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

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source: branches/UKMO/test_moci_test_suite_namelist_read/NEMOGCM/NEMO/OPA_SRC/DYN/dynhpg.F90 @ 9366

Last change on this file since 9366 was 9366, checked in by andmirek, 6 years ago
#2050 first version. Compiled OK in moci test suite
File size: 70.7 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
47	IMPLICIT NONE
48	PRIVATE
49
50	PUBLIC dyn_hpg ! routine called by step module
51	PUBLIC dyn_hpg_init ! routine called by opa module
52	PRIVATE hpg_namelist
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	!!----------------------------------------------------------------------
88	!
89	IF( nn_timing == 1 ) CALL timing_start('dyn_hpg')
90	!
91	IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn)
92	CALL wrk_alloc( jpi,jpj,jpk, ztrdu, ztrdv )
93	ztrdu(:,:,:) = ua(:,:,:)
94	ztrdv(:,:,:) = va(:,:,:)
95	ENDIF
96	!
97	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
98	CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate
99	CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation)
100	CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation)
101	CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial)
102	CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme)
103	CASE ( 5 ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf
104	END SELECT
105	!
106	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
107	ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:)
108	ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:)
109	CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt )
110	CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv )
111	ENDIF
112	!
113	IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, &
114	& tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
115	!
116	IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg')
117	!
118	END SUBROUTINE dyn_hpg
119
120
121	SUBROUTINE dyn_hpg_init
122	!!----------------------------------------------------------------------
123	!! * ROUTINE dyn_hpg_init *
124	!!
125	!! ** Purpose : initializations for the hydrostatic pressure gradient
126	!! computation and consistency control
127	!!
128	!! ** Action : Read the namelist namdyn_hpg and check the consistency
129	!! with the type of vertical coordinate used (zco, zps, sco)
130	!!----------------------------------------------------------------------
131	INTEGER :: ioptio = 0 ! temporary integer
132	INTEGER :: ios ! Local integer output status for namelist read
133	!!
134	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
135	& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf, ln_dynhpg_imp
136	!!----------------------------------------------------------------------
137	!
138	IF(lwm) THEN
139	REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient
140	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
141	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwm )
142	REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient
143	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
144	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwm )
145	ENDIF
146
147	IF(lwm) WRITE ( numond, namdyn_hpg )
148	!
149	CALL hpg_namelist()
150
151	IF(lwp) THEN ! Control print
152	WRITE(numout,*)
153	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
154	WRITE(numout,*) '~~~~~~~~~~~~'
155	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
156	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
157	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
158	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
159	WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf
160	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
161	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
162	WRITE(numout,*) ' time stepping: centered (F) or semi-implicit (T) ln_dynhpg_imp = ', ln_dynhpg_imp
163	ENDIF
164	!
165	IF( ln_hpg_djc ) &
166	& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method &
167	& currently disabled (bugs under investigation). Please select &
168	& either ln_hpg_sco or ln_hpg_prj instead')
169	!
170	IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) &
171	& CALL ctl_stop('dyn_hpg_init : variable volume key_vvl requires:&
172	& the standard jacobian formulation hpg_sco or &
173	& the pressure jacobian formulation hpg_prj')
174
175	IF( ln_hpg_isf .AND. .NOT. ln_isfcav ) &
176	& CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' )
177	IF( .NOT. ln_hpg_isf .AND. ln_isfcav ) &
178	& CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' )
179	!
180	! ! Set nhpg from ln_hpg_... flags
181	IF( ln_hpg_zco ) nhpg = 0
182	IF( ln_hpg_zps ) nhpg = 1
183	IF( ln_hpg_sco ) nhpg = 2
184	IF( ln_hpg_djc ) nhpg = 3
185	IF( ln_hpg_prj ) nhpg = 4
186	IF( ln_hpg_isf ) nhpg = 5
187	!
188	! ! Consistency check
189	ioptio = 0
190	IF( ln_hpg_zco ) ioptio = ioptio + 1
191	IF( ln_hpg_zps ) ioptio = ioptio + 1
192	IF( ln_hpg_sco ) ioptio = ioptio + 1
193	IF( ln_hpg_djc ) ioptio = ioptio + 1
194	IF( ln_hpg_prj ) ioptio = ioptio + 1
195	IF( ln_hpg_isf ) ioptio = ioptio + 1
196	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
197	!
198	! initialisation of ice load
199	riceload(:,:)=0.0
200	!
201	END SUBROUTINE dyn_hpg_init
202
203
204	SUBROUTINE hpg_zco( kt )
205	!!---------------------------------------------------------------------
206	!! * ROUTINE hpg_zco *
207	!!
208	!! ** Method : z-coordinate case, levels are horizontal surfaces.
209	!! The now hydrostatic pressure gradient at a given level, jk,
210	!! is computed by taking the vertical integral of the in-situ
211	!! density gradient along the model level from the suface to that
212	!! level: zhpi = grav .....
213	!! zhpj = grav .....
214	!! add it to the general momentum trend (ua,va).
215	!! ua = ua - 1/e1u * zhpi
216	!! va = va - 1/e2v * zhpj
217	!!
218	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
219	!!----------------------------------------------------------------------
220	INTEGER, INTENT(in) :: kt ! ocean time-step index
221	!!
222	INTEGER :: ji, jj, jk ! dummy loop indices
223	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
224	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
225	!!----------------------------------------------------------------------
226	!
227	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
228	!
229	IF( kt == nit000 ) THEN
230	IF(lwp) WRITE(numout,*)
231	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
232	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
233	ENDIF
234
235	zcoef0 = - grav * 0.5_wp ! Local constant initialization
236
237	! Surface value
238	DO jj = 2, jpjm1
239	DO ji = fs_2, fs_jpim1 ! vector opt.
240	zcoef1 = zcoef0 * fse3w(ji,jj,1)
241	! hydrostatic pressure gradient
242	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
243	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
244	! add to the general momentum trend
245	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
246	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
247	END DO
248	END DO
249
250	!
251	! interior value (2=<jk=<jpkm1)
252	DO jk = 2, jpkm1
253	DO jj = 2, jpjm1
254	DO ji = fs_2, fs_jpim1 ! vector opt.
255	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
256	! hydrostatic pressure gradient
257	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
258	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
259	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
260
261	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
262	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
263	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
264	! add to the general momentum trend
265	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
266	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
267	END DO
268	END DO
269	END DO
270	!
271	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
272	!
273	END SUBROUTINE hpg_zco
274
275
276	SUBROUTINE hpg_zps( kt )
277	!!---------------------------------------------------------------------
278	!! * ROUTINE hpg_zps *
279	!!
280	!! ** Method : z-coordinate plus partial steps case. blahblah...
281	!!
282	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
283	!!----------------------------------------------------------------------
284	INTEGER, INTENT(in) :: kt ! ocean time-step index
285	!!
286	INTEGER :: ji, jj, jk ! dummy loop indices
287	INTEGER :: iku, ikv ! temporary integers
288	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
289	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
290	!!----------------------------------------------------------------------
291	!
292	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
293	!
294	IF( kt == nit000 ) THEN
295	IF(lwp) WRITE(numout,*)
296	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
297	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
298	ENDIF
299
300
301	! Local constant initialization
302	zcoef0 = - grav * 0.5_wp
303
304	! Surface value (also valid in partial step case)
305	DO jj = 2, jpjm1
306	DO ji = fs_2, fs_jpim1 ! vector opt.
307	zcoef1 = zcoef0 * fse3w(ji,jj,1)
308	! hydrostatic pressure gradient
309	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
310	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
311	! add to the general momentum trend
312	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
313	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
314	END DO
315	END DO
316
317
318	! interior value (2=<jk=<jpkm1)
319	DO jk = 2, jpkm1
320	DO jj = 2, jpjm1
321	DO ji = fs_2, fs_jpim1 ! vector opt.
322	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
323	! hydrostatic pressure gradient
324	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
325	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
326	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
327
328	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
329	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
330	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
331	! add to the general momentum trend
332	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
333	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
334	END DO
335	END DO
336	END DO
337
338
339	! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
340	DO jj = 2, jpjm1
341	DO ji = 2, jpim1
342	iku = mbku(ji,jj)
343	ikv = mbkv(ji,jj)
344	zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) )
345	zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) )
346	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
347	ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value
348	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
349	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj)
350	ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
351	ENDIF
352	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
353	va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value
354	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
355	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj)
356	va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
357	ENDIF
358	END DO
359	END DO
360	!
361	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
362	!
363	END SUBROUTINE hpg_zps
364
365	SUBROUTINE hpg_sco( kt )
366	!!---------------------------------------------------------------------
367	!! * ROUTINE hpg_sco *
368	!!
369	!! ** Method : s-coordinate case. Jacobian scheme.
370	!! The now hydrostatic pressure gradient at a given level, jk,
371	!! is computed by taking the vertical integral of the in-situ
372	!! density gradient along the model level from the suface to that
373	!! level. s-coordinates (ln_sco): a corrective term is added
374	!! to the horizontal pressure gradient :
375	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
376	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
377	!! add it to the general momentum trend (ua,va).
378	!! ua = ua - 1/e1u * zhpi
379	!! va = va - 1/e2v * zhpj
380	!!
381	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
382	!!----------------------------------------------------------------------
383	INTEGER, INTENT(in) :: kt ! ocean time-step index
384	!!
385	INTEGER :: ji, jj, jk ! dummy loop indices
386	REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars
387	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
388	!!----------------------------------------------------------------------
389	!
390	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
391	!
392	IF( kt == nit000 ) THEN
393	IF(lwp) WRITE(numout,*)
394	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
395	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
396	ENDIF
397
398	! Local constant initialization
399	zcoef0 = - grav * 0.5_wp
400	! To use density and not density anomaly
401	IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
402	ELSE ; znad = 0._wp ! Fixed volume
403	ENDIF
404
405	! Surface value
406	DO jj = 2, jpjm1
407	DO ji = fs_2, fs_jpim1 ! vector opt.
408	! hydrostatic pressure gradient along s-surfaces
409	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) &
410	& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
411	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) &
412	& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
413	! s-coordinate pressure gradient correction
414	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
415	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
416	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
417	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
418	! add to the general momentum trend
419	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap
420	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap
421	END DO
422	END DO
423
424	! interior value (2=<jk=<jpkm1)
425	DO jk = 2, jpkm1
426	DO jj = 2, jpjm1
427	DO ji = fs_2, fs_jpim1 ! vector opt.
428	! hydrostatic pressure gradient along s-surfaces
429	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
430	& * ( fse3w(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) &
431	& - fse3w(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) )
432	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
433	& * ( fse3w(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) &
434	& - fse3w(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) )
435	! s-coordinate pressure gradient correction
436	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
437	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj)
438	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
439	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj)
440	! add to the general momentum trend
441	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap
442	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap
443	END DO
444	END DO
445	END DO
446	!
447	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
448	!
449	END SUBROUTINE hpg_sco
450
451	SUBROUTINE hpg_isf( kt )
452	!!---------------------------------------------------------------------
453	!! * ROUTINE hpg_sco *
454	!!
455	!! ** Method : s-coordinate case. Jacobian scheme.
456	!! The now hydrostatic pressure gradient at a given level, jk,
457	!! is computed by taking the vertical integral of the in-situ
458	!! density gradient along the model level from the suface to that
459	!! level. s-coordinates (ln_sco): a corrective term is added
460	!! to the horizontal pressure gradient :
461	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
462	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
463	!! add it to the general momentum trend (ua,va).
464	!! ua = ua - 1/e1u * zhpi
465	!! va = va - 1/e2v * zhpj
466	!! iceload is added and partial cell case are added to the top and bottom
467	!!
468	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
469	!!----------------------------------------------------------------------
470	INTEGER, INTENT(in) :: kt ! ocean time-step index
471	!!
472	INTEGER :: ji, jj, jk, iku, ikv, ikt, iktp1i, iktp1j ! dummy loop indices
473	REAL(wp) :: zcoef0, zuap, zvap, znad, ze3wu, ze3wv, zuapint, zvapint, zhpjint, zhpiint, zdzwt, zdzwtjp1, zdzwtip1 ! temporary scalars
474	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj, zrhd
475	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop
476	REAL(wp), POINTER, DIMENSION(:,:) :: ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj
477	!!----------------------------------------------------------------------
478	!
479	CALL wrk_alloc( jpi,jpj, 2, ztstop)
480	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
481	CALL wrk_alloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
482	!
483	IF( kt == nit000 ) THEN
484	IF(lwp) WRITE(numout,*)
485	IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf'
486	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
487	ENDIF
488
489	! Local constant initialization
490	zcoef0 = - grav * 0.5_wp
491	! To use density and not density anomaly
492	! IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
493	! ELSE ; znad = 0._wp ! Fixed volume
494	! ENDIF
495	znad=1._wp
496	! iniitialised to 0. zhpi zhpi
497	zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp
498
499	!==================================================================================
500	!=====Compute iceload and contribution of the half first wet layer =================
501	!===================================================================================
502
503	! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude)
504	ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp
505
506	! compute density of the water displaced by the ice shelf
507	zrhd = rhd ! save rhd
508	DO jk = 1, jpk
509	zdept(:,:)=gdept_1d(jk)
510	CALL eos(ztstop(:,:,:),zdept(:,:),rhd(:,:,jk))
511	END DO
512	WHERE ( tmask(:,:,:) == 1._wp)
513	rhd(:,:,:) = zrhd(:,:,:) ! replace wet cell by the saved rhd
514	END WHERE
515
516	! compute rhd at the ice/oce interface (ice shelf side)
517	CALL eos(ztstop,risfdep,zrhdtop_isf)
518
519	! compute rhd at the ice/oce interface (ocean side)
520	DO ji=1,jpi
521	DO jj=1,jpj
522	ikt=mikt(ji,jj)
523	ztstop(ji,jj,1)=tsn(ji,jj,ikt,1)
524	ztstop(ji,jj,2)=tsn(ji,jj,ikt,2)
525	END DO
526	END DO
527	CALL eos(ztstop,risfdep,zrhdtop_oce)
528	!
529	! Surface value + ice shelf gradient
530	! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v)
531	ziceload = 0._wp
532	DO jj = 1, jpj
533	DO ji = 1, jpi ! vector opt.
534	ikt=mikt(ji,jj)
535	ziceload(ji,jj) = ziceload(ji,jj) + (znad + rhd(ji,jj,1) ) * fse3w(ji,jj,1) * (1._wp - tmask(ji,jj,1))
536	DO jk=2,ikt-1
537	ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + rhd(ji,jj,jk-1) + rhd(ji,jj,jk)) * fse3w(ji,jj,jk) &
538	& * (1._wp - tmask(ji,jj,jk))
539	END DO
540	IF (ikt .GE. 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + rhd(ji,jj,ikt-1)) &
541	& * ( risfdep(ji,jj) - gdept_1d(ikt-1) )
542	END DO
543	END DO
544	riceload(:,:) = 0.0_wp ; riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5
545	! compute zp from z=0 to first T wet point (correction due to zps not yet applied)
546	DO jj = 2, jpjm1
547	DO ji = fs_2, fs_jpim1 ! vector opt.
548	ikt=mikt(ji,jj) ; iktp1i=mikt(ji+1,jj); iktp1j=mikt(ji,jj+1)
549	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
550	! we assume ISF is in isostatic equilibrium
551	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * fse3w(ji+1,jj ,iktp1i) &
552	& * ( 2._wp * znad + rhd(ji+1,jj ,iktp1i) + zrhdtop_oce(ji+1,jj ) ) &
553	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
554	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
555	& + ( ziceload(ji+1,jj) - ziceload(ji,jj)) )
556	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * fse3w(ji ,jj+1,iktp1j) &
557	& * ( 2._wp * znad + rhd(ji ,jj+1,iktp1j) + zrhdtop_oce(ji ,jj+1) ) &
558	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
559	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
560	& + ( ziceload(ji,jj+1) - ziceload(ji,jj) ) )
561	! s-coordinate pressure gradient correction (=0 if z coordinate)
562	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
563	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
564	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
565	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
566	! add to the general momentum trend
567	ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
568	va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
569	END DO
570	END DO
571	!==================================================================================
572	!===== Compute partial cell contribution for the top cell =========================
573	!==================================================================================
574	DO jj = 2, jpjm1
575	DO ji = fs_2, fs_jpim1 ! vector opt.
576	iku = miku(ji,jj) ;
577	zpshpi(ji,jj)=0.0_wp ; zpshpj(ji,jj)=0.0_wp
578	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))
579	! u direction
580	IF ( iku .GT. 1 ) THEN
581	! case iku
582	zhpi(ji,jj,iku) = zcoef0 / e1u(ji,jj) * ze3wu &
583	& * ( rhd (ji+1,jj,iku) + rhd (ji,jj,iku) &
584	& + SIGN(1._wp,ze3wu) * grui(ji,jj) + 2._wp * znad )
585	! corrective term ( = 0 if z coordinate )
586	zuap = -zcoef0 * ( arui(ji,jj) + 2._wp * znad ) * gzui(ji,jj) / e1u(ji,jj)
587	! zhpi will be added in interior loop
588	ua(ji,jj,iku) = ua(ji,jj,iku) + zuap
589	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
590	IF (mbku(ji,jj) == iku + 1) zpshpi(ji,jj) = zhpi(ji,jj,iku)
591
592	! case iku + 1 (remove the zphi term added in the interior loop and compute the one corrected for zps)
593	zhpiint = zcoef0 / e1u(ji,jj) &
594	& * ( fse3w(ji+1,jj ,iku+1) * ( (rhd(ji+1,jj,iku+1) + znad) &
595	& + (rhd(ji+1,jj,iku ) + znad) ) * tmask(ji+1,jj,iku) &
596	& - fse3w(ji ,jj ,iku+1) * ( (rhd(ji ,jj,iku+1) + znad) &
597	& + (rhd(ji ,jj,iku ) + znad) ) * tmask(ji ,jj,iku) )
598	zhpi(ji,jj,iku+1) = zcoef0 / e1u(ji,jj) * ge3rui(ji,jj) - zhpiint
599	END IF
600
601	! v direction
602	ikv = mikv(ji,jj)
603	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))
604	IF ( ikv .GT. 1 ) THEN
605	! case ikv
606	zhpj(ji,jj,ikv) = zcoef0 / e2v(ji,jj) * ze3wv &
607	& * ( rhd(ji,jj+1,ikv) + rhd (ji,jj,ikv) &
608	& + SIGN(1._wp,ze3wv) * grvi(ji,jj) + 2._wp * znad )
609	! corrective term ( = 0 if z coordinate )
610	zvap = -zcoef0 * ( arvi(ji,jj) + 2._wp * znad ) * gzvi(ji,jj) / e2v(ji,jj)
611	! zhpi will be added in interior loop
612	va(ji,jj,ikv) = va(ji,jj,ikv) + zvap
613	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
614	IF (mbkv(ji,jj) == ikv + 1) zpshpj(ji,jj) = zhpj(ji,jj,ikv)
615
616	! case ikv + 1 (remove the zphj term added in the interior loop and compute the one corrected for zps)
617	zhpjint = zcoef0 / e2v(ji,jj) &
618	& * ( fse3w(ji ,jj+1,ikv+1) * ( (rhd(ji,jj+1,ikv+1) + znad) &
619	& + (rhd(ji,jj+1,ikv ) + znad) ) * tmask(ji,jj+1,ikv) &
620	& - fse3w(ji ,jj ,ikv+1) * ( (rhd(ji,jj ,ikv+1) + znad) &
621	& + (rhd(ji,jj ,ikv ) + znad) ) * tmask(ji,jj ,ikv) )
622	zhpj(ji,jj,ikv+1) = zcoef0 / e2v(ji,jj) * ge3rvi(ji,jj) - zhpjint
623	END IF
624	END DO
625	END DO
626
627	!==================================================================================
628	!===== Compute interior value =====================================================
629	!==================================================================================
630
631	DO jj = 2, jpjm1
632	DO ji = fs_2, fs_jpim1 ! vector opt.
633	iku=miku(ji,jj); ikv=mikv(ji,jj)
634	DO jk = 2, jpkm1
635	! hydrostatic pressure gradient along s-surfaces
636	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
637	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) + zhpi(ji,jj,jk-1) &
638	& + zcoef0 / e1u(ji,jj) &
639	& * ( fse3w(ji+1,jj ,jk) * ( (rhd(ji+1,jj,jk ) + znad) &
640	& + (rhd(ji+1,jj,jk-1) + znad) ) * tmask(ji+1,jj,jk-1) &
641	& - fse3w(ji ,jj ,jk) * ( (rhd(ji ,jj,jk ) + znad) &
642	& + (rhd(ji ,jj,jk-1) + znad) ) * tmask(ji ,jj,jk-1) )
643	! s-coordinate pressure gradient correction
644	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
645	zuap = - zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
646	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) * umask(ji,jj,jk-1)
647	ua(ji,jj,jk) = ua(ji,jj,jk) + ( zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
648
649	! hydrostatic pressure gradient along s-surfaces
650	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
651	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) + zhpj(ji,jj,jk-1) &
652	& + zcoef0 / e2v(ji,jj) &
653	& * ( fse3w(ji ,jj+1,jk) * ( (rhd(ji,jj+1,jk ) + znad) &
654	& + (rhd(ji,jj+1,jk-1) + znad) ) * tmask(ji,jj+1,jk-1) &
655	& - fse3w(ji ,jj ,jk) * ( (rhd(ji,jj ,jk ) + znad) &
656	& + (rhd(ji,jj ,jk-1) + znad) ) * tmask(ji,jj ,jk-1) )
657	! s-coordinate pressure gradient correction
658	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
659	zvap = - zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
660	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) * vmask(ji,jj,jk-1)
661	! add to the general momentum trend
662	va(ji,jj,jk) = va(ji,jj,jk) + ( zhpj(ji,jj,jk) + zvap ) * vmask(ji,jj,jk)
663	END DO
664	END DO
665	END DO
666
667	!==================================================================================
668	!===== Compute bottom cell contribution (partial cell) ============================
669	!==================================================================================
670
671	DO jj = 2, jpjm1
672	DO ji = 2, jpim1
673	iku = mbku(ji,jj)
674	ikv = mbkv(ji,jj)
675
676	IF (iku .GT. 1) THEN
677	! remove old value (interior case)
678	zuap = -zcoef0 * ( rhd (ji+1,jj ,iku) + rhd (ji,jj,iku) + 2._wp * znad ) &
679	& * ( fsde3w(ji+1,jj ,iku) - fsde3w(ji,jj,iku) ) / e1u(ji,jj)
680	ua(ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) - zuap
681	! put new value
682	! -zpshpi to avoid double contribution of the partial step in the top layer
683	zuap = -zcoef0 * ( aru(ji,jj) + 2._wp * znad ) * gzu(ji,jj) / e1u(ji,jj)
684	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) + zcoef0 / e1u(ji,jj) * ge3ru(ji,jj) - zpshpi(ji,jj)
685	ua(ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) + zuap
686	END IF
687	! v direction
688	IF (ikv .GT. 1) THEN
689	! remove old value (interior case)
690	zvap = -zcoef0 * ( rhd (ji ,jj+1,ikv) + rhd (ji,jj,ikv) + 2._wp * znad ) &
691	& * ( fsde3w(ji ,jj+1,ikv) - fsde3w(ji,jj,ikv) ) / e2v(ji,jj)
692	va(ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) - zvap
693	! put new value
694	! -zpshpj to avoid double contribution of the partial step in the top layer
695	zvap = -zcoef0 * ( arv(ji,jj) + 2._wp * znad ) * gzv(ji,jj) / e2v(ji,jj)
696	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) + zcoef0 / e2v(ji,jj) * ge3rv(ji,jj) - zpshpj(ji,jj)
697	va(ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) + zvap
698	END IF
699	END DO
700	END DO
701
702	! set back to original density value into the ice shelf cell (maybe useless because it is masked)
703	rhd = zrhd
704	!
705	CALL wrk_dealloc( jpi,jpj,2, ztstop)
706	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
707	CALL wrk_dealloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
708	!
709	END SUBROUTINE hpg_isf
710
711
712	SUBROUTINE hpg_djc( kt )
713	!!---------------------------------------------------------------------
714	!! * ROUTINE hpg_djc *
715	!!
716	!! ** Method : Density Jacobian with Cubic polynomial scheme
717	!!
718	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
719	!!----------------------------------------------------------------------
720	INTEGER, INTENT(in) :: kt ! ocean time-step index
721	!!
722	INTEGER :: ji, jj, jk ! dummy loop indices
723	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
724	REAL(wp) :: z1_10, cffu, cffx ! " "
725	REAL(wp) :: z1_12, cffv, cffy ! " "
726	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
727	REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw
728	REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow
729	REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k
730	!!----------------------------------------------------------------------
731	!
732	CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
733	CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
734	CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
735	!
736
737	IF( kt == nit000 ) THEN
738	IF(lwp) WRITE(numout,*)
739	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
740	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
741	ENDIF
742
743	! Local constant initialization
744	zcoef0 = - grav * 0.5_wp
745	z1_10 = 1._wp / 10._wp
746	z1_12 = 1._wp / 12._wp
747
748	!----------------------------------------------------------------------------------------
749	! compute and store in provisional arrays elementary vertical and horizontal differences
750	!----------------------------------------------------------------------------------------
751
752	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
753
754	DO jk = 2, jpkm1
755	DO jj = 2, jpjm1
756	DO ji = fs_2, fs_jpim1 ! vector opt.
757	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
758	dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1)
759	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
760	dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk )
761	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
762	dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk )
763	END DO
764	END DO
765	END DO
766
767	!-------------------------------------------------------------------------
768	! compute harmonic averages using eq. 5.18
769	!-------------------------------------------------------------------------
770	zep = 1.e-15
771
772	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
773	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
774
775	DO jk = 2, jpkm1
776	DO jj = 2, jpjm1
777	DO ji = fs_2, fs_jpim1 ! vector opt.
778	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
779
780	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
781	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
782
783	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
784	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
785
786	IF( cffw > zep) THEN
787	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
788	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
789	ELSE
790	drhow(ji,jj,jk) = 0._wp
791	ENDIF
792
793	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
794	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
795
796	IF( cffu > zep ) THEN
797	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
798	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
799	ELSE
800	drhou(ji,jj,jk ) = 0._wp
801	ENDIF
802
803	IF( cffx > zep ) THEN
804	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
805	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
806	ELSE
807	dzu(ji,jj,jk) = 0._wp
808	ENDIF
809
810	IF( cffv > zep ) THEN
811	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
812	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
813	ELSE
814	drhov(ji,jj,jk) = 0._wp
815	ENDIF
816
817	IF( cffy > zep ) THEN
818	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
819	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
820	ELSE
821	dzv(ji,jj,jk) = 0._wp
822	ENDIF
823
824	END DO
825	END DO
826	END DO
827
828	!----------------------------------------------------------------------------------
829	! apply boundary conditions at top and bottom using 5.36-5.37
830	!----------------------------------------------------------------------------------
831	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
832	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
833	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
834
835	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
836	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
837	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
838
839
840	!--------------------------------------------------------------
841	! Upper half of top-most grid box, compute and store
842	!-------------------------------------------------------------
843
844	!!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified
845	! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
846
847	DO jj = 2, jpjm1
848	DO ji = fs_2, fs_jpim1 ! vector opt.
849	rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) &
850	& * ( rhd(ji,jj,1) &
851	& + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) &
852	& * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) &
853	& / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) )
854	END DO
855	END DO
856
857	!!bug gm : here also, simplification is possible
858	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
859
860	DO jk = 2, jpkm1
861	DO jj = 2, jpjm1
862	DO ji = fs_2, fs_jpim1 ! vector opt.
863
864	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
865	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) &
866	& - grav * z1_10 * ( &
867	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
868	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
869	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
870	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
871	& )
872
873	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
874	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) &
875	& - grav* z1_10 * ( &
876	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
877	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
878	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
879	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
880	& )
881
882	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
883	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) &
884	& - grav* z1_10 * ( &
885	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
886	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
887	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
888	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
889	& )
890
891	END DO
892	END DO
893	END DO
894	CALL lbc_lnk(rho_k,'W',1.)
895	CALL lbc_lnk(rho_i,'U',1.)
896	CALL lbc_lnk(rho_j,'V',1.)
897
898
899	! ---------------
900	! Surface value
901	! ---------------
902	DO jj = 2, jpjm1
903	DO ji = fs_2, fs_jpim1 ! vector opt.
904	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj)
905	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj)
906	! add to the general momentum trend
907	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
908	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
909	END DO
910	END DO
911
912	! ----------------
913	! interior value (2=<jk=<jpkm1)
914	! ----------------
915	DO jk = 2, jpkm1
916	DO jj = 2, jpjm1
917	DO ji = fs_2, fs_jpim1 ! vector opt.
918	! hydrostatic pressure gradient along s-surfaces
919	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
920	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
921	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj)
922	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
923	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
924	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj)
925	! add to the general momentum trend
926	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
927	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
928	END DO
929	END DO
930	END DO
931	!
932	CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
933	CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
934	CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
935	!
936	END SUBROUTINE hpg_djc
937
938
939	SUBROUTINE hpg_prj( kt )
940	!!---------------------------------------------------------------------
941	!! * ROUTINE hpg_prj *
942	!!
943	!! ** Method : s-coordinate case.
944	!! A Pressure-Jacobian horizontal pressure gradient method
945	!! based on the constrained cubic-spline interpolation for
946	!! all vertical coordinate systems
947	!!
948	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
949	!!----------------------------------------------------------------------
950	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
951	INTEGER, INTENT(in) :: kt ! ocean time-step index
952	!!
953	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
954	REAL(wp) :: zcoef0, znad ! temporary scalars
955	!!
956	!! The local variables for the correction term
957	INTEGER :: jk1, jis, jid, jjs, jjd
958	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
959	REAL(wp) :: zrhdt1
960	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
961	REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh
962	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
963	REAL(wp), POINTER, DIMENSION(:,:) :: zsshu_n, zsshv_n
964	!!----------------------------------------------------------------------
965	!
966	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
967	CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh )
968	CALL wrk_alloc( jpi,jpj, zsshu_n, zsshv_n )
969	!
970	IF( kt == nit000 ) THEN
971	IF(lwp) WRITE(numout,*)
972	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
973	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
974	ENDIF
975
976	!!----------------------------------------------------------------------
977	! Local constant initialization
978	zcoef0 = - grav
979	znad = 0.0_wp
980	IF( lk_vvl ) znad = 1._wp
981
982	! Clean 3-D work arrays
983	zhpi(:,:,:) = 0._wp
984	zrhh(:,:,:) = rhd(:,:,:)
985
986	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
987	DO jj = 1, jpj
988	DO ji = 1, jpi
989	jk = mbathy(ji,jj)
990	IF( jk <= 0 ) THEN; zrhh(ji,jj,:) = 0._wp
991	ELSE IF(jk == 1) THEN; zrhh(ji,jj, jk+1:jpk) = rhd(ji,jj,jk)
992	ELSE IF(jk < jpkm1) THEN
993	DO jkk = jk+1, jpk
994	zrhh(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1), &
995	fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2))
996	END DO
997	ENDIF
998	END DO
999	END DO
1000
1001	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
1002	DO jj = 1, jpj
1003	DO ji = 1, jpi
1004	zdept(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) - sshn(ji,jj) * znad
1005	END DO
1006	END DO
1007
1008	DO jk = 2, jpk
1009	DO jj = 1, jpj
1010	DO ji = 1, jpi
1011	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + fse3w(ji,jj,jk)
1012	END DO
1013	END DO
1014	END DO
1015
1016	fsp(:,:,:) = zrhh (:,:,:)
1017	xsp(:,:,:) = zdept(:,:,:)
1018
1019	! Construct the vertical density profile with the
1020	! constrained cubic spline interpolation
1021	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
1022	CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type)
1023
1024	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
1025	DO jj = 2, jpj
1026	DO ji = 2, jpi
1027	zrhdt1 = zrhh(ji,jj,1) - interp3(zdept(ji,jj,1),asp(ji,jj,1), &
1028	bsp(ji,jj,1), csp(ji,jj,1), &
1029	dsp(ji,jj,1) ) * 0.25_wp * fse3w(ji,jj,1)
1030
1031	! assuming linear profile across the top half surface layer
1032	zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * zrhdt1
1033	END DO
1034	END DO
1035
1036	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
1037	DO jk = 2, jpkm1
1038	DO jj = 2, jpj
1039	DO ji = 2, jpi
1040	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
1041	integ_spline(zdept(ji,jj,jk-1), zdept(ji,jj,jk),&
1042	asp(ji,jj,jk-1), bsp(ji,jj,jk-1), &
1043	csp(ji,jj,jk-1), dsp(ji,jj,jk-1))
1044	END DO
1045	END DO
1046	END DO
1047
1048	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
1049
1050	! Prepare zsshu_n and zsshv_n
1051	DO jj = 2, jpjm1
1052	DO ji = 2, jpim1
1053	zsshu_n(ji,jj) = (e12u(ji,jj) * sshn(ji,jj) + e12u(ji+1, jj) * sshn(ji+1,jj)) * &
1054	& r1_e12u(ji,jj) * umask(ji,jj,1) * 0.5_wp
1055	zsshv_n(ji,jj) = (e12v(ji,jj) * sshn(ji,jj) + e12v(ji+1, jj) * sshn(ji,jj+1)) * &
1056	& r1_e12v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
1057	END DO
1058	END DO
1059
1060	DO jj = 2, jpjm1
1061	DO ji = 2, jpim1
1062	zu(ji,jj,1) = - ( fse3u(ji,jj,1) - zsshu_n(ji,jj) * znad)
1063	zv(ji,jj,1) = - ( fse3v(ji,jj,1) - zsshv_n(ji,jj) * znad)
1064	END DO
1065	END DO
1066
1067	DO jk = 2, jpkm1
1068	DO jj = 2, jpjm1
1069	DO ji = 2, jpim1
1070	zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk)
1071	zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk)
1072	END DO
1073	END DO
1074	END DO
1075
1076	DO jk = 1, jpkm1
1077	DO jj = 2, jpjm1
1078	DO ji = 2, jpim1
1079	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk)
1080	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk)
1081	END DO
1082	END DO
1083	END DO
1084
1085	DO jk = 1, jpkm1
1086	DO jj = 2, jpjm1
1087	DO ji = 2, jpim1
1088	zu(ji,jj,jk) = min(zu(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
1089	zu(ji,jj,jk) = max(zu(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
1090	zv(ji,jj,jk) = min(zv(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
1091	zv(ji,jj,jk) = max(zv(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
1092	END DO
1093	END DO
1094	END DO
1095
1096
1097	DO jk = 1, jpkm1
1098	DO jj = 2, jpjm1
1099	DO ji = 2, jpim1
1100	zpwes = 0._wp; zpwed = 0._wp
1101	zpnss = 0._wp; zpnsd = 0._wp
1102	zuijk = zu(ji,jj,jk)
1103	zvijk = zv(ji,jj,jk)
1104
1105	!!!!! for u equation
1106	IF( jk <= mbku(ji,jj) ) THEN
1107	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
1108	jis = ji + 1; jid = ji
1109	ELSE
1110	jis = ji; jid = ji +1
1111	ENDIF
1112
1113	! integrate the pressure on the shallow side
1114	jk1 = jk
1115	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
1116	IF( jk1 == mbku(ji,jj) ) THEN
1117	zuijk = -zdept(jis,jj,jk1)
1118	EXIT
1119	ENDIF
1120	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
1121	zpwes = zpwes + &
1122	integ_spline(zdept(jis,jj,jk1), zdeps, &
1123	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
1124	csp(jis,jj,jk1), dsp(jis,jj,jk1))
1125	jk1 = jk1 + 1
1126	END DO
1127
1128	! integrate the pressure on the deep side
1129	jk1 = jk
1130	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
1131	IF( jk1 == 1 ) THEN
1132	zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad)
1133	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
1134	bsp(jid,jj,1), csp(jid,jj,1), &
1135	dsp(jid,jj,1)) * zdeps
1136	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
1137	EXIT
1138	ENDIF
1139	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
1140	zpwed = zpwed + &
1141	integ_spline(zdeps, zdept(jid,jj,jk1), &
1142	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
1143	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
1144	jk1 = jk1 - 1
1145	END DO
1146
1147	! update the momentum trends in u direction
1148
1149	zdpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk))
1150	IF( lk_vvl ) THEN
1151	zdpdx2 = zcoef0 / e1u(ji,jj) * &
1152	( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) )
1153	ELSE
1154	zdpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
1155	ENDIF
1156
1157	ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * &
1158	& umask(ji,jj,jk) * tmask(ji,jj,jk) * tmask(ji+1,jj,jk)
1159	ENDIF
1160
1161	!!!!! for v equation
1162	IF( jk <= mbkv(ji,jj) ) THEN
1163	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
1164	jjs = jj + 1; jjd = jj
1165	ELSE
1166	jjs = jj ; jjd = jj + 1
1167	ENDIF
1168
1169	! integrate the pressure on the shallow side
1170	jk1 = jk
1171	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
1172	IF( jk1 == mbkv(ji,jj) ) THEN
1173	zvijk = -zdept(ji,jjs,jk1)
1174	EXIT
1175	ENDIF
1176	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
1177	zpnss = zpnss + &
1178	integ_spline(zdept(ji,jjs,jk1), zdeps, &
1179	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
1180	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
1181	jk1 = jk1 + 1
1182	END DO
1183
1184	! integrate the pressure on the deep side
1185	jk1 = jk
1186	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
1187	IF( jk1 == 1 ) THEN
1188	zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad)
1189	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
1190	bsp(ji,jjd,1), csp(ji,jjd,1), &
1191	dsp(ji,jjd,1) ) * zdeps
1192	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
1193	EXIT
1194	ENDIF
1195	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
1196	zpnsd = zpnsd + &
1197	integ_spline(zdeps, zdept(ji,jjd,jk1), &
1198	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
1199	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
1200	jk1 = jk1 - 1
1201	END DO
1202
1203
1204	! update the momentum trends in v direction
1205
1206	zdpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk))
1207	IF( lk_vvl ) THEN
1208	zdpdy2 = zcoef0 / e2v(ji,jj) * &
1209	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) )
1210	ELSE
1211	zdpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
1212	ENDIF
1213
1214	va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2)*&
1215	& vmask(ji,jj,jk)tmask(ji,jj,jk)tmask(ji,jj+1,jk)
1216	ENDIF
1217
1218
1219	END DO
1220	END DO
1221	END DO
1222	!
1223	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
1224	CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh )
1225	CALL wrk_dealloc( jpi,jpj, zsshu_n, zsshv_n )
1226	!
1227	END SUBROUTINE hpg_prj
1228
1229
1230	SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type)
1231	!!----------------------------------------------------------------------
1232	!! * ROUTINE cspline *
1233	!!
1234	!! ** Purpose : constrained cubic spline interpolation
1235	!!
1236	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
1237	!!
1238	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
1239	!!----------------------------------------------------------------------
1240	IMPLICIT NONE
1241	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate
1242	REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of
1243	! the interpoated function
1244	INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline
1245	! 2: Linear
1246	!
1247	INTEGER :: ji, jj, jk ! dummy loop indices
1248	INTEGER :: jpi, jpj, jpkm1
1249	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
1250	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
1251	REAL(wp) :: zdf(size(fsp,3))
1252	!!----------------------------------------------------------------------
1253
1254	jpi = size(fsp,1)
1255	jpj = size(fsp,2)
1256	jpkm1 = size(fsp,3) - 1
1257
1258
1259	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
1260	DO ji = 1, jpi
1261	DO jj = 1, jpj
1262	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
1263	! DO jk = 2, jpkm1-1
1264	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
1265	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1266	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
1267	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
1268	!
1269	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
1270	!
1271	! IF(zdf1 * zdf2 <= 0._wp) THEN
1272	! zdf(jk) = 0._wp
1273	! ELSE
1274	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
1275	! ENDIF
1276	! END DO
1277
1278	!!Simply geometric average
1279	DO jk = 2, jpkm1-1
1280	zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1))
1281	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk))
1282
1283	IF(zdf1 * zdf2 <= 0._wp) THEN
1284	zdf(jk) = 0._wp
1285	ELSE
1286	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
1287	ENDIF
1288	END DO
1289
1290	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
1291	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
1292	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
1293	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - &
1294	& 0.5_wp * zdf(jpkm1 - 1)
1295
1296	DO jk = 1, jpkm1 - 1
1297	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1298	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
1299	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
1300	zddf1 = -2._wp * ztmp1 + ztmp2
1301	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
1302	zddf2 = 2._wp * ztmp1 - ztmp2
1303
1304	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
1305	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
1306	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
1307	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
1308	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
1309	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
1310	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
1311	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
1312	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
1313	END DO
1314	END DO
1315	END DO
1316
1317	ELSE IF (polynomial_type == 2) THEN ! Linear
1318	DO ji = 1, jpi
1319	DO jj = 1, jpj
1320	DO jk = 1, jpkm1-1
1321	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1322	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
1323
1324	dsp(ji,jj,jk) = 0._wp
1325	csp(ji,jj,jk) = 0._wp
1326	bsp(ji,jj,jk) = ztmp1 / zdxtmp
1327	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
1328	END DO
1329	END DO
1330	END DO
1331
1332	ELSE
1333	CALL ctl_stop( 'invalid polynomial type in cspline' )
1334	ENDIF
1335
1336	END SUBROUTINE cspline
1337
1338
1339	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
1340	!!----------------------------------------------------------------------
1341	!! * ROUTINE interp1 *
1342	!!
1343	!! ** Purpose : 1-d linear interpolation
1344	!!
1345	!! ** Method : interpolation is straight forward
1346	!! extrapolation is also permitted (no value limit)
1347	!!----------------------------------------------------------------------
1348	IMPLICIT NONE
1349	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
1350	REAL(wp) :: f ! result of the interpolation (extrapolation)
1351	REAL(wp) :: zdeltx
1352	!!----------------------------------------------------------------------
1353
1354	zdeltx = xr - xl
1355	IF(abs(zdeltx) <= 10._wp * EPSILON(x)) THEN
1356	f = 0.5_wp * (fl + fr)
1357	ELSE
1358	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
1359	ENDIF
1360
1361	END FUNCTION interp1
1362
1363
1364	FUNCTION interp2(x, a, b, c, d) RESULT(f)
1365	!!----------------------------------------------------------------------
1366	!! * ROUTINE interp1 *
1367	!!
1368	!! ** Purpose : 1-d constrained cubic spline interpolation
1369	!!
1370	!! ** Method : cubic spline interpolation
1371	!!
1372	!!----------------------------------------------------------------------
1373	IMPLICIT NONE
1374	REAL(wp), INTENT(in) :: x, a, b, c, d
1375	REAL(wp) :: f ! value from the interpolation
1376	!!----------------------------------------------------------------------
1377
1378	f = a + x* ( b + x * ( c + d * x ) )
1379
1380	END FUNCTION interp2
1381
1382
1383	FUNCTION interp3(x, a, b, c, d) RESULT(f)
1384	!!----------------------------------------------------------------------
1385	!! * ROUTINE interp1 *
1386	!!
1387	!! ** Purpose : Calculate the first order of deriavtive of
1388	!! a cubic spline function y=a+bx+cx^2+d*x^3
1389	!!
1390	!! ** Method : f=dy/dx=b+2cx+3dx^2
1391	!!
1392	!!----------------------------------------------------------------------
1393	IMPLICIT NONE
1394	REAL(wp), INTENT(in) :: x, a, b, c, d
1395	REAL(wp) :: f ! value from the interpolation
1396	!!----------------------------------------------------------------------
1397
1398	f = b + x * ( 2._wp * c + 3._wp * d * x)
1399
1400	END FUNCTION interp3
1401
1402
1403	FUNCTION integ_spline(xl, xr, a, b, c, d) RESULT(f)
1404	!!----------------------------------------------------------------------
1405	!! * ROUTINE interp1 *
1406	!!
1407	!! ** Purpose : 1-d constrained cubic spline integration
1408	!!
1409	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
1410	!!
1411	!!----------------------------------------------------------------------
1412	IMPLICIT NONE
1413	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
1414	REAL(wp) :: za1, za2, za3
1415	REAL(wp) :: f ! integration result
1416	!!----------------------------------------------------------------------
1417
1418	za1 = 0.5_wp * b
1419	za2 = c / 3.0_wp
1420	za3 = 0.25_wp * d
1421
1422	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
1423	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
1424
1425	END FUNCTION integ_spline
1426
1427	SUBROUTINE hpg_namelist()
1428	!!---------------------------------------------------------------------
1429	!! * ROUTINE hpg_namelist *
1430	!!
1431	!! ** Purpose : Broadcast namelist variables read by procesor lwm
1432	!!
1433	!! ** Method : use lib_mpp
1434	!!----------------------------------------------------------------------
1435	#if defined key_mpp_mpi
1436	CALL mpp_bcast(ln_hpg_zco)
1437	CALL mpp_bcast(ln_hpg_zps)
1438	CALL mpp_bcast(ln_hpg_sco)
1439	CALL mpp_bcast(ln_hpg_djc)
1440	CALL mpp_bcast(ln_hpg_prj)
1441	CALL mpp_bcast(ln_hpg_isf)
1442	CALL mpp_bcast(ln_dynhpg_imp)
1443	#endif
1444	END SUBROUTINE hpg_namelist
1445
1446	!!======================================================================
1447	END MODULE dynhpg
1448

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