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dynhpg.F90 in NEMO/branches/2019/dev_r10721_KERNEL-02_Storkey_Coward_IMMERSE_first_steps/src/OCE/DYN – NEMO

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source: NEMO/branches/2019/dev_r10721_KERNEL-02_Storkey_Coward_IMMERSE_first_steps/src/OCE/DYN/dynhpg.F90 @ 10928

Last change on this file since 10928 was 10928, checked in by davestorkey, 4 years ago
2019/dev_r10721_KERNEL-02_Storkey_Coward_IMMERSE_first_steps : Finish converting DYN module, including some updates to previously processed modules, but excluding dynnxt.F90 (which needs to be completely rewritten) and wet_dry.F90 - I need to talk to Enda about this.
Property svn:keywords set to `Id`
File size: 75.5 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 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 license (see ./LICENSE)
80	!!----------------------------------------------------------------------
81	CONTAINS
82
83	SUBROUTINE dyn_hpg( kt, Kmm, puu, pvv, Krhs )
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 (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) 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	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
95	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
96	!
97	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: ztrdu, ztrdv
98	!!----------------------------------------------------------------------
99	!
100	IF( ln_timing ) CALL timing_start('dyn_hpg')
101	!
102	IF( l_trddyn ) THEN ! Temporary saving of puu(:,:,:,Krhs) and pvv(:,:,:,Krhs) trends (l_trddyn)
103	ALLOCATE( ztrdu(jpi,jpj,jpk) , ztrdv(jpi,jpj,jpk) )
104	ztrdu(:,:,:) = puu(:,:,:,Krhs)
105	ztrdv(:,:,:) = pvv(:,:,:,Krhs)
106	ENDIF
107	!
108	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
109	CASE ( np_zco ) ; CALL hpg_zco ( kt, Kmm, puu, pvv, Krhs ) ! z-coordinate
110	CASE ( np_zps ) ; CALL hpg_zps ( kt, Kmm, puu, pvv, Krhs ) ! z-coordinate plus partial steps (interpolation)
111	CASE ( np_sco ) ; CALL hpg_sco ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate (standard jacobian formulation)
112	CASE ( np_djc ) ; CALL hpg_djc ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate (Density Jacobian with Cubic polynomial)
113	CASE ( np_prj ) ; CALL hpg_prj ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate (Pressure Jacobian scheme)
114	CASE ( np_isf ) ; CALL hpg_isf ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate similar to sco modify for ice shelf
115	END SELECT
116	!
117	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
118	ztrdu(:,:,:) = puu(:,:,:,Krhs) - ztrdu(:,:,:)
119	ztrdv(:,:,:) = pvv(:,:,:,Krhs) - ztrdv(:,:,:)
120	CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt )
121	DEALLOCATE( ztrdu , ztrdv )
122	ENDIF
123	!
124	IF(ln_ctl) CALL prt_ctl( tab3d_1=puu(:,:,:,Krhs), clinfo1=' hpg - Ua: ', mask1=umask, &
125	& tab3d_2=pvv(:,:,:,Krhs), clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
126	!
127	IF( ln_timing ) CALL timing_stop('dyn_hpg')
128	!
129	END SUBROUTINE dyn_hpg
130
131
132	SUBROUTINE dyn_hpg_init( Kmm )
133	!!----------------------------------------------------------------------
134	!! * ROUTINE dyn_hpg_init *
135	!!
136	!! ** Purpose : initializations for the hydrostatic pressure gradient
137	!! computation and consistency control
138	!!
139	!! ** Action : Read the namelist namdyn_hpg and check the consistency
140	!! with the type of vertical coordinate used (zco, zps, sco)
141	!!----------------------------------------------------------------------
142	INTEGER, INTENT( in ) :: Kmm ! ocean time level index
143	!
144	INTEGER :: ioptio = 0 ! temporary integer
145	INTEGER :: ios ! Local integer output status for namelist read
146	!!
147	INTEGER :: ji, jj, jk, ikt ! dummy loop indices ISF
148	REAL(wp) :: znad
149	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: zts_top, zrhd ! hypothesys on isf density
150	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zrhdtop_isf ! density at bottom of ISF
151	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: ziceload ! density at bottom of ISF
152	!!
153	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
154	& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf
155	!!----------------------------------------------------------------------
156	!
157	REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient
158	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
159	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp )
160	!
161	REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient
162	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
163	902 IF( ios > 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp )
164	IF(lwm) WRITE ( numond, namdyn_hpg )
165	!
166	IF(lwp) THEN ! Control print
167	WRITE(numout,*)
168	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
169	WRITE(numout,*) '~~~~~~~~~~~~'
170	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
171	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
172	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
173	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
174	WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf
175	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
176	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
177	ENDIF
178	!
179	IF( ln_hpg_djc ) &
180	& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method', &
181	& ' currently disabled (bugs under investigation).' , &
182	& ' Please select either ln_hpg_sco or ln_hpg_prj instead' )
183	!
184	IF( .NOT.ln_linssh .AND. .NOT.(ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) &
185	& CALL ctl_stop('dyn_hpg_init : non-linear free surface requires either ', &
186	& ' the standard jacobian formulation hpg_sco or ' , &
187	& ' the pressure jacobian formulation hpg_prj' )
188	!
189	IF( ln_hpg_isf ) THEN
190	IF( .NOT. ln_isfcav ) CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' )
191	ELSE
192	IF( ln_isfcav ) CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' )
193	ENDIF
194	!
195	! ! Set nhpg from ln_hpg_... flags & consistency check
196	nhpg = np_ERROR
197	ioptio = 0
198	IF( ln_hpg_zco ) THEN ; nhpg = np_zco ; ioptio = ioptio +1 ; ENDIF
199	IF( ln_hpg_zps ) THEN ; nhpg = np_zps ; ioptio = ioptio +1 ; ENDIF
200	IF( ln_hpg_sco ) THEN ; nhpg = np_sco ; ioptio = ioptio +1 ; ENDIF
201	IF( ln_hpg_djc ) THEN ; nhpg = np_djc ; ioptio = ioptio +1 ; ENDIF
202	IF( ln_hpg_prj ) THEN ; nhpg = np_prj ; ioptio = ioptio +1 ; ENDIF
203	IF( ln_hpg_isf ) THEN ; nhpg = np_isf ; ioptio = ioptio +1 ; ENDIF
204	!
205	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
206	!
207	IF(lwp) THEN
208	WRITE(numout,*)
209	SELECT CASE( nhpg )
210	CASE( np_zco ) ; WRITE(numout,*) ' ==>>> z-coord. - full steps '
211	CASE( np_zps ) ; WRITE(numout,*) ' ==>>> z-coord. - partial steps (interpolation)'
212	CASE( np_sco ) ; WRITE(numout,*) ' ==>>> s-coord. (standard jacobian formulation)'
213	CASE( np_djc ) ; WRITE(numout,*) ' ==>>> s-coord. (Density Jacobian: Cubic polynomial)'
214	CASE( np_prj ) ; WRITE(numout,*) ' ==>>> s-coord. (Pressure Jacobian: Cubic polynomial)'
215	CASE( np_isf ) ; WRITE(numout,*) ' ==>>> s-coord. (standard jacobian formulation) for isf'
216	END SELECT
217	WRITE(numout,*)
218	ENDIF
219	!
220	IF ( .NOT. ln_isfcav ) THEN !--- no ice shelf load
221	riceload(:,:) = 0._wp
222	!
223	ELSE !--- set an ice shelf load
224	!
225	IF(lwp) WRITE(numout,*)
226	IF(lwp) WRITE(numout,*) ' ice shelf case: set the ice-shelf load'
227	ALLOCATE( zts_top(jpi,jpj,jpts) , zrhd(jpi,jpj,jpk) , zrhdtop_isf(jpi,jpj) , ziceload(jpi,jpj) )
228	!
229	znad = 1._wp !- To use density and not density anomaly
230	!
231	! !- assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude)
232	zts_top(:,:,jp_tem) = -1.9_wp ; zts_top(:,:,jp_sal) = 34.4_wp
233	!
234	DO jk = 1, jpk !- compute density of the water displaced by the ice shelf
235	CALL eos( zts_top(:,:,:), gdept(:,:,jk,Kmm), zrhd(:,:,jk) )
236	END DO
237	!
238	! !- compute rhd at the ice/oce interface (ice shelf side)
239	CALL eos( zts_top , risfdep, zrhdtop_isf )
240	!
241	! !- Surface value + ice shelf gradient
242	ziceload = 0._wp ! compute pressure due to ice shelf load
243	DO jj = 1, jpj ! (used to compute hpgi/j for all the level from 1 to miku/v)
244	DO ji = 1, jpi ! divided by 2 later
245	ikt = mikt(ji,jj)
246	ziceload(ji,jj) = ziceload(ji,jj) + (znad + zrhd(ji,jj,1) ) * e3w(ji,jj,1,Kmm) * (1._wp - tmask(ji,jj,1))
247	DO jk = 2, ikt-1
248	ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhd(ji,jj,jk-1) + zrhd(ji,jj,jk)) * e3w(ji,jj,jk,Kmm) &
249	& * (1._wp - tmask(ji,jj,jk))
250	END DO
251	IF (ikt >= 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + zrhd(ji,jj,ikt-1)) &
252	& * ( risfdep(ji,jj) - gdept(ji,jj,ikt-1,Kmm) )
253	END DO
254	END DO
255	riceload(:,:) = ziceload(:,:) ! need to be saved for diaar5
256	!
257	DEALLOCATE( zts_top , zrhd , zrhdtop_isf , ziceload )
258	ENDIF
259	!
260	END SUBROUTINE dyn_hpg_init
261
262
263	SUBROUTINE hpg_zco( kt, Kmm, puu, pvv, Krhs )
264	!!---------------------------------------------------------------------
265	!! * ROUTINE hpg_zco *
266	!!
267	!! ** Method : z-coordinate case, levels are horizontal surfaces.
268	!! The now hydrostatic pressure gradient at a given level, jk,
269	!! is computed by taking the vertical integral of the in-situ
270	!! density gradient along the model level from the suface to that
271	!! level: zhpi = grav .....
272	!! zhpj = grav .....
273	!! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)).
274	!! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi
275	!! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj
276	!!
277	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
278	!!----------------------------------------------------------------------
279	INTEGER , INTENT( in ) :: kt ! ocean time-step index
280	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
281	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
282	!
283	INTEGER :: ji, jj, jk ! dummy loop indices
284	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
285	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
286	!!----------------------------------------------------------------------
287	!
288	IF( kt == nit000 ) THEN
289	IF(lwp) WRITE(numout,*)
290	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
291	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
292	ENDIF
293
294	zcoef0 = - grav * 0.5_wp ! Local constant initialization
295
296	! Surface value
297	DO jj = 2, jpjm1
298	DO ji = fs_2, fs_jpim1 ! vector opt.
299	zcoef1 = zcoef0 * e3w(ji,jj,1,Kmm)
300	! hydrostatic pressure gradient
301	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
302	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
303	! add to the general momentum trend
304	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1)
305	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1)
306	END DO
307	END DO
308
309	!
310	! interior value (2=<jk=<jpkm1)
311	DO jk = 2, jpkm1
312	DO jj = 2, jpjm1
313	DO ji = fs_2, fs_jpim1 ! vector opt.
314	zcoef1 = zcoef0 * e3w(ji,jj,jk,Kmm)
315	! hydrostatic pressure gradient
316	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
317	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
318	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
319
320	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
321	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
322	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
323	! add to the general momentum trend
324	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk)
325	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk)
326	END DO
327	END DO
328	END DO
329	!
330	END SUBROUTINE hpg_zco
331
332
333	SUBROUTINE hpg_zps( kt, Kmm, puu, pvv, Krhs )
334	!!---------------------------------------------------------------------
335	!! * ROUTINE hpg_zps *
336	!!
337	!! ** Method : z-coordinate plus partial steps case. blahblah...
338	!!
339	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
340	!!----------------------------------------------------------------------
341	INTEGER , INTENT( in ) :: kt ! ocean time-step index
342	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
343	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
344	!!
345	INTEGER :: ji, jj, jk ! dummy loop indices
346	INTEGER :: iku, ikv ! temporary integers
347	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
348	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
349	!!----------------------------------------------------------------------
350	!
351	IF( kt == nit000 ) THEN
352	IF(lwp) WRITE(numout,*)
353	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
354	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
355	ENDIF
356
357	! Partial steps: bottom before horizontal gradient of t, s, rd at the last ocean level
358	!jc CALL zps_hde ( kt, jpts, ts(:,:,:,:,Kmm), gtsu, gtsv, rhd, gru , grv )
359
360	! Local constant initialization
361	zcoef0 = - grav * 0.5_wp
362
363	! Surface value (also valid in partial step case)
364	DO jj = 2, jpjm1
365	DO ji = fs_2, fs_jpim1 ! vector opt.
366	zcoef1 = zcoef0 * e3w(ji,jj,1,Kmm)
367	! hydrostatic pressure gradient
368	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
369	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
370	! add to the general momentum trend
371	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1)
372	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1)
373	END DO
374	END DO
375
376	! interior value (2=<jk=<jpkm1)
377	DO jk = 2, jpkm1
378	DO jj = 2, jpjm1
379	DO ji = fs_2, fs_jpim1 ! vector opt.
380	zcoef1 = zcoef0 * e3w(ji,jj,jk,Kmm)
381	! hydrostatic pressure gradient
382	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
383	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
384	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
385
386	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
387	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
388	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
389	! add to the general momentum trend
390	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk)
391	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk)
392	END DO
393	END DO
394	END DO
395
396	! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
397	DO jj = 2, jpjm1
398	DO ji = 2, jpim1
399	iku = mbku(ji,jj)
400	ikv = mbkv(ji,jj)
401	zcoef2 = zcoef0 * MIN( e3w(ji,jj,iku,Kmm), e3w(ji+1,jj ,iku,Kmm) )
402	zcoef3 = zcoef0 * MIN( e3w(ji,jj,ikv,Kmm), e3w(ji ,jj+1,ikv,Kmm) )
403	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
404	puu (ji,jj,iku,Krhs) = puu(ji,jj,iku,Krhs) - zhpi(ji,jj,iku) ! subtract old value
405	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
406	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) * r1_e1u(ji,jj)
407	puu (ji,jj,iku,Krhs) = puu(ji,jj,iku,Krhs) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
408	ENDIF
409	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
410	pvv (ji,jj,ikv,Krhs) = pvv(ji,jj,ikv,Krhs) - zhpj(ji,jj,ikv) ! subtract old value
411	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
412	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) * r1_e2v(ji,jj)
413	pvv (ji,jj,ikv,Krhs) = pvv(ji,jj,ikv,Krhs) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
414	ENDIF
415	END DO
416	END DO
417	!
418	END SUBROUTINE hpg_zps
419
420
421	SUBROUTINE hpg_sco( kt, Kmm, puu, pvv, Krhs )
422	!!---------------------------------------------------------------------
423	!! * ROUTINE hpg_sco *
424	!!
425	!! ** Method : s-coordinate case. Jacobian scheme.
426	!! The now hydrostatic pressure gradient at a given level, jk,
427	!! is computed by taking the vertical integral of the in-situ
428	!! density gradient along the model level from the suface to that
429	!! level. s-coordinates (ln_sco): a corrective term is added
430	!! to the horizontal pressure gradient :
431	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
432	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
433	!! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)).
434	!! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi
435	!! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj
436	!!
437	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
438	!!----------------------------------------------------------------------
439	INTEGER , INTENT( in ) :: kt ! ocean time-step index
440	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
441	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
442	!!
443	INTEGER :: ji, jj, jk, jii, jjj ! dummy loop indices
444	REAL(wp) :: zcoef0, zuap, zvap, znad, ztmp ! temporary scalars
445	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
446	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
447	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter
448	!!----------------------------------------------------------------------
449	!
450	IF( ln_wd_il ) ALLOCATE(zcpx(jpi,jpj), zcpy(jpi,jpj))
451	!
452	IF( kt == nit000 ) THEN
453	IF(lwp) WRITE(numout,*)
454	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
455	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
456	ENDIF
457	!
458	zcoef0 = - grav * 0.5_wp
459	IF ( ln_linssh ) THEN ; znad = 0._wp ! Fixed volume: density anomaly
460	ELSE ; znad = 1._wp ! Variable volume: density
461	ENDIF
462	!
463	IF( ln_wd_il ) THEN
464	DO jj = 2, jpjm1
465	DO ji = 2, jpim1
466	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
467	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
468	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) &
469	& > rn_wdmin1 + rn_wdmin2
470	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji+1,jj,Kmm) ) > 1.E-12 ) .AND. ( &
471	& MAX( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
472	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
473
474	IF(ll_tmp1) THEN
475	zcpx(ji,jj) = 1.0_wp
476	ELSE IF(ll_tmp2) THEN
477	! no worries about ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm) = 0, it won't happen ! here
478	zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
479	& / (ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm)) )
480	ELSE
481	zcpx(ji,jj) = 0._wp
482	END IF
483
484	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
485	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
486	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) &
487	& > rn_wdmin1 + rn_wdmin2
488	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. ( &
489	& MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
490	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
491
492	IF(ll_tmp1) THEN
493	zcpy(ji,jj) = 1.0_wp
494	ELSE IF(ll_tmp2) THEN
495	! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here
496	zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
497	& / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) )
498	ELSE
499	zcpy(ji,jj) = 0._wp
500	END IF
501	END DO
502	END DO
503	CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1., zcpy, 'V', 1. )
504	END IF
505
506	! Surface value
507	DO jj = 2, jpjm1
508	DO ji = fs_2, fs_jpim1 ! vector opt.
509	! hydrostatic pressure gradient along s-surfaces
510	zhpi(ji,jj,1) = zcoef0 * ( e3w(ji+1,jj ,1,Kmm) * ( znad + rhd(ji+1,jj ,1) ) &
511	& - e3w(ji ,jj ,1,Kmm) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e1u(ji,jj)
512	zhpj(ji,jj,1) = zcoef0 * ( e3w(ji ,jj+1,1,Kmm) * ( znad + rhd(ji ,jj+1,1) ) &
513	& - e3w(ji ,jj ,1,Kmm) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e2v(ji,jj)
514	! s-coordinate pressure gradient correction
515	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
516	& * ( gde3w(ji+1,jj,1) - gde3w(ji,jj,1) ) * r1_e1u(ji,jj)
517	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
518	& * ( gde3w(ji,jj+1,1) - gde3w(ji,jj,1) ) * r1_e2v(ji,jj)
519	!
520	IF( ln_wd_il ) THEN
521	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
522	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
523	zuap = zuap * zcpx(ji,jj)
524	zvap = zvap * zcpy(ji,jj)
525	ENDIF
526	!
527	! add to the general momentum trend
528	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1) + zuap
529	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1) + zvap
530	END DO
531	END DO
532
533	! interior value (2=<jk=<jpkm1)
534	DO jk = 2, jpkm1
535	DO jj = 2, jpjm1
536	DO ji = fs_2, fs_jpim1 ! vector opt.
537	! hydrostatic pressure gradient along s-surfaces
538	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 * r1_e1u(ji,jj) &
539	& * ( e3w(ji+1,jj,jk,Kmm) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) &
540	& - e3w(ji ,jj,jk,Kmm) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) )
541	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 * r1_e2v(ji,jj) &
542	& * ( e3w(ji,jj+1,jk,Kmm) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) &
543	& - e3w(ji,jj ,jk,Kmm) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) )
544	! s-coordinate pressure gradient correction
545	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
546	& * ( gde3w(ji+1,jj ,jk) - gde3w(ji,jj,jk) ) * r1_e1u(ji,jj)
547	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
548	& * ( gde3w(ji ,jj+1,jk) - gde3w(ji,jj,jk) ) * r1_e2v(ji,jj)
549	!
550	IF( ln_wd_il ) THEN
551	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
552	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
553	zuap = zuap * zcpx(ji,jj)
554	zvap = zvap * zcpy(ji,jj)
555	ENDIF
556	!
557	! add to the general momentum trend
558	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk) + zuap
559	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk) + zvap
560	END DO
561	END DO
562	END DO
563	!
564	IF( ln_wd_il ) DEALLOCATE( zcpx , zcpy )
565	!
566	END SUBROUTINE hpg_sco
567
568
569	SUBROUTINE hpg_isf( kt, Kmm, puu, pvv, Krhs )
570	!!---------------------------------------------------------------------
571	!! * ROUTINE hpg_isf *
572	!!
573	!! ** Method : s-coordinate case. Jacobian scheme.
574	!! The now hydrostatic pressure gradient at a given level, jk,
575	!! is computed by taking the vertical integral of the in-situ
576	!! density gradient along the model level from the suface to that
577	!! level. s-coordinates (ln_sco): a corrective term is added
578	!! to the horizontal pressure gradient :
579	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
580	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
581	!! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)).
582	!! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi
583	!! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj
584	!! iceload is added and partial cell case are added to the top and bottom
585	!!
586	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
587	!!----------------------------------------------------------------------
588	INTEGER , INTENT( in ) :: kt ! ocean time-step index
589	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
590	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
591	!!
592	INTEGER :: ji, jj, jk, ikt, iktp1i, iktp1j ! dummy loop indices
593	REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars
594	REAL(wp), DIMENSION(jpi,jpj,jpk ) :: zhpi, zhpj
595	REAL(wp), DIMENSION(jpi,jpj,jpts) :: zts_top
596	REAL(wp), DIMENSION(jpi,jpj) :: zrhdtop_oce
597	!!----------------------------------------------------------------------
598	!
599	zcoef0 = - grav * 0.5_wp ! Local constant initialization
600	!
601	znad=1._wp ! To use density and not density anomaly
602	!
603	! ! iniitialised to 0. zhpi zhpi
604	zhpi(:,:,:) = 0._wp ; zhpj(:,:,:) = 0._wp
605
606	! compute rhd at the ice/oce interface (ocean side)
607	! usefull to reduce residual current in the test case ISOMIP with no melting
608	DO ji = 1, jpi
609	DO jj = 1, jpj
610	ikt = mikt(ji,jj)
611	zts_top(ji,jj,1) = ts(ji,jj,ikt,1,Kmm)
612	zts_top(ji,jj,2) = ts(ji,jj,ikt,2,Kmm)
613	END DO
614	END DO
615	CALL eos( zts_top, risfdep, zrhdtop_oce )
616
617	!==================================================================================
618	!===== Compute surface value =====================================================
619	!==================================================================================
620	DO jj = 2, jpjm1
621	DO ji = fs_2, fs_jpim1 ! vector opt.
622	ikt = mikt(ji,jj)
623	iktp1i = mikt(ji+1,jj)
624	iktp1j = mikt(ji,jj+1)
625	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
626	! we assume ISF is in isostatic equilibrium
627	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * e3w(ji+1,jj,iktp1i,Kmm) &
628	& * ( 2._wp * znad + rhd(ji+1,jj,iktp1i) + zrhdtop_oce(ji+1,jj) ) &
629	& - 0.5_wp * e3w(ji,jj,ikt,Kmm) &
630	& * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) &
631	& + ( riceload(ji+1,jj) - riceload(ji,jj)) )
632	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * e3w(ji,jj+1,iktp1j,Kmm) &
633	& * ( 2._wp * znad + rhd(ji,jj+1,iktp1j) + zrhdtop_oce(ji,jj+1) ) &
634	& - 0.5_wp * e3w(ji,jj,ikt,Kmm) &
635	& * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) &
636	& + ( riceload(ji,jj+1) - riceload(ji,jj)) )
637	! s-coordinate pressure gradient correction (=0 if z coordinate)
638	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
639	& * ( gde3w(ji+1,jj,1) - gde3w(ji,jj,1) ) * r1_e1u(ji,jj)
640	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
641	& * ( gde3w(ji,jj+1,1) - gde3w(ji,jj,1) ) * r1_e2v(ji,jj)
642	! add to the general momentum trend
643	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
644	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
645	END DO
646	END DO
647	!==================================================================================
648	!===== Compute interior value =====================================================
649	!==================================================================================
650	! interior value (2=<jk=<jpkm1)
651	DO jk = 2, jpkm1
652	DO jj = 2, jpjm1
653	DO ji = fs_2, fs_jpim1 ! vector opt.
654	! hydrostatic pressure gradient along s-surfaces
655	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
656	& * ( e3w(ji+1,jj,jk,Kmm) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2znad ) wmask(ji+1,jj,jk) &
657	& - e3w(ji ,jj,jk,Kmm) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2znad ) wmask(ji ,jj,jk) )
658	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
659	& * ( e3w(ji,jj+1,jk,Kmm) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2znad ) wmask(ji,jj+1,jk) &
660	& - e3w(ji,jj ,jk,Kmm) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2znad ) wmask(ji,jj ,jk) )
661	! s-coordinate pressure gradient correction
662	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
663	& * ( gde3w(ji+1,jj ,jk) - gde3w(ji,jj,jk) ) / e1u(ji,jj)
664	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
665	& * ( gde3w(ji ,jj+1,jk) - gde3w(ji,jj,jk) ) / e2v(ji,jj)
666	! add to the general momentum trend
667	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + (zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
668	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + (zhpj(ji,jj,jk) + zvap) * vmask(ji,jj,jk)
669	END DO
670	END DO
671	END DO
672	!
673	END SUBROUTINE hpg_isf
674
675
676	SUBROUTINE hpg_djc( kt, Kmm, puu, pvv, Krhs )
677	!!---------------------------------------------------------------------
678	!! * ROUTINE hpg_djc *
679	!!
680	!! ** Method : Density Jacobian with Cubic polynomial scheme
681	!!
682	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
683	!!----------------------------------------------------------------------
684	INTEGER , INTENT( in ) :: kt ! ocean time-step index
685	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
686	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
687	!!
688	INTEGER :: ji, jj, jk ! dummy loop indices
689	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
690	REAL(wp) :: z1_10, cffu, cffx ! " "
691	REAL(wp) :: z1_12, cffv, cffy ! " "
692	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
693	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
694	REAL(wp), DIMENSION(jpi,jpj,jpk) :: dzx, dzy, dzz, dzu, dzv, dzw
695	REAL(wp), DIMENSION(jpi,jpj,jpk) :: drhox, drhoy, drhoz, drhou, drhov, drhow
696	REAL(wp), DIMENSION(jpi,jpj,jpk) :: rho_i, rho_j, rho_k
697	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter
698	!!----------------------------------------------------------------------
699	!
700	IF( ln_wd_il ) THEN
701	ALLOCATE( zcpx(jpi,jpj) , zcpy(jpi,jpj) )
702	DO jj = 2, jpjm1
703	DO ji = 2, jpim1
704	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
705	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
706	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) &
707	& > rn_wdmin1 + rn_wdmin2
708	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji+1,jj,Kmm) ) > 1.E-12 ) .AND. ( &
709	& MAX( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
710	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
711	IF(ll_tmp1) THEN
712	zcpx(ji,jj) = 1.0_wp
713	ELSE IF(ll_tmp2) THEN
714	! no worries about ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm) = 0, it won't happen ! here
715	zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
716	& / (ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm)) )
717	ELSE
718	zcpx(ji,jj) = 0._wp
719	END IF
720
721	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
722	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
723	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) &
724	& > rn_wdmin1 + rn_wdmin2
725	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. ( &
726	& MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
727	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
728
729	IF(ll_tmp1) THEN
730	zcpy(ji,jj) = 1.0_wp
731	ELSE IF(ll_tmp2) THEN
732	! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here
733	zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
734	& / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) )
735	ELSE
736	zcpy(ji,jj) = 0._wp
737	END IF
738	END DO
739	END DO
740	CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1., zcpy, 'V', 1. )
741	END IF
742
743	IF( kt == nit000 ) THEN
744	IF(lwp) WRITE(numout,*)
745	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
746	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
747	ENDIF
748
749	! Local constant initialization
750	zcoef0 = - grav * 0.5_wp
751	z1_10 = 1._wp / 10._wp
752	z1_12 = 1._wp / 12._wp
753
754	!----------------------------------------------------------------------------------------
755	! compute and store in provisional arrays elementary vertical and horizontal differences
756	!----------------------------------------------------------------------------------------
757
758	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
759
760	DO jk = 2, jpkm1
761	DO jj = 2, jpjm1
762	DO ji = fs_2, fs_jpim1 ! vector opt.
763	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
764	dzz (ji,jj,jk) = gde3w(ji ,jj ,jk) - gde3w(ji,jj,jk-1)
765	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
766	dzx (ji,jj,jk) = gde3w(ji+1,jj ,jk) - gde3w(ji,jj,jk )
767	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
768	dzy (ji,jj,jk) = gde3w(ji ,jj+1,jk) - gde3w(ji,jj,jk )
769	END DO
770	END DO
771	END DO
772
773	!-------------------------------------------------------------------------
774	! compute harmonic averages using eq. 5.18
775	!-------------------------------------------------------------------------
776	zep = 1.e-15
777
778	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
779	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
780
781	DO jk = 2, jpkm1
782	DO jj = 2, jpjm1
783	DO ji = fs_2, fs_jpim1 ! vector opt.
784	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
785
786	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
787	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
788
789	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
790	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
791
792	IF( cffw > zep) THEN
793	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
794	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
795	ELSE
796	drhow(ji,jj,jk) = 0._wp
797	ENDIF
798
799	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
800	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
801
802	IF( cffu > zep ) THEN
803	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
804	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
805	ELSE
806	drhou(ji,jj,jk ) = 0._wp
807	ENDIF
808
809	IF( cffx > zep ) THEN
810	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
811	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
812	ELSE
813	dzu(ji,jj,jk) = 0._wp
814	ENDIF
815
816	IF( cffv > zep ) THEN
817	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
818	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
819	ELSE
820	drhov(ji,jj,jk) = 0._wp
821	ENDIF
822
823	IF( cffy > zep ) THEN
824	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
825	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
826	ELSE
827	dzv(ji,jj,jk) = 0._wp
828	ENDIF
829
830	END DO
831	END DO
832	END DO
833
834	!----------------------------------------------------------------------------------
835	! apply boundary conditions at top and bottom using 5.36-5.37
836	!----------------------------------------------------------------------------------
837	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
838	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
839	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
840
841	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
842	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
843	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
844
845
846	!--------------------------------------------------------------
847	! Upper half of top-most grid box, compute and store
848	!-------------------------------------------------------------
849
850	!!bug gm : e3w-gde3w = 0.5*e3w .... and gde3w(2)-gde3w(1)=e3w(2) .... to be verified
851	! true if gde3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
852
853	DO jj = 2, jpjm1
854	DO ji = fs_2, fs_jpim1 ! vector opt.
855	rho_k(ji,jj,1) = -grav * ( e3w(ji,jj,1,Kmm) - gde3w(ji,jj,1) ) &
856	& * ( rhd(ji,jj,1) &
857	& + 0.5_wp * ( rhd (ji,jj,2) - rhd (ji,jj,1) ) &
858	& * ( e3w (ji,jj,1,Kmm) - gde3w(ji,jj,1) ) &
859	& / ( gde3w(ji,jj,2) - gde3w(ji,jj,1) ) )
860	END DO
861	END DO
862
863	!!bug gm : here also, simplification is possible
864	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
865
866	DO jk = 2, jpkm1
867	DO jj = 2, jpjm1
868	DO ji = fs_2, fs_jpim1 ! vector opt.
869
870	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
871	& * ( gde3w(ji,jj,jk) - gde3w(ji,jj,jk-1) ) &
872	& - grav * z1_10 * ( &
873	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
874	& * ( gde3w(ji,jj,jk) - gde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
875	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
876	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
877	& )
878
879	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
880	& * ( gde3w(ji+1,jj,jk) - gde3w(ji,jj,jk) ) &
881	& - grav* z1_10 * ( &
882	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
883	& * ( gde3w(ji+1,jj,jk) - gde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
884	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
885	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
886	& )
887
888	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
889	& * ( gde3w(ji,jj+1,jk) - gde3w(ji,jj,jk) ) &
890	& - grav* z1_10 * ( &
891	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
892	& * ( gde3w(ji,jj+1,jk) - gde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
893	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
894	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
895	& )
896
897	END DO
898	END DO
899	END DO
900	CALL lbc_lnk_multi( 'dynhpg', rho_k, 'W', 1., rho_i, 'U', 1., rho_j, 'V', 1. )
901
902	! ---------------
903	! Surface value
904	! ---------------
905	DO jj = 2, jpjm1
906	DO ji = fs_2, fs_jpim1 ! vector opt.
907	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) * r1_e1u(ji,jj)
908	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) * r1_e2v(ji,jj)
909	IF( ln_wd_il ) THEN
910	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
911	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
912	ENDIF
913	! add to the general momentum trend
914	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1)
915	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1)
916	END DO
917	END DO
918
919	! ----------------
920	! interior value (2=<jk=<jpkm1)
921	! ----------------
922	DO jk = 2, jpkm1
923	DO jj = 2, jpjm1
924	DO ji = fs_2, fs_jpim1 ! vector opt.
925	! hydrostatic pressure gradient along s-surfaces
926	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
927	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
928	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) * r1_e1u(ji,jj)
929	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
930	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
931	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) * r1_e2v(ji,jj)
932	IF( ln_wd_il ) THEN
933	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
934	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
935	ENDIF
936	! add to the general momentum trend
937	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk)
938	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk)
939	END DO
940	END DO
941	END DO
942	!
943	IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy )
944	!
945	END SUBROUTINE hpg_djc
946
947
948	SUBROUTINE hpg_prj( kt, Kmm, puu, pvv, Krhs )
949	!!---------------------------------------------------------------------
950	!! * ROUTINE hpg_prj *
951	!!
952	!! ** Method : s-coordinate case.
953	!! A Pressure-Jacobian horizontal pressure gradient method
954	!! based on the constrained cubic-spline interpolation for
955	!! all vertical coordinate systems
956	!!
957	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
958	!!----------------------------------------------------------------------
959	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
960	INTEGER , INTENT( in ) :: kt ! ocean time-step index
961	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
962	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
963	!!
964	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
965	REAL(wp) :: zcoef0, znad ! local scalars
966	!
967	!! The local variables for the correction term
968	INTEGER :: jk1, jis, jid, jjs, jjd
969	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
970	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
971	REAL(wp) :: zrhdt1
972	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
973	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdept, zrhh
974	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
975	REAL(wp), DIMENSION(jpi,jpj) :: zsshu_n, zsshv_n
976	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter
977	!!----------------------------------------------------------------------
978	!
979	IF( kt == nit000 ) THEN
980	IF(lwp) WRITE(numout,*)
981	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
982	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
983	ENDIF
984
985	! Local constant initialization
986	zcoef0 = - grav
987	znad = 1._wp
988	IF( ln_linssh ) znad = 0._wp
989
990	IF( ln_wd_il ) THEN
991	ALLOCATE( zcpx(jpi,jpj) , zcpy(jpi,jpj) )
992	DO jj = 2, jpjm1
993	DO ji = 2, jpim1
994	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
995	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
996	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) &
997	& > rn_wdmin1 + rn_wdmin2
998	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji+1,jj,Kmm) ) > 1.E-12 ) .AND. ( &
999	& MAX( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
1000	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
1001
1002	IF(ll_tmp1) THEN
1003	zcpx(ji,jj) = 1.0_wp
1004	ELSE IF(ll_tmp2) THEN
1005	! no worries about ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm) = 0, it won't happen ! here
1006	zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
1007	& / (ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm)) )
1008
1009	zcpx(ji,jj) = max(min( zcpx(ji,jj) , 1.0_wp),0.0_wp)
1010	ELSE
1011	zcpx(ji,jj) = 0._wp
1012	END IF
1013
1014	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
1015	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
1016	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) &
1017	& > rn_wdmin1 + rn_wdmin2
1018	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. ( &
1019	& MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
1020	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
1021
1022	IF(ll_tmp1) THEN
1023	zcpy(ji,jj) = 1.0_wp
1024	ELSE IF(ll_tmp2) THEN
1025	! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here
1026	zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
1027	& / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) )
1028	zcpy(ji,jj) = max(min( zcpy(ji,jj) , 1.0_wp),0.0_wp)
1029
1030	ELSE
1031	zcpy(ji,jj) = 0._wp
1032	ENDIF
1033	END DO
1034	END DO
1035	CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1., zcpy, 'V', 1. )
1036	ENDIF
1037
1038	! Clean 3-D work arrays
1039	zhpi(:,:,:) = 0._wp
1040	zrhh(:,:,:) = rhd(:,:,:)
1041
1042	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
1043	DO jj = 1, jpj
1044	DO ji = 1, jpi
1045	jk = mbkt(ji,jj)+1
1046	IF( jk <= 0 ) THEN ; zrhh(ji,jj, : ) = 0._wp
1047	ELSEIF( jk == 1 ) THEN ; zrhh(ji,jj,jk+1:jpk) = rhd(ji,jj,jk)
1048	ELSEIF( jk < jpkm1 ) THEN
1049	DO jkk = jk+1, jpk
1050	zrhh(ji,jj,jkk) = interp1(gde3w(ji,jj,jkk ), gde3w(ji,jj,jkk-1), &
1051	& gde3w(ji,jj,jkk-2), rhd (ji,jj,jkk-1), rhd(ji,jj,jkk-2))
1052	END DO
1053	ENDIF
1054	END DO
1055	END DO
1056
1057	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
1058	DO jj = 1, jpj
1059	DO ji = 1, jpi
1060	zdept(ji,jj,1) = 0.5_wp * e3w(ji,jj,1,Kmm) - ssh(ji,jj,Kmm) * znad
1061	END DO
1062	END DO
1063
1064	DO jk = 2, jpk
1065	DO jj = 1, jpj
1066	DO ji = 1, jpi
1067	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + e3w(ji,jj,jk,Kmm)
1068	END DO
1069	END DO
1070	END DO
1071
1072	fsp(:,:,:) = zrhh (:,:,:)
1073	xsp(:,:,:) = zdept(:,:,:)
1074
1075	! Construct the vertical density profile with the
1076	! constrained cubic spline interpolation
1077	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
1078	CALL cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
1079
1080	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
1081	DO jj = 2, jpj
1082	DO ji = 2, jpi
1083	zrhdt1 = zrhh(ji,jj,1) - interp3( zdept(ji,jj,1), asp(ji,jj,1), bsp(ji,jj,1), &
1084	& csp(ji,jj,1), dsp(ji,jj,1) ) * 0.25_wp * e3w(ji,jj,1,Kmm)
1085
1086	! assuming linear profile across the top half surface layer
1087	zhpi(ji,jj,1) = 0.5_wp * e3w(ji,jj,1,Kmm) * zrhdt1
1088	END DO
1089	END DO
1090
1091	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
1092	DO jk = 2, jpkm1
1093	DO jj = 2, jpj
1094	DO ji = 2, jpi
1095	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
1096	& integ_spline( zdept(ji,jj,jk-1), zdept(ji,jj,jk), &
1097	& asp (ji,jj,jk-1), bsp (ji,jj,jk-1), &
1098	& csp (ji,jj,jk-1), dsp (ji,jj,jk-1) )
1099	END DO
1100	END DO
1101	END DO
1102
1103	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
1104
1105	! Prepare zsshu_n and zsshv_n
1106	DO jj = 2, jpjm1
1107	DO ji = 2, jpim1
1108	!!gm BUG ? if it is ssh at u- & v-point then it should be:
1109	! zsshu_n(ji,jj) = (e1e2t(ji,jj) * ssh(ji,jj,Kmm) + e1e2t(ji+1,jj) * ssh(ji+1,jj,Kmm)) * &
1110	! & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
1111	! zsshv_n(ji,jj) = (e1e2t(ji,jj) * ssh(ji,jj,Kmm) + e1e2t(ji,jj+1) * ssh(ji,jj+1,Kmm)) * &
1112	! & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
1113	!!gm not this:
1114	zsshu_n(ji,jj) = (e1e2u(ji,jj) * ssh(ji,jj,Kmm) + e1e2u(ji+1, jj) * ssh(ji+1,jj,Kmm)) * &
1115	& r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
1116	zsshv_n(ji,jj) = (e1e2v(ji,jj) * ssh(ji,jj,Kmm) + e1e2v(ji+1, jj) * ssh(ji,jj+1,Kmm)) * &
1117	& r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
1118	END DO
1119	END DO
1120
1121	CALL lbc_lnk_multi ('dynhpg', zsshu_n, 'U', 1., zsshv_n, 'V', 1. )
1122
1123	DO jj = 2, jpjm1
1124	DO ji = 2, jpim1
1125	zu(ji,jj,1) = - ( e3u(ji,jj,1,Kmm) - zsshu_n(ji,jj) * znad)
1126	zv(ji,jj,1) = - ( e3v(ji,jj,1,Kmm) - zsshv_n(ji,jj) * znad)
1127	END DO
1128	END DO
1129
1130	DO jk = 2, jpkm1
1131	DO jj = 2, jpjm1
1132	DO ji = 2, jpim1
1133	zu(ji,jj,jk) = zu(ji,jj,jk-1) - e3u(ji,jj,jk,Kmm)
1134	zv(ji,jj,jk) = zv(ji,jj,jk-1) - e3v(ji,jj,jk,Kmm)
1135	END DO
1136	END DO
1137	END DO
1138
1139	DO jk = 1, jpkm1
1140	DO jj = 2, jpjm1
1141	DO ji = 2, jpim1
1142	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * e3u(ji,jj,jk,Kmm)
1143	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * e3v(ji,jj,jk,Kmm)
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	zu(ji,jj,jk) = MIN( zu(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
1152	zu(ji,jj,jk) = MAX( zu(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
1153	zv(ji,jj,jk) = MIN( zv(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
1154	zv(ji,jj,jk) = MAX( zv(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
1155	END DO
1156	END DO
1157	END DO
1158
1159
1160	DO jk = 1, jpkm1
1161	DO jj = 2, jpjm1
1162	DO ji = 2, jpim1
1163	zpwes = 0._wp; zpwed = 0._wp
1164	zpnss = 0._wp; zpnsd = 0._wp
1165	zuijk = zu(ji,jj,jk)
1166	zvijk = zv(ji,jj,jk)
1167
1168	!!!!! for u equation
1169	IF( jk <= mbku(ji,jj) ) THEN
1170	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
1171	jis = ji + 1; jid = ji
1172	ELSE
1173	jis = ji; jid = ji +1
1174	ENDIF
1175
1176	! integrate the pressure on the shallow side
1177	jk1 = jk
1178	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
1179	IF( jk1 == mbku(ji,jj) ) THEN
1180	zuijk = -zdept(jis,jj,jk1)
1181	EXIT
1182	ENDIF
1183	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
1184	zpwes = zpwes + &
1185	integ_spline(zdept(jis,jj,jk1), zdeps, &
1186	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
1187	csp(jis,jj,jk1), dsp(jis,jj,jk1))
1188	jk1 = jk1 + 1
1189	END DO
1190
1191	! integrate the pressure on the deep side
1192	jk1 = jk
1193	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
1194	IF( jk1 == 1 ) THEN
1195	zdeps = zdept(jid,jj,1) + MIN(zuijk, ssh(jid,jj,Kmm)*znad)
1196	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
1197	bsp(jid,jj,1), csp(jid,jj,1), &
1198	dsp(jid,jj,1)) * zdeps
1199	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
1200	EXIT
1201	ENDIF
1202	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
1203	zpwed = zpwed + &
1204	integ_spline(zdeps, zdept(jid,jj,jk1), &
1205	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
1206	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
1207	jk1 = jk1 - 1
1208	END DO
1209
1210	! update the momentum trends in u direction
1211
1212	zdpdx1 = zcoef0 * r1_e1u(ji,jj) * ( zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk) )
1213	IF( .NOT.ln_linssh ) THEN
1214	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * &
1215	& ( REAL(jis-jid, wp) * (zpwes + zpwed) + (ssh(ji+1,jj,Kmm)-ssh(ji,jj,Kmm)) )
1216	ELSE
1217	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
1218	ENDIF
1219	IF( ln_wd_il ) THEN
1220	zdpdx1 = zdpdx1 * zcpx(ji,jj) * wdrampu(ji,jj)
1221	zdpdx2 = zdpdx2 * zcpx(ji,jj) * wdrampu(ji,jj)
1222	ENDIF
1223	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + (zdpdx1 + zdpdx2) * umask(ji,jj,jk)
1224	ENDIF
1225
1226	!!!!! for v equation
1227	IF( jk <= mbkv(ji,jj) ) THEN
1228	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
1229	jjs = jj + 1; jjd = jj
1230	ELSE
1231	jjs = jj ; jjd = jj + 1
1232	ENDIF
1233
1234	! integrate the pressure on the shallow side
1235	jk1 = jk
1236	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
1237	IF( jk1 == mbkv(ji,jj) ) THEN
1238	zvijk = -zdept(ji,jjs,jk1)
1239	EXIT
1240	ENDIF
1241	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
1242	zpnss = zpnss + &
1243	integ_spline(zdept(ji,jjs,jk1), zdeps, &
1244	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
1245	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
1246	jk1 = jk1 + 1
1247	END DO
1248
1249	! integrate the pressure on the deep side
1250	jk1 = jk
1251	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
1252	IF( jk1 == 1 ) THEN
1253	zdeps = zdept(ji,jjd,1) + MIN(zvijk, ssh(ji,jjd,Kmm)*znad)
1254	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
1255	bsp(ji,jjd,1), csp(ji,jjd,1), &
1256	dsp(ji,jjd,1) ) * zdeps
1257	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
1258	EXIT
1259	ENDIF
1260	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
1261	zpnsd = zpnsd + &
1262	integ_spline(zdeps, zdept(ji,jjd,jk1), &
1263	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
1264	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
1265	jk1 = jk1 - 1
1266	END DO
1267
1268
1269	! update the momentum trends in v direction
1270
1271	zdpdy1 = zcoef0 * r1_e2v(ji,jj) * ( zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk) )
1272	IF( .NOT.ln_linssh ) THEN
1273	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * &
1274	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (ssh(ji,jj+1,Kmm)-ssh(ji,jj,Kmm)) )
1275	ELSE
1276	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
1277	ENDIF
1278	IF( ln_wd_il ) THEN
1279	zdpdy1 = zdpdy1 * zcpy(ji,jj) * wdrampv(ji,jj)
1280	zdpdy2 = zdpdy2 * zcpy(ji,jj) * wdrampv(ji,jj)
1281	ENDIF
1282
1283	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + (zdpdy1 + zdpdy2) * vmask(ji,jj,jk)
1284	ENDIF
1285	!
1286	END DO
1287	END DO
1288	END DO
1289	!
1290	IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy )
1291	!
1292	END SUBROUTINE hpg_prj
1293
1294
1295	SUBROUTINE cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
1296	!!----------------------------------------------------------------------
1297	!! * ROUTINE cspline *
1298	!!
1299	!! ** Purpose : constrained cubic spline interpolation
1300	!!
1301	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
1302	!!
1303	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
1304	!!----------------------------------------------------------------------
1305	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: fsp, xsp ! value and coordinate
1306	REAL(wp), DIMENSION(:,:,:), INTENT( out) :: asp, bsp, csp, dsp ! coefficients of the interpoated function
1307	INTEGER , INTENT(in ) :: polynomial_type ! 1: cubic spline ; 2: Linear
1308	!
1309	INTEGER :: ji, jj, jk ! dummy loop indices
1310	INTEGER :: jpi, jpj, jpkm1
1311	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
1312	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
1313	REAL(wp) :: zdf(size(fsp,3))
1314	!!----------------------------------------------------------------------
1315	!
1316	!!gm WHAT !!!!! THIS IS VERY DANGEROUS !!!!!
1317	jpi = size(fsp,1)
1318	jpj = size(fsp,2)
1319	jpkm1 = MAX( 1, size(fsp,3) - 1 )
1320	!
1321	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
1322	DO ji = 1, jpi
1323	DO jj = 1, jpj
1324	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
1325	! DO jk = 2, jpkm1-1
1326	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
1327	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1328	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
1329	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
1330	!
1331	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
1332	!
1333	! IF(zdf1 * zdf2 <= 0._wp) THEN
1334	! zdf(jk) = 0._wp
1335	! ELSE
1336	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
1337	! ENDIF
1338	! END DO
1339
1340	!!Simply geometric average
1341	DO jk = 2, jpkm1-1
1342	zdf1 = (fsp(ji,jj,jk ) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk ) - xsp(ji,jj,jk-1))
1343	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk )) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk ))
1344
1345	IF(zdf1 * zdf2 <= 0._wp) THEN
1346	zdf(jk) = 0._wp
1347	ELSE
1348	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
1349	ENDIF
1350	END DO
1351
1352	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
1353	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
1354	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
1355	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - 0.5_wp * zdf(jpkm1 - 1)
1356
1357	DO jk = 1, jpkm1 - 1
1358	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1359	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
1360	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
1361	zddf1 = -2._wp * ztmp1 + ztmp2
1362	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
1363	zddf2 = 2._wp * ztmp1 - ztmp2
1364
1365	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
1366	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
1367	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
1368	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
1369	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
1370	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
1371	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
1372	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
1373	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
1374	END DO
1375	END DO
1376	END DO
1377
1378	ELSEIF ( polynomial_type == 2 ) THEN ! Linear
1379	DO ji = 1, jpi
1380	DO jj = 1, jpj
1381	DO jk = 1, jpkm1-1
1382	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1383	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
1384
1385	dsp(ji,jj,jk) = 0._wp
1386	csp(ji,jj,jk) = 0._wp
1387	bsp(ji,jj,jk) = ztmp1 / zdxtmp
1388	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
1389	END DO
1390	END DO
1391	END DO
1392	!
1393	ELSE
1394	CALL ctl_stop( 'invalid polynomial type in cspline' )
1395	ENDIF
1396	!
1397	END SUBROUTINE cspline
1398
1399
1400	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
1401	!!----------------------------------------------------------------------
1402	!! * ROUTINE interp1 *
1403	!!
1404	!! ** Purpose : 1-d linear interpolation
1405	!!
1406	!! ** Method : interpolation is straight forward
1407	!! extrapolation is also permitted (no value limit)
1408	!!----------------------------------------------------------------------
1409	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
1410	REAL(wp) :: f ! result of the interpolation (extrapolation)
1411	REAL(wp) :: zdeltx
1412	!!----------------------------------------------------------------------
1413	!
1414	zdeltx = xr - xl
1415	IF( abs(zdeltx) <= 10._wp * EPSILON(x) ) THEN
1416	f = 0.5_wp * (fl + fr)
1417	ELSE
1418	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
1419	ENDIF
1420	!
1421	END FUNCTION interp1
1422
1423
1424	FUNCTION interp2( x, a, b, c, d ) RESULT(f)
1425	!!----------------------------------------------------------------------
1426	!! * ROUTINE interp1 *
1427	!!
1428	!! ** Purpose : 1-d constrained cubic spline interpolation
1429	!!
1430	!! ** Method : cubic spline interpolation
1431	!!
1432	!!----------------------------------------------------------------------
1433	REAL(wp), INTENT(in) :: x, a, b, c, d
1434	REAL(wp) :: f ! value from the interpolation
1435	!!----------------------------------------------------------------------
1436	!
1437	f = a + x* ( b + x * ( c + d * x ) )
1438	!
1439	END FUNCTION interp2
1440
1441
1442	FUNCTION interp3( x, a, b, c, d ) RESULT(f)
1443	!!----------------------------------------------------------------------
1444	!! * ROUTINE interp1 *
1445	!!
1446	!! ** Purpose : Calculate the first order of derivative of
1447	!! a cubic spline function y=a+bx+cx^2+d*x^3
1448	!!
1449	!! ** Method : f=dy/dx=b+2cx+3dx^2
1450	!!
1451	!!----------------------------------------------------------------------
1452	REAL(wp), INTENT(in) :: x, a, b, c, d
1453	REAL(wp) :: f ! value from the interpolation
1454	!!----------------------------------------------------------------------
1455	!
1456	f = b + x * ( 2._wp * c + 3._wp * d * x)
1457	!
1458	END FUNCTION interp3
1459
1460
1461	FUNCTION integ_spline( xl, xr, a, b, c, d ) RESULT(f)
1462	!!----------------------------------------------------------------------
1463	!! * ROUTINE interp1 *
1464	!!
1465	!! ** Purpose : 1-d constrained cubic spline integration
1466	!!
1467	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
1468	!!
1469	!!----------------------------------------------------------------------
1470	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
1471	REAL(wp) :: za1, za2, za3
1472	REAL(wp) :: f ! integration result
1473	!!----------------------------------------------------------------------
1474	!
1475	za1 = 0.5_wp * b
1476	za2 = c / 3.0_wp
1477	za3 = 0.25_wp * d
1478	!
1479	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
1480	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
1481	!
1482	END FUNCTION integ_spline
1483
1484	!!======================================================================
1485	END MODULE dynhpg
1486

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