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dynhpg.F90 in branches/2014/dev_r4650_UKMO10_Tidally_Meaned_Diagnostics/NEMOGCM/NEMO/OPA_SRC/DYN – NEMO

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source: branches/2014/dev_r4650_UKMO10_Tidally_Meaned_Diagnostics/NEMOGCM/NEMO/OPA_SRC/DYN/dynhpg.F90 @ 5989

Last change on this file since 5989 was 5989, checked in by deazer, 8 years ago
Merging TMB and 25h diagnostics to head of trunk added brief documentation
Property svn:keywords set to `Id`
File size: 70.3 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
[5260]	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)
[5260]	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
[5260]	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
[5260]	36	USE trd_oce ! trends: ocean variables
	37	USE trddyn ! trend manager: dynamics
[5989]	38	!jc USE zpshde ! partial step: hor. derivative (zps_hde routine)
[5260]	39	!
[2715]	40	USE in_out_manager ! I/O manager
[258]	41	USE prtctl ! Print control
[5260]	42	USE lbclnk ! lateral boundary condition
[2715]	43	USE lib_mpp ! MPP library
[5260]	44	USE eosbn2 ! compute density
[3294]	45	USE wrk_nemo ! Memory Allocation
	46	USE timing ! Timing
[3]	47
	48	IMPLICIT NONE
	49	PRIVATE
	50
[2528]	51	PUBLIC dyn_hpg ! routine called by step module
	52	PUBLIC dyn_hpg_init ! routine called by opa module
[3]	53
[4147]	54	! !!* Namelist namdyn_hpg : hydrostatic pressure gradient
	55	LOGICAL , PUBLIC :: ln_hpg_zco !: z-coordinate - full steps
	56	LOGICAL , PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation)
	57	LOGICAL , PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation)
	58	LOGICAL , PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial)
	59	LOGICAL , PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme)
[5260]	60	LOGICAL , PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf
[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
[5260]	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)
[5260]	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(:,:,:)
[5260]	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, &
[5989]	134	& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf
[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
[5260]	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
[455]	157	ENDIF
[2528]	158	!
[3294]	159	IF( ln_hpg_djc ) &
	160	& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method &
	161	& currently disabled (bugs under investigation). Please select &
	162	& either ln_hpg_sco or ln_hpg_prj instead')
[2528]	163	!
[5260]	164	IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) &
[3294]	165	& CALL ctl_stop('dyn_hpg_init : variable volume key_vvl requires:&
	166	& the standard jacobian formulation hpg_sco or &
	167	& the pressure jacobian formulation hpg_prj')
[5260]	168
	169	IF( ln_hpg_isf .AND. .NOT. ln_isfcav ) &
	170	& CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' )
	171	IF( .NOT. ln_hpg_isf .AND. ln_isfcav ) &
	172	& CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' )
[3294]	173	!
[503]	174	! ! Set nhpg from ln_hpg_... flags
[455]	175	IF( ln_hpg_zco ) nhpg = 0
	176	IF( ln_hpg_zps ) nhpg = 1
	177	IF( ln_hpg_sco ) nhpg = 2
[3294]	178	IF( ln_hpg_djc ) nhpg = 3
	179	IF( ln_hpg_prj ) nhpg = 4
[5260]	180	IF( ln_hpg_isf ) nhpg = 5
[2528]	181	!
[3294]	182	! ! Consistency check
[3764]	183	ioptio = 0
[455]	184	IF( ln_hpg_zco ) ioptio = ioptio + 1
	185	IF( ln_hpg_zps ) ioptio = ioptio + 1
	186	IF( ln_hpg_sco ) ioptio = ioptio + 1
	187	IF( ln_hpg_djc ) ioptio = ioptio + 1
[3294]	188	IF( ln_hpg_prj ) ioptio = ioptio + 1
[5260]	189	IF( ln_hpg_isf ) ioptio = ioptio + 1
[2715]	190	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
[5260]	191	!
	192	! initialisation of ice load
	193	riceload(:,:)=0.0
[503]	194	!
[2528]	195	END SUBROUTINE dyn_hpg_init
[455]	196
	197
	198	SUBROUTINE hpg_zco( kt )
	199	!!---------------------------------------------------------------------
	200	!! * ROUTINE hpg_zco *
	201	!!
	202	!! ** Method : z-coordinate case, levels are horizontal surfaces.
	203	!! The now hydrostatic pressure gradient at a given level, jk,
	204	!! is computed by taking the vertical integral of the in-situ
	205	!! density gradient along the model level from the suface to that
	206	!! level: zhpi = grav .....
	207	!! zhpj = grav .....
[3]	208	!! add it to the general momentum trend (ua,va).
[455]	209	!! ua = ua - 1/e1u * zhpi
	210	!! va = va - 1/e2v * zhpj
[3764]	211	!!
[3]	212	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[503]	213	!!----------------------------------------------------------------------
	214	INTEGER, INTENT(in) :: kt ! ocean time-step index
	215	!!
	216	INTEGER :: ji, jj, jk ! dummy loop indices
	217	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
[3764]	218	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3]	219	!!----------------------------------------------------------------------
[3764]	220	!
[3294]	221	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
	222	!
[3]	223	IF( kt == nit000 ) THEN
	224	IF(lwp) WRITE(numout,*)
[455]	225	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
	226	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
[3]	227	ENDIF
	228
[3764]	229	zcoef0 = - grav * 0.5_wp ! Local constant initialization
	230
[455]	231	! Surface value
[3]	232	DO jj = 2, jpjm1
	233	DO ji = fs_2, fs_jpim1 ! vector opt.
[455]	234	zcoef1 = zcoef0 * fse3w(ji,jj,1)
	235	! hydrostatic pressure gradient
	236	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
	237	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
[3]	238	! add to the general momentum trend
[455]	239	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
	240	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
	241	END DO
	242	END DO
[3294]	243
[503]	244	!
[455]	245	! interior value (2=<jk=<jpkm1)
[3]	246	DO jk = 2, jpkm1
[455]	247	DO jj = 2, jpjm1
[3]	248	DO ji = fs_2, fs_jpim1 ! vector opt.
[455]	249	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
	250	! hydrostatic pressure gradient
	251	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
	252	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
	253	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
	254
	255	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
	256	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
	257	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
[3]	258	! add to the general momentum trend
[455]	259	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	260	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
[3]	261	END DO
	262	END DO
	263	END DO
[503]	264	!
[3294]	265	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
	266	!
[455]	267	END SUBROUTINE hpg_zco
[216]	268
[3]	269
[455]	270	SUBROUTINE hpg_zps( kt )
[3]	271	!!---------------------------------------------------------------------
[455]	272	!! * ROUTINE hpg_zps *
[3764]	273	!!
[455]	274	!! ** Method : z-coordinate plus partial steps case. blahblah...
[3764]	275	!!
[3]	276	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[3764]	277	!!----------------------------------------------------------------------
[503]	278	INTEGER, INTENT(in) :: kt ! ocean time-step index
	279	!!
	280	INTEGER :: ji, jj, jk ! dummy loop indices
	281	INTEGER :: iku, ikv ! temporary integers
	282	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
[3764]	283	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3]	284	!!----------------------------------------------------------------------
[3294]	285	!
	286	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
	287	!
[3]	288	IF( kt == nit000 ) THEN
	289	IF(lwp) WRITE(numout,*)
[455]	290	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
[503]	291	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
[3]	292	ENDIF
	293
[5989]	294	! Partial steps: bottom before horizontal gradient of t, s, rd at the last ocean level
	295	!jc CALL zps_hde ( kt, jpts, tsn, gtsu, gtsv, rhd, gru , grv )
[3294]	296
[503]	297	! Local constant initialization
[2528]	298	zcoef0 = - grav * 0.5_wp
[3]	299
[2528]	300	! Surface value (also valid in partial step case)
[3]	301	DO jj = 2, jpjm1
	302	DO ji = fs_2, fs_jpim1 ! vector opt.
[170]	303	zcoef1 = zcoef0 * fse3w(ji,jj,1)
[3]	304	! hydrostatic pressure gradient
[455]	305	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
	306	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
[3]	307	! add to the general momentum trend
	308	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
	309	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
	310	END DO
	311	END DO
	312
[3294]	313
[503]	314	! interior value (2=<jk=<jpkm1)
[3]	315	DO jk = 2, jpkm1
	316	DO jj = 2, jpjm1
	317	DO ji = fs_2, fs_jpim1 ! vector opt.
[170]	318	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
[3]	319	! hydrostatic pressure gradient
	320	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
[455]	321	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
	322	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
[3]	323
	324	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
[455]	325	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
	326	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
[3]	327	! add to the general momentum trend
	328	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	329	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
[455]	330	END DO
[3]	331	END DO
	332	END DO
	333
[3294]	334
[2528]	335	! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
[3]	336	DO jj = 2, jpjm1
	337	DO ji = 2, jpim1
[2528]	338	iku = mbku(ji,jj)
	339	ikv = mbkv(ji,jj)
[3]	340	zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) )
	341	zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) )
[2528]	342	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
	343	ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value
	344	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
	345	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj)
	346	ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
[3]	347	ENDIF
[2528]	348	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
	349	va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value
	350	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
	351	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj)
	352	va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
[3]	353	ENDIF
	354	END DO
	355	END DO
[503]	356	!
[3294]	357	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
	358	!
[455]	359	END SUBROUTINE hpg_zps
[216]	360
[455]	361	SUBROUTINE hpg_sco( kt )
[3]	362	!!---------------------------------------------------------------------
[455]	363	!! * ROUTINE hpg_sco *
[3]	364	!!
[455]	365	!! ** Method : s-coordinate case. Jacobian scheme.
	366	!! The now hydrostatic pressure gradient at a given level, jk,
	367	!! is computed by taking the vertical integral of the in-situ
[3]	368	!! density gradient along the model level from the suface to that
[455]	369	!! level. s-coordinates (ln_sco): a corrective term is added
	370	!! to the horizontal pressure gradient :
	371	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
	372	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
[3]	373	!! add it to the general momentum trend (ua,va).
[455]	374	!! ua = ua - 1/e1u * zhpi
	375	!! va = va - 1/e2v * zhpj
[3]	376	!!
	377	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[503]	378	!!----------------------------------------------------------------------
	379	INTEGER, INTENT(in) :: kt ! ocean time-step index
	380	!!
[592]	381	INTEGER :: ji, jj, jk ! dummy loop indices
	382	REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars
[3764]	383	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3]	384	!!----------------------------------------------------------------------
[3294]	385	!
	386	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
	387	!
[3]	388	IF( kt == nit000 ) THEN
	389	IF(lwp) WRITE(numout,*)
[455]	390	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
	391	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
[3]	392	ENDIF
	393
[503]	394	! Local constant initialization
[2528]	395	zcoef0 = - grav * 0.5_wp
[592]	396	! To use density and not density anomaly
[2528]	397	IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
	398	ELSE ; znad = 0._wp ! Fixed volume
[592]	399	ENDIF
[455]	400
[503]	401	! Surface value
[455]	402	DO jj = 2, jpjm1
[3764]	403	DO ji = fs_2, fs_jpim1 ! vector opt.
[455]	404	! hydrostatic pressure gradient along s-surfaces
[592]	405	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) &
	406	& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
	407	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) &
	408	& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
[455]	409	! s-coordinate pressure gradient correction
[2528]	410	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
[455]	411	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
[2528]	412	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
[455]	413	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
	414	! add to the general momentum trend
	415	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap
	416	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap
[3764]	417	END DO
	418	END DO
	419
[503]	420	! interior value (2=<jk=<jpkm1)
[3764]	421	DO jk = 2, jpkm1
	422	DO jj = 2, jpjm1
	423	DO ji = fs_2, fs_jpim1 ! vector opt.
[455]	424	! hydrostatic pressure gradient along s-surfaces
[3764]	425	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
	426	& * ( fse3w(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) &
[592]	427	& - fse3w(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) )
[455]	428	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
[592]	429	& * ( fse3w(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) &
	430	& - fse3w(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) )
[455]	431	! s-coordinate pressure gradient correction
[2528]	432	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
[455]	433	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj)
[2528]	434	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
[455]	435	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj)
	436	! add to the general momentum trend
	437	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap
	438	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap
	439	END DO
	440	END DO
	441	END DO
[503]	442	!
[3294]	443	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
	444	!
[455]	445	END SUBROUTINE hpg_sco
	446
[5260]	447	SUBROUTINE hpg_isf( kt )
	448	!!---------------------------------------------------------------------
	449	!! * ROUTINE hpg_sco *
	450	!!
	451	!! ** Method : s-coordinate case. Jacobian scheme.
	452	!! The now hydrostatic pressure gradient at a given level, jk,
	453	!! is computed by taking the vertical integral of the in-situ
	454	!! density gradient along the model level from the suface to that
	455	!! level. s-coordinates (ln_sco): a corrective term is added
	456	!! to the horizontal pressure gradient :
	457	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
	458	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
	459	!! add it to the general momentum trend (ua,va).
	460	!! ua = ua - 1/e1u * zhpi
	461	!! va = va - 1/e2v * zhpj
	462	!! iceload is added and partial cell case are added to the top and bottom
	463	!!
	464	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
	465	!!----------------------------------------------------------------------
	466	INTEGER, INTENT(in) :: kt ! ocean time-step index
	467	!!
	468	INTEGER :: ji, jj, jk, iku, ikv, ikt, iktp1i, iktp1j ! dummy loop indices
	469	REAL(wp) :: zcoef0, zuap, zvap, znad, ze3wu, ze3wv, zuapint, zvapint, zhpjint, zhpiint, zdzwt, zdzwtjp1, zdzwtip1 ! temporary scalars
	470	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj, zrhd
	471	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop
	472	REAL(wp), POINTER, DIMENSION(:,:) :: ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj
	473	!!----------------------------------------------------------------------
	474	!
	475	CALL wrk_alloc( jpi,jpj, 2, ztstop)
	476	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
	477	CALL wrk_alloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
	478	!
	479	IF( kt == nit000 ) THEN
	480	IF(lwp) WRITE(numout,*)
	481	IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf'
	482	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
	483	ENDIF
	484
	485	! Local constant initialization
	486	zcoef0 = - grav * 0.5_wp
	487	! To use density and not density anomaly
	488	! IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
	489	! ELSE ; znad = 0._wp ! Fixed volume
	490	! ENDIF
	491	znad=1._wp
	492	! iniitialised to 0. zhpi zhpi
	493	zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp
	494
[5989]	495	! Partial steps: top & bottom before horizontal gradient
	496	!jc CALL zps_hde_isf( kt, jpts, tsn, gtsu, gtsv, gtui, gtvi, &
	497	!jc & rhd, gru , grv , aru , arv , gzu , gzv , ge3ru , ge3rv , &
	498	!jc & grui, grvi, arui, arvi, gzui, gzvi, ge3rui, ge3rvi )
	499
[5260]	500	!==================================================================================
	501	!=====Compute iceload and contribution of the half first wet layer =================
	502	!===================================================================================
	503
	504	! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude)
	505	ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp
	506
	507	! compute density of the water displaced by the ice shelf
	508	zrhd = rhd ! save rhd
	509	DO jk = 1, jpk
	510	zdept(:,:)=gdept_1d(jk)
	511	CALL eos(ztstop(:,:,:),zdept(:,:),rhd(:,:,jk))
	512	END DO
	513	WHERE ( tmask(:,:,:) == 1._wp)
	514	rhd(:,:,:) = zrhd(:,:,:) ! replace wet cell by the saved rhd
	515	END WHERE
	516
	517	! compute rhd at the ice/oce interface (ice shelf side)
	518	CALL eos(ztstop,risfdep,zrhdtop_isf)
	519
	520	! compute rhd at the ice/oce interface (ocean side)
	521	DO ji=1,jpi
	522	DO jj=1,jpj
	523	ikt=mikt(ji,jj)
	524	ztstop(ji,jj,1)=tsn(ji,jj,ikt,1)
	525	ztstop(ji,jj,2)=tsn(ji,jj,ikt,2)
	526	END DO
	527	END DO
	528	CALL eos(ztstop,risfdep,zrhdtop_oce)
	529	!
	530	! Surface value + ice shelf gradient
	531	! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v)
	532	ziceload = 0._wp
	533	DO jj = 1, jpj
	534	DO ji = 1, jpi ! vector opt.
	535	ikt=mikt(ji,jj)
	536	ziceload(ji,jj) = ziceload(ji,jj) + (znad + rhd(ji,jj,1) ) * fse3w(ji,jj,1) * (1._wp - tmask(ji,jj,1))
	537	DO jk=2,ikt-1
	538	ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + rhd(ji,jj,jk-1) + rhd(ji,jj,jk)) * fse3w(ji,jj,jk) &
	539	& * (1._wp - tmask(ji,jj,jk))
	540	END DO
	541	IF (ikt .GE. 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + rhd(ji,jj,ikt-1)) &
	542	& * ( risfdep(ji,jj) - gdept_1d(ikt-1) )
	543	END DO
	544	END DO
	545	riceload(:,:) = 0.0_wp ; riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5
	546	! compute zp from z=0 to first T wet point (correction due to zps not yet applied)
	547	DO jj = 2, jpjm1
	548	DO ji = fs_2, fs_jpim1 ! vector opt.
	549	ikt=mikt(ji,jj) ; iktp1i=mikt(ji+1,jj); iktp1j=mikt(ji,jj+1)
	550	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
	551	! we assume ISF is in isostatic equilibrium
	552	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * fse3w(ji+1,jj ,iktp1i) &
	553	& * ( 2._wp * znad + rhd(ji+1,jj ,iktp1i) + zrhdtop_oce(ji+1,jj ) ) &
	554	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
	555	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
	556	& + ( ziceload(ji+1,jj) - ziceload(ji,jj)) )
	557	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * fse3w(ji ,jj+1,iktp1j) &
	558	& * ( 2._wp * znad + rhd(ji ,jj+1,iktp1j) + zrhdtop_oce(ji ,jj+1) ) &
	559	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
	560	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
	561	& + ( ziceload(ji,jj+1) - ziceload(ji,jj) ) )
	562	! s-coordinate pressure gradient correction (=0 if z coordinate)
	563	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
	564	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
	565	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
	566	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
	567	! add to the general momentum trend
	568	ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
	569	va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
	570	END DO
	571	END DO
	572	!==================================================================================
	573	!===== Compute partial cell contribution for the top cell =========================
	574	!==================================================================================
	575	DO jj = 2, jpjm1
	576	DO ji = fs_2, fs_jpim1 ! vector opt.
	577	iku = miku(ji,jj) ;
	578	zpshpi(ji,jj)=0.0_wp ; zpshpj(ji,jj)=0.0_wp
	579	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))
	580	! u direction
	581	IF ( iku .GT. 1 ) THEN
	582	! case iku
	583	zhpi(ji,jj,iku) = zcoef0 / e1u(ji,jj) * ze3wu &
	584	& * ( rhd (ji+1,jj,iku) + rhd (ji,jj,iku) &
	585	& + SIGN(1._wp,ze3wu) * grui(ji,jj) + 2._wp * znad )
	586	! corrective term ( = 0 if z coordinate )
	587	zuap = -zcoef0 * ( arui(ji,jj) + 2._wp * znad ) * gzui(ji,jj) / e1u(ji,jj)
	588	! zhpi will be added in interior loop
	589	ua(ji,jj,iku) = ua(ji,jj,iku) + zuap
	590	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
	591	IF (mbku(ji,jj) == iku + 1) zpshpi(ji,jj) = zhpi(ji,jj,iku)
	592
	593	! case iku + 1 (remove the zphi term added in the interior loop and compute the one corrected for zps)
	594	zhpiint = zcoef0 / e1u(ji,jj) &
	595	& * ( fse3w(ji+1,jj ,iku+1) * ( (rhd(ji+1,jj,iku+1) + znad) &
	596	& + (rhd(ji+1,jj,iku ) + znad) ) * tmask(ji+1,jj,iku) &
	597	& - fse3w(ji ,jj ,iku+1) * ( (rhd(ji ,jj,iku+1) + znad) &
	598	& + (rhd(ji ,jj,iku ) + znad) ) * tmask(ji ,jj,iku) )
	599	zhpi(ji,jj,iku+1) = zcoef0 / e1u(ji,jj) * ge3rui(ji,jj) - zhpiint
	600	END IF
	601
	602	! v direction
	603	ikv = mikv(ji,jj)
	604	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))
	605	IF ( ikv .GT. 1 ) THEN
	606	! case ikv
	607	zhpj(ji,jj,ikv) = zcoef0 / e2v(ji,jj) * ze3wv &
	608	& * ( rhd(ji,jj+1,ikv) + rhd (ji,jj,ikv) &
	609	& + SIGN(1._wp,ze3wv) * grvi(ji,jj) + 2._wp * znad )
	610	! corrective term ( = 0 if z coordinate )
	611	zvap = -zcoef0 * ( arvi(ji,jj) + 2._wp * znad ) * gzvi(ji,jj) / e2v(ji,jj)
	612	! zhpi will be added in interior loop
	613	va(ji,jj,ikv) = va(ji,jj,ikv) + zvap
	614	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
	615	IF (mbkv(ji,jj) == ikv + 1) zpshpj(ji,jj) = zhpj(ji,jj,ikv)
	616
	617	! case ikv + 1 (remove the zphj term added in the interior loop and compute the one corrected for zps)
	618	zhpjint = zcoef0 / e2v(ji,jj) &
	619	& * ( fse3w(ji ,jj+1,ikv+1) * ( (rhd(ji,jj+1,ikv+1) + znad) &
	620	& + (rhd(ji,jj+1,ikv ) + znad) ) * tmask(ji,jj+1,ikv) &
	621	& - fse3w(ji ,jj ,ikv+1) * ( (rhd(ji,jj ,ikv+1) + znad) &
	622	& + (rhd(ji,jj ,ikv ) + znad) ) * tmask(ji,jj ,ikv) )
	623	zhpj(ji,jj,ikv+1) = zcoef0 / e2v(ji,jj) * ge3rvi(ji,jj) - zhpjint
	624	END IF
	625	END DO
	626	END DO
	627
	628	!==================================================================================
	629	!===== Compute interior value =====================================================
	630	!==================================================================================
	631
	632	DO jj = 2, jpjm1
	633	DO ji = fs_2, fs_jpim1 ! vector opt.
	634	iku=miku(ji,jj); ikv=mikv(ji,jj)
	635	DO jk = 2, jpkm1
	636	! hydrostatic pressure gradient along s-surfaces
	637	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
	638	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) + zhpi(ji,jj,jk-1) &
	639	& + zcoef0 / e1u(ji,jj) &
	640	& * ( fse3w(ji+1,jj ,jk) * ( (rhd(ji+1,jj,jk ) + znad) &
	641	& + (rhd(ji+1,jj,jk-1) + znad) ) * tmask(ji+1,jj,jk-1) &
	642	& - fse3w(ji ,jj ,jk) * ( (rhd(ji ,jj,jk ) + znad) &
	643	& + (rhd(ji ,jj,jk-1) + znad) ) * tmask(ji ,jj,jk-1) )
	644	! s-coordinate pressure gradient correction
	645	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
	646	zuap = - zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
	647	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) * umask(ji,jj,jk-1)
	648	ua(ji,jj,jk) = ua(ji,jj,jk) + ( zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
	649
	650	! hydrostatic pressure gradient along s-surfaces
	651	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
	652	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) + zhpj(ji,jj,jk-1) &
	653	& + zcoef0 / e2v(ji,jj) &
	654	& * ( fse3w(ji ,jj+1,jk) * ( (rhd(ji,jj+1,jk ) + znad) &
	655	& + (rhd(ji,jj+1,jk-1) + znad) ) * tmask(ji,jj+1,jk-1) &
	656	& - fse3w(ji ,jj ,jk) * ( (rhd(ji,jj ,jk ) + znad) &
	657	& + (rhd(ji,jj ,jk-1) + znad) ) * tmask(ji,jj ,jk-1) )
	658	! s-coordinate pressure gradient correction
	659	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
	660	zvap = - zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
	661	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) * vmask(ji,jj,jk-1)
	662	! add to the general momentum trend
	663	va(ji,jj,jk) = va(ji,jj,jk) + ( zhpj(ji,jj,jk) + zvap ) * vmask(ji,jj,jk)
	664	END DO
	665	END DO
	666	END DO
	667
	668	!==================================================================================
	669	!===== Compute bottom cell contribution (partial cell) ============================
	670	!==================================================================================
	671
	672	DO jj = 2, jpjm1
	673	DO ji = 2, jpim1
	674	iku = mbku(ji,jj)
	675	ikv = mbkv(ji,jj)
	676
	677	IF (iku .GT. 1) THEN
	678	! remove old value (interior case)
	679	zuap = -zcoef0 * ( rhd (ji+1,jj ,iku) + rhd (ji,jj,iku) + 2._wp * znad ) &
	680	& * ( fsde3w(ji+1,jj ,iku) - fsde3w(ji,jj,iku) ) / e1u(ji,jj)
	681	ua(ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) - zuap
	682	! put new value
	683	! -zpshpi to avoid double contribution of the partial step in the top layer
	684	zuap = -zcoef0 * ( aru(ji,jj) + 2._wp * znad ) * gzu(ji,jj) / e1u(ji,jj)
	685	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) + zcoef0 / e1u(ji,jj) * ge3ru(ji,jj) - zpshpi(ji,jj)
	686	ua(ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) + zuap
	687	END IF
	688	! v direction
	689	IF (ikv .GT. 1) THEN
	690	! remove old value (interior case)
	691	zvap = -zcoef0 * ( rhd (ji ,jj+1,ikv) + rhd (ji,jj,ikv) + 2._wp * znad ) &
	692	& * ( fsde3w(ji ,jj+1,ikv) - fsde3w(ji,jj,ikv) ) / e2v(ji,jj)
	693	va(ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) - zvap
	694	! put new value
	695	! -zpshpj to avoid double contribution of the partial step in the top layer
	696	zvap = -zcoef0 * ( arv(ji,jj) + 2._wp * znad ) * gzv(ji,jj) / e2v(ji,jj)
	697	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) + zcoef0 / e2v(ji,jj) * ge3rv(ji,jj) - zpshpj(ji,jj)
	698	va(ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) + zvap
	699	END IF
	700	END DO
	701	END DO
	702
	703	! set back to original density value into the ice shelf cell (maybe useless because it is masked)
	704	rhd = zrhd
	705	!
	706	CALL wrk_dealloc( jpi,jpj,2, ztstop)
	707	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
	708	CALL wrk_dealloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
	709	!
	710	END SUBROUTINE hpg_isf
	711
	712
[455]	713	SUBROUTINE hpg_djc( kt )
	714	!!---------------------------------------------------------------------
	715	!! * ROUTINE hpg_djc *
	716	!!
	717	!! ** Method : Density Jacobian with Cubic polynomial scheme
[3764]	718	!!
[503]	719	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
[455]	720	!!----------------------------------------------------------------------
[503]	721	INTEGER, INTENT(in) :: kt ! ocean time-step index
	722	!!
	723	INTEGER :: ji, jj, jk ! dummy loop indices
	724	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
	725	REAL(wp) :: z1_10, cffu, cffx ! " "
	726	REAL(wp) :: z1_12, cffv, cffy ! " "
[3764]	727	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3294]	728	REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw
	729	REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow
	730	REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k
[455]	731	!!----------------------------------------------------------------------
[3294]	732	!
[3764]	733	CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
	734	CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
	735	CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
[3294]	736	!
[455]	737
	738	IF( kt == nit000 ) THEN
	739	IF(lwp) WRITE(numout,*)
	740	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
	741	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
[216]	742	ENDIF
	743
[503]	744	! Local constant initialization
[2528]	745	zcoef0 = - grav * 0.5_wp
	746	z1_10 = 1._wp / 10._wp
	747	z1_12 = 1._wp / 12._wp
[455]	748
	749	!----------------------------------------------------------------------------------------
	750	! compute and store in provisional arrays elementary vertical and horizontal differences
	751	!----------------------------------------------------------------------------------------
	752
	753	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
	754
	755	DO jk = 2, jpkm1
	756	DO jj = 2, jpjm1
	757	DO ji = fs_2, fs_jpim1 ! vector opt.
	758	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
	759	dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1)
	760	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
	761	dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk )
	762	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
	763	dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk )
	764	END DO
	765	END DO
	766	END DO
	767
	768	!-------------------------------------------------------------------------
	769	! compute harmonic averages using eq. 5.18
	770	!-------------------------------------------------------------------------
	771	zep = 1.e-15
	772
[503]	773	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
	774	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
[455]	775
	776	DO jk = 2, jpkm1
	777	DO jj = 2, jpjm1
	778	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	779	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
[455]	780
[2528]	781	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
	782	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
[3764]	783
[2528]	784	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
	785	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
[455]	786
	787	IF( cffw > zep) THEN
[2528]	788	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
	789	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
[455]	790	ELSE
[2528]	791	drhow(ji,jj,jk) = 0._wp
[455]	792	ENDIF
	793
[2528]	794	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
	795	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
[455]	796
	797	IF( cffu > zep ) THEN
[2528]	798	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
	799	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
[455]	800	ELSE
[2528]	801	drhou(ji,jj,jk ) = 0._wp
[455]	802	ENDIF
	803
	804	IF( cffx > zep ) THEN
[2528]	805	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
	806	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
[455]	807	ELSE
[2528]	808	dzu(ji,jj,jk) = 0._wp
[455]	809	ENDIF
	810
	811	IF( cffv > zep ) THEN
[2528]	812	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
	813	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
[455]	814	ELSE
[2528]	815	drhov(ji,jj,jk) = 0._wp
[455]	816	ENDIF
	817
	818	IF( cffy > zep ) THEN
[2528]	819	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
	820	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
[455]	821	ELSE
[2528]	822	dzv(ji,jj,jk) = 0._wp
[455]	823	ENDIF
	824
	825	END DO
	826	END DO
	827	END DO
	828
	829	!----------------------------------------------------------------------------------
	830	! apply boundary conditions at top and bottom using 5.36-5.37
	831	!----------------------------------------------------------------------------------
[2528]	832	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
	833	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
	834	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
[455]	835
[2528]	836	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
	837	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
	838	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
[455]	839
	840
	841	!--------------------------------------------------------------
	842	! Upper half of top-most grid box, compute and store
	843	!-------------------------------------------------------------
	844
	845	!!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified
	846	! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
	847
	848	DO jj = 2, jpjm1
	849	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	850	rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) &
	851	& * ( rhd(ji,jj,1) &
	852	& + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) &
	853	& * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) &
[3764]	854	& / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) )
[455]	855	END DO
	856	END DO
	857
	858	!!bug gm : here also, simplification is possible
	859	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
	860
	861	DO jk = 2, jpkm1
	862	DO jj = 2, jpjm1
	863	DO ji = fs_2, fs_jpim1 ! vector opt.
	864
	865	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
	866	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) &
	867	& - grav * z1_10 * ( &
	868	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
	869	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
	870	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
	871	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
	872	& )
	873
	874	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
	875	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) &
	876	& - grav* z1_10 * ( &
	877	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
	878	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
	879	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
	880	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
	881	& )
	882
	883	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
	884	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) &
	885	& - grav* z1_10 * ( &
	886	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
	887	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
	888	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
	889	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
	890	& )
	891
	892	END DO
	893	END DO
	894	END DO
	895	CALL lbc_lnk(rho_k,'W',1.)
	896	CALL lbc_lnk(rho_i,'U',1.)
	897	CALL lbc_lnk(rho_j,'V',1.)
	898
	899
	900	! ---------------
	901	! Surface value
	902	! ---------------
	903	DO jj = 2, jpjm1
	904	DO ji = fs_2, fs_jpim1 ! vector opt.
	905	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj)
	906	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj)
	907	! add to the general momentum trend
	908	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
	909	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
	910	END DO
	911	END DO
	912
	913	! ----------------
	914	! interior value (2=<jk=<jpkm1)
	915	! ----------------
	916	DO jk = 2, jpkm1
[3764]	917	DO jj = 2, jpjm1
[455]	918	DO ji = fs_2, fs_jpim1 ! vector opt.
	919	! hydrostatic pressure gradient along s-surfaces
	920	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
	921	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
	922	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj)
	923	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
	924	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
	925	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj)
	926	! add to the general momentum trend
	927	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	928	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
	929	END DO
	930	END DO
	931	END DO
[503]	932	!
[3764]	933	CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
	934	CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
	935	CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
[2715]	936	!
[455]	937	END SUBROUTINE hpg_djc
	938
	939
[3294]	940	SUBROUTINE hpg_prj( kt )
[455]	941	!!---------------------------------------------------------------------
[3294]	942	!! * ROUTINE hpg_prj *
[455]	943	!!
[3294]	944	!! ** Method : s-coordinate case.
	945	!! A Pressure-Jacobian horizontal pressure gradient method
	946	!! based on the constrained cubic-spline interpolation for
	947	!! all vertical coordinate systems
[455]	948	!!
[3294]	949	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[455]	950	!!----------------------------------------------------------------------
[3294]	951	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
	952	INTEGER, INTENT(in) :: kt ! ocean time-step index
[503]	953	!!
[3294]	954	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
	955	REAL(wp) :: zcoef0, znad ! temporary scalars
[503]	956	!!
[3294]	957	!! The local variables for the correction term
	958	INTEGER :: jk1, jis, jid, jjs, jjd
	959	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
[3764]	960	REAL(wp) :: zrhdt1
[3294]	961	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
[3764]	962	REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh
[3294]	963	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
[5260]	964	REAL(wp), POINTER, DIMENSION(:,:) :: zsshu_n, zsshv_n
[455]	965	!!----------------------------------------------------------------------
[3294]	966	!
[3764]	967	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
	968	CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh )
[5260]	969	CALL wrk_alloc( jpi,jpj, zsshu_n, zsshv_n )
[3294]	970	!
[455]	971	IF( kt == nit000 ) THEN
	972	IF(lwp) WRITE(numout,*)
[3294]	973	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
	974	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
[3]	975	ENDIF
	976
[3294]	977	!!----------------------------------------------------------------------
	978	! Local constant initialization
[3764]	979	zcoef0 = - grav
[3294]	980	znad = 0.0_wp
	981	IF( lk_vvl ) znad = 1._wp
[3]	982
[3294]	983	! Clean 3-D work arrays
	984	zhpi(:,:,:) = 0._wp
	985	zrhh(:,:,:) = rhd(:,:,:)
[3764]	986
[3294]	987	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
	988	DO jj = 1, jpj
[3764]	989	DO ji = 1, jpi
[3294]	990	jk = mbathy(ji,jj)
	991	IF( jk <= 0 ) THEN; zrhh(ji,jj,:) = 0._wp
	992	ELSE IF(jk == 1) THEN; zrhh(ji,jj, jk+1:jpk) = rhd(ji,jj,jk)
	993	ELSE IF(jk < jpkm1) THEN
	994	DO jkk = jk+1, jpk
	995	zrhh(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1), &
	996	fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2))
[3764]	997	END DO
[3294]	998	ENDIF
	999	END DO
	1000	END DO
[3]	1001
[3632]	1002	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
[5260]	1003	DO jj = 1, jpj
	1004	DO ji = 1, jpi
	1005	zdept(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) - sshn(ji,jj) * znad
	1006	END DO
	1007	END DO
[455]	1008
[5260]	1009	DO jk = 2, jpk
	1010	DO jj = 1, jpj
	1011	DO ji = 1, jpi
	1012	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + fse3w(ji,jj,jk)
	1013	END DO
	1014	END DO
	1015	END DO
[455]	1016
[5260]	1017	fsp(:,:,:) = zrhh (:,:,:)
[3632]	1018	xsp(:,:,:) = zdept(:,:,:)
	1019
[3764]	1020	! Construct the vertical density profile with the
[3294]	1021	! constrained cubic spline interpolation
	1022	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
[3764]	1023	CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type)
[3294]	1024
	1025	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
	1026	DO jj = 2, jpj
[3764]	1027	DO ji = 2, jpi
[3632]	1028	zrhdt1 = zrhh(ji,jj,1) - interp3(zdept(ji,jj,1),asp(ji,jj,1), &
[3294]	1029	bsp(ji,jj,1), csp(ji,jj,1), &
[3632]	1030	dsp(ji,jj,1) ) * 0.25_wp * fse3w(ji,jj,1)
[3294]	1031
	1032	! assuming linear profile across the top half surface layer
[3764]	1033	zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * zrhdt1
[3294]	1034	END DO
[455]	1035	END DO
	1036
[3294]	1037	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
[3764]	1038	DO jk = 2, jpkm1
	1039	DO jj = 2, jpj
[3294]	1040	DO ji = 2, jpi
	1041	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
[3632]	1042	integ_spline(zdept(ji,jj,jk-1), zdept(ji,jj,jk),&
[3294]	1043	asp(ji,jj,jk-1), bsp(ji,jj,jk-1), &
	1044	csp(ji,jj,jk-1), dsp(ji,jj,jk-1))
	1045	END DO
	1046	END DO
[455]	1047	END DO
	1048
[3294]	1049	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
[5260]	1050
	1051	! Prepare zsshu_n and zsshv_n
[3764]	1052	DO jj = 2, jpjm1
	1053	DO ji = 2, jpim1
[5989]	1054	zsshu_n(ji,jj) = (e1e2u(ji,jj) * sshn(ji,jj) + e1e2u(ji+1, jj) * sshn(ji+1,jj)) * &
	1055	& r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
	1056	zsshv_n(ji,jj) = (e1e2v(ji,jj) * sshn(ji,jj) + e1e2v(ji+1, jj) * sshn(ji,jj+1)) * &
	1057	& r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
[3294]	1058	END DO
[455]	1059	END DO
	1060
[5260]	1061	DO jj = 2, jpjm1
	1062	DO ji = 2, jpim1
	1063	zu(ji,jj,1) = - ( fse3u(ji,jj,1) - zsshu_n(ji,jj) * znad)
	1064	zv(ji,jj,1) = - ( fse3v(ji,jj,1) - zsshv_n(ji,jj) * znad)
	1065	END DO
	1066	END DO
	1067
[3764]	1068	DO jk = 2, jpkm1
	1069	DO jj = 2, jpjm1
	1070	DO ji = 2, jpim1
[3294]	1071	zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk)
	1072	zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk)
	1073	END DO
	1074	END DO
[455]	1075	END DO
[3764]	1076
	1077	DO jk = 1, jpkm1
	1078	DO jj = 2, jpjm1
	1079	DO ji = 2, jpim1
[3294]	1080	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk)
	1081	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk)
	1082	END DO
	1083	END DO
	1084	END DO
[455]	1085
[3632]	1086	DO jk = 1, jpkm1
	1087	DO jj = 2, jpjm1
	1088	DO ji = 2, jpim1
	1089	zu(ji,jj,jk) = min(zu(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
	1090	zu(ji,jj,jk) = max(zu(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
	1091	zv(ji,jj,jk) = min(zv(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
	1092	zv(ji,jj,jk) = max(zv(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
	1093	END DO
	1094	END DO
	1095	END DO
	1096
	1097
[3764]	1098	DO jk = 1, jpkm1
	1099	DO jj = 2, jpjm1
	1100	DO ji = 2, jpim1
[3294]	1101	zpwes = 0._wp; zpwed = 0._wp
	1102	zpnss = 0._wp; zpnsd = 0._wp
	1103	zuijk = zu(ji,jj,jk)
	1104	zvijk = zv(ji,jj,jk)
	1105
	1106	!!!!! for u equation
	1107	IF( jk <= mbku(ji,jj) ) THEN
[3632]	1108	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
[3294]	1109	jis = ji + 1; jid = ji
	1110	ELSE
	1111	jis = ji; jid = ji +1
	1112	ENDIF
	1113
	1114	! integrate the pressure on the shallow side
[3764]	1115	jk1 = jk
[3632]	1116	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
[3294]	1117	IF( jk1 == mbku(ji,jj) ) THEN
[3632]	1118	zuijk = -zdept(jis,jj,jk1)
[3294]	1119	EXIT
	1120	ENDIF
[3632]	1121	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
[3764]	1122	zpwes = zpwes + &
[3632]	1123	integ_spline(zdept(jis,jj,jk1), zdeps, &
[3294]	1124	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
	1125	csp(jis,jj,jk1), dsp(jis,jj,jk1))
	1126	jk1 = jk1 + 1
	1127	END DO
[3764]	1128
[3294]	1129	! integrate the pressure on the deep side
[3764]	1130	jk1 = jk
[3632]	1131	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
[3294]	1132	IF( jk1 == 1 ) THEN
[3632]	1133	zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad)
	1134	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
	1135	bsp(jid,jj,1), csp(jid,jj,1), &
	1136	dsp(jid,jj,1)) * zdeps
	1137	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
[3294]	1138	EXIT
	1139	ENDIF
[3632]	1140	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
[3764]	1141	zpwed = zpwed + &
[3632]	1142	integ_spline(zdeps, zdept(jid,jj,jk1), &
[3294]	1143	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
	1144	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
	1145	jk1 = jk1 - 1
	1146	END DO
[3764]	1147
[3294]	1148	! update the momentum trends in u direction
	1149
	1150	zdpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk))
	1151	IF( lk_vvl ) THEN
[3764]	1152	zdpdx2 = zcoef0 / e1u(ji,jj) * &
	1153	( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) )
[3294]	1154	ELSE
[3764]	1155	zdpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
[3294]	1156	ENDIF
	1157
	1158	ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * &
	1159	& umask(ji,jj,jk) * tmask(ji,jj,jk) * tmask(ji+1,jj,jk)
	1160	ENDIF
[3764]	1161
[3294]	1162	!!!!! for v equation
	1163	IF( jk <= mbkv(ji,jj) ) THEN
[3632]	1164	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
[3294]	1165	jjs = jj + 1; jjd = jj
	1166	ELSE
	1167	jjs = jj ; jjd = jj + 1
	1168	ENDIF
	1169
	1170	! integrate the pressure on the shallow side
[3764]	1171	jk1 = jk
[3632]	1172	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
[3294]	1173	IF( jk1 == mbkv(ji,jj) ) THEN
[3632]	1174	zvijk = -zdept(ji,jjs,jk1)
[3294]	1175	EXIT
	1176	ENDIF
[3632]	1177	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
[3764]	1178	zpnss = zpnss + &
[3632]	1179	integ_spline(zdept(ji,jjs,jk1), zdeps, &
[3294]	1180	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
	1181	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
	1182	jk1 = jk1 + 1
	1183	END DO
[3764]	1184
[3294]	1185	! integrate the pressure on the deep side
[3764]	1186	jk1 = jk
[3632]	1187	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
[3294]	1188	IF( jk1 == 1 ) THEN
[3632]	1189	zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad)
	1190	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
	1191	bsp(ji,jjd,1), csp(ji,jjd,1), &
	1192	dsp(ji,jjd,1) ) * zdeps
	1193	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
[3294]	1194	EXIT
	1195	ENDIF
[3632]	1196	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
[3764]	1197	zpnsd = zpnsd + &
[3632]	1198	integ_spline(zdeps, zdept(ji,jjd,jk1), &
[3294]	1199	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
	1200	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
	1201	jk1 = jk1 - 1
	1202	END DO
	1203
[3764]	1204
[3294]	1205	! update the momentum trends in v direction
	1206
	1207	zdpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk))
	1208	IF( lk_vvl ) THEN
	1209	zdpdy2 = zcoef0 / e2v(ji,jj) * &
[3764]	1210	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) )
[3294]	1211	ELSE
[3764]	1212	zdpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
[3294]	1213	ENDIF
	1214
	1215	va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2)*&
	1216	& vmask(ji,jj,jk)tmask(ji,jj,jk)tmask(ji,jj+1,jk)
	1217	ENDIF
	1218
[3764]	1219
[3294]	1220	END DO
	1221	END DO
[455]	1222	END DO
[503]	1223	!
[3764]	1224	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
	1225	CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh )
[5260]	1226	CALL wrk_dealloc( jpi,jpj, zsshu_n, zsshv_n )
[2715]	1227	!
[3294]	1228	END SUBROUTINE hpg_prj
[455]	1229
[5260]	1230
[3294]	1231	SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type)
	1232	!!----------------------------------------------------------------------
	1233	!! * ROUTINE cspline *
[3764]	1234	!!
[3294]	1235	!! ** Purpose : constrained cubic spline interpolation
[3764]	1236	!!
	1237	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
[5260]	1238	!!
[3294]	1239	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
	1240	!!----------------------------------------------------------------------
	1241	IMPLICIT NONE
	1242	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate
[3764]	1243	REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of
[3294]	1244	! the interpoated function
[3764]	1245	INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline
[3294]	1246	! 2: Linear
[5260]	1247	!
[3294]	1248	INTEGER :: ji, jj, jk ! dummy loop indices
	1249	INTEGER :: jpi, jpj, jpkm1
	1250	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
	1251	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
	1252	REAL(wp) :: zdf(size(fsp,3))
	1253	!!----------------------------------------------------------------------
	1254
	1255	jpi = size(fsp,1)
	1256	jpj = size(fsp,2)
	1257	jpkm1 = size(fsp,3) - 1
	1258
[3764]	1259
[3294]	1260	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
	1261	DO ji = 1, jpi
	1262	DO jj = 1, jpj
[3764]	1263	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
[3294]	1264	! DO jk = 2, jpkm1-1
[3764]	1265	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
	1266	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1267	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
	1268	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
	1269	!
	1270	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
[3764]	1271	!
[3294]	1272	! IF(zdf1 * zdf2 <= 0._wp) THEN
	1273	! zdf(jk) = 0._wp
	1274	! ELSE
	1275	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
	1276	! ENDIF
	1277	! END DO
[3764]	1278
[3294]	1279	!!Simply geometric average
	1280	DO jk = 2, jpkm1-1
	1281	zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1))
	1282	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk))
[3764]	1283
[3294]	1284	IF(zdf1 * zdf2 <= 0._wp) THEN
	1285	zdf(jk) = 0._wp
	1286	ELSE
	1287	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
	1288	ENDIF
	1289	END DO
[3764]	1290
[3294]	1291	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
	1292	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
	1293	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
	1294	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - &
	1295	& 0.5_wp * zdf(jpkm1 - 1)
[3764]	1296
[3294]	1297	DO jk = 1, jpkm1 - 1
[3764]	1298	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1299	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
	1300	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
[3764]	1301	zddf1 = -2._wp * ztmp1 + ztmp2
[3294]	1302	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
[3764]	1303	zddf2 = 2._wp * ztmp1 - ztmp2
	1304
[3294]	1305	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
	1306	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
[3764]	1307	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
[3294]	1308	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
	1309	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
	1310	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
	1311	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
	1312	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
	1313	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
	1314	END DO
	1315	END DO
	1316	END DO
[3764]	1317
[3294]	1318	ELSE IF (polynomial_type == 2) THEN ! Linear
	1319	DO ji = 1, jpi
	1320	DO jj = 1, jpj
	1321	DO jk = 1, jpkm1-1
[3764]	1322	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1323	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
[3764]	1324
[3294]	1325	dsp(ji,jj,jk) = 0._wp
	1326	csp(ji,jj,jk) = 0._wp
	1327	bsp(ji,jj,jk) = ztmp1 / zdxtmp
	1328	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
	1329	END DO
	1330	END DO
	1331	END DO
	1332
	1333	ELSE
	1334	CALL ctl_stop( 'invalid polynomial type in cspline' )
	1335	ENDIF
	1336
	1337	END SUBROUTINE cspline
	1338
	1339
[3764]	1340	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
[3294]	1341	!!----------------------------------------------------------------------
	1342	!! * ROUTINE interp1 *
[3764]	1343	!!
[3294]	1344	!! ** Purpose : 1-d linear interpolation
[3764]	1345	!!
[5260]	1346	!! ** Method : interpolation is straight forward
[3764]	1347	!! extrapolation is also permitted (no value limit)
[3294]	1348	!!----------------------------------------------------------------------
	1349	IMPLICIT NONE
[3764]	1350	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
[3294]	1351	REAL(wp) :: f ! result of the interpolation (extrapolation)
	1352	REAL(wp) :: zdeltx
	1353	!!----------------------------------------------------------------------
	1354
	1355	zdeltx = xr - xl
	1356	IF(abs(zdeltx) <= 10._wp * EPSILON(x)) THEN
	1357	f = 0.5_wp * (fl + fr)
	1358	ELSE
	1359	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
	1360	ENDIF
[3764]	1361
[3294]	1362	END FUNCTION interp1
	1363
[5260]	1364
[3764]	1365	FUNCTION interp2(x, a, b, c, d) RESULT(f)
[3294]	1366	!!----------------------------------------------------------------------
	1367	!! * ROUTINE interp1 *
[3764]	1368	!!
[3294]	1369	!! ** Purpose : 1-d constrained cubic spline interpolation
[3764]	1370	!!
[3294]	1371	!! ** Method : cubic spline interpolation
	1372	!!
	1373	!!----------------------------------------------------------------------
	1374	IMPLICIT NONE
[3764]	1375	REAL(wp), INTENT(in) :: x, a, b, c, d
[3294]	1376	REAL(wp) :: f ! value from the interpolation
	1377	!!----------------------------------------------------------------------
	1378
[3764]	1379	f = a + x* ( b + x * ( c + d * x ) )
[3294]	1380
	1381	END FUNCTION interp2
	1382
	1383
[3764]	1384	FUNCTION interp3(x, a, b, c, d) RESULT(f)
[3294]	1385	!!----------------------------------------------------------------------
	1386	!! * ROUTINE interp1 *
[3764]	1387	!!
[3294]	1388	!! ** Purpose : Calculate the first order of deriavtive of
	1389	!! a cubic spline function y=a+bx+cx^2+d*x^3
[3764]	1390	!!
[3294]	1391	!! ** Method : f=dy/dx=b+2cx+3dx^2
	1392	!!
	1393	!!----------------------------------------------------------------------
	1394	IMPLICIT NONE
[3764]	1395	REAL(wp), INTENT(in) :: x, a, b, c, d
[3294]	1396	REAL(wp) :: f ! value from the interpolation
	1397	!!----------------------------------------------------------------------
	1398
	1399	f = b + x * ( 2._wp * c + 3._wp * d * x)
	1400
	1401	END FUNCTION interp3
	1402
[3764]	1403
	1404	FUNCTION integ_spline(xl, xr, a, b, c, d) RESULT(f)
[3294]	1405	!!----------------------------------------------------------------------
	1406	!! * ROUTINE interp1 *
[3764]	1407	!!
[3294]	1408	!! ** Purpose : 1-d constrained cubic spline integration
	1409	!!
[3764]	1410	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
	1411	!!
[3294]	1412	!!----------------------------------------------------------------------
	1413	IMPLICIT NONE
[3764]	1414	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
	1415	REAL(wp) :: za1, za2, za3
[3294]	1416	REAL(wp) :: f ! integration result
	1417	!!----------------------------------------------------------------------
	1418
[3764]	1419	za1 = 0.5_wp * b
	1420	za2 = c / 3.0_wp
	1421	za3 = 0.25_wp * d
[3294]	1422
	1423	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
	1424	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
	1425
[3632]	1426	END FUNCTION integ_spline
[3294]	1427
[3]	1428	!!======================================================================
	1429	END MODULE dynhpg
[3632]	1430

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