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dynhpg.F90 @ 6808

Last change on this file since 6808 was 6808, checked in by jamesharle, 8 years ago
merge with trunk@6232 for consistency with SSB code
Property svn:keywords set to `Id`
File size: 70.7 KB

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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 wet_dry ! wetting and drying
36	USE phycst ! physical constants
37	USE trd_oce ! trends: ocean variables
38	USE trddyn ! trend manager: dynamics
39	!jc USE zpshde ! partial step: hor. derivative (zps_hde routine)
40	!
41	USE in_out_manager ! I/O manager
42	USE prtctl ! Print control
43	USE lbclnk ! lateral boundary condition
44	USE lib_mpp ! MPP library
45	USE eosbn2 ! compute density
46	USE wrk_nemo ! Memory Allocation
47	USE timing ! Timing
48	USE iom
49
50	IMPLICIT NONE
51	PRIVATE
52
53	PUBLIC dyn_hpg ! routine called by step module
54	PUBLIC dyn_hpg_init ! routine called by opa module
55
56	! !!* Namelist namdyn_hpg : hydrostatic pressure gradient
57	LOGICAL , PUBLIC :: ln_hpg_zco !: z-coordinate - full steps
58	LOGICAL , PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation)
59	LOGICAL , PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation)
60	LOGICAL , PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial)
61	LOGICAL , PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme)
62	LOGICAL , PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf
63
64	INTEGER , PUBLIC :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM)
65
66	!! * Substitutions
67	# include "vectopt_loop_substitute.h90"
68	!!----------------------------------------------------------------------
69	!! NEMO/OPA 3.3 , NEMO Consortium (2010)
70	!! $Id$
71	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
72	!!----------------------------------------------------------------------
73	CONTAINS
74
75	SUBROUTINE dyn_hpg( kt )
76	!!---------------------------------------------------------------------
77	!! * ROUTINE dyn_hpg *
78	!!
79	!! ** Method : Call the hydrostatic pressure gradient routine
80	!! using the scheme defined in the namelist
81	!!
82	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
83	!! - send trends to trd_dyn for futher diagnostics (l_trddyn=T)
84	!!----------------------------------------------------------------------
85	INTEGER, INTENT(in) :: kt ! ocean time-step index
86	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdu, ztrdv
87	!!----------------------------------------------------------------------
88	!
89	IF( nn_timing == 1 ) CALL timing_start('dyn_hpg')
90	!
91	IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn)
92	CALL wrk_alloc( jpi,jpj,jpk, ztrdu, ztrdv )
93	ztrdu(:,:,:) = ua(:,:,:)
94	ztrdv(:,:,:) = va(:,:,:)
95	ENDIF
96	!
97	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
98	CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate
99	CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation)
100	CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation)
101	CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial)
102	CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme)
103	CASE ( 5 ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf
104	END SELECT
105	!
106	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
107	ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:)
108	ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:)
109	CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt )
110	CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv )
111	ENDIF
112	!
113	IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, &
114	& tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
115	!
116	IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg')
117	!
118	END SUBROUTINE dyn_hpg
119
120
121	SUBROUTINE dyn_hpg_init
122	!!----------------------------------------------------------------------
123	!! * ROUTINE dyn_hpg_init *
124	!!
125	!! ** Purpose : initializations for the hydrostatic pressure gradient
126	!! computation and consistency control
127	!!
128	!! ** Action : Read the namelist namdyn_hpg and check the consistency
129	!! with the type of vertical coordinate used (zco, zps, sco)
130	!!----------------------------------------------------------------------
131	INTEGER :: ioptio = 0 ! temporary integer
132	INTEGER :: ios ! Local integer output status for namelist read
133	!!
134	INTEGER :: ji, jj, jk, ikt ! dummy loop indices ISF
135	REAL(wp) :: znad
136	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop, zrhd ! hypothesys on isf density
137	REAL(wp), POINTER, DIMENSION(:,:) :: zrhdtop_isf ! density at bottom of ISF
138	REAL(wp), POINTER, DIMENSION(:,:) :: ziceload ! density at bottom of ISF
139	!!
140	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
141	& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf
142	!!----------------------------------------------------------------------
143	!
144	REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient
145	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
146	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp )
147	!
148	REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient
149	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
150	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp )
151	IF(lwm) WRITE ( numond, namdyn_hpg )
152	!
153	IF(lwp) THEN ! Control print
154	WRITE(numout,*)
155	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
156	WRITE(numout,*) '~~~~~~~~~~~~'
157	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
158	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
159	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
160	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
161	WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf
162	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
163	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
164	ENDIF
165	!
166	IF( ln_hpg_djc ) &
167	& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method &
168	& currently disabled (bugs under investigation). Please select &
169	& either ln_hpg_sco or ln_hpg_prj instead')
170	!
171	IF( .NOT.ln_linssh .AND. .NOT.(ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) &
172	& CALL ctl_stop('dyn_hpg_init : non-linear free surface requires either ', &
173	& ' the standard jacobian formulation hpg_sco or ' , &
174	& ' the pressure jacobian formulation hpg_prj' )
175
176	IF( ln_hpg_isf .AND. .NOT. ln_isfcav ) &
177	& CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' )
178	IF( .NOT. ln_hpg_isf .AND. ln_isfcav ) &
179	& CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' )
180	!
181	! ! Set nhpg from ln_hpg_... flags
182	IF( ln_hpg_zco ) nhpg = 0
183	IF( ln_hpg_zps ) nhpg = 1
184	IF( ln_hpg_sco ) nhpg = 2
185	IF( ln_hpg_djc ) nhpg = 3
186	IF( ln_hpg_prj ) nhpg = 4
187	IF( ln_hpg_isf ) nhpg = 5
188	!
189	! ! Consistency check
190	ioptio = 0
191	IF( ln_hpg_zco ) ioptio = ioptio + 1
192	IF( ln_hpg_zps ) ioptio = ioptio + 1
193	IF( ln_hpg_sco ) ioptio = ioptio + 1
194	IF( ln_hpg_djc ) ioptio = ioptio + 1
195	IF( ln_hpg_prj ) ioptio = ioptio + 1
196	IF( ln_hpg_isf ) ioptio = ioptio + 1
197	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
198	!
199	! initialisation of ice shelf load
200	IF ( .NOT. ln_isfcav ) riceload(:,:)=0.0
201	IF ( ln_isfcav ) THEN
202	CALL wrk_alloc( jpi,jpj, 2, ztstop)
203	CALL wrk_alloc( jpi,jpj,jpk, zrhd )
204	CALL wrk_alloc( jpi,jpj, zrhdtop_isf, ziceload)
205	!
206	IF(lwp) WRITE(numout,*)
207	IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf'
208	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~'
209
210	! To use density and not density anomaly
211	znad=1._wp
212
213	! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude)
214	ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp
215
216	! compute density of the water displaced by the ice shelf
217	DO jk = 1, jpk
218	CALL eos(ztstop(:,:,:),gdept_n(:,:,jk),zrhd(:,:,jk))
219	END DO
220
221	! compute rhd at the ice/oce interface (ice shelf side)
222	CALL eos(ztstop,risfdep,zrhdtop_isf)
223
224	! Surface value + ice shelf gradient
225	! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v)
226	! divided by 2 later
227	ziceload = 0._wp
228	DO jj = 1, jpj
229	DO ji = 1, jpi
230	ikt=mikt(ji,jj)
231	ziceload(ji,jj) = ziceload(ji,jj) + (znad + zrhd(ji,jj,1) ) * e3w_n(ji,jj,1) * (1._wp - tmask(ji,jj,1))
232	DO jk=2,ikt-1
233	ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhd(ji,jj,jk-1) + zrhd(ji,jj,jk)) * e3w_n(ji,jj,jk) &
234	& * (1._wp - tmask(ji,jj,jk))
235	END DO
236	IF (ikt >= 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + zrhd(ji,jj,ikt-1)) &
237	& * ( risfdep(ji,jj) - gdept_1d(ikt-1) )
238	END DO
239	END DO
240	riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5
241
242	CALL wrk_dealloc( jpi,jpj, 2, ztstop)
243	CALL wrk_dealloc( jpi,jpj,jpk, zrhd )
244	CALL wrk_dealloc( jpi,jpj, zrhdtop_isf, ziceload)
245	END IF
246	!
247	END SUBROUTINE dyn_hpg_init
248
249
250	SUBROUTINE hpg_zco( kt )
251	!!---------------------------------------------------------------------
252	!! * ROUTINE hpg_zco *
253	!!
254	!! ** Method : z-coordinate case, levels are horizontal surfaces.
255	!! The now hydrostatic pressure gradient at a given level, jk,
256	!! is computed by taking the vertical integral of the in-situ
257	!! density gradient along the model level from the suface to that
258	!! level: zhpi = grav .....
259	!! zhpj = grav .....
260	!! add it to the general momentum trend (ua,va).
261	!! ua = ua - 1/e1u * zhpi
262	!! va = va - 1/e2v * zhpj
263	!!
264	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
265	!!----------------------------------------------------------------------
266	INTEGER, INTENT(in) :: kt ! ocean time-step index
267	!
268	INTEGER :: ji, jj, jk ! dummy loop indices
269	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
270	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
271	!!----------------------------------------------------------------------
272	!
273	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
274	!
275	IF( kt == nit000 ) THEN
276	IF(lwp) WRITE(numout,*)
277	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
278	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
279	ENDIF
280
281	zcoef0 = - grav * 0.5_wp ! Local constant initialization
282
283	! Surface value
284	DO jj = 2, jpjm1
285	DO ji = fs_2, fs_jpim1 ! vector opt.
286	zcoef1 = zcoef0 * e3w_n(ji,jj,1)
287	! hydrostatic pressure gradient
288	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
289	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
290	! add to the general momentum trend
291	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
292	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
293	END DO
294	END DO
295
296	!
297	! interior value (2=<jk=<jpkm1)
298	DO jk = 2, jpkm1
299	DO jj = 2, jpjm1
300	DO ji = fs_2, fs_jpim1 ! vector opt.
301	zcoef1 = zcoef0 * e3w_n(ji,jj,jk)
302	! hydrostatic pressure gradient
303	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
304	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
305	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
306
307	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
308	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
309	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
310	! add to the general momentum trend
311	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
312	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
313	END DO
314	END DO
315	END DO
316	!
317	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
318	!
319	END SUBROUTINE hpg_zco
320
321
322	SUBROUTINE hpg_zps( kt )
323	!!---------------------------------------------------------------------
324	!! * ROUTINE hpg_zps *
325	!!
326	!! ** Method : z-coordinate plus partial steps case. blahblah...
327	!!
328	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
329	!!----------------------------------------------------------------------
330	INTEGER, INTENT(in) :: kt ! ocean time-step index
331	!!
332	INTEGER :: ji, jj, jk ! dummy loop indices
333	INTEGER :: iku, ikv ! temporary integers
334	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
335	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
336	!!----------------------------------------------------------------------
337	!
338	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
339	!
340	IF( kt == nit000 ) THEN
341	IF(lwp) WRITE(numout,*)
342	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
343	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
344	ENDIF
345
346	! Partial steps: bottom before horizontal gradient of t, s, rd at the last ocean level
347	!jc CALL zps_hde ( kt, jpts, tsn, gtsu, gtsv, rhd, gru , grv )
348
349	! Local constant initialization
350	zcoef0 = - grav * 0.5_wp
351
352	! Surface value (also valid in partial step case)
353	DO jj = 2, jpjm1
354	DO ji = fs_2, fs_jpim1 ! vector opt.
355	zcoef1 = zcoef0 * e3w_n(ji,jj,1)
356	! hydrostatic pressure gradient
357	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
358	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
359	! add to the general momentum trend
360	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
361	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
362	END DO
363	END DO
364
365	! interior value (2=<jk=<jpkm1)
366	DO jk = 2, jpkm1
367	DO jj = 2, jpjm1
368	DO ji = fs_2, fs_jpim1 ! vector opt.
369	zcoef1 = zcoef0 * e3w_n(ji,jj,jk)
370	! hydrostatic pressure gradient
371	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
372	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
373	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
374
375	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
376	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
377	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
378	! add to the general momentum trend
379	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
380	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
381	END DO
382	END DO
383	END DO
384
385	! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
386	DO jj = 2, jpjm1
387	DO ji = 2, jpim1
388	iku = mbku(ji,jj)
389	ikv = mbkv(ji,jj)
390	zcoef2 = zcoef0 * MIN( e3w_n(ji,jj,iku), e3w_n(ji+1,jj ,iku) )
391	zcoef3 = zcoef0 * MIN( e3w_n(ji,jj,ikv), e3w_n(ji ,jj+1,ikv) )
392	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
393	ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value
394	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
395	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) * r1_e1u(ji,jj)
396	ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
397	ENDIF
398	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
399	va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value
400	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
401	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) * r1_e2v(ji,jj)
402	va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
403	ENDIF
404	END DO
405	END DO
406	!
407	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
408	!
409	END SUBROUTINE hpg_zps
410
411
412	SUBROUTINE hpg_sco( kt )
413	!!---------------------------------------------------------------------
414	!! * ROUTINE hpg_sco *
415	!!
416	!! ** Method : s-coordinate case. Jacobian scheme.
417	!! The now hydrostatic pressure gradient at a given level, jk,
418	!! is computed by taking the vertical integral of the in-situ
419	!! density gradient along the model level from the suface to that
420	!! level. s-coordinates (ln_sco): a corrective term is added
421	!! to the horizontal pressure gradient :
422	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
423	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
424	!! add it to the general momentum trend (ua,va).
425	!! ua = ua - 1/e1u * zhpi
426	!! va = va - 1/e2v * zhpj
427	!!
428	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
429	!!----------------------------------------------------------------------
430	INTEGER, INTENT(in) :: kt ! ocean time-step index
431	!!
432	INTEGER :: ji, jj, jk, jii, jjj ! dummy loop indices
433	REAL(wp) :: zcoef0, zuap, zvap, znad, ztmp ! temporary scalars
434	LOGICAL :: ll_tmp1, ll_tmp2, ll_tmp3 ! local logical variables
435	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
436	REAL(wp), POINTER, DIMENSION(:,:) :: zcpx, zcpy !W/D pressure filter
437	!!----------------------------------------------------------------------
438	!
439	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
440	IF(ln_wd) CALL wrk_alloc( jpi,jpj, zcpx, zcpy )
441	!
442	IF( kt == nit000 ) THEN
443	IF(lwp) WRITE(numout,*)
444	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
445	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
446	ENDIF
447	!
448	zcoef0 = - grav * 0.5_wp
449	IF ( ln_linssh ) THEN ; znad = 0._wp ! Fixed volume: density anomaly
450	ELSE ; znad = 1._wp ! Variable volume: density
451	ENDIF
452	!
453	IF(ln_wd) THEN
454	DO jj = 2, jpjm1
455	DO ji = 2, jpim1
456	ll_tmp1 = MIN(sshn(ji,jj), sshn(ji+1,jj)) > MAX(-bathy(ji,jj), -bathy(ji+1,jj))
457	ll_tmp2 = MAX(sshn(ji,jj) + bathy(ji,jj), sshn(ji+1,jj) + bathy(ji+1,jj)) > rn_wdmin1 + rn_wdmin2
458	ll_tmp3 = MAX(sshn(ji,jj), sshn(ji+1,jj)) > MAX(-bathy(ji,jj), -bathy(ji+1,jj)) + &
459	& rn_wdmin1 + rn_wdmin2
460
461	IF(ll_tmp1.AND.ll_tmp2) THEN
462	zcpx(ji,jj) = 1.0_wp
463	wduflt(ji,jj) = 1.0_wp
464	ELSE IF(ll_tmp3) THEN
465	! no worries about sshn(ji+1,jj)-sshn(ji,jj) = 0, it won't happen ! here
466	zcpx(ji,jj) = ABS((sshn(ji+1,jj) + bathy(ji+1,jj) - sshn(ji,jj) - bathy(ji,jj)) / &
467	& (sshn(ji+1,jj) - sshn(ji,jj)))
468	wduflt(ji,jj) = 1.0_wp
469	ELSE
470	zcpx(ji,jj) = 0._wp
471	wduflt(ji,jj) = 0.0_wp
472	END IF
473
474	ll_tmp1 = MIN(sshn(ji,jj), sshn(ji,jj+1)) > MAX(-bathy(ji,jj), -bathy(ji,jj+1))
475	ll_tmp2 = MAX(sshn(ji,jj) + bathy(ji,jj), sshn(ji,jj+1) + bathy(ji,jj+1)) > rn_wdmin1 + rn_wdmin2
476	ll_tmp3 = MAX(sshn(ji,jj), sshn(ji,jj+1)) > MAX(-bathy(ji,jj), -bathy(ji,jj+1)) + &
477	& rn_wdmin1 + rn_wdmin2
478
479	IF(ll_tmp1.AND.ll_tmp2) THEN
480	zcpy(ji,jj) = 1.0_wp
481	wdvflt(ji,jj) = 1.0_wp
482	ELSE IF(ll_tmp3) THEN
483	! no worries about sshn(ji,jj+1)-sshn(ji,jj) = 0, it won't happen ! here
484	zcpy(ji,jj) = ABS((sshn(ji,jj+1) + bathy(ji,jj+1) - sshn(ji,jj) - bathy(ji,jj)) / &
485	& (sshn(ji,jj+1) - sshn(ji,jj)))
486	wdvflt(ji,jj) = 1.0_wp
487	ELSE
488	zcpy(ji,jj) = 0._wp
489	wdvflt(ji,jj) = 0.0_wp
490	END IF
491	END DO
492	END DO
493	CALL lbc_lnk( zcpx, 'U', 1._wp ) ; CALL lbc_lnk( zcpy, 'V', 1._wp )
494	ENDIF
495
496
497	! Surface value
498	DO jj = 2, jpjm1
499	DO ji = fs_2, fs_jpim1 ! vector opt.
500	! hydrostatic pressure gradient along s-surfaces
501	zhpi(ji,jj,1) = zcoef0 * ( e3w_n(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) &
502	& - e3w_n(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e1u(ji,jj)
503	zhpj(ji,jj,1) = zcoef0 * ( e3w_n(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) &
504	& - e3w_n(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e2v(ji,jj)
505	! s-coordinate pressure gradient correction
506	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
507	& * ( gde3w_n(ji+1,jj,1) - gde3w_n(ji,jj,1) ) * r1_e1u(ji,jj)
508	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
509	& * ( gde3w_n(ji,jj+1,1) - gde3w_n(ji,jj,1) ) * r1_e2v(ji,jj)
510
511
512	IF(ln_wd) THEN
513
514	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
515	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
516	zuap = zuap * zcpx(ji,jj)
517	zvap = zvap * zcpy(ji,jj)
518	ENDIF
519
520	! add to the general momentum trend
521	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap
522	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap
523	END DO
524	END DO
525
526	! interior value (2=<jk=<jpkm1)
527	DO jk = 2, jpkm1
528	DO jj = 2, jpjm1
529	DO ji = fs_2, fs_jpim1 ! vector opt.
530	! hydrostatic pressure gradient along s-surfaces
531	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 * r1_e1u(ji,jj) &
532	& * ( e3w_n(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) &
533	& - e3w_n(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) )
534	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 * r1_e2v(ji,jj) &
535	& * ( e3w_n(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) &
536	& - e3w_n(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) )
537	! s-coordinate pressure gradient correction
538	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
539	& * ( gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk) ) * r1_e1u(ji,jj)
540	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
541	& * ( gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk) ) * r1_e2v(ji,jj)
542
543	IF(ln_wd) THEN
544	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
545	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
546	zuap = zuap * zcpx(ji,jj)
547	zvap = zvap * zcpy(ji,jj)
548	ENDIF
549
550	! add to the general momentum trend
551	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap
552	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap
553	END DO
554	END DO
555	END DO
556	!
557	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
558	IF(ln_wd) CALL wrk_dealloc( jpi,jpj, zcpx, zcpy )
559	!
560	END SUBROUTINE hpg_sco
561
562
563	SUBROUTINE hpg_isf( kt )
564	!!---------------------------------------------------------------------
565	!! * ROUTINE hpg_isf *
566	!!
567	!! ** Method : s-coordinate case. Jacobian scheme.
568	!! The now hydrostatic pressure gradient at a given level, jk,
569	!! is computed by taking the vertical integral of the in-situ
570	!! density gradient along the model level from the suface to that
571	!! level. s-coordinates (ln_sco): a corrective term is added
572	!! to the horizontal pressure gradient :
573	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
574	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
575	!! add it to the general momentum trend (ua,va).
576	!! ua = ua - 1/e1u * zhpi
577	!! va = va - 1/e2v * zhpj
578	!! iceload is added and partial cell case are added to the top and bottom
579	!!
580	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
581	!!----------------------------------------------------------------------
582	INTEGER, INTENT(in) :: kt ! ocean time-step index
583	!!
584	INTEGER :: ji, jj, jk, ikt, iktp1i, iktp1j ! dummy loop indices
585	REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars
586	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
587	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop
588	REAL(wp), POINTER, DIMENSION(:,:) :: zrhdtop_oce
589	!!----------------------------------------------------------------------
590	!
591	CALL wrk_alloc( jpi,jpj, 2, ztstop)
592	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj)
593	CALL wrk_alloc( jpi,jpj, zrhdtop_oce )
594	!
595	! Local constant initialization
596	zcoef0 = - grav * 0.5_wp
597
598	! To use density and not density anomaly
599	znad=1._wp
600
601	! iniitialised to 0. zhpi zhpi
602	zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp
603
604	! compute rhd at the ice/oce interface (ocean side)
605	! usefull to reduce residual current in the test case ISOMIP with no melting
606	DO ji=1,jpi
607	DO jj=1,jpj
608	ikt=mikt(ji,jj)
609	ztstop(ji,jj,1)=tsn(ji,jj,ikt,1)
610	ztstop(ji,jj,2)=tsn(ji,jj,ikt,2)
611	END DO
612	END DO
613	CALL eos( ztstop, risfdep, zrhdtop_oce )
614
615	!==================================================================================
616	!===== Compute surface value =====================================================
617	!==================================================================================
618	DO jj = 2, jpjm1
619	DO ji = fs_2, fs_jpim1 ! vector opt.
620	ikt = mikt(ji,jj)
621	iktp1i = mikt(ji+1,jj)
622	iktp1j = mikt(ji,jj+1)
623	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
624	! we assume ISF is in isostatic equilibrium
625	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * e3w_n(ji+1,jj,iktp1i) &
626	& * ( 2._wp * znad + rhd(ji+1,jj,iktp1i) + zrhdtop_oce(ji+1,jj) ) &
627	& - 0.5_wp * e3w_n(ji,jj,ikt) &
628	& * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) &
629	& + ( riceload(ji+1,jj) - riceload(ji,jj)) )
630	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * e3w_n(ji,jj+1,iktp1j) &
631	& * ( 2._wp * znad + rhd(ji,jj+1,iktp1j) + zrhdtop_oce(ji,jj+1) ) &
632	& - 0.5_wp * e3w_n(ji,jj,ikt) &
633	& * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) &
634	& + ( riceload(ji,jj+1) - riceload(ji,jj)) )
635	! s-coordinate pressure gradient correction (=0 if z coordinate)
636	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
637	& * ( gde3w_n(ji+1,jj,1) - gde3w_n(ji,jj,1) ) * r1_e1u(ji,jj)
638	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
639	& * ( gde3w_n(ji,jj+1,1) - gde3w_n(ji,jj,1) ) * r1_e2v(ji,jj)
640	! add to the general momentum trend
641	ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
642	va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
643	END DO
644	END DO
645	!==================================================================================
646	!===== Compute interior value =====================================================
647	!==================================================================================
648	! interior value (2=<jk=<jpkm1)
649	DO jk = 2, jpkm1
650	DO jj = 2, jpjm1
651	DO ji = fs_2, fs_jpim1 ! vector opt.
652	! hydrostatic pressure gradient along s-surfaces
653	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
654	& * ( e3w_n(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2znad ) wmask(ji+1,jj,jk) &
655	& - e3w_n(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2znad ) wmask(ji ,jj,jk) )
656	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
657	& * ( e3w_n(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2znad ) wmask(ji,jj+1,jk) &
658	& - e3w_n(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2znad ) wmask(ji,jj ,jk) )
659	! s-coordinate pressure gradient correction
660	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
661	& * ( gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk) ) / e1u(ji,jj)
662	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
663	& * ( gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk) ) / e2v(ji,jj)
664	! add to the general momentum trend
665	ua(ji,jj,jk) = ua(ji,jj,jk) + (zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
666	va(ji,jj,jk) = va(ji,jj,jk) + (zhpj(ji,jj,jk) + zvap) * vmask(ji,jj,jk)
667	END DO
668	END DO
669	END DO
670	!
671	CALL wrk_dealloc( jpi,jpj,2 , ztstop)
672	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj)
673	CALL wrk_dealloc( jpi,jpj , zrhdtop_oce )
674	!
675	END SUBROUTINE hpg_isf
676
677
678	SUBROUTINE hpg_djc( kt )
679	!!---------------------------------------------------------------------
680	!! * ROUTINE hpg_djc *
681	!!
682	!! ** Method : Density Jacobian with Cubic polynomial scheme
683	!!
684	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
685	!!----------------------------------------------------------------------
686	INTEGER, INTENT(in) :: kt ! ocean time-step index
687	!!
688	INTEGER :: ji, jj, jk ! dummy loop indices
689	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
690	REAL(wp) :: z1_10, cffu, cffx ! " "
691	REAL(wp) :: z1_12, cffv, cffy ! " "
692	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
693	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
694	REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw
695	REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow
696	REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k
697	REAL(wp), POINTER, DIMENSION(:,:) :: zcpx, zcpy !W/D pressure filter
698	!!----------------------------------------------------------------------
699	!
700	CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
701	CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
702	CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
703	IF(ln_wd) CALL wrk_alloc( jpi,jpj, zcpx, zcpy )
704	!
705	!
706	IF(ln_wd) THEN
707	DO jj = 2, jpjm1
708	DO ji = 2, jpim1
709	ll_tmp1 = MIN(sshn(ji,jj), sshn(ji+1,jj)) > MAX(-bathy(ji,jj), -bathy(ji+1,jj)) &
710	& .and. MAX(sshn(ji,jj) + bathy(ji,jj), sshn(ji+1,jj) + bathy(ji+1,jj)) &
711	& > rn_wdmin1 + rn_wdmin2
712	ll_tmp2 = MAX(sshn(ji,jj), sshn(ji+1,jj)) > MAX(-bathy(ji,jj), -bathy(ji+1,jj)) +&
713	& rn_wdmin1 + rn_wdmin2
714
715	IF(ll_tmp1) THEN
716	zcpx(ji,jj) = 1.0_wp
717	ELSE IF(ll_tmp2) THEN
718	! no worries about sshn(ji+1,jj)-sshn(ji,jj) = 0, it won't happen ! here
719	zcpx(ji,jj) = ABS((sshn(ji+1,jj) + bathy(ji+1,jj) - sshn(ji,jj) - bathy(ji,jj)) /&
720	& (sshn(ji+1,jj) - sshn(ji,jj)))
721	ELSE
722	zcpx(ji,jj) = 0._wp
723	END IF
724
725	ll_tmp1 = MIN(sshn(ji,jj), sshn(ji,jj+1)) > MAX(-bathy(ji,jj), -bathy(ji,jj+1)) &
726	& .and. MAX(sshn(ji,jj) + bathy(ji,jj), sshn(ji,jj+1) + bathy(ji,jj+1)) &
727	& > rn_wdmin1 + rn_wdmin2
728	ll_tmp2 = MAX(sshn(ji,jj), sshn(ji,jj+1)) > MAX(-bathy(ji,jj), -bathy(ji,jj+1)) +&
729	& rn_wdmin1 + rn_wdmin2
730
731	IF(ll_tmp1) THEN
732	zcpy(ji,jj) = 1.0_wp
733	ELSE IF(ll_tmp2) THEN
734	! no worries about sshn(ji,jj+1)-sshn(ji,jj) = 0, it won't happen ! here
735	zcpy(ji,jj) = ABS((sshn(ji,jj+1) + bathy(ji,jj+1) - sshn(ji,jj) - bathy(ji,jj)) /&
736	& (sshn(ji,jj+1) - sshn(ji,jj)))
737	ELSE
738	zcpy(ji,jj) = 0._wp
739	END IF
740	END DO
741	END DO
742	CALL lbc_lnk( zcpx, 'U', 1._wp ) ; CALL lbc_lnk( zcpy, 'V', 1._wp )
743	ENDIF
744
745
746	IF( kt == nit000 ) THEN
747	IF(lwp) WRITE(numout,*)
748	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
749	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
750	ENDIF
751
752	! Local constant initialization
753	zcoef0 = - grav * 0.5_wp
754	z1_10 = 1._wp / 10._wp
755	z1_12 = 1._wp / 12._wp
756
757	!----------------------------------------------------------------------------------------
758	! compute and store in provisional arrays elementary vertical and horizontal differences
759	!----------------------------------------------------------------------------------------
760
761	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
762
763	DO jk = 2, jpkm1
764	DO jj = 2, jpjm1
765	DO ji = fs_2, fs_jpim1 ! vector opt.
766	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
767	dzz (ji,jj,jk) = gde3w_n(ji ,jj ,jk) - gde3w_n(ji,jj,jk-1)
768	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
769	dzx (ji,jj,jk) = gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk )
770	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
771	dzy (ji,jj,jk) = gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk )
772	END DO
773	END DO
774	END DO
775
776	!-------------------------------------------------------------------------
777	! compute harmonic averages using eq. 5.18
778	!-------------------------------------------------------------------------
779	zep = 1.e-15
780
781	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
782	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
783
784	DO jk = 2, jpkm1
785	DO jj = 2, jpjm1
786	DO ji = fs_2, fs_jpim1 ! vector opt.
787	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
788
789	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
790	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
791
792	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
793	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
794
795	IF( cffw > zep) THEN
796	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
797	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
798	ELSE
799	drhow(ji,jj,jk) = 0._wp
800	ENDIF
801
802	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
803	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
804
805	IF( cffu > zep ) THEN
806	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
807	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
808	ELSE
809	drhou(ji,jj,jk ) = 0._wp
810	ENDIF
811
812	IF( cffx > zep ) THEN
813	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
814	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
815	ELSE
816	dzu(ji,jj,jk) = 0._wp
817	ENDIF
818
819	IF( cffv > zep ) THEN
820	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
821	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
822	ELSE
823	drhov(ji,jj,jk) = 0._wp
824	ENDIF
825
826	IF( cffy > zep ) THEN
827	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
828	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
829	ELSE
830	dzv(ji,jj,jk) = 0._wp
831	ENDIF
832
833	END DO
834	END DO
835	END DO
836
837	!----------------------------------------------------------------------------------
838	! apply boundary conditions at top and bottom using 5.36-5.37
839	!----------------------------------------------------------------------------------
840	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
841	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
842	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
843
844	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
845	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
846	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
847
848
849	!--------------------------------------------------------------
850	! Upper half of top-most grid box, compute and store
851	!-------------------------------------------------------------
852
853	!!bug gm : e3w-gde3w = 0.5*e3w .... and gde3w(2)-gde3w(1)=e3w(2) .... to be verified
854	! true if gde3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
855
856	DO jj = 2, jpjm1
857	DO ji = fs_2, fs_jpim1 ! vector opt.
858	rho_k(ji,jj,1) = -grav * ( e3w_n(ji,jj,1) - gde3w_n(ji,jj,1) ) &
859	& * ( rhd(ji,jj,1) &
860	& + 0.5_wp * ( rhd (ji,jj,2) - rhd (ji,jj,1) ) &
861	& * ( e3w_n (ji,jj,1) - gde3w_n(ji,jj,1) ) &
862	& / ( gde3w_n(ji,jj,2) - gde3w_n(ji,jj,1) ) )
863	END DO
864	END DO
865
866	!!bug gm : here also, simplification is possible
867	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
868
869	DO jk = 2, jpkm1
870	DO jj = 2, jpjm1
871	DO ji = fs_2, fs_jpim1 ! vector opt.
872
873	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
874	& * ( gde3w_n(ji,jj,jk) - gde3w_n(ji,jj,jk-1) ) &
875	& - grav * z1_10 * ( &
876	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
877	& * ( gde3w_n(ji,jj,jk) - gde3w_n(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
878	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
879	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
880	& )
881
882	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
883	& * ( gde3w_n(ji+1,jj,jk) - gde3w_n(ji,jj,jk) ) &
884	& - grav* z1_10 * ( &
885	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
886	& * ( gde3w_n(ji+1,jj,jk) - gde3w_n(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
887	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
888	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
889	& )
890
891	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
892	& * ( gde3w_n(ji,jj+1,jk) - gde3w_n(ji,jj,jk) ) &
893	& - grav* z1_10 * ( &
894	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
895	& * ( gde3w_n(ji,jj+1,jk) - gde3w_n(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
896	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
897	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
898	& )
899
900	END DO
901	END DO
902	END DO
903	CALL lbc_lnk(rho_k,'W',1.)
904	CALL lbc_lnk(rho_i,'U',1.)
905	CALL lbc_lnk(rho_j,'V',1.)
906
907
908	! ---------------
909	! Surface value
910	! ---------------
911	DO jj = 2, jpjm1
912	DO ji = fs_2, fs_jpim1 ! vector opt.
913	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) * r1_e1u(ji,jj)
914	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) * r1_e2v(ji,jj)
915	IF(ln_wd) THEN
916	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
917	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
918	ENDIF
919	! add to the general momentum trend
920	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
921	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
922	END DO
923	END DO
924
925	! ----------------
926	! interior value (2=<jk=<jpkm1)
927	! ----------------
928	DO jk = 2, jpkm1
929	DO jj = 2, jpjm1
930	DO ji = fs_2, fs_jpim1 ! vector opt.
931	! hydrostatic pressure gradient along s-surfaces
932	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
933	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
934	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) * r1_e1u(ji,jj)
935	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
936	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
937	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) * r1_e2v(ji,jj)
938	IF(ln_wd) THEN
939	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
940	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
941	ENDIF
942	! add to the general momentum trend
943	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
944	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
945	END DO
946	END DO
947	END DO
948	!
949	CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
950	CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
951	CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
952	IF(ln_wd) CALL wrk_dealloc( jpi,jpj, zcpx, zcpy )
953	!
954	END SUBROUTINE hpg_djc
955
956
957	SUBROUTINE hpg_prj( kt )
958	!!---------------------------------------------------------------------
959	!! * ROUTINE hpg_prj *
960	!!
961	!! ** Method : s-coordinate case.
962	!! A Pressure-Jacobian horizontal pressure gradient method
963	!! based on the constrained cubic-spline interpolation for
964	!! all vertical coordinate systems
965	!!
966	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
967	!!----------------------------------------------------------------------
968	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
969	INTEGER, INTENT(in) :: kt ! ocean time-step index
970	!!
971	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
972	REAL(wp) :: zcoef0, znad ! local scalars
973	!
974	!! The local variables for the correction term
975	INTEGER :: jk1, jis, jid, jjs, jjd
976	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
977	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
978	REAL(wp) :: zrhdt1
979	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
980	REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh
981	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
982	REAL(wp), POINTER, DIMENSION(:,:) :: zsshu_n, zsshv_n
983	REAL(wp), POINTER, DIMENSION(:,:) :: zcpx, zcpy !W/D pressure filter
984	!!----------------------------------------------------------------------
985	!
986	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
987	CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh )
988	CALL wrk_alloc( jpi,jpj, zsshu_n, zsshv_n )
989	IF(ln_wd) CALL wrk_alloc( jpi,jpj, zcpx, zcpy )
990	!
991	IF( kt == nit000 ) THEN
992	IF(lwp) WRITE(numout,*)
993	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
994	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
995	ENDIF
996
997	! Local constant initialization
998	zcoef0 = - grav
999	znad = 1._wp
1000	IF( ln_linssh ) znad = 0._wp
1001
1002	IF(ln_wd) THEN
1003	DO jj = 2, jpjm1
1004	DO ji = 2, jpim1
1005	ll_tmp1 = MIN(sshn(ji,jj), sshn(ji+1,jj)) > MAX(-bathy(ji,jj), -bathy(ji+1,jj)) &
1006	& .and. MAX(sshn(ji,jj) + bathy(ji,jj), sshn(ji+1,jj) + bathy(ji+1,jj)) &
1007	& > rn_wdmin1 + rn_wdmin2
1008	ll_tmp2 = MAX(sshn(ji,jj), sshn(ji+1,jj)) > MAX(-bathy(ji,jj), -bathy(ji+1,jj)) +&
1009	& rn_wdmin1 + rn_wdmin2
1010
1011	IF(ll_tmp1) THEN
1012	zcpx(ji,jj) = 1.0_wp
1013	ELSE IF(ll_tmp2) THEN
1014	! no worries about sshn(ji+1,jj)-sshn(ji,jj) = 0, it won't happen ! here
1015	zcpx(ji,jj) = ABS((sshn(ji+1,jj) + bathy(ji+1,jj) - sshn(ji,jj) - bathy(ji,jj)) /&
1016	& (sshn(ji+1,jj) - sshn(ji,jj)))
1017	ELSE
1018	zcpx(ji,jj) = 0._wp
1019	END IF
1020
1021	ll_tmp1 = MIN(sshn(ji,jj), sshn(ji,jj+1)) > MAX(-bathy(ji,jj), -bathy(ji,jj+1)) &
1022	& .and. MAX(sshn(ji,jj) + bathy(ji,jj), sshn(ji,jj+1) + bathy(ji,jj+1)) &
1023	& > rn_wdmin1 + rn_wdmin2
1024	ll_tmp2 = MAX(sshn(ji,jj), sshn(ji,jj+1)) > MAX(-bathy(ji,jj), -bathy(ji,jj+1)) +&
1025	& rn_wdmin1 + rn_wdmin2
1026
1027	IF(ll_tmp1.OR.ll_tmp2) THEN
1028	zcpy(ji,jj) = 1.0_wp
1029	ELSE IF(ll_tmp2) THEN
1030	! no worries about sshn(ji,jj+1)-sshn(ji,jj) = 0, it won't happen ! here
1031	zcpy(ji,jj) = ABS((sshn(ji,jj+1) + bathy(ji,jj+1) - sshn(ji,jj) - bathy(ji,jj)) /&
1032	& (sshn(ji,jj+1) - sshn(ji,jj)))
1033	ELSE
1034	zcpy(ji,jj) = 0._wp
1035	END IF
1036	END DO
1037	END DO
1038	CALL lbc_lnk( zcpx, 'U', 1._wp ) ; CALL lbc_lnk( zcpy, 'V', 1._wp )
1039	ENDIF
1040
1041	! Clean 3-D work arrays
1042	zhpi(:,:,:) = 0._wp
1043	zrhh(:,:,:) = rhd(:,:,:)
1044
1045	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
1046	DO jj = 1, jpj
1047	DO ji = 1, jpi
1048	jk = mbathy(ji,jj)
1049	IF( jk <= 0 ) THEN ; zrhh(ji,jj, : ) = 0._wp
1050	ELSEIF( jk == 1 ) THEN ; zrhh(ji,jj,jk+1:jpk) = rhd(ji,jj,jk)
1051	ELSEIF( jk < jpkm1 ) THEN
1052	DO jkk = jk+1, jpk
1053	zrhh(ji,jj,jkk) = interp1(gde3w_n(ji,jj,jkk ), gde3w_n(ji,jj,jkk-1), &
1054	& gde3w_n(ji,jj,jkk-2), rhd (ji,jj,jkk-1), rhd(ji,jj,jkk-2))
1055	END DO
1056	ENDIF
1057	END DO
1058	END DO
1059
1060	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
1061	DO jj = 1, jpj
1062	DO ji = 1, jpi
1063	zdept(ji,jj,1) = 0.5_wp * e3w_n(ji,jj,1) - sshn(ji,jj) * znad
1064	END DO
1065	END DO
1066
1067	DO jk = 2, jpk
1068	DO jj = 1, jpj
1069	DO ji = 1, jpi
1070	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + e3w_n(ji,jj,jk)
1071	END DO
1072	END DO
1073	END DO
1074
1075	fsp(:,:,:) = zrhh (:,:,:)
1076	xsp(:,:,:) = zdept(:,:,:)
1077
1078	! Construct the vertical density profile with the
1079	! constrained cubic spline interpolation
1080	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
1081	CALL cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
1082
1083	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
1084	DO jj = 2, jpj
1085	DO ji = 2, jpi
1086	zrhdt1 = zrhh(ji,jj,1) - interp3( zdept(ji,jj,1), asp(ji,jj,1), bsp(ji,jj,1), &
1087	& csp(ji,jj,1), dsp(ji,jj,1) ) * 0.25_wp * e3w_n(ji,jj,1)
1088
1089	! assuming linear profile across the top half surface layer
1090	zhpi(ji,jj,1) = 0.5_wp * e3w_n(ji,jj,1) * zrhdt1
1091	END DO
1092	END DO
1093
1094	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
1095	DO jk = 2, jpkm1
1096	DO jj = 2, jpj
1097	DO ji = 2, jpi
1098	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
1099	& integ_spline( zdept(ji,jj,jk-1), zdept(ji,jj,jk), &
1100	& asp (ji,jj,jk-1), bsp (ji,jj,jk-1), &
1101	& csp (ji,jj,jk-1), dsp (ji,jj,jk-1) )
1102	END DO
1103	END DO
1104	END DO
1105
1106	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
1107
1108	! Prepare zsshu_n and zsshv_n
1109	DO jj = 2, jpjm1
1110	DO ji = 2, jpim1
1111	!!gm BUG ? if it is ssh at u- & v-point then it should be:
1112	! zsshu_n(ji,jj) = (e1e2t(ji,jj) * sshn(ji,jj) + e1e2t(ji+1,jj) * sshn(ji+1,jj)) * &
1113	! & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
1114	! zsshv_n(ji,jj) = (e1e2t(ji,jj) * sshn(ji,jj) + e1e2t(ji,jj+1) * sshn(ji,jj+1)) * &
1115	! & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
1116	!!gm not this:
1117	zsshu_n(ji,jj) = (e1e2u(ji,jj) * sshn(ji,jj) + e1e2u(ji+1, jj) * sshn(ji+1,jj)) * &
1118	& r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
1119	zsshv_n(ji,jj) = (e1e2v(ji,jj) * sshn(ji,jj) + e1e2v(ji+1, jj) * sshn(ji,jj+1)) * &
1120	& r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
1121	END DO
1122	END DO
1123
1124	CALL lbc_lnk (zsshu_n, 'U', 1.)
1125	CALL lbc_lnk (zsshv_n, 'V', 1.)
1126
1127	DO jj = 2, jpjm1
1128	DO ji = 2, jpim1
1129	zu(ji,jj,1) = - ( e3u_n(ji,jj,1) - zsshu_n(ji,jj) * znad)
1130	zv(ji,jj,1) = - ( e3v_n(ji,jj,1) - zsshv_n(ji,jj) * znad)
1131	END DO
1132	END DO
1133
1134	DO jk = 2, jpkm1
1135	DO jj = 2, jpjm1
1136	DO ji = 2, jpim1
1137	zu(ji,jj,jk) = zu(ji,jj,jk-1) - e3u_n(ji,jj,jk)
1138	zv(ji,jj,jk) = zv(ji,jj,jk-1) - e3v_n(ji,jj,jk)
1139	END DO
1140	END DO
1141	END DO
1142
1143	DO jk = 1, jpkm1
1144	DO jj = 2, jpjm1
1145	DO ji = 2, jpim1
1146	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * e3u_n(ji,jj,jk)
1147	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * e3v_n(ji,jj,jk)
1148	END DO
1149	END DO
1150	END DO
1151
1152	DO jk = 1, jpkm1
1153	DO jj = 2, jpjm1
1154	DO ji = 2, jpim1
1155	zu(ji,jj,jk) = MIN( zu(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
1156	zu(ji,jj,jk) = MAX( zu(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
1157	zv(ji,jj,jk) = MIN( zv(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
1158	zv(ji,jj,jk) = MAX( zv(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
1159	END DO
1160	END DO
1161	END DO
1162
1163
1164	DO jk = 1, jpkm1
1165	DO jj = 2, jpjm1
1166	DO ji = 2, jpim1
1167	zpwes = 0._wp; zpwed = 0._wp
1168	zpnss = 0._wp; zpnsd = 0._wp
1169	zuijk = zu(ji,jj,jk)
1170	zvijk = zv(ji,jj,jk)
1171
1172	!!!!! for u equation
1173	IF( jk <= mbku(ji,jj) ) THEN
1174	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
1175	jis = ji + 1; jid = ji
1176	ELSE
1177	jis = ji; jid = ji +1
1178	ENDIF
1179
1180	! integrate the pressure on the shallow side
1181	jk1 = jk
1182	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
1183	IF( jk1 == mbku(ji,jj) ) THEN
1184	zuijk = -zdept(jis,jj,jk1)
1185	EXIT
1186	ENDIF
1187	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
1188	zpwes = zpwes + &
1189	integ_spline(zdept(jis,jj,jk1), zdeps, &
1190	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
1191	csp(jis,jj,jk1), dsp(jis,jj,jk1))
1192	jk1 = jk1 + 1
1193	END DO
1194
1195	! integrate the pressure on the deep side
1196	jk1 = jk
1197	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
1198	IF( jk1 == 1 ) THEN
1199	zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad)
1200	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
1201	bsp(jid,jj,1), csp(jid,jj,1), &
1202	dsp(jid,jj,1)) * zdeps
1203	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
1204	EXIT
1205	ENDIF
1206	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
1207	zpwed = zpwed + &
1208	integ_spline(zdeps, zdept(jid,jj,jk1), &
1209	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
1210	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
1211	jk1 = jk1 - 1
1212	END DO
1213
1214	! update the momentum trends in u direction
1215
1216	zdpdx1 = zcoef0 * r1_e1u(ji,jj) * ( zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk) )
1217	IF( .NOT.ln_linssh ) THEN
1218	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * &
1219	& ( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) )
1220	ELSE
1221	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
1222	ENDIF
1223	IF(ln_wd) THEN
1224	zdpdx1 = zdpdx1 * zcpx(ji,jj)
1225	zdpdx2 = zdpdx2 * zcpx(ji,jj)
1226	ENDIF
1227	ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * umask(ji,jj,jk)
1228	ENDIF
1229
1230	!!!!! for v equation
1231	IF( jk <= mbkv(ji,jj) ) THEN
1232	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
1233	jjs = jj + 1; jjd = jj
1234	ELSE
1235	jjs = jj ; jjd = jj + 1
1236	ENDIF
1237
1238	! integrate the pressure on the shallow side
1239	jk1 = jk
1240	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
1241	IF( jk1 == mbkv(ji,jj) ) THEN
1242	zvijk = -zdept(ji,jjs,jk1)
1243	EXIT
1244	ENDIF
1245	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
1246	zpnss = zpnss + &
1247	integ_spline(zdept(ji,jjs,jk1), zdeps, &
1248	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
1249	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
1250	jk1 = jk1 + 1
1251	END DO
1252
1253	! integrate the pressure on the deep side
1254	jk1 = jk
1255	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
1256	IF( jk1 == 1 ) THEN
1257	zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad)
1258	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
1259	bsp(ji,jjd,1), csp(ji,jjd,1), &
1260	dsp(ji,jjd,1) ) * zdeps
1261	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
1262	EXIT
1263	ENDIF
1264	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
1265	zpnsd = zpnsd + &
1266	integ_spline(zdeps, zdept(ji,jjd,jk1), &
1267	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
1268	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
1269	jk1 = jk1 - 1
1270	END DO
1271
1272
1273	! update the momentum trends in v direction
1274
1275	zdpdy1 = zcoef0 * r1_e2v(ji,jj) * ( zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk) )
1276	IF( .NOT.ln_linssh ) THEN
1277	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * &
1278	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) )
1279	ELSE
1280	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
1281	ENDIF
1282	IF(ln_wd) THEN
1283	zdpdy1 = zdpdy1 * zcpy(ji,jj)
1284	zdpdy2 = zdpdy2 * zcpy(ji,jj)
1285	ENDIF
1286
1287	va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2) * vmask(ji,jj,jk)
1288	ENDIF
1289	!
1290	END DO
1291	END DO
1292	END DO
1293	!
1294	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
1295	CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh )
1296	CALL wrk_dealloc( jpi,jpj, zsshu_n, zsshv_n )
1297	IF(ln_wd) CALL wrk_dealloc( jpi,jpj, zcpx, zcpy )
1298	!
1299	END SUBROUTINE hpg_prj
1300
1301
1302	SUBROUTINE cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
1303	!!----------------------------------------------------------------------
1304	!! * ROUTINE cspline *
1305	!!
1306	!! ** Purpose : constrained cubic spline interpolation
1307	!!
1308	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
1309	!!
1310	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
1311	!!----------------------------------------------------------------------
1312	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: fsp, xsp ! value and coordinate
1313	REAL(wp), DIMENSION(:,:,:), INTENT( out) :: asp, bsp, csp, dsp ! coefficients of the interpoated function
1314	INTEGER , INTENT(in ) :: polynomial_type ! 1: cubic spline ; 2: Linear
1315	!
1316	INTEGER :: ji, jj, jk ! dummy loop indices
1317	INTEGER :: jpi, jpj, jpkm1
1318	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
1319	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
1320	REAL(wp) :: zdf(size(fsp,3))
1321	!!----------------------------------------------------------------------
1322	!
1323	!!gm WHAT !!!!! THIS IS VERY DANGEROUS !!!!!
1324	jpi = size(fsp,1)
1325	jpj = size(fsp,2)
1326	jpkm1 = size(fsp,3) - 1
1327	!
1328	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
1329	DO ji = 1, jpi
1330	DO jj = 1, jpj
1331	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
1332	! DO jk = 2, jpkm1-1
1333	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
1334	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1335	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
1336	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
1337	!
1338	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
1339	!
1340	! IF(zdf1 * zdf2 <= 0._wp) THEN
1341	! zdf(jk) = 0._wp
1342	! ELSE
1343	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
1344	! ENDIF
1345	! END DO
1346
1347	!!Simply geometric average
1348	DO jk = 2, jpkm1-1
1349	zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1))
1350	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk))
1351
1352	IF(zdf1 * zdf2 <= 0._wp) THEN
1353	zdf(jk) = 0._wp
1354	ELSE
1355	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
1356	ENDIF
1357	END DO
1358
1359	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
1360	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
1361	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
1362	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - 0.5_wp * zdf(jpkm1 - 1)
1363
1364	DO jk = 1, jpkm1 - 1
1365	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1366	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
1367	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
1368	zddf1 = -2._wp * ztmp1 + ztmp2
1369	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
1370	zddf2 = 2._wp * ztmp1 - ztmp2
1371
1372	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
1373	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
1374	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
1375	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
1376	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
1377	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
1378	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
1379	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
1380	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
1381	END DO
1382	END DO
1383	END DO
1384
1385	ELSEIF ( polynomial_type == 2 ) THEN ! Linear
1386	DO ji = 1, jpi
1387	DO jj = 1, jpj
1388	DO jk = 1, jpkm1-1
1389	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1390	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
1391
1392	dsp(ji,jj,jk) = 0._wp
1393	csp(ji,jj,jk) = 0._wp
1394	bsp(ji,jj,jk) = ztmp1 / zdxtmp
1395	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
1396	END DO
1397	END DO
1398	END DO
1399
1400	ELSE
1401	CALL ctl_stop( 'invalid polynomial type in cspline' )
1402	ENDIF
1403
1404	END SUBROUTINE cspline
1405
1406
1407	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
1408	!!----------------------------------------------------------------------
1409	!! * ROUTINE interp1 *
1410	!!
1411	!! ** Purpose : 1-d linear interpolation
1412	!!
1413	!! ** Method : interpolation is straight forward
1414	!! extrapolation is also permitted (no value limit)
1415	!!----------------------------------------------------------------------
1416	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
1417	REAL(wp) :: f ! result of the interpolation (extrapolation)
1418	REAL(wp) :: zdeltx
1419	!!----------------------------------------------------------------------
1420	!
1421	zdeltx = xr - xl
1422	IF( abs(zdeltx) <= 10._wp * EPSILON(x) ) THEN
1423	f = 0.5_wp * (fl + fr)
1424	ELSE
1425	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
1426	ENDIF
1427	!
1428	END FUNCTION interp1
1429
1430
1431	FUNCTION interp2( x, a, b, c, d ) RESULT(f)
1432	!!----------------------------------------------------------------------
1433	!! * ROUTINE interp1 *
1434	!!
1435	!! ** Purpose : 1-d constrained cubic spline interpolation
1436	!!
1437	!! ** Method : cubic spline interpolation
1438	!!
1439	!!----------------------------------------------------------------------
1440	REAL(wp), INTENT(in) :: x, a, b, c, d
1441	REAL(wp) :: f ! value from the interpolation
1442	!!----------------------------------------------------------------------
1443	!
1444	f = a + x* ( b + x * ( c + d * x ) )
1445	!
1446	END FUNCTION interp2
1447
1448
1449	FUNCTION interp3( x, a, b, c, d ) RESULT(f)
1450	!!----------------------------------------------------------------------
1451	!! * ROUTINE interp1 *
1452	!!
1453	!! ** Purpose : Calculate the first order of deriavtive of
1454	!! a cubic spline function y=a+bx+cx^2+d*x^3
1455	!!
1456	!! ** Method : f=dy/dx=b+2cx+3dx^2
1457	!!
1458	!!----------------------------------------------------------------------
1459	REAL(wp), INTENT(in) :: x, a, b, c, d
1460	REAL(wp) :: f ! value from the interpolation
1461	!!----------------------------------------------------------------------
1462	!
1463	f = b + x * ( 2._wp * c + 3._wp * d * x)
1464	!
1465	END FUNCTION interp3
1466
1467
1468	FUNCTION integ_spline( xl, xr, a, b, c, d ) RESULT(f)
1469	!!----------------------------------------------------------------------
1470	!! * ROUTINE interp1 *
1471	!!
1472	!! ** Purpose : 1-d constrained cubic spline integration
1473	!!
1474	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
1475	!!
1476	!!----------------------------------------------------------------------
1477	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
1478	REAL(wp) :: za1, za2, za3
1479	REAL(wp) :: f ! integration result
1480	!!----------------------------------------------------------------------
1481	!
1482	za1 = 0.5_wp * b
1483	za2 = c / 3.0_wp
1484	za3 = 0.25_wp * d
1485	!
1486	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
1487	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
1488	!
1489	END FUNCTION integ_spline
1490
1491	!!======================================================================
1492	END MODULE dynhpg
1493

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