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dynhpg.F90 in branches/UKMO/dev_r5518_GO6_package_inc_asm/NEMOGCM/NEMO/OPA_SRC/DYN – NEMO

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source: branches/UKMO/dev_r5518_GO6_package_inc_asm/NEMOGCM/NEMO/OPA_SRC/DYN/dynhpg.F90 @ 8036

Last change on this file since 8036 was 8036, checked in by jwhile, 7 years ago
Further merge of r5518_pcbias
File size: 70.8 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	z_rhd_st(:,:,:) = rhd(:,:,:) ! store orig density
102	rhd(:,:,:) = rhd_pc(:,:,:) ! use pressure corrected density
103	z_gru_st(:,:) = gru(:,:)
104	gru(:,:) = gru_pc(:,:)
105	z_grv_st(:,:) = grv(:,:)
106	grv(:,:) = grv_pc(:,:)
107	ENDIF
108	!
109	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
110	CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate
111	CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation)
112	CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation)
113	CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial)
114	CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme)
115	CASE ( 5 ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf
116	END SELECT
117	!
118	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
119	ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:)
120	ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:)
121	CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt )
122	CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv )
123	ENDIF
124	!
125	IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, &
126	& tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
127	!
128	IF ( ln_bias .AND. ln_bias_pc_app ) THEN
129	rhd(:,:,:) = z_rhd_st(:,:,:) ! restore original density
130	gru(:,:) = z_gru_st(:,:)
131	grv(:,:) = z_grv_st(:,:)
132	ENDIF
133	!
134	IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg')
135	!
136	END SUBROUTINE dyn_hpg
137
138
139	SUBROUTINE dyn_hpg_init
140	!!----------------------------------------------------------------------
141	!! * ROUTINE dyn_hpg_init *
142	!!
143	!! ** Purpose : initializations for the hydrostatic pressure gradient
144	!! computation and consistency control
145	!!
146	!! ** Action : Read the namelist namdyn_hpg and check the consistency
147	!! with the type of vertical coordinate used (zco, zps, sco)
148	!!----------------------------------------------------------------------
149	INTEGER :: ioptio = 0 ! temporary integer
150	INTEGER :: ios ! Local integer output status for namelist read
151	!!
152	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
153	& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf, ln_dynhpg_imp
154	!!----------------------------------------------------------------------
155	!
156	REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient
157	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
158	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp )
159
160	REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient
161	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
162	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp )
163	IF(lwm) WRITE ( numond, namdyn_hpg )
164	!
165	IF(lwp) THEN ! Control print
166	WRITE(numout,*)
167	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
168	WRITE(numout,*) '~~~~~~~~~~~~'
169	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
170	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
171	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
172	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
173	WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf
174	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
175	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
176	WRITE(numout,*) ' time stepping: centered (F) or semi-implicit (T) ln_dynhpg_imp = ', ln_dynhpg_imp
177	ENDIF
178	!
179	IF( ln_hpg_djc ) &
180	& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method &
181	& currently disabled (bugs under investigation). Please select &
182	& either ln_hpg_sco or ln_hpg_prj instead')
183	!
184	IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) &
185	& CALL ctl_stop('dyn_hpg_init : variable volume key_vvl requires:&
186	& the standard jacobian formulation hpg_sco or &
187	& the pressure jacobian formulation hpg_prj')
188
189	IF( ln_hpg_isf .AND. .NOT. ln_isfcav ) &
190	& CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' )
191	IF( .NOT. ln_hpg_isf .AND. ln_isfcav ) &
192	& CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' )
193	!
194	! ! Set nhpg from ln_hpg_... flags
195	IF( ln_hpg_zco ) nhpg = 0
196	IF( ln_hpg_zps ) nhpg = 1
197	IF( ln_hpg_sco ) nhpg = 2
198	IF( ln_hpg_djc ) nhpg = 3
199	IF( ln_hpg_prj ) nhpg = 4
200	IF( ln_hpg_isf ) nhpg = 5
201	!
202	! ! Consistency check
203	ioptio = 0
204	IF( ln_hpg_zco ) ioptio = ioptio + 1
205	IF( ln_hpg_zps ) ioptio = ioptio + 1
206	IF( ln_hpg_sco ) ioptio = ioptio + 1
207	IF( ln_hpg_djc ) ioptio = ioptio + 1
208	IF( ln_hpg_prj ) ioptio = ioptio + 1
209	IF( ln_hpg_isf ) ioptio = ioptio + 1
210	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
211	!
212	! initialisation of ice load
213	riceload(:,:)=0.0
214	!
215	END SUBROUTINE dyn_hpg_init
216
217
218	SUBROUTINE hpg_zco( kt )
219	!!---------------------------------------------------------------------
220	!! * ROUTINE hpg_zco *
221	!!
222	!! ** Method : z-coordinate case, levels are horizontal surfaces.
223	!! The now hydrostatic pressure gradient at a given level, jk,
224	!! is computed by taking the vertical integral of the in-situ
225	!! density gradient along the model level from the suface to that
226	!! level: zhpi = grav .....
227	!! zhpj = grav .....
228	!! add it to the general momentum trend (ua,va).
229	!! ua = ua - 1/e1u * zhpi
230	!! va = va - 1/e2v * zhpj
231	!!
232	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
233	!!----------------------------------------------------------------------
234	INTEGER, INTENT(in) :: kt ! ocean time-step index
235	!!
236	INTEGER :: ji, jj, jk ! dummy loop indices
237	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
238	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
239	!!----------------------------------------------------------------------
240	!
241	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
242	!
243	IF( kt == nit000 ) THEN
244	IF(lwp) WRITE(numout,*)
245	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
246	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
247	ENDIF
248
249	zcoef0 = - grav * 0.5_wp ! Local constant initialization
250
251	! Surface value
252	DO jj = 2, jpjm1
253	DO ji = fs_2, fs_jpim1 ! vector opt.
254	zcoef1 = zcoef0 * fse3w(ji,jj,1)
255	! hydrostatic pressure gradient
256	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
257	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
258	! add to the general momentum trend
259	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
260	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
261	END DO
262	END DO
263
264	!
265	! interior value (2=<jk=<jpkm1)
266	DO jk = 2, jpkm1
267	DO jj = 2, jpjm1
268	DO ji = fs_2, fs_jpim1 ! vector opt.
269	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
270	! hydrostatic pressure gradient
271	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
272	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
273	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
274
275	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
276	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
277	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
278	! add to the general momentum trend
279	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
280	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
281	END DO
282	END DO
283	END DO
284	!
285	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
286	!
287	END SUBROUTINE hpg_zco
288
289
290	SUBROUTINE hpg_zps( kt )
291	!!---------------------------------------------------------------------
292	!! * ROUTINE hpg_zps *
293	!!
294	!! ** Method : z-coordinate plus partial steps case. blahblah...
295	!!
296	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
297	!!----------------------------------------------------------------------
298	INTEGER, INTENT(in) :: kt ! ocean time-step index
299	!!
300	INTEGER :: ji, jj, jk ! dummy loop indices
301	INTEGER :: iku, ikv ! temporary integers
302	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
303	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
304	!!----------------------------------------------------------------------
305	!
306	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
307	!
308	IF( kt == nit000 ) THEN
309	IF(lwp) WRITE(numout,*)
310	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
311	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
312	ENDIF
313
314
315	! Local constant initialization
316	zcoef0 = - grav * 0.5_wp
317
318	! Surface value (also valid in partial step case)
319	DO jj = 2, jpjm1
320	DO ji = fs_2, fs_jpim1 ! vector opt.
321	zcoef1 = zcoef0 * fse3w(ji,jj,1)
322	! hydrostatic pressure gradient
323	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
324	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
325	! add to the general momentum trend
326	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
327	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
328	END DO
329	END DO
330
331
332	! interior value (2=<jk=<jpkm1)
333	DO jk = 2, jpkm1
334	DO jj = 2, jpjm1
335	DO ji = fs_2, fs_jpim1 ! vector opt.
336	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
337	! hydrostatic pressure gradient
338	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
339	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
340	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
341
342	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
343	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
344	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
345	! add to the general momentum trend
346	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
347	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
348	END DO
349	END DO
350	END DO
351
352
353	! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
354	DO jj = 2, jpjm1
355	DO ji = 2, jpim1
356	iku = mbku(ji,jj)
357	ikv = mbkv(ji,jj)
358	zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) )
359	zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) )
360	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
361	ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value
362	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
363	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj)
364	ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
365	ENDIF
366	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
367	va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value
368	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
369	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj)
370	va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
371	ENDIF
372	END DO
373	END DO
374	!
375	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
376	!
377	END SUBROUTINE hpg_zps
378
379	SUBROUTINE hpg_sco( kt )
380	!!---------------------------------------------------------------------
381	!! * ROUTINE hpg_sco *
382	!!
383	!! ** Method : s-coordinate case. Jacobian scheme.
384	!! The now hydrostatic pressure gradient at a given level, jk,
385	!! is computed by taking the vertical integral of the in-situ
386	!! density gradient along the model level from the suface to that
387	!! level. s-coordinates (ln_sco): a corrective term is added
388	!! to the horizontal pressure gradient :
389	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
390	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
391	!! add it to the general momentum trend (ua,va).
392	!! ua = ua - 1/e1u * zhpi
393	!! va = va - 1/e2v * zhpj
394	!!
395	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
396	!!----------------------------------------------------------------------
397	INTEGER, INTENT(in) :: kt ! ocean time-step index
398	!!
399	INTEGER :: ji, jj, jk ! dummy loop indices
400	REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars
401	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
402	!!----------------------------------------------------------------------
403	!
404	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
405	!
406	IF( kt == nit000 ) THEN
407	IF(lwp) WRITE(numout,*)
408	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
409	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
410	ENDIF
411
412	! Local constant initialization
413	zcoef0 = - grav * 0.5_wp
414	! To use density and not density anomaly
415	IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
416	ELSE ; znad = 0._wp ! Fixed volume
417	ENDIF
418
419	! Surface value
420	DO jj = 2, jpjm1
421	DO ji = fs_2, fs_jpim1 ! vector opt.
422	! hydrostatic pressure gradient along s-surfaces
423	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) &
424	& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
425	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) &
426	& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
427	! s-coordinate pressure gradient correction
428	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
429	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
430	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
431	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
432	! add to the general momentum trend
433	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap
434	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap
435	END DO
436	END DO
437
438	! interior value (2=<jk=<jpkm1)
439	DO jk = 2, jpkm1
440	DO jj = 2, jpjm1
441	DO ji = fs_2, fs_jpim1 ! vector opt.
442	! hydrostatic pressure gradient along s-surfaces
443	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
444	& * ( fse3w(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) &
445	& - fse3w(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) )
446	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
447	& * ( fse3w(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) &
448	& - fse3w(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) )
449	! s-coordinate pressure gradient correction
450	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
451	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj)
452	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
453	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj)
454	! add to the general momentum trend
455	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap
456	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap
457	END DO
458	END DO
459	END DO
460	!
461	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
462	!
463	END SUBROUTINE hpg_sco
464
465	SUBROUTINE hpg_isf( kt )
466	!!---------------------------------------------------------------------
467	!! * ROUTINE hpg_sco *
468	!!
469	!! ** Method : s-coordinate case. Jacobian scheme.
470	!! The now hydrostatic pressure gradient at a given level, jk,
471	!! is computed by taking the vertical integral of the in-situ
472	!! density gradient along the model level from the suface to that
473	!! level. s-coordinates (ln_sco): a corrective term is added
474	!! to the horizontal pressure gradient :
475	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
476	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
477	!! add it to the general momentum trend (ua,va).
478	!! ua = ua - 1/e1u * zhpi
479	!! va = va - 1/e2v * zhpj
480	!! iceload is added and partial cell case are added to the top and bottom
481	!!
482	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
483	!!----------------------------------------------------------------------
484	INTEGER, INTENT(in) :: kt ! ocean time-step index
485	!!
486	INTEGER :: ji, jj, jk, iku, ikv, ikt, iktp1i, iktp1j ! dummy loop indices
487	REAL(wp) :: zcoef0, zuap, zvap, znad, ze3wu, ze3wv, zuapint, zvapint, zhpjint, zhpiint, zdzwt, zdzwtjp1, zdzwtip1 ! temporary scalars
488	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj, zrhd
489	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop
490	REAL(wp), POINTER, DIMENSION(:,:) :: ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj
491	!!----------------------------------------------------------------------
492	!
493	CALL wrk_alloc( jpi,jpj, 2, ztstop)
494	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
495	CALL wrk_alloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
496	!
497	IF( kt == nit000 ) THEN
498	IF(lwp) WRITE(numout,*)
499	IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf'
500	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
501	ENDIF
502
503	! Local constant initialization
504	zcoef0 = - grav * 0.5_wp
505	! To use density and not density anomaly
506	! IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
507	! ELSE ; znad = 0._wp ! Fixed volume
508	! ENDIF
509	znad=1._wp
510	! iniitialised to 0. zhpi zhpi
511	zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp
512
513	!==================================================================================
514	!=====Compute iceload and contribution of the half first wet layer =================
515	!===================================================================================
516
517	! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude)
518	ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp
519
520	! compute density of the water displaced by the ice shelf
521	zrhd = rhd ! save rhd
522	DO jk = 1, jpk
523	zdept(:,:)=gdept_1d(jk)
524	CALL eos(ztstop(:,:,:),zdept(:,:),rhd(:,:,jk))
525	END DO
526	WHERE ( tmask(:,:,:) == 1._wp)
527	rhd(:,:,:) = zrhd(:,:,:) ! replace wet cell by the saved rhd
528	END WHERE
529
530	! compute rhd at the ice/oce interface (ice shelf side)
531	CALL eos(ztstop,risfdep,zrhdtop_isf)
532
533	! compute rhd at the ice/oce interface (ocean side)
534	DO ji=1,jpi
535	DO jj=1,jpj
536	ikt=mikt(ji,jj)
537	ztstop(ji,jj,1)=tsn(ji,jj,ikt,1)
538	ztstop(ji,jj,2)=tsn(ji,jj,ikt,2)
539	END DO
540	END DO
541	CALL eos(ztstop,risfdep,zrhdtop_oce)
542	!
543	! Surface value + ice shelf gradient
544	! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v)
545	ziceload = 0._wp
546	DO jj = 1, jpj
547	DO ji = 1, jpi ! vector opt.
548	ikt=mikt(ji,jj)
549	ziceload(ji,jj) = ziceload(ji,jj) + (znad + rhd(ji,jj,1) ) * fse3w(ji,jj,1) * (1._wp - tmask(ji,jj,1))
550	DO jk=2,ikt-1
551	ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + rhd(ji,jj,jk-1) + rhd(ji,jj,jk)) * fse3w(ji,jj,jk) &
552	& * (1._wp - tmask(ji,jj,jk))
553	END DO
554	IF (ikt .GE. 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + rhd(ji,jj,ikt-1)) &
555	& * ( risfdep(ji,jj) - gdept_1d(ikt-1) )
556	END DO
557	END DO
558	riceload(:,:) = 0.0_wp ; riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5
559	! compute zp from z=0 to first T wet point (correction due to zps not yet applied)
560	DO jj = 2, jpjm1
561	DO ji = fs_2, fs_jpim1 ! vector opt.
562	ikt=mikt(ji,jj) ; iktp1i=mikt(ji+1,jj); iktp1j=mikt(ji,jj+1)
563	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
564	! we assume ISF is in isostatic equilibrium
565	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * fse3w(ji+1,jj ,iktp1i) &
566	& * ( 2._wp * znad + rhd(ji+1,jj ,iktp1i) + zrhdtop_oce(ji+1,jj ) ) &
567	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
568	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
569	& + ( ziceload(ji+1,jj) - ziceload(ji,jj)) )
570	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * fse3w(ji ,jj+1,iktp1j) &
571	& * ( 2._wp * znad + rhd(ji ,jj+1,iktp1j) + zrhdtop_oce(ji ,jj+1) ) &
572	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
573	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
574	& + ( ziceload(ji,jj+1) - ziceload(ji,jj) ) )
575	! s-coordinate pressure gradient correction (=0 if z coordinate)
576	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
577	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
578	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
579	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
580	! add to the general momentum trend
581	ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
582	va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
583	END DO
584	END DO
585	!==================================================================================
586	!===== Compute partial cell contribution for the top cell =========================
587	!==================================================================================
588	DO jj = 2, jpjm1
589	DO ji = fs_2, fs_jpim1 ! vector opt.
590	iku = miku(ji,jj) ;
591	zpshpi(ji,jj)=0.0_wp ; zpshpj(ji,jj)=0.0_wp
592	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))
593	! u direction
594	IF ( iku .GT. 1 ) THEN
595	! case iku
596	zhpi(ji,jj,iku) = zcoef0 / e1u(ji,jj) * ze3wu &
597	& * ( rhd (ji+1,jj,iku) + rhd (ji,jj,iku) &
598	& + SIGN(1._wp,ze3wu) * grui(ji,jj) + 2._wp * znad )
599	! corrective term ( = 0 if z coordinate )
600	zuap = -zcoef0 * ( arui(ji,jj) + 2._wp * znad ) * gzui(ji,jj) / e1u(ji,jj)
601	! zhpi will be added in interior loop
602	ua(ji,jj,iku) = ua(ji,jj,iku) + zuap
603	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
604	IF (mbku(ji,jj) == iku + 1) zpshpi(ji,jj) = zhpi(ji,jj,iku)
605
606	! case iku + 1 (remove the zphi term added in the interior loop and compute the one corrected for zps)
607	zhpiint = zcoef0 / e1u(ji,jj) &
608	& * ( fse3w(ji+1,jj ,iku+1) * ( (rhd(ji+1,jj,iku+1) + znad) &
609	& + (rhd(ji+1,jj,iku ) + znad) ) * tmask(ji+1,jj,iku) &
610	& - fse3w(ji ,jj ,iku+1) * ( (rhd(ji ,jj,iku+1) + znad) &
611	& + (rhd(ji ,jj,iku ) + znad) ) * tmask(ji ,jj,iku) )
612	zhpi(ji,jj,iku+1) = zcoef0 / e1u(ji,jj) * ge3rui(ji,jj) - zhpiint
613	END IF
614
615	! v direction
616	ikv = mikv(ji,jj)
617	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))
618	IF ( ikv .GT. 1 ) THEN
619	! case ikv
620	zhpj(ji,jj,ikv) = zcoef0 / e2v(ji,jj) * ze3wv &
621	& * ( rhd(ji,jj+1,ikv) + rhd (ji,jj,ikv) &
622	& + SIGN(1._wp,ze3wv) * grvi(ji,jj) + 2._wp * znad )
623	! corrective term ( = 0 if z coordinate )
624	zvap = -zcoef0 * ( arvi(ji,jj) + 2._wp * znad ) * gzvi(ji,jj) / e2v(ji,jj)
625	! zhpi will be added in interior loop
626	va(ji,jj,ikv) = va(ji,jj,ikv) + zvap
627	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
628	IF (mbkv(ji,jj) == ikv + 1) zpshpj(ji,jj) = zhpj(ji,jj,ikv)
629
630	! case ikv + 1 (remove the zphj term added in the interior loop and compute the one corrected for zps)
631	zhpjint = zcoef0 / e2v(ji,jj) &
632	& * ( fse3w(ji ,jj+1,ikv+1) * ( (rhd(ji,jj+1,ikv+1) + znad) &
633	& + (rhd(ji,jj+1,ikv ) + znad) ) * tmask(ji,jj+1,ikv) &
634	& - fse3w(ji ,jj ,ikv+1) * ( (rhd(ji,jj ,ikv+1) + znad) &
635	& + (rhd(ji,jj ,ikv ) + znad) ) * tmask(ji,jj ,ikv) )
636	zhpj(ji,jj,ikv+1) = zcoef0 / e2v(ji,jj) * ge3rvi(ji,jj) - zhpjint
637	END IF
638	END DO
639	END DO
640
641	!==================================================================================
642	!===== Compute interior value =====================================================
643	!==================================================================================
644
645	DO jj = 2, jpjm1
646	DO ji = fs_2, fs_jpim1 ! vector opt.
647	iku=miku(ji,jj); ikv=mikv(ji,jj)
648	DO jk = 2, jpkm1
649	! hydrostatic pressure gradient along s-surfaces
650	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
651	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) + zhpi(ji,jj,jk-1) &
652	& + zcoef0 / e1u(ji,jj) &
653	& * ( fse3w(ji+1,jj ,jk) * ( (rhd(ji+1,jj,jk ) + znad) &
654	& + (rhd(ji+1,jj,jk-1) + znad) ) * tmask(ji+1,jj,jk-1) &
655	& - fse3w(ji ,jj ,jk) * ( (rhd(ji ,jj,jk ) + znad) &
656	& + (rhd(ji ,jj,jk-1) + znad) ) * tmask(ji ,jj,jk-1) )
657	! s-coordinate pressure gradient correction
658	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
659	zuap = - zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
660	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) * umask(ji,jj,jk-1)
661	ua(ji,jj,jk) = ua(ji,jj,jk) + ( zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
662
663	! hydrostatic pressure gradient along s-surfaces
664	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
665	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) + zhpj(ji,jj,jk-1) &
666	& + zcoef0 / e2v(ji,jj) &
667	& * ( fse3w(ji ,jj+1,jk) * ( (rhd(ji,jj+1,jk ) + znad) &
668	& + (rhd(ji,jj+1,jk-1) + znad) ) * tmask(ji,jj+1,jk-1) &
669	& - fse3w(ji ,jj ,jk) * ( (rhd(ji,jj ,jk ) + znad) &
670	& + (rhd(ji,jj ,jk-1) + znad) ) * tmask(ji,jj ,jk-1) )
671	! s-coordinate pressure gradient correction
672	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
673	zvap = - zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
674	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) * vmask(ji,jj,jk-1)
675	! add to the general momentum trend
676	va(ji,jj,jk) = va(ji,jj,jk) + ( zhpj(ji,jj,jk) + zvap ) * vmask(ji,jj,jk)
677	END DO
678	END DO
679	END DO
680
681	!==================================================================================
682	!===== Compute bottom cell contribution (partial cell) ============================
683	!==================================================================================
684
685	DO jj = 2, jpjm1
686	DO ji = 2, jpim1
687	iku = mbku(ji,jj)
688	ikv = mbkv(ji,jj)
689
690	IF (iku .GT. 1) THEN
691	! remove old value (interior case)
692	zuap = -zcoef0 * ( rhd (ji+1,jj ,iku) + rhd (ji,jj,iku) + 2._wp * znad ) &
693	& * ( fsde3w(ji+1,jj ,iku) - fsde3w(ji,jj,iku) ) / e1u(ji,jj)
694	ua(ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) - zuap
695	! put new value
696	! -zpshpi to avoid double contribution of the partial step in the top layer
697	zuap = -zcoef0 * ( aru(ji,jj) + 2._wp * znad ) * gzu(ji,jj) / e1u(ji,jj)
698	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) + zcoef0 / e1u(ji,jj) * ge3ru(ji,jj) - zpshpi(ji,jj)
699	ua(ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) + zuap
700	END IF
701	! v direction
702	IF (ikv .GT. 1) THEN
703	! remove old value (interior case)
704	zvap = -zcoef0 * ( rhd (ji ,jj+1,ikv) + rhd (ji,jj,ikv) + 2._wp * znad ) &
705	& * ( fsde3w(ji ,jj+1,ikv) - fsde3w(ji,jj,ikv) ) / e2v(ji,jj)
706	va(ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) - zvap
707	! put new value
708	! -zpshpj to avoid double contribution of the partial step in the top layer
709	zvap = -zcoef0 * ( arv(ji,jj) + 2._wp * znad ) * gzv(ji,jj) / e2v(ji,jj)
710	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) + zcoef0 / e2v(ji,jj) * ge3rv(ji,jj) - zpshpj(ji,jj)
711	va(ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) + zvap
712	END IF
713	END DO
714	END DO
715
716	! set back to original density value into the ice shelf cell (maybe useless because it is masked)
717	rhd = zrhd
718	!
719	CALL wrk_dealloc( jpi,jpj,2, ztstop)
720	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
721	CALL wrk_dealloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
722	!
723	END SUBROUTINE hpg_isf
724
725
726	SUBROUTINE hpg_djc( kt )
727	!!---------------------------------------------------------------------
728	!! * ROUTINE hpg_djc *
729	!!
730	!! ** Method : Density Jacobian with Cubic polynomial scheme
731	!!
732	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
733	!!----------------------------------------------------------------------
734	INTEGER, INTENT(in) :: kt ! ocean time-step index
735	!!
736	INTEGER :: ji, jj, jk ! dummy loop indices
737	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
738	REAL(wp) :: z1_10, cffu, cffx ! " "
739	REAL(wp) :: z1_12, cffv, cffy ! " "
740	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
741	REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw
742	REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow
743	REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k
744	!!----------------------------------------------------------------------
745	!
746	CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
747	CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
748	CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
749	!
750
751	IF( kt == nit000 ) THEN
752	IF(lwp) WRITE(numout,*)
753	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
754	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
755	ENDIF
756
757	! Local constant initialization
758	zcoef0 = - grav * 0.5_wp
759	z1_10 = 1._wp / 10._wp
760	z1_12 = 1._wp / 12._wp
761
762	!----------------------------------------------------------------------------------------
763	! compute and store in provisional arrays elementary vertical and horizontal differences
764	!----------------------------------------------------------------------------------------
765
766	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
767
768	DO jk = 2, jpkm1
769	DO jj = 2, jpjm1
770	DO ji = fs_2, fs_jpim1 ! vector opt.
771	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
772	dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1)
773	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
774	dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk )
775	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
776	dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk )
777	END DO
778	END DO
779	END DO
780
781	!-------------------------------------------------------------------------
782	! compute harmonic averages using eq. 5.18
783	!-------------------------------------------------------------------------
784	zep = 1.e-15
785
786	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
787	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
788
789	DO jk = 2, jpkm1
790	DO jj = 2, jpjm1
791	DO ji = fs_2, fs_jpim1 ! vector opt.
792	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
793
794	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
795	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
796
797	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
798	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
799
800	IF( cffw > zep) THEN
801	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
802	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
803	ELSE
804	drhow(ji,jj,jk) = 0._wp
805	ENDIF
806
807	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
808	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
809
810	IF( cffu > zep ) THEN
811	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
812	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
813	ELSE
814	drhou(ji,jj,jk ) = 0._wp
815	ENDIF
816
817	IF( cffx > zep ) THEN
818	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
819	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
820	ELSE
821	dzu(ji,jj,jk) = 0._wp
822	ENDIF
823
824	IF( cffv > zep ) THEN
825	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
826	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
827	ELSE
828	drhov(ji,jj,jk) = 0._wp
829	ENDIF
830
831	IF( cffy > zep ) THEN
832	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
833	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
834	ELSE
835	dzv(ji,jj,jk) = 0._wp
836	ENDIF
837
838	END DO
839	END DO
840	END DO
841
842	!----------------------------------------------------------------------------------
843	! apply boundary conditions at top and bottom using 5.36-5.37
844	!----------------------------------------------------------------------------------
845	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
846	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
847	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
848
849	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
850	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
851	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
852
853
854	!--------------------------------------------------------------
855	! Upper half of top-most grid box, compute and store
856	!-------------------------------------------------------------
857
858	!!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified
859	! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
860
861	DO jj = 2, jpjm1
862	DO ji = fs_2, fs_jpim1 ! vector opt.
863	rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) &
864	& * ( rhd(ji,jj,1) &
865	& + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) &
866	& * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) &
867	& / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) )
868	END DO
869	END DO
870
871	!!bug gm : here also, simplification is possible
872	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
873
874	DO jk = 2, jpkm1
875	DO jj = 2, jpjm1
876	DO ji = fs_2, fs_jpim1 ! vector opt.
877
878	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
879	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) &
880	& - grav * z1_10 * ( &
881	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
882	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
883	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
884	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
885	& )
886
887	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
888	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) &
889	& - grav* z1_10 * ( &
890	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
891	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
892	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
893	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
894	& )
895
896	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
897	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) &
898	& - grav* z1_10 * ( &
899	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
900	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
901	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
902	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
903	& )
904
905	END DO
906	END DO
907	END DO
908	CALL lbc_lnk(rho_k,'W',1.)
909	CALL lbc_lnk(rho_i,'U',1.)
910	CALL lbc_lnk(rho_j,'V',1.)
911
912
913	! ---------------
914	! Surface value
915	! ---------------
916	DO jj = 2, jpjm1
917	DO ji = fs_2, fs_jpim1 ! vector opt.
918	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj)
919	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj)
920	! add to the general momentum trend
921	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
922	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
923	END DO
924	END DO
925
926	! ----------------
927	! interior value (2=<jk=<jpkm1)
928	! ----------------
929	DO jk = 2, jpkm1
930	DO jj = 2, jpjm1
931	DO ji = fs_2, fs_jpim1 ! vector opt.
932	! hydrostatic pressure gradient along s-surfaces
933	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
934	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
935	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj)
936	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
937	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
938	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj)
939	! add to the general momentum trend
940	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
941	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
942	END DO
943	END DO
944	END DO
945	!
946	CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
947	CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
948	CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
949	!
950	END SUBROUTINE hpg_djc
951
952
953	SUBROUTINE hpg_prj( kt )
954	!!---------------------------------------------------------------------
955	!! * ROUTINE hpg_prj *
956	!!
957	!! ** Method : s-coordinate case.
958	!! A Pressure-Jacobian horizontal pressure gradient method
959	!! based on the constrained cubic-spline interpolation for
960	!! all vertical coordinate systems
961	!!
962	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
963	!!----------------------------------------------------------------------
964	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
965	INTEGER, INTENT(in) :: kt ! ocean time-step index
966	!!
967	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
968	REAL(wp) :: zcoef0, znad ! temporary scalars
969	!!
970	!! The local variables for the correction term
971	INTEGER :: jk1, jis, jid, jjs, jjd
972	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
973	REAL(wp) :: zrhdt1
974	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
975	REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh
976	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
977	REAL(wp), POINTER, DIMENSION(:,:) :: zsshu_n, zsshv_n
978	!!----------------------------------------------------------------------
979	!
980	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
981	CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh )
982	CALL wrk_alloc( jpi,jpj, zsshu_n, zsshv_n )
983	!
984	IF( kt == nit000 ) THEN
985	IF(lwp) WRITE(numout,*)
986	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
987	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
988	ENDIF
989
990	!!----------------------------------------------------------------------
991	! Local constant initialization
992	zcoef0 = - grav
993	znad = 0.0_wp
994	IF( lk_vvl ) znad = 1._wp
995
996	! Clean 3-D work arrays
997	zhpi(:,:,:) = 0._wp
998	zrhh(:,:,:) = rhd(:,:,:)
999
1000	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
1001	DO jj = 1, jpj
1002	DO ji = 1, jpi
1003	jk = mbathy(ji,jj)
1004	IF( jk <= 0 ) THEN; zrhh(ji,jj,:) = 0._wp
1005	ELSE IF(jk == 1) THEN; zrhh(ji,jj, jk+1:jpk) = rhd(ji,jj,jk)
1006	ELSE IF(jk < jpkm1) THEN
1007	DO jkk = jk+1, jpk
1008	zrhh(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1), &
1009	fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2))
1010	END DO
1011	ENDIF
1012	END DO
1013	END DO
1014
1015	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
1016	DO jj = 1, jpj
1017	DO ji = 1, jpi
1018	zdept(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) - sshn(ji,jj) * znad
1019	END DO
1020	END DO
1021
1022	DO jk = 2, jpk
1023	DO jj = 1, jpj
1024	DO ji = 1, jpi
1025	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + fse3w(ji,jj,jk)
1026	END DO
1027	END DO
1028	END DO
1029
1030	fsp(:,:,:) = zrhh (:,:,:)
1031	xsp(:,:,:) = zdept(:,:,:)
1032
1033	! Construct the vertical density profile with the
1034	! constrained cubic spline interpolation
1035	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
1036	CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type)
1037
1038	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
1039	DO jj = 2, jpj
1040	DO ji = 2, jpi
1041	zrhdt1 = zrhh(ji,jj,1) - interp3(zdept(ji,jj,1),asp(ji,jj,1), &
1042	bsp(ji,jj,1), csp(ji,jj,1), &
1043	dsp(ji,jj,1) ) * 0.25_wp * fse3w(ji,jj,1)
1044
1045	! assuming linear profile across the top half surface layer
1046	zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * zrhdt1
1047	END DO
1048	END DO
1049
1050	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
1051	DO jk = 2, jpkm1
1052	DO jj = 2, jpj
1053	DO ji = 2, jpi
1054	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
1055	integ_spline(zdept(ji,jj,jk-1), zdept(ji,jj,jk),&
1056	asp(ji,jj,jk-1), bsp(ji,jj,jk-1), &
1057	csp(ji,jj,jk-1), dsp(ji,jj,jk-1))
1058	END DO
1059	END DO
1060	END DO
1061
1062	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
1063
1064	! Prepare zsshu_n and zsshv_n
1065	DO jj = 2, jpjm1
1066	DO ji = 2, jpim1
1067	zsshu_n(ji,jj) = (e12u(ji,jj) * sshn(ji,jj) + e12u(ji+1, jj) * sshn(ji+1,jj)) * &
1068	& r1_e12u(ji,jj) * umask(ji,jj,1) * 0.5_wp
1069	zsshv_n(ji,jj) = (e12v(ji,jj) * sshn(ji,jj) + e12v(ji+1, jj) * sshn(ji,jj+1)) * &
1070	& r1_e12v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
1071	END DO
1072	END DO
1073
1074	DO jj = 2, jpjm1
1075	DO ji = 2, jpim1
1076	zu(ji,jj,1) = - ( fse3u(ji,jj,1) - zsshu_n(ji,jj) * znad)
1077	zv(ji,jj,1) = - ( fse3v(ji,jj,1) - zsshv_n(ji,jj) * znad)
1078	END DO
1079	END DO
1080
1081	DO jk = 2, jpkm1
1082	DO jj = 2, jpjm1
1083	DO ji = 2, jpim1
1084	zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk)
1085	zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk)
1086	END DO
1087	END DO
1088	END DO
1089
1090	DO jk = 1, jpkm1
1091	DO jj = 2, jpjm1
1092	DO ji = 2, jpim1
1093	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk)
1094	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk)
1095	END DO
1096	END DO
1097	END DO
1098
1099	DO jk = 1, jpkm1
1100	DO jj = 2, jpjm1
1101	DO ji = 2, jpim1
1102	zu(ji,jj,jk) = min(zu(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
1103	zu(ji,jj,jk) = max(zu(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
1104	zv(ji,jj,jk) = min(zv(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
1105	zv(ji,jj,jk) = max(zv(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
1106	END DO
1107	END DO
1108	END DO
1109
1110
1111	DO jk = 1, jpkm1
1112	DO jj = 2, jpjm1
1113	DO ji = 2, jpim1
1114	zpwes = 0._wp; zpwed = 0._wp
1115	zpnss = 0._wp; zpnsd = 0._wp
1116	zuijk = zu(ji,jj,jk)
1117	zvijk = zv(ji,jj,jk)
1118
1119	!!!!! for u equation
1120	IF( jk <= mbku(ji,jj) ) THEN
1121	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
1122	jis = ji + 1; jid = ji
1123	ELSE
1124	jis = ji; jid = ji +1
1125	ENDIF
1126
1127	! integrate the pressure on the shallow side
1128	jk1 = jk
1129	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
1130	IF( jk1 == mbku(ji,jj) ) THEN
1131	zuijk = -zdept(jis,jj,jk1)
1132	EXIT
1133	ENDIF
1134	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
1135	zpwes = zpwes + &
1136	integ_spline(zdept(jis,jj,jk1), zdeps, &
1137	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
1138	csp(jis,jj,jk1), dsp(jis,jj,jk1))
1139	jk1 = jk1 + 1
1140	END DO
1141
1142	! integrate the pressure on the deep side
1143	jk1 = jk
1144	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
1145	IF( jk1 == 1 ) THEN
1146	zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad)
1147	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
1148	bsp(jid,jj,1), csp(jid,jj,1), &
1149	dsp(jid,jj,1)) * zdeps
1150	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
1151	EXIT
1152	ENDIF
1153	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
1154	zpwed = zpwed + &
1155	integ_spline(zdeps, zdept(jid,jj,jk1), &
1156	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
1157	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
1158	jk1 = jk1 - 1
1159	END DO
1160
1161	! update the momentum trends in u direction
1162
1163	zdpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk))
1164	IF( lk_vvl ) THEN
1165	zdpdx2 = zcoef0 / e1u(ji,jj) * &
1166	( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) )
1167	ELSE
1168	zdpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
1169	ENDIF
1170
1171	ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * &
1172	& umask(ji,jj,jk) * tmask(ji,jj,jk) * tmask(ji+1,jj,jk)
1173	ENDIF
1174
1175	!!!!! for v equation
1176	IF( jk <= mbkv(ji,jj) ) THEN
1177	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
1178	jjs = jj + 1; jjd = jj
1179	ELSE
1180	jjs = jj ; jjd = jj + 1
1181	ENDIF
1182
1183	! integrate the pressure on the shallow side
1184	jk1 = jk
1185	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
1186	IF( jk1 == mbkv(ji,jj) ) THEN
1187	zvijk = -zdept(ji,jjs,jk1)
1188	EXIT
1189	ENDIF
1190	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
1191	zpnss = zpnss + &
1192	integ_spline(zdept(ji,jjs,jk1), zdeps, &
1193	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
1194	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
1195	jk1 = jk1 + 1
1196	END DO
1197
1198	! integrate the pressure on the deep side
1199	jk1 = jk
1200	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
1201	IF( jk1 == 1 ) THEN
1202	zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad)
1203	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
1204	bsp(ji,jjd,1), csp(ji,jjd,1), &
1205	dsp(ji,jjd,1) ) * zdeps
1206	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
1207	EXIT
1208	ENDIF
1209	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
1210	zpnsd = zpnsd + &
1211	integ_spline(zdeps, zdept(ji,jjd,jk1), &
1212	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
1213	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
1214	jk1 = jk1 - 1
1215	END DO
1216
1217
1218	! update the momentum trends in v direction
1219
1220	zdpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk))
1221	IF( lk_vvl ) THEN
1222	zdpdy2 = zcoef0 / e2v(ji,jj) * &
1223	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) )
1224	ELSE
1225	zdpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
1226	ENDIF
1227
1228	va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2)*&
1229	& vmask(ji,jj,jk)tmask(ji,jj,jk)tmask(ji,jj+1,jk)
1230	ENDIF
1231
1232
1233	END DO
1234	END DO
1235	END DO
1236	!
1237	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
1238	CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh )
1239	CALL wrk_dealloc( jpi,jpj, zsshu_n, zsshv_n )
1240	!
1241	END SUBROUTINE hpg_prj
1242
1243
1244	SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type)
1245	!!----------------------------------------------------------------------
1246	!! * ROUTINE cspline *
1247	!!
1248	!! ** Purpose : constrained cubic spline interpolation
1249	!!
1250	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
1251	!!
1252	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
1253	!!----------------------------------------------------------------------
1254	IMPLICIT NONE
1255	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate
1256	REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of
1257	! the interpoated function
1258	INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline
1259	! 2: Linear
1260	!
1261	INTEGER :: ji, jj, jk ! dummy loop indices
1262	INTEGER :: jpi, jpj, jpkm1
1263	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
1264	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
1265	REAL(wp) :: zdf(size(fsp,3))
1266	!!----------------------------------------------------------------------
1267
1268	jpi = size(fsp,1)
1269	jpj = size(fsp,2)
1270	jpkm1 = size(fsp,3) - 1
1271
1272
1273	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
1274	DO ji = 1, jpi
1275	DO jj = 1, jpj
1276	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
1277	! DO jk = 2, jpkm1-1
1278	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
1279	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1280	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
1281	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
1282	!
1283	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
1284	!
1285	! IF(zdf1 * zdf2 <= 0._wp) THEN
1286	! zdf(jk) = 0._wp
1287	! ELSE
1288	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
1289	! ENDIF
1290	! END DO
1291
1292	!!Simply geometric average
1293	DO jk = 2, jpkm1-1
1294	zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1))
1295	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk))
1296
1297	IF(zdf1 * zdf2 <= 0._wp) THEN
1298	zdf(jk) = 0._wp
1299	ELSE
1300	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
1301	ENDIF
1302	END DO
1303
1304	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
1305	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
1306	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
1307	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - &
1308	& 0.5_wp * zdf(jpkm1 - 1)
1309
1310	DO jk = 1, jpkm1 - 1
1311	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1312	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
1313	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
1314	zddf1 = -2._wp * ztmp1 + ztmp2
1315	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
1316	zddf2 = 2._wp * ztmp1 - ztmp2
1317
1318	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
1319	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
1320	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
1321	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
1322	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
1323	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
1324	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
1325	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
1326	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
1327	END DO
1328	END DO
1329	END DO
1330
1331	ELSE IF (polynomial_type == 2) THEN ! Linear
1332	DO ji = 1, jpi
1333	DO jj = 1, jpj
1334	DO jk = 1, jpkm1-1
1335	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1336	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
1337
1338	dsp(ji,jj,jk) = 0._wp
1339	csp(ji,jj,jk) = 0._wp
1340	bsp(ji,jj,jk) = ztmp1 / zdxtmp
1341	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
1342	END DO
1343	END DO
1344	END DO
1345
1346	ELSE
1347	CALL ctl_stop( 'invalid polynomial type in cspline' )
1348	ENDIF
1349
1350	END SUBROUTINE cspline
1351
1352
1353	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
1354	!!----------------------------------------------------------------------
1355	!! * ROUTINE interp1 *
1356	!!
1357	!! ** Purpose : 1-d linear interpolation
1358	!!
1359	!! ** Method : interpolation is straight forward
1360	!! extrapolation is also permitted (no value limit)
1361	!!----------------------------------------------------------------------
1362	IMPLICIT NONE
1363	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
1364	REAL(wp) :: f ! result of the interpolation (extrapolation)
1365	REAL(wp) :: zdeltx
1366	!!----------------------------------------------------------------------
1367
1368	zdeltx = xr - xl
1369	IF(abs(zdeltx) <= 10._wp * EPSILON(x)) THEN
1370	f = 0.5_wp * (fl + fr)
1371	ELSE
1372	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
1373	ENDIF
1374
1375	END FUNCTION interp1
1376
1377
1378	FUNCTION interp2(x, a, b, c, d) RESULT(f)
1379	!!----------------------------------------------------------------------
1380	!! * ROUTINE interp1 *
1381	!!
1382	!! ** Purpose : 1-d constrained cubic spline interpolation
1383	!!
1384	!! ** Method : cubic spline interpolation
1385	!!
1386	!!----------------------------------------------------------------------
1387	IMPLICIT NONE
1388	REAL(wp), INTENT(in) :: x, a, b, c, d
1389	REAL(wp) :: f ! value from the interpolation
1390	!!----------------------------------------------------------------------
1391
1392	f = a + x* ( b + x * ( c + d * x ) )
1393
1394	END FUNCTION interp2
1395
1396
1397	FUNCTION interp3(x, a, b, c, d) RESULT(f)
1398	!!----------------------------------------------------------------------
1399	!! * ROUTINE interp1 *
1400	!!
1401	!! ** Purpose : Calculate the first order of deriavtive of
1402	!! a cubic spline function y=a+bx+cx^2+d*x^3
1403	!!
1404	!! ** Method : f=dy/dx=b+2cx+3dx^2
1405	!!
1406	!!----------------------------------------------------------------------
1407	IMPLICIT NONE
1408	REAL(wp), INTENT(in) :: x, a, b, c, d
1409	REAL(wp) :: f ! value from the interpolation
1410	!!----------------------------------------------------------------------
1411
1412	f = b + x * ( 2._wp * c + 3._wp * d * x)
1413
1414	END FUNCTION interp3
1415
1416
1417	FUNCTION integ_spline(xl, xr, a, b, c, d) RESULT(f)
1418	!!----------------------------------------------------------------------
1419	!! * ROUTINE interp1 *
1420	!!
1421	!! ** Purpose : 1-d constrained cubic spline integration
1422	!!
1423	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
1424	!!
1425	!!----------------------------------------------------------------------
1426	IMPLICIT NONE
1427	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
1428	REAL(wp) :: za1, za2, za3
1429	REAL(wp) :: f ! integration result
1430	!!----------------------------------------------------------------------
1431
1432	za1 = 0.5_wp * b
1433	za2 = c / 3.0_wp
1434	za3 = 0.25_wp * d
1435
1436	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
1437	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
1438
1439	END FUNCTION integ_spline
1440
1441	!!======================================================================
1442	END MODULE dynhpg
1443

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