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dynhpg.F90 in branches/2016/dev_r6519_HPC_4/NEMOGCM/NEMO/OPA_SRC/DYN – NEMO

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source: branches/2016/dev_r6519_HPC_4/NEMOGCM/NEMO/OPA_SRC/DYN/dynhpg.F90 @ 7037

Last change on this file since 7037 was 7037, checked in by mocavero, 8 years ago
ORCA2_LIM_PISCES hybrid version update
Property svn:keywords set to `Id`
File size: 71.2 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 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	!$OMP PARALLEL WORKSHARE
94	ztrdu(:,:,:) = ua(:,:,:)
95	ztrdv(:,:,:) = va(:,:,:)
96	!$OMP END PARALLEL WORKSHARE
97	ENDIF
98	!
99	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
100	CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate
101	CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation)
102	CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation)
103	CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial)
104	CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme)
105	CASE ( 5 ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf
106	END SELECT
107	!
108	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
109	!$OMP PARALLEL WORKSHARE
110	ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:)
111	ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:)
112	!$OMP END PARALLEL WORKSHARE
113	CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt )
114	CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv )
115	ENDIF
116	!
117	IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, &
118	& tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
119	!
120	IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg')
121	!
122	END SUBROUTINE dyn_hpg
123
124
125	SUBROUTINE dyn_hpg_init
126	!!----------------------------------------------------------------------
127	!! * ROUTINE dyn_hpg_init *
128	!!
129	!! ** Purpose : initializations for the hydrostatic pressure gradient
130	!! computation and consistency control
131	!!
132	!! ** Action : Read the namelist namdyn_hpg and check the consistency
133	!! with the type of vertical coordinate used (zco, zps, sco)
134	!!----------------------------------------------------------------------
135	INTEGER :: ioptio = 0 ! temporary integer
136	INTEGER :: ios ! Local integer output status for namelist read
137	!!
138	INTEGER :: ji, jj, jk, ikt ! dummy loop indices ISF
139	REAL(wp) :: znad
140	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop, zrhd ! hypothesys on isf density
141	REAL(wp), POINTER, DIMENSION(:,:) :: zrhdtop_isf ! density at bottom of ISF
142	REAL(wp), POINTER, DIMENSION(:,:) :: ziceload ! density at bottom of ISF
143	!!
144	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
145	& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf
146	!!----------------------------------------------------------------------
147	!
148	REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient
149	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
150	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp )
151	!
152	REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient
153	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
154	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp )
155	IF(lwm) WRITE ( numond, namdyn_hpg )
156	!
157	IF(lwp) THEN ! Control print
158	WRITE(numout,*)
159	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
160	WRITE(numout,*) '~~~~~~~~~~~~'
161	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
162	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
163	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
164	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
165	WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf
166	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
167	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
168	ENDIF
169	!
170	IF( ln_hpg_djc ) &
171	& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method &
172	& currently disabled (bugs under investigation). Please select &
173	& either ln_hpg_sco or ln_hpg_prj instead')
174	!
175	IF( .NOT.ln_linssh .AND. .NOT.(ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) &
176	& CALL ctl_stop('dyn_hpg_init : non-linear free surface requires either ', &
177	& ' the standard jacobian formulation hpg_sco or ' , &
178	& ' the pressure jacobian formulation hpg_prj' )
179
180	IF( ln_hpg_isf .AND. .NOT. ln_isfcav ) &
181	& CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' )
182	IF( .NOT. ln_hpg_isf .AND. ln_isfcav ) &
183	& CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' )
184	!
185	! ! Set nhpg from ln_hpg_... flags
186	IF( ln_hpg_zco ) nhpg = 0
187	IF( ln_hpg_zps ) nhpg = 1
188	IF( ln_hpg_sco ) nhpg = 2
189	IF( ln_hpg_djc ) nhpg = 3
190	IF( ln_hpg_prj ) nhpg = 4
191	IF( ln_hpg_isf ) nhpg = 5
192	!
193	! ! Consistency check
194	ioptio = 0
195	IF( ln_hpg_zco ) ioptio = ioptio + 1
196	IF( ln_hpg_zps ) ioptio = ioptio + 1
197	IF( ln_hpg_sco ) ioptio = ioptio + 1
198	IF( ln_hpg_djc ) ioptio = ioptio + 1
199	IF( ln_hpg_prj ) ioptio = ioptio + 1
200	IF( ln_hpg_isf ) ioptio = ioptio + 1
201	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
202	!
203	! initialisation of ice shelf load
204	IF ( .NOT. ln_isfcav ) riceload(:,:)=0.0
205	IF ( ln_isfcav ) THEN
206	CALL wrk_alloc( jpi,jpj, 2, ztstop)
207	CALL wrk_alloc( jpi,jpj,jpk, zrhd )
208	CALL wrk_alloc( jpi,jpj, zrhdtop_isf, ziceload)
209	!
210	IF(lwp) WRITE(numout,*)
211	IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf'
212	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~'
213
214	! To use density and not density anomaly
215	znad=1._wp
216
217	! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude)
218	ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp
219
220	! compute density of the water displaced by the ice shelf
221	DO jk = 1, jpk
222	CALL eos(ztstop(:,:,:),gdept_n(:,:,jk),zrhd(:,:,jk))
223	END DO
224
225	! compute rhd at the ice/oce interface (ice shelf side)
226	CALL eos(ztstop,risfdep,zrhdtop_isf)
227
228	! Surface value + ice shelf gradient
229	! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v)
230	! divided by 2 later
231	ziceload = 0._wp
232	!$OMP PARALLEL
233	!$OMP DO schedule(static) private(jj,ji,ikt,jk)
234	DO jj = 1, jpj
235	DO ji = 1, jpi
236	ikt=mikt(ji,jj)
237	ziceload(ji,jj) = ziceload(ji,jj) + (znad + zrhd(ji,jj,1) ) * e3w_n(ji,jj,1) * (1._wp - tmask(ji,jj,1))
238	DO jk=2,ikt-1
239	ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhd(ji,jj,jk-1) + zrhd(ji,jj,jk)) * e3w_n(ji,jj,jk) &
240	& * (1._wp - tmask(ji,jj,jk))
241	END DO
242	IF (ikt >= 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + zrhd(ji,jj,ikt-1)) &
243	& * ( risfdep(ji,jj) - gdept_1d(ikt-1) )
244	END DO
245	END DO
246	!$OMP WORKSHARE
247	riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5
248	!$OMP END WORKSHARE NOWAIT
249	!$OMP END PARALLEL
250
251	CALL wrk_dealloc( jpi,jpj, 2, ztstop)
252	CALL wrk_dealloc( jpi,jpj,jpk, zrhd )
253	CALL wrk_dealloc( jpi,jpj, zrhdtop_isf, ziceload)
254	END IF
255	!
256	END SUBROUTINE dyn_hpg_init
257
258
259	SUBROUTINE hpg_zco( kt )
260	!!---------------------------------------------------------------------
261	!! * ROUTINE hpg_zco *
262	!!
263	!! ** Method : z-coordinate case, levels are horizontal surfaces.
264	!! The now hydrostatic pressure gradient at a given level, jk,
265	!! is computed by taking the vertical integral of the in-situ
266	!! density gradient along the model level from the suface to that
267	!! level: zhpi = grav .....
268	!! zhpj = grav .....
269	!! add it to the general momentum trend (ua,va).
270	!! ua = ua - 1/e1u * zhpi
271	!! va = va - 1/e2v * zhpj
272	!!
273	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
274	!!----------------------------------------------------------------------
275	INTEGER, INTENT(in) :: kt ! ocean time-step index
276	!
277	INTEGER :: ji, jj, jk ! dummy loop indices
278	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
279	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
280	!!----------------------------------------------------------------------
281	!
282	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
283	!
284	IF( kt == nit000 ) THEN
285	IF(lwp) WRITE(numout,*)
286	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
287	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
288	ENDIF
289
290	zcoef0 = - grav * 0.5_wp ! Local constant initialization
291
292	! Surface value
293	!$OMP PARALLEL
294	!$OMP DO private(ji,jj, zcoef1)
295	DO jj = 2, jpjm1
296	DO ji = fs_2, fs_jpim1 ! vector opt.
297	zcoef1 = zcoef0 * e3w_n(ji,jj,1)
298	! hydrostatic pressure gradient
299	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
300	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
301	! add to the general momentum trend
302	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
303	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
304	END DO
305	END DO
306
307	!
308	! interior value (2=<jk=<jpkm1)
309	DO jk = 2, jpkm1
310	!$OMP DO private(ji,jj, zcoef1)
311	DO jj = 2, jpjm1
312	DO ji = fs_2, fs_jpim1 ! vector opt.
313	zcoef1 = zcoef0 * e3w_n(ji,jj,jk)
314	! hydrostatic pressure gradient
315	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
316	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
317	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
318
319	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
320	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
321	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
322	! add to the general momentum trend
323	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
324	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
325	END DO
326	END DO
327	!$OMP END DO NOWAIT
328	END DO
329	!$OMP END PARALLEL
330	!
331	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
332	!
333	END SUBROUTINE hpg_zco
334
335
336	SUBROUTINE hpg_zps( kt )
337	!!---------------------------------------------------------------------
338	!! * ROUTINE hpg_zps *
339	!!
340	!! ** Method : z-coordinate plus partial steps case. blahblah...
341	!!
342	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
343	!!----------------------------------------------------------------------
344	INTEGER, INTENT(in) :: kt ! ocean time-step index
345	!!
346	INTEGER :: ji, jj, jk ! dummy loop indices
347	INTEGER :: iku, ikv ! temporary integers
348	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
349	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
350	!!----------------------------------------------------------------------
351	!
352	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
353	!
354	IF( kt == nit000 ) THEN
355	IF(lwp) WRITE(numout,*)
356	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
357	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
358	ENDIF
359
360	! Partial steps: bottom before horizontal gradient of t, s, rd at the last ocean level
361	!jc CALL zps_hde ( kt, jpts, tsn, gtsu, gtsv, rhd, gru , grv )
362
363	! Local constant initialization
364	zcoef0 = - grav * 0.5_wp
365
366	! Surface value (also valid in partial step case)
367	!$OMP PARALLEL
368	!$OMP DO private(ji,jj, zcoef1)
369	DO jj = 2, jpjm1
370	DO ji = fs_2, fs_jpim1 ! vector opt.
371	zcoef1 = zcoef0 * e3w_n(ji,jj,1)
372	! hydrostatic pressure gradient
373	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
374	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
375	! add to the general momentum trend
376	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
377	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
378	END DO
379	END DO
380
381	! interior value (2=<jk=<jpkm1)
382	DO jk = 2, jpkm1
383	!$OMP DO private(ji,jj, zcoef1)
384	DO jj = 2, jpjm1
385	DO ji = fs_2, fs_jpim1 ! vector opt.
386	zcoef1 = zcoef0 * e3w_n(ji,jj,jk)
387	! hydrostatic pressure gradient
388	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
389	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
390	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
391
392	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
393	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
394	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
395	! add to the general momentum trend
396	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
397	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
398	END DO
399	END DO
400	END DO
401
402	! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
403	!$OMP DO private(ji,jj,iku,ikv,zcoef2,zcoef3)
404	DO jj = 2, jpjm1
405	DO ji = 2, jpim1
406	iku = mbku(ji,jj)
407	ikv = mbkv(ji,jj)
408	zcoef2 = zcoef0 * MIN( e3w_n(ji,jj,iku), e3w_n(ji+1,jj ,iku) )
409	zcoef3 = zcoef0 * MIN( e3w_n(ji,jj,ikv), e3w_n(ji ,jj+1,ikv) )
410	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
411	ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value
412	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
413	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) * r1_e1u(ji,jj)
414	ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
415	ENDIF
416	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
417	va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value
418	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
419	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) * r1_e2v(ji,jj)
420	va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
421	ENDIF
422	END DO
423	END DO
424	!$OMP END DO NOWAIT
425	!$OMP END PARALLEL
426	!
427	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
428	!
429	END SUBROUTINE hpg_zps
430
431
432	SUBROUTINE hpg_sco( kt )
433	!!---------------------------------------------------------------------
434	!! * ROUTINE hpg_sco *
435	!!
436	!! ** Method : s-coordinate case. Jacobian scheme.
437	!! The now hydrostatic pressure gradient at a given level, jk,
438	!! is computed by taking the vertical integral of the in-situ
439	!! density gradient along the model level from the suface to that
440	!! level. s-coordinates (ln_sco): a corrective term is added
441	!! to the horizontal pressure gradient :
442	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
443	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
444	!! add it to the general momentum trend (ua,va).
445	!! ua = ua - 1/e1u * zhpi
446	!! va = va - 1/e2v * zhpj
447	!!
448	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
449	!!----------------------------------------------------------------------
450	INTEGER, INTENT(in) :: kt ! ocean time-step index
451	!!
452	INTEGER :: ji, jj, jk, jii, jjj ! dummy loop indices
453	REAL(wp) :: zcoef0, zuap, zvap, znad, ztmp ! temporary scalars
454	LOGICAL :: ll_tmp1, ll_tmp2, ll_tmp3 ! local logical variables
455	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
456	REAL(wp), POINTER, DIMENSION(:,:) :: zcpx, zcpy !W/D pressure filter
457	!!----------------------------------------------------------------------
458	!
459	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
460	IF(ln_wd) CALL wrk_alloc( jpi,jpj, zcpx, zcpy )
461	!
462	IF( kt == nit000 ) THEN
463	IF(lwp) WRITE(numout,*)
464	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
465	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
466	ENDIF
467	!
468	zcoef0 = - grav * 0.5_wp
469	IF ( ln_linssh ) THEN ; znad = 0._wp ! Fixed volume: density anomaly
470	ELSE ; znad = 1._wp ! Variable volume: density
471	ENDIF
472	!
473	IF(ln_wd) THEN
474	DO jj = 2, jpjm1
475	DO ji = 2, jpim1
476	ll_tmp1 = MIN(sshn(ji,jj), sshn(ji+1,jj)) > MAX(-bathy(ji,jj), -bathy(ji+1,jj))
477	ll_tmp2 = MAX(sshn(ji,jj) + bathy(ji,jj), sshn(ji+1,jj) + bathy(ji+1,jj)) > rn_wdmin1 + rn_wdmin2
478	ll_tmp3 = MAX(sshn(ji,jj), sshn(ji+1,jj)) > MAX(-bathy(ji,jj), -bathy(ji+1,jj)) + &
479	& rn_wdmin1 + rn_wdmin2
480
481	IF(ll_tmp1.AND.ll_tmp2) THEN
482	zcpx(ji,jj) = 1.0_wp
483	wduflt(ji,jj) = 1.0_wp
484	ELSE IF(ll_tmp3) THEN
485	! no worries about sshn(ji+1,jj)-sshn(ji,jj) = 0, it won't happen ! here
486	zcpx(ji,jj) = ABS((sshn(ji+1,jj) + bathy(ji+1,jj) - sshn(ji,jj) - bathy(ji,jj)) / &
487	& (sshn(ji+1,jj) - sshn(ji,jj)))
488	wduflt(ji,jj) = 1.0_wp
489	ELSE
490	zcpx(ji,jj) = 0._wp
491	wduflt(ji,jj) = 0.0_wp
492	END IF
493
494	ll_tmp1 = MIN(sshn(ji,jj), sshn(ji,jj+1)) > MAX(-bathy(ji,jj), -bathy(ji,jj+1))
495	ll_tmp2 = MAX(sshn(ji,jj) + bathy(ji,jj), sshn(ji,jj+1) + bathy(ji,jj+1)) > rn_wdmin1 + rn_wdmin2
496	ll_tmp3 = MAX(sshn(ji,jj), sshn(ji,jj+1)) > MAX(-bathy(ji,jj), -bathy(ji,jj+1)) + &
497	& rn_wdmin1 + rn_wdmin2
498
499	IF(ll_tmp1.AND.ll_tmp2) THEN
500	zcpy(ji,jj) = 1.0_wp
501	wdvflt(ji,jj) = 1.0_wp
502	ELSE IF(ll_tmp3) THEN
503	! no worries about sshn(ji,jj+1)-sshn(ji,jj) = 0, it won't happen ! here
504	zcpy(ji,jj) = ABS((sshn(ji,jj+1) + bathy(ji,jj+1) - sshn(ji,jj) - bathy(ji,jj)) / &
505	& (sshn(ji,jj+1) - sshn(ji,jj)))
506	wdvflt(ji,jj) = 1.0_wp
507	ELSE
508	zcpy(ji,jj) = 0._wp
509	wdvflt(ji,jj) = 0.0_wp
510	END IF
511	END DO
512	END DO
513	CALL lbc_lnk( zcpx, 'U', 1._wp ) ; CALL lbc_lnk( zcpy, 'V', 1._wp )
514	ENDIF
515
516
517	! Surface value
518	DO jj = 2, jpjm1
519	DO ji = fs_2, fs_jpim1 ! vector opt.
520	! hydrostatic pressure gradient along s-surfaces
521	zhpi(ji,jj,1) = zcoef0 * ( e3w_n(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) &
522	& - e3w_n(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e1u(ji,jj)
523	zhpj(ji,jj,1) = zcoef0 * ( e3w_n(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) &
524	& - e3w_n(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e2v(ji,jj)
525	! s-coordinate pressure gradient correction
526	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
527	& * ( gde3w_n(ji+1,jj,1) - gde3w_n(ji,jj,1) ) * r1_e1u(ji,jj)
528	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
529	& * ( gde3w_n(ji,jj+1,1) - gde3w_n(ji,jj,1) ) * r1_e2v(ji,jj)
530
531
532	IF(ln_wd) THEN
533
534	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
535	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
536	zuap = zuap * zcpx(ji,jj)
537	zvap = zvap * zcpy(ji,jj)
538	ENDIF
539
540	! add to the general momentum trend
541	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap
542	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap
543	END DO
544	END DO
545
546	! interior value (2=<jk=<jpkm1)
547	DO jk = 2, jpkm1
548	DO jj = 2, jpjm1
549	DO ji = fs_2, fs_jpim1 ! vector opt.
550	! hydrostatic pressure gradient along s-surfaces
551	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 * r1_e1u(ji,jj) &
552	& * ( e3w_n(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) &
553	& - e3w_n(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) )
554	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 * r1_e2v(ji,jj) &
555	& * ( e3w_n(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) &
556	& - e3w_n(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) )
557	! s-coordinate pressure gradient correction
558	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
559	& * ( gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk) ) * r1_e1u(ji,jj)
560	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
561	& * ( gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk) ) * r1_e2v(ji,jj)
562
563	IF(ln_wd) THEN
564	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
565	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
566	zuap = zuap * zcpx(ji,jj)
567	zvap = zvap * zcpy(ji,jj)
568	ENDIF
569
570	! add to the general momentum trend
571	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap
572	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap
573	END DO
574	END DO
575	END DO
576	!
577	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
578	IF(ln_wd) CALL wrk_dealloc( jpi,jpj, zcpx, zcpy )
579	!
580	END SUBROUTINE hpg_sco
581
582
583	SUBROUTINE hpg_isf( kt )
584	!!---------------------------------------------------------------------
585	!! * ROUTINE hpg_isf *
586	!!
587	!! ** Method : s-coordinate case. Jacobian scheme.
588	!! The now hydrostatic pressure gradient at a given level, jk,
589	!! is computed by taking the vertical integral of the in-situ
590	!! density gradient along the model level from the suface to that
591	!! level. s-coordinates (ln_sco): a corrective term is added
592	!! to the horizontal pressure gradient :
593	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
594	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
595	!! add it to the general momentum trend (ua,va).
596	!! ua = ua - 1/e1u * zhpi
597	!! va = va - 1/e2v * zhpj
598	!! iceload is added and partial cell case are added to the top and bottom
599	!!
600	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
601	!!----------------------------------------------------------------------
602	INTEGER, INTENT(in) :: kt ! ocean time-step index
603	!!
604	INTEGER :: ji, jj, jk, ikt, iktp1i, iktp1j ! dummy loop indices
605	REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars
606	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
607	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop
608	REAL(wp), POINTER, DIMENSION(:,:) :: zrhdtop_oce
609	!!----------------------------------------------------------------------
610	!
611	CALL wrk_alloc( jpi,jpj, 2, ztstop)
612	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj)
613	CALL wrk_alloc( jpi,jpj, zrhdtop_oce )
614	!
615	! Local constant initialization
616	zcoef0 = - grav * 0.5_wp
617
618	! To use density and not density anomaly
619	znad=1._wp
620
621	! iniitialised to 0. zhpi zhpi
622	zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp
623
624	! compute rhd at the ice/oce interface (ocean side)
625	! usefull to reduce residual current in the test case ISOMIP with no melting
626	DO ji=1,jpi
627	DO jj=1,jpj
628	ikt=mikt(ji,jj)
629	ztstop(ji,jj,1)=tsn(ji,jj,ikt,1)
630	ztstop(ji,jj,2)=tsn(ji,jj,ikt,2)
631	END DO
632	END DO
633	CALL eos( ztstop, risfdep, zrhdtop_oce )
634
635	!==================================================================================
636	!===== Compute surface value =====================================================
637	!==================================================================================
638	DO jj = 2, jpjm1
639	DO ji = fs_2, fs_jpim1 ! vector opt.
640	ikt = mikt(ji,jj)
641	iktp1i = mikt(ji+1,jj)
642	iktp1j = mikt(ji,jj+1)
643	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
644	! we assume ISF is in isostatic equilibrium
645	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * e3w_n(ji+1,jj,iktp1i) &
646	& * ( 2._wp * znad + rhd(ji+1,jj,iktp1i) + zrhdtop_oce(ji+1,jj) ) &
647	& - 0.5_wp * e3w_n(ji,jj,ikt) &
648	& * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) &
649	& + ( riceload(ji+1,jj) - riceload(ji,jj)) )
650	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * e3w_n(ji,jj+1,iktp1j) &
651	& * ( 2._wp * znad + rhd(ji,jj+1,iktp1j) + zrhdtop_oce(ji,jj+1) ) &
652	& - 0.5_wp * e3w_n(ji,jj,ikt) &
653	& * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) &
654	& + ( riceload(ji,jj+1) - riceload(ji,jj)) )
655	! s-coordinate pressure gradient correction (=0 if z coordinate)
656	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
657	& * ( gde3w_n(ji+1,jj,1) - gde3w_n(ji,jj,1) ) * r1_e1u(ji,jj)
658	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
659	& * ( gde3w_n(ji,jj+1,1) - gde3w_n(ji,jj,1) ) * r1_e2v(ji,jj)
660	! add to the general momentum trend
661	ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
662	va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
663	END DO
664	END DO
665	!==================================================================================
666	!===== Compute interior value =====================================================
667	!==================================================================================
668	! interior value (2=<jk=<jpkm1)
669	DO jk = 2, jpkm1
670	DO jj = 2, jpjm1
671	DO ji = fs_2, fs_jpim1 ! vector opt.
672	! hydrostatic pressure gradient along s-surfaces
673	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
674	& * ( e3w_n(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2znad ) wmask(ji+1,jj,jk) &
675	& - e3w_n(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2znad ) wmask(ji ,jj,jk) )
676	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
677	& * ( e3w_n(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2znad ) wmask(ji,jj+1,jk) &
678	& - e3w_n(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2znad ) wmask(ji,jj ,jk) )
679	! s-coordinate pressure gradient correction
680	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
681	& * ( gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk) ) / e1u(ji,jj)
682	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
683	& * ( gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk) ) / e2v(ji,jj)
684	! add to the general momentum trend
685	ua(ji,jj,jk) = ua(ji,jj,jk) + (zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
686	va(ji,jj,jk) = va(ji,jj,jk) + (zhpj(ji,jj,jk) + zvap) * vmask(ji,jj,jk)
687	END DO
688	END DO
689	END DO
690	!
691	CALL wrk_dealloc( jpi,jpj,2 , ztstop)
692	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj)
693	CALL wrk_dealloc( jpi,jpj , zrhdtop_oce )
694	!
695	END SUBROUTINE hpg_isf
696
697
698	SUBROUTINE hpg_djc( kt )
699	!!---------------------------------------------------------------------
700	!! * ROUTINE hpg_djc *
701	!!
702	!! ** Method : Density Jacobian with Cubic polynomial scheme
703	!!
704	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
705	!!----------------------------------------------------------------------
706	INTEGER, INTENT(in) :: kt ! ocean time-step index
707	!!
708	INTEGER :: ji, jj, jk ! dummy loop indices
709	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
710	REAL(wp) :: z1_10, cffu, cffx ! " "
711	REAL(wp) :: z1_12, cffv, cffy ! " "
712	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
713	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
714	REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw
715	REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow
716	REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k
717	REAL(wp), POINTER, DIMENSION(:,:) :: zcpx, zcpy !W/D pressure filter
718	!!----------------------------------------------------------------------
719	!
720	CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
721	CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
722	CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
723	IF(ln_wd) CALL wrk_alloc( jpi,jpj, zcpx, zcpy )
724	!
725	!
726	IF(ln_wd) THEN
727	DO jj = 2, jpjm1
728	DO ji = 2, jpim1
729	ll_tmp1 = MIN(sshn(ji,jj), sshn(ji+1,jj)) > MAX(-bathy(ji,jj), -bathy(ji+1,jj)) &
730	& .and. MAX(sshn(ji,jj) + bathy(ji,jj), sshn(ji+1,jj) + bathy(ji+1,jj)) &
731	& > rn_wdmin1 + rn_wdmin2
732	ll_tmp2 = MAX(sshn(ji,jj), sshn(ji+1,jj)) > MAX(-bathy(ji,jj), -bathy(ji+1,jj)) +&
733	& rn_wdmin1 + rn_wdmin2
734
735	IF(ll_tmp1) THEN
736	zcpx(ji,jj) = 1.0_wp
737	ELSE IF(ll_tmp2) THEN
738	! no worries about sshn(ji+1,jj)-sshn(ji,jj) = 0, it won't happen ! here
739	zcpx(ji,jj) = ABS((sshn(ji+1,jj) + bathy(ji+1,jj) - sshn(ji,jj) - bathy(ji,jj)) /&
740	& (sshn(ji+1,jj) - sshn(ji,jj)))
741	ELSE
742	zcpx(ji,jj) = 0._wp
743	END IF
744
745	ll_tmp1 = MIN(sshn(ji,jj), sshn(ji,jj+1)) > MAX(-bathy(ji,jj), -bathy(ji,jj+1)) &
746	& .and. MAX(sshn(ji,jj) + bathy(ji,jj), sshn(ji,jj+1) + bathy(ji,jj+1)) &
747	& > rn_wdmin1 + rn_wdmin2
748	ll_tmp2 = MAX(sshn(ji,jj), sshn(ji,jj+1)) > MAX(-bathy(ji,jj), -bathy(ji,jj+1)) +&
749	& rn_wdmin1 + rn_wdmin2
750
751	IF(ll_tmp1) THEN
752	zcpy(ji,jj) = 1.0_wp
753	ELSE IF(ll_tmp2) THEN
754	! no worries about sshn(ji,jj+1)-sshn(ji,jj) = 0, it won't happen ! here
755	zcpy(ji,jj) = ABS((sshn(ji,jj+1) + bathy(ji,jj+1) - sshn(ji,jj) - bathy(ji,jj)) /&
756	& (sshn(ji,jj+1) - sshn(ji,jj)))
757	ELSE
758	zcpy(ji,jj) = 0._wp
759	END IF
760	END DO
761	END DO
762	CALL lbc_lnk( zcpx, 'U', 1._wp ) ; CALL lbc_lnk( zcpy, 'V', 1._wp )
763	ENDIF
764
765
766	IF( kt == nit000 ) THEN
767	IF(lwp) WRITE(numout,*)
768	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
769	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
770	ENDIF
771
772	! Local constant initialization
773	zcoef0 = - grav * 0.5_wp
774	z1_10 = 1._wp / 10._wp
775	z1_12 = 1._wp / 12._wp
776
777	!----------------------------------------------------------------------------------------
778	! compute and store in provisional arrays elementary vertical and horizontal differences
779	!----------------------------------------------------------------------------------------
780
781	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
782
783	DO jk = 2, jpkm1
784	DO jj = 2, jpjm1
785	DO ji = fs_2, fs_jpim1 ! vector opt.
786	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
787	dzz (ji,jj,jk) = gde3w_n(ji ,jj ,jk) - gde3w_n(ji,jj,jk-1)
788	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
789	dzx (ji,jj,jk) = gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk )
790	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
791	dzy (ji,jj,jk) = gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk )
792	END DO
793	END DO
794	END DO
795
796	!-------------------------------------------------------------------------
797	! compute harmonic averages using eq. 5.18
798	!-------------------------------------------------------------------------
799	zep = 1.e-15
800
801	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
802	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
803
804	DO jk = 2, jpkm1
805	DO jj = 2, jpjm1
806	DO ji = fs_2, fs_jpim1 ! vector opt.
807	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
808
809	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
810	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
811
812	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
813	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
814
815	IF( cffw > zep) THEN
816	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
817	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
818	ELSE
819	drhow(ji,jj,jk) = 0._wp
820	ENDIF
821
822	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
823	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
824
825	IF( cffu > zep ) THEN
826	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
827	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
828	ELSE
829	drhou(ji,jj,jk ) = 0._wp
830	ENDIF
831
832	IF( cffx > zep ) THEN
833	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
834	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
835	ELSE
836	dzu(ji,jj,jk) = 0._wp
837	ENDIF
838
839	IF( cffv > zep ) THEN
840	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
841	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
842	ELSE
843	drhov(ji,jj,jk) = 0._wp
844	ENDIF
845
846	IF( cffy > zep ) THEN
847	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
848	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
849	ELSE
850	dzv(ji,jj,jk) = 0._wp
851	ENDIF
852
853	END DO
854	END DO
855	END DO
856
857	!----------------------------------------------------------------------------------
858	! apply boundary conditions at top and bottom using 5.36-5.37
859	!----------------------------------------------------------------------------------
860	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
861	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
862	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
863
864	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
865	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
866	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
867
868
869	!--------------------------------------------------------------
870	! Upper half of top-most grid box, compute and store
871	!-------------------------------------------------------------
872
873	!!bug gm : e3w-gde3w = 0.5*e3w .... and gde3w(2)-gde3w(1)=e3w(2) .... to be verified
874	! true if gde3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
875
876	DO jj = 2, jpjm1
877	DO ji = fs_2, fs_jpim1 ! vector opt.
878	rho_k(ji,jj,1) = -grav * ( e3w_n(ji,jj,1) - gde3w_n(ji,jj,1) ) &
879	& * ( rhd(ji,jj,1) &
880	& + 0.5_wp * ( rhd (ji,jj,2) - rhd (ji,jj,1) ) &
881	& * ( e3w_n (ji,jj,1) - gde3w_n(ji,jj,1) ) &
882	& / ( gde3w_n(ji,jj,2) - gde3w_n(ji,jj,1) ) )
883	END DO
884	END DO
885
886	!!bug gm : here also, simplification is possible
887	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
888
889	DO jk = 2, jpkm1
890	DO jj = 2, jpjm1
891	DO ji = fs_2, fs_jpim1 ! vector opt.
892
893	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
894	& * ( gde3w_n(ji,jj,jk) - gde3w_n(ji,jj,jk-1) ) &
895	& - grav * z1_10 * ( &
896	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
897	& * ( gde3w_n(ji,jj,jk) - gde3w_n(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
898	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
899	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
900	& )
901
902	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
903	& * ( gde3w_n(ji+1,jj,jk) - gde3w_n(ji,jj,jk) ) &
904	& - grav* z1_10 * ( &
905	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
906	& * ( gde3w_n(ji+1,jj,jk) - gde3w_n(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
907	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
908	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
909	& )
910
911	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
912	& * ( gde3w_n(ji,jj+1,jk) - gde3w_n(ji,jj,jk) ) &
913	& - grav* z1_10 * ( &
914	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
915	& * ( gde3w_n(ji,jj+1,jk) - gde3w_n(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
916	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
917	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
918	& )
919
920	END DO
921	END DO
922	END DO
923	CALL lbc_lnk(rho_k,'W',1.)
924	CALL lbc_lnk(rho_i,'U',1.)
925	CALL lbc_lnk(rho_j,'V',1.)
926
927
928	! ---------------
929	! Surface value
930	! ---------------
931	DO jj = 2, jpjm1
932	DO ji = fs_2, fs_jpim1 ! vector opt.
933	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) * r1_e1u(ji,jj)
934	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) * r1_e2v(ji,jj)
935	IF(ln_wd) THEN
936	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
937	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
938	ENDIF
939	! add to the general momentum trend
940	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
941	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
942	END DO
943	END DO
944
945	! ----------------
946	! interior value (2=<jk=<jpkm1)
947	! ----------------
948	DO jk = 2, jpkm1
949	DO jj = 2, jpjm1
950	DO ji = fs_2, fs_jpim1 ! vector opt.
951	! hydrostatic pressure gradient along s-surfaces
952	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
953	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
954	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) * r1_e1u(ji,jj)
955	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
956	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
957	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) * r1_e2v(ji,jj)
958	IF(ln_wd) THEN
959	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
960	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
961	ENDIF
962	! add to the general momentum trend
963	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
964	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
965	END DO
966	END DO
967	END DO
968	!
969	CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
970	CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
971	CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
972	IF(ln_wd) CALL wrk_dealloc( jpi,jpj, zcpx, zcpy )
973	!
974	END SUBROUTINE hpg_djc
975
976
977	SUBROUTINE hpg_prj( kt )
978	!!---------------------------------------------------------------------
979	!! * ROUTINE hpg_prj *
980	!!
981	!! ** Method : s-coordinate case.
982	!! A Pressure-Jacobian horizontal pressure gradient method
983	!! based on the constrained cubic-spline interpolation for
984	!! all vertical coordinate systems
985	!!
986	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
987	!!----------------------------------------------------------------------
988	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
989	INTEGER, INTENT(in) :: kt ! ocean time-step index
990	!!
991	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
992	REAL(wp) :: zcoef0, znad ! local scalars
993	!
994	!! The local variables for the correction term
995	INTEGER :: jk1, jis, jid, jjs, jjd
996	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
997	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
998	REAL(wp) :: zrhdt1
999	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
1000	REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh
1001	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
1002	REAL(wp), POINTER, DIMENSION(:,:) :: zsshu_n, zsshv_n
1003	REAL(wp), POINTER, DIMENSION(:,:) :: zcpx, zcpy !W/D pressure filter
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	IF(ln_wd) CALL wrk_alloc( jpi,jpj, zcpx, zcpy )
1010	!
1011	IF( kt == nit000 ) THEN
1012	IF(lwp) WRITE(numout,*)
1013	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
1014	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
1015	ENDIF
1016
1017	! Local constant initialization
1018	zcoef0 = - grav
1019	znad = 1._wp
1020	IF( ln_linssh ) znad = 0._wp
1021
1022	IF(ln_wd) THEN
1023	DO jj = 2, jpjm1
1024	DO ji = 2, jpim1
1025	ll_tmp1 = MIN(sshn(ji,jj), sshn(ji+1,jj)) > MAX(-bathy(ji,jj), -bathy(ji+1,jj)) &
1026	& .and. MAX(sshn(ji,jj) + bathy(ji,jj), sshn(ji+1,jj) + bathy(ji+1,jj)) &
1027	& > rn_wdmin1 + rn_wdmin2
1028	ll_tmp2 = MAX(sshn(ji,jj), sshn(ji+1,jj)) > MAX(-bathy(ji,jj), -bathy(ji+1,jj)) +&
1029	& rn_wdmin1 + rn_wdmin2
1030
1031	IF(ll_tmp1) THEN
1032	zcpx(ji,jj) = 1.0_wp
1033	ELSE IF(ll_tmp2) THEN
1034	! no worries about sshn(ji+1,jj)-sshn(ji,jj) = 0, it won't happen ! here
1035	zcpx(ji,jj) = ABS((sshn(ji+1,jj) + bathy(ji+1,jj) - sshn(ji,jj) - bathy(ji,jj)) /&
1036	& (sshn(ji+1,jj) - sshn(ji,jj)))
1037	ELSE
1038	zcpx(ji,jj) = 0._wp
1039	END IF
1040
1041	ll_tmp1 = MIN(sshn(ji,jj), sshn(ji,jj+1)) > MAX(-bathy(ji,jj), -bathy(ji,jj+1)) &
1042	& .and. MAX(sshn(ji,jj) + bathy(ji,jj), sshn(ji,jj+1) + bathy(ji,jj+1)) &
1043	& > rn_wdmin1 + rn_wdmin2
1044	ll_tmp2 = MAX(sshn(ji,jj), sshn(ji,jj+1)) > MAX(-bathy(ji,jj), -bathy(ji,jj+1)) +&
1045	& rn_wdmin1 + rn_wdmin2
1046
1047	IF(ll_tmp1.OR.ll_tmp2) THEN
1048	zcpy(ji,jj) = 1.0_wp
1049	ELSE IF(ll_tmp2) THEN
1050	! no worries about sshn(ji,jj+1)-sshn(ji,jj) = 0, it won't happen ! here
1051	zcpy(ji,jj) = ABS((sshn(ji,jj+1) + bathy(ji,jj+1) - sshn(ji,jj) - bathy(ji,jj)) /&
1052	& (sshn(ji,jj+1) - sshn(ji,jj)))
1053	ELSE
1054	zcpy(ji,jj) = 0._wp
1055	END IF
1056	END DO
1057	END DO
1058	CALL lbc_lnk( zcpx, 'U', 1._wp ) ; CALL lbc_lnk( zcpy, 'V', 1._wp )
1059	ENDIF
1060
1061	! Clean 3-D work arrays
1062	zhpi(:,:,:) = 0._wp
1063	zrhh(:,:,:) = rhd(:,:,:)
1064
1065	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
1066	DO jj = 1, jpj
1067	DO ji = 1, jpi
1068	jk = mbathy(ji,jj)
1069	IF( jk <= 0 ) THEN ; zrhh(ji,jj, : ) = 0._wp
1070	ELSEIF( jk == 1 ) THEN ; zrhh(ji,jj,jk+1:jpk) = rhd(ji,jj,jk)
1071	ELSEIF( jk < jpkm1 ) THEN
1072	DO jkk = jk+1, jpk
1073	zrhh(ji,jj,jkk) = interp1(gde3w_n(ji,jj,jkk ), gde3w_n(ji,jj,jkk-1), &
1074	& gde3w_n(ji,jj,jkk-2), rhd (ji,jj,jkk-1), rhd(ji,jj,jkk-2))
1075	END DO
1076	ENDIF
1077	END DO
1078	END DO
1079
1080	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
1081	DO jj = 1, jpj
1082	DO ji = 1, jpi
1083	zdept(ji,jj,1) = 0.5_wp * e3w_n(ji,jj,1) - sshn(ji,jj) * znad
1084	END DO
1085	END DO
1086
1087	DO jk = 2, jpk
1088	DO jj = 1, jpj
1089	DO ji = 1, jpi
1090	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + e3w_n(ji,jj,jk)
1091	END DO
1092	END DO
1093	END DO
1094
1095	fsp(:,:,:) = zrhh (:,:,:)
1096	xsp(:,:,:) = zdept(:,:,:)
1097
1098	! Construct the vertical density profile with the
1099	! constrained cubic spline interpolation
1100	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
1101	CALL cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
1102
1103	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
1104	DO jj = 2, jpj
1105	DO ji = 2, jpi
1106	zrhdt1 = zrhh(ji,jj,1) - interp3( zdept(ji,jj,1), asp(ji,jj,1), bsp(ji,jj,1), &
1107	& csp(ji,jj,1), dsp(ji,jj,1) ) * 0.25_wp * e3w_n(ji,jj,1)
1108
1109	! assuming linear profile across the top half surface layer
1110	zhpi(ji,jj,1) = 0.5_wp * e3w_n(ji,jj,1) * zrhdt1
1111	END DO
1112	END DO
1113
1114	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
1115	DO jk = 2, jpkm1
1116	DO jj = 2, jpj
1117	DO ji = 2, jpi
1118	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
1119	& integ_spline( zdept(ji,jj,jk-1), zdept(ji,jj,jk), &
1120	& asp (ji,jj,jk-1), bsp (ji,jj,jk-1), &
1121	& csp (ji,jj,jk-1), dsp (ji,jj,jk-1) )
1122	END DO
1123	END DO
1124	END DO
1125
1126	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
1127
1128	! Prepare zsshu_n and zsshv_n
1129	DO jj = 2, jpjm1
1130	DO ji = 2, jpim1
1131	!!gm BUG ? if it is ssh at u- & v-point then it should be:
1132	! zsshu_n(ji,jj) = (e1e2t(ji,jj) * sshn(ji,jj) + e1e2t(ji+1,jj) * sshn(ji+1,jj)) * &
1133	! & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
1134	! zsshv_n(ji,jj) = (e1e2t(ji,jj) * sshn(ji,jj) + e1e2t(ji,jj+1) * sshn(ji,jj+1)) * &
1135	! & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
1136	!!gm not this:
1137	zsshu_n(ji,jj) = (e1e2u(ji,jj) * sshn(ji,jj) + e1e2u(ji+1, jj) * sshn(ji+1,jj)) * &
1138	& r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
1139	zsshv_n(ji,jj) = (e1e2v(ji,jj) * sshn(ji,jj) + e1e2v(ji+1, jj) * sshn(ji,jj+1)) * &
1140	& r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
1141	END DO
1142	END DO
1143
1144	CALL lbc_lnk (zsshu_n, 'U', 1.)
1145	CALL lbc_lnk (zsshv_n, 'V', 1.)
1146
1147	DO jj = 2, jpjm1
1148	DO ji = 2, jpim1
1149	zu(ji,jj,1) = - ( e3u_n(ji,jj,1) - zsshu_n(ji,jj) * znad)
1150	zv(ji,jj,1) = - ( e3v_n(ji,jj,1) - zsshv_n(ji,jj) * znad)
1151	END DO
1152	END DO
1153
1154	DO jk = 2, jpkm1
1155	DO jj = 2, jpjm1
1156	DO ji = 2, jpim1
1157	zu(ji,jj,jk) = zu(ji,jj,jk-1) - e3u_n(ji,jj,jk)
1158	zv(ji,jj,jk) = zv(ji,jj,jk-1) - e3v_n(ji,jj,jk)
1159	END DO
1160	END DO
1161	END DO
1162
1163	DO jk = 1, jpkm1
1164	DO jj = 2, jpjm1
1165	DO ji = 2, jpim1
1166	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * e3u_n(ji,jj,jk)
1167	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * e3v_n(ji,jj,jk)
1168	END DO
1169	END DO
1170	END DO
1171
1172	DO jk = 1, jpkm1
1173	DO jj = 2, jpjm1
1174	DO ji = 2, jpim1
1175	zu(ji,jj,jk) = MIN( zu(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
1176	zu(ji,jj,jk) = MAX( zu(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
1177	zv(ji,jj,jk) = MIN( zv(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
1178	zv(ji,jj,jk) = MAX( zv(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
1179	END DO
1180	END DO
1181	END DO
1182
1183
1184	DO jk = 1, jpkm1
1185	DO jj = 2, jpjm1
1186	DO ji = 2, jpim1
1187	zpwes = 0._wp; zpwed = 0._wp
1188	zpnss = 0._wp; zpnsd = 0._wp
1189	zuijk = zu(ji,jj,jk)
1190	zvijk = zv(ji,jj,jk)
1191
1192	!!!!! for u equation
1193	IF( jk <= mbku(ji,jj) ) THEN
1194	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
1195	jis = ji + 1; jid = ji
1196	ELSE
1197	jis = ji; jid = ji +1
1198	ENDIF
1199
1200	! integrate the pressure on the shallow side
1201	jk1 = jk
1202	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
1203	IF( jk1 == mbku(ji,jj) ) THEN
1204	zuijk = -zdept(jis,jj,jk1)
1205	EXIT
1206	ENDIF
1207	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
1208	zpwes = zpwes + &
1209	integ_spline(zdept(jis,jj,jk1), zdeps, &
1210	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
1211	csp(jis,jj,jk1), dsp(jis,jj,jk1))
1212	jk1 = jk1 + 1
1213	END DO
1214
1215	! integrate the pressure on the deep side
1216	jk1 = jk
1217	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
1218	IF( jk1 == 1 ) THEN
1219	zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad)
1220	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
1221	bsp(jid,jj,1), csp(jid,jj,1), &
1222	dsp(jid,jj,1)) * zdeps
1223	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
1224	EXIT
1225	ENDIF
1226	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
1227	zpwed = zpwed + &
1228	integ_spline(zdeps, zdept(jid,jj,jk1), &
1229	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
1230	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
1231	jk1 = jk1 - 1
1232	END DO
1233
1234	! update the momentum trends in u direction
1235
1236	zdpdx1 = zcoef0 * r1_e1u(ji,jj) * ( zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk) )
1237	IF( .NOT.ln_linssh ) THEN
1238	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * &
1239	& ( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) )
1240	ELSE
1241	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
1242	ENDIF
1243	IF(ln_wd) THEN
1244	zdpdx1 = zdpdx1 * zcpx(ji,jj)
1245	zdpdx2 = zdpdx2 * zcpx(ji,jj)
1246	ENDIF
1247	ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * umask(ji,jj,jk)
1248	ENDIF
1249
1250	!!!!! for v equation
1251	IF( jk <= mbkv(ji,jj) ) THEN
1252	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
1253	jjs = jj + 1; jjd = jj
1254	ELSE
1255	jjs = jj ; jjd = jj + 1
1256	ENDIF
1257
1258	! integrate the pressure on the shallow side
1259	jk1 = jk
1260	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
1261	IF( jk1 == mbkv(ji,jj) ) THEN
1262	zvijk = -zdept(ji,jjs,jk1)
1263	EXIT
1264	ENDIF
1265	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
1266	zpnss = zpnss + &
1267	integ_spline(zdept(ji,jjs,jk1), zdeps, &
1268	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
1269	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
1270	jk1 = jk1 + 1
1271	END DO
1272
1273	! integrate the pressure on the deep side
1274	jk1 = jk
1275	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
1276	IF( jk1 == 1 ) THEN
1277	zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad)
1278	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
1279	bsp(ji,jjd,1), csp(ji,jjd,1), &
1280	dsp(ji,jjd,1) ) * zdeps
1281	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
1282	EXIT
1283	ENDIF
1284	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
1285	zpnsd = zpnsd + &
1286	integ_spline(zdeps, zdept(ji,jjd,jk1), &
1287	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
1288	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
1289	jk1 = jk1 - 1
1290	END DO
1291
1292
1293	! update the momentum trends in v direction
1294
1295	zdpdy1 = zcoef0 * r1_e2v(ji,jj) * ( zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk) )
1296	IF( .NOT.ln_linssh ) THEN
1297	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * &
1298	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) )
1299	ELSE
1300	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
1301	ENDIF
1302	IF(ln_wd) THEN
1303	zdpdy1 = zdpdy1 * zcpy(ji,jj)
1304	zdpdy2 = zdpdy2 * zcpy(ji,jj)
1305	ENDIF
1306
1307	va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2) * vmask(ji,jj,jk)
1308	ENDIF
1309	!
1310	END DO
1311	END DO
1312	END DO
1313	!
1314	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
1315	CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh )
1316	CALL wrk_dealloc( jpi,jpj, zsshu_n, zsshv_n )
1317	IF(ln_wd) CALL wrk_dealloc( jpi,jpj, zcpx, zcpy )
1318	!
1319	END SUBROUTINE hpg_prj
1320
1321
1322	SUBROUTINE cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
1323	!!----------------------------------------------------------------------
1324	!! * ROUTINE cspline *
1325	!!
1326	!! ** Purpose : constrained cubic spline interpolation
1327	!!
1328	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
1329	!!
1330	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
1331	!!----------------------------------------------------------------------
1332	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: fsp, xsp ! value and coordinate
1333	REAL(wp), DIMENSION(:,:,:), INTENT( out) :: asp, bsp, csp, dsp ! coefficients of the interpoated function
1334	INTEGER , INTENT(in ) :: polynomial_type ! 1: cubic spline ; 2: Linear
1335	!
1336	INTEGER :: ji, jj, jk ! dummy loop indices
1337	INTEGER :: jpi, jpj, jpkm1
1338	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
1339	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
1340	REAL(wp) :: zdf(size(fsp,3))
1341	!!----------------------------------------------------------------------
1342	!
1343	!!gm WHAT !!!!! THIS IS VERY DANGEROUS !!!!!
1344	jpi = size(fsp,1)
1345	jpj = size(fsp,2)
1346	jpkm1 = size(fsp,3) - 1
1347	!
1348	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
1349	DO ji = 1, jpi
1350	DO jj = 1, jpj
1351	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
1352	! DO jk = 2, jpkm1-1
1353	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
1354	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1355	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
1356	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
1357	!
1358	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
1359	!
1360	! IF(zdf1 * zdf2 <= 0._wp) THEN
1361	! zdf(jk) = 0._wp
1362	! ELSE
1363	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
1364	! ENDIF
1365	! END DO
1366
1367	!!Simply geometric average
1368	DO jk = 2, jpkm1-1
1369	zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1))
1370	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk))
1371
1372	IF(zdf1 * zdf2 <= 0._wp) THEN
1373	zdf(jk) = 0._wp
1374	ELSE
1375	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
1376	ENDIF
1377	END DO
1378
1379	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
1380	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
1381	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
1382	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - 0.5_wp * zdf(jpkm1 - 1)
1383
1384	DO jk = 1, jpkm1 - 1
1385	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1386	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
1387	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
1388	zddf1 = -2._wp * ztmp1 + ztmp2
1389	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
1390	zddf2 = 2._wp * ztmp1 - ztmp2
1391
1392	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
1393	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
1394	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
1395	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
1396	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
1397	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
1398	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
1399	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
1400	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
1401	END DO
1402	END DO
1403	END DO
1404
1405	ELSEIF ( polynomial_type == 2 ) THEN ! Linear
1406	DO ji = 1, jpi
1407	DO jj = 1, jpj
1408	DO jk = 1, jpkm1-1
1409	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1410	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
1411
1412	dsp(ji,jj,jk) = 0._wp
1413	csp(ji,jj,jk) = 0._wp
1414	bsp(ji,jj,jk) = ztmp1 / zdxtmp
1415	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
1416	END DO
1417	END DO
1418	END DO
1419
1420	ELSE
1421	CALL ctl_stop( 'invalid polynomial type in cspline' )
1422	ENDIF
1423
1424	END SUBROUTINE cspline
1425
1426
1427	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
1428	!!----------------------------------------------------------------------
1429	!! * ROUTINE interp1 *
1430	!!
1431	!! ** Purpose : 1-d linear interpolation
1432	!!
1433	!! ** Method : interpolation is straight forward
1434	!! extrapolation is also permitted (no value limit)
1435	!!----------------------------------------------------------------------
1436	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
1437	REAL(wp) :: f ! result of the interpolation (extrapolation)
1438	REAL(wp) :: zdeltx
1439	!!----------------------------------------------------------------------
1440	!
1441	zdeltx = xr - xl
1442	IF( abs(zdeltx) <= 10._wp * EPSILON(x) ) THEN
1443	f = 0.5_wp * (fl + fr)
1444	ELSE
1445	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
1446	ENDIF
1447	!
1448	END FUNCTION interp1
1449
1450
1451	FUNCTION interp2( x, a, b, c, d ) RESULT(f)
1452	!!----------------------------------------------------------------------
1453	!! * ROUTINE interp1 *
1454	!!
1455	!! ** Purpose : 1-d constrained cubic spline interpolation
1456	!!
1457	!! ** Method : cubic spline interpolation
1458	!!
1459	!!----------------------------------------------------------------------
1460	REAL(wp), INTENT(in) :: x, a, b, c, d
1461	REAL(wp) :: f ! value from the interpolation
1462	!!----------------------------------------------------------------------
1463	!
1464	f = a + x* ( b + x * ( c + d * x ) )
1465	!
1466	END FUNCTION interp2
1467
1468
1469	FUNCTION interp3( x, a, b, c, d ) RESULT(f)
1470	!!----------------------------------------------------------------------
1471	!! * ROUTINE interp1 *
1472	!!
1473	!! ** Purpose : Calculate the first order of deriavtive of
1474	!! a cubic spline function y=a+bx+cx^2+d*x^3
1475	!!
1476	!! ** Method : f=dy/dx=b+2cx+3dx^2
1477	!!
1478	!!----------------------------------------------------------------------
1479	REAL(wp), INTENT(in) :: x, a, b, c, d
1480	REAL(wp) :: f ! value from the interpolation
1481	!!----------------------------------------------------------------------
1482	!
1483	f = b + x * ( 2._wp * c + 3._wp * d * x)
1484	!
1485	END FUNCTION interp3
1486
1487
1488	FUNCTION integ_spline( xl, xr, a, b, c, d ) RESULT(f)
1489	!!----------------------------------------------------------------------
1490	!! * ROUTINE interp1 *
1491	!!
1492	!! ** Purpose : 1-d constrained cubic spline integration
1493	!!
1494	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
1495	!!
1496	!!----------------------------------------------------------------------
1497	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
1498	REAL(wp) :: za1, za2, za3
1499	REAL(wp) :: f ! integration result
1500	!!----------------------------------------------------------------------
1501	!
1502	za1 = 0.5_wp * b
1503	za2 = c / 3.0_wp
1504	za3 = 0.25_wp * d
1505	!
1506	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
1507	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
1508	!
1509	END FUNCTION integ_spline
1510
1511	!!======================================================================
1512	END MODULE dynhpg
1513

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