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dynhpg.F90 @ 7910

Last change on this file since 7910 was 7910, checked in by timgraham, 7 years ago
All wrk_alloc removed
Property svn:keywords set to `Id`
File size: 70.0 KB

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1	MODULE dynhpg
2	!!======================================================================
3	!! * MODULE dynhpg *
4	!! Ocean dynamics: hydrostatic pressure gradient trend
5	!!======================================================================
6	!! History : OPA ! 1987-09 (P. Andrich, M.-A. Foujols) hpg_zco: Original code
7	!! 5.0 ! 1991-11 (G. Madec)
8	!! 7.0 ! 1996-01 (G. Madec) hpg_sco: Original code for s-coordinates
9	!! 8.0 ! 1997-05 (G. Madec) split dynber into dynkeg and dynhpg
10	!! 8.5 ! 2002-07 (G. Madec) F90: Free form and module
11	!! 8.5 ! 2002-08 (A. Bozec) hpg_zps: Original code
12	!! NEMO 1.0 ! 2005-10 (A. Beckmann, B.W. An) various s-coordinate options
13	!! ! Original code for hpg_ctl, hpg_hel hpg_wdj, hpg_djc, hpg_rot
14	!! - ! 2005-11 (G. Madec) style & small optimisation
15	!! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase
16	!! 3.4 ! 2011-11 (H. Liu) hpg_prj: Original code for s-coordinates
17	!! ! (A. Coward) suppression of hel, wdj and rot options
18	!! 3.6 ! 2014-11 (P. Mathiot) hpg_isf: original code for ice shelf cavity
19	!!----------------------------------------------------------------------
20
21	!!----------------------------------------------------------------------
22	!! dyn_hpg : update the momentum trend with the now horizontal
23	!! gradient of the hydrostatic pressure
24	!! dyn_hpg_init : initialisation and control of options
25	!! hpg_zco : z-coordinate scheme
26	!! hpg_zps : z-coordinate plus partial steps (interpolation)
27	!! hpg_sco : s-coordinate (standard jacobian formulation)
28	!! hpg_isf : s-coordinate (sco formulation) adapted to ice shelf
29	!! hpg_djc : s-coordinate (Density Jacobian with Cubic polynomial)
30	!! hpg_prj : s-coordinate (Pressure Jacobian with Cubic polynomial)
31	!!----------------------------------------------------------------------
32	USE oce ! ocean dynamics and tracers
33	USE sbc_oce ! surface variable (only for the flag with ice shelf)
34	USE dom_oce ! ocean space and time domain
35	USE wet_dry ! wetting and drying
36	USE phycst ! physical constants
37	USE trd_oce ! trends: ocean variables
38	USE trddyn ! trend manager: dynamics
39	!jc USE zpshde ! partial step: hor. derivative (zps_hde routine)
40	!
41	USE in_out_manager ! I/O manager
42	USE prtctl ! Print control
43	USE lbclnk ! lateral boundary condition
44	USE lib_mpp ! MPP library
45	USE eosbn2 ! compute density
46	USE timing ! Timing
47	USE iom
48
49	IMPLICIT NONE
50	PRIVATE
51
52	PUBLIC dyn_hpg ! routine called by step module
53	PUBLIC dyn_hpg_init ! routine called by opa module
54
55	! !!* Namelist namdyn_hpg : hydrostatic pressure gradient
56	LOGICAL , PUBLIC :: ln_hpg_zco !: z-coordinate - full steps
57	LOGICAL , PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation)
58	LOGICAL , PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation)
59	LOGICAL , PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial)
60	LOGICAL , PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme)
61	LOGICAL , PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf
62
63	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 "vectopt_loop_substitute.h90"
67	!!----------------------------------------------------------------------
68	!! NEMO/OPA 3.3 , NEMO Consortium (2010)
69	!! $Id$
70	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
71	!!----------------------------------------------------------------------
72	CONTAINS
73
74	SUBROUTINE dyn_hpg( kt )
75	!!---------------------------------------------------------------------
76	!! * ROUTINE dyn_hpg *
77	!!
78	!! ** Method : Call the hydrostatic pressure gradient routine
79	!! using the scheme defined in the namelist
80	!!
81	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
82	!! - send trends to trd_dyn for futher diagnostics (l_trddyn=T)
83	!!----------------------------------------------------------------------
84	INTEGER, INTENT(in) :: kt ! ocean time-step index
85	REAL(wp), DIMENSION(jpi,jpj,jpk) :: ztrdu, ztrdv
86	!!----------------------------------------------------------------------
87	!
88	IF( nn_timing == 1 ) CALL timing_start('dyn_hpg')
89	!
90	IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn)
91	ztrdu(:,:,:) = ua(:,:,:)
92	ztrdv(:,:,:) = va(:,:,:)
93	ENDIF
94	!
95	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
96	CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate
97	CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation)
98	CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation)
99	CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial)
100	CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme)
101	CASE ( 5 ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf
102	END SELECT
103	!
104	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
105	ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:)
106	ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:)
107	CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt )
108	ENDIF
109	!
110	IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, &
111	& tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
112	!
113	IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg')
114	!
115	END SUBROUTINE dyn_hpg
116
117
118	SUBROUTINE dyn_hpg_init
119	!!----------------------------------------------------------------------
120	!! * ROUTINE dyn_hpg_init *
121	!!
122	!! ** Purpose : initializations for the hydrostatic pressure gradient
123	!! computation and consistency control
124	!!
125	!! ** Action : Read the namelist namdyn_hpg and check the consistency
126	!! with the type of vertical coordinate used (zco, zps, sco)
127	!!----------------------------------------------------------------------
128	INTEGER :: ioptio = 0 ! temporary integer
129	INTEGER :: ios ! Local integer output status for namelist read
130	!!
131	INTEGER :: ji, jj, jk, ikt ! dummy loop indices ISF
132	REAL(wp) :: znad
133	REAL(wp), DIMENSION(jpi,jpj,2) :: ztstop ! hypothesys on isf density
134	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zrhd ! hypothesys on isf density
135	REAL(wp), DIMENSION(jpi,jpj) :: zrhdtop_isf ! density at bottom of ISF
136	REAL(wp), DIMENSION(jpi,jpj) :: ziceload ! density at bottom of ISF
137	!!
138	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
139	& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf
140	!!----------------------------------------------------------------------
141	!
142	REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient
143	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
144	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp )
145	!
146	REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient
147	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
148	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp )
149	IF(lwm) WRITE ( numond, namdyn_hpg )
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	ENDIF
163	!
164	IF( ln_hpg_djc ) &
165	& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method &
166	& currently disabled (bugs under investigation). Please select &
167	& either ln_hpg_sco or ln_hpg_prj instead')
168	!
169	IF( .NOT.ln_linssh .AND. .NOT.(ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) &
170	& CALL ctl_stop('dyn_hpg_init : non-linear free surface requires either ', &
171	& ' the standard jacobian formulation hpg_sco or ' , &
172	& ' the pressure jacobian formulation hpg_prj' )
173
174	IF( ln_hpg_isf .AND. .NOT. ln_isfcav ) &
175	& CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' )
176	IF( .NOT. ln_hpg_isf .AND. ln_isfcav ) &
177	& CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' )
178	!
179	! ! Set nhpg from ln_hpg_... flags
180	IF( ln_hpg_zco ) nhpg = 0
181	IF( ln_hpg_zps ) nhpg = 1
182	IF( ln_hpg_sco ) nhpg = 2
183	IF( ln_hpg_djc ) nhpg = 3
184	IF( ln_hpg_prj ) nhpg = 4
185	IF( ln_hpg_isf ) nhpg = 5
186	!
187	! ! Consistency check
188	ioptio = 0
189	IF( ln_hpg_zco ) ioptio = ioptio + 1
190	IF( ln_hpg_zps ) ioptio = ioptio + 1
191	IF( ln_hpg_sco ) ioptio = ioptio + 1
192	IF( ln_hpg_djc ) ioptio = ioptio + 1
193	IF( ln_hpg_prj ) ioptio = ioptio + 1
194	IF( ln_hpg_isf ) ioptio = ioptio + 1
195	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
196	!
197	! initialisation of ice shelf load
198	IF ( .NOT. ln_isfcav ) riceload(:,:)=0.0
199	IF ( ln_isfcav ) THEN
200	!
201	IF(lwp) WRITE(numout,*)
202	IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf'
203	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~'
204
205	! To use density and not density anomaly
206	znad=1._wp
207
208	! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude)
209	ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp
210
211	! compute density of the water displaced by the ice shelf
212	DO jk = 1, jpk
213	CALL eos(ztstop(:,:,:),gdept_n(:,:,jk),zrhd(:,:,jk))
214	END DO
215
216	! compute rhd at the ice/oce interface (ice shelf side)
217	CALL eos(ztstop,risfdep,zrhdtop_isf)
218
219	! Surface value + ice shelf gradient
220	! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v)
221	! divided by 2 later
222	ziceload = 0._wp
223	DO jj = 1, jpj
224	DO ji = 1, jpi
225	ikt=mikt(ji,jj)
226	ziceload(ji,jj) = ziceload(ji,jj) + (znad + zrhd(ji,jj,1) ) * e3w_n(ji,jj,1) * (1._wp - tmask(ji,jj,1))
227	DO jk=2,ikt-1
228	ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhd(ji,jj,jk-1) + zrhd(ji,jj,jk)) * e3w_n(ji,jj,jk) &
229	& * (1._wp - tmask(ji,jj,jk))
230	END DO
231	IF (ikt >= 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + zrhd(ji,jj,ikt-1)) &
232	& * ( risfdep(ji,jj) - gdept_1d(ikt-1) )
233	END DO
234	END DO
235	riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5
236
237	END IF
238	!
239	END SUBROUTINE dyn_hpg_init
240
241
242	SUBROUTINE hpg_zco( kt )
243	!!---------------------------------------------------------------------
244	!! * ROUTINE hpg_zco *
245	!!
246	!! ** Method : z-coordinate case, levels are horizontal surfaces.
247	!! The now hydrostatic pressure gradient at a given level, jk,
248	!! is computed by taking the vertical integral of the in-situ
249	!! density gradient along the model level from the suface to that
250	!! level: zhpi = grav .....
251	!! zhpj = grav .....
252	!! add it to the general momentum trend (ua,va).
253	!! ua = ua - 1/e1u * zhpi
254	!! va = va - 1/e2v * zhpj
255	!!
256	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
257	!!----------------------------------------------------------------------
258	INTEGER, INTENT(in) :: kt ! ocean time-step index
259	!
260	INTEGER :: ji, jj, jk ! dummy loop indices
261	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
262	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
263	!!----------------------------------------------------------------------
264	!
265	!
266	IF( kt == nit000 ) THEN
267	IF(lwp) WRITE(numout,*)
268	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
269	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
270	ENDIF
271
272	zcoef0 = - grav * 0.5_wp ! Local constant initialization
273
274	! Surface value
275	DO jj = 2, jpjm1
276	DO ji = fs_2, fs_jpim1 ! vector opt.
277	zcoef1 = zcoef0 * e3w_n(ji,jj,1)
278	! hydrostatic pressure gradient
279	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
280	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
281	! add to the general momentum trend
282	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
283	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
284	END DO
285	END DO
286
287	!
288	! interior value (2=<jk=<jpkm1)
289	DO jk = 2, jpkm1
290	DO jj = 2, jpjm1
291	DO ji = fs_2, fs_jpim1 ! vector opt.
292	zcoef1 = zcoef0 * e3w_n(ji,jj,jk)
293	! hydrostatic pressure gradient
294	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
295	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
296	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
297
298	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
299	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
300	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
301	! add to the general momentum trend
302	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
303	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
304	END DO
305	END DO
306	END DO
307	!
308	!
309	END SUBROUTINE hpg_zco
310
311
312	SUBROUTINE hpg_zps( kt )
313	!!---------------------------------------------------------------------
314	!! * ROUTINE hpg_zps *
315	!!
316	!! ** Method : z-coordinate plus partial steps case. blahblah...
317	!!
318	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
319	!!----------------------------------------------------------------------
320	INTEGER, INTENT(in) :: kt ! ocean time-step index
321	!!
322	INTEGER :: ji, jj, jk ! dummy loop indices
323	INTEGER :: iku, ikv ! temporary integers
324	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
325	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
326	!!----------------------------------------------------------------------
327	!
328	!
329	IF( kt == nit000 ) THEN
330	IF(lwp) WRITE(numout,*)
331	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
332	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
333	ENDIF
334
335	! Partial steps: bottom before horizontal gradient of t, s, rd at the last ocean level
336	!jc CALL zps_hde ( kt, jpts, tsn, gtsu, gtsv, rhd, gru , grv )
337
338	! Local constant initialization
339	zcoef0 = - grav * 0.5_wp
340
341	! Surface value (also valid in partial step case)
342	DO jj = 2, jpjm1
343	DO ji = fs_2, fs_jpim1 ! vector opt.
344	zcoef1 = zcoef0 * e3w_n(ji,jj,1)
345	! hydrostatic pressure gradient
346	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
347	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
348	! add to the general momentum trend
349	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
350	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
351	END DO
352	END DO
353
354	! interior value (2=<jk=<jpkm1)
355	DO jk = 2, jpkm1
356	DO jj = 2, jpjm1
357	DO ji = fs_2, fs_jpim1 ! vector opt.
358	zcoef1 = zcoef0 * e3w_n(ji,jj,jk)
359	! hydrostatic pressure gradient
360	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
361	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
362	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
363
364	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
365	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
366	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
367	! add to the general momentum trend
368	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
369	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
370	END DO
371	END DO
372	END DO
373
374	! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
375	DO jj = 2, jpjm1
376	DO ji = 2, jpim1
377	iku = mbku(ji,jj)
378	ikv = mbkv(ji,jj)
379	zcoef2 = zcoef0 * MIN( e3w_n(ji,jj,iku), e3w_n(ji+1,jj ,iku) )
380	zcoef3 = zcoef0 * MIN( e3w_n(ji,jj,ikv), e3w_n(ji ,jj+1,ikv) )
381	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
382	ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value
383	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
384	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) * r1_e1u(ji,jj)
385	ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
386	ENDIF
387	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
388	va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value
389	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
390	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) * r1_e2v(ji,jj)
391	va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
392	ENDIF
393	END DO
394	END DO
395	!
396	!
397	END SUBROUTINE hpg_zps
398
399
400	SUBROUTINE hpg_sco( kt )
401	!!---------------------------------------------------------------------
402	!! * ROUTINE hpg_sco *
403	!!
404	!! ** Method : s-coordinate case. Jacobian scheme.
405	!! The now hydrostatic pressure gradient at a given level, jk,
406	!! is computed by taking the vertical integral of the in-situ
407	!! density gradient along the model level from the suface to that
408	!! level. s-coordinates (ln_sco): a corrective term is added
409	!! to the horizontal pressure gradient :
410	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
411	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
412	!! add it to the general momentum trend (ua,va).
413	!! ua = ua - 1/e1u * zhpi
414	!! va = va - 1/e2v * zhpj
415	!!
416	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
417	!!----------------------------------------------------------------------
418	INTEGER, INTENT(in) :: kt ! ocean time-step index
419	!!
420	INTEGER :: ji, jj, jk, jii, jjj ! dummy loop indices
421	REAL(wp) :: zcoef0, zuap, zvap, znad, ztmp ! temporary scalars
422	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
423	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
424	REAL(wp), DIMENSION(jpi,jpj) :: zcpx, zcpy !W/D pressure filter
425	!!----------------------------------------------------------------------
426	!
427	!
428	IF( kt == nit000 ) THEN
429	IF(lwp) WRITE(numout,*)
430	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
431	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
432	ENDIF
433	!
434	zcoef0 = - grav * 0.5_wp
435	IF ( ln_linssh ) THEN ; znad = 0._wp ! Fixed volume: density anomaly
436	ELSE ; znad = 1._wp ! Variable volume: density
437	ENDIF
438	!
439	IF( ln_wd ) THEN
440	DO jj = 2, jpjm1
441	DO ji = 2, jpim1
442	ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji+1,jj) ) > &
443	& MAX( -ht_wd(ji,jj) , -ht_wd(ji+1,jj) ) .AND. &
444	& MAX( sshn(ji,jj) + ht_wd(ji,jj), sshn(ji+1,jj) + ht_wd(ji+1,jj) ) &
445	& > rn_wdmin1 + rn_wdmin2
446	ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji+1,jj) ) > 1.E-12 ) .AND. ( &
447	& MAX( sshn(ji,jj) , sshn(ji+1,jj) ) > &
448	& MAX( -ht_wd(ji,jj) , -ht_wd(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
449
450	IF(ll_tmp1) THEN
451	zcpx(ji,jj) = 1.0_wp
452	ELSE IF(ll_tmp2) THEN
453	! no worries about sshn(ji+1,jj) - sshn(ji ,jj) = 0, it won't happen ! here
454	zcpx(ji,jj) = ABS( (sshn(ji+1,jj) + ht_wd(ji+1,jj) - sshn(ji,jj) - ht_wd(ji,jj)) &
455	& / (sshn(ji+1,jj) - sshn(ji ,jj)) )
456	ELSE
457	zcpx(ji,jj) = 0._wp
458	END IF
459
460	ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji,jj+1) ) > &
461	& MAX( -ht_wd(ji,jj) , -ht_wd(ji,jj+1) ) .AND. &
462	& MAX( sshn(ji,jj) + ht_wd(ji,jj), sshn(ji,jj+1) + ht_wd(ji,jj+1) ) &
463	& > rn_wdmin1 + rn_wdmin2
464	ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji,jj+1) ) > 1.E-12 ) .AND. ( &
465	& MAX( sshn(ji,jj) , sshn(ji,jj+1) ) > &
466	& MAX( -ht_wd(ji,jj) , -ht_wd(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
467
468	IF(ll_tmp1) THEN
469	zcpy(ji,jj) = 1.0_wp
470	ELSE IF(ll_tmp2) THEN
471	! no worries about sshn(ji,jj+1) - sshn(ji,jj ) = 0, it won't happen ! here
472	zcpy(ji,jj) = ABS( (sshn(ji,jj+1) + ht_wd(ji,jj+1) - sshn(ji,jj) - ht_wd(ji,jj)) &
473	& / (sshn(ji,jj+1) - sshn(ji,jj )) )
474	ELSE
475	zcpy(ji,jj) = 0._wp
476	END IF
477	END DO
478	END DO
479	CALL lbc_lnk( zcpx, 'U', 1._wp ) ; CALL lbc_lnk( zcpy, 'V', 1._wp )
480	END IF
481
482	! Surface value
483	DO jj = 2, jpjm1
484	DO ji = fs_2, fs_jpim1 ! vector opt.
485	! hydrostatic pressure gradient along s-surfaces
486	zhpi(ji,jj,1) = zcoef0 * ( e3w_n(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) &
487	& - e3w_n(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e1u(ji,jj)
488	zhpj(ji,jj,1) = zcoef0 * ( e3w_n(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) &
489	& - e3w_n(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e2v(ji,jj)
490	! s-coordinate pressure gradient correction
491	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
492	& * ( gde3w_n(ji+1,jj,1) - gde3w_n(ji,jj,1) ) * r1_e1u(ji,jj)
493	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
494	& * ( gde3w_n(ji,jj+1,1) - gde3w_n(ji,jj,1) ) * r1_e2v(ji,jj)
495
496
497	IF( ln_wd ) THEN
498
499	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
500	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
501	zuap = zuap * zcpx(ji,jj)
502	zvap = zvap * zcpy(ji,jj)
503	ENDIF
504
505	! add to the general momentum trend
506	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap
507	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap
508	END DO
509	END DO
510
511	! interior value (2=<jk=<jpkm1)
512	DO jk = 2, jpkm1
513	DO jj = 2, jpjm1
514	DO ji = fs_2, fs_jpim1 ! vector opt.
515	! hydrostatic pressure gradient along s-surfaces
516	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 * r1_e1u(ji,jj) &
517	& * ( e3w_n(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) &
518	& - e3w_n(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) )
519	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 * r1_e2v(ji,jj) &
520	& * ( e3w_n(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) &
521	& - e3w_n(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) )
522	! s-coordinate pressure gradient correction
523	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
524	& * ( gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk) ) * r1_e1u(ji,jj)
525	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
526	& * ( gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk) ) * r1_e2v(ji,jj)
527
528	IF( ln_wd ) THEN
529	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
530	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
531	zuap = zuap * zcpx(ji,jj)
532	zvap = zvap * zcpy(ji,jj)
533	ENDIF
534
535	! add to the general momentum trend
536	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap
537	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap
538	END DO
539	END DO
540	END DO
541	!
542	!
543	END SUBROUTINE hpg_sco
544
545
546	SUBROUTINE hpg_isf( kt )
547	!!---------------------------------------------------------------------
548	!! * ROUTINE hpg_isf *
549	!!
550	!! ** Method : s-coordinate case. Jacobian scheme.
551	!! The now hydrostatic pressure gradient at a given level, jk,
552	!! is computed by taking the vertical integral of the in-situ
553	!! density gradient along the model level from the suface to that
554	!! level. s-coordinates (ln_sco): a corrective term is added
555	!! to the horizontal pressure gradient :
556	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
557	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
558	!! add it to the general momentum trend (ua,va).
559	!! ua = ua - 1/e1u * zhpi
560	!! va = va - 1/e2v * zhpj
561	!! iceload is added and partial cell case are added to the top and bottom
562	!!
563	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
564	!!----------------------------------------------------------------------
565	INTEGER, INTENT(in) :: kt ! ocean time-step index
566	!!
567	INTEGER :: ji, jj, jk, ikt, iktp1i, iktp1j ! dummy loop indices
568	REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars
569	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
570	REAL(wp), DIMENSION(jpi,jpj,2) :: ztstop
571	REAL(wp), DIMENSION(jpi,jpj) :: zrhdtop_oce
572	!!----------------------------------------------------------------------
573	!
574	!
575	! Local constant initialization
576	zcoef0 = - grav * 0.5_wp
577
578	! To use density and not density anomaly
579	znad=1._wp
580
581	! iniitialised to 0. zhpi zhpi
582	zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp
583
584	! compute rhd at the ice/oce interface (ocean side)
585	! usefull to reduce residual current in the test case ISOMIP with no melting
586	DO ji=1,jpi
587	DO jj=1,jpj
588	ikt=mikt(ji,jj)
589	ztstop(ji,jj,1)=tsn(ji,jj,ikt,1)
590	ztstop(ji,jj,2)=tsn(ji,jj,ikt,2)
591	END DO
592	END DO
593	CALL eos( ztstop, risfdep, zrhdtop_oce )
594
595	!==================================================================================
596	!===== Compute surface value =====================================================
597	!==================================================================================
598	DO jj = 2, jpjm1
599	DO ji = fs_2, fs_jpim1 ! vector opt.
600	ikt = mikt(ji,jj)
601	iktp1i = mikt(ji+1,jj)
602	iktp1j = mikt(ji,jj+1)
603	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
604	! we assume ISF is in isostatic equilibrium
605	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * e3w_n(ji+1,jj,iktp1i) &
606	& * ( 2._wp * znad + rhd(ji+1,jj,iktp1i) + zrhdtop_oce(ji+1,jj) ) &
607	& - 0.5_wp * e3w_n(ji,jj,ikt) &
608	& * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) &
609	& + ( riceload(ji+1,jj) - riceload(ji,jj)) )
610	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * e3w_n(ji,jj+1,iktp1j) &
611	& * ( 2._wp * znad + rhd(ji,jj+1,iktp1j) + zrhdtop_oce(ji,jj+1) ) &
612	& - 0.5_wp * e3w_n(ji,jj,ikt) &
613	& * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) &
614	& + ( riceload(ji,jj+1) - riceload(ji,jj)) )
615	! s-coordinate pressure gradient correction (=0 if z coordinate)
616	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
617	& * ( gde3w_n(ji+1,jj,1) - gde3w_n(ji,jj,1) ) * r1_e1u(ji,jj)
618	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
619	& * ( gde3w_n(ji,jj+1,1) - gde3w_n(ji,jj,1) ) * r1_e2v(ji,jj)
620	! add to the general momentum trend
621	ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
622	va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
623	END DO
624	END DO
625	!==================================================================================
626	!===== Compute interior value =====================================================
627	!==================================================================================
628	! interior value (2=<jk=<jpkm1)
629	DO jk = 2, jpkm1
630	DO jj = 2, jpjm1
631	DO ji = fs_2, fs_jpim1 ! vector opt.
632	! hydrostatic pressure gradient along s-surfaces
633	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
634	& * ( e3w_n(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2znad ) wmask(ji+1,jj,jk) &
635	& - e3w_n(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2znad ) wmask(ji ,jj,jk) )
636	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
637	& * ( e3w_n(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2znad ) wmask(ji,jj+1,jk) &
638	& - e3w_n(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2znad ) wmask(ji,jj ,jk) )
639	! s-coordinate pressure gradient correction
640	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
641	& * ( gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk) ) / e1u(ji,jj)
642	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
643	& * ( gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk) ) / e2v(ji,jj)
644	! add to the general momentum trend
645	ua(ji,jj,jk) = ua(ji,jj,jk) + (zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
646	va(ji,jj,jk) = va(ji,jj,jk) + (zhpj(ji,jj,jk) + zvap) * vmask(ji,jj,jk)
647	END DO
648	END DO
649	END DO
650	!
651	!
652	END SUBROUTINE hpg_isf
653
654
655	SUBROUTINE hpg_djc( kt )
656	!!---------------------------------------------------------------------
657	!! * ROUTINE hpg_djc *
658	!!
659	!! ** Method : Density Jacobian with Cubic polynomial scheme
660	!!
661	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
662	!!----------------------------------------------------------------------
663	INTEGER, INTENT(in) :: kt ! ocean time-step index
664	!!
665	INTEGER :: ji, jj, jk ! dummy loop indices
666	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
667	REAL(wp) :: z1_10, cffu, cffx ! " "
668	REAL(wp) :: z1_12, cffv, cffy ! " "
669	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
670	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
671	REAL(wp), DIMENSION(jpi,jpj,jpk) :: dzx, dzy, dzz, dzu, dzv, dzw
672	REAL(wp), DIMENSION(jpi,jpj,jpk) :: drhox, drhoy, drhoz, drhou, drhov, drhow
673	REAL(wp), DIMENSION(jpi,jpj,jpk) :: rho_i, rho_j, rho_k
674	REAL(wp), DIMENSION(jpi,jpj) :: zcpx, zcpy !W/D pressure filter
675	!!----------------------------------------------------------------------
676	!
677	!
678	!
679	IF( ln_wd ) THEN
680	DO jj = 2, jpjm1
681	DO ji = 2, jpim1
682	ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji+1,jj) ) > &
683	& MAX( -ht_wd(ji,jj) , -ht_wd(ji+1,jj) ) .AND. &
684	& MAX( sshn(ji,jj) + ht_wd(ji,jj), sshn(ji+1,jj) + ht_wd(ji+1,jj) ) &
685	& > rn_wdmin1 + rn_wdmin2
686	ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji+1,jj) ) > 1.E-12 ) .AND. ( &
687	& MAX( sshn(ji,jj) , sshn(ji+1,jj) ) > &
688	& MAX( -ht_wd(ji,jj) , -ht_wd(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
689
690	IF(ll_tmp1) THEN
691	zcpx(ji,jj) = 1.0_wp
692	ELSE IF(ll_tmp2) THEN
693	! no worries about sshn(ji+1,jj) - sshn(ji ,jj) = 0, it won't happen ! here
694	zcpx(ji,jj) = ABS( (sshn(ji+1,jj) + ht_wd(ji+1,jj) - sshn(ji,jj) - ht_wd(ji,jj)) &
695	& / (sshn(ji+1,jj) - sshn(ji ,jj)) )
696	ELSE
697	zcpx(ji,jj) = 0._wp
698	END IF
699
700	ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji,jj+1) ) > &
701	& MAX( -ht_wd(ji,jj) , -ht_wd(ji,jj+1) ) .AND. &
702	& MAX( sshn(ji,jj) + ht_wd(ji,jj), sshn(ji,jj+1) + ht_wd(ji,jj+1) ) &
703	& > rn_wdmin1 + rn_wdmin2
704	ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji,jj+1) ) > 1.E-12 ) .AND. ( &
705	& MAX( sshn(ji,jj) , sshn(ji,jj+1) ) > &
706	& MAX( -ht_wd(ji,jj) , -ht_wd(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
707
708	IF(ll_tmp1) THEN
709	zcpy(ji,jj) = 1.0_wp
710	ELSE IF(ll_tmp2) THEN
711	! no worries about sshn(ji,jj+1) - sshn(ji,jj ) = 0, it won't happen ! here
712	zcpy(ji,jj) = ABS( (sshn(ji,jj+1) + ht_wd(ji,jj+1) - sshn(ji,jj) - ht_wd(ji,jj)) &
713	& / (sshn(ji,jj+1) - sshn(ji,jj )) )
714	ELSE
715	zcpy(ji,jj) = 0._wp
716	END IF
717	END DO
718	END DO
719	CALL lbc_lnk( zcpx, 'U', 1._wp ) ; CALL lbc_lnk( zcpy, 'V', 1._wp )
720	END IF
721
722	IF( kt == nit000 ) THEN
723	IF(lwp) WRITE(numout,*)
724	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
725	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
726	ENDIF
727
728	! Local constant initialization
729	zcoef0 = - grav * 0.5_wp
730	z1_10 = 1._wp / 10._wp
731	z1_12 = 1._wp / 12._wp
732
733	!----------------------------------------------------------------------------------------
734	! compute and store in provisional arrays elementary vertical and horizontal differences
735	!----------------------------------------------------------------------------------------
736
737	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
738
739	DO jk = 2, jpkm1
740	DO jj = 2, jpjm1
741	DO ji = fs_2, fs_jpim1 ! vector opt.
742	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
743	dzz (ji,jj,jk) = gde3w_n(ji ,jj ,jk) - gde3w_n(ji,jj,jk-1)
744	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
745	dzx (ji,jj,jk) = gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk )
746	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
747	dzy (ji,jj,jk) = gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk )
748	END DO
749	END DO
750	END DO
751
752	!-------------------------------------------------------------------------
753	! compute harmonic averages using eq. 5.18
754	!-------------------------------------------------------------------------
755	zep = 1.e-15
756
757	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
758	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
759
760	DO jk = 2, jpkm1
761	DO jj = 2, jpjm1
762	DO ji = fs_2, fs_jpim1 ! vector opt.
763	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
764
765	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
766	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
767
768	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
769	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
770
771	IF( cffw > zep) THEN
772	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
773	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
774	ELSE
775	drhow(ji,jj,jk) = 0._wp
776	ENDIF
777
778	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
779	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
780
781	IF( cffu > zep ) THEN
782	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
783	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
784	ELSE
785	drhou(ji,jj,jk ) = 0._wp
786	ENDIF
787
788	IF( cffx > zep ) THEN
789	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
790	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
791	ELSE
792	dzu(ji,jj,jk) = 0._wp
793	ENDIF
794
795	IF( cffv > zep ) THEN
796	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
797	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
798	ELSE
799	drhov(ji,jj,jk) = 0._wp
800	ENDIF
801
802	IF( cffy > zep ) THEN
803	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
804	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
805	ELSE
806	dzv(ji,jj,jk) = 0._wp
807	ENDIF
808
809	END DO
810	END DO
811	END DO
812
813	!----------------------------------------------------------------------------------
814	! apply boundary conditions at top and bottom using 5.36-5.37
815	!----------------------------------------------------------------------------------
816	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
817	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
818	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
819
820	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
821	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
822	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
823
824
825	!--------------------------------------------------------------
826	! Upper half of top-most grid box, compute and store
827	!-------------------------------------------------------------
828
829	!!bug gm : e3w-gde3w = 0.5*e3w .... and gde3w(2)-gde3w(1)=e3w(2) .... to be verified
830	! true if gde3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
831
832	DO jj = 2, jpjm1
833	DO ji = fs_2, fs_jpim1 ! vector opt.
834	rho_k(ji,jj,1) = -grav * ( e3w_n(ji,jj,1) - gde3w_n(ji,jj,1) ) &
835	& * ( rhd(ji,jj,1) &
836	& + 0.5_wp * ( rhd (ji,jj,2) - rhd (ji,jj,1) ) &
837	& * ( e3w_n (ji,jj,1) - gde3w_n(ji,jj,1) ) &
838	& / ( gde3w_n(ji,jj,2) - gde3w_n(ji,jj,1) ) )
839	END DO
840	END DO
841
842	!!bug gm : here also, simplification is possible
843	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
844
845	DO jk = 2, jpkm1
846	DO jj = 2, jpjm1
847	DO ji = fs_2, fs_jpim1 ! vector opt.
848
849	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
850	& * ( gde3w_n(ji,jj,jk) - gde3w_n(ji,jj,jk-1) ) &
851	& - grav * z1_10 * ( &
852	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
853	& * ( gde3w_n(ji,jj,jk) - gde3w_n(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
854	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
855	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
856	& )
857
858	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
859	& * ( gde3w_n(ji+1,jj,jk) - gde3w_n(ji,jj,jk) ) &
860	& - grav* z1_10 * ( &
861	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
862	& * ( gde3w_n(ji+1,jj,jk) - gde3w_n(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
863	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
864	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
865	& )
866
867	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
868	& * ( gde3w_n(ji,jj+1,jk) - gde3w_n(ji,jj,jk) ) &
869	& - grav* z1_10 * ( &
870	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
871	& * ( gde3w_n(ji,jj+1,jk) - gde3w_n(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
872	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
873	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
874	& )
875
876	END DO
877	END DO
878	END DO
879	CALL lbc_lnk(rho_k,'W',1.)
880	CALL lbc_lnk(rho_i,'U',1.)
881	CALL lbc_lnk(rho_j,'V',1.)
882
883
884	! ---------------
885	! Surface value
886	! ---------------
887	DO jj = 2, jpjm1
888	DO ji = fs_2, fs_jpim1 ! vector opt.
889	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) * r1_e1u(ji,jj)
890	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) * r1_e2v(ji,jj)
891	IF( ln_wd ) THEN
892	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
893	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
894	ENDIF
895	! add to the general momentum trend
896	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
897	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
898	END DO
899	END DO
900
901	! ----------------
902	! interior value (2=<jk=<jpkm1)
903	! ----------------
904	DO jk = 2, jpkm1
905	DO jj = 2, jpjm1
906	DO ji = fs_2, fs_jpim1 ! vector opt.
907	! hydrostatic pressure gradient along s-surfaces
908	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
909	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
910	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) * r1_e1u(ji,jj)
911	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
912	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
913	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) * r1_e2v(ji,jj)
914	IF( ln_wd ) THEN
915	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
916	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
917	ENDIF
918	! add to the general momentum trend
919	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
920	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
921	END DO
922	END DO
923	END DO
924	!
925	!
926	END SUBROUTINE hpg_djc
927
928
929	SUBROUTINE hpg_prj( kt )
930	!!---------------------------------------------------------------------
931	!! * ROUTINE hpg_prj *
932	!!
933	!! ** Method : s-coordinate case.
934	!! A Pressure-Jacobian horizontal pressure gradient method
935	!! based on the constrained cubic-spline interpolation for
936	!! all vertical coordinate systems
937	!!
938	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
939	!!----------------------------------------------------------------------
940	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
941	INTEGER, INTENT(in) :: kt ! ocean time-step index
942	!!
943	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
944	REAL(wp) :: zcoef0, znad ! local scalars
945	!
946	!! The local variables for the correction term
947	INTEGER :: jk1, jis, jid, jjs, jjd
948	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
949	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
950	REAL(wp) :: zrhdt1
951	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
952	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdept, zrhh
953	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
954	REAL(wp), DIMENSION(jpi,jpj) :: zsshu_n, zsshv_n
955	REAL(wp), DIMENSION(jpi,jpj) :: zcpx, zcpy !W/D pressure filter
956	!!----------------------------------------------------------------------
957	!
958	!
959	IF( kt == nit000 ) THEN
960	IF(lwp) WRITE(numout,*)
961	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
962	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
963	ENDIF
964
965	! Local constant initialization
966	zcoef0 = - grav
967	znad = 1._wp
968	IF( ln_linssh ) znad = 0._wp
969
970	IF( ln_wd ) THEN
971	DO jj = 2, jpjm1
972	DO ji = 2, jpim1
973	ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji+1,jj) ) > &
974	& MAX( -ht_wd(ji,jj) , -ht_wd(ji+1,jj) ) .AND. &
975	& MAX( sshn(ji,jj) + ht_wd(ji,jj), sshn(ji+1,jj) + ht_wd(ji+1,jj) ) &
976	& > rn_wdmin1 + rn_wdmin2
977	ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji+1,jj) ) > 1.E-12 ) .AND. ( &
978	& MAX( sshn(ji,jj) , sshn(ji+1,jj) ) > &
979	& MAX( -ht_wd(ji,jj) , -ht_wd(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
980
981	IF(ll_tmp1) THEN
982	zcpx(ji,jj) = 1.0_wp
983	ELSE IF(ll_tmp2) THEN
984	! no worries about sshn(ji+1,jj) - sshn(ji ,jj) = 0, it won't happen ! here
985	zcpx(ji,jj) = ABS( (sshn(ji+1,jj) + ht_wd(ji+1,jj) - sshn(ji,jj) - ht_wd(ji,jj)) &
986	& / (sshn(ji+1,jj) - sshn(ji ,jj)) )
987	ELSE
988	zcpx(ji,jj) = 0._wp
989	END IF
990
991	ll_tmp1 = MIN( sshn(ji,jj) , sshn(ji,jj+1) ) > &
992	& MAX( -ht_wd(ji,jj) , -ht_wd(ji,jj+1) ) .AND. &
993	& MAX( sshn(ji,jj) + ht_wd(ji,jj), sshn(ji,jj+1) + ht_wd(ji,jj+1) ) &
994	& > rn_wdmin1 + rn_wdmin2
995	ll_tmp2 = ( ABS( sshn(ji,jj) - sshn(ji,jj+1) ) > 1.E-12 ) .AND. ( &
996	& MAX( sshn(ji,jj) , sshn(ji,jj+1) ) > &
997	& MAX( -ht_wd(ji,jj) , -ht_wd(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
998
999	IF(ll_tmp1) THEN
1000	zcpy(ji,jj) = 1.0_wp
1001	ELSE IF(ll_tmp2) THEN
1002	! no worries about sshn(ji,jj+1) - sshn(ji,jj ) = 0, it won't happen ! here
1003	zcpy(ji,jj) = ABS( (sshn(ji,jj+1) + ht_wd(ji,jj+1) - sshn(ji,jj) - ht_wd(ji,jj)) &
1004	& / (sshn(ji,jj+1) - sshn(ji,jj )) )
1005	ELSE
1006	zcpy(ji,jj) = 0._wp
1007	END IF
1008	END DO
1009	END DO
1010	CALL lbc_lnk( zcpx, 'U', 1._wp ) ; CALL lbc_lnk( zcpy, 'V', 1._wp )
1011	END IF
1012
1013	! Clean 3-D work arrays
1014	zhpi(:,:,:) = 0._wp
1015	zrhh(:,:,:) = rhd(:,:,:)
1016
1017	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
1018	DO jj = 1, jpj
1019	DO ji = 1, jpi
1020	jk = mbkt(ji,jj)+1
1021	IF( jk <= 0 ) THEN ; zrhh(ji,jj, : ) = 0._wp
1022	ELSEIF( jk == 1 ) THEN ; zrhh(ji,jj,jk+1:jpk) = rhd(ji,jj,jk)
1023	ELSEIF( jk < jpkm1 ) THEN
1024	DO jkk = jk+1, jpk
1025	zrhh(ji,jj,jkk) = interp1(gde3w_n(ji,jj,jkk ), gde3w_n(ji,jj,jkk-1), &
1026	& gde3w_n(ji,jj,jkk-2), rhd (ji,jj,jkk-1), rhd(ji,jj,jkk-2))
1027	END DO
1028	ENDIF
1029	END DO
1030	END DO
1031
1032	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
1033	DO jj = 1, jpj
1034	DO ji = 1, jpi
1035	zdept(ji,jj,1) = 0.5_wp * e3w_n(ji,jj,1) - sshn(ji,jj) * znad
1036	END DO
1037	END DO
1038
1039	DO jk = 2, jpk
1040	DO jj = 1, jpj
1041	DO ji = 1, jpi
1042	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + e3w_n(ji,jj,jk)
1043	END DO
1044	END DO
1045	END DO
1046
1047	fsp(:,:,:) = zrhh (:,:,:)
1048	xsp(:,:,:) = zdept(:,:,:)
1049
1050	! Construct the vertical density profile with the
1051	! constrained cubic spline interpolation
1052	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
1053	CALL cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
1054
1055	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
1056	DO jj = 2, jpj
1057	DO ji = 2, jpi
1058	zrhdt1 = zrhh(ji,jj,1) - interp3( zdept(ji,jj,1), asp(ji,jj,1), bsp(ji,jj,1), &
1059	& csp(ji,jj,1), dsp(ji,jj,1) ) * 0.25_wp * e3w_n(ji,jj,1)
1060
1061	! assuming linear profile across the top half surface layer
1062	zhpi(ji,jj,1) = 0.5_wp * e3w_n(ji,jj,1) * zrhdt1
1063	END DO
1064	END DO
1065
1066	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
1067	DO jk = 2, jpkm1
1068	DO jj = 2, jpj
1069	DO ji = 2, jpi
1070	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
1071	& integ_spline( zdept(ji,jj,jk-1), zdept(ji,jj,jk), &
1072	& asp (ji,jj,jk-1), bsp (ji,jj,jk-1), &
1073	& csp (ji,jj,jk-1), dsp (ji,jj,jk-1) )
1074	END DO
1075	END DO
1076	END DO
1077
1078	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
1079
1080	! Prepare zsshu_n and zsshv_n
1081	DO jj = 2, jpjm1
1082	DO ji = 2, jpim1
1083	!!gm BUG ? if it is ssh at u- & v-point then it should be:
1084	! zsshu_n(ji,jj) = (e1e2t(ji,jj) * sshn(ji,jj) + e1e2t(ji+1,jj) * sshn(ji+1,jj)) * &
1085	! & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
1086	! zsshv_n(ji,jj) = (e1e2t(ji,jj) * sshn(ji,jj) + e1e2t(ji,jj+1) * sshn(ji,jj+1)) * &
1087	! & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
1088	!!gm not this:
1089	zsshu_n(ji,jj) = (e1e2u(ji,jj) * sshn(ji,jj) + e1e2u(ji+1, jj) * sshn(ji+1,jj)) * &
1090	& r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
1091	zsshv_n(ji,jj) = (e1e2v(ji,jj) * sshn(ji,jj) + e1e2v(ji+1, jj) * sshn(ji,jj+1)) * &
1092	& r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
1093	END DO
1094	END DO
1095
1096	CALL lbc_lnk (zsshu_n, 'U', 1.)
1097	CALL lbc_lnk (zsshv_n, 'V', 1.)
1098
1099	DO jj = 2, jpjm1
1100	DO ji = 2, jpim1
1101	zu(ji,jj,1) = - ( e3u_n(ji,jj,1) - zsshu_n(ji,jj) * znad)
1102	zv(ji,jj,1) = - ( e3v_n(ji,jj,1) - zsshv_n(ji,jj) * znad)
1103	END DO
1104	END DO
1105
1106	DO jk = 2, jpkm1
1107	DO jj = 2, jpjm1
1108	DO ji = 2, jpim1
1109	zu(ji,jj,jk) = zu(ji,jj,jk-1) - e3u_n(ji,jj,jk)
1110	zv(ji,jj,jk) = zv(ji,jj,jk-1) - e3v_n(ji,jj,jk)
1111	END DO
1112	END DO
1113	END DO
1114
1115	DO jk = 1, jpkm1
1116	DO jj = 2, jpjm1
1117	DO ji = 2, jpim1
1118	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * e3u_n(ji,jj,jk)
1119	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * e3v_n(ji,jj,jk)
1120	END DO
1121	END DO
1122	END DO
1123
1124	DO jk = 1, jpkm1
1125	DO jj = 2, jpjm1
1126	DO ji = 2, jpim1
1127	zu(ji,jj,jk) = MIN( zu(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
1128	zu(ji,jj,jk) = MAX( zu(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
1129	zv(ji,jj,jk) = MIN( zv(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
1130	zv(ji,jj,jk) = MAX( zv(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
1131	END DO
1132	END DO
1133	END DO
1134
1135
1136	DO jk = 1, jpkm1
1137	DO jj = 2, jpjm1
1138	DO ji = 2, jpim1
1139	zpwes = 0._wp; zpwed = 0._wp
1140	zpnss = 0._wp; zpnsd = 0._wp
1141	zuijk = zu(ji,jj,jk)
1142	zvijk = zv(ji,jj,jk)
1143
1144	!!!!! for u equation
1145	IF( jk <= mbku(ji,jj) ) THEN
1146	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
1147	jis = ji + 1; jid = ji
1148	ELSE
1149	jis = ji; jid = ji +1
1150	ENDIF
1151
1152	! integrate the pressure on the shallow side
1153	jk1 = jk
1154	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
1155	IF( jk1 == mbku(ji,jj) ) THEN
1156	zuijk = -zdept(jis,jj,jk1)
1157	EXIT
1158	ENDIF
1159	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
1160	zpwes = zpwes + &
1161	integ_spline(zdept(jis,jj,jk1), zdeps, &
1162	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
1163	csp(jis,jj,jk1), dsp(jis,jj,jk1))
1164	jk1 = jk1 + 1
1165	END DO
1166
1167	! integrate the pressure on the deep side
1168	jk1 = jk
1169	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
1170	IF( jk1 == 1 ) THEN
1171	zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad)
1172	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
1173	bsp(jid,jj,1), csp(jid,jj,1), &
1174	dsp(jid,jj,1)) * zdeps
1175	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
1176	EXIT
1177	ENDIF
1178	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
1179	zpwed = zpwed + &
1180	integ_spline(zdeps, zdept(jid,jj,jk1), &
1181	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
1182	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
1183	jk1 = jk1 - 1
1184	END DO
1185
1186	! update the momentum trends in u direction
1187
1188	zdpdx1 = zcoef0 * r1_e1u(ji,jj) * ( zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk) )
1189	IF( .NOT.ln_linssh ) THEN
1190	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * &
1191	& ( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) )
1192	ELSE
1193	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
1194	ENDIF
1195	IF( ln_wd ) THEN
1196	zdpdx1 = zdpdx1 * zcpx(ji,jj)
1197	zdpdx2 = zdpdx2 * zcpx(ji,jj)
1198	ENDIF
1199	ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * umask(ji,jj,jk)
1200	ENDIF
1201
1202	!!!!! for v equation
1203	IF( jk <= mbkv(ji,jj) ) THEN
1204	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
1205	jjs = jj + 1; jjd = jj
1206	ELSE
1207	jjs = jj ; jjd = jj + 1
1208	ENDIF
1209
1210	! integrate the pressure on the shallow side
1211	jk1 = jk
1212	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
1213	IF( jk1 == mbkv(ji,jj) ) THEN
1214	zvijk = -zdept(ji,jjs,jk1)
1215	EXIT
1216	ENDIF
1217	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
1218	zpnss = zpnss + &
1219	integ_spline(zdept(ji,jjs,jk1), zdeps, &
1220	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
1221	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
1222	jk1 = jk1 + 1
1223	END DO
1224
1225	! integrate the pressure on the deep side
1226	jk1 = jk
1227	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
1228	IF( jk1 == 1 ) THEN
1229	zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad)
1230	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
1231	bsp(ji,jjd,1), csp(ji,jjd,1), &
1232	dsp(ji,jjd,1) ) * zdeps
1233	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
1234	EXIT
1235	ENDIF
1236	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
1237	zpnsd = zpnsd + &
1238	integ_spline(zdeps, zdept(ji,jjd,jk1), &
1239	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
1240	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
1241	jk1 = jk1 - 1
1242	END DO
1243
1244
1245	! update the momentum trends in v direction
1246
1247	zdpdy1 = zcoef0 * r1_e2v(ji,jj) * ( zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk) )
1248	IF( .NOT.ln_linssh ) THEN
1249	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * &
1250	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) )
1251	ELSE
1252	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
1253	ENDIF
1254	IF( ln_wd ) THEN
1255	zdpdy1 = zdpdy1 * zcpy(ji,jj)
1256	zdpdy2 = zdpdy2 * zcpy(ji,jj)
1257	ENDIF
1258
1259	va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2) * vmask(ji,jj,jk)
1260	ENDIF
1261	!
1262	END DO
1263	END DO
1264	END DO
1265	!
1266	!
1267	END SUBROUTINE hpg_prj
1268
1269
1270	SUBROUTINE cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
1271	!!----------------------------------------------------------------------
1272	!! * ROUTINE cspline *
1273	!!
1274	!! ** Purpose : constrained cubic spline interpolation
1275	!!
1276	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
1277	!!
1278	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
1279	!!----------------------------------------------------------------------
1280	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: fsp, xsp ! value and coordinate
1281	REAL(wp), DIMENSION(:,:,:), INTENT( out) :: asp, bsp, csp, dsp ! coefficients of the interpoated function
1282	INTEGER , INTENT(in ) :: polynomial_type ! 1: cubic spline ; 2: Linear
1283	!
1284	INTEGER :: ji, jj, jk ! dummy loop indices
1285	INTEGER :: jpi, jpj, jpkm1
1286	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
1287	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
1288	REAL(wp) :: zdf(size(fsp,3))
1289	!!----------------------------------------------------------------------
1290	!
1291	!!gm WHAT !!!!! THIS IS VERY DANGEROUS !!!!!
1292	jpi = size(fsp,1)
1293	jpj = size(fsp,2)
1294	jpkm1 = MAX( 1, size(fsp,3) - 1 )
1295	!
1296	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
1297	DO ji = 1, jpi
1298	DO jj = 1, jpj
1299	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
1300	! DO jk = 2, jpkm1-1
1301	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
1302	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1303	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
1304	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
1305	!
1306	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
1307	!
1308	! IF(zdf1 * zdf2 <= 0._wp) THEN
1309	! zdf(jk) = 0._wp
1310	! ELSE
1311	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
1312	! ENDIF
1313	! END DO
1314
1315	!!Simply geometric average
1316	DO jk = 2, jpkm1-1
1317	zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1))
1318	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk))
1319
1320	IF(zdf1 * zdf2 <= 0._wp) THEN
1321	zdf(jk) = 0._wp
1322	ELSE
1323	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
1324	ENDIF
1325	END DO
1326
1327	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
1328	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
1329	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
1330	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - 0.5_wp * zdf(jpkm1 - 1)
1331
1332	DO jk = 1, jpkm1 - 1
1333	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1334	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
1335	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
1336	zddf1 = -2._wp * ztmp1 + ztmp2
1337	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
1338	zddf2 = 2._wp * ztmp1 - ztmp2
1339
1340	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
1341	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
1342	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
1343	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
1344	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
1345	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
1346	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
1347	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
1348	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
1349	END DO
1350	END DO
1351	END DO
1352
1353	ELSEIF ( polynomial_type == 2 ) THEN ! Linear
1354	DO ji = 1, jpi
1355	DO jj = 1, jpj
1356	DO jk = 1, jpkm1-1
1357	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
1358	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
1359
1360	dsp(ji,jj,jk) = 0._wp
1361	csp(ji,jj,jk) = 0._wp
1362	bsp(ji,jj,jk) = ztmp1 / zdxtmp
1363	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
1364	END DO
1365	END DO
1366	END DO
1367
1368	ELSE
1369	CALL ctl_stop( 'invalid polynomial type in cspline' )
1370	ENDIF
1371
1372	END SUBROUTINE cspline
1373
1374
1375	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
1376	!!----------------------------------------------------------------------
1377	!! * ROUTINE interp1 *
1378	!!
1379	!! ** Purpose : 1-d linear interpolation
1380	!!
1381	!! ** Method : interpolation is straight forward
1382	!! extrapolation is also permitted (no value limit)
1383	!!----------------------------------------------------------------------
1384	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
1385	REAL(wp) :: f ! result of the interpolation (extrapolation)
1386	REAL(wp) :: zdeltx
1387	!!----------------------------------------------------------------------
1388	!
1389	zdeltx = xr - xl
1390	IF( abs(zdeltx) <= 10._wp * EPSILON(x) ) THEN
1391	f = 0.5_wp * (fl + fr)
1392	ELSE
1393	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
1394	ENDIF
1395	!
1396	END FUNCTION interp1
1397
1398
1399	FUNCTION interp2( x, a, b, c, d ) RESULT(f)
1400	!!----------------------------------------------------------------------
1401	!! * ROUTINE interp1 *
1402	!!
1403	!! ** Purpose : 1-d constrained cubic spline interpolation
1404	!!
1405	!! ** Method : cubic spline interpolation
1406	!!
1407	!!----------------------------------------------------------------------
1408	REAL(wp), INTENT(in) :: x, a, b, c, d
1409	REAL(wp) :: f ! value from the interpolation
1410	!!----------------------------------------------------------------------
1411	!
1412	f = a + x* ( b + x * ( c + d * x ) )
1413	!
1414	END FUNCTION interp2
1415
1416
1417	FUNCTION interp3( x, a, b, c, d ) RESULT(f)
1418	!!----------------------------------------------------------------------
1419	!! * ROUTINE interp1 *
1420	!!
1421	!! ** Purpose : Calculate the first order of deriavtive of
1422	!! a cubic spline function y=a+bx+cx^2+d*x^3
1423	!!
1424	!! ** Method : f=dy/dx=b+2cx+3dx^2
1425	!!
1426	!!----------------------------------------------------------------------
1427	REAL(wp), INTENT(in) :: x, a, b, c, d
1428	REAL(wp) :: f ! value from the interpolation
1429	!!----------------------------------------------------------------------
1430	!
1431	f = b + x * ( 2._wp * c + 3._wp * d * x)
1432	!
1433	END FUNCTION interp3
1434
1435
1436	FUNCTION integ_spline( xl, xr, a, b, c, d ) RESULT(f)
1437	!!----------------------------------------------------------------------
1438	!! * ROUTINE interp1 *
1439	!!
1440	!! ** Purpose : 1-d constrained cubic spline integration
1441	!!
1442	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
1443	!!
1444	!!----------------------------------------------------------------------
1445	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
1446	REAL(wp) :: za1, za2, za3
1447	REAL(wp) :: f ! integration result
1448	!!----------------------------------------------------------------------
1449	!
1450	za1 = 0.5_wp * b
1451	za2 = c / 3.0_wp
1452	za3 = 0.25_wp * d
1453	!
1454	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
1455	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
1456	!
1457	END FUNCTION integ_spline
1458
1459	!!======================================================================
1460	END MODULE dynhpg
1461

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source: branches/2017/dev_r7881_no_wrk_alloc/NEMOGCM/NEMO/OPA_SRC/DYN/dynhpg.F90 @ 7910

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