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dynhpg.F90 in NEMO/branches/2018/dev_r9838_ENHANCE04_RK3/src/OCE/DYN – NEMO

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source: NEMO/branches/2018/dev_r9838_ENHANCE04_RK3/src/OCE/DYN/dynhpg.F90 @ 10009

Last change on this file since 10009 was 10009, checked in by gm, 6 years ago
#1911 (ENHANCE-04): RK3 branch - step II.1 time-level dimension on ssh
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File size: 73.0 KB

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1	MODULE dynhpg
2	!!======================================================================
3	!! * MODULE dynhpg *
4	!! Ocean dynamics: hydrostatic pressure gradient trend
5	!!======================================================================
6	!! History : OPA ! 1987-09 (P. Andrich, M.-A. Foujols) hpg_zco: Original code
7	!! 5.0 ! 1991-11 (G. Madec)
8	!! 7.0 ! 1996-01 (G. Madec) hpg_sco: Original code for s-coordinates
9	!! 8.0 ! 1997-05 (G. Madec) split dynber into dynkeg and dynhpg
10	!! 8.5 ! 2002-07 (G. Madec) F90: Free form and module
11	!! 8.5 ! 2002-08 (A. Bozec) hpg_zps: Original code
12	!! NEMO 1.0 ! 2005-10 (A. Beckmann, B.W. An) various s-coordinate options
13	!! ! Original code for hpg_ctl, hpg_hel hpg_wdj, hpg_djc, hpg_rot
14	!! - ! 2005-11 (G. Madec) style & small optimisation
15	!! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase
16	!! 3.4 ! 2011-11 (H. Liu) hpg_prj: Original code for s-coordinates
17	!! ! (A. Coward) suppression of hel, wdj and rot options
18	!! 3.6 ! 2014-11 (P. Mathiot) hpg_isf: original code for ice shelf cavity
19	!!----------------------------------------------------------------------
20
21	!!----------------------------------------------------------------------
22	!! dyn_hpg : update the momentum trend with the now horizontal
23	!! gradient of the hydrostatic pressure
24	!! dyn_hpg_init : initialisation and control of options
25	!! hpg_zco : z-coordinate scheme
26	!! hpg_zps : z-coordinate plus partial steps (interpolation)
27	!! hpg_sco : s-coordinate (standard jacobian formulation)
28	!! hpg_isf : s-coordinate (sco formulation) adapted to ice shelf
29	!! hpg_djc : s-coordinate (Density Jacobian with Cubic polynomial)
30	!! hpg_prj : s-coordinate (Pressure Jacobian with Cubic polynomial)
31	!!----------------------------------------------------------------------
32	USE oce ! ocean dynamics and tracers
33	USE sbc_oce ! surface variable (only for the flag with ice shelf)
34	USE dom_oce ! ocean space and time domain
35	USE wet_dry ! wetting and drying
36	USE phycst ! physical constants
37	USE trd_oce ! trends: ocean variables
38	USE trddyn ! trend manager: dynamics
39	!jc USE zpshde ! partial step: hor. derivative (zps_hde routine)
40	!
41	USE in_out_manager ! I/O manager
42	USE prtctl ! Print control
43	USE lbclnk ! lateral boundary condition
44	USE lib_mpp ! MPP library
45	USE eosbn2 ! compute density
46	USE timing ! Timing
47	USE iom
48
49	IMPLICIT NONE
50	PRIVATE
51
52	PUBLIC dyn_hpg ! routine called by step module
53	PUBLIC dyn_hpg_init ! routine called by opa module
54
55	! !!* Namelist namdyn_hpg : hydrostatic pressure gradient
56	LOGICAL, PUBLIC :: ln_hpg_zco !: z-coordinate - full steps
57	LOGICAL, PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation)
58	LOGICAL, PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation)
59	LOGICAL, PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial)
60	LOGICAL, PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme)
61	LOGICAL, PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf
62
63	! !! Flag to control the type of hydrostatic pressure gradient
64	INTEGER, PARAMETER :: np_ERROR =-10 ! error in specification of lateral diffusion
65	INTEGER, PARAMETER :: np_zco = 0 ! z-coordinate - full steps
66	INTEGER, PARAMETER :: np_zps = 1 ! z-coordinate - partial steps (interpolation)
67	INTEGER, PARAMETER :: np_sco = 2 ! s-coordinate (standard jacobian formulation)
68	INTEGER, PARAMETER :: np_djc = 3 ! s-coordinate (Density Jacobian with Cubic polynomial)
69	INTEGER, PARAMETER :: np_prj = 4 ! s-coordinate (Pressure Jacobian scheme)
70	INTEGER, PARAMETER :: np_isf = 5 ! s-coordinate similar to sco modify for isf
71	!
72	INTEGER, PUBLIC :: nhpg !: type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM)
73
74	!! * Substitutions
75	# include "vectopt_loop_substitute.h90"
76	!!----------------------------------------------------------------------
77	!! NEMO/OCE 4.0 , NEMO Consortium (2018)
78	!! $Id$
79	!! Software governed by the CeCILL licence (./LICENSE)
80	!!----------------------------------------------------------------------
81	CONTAINS
82
83	SUBROUTINE dyn_hpg( kt )
84	!!---------------------------------------------------------------------
85	!! * ROUTINE dyn_hpg *
86	!!
87	!! ** Method : Call the hydrostatic pressure gradient routine
88	!! using the scheme defined in the namelist
89	!!
90	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
91	!! - send trends to trd_dyn for futher diagnostics (l_trddyn=T)
92	!!----------------------------------------------------------------------
93	INTEGER, INTENT(in) :: kt ! ocean time-step index
94	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: ztrdu, ztrdv
95	!!----------------------------------------------------------------------
96	!
97	IF( ln_timing ) CALL timing_start('dyn_hpg')
98	!
99	IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn)
100	ALLOCATE( ztrdu(jpi,jpj,jpk) , ztrdv(jpi,jpj,jpk) )
101	ztrdu(:,:,:) = ua(:,:,:)
102	ztrdv(:,:,:) = va(:,:,:)
103	ENDIF
104	!
105	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
106	CASE ( np_zco ) ; CALL hpg_zco ( kt ) ! z-coordinate
107	CASE ( np_zps ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation)
108	CASE ( np_sco ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation)
109	CASE ( np_djc ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial)
110	CASE ( np_prj ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme)
111	CASE ( np_isf ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf
112	END SELECT
113	!
114	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
115	ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:)
116	ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:)
117	CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt )
118	DEALLOCATE( ztrdu , ztrdv )
119	ENDIF
120	!
121	IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, &
122	& tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
123	!
124	IF( ln_timing ) CALL timing_stop('dyn_hpg')
125	!
126	END SUBROUTINE dyn_hpg
127
128
129	SUBROUTINE dyn_hpg_init
130	!!----------------------------------------------------------------------
131	!! * ROUTINE dyn_hpg_init *
132	!!
133	!! ** Purpose : initializations for the hydrostatic pressure gradient
134	!! computation and consistency control
135	!!
136	!! ** Action : Read the namelist namdyn_hpg and check the consistency
137	!! with the type of vertical coordinate used (zco, zps, sco)
138	!!----------------------------------------------------------------------
139	INTEGER :: ioptio = 0 ! temporary integer
140	INTEGER :: ios ! Local integer output status for namelist read
141	!!
142	INTEGER :: ji, jj, jk, ikt ! dummy loop indices ISF
143	REAL(wp) :: znad
144	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: zts_top, zrhd ! hypothesys on isf density
145	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zrhdtop_isf ! density at bottom of ISF
146	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: ziceload ! density at bottom of ISF
147	!!
148	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
149	& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf
150	!!----------------------------------------------------------------------
151	!
152	REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient
153	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
154	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp )
155	!
156	REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient
157	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
158	902 IF( ios > 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp )
159	IF(lwm) WRITE ( numond, namdyn_hpg )
160	!
161	IF(lwp) THEN ! Control print
162	WRITE(numout,*)
163	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
164	WRITE(numout,*) '~~~~~~~~~~~~'
165	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
166	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
167	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
168	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
169	WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf
170	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
171	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
172	ENDIF
173	!
174	IF( ln_hpg_djc ) &
175	& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method', &
176	& ' currently disabled (bugs under investigation).' , &
177	& ' Please select either ln_hpg_sco or ln_hpg_prj instead' )
178	!
179	IF( .NOT.ln_linssh .AND. .NOT.(ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) &
180	& CALL ctl_stop('dyn_hpg_init : non-linear free surface requires either ', &
181	& ' the standard jacobian formulation hpg_sco or ' , &
182	& ' the pressure jacobian formulation hpg_prj' )
183	!
184	IF( ln_hpg_isf ) THEN
185	IF( .NOT. ln_isfcav ) CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' )
186	ELSE
187	IF( ln_isfcav ) CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' )
188	ENDIF
189	!
190	! ! Set nhpg from ln_hpg_... flags & consistency check
191	nhpg = np_ERROR
192	ioptio = 0
193	IF( ln_hpg_zco ) THEN ; nhpg = np_zco ; ioptio = ioptio +1 ; ENDIF
194	IF( ln_hpg_zps ) THEN ; nhpg = np_zps ; ioptio = ioptio +1 ; ENDIF
195	IF( ln_hpg_sco ) THEN ; nhpg = np_sco ; ioptio = ioptio +1 ; ENDIF
196	IF( ln_hpg_djc ) THEN ; nhpg = np_djc ; ioptio = ioptio +1 ; ENDIF
197	IF( ln_hpg_prj ) THEN ; nhpg = np_prj ; ioptio = ioptio +1 ; ENDIF
198	IF( ln_hpg_isf ) THEN ; nhpg = np_isf ; ioptio = ioptio +1 ; ENDIF
199	!
200	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
201	!
202	IF(lwp) THEN
203	WRITE(numout,*)
204	SELECT CASE( nhpg )
205	CASE( np_zco ) ; WRITE(numout,*) ' ==>>> z-coord. - full steps '
206	CASE( np_zps ) ; WRITE(numout,*) ' ==>>> z-coord. - partial steps (interpolation)'
207	CASE( np_sco ) ; WRITE(numout,*) ' ==>>> s-coord. (standard jacobian formulation)'
208	CASE( np_djc ) ; WRITE(numout,*) ' ==>>> s-coord. (Density Jacobian: Cubic polynomial)'
209	CASE( np_prj ) ; WRITE(numout,*) ' ==>>> s-coord. (Pressure Jacobian: Cubic polynomial)'
210	CASE( np_isf ) ; WRITE(numout,*) ' ==>>> s-coord. (standard jacobian formulation) for isf'
211	END SELECT
212	WRITE(numout,*)
213	ENDIF
214	!
215	IF ( .NOT. ln_isfcav ) THEN !--- no ice shelf load
216	riceload(:,:) = 0._wp
217	!
218	ELSE !--- set an ice shelf load
219	!
220	IF(lwp) WRITE(numout,*)
221	IF(lwp) WRITE(numout,*) ' ice shelf case: set the ice-shelf load'
222	ALLOCATE( zts_top(jpi,jpj,jpts) , zrhd(jpi,jpj,jpk) , zrhdtop_isf(jpi,jpj) , ziceload(jpi,jpj) )
223	!
224	znad = 1._wp !- To use density and not density anomaly
225	!
226	! !- assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude)
227	zts_top(:,:,jp_tem) = -1.9_wp ; zts_top(:,:,jp_sal) = 34.4_wp
228	!
229	DO jk = 1, jpk !- compute density of the water displaced by the ice shelf
230	CALL eos( zts_top(:,:,:), gdept_n(:,:,jk), zrhd(:,:,jk) )
231	END DO
232	!
233	! !- compute rhd at the ice/oce interface (ice shelf side)
234	CALL eos( zts_top , risfdep, zrhdtop_isf )
235	!
236	! !- Surface value + ice shelf gradient
237	ziceload = 0._wp ! compute pressure due to ice shelf load
238	DO jj = 1, jpj ! (used to compute hpgi/j for all the level from 1 to miku/v)
239	DO ji = 1, jpi ! divided by 2 later
240	ikt = mikt(ji,jj)
241	ziceload(ji,jj) = ziceload(ji,jj) + (znad + zrhd(ji,jj,1) ) * e3w_n(ji,jj,1) * (1._wp - tmask(ji,jj,1))
242	DO jk = 2, ikt-1
243	ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhd(ji,jj,jk-1) + zrhd(ji,jj,jk)) * e3w_n(ji,jj,jk) &
244	& * (1._wp - tmask(ji,jj,jk))
245	END DO
246	IF (ikt >= 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + zrhd(ji,jj,ikt-1)) &
247	& * ( risfdep(ji,jj) - gdept_1d(ikt-1) )
248	END DO
249	END DO
250	riceload(:,:) = ziceload(:,:) ! need to be saved for diaar5
251	!
252	DEALLOCATE( zts_top , zrhd , zrhdtop_isf , ziceload )
253	ENDIF
254	!
255	END SUBROUTINE dyn_hpg_init
256
257
258	SUBROUTINE hpg_zco( kt )
259	!!---------------------------------------------------------------------
260	!! * ROUTINE hpg_zco *
261	!!
262	!! ** Method : z-coordinate case, levels are horizontal surfaces.
263	!! The now hydrostatic pressure gradient at a given level, jk,
264	!! is computed by taking the vertical integral of the in-situ
265	!! density gradient along the model level from the suface to that
266	!! level: zhpi = grav .....
267	!! zhpj = grav .....
268	!! add it to the general momentum trend (ua,va).
269	!! ua = ua - 1/e1u * zhpi
270	!! va = va - 1/e2v * zhpj
271	!!
272	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
273	!!----------------------------------------------------------------------
274	INTEGER, INTENT(in) :: kt ! ocean time-step index
275	!
276	INTEGER :: ji, jj, jk ! dummy loop indices
277	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
278	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
279	!!----------------------------------------------------------------------
280	!
281	IF( kt == nit000 ) THEN
282	IF(lwp) WRITE(numout,*)
283	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
284	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
285	ENDIF
286
287	zcoef0 = - grav * 0.5_wp ! Local constant initialization
288
289	! Surface value
290	DO jj = 2, jpjm1
291	DO ji = fs_2, fs_jpim1 ! vector opt.
292	zcoef1 = zcoef0 * e3w_n(ji,jj,1)
293	! hydrostatic pressure gradient
294	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
295	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
296	! add to the general momentum trend
297	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
298	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
299	END DO
300	END DO
301
302	!
303	! interior value (2=<jk=<jpkm1)
304	DO jk = 2, jpkm1
305	DO jj = 2, jpjm1
306	DO ji = fs_2, fs_jpim1 ! vector opt.
307	zcoef1 = zcoef0 * e3w_n(ji,jj,jk)
308	! hydrostatic pressure gradient
309	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
310	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
311	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
312
313	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
314	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
315	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
316	! add to the general momentum trend
317	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
318	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
319	END DO
320	END DO
321	END DO
322	!
323	END SUBROUTINE hpg_zco
324
325
326	SUBROUTINE hpg_zps( kt )
327	!!---------------------------------------------------------------------
328	!! * ROUTINE hpg_zps *
329	!!
330	!! ** Method : z-coordinate plus partial steps case. blahblah...
331	!!
332	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
333	!!----------------------------------------------------------------------
334	INTEGER, INTENT(in) :: kt ! ocean time-step index
335	!!
336	INTEGER :: ji, jj, jk ! dummy loop indices
337	INTEGER :: iku, ikv ! temporary integers
338	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
339	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
340	!!----------------------------------------------------------------------
341	!
342	IF( kt == nit000 ) THEN
343	IF(lwp) WRITE(numout,*)
344	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
345	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
346	ENDIF
347
348	! Partial steps: bottom before horizontal gradient of t, s, rd at the last ocean level
349	!jc CALL zps_hde ( kt, jpts, tsn, gtsu, gtsv, rhd, gru , grv )
350
351	! Local constant initialization
352	zcoef0 = - grav * 0.5_wp
353
354	! Surface value (also valid in partial step case)
355	DO jj = 2, jpjm1
356	DO ji = fs_2, fs_jpim1 ! vector opt.
357	zcoef1 = zcoef0 * e3w_n(ji,jj,1)
358	! hydrostatic pressure gradient
359	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
360	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
361	! add to the general momentum trend
362	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
363	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
364	END DO
365	END DO
366
367	! interior value (2=<jk=<jpkm1)
368	DO jk = 2, jpkm1
369	DO jj = 2, jpjm1
370	DO ji = fs_2, fs_jpim1 ! vector opt.
371	zcoef1 = zcoef0 * e3w_n(ji,jj,jk)
372	! hydrostatic pressure gradient
373	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
374	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
375	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
376
377	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
378	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
379	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
380	! add to the general momentum trend
381	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
382	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
383	END DO
384	END DO
385	END DO
386
387	! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
388	DO jj = 2, jpjm1
389	DO ji = 2, jpim1
390	iku = mbku(ji,jj)
391	ikv = mbkv(ji,jj)
392	zcoef2 = zcoef0 * MIN( e3w_n(ji,jj,iku), e3w_n(ji+1,jj ,iku) )
393	zcoef3 = zcoef0 * MIN( e3w_n(ji,jj,ikv), e3w_n(ji ,jj+1,ikv) )
394	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
395	ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value
396	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
397	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) * r1_e1u(ji,jj)
398	ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
399	ENDIF
400	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
401	va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value
402	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
403	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) * r1_e2v(ji,jj)
404	va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
405	ENDIF
406	END DO
407	END DO
408	!
409	END SUBROUTINE hpg_zps
410
411
412	SUBROUTINE hpg_sco( kt )
413	!!---------------------------------------------------------------------
414	!! * ROUTINE hpg_sco *
415	!!
416	!! ** Method : s-coordinate case. Jacobian scheme.
417	!! The now hydrostatic pressure gradient at a given level, jk,
418	!! is computed by taking the vertical integral of the in-situ
419	!! density gradient along the model level from the suface to that
420	!! level. s-coordinates (ln_sco): a corrective term is added
421	!! to the horizontal pressure gradient :
422	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
423	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
424	!! add it to the general momentum trend (ua,va).
425	!! ua = ua - 1/e1u * zhpi
426	!! va = va - 1/e2v * zhpj
427	!!
428	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
429	!!----------------------------------------------------------------------
430	INTEGER, INTENT(in) :: kt ! ocean time-step index
431	!!
432	INTEGER :: ji, jj, jk, jii, jjj ! dummy loop indices
433	REAL(wp) :: zcoef0, zuap, zvap, znad, ztmp ! temporary scalars
434	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
435	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
436	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter
437	!!----------------------------------------------------------------------
438	!
439	IF( ln_wd_il ) ALLOCATE(zcpx(jpi,jpj), zcpy(jpi,jpj))
440	!
441	IF( kt == nit000 ) THEN
442	IF(lwp) WRITE(numout,*)
443	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
444	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
445	ENDIF
446	!
447	zcoef0 = - grav * 0.5_wp
448	IF ( ln_linssh ) THEN ; znad = 0._wp ! Fixed volume: density anomaly
449	ELSE ; znad = 1._wp ! Variable volume: density
450	ENDIF
451	!
452	IF( ln_wd_il ) THEN
453	DO jj = 2, jpjm1
454	DO ji = 2, jpim1
455	ll_tmp1 = MIN( ssh(ji,jj,Nnn) , ssh(ji+1,jj,Nnn) ) &
456	& > MAX( - ht_0(ji,jj) , - ht_0(ji+1,jj) ) .AND. &
457	& MAX( ssh(ji,jj,Nnn) + ht_0(ji,jj) , ssh(ji+1,jj,Nnn) + ht_0(ji+1,jj) ) > rn_wdmin1 + rn_wdmin2
458	!
459	ll_tmp2 = ABS( ssh(ji,jj,Nnn) - ssh(ji+1,jj,Nnn) ) > 1.E-12 .AND. &
460	& MAX( ssh(ji,jj,Nnn) , ssh(ji+1,jj,Nnn) ) > MAX( ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2
461
462	IF(ll_tmp1) THEN
463	zcpx(ji,jj) = 1.0_wp
464	ELSE IF(ll_tmp2) THEN
465	! no worries about ssh(ji+1,jj,,Nnn) - ssh(ji,jj,Nnn) = 0, it won't happen ! here
466	zcpx(ji,jj) = ABS( ( ssh(ji+1,jj,Nnn) + ht_0(ji+1,jj) - ssh(ji,jj,Nnn) - ht_0(ji,jj) ) &
467	& / ( ssh(ji+1,jj,Nnn) - ssh(ji,jj,Nnn) ) )
468	ELSE
469	zcpx(ji,jj) = 0._wp
470	END IF
471
472	ll_tmp1 = MIN( ssh (ji,jj,Nnn) , ssh (ji,jj+1,Nnn) ) &
473	& > MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
474	& MAX( ssh(ji,jj,Nnn) + ht_0(ji,jj), ssh (ji,jj+1,Nnn) + ht_0(ji,jj+1) ) &
475	& > rn_wdmin1 + rn_wdmin2
476	ll_tmp2 = ( ABS( ssh (ji,jj,Nnn) - ssh (ji,jj+1,Nnn) ) > 1.E-12 ) .AND. &
477	& ( MAX( ssh (ji,jj,Nnn) , ssh (ji,jj+1,Nnn) ) > &
478	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
479
480	IF(ll_tmp1) THEN
481	zcpy(ji,jj) = 1.0_wp
482	ELSE IF(ll_tmp2) THEN
483	! no worries about ssh(ji,jj+1,Nnn) - ssh(ji,jj ,Nnn) = 0, it won't happen ! here
484	zcpy(ji,jj) = ABS( ( ssh(ji,jj+1,Nnn) + ht_0(ji,jj+1) - ssh(ji,jj,Nnn) - ht_0(ji,jj) ) &
485	& / ( ssh(ji,jj+1,Nnn) - ssh(ji,jj,Nnn) ) )
486	ELSE
487	zcpy(ji,jj) = 0._wp
488	END IF
489	END DO
490	END DO
491	CALL lbc_lnk_multi( zcpx, 'U', 1., zcpy, 'V', 1. )
492	END IF
493
494	! Surface value
495	DO jj = 2, jpjm1
496	DO ji = fs_2, fs_jpim1 ! vector opt.
497	! hydrostatic pressure gradient along s-surfaces
498	zhpi(ji,jj,1) = zcoef0 * ( e3w_n(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) &
499	& - e3w_n(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e1u(ji,jj)
500	zhpj(ji,jj,1) = zcoef0 * ( e3w_n(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) &
501	& - e3w_n(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e2v(ji,jj)
502	! s-coordinate pressure gradient correction
503	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
504	& * ( gde3w_n(ji+1,jj,1) - gde3w_n(ji,jj,1) ) * r1_e1u(ji,jj)
505	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
506	& * ( gde3w_n(ji,jj+1,1) - gde3w_n(ji,jj,1) ) * r1_e2v(ji,jj)
507	!
508	IF( ln_wd_il ) THEN
509	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
510	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
511	zuap = zuap * zcpx(ji,jj)
512	zvap = zvap * zcpy(ji,jj)
513	ENDIF
514	!
515	! add to the general momentum trend
516	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap
517	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap
518	END DO
519	END DO
520
521	! interior value (2=<jk=<jpkm1)
522	DO jk = 2, jpkm1
523	DO jj = 2, jpjm1
524	DO ji = fs_2, fs_jpim1 ! vector opt.
525	! hydrostatic pressure gradient along s-surfaces
526	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 * r1_e1u(ji,jj) &
527	& * ( e3w_n(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) &
528	& - e3w_n(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) )
529	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 * r1_e2v(ji,jj) &
530	& * ( e3w_n(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) &
531	& - e3w_n(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) )
532	! s-coordinate pressure gradient correction
533	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
534	& * ( gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk) ) * r1_e1u(ji,jj)
535	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
536	& * ( gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk) ) * r1_e2v(ji,jj)
537	!
538	IF( ln_wd_il ) THEN
539	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
540	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
541	zuap = zuap * zcpx(ji,jj)
542	zvap = zvap * zcpy(ji,jj)
543	ENDIF
544	!
545	! add to the general momentum trend
546	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap
547	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap
548	END DO
549	END DO
550	END DO
551	!
552	IF( ln_wd_il ) DEALLOCATE( zcpx , zcpy )
553	!
554	END SUBROUTINE hpg_sco
555
556
557	SUBROUTINE hpg_isf( kt )
558	!!---------------------------------------------------------------------
559	!! * ROUTINE hpg_isf *
560	!!
561	!! ** Method : s-coordinate case. Jacobian scheme.
562	!! The now hydrostatic pressure gradient at a given level, jk,
563	!! is computed by taking the vertical integral of the in-situ
564	!! density gradient along the model level from the suface to that
565	!! level. s-coordinates (ln_sco): a corrective term is added
566	!! to the horizontal pressure gradient :
567	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
568	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
569	!! add it to the general momentum trend (ua,va).
570	!! ua = ua - 1/e1u * zhpi
571	!! va = va - 1/e2v * zhpj
572	!! iceload is added and partial cell case are added to the top and bottom
573	!!
574	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
575	!!----------------------------------------------------------------------
576	INTEGER, INTENT(in) :: kt ! ocean time-step index
577	!!
578	INTEGER :: ji, jj, jk, ikt, iktp1i, iktp1j ! dummy loop indices
579	REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars
580	REAL(wp), DIMENSION(jpi,jpj,jpk ) :: zhpi, zhpj
581	REAL(wp), DIMENSION(jpi,jpj,jpts) :: zts_top
582	REAL(wp), DIMENSION(jpi,jpj) :: zrhdtop_oce
583	!!----------------------------------------------------------------------
584	!
585	zcoef0 = - grav * 0.5_wp ! Local constant initialization
586	!
587	znad=1._wp ! To use density and not density anomaly
588	!
589	! ! iniitialised to 0. zhpi zhpi
590	zhpi(:,:,:) = 0._wp ; zhpj(:,:,:) = 0._wp
591
592	! compute rhd at the ice/oce interface (ocean side)
593	! usefull to reduce residual current in the test case ISOMIP with no melting
594	DO ji = 1, jpi
595	DO jj = 1, jpj
596	ikt = mikt(ji,jj)
597	zts_top(ji,jj,1) = tsn(ji,jj,ikt,1)
598	zts_top(ji,jj,2) = tsn(ji,jj,ikt,2)
599	END DO
600	END DO
601	CALL eos( zts_top, risfdep, zrhdtop_oce )
602
603	!==================================================================================
604	!===== Compute surface value =====================================================
605	!==================================================================================
606	DO jj = 2, jpjm1
607	DO ji = fs_2, fs_jpim1 ! vector opt.
608	ikt = mikt(ji,jj)
609	iktp1i = mikt(ji+1,jj)
610	iktp1j = mikt(ji,jj+1)
611	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
612	! we assume ISF is in isostatic equilibrium
613	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * e3w_n(ji+1,jj,iktp1i) &
614	& * ( 2._wp * znad + rhd(ji+1,jj,iktp1i) + zrhdtop_oce(ji+1,jj) ) &
615	& - 0.5_wp * e3w_n(ji,jj,ikt) &
616	& * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) &
617	& + ( riceload(ji+1,jj) - riceload(ji,jj)) )
618	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * e3w_n(ji,jj+1,iktp1j) &
619	& * ( 2._wp * znad + rhd(ji,jj+1,iktp1j) + zrhdtop_oce(ji,jj+1) ) &
620	& - 0.5_wp * e3w_n(ji,jj,ikt) &
621	& * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) &
622	& + ( riceload(ji,jj+1) - riceload(ji,jj)) )
623	! s-coordinate pressure gradient correction (=0 if z coordinate)
624	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
625	& * ( gde3w_n(ji+1,jj,1) - gde3w_n(ji,jj,1) ) * r1_e1u(ji,jj)
626	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
627	& * ( gde3w_n(ji,jj+1,1) - gde3w_n(ji,jj,1) ) * r1_e2v(ji,jj)
628	! add to the general momentum trend
629	ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
630	va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
631	END DO
632	END DO
633	!==================================================================================
634	!===== Compute interior value =====================================================
635	!==================================================================================
636	! interior value (2=<jk=<jpkm1)
637	DO jk = 2, jpkm1
638	DO jj = 2, jpjm1
639	DO ji = fs_2, fs_jpim1 ! vector opt.
640	! hydrostatic pressure gradient along s-surfaces
641	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
642	& * ( e3w_n(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2znad ) wmask(ji+1,jj,jk) &
643	& - e3w_n(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2znad ) wmask(ji ,jj,jk) )
644	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
645	& * ( e3w_n(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2znad ) wmask(ji,jj+1,jk) &
646	& - e3w_n(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2znad ) wmask(ji,jj ,jk) )
647	! s-coordinate pressure gradient correction
648	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
649	& * ( gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk) ) / e1u(ji,jj)
650	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
651	& * ( gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk) ) / e2v(ji,jj)
652	! add to the general momentum trend
653	ua(ji,jj,jk) = ua(ji,jj,jk) + (zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
654	va(ji,jj,jk) = va(ji,jj,jk) + (zhpj(ji,jj,jk) + zvap) * vmask(ji,jj,jk)
655	END DO
656	END DO
657	END DO
658	!
659	END SUBROUTINE hpg_isf
660
661
662	SUBROUTINE hpg_djc( kt )
663	!!---------------------------------------------------------------------
664	!! * ROUTINE hpg_djc *
665	!!
666	!! ** Method : Density Jacobian with Cubic polynomial scheme
667	!!
668	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
669	!!----------------------------------------------------------------------
670	INTEGER, INTENT(in) :: kt ! ocean time-step index
671	!!
672	INTEGER :: ji, jj, jk ! dummy loop indices
673	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
674	REAL(wp) :: z1_10, cffu, cffx ! " "
675	REAL(wp) :: z1_12, cffv, cffy ! " "
676	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
677	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
678	REAL(wp), DIMENSION(jpi,jpj,jpk) :: dzx, dzy, dzz, dzu, dzv, dzw
679	REAL(wp), DIMENSION(jpi,jpj,jpk) :: drhox, drhoy, drhoz, drhou, drhov, drhow
680	REAL(wp), DIMENSION(jpi,jpj,jpk) :: rho_i, rho_j, rho_k
681	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter
682	!!----------------------------------------------------------------------
683	!
684	IF( ln_wd_il ) THEN
685	ALLOCATE( zcpx(jpi,jpj) , zcpy(jpi,jpj) )
686	DO jj = 2, jpjm1
687	DO ji = 2, jpim1
688	ll_tmp1 = MIN( ssh (ji,jj,Nnn) , ssh (ji+1,jj,Nnn) ) &
689	& > MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
690	& MAX( ssh (ji,jj,Nnn) + ht_0(ji,jj), ssh (ji+1,jj,Nnn) + ht_0(ji+1,jj) ) &
691	& > rn_wdmin1 + rn_wdmin2
692	ll_tmp2 = ( ABS( ssh (ji,jj,Nnn) - ssh (ji+1,jj,Nnn) ) > 1.E-12 ) .AND. ( &
693	& MAX( ssh (ji,jj,Nnn) , ssh (ji+1,jj,Nnn) ) > &
694	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
695	IF(ll_tmp1) THEN
696	zcpx(ji,jj) = 1.0_wp
697	ELSE IF(ll_tmp2) THEN
698	! no worries about ssh(ji+1,jj,Nnn) - ssh(ji ,jj,Nnn) = 0, it won't happen ! here
699	zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Nnn) + ht_0(ji+1,jj) - ssh(ji,jj,Nnn) - ht_0(ji,jj) ) &
700	& / (ssh(ji+1,jj,Nnn) - ssh(ji,jj,Nnn) ) )
701	ELSE
702	zcpx(ji,jj) = 0._wp
703	END IF
704
705	ll_tmp1 = MIN( ssh (ji,jj,Nnn) , ssh (ji,jj+1,Nnn) ) > &
706	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
707	& MAX( ssh (ji,jj,Nnn) + ht_0(ji,jj), ssh (ji,jj+1,Nnn) + ht_0(ji,jj+1) ) &
708	& > rn_wdmin1 + rn_wdmin2
709	ll_tmp2 = ( ABS( ssh (ji,jj,Nnn) - ssh (ji,jj+1,Nnn) ) > 1.E-12 ) .AND. ( &
710	& MAX( ssh (ji,jj,Nnn) , ssh (ji,jj+1,Nnn) ) > &
711	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
712
713	IF(ll_tmp1) THEN
714	zcpy(ji,jj) = 1.0_wp
715	ELSE IF(ll_tmp2) THEN
716	! no worries about ssh(ji,jj+1,Nnn) - ssh(ji,jj,Nnn) = 0, it won't happen ! here
717	zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Nnn) + ht_0(ji,jj+1) - ssh(ji,jj,Nnn) - ht_0(ji,jj) ) &
718	& / (ssh(ji,jj+1,Nnn) - ssh(ji,jj,Nnn) ) )
719	ELSE
720	zcpy(ji,jj) = 0._wp
721	END IF
722	END DO
723	END DO
724	CALL lbc_lnk_multi( zcpx, 'U', 1., zcpy, 'V', 1. )
725	END IF
726
727	IF( kt == nit000 ) THEN
728	IF(lwp) WRITE(numout,*)
729	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
730	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
731	ENDIF
732
733	! Local constant initialization
734	zcoef0 = - grav * 0.5_wp
735	z1_10 = 1._wp / 10._wp
736	z1_12 = 1._wp / 12._wp
737
738	!----------------------------------------------------------------------------------------
739	! compute and store in provisional arrays elementary vertical and horizontal differences
740	!----------------------------------------------------------------------------------------
741
742	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
743
744	DO jk = 2, jpkm1
745	DO jj = 2, jpjm1
746	DO ji = fs_2, fs_jpim1 ! vector opt.
747	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
748	dzz (ji,jj,jk) = gde3w_n(ji ,jj ,jk) - gde3w_n(ji,jj,jk-1)
749	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
750	dzx (ji,jj,jk) = gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk )
751	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
752	dzy (ji,jj,jk) = gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk )
753	END DO
754	END DO
755	END DO
756
757	!-------------------------------------------------------------------------
758	! compute harmonic averages using eq. 5.18
759	!-------------------------------------------------------------------------
760	zep = 1.e-15
761
762	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
763	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
764
765	DO jk = 2, jpkm1
766	DO jj = 2, jpjm1
767	DO ji = fs_2, fs_jpim1 ! vector opt.
768	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
769
770	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
771	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
772
773	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
774	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
775
776	IF( cffw > zep) THEN
777	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
778	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
779	ELSE
780	drhow(ji,jj,jk) = 0._wp
781	ENDIF
782
783	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
784	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
785
786	IF( cffu > zep ) THEN
787	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
788	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
789	ELSE
790	drhou(ji,jj,jk ) = 0._wp
791	ENDIF
792
793	IF( cffx > zep ) THEN
794	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
795	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
796	ELSE
797	dzu(ji,jj,jk) = 0._wp
798	ENDIF
799
800	IF( cffv > zep ) THEN
801	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
802	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
803	ELSE
804	drhov(ji,jj,jk) = 0._wp
805	ENDIF
806
807	IF( cffy > zep ) THEN
808	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
809	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
810	ELSE
811	dzv(ji,jj,jk) = 0._wp
812	ENDIF
813
814	END DO
815	END DO
816	END DO
817
818	!----------------------------------------------------------------------------------
819	! apply boundary conditions at top and bottom using 5.36-5.37
820	!----------------------------------------------------------------------------------
821	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
822	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
823	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
824
825	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
826	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
827	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
828
829
830	!--------------------------------------------------------------
831	! Upper half of top-most grid box, compute and store
832	!-------------------------------------------------------------
833
834	!!bug gm : e3w-gde3w = 0.5*e3w .... and gde3w(2)-gde3w(1)=e3w(2) .... to be verified
835	! true if gde3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
836
837	DO jj = 2, jpjm1
838	DO ji = fs_2, fs_jpim1 ! vector opt.
839	rho_k(ji,jj,1) = -grav * ( e3w_n(ji,jj,1) - gde3w_n(ji,jj,1) ) &
840	& * ( rhd(ji,jj,1) &
841	& + 0.5_wp * ( rhd (ji,jj,2) - rhd (ji,jj,1) ) &
842	& * ( e3w_n (ji,jj,1) - gde3w_n(ji,jj,1) ) &
843	& / ( gde3w_n(ji,jj,2) - gde3w_n(ji,jj,1) ) )
844	END DO
845	END DO
846
847	!!bug gm : here also, simplification is possible
848	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
849
850	DO jk = 2, jpkm1
851	DO jj = 2, jpjm1
852	DO ji = fs_2, fs_jpim1 ! vector opt.
853
854	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
855	& * ( gde3w_n(ji,jj,jk) - gde3w_n(ji,jj,jk-1) ) &
856	& - grav * z1_10 * ( &
857	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
858	& * ( gde3w_n(ji,jj,jk) - gde3w_n(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
859	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
860	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
861	& )
862
863	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
864	& * ( gde3w_n(ji+1,jj,jk) - gde3w_n(ji,jj,jk) ) &
865	& - grav* z1_10 * ( &
866	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
867	& * ( gde3w_n(ji+1,jj,jk) - gde3w_n(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
868	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
869	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
870	& )
871
872	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
873	& * ( gde3w_n(ji,jj+1,jk) - gde3w_n(ji,jj,jk) ) &
874	& - grav* z1_10 * ( &
875	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
876	& * ( gde3w_n(ji,jj+1,jk) - gde3w_n(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
877	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
878	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
879	& )
880
881	END DO
882	END DO
883	END DO
884	CALL lbc_lnk_multi( rho_k, 'W', 1., rho_i, 'U', 1., rho_j, 'V', 1. )
885
886	! ---------------
887	! Surface value
888	! ---------------
889	DO jj = 2, jpjm1
890	DO ji = fs_2, fs_jpim1 ! vector opt.
891	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) * r1_e1u(ji,jj)
892	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) * r1_e2v(ji,jj)
893	IF( ln_wd_il ) THEN
894	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
895	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
896	ENDIF
897	! add to the general momentum trend
898	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
899	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
900	END DO
901	END DO
902
903	! ----------------
904	! interior value (2=<jk=<jpkm1)
905	! ----------------
906	DO jk = 2, jpkm1
907	DO jj = 2, jpjm1
908	DO ji = fs_2, fs_jpim1 ! vector opt.
909	! hydrostatic pressure gradient along s-surfaces
910	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
911	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
912	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) * r1_e1u(ji,jj)
913	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
914	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
915	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) * r1_e2v(ji,jj)
916	IF( ln_wd_il ) THEN
917	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
918	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
919	ENDIF
920	! add to the general momentum trend
921	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
922	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
923	END DO
924	END DO
925	END DO
926	!
927	IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy )
928	!
929	END SUBROUTINE hpg_djc
930
931
932	SUBROUTINE hpg_prj( kt )
933	!!---------------------------------------------------------------------
934	!! * ROUTINE hpg_prj *
935	!!
936	!! ** Method : s-coordinate case.
937	!! A Pressure-Jacobian horizontal pressure gradient method
938	!! based on the constrained cubic-spline interpolation for
939	!! all vertical coordinate systems
940	!!
941	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
942	!!----------------------------------------------------------------------
943	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
944	INTEGER, INTENT(in) :: kt ! ocean time-step index
945	!!
946	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
947	REAL(wp) :: zcoef0, znad ! local scalars
948	!
949	!! The local variables for the correction term
950	INTEGER :: jk1, jis, jid, jjs, jjd
951	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
952	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
953	REAL(wp) :: zrhdt1
954	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
955	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdept, zrhh
956	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
957	REAL(wp), DIMENSION(jpi,jpj) :: zsshu_n, zsshv_n
958	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter
959	!!----------------------------------------------------------------------
960	!
961	IF( kt == nit000 ) THEN
962	IF(lwp) WRITE(numout,*)
963	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
964	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
965	ENDIF
966
967	! Local constant initialization
968	zcoef0 = - grav
969	znad = 1._wp
970	IF( ln_linssh ) znad = 0._wp
971
972	IF( ln_wd_il ) THEN
973	ALLOCATE( zcpx(jpi,jpj) , zcpy(jpi,jpj) )
974	DO jj = 2, jpjm1
975	DO ji = 2, jpim1
976	ll_tmp1 = MIN( ssh (ji,jj,Nnn) , ssh(ji+1,jj,Nnn) ) > &
977	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
978	& MAX( ssh(ji,jj,Nnn) + ht_0(ji,jj), ssh(ji+1,jj,Nnn) + ht_0(ji+1,jj) ) &
979	& > rn_wdmin1 + rn_wdmin2
980	ll_tmp2 = ( ABS( ssh(ji,jj,Nnn) - ssh (ji+1,jj,Nnn) ) > 1.E-12 ) .AND. ( &
981	& MAX( ssh(ji,jj,Nnn) , ssh (ji+1,jj,Nnn) ) > &
982	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
983
984	IF(ll_tmp1) THEN
985	zcpx(ji,jj) = 1.0_wp
986	ELSE IF(ll_tmp2) THEN
987	! no worries about ssh(ji+1,jj,Nnn) - ssh(ji,jj,Nnn) = 0, it won't happen ! here
988	zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Nnn) + ht_0(ji+1,jj) - ssh(ji,jj,Nnn) - ht_0(ji,jj) ) &
989	& / (ssh(ji+1,jj,Nnn) - ssh(ji,jj,Nnn) ) )
990
991	zcpx(ji,jj) = max(min( zcpx(ji,jj) , 1.0_wp),0.0_wp)
992	ELSE
993	zcpx(ji,jj) = 0._wp
994	END IF
995
996	ll_tmp1 = MIN( ssh (ji,jj,Nnn) , ssh(ji,jj+1,Nnn) ) > &
997	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
998	& MAX( ssh (ji,jj,Nnn) + ht_0(ji,jj), ssh(ji,jj+1,Nnn) + ht_0(ji,jj+1) ) &
999	& > rn_wdmin1 + rn_wdmin2
1000	ll_tmp2 = ( ABS( ssh (ji,jj,Nnn) - ssh (ji,jj+1,Nnn) ) > 1.E-12 ) .AND. ( &
1001	& MAX( ssh (ji,jj,Nnn) , ssh (ji,jj+1,Nnn) ) > &
1002	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
1003
1004	IF(ll_tmp1) THEN
1005	zcpy(ji,jj) = 1.0_wp
1006	ELSE IF(ll_tmp2) THEN
1007	! no worries about ssh(ji,jj+1,Nnn) - ssh(ji,jj,Nnn) = 0, it won't happen ! here
1008	zcpy(ji,jj) = ABS( ( ssh(ji,jj+1,Nnn) + ht_0(ji,jj+1) - ssh(ji,jj,Nnn) - ht_0(ji,jj)) &
1009	& / ( ssh(ji,jj+1,Nnn) - ssh(ji,jj,Nnn) ) )
1010	zcpy(ji,jj) = max(min( zcpy(ji,jj) , 1.0_wp),0.0_wp)
1011
1012	ELSE
1013	zcpy(ji,jj) = 0._wp
1014	ENDIF
1015	END DO
1016	END DO
1017	CALL lbc_lnk_multi( zcpx, 'U', 1., zcpy, 'V', 1. )
1018	ENDIF
1019
1020	! Clean 3-D work arrays
1021	zhpi(:,:,:) = 0._wp
1022	zrhh(:,:,:) = rhd(:,:,:)
1023
1024	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
1025	DO jj = 1, jpj
1026	DO ji = 1, jpi
1027	jk = mbkt(ji,jj)+1
1028	IF( jk <= 0 ) THEN ; zrhh(ji,jj, : ) = 0._wp
1029	ELSEIF( jk == 1 ) THEN ; zrhh(ji,jj,jk+1:jpk) = rhd(ji,jj,jk)
1030	ELSEIF( jk < jpkm1 ) THEN
1031	DO jkk = jk+1, jpk
1032	zrhh(ji,jj,jkk) = interp1(gde3w_n(ji,jj,jkk ), gde3w_n(ji,jj,jkk-1), &
1033	& gde3w_n(ji,jj,jkk-2), rhd (ji,jj,jkk-1), rhd(ji,jj,jkk-2))
1034	END DO
1035	ENDIF
1036	END DO
1037	END DO
1038
1039	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
1040	DO jj = 1, jpj
1041	DO ji = 1, jpi
1042	zdept(ji,jj,1) = 0.5_wp * e3w_n(ji,jj,1) - ssh(ji,jj,Nnn) * znad
1043	END DO
1044	END DO
1045
1046	DO jk = 2, jpk
1047	DO jj = 1, jpj
1048	DO ji = 1, jpi
1049	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + e3w_n(ji,jj,jk)
1050	END DO
1051	END DO
1052	END DO
1053
1054	fsp(:,:,:) = zrhh (:,:,:)
1055	xsp(:,:,:) = zdept(:,:,:)
1056
1057	! Construct the vertical density profile with the
1058	! constrained cubic spline interpolation
1059	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
1060	CALL cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
1061
1062	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
1063	DO jj = 2, jpj
1064	DO ji = 2, jpi
1065	zrhdt1 = zrhh(ji,jj,1) - interp3( zdept(ji,jj,1), asp(ji,jj,1), bsp(ji,jj,1), &
1066	& csp(ji,jj,1), dsp(ji,jj,1) ) * 0.25_wp * e3w_n(ji,jj,1)
1067
1068	! assuming linear profile across the top half surface layer
1069	zhpi(ji,jj,1) = 0.5_wp * e3w_n(ji,jj,1) * zrhdt1
1070	END DO
1071	END DO
1072
1073	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
1074	DO jk = 2, jpkm1
1075	DO jj = 2, jpj
1076	DO ji = 2, jpi
1077	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
1078	& integ_spline( zdept(ji,jj,jk-1), zdept(ji,jj,jk), &
1079	& asp (ji,jj,jk-1), bsp (ji,jj,jk-1), &
1080	& csp (ji,jj,jk-1), dsp (ji,jj,jk-1) )
1081	END DO
1082	END DO
1083	END DO
1084
1085	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
1086
1087	! Prepare zsshu_n and zsshv_n
1088	!!gm Vector form
1089	! DO jj = 2, jpjm1
1090	! DO ji = 2, jpim1
1091	! !!gm BUG ? if it is ssh at u- & v-point then it should be:
1092	! ! zsshu_n(ji,jj) = (e1e2t(ji,jj) * ssh(ji,jj,Nnn) + e1e2t(ji+1,jj) * ssh(ji+1,jj,Nnn)) * &
1093	! ! & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
1094	! ! zsshv_n(ji,jj) = (e1e2t(ji,jj) * ssh(ji,jj,Nnn) + e1e2t(ji,jj+1) * ssh(ji,jj+1,Nnn)) * &
1095	! ! & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
1096	! !!gm not this:
1097	! zsshu_n(ji,jj) = (e1e2u(ji,jj) * ssh(ji,jj,Nnn) + e1e2u(ji+1, jj) * ssh(ji+1,jj,Nnn)) * &
1098	! & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
1099	! zsshv_n(ji,jj) = (e1e2v(ji,jj) * ssh(ji,jj,Nnn) + e1e2v(ji+1, jj) * ssh(ji,jj+1,Nnn)) * &
1100	! & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
1101	! END DO
1102	! END DO
1103	!!gm Flux form :
1104	DO jj = 2, jpjm1
1105	DO ji = 2, jpim1
1106	zsshu_n(ji,jj) = 0.5_wp * ( ssh(ji,jj,Nnn) + ssh(ji+1,jj,Nnn) ) * ssumask(ji,jj)
1107	zsshv_n(ji,jj) = 0.5_wp * ( ssh(ji,jj,Nnn) + ssh(ji,jj+1,Nnn) ) * ssvmask(ji,jj)
1108	END DO
1109	END DO
1110	CALL lbc_lnk_multi (zsshu_n, 'U', 1., zsshv_n, 'V', 1. )
1111	!
1112	DO jj = 2, jpjm1
1113	DO ji = 2, jpim1
1114	zu(ji,jj,1) = - ( e3u_n(ji,jj,1) - zsshu_n(ji,jj) * znad)
1115	zv(ji,jj,1) = - ( e3v_n(ji,jj,1) - zsshv_n(ji,jj) * znad)
1116	END DO
1117	END DO
1118	!
1119	DO jk = 2, jpkm1
1120	DO jj = 2, jpjm1
1121	DO ji = 2, jpim1
1122	zu(ji,jj,jk) = zu(ji,jj,jk-1) - e3u_n(ji,jj,jk)
1123	zv(ji,jj,jk) = zv(ji,jj,jk-1) - e3v_n(ji,jj,jk)
1124	END DO
1125	END DO
1126	END DO
1127	!
1128	DO jk = 1, jpkm1
1129	DO jj = 2, jpjm1
1130	DO ji = 2, jpim1
1131	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * e3u_n(ji,jj,jk)
1132	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * e3v_n(ji,jj,jk)
1133	END DO
1134	END DO
1135	END DO
1136
1137	DO jk = 1, jpkm1
1138	DO jj = 2, jpjm1
1139	DO ji = 2, jpim1
1140	zu(ji,jj,jk) = MIN( zu(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
1141	zu(ji,jj,jk) = MAX( zu(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
1142	zv(ji,jj,jk) = MIN( zv(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
1143	zv(ji,jj,jk) = MAX( zv(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
1144	END DO
1145	END DO
1146	END DO
1147
1148	DO jk = 1, jpkm1
1149	DO jj = 2, jpjm1
1150	DO ji = 2, jpim1
1151	zpwes = 0._wp ; zpwed = 0._wp
1152	zpnss = 0._wp ; zpnsd = 0._wp
1153	zuijk = zu(ji,jj,jk)
1154	zvijk = zv(ji,jj,jk)
1155
1156	!!!!! for u equation
1157	IF( jk <= mbku(ji,jj) ) THEN
1158	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
1159	jis = ji + 1; jid = ji
1160	ELSE
1161	jis = ji; jid = ji +1
1162	ENDIF
1163
1164	! integrate the pressure on the shallow side
1165	jk1 = jk
1166	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
1167	IF( jk1 == mbku(ji,jj) ) THEN
1168	zuijk = -zdept(jis,jj,jk1)
1169	EXIT
1170	ENDIF
1171	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
1172	zpwes = zpwes + &
1173	integ_spline(zdept(jis,jj,jk1), zdeps, &
1174	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
1175	csp(jis,jj,jk1), dsp(jis,jj,jk1))
1176	jk1 = jk1 + 1
1177	END DO
1178
1179	! integrate the pressure on the deep side
1180	jk1 = jk
1181	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
1182	IF( jk1 == 1 ) THEN
1183	zdeps = zdept(jid,jj,1) + MIN(zuijk, ssh(jid,jj,Nnn)*znad)
1184	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
1185	bsp(jid,jj,1), csp(jid,jj,1), &
1186	dsp(jid,jj,1)) * zdeps
1187	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
1188	EXIT
1189	ENDIF
1190	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
1191	zpwed = zpwed + &
1192	integ_spline(zdeps, zdept(jid,jj,jk1), &
1193	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
1194	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
1195	jk1 = jk1 - 1
1196	END DO
1197
1198	! update the momentum trends in u direction
1199
1200	zdpdx1 = zcoef0 * r1_e1u(ji,jj) * ( zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk) )
1201	IF( .NOT.ln_linssh ) THEN
1202	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * &
1203	& ( REAL(jis-jid, wp) * (zpwes + zpwed) + (ssh(ji+1,jj,Nnn)-ssh(ji,jj,Nnn)) )
1204	ELSE
1205	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
1206	ENDIF
1207	IF( ln_wd_il ) THEN
1208	zdpdx1 = zdpdx1 * zcpx(ji,jj) * wdrampu(ji,jj)
1209	zdpdx2 = zdpdx2 * zcpx(ji,jj) * wdrampu(ji,jj)
1210	ENDIF
1211	ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * umask(ji,jj,jk)
1212	ENDIF
1213
1214	!!!!! for v equation
1215	IF( jk <= mbkv(ji,jj) ) THEN
1216	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
1217	jjs = jj + 1; jjd = jj
1218	ELSE
1219	jjs = jj ; jjd = jj + 1
1220	ENDIF
1221
1222	! integrate the pressure on the shallow side
1223	jk1 = jk
1224	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
1225	IF( jk1 == mbkv(ji,jj) ) THEN
1226	zvijk = -zdept(ji,jjs,jk1)
1227	EXIT
1228	ENDIF
1229	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
1230	zpnss = zpnss + &
1231	integ_spline(zdept(ji,jjs,jk1), zdeps, &
1232	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
1233	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
1234	jk1 = jk1 + 1
1235	END DO
1236
1237	! integrate the pressure on the deep side
1238	jk1 = jk
1239	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
1240	IF( jk1 == 1 ) THEN
1241	zdeps = zdept(ji,jjd,1) + MIN(zvijk, ssh(ji,jjd,Nnn)*znad)
1242	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
1243	bsp(ji,jjd,1), csp(ji,jjd,1), &
1244	dsp(ji,jjd,1) ) * zdeps
1245	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
1246	EXIT
1247	ENDIF
1248	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
1249	zpnsd = zpnsd + &
1250	integ_spline(zdeps, zdept(ji,jjd,jk1), &
1251	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
1252	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
1253	jk1 = jk1 - 1
1254	END DO
1255
1256
1257	! update the momentum trends in v direction
1258
1259	zdpdy1 = zcoef0 * r1_e2v(ji,jj) * ( zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk) )
1260	IF( .NOT.ln_linssh ) THEN
1261	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * &
1262	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (ssh(ji,jj+1,Nnn)-ssh(ji,jj,Nnn)) )
1263	ELSE
1264	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
1265	ENDIF
1266	IF( ln_wd_il ) THEN
1267	zdpdy1 = zdpdy1 * zcpy(ji,jj) * wdrampv(ji,jj)
1268	zdpdy2 = zdpdy2 * zcpy(ji,jj) * wdrampv(ji,jj)
1269	ENDIF
1270
1271	va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2) * vmask(ji,jj,jk)
1272	ENDIF
1273	!
1274	END DO
1275	END DO
1276	END DO
1277	!
1278	IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy )
1279	!
1280	END SUBROUTINE hpg_prj
1281
1282
1283	SUBROUTINE cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
1284	!!----------------------------------------------------------------------
1285	!! * ROUTINE cspline *
1286	!!
1287	!! ** Purpose : constrained cubic spline interpolation
1288	!!
1289	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
1290	!!
1291	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
1292	!!----------------------------------------------------------------------
1293	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: fsp, xsp ! value and coordinate
1294	REAL(wp), DIMENSION(:,:,:), INTENT( out) :: asp, bsp, csp, dsp ! coefficients of the interpoated function
1295	INTEGER , INTENT(in ) :: polynomial_type ! 1: cubic spline ; 2: Linear
1296	!
1297	INTEGER :: ji, jj, jk ! dummy loop indices
1298	INTEGER :: jpi, jpj, jpkm1
1299	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
1300	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
1301	REAL(wp) :: zdf(size(fsp,3))
1302	!!----------------------------------------------------------------------
1303	!
1304	!!gm WHAT !!!!! THIS IS VERY DANGEROUS !!!!!
1305	jpi = size(fsp,1)
1306	jpj = size(fsp,2)
1307	jpkm1 = MAX( 1, size(fsp,3) - 1 )
1308	!
1309	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
1310	DO ji = 1, jpi
1311	DO jj = 1, jpj
1312	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
1313	! DO jk = 2, jpkm1-1
1314	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
1315	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1316	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
1317	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
1318	!
1319	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
1320	!
1321	! IF(zdf1 * zdf2 <= 0._wp) THEN
1322	! zdf(jk) = 0._wp
1323	! ELSE
1324	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
1325	! ENDIF
1326	! END DO
1327
1328	!!Simply geometric average
1329	DO jk = 2, jpkm1-1
1330	zdf1 = (fsp(ji,jj,jk ) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk ) - xsp(ji,jj,jk-1))
1331	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk )) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk ))
1332
1333	IF(zdf1 * zdf2 <= 0._wp) THEN
1334	zdf(jk) = 0._wp
1335	ELSE
1336	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
1337	ENDIF
1338	END DO
1339
1340	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
1341	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
1342	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
1343	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - 0.5_wp * zdf(jpkm1 - 1)
1344
1345	DO jk = 1, jpkm1 - 1
1346	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1347	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
1348	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
1349	zddf1 = -2._wp * ztmp1 + ztmp2
1350	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
1351	zddf2 = 2._wp * ztmp1 - ztmp2
1352
1353	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
1354	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
1355	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
1356	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
1357	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
1358	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
1359	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
1360	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
1361	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
1362	END DO
1363	END DO
1364	END DO
1365
1366	ELSEIF ( polynomial_type == 2 ) THEN ! Linear
1367	DO ji = 1, jpi
1368	DO jj = 1, jpj
1369	DO jk = 1, jpkm1-1
1370	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1371	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
1372
1373	dsp(ji,jj,jk) = 0._wp
1374	csp(ji,jj,jk) = 0._wp
1375	bsp(ji,jj,jk) = ztmp1 / zdxtmp
1376	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
1377	END DO
1378	END DO
1379	END DO
1380	!
1381	ELSE
1382	CALL ctl_stop( 'invalid polynomial type in cspline' )
1383	ENDIF
1384	!
1385	END SUBROUTINE cspline
1386
1387
1388	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
1389	!!----------------------------------------------------------------------
1390	!! * ROUTINE interp1 *
1391	!!
1392	!! ** Purpose : 1-d linear interpolation
1393	!!
1394	!! ** Method : interpolation is straight forward
1395	!! extrapolation is also permitted (no value limit)
1396	!!----------------------------------------------------------------------
1397	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
1398	REAL(wp) :: f ! result of the interpolation (extrapolation)
1399	REAL(wp) :: zdeltx
1400	!!----------------------------------------------------------------------
1401	!
1402	zdeltx = xr - xl
1403	IF( abs(zdeltx) <= 10._wp * EPSILON(x) ) THEN
1404	f = 0.5_wp * (fl + fr)
1405	ELSE
1406	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
1407	ENDIF
1408	!
1409	END FUNCTION interp1
1410
1411
1412	FUNCTION interp2( x, a, b, c, d ) RESULT(f)
1413	!!----------------------------------------------------------------------
1414	!! * ROUTINE interp1 *
1415	!!
1416	!! ** Purpose : 1-d constrained cubic spline interpolation
1417	!!
1418	!! ** Method : cubic spline interpolation
1419	!!
1420	!!----------------------------------------------------------------------
1421	REAL(wp), INTENT(in) :: x, a, b, c, d
1422	REAL(wp) :: f ! value from the interpolation
1423	!!----------------------------------------------------------------------
1424	!
1425	f = a + x* ( b + x * ( c + d * x ) )
1426	!
1427	END FUNCTION interp2
1428
1429
1430	FUNCTION interp3( x, a, b, c, d ) RESULT(f)
1431	!!----------------------------------------------------------------------
1432	!! * ROUTINE interp1 *
1433	!!
1434	!! ** Purpose : Calculate the first order of derivative of
1435	!! a cubic spline function y=a+bx+cx^2+d*x^3
1436	!!
1437	!! ** Method : f=dy/dx=b+2cx+3dx^2
1438	!!
1439	!!----------------------------------------------------------------------
1440	REAL(wp), INTENT(in) :: x, a, b, c, d
1441	REAL(wp) :: f ! value from the interpolation
1442	!!----------------------------------------------------------------------
1443	!
1444	f = b + x * ( 2._wp * c + 3._wp * d * x)
1445	!
1446	END FUNCTION interp3
1447
1448
1449	FUNCTION integ_spline( xl, xr, a, b, c, d ) RESULT(f)
1450	!!----------------------------------------------------------------------
1451	!! * ROUTINE interp1 *
1452	!!
1453	!! ** Purpose : 1-d constrained cubic spline integration
1454	!!
1455	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
1456	!!
1457	!!----------------------------------------------------------------------
1458	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
1459	REAL(wp) :: za1, za2, za3
1460	REAL(wp) :: f ! integration result
1461	!!----------------------------------------------------------------------
1462	!
1463	za1 = 0.5_wp * b
1464	za2 = c / 3.0_wp
1465	za3 = 0.25_wp * d
1466	!
1467	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
1468	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
1469	!
1470	END FUNCTION integ_spline
1471
1472	!!======================================================================
1473	END MODULE dynhpg
1474

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