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dynhpg.F90 in branches/2015/dev_r5094_UKMO_ISFCLEAN/NEMOGCM/NEMO/OPA_SRC/DYN – NEMO

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source: branches/2015/dev_r5094_UKMO_ISFCLEAN/NEMOGCM/NEMO/OPA_SRC/DYN/dynhpg.F90 @ 5098

Last change on this file since 5098 was 5098, checked in by mathiot, 9 years ago
add wmask, wumask, wvmask and restore loop order and add flag to ignore specific isf code if no isf
Property svn:keywords set to `Id`
File size: 69.3 KB

Rev	Line
[3]	1	MODULE dynhpg
	2	!!======================================================================
	3	!! * MODULE dynhpg *
	4	!! Ocean dynamics: hydrostatic pressure gradient trend
	5	!!======================================================================
[2528]	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
[3764]	13	!! ! Original code for hpg_ctl, hpg_hel hpg_wdj, hpg_djc, hpg_rot
[2528]	14	!! - ! 2005-11 (G. Madec) style & small optimisation
	15	!! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase
[3294]	16	!! 3.4 ! 2011-11 (H. Liu) hpg_prj: Original code for s-coordinates
	17	!! ! (A. Coward) suppression of hel, wdj and rot options
[5098]	18	!! 3.6 ! 2014-11 (P. Mathiot) hpg_isf: original code for ice shelf cavity
[503]	19	!!----------------------------------------------------------------------
[3]	20
	21	!!----------------------------------------------------------------------
[455]	22	!! dyn_hpg : update the momentum trend with the now horizontal
[3]	23	!! gradient of the hydrostatic pressure
[2528]	24	!! dyn_hpg_init : initialisation and control of options
[455]	25	!! hpg_zco : z-coordinate scheme
	26	!! hpg_zps : z-coordinate plus partial steps (interpolation)
	27	!! hpg_sco : s-coordinate (standard jacobian formulation)
[5098]	28	!! hpg_isf : s-coordinate (sco formulation) adapted to ice shelf
[455]	29	!! hpg_djc : s-coordinate (Density Jacobian with Cubic polynomial)
[3294]	30	!! hpg_prj : s-coordinate (Pressure Jacobian with Cubic polynomial)
[3]	31	!!----------------------------------------------------------------------
	32	USE oce ! ocean dynamics and tracers
[4990]	33	USE sbc_oce ! surface variable (only for the flag with ice shelf)
[3]	34	USE dom_oce ! ocean space and time domain
	35	USE phycst ! physical constants
[4990]	36	USE trd_oce ! trends: ocean variables
	37	USE trddyn ! trend manager: dynamics
	38	!
[2715]	39	USE in_out_manager ! I/O manager
[258]	40	USE prtctl ! Print control
[4990]	41	USE lbclnk ! lateral boundary condition
[2715]	42	USE lib_mpp ! MPP library
[4990]	43	USE eosbn2 ! compute density
[3294]	44	USE wrk_nemo ! Memory Allocation
	45	USE timing ! Timing
[3]	46
	47	IMPLICIT NONE
	48	PRIVATE
	49
[2528]	50	PUBLIC dyn_hpg ! routine called by step module
	51	PUBLIC dyn_hpg_init ! routine called by opa module
[3]	52
[4147]	53	! !!* Namelist namdyn_hpg : hydrostatic pressure gradient
	54	LOGICAL , PUBLIC :: ln_hpg_zco !: z-coordinate - full steps
	55	LOGICAL , PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation)
	56	LOGICAL , PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation)
	57	LOGICAL , PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial)
	58	LOGICAL , PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme)
[5098]	59	LOGICAL , PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf
[4147]	60	LOGICAL , PUBLIC :: ln_dynhpg_imp !: semi-implicite hpg flag
[455]	61
[3764]	62	INTEGER , PUBLIC :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM)
[455]	63
[3]	64	!! * Substitutions
	65	# include "domzgr_substitute.h90"
	66	# include "vectopt_loop_substitute.h90"
	67	!!----------------------------------------------------------------------
[2528]	68	!! NEMO/OPA 3.3 , NEMO Consortium (2010)
	69	!! $Id$
	70	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
[3]	71	!!----------------------------------------------------------------------
	72	CONTAINS
	73
	74	SUBROUTINE dyn_hpg( kt )
	75	!!---------------------------------------------------------------------
	76	!! * ROUTINE dyn_hpg *
	77	!!
[3764]	78	!! ** Method : Call the hydrostatic pressure gradient routine
[503]	79	!! using the scheme defined in the namelist
[3764]	80	!!
[455]	81	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[4990]	82	!! - send trends to trd_dyn for futher diagnostics (l_trddyn=T)
[503]	83	!!----------------------------------------------------------------------
	84	INTEGER, INTENT(in) :: kt ! ocean time-step index
[3294]	85	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdu, ztrdv
[455]	86	!!----------------------------------------------------------------------
[2528]	87	!
[3294]	88	IF( nn_timing == 1 ) CALL timing_start('dyn_hpg')
[2715]	89	!
[503]	90	IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn)
[3294]	91	CALL wrk_alloc( jpi,jpj,jpk, ztrdu, ztrdv )
[3764]	92	ztrdu(:,:,:) = ua(:,:,:)
	93	ztrdv(:,:,:) = va(:,:,:)
	94	ENDIF
[2528]	95	!
[3294]	96	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
[503]	97	CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate
	98	CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation)
	99	CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation)
[3294]	100	CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial)
	101	CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme)
[5098]	102	CASE ( 5 ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf
[455]	103	END SELECT
[2528]	104	!
[503]	105	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
[455]	106	ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:)
	107	ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:)
[4990]	108	CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt )
[3294]	109	CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv )
[3764]	110	ENDIF
[503]	111	!
	112	IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, &
	113	& tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
	114	!
[3294]	115	IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg')
[2715]	116	!
[455]	117	END SUBROUTINE dyn_hpg
	118
	119
[2528]	120	SUBROUTINE dyn_hpg_init
[455]	121	!!----------------------------------------------------------------------
[2528]	122	!! * ROUTINE dyn_hpg_init *
[455]	123	!!
	124	!! ** Purpose : initializations for the hydrostatic pressure gradient
	125	!! computation and consistency control
	126	!!
[1601]	127	!! ** Action : Read the namelist namdyn_hpg and check the consistency
[455]	128	!! with the type of vertical coordinate used (zco, zps, sco)
	129	!!----------------------------------------------------------------------
	130	INTEGER :: ioptio = 0 ! temporary integer
[4147]	131	INTEGER :: ios ! Local integer output status for namelist read
[1601]	132	!!
[3294]	133	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
[5098]	134	& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf, ln_dynhpg_imp
[455]	135	!!----------------------------------------------------------------------
[2528]	136	!
[4147]	137	REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient
	138	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
	139	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp )
	140
	141	REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient
	142	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
	143	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp )
[4624]	144	IF(lwm) WRITE ( numond, namdyn_hpg )
[2528]	145	!
	146	IF(lwp) THEN ! Control print
[455]	147	WRITE(numout,*)
[2528]	148	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
	149	WRITE(numout,*) '~~~~~~~~~~~~'
[1601]	150	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
	151	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
	152	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
	153	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
[5098]	154	WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf
[1601]	155	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
[3294]	156	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
[1601]	157	WRITE(numout,*) ' time stepping: centered (F) or semi-implicit (T) ln_dynhpg_imp = ', ln_dynhpg_imp
[455]	158	ENDIF
[2528]	159	!
[3294]	160	IF( ln_hpg_djc ) &
	161	& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method &
	162	& currently disabled (bugs under investigation). Please select &
	163	& either ln_hpg_sco or ln_hpg_prj instead')
[2528]	164	!
[5098]	165	IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) &
[3294]	166	& CALL ctl_stop('dyn_hpg_init : variable volume key_vvl requires:&
	167	& the standard jacobian formulation hpg_sco or &
	168	& the pressure jacobian formulation hpg_prj')
	169	!
[503]	170	! ! Set nhpg from ln_hpg_... flags
[455]	171	IF( ln_hpg_zco ) nhpg = 0
	172	IF( ln_hpg_zps ) nhpg = 1
	173	IF( ln_hpg_sco ) nhpg = 2
[3294]	174	IF( ln_hpg_djc ) nhpg = 3
	175	IF( ln_hpg_prj ) nhpg = 4
[5098]	176	IF( ln_hpg_isf ) nhpg = 5
[2528]	177	!
[3294]	178	! ! Consistency check
[3764]	179	ioptio = 0
[455]	180	IF( ln_hpg_zco ) ioptio = ioptio + 1
	181	IF( ln_hpg_zps ) ioptio = ioptio + 1
	182	IF( ln_hpg_sco ) ioptio = ioptio + 1
	183	IF( ln_hpg_djc ) ioptio = ioptio + 1
[3294]	184	IF( ln_hpg_prj ) ioptio = ioptio + 1
[5098]	185	IF( ln_hpg_isf ) ioptio = ioptio + 1
[2715]	186	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
[5098]	187	IF( ( .NOT. ln_hpg_isf ) .AND. ln_isfcav ) &
	188	& CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' )
[503]	189	!
[2528]	190	END SUBROUTINE dyn_hpg_init
[455]	191
	192
	193	SUBROUTINE hpg_zco( kt )
	194	!!---------------------------------------------------------------------
	195	!! * ROUTINE hpg_zco *
	196	!!
	197	!! ** Method : z-coordinate case, levels are horizontal surfaces.
	198	!! The now hydrostatic pressure gradient at a given level, jk,
	199	!! is computed by taking the vertical integral of the in-situ
	200	!! density gradient along the model level from the suface to that
	201	!! level: zhpi = grav .....
	202	!! zhpj = grav .....
[3]	203	!! add it to the general momentum trend (ua,va).
[455]	204	!! ua = ua - 1/e1u * zhpi
	205	!! va = va - 1/e2v * zhpj
[3764]	206	!!
[3]	207	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[503]	208	!!----------------------------------------------------------------------
	209	INTEGER, INTENT(in) :: kt ! ocean time-step index
	210	!!
	211	INTEGER :: ji, jj, jk ! dummy loop indices
	212	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
[3764]	213	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3]	214	!!----------------------------------------------------------------------
[3764]	215	!
[3294]	216	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
	217	!
[3]	218	IF( kt == nit000 ) THEN
	219	IF(lwp) WRITE(numout,*)
[455]	220	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
	221	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
[3]	222	ENDIF
	223
[3764]	224	zcoef0 = - grav * 0.5_wp ! Local constant initialization
	225
[455]	226	! Surface value
[3]	227	DO jj = 2, jpjm1
	228	DO ji = fs_2, fs_jpim1 ! vector opt.
[455]	229	zcoef1 = zcoef0 * fse3w(ji,jj,1)
	230	! hydrostatic pressure gradient
	231	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
	232	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
[3]	233	! add to the general momentum trend
[455]	234	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
	235	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
	236	END DO
	237	END DO
[3294]	238
[503]	239	!
[455]	240	! interior value (2=<jk=<jpkm1)
[3]	241	DO jk = 2, jpkm1
[455]	242	DO jj = 2, jpjm1
[3]	243	DO ji = fs_2, fs_jpim1 ! vector opt.
[455]	244	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
	245	! hydrostatic pressure gradient
	246	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
	247	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
	248	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
	249
	250	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
	251	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
	252	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
[3]	253	! add to the general momentum trend
[455]	254	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	255	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
[3]	256	END DO
	257	END DO
	258	END DO
[503]	259	!
[3294]	260	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
	261	!
[455]	262	END SUBROUTINE hpg_zco
[216]	263
[3]	264
[455]	265	SUBROUTINE hpg_zps( kt )
[3]	266	!!---------------------------------------------------------------------
[455]	267	!! * ROUTINE hpg_zps *
[3764]	268	!!
[455]	269	!! ** Method : z-coordinate plus partial steps case. blahblah...
[3764]	270	!!
[3]	271	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[3764]	272	!!----------------------------------------------------------------------
[503]	273	INTEGER, INTENT(in) :: kt ! ocean time-step index
	274	!!
	275	INTEGER :: ji, jj, jk ! dummy loop indices
	276	INTEGER :: iku, ikv ! temporary integers
	277	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
[3764]	278	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3]	279	!!----------------------------------------------------------------------
[3294]	280	!
	281	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
	282	!
[3]	283	IF( kt == nit000 ) THEN
	284	IF(lwp) WRITE(numout,*)
[455]	285	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
[503]	286	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
[3]	287	ENDIF
	288
[3294]	289
[503]	290	! Local constant initialization
[2528]	291	zcoef0 = - grav * 0.5_wp
[3]	292
[2528]	293	! Surface value (also valid in partial step case)
[3]	294	DO jj = 2, jpjm1
	295	DO ji = fs_2, fs_jpim1 ! vector opt.
[170]	296	zcoef1 = zcoef0 * fse3w(ji,jj,1)
[3]	297	! hydrostatic pressure gradient
[455]	298	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
	299	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
[3]	300	! add to the general momentum trend
	301	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
	302	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
	303	END DO
	304	END DO
	305
[3294]	306
[503]	307	! interior value (2=<jk=<jpkm1)
[3]	308	DO jk = 2, jpkm1
	309	DO jj = 2, jpjm1
	310	DO ji = fs_2, fs_jpim1 ! vector opt.
[170]	311	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
[3]	312	! hydrostatic pressure gradient
	313	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
[455]	314	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
	315	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
[3]	316
	317	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
[455]	318	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
	319	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
[3]	320	! add to the general momentum trend
	321	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	322	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
[455]	323	END DO
[3]	324	END DO
	325	END DO
	326
[3294]	327
[2528]	328	! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
[3]	329	DO jj = 2, jpjm1
	330	DO ji = 2, jpim1
[2528]	331	iku = mbku(ji,jj)
	332	ikv = mbkv(ji,jj)
[3]	333	zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) )
	334	zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) )
[2528]	335	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
	336	ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value
	337	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
	338	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj)
	339	ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
[3]	340	ENDIF
[2528]	341	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
	342	va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value
	343	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
	344	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj)
	345	va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
[3]	346	ENDIF
	347	END DO
	348	END DO
[503]	349	!
[3294]	350	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
	351	!
[455]	352	END SUBROUTINE hpg_zps
[216]	353
[455]	354	SUBROUTINE hpg_sco( kt )
[3]	355	!!---------------------------------------------------------------------
[455]	356	!! * ROUTINE hpg_sco *
[3]	357	!!
[455]	358	!! ** Method : s-coordinate case. Jacobian scheme.
	359	!! The now hydrostatic pressure gradient at a given level, jk,
	360	!! is computed by taking the vertical integral of the in-situ
[3]	361	!! density gradient along the model level from the suface to that
[455]	362	!! level. s-coordinates (ln_sco): a corrective term is added
	363	!! to the horizontal pressure gradient :
	364	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
	365	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
[3]	366	!! add it to the general momentum trend (ua,va).
[455]	367	!! ua = ua - 1/e1u * zhpi
	368	!! va = va - 1/e2v * zhpj
[3]	369	!!
	370	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[503]	371	!!----------------------------------------------------------------------
	372	INTEGER, INTENT(in) :: kt ! ocean time-step index
	373	!!
[5098]	374	INTEGER :: ji, jj, jk ! dummy loop indices
	375	REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars
	376	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
	377	!!----------------------------------------------------------------------
	378	!
	379	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
	380	!
	381	IF( kt == nit000 ) THEN
	382	IF(lwp) WRITE(numout,*)
	383	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
	384	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
	385	ENDIF
	386
	387	! Local constant initialization
	388	zcoef0 = - grav * 0.5_wp
	389	! To use density and not density anomaly
	390	IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
	391	ELSE ; znad = 0._wp ! Fixed volume
	392	ENDIF
	393
	394	! Surface value
	395	DO jj = 2, jpjm1
	396	DO ji = fs_2, fs_jpim1 ! vector opt.
	397	! hydrostatic pressure gradient along s-surfaces
	398	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) &
	399	& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
	400	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) &
	401	& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
	402	! s-coordinate pressure gradient correction
	403	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
	404	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
	405	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
	406	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
	407	! add to the general momentum trend
	408	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap
	409	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap
	410	END DO
	411	END DO
	412
	413	! interior value (2=<jk=<jpkm1)
	414	DO jk = 2, jpkm1
	415	DO jj = 2, jpjm1
	416	DO ji = fs_2, fs_jpim1 ! vector opt.
	417	! hydrostatic pressure gradient along s-surfaces
	418	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
	419	& * ( fse3w(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) &
	420	& - fse3w(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) )
	421	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
	422	& * ( fse3w(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) &
	423	& - fse3w(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) )
	424	! s-coordinate pressure gradient correction
	425	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
	426	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj)
	427	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
	428	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj)
	429	! add to the general momentum trend
	430	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap
	431	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap
	432	END DO
	433	END DO
	434	END DO
	435	!
	436	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
	437	!
	438	END SUBROUTINE hpg_sco
	439
	440	SUBROUTINE hpg_isf( kt )
	441	!!---------------------------------------------------------------------
	442	!! * ROUTINE hpg_sco *
	443	!!
	444	!! ** Method : s-coordinate case. Jacobian scheme.
	445	!! The now hydrostatic pressure gradient at a given level, jk,
	446	!! is computed by taking the vertical integral of the in-situ
	447	!! density gradient along the model level from the suface to that
	448	!! level. s-coordinates (ln_sco): a corrective term is added
	449	!! to the horizontal pressure gradient :
	450	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
	451	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
	452	!! add it to the general momentum trend (ua,va).
	453	!! ua = ua - 1/e1u * zhpi
	454	!! va = va - 1/e2v * zhpj
	455	!! iceload is added and partial cell case are added to the top and bottom
	456	!!
	457	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
	458	!!----------------------------------------------------------------------
	459	INTEGER, INTENT(in) :: kt ! ocean time-step index
	460	!!
[4990]	461	INTEGER :: ji, jj, jk, iku, ikv, ikt, iktp1i, iktp1j ! dummy loop indices
	462	REAL(wp) :: zcoef0, zuap, zvap, znad, ze3wu, ze3wv, zuapint, zvapint, zhpjint, zhpiint, zdzwt, zdzwtjp1, zdzwtip1 ! temporary scalars
	463	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj, zrhd
	464	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop
	465	REAL(wp), POINTER, DIMENSION(:,:) :: ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj
[3]	466	!!----------------------------------------------------------------------
[3294]	467	!
[4990]	468	CALL wrk_alloc( jpi,jpj, 2, ztstop)
	469	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
	470	CALL wrk_alloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
[3294]	471	!
[4990]	472	IF( kt == nit000 ) THEN
[3]	473	IF(lwp) WRITE(numout,*)
[5098]	474	IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf'
[455]	475	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
[3]	476	ENDIF
	477
[503]	478	! Local constant initialization
[2528]	479	zcoef0 = - grav * 0.5_wp
[592]	480	! To use density and not density anomaly
[4990]	481	! IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
	482	! ELSE ; znad = 0._wp ! Fixed volume
	483	! ENDIF
	484	znad=1._wp
	485	! iniitialised to 0. zhpi zhpi
	486	zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp
[455]	487
[4990]	488	!==================================================================================
	489	!=====Compute iceload and contribution of the half first wet layer =================
	490	!===================================================================================
	491
	492	! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude)
	493	ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp
	494
	495	! compute density of the water displaced by the ice shelf
	496	zrhd = rhd ! save rhd
	497	DO jk = 1, jpk
	498	zdept(:,:)=gdept_1d(jk)
	499	CALL eos(ztstop(:,:,:),zdept(:,:),rhd(:,:,jk))
	500	END DO
	501	WHERE ( tmask(:,:,:) == 1._wp)
	502	rhd(:,:,:) = zrhd(:,:,:) ! replace wet cell by the saved rhd
	503	END WHERE
	504
	505	! compute rhd at the ice/oce interface (ice shelf side)
	506	CALL eos(ztstop,risfdep,zrhdtop_isf)
	507
	508	! compute rhd at the ice/oce interface (ocean side)
	509	DO ji=1,jpi
	510	DO jj=1,jpj
	511	ikt=mikt(ji,jj)
	512	ztstop(ji,jj,1)=tsn(ji,jj,ikt,1)
	513	ztstop(ji,jj,2)=tsn(ji,jj,ikt,2)
	514	END DO
	515	END DO
	516	CALL eos(ztstop,risfdep,zrhdtop_oce)
	517	!
	518	! Surface value + ice shelf gradient
	519	! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v)
	520	ziceload = 0._wp
	521	DO jj = 1, jpj
	522	DO ji = 1, jpi ! vector opt.
	523	ikt=mikt(ji,jj)
	524	ziceload(ji,jj) = ziceload(ji,jj) + (znad + rhd(ji,jj,1) ) * fse3w(ji,jj,1) * (1._wp - tmask(ji,jj,1))
	525	DO jk=2,ikt-1
	526	ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + rhd(ji,jj,jk-1) + rhd(ji,jj,jk)) * fse3w(ji,jj,jk) &
	527	& * (1._wp - tmask(ji,jj,jk))
	528	END DO
	529	IF (ikt .GE. 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + rhd(ji,jj,ikt-1)) &
	530	& * ( risfdep(ji,jj) - gdept_1d(ikt-1) )
	531	END DO
	532	END DO
	533	riceload(:,:) = 0.0_wp ; riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5
	534	! compute zp from z=0 to first T wet point (correction due to zps not yet applied)
[455]	535	DO jj = 2, jpjm1
[3764]	536	DO ji = fs_2, fs_jpim1 ! vector opt.
[4990]	537	ikt=mikt(ji,jj) ; iktp1i=mikt(ji+1,jj); iktp1j=mikt(ji,jj+1)
	538	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
	539	! we assume ISF is in isostatic equilibrium
	540	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * fse3w(ji+1,jj ,iktp1i) &
	541	& * ( 2._wp * znad + rhd(ji+1,jj ,iktp1i) + zrhdtop_oce(ji+1,jj ) ) &
	542	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
	543	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
	544	& + ( ziceload(ji+1,jj) - ziceload(ji,jj)) )
	545	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * fse3w(ji ,jj+1,iktp1j) &
	546	& * ( 2._wp * znad + rhd(ji ,jj+1,iktp1j) + zrhdtop_oce(ji ,jj+1) ) &
	547	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
	548	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
	549	& + ( ziceload(ji,jj+1) - ziceload(ji,jj) ) )
	550	! s-coordinate pressure gradient correction (=0 if z coordinate)
[2528]	551	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
[455]	552	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
[2528]	553	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
[455]	554	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
	555	! add to the general momentum trend
[4990]	556	ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
	557	va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
[3764]	558	END DO
	559	END DO
[4990]	560	!==================================================================================
	561	!===== Compute partial cell contribution for the top cell =========================
	562	!==================================================================================
	563	DO jj = 2, jpjm1
	564	DO ji = fs_2, fs_jpim1 ! vector opt.
	565	iku = miku(ji,jj) ;
	566	zpshpi(ji,jj)=0.0_wp ; zpshpj(ji,jj)=0.0_wp
	567	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))
	568	! u direction
	569	IF ( iku .GT. 1 ) THEN
	570	! case iku
	571	zhpi(ji,jj,iku) = zcoef0 / e1u(ji,jj) * ze3wu &
	572	& * ( rhd (ji+1,jj,iku) + rhd (ji,jj,iku) &
	573	& + SIGN(1._wp,ze3wu) * grui(ji,jj) + 2._wp * znad )
	574	! corrective term ( = 0 if z coordinate )
	575	zuap = -zcoef0 * ( arui(ji,jj) + 2._wp * znad ) * gzui(ji,jj) / e1u(ji,jj)
	576	! zhpi will be added in interior loop
	577	ua(ji,jj,iku) = ua(ji,jj,iku) + zuap
	578	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
	579	IF (mbku(ji,jj) == iku + 1) zpshpi(ji,jj) = zhpi(ji,jj,iku)
[3764]	580
[4990]	581	! case iku + 1 (remove the zphi term added in the interior loop and compute the one corrected for zps)
	582	zhpiint = zcoef0 / e1u(ji,jj) &
	583	& * ( fse3w(ji+1,jj ,iku+1) * ( (rhd(ji+1,jj,iku+1) + znad) &
	584	& + (rhd(ji+1,jj,iku ) + znad) ) * tmask(ji+1,jj,iku) &
	585	& - fse3w(ji ,jj ,iku+1) * ( (rhd(ji ,jj,iku+1) + znad) &
	586	& + (rhd(ji ,jj,iku ) + znad) ) * tmask(ji ,jj,iku) )
	587	zhpi(ji,jj,iku+1) = zcoef0 / e1u(ji,jj) * ge3rui(ji,jj) - zhpiint
	588	END IF
	589
	590	! v direction
	591	ikv = mikv(ji,jj)
	592	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))
	593	IF ( ikv .GT. 1 ) THEN
	594	! case ikv
	595	zhpj(ji,jj,ikv) = zcoef0 / e2v(ji,jj) * ze3wv &
	596	& * ( rhd(ji,jj+1,ikv) + rhd (ji,jj,ikv) &
	597	& + SIGN(1._wp,ze3wv) * grvi(ji,jj) + 2._wp * znad )
	598	! corrective term ( = 0 if z coordinate )
	599	zvap = -zcoef0 * ( arvi(ji,jj) + 2._wp * znad ) * gzvi(ji,jj) / e2v(ji,jj)
	600	! zhpi will be added in interior loop
	601	va(ji,jj,ikv) = va(ji,jj,ikv) + zvap
	602	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
	603	IF (mbkv(ji,jj) == ikv + 1) zpshpj(ji,jj) = zhpj(ji,jj,ikv)
	604
	605	! case ikv + 1 (remove the zphj term added in the interior loop and compute the one corrected for zps)
	606	zhpjint = zcoef0 / e2v(ji,jj) &
	607	& * ( fse3w(ji ,jj+1,ikv+1) * ( (rhd(ji,jj+1,ikv+1) + znad) &
	608	& + (rhd(ji,jj+1,ikv ) + znad) ) * tmask(ji,jj+1,ikv) &
	609	& - fse3w(ji ,jj ,ikv+1) * ( (rhd(ji,jj ,ikv+1) + znad) &
	610	& + (rhd(ji,jj ,ikv ) + znad) ) * tmask(ji,jj ,ikv) )
	611	zhpj(ji,jj,ikv+1) = zcoef0 / e2v(ji,jj) * ge3rvi(ji,jj) - zhpjint
	612	END IF
	613	END DO
	614	END DO
	615
	616	!==================================================================================
	617	!===== Compute interior value =====================================================
	618	!==================================================================================
	619
	620	DO jj = 2, jpjm1
	621	DO ji = fs_2, fs_jpim1 ! vector opt.
	622	iku=miku(ji,jj); ikv=mikv(ji,jj)
	623	DO jk = 2, jpkm1
[455]	624	! hydrostatic pressure gradient along s-surfaces
[4990]	625	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
	626	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) + zhpi(ji,jj,jk-1) &
	627	& + zcoef0 / e1u(ji,jj) &
	628	& * ( fse3w(ji+1,jj ,jk) * ( (rhd(ji+1,jj,jk ) + znad) &
	629	& + (rhd(ji+1,jj,jk-1) + znad) ) * tmask(ji+1,jj,jk-1) &
	630	& - fse3w(ji ,jj ,jk) * ( (rhd(ji ,jj,jk ) + znad) &
	631	& + (rhd(ji ,jj,jk-1) + znad) ) * tmask(ji ,jj,jk-1) )
[455]	632	! s-coordinate pressure gradient correction
[4990]	633	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
	634	zuap = - zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
	635	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) * umask(ji,jj,jk-1)
	636	ua(ji,jj,jk) = ua(ji,jj,jk) + ( zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
	637
	638	! hydrostatic pressure gradient along s-surfaces
	639	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
	640	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) + zhpj(ji,jj,jk-1) &
	641	& + zcoef0 / e2v(ji,jj) &
	642	& * ( fse3w(ji ,jj+1,jk) * ( (rhd(ji,jj+1,jk ) + znad) &
	643	& + (rhd(ji,jj+1,jk-1) + znad) ) * tmask(ji,jj+1,jk-1) &
	644	& - fse3w(ji ,jj ,jk) * ( (rhd(ji,jj ,jk ) + znad) &
	645	& + (rhd(ji,jj ,jk-1) + znad) ) * tmask(ji,jj ,jk-1) )
	646	! s-coordinate pressure gradient correction
	647	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
	648	zvap = - zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
	649	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) * vmask(ji,jj,jk-1)
[455]	650	! add to the general momentum trend
[4990]	651	va(ji,jj,jk) = va(ji,jj,jk) + ( zhpj(ji,jj,jk) + zvap ) * vmask(ji,jj,jk)
[455]	652	END DO
	653	END DO
	654	END DO
[4990]	655
	656	!==================================================================================
	657	!===== Compute bottom cell contribution (partial cell) ============================
	658	!==================================================================================
	659
	660	DO jj = 2, jpjm1
	661	DO ji = 2, jpim1
	662	iku = mbku(ji,jj)
	663	ikv = mbkv(ji,jj)
	664
	665	IF (iku .GT. 1) THEN
	666	! remove old value (interior case)
	667	zuap = -zcoef0 * ( rhd (ji+1,jj ,iku) + rhd (ji,jj,iku) + 2._wp * znad ) &
	668	& * ( fsde3w(ji+1,jj ,iku) - fsde3w(ji,jj,iku) ) / e1u(ji,jj)
	669	ua(ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) - zuap
	670	! put new value
	671	! -zpshpi to avoid double contribution of the partial step in the top layer
	672	zuap = -zcoef0 * ( aru(ji,jj) + 2._wp * znad ) * gzu(ji,jj) / e1u(ji,jj)
	673	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) + zcoef0 / e1u(ji,jj) * ge3ru(ji,jj) - zpshpi(ji,jj)
	674	ua(ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) + zuap
	675	END IF
	676	! v direction
	677	IF (ikv .GT. 1) THEN
	678	! remove old value (interior case)
	679	zvap = -zcoef0 * ( rhd (ji ,jj+1,ikv) + rhd (ji,jj,ikv) + 2._wp * znad ) &
	680	& * ( fsde3w(ji ,jj+1,ikv) - fsde3w(ji,jj,ikv) ) / e2v(ji,jj)
	681	va(ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) - zvap
	682	! put new value
	683	! -zpshpj to avoid double contribution of the partial step in the top layer
	684	zvap = -zcoef0 * ( arv(ji,jj) + 2._wp * znad ) * gzv(ji,jj) / e2v(ji,jj)
	685	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) + zcoef0 / e2v(ji,jj) * ge3rv(ji,jj) - zpshpj(ji,jj)
	686	va(ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) + zvap
	687	END IF
	688	END DO
	689	END DO
	690
	691	! set back to original density value into the ice shelf cell (maybe useless because it is masked)
	692	rhd = zrhd
[503]	693	!
[4990]	694	CALL wrk_dealloc( jpi,jpj,2, ztstop)
	695	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
	696	CALL wrk_dealloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
[3294]	697	!
[5098]	698	END SUBROUTINE hpg_isf
[455]	699
[4990]	700
[455]	701	SUBROUTINE hpg_djc( kt )
	702	!!---------------------------------------------------------------------
	703	!! * ROUTINE hpg_djc *
	704	!!
	705	!! ** Method : Density Jacobian with Cubic polynomial scheme
[3764]	706	!!
[503]	707	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
[455]	708	!!----------------------------------------------------------------------
[503]	709	INTEGER, INTENT(in) :: kt ! ocean time-step index
	710	!!
	711	INTEGER :: ji, jj, jk ! dummy loop indices
	712	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
	713	REAL(wp) :: z1_10, cffu, cffx ! " "
	714	REAL(wp) :: z1_12, cffv, cffy ! " "
[3764]	715	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3294]	716	REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw
	717	REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow
	718	REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k
[455]	719	!!----------------------------------------------------------------------
[3294]	720	!
[3764]	721	CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
	722	CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
	723	CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
[3294]	724	!
[455]	725
	726	IF( kt == nit000 ) THEN
	727	IF(lwp) WRITE(numout,*)
	728	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
	729	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
[216]	730	ENDIF
	731
[503]	732	! Local constant initialization
[2528]	733	zcoef0 = - grav * 0.5_wp
	734	z1_10 = 1._wp / 10._wp
	735	z1_12 = 1._wp / 12._wp
[455]	736
	737	!----------------------------------------------------------------------------------------
	738	! compute and store in provisional arrays elementary vertical and horizontal differences
	739	!----------------------------------------------------------------------------------------
	740
	741	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
	742
	743	DO jk = 2, jpkm1
	744	DO jj = 2, jpjm1
	745	DO ji = fs_2, fs_jpim1 ! vector opt.
	746	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
	747	dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1)
	748	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
	749	dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk )
	750	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
	751	dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk )
	752	END DO
	753	END DO
	754	END DO
	755
	756	!-------------------------------------------------------------------------
	757	! compute harmonic averages using eq. 5.18
	758	!-------------------------------------------------------------------------
	759	zep = 1.e-15
	760
[503]	761	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
	762	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
[455]	763
	764	DO jk = 2, jpkm1
	765	DO jj = 2, jpjm1
	766	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	767	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
[455]	768
[2528]	769	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
	770	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
[3764]	771
[2528]	772	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
	773	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
[455]	774
	775	IF( cffw > zep) THEN
[2528]	776	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
	777	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
[455]	778	ELSE
[2528]	779	drhow(ji,jj,jk) = 0._wp
[455]	780	ENDIF
	781
[2528]	782	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
	783	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
[455]	784
	785	IF( cffu > zep ) THEN
[2528]	786	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
	787	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
[455]	788	ELSE
[2528]	789	drhou(ji,jj,jk ) = 0._wp
[455]	790	ENDIF
	791
	792	IF( cffx > zep ) THEN
[2528]	793	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
	794	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
[455]	795	ELSE
[2528]	796	dzu(ji,jj,jk) = 0._wp
[455]	797	ENDIF
	798
	799	IF( cffv > zep ) THEN
[2528]	800	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
	801	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
[455]	802	ELSE
[2528]	803	drhov(ji,jj,jk) = 0._wp
[455]	804	ENDIF
	805
	806	IF( cffy > zep ) THEN
[2528]	807	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
	808	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
[455]	809	ELSE
[2528]	810	dzv(ji,jj,jk) = 0._wp
[455]	811	ENDIF
	812
	813	END DO
	814	END DO
	815	END DO
	816
	817	!----------------------------------------------------------------------------------
	818	! apply boundary conditions at top and bottom using 5.36-5.37
	819	!----------------------------------------------------------------------------------
[2528]	820	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
	821	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
	822	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
[455]	823
[2528]	824	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
	825	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
	826	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
[455]	827
	828
	829	!--------------------------------------------------------------
	830	! Upper half of top-most grid box, compute and store
	831	!-------------------------------------------------------------
	832
	833	!!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified
	834	! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
	835
	836	DO jj = 2, jpjm1
	837	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	838	rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) &
	839	& * ( rhd(ji,jj,1) &
	840	& + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) &
	841	& * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) &
[3764]	842	& / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) )
[455]	843	END DO
	844	END DO
	845
	846	!!bug gm : here also, simplification is possible
	847	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
	848
	849	DO jk = 2, jpkm1
	850	DO jj = 2, jpjm1
	851	DO ji = fs_2, fs_jpim1 ! vector opt.
	852
	853	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
	854	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) &
	855	& - grav * z1_10 * ( &
	856	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
	857	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
	858	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
	859	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
	860	& )
	861
	862	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
	863	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) &
	864	& - grav* z1_10 * ( &
	865	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
	866	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
	867	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
	868	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
	869	& )
	870
	871	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
	872	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) &
	873	& - grav* z1_10 * ( &
	874	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
	875	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
	876	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
	877	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
	878	& )
	879
	880	END DO
	881	END DO
	882	END DO
	883	CALL lbc_lnk(rho_k,'W',1.)
	884	CALL lbc_lnk(rho_i,'U',1.)
	885	CALL lbc_lnk(rho_j,'V',1.)
	886
	887
	888	! ---------------
	889	! Surface value
	890	! ---------------
	891	DO jj = 2, jpjm1
	892	DO ji = fs_2, fs_jpim1 ! vector opt.
	893	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj)
	894	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj)
	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
[3764]	905	DO jj = 2, jpjm1
[455]	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) ) ) / 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) ) ) / e2v(ji,jj)
	914	! add to the general momentum trend
	915	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	916	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
	917	END DO
	918	END DO
	919	END DO
[503]	920	!
[3764]	921	CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
	922	CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
	923	CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
[2715]	924	!
[455]	925	END SUBROUTINE hpg_djc
	926
	927
[3294]	928	SUBROUTINE hpg_prj( kt )
[455]	929	!!---------------------------------------------------------------------
[3294]	930	!! * ROUTINE hpg_prj *
[455]	931	!!
[3294]	932	!! ** Method : s-coordinate case.
	933	!! A Pressure-Jacobian horizontal pressure gradient method
	934	!! based on the constrained cubic-spline interpolation for
	935	!! all vertical coordinate systems
[455]	936	!!
[3294]	937	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[455]	938	!!----------------------------------------------------------------------
[3294]	939	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
	940	INTEGER, INTENT(in) :: kt ! ocean time-step index
[503]	941	!!
[3294]	942	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
	943	REAL(wp) :: zcoef0, znad ! temporary scalars
[503]	944	!!
[3294]	945	!! The local variables for the correction term
	946	INTEGER :: jk1, jis, jid, jjs, jjd
	947	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
[3764]	948	REAL(wp) :: zrhdt1
[3294]	949	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
[3764]	950	REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh
[3294]	951	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
[455]	952	!!----------------------------------------------------------------------
[3294]	953	!
[3764]	954	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
	955	CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh )
[3294]	956	!
[455]	957	IF( kt == nit000 ) THEN
	958	IF(lwp) WRITE(numout,*)
[3294]	959	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
	960	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
[3]	961	ENDIF
	962
[3294]	963	!!----------------------------------------------------------------------
	964	! Local constant initialization
[3764]	965	zcoef0 = - grav
[3294]	966	znad = 0.0_wp
	967	IF( lk_vvl ) znad = 1._wp
[3]	968
[3294]	969	! Clean 3-D work arrays
	970	zhpi(:,:,:) = 0._wp
	971	zrhh(:,:,:) = rhd(:,:,:)
[3764]	972
[3294]	973	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
	974	DO jj = 1, jpj
[3764]	975	DO ji = 1, jpi
[3294]	976	jk = mbathy(ji,jj)
	977	IF( jk <= 0 ) THEN; zrhh(ji,jj,:) = 0._wp
	978	ELSE IF(jk == 1) THEN; zrhh(ji,jj, jk+1:jpk) = rhd(ji,jj,jk)
	979	ELSE IF(jk < jpkm1) THEN
	980	DO jkk = jk+1, jpk
	981	zrhh(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1), &
	982	fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2))
[3764]	983	END DO
[3294]	984	ENDIF
	985	END DO
	986	END DO
[3]	987
[3632]	988	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
[4990]	989	DO jj = 1, jpj
	990	DO ji = 1, jpi
	991	zdept(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) - sshn(ji,jj) * znad
	992	END DO
	993	END DO
[455]	994
[4990]	995	DO jk = 2, jpk
	996	DO jj = 1, jpj
	997	DO ji = 1, jpi
	998	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + fse3w(ji,jj,jk)
	999	END DO
	1000	END DO
	1001	END DO
[455]	1002
[4990]	1003	fsp(:,:,:) = zrhh (:,:,:)
[3632]	1004	xsp(:,:,:) = zdept(:,:,:)
	1005
[3764]	1006	! Construct the vertical density profile with the
[3294]	1007	! constrained cubic spline interpolation
	1008	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
[3764]	1009	CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type)
[3294]	1010
	1011	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
	1012	DO jj = 2, jpj
[3764]	1013	DO ji = 2, jpi
[3632]	1014	zrhdt1 = zrhh(ji,jj,1) - interp3(zdept(ji,jj,1),asp(ji,jj,1), &
[3294]	1015	bsp(ji,jj,1), csp(ji,jj,1), &
[3632]	1016	dsp(ji,jj,1) ) * 0.25_wp * fse3w(ji,jj,1)
[3294]	1017
	1018	! assuming linear profile across the top half surface layer
[3764]	1019	zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * zrhdt1
[3294]	1020	END DO
[455]	1021	END DO
	1022
[3294]	1023	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
[3764]	1024	DO jk = 2, jpkm1
	1025	DO jj = 2, jpj
[3294]	1026	DO ji = 2, jpi
	1027	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
[3632]	1028	integ_spline(zdept(ji,jj,jk-1), zdept(ji,jj,jk),&
[3294]	1029	asp(ji,jj,jk-1), bsp(ji,jj,jk-1), &
	1030	csp(ji,jj,jk-1), dsp(ji,jj,jk-1))
	1031	END DO
	1032	END DO
[455]	1033	END DO
	1034
[3294]	1035	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
[3764]	1036	DO jj = 2, jpjm1
	1037	DO ji = 2, jpim1
[4292]	1038	zu(ji,jj,1) = - ( fse3u(ji,jj,1) - sshn(ji,jj) * znad) ! probable bug: changed from sshu_n for ztilde compilation
	1039	zv(ji,jj,1) = - ( fse3v(ji,jj,1) - sshn(ji,jj) * znad) ! probable bug: changed from sshv_n for ztilde compilation
[3294]	1040	END DO
[455]	1041	END DO
	1042
[3764]	1043	DO jk = 2, jpkm1
	1044	DO jj = 2, jpjm1
	1045	DO ji = 2, jpim1
[3294]	1046	zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk)
	1047	zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk)
	1048	END DO
	1049	END DO
[455]	1050	END DO
[3764]	1051
	1052	DO jk = 1, jpkm1
	1053	DO jj = 2, jpjm1
	1054	DO ji = 2, jpim1
[3294]	1055	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk)
	1056	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk)
	1057	END DO
	1058	END DO
	1059	END DO
[455]	1060
[3632]	1061	DO jk = 1, jpkm1
	1062	DO jj = 2, jpjm1
	1063	DO ji = 2, jpim1
	1064	zu(ji,jj,jk) = min(zu(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
	1065	zu(ji,jj,jk) = max(zu(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
	1066	zv(ji,jj,jk) = min(zv(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
	1067	zv(ji,jj,jk) = max(zv(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
	1068	END DO
	1069	END DO
	1070	END DO
	1071
	1072
[3764]	1073	DO jk = 1, jpkm1
	1074	DO jj = 2, jpjm1
	1075	DO ji = 2, jpim1
[3294]	1076	zpwes = 0._wp; zpwed = 0._wp
	1077	zpnss = 0._wp; zpnsd = 0._wp
	1078	zuijk = zu(ji,jj,jk)
	1079	zvijk = zv(ji,jj,jk)
	1080
	1081	!!!!! for u equation
	1082	IF( jk <= mbku(ji,jj) ) THEN
[3632]	1083	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
[3294]	1084	jis = ji + 1; jid = ji
	1085	ELSE
	1086	jis = ji; jid = ji +1
	1087	ENDIF
	1088
	1089	! integrate the pressure on the shallow side
[3764]	1090	jk1 = jk
[3632]	1091	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
[3294]	1092	IF( jk1 == mbku(ji,jj) ) THEN
[3632]	1093	zuijk = -zdept(jis,jj,jk1)
[3294]	1094	EXIT
	1095	ENDIF
[3632]	1096	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
[3764]	1097	zpwes = zpwes + &
[3632]	1098	integ_spline(zdept(jis,jj,jk1), zdeps, &
[3294]	1099	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
	1100	csp(jis,jj,jk1), dsp(jis,jj,jk1))
	1101	jk1 = jk1 + 1
	1102	END DO
[3764]	1103
[3294]	1104	! integrate the pressure on the deep side
[3764]	1105	jk1 = jk
[3632]	1106	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
[3294]	1107	IF( jk1 == 1 ) THEN
[3632]	1108	zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad)
	1109	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
	1110	bsp(jid,jj,1), csp(jid,jj,1), &
	1111	dsp(jid,jj,1)) * zdeps
	1112	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
[3294]	1113	EXIT
	1114	ENDIF
[3632]	1115	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
[3764]	1116	zpwed = zpwed + &
[3632]	1117	integ_spline(zdeps, zdept(jid,jj,jk1), &
[3294]	1118	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
	1119	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
	1120	jk1 = jk1 - 1
	1121	END DO
[3764]	1122
[3294]	1123	! update the momentum trends in u direction
	1124
	1125	zdpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk))
	1126	IF( lk_vvl ) THEN
[3764]	1127	zdpdx2 = zcoef0 / e1u(ji,jj) * &
	1128	( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) )
[3294]	1129	ELSE
[3764]	1130	zdpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
[3294]	1131	ENDIF
	1132
	1133	ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * &
	1134	& umask(ji,jj,jk) * tmask(ji,jj,jk) * tmask(ji+1,jj,jk)
	1135	ENDIF
[3764]	1136
[3294]	1137	!!!!! for v equation
	1138	IF( jk <= mbkv(ji,jj) ) THEN
[3632]	1139	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
[3294]	1140	jjs = jj + 1; jjd = jj
	1141	ELSE
	1142	jjs = jj ; jjd = jj + 1
	1143	ENDIF
	1144
	1145	! integrate the pressure on the shallow side
[3764]	1146	jk1 = jk
[3632]	1147	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
[3294]	1148	IF( jk1 == mbkv(ji,jj) ) THEN
[3632]	1149	zvijk = -zdept(ji,jjs,jk1)
[3294]	1150	EXIT
	1151	ENDIF
[3632]	1152	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
[3764]	1153	zpnss = zpnss + &
[3632]	1154	integ_spline(zdept(ji,jjs,jk1), zdeps, &
[3294]	1155	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
	1156	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
	1157	jk1 = jk1 + 1
	1158	END DO
[3764]	1159
[3294]	1160	! integrate the pressure on the deep side
[3764]	1161	jk1 = jk
[3632]	1162	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
[3294]	1163	IF( jk1 == 1 ) THEN
[3632]	1164	zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad)
	1165	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
	1166	bsp(ji,jjd,1), csp(ji,jjd,1), &
	1167	dsp(ji,jjd,1) ) * zdeps
	1168	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
[3294]	1169	EXIT
	1170	ENDIF
[3632]	1171	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
[3764]	1172	zpnsd = zpnsd + &
[3632]	1173	integ_spline(zdeps, zdept(ji,jjd,jk1), &
[3294]	1174	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
	1175	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
	1176	jk1 = jk1 - 1
	1177	END DO
	1178
[3764]	1179
[3294]	1180	! update the momentum trends in v direction
	1181
	1182	zdpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk))
	1183	IF( lk_vvl ) THEN
	1184	zdpdy2 = zcoef0 / e2v(ji,jj) * &
[3764]	1185	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) )
[3294]	1186	ELSE
[3764]	1187	zdpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
[3294]	1188	ENDIF
	1189
	1190	va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2)*&
	1191	& vmask(ji,jj,jk)tmask(ji,jj,jk)tmask(ji,jj+1,jk)
	1192	ENDIF
	1193
[3764]	1194
[3294]	1195	END DO
	1196	END DO
[455]	1197	END DO
[503]	1198	!
[3764]	1199	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
	1200	CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh )
[2715]	1201	!
[3294]	1202	END SUBROUTINE hpg_prj
[455]	1203
[4990]	1204
[3294]	1205	SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type)
	1206	!!----------------------------------------------------------------------
	1207	!! * ROUTINE cspline *
[3764]	1208	!!
[3294]	1209	!! ** Purpose : constrained cubic spline interpolation
[3764]	1210	!!
	1211	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
[4990]	1212	!!
[3294]	1213	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
	1214	!!----------------------------------------------------------------------
	1215	IMPLICIT NONE
	1216	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate
[3764]	1217	REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of
[3294]	1218	! the interpoated function
[3764]	1219	INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline
[3294]	1220	! 2: Linear
[4990]	1221	!
[3294]	1222	INTEGER :: ji, jj, jk ! dummy loop indices
	1223	INTEGER :: jpi, jpj, jpkm1
	1224	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
	1225	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
	1226	REAL(wp) :: zdf(size(fsp,3))
	1227	!!----------------------------------------------------------------------
	1228
	1229	jpi = size(fsp,1)
	1230	jpj = size(fsp,2)
	1231	jpkm1 = size(fsp,3) - 1
	1232
[3764]	1233
[3294]	1234	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
	1235	DO ji = 1, jpi
	1236	DO jj = 1, jpj
[3764]	1237	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
[3294]	1238	! DO jk = 2, jpkm1-1
[3764]	1239	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
	1240	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1241	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
	1242	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
	1243	!
	1244	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
[3764]	1245	!
[3294]	1246	! IF(zdf1 * zdf2 <= 0._wp) THEN
	1247	! zdf(jk) = 0._wp
	1248	! ELSE
	1249	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
	1250	! ENDIF
	1251	! END DO
[3764]	1252
[3294]	1253	!!Simply geometric average
	1254	DO jk = 2, jpkm1-1
	1255	zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1))
	1256	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk))
[3764]	1257
[3294]	1258	IF(zdf1 * zdf2 <= 0._wp) THEN
	1259	zdf(jk) = 0._wp
	1260	ELSE
	1261	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
	1262	ENDIF
	1263	END DO
[3764]	1264
[3294]	1265	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
	1266	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
	1267	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
	1268	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - &
	1269	& 0.5_wp * zdf(jpkm1 - 1)
[3764]	1270
[3294]	1271	DO jk = 1, jpkm1 - 1
[3764]	1272	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1273	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
	1274	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
[3764]	1275	zddf1 = -2._wp * ztmp1 + ztmp2
[3294]	1276	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
[3764]	1277	zddf2 = 2._wp * ztmp1 - ztmp2
	1278
[3294]	1279	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
	1280	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
[3764]	1281	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
[3294]	1282	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
	1283	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
	1284	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
	1285	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
	1286	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
	1287	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
	1288	END DO
	1289	END DO
	1290	END DO
[3764]	1291
[3294]	1292	ELSE IF (polynomial_type == 2) THEN ! Linear
	1293	DO ji = 1, jpi
	1294	DO jj = 1, jpj
	1295	DO jk = 1, jpkm1-1
[3764]	1296	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1297	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
[3764]	1298
[3294]	1299	dsp(ji,jj,jk) = 0._wp
	1300	csp(ji,jj,jk) = 0._wp
	1301	bsp(ji,jj,jk) = ztmp1 / zdxtmp
	1302	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
	1303	END DO
	1304	END DO
	1305	END DO
	1306
	1307	ELSE
	1308	CALL ctl_stop( 'invalid polynomial type in cspline' )
	1309	ENDIF
	1310
	1311	END SUBROUTINE cspline
	1312
	1313
[3764]	1314	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
[3294]	1315	!!----------------------------------------------------------------------
	1316	!! * ROUTINE interp1 *
[3764]	1317	!!
[3294]	1318	!! ** Purpose : 1-d linear interpolation
[3764]	1319	!!
[4990]	1320	!! ** Method : interpolation is straight forward
[3764]	1321	!! extrapolation is also permitted (no value limit)
[3294]	1322	!!----------------------------------------------------------------------
	1323	IMPLICIT NONE
[3764]	1324	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
[3294]	1325	REAL(wp) :: f ! result of the interpolation (extrapolation)
	1326	REAL(wp) :: zdeltx
	1327	!!----------------------------------------------------------------------
	1328
	1329	zdeltx = xr - xl
	1330	IF(abs(zdeltx) <= 10._wp * EPSILON(x)) THEN
	1331	f = 0.5_wp * (fl + fr)
	1332	ELSE
	1333	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
	1334	ENDIF
[3764]	1335
[3294]	1336	END FUNCTION interp1
	1337
[4990]	1338
[3764]	1339	FUNCTION interp2(x, a, b, c, d) RESULT(f)
[3294]	1340	!!----------------------------------------------------------------------
	1341	!! * ROUTINE interp1 *
[3764]	1342	!!
[3294]	1343	!! ** Purpose : 1-d constrained cubic spline interpolation
[3764]	1344	!!
[3294]	1345	!! ** Method : cubic spline interpolation
	1346	!!
	1347	!!----------------------------------------------------------------------
	1348	IMPLICIT NONE
[3764]	1349	REAL(wp), INTENT(in) :: x, a, b, c, d
[3294]	1350	REAL(wp) :: f ! value from the interpolation
	1351	!!----------------------------------------------------------------------
	1352
[3764]	1353	f = a + x* ( b + x * ( c + d * x ) )
[3294]	1354
	1355	END FUNCTION interp2
	1356
	1357
[3764]	1358	FUNCTION interp3(x, a, b, c, d) RESULT(f)
[3294]	1359	!!----------------------------------------------------------------------
	1360	!! * ROUTINE interp1 *
[3764]	1361	!!
[3294]	1362	!! ** Purpose : Calculate the first order of deriavtive of
	1363	!! a cubic spline function y=a+bx+cx^2+d*x^3
[3764]	1364	!!
[3294]	1365	!! ** Method : f=dy/dx=b+2cx+3dx^2
	1366	!!
	1367	!!----------------------------------------------------------------------
	1368	IMPLICIT NONE
[3764]	1369	REAL(wp), INTENT(in) :: x, a, b, c, d
[3294]	1370	REAL(wp) :: f ! value from the interpolation
	1371	!!----------------------------------------------------------------------
	1372
	1373	f = b + x * ( 2._wp * c + 3._wp * d * x)
	1374
	1375	END FUNCTION interp3
	1376
[3764]	1377
	1378	FUNCTION integ_spline(xl, xr, a, b, c, d) RESULT(f)
[3294]	1379	!!----------------------------------------------------------------------
	1380	!! * ROUTINE interp1 *
[3764]	1381	!!
[3294]	1382	!! ** Purpose : 1-d constrained cubic spline integration
	1383	!!
[3764]	1384	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
	1385	!!
[3294]	1386	!!----------------------------------------------------------------------
	1387	IMPLICIT NONE
[3764]	1388	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
	1389	REAL(wp) :: za1, za2, za3
[3294]	1390	REAL(wp) :: f ! integration result
	1391	!!----------------------------------------------------------------------
	1392
[3764]	1393	za1 = 0.5_wp * b
	1394	za2 = c / 3.0_wp
	1395	za3 = 0.25_wp * d
[3294]	1396
	1397	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
	1398	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
	1399
[3632]	1400	END FUNCTION integ_spline
[3294]	1401
[3]	1402	!!======================================================================
	1403	END MODULE dynhpg
[3632]	1404

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