * tmask(ji,jj,jk) * tmask(ji+1,jj,jk)
1179	ENDIF
1180
1181	!!!!! for v equation
1182	IF( jk <= mbkv(ji,jj) ) THEN
1183	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
1184	jjs = jj + 1; jjd = jj
1185	ELSE
1186	jjs = jj ; jjd = jj + 1
1187	ENDIF
1188
1189	! integrate the pressure on the shallow side
1190	jk1 = jk
1191	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
1192	IF( jk1 == mbkv(ji,jj) ) THEN
1193	zvijk = -zdept(ji,jjs,jk1)
1194	EXIT
1195	ENDIF
1196	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
1197	zpnss = zpnss + &
1198	integ_spline(zdept(ji,jjs,jk1), zdeps, &
1199	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
1200	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
1201	jk1 = jk1 + 1
1202	END DO
1203
1204	! integrate the pressure on the deep side
1205	jk1 = jk
1206	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
1207	IF( jk1 == 1 ) THEN
1208	zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad)
1209	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
1210	bsp(ji,jjd,1), csp(ji,jjd,1), &
1211	dsp(ji,jjd,1) ) * zdeps
1212	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
1213	EXIT
1214	ENDIF
1215	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
1216	zpnsd = zpnsd + &
1217	integ_spline(zdeps, zdept(ji,jjd,jk1), &
1218	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
1219	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
1220	jk1 = jk1 - 1
1221	END DO
1222
1223
1224	! update the momentum trends in v direction
1225
1226	zdpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk))
1227	IF( lk_vvl ) THEN
1228	zdpdy2 = zcoef0 / e2v(ji,jj) * &
1229	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) )
1230	ELSE
1231	zdpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
1232	ENDIF
1233
1234	va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2)*&
1235	& vmask(ji,jj,jk)tmask(ji,jj,jk)tmask(ji,jj+1,jk)
1236	ENDIF
1237
1238
1239	END DO
1240	END DO
1241	END DO
1242	!
1243	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
1244	CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh )
1245	CALL wrk_dealloc( jpi,jpj, zsshu_n, zsshv_n )
1246	!
1247	END SUBROUTINE hpg_prj
1248
1249
1250	SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type)
1251	!!----------------------------------------------------------------------
1252	!! * ROUTINE cspline *
1253	!!
1254	!! ** Purpose : constrained cubic spline interpolation
1255	!!
1256	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
1257	!!
1258	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
1259	!!----------------------------------------------------------------------
1260	IMPLICIT NONE
1261	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate
1262	REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of
1263	! the interpoated function
1264	INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline
1265	! 2: Linear
1266	!
1267	INTEGER :: ji, jj, jk ! dummy loop indices
1268	INTEGER :: jpi, jpj, jpkm1
1269	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
1270	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
1271	REAL(wp) :: zdf(size(fsp,3))
1272	!!----------------------------------------------------------------------
1273
1274	jpi = size(fsp,1)
1275	jpj = size(fsp,2)
1276	jpkm1 = size(fsp,3) - 1
1277
1278
1279	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
1280	DO ji = 1, jpi
1281	DO jj = 1, jpj
1282	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
1283	! DO jk = 2, jpkm1-1
1284	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
1285	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1286	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
1287	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
1288	!
1289	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
1290	!
1291	! IF(zdf1 * zdf2 <= 0._wp) THEN
1292	! zdf(jk) = 0._wp
1293	! ELSE
1294	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
1295	! ENDIF
1296	! END DO
1297
1298	!!Simply geometric average
1299	DO jk = 2, jpkm1-1
1300	zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1))
1301	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk))
1302
1303	IF(zdf1 * zdf2 <= 0._wp) THEN
1304	zdf(jk) = 0._wp
1305	ELSE
1306	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
1307	ENDIF
1308	END DO
1309
1310	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
1311	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
1312	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
1313	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - &
1314	& 0.5_wp * zdf(jpkm1 - 1)
1315
1316	DO jk = 1, jpkm1 - 1
1317	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1318	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
1319	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
1320	zddf1 = -2._wp * ztmp1 + ztmp2
1321	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
1322	zddf2 = 2._wp * ztmp1 - ztmp2
1323
1324	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
1325	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
1326	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
1327	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
1328	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
1329	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
1330	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
1331	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
1332	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
1333	END DO
1334	END DO
1335	END DO
1336
1337	ELSE IF (polynomial_type == 2) THEN ! Linear
1338	DO ji = 1, jpi
1339	DO jj = 1, jpj
1340	DO jk = 1, jpkm1-1
1341	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1342	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
1343
1344	dsp(ji,jj,jk) = 0._wp
1345	csp(ji,jj,jk) = 0._wp
1346	bsp(ji,jj,jk) = ztmp1 / zdxtmp
1347	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
1348	END DO
1349	END DO
1350	END DO
1351
1352	ELSE
1353	CALL ctl_stop( 'invalid polynomial type in cspline' )
1354	ENDIF
1355
1356	END SUBROUTINE cspline
1357
1358
1359	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
1360	!!----------------------------------------------------------------------
1361	!! * ROUTINE interp1 *
1362	!!
1363	!! ** Purpose : 1-d linear interpolation
1364	!!
1365	!! ** Method : interpolation is straight forward
1366	!! extrapolation is also permitted (no value limit)
1367	!!----------------------------------------------------------------------
1368	IMPLICIT NONE
1369	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
1370	REAL(wp) :: f ! result of the interpolation (extrapolation)
1371	REAL(wp) :: zdeltx
1372	!!----------------------------------------------------------------------
1373
1374	zdeltx = xr - xl
1375	IF(abs(zdeltx) <= 10._wp * EPSILON(x)) THEN
1376	f = 0.5_wp * (fl + fr)
1377	ELSE
1378	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
1379	ENDIF
1380
1381	END FUNCTION interp1
1382
1383
1384	FUNCTION interp2(x, a, b, c, d) RESULT(f)
1385	!!----------------------------------------------------------------------
1386	!! * ROUTINE interp1 *
1387	!!
1388	!! ** Purpose : 1-d constrained cubic spline interpolation
1389	!!
1390	!! ** Method : cubic spline interpolation
1391	!!
1392	!!----------------------------------------------------------------------
1393	IMPLICIT NONE
1394	REAL(wp), INTENT(in) :: x, a, b, c, d
1395	REAL(wp) :: f ! value from the interpolation
1396	!!----------------------------------------------------------------------
1397
1398	f = a + x* ( b + x * ( c + d * x ) )
1399
1400	END FUNCTION interp2
1401
1402
1403	FUNCTION interp3(x, a, b, c, d) RESULT(f)
1404	!!----------------------------------------------------------------------
1405	!! * ROUTINE interp1 *
1406	!!
1407	!! ** Purpose : Calculate the first order of deriavtive of
1408	!! a cubic spline function y=a+bx+cx^2+d*x^3
1409	!!
1410	!! ** Method : f=dy/dx=b+2cx+3dx^2
1411	!!
1412	!!----------------------------------------------------------------------
1413	IMPLICIT NONE
1414	REAL(wp), INTENT(in) :: x, a, b, c, d
1415	REAL(wp) :: f ! value from the interpolation
1416	!!----------------------------------------------------------------------
1417
1418	f = b + x * ( 2._wp * c + 3._wp * d * x)
1419
1420	END FUNCTION interp3
1421
1422
1423	FUNCTION integ_spline(xl, xr, a, b, c, d) RESULT(f)
1424	!!----------------------------------------------------------------------
1425	!! * ROUTINE interp1 *
1426	!!
1427	!! ** Purpose : 1-d constrained cubic spline integration
1428	!!
1429	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
1430	!!
1431	!!----------------------------------------------------------------------
1432	IMPLICIT NONE
1433	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
1434	REAL(wp) :: za1, za2, za3
1435	REAL(wp) :: f ! integration result
1436	!!----------------------------------------------------------------------
1437
1438	za1 = 0.5_wp * b
1439	za2 = c / 3.0_wp
1440	za3 = 0.25_wp * d
1441
1442	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
1443	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
1444
1445	END FUNCTION integ_spline
1446
1447	!!======================================================================
1448	END MODULE dynhpg
1449

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