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dynhpg.F90 in branches/UKMO/dev_r5518_GO6_package_FOAMv14_updated_pcbias/NEMOGCM/NEMO/OPA_SRC/DYN – NEMO

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source: branches/UKMO/dev_r5518_GO6_package_FOAMv14_updated_pcbias/NEMOGCM/NEMO/OPA_SRC/DYN/dynhpg.F90 @ 11478

Last change on this file since 11478 was 11478, checked in by mattmartin, 5 years ago
Include initial version of updated pressure correction by Mike Bell.
File size: 74.4 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	!! 3.6 ! 2019-08 (M. Bell) Revisions to bias pressure correction
20	!!----------------------------------------------------------------------
21
22	!!----------------------------------------------------------------------
23	!! dyn_hpg : update the momentum trend with the now horizontal
24	!! gradient of the hydrostatic pressure
25	!! dyn_hpg_init : initialisation and control of options
26	!! hpg_zco : z-coordinate scheme
27	!! hpg_zps : z-coordinate plus partial steps (interpolation)
28	!! hpg_sco : s-coordinate (standard jacobian formulation)
29	!! hpg_isf : s-coordinate (sco formulation) adapted to ice shelf
30	!! hpg_djc : s-coordinate (Density Jacobian with Cubic polynomial)
31	!! hpg_prj : s-coordinate (Pressure Jacobian with Cubic polynomial)
32	!!----------------------------------------------------------------------
33	USE oce ! ocean dynamics and tracers
34	USE sbc_oce ! surface variable (only for the flag with ice shelf)
35	USE dom_oce ! ocean space and time domain
36	USE phycst ! physical constants
37	USE trd_oce ! trends: ocean variables
38	USE trddyn ! trend manager: dynamics
39	!
40	USE in_out_manager ! I/O manager
41	USE prtctl ! Print control
42	USE lbclnk ! lateral boundary condition
43	USE lib_mpp ! MPP library
44	USE eosbn2 ! compute density
45	USE wrk_nemo ! Memory Allocation
46	USE timing ! Timing
47	USE biaspar ! bias correction variables
48
49	IMPLICIT NONE
50	PRIVATE
51
52	PUBLIC dyn_hpg ! routine called by step module
53	PUBLIC dyn_hpg_init ! routine called by opa module
54
55	! !!* Namelist namdyn_hpg : hydrostatic pressure gradient
56	LOGICAL , PUBLIC :: ln_hpg_zco !: z-coordinate - full steps
57	LOGICAL , PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation)
58	LOGICAL , PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation)
59	LOGICAL , PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial)
60	LOGICAL , PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme)
61	LOGICAL , PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf
62	LOGICAL , PUBLIC :: ln_dynhpg_imp !: semi-implicite hpg flag
63
64	INTEGER , PUBLIC :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM)
65
66	!! * Substitutions
67	# include "domzgr_substitute.h90"
68	# include "vectopt_loop_substitute.h90"
69	!!----------------------------------------------------------------------
70	!! NEMO/OPA 3.3 , NEMO Consortium (2010)
71	!! $Id$
72	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
73	!!----------------------------------------------------------------------
74	CONTAINS
75
76	SUBROUTINE dyn_hpg( kt )
77	!!---------------------------------------------------------------------
78	!! * ROUTINE dyn_hpg *
79	!!
80	!! ** Method : Call the hydrostatic pressure gradient routine
81	!! using the scheme defined in the namelist
82	!!
83	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
84	!! - send trends to trd_dyn for futher diagnostics (l_trddyn=T)
85	!!----------------------------------------------------------------------
86	INTEGER, INTENT(in) :: kt ! ocean time-step index
87	INTEGER :: ji, jj, jk ! dummy loop indices
88	INTEGER :: iku, ikv ! k indices for bottom level at u and v points
89	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdu, ztrdv
90	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: z_rhd_st ! tmp density storage for pressure corr
91	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: z_ua, z_va ! tmp store for ua and va including hpg but not pressure correction
92	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: z_ua_bpc, z_va_bpc ! ua calculated with bias pressure correction
93
94	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: z_gru_st, z_grv_st ! tmp ua and va trends storage for pressure corr
95	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: z_ua_bpc_bot, z_va_bpc_bot ! bias pc fields calculated at the ocean bottom
96
97	!!----------------------------------------------------------------------
98	!
99	IF( nn_timing == 1 ) CALL timing_start('dyn_hpg')
100	!
101	IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn)
102	CALL wrk_alloc( jpi,jpj,jpk, ztrdu, ztrdv )
103	ztrdu(:,:,:) = ua(:,:,:)
104	ztrdv(:,:,:) = va(:,:,:)
105	ENDIF
106	!
107
108	IF ( ln_bias .AND. ln_bias_pc_app ) THEN
109
110	!Allocate space for tempory variables
111	ALLOCATE( z_rhd_st(jpi,jpj,jpk), &
112	& z_gru_st(jpi,jpj), &
113	& z_grv_st(jpi,jpj), &
114	& z_ua(jpi,jpj,jpk), z_va(jpi,jpj,jpk), &
115	& z_ua_bpc(jpi,jpj,jpk), z_va_bpc(jpi,jpj,jpk), &
116	& z_ua_bpc_bot(jpi,jpj), z_va_bpc_bot(jpi,jpj) &
117	& )
118
119	! save the original acceleration trends (z_ua_bpc, z_va_bpc are used as temporary storage)
120	z_ua_bpc(:,:,:) = ua(:,:,:)
121	z_va_bpc(:,:,:) = va(:,:,:)
122	END IF
123
124	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
125	CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate
126	CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation)
127	CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation)
128	CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial)
129	CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme)
130	CASE ( 5 ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf
131	END SELECT
132	!
133
134	IF ( ln_bias .AND. ln_bias_pc_app ) THEN
135
136	z_rhd_st(:,:,:) = rhd(:,:,:) ! store orig density
137	rhd(:,:,:) = rhd_pc(:,:,:) ! use pressure corrected density
138	z_gru_st(:,:) = gru(:,:)
139	gru(:,:) = gru_pc(:,:)
140	z_grv_st(:,:) = grv(:,:)
141	grv(:,:) = grv_pc(:,:)
142
143	! save the acceleration trends including hpg field but calculated without the bpc fields
144	z_ua(:,:,:) = ua(:,:,:)
145	z_va(:,:,:) = va(:,:,:)
146
147	! reset the acceleration trends to their original values
148	ua(:,:,:) = z_ua_bpc(:,:,:)
149	va(:,:,:) = z_va_bpc(:,:,:)
150
151	! re-calculate the horizontal pressure gradients with the bpc fields
152	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
153	CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate
154	CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation)
155	CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation)
156	CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial)
157	CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme)
158	CASE ( 5 ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf
159	END SELECT
160
161	! calculate the bpc contribution to ua and va
162	z_ua_bpc(:,:,:) = ua(:,:,:) - z_ua(:,:,:)
163	z_va_bpc(:,:,:) = va(:,:,:) - z_va(:,:,:)
164
165	! calculate the bpc contribution to ua and va at the bottom
166	DO jj = 2, jpjm1
167	DO ji = 2, jpim1
168	iku = mbku(ji,jj)
169	ikv = mbkv(ji,jj)
170	z_ua_bpc_bot(ji,jj) = z_ua_bpc(ji,jj,iku)
171	z_va_bpc_bot(ji,jj) = z_va_bpc(ji,jj,ikv)
172	END DO ! ji
173	END DO ! jj
174
175	! subtract off the bottom values of bpc contribution to ua and va
176	DO jk = 1, jpk - 1
177	z_ua_bpc(:,:,jk) = z_ua_bpc(:,:,jk) - z_ua_bpc_bot(:,:)
178	z_va_bpc(:,:,jk) = z_va_bpc(:,:,jk) - z_va_bpc_bot(:,:)
179	END DO
180
181	! calculate ua using the original hpg (z_ua) and the bias hpg with the bottom pressure gradients subtracted off
182	ua(:,:,:) = z_ua(:,:,:) + z_ua_bpc(:,:,:)
183	va(:,:,:) = z_va(:,:,:) + z_va_bpc(:,:,:)
184
185	IF(lwp) THEN
186	WRITE(numout,*) " ! restore original density"
187	ENDIF
188
189	! restore original density, gru and grv fields
190	rhd(:,:,:) = z_rhd_st(:,:,:)
191	gru(:,:) = z_gru_st(:,:)
192	grv(:,:) = z_grv_st(:,:)
193
194	!Deallocate tempory variables
195	DEALLOCATE( z_rhd_st, z_gru_st, z_grv_st, &
196	& z_ua, z_va, z_ua_bpc, z_va_bpc, &
197	& z_ua_bpc_bot, z_va_bpc_bot &
198	& )
199
200	ENDIF ! ln_bias .AND. ln_bias_pc_app
201
202
203	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
204	ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:)
205	ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:)
206	CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt )
207	CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv )
208	ENDIF
209	!
210	IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, &
211	& tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
212	!
213	IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg')
214	!
215	END SUBROUTINE dyn_hpg
216
217
218	SUBROUTINE dyn_hpg_init
219	!!----------------------------------------------------------------------
220	!! * ROUTINE dyn_hpg_init *
221	!!
222	!! ** Purpose : initializations for the hydrostatic pressure gradient
223	!! computation and consistency control
224	!!
225	!! ** Action : Read the namelist namdyn_hpg and check the consistency
226	!! with the type of vertical coordinate used (zco, zps, sco)
227	!!----------------------------------------------------------------------
228	INTEGER :: ioptio = 0 ! temporary integer
229	INTEGER :: ios ! Local integer output status for namelist read
230	!!
231	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
232	& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf, ln_dynhpg_imp
233	!!----------------------------------------------------------------------
234	!
235	REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient
236	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
237	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp )
238
239	REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient
240	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
241	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp )
242	IF(lwm) WRITE ( numond, namdyn_hpg )
243	!
244	IF(lwp) THEN ! Control print
245	WRITE(numout,*)
246	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
247	WRITE(numout,*) '~~~~~~~~~~~~'
248	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
249	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
250	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
251	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
252	WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf
253	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
254	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
255	WRITE(numout,*) ' time stepping: centered (F) or semi-implicit (T) ln_dynhpg_imp = ', ln_dynhpg_imp
256	ENDIF
257	!
258	IF( ln_hpg_djc ) &
259	& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method &
260	& currently disabled (bugs under investigation). Please select &
261	& either ln_hpg_sco or ln_hpg_prj instead')
262	!
263	IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) &
264	& CALL ctl_stop('dyn_hpg_init : variable volume key_vvl requires:&
265	& the standard jacobian formulation hpg_sco or &
266	& the pressure jacobian formulation hpg_prj')
267
268	IF( ln_hpg_isf .AND. .NOT. ln_isfcav ) &
269	& CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' )
270	IF( .NOT. ln_hpg_isf .AND. ln_isfcav ) &
271	& CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' )
272	!
273	! ! Set nhpg from ln_hpg_... flags
274	IF( ln_hpg_zco ) nhpg = 0
275	IF( ln_hpg_zps ) nhpg = 1
276	IF( ln_hpg_sco ) nhpg = 2
277	IF( ln_hpg_djc ) nhpg = 3
278	IF( ln_hpg_prj ) nhpg = 4
279	IF( ln_hpg_isf ) nhpg = 5
280	!
281	! ! Consistency check
282	ioptio = 0
283	IF( ln_hpg_zco ) ioptio = ioptio + 1
284	IF( ln_hpg_zps ) ioptio = ioptio + 1
285	IF( ln_hpg_sco ) ioptio = ioptio + 1
286	IF( ln_hpg_djc ) ioptio = ioptio + 1
287	IF( ln_hpg_prj ) ioptio = ioptio + 1
288	IF( ln_hpg_isf ) ioptio = ioptio + 1
289	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
290	!
291	! initialisation of ice load
292	riceload(:,:)=0.0
293	!
294	END SUBROUTINE dyn_hpg_init
295
296
297	SUBROUTINE hpg_zco( kt )
298	!!---------------------------------------------------------------------
299	!! * ROUTINE hpg_zco *
300	!!
301	!! ** Method : z-coordinate case, levels are horizontal surfaces.
302	!! The now hydrostatic pressure gradient at a given level, jk,
303	!! is computed by taking the vertical integral of the in-situ
304	!! density gradient along the model level from the suface to that
305	!! level: zhpi = grav .....
306	!! zhpj = grav .....
307	!! add it to the general momentum trend (ua,va).
308	!! ua = ua - 1/e1u * zhpi
309	!! va = va - 1/e2v * zhpj
310	!!
311	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
312	!!----------------------------------------------------------------------
313	INTEGER, INTENT(in) :: kt ! ocean time-step index
314	!!
315	INTEGER :: ji, jj, jk ! dummy loop indices
316	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
317	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
318	!!----------------------------------------------------------------------
319	!
320	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
321	!
322	IF( kt == nit000 ) THEN
323	IF(lwp) WRITE(numout,*)
324	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
325	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
326	ENDIF
327
328	zcoef0 = - grav * 0.5_wp ! Local constant initialization
329
330	! Surface value
331	DO jj = 2, jpjm1
332	DO ji = fs_2, fs_jpim1 ! vector opt.
333	zcoef1 = zcoef0 * fse3w(ji,jj,1)
334	! hydrostatic pressure gradient
335	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
336	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
337	! add to the general momentum trend
338	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
339	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
340	END DO
341	END DO
342
343	!
344	! interior value (2=<jk=<jpkm1)
345	DO jk = 2, jpkm1
346	DO jj = 2, jpjm1
347	DO ji = fs_2, fs_jpim1 ! vector opt.
348	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
349	! hydrostatic pressure gradient
350	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
351	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
352	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
353
354	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
355	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
356	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
357	! add to the general momentum trend
358	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
359	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
360	END DO
361	END DO
362	END DO
363	!
364	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
365	!
366	END SUBROUTINE hpg_zco
367
368
369	SUBROUTINE hpg_zps( kt )
370	!!---------------------------------------------------------------------
371	!! * ROUTINE hpg_zps *
372	!!
373	!! ** Method : z-coordinate plus partial steps case. blahblah...
374	!!
375	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
376	!!----------------------------------------------------------------------
377	INTEGER, INTENT(in) :: kt ! ocean time-step index
378	!!
379	INTEGER :: ji, jj, jk ! dummy loop indices
380	INTEGER :: iku, ikv ! temporary integers
381	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
382	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
383	!!----------------------------------------------------------------------
384	!
385	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
386	!
387	IF( kt == nit000 ) THEN
388	IF(lwp) WRITE(numout,*)
389	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
390	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
391	ENDIF
392
393
394	! Local constant initialization
395	zcoef0 = - grav * 0.5_wp
396
397	! Surface value (also valid in partial step case)
398	DO jj = 2, jpjm1
399	DO ji = fs_2, fs_jpim1 ! vector opt.
400	zcoef1 = zcoef0 * fse3w(ji,jj,1)
401	! hydrostatic pressure gradient
402	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
403	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
404	! add to the general momentum trend
405	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
406	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
407	END DO
408	END DO
409
410
411	! interior value (2=<jk=<jpkm1)
412	DO jk = 2, jpkm1
413	DO jj = 2, jpjm1
414	DO ji = fs_2, fs_jpim1 ! vector opt.
415	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
416	! hydrostatic pressure gradient
417	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
418	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
419	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
420
421	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
422	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
423	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
424	! add to the general momentum trend
425	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
426	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
427	END DO
428	END DO
429	END DO
430
431
432	! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
433	DO jj = 2, jpjm1
434	DO ji = 2, jpim1
435	iku = mbku(ji,jj)
436	ikv = mbkv(ji,jj)
437	zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) )
438	zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) )
439	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
440	ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value
441	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
442	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj)
443	ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
444	ENDIF
445	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
446	va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value
447	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
448	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj)
449	va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
450	ENDIF
451	END DO
452	END DO
453	!
454	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
455	!
456	END SUBROUTINE hpg_zps
457
458	SUBROUTINE hpg_sco( kt )
459	!!---------------------------------------------------------------------
460	!! * ROUTINE hpg_sco *
461	!!
462	!! ** Method : s-coordinate case. Jacobian scheme.
463	!! The now hydrostatic pressure gradient at a given level, jk,
464	!! is computed by taking the vertical integral of the in-situ
465	!! density gradient along the model level from the suface to that
466	!! level. s-coordinates (ln_sco): a corrective term is added
467	!! to the horizontal pressure gradient :
468	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
469	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
470	!! add it to the general momentum trend (ua,va).
471	!! ua = ua - 1/e1u * zhpi
472	!! va = va - 1/e2v * zhpj
473	!!
474	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
475	!!----------------------------------------------------------------------
476	INTEGER, INTENT(in) :: kt ! ocean time-step index
477	!!
478	INTEGER :: ji, jj, jk ! dummy loop indices
479	REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars
480	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
481	!!----------------------------------------------------------------------
482	!
483	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
484	!
485	IF( kt == nit000 ) THEN
486	IF(lwp) WRITE(numout,*)
487	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
488	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
489	ENDIF
490
491	! Local constant initialization
492	zcoef0 = - grav * 0.5_wp
493	! To use density and not density anomaly
494	IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
495	ELSE ; znad = 0._wp ! Fixed volume
496	ENDIF
497
498	! Surface value
499	DO jj = 2, jpjm1
500	DO ji = fs_2, fs_jpim1 ! vector opt.
501	! hydrostatic pressure gradient along s-surfaces
502	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) &
503	& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
504	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) &
505	& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
506	! s-coordinate pressure gradient correction
507	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
508	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
509	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
510	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
511	! add to the general momentum trend
512	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap
513	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap
514	END DO
515	END DO
516
517	! interior value (2=<jk=<jpkm1)
518	DO jk = 2, jpkm1
519	DO jj = 2, jpjm1
520	DO ji = fs_2, fs_jpim1 ! vector opt.
521	! hydrostatic pressure gradient along s-surfaces
522	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
523	& * ( fse3w(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) &
524	& - fse3w(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) )
525	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
526	& * ( fse3w(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) &
527	& - fse3w(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) )
528	! s-coordinate pressure gradient correction
529	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
530	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj)
531	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
532	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj)
533	! add to the general momentum trend
534	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap
535	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap
536	END DO
537	END DO
538	END DO
539	!
540	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
541	!
542	END SUBROUTINE hpg_sco
543
544	SUBROUTINE hpg_isf( kt )
545	!!---------------------------------------------------------------------
546	!! * ROUTINE hpg_sco *
547	!!
548	!! ** Method : s-coordinate case. Jacobian scheme.
549	!! The now hydrostatic pressure gradient at a given level, jk,
550	!! is computed by taking the vertical integral of the in-situ
551	!! density gradient along the model level from the suface to that
552	!! level. s-coordinates (ln_sco): a corrective term is added
553	!! to the horizontal pressure gradient :
554	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
555	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
556	!! add it to the general momentum trend (ua,va).
557	!! ua = ua - 1/e1u * zhpi
558	!! va = va - 1/e2v * zhpj
559	!! iceload is added and partial cell case are added to the top and bottom
560	!!
561	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
562	!!----------------------------------------------------------------------
563	INTEGER, INTENT(in) :: kt ! ocean time-step index
564	!!
565	INTEGER :: ji, jj, jk, iku, ikv, ikt, iktp1i, iktp1j ! dummy loop indices
566	REAL(wp) :: zcoef0, zuap, zvap, znad, ze3wu, ze3wv, zuapint, zvapint, zhpjint, zhpiint, zdzwt, zdzwtjp1, zdzwtip1 ! temporary scalars
567	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj, zrhd
568	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop
569	REAL(wp), POINTER, DIMENSION(:,:) :: ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj
570	!!----------------------------------------------------------------------
571	!
572	CALL wrk_alloc( jpi,jpj, 2, ztstop)
573	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
574	CALL wrk_alloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
575	!
576	IF( kt == nit000 ) THEN
577	IF(lwp) WRITE(numout,*)
578	IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf'
579	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
580	ENDIF
581
582	! Local constant initialization
583	zcoef0 = - grav * 0.5_wp
584	! To use density and not density anomaly
585	! IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
586	! ELSE ; znad = 0._wp ! Fixed volume
587	! ENDIF
588	znad=1._wp
589	! iniitialised to 0. zhpi zhpi
590	zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp
591
592	!==================================================================================
593	!=====Compute iceload and contribution of the half first wet layer =================
594	!===================================================================================
595
596	! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude)
597	ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp
598
599	! compute density of the water displaced by the ice shelf
600	zrhd = rhd ! save rhd
601	DO jk = 1, jpk
602	zdept(:,:)=gdept_1d(jk)
603	CALL eos(ztstop(:,:,:),zdept(:,:),rhd(:,:,jk))
604	END DO
605	WHERE ( tmask(:,:,:) == 1._wp)
606	rhd(:,:,:) = zrhd(:,:,:) ! replace wet cell by the saved rhd
607	END WHERE
608
609	! compute rhd at the ice/oce interface (ice shelf side)
610	CALL eos(ztstop,risfdep,zrhdtop_isf)
611
612	! compute rhd at the ice/oce interface (ocean side)
613	DO ji=1,jpi
614	DO jj=1,jpj
615	ikt=mikt(ji,jj)
616	ztstop(ji,jj,1)=tsn(ji,jj,ikt,1)
617	ztstop(ji,jj,2)=tsn(ji,jj,ikt,2)
618	END DO
619	END DO
620	CALL eos(ztstop,risfdep,zrhdtop_oce)
621	!
622	! Surface value + ice shelf gradient
623	! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v)
624	ziceload = 0._wp
625	DO jj = 1, jpj
626	DO ji = 1, jpi ! vector opt.
627	ikt=mikt(ji,jj)
628	ziceload(ji,jj) = ziceload(ji,jj) + (znad + rhd(ji,jj,1) ) * fse3w(ji,jj,1) * (1._wp - tmask(ji,jj,1))
629	DO jk=2,ikt-1
630	ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + rhd(ji,jj,jk-1) + rhd(ji,jj,jk)) * fse3w(ji,jj,jk) &
631	& * (1._wp - tmask(ji,jj,jk))
632	END DO
633	IF (ikt .GE. 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + rhd(ji,jj,ikt-1)) &
634	& * ( risfdep(ji,jj) - gdept_1d(ikt-1) )
635	END DO
636	END DO
637	riceload(:,:) = 0.0_wp ; riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5
638	! compute zp from z=0 to first T wet point (correction due to zps not yet applied)
639	DO jj = 2, jpjm1
640	DO ji = fs_2, fs_jpim1 ! vector opt.
641	ikt=mikt(ji,jj) ; iktp1i=mikt(ji+1,jj); iktp1j=mikt(ji,jj+1)
642	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
643	! we assume ISF is in isostatic equilibrium
644	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * fse3w(ji+1,jj ,iktp1i) &
645	& * ( 2._wp * znad + rhd(ji+1,jj ,iktp1i) + zrhdtop_oce(ji+1,jj ) ) &
646	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
647	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
648	& + ( ziceload(ji+1,jj) - ziceload(ji,jj)) )
649	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * fse3w(ji ,jj+1,iktp1j) &
650	& * ( 2._wp * znad + rhd(ji ,jj+1,iktp1j) + zrhdtop_oce(ji ,jj+1) ) &
651	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
652	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
653	& + ( ziceload(ji,jj+1) - ziceload(ji,jj) ) )
654	! s-coordinate pressure gradient correction (=0 if z coordinate)
655	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
656	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
657	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
658	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
659	! add to the general momentum trend
660	ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
661	va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
662	END DO
663	END DO
664	!==================================================================================
665	!===== Compute partial cell contribution for the top cell =========================
666	!==================================================================================
667	DO jj = 2, jpjm1
668	DO ji = fs_2, fs_jpim1 ! vector opt.
669	iku = miku(ji,jj) ;
670	zpshpi(ji,jj)=0.0_wp ; zpshpj(ji,jj)=0.0_wp
671	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))
672	! u direction
673	IF ( iku .GT. 1 ) THEN
674	! case iku
675	zhpi(ji,jj,iku) = zcoef0 / e1u(ji,jj) * ze3wu &
676	& * ( rhd (ji+1,jj,iku) + rhd (ji,jj,iku) &
677	& + SIGN(1._wp,ze3wu) * grui(ji,jj) + 2._wp * znad )
678	! corrective term ( = 0 if z coordinate )
679	zuap = -zcoef0 * ( arui(ji,jj) + 2._wp * znad ) * gzui(ji,jj) / e1u(ji,jj)
680	! zhpi will be added in interior loop
681	ua(ji,jj,iku) = ua(ji,jj,iku) + zuap
682	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
683	IF (mbku(ji,jj) == iku + 1) zpshpi(ji,jj) = zhpi(ji,jj,iku)
684
685	! case iku + 1 (remove the zphi term added in the interior loop and compute the one corrected for zps)
686	zhpiint = zcoef0 / e1u(ji,jj) &
687	& * ( fse3w(ji+1,jj ,iku+1) * ( (rhd(ji+1,jj,iku+1) + znad) &
688	& + (rhd(ji+1,jj,iku ) + znad) ) * tmask(ji+1,jj,iku) &
689	& - fse3w(ji ,jj ,iku+1) * ( (rhd(ji ,jj,iku+1) + znad) &
690	& + (rhd(ji ,jj,iku ) + znad) ) * tmask(ji ,jj,iku) )
691	zhpi(ji,jj,iku+1) = zcoef0 / e1u(ji,jj) * ge3rui(ji,jj) - zhpiint
692	END IF
693
694	! v direction
695	ikv = mikv(ji,jj)
696	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))
697	IF ( ikv .GT. 1 ) THEN
698	! case ikv
699	zhpj(ji,jj,ikv) = zcoef0 / e2v(ji,jj) * ze3wv &
700	& * ( rhd(ji,jj+1,ikv) + rhd (ji,jj,ikv) &
701	& + SIGN(1._wp,ze3wv) * grvi(ji,jj) + 2._wp * znad )
702	! corrective term ( = 0 if z coordinate )
703	zvap = -zcoef0 * ( arvi(ji,jj) + 2._wp * znad ) * gzvi(ji,jj) / e2v(ji,jj)
704	! zhpi will be added in interior loop
705	va(ji,jj,ikv) = va(ji,jj,ikv) + zvap
706	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
707	IF (mbkv(ji,jj) == ikv + 1) zpshpj(ji,jj) = zhpj(ji,jj,ikv)
708
709	! case ikv + 1 (remove the zphj term added in the interior loop and compute the one corrected for zps)
710	zhpjint = zcoef0 / e2v(ji,jj) &
711	& * ( fse3w(ji ,jj+1,ikv+1) * ( (rhd(ji,jj+1,ikv+1) + znad) &
712	& + (rhd(ji,jj+1,ikv ) + znad) ) * tmask(ji,jj+1,ikv) &
713	& - fse3w(ji ,jj ,ikv+1) * ( (rhd(ji,jj ,ikv+1) + znad) &
714	& + (rhd(ji,jj ,ikv ) + znad) ) * tmask(ji,jj ,ikv) )
715	zhpj(ji,jj,ikv+1) = zcoef0 / e2v(ji,jj) * ge3rvi(ji,jj) - zhpjint
716	END IF
717	END DO
718	END DO
719
720	!==================================================================================
721	!===== Compute interior value =====================================================
722	!==================================================================================
723
724	DO jj = 2, jpjm1
725	DO ji = fs_2, fs_jpim1 ! vector opt.
726	iku=miku(ji,jj); ikv=mikv(ji,jj)
727	DO jk = 2, jpkm1
728	! hydrostatic pressure gradient along s-surfaces
729	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
730	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) + zhpi(ji,jj,jk-1) &
731	& + zcoef0 / e1u(ji,jj) &
732	& * ( fse3w(ji+1,jj ,jk) * ( (rhd(ji+1,jj,jk ) + znad) &
733	& + (rhd(ji+1,jj,jk-1) + znad) ) * tmask(ji+1,jj,jk-1) &
734	& - fse3w(ji ,jj ,jk) * ( (rhd(ji ,jj,jk ) + znad) &
735	& + (rhd(ji ,jj,jk-1) + znad) ) * tmask(ji ,jj,jk-1) )
736	! s-coordinate pressure gradient correction
737	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
738	zuap = - zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
739	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) * umask(ji,jj,jk-1)
740	ua(ji,jj,jk) = ua(ji,jj,jk) + ( zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
741
742	! hydrostatic pressure gradient along s-surfaces
743	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
744	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) + zhpj(ji,jj,jk-1) &
745	& + zcoef0 / e2v(ji,jj) &
746	& * ( fse3w(ji ,jj+1,jk) * ( (rhd(ji,jj+1,jk ) + znad) &
747	& + (rhd(ji,jj+1,jk-1) + znad) ) * tmask(ji,jj+1,jk-1) &
748	& - fse3w(ji ,jj ,jk) * ( (rhd(ji,jj ,jk ) + znad) &
749	& + (rhd(ji,jj ,jk-1) + znad) ) * tmask(ji,jj ,jk-1) )
750	! s-coordinate pressure gradient correction
751	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
752	zvap = - zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
753	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) * vmask(ji,jj,jk-1)
754	! add to the general momentum trend
755	va(ji,jj,jk) = va(ji,jj,jk) + ( zhpj(ji,jj,jk) + zvap ) * vmask(ji,jj,jk)
756	END DO
757	END DO
758	END DO
759
760	!==================================================================================
761	!===== Compute bottom cell contribution (partial cell) ============================
762	!==================================================================================
763
764	DO jj = 2, jpjm1
765	DO ji = 2, jpim1
766	iku = mbku(ji,jj)
767	ikv = mbkv(ji,jj)
768
769	IF (iku .GT. 1) THEN
770	! remove old value (interior case)
771	zuap = -zcoef0 * ( rhd (ji+1,jj ,iku) + rhd (ji,jj,iku) + 2._wp * znad ) &
772	& * ( fsde3w(ji+1,jj ,iku) - fsde3w(ji,jj,iku) ) / e1u(ji,jj)
773	ua(ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) - zuap
774	! put new value
775	! -zpshpi to avoid double contribution of the partial step in the top layer
776	zuap = -zcoef0 * ( aru(ji,jj) + 2._wp * znad ) * gzu(ji,jj) / e1u(ji,jj)
777	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) + zcoef0 / e1u(ji,jj) * ge3ru(ji,jj) - zpshpi(ji,jj)
778	ua(ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) + zuap
779	END IF
780	! v direction
781	IF (ikv .GT. 1) THEN
782	! remove old value (interior case)
783	zvap = -zcoef0 * ( rhd (ji ,jj+1,ikv) + rhd (ji,jj,ikv) + 2._wp * znad ) &
784	& * ( fsde3w(ji ,jj+1,ikv) - fsde3w(ji,jj,ikv) ) / e2v(ji,jj)
785	va(ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) - zvap
786	! put new value
787	! -zpshpj to avoid double contribution of the partial step in the top layer
788	zvap = -zcoef0 * ( arv(ji,jj) + 2._wp * znad ) * gzv(ji,jj) / e2v(ji,jj)
789	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) + zcoef0 / e2v(ji,jj) * ge3rv(ji,jj) - zpshpj(ji,jj)
790	va(ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) + zvap
791	END IF
792	END DO
793	END DO
794
795	! set back to original density value into the ice shelf cell (maybe useless because it is masked)
796	rhd = zrhd
797	!
798	CALL wrk_dealloc( jpi,jpj,2, ztstop)
799	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
800	CALL wrk_dealloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
801	!
802	END SUBROUTINE hpg_isf
803
804
805	SUBROUTINE hpg_djc( kt )
806	!!---------------------------------------------------------------------
807	!! * ROUTINE hpg_djc *
808	!!
809	!! ** Method : Density Jacobian with Cubic polynomial scheme
810	!!
811	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
812	!!----------------------------------------------------------------------
813	INTEGER, INTENT(in) :: kt ! ocean time-step index
814	!!
815	INTEGER :: ji, jj, jk ! dummy loop indices
816	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
817	REAL(wp) :: z1_10, cffu, cffx ! " "
818	REAL(wp) :: z1_12, cffv, cffy ! " "
819	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
820	REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw
821	REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow
822	REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k
823	!!----------------------------------------------------------------------
824	!
825	CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
826	CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
827	CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
828	!
829
830	IF( kt == nit000 ) THEN
831	IF(lwp) WRITE(numout,*)
832	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
833	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
834	ENDIF
835
836	! Local constant initialization
837	zcoef0 = - grav * 0.5_wp
838	z1_10 = 1._wp / 10._wp
839	z1_12 = 1._wp / 12._wp
840
841	!----------------------------------------------------------------------------------------
842	! compute and store in provisional arrays elementary vertical and horizontal differences
843	!----------------------------------------------------------------------------------------
844
845	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
846
847	DO jk = 2, jpkm1
848	DO jj = 2, jpjm1
849	DO ji = fs_2, fs_jpim1 ! vector opt.
850	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
851	dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1)
852	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
853	dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk )
854	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
855	dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk )
856	END DO
857	END DO
858	END DO
859
860	!-------------------------------------------------------------------------
861	! compute harmonic averages using eq. 5.18
862	!-------------------------------------------------------------------------
863	zep = 1.e-15
864
865	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
866	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
867
868	DO jk = 2, jpkm1
869	DO jj = 2, jpjm1
870	DO ji = fs_2, fs_jpim1 ! vector opt.
871	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
872
873	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
874	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
875
876	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
877	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
878
879	IF( cffw > zep) THEN
880	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
881	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
882	ELSE
883	drhow(ji,jj,jk) = 0._wp
884	ENDIF
885
886	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
887	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
888
889	IF( cffu > zep ) THEN
890	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
891	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
892	ELSE
893	drhou(ji,jj,jk ) = 0._wp
894	ENDIF
895
896	IF( cffx > zep ) THEN
897	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
898	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
899	ELSE
900	dzu(ji,jj,jk) = 0._wp
901	ENDIF
902
903	IF( cffv > zep ) THEN
904	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
905	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
906	ELSE
907	drhov(ji,jj,jk) = 0._wp
908	ENDIF
909
910	IF( cffy > zep ) THEN
911	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
912	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
913	ELSE
914	dzv(ji,jj,jk) = 0._wp
915	ENDIF
916
917	END DO
918	END DO
919	END DO
920
921	!----------------------------------------------------------------------------------
922	! apply boundary conditions at top and bottom using 5.36-5.37
923	!----------------------------------------------------------------------------------
924	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
925	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
926	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
927
928	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
929	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
930	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
931
932
933	!--------------------------------------------------------------
934	! Upper half of top-most grid box, compute and store
935	!-------------------------------------------------------------
936
937	!!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified
938	! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
939
940	DO jj = 2, jpjm1
941	DO ji = fs_2, fs_jpim1 ! vector opt.
942	rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) &
943	& * ( rhd(ji,jj,1) &
944	& + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) &
945	& * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) &
946	& / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) )
947	END DO
948	END DO
949
950	!!bug gm : here also, simplification is possible
951	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
952
953	DO jk = 2, jpkm1
954	DO jj = 2, jpjm1
955	DO ji = fs_2, fs_jpim1 ! vector opt.
956
957	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
958	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) &
959	& - grav * z1_10 * ( &
960	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
961	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
962	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
963	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
964	& )
965
966	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
967	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) &
968	& - grav* z1_10 * ( &
969	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
970	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
971	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
972	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
973	& )
974
975	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
976	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) &
977	& - grav* z1_10 * ( &
978	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
979	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
980	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
981	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
982	& )
983
984	END DO
985	END DO
986	END DO
987	CALL lbc_lnk(rho_k,'W',1.)
988	CALL lbc_lnk(rho_i,'U',1.)
989	CALL lbc_lnk(rho_j,'V',1.)
990
991
992	! ---------------
993	! Surface value
994	! ---------------
995	DO jj = 2, jpjm1
996	DO ji = fs_2, fs_jpim1 ! vector opt.
997	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj)
998	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj)
999	! add to the general momentum trend
1000	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
1001	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
1002	END DO
1003	END DO
1004
1005	! ----------------
1006	! interior value (2=<jk=<jpkm1)
1007	! ----------------
1008	DO jk = 2, jpkm1
1009	DO jj = 2, jpjm1
1010	DO ji = fs_2, fs_jpim1 ! vector opt.
1011	! hydrostatic pressure gradient along s-surfaces
1012	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
1013	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
1014	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj)
1015	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
1016	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
1017	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj)
1018	! add to the general momentum trend
1019	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
1020	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
1021	END DO
1022	END DO
1023	END DO
1024	!
1025	CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
1026	CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
1027	CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
1028	!
1029	END SUBROUTINE hpg_djc
1030
1031
1032	SUBROUTINE hpg_prj( kt )
1033	!!---------------------------------------------------------------------
1034	!! * ROUTINE hpg_prj *
1035	!!
1036	!! ** Method : s-coordinate case.
1037	!! A Pressure-Jacobian horizontal pressure gradient method
1038	!! based on the constrained cubic-spline interpolation for
1039	!! all vertical coordinate systems
1040	!!
1041	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
1042	!!----------------------------------------------------------------------
1043	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
1044	INTEGER, INTENT(in) :: kt ! ocean time-step index
1045	!!
1046	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
1047	REAL(wp) :: zcoef0, znad ! temporary scalars
1048	!!
1049	!! The local variables for the correction term
1050	INTEGER :: jk1, jis, jid, jjs, jjd
1051	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
1052	REAL(wp) :: zrhdt1
1053	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
1054	REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh
1055	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
1056	REAL(wp), POINTER, DIMENSION(:,:) :: zsshu_n, zsshv_n
1057	!!----------------------------------------------------------------------
1058	!
1059	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
1060	CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh )
1061	CALL wrk_alloc( jpi,jpj, zsshu_n, zsshv_n )
1062	!
1063	IF( kt == nit000 ) THEN
1064	IF(lwp) WRITE(numout,*)
1065	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
1066	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
1067	ENDIF
1068
1069	!!----------------------------------------------------------------------
1070	! Local constant initialization
1071	zcoef0 = - grav
1072	znad = 0.0_wp
1073	IF( lk_vvl ) znad = 1._wp
1074
1075	! Clean 3-D work arrays
1076	zhpi(:,:,:) = 0._wp
1077	zrhh(:,:,:) = rhd(:,:,:)
1078
1079	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
1080	DO jj = 1, jpj
1081	DO ji = 1, jpi
1082	jk = mbathy(ji,jj)
1083	IF( jk <= 0 ) THEN; zrhh(ji,jj,:) = 0._wp
1084	ELSE IF(jk == 1) THEN; zrhh(ji,jj, jk+1:jpk) = rhd(ji,jj,jk)
1085	ELSE IF(jk < jpkm1) THEN
1086	DO jkk = jk+1, jpk
1087	zrhh(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1), &
1088	fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2))
1089	END DO
1090	ENDIF
1091	END DO
1092	END DO
1093
1094	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
1095	DO jj = 1, jpj
1096	DO ji = 1, jpi
1097	zdept(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) - sshn(ji,jj) * znad
1098	END DO
1099	END DO
1100
1101	DO jk = 2, jpk
1102	DO jj = 1, jpj
1103	DO ji = 1, jpi
1104	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + fse3w(ji,jj,jk)
1105	END DO
1106	END DO
1107	END DO
1108
1109	fsp(:,:,:) = zrhh (:,:,:)
1110	xsp(:,:,:) = zdept(:,:,:)
1111
1112	! Construct the vertical density profile with the
1113	! constrained cubic spline interpolation
1114	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
1115	CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type)
1116
1117	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
1118	DO jj = 2, jpj
1119	DO ji = 2, jpi
1120	zrhdt1 = zrhh(ji,jj,1) - interp3(zdept(ji,jj,1),asp(ji,jj,1), &
1121	bsp(ji,jj,1), csp(ji,jj,1), &
1122	dsp(ji,jj,1) ) * 0.25_wp * fse3w(ji,jj,1)
1123
1124	! assuming linear profile across the top half surface layer
1125	zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * zrhdt1
1126	END DO
1127	END DO
1128
1129	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
1130	DO jk = 2, jpkm1
1131	DO jj = 2, jpj
1132	DO ji = 2, jpi
1133	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
1134	integ_spline(zdept(ji,jj,jk-1), zdept(ji,jj,jk),&
1135	asp(ji,jj,jk-1), bsp(ji,jj,jk-1), &
1136	csp(ji,jj,jk-1), dsp(ji,jj,jk-1))
1137	END DO
1138	END DO
1139	END DO
1140
1141	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
1142
1143	! Prepare zsshu_n and zsshv_n
1144	DO jj = 2, jpjm1
1145	DO ji = 2, jpim1
1146	zsshu_n(ji,jj) = (e12u(ji,jj) * sshn(ji,jj) + e12u(ji+1, jj) * sshn(ji+1,jj)) * &
1147	& r1_e12u(ji,jj) * umask(ji,jj,1) * 0.5_wp
1148	zsshv_n(ji,jj) = (e12v(ji,jj) * sshn(ji,jj) + e12v(ji+1, jj) * sshn(ji,jj+1)) * &
1149	& r1_e12v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
1150	END DO
1151	END DO
1152
1153	DO jj = 2, jpjm1
1154	DO ji = 2, jpim1
1155	zu(ji,jj,1) = - ( fse3u(ji,jj,1) - zsshu_n(ji,jj) * znad)
1156	zv(ji,jj,1) = - ( fse3v(ji,jj,1) - zsshv_n(ji,jj) * znad)
1157	END DO
1158	END DO
1159
1160	DO jk = 2, jpkm1
1161	DO jj = 2, jpjm1
1162	DO ji = 2, jpim1
1163	zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk)
1164	zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk)
1165	END DO
1166	END DO
1167	END DO
1168
1169	DO jk = 1, jpkm1
1170	DO jj = 2, jpjm1
1171	DO ji = 2, jpim1
1172	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk)
1173	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk)
1174	END DO
1175	END DO
1176	END DO
1177
1178	DO jk = 1, jpkm1
1179	DO jj = 2, jpjm1
1180	DO ji = 2, jpim1
1181	zu(ji,jj,jk) = min(zu(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
1182	zu(ji,jj,jk) = max(zu(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
1183	zv(ji,jj,jk) = min(zv(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
1184	zv(ji,jj,jk) = max(zv(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
1185	END DO
1186	END DO
1187	END DO
1188
1189
1190	DO jk = 1, jpkm1
1191	DO jj = 2, jpjm1
1192	DO ji = 2, jpim1
1193	zpwes = 0._wp; zpwed = 0._wp
1194	zpnss = 0._wp; zpnsd = 0._wp
1195	zuijk = zu(ji,jj,jk)
1196	zvijk = zv(ji,jj,jk)
1197
1198	!!!!! for u equation
1199	IF( jk <= mbku(ji,jj) ) THEN
1200	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
1201	jis = ji + 1; jid = ji
1202	ELSE
1203	jis = ji; jid = ji +1
1204	ENDIF
1205
1206	! integrate the pressure on the shallow side
1207	jk1 = jk
1208	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
1209	IF( jk1 == mbku(ji,jj) ) THEN
1210	zuijk = -zdept(jis,jj,jk1)
1211	EXIT
1212	ENDIF
1213	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
1214	zpwes = zpwes + &
1215	integ_spline(zdept(jis,jj,jk1), zdeps, &
1216	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
1217	csp(jis,jj,jk1), dsp(jis,jj,jk1))
1218	jk1 = jk1 + 1
1219	END DO
1220
1221	! integrate the pressure on the deep side
1222	jk1 = jk
1223	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
1224	IF( jk1 == 1 ) THEN
1225	zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad)
1226	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
1227	bsp(jid,jj,1), csp(jid,jj,1), &
1228	dsp(jid,jj,1)) * zdeps
1229	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
1230	EXIT
1231	ENDIF
1232	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
1233	zpwed = zpwed + &
1234	integ_spline(zdeps, zdept(jid,jj,jk1), &
1235	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
1236	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
1237	jk1 = jk1 - 1
1238	END DO
1239
1240	! update the momentum trends in u direction
1241
1242	zdpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk))
1243	IF( lk_vvl ) THEN
1244	zdpdx2 = zcoef0 / e1u(ji,jj) * &
1245	( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) )
1246	ELSE
1247	zdpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
1248	ENDIF
1249
1250	ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * &
1251	& umask(ji,jj,jk) * tmask(ji,jj,jk) * tmask(ji+1,jj,jk)
1252	ENDIF
1253
1254	!!!!! for v equation
1255	IF( jk <= mbkv(ji,jj) ) THEN
1256	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
1257	jjs = jj + 1; jjd = jj
1258	ELSE
1259	jjs = jj ; jjd = jj + 1
1260	ENDIF
1261
1262	! integrate the pressure on the shallow side
1263	jk1 = jk
1264	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
1265	IF( jk1 == mbkv(ji,jj) ) THEN
1266	zvijk = -zdept(ji,jjs,jk1)
1267	EXIT
1268	ENDIF
1269	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
1270	zpnss = zpnss + &
1271	integ_spline(zdept(ji,jjs,jk1), zdeps, &
1272	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
1273	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
1274	jk1 = jk1 + 1
1275	END DO
1276
1277	! integrate the pressure on the deep side
1278	jk1 = jk
1279	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
1280	IF( jk1 == 1 ) THEN
1281	zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad)
1282	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
1283	bsp(ji,jjd,1), csp(ji,jjd,1), &
1284	dsp(ji,jjd,1) ) * zdeps
1285	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
1286	EXIT
1287	ENDIF
1288	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
1289	zpnsd = zpnsd + &
1290	integ_spline(zdeps, zdept(ji,jjd,jk1), &
1291	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
1292	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
1293	jk1 = jk1 - 1
1294	END DO
1295
1296
1297	! update the momentum trends in v direction
1298
1299	zdpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk))
1300	IF( lk_vvl ) THEN
1301	zdpdy2 = zcoef0 / e2v(ji,jj) * &
1302	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) )
1303	ELSE
1304	zdpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
1305	ENDIF
1306
1307	va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2)*&
1308	& vmask(ji,jj,jk)tmask(ji,jj,jk)tmask(ji,jj+1,jk)
1309	ENDIF
1310
1311
1312	END DO
1313	END DO
1314	END DO
1315	!
1316	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
1317	CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh )
1318	CALL wrk_dealloc( jpi,jpj, zsshu_n, zsshv_n )
1319	!
1320	END SUBROUTINE hpg_prj
1321
1322
1323	SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type)
1324	!!----------------------------------------------------------------------
1325	!! * ROUTINE cspline *
1326	!!
1327	!! ** Purpose : constrained cubic spline interpolation
1328	!!
1329	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
1330	!!
1331	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
1332	!!----------------------------------------------------------------------
1333	IMPLICIT NONE
1334	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate
1335	REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of
1336	! the interpoated function
1337	INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline
1338	! 2: Linear
1339	!
1340	INTEGER :: ji, jj, jk ! dummy loop indices
1341	INTEGER :: jpi, jpj, jpkm1
1342	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
1343	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
1344	REAL(wp) :: zdf(size(fsp,3))
1345	!!----------------------------------------------------------------------
1346
1347	jpi = size(fsp,1)
1348	jpj = size(fsp,2)
1349	jpkm1 = size(fsp,3) - 1
1350
1351
1352	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
1353	DO ji = 1, jpi
1354	DO jj = 1, jpj
1355	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
1356	! DO jk = 2, jpkm1-1
1357	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
1358	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1359	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
1360	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
1361	!
1362	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
1363	!
1364	! IF(zdf1 * zdf2 <= 0._wp) THEN
1365	! zdf(jk) = 0._wp
1366	! ELSE
1367	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
1368	! ENDIF
1369	! END DO
1370
1371	!!Simply geometric average
1372	DO jk = 2, jpkm1-1
1373	zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1))
1374	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk))
1375
1376	IF(zdf1 * zdf2 <= 0._wp) THEN
1377	zdf(jk) = 0._wp
1378	ELSE
1379	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
1380	ENDIF
1381	END DO
1382
1383	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
1384	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
1385	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
1386	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - &
1387	& 0.5_wp * zdf(jpkm1 - 1)
1388
1389	DO jk = 1, jpkm1 - 1
1390	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1391	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
1392	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
1393	zddf1 = -2._wp * ztmp1 + ztmp2
1394	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
1395	zddf2 = 2._wp * ztmp1 - ztmp2
1396
1397	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
1398	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
1399	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
1400	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
1401	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
1402	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
1403	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
1404	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
1405	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
1406	END DO
1407	END DO
1408	END DO
1409
1410	ELSE IF (polynomial_type == 2) THEN ! Linear
1411	DO ji = 1, jpi
1412	DO jj = 1, jpj
1413	DO jk = 1, jpkm1-1
1414	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1415	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
1416
1417	dsp(ji,jj,jk) = 0._wp
1418	csp(ji,jj,jk) = 0._wp
1419	bsp(ji,jj,jk) = ztmp1 / zdxtmp
1420	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
1421	END DO
1422	END DO
1423	END DO
1424
1425	ELSE
1426	CALL ctl_stop( 'invalid polynomial type in cspline' )
1427	ENDIF
1428
1429	END SUBROUTINE cspline
1430
1431
1432	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
1433	!!----------------------------------------------------------------------
1434	!! * ROUTINE interp1 *
1435	!!
1436	!! ** Purpose : 1-d linear interpolation
1437	!!
1438	!! ** Method : interpolation is straight forward
1439	!! extrapolation is also permitted (no value limit)
1440	!!----------------------------------------------------------------------
1441	IMPLICIT NONE
1442	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
1443	REAL(wp) :: f ! result of the interpolation (extrapolation)
1444	REAL(wp) :: zdeltx
1445	!!----------------------------------------------------------------------
1446
1447	zdeltx = xr - xl
1448	IF(abs(zdeltx) <= 10._wp * EPSILON(x)) THEN
1449	f = 0.5_wp * (fl + fr)
1450	ELSE
1451	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
1452	ENDIF
1453
1454	END FUNCTION interp1
1455
1456
1457	FUNCTION interp2(x, a, b, c, d) RESULT(f)
1458	!!----------------------------------------------------------------------
1459	!! * ROUTINE interp1 *
1460	!!
1461	!! ** Purpose : 1-d constrained cubic spline interpolation
1462	!!
1463	!! ** Method : cubic spline interpolation
1464	!!
1465	!!----------------------------------------------------------------------
1466	IMPLICIT NONE
1467	REAL(wp), INTENT(in) :: x, a, b, c, d
1468	REAL(wp) :: f ! value from the interpolation
1469	!!----------------------------------------------------------------------
1470
1471	f = a + x* ( b + x * ( c + d * x ) )
1472
1473	END FUNCTION interp2
1474
1475
1476	FUNCTION interp3(x, a, b, c, d) RESULT(f)
1477	!!----------------------------------------------------------------------
1478	!! * ROUTINE interp1 *
1479	!!
1480	!! ** Purpose : Calculate the first order of deriavtive of
1481	!! a cubic spline function y=a+bx+cx^2+d*x^3
1482	!!
1483	!! ** Method : f=dy/dx=b+2cx+3dx^2
1484	!!
1485	!!----------------------------------------------------------------------
1486	IMPLICIT NONE
1487	REAL(wp), INTENT(in) :: x, a, b, c, d
1488	REAL(wp) :: f ! value from the interpolation
1489	!!----------------------------------------------------------------------
1490
1491	f = b + x * ( 2._wp * c + 3._wp * d * x)
1492
1493	END FUNCTION interp3
1494
1495
1496	FUNCTION integ_spline(xl, xr, a, b, c, d) RESULT(f)
1497	!!----------------------------------------------------------------------
1498	!! * ROUTINE interp1 *
1499	!!
1500	!! ** Purpose : 1-d constrained cubic spline integration
1501	!!
1502	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
1503	!!
1504	!!----------------------------------------------------------------------
1505	IMPLICIT NONE
1506	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
1507	REAL(wp) :: za1, za2, za3
1508	REAL(wp) :: f ! integration result
1509	!!----------------------------------------------------------------------
1510
1511	za1 = 0.5_wp * b
1512	za2 = c / 3.0_wp
1513	za3 = 0.25_wp * d
1514
1515	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
1516	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
1517
1518	END FUNCTION integ_spline
1519
1520	!!======================================================================
1521	END MODULE dynhpg
1522

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