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dynhpg.F90 in NEMO/branches/2019/UKMO_MERGE_2019/src/OCE/DYN – NEMO

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source: NEMO/branches/2019/UKMO_MERGE_2019/src/OCE/DYN/dynhpg.F90 @ 12077

Last change on this file since 12077 was 12077, checked in by mathiot, 4 years ago
include ENHANCE-02_ISF_nemo in UKMO merge branch
Property svn:keywords set to `Id`
File size: 73.5 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 isf_oce , ONLY : risfload ! ice shelf (risfload variable)
34	USE isfload , ONLY : isf_load ! ice shelf (isf_load routine )
35	USE sbc_oce ! surface variable (only for the flag with ice shelf)
36	USE dom_oce ! ocean space and time domain
37	USE wet_dry ! wetting and drying
38	USE phycst ! physical constants
39	USE trd_oce ! trends: ocean variables
40	USE trddyn ! trend manager: dynamics
41	USE zpshde ! partial step: hor. derivative (zps_hde routine)
42	!
43	USE in_out_manager ! I/O manager
44	USE prtctl ! Print control
45	USE lbclnk ! lateral boundary condition
46	USE lib_mpp ! MPP library
47	USE eosbn2 ! compute density
48	USE timing ! Timing
49	USE iom
50
51	IMPLICIT NONE
52	PRIVATE
53
54	PUBLIC dyn_hpg ! routine called by step module
55	PUBLIC dyn_hpg_init ! routine called by opa module
56
57	! !!* Namelist namdyn_hpg : hydrostatic pressure gradient
58	LOGICAL, PUBLIC :: ln_hpg_zco !: z-coordinate - full steps
59	LOGICAL, PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation)
60	LOGICAL, PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation)
61	LOGICAL, PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial)
62	LOGICAL, PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme)
63	LOGICAL, PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf
64
65	! !! Flag to control the type of hydrostatic pressure gradient
66	INTEGER, PARAMETER :: np_ERROR =-10 ! error in specification of lateral diffusion
67	INTEGER, PARAMETER :: np_zco = 0 ! z-coordinate - full steps
68	INTEGER, PARAMETER :: np_zps = 1 ! z-coordinate - partial steps (interpolation)
69	INTEGER, PARAMETER :: np_sco = 2 ! s-coordinate (standard jacobian formulation)
70	INTEGER, PARAMETER :: np_djc = 3 ! s-coordinate (Density Jacobian with Cubic polynomial)
71	INTEGER, PARAMETER :: np_prj = 4 ! s-coordinate (Pressure Jacobian scheme)
72	INTEGER, PARAMETER :: np_isf = 5 ! s-coordinate similar to sco modify for isf
73	!
74	INTEGER, PUBLIC :: nhpg !: type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM)
75
76	!! * Substitutions
77	# include "vectopt_loop_substitute.h90"
78	!!----------------------------------------------------------------------
79	!! NEMO/OCE 4.0 , NEMO Consortium (2018)
80	!! $Id$
81	!! Software governed by the CeCILL license (see ./LICENSE)
82	!!----------------------------------------------------------------------
83	CONTAINS
84
85	SUBROUTINE dyn_hpg( kt, Kmm, puu, pvv, Krhs )
86	!!---------------------------------------------------------------------
87	!! * ROUTINE dyn_hpg *
88	!!
89	!! ** Method : Call the hydrostatic pressure gradient routine
90	!! using the scheme defined in the namelist
91	!!
92	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
93	!! - send trends to trd_dyn for futher diagnostics (l_trddyn=T)
94	!!----------------------------------------------------------------------
95	INTEGER , INTENT( in ) :: kt ! ocean time-step index
96	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
97	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
98	!
99	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: ztrdu, ztrdv
100	!!----------------------------------------------------------------------
101	!
102	IF( ln_timing ) CALL timing_start('dyn_hpg')
103	!
104	IF( l_trddyn ) THEN ! Temporary saving of puu(:,:,:,Krhs) and pvv(:,:,:,Krhs) trends (l_trddyn)
105	ALLOCATE( ztrdu(jpi,jpj,jpk) , ztrdv(jpi,jpj,jpk) )
106	ztrdu(:,:,:) = puu(:,:,:,Krhs)
107	ztrdv(:,:,:) = pvv(:,:,:,Krhs)
108	ENDIF
109	!
110	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
111	CASE ( np_zco ) ; CALL hpg_zco ( kt, Kmm, puu, pvv, Krhs ) ! z-coordinate
112	CASE ( np_zps ) ; CALL hpg_zps ( kt, Kmm, puu, pvv, Krhs ) ! z-coordinate plus partial steps (interpolation)
113	CASE ( np_sco ) ; CALL hpg_sco ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate (standard jacobian formulation)
114	CASE ( np_djc ) ; CALL hpg_djc ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate (Density Jacobian with Cubic polynomial)
115	CASE ( np_prj ) ; CALL hpg_prj ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate (Pressure Jacobian scheme)
116	CASE ( np_isf ) ; CALL hpg_isf ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate similar to sco modify for ice shelf
117	END SELECT
118	!
119	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
120	ztrdu(:,:,:) = puu(:,:,:,Krhs) - ztrdu(:,:,:)
121	ztrdv(:,:,:) = pvv(:,:,:,Krhs) - ztrdv(:,:,:)
122	CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt, Kmm )
123	DEALLOCATE( ztrdu , ztrdv )
124	ENDIF
125	!
126	IF(ln_ctl) CALL prt_ctl( tab3d_1=puu(:,:,:,Krhs), clinfo1=' hpg - Ua: ', mask1=umask, &
127	& tab3d_2=pvv(:,:,:,Krhs), clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
128	!
129	IF( ln_timing ) CALL timing_stop('dyn_hpg')
130	!
131	END SUBROUTINE dyn_hpg
132
133
134	SUBROUTINE dyn_hpg_init( Kmm )
135	!!----------------------------------------------------------------------
136	!! * ROUTINE dyn_hpg_init *
137	!!
138	!! ** Purpose : initializations for the hydrostatic pressure gradient
139	!! computation and consistency control
140	!!
141	!! ** Action : Read the namelist namdyn_hpg and check the consistency
142	!! with the type of vertical coordinate used (zco, zps, sco)
143	!!----------------------------------------------------------------------
144	INTEGER, INTENT( in ) :: Kmm ! ocean time level index
145	!
146	INTEGER :: ioptio = 0 ! temporary integer
147	INTEGER :: ios ! Local integer output status for namelist read
148	!!
149	INTEGER :: ji, jj, jk, ikt ! dummy loop indices ISF
150	REAL(wp) :: znad
151	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: zts_top, zrhd ! hypothesys on isf density
152	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zrhdtop_isf ! density at bottom of ISF
153	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: ziceload ! density at bottom of ISF
154	!!
155	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
156	& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf
157	!!----------------------------------------------------------------------
158	!
159	REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient
160	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
161	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist' )
162	!
163	REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient
164	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
165	902 IF( ios > 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist' )
166	IF(lwm) WRITE ( numond, namdyn_hpg )
167	!
168	IF(lwp) THEN ! Control print
169	WRITE(numout,*)
170	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
171	WRITE(numout,*) '~~~~~~~~~~~~'
172	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
173	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
174	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
175	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
176	WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf
177	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
178	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
179	ENDIF
180	!
181	IF( ln_hpg_djc ) &
182	& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method', &
183	& ' currently disabled (bugs under investigation).' , &
184	& ' Please select either ln_hpg_sco or ln_hpg_prj instead' )
185	!
186	IF( .NOT.ln_linssh .AND. .NOT.(ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) &
187	& CALL ctl_stop('dyn_hpg_init : non-linear free surface requires either ', &
188	& ' the standard jacobian formulation hpg_sco or ' , &
189	& ' the pressure jacobian formulation hpg_prj' )
190	!
191	IF( ln_hpg_isf ) THEN
192	IF( .NOT. ln_isfcav ) CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' )
193	ELSE
194	IF( ln_isfcav ) CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' )
195	ENDIF
196	!
197	! ! Set nhpg from ln_hpg_... flags & consistency check
198	nhpg = np_ERROR
199	ioptio = 0
200	IF( ln_hpg_zco ) THEN ; nhpg = np_zco ; ioptio = ioptio +1 ; ENDIF
201	IF( ln_hpg_zps ) THEN ; nhpg = np_zps ; ioptio = ioptio +1 ; ENDIF
202	IF( ln_hpg_sco ) THEN ; nhpg = np_sco ; ioptio = ioptio +1 ; ENDIF
203	IF( ln_hpg_djc ) THEN ; nhpg = np_djc ; ioptio = ioptio +1 ; ENDIF
204	IF( ln_hpg_prj ) THEN ; nhpg = np_prj ; ioptio = ioptio +1 ; ENDIF
205	IF( ln_hpg_isf ) THEN ; nhpg = np_isf ; ioptio = ioptio +1 ; ENDIF
206	!
207	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
208	!
209	IF(lwp) THEN
210	WRITE(numout,*)
211	SELECT CASE( nhpg )
212	CASE( np_zco ) ; WRITE(numout,*) ' ==>>> z-coord. - full steps '
213	CASE( np_zps ) ; WRITE(numout,*) ' ==>>> z-coord. - partial steps (interpolation)'
214	CASE( np_sco ) ; WRITE(numout,*) ' ==>>> s-coord. (standard jacobian formulation)'
215	CASE( np_djc ) ; WRITE(numout,*) ' ==>>> s-coord. (Density Jacobian: Cubic polynomial)'
216	CASE( np_prj ) ; WRITE(numout,*) ' ==>>> s-coord. (Pressure Jacobian: Cubic polynomial)'
217	CASE( np_isf ) ; WRITE(numout,*) ' ==>>> s-coord. (standard jacobian formulation) for isf'
218	END SELECT
219	WRITE(numout,*)
220	ENDIF
221	!
222	END SUBROUTINE dyn_hpg_init
223
224
225	SUBROUTINE hpg_zco( kt, Kmm, puu, pvv, Krhs )
226	!!---------------------------------------------------------------------
227	!! * ROUTINE hpg_zco *
228	!!
229	!! ** Method : z-coordinate case, levels are horizontal surfaces.
230	!! The now hydrostatic pressure gradient at a given level, jk,
231	!! is computed by taking the vertical integral of the in-situ
232	!! density gradient along the model level from the suface to that
233	!! level: zhpi = grav .....
234	!! zhpj = grav .....
235	!! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)).
236	!! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi
237	!! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj
238	!!
239	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
240	!!----------------------------------------------------------------------
241	INTEGER , INTENT( in ) :: kt ! ocean time-step index
242	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
243	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
244	!
245	INTEGER :: ji, jj, jk ! dummy loop indices
246	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
247	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
248	!!----------------------------------------------------------------------
249	!
250	IF( kt == nit000 ) THEN
251	IF(lwp) WRITE(numout,*)
252	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
253	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
254	ENDIF
255
256	zcoef0 = - grav * 0.5_wp ! Local constant initialization
257
258	! Surface value
259	DO jj = 2, jpjm1
260	DO ji = fs_2, fs_jpim1 ! vector opt.
261	zcoef1 = zcoef0 * e3w(ji,jj,1,Kmm)
262	! hydrostatic pressure gradient
263	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
264	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
265	! add to the general momentum trend
266	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1)
267	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1)
268	END DO
269	END DO
270
271	!
272	! interior value (2=<jk=<jpkm1)
273	DO jk = 2, jpkm1
274	DO jj = 2, jpjm1
275	DO ji = fs_2, fs_jpim1 ! vector opt.
276	zcoef1 = zcoef0 * e3w(ji,jj,jk,Kmm)
277	! hydrostatic pressure gradient
278	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
279	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
280	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
281
282	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
283	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
284	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
285	! add to the general momentum trend
286	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk)
287	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk)
288	END DO
289	END DO
290	END DO
291	!
292	END SUBROUTINE hpg_zco
293
294
295	SUBROUTINE hpg_zps( kt, Kmm, puu, pvv, Krhs )
296	!!---------------------------------------------------------------------
297	!! * ROUTINE hpg_zps *
298	!!
299	!! ** Method : z-coordinate plus partial steps case. blahblah...
300	!!
301	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
302	!!----------------------------------------------------------------------
303	INTEGER , INTENT( in ) :: kt ! ocean time-step index
304	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
305	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
306	!!
307	INTEGER :: ji, jj, jk ! dummy loop indices
308	INTEGER :: iku, ikv ! temporary integers
309	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
310	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
311	REAL(wp), DIMENSION(jpi,jpj) :: zgtsu, zgtsv, zgru, zgrv
312	!!----------------------------------------------------------------------
313	!
314	IF( kt == nit000 ) THEN
315	IF(lwp) WRITE(numout,*)
316	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
317	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
318	ENDIF
319
320	! Partial steps: Compute NOW horizontal gradient of t, s, rd at the last ocean level
321	CALL zps_hde( kt, Kmm, jpts, ts(:,:,:,:,Kmm), zgtsu, zgtsv, rhd, zgru , zgrv )
322
323	! Local constant initialization
324	zcoef0 = - grav * 0.5_wp
325
326	! Surface value (also valid in partial step case)
327	DO jj = 2, jpjm1
328	DO ji = fs_2, fs_jpim1 ! vector opt.
329	zcoef1 = zcoef0 * e3w(ji,jj,1,Kmm)
330	! hydrostatic pressure gradient
331	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
332	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
333	! add to the general momentum trend
334	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1)
335	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1)
336	END DO
337	END DO
338
339	! interior value (2=<jk=<jpkm1)
340	DO jk = 2, jpkm1
341	DO jj = 2, jpjm1
342	DO ji = fs_2, fs_jpim1 ! vector opt.
343	zcoef1 = zcoef0 * e3w(ji,jj,jk,Kmm)
344	! hydrostatic pressure gradient
345	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
346	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
347	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
348
349	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
350	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
351	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
352	! add to the general momentum trend
353	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk)
354	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk)
355	END DO
356	END DO
357	END DO
358
359	! partial steps correction at the last level (use zgru & zgrv computed in zpshde.F90)
360	DO jj = 2, jpjm1
361	DO ji = 2, jpim1
362	iku = mbku(ji,jj)
363	ikv = mbkv(ji,jj)
364	zcoef2 = zcoef0 * MIN( e3w(ji,jj,iku,Kmm), e3w(ji+1,jj ,iku,Kmm) )
365	zcoef3 = zcoef0 * MIN( e3w(ji,jj,ikv,Kmm), e3w(ji ,jj+1,ikv,Kmm) )
366	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
367	puu (ji,jj,iku,Krhs) = puu(ji,jj,iku,Krhs) - zhpi(ji,jj,iku) ! subtract old value
368	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
369	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + zgru(ji,jj) ) * r1_e1u(ji,jj)
370	puu (ji,jj,iku,Krhs) = puu(ji,jj,iku,Krhs) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
371	ENDIF
372	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
373	pvv (ji,jj,ikv,Krhs) = pvv(ji,jj,ikv,Krhs) - zhpj(ji,jj,ikv) ! subtract old value
374	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
375	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + zgrv(ji,jj) ) * r1_e2v(ji,jj)
376	pvv (ji,jj,ikv,Krhs) = pvv(ji,jj,ikv,Krhs) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
377	ENDIF
378	END DO
379	END DO
380	!
381	END SUBROUTINE hpg_zps
382
383
384	SUBROUTINE hpg_sco( kt, Kmm, puu, pvv, Krhs )
385	!!---------------------------------------------------------------------
386	!! * ROUTINE hpg_sco *
387	!!
388	!! ** Method : s-coordinate case. Jacobian scheme.
389	!! The now hydrostatic pressure gradient at a given level, jk,
390	!! is computed by taking the vertical integral of the in-situ
391	!! density gradient along the model level from the suface to that
392	!! level. s-coordinates (ln_sco): a corrective term is added
393	!! to the horizontal pressure gradient :
394	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
395	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
396	!! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)).
397	!! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi
398	!! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj
399	!!
400	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
401	!!----------------------------------------------------------------------
402	INTEGER , INTENT( in ) :: kt ! ocean time-step index
403	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
404	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
405	!!
406	INTEGER :: ji, jj, jk, jii, jjj ! dummy loop indices
407	REAL(wp) :: zcoef0, zuap, zvap, znad, ztmp ! temporary scalars
408	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
409	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
410	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter
411	!!----------------------------------------------------------------------
412	!
413	IF( ln_wd_il ) ALLOCATE(zcpx(jpi,jpj), zcpy(jpi,jpj))
414	!
415	IF( kt == nit000 ) THEN
416	IF(lwp) WRITE(numout,*)
417	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
418	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
419	ENDIF
420	!
421	zcoef0 = - grav * 0.5_wp
422	IF ( ln_linssh ) THEN ; znad = 0._wp ! Fixed volume: density anomaly
423	ELSE ; znad = 1._wp ! Variable volume: density
424	ENDIF
425	!
426	IF( ln_wd_il ) THEN
427	DO jj = 2, jpjm1
428	DO ji = 2, jpim1
429	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
430	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
431	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) &
432	& > rn_wdmin1 + rn_wdmin2
433	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji+1,jj,Kmm) ) > 1.E-12 ) .AND. ( &
434	& MAX( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
435	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
436
437	IF(ll_tmp1) THEN
438	zcpx(ji,jj) = 1.0_wp
439	ELSE IF(ll_tmp2) THEN
440	! no worries about ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm) = 0, it won't happen ! here
441	zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
442	& / (ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm)) )
443	ELSE
444	zcpx(ji,jj) = 0._wp
445	END IF
446
447	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
448	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
449	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) &
450	& > rn_wdmin1 + rn_wdmin2
451	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. ( &
452	& MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
453	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
454
455	IF(ll_tmp1) THEN
456	zcpy(ji,jj) = 1.0_wp
457	ELSE IF(ll_tmp2) THEN
458	! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here
459	zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
460	& / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) )
461	ELSE
462	zcpy(ji,jj) = 0._wp
463	END IF
464	END DO
465	END DO
466	CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1., zcpy, 'V', 1. )
467	END IF
468
469	! Surface value
470	DO jj = 2, jpjm1
471	DO ji = fs_2, fs_jpim1 ! vector opt.
472	! hydrostatic pressure gradient along s-surfaces
473	zhpi(ji,jj,1) = zcoef0 * ( e3w(ji+1,jj ,1,Kmm) * ( znad + rhd(ji+1,jj ,1) ) &
474	& - e3w(ji ,jj ,1,Kmm) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e1u(ji,jj)
475	zhpj(ji,jj,1) = zcoef0 * ( e3w(ji ,jj+1,1,Kmm) * ( znad + rhd(ji ,jj+1,1) ) &
476	& - e3w(ji ,jj ,1,Kmm) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e2v(ji,jj)
477	! s-coordinate pressure gradient correction
478	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
479	& * ( gde3w(ji+1,jj,1) - gde3w(ji,jj,1) ) * r1_e1u(ji,jj)
480	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
481	& * ( gde3w(ji,jj+1,1) - gde3w(ji,jj,1) ) * r1_e2v(ji,jj)
482	!
483	IF( ln_wd_il ) THEN
484	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
485	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
486	zuap = zuap * zcpx(ji,jj)
487	zvap = zvap * zcpy(ji,jj)
488	ENDIF
489	!
490	! add to the general momentum trend
491	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1) + zuap
492	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1) + zvap
493	END DO
494	END DO
495
496	! interior value (2=<jk=<jpkm1)
497	DO jk = 2, jpkm1
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,jk) = zhpi(ji,jj,jk-1) + zcoef0 * r1_e1u(ji,jj) &
502	& * ( e3w(ji+1,jj,jk,Kmm) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) &
503	& - e3w(ji ,jj,jk,Kmm) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) )
504	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 * r1_e2v(ji,jj) &
505	& * ( e3w(ji,jj+1,jk,Kmm) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) &
506	& - e3w(ji,jj ,jk,Kmm) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) )
507	! s-coordinate pressure gradient correction
508	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
509	& * ( gde3w(ji+1,jj ,jk) - gde3w(ji,jj,jk) ) * r1_e1u(ji,jj)
510	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
511	& * ( gde3w(ji ,jj+1,jk) - gde3w(ji,jj,jk) ) * r1_e2v(ji,jj)
512	!
513	IF( ln_wd_il ) THEN
514	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
515	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * 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	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk) + zuap
522	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk) + zvap
523	END DO
524	END DO
525	END DO
526	!
527	IF( ln_wd_il ) DEALLOCATE( zcpx , zcpy )
528	!
529	END SUBROUTINE hpg_sco
530
531
532	SUBROUTINE hpg_isf( kt, Kmm, puu, pvv, Krhs )
533	!!---------------------------------------------------------------------
534	!! * ROUTINE hpg_isf *
535	!!
536	!! ** Method : s-coordinate case. Jacobian scheme.
537	!! The now hydrostatic pressure gradient at a given level, jk,
538	!! is computed by taking the vertical integral of the in-situ
539	!! density gradient along the model level from the suface to that
540	!! level. s-coordinates (ln_sco): a corrective term is added
541	!! to the horizontal pressure gradient :
542	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
543	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
544	!! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)).
545	!! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi
546	!! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj
547	!! iceload is added
548	!!
549	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
550	!!----------------------------------------------------------------------
551	INTEGER , INTENT( in ) :: kt ! ocean time-step index
552	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
553	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
554	!!
555	INTEGER :: ji, jj, jk, ikt, iktp1i, iktp1j ! dummy loop indices
556	REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars
557	REAL(wp), DIMENSION(jpi,jpj,jpk ) :: zhpi, zhpj
558	REAL(wp), DIMENSION(jpi,jpj,jpts) :: zts_top
559	REAL(wp), DIMENSION(jpi,jpj) :: zrhdtop_oce
560	!!----------------------------------------------------------------------
561	!
562	zcoef0 = - grav * 0.5_wp ! Local constant initialization
563	!
564	znad=1._wp ! To use density and not density anomaly
565	!
566	! ! iniitialised to 0. zhpi zhpi
567	zhpi(:,:,:) = 0._wp ; zhpj(:,:,:) = 0._wp
568
569	! compute rhd at the ice/oce interface (ocean side)
570	! usefull to reduce residual current in the test case ISOMIP with no melting
571	DO ji = 1, jpi
572	DO jj = 1, jpj
573	ikt = mikt(ji,jj)
574	zts_top(ji,jj,1) = ts(ji,jj,ikt,1,Kmm)
575	zts_top(ji,jj,2) = ts(ji,jj,ikt,2,Kmm)
576	END DO
577	END DO
578	CALL eos( zts_top, risfdep, zrhdtop_oce )
579
580	!==================================================================================
581	!===== Compute surface value =====================================================
582	!==================================================================================
583	DO jj = 2, jpjm1
584	DO ji = fs_2, fs_jpim1 ! vector opt.
585	ikt = mikt(ji,jj)
586	iktp1i = mikt(ji+1,jj)
587	iktp1j = mikt(ji,jj+1)
588	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
589	! we assume ISF is in isostatic equilibrium
590	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * e3w(ji+1,jj,iktp1i,Kmm) &
591	& * ( 2._wp * znad + rhd(ji+1,jj,iktp1i) + zrhdtop_oce(ji+1,jj) ) &
592	& - 0.5_wp * e3w(ji,jj,ikt,Kmm) &
593	& * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) &
594	& + ( risfload(ji+1,jj) - risfload(ji,jj)) )
595	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * e3w(ji,jj+1,iktp1j,Kmm) &
596	& * ( 2._wp * znad + rhd(ji,jj+1,iktp1j) + zrhdtop_oce(ji,jj+1) ) &
597	& - 0.5_wp * e3w(ji,jj,ikt,Kmm) &
598	& * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) &
599	& + ( risfload(ji,jj+1) - risfload(ji,jj)) )
600	! s-coordinate pressure gradient correction (=0 if z coordinate)
601	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
602	& * ( gde3w(ji+1,jj,1) - gde3w(ji,jj,1) ) * r1_e1u(ji,jj)
603	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
604	& * ( gde3w(ji,jj+1,1) - gde3w(ji,jj,1) ) * r1_e2v(ji,jj)
605	! add to the general momentum trend
606	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
607	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
608	END DO
609	END DO
610	!==================================================================================
611	!===== Compute interior value =====================================================
612	!==================================================================================
613	! interior value (2=<jk=<jpkm1)
614	DO jk = 2, jpkm1
615	DO jj = 2, jpjm1
616	DO ji = fs_2, fs_jpim1 ! vector opt.
617	! hydrostatic pressure gradient along s-surfaces
618	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
619	& * ( e3w(ji+1,jj,jk,Kmm) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2znad ) wmask(ji+1,jj,jk) &
620	& - e3w(ji ,jj,jk,Kmm) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2znad ) wmask(ji ,jj,jk) )
621	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
622	& * ( e3w(ji,jj+1,jk,Kmm) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2znad ) wmask(ji,jj+1,jk) &
623	& - e3w(ji,jj ,jk,Kmm) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2znad ) wmask(ji,jj ,jk) )
624	! s-coordinate pressure gradient correction
625	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
626	& * ( gde3w(ji+1,jj ,jk) - gde3w(ji,jj,jk) ) / e1u(ji,jj)
627	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
628	& * ( gde3w(ji ,jj+1,jk) - gde3w(ji,jj,jk) ) / e2v(ji,jj)
629	! add to the general momentum trend
630	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + (zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
631	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + (zhpj(ji,jj,jk) + zvap) * vmask(ji,jj,jk)
632	END DO
633	END DO
634	END DO
635	!
636	END SUBROUTINE hpg_isf
637
638
639	SUBROUTINE hpg_djc( kt, Kmm, puu, pvv, Krhs )
640	!!---------------------------------------------------------------------
641	!! * ROUTINE hpg_djc *
642	!!
643	!! ** Method : Density Jacobian with Cubic polynomial scheme
644	!!
645	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
646	!!----------------------------------------------------------------------
647	INTEGER , INTENT( in ) :: kt ! ocean time-step index
648	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
649	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
650	!!
651	INTEGER :: ji, jj, jk ! dummy loop indices
652	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
653	REAL(wp) :: z1_10, cffu, cffx ! " "
654	REAL(wp) :: z1_12, cffv, cffy ! " "
655	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
656	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
657	REAL(wp), DIMENSION(jpi,jpj,jpk) :: dzx, dzy, dzz, dzu, dzv, dzw
658	REAL(wp), DIMENSION(jpi,jpj,jpk) :: drhox, drhoy, drhoz, drhou, drhov, drhow
659	REAL(wp), DIMENSION(jpi,jpj,jpk) :: rho_i, rho_j, rho_k
660	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter
661	!!----------------------------------------------------------------------
662	!
663	IF( ln_wd_il ) THEN
664	ALLOCATE( zcpx(jpi,jpj) , zcpy(jpi,jpj) )
665	DO jj = 2, jpjm1
666	DO ji = 2, jpim1
667	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
668	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
669	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) &
670	& > rn_wdmin1 + rn_wdmin2
671	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji+1,jj,Kmm) ) > 1.E-12 ) .AND. ( &
672	& MAX( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
673	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
674	IF(ll_tmp1) THEN
675	zcpx(ji,jj) = 1.0_wp
676	ELSE IF(ll_tmp2) THEN
677	! no worries about ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm) = 0, it won't happen ! here
678	zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
679	& / (ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm)) )
680	ELSE
681	zcpx(ji,jj) = 0._wp
682	END IF
683
684	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
685	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
686	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) &
687	& > rn_wdmin1 + rn_wdmin2
688	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. ( &
689	& MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
690	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
691
692	IF(ll_tmp1) THEN
693	zcpy(ji,jj) = 1.0_wp
694	ELSE IF(ll_tmp2) THEN
695	! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here
696	zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
697	& / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) )
698	ELSE
699	zcpy(ji,jj) = 0._wp
700	END IF
701	END DO
702	END DO
703	CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1., zcpy, 'V', 1. )
704	END IF
705
706	IF( kt == nit000 ) THEN
707	IF(lwp) WRITE(numout,*)
708	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
709	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
710	ENDIF
711
712	! Local constant initialization
713	zcoef0 = - grav * 0.5_wp
714	z1_10 = 1._wp / 10._wp
715	z1_12 = 1._wp / 12._wp
716
717	!----------------------------------------------------------------------------------------
718	! compute and store in provisional arrays elementary vertical and horizontal differences
719	!----------------------------------------------------------------------------------------
720
721	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
722
723	DO jk = 2, jpkm1
724	DO jj = 2, jpjm1
725	DO ji = fs_2, fs_jpim1 ! vector opt.
726	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
727	dzz (ji,jj,jk) = gde3w(ji ,jj ,jk) - gde3w(ji,jj,jk-1)
728	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
729	dzx (ji,jj,jk) = gde3w(ji+1,jj ,jk) - gde3w(ji,jj,jk )
730	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
731	dzy (ji,jj,jk) = gde3w(ji ,jj+1,jk) - gde3w(ji,jj,jk )
732	END DO
733	END DO
734	END DO
735
736	!-------------------------------------------------------------------------
737	! compute harmonic averages using eq. 5.18
738	!-------------------------------------------------------------------------
739	zep = 1.e-15
740
741	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
742	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
743
744	DO jk = 2, jpkm1
745	DO jj = 2, jpjm1
746	DO ji = fs_2, fs_jpim1 ! vector opt.
747	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
748
749	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
750	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
751
752	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
753	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
754
755	IF( cffw > zep) THEN
756	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
757	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
758	ELSE
759	drhow(ji,jj,jk) = 0._wp
760	ENDIF
761
762	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
763	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
764
765	IF( cffu > zep ) THEN
766	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
767	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
768	ELSE
769	drhou(ji,jj,jk ) = 0._wp
770	ENDIF
771
772	IF( cffx > zep ) THEN
773	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
774	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
775	ELSE
776	dzu(ji,jj,jk) = 0._wp
777	ENDIF
778
779	IF( cffv > zep ) THEN
780	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
781	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
782	ELSE
783	drhov(ji,jj,jk) = 0._wp
784	ENDIF
785
786	IF( cffy > zep ) THEN
787	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
788	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
789	ELSE
790	dzv(ji,jj,jk) = 0._wp
791	ENDIF
792
793	END DO
794	END DO
795	END DO
796
797	!----------------------------------------------------------------------------------
798	! apply boundary conditions at top and bottom using 5.36-5.37
799	!----------------------------------------------------------------------------------
800	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
801	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
802	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
803
804	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
805	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
806	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
807
808
809	!--------------------------------------------------------------
810	! Upper half of top-most grid box, compute and store
811	!-------------------------------------------------------------
812
813	!!bug gm : e3w-gde3w = 0.5*e3w .... and gde3w(2)-gde3w(1)=e3w(2) .... to be verified
814	! true if gde3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
815
816	DO jj = 2, jpjm1
817	DO ji = fs_2, fs_jpim1 ! vector opt.
818	rho_k(ji,jj,1) = -grav * ( e3w(ji,jj,1,Kmm) - gde3w(ji,jj,1) ) &
819	& * ( rhd(ji,jj,1) &
820	& + 0.5_wp * ( rhd (ji,jj,2) - rhd (ji,jj,1) ) &
821	& * ( e3w (ji,jj,1,Kmm) - gde3w(ji,jj,1) ) &
822	& / ( gde3w(ji,jj,2) - gde3w(ji,jj,1) ) )
823	END DO
824	END DO
825
826	!!bug gm : here also, simplification is possible
827	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
828
829	DO jk = 2, jpkm1
830	DO jj = 2, jpjm1
831	DO ji = fs_2, fs_jpim1 ! vector opt.
832
833	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
834	& * ( gde3w(ji,jj,jk) - gde3w(ji,jj,jk-1) ) &
835	& - grav * z1_10 * ( &
836	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
837	& * ( gde3w(ji,jj,jk) - gde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
838	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
839	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
840	& )
841
842	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
843	& * ( gde3w(ji+1,jj,jk) - gde3w(ji,jj,jk) ) &
844	& - grav* z1_10 * ( &
845	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
846	& * ( gde3w(ji+1,jj,jk) - gde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
847	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
848	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
849	& )
850
851	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
852	& * ( gde3w(ji,jj+1,jk) - gde3w(ji,jj,jk) ) &
853	& - grav* z1_10 * ( &
854	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
855	& * ( gde3w(ji,jj+1,jk) - gde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
856	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
857	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
858	& )
859
860	END DO
861	END DO
862	END DO
863	CALL lbc_lnk_multi( 'dynhpg', rho_k, 'W', 1., rho_i, 'U', 1., rho_j, 'V', 1. )
864
865	! ---------------
866	! Surface value
867	! ---------------
868	DO jj = 2, jpjm1
869	DO ji = fs_2, fs_jpim1 ! vector opt.
870	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) * r1_e1u(ji,jj)
871	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) * r1_e2v(ji,jj)
872	IF( ln_wd_il ) THEN
873	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
874	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
875	ENDIF
876	! add to the general momentum trend
877	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1)
878	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1)
879	END DO
880	END DO
881
882	! ----------------
883	! interior value (2=<jk=<jpkm1)
884	! ----------------
885	DO jk = 2, jpkm1
886	DO jj = 2, jpjm1
887	DO ji = fs_2, fs_jpim1 ! vector opt.
888	! hydrostatic pressure gradient along s-surfaces
889	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
890	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
891	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) * r1_e1u(ji,jj)
892	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
893	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
894	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) * r1_e2v(ji,jj)
895	IF( ln_wd_il ) THEN
896	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
897	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
898	ENDIF
899	! add to the general momentum trend
900	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk)
901	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk)
902	END DO
903	END DO
904	END DO
905	!
906	IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy )
907	!
908	END SUBROUTINE hpg_djc
909
910
911	SUBROUTINE hpg_prj( kt, Kmm, puu, pvv, Krhs )
912	!!---------------------------------------------------------------------
913	!! * ROUTINE hpg_prj *
914	!!
915	!! ** Method : s-coordinate case.
916	!! A Pressure-Jacobian horizontal pressure gradient method
917	!! based on the constrained cubic-spline interpolation for
918	!! all vertical coordinate systems
919	!!
920	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
921	!!----------------------------------------------------------------------
922	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
923	INTEGER , INTENT( in ) :: kt ! ocean time-step index
924	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
925	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
926	!!
927	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
928	REAL(wp) :: zcoef0, znad ! local scalars
929	!
930	!! The local variables for the correction term
931	INTEGER :: jk1, jis, jid, jjs, jjd
932	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
933	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
934	REAL(wp) :: zrhdt1
935	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
936	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdept, zrhh
937	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
938	REAL(wp), DIMENSION(jpi,jpj) :: zsshu_n, zsshv_n
939	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter
940	!!----------------------------------------------------------------------
941	!
942	IF( kt == nit000 ) THEN
943	IF(lwp) WRITE(numout,*)
944	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
945	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
946	ENDIF
947
948	! Local constant initialization
949	zcoef0 = - grav
950	znad = 1._wp
951	IF( ln_linssh ) znad = 0._wp
952
953	IF( ln_wd_il ) THEN
954	ALLOCATE( zcpx(jpi,jpj) , zcpy(jpi,jpj) )
955	DO jj = 2, jpjm1
956	DO ji = 2, jpim1
957	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
958	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
959	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) &
960	& > rn_wdmin1 + rn_wdmin2
961	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji+1,jj,Kmm) ) > 1.E-12 ) .AND. ( &
962	& MAX( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
963	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
964
965	IF(ll_tmp1) THEN
966	zcpx(ji,jj) = 1.0_wp
967	ELSE IF(ll_tmp2) THEN
968	! no worries about ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm) = 0, it won't happen ! here
969	zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
970	& / (ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm)) )
971
972	zcpx(ji,jj) = max(min( zcpx(ji,jj) , 1.0_wp),0.0_wp)
973	ELSE
974	zcpx(ji,jj) = 0._wp
975	END IF
976
977	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
978	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
979	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) &
980	& > rn_wdmin1 + rn_wdmin2
981	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. ( &
982	& MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
983	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
984
985	IF(ll_tmp1) THEN
986	zcpy(ji,jj) = 1.0_wp
987	ELSE IF(ll_tmp2) THEN
988	! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here
989	zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
990	& / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) )
991	zcpy(ji,jj) = max(min( zcpy(ji,jj) , 1.0_wp),0.0_wp)
992
993	ELSE
994	zcpy(ji,jj) = 0._wp
995	ENDIF
996	END DO
997	END DO
998	CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1., zcpy, 'V', 1. )
999	ENDIF
1000
1001	! Clean 3-D work arrays
1002	zhpi(:,:,:) = 0._wp
1003	zrhh(:,:,:) = rhd(:,:,:)
1004
1005	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
1006	DO jj = 1, jpj
1007	DO ji = 1, jpi
1008	jk = mbkt(ji,jj)+1
1009	IF( jk <= 0 ) THEN ; zrhh(ji,jj, : ) = 0._wp
1010	ELSEIF( jk == 1 ) THEN ; zrhh(ji,jj,jk+1:jpk) = rhd(ji,jj,jk)
1011	ELSEIF( jk < jpkm1 ) THEN
1012	DO jkk = jk+1, jpk
1013	zrhh(ji,jj,jkk) = interp1(gde3w(ji,jj,jkk ), gde3w(ji,jj,jkk-1), &
1014	& gde3w(ji,jj,jkk-2), rhd (ji,jj,jkk-1), rhd(ji,jj,jkk-2))
1015	END DO
1016	ENDIF
1017	END DO
1018	END DO
1019
1020	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
1021	DO jj = 1, jpj
1022	DO ji = 1, jpi
1023	zdept(ji,jj,1) = 0.5_wp * e3w(ji,jj,1,Kmm) - ssh(ji,jj,Kmm) * znad
1024	END DO
1025	END DO
1026
1027	DO jk = 2, jpk
1028	DO jj = 1, jpj
1029	DO ji = 1, jpi
1030	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + e3w(ji,jj,jk,Kmm)
1031	END DO
1032	END DO
1033	END DO
1034
1035	fsp(:,:,:) = zrhh (:,:,:)
1036	xsp(:,:,:) = zdept(:,:,:)
1037
1038	! Construct the vertical density profile with the
1039	! constrained cubic spline interpolation
1040	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
1041	CALL cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
1042
1043	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
1044	DO jj = 2, jpj
1045	DO ji = 2, jpi
1046	zrhdt1 = zrhh(ji,jj,1) - interp3( zdept(ji,jj,1), asp(ji,jj,1), bsp(ji,jj,1), &
1047	& csp(ji,jj,1), dsp(ji,jj,1) ) * 0.25_wp * e3w(ji,jj,1,Kmm)
1048
1049	! assuming linear profile across the top half surface layer
1050	zhpi(ji,jj,1) = 0.5_wp * e3w(ji,jj,1,Kmm) * zrhdt1
1051	END DO
1052	END DO
1053
1054	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
1055	DO jk = 2, jpkm1
1056	DO jj = 2, jpj
1057	DO ji = 2, jpi
1058	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
1059	& integ_spline( zdept(ji,jj,jk-1), zdept(ji,jj,jk), &
1060	& asp (ji,jj,jk-1), bsp (ji,jj,jk-1), &
1061	& csp (ji,jj,jk-1), dsp (ji,jj,jk-1) )
1062	END DO
1063	END DO
1064	END DO
1065
1066	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
1067
1068	! Prepare zsshu_n and zsshv_n
1069	DO jj = 2, jpjm1
1070	DO ji = 2, jpim1
1071	!!gm BUG ? if it is ssh at u- & v-point then it should be:
1072	! zsshu_n(ji,jj) = (e1e2t(ji,jj) * ssh(ji,jj,Kmm) + e1e2t(ji+1,jj) * ssh(ji+1,jj,Kmm)) * &
1073	! & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
1074	! zsshv_n(ji,jj) = (e1e2t(ji,jj) * ssh(ji,jj,Kmm) + e1e2t(ji,jj+1) * ssh(ji,jj+1,Kmm)) * &
1075	! & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
1076	!!gm not this:
1077	zsshu_n(ji,jj) = (e1e2u(ji,jj) * ssh(ji,jj,Kmm) + e1e2u(ji+1, jj) * ssh(ji+1,jj,Kmm)) * &
1078	& r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
1079	zsshv_n(ji,jj) = (e1e2v(ji,jj) * ssh(ji,jj,Kmm) + e1e2v(ji+1, jj) * ssh(ji,jj+1,Kmm)) * &
1080	& r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
1081	END DO
1082	END DO
1083
1084	CALL lbc_lnk_multi ('dynhpg', zsshu_n, 'U', 1., zsshv_n, 'V', 1. )
1085
1086	DO jj = 2, jpjm1
1087	DO ji = 2, jpim1
1088	zu(ji,jj,1) = - ( e3u(ji,jj,1,Kmm) - zsshu_n(ji,jj) * znad)
1089	zv(ji,jj,1) = - ( e3v(ji,jj,1,Kmm) - zsshv_n(ji,jj) * znad)
1090	END DO
1091	END DO
1092
1093	DO jk = 2, jpkm1
1094	DO jj = 2, jpjm1
1095	DO ji = 2, jpim1
1096	zu(ji,jj,jk) = zu(ji,jj,jk-1) - e3u(ji,jj,jk,Kmm)
1097	zv(ji,jj,jk) = zv(ji,jj,jk-1) - e3v(ji,jj,jk,Kmm)
1098	END DO
1099	END DO
1100	END DO
1101
1102	DO jk = 1, jpkm1
1103	DO jj = 2, jpjm1
1104	DO ji = 2, jpim1
1105	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * e3u(ji,jj,jk,Kmm)
1106	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * e3v(ji,jj,jk,Kmm)
1107	END DO
1108	END DO
1109	END DO
1110
1111	DO jk = 1, jpkm1
1112	DO jj = 2, jpjm1
1113	DO ji = 2, jpim1
1114	zu(ji,jj,jk) = MIN( zu(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
1115	zu(ji,jj,jk) = MAX( zu(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
1116	zv(ji,jj,jk) = MIN( zv(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
1117	zv(ji,jj,jk) = MAX( zv(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
1118	END DO
1119	END DO
1120	END DO
1121
1122
1123	DO jk = 1, jpkm1
1124	DO jj = 2, jpjm1
1125	DO ji = 2, jpim1
1126	zpwes = 0._wp; zpwed = 0._wp
1127	zpnss = 0._wp; zpnsd = 0._wp
1128	zuijk = zu(ji,jj,jk)
1129	zvijk = zv(ji,jj,jk)
1130
1131	!!!!! for u equation
1132	IF( jk <= mbku(ji,jj) ) THEN
1133	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
1134	jis = ji + 1; jid = ji
1135	ELSE
1136	jis = ji; jid = ji +1
1137	ENDIF
1138
1139	! integrate the pressure on the shallow side
1140	jk1 = jk
1141	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
1142	IF( jk1 == mbku(ji,jj) ) THEN
1143	zuijk = -zdept(jis,jj,jk1)
1144	EXIT
1145	ENDIF
1146	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
1147	zpwes = zpwes + &
1148	integ_spline(zdept(jis,jj,jk1), zdeps, &
1149	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
1150	csp(jis,jj,jk1), dsp(jis,jj,jk1))
1151	jk1 = jk1 + 1
1152	END DO
1153
1154	! integrate the pressure on the deep side
1155	jk1 = jk
1156	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
1157	IF( jk1 == 1 ) THEN
1158	zdeps = zdept(jid,jj,1) + MIN(zuijk, ssh(jid,jj,Kmm)*znad)
1159	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
1160	bsp(jid,jj,1), csp(jid,jj,1), &
1161	dsp(jid,jj,1)) * zdeps
1162	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
1163	EXIT
1164	ENDIF
1165	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
1166	zpwed = zpwed + &
1167	integ_spline(zdeps, zdept(jid,jj,jk1), &
1168	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
1169	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
1170	jk1 = jk1 - 1
1171	END DO
1172
1173	! update the momentum trends in u direction
1174
1175	zdpdx1 = zcoef0 * r1_e1u(ji,jj) * ( zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk) )
1176	IF( .NOT.ln_linssh ) THEN
1177	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * &
1178	& ( REAL(jis-jid, wp) * (zpwes + zpwed) + (ssh(ji+1,jj,Kmm)-ssh(ji,jj,Kmm)) )
1179	ELSE
1180	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
1181	ENDIF
1182	IF( ln_wd_il ) THEN
1183	zdpdx1 = zdpdx1 * zcpx(ji,jj) * wdrampu(ji,jj)
1184	zdpdx2 = zdpdx2 * zcpx(ji,jj) * wdrampu(ji,jj)
1185	ENDIF
1186	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + (zdpdx1 + zdpdx2) * umask(ji,jj,jk)
1187	ENDIF
1188
1189	!!!!! for v equation
1190	IF( jk <= mbkv(ji,jj) ) THEN
1191	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
1192	jjs = jj + 1; jjd = jj
1193	ELSE
1194	jjs = jj ; jjd = jj + 1
1195	ENDIF
1196
1197	! integrate the pressure on the shallow side
1198	jk1 = jk
1199	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
1200	IF( jk1 == mbkv(ji,jj) ) THEN
1201	zvijk = -zdept(ji,jjs,jk1)
1202	EXIT
1203	ENDIF
1204	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
1205	zpnss = zpnss + &
1206	integ_spline(zdept(ji,jjs,jk1), zdeps, &
1207	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
1208	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
1209	jk1 = jk1 + 1
1210	END DO
1211
1212	! integrate the pressure on the deep side
1213	jk1 = jk
1214	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
1215	IF( jk1 == 1 ) THEN
1216	zdeps = zdept(ji,jjd,1) + MIN(zvijk, ssh(ji,jjd,Kmm)*znad)
1217	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
1218	bsp(ji,jjd,1), csp(ji,jjd,1), &
1219	dsp(ji,jjd,1) ) * zdeps
1220	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
1221	EXIT
1222	ENDIF
1223	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
1224	zpnsd = zpnsd + &
1225	integ_spline(zdeps, zdept(ji,jjd,jk1), &
1226	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
1227	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
1228	jk1 = jk1 - 1
1229	END DO
1230
1231
1232	! update the momentum trends in v direction
1233
1234	zdpdy1 = zcoef0 * r1_e2v(ji,jj) * ( zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk) )
1235	IF( .NOT.ln_linssh ) THEN
1236	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * &
1237	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (ssh(ji,jj+1,Kmm)-ssh(ji,jj,Kmm)) )
1238	ELSE
1239	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
1240	ENDIF
1241	IF( ln_wd_il ) THEN
1242	zdpdy1 = zdpdy1 * zcpy(ji,jj) * wdrampv(ji,jj)
1243	zdpdy2 = zdpdy2 * zcpy(ji,jj) * wdrampv(ji,jj)
1244	ENDIF
1245
1246	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + (zdpdy1 + zdpdy2) * vmask(ji,jj,jk)
1247	ENDIF
1248	!
1249	END DO
1250	END DO
1251	END DO
1252	!
1253	IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy )
1254	!
1255	END SUBROUTINE hpg_prj
1256
1257
1258	SUBROUTINE cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
1259	!!----------------------------------------------------------------------
1260	!! * ROUTINE cspline *
1261	!!
1262	!! ** Purpose : constrained cubic spline interpolation
1263	!!
1264	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
1265	!!
1266	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
1267	!!----------------------------------------------------------------------
1268	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: fsp, xsp ! value and coordinate
1269	REAL(wp), DIMENSION(:,:,:), INTENT( out) :: asp, bsp, csp, dsp ! coefficients of the interpoated function
1270	INTEGER , INTENT(in ) :: polynomial_type ! 1: cubic spline ; 2: Linear
1271	!
1272	INTEGER :: ji, jj, jk ! dummy loop indices
1273	INTEGER :: jpi, jpj, jpkm1
1274	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
1275	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
1276	REAL(wp) :: zdf(size(fsp,3))
1277	!!----------------------------------------------------------------------
1278	!
1279	!!gm WHAT !!!!! THIS IS VERY DANGEROUS !!!!!
1280	jpi = size(fsp,1)
1281	jpj = size(fsp,2)
1282	jpkm1 = MAX( 1, size(fsp,3) - 1 )
1283	!
1284	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
1285	DO ji = 1, jpi
1286	DO jj = 1, jpj
1287	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
1288	! DO jk = 2, jpkm1-1
1289	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
1290	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1291	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
1292	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
1293	!
1294	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
1295	!
1296	! IF(zdf1 * zdf2 <= 0._wp) THEN
1297	! zdf(jk) = 0._wp
1298	! ELSE
1299	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
1300	! ENDIF
1301	! END DO
1302
1303	!!Simply geometric average
1304	DO jk = 2, jpkm1-1
1305	zdf1 = (fsp(ji,jj,jk ) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk ) - xsp(ji,jj,jk-1))
1306	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk )) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk ))
1307
1308	IF(zdf1 * zdf2 <= 0._wp) THEN
1309	zdf(jk) = 0._wp
1310	ELSE
1311	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
1312	ENDIF
1313	END DO
1314
1315	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
1316	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
1317	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
1318	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - 0.5_wp * zdf(jpkm1 - 1)
1319
1320	DO jk = 1, jpkm1 - 1
1321	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1322	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
1323	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
1324	zddf1 = -2._wp * ztmp1 + ztmp2
1325	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
1326	zddf2 = 2._wp * ztmp1 - ztmp2
1327
1328	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
1329	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
1330	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
1331	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
1332	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
1333	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
1334	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
1335	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
1336	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
1337	END DO
1338	END DO
1339	END DO
1340
1341	ELSEIF ( polynomial_type == 2 ) THEN ! Linear
1342	DO ji = 1, jpi
1343	DO jj = 1, jpj
1344	DO jk = 1, jpkm1-1
1345	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1346	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
1347
1348	dsp(ji,jj,jk) = 0._wp
1349	csp(ji,jj,jk) = 0._wp
1350	bsp(ji,jj,jk) = ztmp1 / zdxtmp
1351	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
1352	END DO
1353	END DO
1354	END DO
1355	!
1356	ELSE
1357	CALL ctl_stop( 'invalid polynomial type in cspline' )
1358	ENDIF
1359	!
1360	END SUBROUTINE cspline
1361
1362
1363	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
1364	!!----------------------------------------------------------------------
1365	!! * ROUTINE interp1 *
1366	!!
1367	!! ** Purpose : 1-d linear interpolation
1368	!!
1369	!! ** Method : interpolation is straight forward
1370	!! extrapolation is also permitted (no value limit)
1371	!!----------------------------------------------------------------------
1372	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
1373	REAL(wp) :: f ! result of the interpolation (extrapolation)
1374	REAL(wp) :: zdeltx
1375	!!----------------------------------------------------------------------
1376	!
1377	zdeltx = xr - xl
1378	IF( abs(zdeltx) <= 10._wp * EPSILON(x) ) THEN
1379	f = 0.5_wp * (fl + fr)
1380	ELSE
1381	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
1382	ENDIF
1383	!
1384	END FUNCTION interp1
1385
1386
1387	FUNCTION interp2( x, a, b, c, d ) RESULT(f)
1388	!!----------------------------------------------------------------------
1389	!! * ROUTINE interp1 *
1390	!!
1391	!! ** Purpose : 1-d constrained cubic spline interpolation
1392	!!
1393	!! ** Method : cubic spline interpolation
1394	!!
1395	!!----------------------------------------------------------------------
1396	REAL(wp), INTENT(in) :: x, a, b, c, d
1397	REAL(wp) :: f ! value from the interpolation
1398	!!----------------------------------------------------------------------
1399	!
1400	f = a + x* ( b + x * ( c + d * x ) )
1401	!
1402	END FUNCTION interp2
1403
1404
1405	FUNCTION interp3( x, a, b, c, d ) RESULT(f)
1406	!!----------------------------------------------------------------------
1407	!! * ROUTINE interp1 *
1408	!!
1409	!! ** Purpose : Calculate the first order of derivative of
1410	!! a cubic spline function y=a+bx+cx^2+d*x^3
1411	!!
1412	!! ** Method : f=dy/dx=b+2cx+3dx^2
1413	!!
1414	!!----------------------------------------------------------------------
1415	REAL(wp), INTENT(in) :: x, a, b, c, d
1416	REAL(wp) :: f ! value from the interpolation
1417	!!----------------------------------------------------------------------
1418	!
1419	f = b + x * ( 2._wp * c + 3._wp * d * x)
1420	!
1421	END FUNCTION interp3
1422
1423
1424	FUNCTION integ_spline( xl, xr, a, b, c, d ) RESULT(f)
1425	!!----------------------------------------------------------------------
1426	!! * ROUTINE interp1 *
1427	!!
1428	!! ** Purpose : 1-d constrained cubic spline integration
1429	!!
1430	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
1431	!!
1432	!!----------------------------------------------------------------------
1433	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
1434	REAL(wp) :: za1, za2, za3
1435	REAL(wp) :: f ! integration result
1436	!!----------------------------------------------------------------------
1437	!
1438	za1 = 0.5_wp * b
1439	za2 = c / 3.0_wp
1440	za3 = 0.25_wp * d
1441	!
1442	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
1443	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
1444	!
1445	END FUNCTION integ_spline
1446
1447	!!======================================================================
1448	END MODULE dynhpg
1449

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