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dynhpg.F90 in branches/2015/dev_r5836_NOC3_vvl_by_default/NEMOGCM/NEMO/OPA_SRC/DYN – NEMO

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source: branches/2015/dev_r5836_NOC3_vvl_by_default/NEMOGCM/NEMO/OPA_SRC/DYN/dynhpg.F90 @ 5845

Last change on this file since 5845 was 5845, checked in by gm, 8 years ago
#1613: vvl by default: suppression of domzgr_substitute.h90
Property svn:keywords set to `Id`
File size: 75.0 KB

Line
1	MODULE dynhpg
2	!!======================================================================
3	!! * MODULE dynhpg *
4	!! Ocean dynamics: hydrostatic pressure gradient trend
5	!!======================================================================
6	!! History : OPA ! 1987-09 (P. Andrich, M.-A. Foujols) hpg_zco: Original code
7	!! 5.0 ! 1991-11 (G. Madec)
8	!! 7.0 ! 1996-01 (G. Madec) hpg_sco: Original code for s-coordinates
9	!! 8.0 ! 1997-05 (G. Madec) split dynber into dynkeg and dynhpg
10	!! 8.5 ! 2002-07 (G. Madec) F90: Free form and module
11	!! 8.5 ! 2002-08 (A. Bozec) hpg_zps: Original code
12	!! NEMO 1.0 ! 2005-10 (A. Beckmann, B.W. An) various s-coordinate options
13	!! ! Original code for hpg_ctl, hpg_hel hpg_wdj, hpg_djc, hpg_rot
14	!! - ! 2005-11 (G. Madec) style & small optimisation
15	!! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase
16	!! 3.4 ! 2011-11 (H. Liu) hpg_prj: Original code for s-coordinates
17	!! ! (A. Coward) suppression of hel, wdj and rot options
18	!! 3.6 ! 2014-11 (P. Mathiot) hpg_isf: original code for ice shelf cavity
19	!!----------------------------------------------------------------------
20
21	!!----------------------------------------------------------------------
22	!! dyn_hpg : update the momentum trend with the now horizontal
23	!! gradient of the hydrostatic pressure
24	!! dyn_hpg_init : initialisation and control of options
25	!! hpg_zco : z-coordinate scheme
26	!! hpg_zps : z-coordinate plus partial steps (interpolation)
27	!! hpg_sco : s-coordinate (standard jacobian formulation)
28	!! hpg_isf : s-coordinate (sco formulation) adapted to ice shelf
29	!! hpg_djc : s-coordinate (Density Jacobian with Cubic polynomial)
30	!! hpg_prj : s-coordinate (Pressure Jacobian with Cubic polynomial)
31	!!----------------------------------------------------------------------
32	USE oce ! ocean dynamics and tracers
33	USE sbc_oce ! surface variable (only for the flag with ice shelf)
34	USE dom_oce ! ocean space and time domain
35	USE phycst ! physical constants
36	USE trd_oce ! trends: ocean variables
37	USE trddyn ! trend manager: dynamics
38	!
39	USE in_out_manager ! I/O manager
40	USE prtctl ! Print control
41	USE lbclnk ! lateral boundary condition
42	USE lib_mpp ! MPP library
43	USE eosbn2 ! compute density
44	USE wrk_nemo ! Memory Allocation
45	USE timing ! Timing
46
47	IMPLICIT NONE
48	PRIVATE
49
50	PUBLIC dyn_hpg ! routine called by step module
51	PUBLIC dyn_hpg_init ! routine called by opa module
52
53	! !!* Namelist namdyn_hpg : hydrostatic pressure gradient
54	LOGICAL , PUBLIC :: ln_hpg_zco !: z-coordinate - full steps
55	LOGICAL , PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation)
56	LOGICAL , PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation)
57	LOGICAL , PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial)
58	LOGICAL , PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme)
59	LOGICAL , PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf
60	LOGICAL , PUBLIC :: ln_dynhpg_imp !: semi-implicite hpg flag
61
62	INTEGER , PUBLIC :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM)
63
64	!! * Substitutions
65	# include "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, ln_dynhpg_imp
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	WRITE(numout,*) ' time stepping: centered (F) or semi-implicit (T) ln_dynhpg_imp = ', ln_dynhpg_imp
157	ENDIF
158	!
159	IF( ln_hpg_djc ) &
160	& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method &
161	& currently disabled (bugs under investigation). Please select &
162	& either ln_hpg_sco or ln_hpg_prj instead')
163	!
164	IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) &
165	& CALL ctl_stop('dyn_hpg_init : variable volume key_vvl requires:&
166	& the standard jacobian formulation hpg_sco or &
167	& the pressure jacobian formulation hpg_prj')
168
169	IF( ln_hpg_isf .AND. .NOT. ln_isfcav ) &
170	& CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' )
171	IF( .NOT. ln_hpg_isf .AND. ln_isfcav ) &
172	& CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' )
173	!
174	! ! Set nhpg from ln_hpg_... flags
175	IF( ln_hpg_zco ) nhpg = 0
176	IF( ln_hpg_zps ) nhpg = 1
177	IF( ln_hpg_sco ) nhpg = 2
178	IF( ln_hpg_djc ) nhpg = 3
179	IF( ln_hpg_prj ) nhpg = 4
180	IF( ln_hpg_isf ) nhpg = 5
181	!
182	! ! Consistency check
183	ioptio = 0
184	IF( ln_hpg_zco ) ioptio = ioptio + 1
185	IF( ln_hpg_zps ) ioptio = ioptio + 1
186	IF( ln_hpg_sco ) ioptio = ioptio + 1
187	IF( ln_hpg_djc ) ioptio = ioptio + 1
188	IF( ln_hpg_prj ) ioptio = ioptio + 1
189	IF( ln_hpg_isf ) ioptio = ioptio + 1
190	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
191	!
192	! initialisation of ice load
193	riceload(:,:)=0.0
194	!
195	END SUBROUTINE dyn_hpg_init
196
197
198	SUBROUTINE hpg_zco( kt )
199	!!---------------------------------------------------------------------
200	!! * ROUTINE hpg_zco *
201	!!
202	!! ** Method : z-coordinate case, levels are horizontal surfaces.
203	!! The now hydrostatic pressure gradient at a given level, jk,
204	!! is computed by taking the vertical integral of the in-situ
205	!! density gradient along the model level from the suface to that
206	!! level: zhpi = grav .....
207	!! zhpj = grav .....
208	!! add it to the general momentum trend (ua,va).
209	!! ua = ua - 1/e1u * zhpi
210	!! va = va - 1/e2v * zhpj
211	!!
212	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
213	!!----------------------------------------------------------------------
214	INTEGER, INTENT(in) :: kt ! ocean time-step index
215	!
216	INTEGER :: ji, jj, jk ! dummy loop indices
217	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
218	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
219	!!----------------------------------------------------------------------
220	!
221	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
222	!
223	IF( kt == nit000 ) THEN
224	IF(lwp) WRITE(numout,*)
225	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
226	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
227	ENDIF
228
229	zcoef0 = - grav * 0.5_wp ! Local constant initialization
230
231	! Surface value
232	DO jj = 2, jpjm1
233	DO ji = fs_2, fs_jpim1 ! vector opt.
234	zcoef1 = zcoef0 * e3w_n(ji,jj,1)
235	! hydrostatic pressure gradient
236	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
237	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
238	!!gm zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
239	!!gm zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
240	! add to the general momentum trend
241	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
242	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
243	END DO
244	END DO
245
246	!
247	! interior value (2=<jk=<jpkm1)
248	DO jk = 2, jpkm1
249	DO jj = 2, jpjm1
250	DO ji = fs_2, fs_jpim1 ! vector opt.
251	zcoef1 = zcoef0 * e3w_n(ji,jj,jk)
252	! hydrostatic pressure gradient
253	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
254	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
255	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
256	!!gm & - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
257
258	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
259	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
260	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
261	!!gm & - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
262	! add to the general momentum trend
263	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
264	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
265	END DO
266	END DO
267	END DO
268	!
269	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
270	!
271	END SUBROUTINE hpg_zco
272
273
274	SUBROUTINE hpg_zps( kt )
275	!!---------------------------------------------------------------------
276	!! * ROUTINE hpg_zps *
277	!!
278	!! ** Method : z-coordinate plus partial steps case. blahblah...
279	!!
280	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
281	!!----------------------------------------------------------------------
282	INTEGER, INTENT(in) :: kt ! ocean time-step index
283	!!
284	INTEGER :: ji, jj, jk ! dummy loop indices
285	INTEGER :: iku, ikv ! temporary integers
286	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
287	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
288	!!----------------------------------------------------------------------
289	!
290	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
291	!
292	IF( kt == nit000 ) THEN
293	IF(lwp) WRITE(numout,*)
294	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
295	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
296	ENDIF
297
298
299	! Local constant initialization
300	zcoef0 = - grav * 0.5_wp
301
302	! Surface value (also valid in partial step case)
303	DO jj = 2, jpjm1
304	DO ji = fs_2, fs_jpim1 ! vector opt.
305	zcoef1 = zcoef0 * e3w_n(ji,jj,1)
306	! hydrostatic pressure gradient
307	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
308	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
309	!!gm zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
310	!!gm zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
311	! add to the general momentum trend
312	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
313	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
314	END DO
315	END DO
316
317
318	! interior value (2=<jk=<jpkm1)
319	DO jk = 2, jpkm1
320	DO jj = 2, jpjm1
321	DO ji = fs_2, fs_jpim1 ! vector opt.
322	zcoef1 = zcoef0 * e3w_n(ji,jj,jk)
323	! hydrostatic pressure gradient
324	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
325	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
326	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
327	!!gm & - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
328
329	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
330	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
331	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
332	!!gm & - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
333	! add to the general momentum trend
334	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
335	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
336	END DO
337	END DO
338	END DO
339
340
341	! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
342	DO jj = 2, jpjm1
343	DO ji = 2, jpim1
344	iku = mbku(ji,jj)
345	ikv = mbkv(ji,jj)
346	zcoef2 = zcoef0 * MIN( e3w_n(ji,jj,iku), e3w_n(ji+1,jj ,iku) )
347	zcoef3 = zcoef0 * MIN( e3w_n(ji,jj,ikv), e3w_n(ji ,jj+1,ikv) )
348	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
349	ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value
350	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
351	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj)
352	!!gm & + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) * r1_e1u(ji,jj)
353	ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
354	ENDIF
355	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
356	va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value
357	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
358	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj)
359	!!gm & + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) * r1_e2v(ji,jj)
360	va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
361	ENDIF
362	END DO
363	END DO
364	!
365	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
366	!
367	END SUBROUTINE hpg_zps
368
369	SUBROUTINE hpg_sco( kt )
370	!!---------------------------------------------------------------------
371	!! * ROUTINE hpg_sco *
372	!!
373	!! ** Method : s-coordinate case. Jacobian scheme.
374	!! The now hydrostatic pressure gradient at a given level, jk,
375	!! is computed by taking the vertical integral of the in-situ
376	!! density gradient along the model level from the suface to that
377	!! level. s-coordinates (ln_sco): a corrective term is added
378	!! to the horizontal pressure gradient :
379	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
380	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
381	!! add it to the general momentum trend (ua,va).
382	!! ua = ua - 1/e1u * zhpi
383	!! va = va - 1/e2v * zhpj
384	!!
385	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
386	!!----------------------------------------------------------------------
387	INTEGER, INTENT(in) :: kt ! ocean time-step index
388	!!
389	INTEGER :: ji, jj, jk ! dummy loop indices
390	REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars
391	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
392	!!----------------------------------------------------------------------
393	!
394	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
395	!
396	IF( kt == nit000 ) THEN
397	IF(lwp) WRITE(numout,*)
398	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
399	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
400	ENDIF
401
402	! Local constant initialization
403	zcoef0 = - grav * 0.5_wp
404	! To use density and not density anomaly
405	IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
406	ELSE ; znad = 0._wp ! Fixed volume
407	ENDIF
408
409	! Surface value
410	DO jj = 2, jpjm1
411	DO ji = fs_2, fs_jpim1 ! vector opt.
412	! hydrostatic pressure gradient along s-surfaces
413	!!gm zhpi(ji,jj,1) = zcoef0 * r1_e1u(ji,jj) * ( e3w_n(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) &
414	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( e3w_n(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) &
415	& - e3w_n(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
416	!!gm zhpj(ji,jj,1) = zcoef0 * r1_e2v(ji,jj) * ( e3w_n(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) &
417	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( e3w_n(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) &
418	& - e3w_n(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
419	! s-coordinate pressure gradient correction
420	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
421	& * ( gde3w_n(ji+1,jj,1) - gde3w_n(ji,jj,1) ) / e1u(ji,jj)
422	!!gm & * ( gde3w_n(ji+1,jj,1) - gde3w_n(ji,jj,1) ) * r1_e1u(ji,jj)
423	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
424	& * ( gde3w_n(ji,jj+1,1) - gde3w_n(ji,jj,1) ) / e2v(ji,jj)
425	!!gm & * ( gde3w_n(ji,jj+1,1) - gde3w_n(ji,jj,1) ) * r1_e2v(ji,jj)
426	! add to the general momentum trend
427	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap
428	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap
429	END DO
430	END DO
431
432	! interior value (2=<jk=<jpkm1)
433	DO jk = 2, jpkm1
434	DO jj = 2, jpjm1
435	DO ji = fs_2, fs_jpim1 ! vector opt.
436	! hydrostatic pressure gradient along s-surfaces
437	!!gm zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 * r1_e1u(ji,jj) &
438	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
439	& * ( e3w_n(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) &
440	& - e3w_n(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) )
441	!!gm zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
442	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 * r1_e2v(ji,jj) &
443	& * ( e3w_n(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) &
444	& - e3w_n(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) )
445	! s-coordinate pressure gradient correction
446	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
447	& * ( gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk) ) / e1u(ji,jj)
448	!!gm & * ( gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk) ) * r1_e1u(ji,jj)
449	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
450	& * ( gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk) ) / e2v(ji,jj)
451	!!gm & * ( gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk) ) * r1_e2v(ji,jj)
452	! add to the general momentum trend
453	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap
454	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap
455	END DO
456	END DO
457	END DO
458	!
459	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
460	!
461	END SUBROUTINE hpg_sco
462
463	SUBROUTINE hpg_isf( kt )
464	!!---------------------------------------------------------------------
465	!! * ROUTINE hpg_sco *
466	!!
467	!! ** Method : s-coordinate case. Jacobian scheme.
468	!! The now hydrostatic pressure gradient at a given level, jk,
469	!! is computed by taking the vertical integral of the in-situ
470	!! density gradient along the model level from the suface to that
471	!! level. s-coordinates (ln_sco): a corrective term is added
472	!! to the horizontal pressure gradient :
473	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
474	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
475	!! add it to the general momentum trend (ua,va).
476	!! ua = ua - 1/e1u * zhpi
477	!! va = va - 1/e2v * zhpj
478	!! iceload is added and partial cell case are added to the top and bottom
479	!!
480	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
481	!!----------------------------------------------------------------------
482	INTEGER, INTENT(in) :: kt ! ocean time-step index
483	!!
484	INTEGER :: ji, jj, jk, iku, ikv, ikt, iktp1i, iktp1j ! dummy loop indices
485	REAL(wp) :: zcoef0, zuap, zvap, znad, ze3wu, ze3wv, zuapint, zvapint, zhpjint, zhpiint, zdzwt, zdzwtjp1, zdzwtip1 ! temporary scalars
486	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj, zrhd
487	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop
488	REAL(wp), POINTER, DIMENSION(:,:) :: ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj
489	!!----------------------------------------------------------------------
490	!
491	CALL wrk_alloc( jpi,jpj, 2, ztstop)
492	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
493	CALL wrk_alloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
494	!
495	IF( kt == nit000 ) THEN
496	IF(lwp) WRITE(numout,*)
497	IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf'
498	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
499	ENDIF
500
501	! Local constant initialization
502	zcoef0 = - grav * 0.5_wp
503	! To use density and not density anomaly
504	! IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
505	! ELSE ; znad = 0._wp ! Fixed volume
506	! ENDIF
507	znad=1._wp
508	! iniitialised to 0. zhpi zhpi
509	zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp
510
511	!==================================================================================
512	!=====Compute iceload and contribution of the half first wet layer =================
513	!===================================================================================
514
515	! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude)
516	ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp
517
518	! compute density of the water displaced by the ice shelf
519	zrhd = rhd ! save rhd
520	DO jk = 1, jpk
521	zdept(:,:)=gdept_1d(jk)
522	CALL eos(ztstop(:,:,:),zdept(:,:),rhd(:,:,jk))
523	END DO
524	WHERE ( tmask(:,:,:) == 1._wp)
525	rhd(:,:,:) = zrhd(:,:,:) ! replace wet cell by the saved rhd
526	END WHERE
527
528	! compute rhd at the ice/oce interface (ice shelf side)
529	CALL eos(ztstop,risfdep,zrhdtop_isf)
530
531	! compute rhd at the ice/oce interface (ocean side)
532	DO ji=1,jpi
533	DO jj=1,jpj
534	ikt=mikt(ji,jj)
535	ztstop(ji,jj,1)=tsn(ji,jj,ikt,1)
536	ztstop(ji,jj,2)=tsn(ji,jj,ikt,2)
537	END DO
538	END DO
539	CALL eos(ztstop,risfdep,zrhdtop_oce)
540	!
541	! Surface value + ice shelf gradient
542	! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v)
543	ziceload = 0._wp
544	DO jj = 1, jpj
545	DO ji = 1, jpi ! vector opt.
546	ikt=mikt(ji,jj)
547	ziceload(ji,jj) = ziceload(ji,jj) + (znad + rhd(ji,jj,1) ) * e3w_n(ji,jj,1) * (1._wp - tmask(ji,jj,1))
548	DO jk=2,ikt-1
549	ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + rhd(ji,jj,jk-1) + rhd(ji,jj,jk)) * e3w_n(ji,jj,jk) &
550	& * (1._wp - tmask(ji,jj,jk))
551	END DO
552	IF (ikt .GE. 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + rhd(ji,jj,ikt-1)) &
553	& * ( risfdep(ji,jj) - gdept_1d(ikt-1) )
554	END DO
555	END DO
556	riceload(:,:) = 0.0_wp ; riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5
557	! compute zp from z=0 to first T wet point (correction due to zps not yet applied)
558	DO jj = 2, jpjm1
559	DO ji = fs_2, fs_jpim1 ! vector opt.
560	ikt=mikt(ji,jj) ; iktp1i=mikt(ji+1,jj); iktp1j=mikt(ji,jj+1)
561	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
562	! we assume ISF is in isostatic equilibrium
563	!!gm zhpi(ji,jj,1) = zcoef0 * r1_e1u(ji,jj) * ( 0.5_wp * e3w_n(ji+1,jj ,iktp1i) &
564	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * e3w_n(ji+1,jj ,iktp1i) &
565	& * ( 2._wp * znad + rhd(ji+1,jj ,iktp1i) + zrhdtop_oce(ji+1,jj ) ) &
566	& - 0.5_wp * e3w_n(ji ,jj ,ikt ) &
567	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
568	& + ( ziceload(ji+1,jj) - ziceload(ji,jj)) )
569	!!gm zhpj(ji,jj,1) = zcoef0 * r1_e2v(ji,jj) * ( 0.5_wp * e3w_n(ji ,jj+1,iktp1j) &
570	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * e3w_n(ji ,jj+1,iktp1j) &
571	& * ( 2._wp * znad + rhd(ji ,jj+1,iktp1j) + zrhdtop_oce(ji ,jj+1) ) &
572	& - 0.5_wp * e3w_n(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	& * ( gde3w_n(ji+1,jj,1) - gde3w_n(ji,jj,1) ) / e1u(ji,jj)
578	!!gm & * ( gde3w_n(ji+1,jj,1) - gde3w_n(ji,jj,1) ) * r1_e1u(ji,jj)
579	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
580	& * ( gde3w_n(ji,jj+1,1) - gde3w_n(ji,jj,1) ) / e2v(ji,jj)
581	!!gm & * ( gde3w_n(ji,jj+1,1) - gde3w_n(ji,jj,1) ) * r1_e2v(ji,jj)
582	! add to the general momentum trend
583	ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
584	va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
585	END DO
586	END DO
587	!==================================================================================
588	!===== Compute partial cell contribution for the top cell =========================
589	!==================================================================================
590	DO jj = 2, jpjm1
591	DO ji = fs_2, fs_jpim1 ! vector opt.
592	iku = miku(ji,jj)
593	zpshpi(ji,jj) = 0._wp ; zpshpj(ji,jj) = 0._wp
594	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))
595	! u direction
596	IF ( iku .GT. 1 ) THEN
597	! case iku
598	!!gm zhpi(ji,jj,iku) = zcoef0 * r1_e1u(ji,jj) * ze3wu &
599	zhpi(ji,jj,iku) = zcoef0 / e1u(ji,jj) * ze3wu &
600	& * ( rhd (ji+1,jj,iku) + rhd (ji,jj,iku) &
601	& + SIGN(1._wp,ze3wu) * grui(ji,jj) + 2._wp * znad )
602	! corrective term ( = 0 if z coordinate )
603	!!gm zuap = -zcoef0 * ( arui(ji,jj) + 2._wp * znad ) * gzui(ji,jj) * r1_e1u(ji,jj)
604	zuap = -zcoef0 * ( arui(ji,jj) + 2._wp * znad ) * gzui(ji,jj) / e1u(ji,jj)
605	! zhpi will be added in interior loop
606	ua(ji,jj,iku) = ua(ji,jj,iku) + zuap
607	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
608	IF (mbku(ji,jj) == iku + 1) zpshpi(ji,jj) = zhpi(ji,jj,iku)
609
610	! case iku + 1 (remove the zphi term added in the interior loop and compute the one corrected for zps)
611	!!gm zhpiint = zcoef0 * r1_e1u(ji,jj) &
612	zhpiint = zcoef0 / e1u(ji,jj) &
613	& * ( e3w_n(ji+1,jj ,iku+1) * ( (rhd(ji+1,jj,iku+1) + znad) &
614	& + (rhd(ji+1,jj,iku ) + znad) ) * tmask(ji+1,jj,iku) &
615	& - e3w_n(ji ,jj ,iku+1) * ( (rhd(ji ,jj,iku+1) + znad) &
616	& + (rhd(ji ,jj,iku ) + znad) ) * tmask(ji ,jj,iku) )
617	!!gm zhpi(ji,jj,iku+1) = zcoef0 * r1_e1u(ji,jj) * ge3rui(ji,jj) - zhpiint
618	zhpi(ji,jj,iku+1) = zcoef0 / e1u(ji,jj) * ge3rui(ji,jj) - zhpiint
619	END IF
620
621	! v direction
622	ikv = mikv(ji,jj)
623	ze3wv = (gdepw_0(ji,jj+1,ikv+1) - gdept_0(ji,jj+1,ikv)) - (gdepw_0(ji,jj,ikv+1) - gdept_0(ji,jj,ikv))
624	IF ( ikv .GT. 1 ) THEN
625	! case ikv
626	!!gm zhpj(ji,jj,ikv) = zcoef0 * r1_e2v(ji,jj) * ze3wv &
627	zhpj(ji,jj,ikv) = zcoef0 / e2v(ji,jj) * ze3wv &
628	& * ( rhd(ji,jj+1,ikv) + rhd (ji,jj,ikv) &
629	& + SIGN(1._wp,ze3wv) * grvi(ji,jj) + 2._wp * znad )
630	! corrective term ( = 0 if z coordinate )
631	!!gm zvap = -zcoef0 * ( arvi(ji,jj) + 2._wp * znad ) * gzvi(ji,jj) * r1_e2v(ji,jj)
632	zvap = -zcoef0 * ( arvi(ji,jj) + 2._wp * znad ) * gzvi(ji,jj) / e2v(ji,jj)
633	! zhpi will be added in interior loop
634	va(ji,jj,ikv) = va(ji,jj,ikv) + zvap
635	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
636	IF (mbkv(ji,jj) == ikv + 1) zpshpj(ji,jj) = zhpj(ji,jj,ikv)
637
638	! case ikv + 1 (remove the zphj term added in the interior loop and compute the one corrected for zps)
639	!!gm zhpjint = zcoef0 * r1_e2v(ji,jj) &
640	zhpjint = zcoef0 / e2v(ji,jj) &
641	& * ( e3w_n(ji ,jj+1,ikv+1) * ( (rhd(ji,jj+1,ikv+1) + znad) &
642	& + (rhd(ji,jj+1,ikv ) + znad) ) * tmask(ji,jj+1,ikv) &
643	& - e3w_n(ji ,jj ,ikv+1) * ( (rhd(ji,jj ,ikv+1) + znad) &
644	& + (rhd(ji,jj ,ikv ) + znad) ) * tmask(ji,jj ,ikv) )
645	!!gm zhpj(ji,jj,ikv+1) = zcoef0 * r1_e2v(ji,jj) * ge3rvi(ji,jj) - zhpjint
646	zhpj(ji,jj,ikv+1) = zcoef0 / e2v(ji,jj) * ge3rvi(ji,jj) - zhpjint
647	END IF
648	END DO
649	END DO
650
651	!==================================================================================
652	!===== Compute interior value =====================================================
653	!==================================================================================
654
655	DO jj = 2, jpjm1
656	DO ji = fs_2, fs_jpim1 ! vector opt.
657	!!gm useles !
658	iku=miku(ji,jj); ikv=mikv(ji,jj)
659	!!gm
660	DO jk = 2, jpkm1
661	! hydrostatic pressure gradient along s-surfaces
662	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
663	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) + zhpi(ji,jj,jk-1) &
664	!!gm & + zcoef0 * r1_e1u(ji,jj) &
665	& + zcoef0 / e1u(ji,jj) &
666	& * ( e3w_n(ji+1,jj,jk) * ( (rhd(ji+1,jj,jk ) + znad) &
667	& + (rhd(ji+1,jj,jk-1) + znad) ) * tmask(ji+1,jj,jk-1) &
668	& - e3w_n(ji ,jj,jk) * ( (rhd(ji ,jj,jk ) + znad) &
669	& + (rhd(ji ,jj,jk-1) + znad) ) * tmask(ji ,jj,jk-1) )
670	! s-coordinate pressure gradient correction
671	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
672	zuap = - zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
673	& * ( gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk) ) / e1u(ji,jj) * umask(ji,jj,jk-1)
674	!!gm & * ( gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk) ) * r1_e1u(ji,jj) * umask(ji,jj,jk-1)
675	ua(ji,jj,jk) = ua(ji,jj,jk) + ( zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
676
677	! hydrostatic pressure gradient along s-surfaces
678	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
679	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) + zhpj(ji,jj,jk-1) &
680	!!gm & + zcoef0 * r1_e2v(ji,jj) &
681	& + zcoef0 / e2v(ji,jj) &
682	& * ( e3w_n(ji ,jj+1,jk) * ( (rhd(ji,jj+1,jk ) + znad) &
683	& + (rhd(ji,jj+1,jk-1) + znad) ) * tmask(ji,jj+1,jk-1) &
684	& - e3w_n(ji ,jj ,jk) * ( (rhd(ji,jj ,jk ) + znad) &
685	& + (rhd(ji,jj ,jk-1) + znad) ) * tmask(ji,jj ,jk-1) )
686	! s-coordinate pressure gradient correction
687	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
688	zvap = - zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
689	& * ( gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk) ) / e2v(ji,jj) * vmask(ji,jj,jk-1)
690	!!gm & * ( gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk) ) * r1_e2v(ji,jj) * vmask(ji,jj,jk-1)
691	! add to the general momentum trend
692	va(ji,jj,jk) = va(ji,jj,jk) + ( zhpj(ji,jj,jk) + zvap ) * vmask(ji,jj,jk)
693	END DO
694	END DO
695	END DO
696
697	!==================================================================================
698	!===== Compute bottom cell contribution (partial cell) ============================
699	!==================================================================================
700
701	DO jj = 2, jpjm1
702	DO ji = 2, jpim1
703	iku = mbku(ji,jj)
704	ikv = mbkv(ji,jj)
705
706	IF (iku .GT. 1) THEN
707	! remove old value (interior case)
708	zuap = -zcoef0 * ( rhd (ji+1,jj ,iku) + rhd (ji,jj,iku) + 2._wp * znad ) &
709	& * ( gde3w_n(ji+1,jj ,iku) - gde3w_n(ji,jj,iku) ) / e1u(ji,jj)
710	!!gm & * ( gde3w_n(ji+1,jj ,iku) - gde3w_n(ji,jj,iku) ) * r1_e1u(ji,jj)
711	ua(ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) - zuap
712	! put new value
713	! -zpshpi to avoid double contribution of the partial step in the top layer
714	!!gm zuap = -zcoef0 * ( aru(ji,jj) + 2._wp * znad ) * gzu(ji,jj) * r1_e1u(ji,jj)
715	zuap = -zcoef0 * ( aru(ji,jj) + 2._wp * znad ) * gzu(ji,jj) / e1u(ji,jj)
716	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) + zcoef0 / e1u(ji,jj) * ge3ru(ji,jj) - zpshpi(ji,jj)
717	!!gm zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) + zcoef0 * r1_e1u(ji,jj) * ge3ru(ji,jj) - zpshpi(ji,jj)
718	ua(ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) + zuap
719	END IF
720	! v direction
721	IF (ikv .GT. 1) THEN
722	! remove old value (interior case)
723	zvap = -zcoef0 * ( rhd (ji ,jj+1,ikv) + rhd (ji,jj,ikv) + 2._wp * znad ) &
724	& * ( gde3w_n(ji ,jj+1,ikv) - gde3w_n(ji,jj,ikv) ) / e2v(ji,jj)
725	!!gm & * ( gde3w_n(ji ,jj+1,ikv) - gde3w_n(ji,jj,ikv) ) * r1_e2v(ji,jj)
726	va(ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) - zvap
727	! put new value
728	! -zpshpj to avoid double contribution of the partial step in the top layer
729	!!gm zvap = -zcoef0 * ( arv(ji,jj) + 2._wp * znad ) * gzv(ji,jj) * r1_e2v(ji,jj)
730	zvap = -zcoef0 * ( arv(ji,jj) + 2._wp * znad ) * gzv(ji,jj) / e2v(ji,jj)
731	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) + zcoef0 / e2v(ji,jj) * ge3rv(ji,jj) - zpshpj(ji,jj)
732	!!gm zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) + zcoef0 * r1_e2v(ji,jj) * ge3rv(ji,jj) - zpshpj(ji,jj)
733	va(ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) + zvap
734	END IF
735	END DO
736	END DO
737
738	! set back to original density value into the ice shelf cell (maybe useless because it is masked)
739	rhd = zrhd
740	!
741	CALL wrk_dealloc( jpi,jpj,2, ztstop)
742	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
743	CALL wrk_dealloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
744	!
745	END SUBROUTINE hpg_isf
746
747
748	SUBROUTINE hpg_djc( kt )
749	!!---------------------------------------------------------------------
750	!! * ROUTINE hpg_djc *
751	!!
752	!! ** Method : Density Jacobian with Cubic polynomial scheme
753	!!
754	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
755	!!----------------------------------------------------------------------
756	INTEGER, INTENT(in) :: kt ! ocean time-step index
757	!!
758	INTEGER :: ji, jj, jk ! dummy loop indices
759	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
760	REAL(wp) :: z1_10, cffu, cffx ! " "
761	REAL(wp) :: z1_12, cffv, cffy ! " "
762	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
763	REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw
764	REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow
765	REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k
766	!!----------------------------------------------------------------------
767	!
768	CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
769	CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
770	CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
771	!
772
773	IF( kt == nit000 ) THEN
774	IF(lwp) WRITE(numout,*)
775	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
776	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
777	ENDIF
778
779	! Local constant initialization
780	zcoef0 = - grav * 0.5_wp
781	z1_10 = 1._wp / 10._wp
782	z1_12 = 1._wp / 12._wp
783
784	!----------------------------------------------------------------------------------------
785	! compute and store in provisional arrays elementary vertical and horizontal differences
786	!----------------------------------------------------------------------------------------
787
788	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
789
790	DO jk = 2, jpkm1
791	DO jj = 2, jpjm1
792	DO ji = fs_2, fs_jpim1 ! vector opt.
793	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
794	dzz (ji,jj,jk) = gde3w_n(ji ,jj ,jk) - gde3w_n(ji,jj,jk-1)
795	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
796	dzx (ji,jj,jk) = gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk )
797	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
798	dzy (ji,jj,jk) = gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk )
799	END DO
800	END DO
801	END DO
802
803	!-------------------------------------------------------------------------
804	! compute harmonic averages using eq. 5.18
805	!-------------------------------------------------------------------------
806	zep = 1.e-15
807
808	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
809	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
810
811	DO jk = 2, jpkm1
812	DO jj = 2, jpjm1
813	DO ji = fs_2, fs_jpim1 ! vector opt.
814	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
815
816	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
817	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
818
819	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
820	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
821
822	IF( cffw > zep) THEN
823	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
824	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
825	ELSE
826	drhow(ji,jj,jk) = 0._wp
827	ENDIF
828
829	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
830	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
831
832	IF( cffu > zep ) THEN
833	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
834	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
835	ELSE
836	drhou(ji,jj,jk ) = 0._wp
837	ENDIF
838
839	IF( cffx > zep ) THEN
840	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
841	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
842	ELSE
843	dzu(ji,jj,jk) = 0._wp
844	ENDIF
845
846	IF( cffv > zep ) THEN
847	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
848	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
849	ELSE
850	drhov(ji,jj,jk) = 0._wp
851	ENDIF
852
853	IF( cffy > zep ) THEN
854	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
855	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
856	ELSE
857	dzv(ji,jj,jk) = 0._wp
858	ENDIF
859
860	END DO
861	END DO
862	END DO
863
864	!----------------------------------------------------------------------------------
865	! apply boundary conditions at top and bottom using 5.36-5.37
866	!----------------------------------------------------------------------------------
867	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
868	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
869	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
870
871	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
872	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
873	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
874
875
876	!--------------------------------------------------------------
877	! Upper half of top-most grid box, compute and store
878	!-------------------------------------------------------------
879
880	!!bug gm : e3w-gde3w = 0.5*e3w .... and gde3w(2)-gde3w(1)=e3w(2) .... to be verified
881	! true if gde3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
882
883	DO jj = 2, jpjm1
884	DO ji = fs_2, fs_jpim1 ! vector opt.
885	rho_k(ji,jj,1) = -grav * ( e3w_n(ji,jj,1) - gde3w_n(ji,jj,1) ) &
886	& * ( rhd(ji,jj,1) &
887	& + 0.5_wp * ( rhd (ji,jj,2) - rhd (ji,jj,1) ) &
888	& * ( e3w_n (ji,jj,1) - gde3w_n(ji,jj,1) ) &
889	& / ( gde3w_n(ji,jj,2) - gde3w_n(ji,jj,1) ) )
890	END DO
891	END DO
892
893	!!bug gm : here also, simplification is possible
894	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
895
896	DO jk = 2, jpkm1
897	DO jj = 2, jpjm1
898	DO ji = fs_2, fs_jpim1 ! vector opt.
899
900	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
901	& * ( gde3w_n(ji,jj,jk) - gde3w_n(ji,jj,jk-1) ) &
902	& - grav * z1_10 * ( &
903	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
904	& * ( gde3w_n(ji,jj,jk) - gde3w_n(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
905	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
906	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
907	& )
908
909	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
910	& * ( gde3w_n(ji+1,jj,jk) - gde3w_n(ji,jj,jk) ) &
911	& - grav* z1_10 * ( &
912	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
913	& * ( gde3w_n(ji+1,jj,jk) - gde3w_n(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
914	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
915	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
916	& )
917
918	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
919	& * ( gde3w_n(ji,jj+1,jk) - gde3w_n(ji,jj,jk) ) &
920	& - grav* z1_10 * ( &
921	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
922	& * ( gde3w_n(ji,jj+1,jk) - gde3w_n(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
923	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
924	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
925	& )
926
927	END DO
928	END DO
929	END DO
930	CALL lbc_lnk(rho_k,'W',1.)
931	CALL lbc_lnk(rho_i,'U',1.)
932	CALL lbc_lnk(rho_j,'V',1.)
933
934
935	! ---------------
936	! Surface value
937	! ---------------
938	DO jj = 2, jpjm1
939	DO ji = fs_2, fs_jpim1 ! vector opt.
940	!!gm zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) * r1_e1u(ji,jj)
941	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj)
942	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj)
943	!!gm zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) * r1_e2v(ji,jj)
944	! add to the general momentum trend
945	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
946	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
947	END DO
948	END DO
949
950	! ----------------
951	! interior value (2=<jk=<jpkm1)
952	! ----------------
953	DO jk = 2, jpkm1
954	DO jj = 2, jpjm1
955	DO ji = fs_2, fs_jpim1 ! vector opt.
956	! hydrostatic pressure gradient along s-surfaces
957	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
958	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
959	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj)
960	!!gm & - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) * r1_e1u(ji,jj)
961	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
962	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
963	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj)
964	!!gm & -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) * r1_e2v(ji,jj)
965	! add to the general momentum trend
966	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
967	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
968	END DO
969	END DO
970	END DO
971	!
972	CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
973	CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
974	CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
975	!
976	END SUBROUTINE hpg_djc
977
978
979	SUBROUTINE hpg_prj( kt )
980	!!---------------------------------------------------------------------
981	!! * ROUTINE hpg_prj *
982	!!
983	!! ** Method : s-coordinate case.
984	!! A Pressure-Jacobian horizontal pressure gradient method
985	!! based on the constrained cubic-spline interpolation for
986	!! all vertical coordinate systems
987	!!
988	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
989	!!----------------------------------------------------------------------
990	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
991	INTEGER, INTENT(in) :: kt ! ocean time-step index
992	!!
993	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
994	REAL(wp) :: zcoef0, znad ! temporary scalars
995	!!
996	!! The local variables for the correction term
997	INTEGER :: jk1, jis, jid, jjs, jjd
998	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
999	REAL(wp) :: zrhdt1
1000	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
1001	REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh
1002	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
1003	REAL(wp), POINTER, DIMENSION(:,:) :: zsshu_n, zsshv_n
1004	!!----------------------------------------------------------------------
1005	!
1006	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
1007	CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh )
1008	CALL wrk_alloc( jpi,jpj, zsshu_n, zsshv_n )
1009	!
1010	IF( kt == nit000 ) THEN
1011	IF(lwp) WRITE(numout,*)
1012	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
1013	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
1014	ENDIF
1015
1016	!!----------------------------------------------------------------------
1017	! Local constant initialization
1018	zcoef0 = - grav
1019	znad = 0.0_wp
1020	IF( lk_vvl ) znad = 1._wp
1021
1022	! Clean 3-D work arrays
1023	zhpi(:,:,:) = 0._wp
1024	zrhh(:,:,:) = rhd(:,:,:)
1025
1026	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
1027	DO jj = 1, jpj
1028	DO ji = 1, jpi
1029	jk = mbathy(ji,jj)
1030	IF( jk <= 0 ) THEN ; zrhh(ji,jj, : ) = 0._wp
1031	ELSEIF( jk == 1 ) THEN ; zrhh(ji,jj,jk+1:jpk) = rhd(ji,jj,jk)
1032	ELSEIF( jk < jpkm1 ) THEN
1033	DO jkk = jk+1, jpk
1034	zrhh(ji,jj,jkk) = interp1(gde3w_n(ji,jj,jkk ), gde3w_n(ji,jj,jkk-1), &
1035	& gde3w_n(ji,jj,jkk-2), rhd (ji,jj,jkk-1), rhd(ji,jj,jkk-2))
1036	END DO
1037	ENDIF
1038	END DO
1039	END DO
1040
1041	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
1042	DO jj = 1, jpj
1043	DO ji = 1, jpi
1044	zdept(ji,jj,1) = 0.5_wp * e3w_n(ji,jj,1) - sshn(ji,jj) * znad
1045	END DO
1046	END DO
1047
1048	DO jk = 2, jpk
1049	DO jj = 1, jpj
1050	DO ji = 1, jpi
1051	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + e3w_n(ji,jj,jk)
1052	END DO
1053	END DO
1054	END DO
1055
1056	fsp(:,:,:) = zrhh (:,:,:)
1057	xsp(:,:,:) = zdept(:,:,:)
1058
1059	! Construct the vertical density profile with the
1060	! constrained cubic spline interpolation
1061	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
1062	CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type)
1063
1064	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
1065	DO jj = 2, jpj
1066	DO ji = 2, jpi
1067	zrhdt1 = zrhh(ji,jj,1) - interp3(zdept(ji,jj,1),asp(ji,jj,1), &
1068	bsp(ji,jj,1), csp(ji,jj,1), &
1069	dsp(ji,jj,1) ) * 0.25_wp * e3w_n(ji,jj,1)
1070
1071	! assuming linear profile across the top half surface layer
1072	zhpi(ji,jj,1) = 0.5_wp * e3w_n(ji,jj,1) * zrhdt1
1073	END DO
1074	END DO
1075
1076	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
1077	DO jk = 2, jpkm1
1078	DO jj = 2, jpj
1079	DO ji = 2, jpi
1080	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
1081	integ_spline(zdept(ji,jj,jk-1), zdept(ji,jj,jk),&
1082	asp(ji,jj,jk-1), bsp(ji,jj,jk-1), &
1083	csp(ji,jj,jk-1), dsp(ji,jj,jk-1))
1084	END DO
1085	END DO
1086	END DO
1087
1088	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
1089
1090	! Prepare zsshu_n and zsshv_n
1091	DO jj = 2, jpjm1
1092	DO ji = 2, jpim1
1093	zsshu_n(ji,jj) = (e1e2u(ji,jj) * sshn(ji,jj) + e1e2u(ji+1, jj) * sshn(ji+1,jj)) * &
1094	& r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
1095	zsshv_n(ji,jj) = (e1e2v(ji,jj) * sshn(ji,jj) + e1e2v(ji+1, jj) * sshn(ji,jj+1)) * &
1096	& r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
1097	END DO
1098	END DO
1099
1100	DO jj = 2, jpjm1
1101	DO ji = 2, jpim1
1102	zu(ji,jj,1) = - ( e3u_n(ji,jj,1) - zsshu_n(ji,jj) * znad)
1103	zv(ji,jj,1) = - ( e3v_n(ji,jj,1) - zsshv_n(ji,jj) * znad)
1104	END DO
1105	END DO
1106
1107	DO jk = 2, jpkm1
1108	DO jj = 2, jpjm1
1109	DO ji = 2, jpim1
1110	zu(ji,jj,jk) = zu(ji,jj,jk-1)- e3u_n(ji,jj,jk)
1111	zv(ji,jj,jk) = zv(ji,jj,jk-1)- e3v_n(ji,jj,jk)
1112	END DO
1113	END DO
1114	END DO
1115
1116	DO jk = 1, jpkm1
1117	DO jj = 2, jpjm1
1118	DO ji = 2, jpim1
1119	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * e3u_n(ji,jj,jk)
1120	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * e3v_n(ji,jj,jk)
1121	END DO
1122	END DO
1123	END DO
1124
1125	DO jk = 1, jpkm1
1126	DO jj = 2, jpjm1
1127	DO ji = 2, jpim1
1128	zu(ji,jj,jk) = min(zu(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
1129	zu(ji,jj,jk) = max(zu(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
1130	zv(ji,jj,jk) = min(zv(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
1131	zv(ji,jj,jk) = max(zv(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
1132	END DO
1133	END DO
1134	END DO
1135
1136
1137	DO jk = 1, jpkm1
1138	DO jj = 2, jpjm1
1139	DO ji = 2, jpim1
1140	zpwes = 0._wp; zpwed = 0._wp
1141	zpnss = 0._wp; zpnsd = 0._wp
1142	zuijk = zu(ji,jj,jk)
1143	zvijk = zv(ji,jj,jk)
1144
1145	!!!!! for u equation
1146	IF( jk <= mbku(ji,jj) ) THEN
1147	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
1148	jis = ji + 1; jid = ji
1149	ELSE
1150	jis = ji; jid = ji +1
1151	ENDIF
1152
1153	! integrate the pressure on the shallow side
1154	jk1 = jk
1155	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
1156	IF( jk1 == mbku(ji,jj) ) THEN
1157	zuijk = -zdept(jis,jj,jk1)
1158	EXIT
1159	ENDIF
1160	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
1161	zpwes = zpwes + &
1162	integ_spline(zdept(jis,jj,jk1), zdeps, &
1163	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
1164	csp(jis,jj,jk1), dsp(jis,jj,jk1))
1165	jk1 = jk1 + 1
1166	END DO
1167
1168	! integrate the pressure on the deep side
1169	jk1 = jk
1170	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
1171	IF( jk1 == 1 ) THEN
1172	zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad)
1173	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
1174	bsp(jid,jj,1), csp(jid,jj,1), &
1175	dsp(jid,jj,1)) * zdeps
1176	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
1177	EXIT
1178	ENDIF
1179	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
1180	zpwed = zpwed + &
1181	integ_spline(zdeps, zdept(jid,jj,jk1), &
1182	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
1183	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
1184	jk1 = jk1 - 1
1185	END DO
1186
1187	! update the momentum trends in u direction
1188
1189	!!gm zdpdx1 = zcoef0 * r1_e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk))
1190	zdpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk))
1191	IF( lk_vvl ) THEN
1192	!!gm zdpdx2 = zcoef0 * r1_e1u(ji,jj) * &
1193	zdpdx2 = zcoef0 / e1u(ji,jj) * &
1194	( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) )
1195	ELSE
1196	!!gm zdpdx2 = zcoef0 * r1_e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
1197	zdpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
1198	ENDIF
1199
1200	ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * &
1201	& umask(ji,jj,jk) * tmask(ji,jj,jk) * tmask(ji+1,jj,jk)
1202	ENDIF
1203
1204	!!!!! for v equation
1205	IF( jk <= mbkv(ji,jj) ) THEN
1206	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
1207	jjs = jj + 1; jjd = jj
1208	ELSE
1209	jjs = jj ; jjd = jj + 1
1210	ENDIF
1211
1212	! integrate the pressure on the shallow side
1213	jk1 = jk
1214	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
1215	IF( jk1 == mbkv(ji,jj) ) THEN
1216	zvijk = -zdept(ji,jjs,jk1)
1217	EXIT
1218	ENDIF
1219	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
1220	zpnss = zpnss + &
1221	integ_spline(zdept(ji,jjs,jk1), zdeps, &
1222	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
1223	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
1224	jk1 = jk1 + 1
1225	END DO
1226
1227	! integrate the pressure on the deep side
1228	jk1 = jk
1229	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
1230	IF( jk1 == 1 ) THEN
1231	zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad)
1232	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
1233	bsp(ji,jjd,1), csp(ji,jjd,1), &
1234	dsp(ji,jjd,1) ) * zdeps
1235	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
1236	EXIT
1237	ENDIF
1238	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
1239	zpnsd = zpnsd + &
1240	integ_spline(zdeps, zdept(ji,jjd,jk1), &
1241	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
1242	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
1243	jk1 = jk1 - 1
1244	END DO
1245
1246
1247	! update the momentum trends in v direction
1248
1249	!!gm zdpdy1 = zcoef0 * r1_e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk))
1250	zdpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk))
1251	IF( lk_vvl ) THEN
1252	!!gm zdpdy2 = zcoef0 * r1_e2v(ji,jj) * &
1253	zdpdy2 = zcoef0 / e2v(ji,jj) * &
1254	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) )
1255	ELSE
1256	!!gm zdpdy2 = zcoef0 * r1_e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
1257	zdpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
1258	ENDIF
1259
1260	va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2)*&
1261	& vmask(ji,jj,jk)tmask(ji,jj,jk)tmask(ji,jj+1,jk)
1262	ENDIF
1263
1264
1265	END DO
1266	END DO
1267	END DO
1268	!
1269	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
1270	CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh )
1271	CALL wrk_dealloc( jpi,jpj, zsshu_n, zsshv_n )
1272	!
1273	END SUBROUTINE hpg_prj
1274
1275
1276	SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type)
1277	!!----------------------------------------------------------------------
1278	!! * ROUTINE cspline *
1279	!!
1280	!! ** Purpose : constrained cubic spline interpolation
1281	!!
1282	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
1283	!!
1284	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
1285	!!----------------------------------------------------------------------
1286	IMPLICIT NONE
1287	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate
1288	REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of
1289	! the interpoated function
1290	INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline
1291	! 2: Linear
1292	!
1293	INTEGER :: ji, jj, jk ! dummy loop indices
1294	INTEGER :: jpi, jpj, jpkm1
1295	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
1296	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
1297	REAL(wp) :: zdf(size(fsp,3))
1298	!!----------------------------------------------------------------------
1299
1300	jpi = size(fsp,1)
1301	jpj = size(fsp,2)
1302	jpkm1 = size(fsp,3) - 1
1303
1304
1305	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
1306	DO ji = 1, jpi
1307	DO jj = 1, jpj
1308	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
1309	! DO jk = 2, jpkm1-1
1310	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
1311	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1312	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
1313	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
1314	!
1315	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
1316	!
1317	! IF(zdf1 * zdf2 <= 0._wp) THEN
1318	! zdf(jk) = 0._wp
1319	! ELSE
1320	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
1321	! ENDIF
1322	! END DO
1323
1324	!!Simply geometric average
1325	DO jk = 2, jpkm1-1
1326	zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1))
1327	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk))
1328
1329	IF(zdf1 * zdf2 <= 0._wp) THEN
1330	zdf(jk) = 0._wp
1331	ELSE
1332	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
1333	ENDIF
1334	END DO
1335
1336	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
1337	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
1338	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
1339	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - &
1340	& 0.5_wp * zdf(jpkm1 - 1)
1341
1342	DO jk = 1, jpkm1 - 1
1343	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1344	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
1345	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
1346	zddf1 = -2._wp * ztmp1 + ztmp2
1347	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
1348	zddf2 = 2._wp * ztmp1 - ztmp2
1349
1350	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
1351	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
1352	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
1353	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
1354	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
1355	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
1356	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
1357	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
1358	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
1359	END DO
1360	END DO
1361	END DO
1362
1363	ELSE IF (polynomial_type == 2) THEN ! Linear
1364	DO ji = 1, jpi
1365	DO jj = 1, jpj
1366	DO jk = 1, jpkm1-1
1367	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1368	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
1369
1370	dsp(ji,jj,jk) = 0._wp
1371	csp(ji,jj,jk) = 0._wp
1372	bsp(ji,jj,jk) = ztmp1 / zdxtmp
1373	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
1374	END DO
1375	END DO
1376	END DO
1377
1378	ELSE
1379	CALL ctl_stop( 'invalid polynomial type in cspline' )
1380	ENDIF
1381
1382	END SUBROUTINE cspline
1383
1384
1385	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
1386	!!----------------------------------------------------------------------
1387	!! * ROUTINE interp1 *
1388	!!
1389	!! ** Purpose : 1-d linear interpolation
1390	!!
1391	!! ** Method : interpolation is straight forward
1392	!! extrapolation is also permitted (no value limit)
1393	!!----------------------------------------------------------------------
1394	IMPLICIT NONE
1395	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
1396	REAL(wp) :: f ! result of the interpolation (extrapolation)
1397	REAL(wp) :: zdeltx
1398	!!----------------------------------------------------------------------
1399
1400	zdeltx = xr - xl
1401	IF(abs(zdeltx) <= 10._wp * EPSILON(x)) THEN
1402	f = 0.5_wp * (fl + fr)
1403	ELSE
1404	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
1405	ENDIF
1406
1407	END FUNCTION interp1
1408
1409
1410	FUNCTION interp2(x, a, b, c, d) RESULT(f)
1411	!!----------------------------------------------------------------------
1412	!! * ROUTINE interp1 *
1413	!!
1414	!! ** Purpose : 1-d constrained cubic spline interpolation
1415	!!
1416	!! ** Method : cubic spline interpolation
1417	!!
1418	!!----------------------------------------------------------------------
1419	IMPLICIT NONE
1420	REAL(wp), INTENT(in) :: x, a, b, c, d
1421	REAL(wp) :: f ! value from the interpolation
1422	!!----------------------------------------------------------------------
1423
1424	f = a + x* ( b + x * ( c + d * x ) )
1425
1426	END FUNCTION interp2
1427
1428
1429	FUNCTION interp3(x, a, b, c, d) RESULT(f)
1430	!!----------------------------------------------------------------------
1431	!! * ROUTINE interp1 *
1432	!!
1433	!! ** Purpose : Calculate the first order of deriavtive of
1434	!! a cubic spline function y=a+bx+cx^2+d*x^3
1435	!!
1436	!! ** Method : f=dy/dx=b+2cx+3dx^2
1437	!!
1438	!!----------------------------------------------------------------------
1439	IMPLICIT NONE
1440	REAL(wp), INTENT(in) :: x, a, b, c, d
1441	REAL(wp) :: f ! value from the interpolation
1442	!!----------------------------------------------------------------------
1443
1444	f = b + x * ( 2._wp * c + 3._wp * d * x)
1445
1446	END FUNCTION interp3
1447
1448
1449	FUNCTION integ_spline(xl, xr, a, b, c, d) RESULT(f)
1450	!!----------------------------------------------------------------------
1451	!! * ROUTINE interp1 *
1452	!!
1453	!! ** Purpose : 1-d constrained cubic spline integration
1454	!!
1455	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
1456	!!
1457	!!----------------------------------------------------------------------
1458	IMPLICIT NONE
1459	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
1460	REAL(wp) :: za1, za2, za3
1461	REAL(wp) :: f ! integration result
1462	!!----------------------------------------------------------------------
1463
1464	za1 = 0.5_wp * b
1465	za2 = c / 3.0_wp
1466	za3 = 0.25_wp * d
1467
1468	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
1469	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
1470
1471	END FUNCTION integ_spline
1472
1473	!!======================================================================
1474	END MODULE dynhpg
1475

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