New URL for NEMO forge! http://forge.nemo-ocean.eu

Since March 2022 along with NEMO 4.2 release, the code development moved to a self-hosted GitLab.
This present forge is now archived and remained online for history.

dynhpg.F90 in branches/2015/dev_r5847_MERCATOR9_solveur_simplification/NEMOGCM/NEMO/OPA_SRC/DYN – NEMO

Context Navigation

source: branches/2015/dev_r5847_MERCATOR9_solveur_simplification/NEMOGCM/NEMO/OPA_SRC/DYN/dynhpg.F90 @ 5869

Last change on this file since 5869 was 5869, checked in by jchanut, 8 years ago
Free surface simplification #1620. Step 2: suppress implicit pressure gradient
Property svn:keywords set to `Id`
File size: 69.7 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
61	INTEGER , PUBLIC :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM)
62
63	!! * Substitutions
64	# include "domzgr_substitute.h90"
65	# include "vectopt_loop_substitute.h90"
66	!!----------------------------------------------------------------------
67	!! NEMO/OPA 3.3 , NEMO Consortium (2010)
68	!! $Id$
69	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
70	!!----------------------------------------------------------------------
71	CONTAINS
72
73	SUBROUTINE dyn_hpg( kt )
74	!!---------------------------------------------------------------------
75	!! * ROUTINE dyn_hpg *
76	!!
77	!! ** Method : Call the hydrostatic pressure gradient routine
78	!! using the scheme defined in the namelist
79	!!
80	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
81	!! - send trends to trd_dyn for futher diagnostics (l_trddyn=T)
82	!!----------------------------------------------------------------------
83	INTEGER, INTENT(in) :: kt ! ocean time-step index
84	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdu, ztrdv
85	!!----------------------------------------------------------------------
86	!
87	IF( nn_timing == 1 ) CALL timing_start('dyn_hpg')
88	!
89	IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn)
90	CALL wrk_alloc( jpi,jpj,jpk, ztrdu, ztrdv )
91	ztrdu(:,:,:) = ua(:,:,:)
92	ztrdv(:,:,:) = va(:,:,:)
93	ENDIF
94	!
95	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
96	CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate
97	CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation)
98	CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation)
99	CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial)
100	CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme)
101	CASE ( 5 ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf
102	END SELECT
103	!
104	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
105	ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:)
106	ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:)
107	CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt )
108	CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv )
109	ENDIF
110	!
111	IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, &
112	& tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
113	!
114	IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg')
115	!
116	END SUBROUTINE dyn_hpg
117
118
119	SUBROUTINE dyn_hpg_init
120	!!----------------------------------------------------------------------
121	!! * ROUTINE dyn_hpg_init *
122	!!
123	!! ** Purpose : initializations for the hydrostatic pressure gradient
124	!! computation and consistency control
125	!!
126	!! ** Action : Read the namelist namdyn_hpg and check the consistency
127	!! with the type of vertical coordinate used (zco, zps, sco)
128	!!----------------------------------------------------------------------
129	INTEGER :: ioptio = 0 ! temporary integer
130	INTEGER :: ios ! Local integer output status for namelist read
131	!!
132	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
133	& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf
134	!!----------------------------------------------------------------------
135	!
136	REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient
137	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
138	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp )
139
140	REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient
141	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
142	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp )
143	IF(lwm) WRITE ( numond, namdyn_hpg )
144	!
145	IF(lwp) THEN ! Control print
146	WRITE(numout,*)
147	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
148	WRITE(numout,*) '~~~~~~~~~~~~'
149	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
150	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
151	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
152	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
153	WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf
154	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
155	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
156	ENDIF
157	!
158	IF( ln_hpg_djc ) &
159	& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method &
160	& currently disabled (bugs under investigation). Please select &
161	& either ln_hpg_sco or ln_hpg_prj instead')
162	!
163	IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) &
164	& CALL ctl_stop('dyn_hpg_init : variable volume key_vvl requires:&
165	& the standard jacobian formulation hpg_sco or &
166	& the pressure jacobian formulation hpg_prj')
167
168	IF( ln_hpg_isf .AND. .NOT. ln_isfcav ) &
169	& CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' )
170	IF( .NOT. ln_hpg_isf .AND. ln_isfcav ) &
171	& CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' )
172	!
173	! ! Set nhpg from ln_hpg_... flags
174	IF( ln_hpg_zco ) nhpg = 0
175	IF( ln_hpg_zps ) nhpg = 1
176	IF( ln_hpg_sco ) nhpg = 2
177	IF( ln_hpg_djc ) nhpg = 3
178	IF( ln_hpg_prj ) nhpg = 4
179	IF( ln_hpg_isf ) nhpg = 5
180	!
181	! ! Consistency check
182	ioptio = 0
183	IF( ln_hpg_zco ) ioptio = ioptio + 1
184	IF( ln_hpg_zps ) ioptio = ioptio + 1
185	IF( ln_hpg_sco ) ioptio = ioptio + 1
186	IF( ln_hpg_djc ) ioptio = ioptio + 1
187	IF( ln_hpg_prj ) ioptio = ioptio + 1
188	IF( ln_hpg_isf ) ioptio = ioptio + 1
189	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
190	!
191	! initialisation of ice load
192	riceload(:,:)=0.0
193	!
194	END SUBROUTINE dyn_hpg_init
195
196
197	SUBROUTINE hpg_zco( kt )
198	!!---------------------------------------------------------------------
199	!! * ROUTINE hpg_zco *
200	!!
201	!! ** Method : z-coordinate case, levels are horizontal surfaces.
202	!! The now hydrostatic pressure gradient at a given level, jk,
203	!! is computed by taking the vertical integral of the in-situ
204	!! density gradient along the model level from the suface to that
205	!! level: zhpi = grav .....
206	!! zhpj = grav .....
207	!! add it to the general momentum trend (ua,va).
208	!! ua = ua - 1/e1u * zhpi
209	!! va = va - 1/e2v * zhpj
210	!!
211	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
212	!!----------------------------------------------------------------------
213	INTEGER, INTENT(in) :: kt ! ocean time-step index
214	!!
215	INTEGER :: ji, jj, jk ! dummy loop indices
216	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
217	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
218	!!----------------------------------------------------------------------
219	!
220	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
221	!
222	IF( kt == nit000 ) THEN
223	IF(lwp) WRITE(numout,*)
224	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
225	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
226	ENDIF
227
228	zcoef0 = - grav * 0.5_wp ! Local constant initialization
229
230	! Surface value
231	DO jj = 2, jpjm1
232	DO ji = fs_2, fs_jpim1 ! vector opt.
233	zcoef1 = zcoef0 * fse3w(ji,jj,1)
234	! hydrostatic pressure gradient
235	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
236	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
237	! add to the general momentum trend
238	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
239	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
240	END DO
241	END DO
242
243	!
244	! interior value (2=<jk=<jpkm1)
245	DO jk = 2, jpkm1
246	DO jj = 2, jpjm1
247	DO ji = fs_2, fs_jpim1 ! vector opt.
248	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
249	! hydrostatic pressure gradient
250	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
251	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
252	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
253
254	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
255	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
256	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
257	! add to the general momentum trend
258	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
259	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
260	END DO
261	END DO
262	END DO
263	!
264	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
265	!
266	END SUBROUTINE hpg_zco
267
268
269	SUBROUTINE hpg_zps( kt )
270	!!---------------------------------------------------------------------
271	!! * ROUTINE hpg_zps *
272	!!
273	!! ** Method : z-coordinate plus partial steps case. blahblah...
274	!!
275	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
276	!!----------------------------------------------------------------------
277	INTEGER, INTENT(in) :: kt ! ocean time-step index
278	!!
279	INTEGER :: ji, jj, jk ! dummy loop indices
280	INTEGER :: iku, ikv ! temporary integers
281	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
282	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
283	!!----------------------------------------------------------------------
284	!
285	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
286	!
287	IF( kt == nit000 ) THEN
288	IF(lwp) WRITE(numout,*)
289	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
290	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
291	ENDIF
292
293
294	! Local constant initialization
295	zcoef0 = - grav * 0.5_wp
296
297	! Surface value (also valid in partial step case)
298	DO jj = 2, jpjm1
299	DO ji = fs_2, fs_jpim1 ! vector opt.
300	zcoef1 = zcoef0 * fse3w(ji,jj,1)
301	! hydrostatic pressure gradient
302	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
303	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
304	! add to the general momentum trend
305	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
306	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
307	END DO
308	END DO
309
310
311	! interior value (2=<jk=<jpkm1)
312	DO jk = 2, jpkm1
313	DO jj = 2, jpjm1
314	DO ji = fs_2, fs_jpim1 ! vector opt.
315	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
316	! hydrostatic pressure gradient
317	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
318	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
319	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
320
321	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
322	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
323	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
324	! add to the general momentum trend
325	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
326	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
327	END DO
328	END DO
329	END DO
330
331
332	! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
333	DO jj = 2, jpjm1
334	DO ji = 2, jpim1
335	iku = mbku(ji,jj)
336	ikv = mbkv(ji,jj)
337	zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) )
338	zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) )
339	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
340	ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value
341	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
342	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj)
343	ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
344	ENDIF
345	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
346	va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value
347	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
348	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj)
349	va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
350	ENDIF
351	END DO
352	END DO
353	!
354	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
355	!
356	END SUBROUTINE hpg_zps
357
358	SUBROUTINE hpg_sco( kt )
359	!!---------------------------------------------------------------------
360	!! * ROUTINE hpg_sco *
361	!!
362	!! ** Method : s-coordinate case. Jacobian scheme.
363	!! The now hydrostatic pressure gradient at a given level, jk,
364	!! is computed by taking the vertical integral of the in-situ
365	!! density gradient along the model level from the suface to that
366	!! level. s-coordinates (ln_sco): a corrective term is added
367	!! to the horizontal pressure gradient :
368	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
369	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
370	!! add it to the general momentum trend (ua,va).
371	!! ua = ua - 1/e1u * zhpi
372	!! va = va - 1/e2v * zhpj
373	!!
374	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
375	!!----------------------------------------------------------------------
376	INTEGER, INTENT(in) :: kt ! ocean time-step index
377	!!
378	INTEGER :: ji, jj, jk ! dummy loop indices
379	REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars
380	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
381	!!----------------------------------------------------------------------
382	!
383	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
384	!
385	IF( kt == nit000 ) THEN
386	IF(lwp) WRITE(numout,*)
387	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
388	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
389	ENDIF
390
391	! Local constant initialization
392	zcoef0 = - grav * 0.5_wp
393	! To use density and not density anomaly
394	IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
395	ELSE ; znad = 0._wp ! Fixed volume
396	ENDIF
397
398	! Surface value
399	DO jj = 2, jpjm1
400	DO ji = fs_2, fs_jpim1 ! vector opt.
401	! hydrostatic pressure gradient along s-surfaces
402	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) &
403	& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
404	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) &
405	& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
406	! s-coordinate pressure gradient correction
407	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
408	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
409	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
410	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
411	! add to the general momentum trend
412	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap
413	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap
414	END DO
415	END DO
416
417	! interior value (2=<jk=<jpkm1)
418	DO jk = 2, jpkm1
419	DO jj = 2, jpjm1
420	DO ji = fs_2, fs_jpim1 ! vector opt.
421	! hydrostatic pressure gradient along s-surfaces
422	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
423	& * ( fse3w(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) &
424	& - fse3w(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) )
425	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
426	& * ( fse3w(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) &
427	& - fse3w(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) )
428	! s-coordinate pressure gradient correction
429	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
430	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj)
431	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
432	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj)
433	! add to the general momentum trend
434	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap
435	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap
436	END DO
437	END DO
438	END DO
439	!
440	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
441	!
442	END SUBROUTINE hpg_sco
443
444	SUBROUTINE hpg_isf( kt )
445	!!---------------------------------------------------------------------
446	!! * ROUTINE hpg_sco *
447	!!
448	!! ** Method : s-coordinate case. Jacobian scheme.
449	!! The now hydrostatic pressure gradient at a given level, jk,
450	!! is computed by taking the vertical integral of the in-situ
451	!! density gradient along the model level from the suface to that
452	!! level. s-coordinates (ln_sco): a corrective term is added
453	!! to the horizontal pressure gradient :
454	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
455	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
456	!! add it to the general momentum trend (ua,va).
457	!! ua = ua - 1/e1u * zhpi
458	!! va = va - 1/e2v * zhpj
459	!! iceload is added and partial cell case are added to the top and bottom
460	!!
461	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
462	!!----------------------------------------------------------------------
463	INTEGER, INTENT(in) :: kt ! ocean time-step index
464	!!
465	INTEGER :: ji, jj, jk, iku, ikv, ikt, iktp1i, iktp1j ! dummy loop indices
466	REAL(wp) :: zcoef0, zuap, zvap, znad, ze3wu, ze3wv, zuapint, zvapint, zhpjint, zhpiint, zdzwt, zdzwtjp1, zdzwtip1 ! temporary scalars
467	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj, zrhd
468	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop
469	REAL(wp), POINTER, DIMENSION(:,:) :: ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj
470	!!----------------------------------------------------------------------
471	!
472	CALL wrk_alloc( jpi,jpj, 2, ztstop)
473	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
474	CALL wrk_alloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
475	!
476	IF( kt == nit000 ) THEN
477	IF(lwp) WRITE(numout,*)
478	IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf'
479	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
480	ENDIF
481
482	! Local constant initialization
483	zcoef0 = - grav * 0.5_wp
484	! To use density and not density anomaly
485	! IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
486	! ELSE ; znad = 0._wp ! Fixed volume
487	! ENDIF
488	znad=1._wp
489	! iniitialised to 0. zhpi zhpi
490	zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp
491
492	!==================================================================================
493	!=====Compute iceload and contribution of the half first wet layer =================
494	!===================================================================================
495
496	! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude)
497	ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp
498
499	! compute density of the water displaced by the ice shelf
500	zrhd = rhd ! save rhd
501	DO jk = 1, jpk
502	zdept(:,:)=gdept_1d(jk)
503	CALL eos(ztstop(:,:,:),zdept(:,:),rhd(:,:,jk))
504	END DO
505	WHERE ( tmask(:,:,:) == 1._wp)
506	rhd(:,:,:) = zrhd(:,:,:) ! replace wet cell by the saved rhd
507	END WHERE
508
509	! compute rhd at the ice/oce interface (ice shelf side)
510	CALL eos(ztstop,risfdep,zrhdtop_isf)
511
512	! compute rhd at the ice/oce interface (ocean side)
513	DO ji=1,jpi
514	DO jj=1,jpj
515	ikt=mikt(ji,jj)
516	ztstop(ji,jj,1)=tsn(ji,jj,ikt,1)
517	ztstop(ji,jj,2)=tsn(ji,jj,ikt,2)
518	END DO
519	END DO
520	CALL eos(ztstop,risfdep,zrhdtop_oce)
521	!
522	! Surface value + ice shelf gradient
523	! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v)
524	ziceload = 0._wp
525	DO jj = 1, jpj
526	DO ji = 1, jpi ! vector opt.
527	ikt=mikt(ji,jj)
528	ziceload(ji,jj) = ziceload(ji,jj) + (znad + rhd(ji,jj,1) ) * fse3w(ji,jj,1) * (1._wp - tmask(ji,jj,1))
529	DO jk=2,ikt-1
530	ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + rhd(ji,jj,jk-1) + rhd(ji,jj,jk)) * fse3w(ji,jj,jk) &
531	& * (1._wp - tmask(ji,jj,jk))
532	END DO
533	IF (ikt .GE. 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + rhd(ji,jj,ikt-1)) &
534	& * ( risfdep(ji,jj) - gdept_1d(ikt-1) )
535	END DO
536	END DO
537	riceload(:,:) = 0.0_wp ; riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5
538	! compute zp from z=0 to first T wet point (correction due to zps not yet applied)
539	DO jj = 2, jpjm1
540	DO ji = fs_2, fs_jpim1 ! vector opt.
541	ikt=mikt(ji,jj) ; iktp1i=mikt(ji+1,jj); iktp1j=mikt(ji,jj+1)
542	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
543	! we assume ISF is in isostatic equilibrium
544	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * fse3w(ji+1,jj ,iktp1i) &
545	& * ( 2._wp * znad + rhd(ji+1,jj ,iktp1i) + zrhdtop_oce(ji+1,jj ) ) &
546	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
547	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
548	& + ( ziceload(ji+1,jj) - ziceload(ji,jj)) )
549	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * fse3w(ji ,jj+1,iktp1j) &
550	& * ( 2._wp * znad + rhd(ji ,jj+1,iktp1j) + zrhdtop_oce(ji ,jj+1) ) &
551	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
552	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
553	& + ( ziceload(ji,jj+1) - ziceload(ji,jj) ) )
554	! s-coordinate pressure gradient correction (=0 if z coordinate)
555	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
556	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
557	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
558	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
559	! add to the general momentum trend
560	ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
561	va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
562	END DO
563	END DO
564	!==================================================================================
565	!===== Compute partial cell contribution for the top cell =========================
566	!==================================================================================
567	DO jj = 2, jpjm1
568	DO ji = fs_2, fs_jpim1 ! vector opt.
569	iku = miku(ji,jj) ;
570	zpshpi(ji,jj)=0.0_wp ; zpshpj(ji,jj)=0.0_wp
571	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))
572	! u direction
573	IF ( iku .GT. 1 ) THEN
574	! case iku
575	zhpi(ji,jj,iku) = zcoef0 / e1u(ji,jj) * ze3wu &
576	& * ( rhd (ji+1,jj,iku) + rhd (ji,jj,iku) &
577	& + SIGN(1._wp,ze3wu) * grui(ji,jj) + 2._wp * znad )
578	! corrective term ( = 0 if z coordinate )
579	zuap = -zcoef0 * ( arui(ji,jj) + 2._wp * znad ) * gzui(ji,jj) / e1u(ji,jj)
580	! zhpi will be added in interior loop
581	ua(ji,jj,iku) = ua(ji,jj,iku) + zuap
582	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
583	IF (mbku(ji,jj) == iku + 1) zpshpi(ji,jj) = zhpi(ji,jj,iku)
584
585	! case iku + 1 (remove the zphi term added in the interior loop and compute the one corrected for zps)
586	zhpiint = zcoef0 / e1u(ji,jj) &
587	& * ( fse3w(ji+1,jj ,iku+1) * ( (rhd(ji+1,jj,iku+1) + znad) &
588	& + (rhd(ji+1,jj,iku ) + znad) ) * tmask(ji+1,jj,iku) &
589	& - fse3w(ji ,jj ,iku+1) * ( (rhd(ji ,jj,iku+1) + znad) &
590	& + (rhd(ji ,jj,iku ) + znad) ) * tmask(ji ,jj,iku) )
591	zhpi(ji,jj,iku+1) = zcoef0 / e1u(ji,jj) * ge3rui(ji,jj) - zhpiint
592	END IF
593
594	! v direction
595	ikv = mikv(ji,jj)
596	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))
597	IF ( ikv .GT. 1 ) THEN
598	! case ikv
599	zhpj(ji,jj,ikv) = zcoef0 / e2v(ji,jj) * ze3wv &
600	& * ( rhd(ji,jj+1,ikv) + rhd (ji,jj,ikv) &
601	& + SIGN(1._wp,ze3wv) * grvi(ji,jj) + 2._wp * znad )
602	! corrective term ( = 0 if z coordinate )
603	zvap = -zcoef0 * ( arvi(ji,jj) + 2._wp * znad ) * gzvi(ji,jj) / e2v(ji,jj)
604	! zhpi will be added in interior loop
605	va(ji,jj,ikv) = va(ji,jj,ikv) + zvap
606	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
607	IF (mbkv(ji,jj) == ikv + 1) zpshpj(ji,jj) = zhpj(ji,jj,ikv)
608
609	! case ikv + 1 (remove the zphj term added in the interior loop and compute the one corrected for zps)
610	zhpjint = zcoef0 / e2v(ji,jj) &
611	& * ( fse3w(ji ,jj+1,ikv+1) * ( (rhd(ji,jj+1,ikv+1) + znad) &
612	& + (rhd(ji,jj+1,ikv ) + znad) ) * tmask(ji,jj+1,ikv) &
613	& - fse3w(ji ,jj ,ikv+1) * ( (rhd(ji,jj ,ikv+1) + znad) &
614	& + (rhd(ji,jj ,ikv ) + znad) ) * tmask(ji,jj ,ikv) )
615	zhpj(ji,jj,ikv+1) = zcoef0 / e2v(ji,jj) * ge3rvi(ji,jj) - zhpjint
616	END IF
617	END DO
618	END DO
619
620	!==================================================================================
621	!===== Compute interior value =====================================================
622	!==================================================================================
623
624	DO jj = 2, jpjm1
625	DO ji = fs_2, fs_jpim1 ! vector opt.
626	iku=miku(ji,jj); ikv=mikv(ji,jj)
627	DO jk = 2, jpkm1
628	! hydrostatic pressure gradient along s-surfaces
629	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
630	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) + zhpi(ji,jj,jk-1) &
631	& + zcoef0 / e1u(ji,jj) &
632	& * ( fse3w(ji+1,jj ,jk) * ( (rhd(ji+1,jj,jk ) + znad) &
633	& + (rhd(ji+1,jj,jk-1) + znad) ) * tmask(ji+1,jj,jk-1) &
634	& - fse3w(ji ,jj ,jk) * ( (rhd(ji ,jj,jk ) + znad) &
635	& + (rhd(ji ,jj,jk-1) + znad) ) * tmask(ji ,jj,jk-1) )
636	! s-coordinate pressure gradient correction
637	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
638	zuap = - zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
639	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) * umask(ji,jj,jk-1)
640	ua(ji,jj,jk) = ua(ji,jj,jk) + ( zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
641
642	! hydrostatic pressure gradient along s-surfaces
643	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
644	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) + zhpj(ji,jj,jk-1) &
645	& + zcoef0 / e2v(ji,jj) &
646	& * ( fse3w(ji ,jj+1,jk) * ( (rhd(ji,jj+1,jk ) + znad) &
647	& + (rhd(ji,jj+1,jk-1) + znad) ) * tmask(ji,jj+1,jk-1) &
648	& - fse3w(ji ,jj ,jk) * ( (rhd(ji,jj ,jk ) + znad) &
649	& + (rhd(ji,jj ,jk-1) + znad) ) * tmask(ji,jj ,jk-1) )
650	! s-coordinate pressure gradient correction
651	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
652	zvap = - zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
653	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) * vmask(ji,jj,jk-1)
654	! add to the general momentum trend
655	va(ji,jj,jk) = va(ji,jj,jk) + ( zhpj(ji,jj,jk) + zvap ) * vmask(ji,jj,jk)
656	END DO
657	END DO
658	END DO
659
660	!==================================================================================
661	!===== Compute bottom cell contribution (partial cell) ============================
662	!==================================================================================
663
664	DO jj = 2, jpjm1
665	DO ji = 2, jpim1
666	iku = mbku(ji,jj)
667	ikv = mbkv(ji,jj)
668
669	IF (iku .GT. 1) THEN
670	! remove old value (interior case)
671	zuap = -zcoef0 * ( rhd (ji+1,jj ,iku) + rhd (ji,jj,iku) + 2._wp * znad ) &
672	& * ( fsde3w(ji+1,jj ,iku) - fsde3w(ji,jj,iku) ) / e1u(ji,jj)
673	ua(ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) - zuap
674	! put new value
675	! -zpshpi to avoid double contribution of the partial step in the top layer
676	zuap = -zcoef0 * ( aru(ji,jj) + 2._wp * znad ) * gzu(ji,jj) / e1u(ji,jj)
677	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) + zcoef0 / e1u(ji,jj) * ge3ru(ji,jj) - zpshpi(ji,jj)
678	ua(ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) + zuap
679	END IF
680	! v direction
681	IF (ikv .GT. 1) THEN
682	! remove old value (interior case)
683	zvap = -zcoef0 * ( rhd (ji ,jj+1,ikv) + rhd (ji,jj,ikv) + 2._wp * znad ) &
684	& * ( fsde3w(ji ,jj+1,ikv) - fsde3w(ji,jj,ikv) ) / e2v(ji,jj)
685	va(ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) - zvap
686	! put new value
687	! -zpshpj to avoid double contribution of the partial step in the top layer
688	zvap = -zcoef0 * ( arv(ji,jj) + 2._wp * znad ) * gzv(ji,jj) / e2v(ji,jj)
689	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) + zcoef0 / e2v(ji,jj) * ge3rv(ji,jj) - zpshpj(ji,jj)
690	va(ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) + zvap
691	END IF
692	END DO
693	END DO
694
695	! set back to original density value into the ice shelf cell (maybe useless because it is masked)
696	rhd = zrhd
697	!
698	CALL wrk_dealloc( jpi,jpj,2, ztstop)
699	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
700	CALL wrk_dealloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
701	!
702	END SUBROUTINE hpg_isf
703
704
705	SUBROUTINE hpg_djc( kt )
706	!!---------------------------------------------------------------------
707	!! * ROUTINE hpg_djc *
708	!!
709	!! ** Method : Density Jacobian with Cubic polynomial scheme
710	!!
711	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
712	!!----------------------------------------------------------------------
713	INTEGER, INTENT(in) :: kt ! ocean time-step index
714	!!
715	INTEGER :: ji, jj, jk ! dummy loop indices
716	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
717	REAL(wp) :: z1_10, cffu, cffx ! " "
718	REAL(wp) :: z1_12, cffv, cffy ! " "
719	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
720	REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw
721	REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow
722	REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k
723	!!----------------------------------------------------------------------
724	!
725	CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
726	CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
727	CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
728	!
729
730	IF( kt == nit000 ) THEN
731	IF(lwp) WRITE(numout,*)
732	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
733	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
734	ENDIF
735
736	! Local constant initialization
737	zcoef0 = - grav * 0.5_wp
738	z1_10 = 1._wp / 10._wp
739	z1_12 = 1._wp / 12._wp
740
741	!----------------------------------------------------------------------------------------
742	! compute and store in provisional arrays elementary vertical and horizontal differences
743	!----------------------------------------------------------------------------------------
744
745	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
746
747	DO jk = 2, jpkm1
748	DO jj = 2, jpjm1
749	DO ji = fs_2, fs_jpim1 ! vector opt.
750	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
751	dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1)
752	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
753	dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk )
754	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
755	dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk )
756	END DO
757	END DO
758	END DO
759
760	!-------------------------------------------------------------------------
761	! compute harmonic averages using eq. 5.18
762	!-------------------------------------------------------------------------
763	zep = 1.e-15
764
765	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
766	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
767
768	DO jk = 2, jpkm1
769	DO jj = 2, jpjm1
770	DO ji = fs_2, fs_jpim1 ! vector opt.
771	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
772
773	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
774	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
775
776	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
777	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
778
779	IF( cffw > zep) THEN
780	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
781	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
782	ELSE
783	drhow(ji,jj,jk) = 0._wp
784	ENDIF
785
786	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
787	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
788
789	IF( cffu > zep ) THEN
790	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
791	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
792	ELSE
793	drhou(ji,jj,jk ) = 0._wp
794	ENDIF
795
796	IF( cffx > zep ) THEN
797	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
798	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
799	ELSE
800	dzu(ji,jj,jk) = 0._wp
801	ENDIF
802
803	IF( cffv > zep ) THEN
804	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
805	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
806	ELSE
807	drhov(ji,jj,jk) = 0._wp
808	ENDIF
809
810	IF( cffy > zep ) THEN
811	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
812	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
813	ELSE
814	dzv(ji,jj,jk) = 0._wp
815	ENDIF
816
817	END DO
818	END DO
819	END DO
820
821	!----------------------------------------------------------------------------------
822	! apply boundary conditions at top and bottom using 5.36-5.37
823	!----------------------------------------------------------------------------------
824	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
825	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
826	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
827
828	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
829	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
830	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
831
832
833	!--------------------------------------------------------------
834	! Upper half of top-most grid box, compute and store
835	!-------------------------------------------------------------
836
837	!!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified
838	! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
839
840	DO jj = 2, jpjm1
841	DO ji = fs_2, fs_jpim1 ! vector opt.
842	rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) &
843	& * ( rhd(ji,jj,1) &
844	& + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) &
845	& * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) &
846	& / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) )
847	END DO
848	END DO
849
850	!!bug gm : here also, simplification is possible
851	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
852
853	DO jk = 2, jpkm1
854	DO jj = 2, jpjm1
855	DO ji = fs_2, fs_jpim1 ! vector opt.
856
857	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
858	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) &
859	& - grav * z1_10 * ( &
860	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
861	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
862	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
863	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
864	& )
865
866	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
867	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) &
868	& - grav* z1_10 * ( &
869	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
870	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
871	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
872	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
873	& )
874
875	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
876	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) &
877	& - grav* z1_10 * ( &
878	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
879	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
880	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
881	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
882	& )
883
884	END DO
885	END DO
886	END DO
887	CALL lbc_lnk(rho_k,'W',1.)
888	CALL lbc_lnk(rho_i,'U',1.)
889	CALL lbc_lnk(rho_j,'V',1.)
890
891
892	! ---------------
893	! Surface value
894	! ---------------
895	DO jj = 2, jpjm1
896	DO ji = fs_2, fs_jpim1 ! vector opt.
897	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj)
898	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj)
899	! add to the general momentum trend
900	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
901	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
902	END DO
903	END DO
904
905	! ----------------
906	! interior value (2=<jk=<jpkm1)
907	! ----------------
908	DO jk = 2, jpkm1
909	DO jj = 2, jpjm1
910	DO ji = fs_2, fs_jpim1 ! vector opt.
911	! hydrostatic pressure gradient along s-surfaces
912	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
913	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
914	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj)
915	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
916	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
917	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj)
918	! add to the general momentum trend
919	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
920	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
921	END DO
922	END DO
923	END DO
924	!
925	CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
926	CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
927	CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
928	!
929	END SUBROUTINE hpg_djc
930
931
932	SUBROUTINE hpg_prj( kt )
933	!!---------------------------------------------------------------------
934	!! * ROUTINE hpg_prj *
935	!!
936	!! ** Method : s-coordinate case.
937	!! A Pressure-Jacobian horizontal pressure gradient method
938	!! based on the constrained cubic-spline interpolation for
939	!! all vertical coordinate systems
940	!!
941	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
942	!!----------------------------------------------------------------------
943	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
944	INTEGER, INTENT(in) :: kt ! ocean time-step index
945	!!
946	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
947	REAL(wp) :: zcoef0, znad ! temporary scalars
948	!!
949	!! The local variables for the correction term
950	INTEGER :: jk1, jis, jid, jjs, jjd
951	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
952	REAL(wp) :: zrhdt1
953	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
954	REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh
955	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
956	REAL(wp), POINTER, DIMENSION(:,:) :: zsshu_n, zsshv_n
957	!!----------------------------------------------------------------------
958	!
959	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
960	CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh )
961	CALL wrk_alloc( jpi,jpj, zsshu_n, zsshv_n )
962	!
963	IF( kt == nit000 ) THEN
964	IF(lwp) WRITE(numout,*)
965	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
966	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
967	ENDIF
968
969	!!----------------------------------------------------------------------
970	! Local constant initialization
971	zcoef0 = - grav
972	znad = 0.0_wp
973	IF( lk_vvl ) znad = 1._wp
974
975	! Clean 3-D work arrays
976	zhpi(:,:,:) = 0._wp
977	zrhh(:,:,:) = rhd(:,:,:)
978
979	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
980	DO jj = 1, jpj
981	DO ji = 1, jpi
982	jk = mbathy(ji,jj)
983	IF( jk <= 0 ) THEN; zrhh(ji,jj,:) = 0._wp
984	ELSE IF(jk == 1) THEN; zrhh(ji,jj, jk+1:jpk) = rhd(ji,jj,jk)
985	ELSE IF(jk < jpkm1) THEN
986	DO jkk = jk+1, jpk
987	zrhh(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1), &
988	fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2))
989	END DO
990	ENDIF
991	END DO
992	END DO
993
994	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
995	DO jj = 1, jpj
996	DO ji = 1, jpi
997	zdept(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) - sshn(ji,jj) * znad
998	END DO
999	END DO
1000
1001	DO jk = 2, jpk
1002	DO jj = 1, jpj
1003	DO ji = 1, jpi
1004	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + fse3w(ji,jj,jk)
1005	END DO
1006	END DO
1007	END DO
1008
1009	fsp(:,:,:) = zrhh (:,:,:)
1010	xsp(:,:,:) = zdept(:,:,:)
1011
1012	! Construct the vertical density profile with the
1013	! constrained cubic spline interpolation
1014	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
1015	CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type)
1016
1017	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
1018	DO jj = 2, jpj
1019	DO ji = 2, jpi
1020	zrhdt1 = zrhh(ji,jj,1) - interp3(zdept(ji,jj,1),asp(ji,jj,1), &
1021	bsp(ji,jj,1), csp(ji,jj,1), &
1022	dsp(ji,jj,1) ) * 0.25_wp * fse3w(ji,jj,1)
1023
1024	! assuming linear profile across the top half surface layer
1025	zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * zrhdt1
1026	END DO
1027	END DO
1028
1029	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
1030	DO jk = 2, jpkm1
1031	DO jj = 2, jpj
1032	DO ji = 2, jpi
1033	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
1034	integ_spline(zdept(ji,jj,jk-1), zdept(ji,jj,jk),&
1035	asp(ji,jj,jk-1), bsp(ji,jj,jk-1), &
1036	csp(ji,jj,jk-1), dsp(ji,jj,jk-1))
1037	END DO
1038	END DO
1039	END DO
1040
1041	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
1042
1043	! Prepare zsshu_n and zsshv_n
1044	DO jj = 2, jpjm1
1045	DO ji = 2, jpim1
1046	zsshu_n(ji,jj) = (e1e2u(ji,jj) * sshn(ji,jj) + e1e2u(ji+1, jj) * sshn(ji+1,jj)) * &
1047	& r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
1048	zsshv_n(ji,jj) = (e1e2v(ji,jj) * sshn(ji,jj) + e1e2v(ji+1, jj) * sshn(ji,jj+1)) * &
1049	& r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
1050	END DO
1051	END DO
1052
1053	DO jj = 2, jpjm1
1054	DO ji = 2, jpim1
1055	zu(ji,jj,1) = - ( fse3u(ji,jj,1) - zsshu_n(ji,jj) * znad)
1056	zv(ji,jj,1) = - ( fse3v(ji,jj,1) - zsshv_n(ji,jj) * znad)
1057	END DO
1058	END DO
1059
1060	DO jk = 2, jpkm1
1061	DO jj = 2, jpjm1
1062	DO ji = 2, jpim1
1063	zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk)
1064	zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk)
1065	END DO
1066	END DO
1067	END DO
1068
1069	DO jk = 1, jpkm1
1070	DO jj = 2, jpjm1
1071	DO ji = 2, jpim1
1072	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk)
1073	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk)
1074	END DO
1075	END DO
1076	END DO
1077
1078	DO jk = 1, jpkm1
1079	DO jj = 2, jpjm1
1080	DO ji = 2, jpim1
1081	zu(ji,jj,jk) = min(zu(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
1082	zu(ji,jj,jk) = max(zu(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
1083	zv(ji,jj,jk) = min(zv(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
1084	zv(ji,jj,jk) = max(zv(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
1085	END DO
1086	END DO
1087	END DO
1088
1089
1090	DO jk = 1, jpkm1
1091	DO jj = 2, jpjm1
1092	DO ji = 2, jpim1
1093	zpwes = 0._wp; zpwed = 0._wp
1094	zpnss = 0._wp; zpnsd = 0._wp
1095	zuijk = zu(ji,jj,jk)
1096	zvijk = zv(ji,jj,jk)
1097
1098	!!!!! for u equation
1099	IF( jk <= mbku(ji,jj) ) THEN
1100	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
1101	jis = ji + 1; jid = ji
1102	ELSE
1103	jis = ji; jid = ji +1
1104	ENDIF
1105
1106	! integrate the pressure on the shallow side
1107	jk1 = jk
1108	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
1109	IF( jk1 == mbku(ji,jj) ) THEN
1110	zuijk = -zdept(jis,jj,jk1)
1111	EXIT
1112	ENDIF
1113	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
1114	zpwes = zpwes + &
1115	integ_spline(zdept(jis,jj,jk1), zdeps, &
1116	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
1117	csp(jis,jj,jk1), dsp(jis,jj,jk1))
1118	jk1 = jk1 + 1
1119	END DO
1120
1121	! integrate the pressure on the deep side
1122	jk1 = jk
1123	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
1124	IF( jk1 == 1 ) THEN
1125	zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad)
1126	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
1127	bsp(jid,jj,1), csp(jid,jj,1), &
1128	dsp(jid,jj,1)) * zdeps
1129	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
1130	EXIT
1131	ENDIF
1132	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
1133	zpwed = zpwed + &
1134	integ_spline(zdeps, zdept(jid,jj,jk1), &
1135	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
1136	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
1137	jk1 = jk1 - 1
1138	END DO
1139
1140	! update the momentum trends in u direction
1141
1142	zdpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk))
1143	IF( lk_vvl ) THEN
1144	zdpdx2 = zcoef0 / e1u(ji,jj) * &
1145	( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) )
1146	ELSE
1147	zdpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
1148	ENDIF
1149
1150	ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * &
1151	& umask(ji,jj,jk) * tmask(ji,jj,jk) * tmask(ji+1,jj,jk)
1152	ENDIF
1153
1154	!!!!! for v equation
1155	IF( jk <= mbkv(ji,jj) ) THEN
1156	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
1157	jjs = jj + 1; jjd = jj
1158	ELSE
1159	jjs = jj ; jjd = jj + 1
1160	ENDIF
1161
1162	! integrate the pressure on the shallow side
1163	jk1 = jk
1164	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
1165	IF( jk1 == mbkv(ji,jj) ) THEN
1166	zvijk = -zdept(ji,jjs,jk1)
1167	EXIT
1168	ENDIF
1169	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
1170	zpnss = zpnss + &
1171	integ_spline(zdept(ji,jjs,jk1), zdeps, &
1172	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
1173	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
1174	jk1 = jk1 + 1
1175	END DO
1176
1177	! integrate the pressure on the deep side
1178	jk1 = jk
1179	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
1180	IF( jk1 == 1 ) THEN
1181	zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad)
1182	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
1183	bsp(ji,jjd,1), csp(ji,jjd,1), &
1184	dsp(ji,jjd,1) ) * zdeps
1185	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
1186	EXIT
1187	ENDIF
1188	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
1189	zpnsd = zpnsd + &
1190	integ_spline(zdeps, zdept(ji,jjd,jk1), &
1191	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
1192	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
1193	jk1 = jk1 - 1
1194	END DO
1195
1196
1197	! update the momentum trends in v direction
1198
1199	zdpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk))
1200	IF( lk_vvl ) THEN
1201	zdpdy2 = zcoef0 / e2v(ji,jj) * &
1202	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) )
1203	ELSE
1204	zdpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
1205	ENDIF
1206
1207	va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2)*&
1208	& vmask(ji,jj,jk)tmask(ji,jj,jk)tmask(ji,jj+1,jk)
1209	ENDIF
1210
1211
1212	END DO
1213	END DO
1214	END DO
1215	!
1216	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
1217	CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh )
1218	CALL wrk_dealloc( jpi,jpj, zsshu_n, zsshv_n )
1219	!
1220	END SUBROUTINE hpg_prj
1221
1222
1223	SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type)
1224	!!----------------------------------------------------------------------
1225	!! * ROUTINE cspline *
1226	!!
1227	!! ** Purpose : constrained cubic spline interpolation
1228	!!
1229	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
1230	!!
1231	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
1232	!!----------------------------------------------------------------------
1233	IMPLICIT NONE
1234	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate
1235	REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of
1236	! the interpoated function
1237	INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline
1238	! 2: Linear
1239	!
1240	INTEGER :: ji, jj, jk ! dummy loop indices
1241	INTEGER :: jpi, jpj, jpkm1
1242	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
1243	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
1244	REAL(wp) :: zdf(size(fsp,3))
1245	!!----------------------------------------------------------------------
1246
1247	jpi = size(fsp,1)
1248	jpj = size(fsp,2)
1249	jpkm1 = size(fsp,3) - 1
1250
1251
1252	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
1253	DO ji = 1, jpi
1254	DO jj = 1, jpj
1255	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
1256	! DO jk = 2, jpkm1-1
1257	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
1258	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1259	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
1260	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
1261	!
1262	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
1263	!
1264	! IF(zdf1 * zdf2 <= 0._wp) THEN
1265	! zdf(jk) = 0._wp
1266	! ELSE
1267	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
1268	! ENDIF
1269	! END DO
1270
1271	!!Simply geometric average
1272	DO jk = 2, jpkm1-1
1273	zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1))
1274	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk))
1275
1276	IF(zdf1 * zdf2 <= 0._wp) THEN
1277	zdf(jk) = 0._wp
1278	ELSE
1279	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
1280	ENDIF
1281	END DO
1282
1283	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
1284	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
1285	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
1286	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - &
1287	& 0.5_wp * zdf(jpkm1 - 1)
1288
1289	DO jk = 1, jpkm1 - 1
1290	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1291	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
1292	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
1293	zddf1 = -2._wp * ztmp1 + ztmp2
1294	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
1295	zddf2 = 2._wp * ztmp1 - ztmp2
1296
1297	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
1298	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
1299	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
1300	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
1301	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
1302	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
1303	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
1304	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
1305	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
1306	END DO
1307	END DO
1308	END DO
1309
1310	ELSE IF (polynomial_type == 2) THEN ! Linear
1311	DO ji = 1, jpi
1312	DO jj = 1, jpj
1313	DO jk = 1, jpkm1-1
1314	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1315	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
1316
1317	dsp(ji,jj,jk) = 0._wp
1318	csp(ji,jj,jk) = 0._wp
1319	bsp(ji,jj,jk) = ztmp1 / zdxtmp
1320	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
1321	END DO
1322	END DO
1323	END DO
1324
1325	ELSE
1326	CALL ctl_stop( 'invalid polynomial type in cspline' )
1327	ENDIF
1328
1329	END SUBROUTINE cspline
1330
1331
1332	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
1333	!!----------------------------------------------------------------------
1334	!! * ROUTINE interp1 *
1335	!!
1336	!! ** Purpose : 1-d linear interpolation
1337	!!
1338	!! ** Method : interpolation is straight forward
1339	!! extrapolation is also permitted (no value limit)
1340	!!----------------------------------------------------------------------
1341	IMPLICIT NONE
1342	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
1343	REAL(wp) :: f ! result of the interpolation (extrapolation)
1344	REAL(wp) :: zdeltx
1345	!!----------------------------------------------------------------------
1346
1347	zdeltx = xr - xl
1348	IF(abs(zdeltx) <= 10._wp * EPSILON(x)) THEN
1349	f = 0.5_wp * (fl + fr)
1350	ELSE
1351	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
1352	ENDIF
1353
1354	END FUNCTION interp1
1355
1356
1357	FUNCTION interp2(x, a, b, c, d) RESULT(f)
1358	!!----------------------------------------------------------------------
1359	!! * ROUTINE interp1 *
1360	!!
1361	!! ** Purpose : 1-d constrained cubic spline interpolation
1362	!!
1363	!! ** Method : cubic spline interpolation
1364	!!
1365	!!----------------------------------------------------------------------
1366	IMPLICIT NONE
1367	REAL(wp), INTENT(in) :: x, a, b, c, d
1368	REAL(wp) :: f ! value from the interpolation
1369	!!----------------------------------------------------------------------
1370
1371	f = a + x* ( b + x * ( c + d * x ) )
1372
1373	END FUNCTION interp2
1374
1375
1376	FUNCTION interp3(x, a, b, c, d) RESULT(f)
1377	!!----------------------------------------------------------------------
1378	!! * ROUTINE interp1 *
1379	!!
1380	!! ** Purpose : Calculate the first order of deriavtive of
1381	!! a cubic spline function y=a+bx+cx^2+d*x^3
1382	!!
1383	!! ** Method : f=dy/dx=b+2cx+3dx^2
1384	!!
1385	!!----------------------------------------------------------------------
1386	IMPLICIT NONE
1387	REAL(wp), INTENT(in) :: x, a, b, c, d
1388	REAL(wp) :: f ! value from the interpolation
1389	!!----------------------------------------------------------------------
1390
1391	f = b + x * ( 2._wp * c + 3._wp * d * x)
1392
1393	END FUNCTION interp3
1394
1395
1396	FUNCTION integ_spline(xl, xr, a, b, c, d) RESULT(f)
1397	!!----------------------------------------------------------------------
1398	!! * ROUTINE interp1 *
1399	!!
1400	!! ** Purpose : 1-d constrained cubic spline integration
1401	!!
1402	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
1403	!!
1404	!!----------------------------------------------------------------------
1405	IMPLICIT NONE
1406	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
1407	REAL(wp) :: za1, za2, za3
1408	REAL(wp) :: f ! integration result
1409	!!----------------------------------------------------------------------
1410
1411	za1 = 0.5_wp * b
1412	za2 = c / 3.0_wp
1413	za3 = 0.25_wp * d
1414
1415	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
1416	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
1417
1418	END FUNCTION integ_spline
1419
1420	!!======================================================================
1421	END MODULE dynhpg
1422

Note: See TracBrowser for help on using the repository browser.

Download in other formats: