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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 @ 11822

Last change on this file since 11822 was 11822, checked in by acc, 4 years ago
Branch 2019/dev_r10721_KERNEL-02_Storkey_Coward_IMMERSE_first_steps. Sette tested updates to branch to align with trunk changes between 10721 and 11740. Sette tests are passing but results differ from branch before these changes (except for GYRE_PISCES and VORTEX) and branch results already differed from trunk because of algorithmic fixes. Will need more checks to confirm correctness.
Property svn:keywords set to `Id`
File size: 75.6 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	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, Kmm )
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' )
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' )
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	REAL(wp), DIMENSION(jpi,jpj) :: zgtsu, zgtsv, zgru, zgrv
350	!!----------------------------------------------------------------------
351	!
352	IF( kt == nit000 ) THEN
353	IF(lwp) WRITE(numout,*)
354	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
355	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
356	ENDIF
357
358	! Partial steps: Compute NOW horizontal gradient of t, s, rd at the last ocean level
359	CALL zps_hde( kt, Kmm, jpts, ts(:,:,:,:,Kmm), zgtsu, zgtsv, rhd, zgru , zgrv )
360
361	! Local constant initialization
362	zcoef0 = - grav * 0.5_wp
363
364	! Surface value (also valid in partial step case)
365	DO jj = 2, jpjm1
366	DO ji = fs_2, fs_jpim1 ! vector opt.
367	zcoef1 = zcoef0 * e3w(ji,jj,1,Kmm)
368	! hydrostatic pressure gradient
369	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
370	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
371	! add to the general momentum trend
372	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1)
373	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1)
374	END DO
375	END DO
376
377	! interior value (2=<jk=<jpkm1)
378	DO jk = 2, jpkm1
379	DO jj = 2, jpjm1
380	DO ji = fs_2, fs_jpim1 ! vector opt.
381	zcoef1 = zcoef0 * e3w(ji,jj,jk,Kmm)
382	! hydrostatic pressure gradient
383	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
384	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
385	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
386
387	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
388	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
389	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
390	! add to the general momentum trend
391	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk)
392	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk)
393	END DO
394	END DO
395	END DO
396
397	! partial steps correction at the last level (use zgru & zgrv computed in zpshde.F90)
398	DO jj = 2, jpjm1
399	DO ji = 2, jpim1
400	iku = mbku(ji,jj)
401	ikv = mbkv(ji,jj)
402	zcoef2 = zcoef0 * MIN( e3w(ji,jj,iku,Kmm), e3w(ji+1,jj ,iku,Kmm) )
403	zcoef3 = zcoef0 * MIN( e3w(ji,jj,ikv,Kmm), e3w(ji ,jj+1,ikv,Kmm) )
404	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
405	puu (ji,jj,iku,Krhs) = puu(ji,jj,iku,Krhs) - zhpi(ji,jj,iku) ! subtract old value
406	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
407	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + zgru(ji,jj) ) * r1_e1u(ji,jj)
408	puu (ji,jj,iku,Krhs) = puu(ji,jj,iku,Krhs) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
409	ENDIF
410	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
411	pvv (ji,jj,ikv,Krhs) = pvv(ji,jj,ikv,Krhs) - zhpj(ji,jj,ikv) ! subtract old value
412	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
413	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + zgrv(ji,jj) ) * r1_e2v(ji,jj)
414	pvv (ji,jj,ikv,Krhs) = pvv(ji,jj,ikv,Krhs) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
415	ENDIF
416	END DO
417	END DO
418	!
419	END SUBROUTINE hpg_zps
420
421
422	SUBROUTINE hpg_sco( kt, Kmm, puu, pvv, Krhs )
423	!!---------------------------------------------------------------------
424	!! * ROUTINE hpg_sco *
425	!!
426	!! ** Method : s-coordinate case. Jacobian scheme.
427	!! The now hydrostatic pressure gradient at a given level, jk,
428	!! is computed by taking the vertical integral of the in-situ
429	!! density gradient along the model level from the suface to that
430	!! level. s-coordinates (ln_sco): a corrective term is added
431	!! to the horizontal pressure gradient :
432	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
433	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
434	!! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)).
435	!! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi
436	!! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj
437	!!
438	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
439	!!----------------------------------------------------------------------
440	INTEGER , INTENT( in ) :: kt ! ocean time-step index
441	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
442	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
443	!!
444	INTEGER :: ji, jj, jk, jii, jjj ! dummy loop indices
445	REAL(wp) :: zcoef0, zuap, zvap, znad, ztmp ! temporary scalars
446	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
447	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
448	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter
449	!!----------------------------------------------------------------------
450	!
451	IF( ln_wd_il ) ALLOCATE(zcpx(jpi,jpj), zcpy(jpi,jpj))
452	!
453	IF( kt == nit000 ) THEN
454	IF(lwp) WRITE(numout,*)
455	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
456	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
457	ENDIF
458	!
459	zcoef0 = - grav * 0.5_wp
460	IF ( ln_linssh ) THEN ; znad = 0._wp ! Fixed volume: density anomaly
461	ELSE ; znad = 1._wp ! Variable volume: density
462	ENDIF
463	!
464	IF( ln_wd_il ) THEN
465	DO jj = 2, jpjm1
466	DO ji = 2, jpim1
467	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
468	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
469	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) &
470	& > rn_wdmin1 + rn_wdmin2
471	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji+1,jj,Kmm) ) > 1.E-12 ) .AND. ( &
472	& MAX( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
473	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
474
475	IF(ll_tmp1) THEN
476	zcpx(ji,jj) = 1.0_wp
477	ELSE IF(ll_tmp2) THEN
478	! no worries about ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm) = 0, it won't happen ! here
479	zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
480	& / (ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm)) )
481	ELSE
482	zcpx(ji,jj) = 0._wp
483	END IF
484
485	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
486	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
487	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) &
488	& > rn_wdmin1 + rn_wdmin2
489	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. ( &
490	& MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
491	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
492
493	IF(ll_tmp1) THEN
494	zcpy(ji,jj) = 1.0_wp
495	ELSE IF(ll_tmp2) THEN
496	! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here
497	zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
498	& / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) )
499	ELSE
500	zcpy(ji,jj) = 0._wp
501	END IF
502	END DO
503	END DO
504	CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1., zcpy, 'V', 1. )
505	END IF
506
507	! Surface value
508	DO jj = 2, jpjm1
509	DO ji = fs_2, fs_jpim1 ! vector opt.
510	! hydrostatic pressure gradient along s-surfaces
511	zhpi(ji,jj,1) = zcoef0 * ( e3w(ji+1,jj ,1,Kmm) * ( znad + rhd(ji+1,jj ,1) ) &
512	& - e3w(ji ,jj ,1,Kmm) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e1u(ji,jj)
513	zhpj(ji,jj,1) = zcoef0 * ( e3w(ji ,jj+1,1,Kmm) * ( znad + rhd(ji ,jj+1,1) ) &
514	& - e3w(ji ,jj ,1,Kmm) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e2v(ji,jj)
515	! s-coordinate pressure gradient correction
516	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
517	& * ( gde3w(ji+1,jj,1) - gde3w(ji,jj,1) ) * r1_e1u(ji,jj)
518	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
519	& * ( gde3w(ji,jj+1,1) - gde3w(ji,jj,1) ) * r1_e2v(ji,jj)
520	!
521	IF( ln_wd_il ) THEN
522	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
523	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
524	zuap = zuap * zcpx(ji,jj)
525	zvap = zvap * zcpy(ji,jj)
526	ENDIF
527	!
528	! add to the general momentum trend
529	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1) + zuap
530	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1) + zvap
531	END DO
532	END DO
533
534	! interior value (2=<jk=<jpkm1)
535	DO jk = 2, jpkm1
536	DO jj = 2, jpjm1
537	DO ji = fs_2, fs_jpim1 ! vector opt.
538	! hydrostatic pressure gradient along s-surfaces
539	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 * r1_e1u(ji,jj) &
540	& * ( e3w(ji+1,jj,jk,Kmm) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) &
541	& - e3w(ji ,jj,jk,Kmm) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) )
542	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 * r1_e2v(ji,jj) &
543	& * ( e3w(ji,jj+1,jk,Kmm) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) &
544	& - e3w(ji,jj ,jk,Kmm) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) )
545	! s-coordinate pressure gradient correction
546	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
547	& * ( gde3w(ji+1,jj ,jk) - gde3w(ji,jj,jk) ) * r1_e1u(ji,jj)
548	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
549	& * ( gde3w(ji ,jj+1,jk) - gde3w(ji,jj,jk) ) * r1_e2v(ji,jj)
550	!
551	IF( ln_wd_il ) THEN
552	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
553	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
554	zuap = zuap * zcpx(ji,jj)
555	zvap = zvap * zcpy(ji,jj)
556	ENDIF
557	!
558	! add to the general momentum trend
559	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk) + zuap
560	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk) + zvap
561	END DO
562	END DO
563	END DO
564	!
565	IF( ln_wd_il ) DEALLOCATE( zcpx , zcpy )
566	!
567	END SUBROUTINE hpg_sco
568
569
570	SUBROUTINE hpg_isf( kt, Kmm, puu, pvv, Krhs )
571	!!---------------------------------------------------------------------
572	!! * ROUTINE hpg_isf *
573	!!
574	!! ** Method : s-coordinate case. Jacobian scheme.
575	!! The now hydrostatic pressure gradient at a given level, jk,
576	!! is computed by taking the vertical integral of the in-situ
577	!! density gradient along the model level from the suface to that
578	!! level. s-coordinates (ln_sco): a corrective term is added
579	!! to the horizontal pressure gradient :
580	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
581	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
582	!! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)).
583	!! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi
584	!! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj
585	!! iceload is added and partial cell case are added to the top and bottom
586	!!
587	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
588	!!----------------------------------------------------------------------
589	INTEGER , INTENT( in ) :: kt ! ocean time-step index
590	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
591	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
592	!!
593	INTEGER :: ji, jj, jk, ikt, iktp1i, iktp1j ! dummy loop indices
594	REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars
595	REAL(wp), DIMENSION(jpi,jpj,jpk ) :: zhpi, zhpj
596	REAL(wp), DIMENSION(jpi,jpj,jpts) :: zts_top
597	REAL(wp), DIMENSION(jpi,jpj) :: zrhdtop_oce
598	!!----------------------------------------------------------------------
599	!
600	zcoef0 = - grav * 0.5_wp ! Local constant initialization
601	!
602	znad=1._wp ! To use density and not density anomaly
603	!
604	! ! iniitialised to 0. zhpi zhpi
605	zhpi(:,:,:) = 0._wp ; zhpj(:,:,:) = 0._wp
606
607	! compute rhd at the ice/oce interface (ocean side)
608	! usefull to reduce residual current in the test case ISOMIP with no melting
609	DO ji = 1, jpi
610	DO jj = 1, jpj
611	ikt = mikt(ji,jj)
612	zts_top(ji,jj,1) = ts(ji,jj,ikt,1,Kmm)
613	zts_top(ji,jj,2) = ts(ji,jj,ikt,2,Kmm)
614	END DO
615	END DO
616	CALL eos( zts_top, risfdep, zrhdtop_oce )
617
618	!==================================================================================
619	!===== Compute surface value =====================================================
620	!==================================================================================
621	DO jj = 2, jpjm1
622	DO ji = fs_2, fs_jpim1 ! vector opt.
623	ikt = mikt(ji,jj)
624	iktp1i = mikt(ji+1,jj)
625	iktp1j = mikt(ji,jj+1)
626	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
627	! we assume ISF is in isostatic equilibrium
628	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * e3w(ji+1,jj,iktp1i,Kmm) &
629	& * ( 2._wp * znad + rhd(ji+1,jj,iktp1i) + zrhdtop_oce(ji+1,jj) ) &
630	& - 0.5_wp * e3w(ji,jj,ikt,Kmm) &
631	& * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) &
632	& + ( riceload(ji+1,jj) - riceload(ji,jj)) )
633	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * e3w(ji,jj+1,iktp1j,Kmm) &
634	& * ( 2._wp * znad + rhd(ji,jj+1,iktp1j) + zrhdtop_oce(ji,jj+1) ) &
635	& - 0.5_wp * e3w(ji,jj,ikt,Kmm) &
636	& * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) &
637	& + ( riceload(ji,jj+1) - riceload(ji,jj)) )
638	! s-coordinate pressure gradient correction (=0 if z coordinate)
639	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
640	& * ( gde3w(ji+1,jj,1) - gde3w(ji,jj,1) ) * r1_e1u(ji,jj)
641	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
642	& * ( gde3w(ji,jj+1,1) - gde3w(ji,jj,1) ) * r1_e2v(ji,jj)
643	! add to the general momentum trend
644	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
645	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
646	END DO
647	END DO
648	!==================================================================================
649	!===== Compute interior value =====================================================
650	!==================================================================================
651	! interior value (2=<jk=<jpkm1)
652	DO jk = 2, jpkm1
653	DO jj = 2, jpjm1
654	DO ji = fs_2, fs_jpim1 ! vector opt.
655	! hydrostatic pressure gradient along s-surfaces
656	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
657	& * ( e3w(ji+1,jj,jk,Kmm) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2znad ) wmask(ji+1,jj,jk) &
658	& - e3w(ji ,jj,jk,Kmm) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2znad ) wmask(ji ,jj,jk) )
659	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
660	& * ( e3w(ji,jj+1,jk,Kmm) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2znad ) wmask(ji,jj+1,jk) &
661	& - e3w(ji,jj ,jk,Kmm) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2znad ) wmask(ji,jj ,jk) )
662	! s-coordinate pressure gradient correction
663	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
664	& * ( gde3w(ji+1,jj ,jk) - gde3w(ji,jj,jk) ) / e1u(ji,jj)
665	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
666	& * ( gde3w(ji ,jj+1,jk) - gde3w(ji,jj,jk) ) / e2v(ji,jj)
667	! add to the general momentum trend
668	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + (zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
669	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + (zhpj(ji,jj,jk) + zvap) * vmask(ji,jj,jk)
670	END DO
671	END DO
672	END DO
673	!
674	END SUBROUTINE hpg_isf
675
676
677	SUBROUTINE hpg_djc( kt, Kmm, puu, pvv, Krhs )
678	!!---------------------------------------------------------------------
679	!! * ROUTINE hpg_djc *
680	!!
681	!! ** Method : Density Jacobian with Cubic polynomial scheme
682	!!
683	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
684	!!----------------------------------------------------------------------
685	INTEGER , INTENT( in ) :: kt ! ocean time-step index
686	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
687	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
688	!!
689	INTEGER :: ji, jj, jk ! dummy loop indices
690	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
691	REAL(wp) :: z1_10, cffu, cffx ! " "
692	REAL(wp) :: z1_12, cffv, cffy ! " "
693	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
694	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
695	REAL(wp), DIMENSION(jpi,jpj,jpk) :: dzx, dzy, dzz, dzu, dzv, dzw
696	REAL(wp), DIMENSION(jpi,jpj,jpk) :: drhox, drhoy, drhoz, drhou, drhov, drhow
697	REAL(wp), DIMENSION(jpi,jpj,jpk) :: rho_i, rho_j, rho_k
698	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter
699	!!----------------------------------------------------------------------
700	!
701	IF( ln_wd_il ) THEN
702	ALLOCATE( zcpx(jpi,jpj) , zcpy(jpi,jpj) )
703	DO jj = 2, jpjm1
704	DO ji = 2, jpim1
705	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
706	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
707	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) &
708	& > rn_wdmin1 + rn_wdmin2
709	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji+1,jj,Kmm) ) > 1.E-12 ) .AND. ( &
710	& MAX( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
711	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
712	IF(ll_tmp1) THEN
713	zcpx(ji,jj) = 1.0_wp
714	ELSE IF(ll_tmp2) THEN
715	! no worries about ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm) = 0, it won't happen ! here
716	zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
717	& / (ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm)) )
718	ELSE
719	zcpx(ji,jj) = 0._wp
720	END IF
721
722	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
723	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
724	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) &
725	& > rn_wdmin1 + rn_wdmin2
726	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. ( &
727	& MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
728	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
729
730	IF(ll_tmp1) THEN
731	zcpy(ji,jj) = 1.0_wp
732	ELSE IF(ll_tmp2) THEN
733	! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here
734	zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
735	& / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) )
736	ELSE
737	zcpy(ji,jj) = 0._wp
738	END IF
739	END DO
740	END DO
741	CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1., zcpy, 'V', 1. )
742	END IF
743
744	IF( kt == nit000 ) THEN
745	IF(lwp) WRITE(numout,*)
746	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
747	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
748	ENDIF
749
750	! Local constant initialization
751	zcoef0 = - grav * 0.5_wp
752	z1_10 = 1._wp / 10._wp
753	z1_12 = 1._wp / 12._wp
754
755	!----------------------------------------------------------------------------------------
756	! compute and store in provisional arrays elementary vertical and horizontal differences
757	!----------------------------------------------------------------------------------------
758
759	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
760
761	DO jk = 2, jpkm1
762	DO jj = 2, jpjm1
763	DO ji = fs_2, fs_jpim1 ! vector opt.
764	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
765	dzz (ji,jj,jk) = gde3w(ji ,jj ,jk) - gde3w(ji,jj,jk-1)
766	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
767	dzx (ji,jj,jk) = gde3w(ji+1,jj ,jk) - gde3w(ji,jj,jk )
768	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
769	dzy (ji,jj,jk) = gde3w(ji ,jj+1,jk) - gde3w(ji,jj,jk )
770	END DO
771	END DO
772	END DO
773
774	!-------------------------------------------------------------------------
775	! compute harmonic averages using eq. 5.18
776	!-------------------------------------------------------------------------
777	zep = 1.e-15
778
779	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
780	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
781
782	DO jk = 2, jpkm1
783	DO jj = 2, jpjm1
784	DO ji = fs_2, fs_jpim1 ! vector opt.
785	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
786
787	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
788	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
789
790	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
791	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
792
793	IF( cffw > zep) THEN
794	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
795	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
796	ELSE
797	drhow(ji,jj,jk) = 0._wp
798	ENDIF
799
800	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
801	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
802
803	IF( cffu > zep ) THEN
804	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
805	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
806	ELSE
807	drhou(ji,jj,jk ) = 0._wp
808	ENDIF
809
810	IF( cffx > zep ) THEN
811	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
812	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
813	ELSE
814	dzu(ji,jj,jk) = 0._wp
815	ENDIF
816
817	IF( cffv > zep ) THEN
818	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
819	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
820	ELSE
821	drhov(ji,jj,jk) = 0._wp
822	ENDIF
823
824	IF( cffy > zep ) THEN
825	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
826	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
827	ELSE
828	dzv(ji,jj,jk) = 0._wp
829	ENDIF
830
831	END DO
832	END DO
833	END DO
834
835	!----------------------------------------------------------------------------------
836	! apply boundary conditions at top and bottom using 5.36-5.37
837	!----------------------------------------------------------------------------------
838	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
839	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
840	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
841
842	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
843	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
844	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
845
846
847	!--------------------------------------------------------------
848	! Upper half of top-most grid box, compute and store
849	!-------------------------------------------------------------
850
851	!!bug gm : e3w-gde3w = 0.5*e3w .... and gde3w(2)-gde3w(1)=e3w(2) .... to be verified
852	! true if gde3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
853
854	DO jj = 2, jpjm1
855	DO ji = fs_2, fs_jpim1 ! vector opt.
856	rho_k(ji,jj,1) = -grav * ( e3w(ji,jj,1,Kmm) - gde3w(ji,jj,1) ) &
857	& * ( rhd(ji,jj,1) &
858	& + 0.5_wp * ( rhd (ji,jj,2) - rhd (ji,jj,1) ) &
859	& * ( e3w (ji,jj,1,Kmm) - gde3w(ji,jj,1) ) &
860	& / ( gde3w(ji,jj,2) - gde3w(ji,jj,1) ) )
861	END DO
862	END DO
863
864	!!bug gm : here also, simplification is possible
865	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
866
867	DO jk = 2, jpkm1
868	DO jj = 2, jpjm1
869	DO ji = fs_2, fs_jpim1 ! vector opt.
870
871	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
872	& * ( gde3w(ji,jj,jk) - gde3w(ji,jj,jk-1) ) &
873	& - grav * z1_10 * ( &
874	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
875	& * ( gde3w(ji,jj,jk) - gde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
876	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
877	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
878	& )
879
880	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
881	& * ( gde3w(ji+1,jj,jk) - gde3w(ji,jj,jk) ) &
882	& - grav* z1_10 * ( &
883	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
884	& * ( gde3w(ji+1,jj,jk) - gde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
885	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
886	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
887	& )
888
889	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
890	& * ( gde3w(ji,jj+1,jk) - gde3w(ji,jj,jk) ) &
891	& - grav* z1_10 * ( &
892	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
893	& * ( gde3w(ji,jj+1,jk) - gde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
894	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
895	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
896	& )
897
898	END DO
899	END DO
900	END DO
901	CALL lbc_lnk_multi( 'dynhpg', rho_k, 'W', 1., rho_i, 'U', 1., rho_j, 'V', 1. )
902
903	! ---------------
904	! Surface value
905	! ---------------
906	DO jj = 2, jpjm1
907	DO ji = fs_2, fs_jpim1 ! vector opt.
908	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) * r1_e1u(ji,jj)
909	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) * r1_e2v(ji,jj)
910	IF( ln_wd_il ) THEN
911	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
912	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
913	ENDIF
914	! add to the general momentum trend
915	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1)
916	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1)
917	END DO
918	END DO
919
920	! ----------------
921	! interior value (2=<jk=<jpkm1)
922	! ----------------
923	DO jk = 2, jpkm1
924	DO jj = 2, jpjm1
925	DO ji = fs_2, fs_jpim1 ! vector opt.
926	! hydrostatic pressure gradient along s-surfaces
927	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
928	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
929	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) * r1_e1u(ji,jj)
930	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
931	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
932	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) * r1_e2v(ji,jj)
933	IF( ln_wd_il ) THEN
934	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
935	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
936	ENDIF
937	! add to the general momentum trend
938	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk)
939	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk)
940	END DO
941	END DO
942	END DO
943	!
944	IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy )
945	!
946	END SUBROUTINE hpg_djc
947
948
949	SUBROUTINE hpg_prj( kt, Kmm, puu, pvv, Krhs )
950	!!---------------------------------------------------------------------
951	!! * ROUTINE hpg_prj *
952	!!
953	!! ** Method : s-coordinate case.
954	!! A Pressure-Jacobian horizontal pressure gradient method
955	!! based on the constrained cubic-spline interpolation for
956	!! all vertical coordinate systems
957	!!
958	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
959	!!----------------------------------------------------------------------
960	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
961	INTEGER , INTENT( in ) :: kt ! ocean time-step index
962	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
963	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
964	!!
965	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
966	REAL(wp) :: zcoef0, znad ! local scalars
967	!
968	!! The local variables for the correction term
969	INTEGER :: jk1, jis, jid, jjs, jjd
970	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
971	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
972	REAL(wp) :: zrhdt1
973	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
974	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdept, zrhh
975	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
976	REAL(wp), DIMENSION(jpi,jpj) :: zsshu_n, zsshv_n
977	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter
978	!!----------------------------------------------------------------------
979	!
980	IF( kt == nit000 ) THEN
981	IF(lwp) WRITE(numout,*)
982	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
983	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
984	ENDIF
985
986	! Local constant initialization
987	zcoef0 = - grav
988	znad = 1._wp
989	IF( ln_linssh ) znad = 0._wp
990
991	IF( ln_wd_il ) THEN
992	ALLOCATE( zcpx(jpi,jpj) , zcpy(jpi,jpj) )
993	DO jj = 2, jpjm1
994	DO ji = 2, jpim1
995	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
996	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
997	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) &
998	& > rn_wdmin1 + rn_wdmin2
999	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji+1,jj,Kmm) ) > 1.E-12 ) .AND. ( &
1000	& MAX( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
1001	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
1002
1003	IF(ll_tmp1) THEN
1004	zcpx(ji,jj) = 1.0_wp
1005	ELSE IF(ll_tmp2) THEN
1006	! no worries about ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm) = 0, it won't happen ! here
1007	zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
1008	& / (ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm)) )
1009
1010	zcpx(ji,jj) = max(min( zcpx(ji,jj) , 1.0_wp),0.0_wp)
1011	ELSE
1012	zcpx(ji,jj) = 0._wp
1013	END IF
1014
1015	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
1016	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
1017	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) &
1018	& > rn_wdmin1 + rn_wdmin2
1019	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. ( &
1020	& MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
1021	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
1022
1023	IF(ll_tmp1) THEN
1024	zcpy(ji,jj) = 1.0_wp
1025	ELSE IF(ll_tmp2) THEN
1026	! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here
1027	zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
1028	& / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) )
1029	zcpy(ji,jj) = max(min( zcpy(ji,jj) , 1.0_wp),0.0_wp)
1030
1031	ELSE
1032	zcpy(ji,jj) = 0._wp
1033	ENDIF
1034	END DO
1035	END DO
1036	CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1., zcpy, 'V', 1. )
1037	ENDIF
1038
1039	! Clean 3-D work arrays
1040	zhpi(:,:,:) = 0._wp
1041	zrhh(:,:,:) = rhd(:,:,:)
1042
1043	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
1044	DO jj = 1, jpj
1045	DO ji = 1, jpi
1046	jk = mbkt(ji,jj)+1
1047	IF( jk <= 0 ) THEN ; zrhh(ji,jj, : ) = 0._wp
1048	ELSEIF( jk == 1 ) THEN ; zrhh(ji,jj,jk+1:jpk) = rhd(ji,jj,jk)
1049	ELSEIF( jk < jpkm1 ) THEN
1050	DO jkk = jk+1, jpk
1051	zrhh(ji,jj,jkk) = interp1(gde3w(ji,jj,jkk ), gde3w(ji,jj,jkk-1), &
1052	& gde3w(ji,jj,jkk-2), rhd (ji,jj,jkk-1), rhd(ji,jj,jkk-2))
1053	END DO
1054	ENDIF
1055	END DO
1056	END DO
1057
1058	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
1059	DO jj = 1, jpj
1060	DO ji = 1, jpi
1061	zdept(ji,jj,1) = 0.5_wp * e3w(ji,jj,1,Kmm) - ssh(ji,jj,Kmm) * znad
1062	END DO
1063	END DO
1064
1065	DO jk = 2, jpk
1066	DO jj = 1, jpj
1067	DO ji = 1, jpi
1068	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + e3w(ji,jj,jk,Kmm)
1069	END DO
1070	END DO
1071	END DO
1072
1073	fsp(:,:,:) = zrhh (:,:,:)
1074	xsp(:,:,:) = zdept(:,:,:)
1075
1076	! Construct the vertical density profile with the
1077	! constrained cubic spline interpolation
1078	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
1079	CALL cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
1080
1081	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
1082	DO jj = 2, jpj
1083	DO ji = 2, jpi
1084	zrhdt1 = zrhh(ji,jj,1) - interp3( zdept(ji,jj,1), asp(ji,jj,1), bsp(ji,jj,1), &
1085	& csp(ji,jj,1), dsp(ji,jj,1) ) * 0.25_wp * e3w(ji,jj,1,Kmm)
1086
1087	! assuming linear profile across the top half surface layer
1088	zhpi(ji,jj,1) = 0.5_wp * e3w(ji,jj,1,Kmm) * zrhdt1
1089	END DO
1090	END DO
1091
1092	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
1093	DO jk = 2, jpkm1
1094	DO jj = 2, jpj
1095	DO ji = 2, jpi
1096	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
1097	& integ_spline( zdept(ji,jj,jk-1), zdept(ji,jj,jk), &
1098	& asp (ji,jj,jk-1), bsp (ji,jj,jk-1), &
1099	& csp (ji,jj,jk-1), dsp (ji,jj,jk-1) )
1100	END DO
1101	END DO
1102	END DO
1103
1104	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
1105
1106	! Prepare zsshu_n and zsshv_n
1107	DO jj = 2, jpjm1
1108	DO ji = 2, jpim1
1109	!!gm BUG ? if it is ssh at u- & v-point then it should be:
1110	! zsshu_n(ji,jj) = (e1e2t(ji,jj) * ssh(ji,jj,Kmm) + e1e2t(ji+1,jj) * ssh(ji+1,jj,Kmm)) * &
1111	! & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
1112	! zsshv_n(ji,jj) = (e1e2t(ji,jj) * ssh(ji,jj,Kmm) + e1e2t(ji,jj+1) * ssh(ji,jj+1,Kmm)) * &
1113	! & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
1114	!!gm not this:
1115	zsshu_n(ji,jj) = (e1e2u(ji,jj) * ssh(ji,jj,Kmm) + e1e2u(ji+1, jj) * ssh(ji+1,jj,Kmm)) * &
1116	& r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
1117	zsshv_n(ji,jj) = (e1e2v(ji,jj) * ssh(ji,jj,Kmm) + e1e2v(ji+1, jj) * ssh(ji,jj+1,Kmm)) * &
1118	& r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
1119	END DO
1120	END DO
1121
1122	CALL lbc_lnk_multi ('dynhpg', zsshu_n, 'U', 1., zsshv_n, 'V', 1. )
1123
1124	DO jj = 2, jpjm1
1125	DO ji = 2, jpim1
1126	zu(ji,jj,1) = - ( e3u(ji,jj,1,Kmm) - zsshu_n(ji,jj) * znad)
1127	zv(ji,jj,1) = - ( e3v(ji,jj,1,Kmm) - zsshv_n(ji,jj) * znad)
1128	END DO
1129	END DO
1130
1131	DO jk = 2, jpkm1
1132	DO jj = 2, jpjm1
1133	DO ji = 2, jpim1
1134	zu(ji,jj,jk) = zu(ji,jj,jk-1) - e3u(ji,jj,jk,Kmm)
1135	zv(ji,jj,jk) = zv(ji,jj,jk-1) - e3v(ji,jj,jk,Kmm)
1136	END DO
1137	END DO
1138	END DO
1139
1140	DO jk = 1, jpkm1
1141	DO jj = 2, jpjm1
1142	DO ji = 2, jpim1
1143	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * e3u(ji,jj,jk,Kmm)
1144	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * e3v(ji,jj,jk,Kmm)
1145	END DO
1146	END DO
1147	END DO
1148
1149	DO jk = 1, jpkm1
1150	DO jj = 2, jpjm1
1151	DO ji = 2, jpim1
1152	zu(ji,jj,jk) = MIN( zu(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
1153	zu(ji,jj,jk) = MAX( zu(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
1154	zv(ji,jj,jk) = MIN( zv(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
1155	zv(ji,jj,jk) = MAX( zv(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
1156	END DO
1157	END DO
1158	END DO
1159
1160
1161	DO jk = 1, jpkm1
1162	DO jj = 2, jpjm1
1163	DO ji = 2, jpim1
1164	zpwes = 0._wp; zpwed = 0._wp
1165	zpnss = 0._wp; zpnsd = 0._wp
1166	zuijk = zu(ji,jj,jk)
1167	zvijk = zv(ji,jj,jk)
1168
1169	!!!!! for u equation
1170	IF( jk <= mbku(ji,jj) ) THEN
1171	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
1172	jis = ji + 1; jid = ji
1173	ELSE
1174	jis = ji; jid = ji +1
1175	ENDIF
1176
1177	! integrate the pressure on the shallow side
1178	jk1 = jk
1179	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
1180	IF( jk1 == mbku(ji,jj) ) THEN
1181	zuijk = -zdept(jis,jj,jk1)
1182	EXIT
1183	ENDIF
1184	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
1185	zpwes = zpwes + &
1186	integ_spline(zdept(jis,jj,jk1), zdeps, &
1187	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
1188	csp(jis,jj,jk1), dsp(jis,jj,jk1))
1189	jk1 = jk1 + 1
1190	END DO
1191
1192	! integrate the pressure on the deep side
1193	jk1 = jk
1194	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
1195	IF( jk1 == 1 ) THEN
1196	zdeps = zdept(jid,jj,1) + MIN(zuijk, ssh(jid,jj,Kmm)*znad)
1197	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
1198	bsp(jid,jj,1), csp(jid,jj,1), &
1199	dsp(jid,jj,1)) * zdeps
1200	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
1201	EXIT
1202	ENDIF
1203	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
1204	zpwed = zpwed + &
1205	integ_spline(zdeps, zdept(jid,jj,jk1), &
1206	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
1207	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
1208	jk1 = jk1 - 1
1209	END DO
1210
1211	! update the momentum trends in u direction
1212
1213	zdpdx1 = zcoef0 * r1_e1u(ji,jj) * ( zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk) )
1214	IF( .NOT.ln_linssh ) THEN
1215	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * &
1216	& ( REAL(jis-jid, wp) * (zpwes + zpwed) + (ssh(ji+1,jj,Kmm)-ssh(ji,jj,Kmm)) )
1217	ELSE
1218	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
1219	ENDIF
1220	IF( ln_wd_il ) THEN
1221	zdpdx1 = zdpdx1 * zcpx(ji,jj) * wdrampu(ji,jj)
1222	zdpdx2 = zdpdx2 * zcpx(ji,jj) * wdrampu(ji,jj)
1223	ENDIF
1224	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + (zdpdx1 + zdpdx2) * umask(ji,jj,jk)
1225	ENDIF
1226
1227	!!!!! for v equation
1228	IF( jk <= mbkv(ji,jj) ) THEN
1229	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
1230	jjs = jj + 1; jjd = jj
1231	ELSE
1232	jjs = jj ; jjd = jj + 1
1233	ENDIF
1234
1235	! integrate the pressure on the shallow side
1236	jk1 = jk
1237	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
1238	IF( jk1 == mbkv(ji,jj) ) THEN
1239	zvijk = -zdept(ji,jjs,jk1)
1240	EXIT
1241	ENDIF
1242	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
1243	zpnss = zpnss + &
1244	integ_spline(zdept(ji,jjs,jk1), zdeps, &
1245	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
1246	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
1247	jk1 = jk1 + 1
1248	END DO
1249
1250	! integrate the pressure on the deep side
1251	jk1 = jk
1252	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
1253	IF( jk1 == 1 ) THEN
1254	zdeps = zdept(ji,jjd,1) + MIN(zvijk, ssh(ji,jjd,Kmm)*znad)
1255	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
1256	bsp(ji,jjd,1), csp(ji,jjd,1), &
1257	dsp(ji,jjd,1) ) * zdeps
1258	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
1259	EXIT
1260	ENDIF
1261	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
1262	zpnsd = zpnsd + &
1263	integ_spline(zdeps, zdept(ji,jjd,jk1), &
1264	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
1265	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
1266	jk1 = jk1 - 1
1267	END DO
1268
1269
1270	! update the momentum trends in v direction
1271
1272	zdpdy1 = zcoef0 * r1_e2v(ji,jj) * ( zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk) )
1273	IF( .NOT.ln_linssh ) THEN
1274	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * &
1275	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (ssh(ji,jj+1,Kmm)-ssh(ji,jj,Kmm)) )
1276	ELSE
1277	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
1278	ENDIF
1279	IF( ln_wd_il ) THEN
1280	zdpdy1 = zdpdy1 * zcpy(ji,jj) * wdrampv(ji,jj)
1281	zdpdy2 = zdpdy2 * zcpy(ji,jj) * wdrampv(ji,jj)
1282	ENDIF
1283
1284	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + (zdpdy1 + zdpdy2) * vmask(ji,jj,jk)
1285	ENDIF
1286	!
1287	END DO
1288	END DO
1289	END DO
1290	!
1291	IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy )
1292	!
1293	END SUBROUTINE hpg_prj
1294
1295
1296	SUBROUTINE cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
1297	!!----------------------------------------------------------------------
1298	!! * ROUTINE cspline *
1299	!!
1300	!! ** Purpose : constrained cubic spline interpolation
1301	!!
1302	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
1303	!!
1304	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
1305	!!----------------------------------------------------------------------
1306	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: fsp, xsp ! value and coordinate
1307	REAL(wp), DIMENSION(:,:,:), INTENT( out) :: asp, bsp, csp, dsp ! coefficients of the interpoated function
1308	INTEGER , INTENT(in ) :: polynomial_type ! 1: cubic spline ; 2: Linear
1309	!
1310	INTEGER :: ji, jj, jk ! dummy loop indices
1311	INTEGER :: jpi, jpj, jpkm1
1312	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
1313	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
1314	REAL(wp) :: zdf(size(fsp,3))
1315	!!----------------------------------------------------------------------
1316	!
1317	!!gm WHAT !!!!! THIS IS VERY DANGEROUS !!!!!
1318	jpi = size(fsp,1)
1319	jpj = size(fsp,2)
1320	jpkm1 = MAX( 1, size(fsp,3) - 1 )
1321	!
1322	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
1323	DO ji = 1, jpi
1324	DO jj = 1, jpj
1325	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
1326	! DO jk = 2, jpkm1-1
1327	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
1328	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1329	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
1330	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
1331	!
1332	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
1333	!
1334	! IF(zdf1 * zdf2 <= 0._wp) THEN
1335	! zdf(jk) = 0._wp
1336	! ELSE
1337	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
1338	! ENDIF
1339	! END DO
1340
1341	!!Simply geometric average
1342	DO jk = 2, jpkm1-1
1343	zdf1 = (fsp(ji,jj,jk ) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk ) - xsp(ji,jj,jk-1))
1344	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk )) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk ))
1345
1346	IF(zdf1 * zdf2 <= 0._wp) THEN
1347	zdf(jk) = 0._wp
1348	ELSE
1349	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
1350	ENDIF
1351	END DO
1352
1353	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
1354	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
1355	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
1356	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - 0.5_wp * zdf(jpkm1 - 1)
1357
1358	DO jk = 1, jpkm1 - 1
1359	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1360	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
1361	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
1362	zddf1 = -2._wp * ztmp1 + ztmp2
1363	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
1364	zddf2 = 2._wp * ztmp1 - ztmp2
1365
1366	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
1367	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
1368	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
1369	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
1370	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
1371	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
1372	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
1373	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
1374	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
1375	END DO
1376	END DO
1377	END DO
1378
1379	ELSEIF ( polynomial_type == 2 ) THEN ! Linear
1380	DO ji = 1, jpi
1381	DO jj = 1, jpj
1382	DO jk = 1, jpkm1-1
1383	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1384	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
1385
1386	dsp(ji,jj,jk) = 0._wp
1387	csp(ji,jj,jk) = 0._wp
1388	bsp(ji,jj,jk) = ztmp1 / zdxtmp
1389	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
1390	END DO
1391	END DO
1392	END DO
1393	!
1394	ELSE
1395	CALL ctl_stop( 'invalid polynomial type in cspline' )
1396	ENDIF
1397	!
1398	END SUBROUTINE cspline
1399
1400
1401	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
1402	!!----------------------------------------------------------------------
1403	!! * ROUTINE interp1 *
1404	!!
1405	!! ** Purpose : 1-d linear interpolation
1406	!!
1407	!! ** Method : interpolation is straight forward
1408	!! extrapolation is also permitted (no value limit)
1409	!!----------------------------------------------------------------------
1410	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
1411	REAL(wp) :: f ! result of the interpolation (extrapolation)
1412	REAL(wp) :: zdeltx
1413	!!----------------------------------------------------------------------
1414	!
1415	zdeltx = xr - xl
1416	IF( abs(zdeltx) <= 10._wp * EPSILON(x) ) THEN
1417	f = 0.5_wp * (fl + fr)
1418	ELSE
1419	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
1420	ENDIF
1421	!
1422	END FUNCTION interp1
1423
1424
1425	FUNCTION interp2( x, a, b, c, d ) RESULT(f)
1426	!!----------------------------------------------------------------------
1427	!! * ROUTINE interp1 *
1428	!!
1429	!! ** Purpose : 1-d constrained cubic spline interpolation
1430	!!
1431	!! ** Method : cubic spline interpolation
1432	!!
1433	!!----------------------------------------------------------------------
1434	REAL(wp), INTENT(in) :: x, a, b, c, d
1435	REAL(wp) :: f ! value from the interpolation
1436	!!----------------------------------------------------------------------
1437	!
1438	f = a + x* ( b + x * ( c + d * x ) )
1439	!
1440	END FUNCTION interp2
1441
1442
1443	FUNCTION interp3( x, a, b, c, d ) RESULT(f)
1444	!!----------------------------------------------------------------------
1445	!! * ROUTINE interp1 *
1446	!!
1447	!! ** Purpose : Calculate the first order of derivative of
1448	!! a cubic spline function y=a+bx+cx^2+d*x^3
1449	!!
1450	!! ** Method : f=dy/dx=b+2cx+3dx^2
1451	!!
1452	!!----------------------------------------------------------------------
1453	REAL(wp), INTENT(in) :: x, a, b, c, d
1454	REAL(wp) :: f ! value from the interpolation
1455	!!----------------------------------------------------------------------
1456	!
1457	f = b + x * ( 2._wp * c + 3._wp * d * x)
1458	!
1459	END FUNCTION interp3
1460
1461
1462	FUNCTION integ_spline( xl, xr, a, b, c, d ) RESULT(f)
1463	!!----------------------------------------------------------------------
1464	!! * ROUTINE interp1 *
1465	!!
1466	!! ** Purpose : 1-d constrained cubic spline integration
1467	!!
1468	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
1469	!!
1470	!!----------------------------------------------------------------------
1471	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
1472	REAL(wp) :: za1, za2, za3
1473	REAL(wp) :: f ! integration result
1474	!!----------------------------------------------------------------------
1475	!
1476	za1 = 0.5_wp * b
1477	za2 = c / 3.0_wp
1478	za3 = 0.25_wp * d
1479	!
1480	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
1481	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
1482	!
1483	END FUNCTION integ_spline
1484
1485	!!======================================================================
1486	END MODULE dynhpg
1487

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