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dynhpg.F90 @ 10774

Last change on this file since 10774 was 10774, checked in by andmirek, 5 years ago
GMED 450 add flush after prints
File size: 71.6 KB

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[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
[5120]	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)
[5120]	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
[8400]	46	USE biaspar ! bias correction variables
[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)
[5120]	60	LOGICAL , PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf
[4147]	61	LOGICAL , PUBLIC :: ln_dynhpg_imp !: semi-implicite hpg flag
[455]	62
[3764]	63	INTEGER , PUBLIC :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM)
[455]	64
[3]	65	!! * Substitutions
	66	# include "domzgr_substitute.h90"
	67	# include "vectopt_loop_substitute.h90"
	68	!!----------------------------------------------------------------------
[2528]	69	!! NEMO/OPA 3.3 , NEMO Consortium (2010)
	70	!! $Id$
	71	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
[3]	72	!!----------------------------------------------------------------------
	73	CONTAINS
	74
	75	SUBROUTINE dyn_hpg( kt )
	76	!!---------------------------------------------------------------------
	77	!! * ROUTINE dyn_hpg *
	78	!!
[3764]	79	!! ** Method : Call the hydrostatic pressure gradient routine
[503]	80	!! using the scheme defined in the namelist
[3764]	81	!!
[455]	82	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[4990]	83	!! - send trends to trd_dyn for futher diagnostics (l_trddyn=T)
[503]	84	!!----------------------------------------------------------------------
	85	INTEGER, INTENT(in) :: kt ! ocean time-step index
[3294]	86	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdu, ztrdv
[8400]	87	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: z_rhd_st ! tmp density storage for pressure corr
	88	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: z_gru_st ! tmp ua trends storage for pressure corr
	89	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: z_grv_st ! tmp va trends storage for pressure corr
[455]	90	!!----------------------------------------------------------------------
[2528]	91	!
[3294]	92	IF( nn_timing == 1 ) CALL timing_start('dyn_hpg')
[2715]	93	!
[503]	94	IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn)
[3294]	95	CALL wrk_alloc( jpi,jpj,jpk, ztrdu, ztrdv )
[3764]	96	ztrdu(:,:,:) = ua(:,:,:)
	97	ztrdv(:,:,:) = va(:,:,:)
	98	ENDIF
[2528]	99	!
[8400]	100	IF ( ln_bias .AND. ln_bias_pc_app ) THEN
	101
	102	!Allocate space for tempory variables
	103	ALLOCATE( z_rhd_st(jpi,jpj,jpk), &
	104	& z_gru_st(jpi,jpj), &
	105	& z_grv_st(jpi,jpj) )
	106
	107	z_rhd_st(:,:,:) = rhd(:,:,:) ! store orig density
	108	rhd(:,:,:) = rhd_pc(:,:,:) ! use pressure corrected density
	109	z_gru_st(:,:) = gru(:,:)
	110	gru(:,:) = gru_pc(:,:)
	111	z_grv_st(:,:) = grv(:,:)
	112	grv(:,:) = grv_pc(:,:)
	113
	114	ENDIF
[8447]	115
[3294]	116	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
[503]	117	CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate
	118	CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation)
	119	CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation)
[3294]	120	CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial)
	121	CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme)
[5120]	122	CASE ( 5 ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf
[455]	123	END SELECT
[2528]	124	!
[503]	125	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
[455]	126	ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:)
	127	ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:)
[4990]	128	CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt )
[3294]	129	CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv )
[3764]	130	ENDIF
[503]	131	!
	132	IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, &
	133	& tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
	134	!
[8400]	135	IF ( ln_bias .AND. ln_bias_pc_app ) THEN
[8447]	136	IF(lwp) THEN
	137	WRITE(numout,*) " ! restore original density"
[10774]	138	IF(lflush) CALL flush(numout)
[8447]	139	ENDIF
[8400]	140	rhd(:,:,:) = z_rhd_st(:,:,:) ! restore original density
	141	gru(:,:) = z_gru_st(:,:)
	142	grv(:,:) = z_grv_st(:,:)
	143
	144	!Deallocate tempory variables
	145	DEALLOCATE( z_rhd_st, &
	146	& z_gru_st, &
	147	& z_grv_st )
	148	ENDIF
	149	!
[3294]	150	IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg')
[2715]	151	!
[455]	152	END SUBROUTINE dyn_hpg
	153
	154
[2528]	155	SUBROUTINE dyn_hpg_init
[455]	156	!!----------------------------------------------------------------------
[2528]	157	!! * ROUTINE dyn_hpg_init *
[455]	158	!!
	159	!! ** Purpose : initializations for the hydrostatic pressure gradient
	160	!! computation and consistency control
	161	!!
[1601]	162	!! ** Action : Read the namelist namdyn_hpg and check the consistency
[455]	163	!! with the type of vertical coordinate used (zco, zps, sco)
	164	!!----------------------------------------------------------------------
	165	INTEGER :: ioptio = 0 ! temporary integer
[4147]	166	INTEGER :: ios ! Local integer output status for namelist read
[1601]	167	!!
[3294]	168	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
[5120]	169	& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf, ln_dynhpg_imp
[455]	170	!!----------------------------------------------------------------------
[2528]	171	!
[4147]	172	REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient
	173	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
	174	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp )
	175
	176	REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient
	177	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
	178	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp )
[10759]	179	IF(lwm .AND. nprint > 2) WRITE ( numond, namdyn_hpg )
[2528]	180	!
	181	IF(lwp) THEN ! Control print
[455]	182	WRITE(numout,*)
[2528]	183	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
	184	WRITE(numout,*) '~~~~~~~~~~~~'
[1601]	185	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
	186	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
	187	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
	188	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
[5120]	189	WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf
[1601]	190	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
[3294]	191	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
[1601]	192	WRITE(numout,*) ' time stepping: centered (F) or semi-implicit (T) ln_dynhpg_imp = ', ln_dynhpg_imp
[10774]	193	IF(lflush) CALL flush(numout)
[455]	194	ENDIF
[2528]	195	!
[3294]	196	IF( ln_hpg_djc ) &
	197	& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method &
	198	& currently disabled (bugs under investigation). Please select &
	199	& either ln_hpg_sco or ln_hpg_prj instead')
[2528]	200	!
[5120]	201	IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) &
[3294]	202	& CALL ctl_stop('dyn_hpg_init : variable volume key_vvl requires:&
	203	& the standard jacobian formulation hpg_sco or &
	204	& the pressure jacobian formulation hpg_prj')
[5120]	205
	206	IF( ln_hpg_isf .AND. .NOT. ln_isfcav ) &
	207	& CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' )
	208	IF( .NOT. ln_hpg_isf .AND. ln_isfcav ) &
	209	& CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' )
[3294]	210	!
[503]	211	! ! Set nhpg from ln_hpg_... flags
[455]	212	IF( ln_hpg_zco ) nhpg = 0
	213	IF( ln_hpg_zps ) nhpg = 1
	214	IF( ln_hpg_sco ) nhpg = 2
[3294]	215	IF( ln_hpg_djc ) nhpg = 3
	216	IF( ln_hpg_prj ) nhpg = 4
[5120]	217	IF( ln_hpg_isf ) nhpg = 5
[2528]	218	!
[3294]	219	! ! Consistency check
[3764]	220	ioptio = 0
[455]	221	IF( ln_hpg_zco ) ioptio = ioptio + 1
	222	IF( ln_hpg_zps ) ioptio = ioptio + 1
	223	IF( ln_hpg_sco ) ioptio = ioptio + 1
	224	IF( ln_hpg_djc ) ioptio = ioptio + 1
[3294]	225	IF( ln_hpg_prj ) ioptio = ioptio + 1
[5120]	226	IF( ln_hpg_isf ) ioptio = ioptio + 1
[2715]	227	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
[5120]	228	!
	229	! initialisation of ice load
	230	riceload(:,:)=0.0
[503]	231	!
[2528]	232	END SUBROUTINE dyn_hpg_init
[455]	233
	234
	235	SUBROUTINE hpg_zco( kt )
	236	!!---------------------------------------------------------------------
	237	!! * ROUTINE hpg_zco *
	238	!!
	239	!! ** Method : z-coordinate case, levels are horizontal surfaces.
	240	!! The now hydrostatic pressure gradient at a given level, jk,
	241	!! is computed by taking the vertical integral of the in-situ
	242	!! density gradient along the model level from the suface to that
	243	!! level: zhpi = grav .....
	244	!! zhpj = grav .....
[3]	245	!! add it to the general momentum trend (ua,va).
[455]	246	!! ua = ua - 1/e1u * zhpi
	247	!! va = va - 1/e2v * zhpj
[3764]	248	!!
[3]	249	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[503]	250	!!----------------------------------------------------------------------
	251	INTEGER, INTENT(in) :: kt ! ocean time-step index
	252	!!
	253	INTEGER :: ji, jj, jk ! dummy loop indices
	254	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
[3764]	255	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3]	256	!!----------------------------------------------------------------------
[3764]	257	!
[3294]	258	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
	259	!
[3]	260	IF( kt == nit000 ) THEN
	261	IF(lwp) WRITE(numout,*)
[455]	262	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
	263	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
[10774]	264	IF(lwp .AND. lflush) CALL flush(numout)
[3]	265	ENDIF
	266
[3764]	267	zcoef0 = - grav * 0.5_wp ! Local constant initialization
	268
[455]	269	! Surface value
[3]	270	DO jj = 2, jpjm1
	271	DO ji = fs_2, fs_jpim1 ! vector opt.
[455]	272	zcoef1 = zcoef0 * fse3w(ji,jj,1)
	273	! hydrostatic pressure gradient
	274	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
	275	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
[3]	276	! add to the general momentum trend
[455]	277	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
	278	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
	279	END DO
	280	END DO
[3294]	281
[503]	282	!
[455]	283	! interior value (2=<jk=<jpkm1)
[3]	284	DO jk = 2, jpkm1
[455]	285	DO jj = 2, jpjm1
[3]	286	DO ji = fs_2, fs_jpim1 ! vector opt.
[455]	287	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
	288	! hydrostatic pressure gradient
	289	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
	290	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
	291	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
	292
	293	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
	294	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
	295	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
[3]	296	! add to the general momentum trend
[455]	297	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	298	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
[3]	299	END DO
	300	END DO
	301	END DO
[503]	302	!
[3294]	303	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
	304	!
[455]	305	END SUBROUTINE hpg_zco
[216]	306
[3]	307
[455]	308	SUBROUTINE hpg_zps( kt )
[3]	309	!!---------------------------------------------------------------------
[455]	310	!! * ROUTINE hpg_zps *
[3764]	311	!!
[455]	312	!! ** Method : z-coordinate plus partial steps case. blahblah...
[3764]	313	!!
[3]	314	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[3764]	315	!!----------------------------------------------------------------------
[503]	316	INTEGER, INTENT(in) :: kt ! ocean time-step index
	317	!!
	318	INTEGER :: ji, jj, jk ! dummy loop indices
	319	INTEGER :: iku, ikv ! temporary integers
	320	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
[3764]	321	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3]	322	!!----------------------------------------------------------------------
[3294]	323	!
	324	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
	325	!
[3]	326	IF( kt == nit000 ) THEN
	327	IF(lwp) WRITE(numout,*)
[455]	328	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
[503]	329	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
[10774]	330	IF(lwp .AND. lflush) CALL flush(numout)
[3]	331	ENDIF
	332
[3294]	333
[503]	334	! Local constant initialization
[2528]	335	zcoef0 = - grav * 0.5_wp
[3]	336
[2528]	337	! Surface value (also valid in partial step case)
[3]	338	DO jj = 2, jpjm1
	339	DO ji = fs_2, fs_jpim1 ! vector opt.
[170]	340	zcoef1 = zcoef0 * fse3w(ji,jj,1)
[3]	341	! hydrostatic pressure gradient
[455]	342	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
	343	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
[3]	344	! add to the general momentum trend
	345	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
	346	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
	347	END DO
	348	END DO
	349
[3294]	350
[503]	351	! interior value (2=<jk=<jpkm1)
[3]	352	DO jk = 2, jpkm1
	353	DO jj = 2, jpjm1
	354	DO ji = fs_2, fs_jpim1 ! vector opt.
[170]	355	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
[3]	356	! hydrostatic pressure gradient
	357	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
[455]	358	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
	359	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
[3]	360
	361	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
[455]	362	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
	363	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
[3]	364	! add to the general momentum trend
	365	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	366	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
[455]	367	END DO
[3]	368	END DO
	369	END DO
	370
[3294]	371
[2528]	372	! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
[3]	373	DO jj = 2, jpjm1
	374	DO ji = 2, jpim1
[2528]	375	iku = mbku(ji,jj)
	376	ikv = mbkv(ji,jj)
[3]	377	zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) )
	378	zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) )
[2528]	379	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
	380	ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value
	381	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
	382	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj)
	383	ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
[3]	384	ENDIF
[2528]	385	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
	386	va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value
	387	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
	388	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj)
	389	va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
[3]	390	ENDIF
	391	END DO
	392	END DO
[503]	393	!
[3294]	394	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
	395	!
[455]	396	END SUBROUTINE hpg_zps
[216]	397
[455]	398	SUBROUTINE hpg_sco( kt )
[3]	399	!!---------------------------------------------------------------------
[455]	400	!! * ROUTINE hpg_sco *
[3]	401	!!
[455]	402	!! ** Method : s-coordinate case. Jacobian scheme.
	403	!! The now hydrostatic pressure gradient at a given level, jk,
	404	!! is computed by taking the vertical integral of the in-situ
[3]	405	!! density gradient along the model level from the suface to that
[455]	406	!! level. s-coordinates (ln_sco): a corrective term is added
	407	!! to the horizontal pressure gradient :
	408	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
	409	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
[3]	410	!! add it to the general momentum trend (ua,va).
[455]	411	!! ua = ua - 1/e1u * zhpi
	412	!! va = va - 1/e2v * zhpj
[3]	413	!!
	414	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[503]	415	!!----------------------------------------------------------------------
	416	INTEGER, INTENT(in) :: kt ! ocean time-step index
	417	!!
[5120]	418	INTEGER :: ji, jj, jk ! dummy loop indices
	419	REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars
	420	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
	421	!!----------------------------------------------------------------------
	422	!
	423	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
	424	!
	425	IF( kt == nit000 ) THEN
	426	IF(lwp) WRITE(numout,*)
	427	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
	428	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
[10774]	429	IF(lwp .AND. lflush) CALL flush(numout)
[5120]	430	ENDIF
	431
	432	! Local constant initialization
	433	zcoef0 = - grav * 0.5_wp
	434	! To use density and not density anomaly
	435	IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
	436	ELSE ; znad = 0._wp ! Fixed volume
	437	ENDIF
	438
	439	! Surface value
	440	DO jj = 2, jpjm1
	441	DO ji = fs_2, fs_jpim1 ! vector opt.
	442	! hydrostatic pressure gradient along s-surfaces
	443	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) &
	444	& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
	445	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) &
	446	& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
	447	! s-coordinate pressure gradient correction
	448	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
	449	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
	450	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
	451	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
	452	! add to the general momentum trend
	453	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap
	454	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap
	455	END DO
	456	END DO
	457
	458	! interior value (2=<jk=<jpkm1)
	459	DO jk = 2, jpkm1
	460	DO jj = 2, jpjm1
	461	DO ji = fs_2, fs_jpim1 ! vector opt.
	462	! hydrostatic pressure gradient along s-surfaces
	463	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
	464	& * ( fse3w(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) &
	465	& - fse3w(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) )
	466	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
	467	& * ( fse3w(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) &
	468	& - fse3w(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) )
	469	! s-coordinate pressure gradient correction
	470	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
	471	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj)
	472	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
	473	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj)
	474	! add to the general momentum trend
	475	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap
	476	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap
	477	END DO
	478	END DO
	479	END DO
	480	!
	481	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
	482	!
	483	END SUBROUTINE hpg_sco
	484
	485	SUBROUTINE hpg_isf( kt )
	486	!!---------------------------------------------------------------------
	487	!! * ROUTINE hpg_sco *
	488	!!
	489	!! ** Method : s-coordinate case. Jacobian scheme.
	490	!! The now hydrostatic pressure gradient at a given level, jk,
	491	!! is computed by taking the vertical integral of the in-situ
	492	!! density gradient along the model level from the suface to that
	493	!! level. s-coordinates (ln_sco): a corrective term is added
	494	!! to the horizontal pressure gradient :
	495	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
	496	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
	497	!! add it to the general momentum trend (ua,va).
	498	!! ua = ua - 1/e1u * zhpi
	499	!! va = va - 1/e2v * zhpj
	500	!! iceload is added and partial cell case are added to the top and bottom
	501	!!
	502	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
	503	!!----------------------------------------------------------------------
	504	INTEGER, INTENT(in) :: kt ! ocean time-step index
	505	!!
[4990]	506	INTEGER :: ji, jj, jk, iku, ikv, ikt, iktp1i, iktp1j ! dummy loop indices
	507	REAL(wp) :: zcoef0, zuap, zvap, znad, ze3wu, ze3wv, zuapint, zvapint, zhpjint, zhpiint, zdzwt, zdzwtjp1, zdzwtip1 ! temporary scalars
	508	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj, zrhd
	509	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop
	510	REAL(wp), POINTER, DIMENSION(:,:) :: ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj
[3]	511	!!----------------------------------------------------------------------
[3294]	512	!
[4990]	513	CALL wrk_alloc( jpi,jpj, 2, ztstop)
	514	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
	515	CALL wrk_alloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
[3294]	516	!
[4990]	517	IF( kt == nit000 ) THEN
[3]	518	IF(lwp) WRITE(numout,*)
[5120]	519	IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf'
[455]	520	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
[10774]	521	IF(lwp .AND. lflush) CALL flush(numout)
[3]	522	ENDIF
	523
[503]	524	! Local constant initialization
[2528]	525	zcoef0 = - grav * 0.5_wp
[592]	526	! To use density and not density anomaly
[4990]	527	! IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
	528	! ELSE ; znad = 0._wp ! Fixed volume
	529	! ENDIF
	530	znad=1._wp
	531	! iniitialised to 0. zhpi zhpi
	532	zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp
[455]	533
[4990]	534	!==================================================================================
	535	!=====Compute iceload and contribution of the half first wet layer =================
	536	!===================================================================================
	537
	538	! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude)
	539	ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp
	540
	541	! compute density of the water displaced by the ice shelf
	542	zrhd = rhd ! save rhd
	543	DO jk = 1, jpk
	544	zdept(:,:)=gdept_1d(jk)
	545	CALL eos(ztstop(:,:,:),zdept(:,:),rhd(:,:,jk))
	546	END DO
	547	WHERE ( tmask(:,:,:) == 1._wp)
	548	rhd(:,:,:) = zrhd(:,:,:) ! replace wet cell by the saved rhd
	549	END WHERE
	550
	551	! compute rhd at the ice/oce interface (ice shelf side)
	552	CALL eos(ztstop,risfdep,zrhdtop_isf)
	553
	554	! compute rhd at the ice/oce interface (ocean side)
	555	DO ji=1,jpi
	556	DO jj=1,jpj
	557	ikt=mikt(ji,jj)
	558	ztstop(ji,jj,1)=tsn(ji,jj,ikt,1)
	559	ztstop(ji,jj,2)=tsn(ji,jj,ikt,2)
	560	END DO
	561	END DO
	562	CALL eos(ztstop,risfdep,zrhdtop_oce)
	563	!
	564	! Surface value + ice shelf gradient
	565	! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v)
	566	ziceload = 0._wp
	567	DO jj = 1, jpj
	568	DO ji = 1, jpi ! vector opt.
	569	ikt=mikt(ji,jj)
	570	ziceload(ji,jj) = ziceload(ji,jj) + (znad + rhd(ji,jj,1) ) * fse3w(ji,jj,1) * (1._wp - tmask(ji,jj,1))
	571	DO jk=2,ikt-1
	572	ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + rhd(ji,jj,jk-1) + rhd(ji,jj,jk)) * fse3w(ji,jj,jk) &
	573	& * (1._wp - tmask(ji,jj,jk))
	574	END DO
	575	IF (ikt .GE. 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + rhd(ji,jj,ikt-1)) &
	576	& * ( risfdep(ji,jj) - gdept_1d(ikt-1) )
	577	END DO
	578	END DO
	579	riceload(:,:) = 0.0_wp ; riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5
	580	! compute zp from z=0 to first T wet point (correction due to zps not yet applied)
[455]	581	DO jj = 2, jpjm1
[3764]	582	DO ji = fs_2, fs_jpim1 ! vector opt.
[4990]	583	ikt=mikt(ji,jj) ; iktp1i=mikt(ji+1,jj); iktp1j=mikt(ji,jj+1)
	584	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
	585	! we assume ISF is in isostatic equilibrium
	586	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * fse3w(ji+1,jj ,iktp1i) &
	587	& * ( 2._wp * znad + rhd(ji+1,jj ,iktp1i) + zrhdtop_oce(ji+1,jj ) ) &
	588	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
	589	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
	590	& + ( ziceload(ji+1,jj) - ziceload(ji,jj)) )
	591	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * fse3w(ji ,jj+1,iktp1j) &
	592	& * ( 2._wp * znad + rhd(ji ,jj+1,iktp1j) + zrhdtop_oce(ji ,jj+1) ) &
	593	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
	594	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
	595	& + ( ziceload(ji,jj+1) - ziceload(ji,jj) ) )
	596	! s-coordinate pressure gradient correction (=0 if z coordinate)
[2528]	597	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
[455]	598	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
[2528]	599	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
[455]	600	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
	601	! add to the general momentum trend
[4990]	602	ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
	603	va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
[3764]	604	END DO
	605	END DO
[4990]	606	!==================================================================================
	607	!===== Compute partial cell contribution for the top cell =========================
	608	!==================================================================================
	609	DO jj = 2, jpjm1
	610	DO ji = fs_2, fs_jpim1 ! vector opt.
	611	iku = miku(ji,jj) ;
	612	zpshpi(ji,jj)=0.0_wp ; zpshpj(ji,jj)=0.0_wp
	613	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))
	614	! u direction
	615	IF ( iku .GT. 1 ) THEN
	616	! case iku
	617	zhpi(ji,jj,iku) = zcoef0 / e1u(ji,jj) * ze3wu &
	618	& * ( rhd (ji+1,jj,iku) + rhd (ji,jj,iku) &
	619	& + SIGN(1._wp,ze3wu) * grui(ji,jj) + 2._wp * znad )
	620	! corrective term ( = 0 if z coordinate )
	621	zuap = -zcoef0 * ( arui(ji,jj) + 2._wp * znad ) * gzui(ji,jj) / e1u(ji,jj)
	622	! zhpi will be added in interior loop
	623	ua(ji,jj,iku) = ua(ji,jj,iku) + zuap
	624	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
	625	IF (mbku(ji,jj) == iku + 1) zpshpi(ji,jj) = zhpi(ji,jj,iku)
[3764]	626
[4990]	627	! case iku + 1 (remove the zphi term added in the interior loop and compute the one corrected for zps)
	628	zhpiint = zcoef0 / e1u(ji,jj) &
	629	& * ( fse3w(ji+1,jj ,iku+1) * ( (rhd(ji+1,jj,iku+1) + znad) &
	630	& + (rhd(ji+1,jj,iku ) + znad) ) * tmask(ji+1,jj,iku) &
	631	& - fse3w(ji ,jj ,iku+1) * ( (rhd(ji ,jj,iku+1) + znad) &
	632	& + (rhd(ji ,jj,iku ) + znad) ) * tmask(ji ,jj,iku) )
	633	zhpi(ji,jj,iku+1) = zcoef0 / e1u(ji,jj) * ge3rui(ji,jj) - zhpiint
	634	END IF
	635
	636	! v direction
	637	ikv = mikv(ji,jj)
	638	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))
	639	IF ( ikv .GT. 1 ) THEN
	640	! case ikv
	641	zhpj(ji,jj,ikv) = zcoef0 / e2v(ji,jj) * ze3wv &
	642	& * ( rhd(ji,jj+1,ikv) + rhd (ji,jj,ikv) &
	643	& + SIGN(1._wp,ze3wv) * grvi(ji,jj) + 2._wp * znad )
	644	! corrective term ( = 0 if z coordinate )
	645	zvap = -zcoef0 * ( arvi(ji,jj) + 2._wp * znad ) * gzvi(ji,jj) / e2v(ji,jj)
	646	! zhpi will be added in interior loop
	647	va(ji,jj,ikv) = va(ji,jj,ikv) + zvap
	648	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
	649	IF (mbkv(ji,jj) == ikv + 1) zpshpj(ji,jj) = zhpj(ji,jj,ikv)
	650
	651	! case ikv + 1 (remove the zphj term added in the interior loop and compute the one corrected for zps)
	652	zhpjint = zcoef0 / e2v(ji,jj) &
	653	& * ( fse3w(ji ,jj+1,ikv+1) * ( (rhd(ji,jj+1,ikv+1) + znad) &
	654	& + (rhd(ji,jj+1,ikv ) + znad) ) * tmask(ji,jj+1,ikv) &
	655	& - fse3w(ji ,jj ,ikv+1) * ( (rhd(ji,jj ,ikv+1) + znad) &
	656	& + (rhd(ji,jj ,ikv ) + znad) ) * tmask(ji,jj ,ikv) )
	657	zhpj(ji,jj,ikv+1) = zcoef0 / e2v(ji,jj) * ge3rvi(ji,jj) - zhpjint
	658	END IF
	659	END DO
	660	END DO
	661
	662	!==================================================================================
	663	!===== Compute interior value =====================================================
	664	!==================================================================================
	665
	666	DO jj = 2, jpjm1
	667	DO ji = fs_2, fs_jpim1 ! vector opt.
	668	iku=miku(ji,jj); ikv=mikv(ji,jj)
	669	DO jk = 2, jpkm1
[455]	670	! hydrostatic pressure gradient along s-surfaces
[4990]	671	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
	672	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) + zhpi(ji,jj,jk-1) &
	673	& + zcoef0 / e1u(ji,jj) &
	674	& * ( fse3w(ji+1,jj ,jk) * ( (rhd(ji+1,jj,jk ) + znad) &
	675	& + (rhd(ji+1,jj,jk-1) + znad) ) * tmask(ji+1,jj,jk-1) &
	676	& - fse3w(ji ,jj ,jk) * ( (rhd(ji ,jj,jk ) + znad) &
	677	& + (rhd(ji ,jj,jk-1) + znad) ) * tmask(ji ,jj,jk-1) )
[455]	678	! s-coordinate pressure gradient correction
[4990]	679	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
	680	zuap = - zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
	681	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) * umask(ji,jj,jk-1)
	682	ua(ji,jj,jk) = ua(ji,jj,jk) + ( zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
	683
	684	! hydrostatic pressure gradient along s-surfaces
	685	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
	686	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) + zhpj(ji,jj,jk-1) &
	687	& + zcoef0 / e2v(ji,jj) &
	688	& * ( fse3w(ji ,jj+1,jk) * ( (rhd(ji,jj+1,jk ) + znad) &
	689	& + (rhd(ji,jj+1,jk-1) + znad) ) * tmask(ji,jj+1,jk-1) &
	690	& - fse3w(ji ,jj ,jk) * ( (rhd(ji,jj ,jk ) + znad) &
	691	& + (rhd(ji,jj ,jk-1) + znad) ) * tmask(ji,jj ,jk-1) )
	692	! s-coordinate pressure gradient correction
	693	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
	694	zvap = - zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
	695	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) * vmask(ji,jj,jk-1)
[455]	696	! add to the general momentum trend
[4990]	697	va(ji,jj,jk) = va(ji,jj,jk) + ( zhpj(ji,jj,jk) + zvap ) * vmask(ji,jj,jk)
[455]	698	END DO
	699	END DO
	700	END DO
[4990]	701
	702	!==================================================================================
	703	!===== Compute bottom cell contribution (partial cell) ============================
	704	!==================================================================================
	705
	706	DO jj = 2, jpjm1
	707	DO ji = 2, jpim1
	708	iku = mbku(ji,jj)
	709	ikv = mbkv(ji,jj)
	710
	711	IF (iku .GT. 1) THEN
	712	! remove old value (interior case)
	713	zuap = -zcoef0 * ( rhd (ji+1,jj ,iku) + rhd (ji,jj,iku) + 2._wp * znad ) &
	714	& * ( fsde3w(ji+1,jj ,iku) - fsde3w(ji,jj,iku) ) / e1u(ji,jj)
	715	ua(ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) - zuap
	716	! put new value
	717	! -zpshpi to avoid double contribution of the partial step in the top layer
	718	zuap = -zcoef0 * ( aru(ji,jj) + 2._wp * znad ) * gzu(ji,jj) / e1u(ji,jj)
	719	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) + zcoef0 / e1u(ji,jj) * ge3ru(ji,jj) - zpshpi(ji,jj)
	720	ua(ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) + zuap
	721	END IF
	722	! v direction
	723	IF (ikv .GT. 1) THEN
	724	! remove old value (interior case)
	725	zvap = -zcoef0 * ( rhd (ji ,jj+1,ikv) + rhd (ji,jj,ikv) + 2._wp * znad ) &
	726	& * ( fsde3w(ji ,jj+1,ikv) - fsde3w(ji,jj,ikv) ) / e2v(ji,jj)
	727	va(ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) - zvap
	728	! put new value
	729	! -zpshpj to avoid double contribution of the partial step in the top layer
	730	zvap = -zcoef0 * ( arv(ji,jj) + 2._wp * znad ) * gzv(ji,jj) / e2v(ji,jj)
	731	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) + zcoef0 / e2v(ji,jj) * ge3rv(ji,jj) - zpshpj(ji,jj)
	732	va(ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) + zvap
	733	END IF
	734	END DO
	735	END DO
	736
	737	! set back to original density value into the ice shelf cell (maybe useless because it is masked)
	738	rhd = zrhd
[503]	739	!
[4990]	740	CALL wrk_dealloc( jpi,jpj,2, ztstop)
	741	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
	742	CALL wrk_dealloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
[3294]	743	!
[5120]	744	END SUBROUTINE hpg_isf
[455]	745
[4990]	746
[455]	747	SUBROUTINE hpg_djc( kt )
	748	!!---------------------------------------------------------------------
	749	!! * ROUTINE hpg_djc *
	750	!!
	751	!! ** Method : Density Jacobian with Cubic polynomial scheme
[3764]	752	!!
[503]	753	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
[455]	754	!!----------------------------------------------------------------------
[503]	755	INTEGER, INTENT(in) :: kt ! ocean time-step index
	756	!!
	757	INTEGER :: ji, jj, jk ! dummy loop indices
	758	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
	759	REAL(wp) :: z1_10, cffu, cffx ! " "
	760	REAL(wp) :: z1_12, cffv, cffy ! " "
[3764]	761	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3294]	762	REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw
	763	REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow
	764	REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k
[455]	765	!!----------------------------------------------------------------------
[3294]	766	!
[3764]	767	CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
	768	CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
	769	CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
[3294]	770	!
[455]	771
	772	IF( kt == nit000 ) THEN
	773	IF(lwp) WRITE(numout,*)
	774	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
	775	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
[10774]	776	IF(lwp .AND. lflush) CALL flush(numout)
[216]	777	ENDIF
	778
[503]	779	! Local constant initialization
[2528]	780	zcoef0 = - grav * 0.5_wp
	781	z1_10 = 1._wp / 10._wp
	782	z1_12 = 1._wp / 12._wp
[455]	783
	784	!----------------------------------------------------------------------------------------
	785	! compute and store in provisional arrays elementary vertical and horizontal differences
	786	!----------------------------------------------------------------------------------------
	787
	788	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
	789
	790	DO jk = 2, jpkm1
	791	DO jj = 2, jpjm1
	792	DO ji = fs_2, fs_jpim1 ! vector opt.
	793	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
	794	dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1)
	795	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
	796	dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk )
	797	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
	798	dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk )
	799	END DO
	800	END DO
	801	END DO
	802
	803	!-------------------------------------------------------------------------
	804	! compute harmonic averages using eq. 5.18
	805	!-------------------------------------------------------------------------
	806	zep = 1.e-15
	807
[503]	808	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
	809	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
[455]	810
	811	DO jk = 2, jpkm1
	812	DO jj = 2, jpjm1
	813	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	814	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
[455]	815
[2528]	816	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
	817	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
[3764]	818
[2528]	819	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
	820	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
[455]	821
	822	IF( cffw > zep) THEN
[2528]	823	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
	824	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
[455]	825	ELSE
[2528]	826	drhow(ji,jj,jk) = 0._wp
[455]	827	ENDIF
	828
[2528]	829	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
	830	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
[455]	831
	832	IF( cffu > zep ) THEN
[2528]	833	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
	834	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
[455]	835	ELSE
[2528]	836	drhou(ji,jj,jk ) = 0._wp
[455]	837	ENDIF
	838
	839	IF( cffx > zep ) THEN
[2528]	840	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
	841	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
[455]	842	ELSE
[2528]	843	dzu(ji,jj,jk) = 0._wp
[455]	844	ENDIF
	845
	846	IF( cffv > zep ) THEN
[2528]	847	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
	848	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
[455]	849	ELSE
[2528]	850	drhov(ji,jj,jk) = 0._wp
[455]	851	ENDIF
	852
	853	IF( cffy > zep ) THEN
[2528]	854	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
	855	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
[455]	856	ELSE
[2528]	857	dzv(ji,jj,jk) = 0._wp
[455]	858	ENDIF
	859
	860	END DO
	861	END DO
	862	END DO
	863
	864	!----------------------------------------------------------------------------------
	865	! apply boundary conditions at top and bottom using 5.36-5.37
	866	!----------------------------------------------------------------------------------
[2528]	867	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
	868	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
	869	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
[455]	870
[2528]	871	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
	872	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
	873	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
[455]	874
	875
	876	!--------------------------------------------------------------
	877	! Upper half of top-most grid box, compute and store
	878	!-------------------------------------------------------------
	879
	880	!!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified
	881	! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
	882
	883	DO jj = 2, jpjm1
	884	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	885	rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) &
	886	& * ( rhd(ji,jj,1) &
	887	& + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) &
	888	& * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) &
[3764]	889	& / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) )
[455]	890	END DO
	891	END DO
	892
	893	!!bug gm : here also, simplification is possible
	894	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
	895
	896	DO jk = 2, jpkm1
	897	DO jj = 2, jpjm1
	898	DO ji = fs_2, fs_jpim1 ! vector opt.
	899
	900	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
	901	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) &
	902	& - grav * z1_10 * ( &
	903	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
	904	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
	905	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
	906	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
	907	& )
	908
	909	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
	910	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) &
	911	& - grav* z1_10 * ( &
	912	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
	913	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
	914	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
	915	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
	916	& )
	917
	918	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
	919	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) &
	920	& - grav* z1_10 * ( &
	921	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
	922	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
	923	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
	924	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
	925	& )
	926
	927	END DO
	928	END DO
	929	END DO
	930	CALL lbc_lnk(rho_k,'W',1.)
	931	CALL lbc_lnk(rho_i,'U',1.)
	932	CALL lbc_lnk(rho_j,'V',1.)
	933
	934
	935	! ---------------
	936	! Surface value
	937	! ---------------
	938	DO jj = 2, jpjm1
	939	DO ji = fs_2, fs_jpim1 ! vector opt.
	940	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj)
	941	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj)
	942	! add to the general momentum trend
	943	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
	944	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
	945	END DO
	946	END DO
	947
	948	! ----------------
	949	! interior value (2=<jk=<jpkm1)
	950	! ----------------
	951	DO jk = 2, jpkm1
[3764]	952	DO jj = 2, jpjm1
[455]	953	DO ji = fs_2, fs_jpim1 ! vector opt.
	954	! hydrostatic pressure gradient along s-surfaces
	955	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
	956	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
	957	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj)
	958	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
	959	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
	960	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj)
	961	! add to the general momentum trend
	962	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	963	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
	964	END DO
	965	END DO
	966	END DO
[503]	967	!
[3764]	968	CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
	969	CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
	970	CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
[2715]	971	!
[455]	972	END SUBROUTINE hpg_djc
	973
	974
[3294]	975	SUBROUTINE hpg_prj( kt )
[455]	976	!!---------------------------------------------------------------------
[3294]	977	!! * ROUTINE hpg_prj *
[455]	978	!!
[3294]	979	!! ** Method : s-coordinate case.
	980	!! A Pressure-Jacobian horizontal pressure gradient method
	981	!! based on the constrained cubic-spline interpolation for
	982	!! all vertical coordinate systems
[455]	983	!!
[3294]	984	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[455]	985	!!----------------------------------------------------------------------
[3294]	986	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
	987	INTEGER, INTENT(in) :: kt ! ocean time-step index
[503]	988	!!
[3294]	989	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
	990	REAL(wp) :: zcoef0, znad ! temporary scalars
[503]	991	!!
[3294]	992	!! The local variables for the correction term
	993	INTEGER :: jk1, jis, jid, jjs, jjd
	994	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
[3764]	995	REAL(wp) :: zrhdt1
[3294]	996	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
[3764]	997	REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh
[3294]	998	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
[5224]	999	REAL(wp), POINTER, DIMENSION(:,:) :: zsshu_n, zsshv_n
[455]	1000	!!----------------------------------------------------------------------
[3294]	1001	!
[3764]	1002	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
	1003	CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh )
[5224]	1004	CALL wrk_alloc( jpi,jpj, zsshu_n, zsshv_n )
[3294]	1005	!
[455]	1006	IF( kt == nit000 ) THEN
	1007	IF(lwp) WRITE(numout,*)
[3294]	1008	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
	1009	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
[10774]	1010	IF(lwp .AND. lflush) CALL flush(numout)
[3]	1011	ENDIF
	1012
[3294]	1013	!!----------------------------------------------------------------------
	1014	! Local constant initialization
[3764]	1015	zcoef0 = - grav
[3294]	1016	znad = 0.0_wp
	1017	IF( lk_vvl ) znad = 1._wp
[3]	1018
[3294]	1019	! Clean 3-D work arrays
	1020	zhpi(:,:,:) = 0._wp
	1021	zrhh(:,:,:) = rhd(:,:,:)
[3764]	1022
[3294]	1023	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
	1024	DO jj = 1, jpj
[3764]	1025	DO ji = 1, jpi
[3294]	1026	jk = mbathy(ji,jj)
	1027	IF( jk <= 0 ) THEN; zrhh(ji,jj,:) = 0._wp
	1028	ELSE IF(jk == 1) THEN; zrhh(ji,jj, jk+1:jpk) = rhd(ji,jj,jk)
	1029	ELSE IF(jk < jpkm1) THEN
	1030	DO jkk = jk+1, jpk
	1031	zrhh(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1), &
	1032	fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2))
[3764]	1033	END DO
[3294]	1034	ENDIF
	1035	END DO
	1036	END DO
[3]	1037
[3632]	1038	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
[4990]	1039	DO jj = 1, jpj
	1040	DO ji = 1, jpi
	1041	zdept(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) - sshn(ji,jj) * znad
	1042	END DO
	1043	END DO
[455]	1044
[4990]	1045	DO jk = 2, jpk
	1046	DO jj = 1, jpj
	1047	DO ji = 1, jpi
	1048	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + fse3w(ji,jj,jk)
	1049	END DO
	1050	END DO
	1051	END DO
[455]	1052
[4990]	1053	fsp(:,:,:) = zrhh (:,:,:)
[3632]	1054	xsp(:,:,:) = zdept(:,:,:)
	1055
[3764]	1056	! Construct the vertical density profile with the
[3294]	1057	! constrained cubic spline interpolation
	1058	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
[3764]	1059	CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type)
[3294]	1060
	1061	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
	1062	DO jj = 2, jpj
[3764]	1063	DO ji = 2, jpi
[3632]	1064	zrhdt1 = zrhh(ji,jj,1) - interp3(zdept(ji,jj,1),asp(ji,jj,1), &
[3294]	1065	bsp(ji,jj,1), csp(ji,jj,1), &
[3632]	1066	dsp(ji,jj,1) ) * 0.25_wp * fse3w(ji,jj,1)
[3294]	1067
	1068	! assuming linear profile across the top half surface layer
[3764]	1069	zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * zrhdt1
[3294]	1070	END DO
[455]	1071	END DO
	1072
[3294]	1073	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
[3764]	1074	DO jk = 2, jpkm1
	1075	DO jj = 2, jpj
[3294]	1076	DO ji = 2, jpi
	1077	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
[3632]	1078	integ_spline(zdept(ji,jj,jk-1), zdept(ji,jj,jk),&
[3294]	1079	asp(ji,jj,jk-1), bsp(ji,jj,jk-1), &
	1080	csp(ji,jj,jk-1), dsp(ji,jj,jk-1))
	1081	END DO
	1082	END DO
[455]	1083	END DO
	1084
[3294]	1085	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
[5224]	1086
	1087	! Prepare zsshu_n and zsshv_n
[3764]	1088	DO jj = 2, jpjm1
	1089	DO ji = 2, jpim1
[5224]	1090	zsshu_n(ji,jj) = (e12u(ji,jj) * sshn(ji,jj) + e12u(ji+1, jj) * sshn(ji+1,jj)) * &
	1091	& r1_e12u(ji,jj) * umask(ji,jj,1) * 0.5_wp
	1092	zsshv_n(ji,jj) = (e12v(ji,jj) * sshn(ji,jj) + e12v(ji+1, jj) * sshn(ji,jj+1)) * &
	1093	& r1_e12v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
[3294]	1094	END DO
[455]	1095	END DO
	1096
[5224]	1097	DO jj = 2, jpjm1
	1098	DO ji = 2, jpim1
	1099	zu(ji,jj,1) = - ( fse3u(ji,jj,1) - zsshu_n(ji,jj) * znad)
	1100	zv(ji,jj,1) = - ( fse3v(ji,jj,1) - zsshv_n(ji,jj) * znad)
	1101	END DO
	1102	END DO
	1103
[3764]	1104	DO jk = 2, jpkm1
	1105	DO jj = 2, jpjm1
	1106	DO ji = 2, jpim1
[3294]	1107	zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk)
	1108	zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk)
	1109	END DO
	1110	END DO
[455]	1111	END DO
[3764]	1112
	1113	DO jk = 1, jpkm1
	1114	DO jj = 2, jpjm1
	1115	DO ji = 2, jpim1
[3294]	1116	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk)
	1117	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk)
	1118	END DO
	1119	END DO
	1120	END DO
[455]	1121
[3632]	1122	DO jk = 1, jpkm1
	1123	DO jj = 2, jpjm1
	1124	DO ji = 2, jpim1
	1125	zu(ji,jj,jk) = min(zu(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
	1126	zu(ji,jj,jk) = max(zu(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
	1127	zv(ji,jj,jk) = min(zv(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
	1128	zv(ji,jj,jk) = max(zv(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
	1129	END DO
	1130	END DO
	1131	END DO
	1132
	1133
[3764]	1134	DO jk = 1, jpkm1
	1135	DO jj = 2, jpjm1
	1136	DO ji = 2, jpim1
[3294]	1137	zpwes = 0._wp; zpwed = 0._wp
	1138	zpnss = 0._wp; zpnsd = 0._wp
	1139	zuijk = zu(ji,jj,jk)
	1140	zvijk = zv(ji,jj,jk)
	1141
	1142	!!!!! for u equation
	1143	IF( jk <= mbku(ji,jj) ) THEN
[3632]	1144	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
[3294]	1145	jis = ji + 1; jid = ji
	1146	ELSE
	1147	jis = ji; jid = ji +1
	1148	ENDIF
	1149
	1150	! integrate the pressure on the shallow side
[3764]	1151	jk1 = jk
[3632]	1152	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
[3294]	1153	IF( jk1 == mbku(ji,jj) ) THEN
[3632]	1154	zuijk = -zdept(jis,jj,jk1)
[3294]	1155	EXIT
	1156	ENDIF
[3632]	1157	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
[3764]	1158	zpwes = zpwes + &
[3632]	1159	integ_spline(zdept(jis,jj,jk1), zdeps, &
[3294]	1160	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
	1161	csp(jis,jj,jk1), dsp(jis,jj,jk1))
	1162	jk1 = jk1 + 1
	1163	END DO
[3764]	1164
[3294]	1165	! integrate the pressure on the deep side
[3764]	1166	jk1 = jk
[3632]	1167	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
[3294]	1168	IF( jk1 == 1 ) THEN
[3632]	1169	zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad)
	1170	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
	1171	bsp(jid,jj,1), csp(jid,jj,1), &
	1172	dsp(jid,jj,1)) * zdeps
	1173	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
[3294]	1174	EXIT
	1175	ENDIF
[3632]	1176	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
[3764]	1177	zpwed = zpwed + &
[3632]	1178	integ_spline(zdeps, zdept(jid,jj,jk1), &
[3294]	1179	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
	1180	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
	1181	jk1 = jk1 - 1
	1182	END DO
[3764]	1183
[3294]	1184	! update the momentum trends in u direction
	1185
	1186	zdpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk))
	1187	IF( lk_vvl ) THEN
[3764]	1188	zdpdx2 = zcoef0 / e1u(ji,jj) * &
	1189	( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) )
[3294]	1190	ELSE
[3764]	1191	zdpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
[3294]	1192	ENDIF
	1193
	1194	ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * &
	1195	& umask(ji,jj,jk) * tmask(ji,jj,jk) * tmask(ji+1,jj,jk)
	1196	ENDIF
[3764]	1197
[3294]	1198	!!!!! for v equation
	1199	IF( jk <= mbkv(ji,jj) ) THEN
[3632]	1200	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
[3294]	1201	jjs = jj + 1; jjd = jj
	1202	ELSE
	1203	jjs = jj ; jjd = jj + 1
	1204	ENDIF
	1205
	1206	! integrate the pressure on the shallow side
[3764]	1207	jk1 = jk
[3632]	1208	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
[3294]	1209	IF( jk1 == mbkv(ji,jj) ) THEN
[3632]	1210	zvijk = -zdept(ji,jjs,jk1)
[3294]	1211	EXIT
	1212	ENDIF
[3632]	1213	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
[3764]	1214	zpnss = zpnss + &
[3632]	1215	integ_spline(zdept(ji,jjs,jk1), zdeps, &
[3294]	1216	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
	1217	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
	1218	jk1 = jk1 + 1
	1219	END DO
[3764]	1220
[3294]	1221	! integrate the pressure on the deep side
[3764]	1222	jk1 = jk
[3632]	1223	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
[3294]	1224	IF( jk1 == 1 ) THEN
[3632]	1225	zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad)
	1226	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
	1227	bsp(ji,jjd,1), csp(ji,jjd,1), &
	1228	dsp(ji,jjd,1) ) * zdeps
	1229	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
[3294]	1230	EXIT
	1231	ENDIF
[3632]	1232	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
[3764]	1233	zpnsd = zpnsd + &
[3632]	1234	integ_spline(zdeps, zdept(ji,jjd,jk1), &
[3294]	1235	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
	1236	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
	1237	jk1 = jk1 - 1
	1238	END DO
	1239
[3764]	1240
[3294]	1241	! update the momentum trends in v direction
	1242
	1243	zdpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk))
	1244	IF( lk_vvl ) THEN
	1245	zdpdy2 = zcoef0 / e2v(ji,jj) * &
[3764]	1246	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) )
[3294]	1247	ELSE
[3764]	1248	zdpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
[3294]	1249	ENDIF
	1250
	1251	va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2)*&
	1252	& vmask(ji,jj,jk)tmask(ji,jj,jk)tmask(ji,jj+1,jk)
	1253	ENDIF
	1254
[3764]	1255
[3294]	1256	END DO
	1257	END DO
[455]	1258	END DO
[503]	1259	!
[3764]	1260	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
	1261	CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh )
[5224]	1262	CALL wrk_dealloc( jpi,jpj, zsshu_n, zsshv_n )
[2715]	1263	!
[3294]	1264	END SUBROUTINE hpg_prj
[455]	1265
[4990]	1266
[3294]	1267	SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type)
	1268	!!----------------------------------------------------------------------
	1269	!! * ROUTINE cspline *
[3764]	1270	!!
[3294]	1271	!! ** Purpose : constrained cubic spline interpolation
[3764]	1272	!!
	1273	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
[4990]	1274	!!
[3294]	1275	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
	1276	!!----------------------------------------------------------------------
	1277	IMPLICIT NONE
	1278	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate
[3764]	1279	REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of
[3294]	1280	! the interpoated function
[3764]	1281	INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline
[3294]	1282	! 2: Linear
[4990]	1283	!
[3294]	1284	INTEGER :: ji, jj, jk ! dummy loop indices
	1285	INTEGER :: jpi, jpj, jpkm1
	1286	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
	1287	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
	1288	REAL(wp) :: zdf(size(fsp,3))
	1289	!!----------------------------------------------------------------------
	1290
	1291	jpi = size(fsp,1)
	1292	jpj = size(fsp,2)
	1293	jpkm1 = size(fsp,3) - 1
	1294
[3764]	1295
[3294]	1296	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
	1297	DO ji = 1, jpi
	1298	DO jj = 1, jpj
[3764]	1299	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
[3294]	1300	! DO jk = 2, jpkm1-1
[3764]	1301	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
	1302	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1303	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
	1304	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
	1305	!
	1306	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
[3764]	1307	!
[3294]	1308	! IF(zdf1 * zdf2 <= 0._wp) THEN
	1309	! zdf(jk) = 0._wp
	1310	! ELSE
	1311	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
	1312	! ENDIF
	1313	! END DO
[3764]	1314
[3294]	1315	!!Simply geometric average
	1316	DO jk = 2, jpkm1-1
	1317	zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1))
	1318	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk))
[3764]	1319
[3294]	1320	IF(zdf1 * zdf2 <= 0._wp) THEN
	1321	zdf(jk) = 0._wp
	1322	ELSE
	1323	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
	1324	ENDIF
	1325	END DO
[3764]	1326
[3294]	1327	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
	1328	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
	1329	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
	1330	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - &
	1331	& 0.5_wp * zdf(jpkm1 - 1)
[3764]	1332
[3294]	1333	DO jk = 1, jpkm1 - 1
[3764]	1334	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1335	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
	1336	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
[3764]	1337	zddf1 = -2._wp * ztmp1 + ztmp2
[3294]	1338	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
[3764]	1339	zddf2 = 2._wp * ztmp1 - ztmp2
	1340
[3294]	1341	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
	1342	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
[3764]	1343	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
[3294]	1344	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
	1345	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
	1346	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
	1347	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
	1348	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
	1349	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
	1350	END DO
	1351	END DO
	1352	END DO
[3764]	1353
[3294]	1354	ELSE IF (polynomial_type == 2) THEN ! Linear
	1355	DO ji = 1, jpi
	1356	DO jj = 1, jpj
	1357	DO jk = 1, jpkm1-1
[3764]	1358	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1359	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
[3764]	1360
[3294]	1361	dsp(ji,jj,jk) = 0._wp
	1362	csp(ji,jj,jk) = 0._wp
	1363	bsp(ji,jj,jk) = ztmp1 / zdxtmp
	1364	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
	1365	END DO
	1366	END DO
	1367	END DO
	1368
	1369	ELSE
	1370	CALL ctl_stop( 'invalid polynomial type in cspline' )
	1371	ENDIF
	1372
	1373	END SUBROUTINE cspline
	1374
	1375
[3764]	1376	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
[3294]	1377	!!----------------------------------------------------------------------
	1378	!! * ROUTINE interp1 *
[3764]	1379	!!
[3294]	1380	!! ** Purpose : 1-d linear interpolation
[3764]	1381	!!
[4990]	1382	!! ** Method : interpolation is straight forward
[3764]	1383	!! extrapolation is also permitted (no value limit)
[3294]	1384	!!----------------------------------------------------------------------
	1385	IMPLICIT NONE
[3764]	1386	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
[3294]	1387	REAL(wp) :: f ! result of the interpolation (extrapolation)
	1388	REAL(wp) :: zdeltx
	1389	!!----------------------------------------------------------------------
	1390
	1391	zdeltx = xr - xl
	1392	IF(abs(zdeltx) <= 10._wp * EPSILON(x)) THEN
	1393	f = 0.5_wp * (fl + fr)
	1394	ELSE
	1395	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
	1396	ENDIF
[3764]	1397
[3294]	1398	END FUNCTION interp1
	1399
[4990]	1400
[3764]	1401	FUNCTION interp2(x, a, b, c, d) RESULT(f)
[3294]	1402	!!----------------------------------------------------------------------
	1403	!! * ROUTINE interp1 *
[3764]	1404	!!
[3294]	1405	!! ** Purpose : 1-d constrained cubic spline interpolation
[3764]	1406	!!
[3294]	1407	!! ** Method : cubic spline interpolation
	1408	!!
	1409	!!----------------------------------------------------------------------
	1410	IMPLICIT NONE
[3764]	1411	REAL(wp), INTENT(in) :: x, a, b, c, d
[3294]	1412	REAL(wp) :: f ! value from the interpolation
	1413	!!----------------------------------------------------------------------
	1414
[3764]	1415	f = a + x* ( b + x * ( c + d * x ) )
[3294]	1416
	1417	END FUNCTION interp2
	1418
	1419
[3764]	1420	FUNCTION interp3(x, a, b, c, d) RESULT(f)
[3294]	1421	!!----------------------------------------------------------------------
	1422	!! * ROUTINE interp1 *
[3764]	1423	!!
[3294]	1424	!! ** Purpose : Calculate the first order of deriavtive of
	1425	!! a cubic spline function y=a+bx+cx^2+d*x^3
[3764]	1426	!!
[3294]	1427	!! ** Method : f=dy/dx=b+2cx+3dx^2
	1428	!!
	1429	!!----------------------------------------------------------------------
	1430	IMPLICIT NONE
[3764]	1431	REAL(wp), INTENT(in) :: x, a, b, c, d
[3294]	1432	REAL(wp) :: f ! value from the interpolation
	1433	!!----------------------------------------------------------------------
	1434
	1435	f = b + x * ( 2._wp * c + 3._wp * d * x)
	1436
	1437	END FUNCTION interp3
	1438
[3764]	1439
	1440	FUNCTION integ_spline(xl, xr, a, b, c, d) RESULT(f)
[3294]	1441	!!----------------------------------------------------------------------
	1442	!! * ROUTINE interp1 *
[3764]	1443	!!
[3294]	1444	!! ** Purpose : 1-d constrained cubic spline integration
	1445	!!
[3764]	1446	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
	1447	!!
[3294]	1448	!!----------------------------------------------------------------------
	1449	IMPLICIT NONE
[3764]	1450	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
	1451	REAL(wp) :: za1, za2, za3
[3294]	1452	REAL(wp) :: f ! integration result
	1453	!!----------------------------------------------------------------------
	1454
[3764]	1455	za1 = 0.5_wp * b
	1456	za2 = c / 3.0_wp
	1457	za3 = 0.25_wp * d
[3294]	1458
	1459	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
	1460	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
	1461
[3632]	1462	END FUNCTION integ_spline
[3294]	1463
[3]	1464	!!======================================================================
	1465	END MODULE dynhpg
[3632]	1466

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