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dynhpg.F90 in branches/2015/dev_r5218_CNRS17_coupling/NEMOGCM/NEMO/OPA_SRC/DYN – NEMO

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source: branches/2015/dev_r5218_CNRS17_coupling/NEMOGCM/NEMO/OPA_SRC/DYN/dynhpg.F90 @ 5259

Last change on this file since 5259 was 5259, checked in by smasson, 10 years ago
dev_r5218_CNRS17_coupling: merge with trunk rev 5258
Property svn:keywords set to `Id`
File size: 69.9 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
47	IMPLICIT NONE
48	PRIVATE
49
50	PUBLIC dyn_hpg ! routine called by step module
51	PUBLIC dyn_hpg_init ! routine called by opa module
52
53	! !!* Namelist namdyn_hpg : hydrostatic pressure gradient
54	LOGICAL , PUBLIC :: ln_hpg_zco !: z-coordinate - full steps
55	LOGICAL , PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation)
56	LOGICAL , PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation)
57	LOGICAL , PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial)
58	LOGICAL , PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme)
59	LOGICAL , PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf
60	LOGICAL , PUBLIC :: ln_dynhpg_imp !: semi-implicite hpg flag
61
62	INTEGER , PUBLIC :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM)
63
64	!! * Substitutions
65	# include "domzgr_substitute.h90"
66	# include "vectopt_loop_substitute.h90"
67	!!----------------------------------------------------------------------
68	!! NEMO/OPA 3.3 , NEMO Consortium (2010)
69	!! $Id$
70	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
71	!!----------------------------------------------------------------------
72	CONTAINS
73
74	SUBROUTINE dyn_hpg( kt )
75	!!---------------------------------------------------------------------
76	!! * ROUTINE dyn_hpg *
77	!!
78	!! ** Method : Call the hydrostatic pressure gradient routine
79	!! using the scheme defined in the namelist
80	!!
81	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
82	!! - send trends to trd_dyn for futher diagnostics (l_trddyn=T)
83	!!----------------------------------------------------------------------
84	INTEGER, INTENT(in) :: kt ! ocean time-step index
85	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdu, ztrdv
86	!!----------------------------------------------------------------------
87	!
88	IF( nn_timing == 1 ) CALL timing_start('dyn_hpg')
89	!
90	IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn)
91	CALL wrk_alloc( jpi,jpj,jpk, ztrdu, ztrdv )
92	ztrdu(:,:,:) = ua(:,:,:)
93	ztrdv(:,:,:) = va(:,:,:)
94	ENDIF
95	!
96	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
97	CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate
98	CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation)
99	CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation)
100	CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial)
101	CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme)
102	CASE ( 5 ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf
103	END SELECT
104	!
105	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
106	ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:)
107	ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:)
108	CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt )
109	CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv )
110	ENDIF
111	!
112	IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, &
113	& tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
114	!
115	IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg')
116	!
117	END SUBROUTINE dyn_hpg
118
119
120	SUBROUTINE dyn_hpg_init
121	!!----------------------------------------------------------------------
122	!! * ROUTINE dyn_hpg_init *
123	!!
124	!! ** Purpose : initializations for the hydrostatic pressure gradient
125	!! computation and consistency control
126	!!
127	!! ** Action : Read the namelist namdyn_hpg and check the consistency
128	!! with the type of vertical coordinate used (zco, zps, sco)
129	!!----------------------------------------------------------------------
130	INTEGER :: ioptio = 0 ! temporary integer
131	INTEGER :: ios ! Local integer output status for namelist read
132	!!
133	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
134	& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf, ln_dynhpg_imp
135	!!----------------------------------------------------------------------
136	!
137	REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient
138	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
139	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp )
140
141	REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient
142	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
143	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp )
144	IF(lwm) WRITE ( numond, namdyn_hpg )
145	!
146	IF(lwp) THEN ! Control print
147	WRITE(numout,*)
148	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
149	WRITE(numout,*) '~~~~~~~~~~~~'
150	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
151	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
152	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
153	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
154	WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf
155	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
156	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
157	WRITE(numout,*) ' time stepping: centered (F) or semi-implicit (T) ln_dynhpg_imp = ', ln_dynhpg_imp
158	ENDIF
159	!
160	IF( ln_hpg_djc ) &
161	& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method &
162	& currently disabled (bugs under investigation). Please select &
163	& either ln_hpg_sco or ln_hpg_prj instead')
164	!
165	IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) &
166	& CALL ctl_stop('dyn_hpg_init : variable volume key_vvl requires:&
167	& the standard jacobian formulation hpg_sco or &
168	& the pressure jacobian formulation hpg_prj')
169
170	IF( ln_hpg_isf .AND. .NOT. ln_isfcav ) &
171	& CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' )
172	IF( .NOT. ln_hpg_isf .AND. ln_isfcav ) &
173	& CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' )
174	!
175	! ! Set nhpg from ln_hpg_... flags
176	IF( ln_hpg_zco ) nhpg = 0
177	IF( ln_hpg_zps ) nhpg = 1
178	IF( ln_hpg_sco ) nhpg = 2
179	IF( ln_hpg_djc ) nhpg = 3
180	IF( ln_hpg_prj ) nhpg = 4
181	IF( ln_hpg_isf ) nhpg = 5
182	!
183	! ! Consistency check
184	ioptio = 0
185	IF( ln_hpg_zco ) ioptio = ioptio + 1
186	IF( ln_hpg_zps ) ioptio = ioptio + 1
187	IF( ln_hpg_sco ) ioptio = ioptio + 1
188	IF( ln_hpg_djc ) ioptio = ioptio + 1
189	IF( ln_hpg_prj ) ioptio = ioptio + 1
190	IF( ln_hpg_isf ) ioptio = ioptio + 1
191	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
192	!
193	! initialisation of ice load
194	riceload(:,:)=0.0
195	!
196	END SUBROUTINE dyn_hpg_init
197
198
199	SUBROUTINE hpg_zco( kt )
200	!!---------------------------------------------------------------------
201	!! * ROUTINE hpg_zco *
202	!!
203	!! ** Method : z-coordinate case, levels are horizontal surfaces.
204	!! The now hydrostatic pressure gradient at a given level, jk,
205	!! is computed by taking the vertical integral of the in-situ
206	!! density gradient along the model level from the suface to that
207	!! level: zhpi = grav .....
208	!! zhpj = grav .....
209	!! add it to the general momentum trend (ua,va).
210	!! ua = ua - 1/e1u * zhpi
211	!! va = va - 1/e2v * zhpj
212	!!
213	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
214	!!----------------------------------------------------------------------
215	INTEGER, INTENT(in) :: kt ! ocean time-step index
216	!!
217	INTEGER :: ji, jj, jk ! dummy loop indices
218	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
219	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
220	!!----------------------------------------------------------------------
221	!
222	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
223	!
224	IF( kt == nit000 ) THEN
225	IF(lwp) WRITE(numout,*)
226	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
227	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
228	ENDIF
229
230	zcoef0 = - grav * 0.5_wp ! Local constant initialization
231
232	! Surface value
233	DO jj = 2, jpjm1
234	DO ji = fs_2, fs_jpim1 ! vector opt.
235	zcoef1 = zcoef0 * fse3w(ji,jj,1)
236	! hydrostatic pressure gradient
237	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
238	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
239	! add to the general momentum trend
240	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
241	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
242	END DO
243	END DO
244
245	!
246	! interior value (2=<jk=<jpkm1)
247	DO jk = 2, jpkm1
248	DO jj = 2, jpjm1
249	DO ji = fs_2, fs_jpim1 ! vector opt.
250	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
251	! hydrostatic pressure gradient
252	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
253	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
254	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
255
256	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
257	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
258	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
259	! add to the general momentum trend
260	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
261	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
262	END DO
263	END DO
264	END DO
265	!
266	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
267	!
268	END SUBROUTINE hpg_zco
269
270
271	SUBROUTINE hpg_zps( kt )
272	!!---------------------------------------------------------------------
273	!! * ROUTINE hpg_zps *
274	!!
275	!! ** Method : z-coordinate plus partial steps case. blahblah...
276	!!
277	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
278	!!----------------------------------------------------------------------
279	INTEGER, INTENT(in) :: kt ! ocean time-step index
280	!!
281	INTEGER :: ji, jj, jk ! dummy loop indices
282	INTEGER :: iku, ikv ! temporary integers
283	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
284	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
285	!!----------------------------------------------------------------------
286	!
287	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
288	!
289	IF( kt == nit000 ) THEN
290	IF(lwp) WRITE(numout,*)
291	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
292	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
293	ENDIF
294
295
296	! Local constant initialization
297	zcoef0 = - grav * 0.5_wp
298
299	! Surface value (also valid in partial step case)
300	DO jj = 2, jpjm1
301	DO ji = fs_2, fs_jpim1 ! vector opt.
302	zcoef1 = zcoef0 * fse3w(ji,jj,1)
303	! hydrostatic pressure gradient
304	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
305	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
306	! add to the general momentum trend
307	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
308	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
309	END DO
310	END DO
311
312
313	! interior value (2=<jk=<jpkm1)
314	DO jk = 2, jpkm1
315	DO jj = 2, jpjm1
316	DO ji = fs_2, fs_jpim1 ! vector opt.
317	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
318	! hydrostatic pressure gradient
319	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
320	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
321	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
322
323	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
324	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
325	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
326	! add to the general momentum trend
327	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
328	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
329	END DO
330	END DO
331	END DO
332
333
334	! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
335	DO jj = 2, jpjm1
336	DO ji = 2, jpim1
337	iku = mbku(ji,jj)
338	ikv = mbkv(ji,jj)
339	zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) )
340	zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) )
341	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
342	ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value
343	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
344	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj)
345	ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
346	ENDIF
347	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
348	va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value
349	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
350	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj)
351	va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
352	ENDIF
353	END DO
354	END DO
355	!
356	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
357	!
358	END SUBROUTINE hpg_zps
359
360	SUBROUTINE hpg_sco( kt )
361	!!---------------------------------------------------------------------
362	!! * ROUTINE hpg_sco *
363	!!
364	!! ** Method : s-coordinate case. Jacobian scheme.
365	!! The now hydrostatic pressure gradient at a given level, jk,
366	!! is computed by taking the vertical integral of the in-situ
367	!! density gradient along the model level from the suface to that
368	!! level. s-coordinates (ln_sco): a corrective term is added
369	!! to the horizontal pressure gradient :
370	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
371	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
372	!! add it to the general momentum trend (ua,va).
373	!! ua = ua - 1/e1u * zhpi
374	!! va = va - 1/e2v * zhpj
375	!!
376	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
377	!!----------------------------------------------------------------------
378	INTEGER, INTENT(in) :: kt ! ocean time-step index
379	!!
380	INTEGER :: ji, jj, jk ! dummy loop indices
381	REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars
382	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
383	!!----------------------------------------------------------------------
384	!
385	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
386	!
387	IF( kt == nit000 ) THEN
388	IF(lwp) WRITE(numout,*)
389	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
390	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
391	ENDIF
392
393	! Local constant initialization
394	zcoef0 = - grav * 0.5_wp
395	! To use density and not density anomaly
396	IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
397	ELSE ; znad = 0._wp ! Fixed volume
398	ENDIF
399
400	! Surface value
401	DO jj = 2, jpjm1
402	DO ji = fs_2, fs_jpim1 ! vector opt.
403	! hydrostatic pressure gradient along s-surfaces
404	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) &
405	& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
406	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) &
407	& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
408	! s-coordinate pressure gradient correction
409	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
410	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
411	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
412	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
413	! add to the general momentum trend
414	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap
415	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap
416	END DO
417	END DO
418
419	! interior value (2=<jk=<jpkm1)
420	DO jk = 2, jpkm1
421	DO jj = 2, jpjm1
422	DO ji = fs_2, fs_jpim1 ! vector opt.
423	! hydrostatic pressure gradient along s-surfaces
424	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
425	& * ( fse3w(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) &
426	& - fse3w(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) )
427	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
428	& * ( fse3w(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) &
429	& - fse3w(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) )
430	! s-coordinate pressure gradient correction
431	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
432	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj)
433	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
434	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj)
435	! add to the general momentum trend
436	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap
437	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap
438	END DO
439	END DO
440	END DO
441	!
442	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
443	!
444	END SUBROUTINE hpg_sco
445
446	SUBROUTINE hpg_isf( kt )
447	!!---------------------------------------------------------------------
448	!! * ROUTINE hpg_sco *
449	!!
450	!! ** Method : s-coordinate case. Jacobian scheme.
451	!! The now hydrostatic pressure gradient at a given level, jk,
452	!! is computed by taking the vertical integral of the in-situ
453	!! density gradient along the model level from the suface to that
454	!! level. s-coordinates (ln_sco): a corrective term is added
455	!! to the horizontal pressure gradient :
456	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
457	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
458	!! add it to the general momentum trend (ua,va).
459	!! ua = ua - 1/e1u * zhpi
460	!! va = va - 1/e2v * zhpj
461	!! iceload is added and partial cell case are added to the top and bottom
462	!!
463	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
464	!!----------------------------------------------------------------------
465	INTEGER, INTENT(in) :: kt ! ocean time-step index
466	!!
467	INTEGER :: ji, jj, jk, iku, ikv, ikt, iktp1i, iktp1j ! dummy loop indices
468	REAL(wp) :: zcoef0, zuap, zvap, znad, ze3wu, ze3wv, zuapint, zvapint, zhpjint, zhpiint, zdzwt, zdzwtjp1, zdzwtip1 ! temporary scalars
469	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj, zrhd
470	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop
471	REAL(wp), POINTER, DIMENSION(:,:) :: ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj
472	!!----------------------------------------------------------------------
473	!
474	CALL wrk_alloc( jpi,jpj, 2, ztstop)
475	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
476	CALL wrk_alloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
477	!
478	IF( kt == nit000 ) THEN
479	IF(lwp) WRITE(numout,*)
480	IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf'
481	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
482	ENDIF
483
484	! Local constant initialization
485	zcoef0 = - grav * 0.5_wp
486	! To use density and not density anomaly
487	! IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
488	! ELSE ; znad = 0._wp ! Fixed volume
489	! ENDIF
490	znad=1._wp
491	! iniitialised to 0. zhpi zhpi
492	zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp
493
494	!==================================================================================
495	!=====Compute iceload and contribution of the half first wet layer =================
496	!===================================================================================
497
498	! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude)
499	ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp
500
501	! compute density of the water displaced by the ice shelf
502	zrhd = rhd ! save rhd
503	DO jk = 1, jpk
504	zdept(:,:)=gdept_1d(jk)
505	CALL eos(ztstop(:,:,:),zdept(:,:),rhd(:,:,jk))
506	END DO
507	WHERE ( tmask(:,:,:) == 1._wp)
508	rhd(:,:,:) = zrhd(:,:,:) ! replace wet cell by the saved rhd
509	END WHERE
510
511	! compute rhd at the ice/oce interface (ice shelf side)
512	CALL eos(ztstop,risfdep,zrhdtop_isf)
513
514	! compute rhd at the ice/oce interface (ocean side)
515	DO ji=1,jpi
516	DO jj=1,jpj
517	ikt=mikt(ji,jj)
518	ztstop(ji,jj,1)=tsn(ji,jj,ikt,1)
519	ztstop(ji,jj,2)=tsn(ji,jj,ikt,2)
520	END DO
521	END DO
522	CALL eos(ztstop,risfdep,zrhdtop_oce)
523	!
524	! Surface value + ice shelf gradient
525	! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v)
526	ziceload = 0._wp
527	DO jj = 1, jpj
528	DO ji = 1, jpi ! vector opt.
529	ikt=mikt(ji,jj)
530	ziceload(ji,jj) = ziceload(ji,jj) + (znad + rhd(ji,jj,1) ) * fse3w(ji,jj,1) * (1._wp - tmask(ji,jj,1))
531	DO jk=2,ikt-1
532	ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + rhd(ji,jj,jk-1) + rhd(ji,jj,jk)) * fse3w(ji,jj,jk) &
533	& * (1._wp - tmask(ji,jj,jk))
534	END DO
535	IF (ikt .GE. 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + rhd(ji,jj,ikt-1)) &
536	& * ( risfdep(ji,jj) - gdept_1d(ikt-1) )
537	END DO
538	END DO
539	riceload(:,:) = 0.0_wp ; riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5
540	! compute zp from z=0 to first T wet point (correction due to zps not yet applied)
541	DO jj = 2, jpjm1
542	DO ji = fs_2, fs_jpim1 ! vector opt.
543	ikt=mikt(ji,jj) ; iktp1i=mikt(ji+1,jj); iktp1j=mikt(ji,jj+1)
544	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
545	! we assume ISF is in isostatic equilibrium
546	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * fse3w(ji+1,jj ,iktp1i) &
547	& * ( 2._wp * znad + rhd(ji+1,jj ,iktp1i) + zrhdtop_oce(ji+1,jj ) ) &
548	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
549	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
550	& + ( ziceload(ji+1,jj) - ziceload(ji,jj)) )
551	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * fse3w(ji ,jj+1,iktp1j) &
552	& * ( 2._wp * znad + rhd(ji ,jj+1,iktp1j) + zrhdtop_oce(ji ,jj+1) ) &
553	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
554	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
555	& + ( ziceload(ji,jj+1) - ziceload(ji,jj) ) )
556	! s-coordinate pressure gradient correction (=0 if z coordinate)
557	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
558	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
559	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
560	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
561	! add to the general momentum trend
562	ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
563	va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
564	END DO
565	END DO
566	!==================================================================================
567	!===== Compute partial cell contribution for the top cell =========================
568	!==================================================================================
569	DO jj = 2, jpjm1
570	DO ji = fs_2, fs_jpim1 ! vector opt.
571	iku = miku(ji,jj) ;
572	zpshpi(ji,jj)=0.0_wp ; zpshpj(ji,jj)=0.0_wp
573	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))
574	! u direction
575	IF ( iku .GT. 1 ) THEN
576	! case iku
577	zhpi(ji,jj,iku) = zcoef0 / e1u(ji,jj) * ze3wu &
578	& * ( rhd (ji+1,jj,iku) + rhd (ji,jj,iku) &
579	& + SIGN(1._wp,ze3wu) * grui(ji,jj) + 2._wp * znad )
580	! corrective term ( = 0 if z coordinate )
581	zuap = -zcoef0 * ( arui(ji,jj) + 2._wp * znad ) * gzui(ji,jj) / e1u(ji,jj)
582	! zhpi will be added in interior loop
583	ua(ji,jj,iku) = ua(ji,jj,iku) + zuap
584	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
585	IF (mbku(ji,jj) == iku + 1) zpshpi(ji,jj) = zhpi(ji,jj,iku)
586
587	! case iku + 1 (remove the zphi term added in the interior loop and compute the one corrected for zps)
588	zhpiint = zcoef0 / e1u(ji,jj) &
589	& * ( fse3w(ji+1,jj ,iku+1) * ( (rhd(ji+1,jj,iku+1) + znad) &
590	& + (rhd(ji+1,jj,iku ) + znad) ) * tmask(ji+1,jj,iku) &
591	& - fse3w(ji ,jj ,iku+1) * ( (rhd(ji ,jj,iku+1) + znad) &
592	& + (rhd(ji ,jj,iku ) + znad) ) * tmask(ji ,jj,iku) )
593	zhpi(ji,jj,iku+1) = zcoef0 / e1u(ji,jj) * ge3rui(ji,jj) - zhpiint
594	END IF
595
596	! v direction
597	ikv = mikv(ji,jj)
598	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))
599	IF ( ikv .GT. 1 ) THEN
600	! case ikv
601	zhpj(ji,jj,ikv) = zcoef0 / e2v(ji,jj) * ze3wv &
602	& * ( rhd(ji,jj+1,ikv) + rhd (ji,jj,ikv) &
603	& + SIGN(1._wp,ze3wv) * grvi(ji,jj) + 2._wp * znad )
604	! corrective term ( = 0 if z coordinate )
605	zvap = -zcoef0 * ( arvi(ji,jj) + 2._wp * znad ) * gzvi(ji,jj) / e2v(ji,jj)
606	! zhpi will be added in interior loop
607	va(ji,jj,ikv) = va(ji,jj,ikv) + zvap
608	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
609	IF (mbkv(ji,jj) == ikv + 1) zpshpj(ji,jj) = zhpj(ji,jj,ikv)
610
611	! case ikv + 1 (remove the zphj term added in the interior loop and compute the one corrected for zps)
612	zhpjint = zcoef0 / e2v(ji,jj) &
613	& * ( fse3w(ji ,jj+1,ikv+1) * ( (rhd(ji,jj+1,ikv+1) + znad) &
614	& + (rhd(ji,jj+1,ikv ) + znad) ) * tmask(ji,jj+1,ikv) &
615	& - fse3w(ji ,jj ,ikv+1) * ( (rhd(ji,jj ,ikv+1) + znad) &
616	& + (rhd(ji,jj ,ikv ) + znad) ) * tmask(ji,jj ,ikv) )
617	zhpj(ji,jj,ikv+1) = zcoef0 / e2v(ji,jj) * ge3rvi(ji,jj) - zhpjint
618	END IF
619	END DO
620	END DO
621
622	!==================================================================================
623	!===== Compute interior value =====================================================
624	!==================================================================================
625
626	DO jj = 2, jpjm1
627	DO ji = fs_2, fs_jpim1 ! vector opt.
628	iku=miku(ji,jj); ikv=mikv(ji,jj)
629	DO jk = 2, jpkm1
630	! hydrostatic pressure gradient along s-surfaces
631	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
632	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) + zhpi(ji,jj,jk-1) &
633	& + zcoef0 / e1u(ji,jj) &
634	& * ( fse3w(ji+1,jj ,jk) * ( (rhd(ji+1,jj,jk ) + znad) &
635	& + (rhd(ji+1,jj,jk-1) + znad) ) * tmask(ji+1,jj,jk-1) &
636	& - fse3w(ji ,jj ,jk) * ( (rhd(ji ,jj,jk ) + znad) &
637	& + (rhd(ji ,jj,jk-1) + znad) ) * tmask(ji ,jj,jk-1) )
638	! s-coordinate pressure gradient correction
639	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
640	zuap = - zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
641	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) * umask(ji,jj,jk-1)
642	ua(ji,jj,jk) = ua(ji,jj,jk) + ( zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
643
644	! hydrostatic pressure gradient along s-surfaces
645	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
646	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) + zhpj(ji,jj,jk-1) &
647	& + zcoef0 / e2v(ji,jj) &
648	& * ( fse3w(ji ,jj+1,jk) * ( (rhd(ji,jj+1,jk ) + znad) &
649	& + (rhd(ji,jj+1,jk-1) + znad) ) * tmask(ji,jj+1,jk-1) &
650	& - fse3w(ji ,jj ,jk) * ( (rhd(ji,jj ,jk ) + znad) &
651	& + (rhd(ji,jj ,jk-1) + znad) ) * tmask(ji,jj ,jk-1) )
652	! s-coordinate pressure gradient correction
653	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
654	zvap = - zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
655	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) * vmask(ji,jj,jk-1)
656	! add to the general momentum trend
657	va(ji,jj,jk) = va(ji,jj,jk) + ( zhpj(ji,jj,jk) + zvap ) * vmask(ji,jj,jk)
658	END DO
659	END DO
660	END DO
661
662	!==================================================================================
663	!===== Compute bottom cell contribution (partial cell) ============================
664	!==================================================================================
665
666	DO jj = 2, jpjm1
667	DO ji = 2, jpim1
668	iku = mbku(ji,jj)
669	ikv = mbkv(ji,jj)
670
671	IF (iku .GT. 1) THEN
672	! remove old value (interior case)
673	zuap = -zcoef0 * ( rhd (ji+1,jj ,iku) + rhd (ji,jj,iku) + 2._wp * znad ) &
674	& * ( fsde3w(ji+1,jj ,iku) - fsde3w(ji,jj,iku) ) / e1u(ji,jj)
675	ua(ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) - zuap
676	! put new value
677	! -zpshpi to avoid double contribution of the partial step in the top layer
678	zuap = -zcoef0 * ( aru(ji,jj) + 2._wp * znad ) * gzu(ji,jj) / e1u(ji,jj)
679	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) + zcoef0 / e1u(ji,jj) * ge3ru(ji,jj) - zpshpi(ji,jj)
680	ua(ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) + zuap
681	END IF
682	! v direction
683	IF (ikv .GT. 1) THEN
684	! remove old value (interior case)
685	zvap = -zcoef0 * ( rhd (ji ,jj+1,ikv) + rhd (ji,jj,ikv) + 2._wp * znad ) &
686	& * ( fsde3w(ji ,jj+1,ikv) - fsde3w(ji,jj,ikv) ) / e2v(ji,jj)
687	va(ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) - zvap
688	! put new value
689	! -zpshpj to avoid double contribution of the partial step in the top layer
690	zvap = -zcoef0 * ( arv(ji,jj) + 2._wp * znad ) * gzv(ji,jj) / e2v(ji,jj)
691	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) + zcoef0 / e2v(ji,jj) * ge3rv(ji,jj) - zpshpj(ji,jj)
692	va(ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) + zvap
693	END IF
694	END DO
695	END DO
696
697	! set back to original density value into the ice shelf cell (maybe useless because it is masked)
698	rhd = zrhd
699	!
700	CALL wrk_dealloc( jpi,jpj,2, ztstop)
701	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
702	CALL wrk_dealloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
703	!
704	END SUBROUTINE hpg_isf
705
706
707	SUBROUTINE hpg_djc( kt )
708	!!---------------------------------------------------------------------
709	!! * ROUTINE hpg_djc *
710	!!
711	!! ** Method : Density Jacobian with Cubic polynomial scheme
712	!!
713	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
714	!!----------------------------------------------------------------------
715	INTEGER, INTENT(in) :: kt ! ocean time-step index
716	!!
717	INTEGER :: ji, jj, jk ! dummy loop indices
718	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
719	REAL(wp) :: z1_10, cffu, cffx ! " "
720	REAL(wp) :: z1_12, cffv, cffy ! " "
721	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
722	REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw
723	REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow
724	REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k
725	!!----------------------------------------------------------------------
726	!
727	CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
728	CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
729	CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
730	!
731
732	IF( kt == nit000 ) THEN
733	IF(lwp) WRITE(numout,*)
734	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
735	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
736	ENDIF
737
738	! Local constant initialization
739	zcoef0 = - grav * 0.5_wp
740	z1_10 = 1._wp / 10._wp
741	z1_12 = 1._wp / 12._wp
742
743	!----------------------------------------------------------------------------------------
744	! compute and store in provisional arrays elementary vertical and horizontal differences
745	!----------------------------------------------------------------------------------------
746
747	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
748
749	DO jk = 2, jpkm1
750	DO jj = 2, jpjm1
751	DO ji = fs_2, fs_jpim1 ! vector opt.
752	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
753	dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1)
754	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
755	dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk )
756	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
757	dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk )
758	END DO
759	END DO
760	END DO
761
762	!-------------------------------------------------------------------------
763	! compute harmonic averages using eq. 5.18
764	!-------------------------------------------------------------------------
765	zep = 1.e-15
766
767	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
768	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
769
770	DO jk = 2, jpkm1
771	DO jj = 2, jpjm1
772	DO ji = fs_2, fs_jpim1 ! vector opt.
773	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
774
775	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
776	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
777
778	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
779	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
780
781	IF( cffw > zep) THEN
782	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
783	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
784	ELSE
785	drhow(ji,jj,jk) = 0._wp
786	ENDIF
787
788	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
789	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
790
791	IF( cffu > zep ) THEN
792	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
793	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
794	ELSE
795	drhou(ji,jj,jk ) = 0._wp
796	ENDIF
797
798	IF( cffx > zep ) THEN
799	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
800	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
801	ELSE
802	dzu(ji,jj,jk) = 0._wp
803	ENDIF
804
805	IF( cffv > zep ) THEN
806	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
807	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
808	ELSE
809	drhov(ji,jj,jk) = 0._wp
810	ENDIF
811
812	IF( cffy > zep ) THEN
813	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
814	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
815	ELSE
816	dzv(ji,jj,jk) = 0._wp
817	ENDIF
818
819	END DO
820	END DO
821	END DO
822
823	!----------------------------------------------------------------------------------
824	! apply boundary conditions at top and bottom using 5.36-5.37
825	!----------------------------------------------------------------------------------
826	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
827	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
828	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
829
830	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
831	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
832	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
833
834
835	!--------------------------------------------------------------
836	! Upper half of top-most grid box, compute and store
837	!-------------------------------------------------------------
838
839	!!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified
840	! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
841
842	DO jj = 2, jpjm1
843	DO ji = fs_2, fs_jpim1 ! vector opt.
844	rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) &
845	& * ( rhd(ji,jj,1) &
846	& + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) &
847	& * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) &
848	& / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) )
849	END DO
850	END DO
851
852	!!bug gm : here also, simplification is possible
853	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
854
855	DO jk = 2, jpkm1
856	DO jj = 2, jpjm1
857	DO ji = fs_2, fs_jpim1 ! vector opt.
858
859	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
860	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) &
861	& - grav * z1_10 * ( &
862	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
863	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
864	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
865	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
866	& )
867
868	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
869	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) &
870	& - grav* z1_10 * ( &
871	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
872	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
873	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
874	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
875	& )
876
877	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
878	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) &
879	& - grav* z1_10 * ( &
880	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
881	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
882	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
883	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
884	& )
885
886	END DO
887	END DO
888	END DO
889	CALL lbc_lnk(rho_k,'W',1.)
890	CALL lbc_lnk(rho_i,'U',1.)
891	CALL lbc_lnk(rho_j,'V',1.)
892
893
894	! ---------------
895	! Surface value
896	! ---------------
897	DO jj = 2, jpjm1
898	DO ji = fs_2, fs_jpim1 ! vector opt.
899	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj)
900	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj)
901	! add to the general momentum trend
902	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
903	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
904	END DO
905	END DO
906
907	! ----------------
908	! interior value (2=<jk=<jpkm1)
909	! ----------------
910	DO jk = 2, jpkm1
911	DO jj = 2, jpjm1
912	DO ji = fs_2, fs_jpim1 ! vector opt.
913	! hydrostatic pressure gradient along s-surfaces
914	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
915	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
916	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj)
917	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
918	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
919	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj)
920	! add to the general momentum trend
921	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
922	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
923	END DO
924	END DO
925	END DO
926	!
927	CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
928	CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
929	CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
930	!
931	END SUBROUTINE hpg_djc
932
933
934	SUBROUTINE hpg_prj( kt )
935	!!---------------------------------------------------------------------
936	!! * ROUTINE hpg_prj *
937	!!
938	!! ** Method : s-coordinate case.
939	!! A Pressure-Jacobian horizontal pressure gradient method
940	!! based on the constrained cubic-spline interpolation for
941	!! all vertical coordinate systems
942	!!
943	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
944	!!----------------------------------------------------------------------
945	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
946	INTEGER, INTENT(in) :: kt ! ocean time-step index
947	!!
948	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
949	REAL(wp) :: zcoef0, znad ! temporary scalars
950	!!
951	!! The local variables for the correction term
952	INTEGER :: jk1, jis, jid, jjs, jjd
953	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
954	REAL(wp) :: zrhdt1
955	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
956	REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh
957	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
958	REAL(wp), POINTER, DIMENSION(:,:) :: zsshu_n, zsshv_n
959	!!----------------------------------------------------------------------
960	!
961	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
962	CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh )
963	CALL wrk_alloc( jpi,jpj, zsshu_n, zsshv_n )
964	!
965	IF( kt == nit000 ) THEN
966	IF(lwp) WRITE(numout,*)
967	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
968	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
969	ENDIF
970
971	!!----------------------------------------------------------------------
972	! Local constant initialization
973	zcoef0 = - grav
974	znad = 0.0_wp
975	IF( lk_vvl ) znad = 1._wp
976
977	! Clean 3-D work arrays
978	zhpi(:,:,:) = 0._wp
979	zrhh(:,:,:) = rhd(:,:,:)
980
981	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
982	DO jj = 1, jpj
983	DO ji = 1, jpi
984	jk = mbathy(ji,jj)
985	IF( jk <= 0 ) THEN; zrhh(ji,jj,:) = 0._wp
986	ELSE IF(jk == 1) THEN; zrhh(ji,jj, jk+1:jpk) = rhd(ji,jj,jk)
987	ELSE IF(jk < jpkm1) THEN
988	DO jkk = jk+1, jpk
989	zrhh(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1), &
990	fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2))
991	END DO
992	ENDIF
993	END DO
994	END DO
995
996	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
997	DO jj = 1, jpj
998	DO ji = 1, jpi
999	zdept(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) - sshn(ji,jj) * znad
1000	END DO
1001	END DO
1002
1003	DO jk = 2, jpk
1004	DO jj = 1, jpj
1005	DO ji = 1, jpi
1006	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + fse3w(ji,jj,jk)
1007	END DO
1008	END DO
1009	END DO
1010
1011	fsp(:,:,:) = zrhh (:,:,:)
1012	xsp(:,:,:) = zdept(:,:,:)
1013
1014	! Construct the vertical density profile with the
1015	! constrained cubic spline interpolation
1016	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
1017	CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type)
1018
1019	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
1020	DO jj = 2, jpj
1021	DO ji = 2, jpi
1022	zrhdt1 = zrhh(ji,jj,1) - interp3(zdept(ji,jj,1),asp(ji,jj,1), &
1023	bsp(ji,jj,1), csp(ji,jj,1), &
1024	dsp(ji,jj,1) ) * 0.25_wp * fse3w(ji,jj,1)
1025
1026	! assuming linear profile across the top half surface layer
1027	zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * zrhdt1
1028	END DO
1029	END DO
1030
1031	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
1032	DO jk = 2, jpkm1
1033	DO jj = 2, jpj
1034	DO ji = 2, jpi
1035	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
1036	integ_spline(zdept(ji,jj,jk-1), zdept(ji,jj,jk),&
1037	asp(ji,jj,jk-1), bsp(ji,jj,jk-1), &
1038	csp(ji,jj,jk-1), dsp(ji,jj,jk-1))
1039	END DO
1040	END DO
1041	END DO
1042
1043	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
1044
1045	! Prepare zsshu_n and zsshv_n
1046	DO jj = 2, jpjm1
1047	DO ji = 2, jpim1
1048	zsshu_n(ji,jj) = (e12u(ji,jj) * sshn(ji,jj) + e12u(ji+1, jj) * sshn(ji+1,jj)) * &
1049	& r1_e12u(ji,jj) * umask(ji,jj,1) * 0.5_wp
1050	zsshv_n(ji,jj) = (e12v(ji,jj) * sshn(ji,jj) + e12v(ji+1, jj) * sshn(ji,jj+1)) * &
1051	& r1_e12v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
1052	END DO
1053	END DO
1054
1055	DO jj = 2, jpjm1
1056	DO ji = 2, jpim1
1057	zu(ji,jj,1) = - ( fse3u(ji,jj,1) - zsshu_n(ji,jj) * znad)
1058	zv(ji,jj,1) = - ( fse3v(ji,jj,1) - zsshv_n(ji,jj) * znad)
1059	END DO
1060	END DO
1061
1062	DO jk = 2, jpkm1
1063	DO jj = 2, jpjm1
1064	DO ji = 2, jpim1
1065	zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk)
1066	zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk)
1067	END DO
1068	END DO
1069	END DO
1070
1071	DO jk = 1, jpkm1
1072	DO jj = 2, jpjm1
1073	DO ji = 2, jpim1
1074	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk)
1075	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk)
1076	END DO
1077	END DO
1078	END DO
1079
1080	DO jk = 1, jpkm1
1081	DO jj = 2, jpjm1
1082	DO ji = 2, jpim1
1083	zu(ji,jj,jk) = min(zu(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
1084	zu(ji,jj,jk) = max(zu(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
1085	zv(ji,jj,jk) = min(zv(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
1086	zv(ji,jj,jk) = max(zv(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
1087	END DO
1088	END DO
1089	END DO
1090
1091
1092	DO jk = 1, jpkm1
1093	DO jj = 2, jpjm1
1094	DO ji = 2, jpim1
1095	zpwes = 0._wp; zpwed = 0._wp
1096	zpnss = 0._wp; zpnsd = 0._wp
1097	zuijk = zu(ji,jj,jk)
1098	zvijk = zv(ji,jj,jk)
1099
1100	!!!!! for u equation
1101	IF( jk <= mbku(ji,jj) ) THEN
1102	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
1103	jis = ji + 1; jid = ji
1104	ELSE
1105	jis = ji; jid = ji +1
1106	ENDIF
1107
1108	! integrate the pressure on the shallow side
1109	jk1 = jk
1110	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
1111	IF( jk1 == mbku(ji,jj) ) THEN
1112	zuijk = -zdept(jis,jj,jk1)
1113	EXIT
1114	ENDIF
1115	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
1116	zpwes = zpwes + &
1117	integ_spline(zdept(jis,jj,jk1), zdeps, &
1118	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
1119	csp(jis,jj,jk1), dsp(jis,jj,jk1))
1120	jk1 = jk1 + 1
1121	END DO
1122
1123	! integrate the pressure on the deep side
1124	jk1 = jk
1125	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
1126	IF( jk1 == 1 ) THEN
1127	zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad)
1128	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
1129	bsp(jid,jj,1), csp(jid,jj,1), &
1130	dsp(jid,jj,1)) * zdeps
1131	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
1132	EXIT
1133	ENDIF
1134	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
1135	zpwed = zpwed + &
1136	integ_spline(zdeps, zdept(jid,jj,jk1), &
1137	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
1138	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
1139	jk1 = jk1 - 1
1140	END DO
1141
1142	! update the momentum trends in u direction
1143
1144	zdpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk))
1145	IF( lk_vvl ) THEN
1146	zdpdx2 = zcoef0 / e1u(ji,jj) * &
1147	( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) )
1148	ELSE
1149	zdpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
1150	ENDIF
1151
1152	ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * &
1153	& umask(ji,jj,jk) * tmask(ji,jj,jk) * tmask(ji+1,jj,jk)
1154	ENDIF
1155
1156	!!!!! for v equation
1157	IF( jk <= mbkv(ji,jj) ) THEN
1158	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
1159	jjs = jj + 1; jjd = jj
1160	ELSE
1161	jjs = jj ; jjd = jj + 1
1162	ENDIF
1163
1164	! integrate the pressure on the shallow side
1165	jk1 = jk
1166	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
1167	IF( jk1 == mbkv(ji,jj) ) THEN
1168	zvijk = -zdept(ji,jjs,jk1)
1169	EXIT
1170	ENDIF
1171	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
1172	zpnss = zpnss + &
1173	integ_spline(zdept(ji,jjs,jk1), zdeps, &
1174	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
1175	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
1176	jk1 = jk1 + 1
1177	END DO
1178
1179	! integrate the pressure on the deep side
1180	jk1 = jk
1181	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
1182	IF( jk1 == 1 ) THEN
1183	zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad)
1184	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
1185	bsp(ji,jjd,1), csp(ji,jjd,1), &
1186	dsp(ji,jjd,1) ) * zdeps
1187	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
1188	EXIT
1189	ENDIF
1190	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
1191	zpnsd = zpnsd + &
1192	integ_spline(zdeps, zdept(ji,jjd,jk1), &
1193	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
1194	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
1195	jk1 = jk1 - 1
1196	END DO
1197
1198
1199	! update the momentum trends in v direction
1200
1201	zdpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk))
1202	IF( lk_vvl ) THEN
1203	zdpdy2 = zcoef0 / e2v(ji,jj) * &
1204	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) )
1205	ELSE
1206	zdpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
1207	ENDIF
1208
1209	va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2)*&
1210	& vmask(ji,jj,jk)tmask(ji,jj,jk)tmask(ji,jj+1,jk)
1211	ENDIF
1212
1213
1214	END DO
1215	END DO
1216	END DO
1217	!
1218	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
1219	CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh )
1220	CALL wrk_dealloc( jpi,jpj, zsshu_n, zsshv_n )
1221	!
1222	END SUBROUTINE hpg_prj
1223
1224
1225	SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type)
1226	!!----------------------------------------------------------------------
1227	!! * ROUTINE cspline *
1228	!!
1229	!! ** Purpose : constrained cubic spline interpolation
1230	!!
1231	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
1232	!!
1233	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
1234	!!----------------------------------------------------------------------
1235	IMPLICIT NONE
1236	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate
1237	REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of
1238	! the interpoated function
1239	INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline
1240	! 2: Linear
1241	!
1242	INTEGER :: ji, jj, jk ! dummy loop indices
1243	INTEGER :: jpi, jpj, jpkm1
1244	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
1245	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
1246	REAL(wp) :: zdf(size(fsp,3))
1247	!!----------------------------------------------------------------------
1248
1249	jpi = size(fsp,1)
1250	jpj = size(fsp,2)
1251	jpkm1 = size(fsp,3) - 1
1252
1253
1254	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
1255	DO ji = 1, jpi
1256	DO jj = 1, jpj
1257	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
1258	! DO jk = 2, jpkm1-1
1259	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
1260	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1261	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
1262	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
1263	!
1264	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
1265	!
1266	! IF(zdf1 * zdf2 <= 0._wp) THEN
1267	! zdf(jk) = 0._wp
1268	! ELSE
1269	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
1270	! ENDIF
1271	! END DO
1272
1273	!!Simply geometric average
1274	DO jk = 2, jpkm1-1
1275	zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1))
1276	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk))
1277
1278	IF(zdf1 * zdf2 <= 0._wp) THEN
1279	zdf(jk) = 0._wp
1280	ELSE
1281	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
1282	ENDIF
1283	END DO
1284
1285	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
1286	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
1287	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
1288	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - &
1289	& 0.5_wp * zdf(jpkm1 - 1)
1290
1291	DO jk = 1, jpkm1 - 1
1292	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1293	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
1294	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
1295	zddf1 = -2._wp * ztmp1 + ztmp2
1296	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
1297	zddf2 = 2._wp * ztmp1 - ztmp2
1298
1299	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
1300	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
1301	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
1302	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
1303	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
1304	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
1305	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
1306	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
1307	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
1308	END DO
1309	END DO
1310	END DO
1311
1312	ELSE IF (polynomial_type == 2) THEN ! Linear
1313	DO ji = 1, jpi
1314	DO jj = 1, jpj
1315	DO jk = 1, jpkm1-1
1316	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1317	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
1318
1319	dsp(ji,jj,jk) = 0._wp
1320	csp(ji,jj,jk) = 0._wp
1321	bsp(ji,jj,jk) = ztmp1 / zdxtmp
1322	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
1323	END DO
1324	END DO
1325	END DO
1326
1327	ELSE
1328	CALL ctl_stop( 'invalid polynomial type in cspline' )
1329	ENDIF
1330
1331	END SUBROUTINE cspline
1332
1333
1334	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
1335	!!----------------------------------------------------------------------
1336	!! * ROUTINE interp1 *
1337	!!
1338	!! ** Purpose : 1-d linear interpolation
1339	!!
1340	!! ** Method : interpolation is straight forward
1341	!! extrapolation is also permitted (no value limit)
1342	!!----------------------------------------------------------------------
1343	IMPLICIT NONE
1344	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
1345	REAL(wp) :: f ! result of the interpolation (extrapolation)
1346	REAL(wp) :: zdeltx
1347	!!----------------------------------------------------------------------
1348
1349	zdeltx = xr - xl
1350	IF(abs(zdeltx) <= 10._wp * EPSILON(x)) THEN
1351	f = 0.5_wp * (fl + fr)
1352	ELSE
1353	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
1354	ENDIF
1355
1356	END FUNCTION interp1
1357
1358
1359	FUNCTION interp2(x, a, b, c, d) RESULT(f)
1360	!!----------------------------------------------------------------------
1361	!! * ROUTINE interp1 *
1362	!!
1363	!! ** Purpose : 1-d constrained cubic spline interpolation
1364	!!
1365	!! ** Method : cubic spline interpolation
1366	!!
1367	!!----------------------------------------------------------------------
1368	IMPLICIT NONE
1369	REAL(wp), INTENT(in) :: x, a, b, c, d
1370	REAL(wp) :: f ! value from the interpolation
1371	!!----------------------------------------------------------------------
1372
1373	f = a + x* ( b + x * ( c + d * x ) )
1374
1375	END FUNCTION interp2
1376
1377
1378	FUNCTION interp3(x, a, b, c, d) RESULT(f)
1379	!!----------------------------------------------------------------------
1380	!! * ROUTINE interp1 *
1381	!!
1382	!! ** Purpose : Calculate the first order of deriavtive of
1383	!! a cubic spline function y=a+bx+cx^2+d*x^3
1384	!!
1385	!! ** Method : f=dy/dx=b+2cx+3dx^2
1386	!!
1387	!!----------------------------------------------------------------------
1388	IMPLICIT NONE
1389	REAL(wp), INTENT(in) :: x, a, b, c, d
1390	REAL(wp) :: f ! value from the interpolation
1391	!!----------------------------------------------------------------------
1392
1393	f = b + x * ( 2._wp * c + 3._wp * d * x)
1394
1395	END FUNCTION interp3
1396
1397
1398	FUNCTION integ_spline(xl, xr, a, b, c, d) RESULT(f)
1399	!!----------------------------------------------------------------------
1400	!! * ROUTINE interp1 *
1401	!!
1402	!! ** Purpose : 1-d constrained cubic spline integration
1403	!!
1404	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
1405	!!
1406	!!----------------------------------------------------------------------
1407	IMPLICIT NONE
1408	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
1409	REAL(wp) :: za1, za2, za3
1410	REAL(wp) :: f ! integration result
1411	!!----------------------------------------------------------------------
1412
1413	za1 = 0.5_wp * b
1414	za2 = c / 3.0_wp
1415	za3 = 0.25_wp * d
1416
1417	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
1418	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
1419
1420	END FUNCTION integ_spline
1421
1422	!!======================================================================
1423	END MODULE dynhpg
1424

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