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dynhpg.F90 in branches/UKMO/dev_r5518_pcbias_ipc/NEMOGCM/NEMO/OPA_SRC/DYN – NEMO

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source: branches/UKMO/dev_r5518_pcbias_ipc/NEMOGCM/NEMO/OPA_SRC/DYN/dynhpg.F90 @ 7657

Last change on this file since 7657 was 7657, checked in by isabella, 7 years ago
adding more output messages
File size: 71.1 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 phycst ! physical constants
36	USE trd_oce ! trends: ocean variables
37	USE trddyn ! trend manager: dynamics
38	!
39	USE in_out_manager ! I/O manager
40	USE prtctl ! Print control
41	USE lbclnk ! lateral boundary condition
42	USE lib_mpp ! MPP library
43	USE eosbn2 ! compute density
44	USE wrk_nemo ! Memory Allocation
45	USE timing ! Timing
46	USE biaspar ! bias correction variables
47
48	IMPLICIT NONE
49	PRIVATE
50
51	PUBLIC dyn_hpg ! routine called by step module
52	PUBLIC dyn_hpg_init ! routine called by opa module
53
54	! !!* Namelist namdyn_hpg : hydrostatic pressure gradient
55	LOGICAL , PUBLIC :: ln_hpg_zco !: z-coordinate - full steps
56	LOGICAL , PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation)
57	LOGICAL , PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation)
58	LOGICAL , PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial)
59	LOGICAL , PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme)
60	LOGICAL , PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf
61	LOGICAL , PUBLIC :: ln_dynhpg_imp !: semi-implicite hpg flag
62
63	INTEGER , PUBLIC :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM)
64
65	!! * Substitutions
66	# include "domzgr_substitute.h90"
67	# include "vectopt_loop_substitute.h90"
68	!!----------------------------------------------------------------------
69	!! NEMO/OPA 3.3 , NEMO Consortium (2010)
70	!! $Id$
71	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
72	!!----------------------------------------------------------------------
73	CONTAINS
74
75	SUBROUTINE dyn_hpg( kt )
76	!!---------------------------------------------------------------------
77	!! * ROUTINE dyn_hpg *
78	!!
79	!! ** Method : Call the hydrostatic pressure gradient routine
80	!! using the scheme defined in the namelist
81	!!
82	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
83	!! - send trends to trd_dyn for futher diagnostics (l_trddyn=T)
84	!!----------------------------------------------------------------------
85	INTEGER, INTENT(in) :: kt ! ocean time-step index
86	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdu, ztrdv
87	REAL(wp), DIMENSION(jpi,jpj,jpk) :: z_rhd_st ! tmp density storage for pressure corr
88	REAL(wp), DIMENSION(jpi,jpj) :: z_gru_st ! tmp ua trends storage for pressure corr
89	REAL(wp), DIMENSION(jpi,jpj) :: z_grv_st ! tmp va trends storage for pressure corr
90	!!----------------------------------------------------------------------
91	!
92	IF( nn_timing == 1 ) CALL timing_start('dyn_hpg')
93	!
94	IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn)
95	CALL wrk_alloc( jpi,jpj,jpk, ztrdu, ztrdv )
96	ztrdu(:,:,:) = ua(:,:,:)
97	ztrdv(:,:,:) = va(:,:,:)
98	ENDIF
99	!
100	IF ( ln_bias .AND. ln_bias_pc_app ) THEN
101	IF(lwp) THEN
102	WRITE(numout,*) " ! store orig density, use pressure corrected density using gru_pc and grv_pc"
103	ENDIF
104	z_rhd_st(:,:,:) = rhd(:,:,:) ! store orig density
105	rhd(:,:,:) = rhd_pc(:,:,:) ! use pressure corrected density
106	z_gru_st(:,:) = gru(:,:)
107	gru(:,:) = gru_pc(:,:)
108	z_grv_st(:,:) = grv(:,:)
109	grv(:,:) = grv_pc(:,:)
110	ENDIF
111	!
112	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
113	IF(lwp) THEN
114	WRITE(numout,*) " computing pressure gradient with nhpg = ",nhpg
115	ENDIF
116	CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate
117	CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation)
118	CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation)
119	CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial)
120	CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme)
121	CASE ( 5 ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf
122	END SELECT
123	!
124	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
125	ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:)
126	ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:)
127	CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt )
128	CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv )
129	ENDIF
130	!
131	IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, &
132	& tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
133	!
134	IF ( ln_bias .AND. ln_bias_pc_app ) THEN
135	IF(lwp) THEN
136	WRITE(numout,*) " ! restore original density"
137	ENDIF
138	rhd(:,:,:) = z_rhd_st(:,:,:) ! restore original density
139	gru(:,:) = z_gru_st(:,:)
140	grv(:,:) = z_grv_st(:,:)
141	ENDIF
142	!
143	IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg')
144	!
145	END SUBROUTINE dyn_hpg
146
147
148	SUBROUTINE dyn_hpg_init
149	!!----------------------------------------------------------------------
150	!! * ROUTINE dyn_hpg_init *
151	!!
152	!! ** Purpose : initializations for the hydrostatic pressure gradient
153	!! computation and consistency control
154	!!
155	!! ** Action : Read the namelist namdyn_hpg and check the consistency
156	!! with the type of vertical coordinate used (zco, zps, sco)
157	!!----------------------------------------------------------------------
158	INTEGER :: ioptio = 0 ! temporary integer
159	INTEGER :: ios ! Local integer output status for namelist read
160	!!
161	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
162	& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf, ln_dynhpg_imp
163	!!----------------------------------------------------------------------
164	!
165	REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient
166	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
167	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp )
168
169	REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient
170	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
171	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp )
172	IF(lwm) WRITE ( numond, namdyn_hpg )
173	!
174	IF(lwp) THEN ! Control print
175	WRITE(numout,*)
176	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
177	WRITE(numout,*) '~~~~~~~~~~~~'
178	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
179	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
180	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
181	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
182	WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf
183	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
184	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
185	WRITE(numout,*) ' time stepping: centered (F) or semi-implicit (T) ln_dynhpg_imp = ', ln_dynhpg_imp
186	ENDIF
187	!
188	IF( ln_hpg_djc ) &
189	& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method &
190	& currently disabled (bugs under investigation). Please select &
191	& either ln_hpg_sco or ln_hpg_prj instead')
192	!
193	IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) &
194	& CALL ctl_stop('dyn_hpg_init : variable volume key_vvl requires:&
195	& the standard jacobian formulation hpg_sco or &
196	& the pressure jacobian formulation hpg_prj')
197
198	IF( ln_hpg_isf .AND. .NOT. ln_isfcav ) &
199	& CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' )
200	IF( .NOT. ln_hpg_isf .AND. ln_isfcav ) &
201	& CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' )
202	!
203	! ! Set nhpg from ln_hpg_... flags
204	IF( ln_hpg_zco ) nhpg = 0
205	IF( ln_hpg_zps ) nhpg = 1
206	IF( ln_hpg_sco ) nhpg = 2
207	IF( ln_hpg_djc ) nhpg = 3
208	IF( ln_hpg_prj ) nhpg = 4
209	IF( ln_hpg_isf ) nhpg = 5
210	!
211	! ! Consistency check
212	ioptio = 0
213	IF( ln_hpg_zco ) ioptio = ioptio + 1
214	IF( ln_hpg_zps ) ioptio = ioptio + 1
215	IF( ln_hpg_sco ) ioptio = ioptio + 1
216	IF( ln_hpg_djc ) ioptio = ioptio + 1
217	IF( ln_hpg_prj ) ioptio = ioptio + 1
218	IF( ln_hpg_isf ) ioptio = ioptio + 1
219	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
220	!
221	! initialisation of ice load
222	riceload(:,:)=0.0
223	!
224	END SUBROUTINE dyn_hpg_init
225
226
227	SUBROUTINE hpg_zco( kt )
228	!!---------------------------------------------------------------------
229	!! * ROUTINE hpg_zco *
230	!!
231	!! ** Method : z-coordinate case, levels are horizontal surfaces.
232	!! The now hydrostatic pressure gradient at a given level, jk,
233	!! is computed by taking the vertical integral of the in-situ
234	!! density gradient along the model level from the suface to that
235	!! level: zhpi = grav .....
236	!! zhpj = grav .....
237	!! add it to the general momentum trend (ua,va).
238	!! ua = ua - 1/e1u * zhpi
239	!! va = va - 1/e2v * zhpj
240	!!
241	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
242	!!----------------------------------------------------------------------
243	INTEGER, INTENT(in) :: kt ! ocean time-step index
244	!!
245	INTEGER :: ji, jj, jk ! dummy loop indices
246	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
247	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
248	!!----------------------------------------------------------------------
249	!
250	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
251	!
252	IF( kt == nit000 ) THEN
253	IF(lwp) WRITE(numout,*)
254	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
255	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
256	ENDIF
257
258	zcoef0 = - grav * 0.5_wp ! Local constant initialization
259
260	! Surface value
261	DO jj = 2, jpjm1
262	DO ji = fs_2, fs_jpim1 ! vector opt.
263	zcoef1 = zcoef0 * fse3w(ji,jj,1)
264	! hydrostatic pressure gradient
265	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
266	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
267	! add to the general momentum trend
268	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
269	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
270	END DO
271	END DO
272
273	!
274	! interior value (2=<jk=<jpkm1)
275	DO jk = 2, jpkm1
276	DO jj = 2, jpjm1
277	DO ji = fs_2, fs_jpim1 ! vector opt.
278	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
279	! hydrostatic pressure gradient
280	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
281	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
282	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
283
284	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
285	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
286	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
287	! add to the general momentum trend
288	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
289	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
290	END DO
291	END DO
292	END DO
293	!
294	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
295	!
296	END SUBROUTINE hpg_zco
297
298
299	SUBROUTINE hpg_zps( kt )
300	!!---------------------------------------------------------------------
301	!! * ROUTINE hpg_zps *
302	!!
303	!! ** Method : z-coordinate plus partial steps case. blahblah...
304	!!
305	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
306	!!----------------------------------------------------------------------
307	INTEGER, INTENT(in) :: kt ! ocean time-step index
308	!!
309	INTEGER :: ji, jj, jk ! dummy loop indices
310	INTEGER :: iku, ikv ! temporary integers
311	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
312	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
313	!!----------------------------------------------------------------------
314	!
315	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
316	!
317	IF( kt == nit000 ) THEN
318	IF(lwp) WRITE(numout,*)
319	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
320	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
321	ENDIF
322
323
324	! Local constant initialization
325	zcoef0 = - grav * 0.5_wp
326
327	! Surface value (also valid in partial step case)
328	DO jj = 2, jpjm1
329	DO ji = fs_2, fs_jpim1 ! vector opt.
330	zcoef1 = zcoef0 * fse3w(ji,jj,1)
331	! hydrostatic pressure gradient
332	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
333	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
334	! add to the general momentum trend
335	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
336	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
337	END DO
338	END DO
339
340
341	! interior value (2=<jk=<jpkm1)
342	DO jk = 2, jpkm1
343	DO jj = 2, jpjm1
344	DO ji = fs_2, fs_jpim1 ! vector opt.
345	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
346	! hydrostatic pressure gradient
347	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
348	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
349	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
350
351	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
352	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
353	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
354	! add to the general momentum trend
355	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
356	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
357	END DO
358	END DO
359	END DO
360
361
362	! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
363	DO jj = 2, jpjm1
364	DO ji = 2, jpim1
365	iku = mbku(ji,jj)
366	ikv = mbkv(ji,jj)
367	zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) )
368	zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) )
369	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
370	ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value
371	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
372	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj)
373	ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
374	ENDIF
375	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
376	va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value
377	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
378	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj)
379	va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
380	ENDIF
381	END DO
382	END DO
383	!
384	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
385	!
386	END SUBROUTINE hpg_zps
387
388	SUBROUTINE hpg_sco( kt )
389	!!---------------------------------------------------------------------
390	!! * ROUTINE hpg_sco *
391	!!
392	!! ** Method : s-coordinate case. Jacobian scheme.
393	!! The now hydrostatic pressure gradient at a given level, jk,
394	!! is computed by taking the vertical integral of the in-situ
395	!! density gradient along the model level from the suface to that
396	!! level. s-coordinates (ln_sco): a corrective term is added
397	!! to the horizontal pressure gradient :
398	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
399	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
400	!! add it to the general momentum trend (ua,va).
401	!! ua = ua - 1/e1u * zhpi
402	!! va = va - 1/e2v * zhpj
403	!!
404	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
405	!!----------------------------------------------------------------------
406	INTEGER, INTENT(in) :: kt ! ocean time-step index
407	!!
408	INTEGER :: ji, jj, jk ! dummy loop indices
409	REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars
410	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
411	!!----------------------------------------------------------------------
412	!
413	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
414	!
415	IF( kt == nit000 ) THEN
416	IF(lwp) WRITE(numout,*)
417	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
418	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
419	ENDIF
420
421	! Local constant initialization
422	zcoef0 = - grav * 0.5_wp
423	! To use density and not density anomaly
424	IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
425	ELSE ; znad = 0._wp ! Fixed volume
426	ENDIF
427
428	! Surface value
429	DO jj = 2, jpjm1
430	DO ji = fs_2, fs_jpim1 ! vector opt.
431	! hydrostatic pressure gradient along s-surfaces
432	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) &
433	& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
434	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) &
435	& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
436	! s-coordinate pressure gradient correction
437	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
438	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
439	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
440	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
441	! add to the general momentum trend
442	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap
443	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap
444	END DO
445	END DO
446
447	! interior value (2=<jk=<jpkm1)
448	DO jk = 2, jpkm1
449	DO jj = 2, jpjm1
450	DO ji = fs_2, fs_jpim1 ! vector opt.
451	! hydrostatic pressure gradient along s-surfaces
452	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
453	& * ( fse3w(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) &
454	& - fse3w(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) )
455	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
456	& * ( fse3w(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) &
457	& - fse3w(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) )
458	! s-coordinate pressure gradient correction
459	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
460	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj)
461	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
462	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj)
463	! add to the general momentum trend
464	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap
465	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap
466	END DO
467	END DO
468	END DO
469	!
470	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
471	!
472	END SUBROUTINE hpg_sco
473
474	SUBROUTINE hpg_isf( kt )
475	!!---------------------------------------------------------------------
476	!! * ROUTINE hpg_sco *
477	!!
478	!! ** Method : s-coordinate case. Jacobian scheme.
479	!! The now hydrostatic pressure gradient at a given level, jk,
480	!! is computed by taking the vertical integral of the in-situ
481	!! density gradient along the model level from the suface to that
482	!! level. s-coordinates (ln_sco): a corrective term is added
483	!! to the horizontal pressure gradient :
484	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
485	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
486	!! add it to the general momentum trend (ua,va).
487	!! ua = ua - 1/e1u * zhpi
488	!! va = va - 1/e2v * zhpj
489	!! iceload is added and partial cell case are added to the top and bottom
490	!!
491	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
492	!!----------------------------------------------------------------------
493	INTEGER, INTENT(in) :: kt ! ocean time-step index
494	!!
495	INTEGER :: ji, jj, jk, iku, ikv, ikt, iktp1i, iktp1j ! dummy loop indices
496	REAL(wp) :: zcoef0, zuap, zvap, znad, ze3wu, ze3wv, zuapint, zvapint, zhpjint, zhpiint, zdzwt, zdzwtjp1, zdzwtip1 ! temporary scalars
497	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj, zrhd
498	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop
499	REAL(wp), POINTER, DIMENSION(:,:) :: ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj
500	!!----------------------------------------------------------------------
501	!
502	CALL wrk_alloc( jpi,jpj, 2, ztstop)
503	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
504	CALL wrk_alloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
505	!
506	IF( kt == nit000 ) THEN
507	IF(lwp) WRITE(numout,*)
508	IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf'
509	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
510	ENDIF
511
512	! Local constant initialization
513	zcoef0 = - grav * 0.5_wp
514	! To use density and not density anomaly
515	! IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
516	! ELSE ; znad = 0._wp ! Fixed volume
517	! ENDIF
518	znad=1._wp
519	! iniitialised to 0. zhpi zhpi
520	zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp
521
522	!==================================================================================
523	!=====Compute iceload and contribution of the half first wet layer =================
524	!===================================================================================
525
526	! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude)
527	ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp
528
529	! compute density of the water displaced by the ice shelf
530	zrhd = rhd ! save rhd
531	DO jk = 1, jpk
532	zdept(:,:)=gdept_1d(jk)
533	CALL eos(ztstop(:,:,:),zdept(:,:),rhd(:,:,jk))
534	END DO
535	WHERE ( tmask(:,:,:) == 1._wp)
536	rhd(:,:,:) = zrhd(:,:,:) ! replace wet cell by the saved rhd
537	END WHERE
538
539	! compute rhd at the ice/oce interface (ice shelf side)
540	CALL eos(ztstop,risfdep,zrhdtop_isf)
541
542	! compute rhd at the ice/oce interface (ocean side)
543	DO ji=1,jpi
544	DO jj=1,jpj
545	ikt=mikt(ji,jj)
546	ztstop(ji,jj,1)=tsn(ji,jj,ikt,1)
547	ztstop(ji,jj,2)=tsn(ji,jj,ikt,2)
548	END DO
549	END DO
550	CALL eos(ztstop,risfdep,zrhdtop_oce)
551	!
552	! Surface value + ice shelf gradient
553	! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v)
554	ziceload = 0._wp
555	DO jj = 1, jpj
556	DO ji = 1, jpi ! vector opt.
557	ikt=mikt(ji,jj)
558	ziceload(ji,jj) = ziceload(ji,jj) + (znad + rhd(ji,jj,1) ) * fse3w(ji,jj,1) * (1._wp - tmask(ji,jj,1))
559	DO jk=2,ikt-1
560	ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + rhd(ji,jj,jk-1) + rhd(ji,jj,jk)) * fse3w(ji,jj,jk) &
561	& * (1._wp - tmask(ji,jj,jk))
562	END DO
563	IF (ikt .GE. 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + rhd(ji,jj,ikt-1)) &
564	& * ( risfdep(ji,jj) - gdept_1d(ikt-1) )
565	END DO
566	END DO
567	riceload(:,:) = 0.0_wp ; riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5
568	! compute zp from z=0 to first T wet point (correction due to zps not yet applied)
569	DO jj = 2, jpjm1
570	DO ji = fs_2, fs_jpim1 ! vector opt.
571	ikt=mikt(ji,jj) ; iktp1i=mikt(ji+1,jj); iktp1j=mikt(ji,jj+1)
572	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
573	! we assume ISF is in isostatic equilibrium
574	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * fse3w(ji+1,jj ,iktp1i) &
575	& * ( 2._wp * znad + rhd(ji+1,jj ,iktp1i) + zrhdtop_oce(ji+1,jj ) ) &
576	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
577	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
578	& + ( ziceload(ji+1,jj) - ziceload(ji,jj)) )
579	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * fse3w(ji ,jj+1,iktp1j) &
580	& * ( 2._wp * znad + rhd(ji ,jj+1,iktp1j) + zrhdtop_oce(ji ,jj+1) ) &
581	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
582	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
583	& + ( ziceload(ji,jj+1) - ziceload(ji,jj) ) )
584	! s-coordinate pressure gradient correction (=0 if z coordinate)
585	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
586	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
587	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
588	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
589	! add to the general momentum trend
590	ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
591	va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
592	END DO
593	END DO
594	!==================================================================================
595	!===== Compute partial cell contribution for the top cell =========================
596	!==================================================================================
597	DO jj = 2, jpjm1
598	DO ji = fs_2, fs_jpim1 ! vector opt.
599	iku = miku(ji,jj) ;
600	zpshpi(ji,jj)=0.0_wp ; zpshpj(ji,jj)=0.0_wp
601	ze3wu = (gdepw_0(ji+1,jj,iku+1) - gdept_0(ji+1,jj,iku)) - (gdepw_0(ji,jj,iku+1) - gdept_0(ji,jj,iku))
602	! u direction
603	IF ( iku .GT. 1 ) THEN
604	! case iku
605	zhpi(ji,jj,iku) = zcoef0 / e1u(ji,jj) * ze3wu &
606	& * ( rhd (ji+1,jj,iku) + rhd (ji,jj,iku) &
607	& + SIGN(1._wp,ze3wu) * grui(ji,jj) + 2._wp * znad )
608	! corrective term ( = 0 if z coordinate )
609	zuap = -zcoef0 * ( arui(ji,jj) + 2._wp * znad ) * gzui(ji,jj) / e1u(ji,jj)
610	! zhpi will be added in interior loop
611	ua(ji,jj,iku) = ua(ji,jj,iku) + zuap
612	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
613	IF (mbku(ji,jj) == iku + 1) zpshpi(ji,jj) = zhpi(ji,jj,iku)
614
615	! case iku + 1 (remove the zphi term added in the interior loop and compute the one corrected for zps)
616	zhpiint = zcoef0 / e1u(ji,jj) &
617	& * ( fse3w(ji+1,jj ,iku+1) * ( (rhd(ji+1,jj,iku+1) + znad) &
618	& + (rhd(ji+1,jj,iku ) + znad) ) * tmask(ji+1,jj,iku) &
619	& - fse3w(ji ,jj ,iku+1) * ( (rhd(ji ,jj,iku+1) + znad) &
620	& + (rhd(ji ,jj,iku ) + znad) ) * tmask(ji ,jj,iku) )
621	zhpi(ji,jj,iku+1) = zcoef0 / e1u(ji,jj) * ge3rui(ji,jj) - zhpiint
622	END IF
623
624	! v direction
625	ikv = mikv(ji,jj)
626	ze3wv = (gdepw_0(ji,jj+1,ikv+1) - gdept_0(ji,jj+1,ikv)) - (gdepw_0(ji,jj,ikv+1) - gdept_0(ji,jj,ikv))
627	IF ( ikv .GT. 1 ) THEN
628	! case ikv
629	zhpj(ji,jj,ikv) = zcoef0 / e2v(ji,jj) * ze3wv &
630	& * ( rhd(ji,jj+1,ikv) + rhd (ji,jj,ikv) &
631	& + SIGN(1._wp,ze3wv) * grvi(ji,jj) + 2._wp * znad )
632	! corrective term ( = 0 if z coordinate )
633	zvap = -zcoef0 * ( arvi(ji,jj) + 2._wp * znad ) * gzvi(ji,jj) / e2v(ji,jj)
634	! zhpi will be added in interior loop
635	va(ji,jj,ikv) = va(ji,jj,ikv) + zvap
636	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
637	IF (mbkv(ji,jj) == ikv + 1) zpshpj(ji,jj) = zhpj(ji,jj,ikv)
638
639	! case ikv + 1 (remove the zphj term added in the interior loop and compute the one corrected for zps)
640	zhpjint = zcoef0 / e2v(ji,jj) &
641	& * ( fse3w(ji ,jj+1,ikv+1) * ( (rhd(ji,jj+1,ikv+1) + znad) &
642	& + (rhd(ji,jj+1,ikv ) + znad) ) * tmask(ji,jj+1,ikv) &
643	& - fse3w(ji ,jj ,ikv+1) * ( (rhd(ji,jj ,ikv+1) + znad) &
644	& + (rhd(ji,jj ,ikv ) + znad) ) * tmask(ji,jj ,ikv) )
645	zhpj(ji,jj,ikv+1) = zcoef0 / e2v(ji,jj) * ge3rvi(ji,jj) - zhpjint
646	END IF
647	END DO
648	END DO
649
650	!==================================================================================
651	!===== Compute interior value =====================================================
652	!==================================================================================
653
654	DO jj = 2, jpjm1
655	DO ji = fs_2, fs_jpim1 ! vector opt.
656	iku=miku(ji,jj); ikv=mikv(ji,jj)
657	DO jk = 2, jpkm1
658	! hydrostatic pressure gradient along s-surfaces
659	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
660	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) + zhpi(ji,jj,jk-1) &
661	& + zcoef0 / e1u(ji,jj) &
662	& * ( fse3w(ji+1,jj ,jk) * ( (rhd(ji+1,jj,jk ) + znad) &
663	& + (rhd(ji+1,jj,jk-1) + znad) ) * tmask(ji+1,jj,jk-1) &
664	& - fse3w(ji ,jj ,jk) * ( (rhd(ji ,jj,jk ) + znad) &
665	& + (rhd(ji ,jj,jk-1) + znad) ) * tmask(ji ,jj,jk-1) )
666	! s-coordinate pressure gradient correction
667	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
668	zuap = - zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
669	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) * umask(ji,jj,jk-1)
670	ua(ji,jj,jk) = ua(ji,jj,jk) + ( zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
671
672	! hydrostatic pressure gradient along s-surfaces
673	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
674	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) + zhpj(ji,jj,jk-1) &
675	& + zcoef0 / e2v(ji,jj) &
676	& * ( fse3w(ji ,jj+1,jk) * ( (rhd(ji,jj+1,jk ) + znad) &
677	& + (rhd(ji,jj+1,jk-1) + znad) ) * tmask(ji,jj+1,jk-1) &
678	& - fse3w(ji ,jj ,jk) * ( (rhd(ji,jj ,jk ) + znad) &
679	& + (rhd(ji,jj ,jk-1) + znad) ) * tmask(ji,jj ,jk-1) )
680	! s-coordinate pressure gradient correction
681	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
682	zvap = - zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
683	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) * vmask(ji,jj,jk-1)
684	! add to the general momentum trend
685	va(ji,jj,jk) = va(ji,jj,jk) + ( zhpj(ji,jj,jk) + zvap ) * vmask(ji,jj,jk)
686	END DO
687	END DO
688	END DO
689
690	!==================================================================================
691	!===== Compute bottom cell contribution (partial cell) ============================
692	!==================================================================================
693
694	DO jj = 2, jpjm1
695	DO ji = 2, jpim1
696	iku = mbku(ji,jj)
697	ikv = mbkv(ji,jj)
698
699	IF (iku .GT. 1) THEN
700	! remove old value (interior case)
701	zuap = -zcoef0 * ( rhd (ji+1,jj ,iku) + rhd (ji,jj,iku) + 2._wp * znad ) &
702	& * ( fsde3w(ji+1,jj ,iku) - fsde3w(ji,jj,iku) ) / e1u(ji,jj)
703	ua(ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) - zuap
704	! put new value
705	! -zpshpi to avoid double contribution of the partial step in the top layer
706	zuap = -zcoef0 * ( aru(ji,jj) + 2._wp * znad ) * gzu(ji,jj) / e1u(ji,jj)
707	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) + zcoef0 / e1u(ji,jj) * ge3ru(ji,jj) - zpshpi(ji,jj)
708	ua(ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) + zuap
709	END IF
710	! v direction
711	IF (ikv .GT. 1) THEN
712	! remove old value (interior case)
713	zvap = -zcoef0 * ( rhd (ji ,jj+1,ikv) + rhd (ji,jj,ikv) + 2._wp * znad ) &
714	& * ( fsde3w(ji ,jj+1,ikv) - fsde3w(ji,jj,ikv) ) / e2v(ji,jj)
715	va(ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) - zvap
716	! put new value
717	! -zpshpj to avoid double contribution of the partial step in the top layer
718	zvap = -zcoef0 * ( arv(ji,jj) + 2._wp * znad ) * gzv(ji,jj) / e2v(ji,jj)
719	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) + zcoef0 / e2v(ji,jj) * ge3rv(ji,jj) - zpshpj(ji,jj)
720	va(ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) + zvap
721	END IF
722	END DO
723	END DO
724
725	! set back to original density value into the ice shelf cell (maybe useless because it is masked)
726	rhd = zrhd
727	!
728	CALL wrk_dealloc( jpi,jpj,2, ztstop)
729	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
730	CALL wrk_dealloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
731	!
732	END SUBROUTINE hpg_isf
733
734
735	SUBROUTINE hpg_djc( kt )
736	!!---------------------------------------------------------------------
737	!! * ROUTINE hpg_djc *
738	!!
739	!! ** Method : Density Jacobian with Cubic polynomial scheme
740	!!
741	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
742	!!----------------------------------------------------------------------
743	INTEGER, INTENT(in) :: kt ! ocean time-step index
744	!!
745	INTEGER :: ji, jj, jk ! dummy loop indices
746	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
747	REAL(wp) :: z1_10, cffu, cffx ! " "
748	REAL(wp) :: z1_12, cffv, cffy ! " "
749	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
750	REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw
751	REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow
752	REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k
753	!!----------------------------------------------------------------------
754	!
755	CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
756	CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
757	CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
758	!
759
760	IF( kt == nit000 ) THEN
761	IF(lwp) WRITE(numout,*)
762	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
763	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
764	ENDIF
765
766	! Local constant initialization
767	zcoef0 = - grav * 0.5_wp
768	z1_10 = 1._wp / 10._wp
769	z1_12 = 1._wp / 12._wp
770
771	!----------------------------------------------------------------------------------------
772	! compute and store in provisional arrays elementary vertical and horizontal differences
773	!----------------------------------------------------------------------------------------
774
775	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
776
777	DO jk = 2, jpkm1
778	DO jj = 2, jpjm1
779	DO ji = fs_2, fs_jpim1 ! vector opt.
780	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
781	dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1)
782	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
783	dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk )
784	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
785	dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk )
786	END DO
787	END DO
788	END DO
789
790	!-------------------------------------------------------------------------
791	! compute harmonic averages using eq. 5.18
792	!-------------------------------------------------------------------------
793	zep = 1.e-15
794
795	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
796	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
797
798	DO jk = 2, jpkm1
799	DO jj = 2, jpjm1
800	DO ji = fs_2, fs_jpim1 ! vector opt.
801	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
802
803	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
804	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
805
806	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
807	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
808
809	IF( cffw > zep) THEN
810	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
811	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
812	ELSE
813	drhow(ji,jj,jk) = 0._wp
814	ENDIF
815
816	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
817	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
818
819	IF( cffu > zep ) THEN
820	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
821	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
822	ELSE
823	drhou(ji,jj,jk ) = 0._wp
824	ENDIF
825
826	IF( cffx > zep ) THEN
827	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
828	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
829	ELSE
830	dzu(ji,jj,jk) = 0._wp
831	ENDIF
832
833	IF( cffv > zep ) THEN
834	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
835	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
836	ELSE
837	drhov(ji,jj,jk) = 0._wp
838	ENDIF
839
840	IF( cffy > zep ) THEN
841	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
842	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
843	ELSE
844	dzv(ji,jj,jk) = 0._wp
845	ENDIF
846
847	END DO
848	END DO
849	END DO
850
851	!----------------------------------------------------------------------------------
852	! apply boundary conditions at top and bottom using 5.36-5.37
853	!----------------------------------------------------------------------------------
854	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
855	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
856	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
857
858	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
859	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
860	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
861
862
863	!--------------------------------------------------------------
864	! Upper half of top-most grid box, compute and store
865	!-------------------------------------------------------------
866
867	!!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified
868	! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
869
870	DO jj = 2, jpjm1
871	DO ji = fs_2, fs_jpim1 ! vector opt.
872	rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) &
873	& * ( rhd(ji,jj,1) &
874	& + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) &
875	& * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) &
876	& / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) )
877	END DO
878	END DO
879
880	!!bug gm : here also, simplification is possible
881	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
882
883	DO jk = 2, jpkm1
884	DO jj = 2, jpjm1
885	DO ji = fs_2, fs_jpim1 ! vector opt.
886
887	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
888	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) &
889	& - grav * z1_10 * ( &
890	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
891	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
892	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
893	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
894	& )
895
896	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
897	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) &
898	& - grav* z1_10 * ( &
899	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
900	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
901	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
902	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
903	& )
904
905	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
906	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) &
907	& - grav* z1_10 * ( &
908	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
909	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
910	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
911	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
912	& )
913
914	END DO
915	END DO
916	END DO
917	CALL lbc_lnk(rho_k,'W',1.)
918	CALL lbc_lnk(rho_i,'U',1.)
919	CALL lbc_lnk(rho_j,'V',1.)
920
921
922	! ---------------
923	! Surface value
924	! ---------------
925	DO jj = 2, jpjm1
926	DO ji = fs_2, fs_jpim1 ! vector opt.
927	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj)
928	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj)
929	! add to the general momentum trend
930	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
931	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
932	END DO
933	END DO
934
935	! ----------------
936	! interior value (2=<jk=<jpkm1)
937	! ----------------
938	DO jk = 2, jpkm1
939	DO jj = 2, jpjm1
940	DO ji = fs_2, fs_jpim1 ! vector opt.
941	! hydrostatic pressure gradient along s-surfaces
942	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
943	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
944	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj)
945	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
946	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
947	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj)
948	! add to the general momentum trend
949	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
950	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
951	END DO
952	END DO
953	END DO
954	!
955	CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
956	CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
957	CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
958	!
959	END SUBROUTINE hpg_djc
960
961
962	SUBROUTINE hpg_prj( kt )
963	!!---------------------------------------------------------------------
964	!! * ROUTINE hpg_prj *
965	!!
966	!! ** Method : s-coordinate case.
967	!! A Pressure-Jacobian horizontal pressure gradient method
968	!! based on the constrained cubic-spline interpolation for
969	!! all vertical coordinate systems
970	!!
971	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
972	!!----------------------------------------------------------------------
973	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
974	INTEGER, INTENT(in) :: kt ! ocean time-step index
975	!!
976	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
977	REAL(wp) :: zcoef0, znad ! temporary scalars
978	!!
979	!! The local variables for the correction term
980	INTEGER :: jk1, jis, jid, jjs, jjd
981	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
982	REAL(wp) :: zrhdt1
983	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
984	REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh
985	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
986	REAL(wp), POINTER, DIMENSION(:,:) :: zsshu_n, zsshv_n
987	!!----------------------------------------------------------------------
988	!
989	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
990	CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh )
991	CALL wrk_alloc( jpi,jpj, zsshu_n, zsshv_n )
992	!
993	IF( kt == nit000 ) THEN
994	IF(lwp) WRITE(numout,*)
995	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
996	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
997	ENDIF
998
999	!!----------------------------------------------------------------------
1000	! Local constant initialization
1001	zcoef0 = - grav
1002	znad = 0.0_wp
1003	IF( lk_vvl ) znad = 1._wp
1004
1005	! Clean 3-D work arrays
1006	zhpi(:,:,:) = 0._wp
1007	zrhh(:,:,:) = rhd(:,:,:)
1008
1009	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
1010	DO jj = 1, jpj
1011	DO ji = 1, jpi
1012	jk = mbathy(ji,jj)
1013	IF( jk <= 0 ) THEN; zrhh(ji,jj,:) = 0._wp
1014	ELSE IF(jk == 1) THEN; zrhh(ji,jj, jk+1:jpk) = rhd(ji,jj,jk)
1015	ELSE IF(jk < jpkm1) THEN
1016	DO jkk = jk+1, jpk
1017	zrhh(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1), &
1018	fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2))
1019	END DO
1020	ENDIF
1021	END DO
1022	END DO
1023
1024	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
1025	DO jj = 1, jpj
1026	DO ji = 1, jpi
1027	zdept(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) - sshn(ji,jj) * znad
1028	END DO
1029	END DO
1030
1031	DO jk = 2, jpk
1032	DO jj = 1, jpj
1033	DO ji = 1, jpi
1034	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + fse3w(ji,jj,jk)
1035	END DO
1036	END DO
1037	END DO
1038
1039	fsp(:,:,:) = zrhh (:,:,:)
1040	xsp(:,:,:) = zdept(:,:,:)
1041
1042	! Construct the vertical density profile with the
1043	! constrained cubic spline interpolation
1044	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
1045	CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type)
1046
1047	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
1048	DO jj = 2, jpj
1049	DO ji = 2, jpi
1050	zrhdt1 = zrhh(ji,jj,1) - interp3(zdept(ji,jj,1),asp(ji,jj,1), &
1051	bsp(ji,jj,1), csp(ji,jj,1), &
1052	dsp(ji,jj,1) ) * 0.25_wp * fse3w(ji,jj,1)
1053
1054	! assuming linear profile across the top half surface layer
1055	zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * zrhdt1
1056	END DO
1057	END DO
1058
1059	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
1060	DO jk = 2, jpkm1
1061	DO jj = 2, jpj
1062	DO ji = 2, jpi
1063	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
1064	integ_spline(zdept(ji,jj,jk-1), zdept(ji,jj,jk),&
1065	asp(ji,jj,jk-1), bsp(ji,jj,jk-1), &
1066	csp(ji,jj,jk-1), dsp(ji,jj,jk-1))
1067	END DO
1068	END DO
1069	END DO
1070
1071	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
1072
1073	! Prepare zsshu_n and zsshv_n
1074	DO jj = 2, jpjm1
1075	DO ji = 2, jpim1
1076	zsshu_n(ji,jj) = (e12u(ji,jj) * sshn(ji,jj) + e12u(ji+1, jj) * sshn(ji+1,jj)) * &
1077	& r1_e12u(ji,jj) * umask(ji,jj,1) * 0.5_wp
1078	zsshv_n(ji,jj) = (e12v(ji,jj) * sshn(ji,jj) + e12v(ji+1, jj) * sshn(ji,jj+1)) * &
1079	& r1_e12v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
1080	END DO
1081	END DO
1082
1083	DO jj = 2, jpjm1
1084	DO ji = 2, jpim1
1085	zu(ji,jj,1) = - ( fse3u(ji,jj,1) - zsshu_n(ji,jj) * znad)
1086	zv(ji,jj,1) = - ( fse3v(ji,jj,1) - zsshv_n(ji,jj) * znad)
1087	END DO
1088	END DO
1089
1090	DO jk = 2, jpkm1
1091	DO jj = 2, jpjm1
1092	DO ji = 2, jpim1
1093	zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk)
1094	zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk)
1095	END DO
1096	END DO
1097	END DO
1098
1099	DO jk = 1, jpkm1
1100	DO jj = 2, jpjm1
1101	DO ji = 2, jpim1
1102	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk)
1103	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk)
1104	END DO
1105	END DO
1106	END DO
1107
1108	DO jk = 1, jpkm1
1109	DO jj = 2, jpjm1
1110	DO ji = 2, jpim1
1111	zu(ji,jj,jk) = min(zu(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
1112	zu(ji,jj,jk) = max(zu(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
1113	zv(ji,jj,jk) = min(zv(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
1114	zv(ji,jj,jk) = max(zv(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
1115	END DO
1116	END DO
1117	END DO
1118
1119
1120	DO jk = 1, jpkm1
1121	DO jj = 2, jpjm1
1122	DO ji = 2, jpim1
1123	zpwes = 0._wp; zpwed = 0._wp
1124	zpnss = 0._wp; zpnsd = 0._wp
1125	zuijk = zu(ji,jj,jk)
1126	zvijk = zv(ji,jj,jk)
1127
1128	!!!!! for u equation
1129	IF( jk <= mbku(ji,jj) ) THEN
1130	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
1131	jis = ji + 1; jid = ji
1132	ELSE
1133	jis = ji; jid = ji +1
1134	ENDIF
1135
1136	! integrate the pressure on the shallow side
1137	jk1 = jk
1138	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
1139	IF( jk1 == mbku(ji,jj) ) THEN
1140	zuijk = -zdept(jis,jj,jk1)
1141	EXIT
1142	ENDIF
1143	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
1144	zpwes = zpwes + &
1145	integ_spline(zdept(jis,jj,jk1), zdeps, &
1146	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
1147	csp(jis,jj,jk1), dsp(jis,jj,jk1))
1148	jk1 = jk1 + 1
1149	END DO
1150
1151	! integrate the pressure on the deep side
1152	jk1 = jk
1153	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
1154	IF( jk1 == 1 ) THEN
1155	zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad)
1156	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
1157	bsp(jid,jj,1), csp(jid,jj,1), &
1158	dsp(jid,jj,1)) * zdeps
1159	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
1160	EXIT
1161	ENDIF
1162	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
1163	zpwed = zpwed + &
1164	integ_spline(zdeps, zdept(jid,jj,jk1), &
1165	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
1166	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
1167	jk1 = jk1 - 1
1168	END DO
1169
1170	! update the momentum trends in u direction
1171
1172	zdpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk))
1173	IF( lk_vvl ) THEN
1174	zdpdx2 = zcoef0 / e1u(ji,jj) * &
1175	( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) )
1176	ELSE
1177	zdpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
1178	ENDIF
1179
1180	ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * &
1181	& umask(ji,jj,jk) * tmask(ji,jj,jk) * tmask(ji+1,jj,jk)
1182	ENDIF
1183
1184	!!!!! for v equation
1185	IF( jk <= mbkv(ji,jj) ) THEN
1186	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
1187	jjs = jj + 1; jjd = jj
1188	ELSE
1189	jjs = jj ; jjd = jj + 1
1190	ENDIF
1191
1192	! integrate the pressure on the shallow side
1193	jk1 = jk
1194	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
1195	IF( jk1 == mbkv(ji,jj) ) THEN
1196	zvijk = -zdept(ji,jjs,jk1)
1197	EXIT
1198	ENDIF
1199	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
1200	zpnss = zpnss + &
1201	integ_spline(zdept(ji,jjs,jk1), zdeps, &
1202	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
1203	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
1204	jk1 = jk1 + 1
1205	END DO
1206
1207	! integrate the pressure on the deep side
1208	jk1 = jk
1209	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
1210	IF( jk1 == 1 ) THEN
1211	zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad)
1212	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
1213	bsp(ji,jjd,1), csp(ji,jjd,1), &
1214	dsp(ji,jjd,1) ) * zdeps
1215	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
1216	EXIT
1217	ENDIF
1218	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
1219	zpnsd = zpnsd + &
1220	integ_spline(zdeps, zdept(ji,jjd,jk1), &
1221	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
1222	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
1223	jk1 = jk1 - 1
1224	END DO
1225
1226
1227	! update the momentum trends in v direction
1228
1229	zdpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk))
1230	IF( lk_vvl ) THEN
1231	zdpdy2 = zcoef0 / e2v(ji,jj) * &
1232	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) )
1233	ELSE
1234	zdpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
1235	ENDIF
1236
1237	va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2)*&
1238	& vmask(ji,jj,jk)tmask(ji,jj,jk)tmask(ji,jj+1,jk)
1239	ENDIF
1240
1241
1242	END DO
1243	END DO
1244	END DO
1245	!
1246	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
1247	CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh )
1248	CALL wrk_dealloc( jpi,jpj, zsshu_n, zsshv_n )
1249	!
1250	END SUBROUTINE hpg_prj
1251
1252
1253	SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type)
1254	!!----------------------------------------------------------------------
1255	!! * ROUTINE cspline *
1256	!!
1257	!! ** Purpose : constrained cubic spline interpolation
1258	!!
1259	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
1260	!!
1261	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
1262	!!----------------------------------------------------------------------
1263	IMPLICIT NONE
1264	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate
1265	REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of
1266	! the interpoated function
1267	INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline
1268	! 2: Linear
1269	!
1270	INTEGER :: ji, jj, jk ! dummy loop indices
1271	INTEGER :: jpi, jpj, jpkm1
1272	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
1273	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
1274	REAL(wp) :: zdf(size(fsp,3))
1275	!!----------------------------------------------------------------------
1276
1277	jpi = size(fsp,1)
1278	jpj = size(fsp,2)
1279	jpkm1 = size(fsp,3) - 1
1280
1281
1282	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
1283	DO ji = 1, jpi
1284	DO jj = 1, jpj
1285	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
1286	! DO jk = 2, jpkm1-1
1287	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
1288	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1289	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
1290	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
1291	!
1292	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
1293	!
1294	! IF(zdf1 * zdf2 <= 0._wp) THEN
1295	! zdf(jk) = 0._wp
1296	! ELSE
1297	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
1298	! ENDIF
1299	! END DO
1300
1301	!!Simply geometric average
1302	DO jk = 2, jpkm1-1
1303	zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1))
1304	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk))
1305
1306	IF(zdf1 * zdf2 <= 0._wp) THEN
1307	zdf(jk) = 0._wp
1308	ELSE
1309	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
1310	ENDIF
1311	END DO
1312
1313	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
1314	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
1315	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
1316	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - &
1317	& 0.5_wp * zdf(jpkm1 - 1)
1318
1319	DO jk = 1, jpkm1 - 1
1320	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1321	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
1322	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
1323	zddf1 = -2._wp * ztmp1 + ztmp2
1324	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
1325	zddf2 = 2._wp * ztmp1 - ztmp2
1326
1327	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
1328	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
1329	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
1330	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
1331	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
1332	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
1333	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
1334	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
1335	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
1336	END DO
1337	END DO
1338	END DO
1339
1340	ELSE IF (polynomial_type == 2) THEN ! Linear
1341	DO ji = 1, jpi
1342	DO jj = 1, jpj
1343	DO jk = 1, jpkm1-1
1344	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1345	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
1346
1347	dsp(ji,jj,jk) = 0._wp
1348	csp(ji,jj,jk) = 0._wp
1349	bsp(ji,jj,jk) = ztmp1 / zdxtmp
1350	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
1351	END DO
1352	END DO
1353	END DO
1354
1355	ELSE
1356	CALL ctl_stop( 'invalid polynomial type in cspline' )
1357	ENDIF
1358
1359	END SUBROUTINE cspline
1360
1361
1362	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
1363	!!----------------------------------------------------------------------
1364	!! * ROUTINE interp1 *
1365	!!
1366	!! ** Purpose : 1-d linear interpolation
1367	!!
1368	!! ** Method : interpolation is straight forward
1369	!! extrapolation is also permitted (no value limit)
1370	!!----------------------------------------------------------------------
1371	IMPLICIT NONE
1372	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
1373	REAL(wp) :: f ! result of the interpolation (extrapolation)
1374	REAL(wp) :: zdeltx
1375	!!----------------------------------------------------------------------
1376
1377	zdeltx = xr - xl
1378	IF(abs(zdeltx) <= 10._wp * EPSILON(x)) THEN
1379	f = 0.5_wp * (fl + fr)
1380	ELSE
1381	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
1382	ENDIF
1383
1384	END FUNCTION interp1
1385
1386
1387	FUNCTION interp2(x, a, b, c, d) RESULT(f)
1388	!!----------------------------------------------------------------------
1389	!! * ROUTINE interp1 *
1390	!!
1391	!! ** Purpose : 1-d constrained cubic spline interpolation
1392	!!
1393	!! ** Method : cubic spline interpolation
1394	!!
1395	!!----------------------------------------------------------------------
1396	IMPLICIT NONE
1397	REAL(wp), INTENT(in) :: x, a, b, c, d
1398	REAL(wp) :: f ! value from the interpolation
1399	!!----------------------------------------------------------------------
1400
1401	f = a + x* ( b + x * ( c + d * x ) )
1402
1403	END FUNCTION interp2
1404
1405
1406	FUNCTION interp3(x, a, b, c, d) RESULT(f)
1407	!!----------------------------------------------------------------------
1408	!! * ROUTINE interp1 *
1409	!!
1410	!! ** Purpose : Calculate the first order of deriavtive of
1411	!! a cubic spline function y=a+bx+cx^2+d*x^3
1412	!!
1413	!! ** Method : f=dy/dx=b+2cx+3dx^2
1414	!!
1415	!!----------------------------------------------------------------------
1416	IMPLICIT NONE
1417	REAL(wp), INTENT(in) :: x, a, b, c, d
1418	REAL(wp) :: f ! value from the interpolation
1419	!!----------------------------------------------------------------------
1420
1421	f = b + x * ( 2._wp * c + 3._wp * d * x)
1422
1423	END FUNCTION interp3
1424
1425
1426	FUNCTION integ_spline(xl, xr, a, b, c, d) RESULT(f)
1427	!!----------------------------------------------------------------------
1428	!! * ROUTINE interp1 *
1429	!!
1430	!! ** Purpose : 1-d constrained cubic spline integration
1431	!!
1432	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
1433	!!
1434	!!----------------------------------------------------------------------
1435	IMPLICIT NONE
1436	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
1437	REAL(wp) :: za1, za2, za3
1438	REAL(wp) :: f ! integration result
1439	!!----------------------------------------------------------------------
1440
1441	za1 = 0.5_wp * b
1442	za2 = c / 3.0_wp
1443	za3 = 0.25_wp * d
1444
1445	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
1446	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
1447
1448	END FUNCTION integ_spline
1449
1450	!!======================================================================
1451	END MODULE dynhpg
1452

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