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dynhpg.F90 in branches/UKMO/dev_r5518_GO6_package_inc_asm/NEMOGCM/NEMO/OPA_SRC/DYN – NEMO

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source: branches/UKMO/dev_r5518_GO6_package_inc_asm/NEMOGCM/NEMO/OPA_SRC/DYN/dynhpg.F90 @ 8036

Last change on this file since 8036 was 8036, checked in by jwhile, 7 years ago
Further merge of r5518_pcbias
File size: 70.8 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
[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
[8036]	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
[8036]	87	REAL(wp), DIMENSION(jpi,jpj,jpk) :: z_rhd_st ! tmp density storage for pressure corr
	88	REAL(wp), DIMENSION(jpi,jpj) :: z_gru_st ! tmp ua trends storage for pressure corr
	89	REAL(wp), DIMENSION(jpi,jpj) :: 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	!
[8036]	100	IF ( ln_bias .AND. ln_bias_pc_app ) THEN
	101	z_rhd_st(:,:,:) = rhd(:,:,:) ! store orig density
	102	rhd(:,:,:) = rhd_pc(:,:,:) ! use pressure corrected density
	103	z_gru_st(:,:) = gru(:,:)
	104	gru(:,:) = gru_pc(:,:)
	105	z_grv_st(:,:) = grv(:,:)
	106	grv(:,:) = grv_pc(:,:)
	107	ENDIF
	108	!
[3294]	109	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
[503]	110	CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate
	111	CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation)
	112	CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation)
[3294]	113	CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial)
	114	CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme)
[5120]	115	CASE ( 5 ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf
[455]	116	END SELECT
[2528]	117	!
[503]	118	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
[455]	119	ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:)
	120	ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:)
[4990]	121	CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt )
[3294]	122	CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv )
[3764]	123	ENDIF
[503]	124	!
	125	IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, &
	126	& tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
	127	!
[8036]	128	IF ( ln_bias .AND. ln_bias_pc_app ) THEN
	129	rhd(:,:,:) = z_rhd_st(:,:,:) ! restore original density
	130	gru(:,:) = z_gru_st(:,:)
	131	grv(:,:) = z_grv_st(:,:)
	132	ENDIF
	133	!
[3294]	134	IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg')
[2715]	135	!
[455]	136	END SUBROUTINE dyn_hpg
	137
	138
[2528]	139	SUBROUTINE dyn_hpg_init
[455]	140	!!----------------------------------------------------------------------
[2528]	141	!! * ROUTINE dyn_hpg_init *
[455]	142	!!
	143	!! ** Purpose : initializations for the hydrostatic pressure gradient
	144	!! computation and consistency control
	145	!!
[1601]	146	!! ** Action : Read the namelist namdyn_hpg and check the consistency
[455]	147	!! with the type of vertical coordinate used (zco, zps, sco)
	148	!!----------------------------------------------------------------------
	149	INTEGER :: ioptio = 0 ! temporary integer
[4147]	150	INTEGER :: ios ! Local integer output status for namelist read
[1601]	151	!!
[3294]	152	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
[5120]	153	& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf, ln_dynhpg_imp
[455]	154	!!----------------------------------------------------------------------
[2528]	155	!
[4147]	156	REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient
	157	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
	158	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp )
	159
	160	REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient
	161	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
	162	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp )
[4624]	163	IF(lwm) WRITE ( numond, namdyn_hpg )
[2528]	164	!
	165	IF(lwp) THEN ! Control print
[455]	166	WRITE(numout,*)
[2528]	167	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
	168	WRITE(numout,*) '~~~~~~~~~~~~'
[1601]	169	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
	170	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
	171	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
	172	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
[5120]	173	WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf
[1601]	174	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
[3294]	175	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
[1601]	176	WRITE(numout,*) ' time stepping: centered (F) or semi-implicit (T) ln_dynhpg_imp = ', ln_dynhpg_imp
[455]	177	ENDIF
[2528]	178	!
[3294]	179	IF( ln_hpg_djc ) &
	180	& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method &
	181	& currently disabled (bugs under investigation). Please select &
	182	& either ln_hpg_sco or ln_hpg_prj instead')
[2528]	183	!
[5120]	184	IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) &
[3294]	185	& CALL ctl_stop('dyn_hpg_init : variable volume key_vvl requires:&
	186	& the standard jacobian formulation hpg_sco or &
	187	& the pressure jacobian formulation hpg_prj')
[5120]	188
	189	IF( ln_hpg_isf .AND. .NOT. ln_isfcav ) &
	190	& CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' )
	191	IF( .NOT. ln_hpg_isf .AND. ln_isfcav ) &
	192	& CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' )
[3294]	193	!
[503]	194	! ! Set nhpg from ln_hpg_... flags
[455]	195	IF( ln_hpg_zco ) nhpg = 0
	196	IF( ln_hpg_zps ) nhpg = 1
	197	IF( ln_hpg_sco ) nhpg = 2
[3294]	198	IF( ln_hpg_djc ) nhpg = 3
	199	IF( ln_hpg_prj ) nhpg = 4
[5120]	200	IF( ln_hpg_isf ) nhpg = 5
[2528]	201	!
[3294]	202	! ! Consistency check
[3764]	203	ioptio = 0
[455]	204	IF( ln_hpg_zco ) ioptio = ioptio + 1
	205	IF( ln_hpg_zps ) ioptio = ioptio + 1
	206	IF( ln_hpg_sco ) ioptio = ioptio + 1
	207	IF( ln_hpg_djc ) ioptio = ioptio + 1
[3294]	208	IF( ln_hpg_prj ) ioptio = ioptio + 1
[5120]	209	IF( ln_hpg_isf ) ioptio = ioptio + 1
[2715]	210	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
[5120]	211	!
	212	! initialisation of ice load
	213	riceload(:,:)=0.0
[503]	214	!
[2528]	215	END SUBROUTINE dyn_hpg_init
[455]	216
	217
	218	SUBROUTINE hpg_zco( kt )
	219	!!---------------------------------------------------------------------
	220	!! * ROUTINE hpg_zco *
	221	!!
	222	!! ** Method : z-coordinate case, levels are horizontal surfaces.
	223	!! The now hydrostatic pressure gradient at a given level, jk,
	224	!! is computed by taking the vertical integral of the in-situ
	225	!! density gradient along the model level from the suface to that
	226	!! level: zhpi = grav .....
	227	!! zhpj = grav .....
[3]	228	!! add it to the general momentum trend (ua,va).
[455]	229	!! ua = ua - 1/e1u * zhpi
	230	!! va = va - 1/e2v * zhpj
[3764]	231	!!
[3]	232	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[503]	233	!!----------------------------------------------------------------------
	234	INTEGER, INTENT(in) :: kt ! ocean time-step index
	235	!!
	236	INTEGER :: ji, jj, jk ! dummy loop indices
	237	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
[3764]	238	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3]	239	!!----------------------------------------------------------------------
[3764]	240	!
[3294]	241	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
	242	!
[3]	243	IF( kt == nit000 ) THEN
	244	IF(lwp) WRITE(numout,*)
[455]	245	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
	246	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
[3]	247	ENDIF
	248
[3764]	249	zcoef0 = - grav * 0.5_wp ! Local constant initialization
	250
[455]	251	! Surface value
[3]	252	DO jj = 2, jpjm1
	253	DO ji = fs_2, fs_jpim1 ! vector opt.
[455]	254	zcoef1 = zcoef0 * fse3w(ji,jj,1)
	255	! hydrostatic pressure gradient
	256	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
	257	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
[3]	258	! add to the general momentum trend
[455]	259	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
	260	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
	261	END DO
	262	END DO
[3294]	263
[503]	264	!
[455]	265	! interior value (2=<jk=<jpkm1)
[3]	266	DO jk = 2, jpkm1
[455]	267	DO jj = 2, jpjm1
[3]	268	DO ji = fs_2, fs_jpim1 ! vector opt.
[455]	269	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
	270	! hydrostatic pressure gradient
	271	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
	272	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
	273	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
	274
	275	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
	276	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
	277	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
[3]	278	! add to the general momentum trend
[455]	279	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	280	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
[3]	281	END DO
	282	END DO
	283	END DO
[503]	284	!
[3294]	285	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
	286	!
[455]	287	END SUBROUTINE hpg_zco
[216]	288
[3]	289
[455]	290	SUBROUTINE hpg_zps( kt )
[3]	291	!!---------------------------------------------------------------------
[455]	292	!! * ROUTINE hpg_zps *
[3764]	293	!!
[455]	294	!! ** Method : z-coordinate plus partial steps case. blahblah...
[3764]	295	!!
[3]	296	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[3764]	297	!!----------------------------------------------------------------------
[503]	298	INTEGER, INTENT(in) :: kt ! ocean time-step index
	299	!!
	300	INTEGER :: ji, jj, jk ! dummy loop indices
	301	INTEGER :: iku, ikv ! temporary integers
	302	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
[3764]	303	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3]	304	!!----------------------------------------------------------------------
[3294]	305	!
	306	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
	307	!
[3]	308	IF( kt == nit000 ) THEN
	309	IF(lwp) WRITE(numout,*)
[455]	310	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
[503]	311	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
[3]	312	ENDIF
	313
[3294]	314
[503]	315	! Local constant initialization
[2528]	316	zcoef0 = - grav * 0.5_wp
[3]	317
[2528]	318	! Surface value (also valid in partial step case)
[3]	319	DO jj = 2, jpjm1
	320	DO ji = fs_2, fs_jpim1 ! vector opt.
[170]	321	zcoef1 = zcoef0 * fse3w(ji,jj,1)
[3]	322	! hydrostatic pressure gradient
[455]	323	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
	324	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
[3]	325	! add to the general momentum trend
	326	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
	327	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
	328	END DO
	329	END DO
	330
[3294]	331
[503]	332	! interior value (2=<jk=<jpkm1)
[3]	333	DO jk = 2, jpkm1
	334	DO jj = 2, jpjm1
	335	DO ji = fs_2, fs_jpim1 ! vector opt.
[170]	336	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
[3]	337	! hydrostatic pressure gradient
	338	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
[455]	339	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
	340	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
[3]	341
	342	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
[455]	343	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
	344	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
[3]	345	! add to the general momentum trend
	346	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	347	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
[455]	348	END DO
[3]	349	END DO
	350	END DO
	351
[3294]	352
[2528]	353	! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
[3]	354	DO jj = 2, jpjm1
	355	DO ji = 2, jpim1
[2528]	356	iku = mbku(ji,jj)
	357	ikv = mbkv(ji,jj)
[3]	358	zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) )
	359	zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) )
[2528]	360	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
	361	ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value
	362	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
	363	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj)
	364	ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
[3]	365	ENDIF
[2528]	366	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
	367	va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value
	368	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
	369	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj)
	370	va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
[3]	371	ENDIF
	372	END DO
	373	END DO
[503]	374	!
[3294]	375	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
	376	!
[455]	377	END SUBROUTINE hpg_zps
[216]	378
[455]	379	SUBROUTINE hpg_sco( kt )
[3]	380	!!---------------------------------------------------------------------
[455]	381	!! * ROUTINE hpg_sco *
[3]	382	!!
[455]	383	!! ** Method : s-coordinate case. Jacobian scheme.
	384	!! The now hydrostatic pressure gradient at a given level, jk,
	385	!! is computed by taking the vertical integral of the in-situ
[3]	386	!! density gradient along the model level from the suface to that
[455]	387	!! level. s-coordinates (ln_sco): a corrective term is added
	388	!! to the horizontal pressure gradient :
	389	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
	390	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
[3]	391	!! add it to the general momentum trend (ua,va).
[455]	392	!! ua = ua - 1/e1u * zhpi
	393	!! va = va - 1/e2v * zhpj
[3]	394	!!
	395	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[503]	396	!!----------------------------------------------------------------------
	397	INTEGER, INTENT(in) :: kt ! ocean time-step index
	398	!!
[5120]	399	INTEGER :: ji, jj, jk ! dummy loop indices
	400	REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars
	401	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
	402	!!----------------------------------------------------------------------
	403	!
	404	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
	405	!
	406	IF( kt == nit000 ) THEN
	407	IF(lwp) WRITE(numout,*)
	408	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
	409	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
	410	ENDIF
	411
	412	! Local constant initialization
	413	zcoef0 = - grav * 0.5_wp
	414	! To use density and not density anomaly
	415	IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
	416	ELSE ; znad = 0._wp ! Fixed volume
	417	ENDIF
	418
	419	! Surface value
	420	DO jj = 2, jpjm1
	421	DO ji = fs_2, fs_jpim1 ! vector opt.
	422	! hydrostatic pressure gradient along s-surfaces
	423	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) &
	424	& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
	425	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) &
	426	& - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) )
	427	! s-coordinate pressure gradient correction
	428	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
	429	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
	430	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
	431	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
	432	! add to the general momentum trend
	433	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap
	434	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap
	435	END DO
	436	END DO
	437
	438	! interior value (2=<jk=<jpkm1)
	439	DO jk = 2, jpkm1
	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,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
	444	& * ( fse3w(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) &
	445	& - fse3w(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) )
	446	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
	447	& * ( fse3w(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) &
	448	& - fse3w(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) )
	449	! s-coordinate pressure gradient correction
	450	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
	451	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj)
	452	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
	453	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj)
	454	! add to the general momentum trend
	455	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap
	456	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap
	457	END DO
	458	END DO
	459	END DO
	460	!
	461	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
	462	!
	463	END SUBROUTINE hpg_sco
	464
	465	SUBROUTINE hpg_isf( kt )
	466	!!---------------------------------------------------------------------
	467	!! * ROUTINE hpg_sco *
	468	!!
	469	!! ** Method : s-coordinate case. Jacobian scheme.
	470	!! The now hydrostatic pressure gradient at a given level, jk,
	471	!! is computed by taking the vertical integral of the in-situ
	472	!! density gradient along the model level from the suface to that
	473	!! level. s-coordinates (ln_sco): a corrective term is added
	474	!! to the horizontal pressure gradient :
	475	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
	476	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
	477	!! add it to the general momentum trend (ua,va).
	478	!! ua = ua - 1/e1u * zhpi
	479	!! va = va - 1/e2v * zhpj
	480	!! iceload is added and partial cell case are added to the top and bottom
	481	!!
	482	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
	483	!!----------------------------------------------------------------------
	484	INTEGER, INTENT(in) :: kt ! ocean time-step index
	485	!!
[4990]	486	INTEGER :: ji, jj, jk, iku, ikv, ikt, iktp1i, iktp1j ! dummy loop indices
	487	REAL(wp) :: zcoef0, zuap, zvap, znad, ze3wu, ze3wv, zuapint, zvapint, zhpjint, zhpiint, zdzwt, zdzwtjp1, zdzwtip1 ! temporary scalars
	488	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj, zrhd
	489	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop
	490	REAL(wp), POINTER, DIMENSION(:,:) :: ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj
[3]	491	!!----------------------------------------------------------------------
[3294]	492	!
[4990]	493	CALL wrk_alloc( jpi,jpj, 2, ztstop)
	494	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
	495	CALL wrk_alloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
[3294]	496	!
[4990]	497	IF( kt == nit000 ) THEN
[3]	498	IF(lwp) WRITE(numout,*)
[5120]	499	IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf'
[455]	500	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
[3]	501	ENDIF
	502
[503]	503	! Local constant initialization
[2528]	504	zcoef0 = - grav * 0.5_wp
[592]	505	! To use density and not density anomaly
[4990]	506	! IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
	507	! ELSE ; znad = 0._wp ! Fixed volume
	508	! ENDIF
	509	znad=1._wp
	510	! iniitialised to 0. zhpi zhpi
	511	zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp
[455]	512
[4990]	513	!==================================================================================
	514	!=====Compute iceload and contribution of the half first wet layer =================
	515	!===================================================================================
	516
	517	! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude)
	518	ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp
	519
	520	! compute density of the water displaced by the ice shelf
	521	zrhd = rhd ! save rhd
	522	DO jk = 1, jpk
	523	zdept(:,:)=gdept_1d(jk)
	524	CALL eos(ztstop(:,:,:),zdept(:,:),rhd(:,:,jk))
	525	END DO
	526	WHERE ( tmask(:,:,:) == 1._wp)
	527	rhd(:,:,:) = zrhd(:,:,:) ! replace wet cell by the saved rhd
	528	END WHERE
	529
	530	! compute rhd at the ice/oce interface (ice shelf side)
	531	CALL eos(ztstop,risfdep,zrhdtop_isf)
	532
	533	! compute rhd at the ice/oce interface (ocean side)
	534	DO ji=1,jpi
	535	DO jj=1,jpj
	536	ikt=mikt(ji,jj)
	537	ztstop(ji,jj,1)=tsn(ji,jj,ikt,1)
	538	ztstop(ji,jj,2)=tsn(ji,jj,ikt,2)
	539	END DO
	540	END DO
	541	CALL eos(ztstop,risfdep,zrhdtop_oce)
	542	!
	543	! Surface value + ice shelf gradient
	544	! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v)
	545	ziceload = 0._wp
	546	DO jj = 1, jpj
	547	DO ji = 1, jpi ! vector opt.
	548	ikt=mikt(ji,jj)
	549	ziceload(ji,jj) = ziceload(ji,jj) + (znad + rhd(ji,jj,1) ) * fse3w(ji,jj,1) * (1._wp - tmask(ji,jj,1))
	550	DO jk=2,ikt-1
	551	ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + rhd(ji,jj,jk-1) + rhd(ji,jj,jk)) * fse3w(ji,jj,jk) &
	552	& * (1._wp - tmask(ji,jj,jk))
	553	END DO
	554	IF (ikt .GE. 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + rhd(ji,jj,ikt-1)) &
	555	& * ( risfdep(ji,jj) - gdept_1d(ikt-1) )
	556	END DO
	557	END DO
	558	riceload(:,:) = 0.0_wp ; riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5
	559	! compute zp from z=0 to first T wet point (correction due to zps not yet applied)
[455]	560	DO jj = 2, jpjm1
[3764]	561	DO ji = fs_2, fs_jpim1 ! vector opt.
[4990]	562	ikt=mikt(ji,jj) ; iktp1i=mikt(ji+1,jj); iktp1j=mikt(ji,jj+1)
	563	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
	564	! we assume ISF is in isostatic equilibrium
	565	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * fse3w(ji+1,jj ,iktp1i) &
	566	& * ( 2._wp * znad + rhd(ji+1,jj ,iktp1i) + zrhdtop_oce(ji+1,jj ) ) &
	567	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
	568	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
	569	& + ( ziceload(ji+1,jj) - ziceload(ji,jj)) )
	570	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * fse3w(ji ,jj+1,iktp1j) &
	571	& * ( 2._wp * znad + rhd(ji ,jj+1,iktp1j) + zrhdtop_oce(ji ,jj+1) ) &
	572	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
	573	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
	574	& + ( ziceload(ji,jj+1) - ziceload(ji,jj) ) )
	575	! s-coordinate pressure gradient correction (=0 if z coordinate)
[2528]	576	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
[455]	577	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
[2528]	578	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
[455]	579	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
	580	! add to the general momentum trend
[4990]	581	ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
	582	va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
[3764]	583	END DO
	584	END DO
[4990]	585	!==================================================================================
	586	!===== Compute partial cell contribution for the top cell =========================
	587	!==================================================================================
	588	DO jj = 2, jpjm1
	589	DO ji = fs_2, fs_jpim1 ! vector opt.
	590	iku = miku(ji,jj) ;
	591	zpshpi(ji,jj)=0.0_wp ; zpshpj(ji,jj)=0.0_wp
	592	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))
	593	! u direction
	594	IF ( iku .GT. 1 ) THEN
	595	! case iku
	596	zhpi(ji,jj,iku) = zcoef0 / e1u(ji,jj) * ze3wu &
	597	& * ( rhd (ji+1,jj,iku) + rhd (ji,jj,iku) &
	598	& + SIGN(1._wp,ze3wu) * grui(ji,jj) + 2._wp * znad )
	599	! corrective term ( = 0 if z coordinate )
	600	zuap = -zcoef0 * ( arui(ji,jj) + 2._wp * znad ) * gzui(ji,jj) / e1u(ji,jj)
	601	! zhpi will be added in interior loop
	602	ua(ji,jj,iku) = ua(ji,jj,iku) + zuap
	603	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
	604	IF (mbku(ji,jj) == iku + 1) zpshpi(ji,jj) = zhpi(ji,jj,iku)
[3764]	605
[4990]	606	! case iku + 1 (remove the zphi term added in the interior loop and compute the one corrected for zps)
	607	zhpiint = zcoef0 / e1u(ji,jj) &
	608	& * ( fse3w(ji+1,jj ,iku+1) * ( (rhd(ji+1,jj,iku+1) + znad) &
	609	& + (rhd(ji+1,jj,iku ) + znad) ) * tmask(ji+1,jj,iku) &
	610	& - fse3w(ji ,jj ,iku+1) * ( (rhd(ji ,jj,iku+1) + znad) &
	611	& + (rhd(ji ,jj,iku ) + znad) ) * tmask(ji ,jj,iku) )
	612	zhpi(ji,jj,iku+1) = zcoef0 / e1u(ji,jj) * ge3rui(ji,jj) - zhpiint
	613	END IF
	614
	615	! v direction
	616	ikv = mikv(ji,jj)
	617	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))
	618	IF ( ikv .GT. 1 ) THEN
	619	! case ikv
	620	zhpj(ji,jj,ikv) = zcoef0 / e2v(ji,jj) * ze3wv &
	621	& * ( rhd(ji,jj+1,ikv) + rhd (ji,jj,ikv) &
	622	& + SIGN(1._wp,ze3wv) * grvi(ji,jj) + 2._wp * znad )
	623	! corrective term ( = 0 if z coordinate )
	624	zvap = -zcoef0 * ( arvi(ji,jj) + 2._wp * znad ) * gzvi(ji,jj) / e2v(ji,jj)
	625	! zhpi will be added in interior loop
	626	va(ji,jj,ikv) = va(ji,jj,ikv) + zvap
	627	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
	628	IF (mbkv(ji,jj) == ikv + 1) zpshpj(ji,jj) = zhpj(ji,jj,ikv)
	629
	630	! case ikv + 1 (remove the zphj term added in the interior loop and compute the one corrected for zps)
	631	zhpjint = zcoef0 / e2v(ji,jj) &
	632	& * ( fse3w(ji ,jj+1,ikv+1) * ( (rhd(ji,jj+1,ikv+1) + znad) &
	633	& + (rhd(ji,jj+1,ikv ) + znad) ) * tmask(ji,jj+1,ikv) &
	634	& - fse3w(ji ,jj ,ikv+1) * ( (rhd(ji,jj ,ikv+1) + znad) &
	635	& + (rhd(ji,jj ,ikv ) + znad) ) * tmask(ji,jj ,ikv) )
	636	zhpj(ji,jj,ikv+1) = zcoef0 / e2v(ji,jj) * ge3rvi(ji,jj) - zhpjint
	637	END IF
	638	END DO
	639	END DO
	640
	641	!==================================================================================
	642	!===== Compute interior value =====================================================
	643	!==================================================================================
	644
	645	DO jj = 2, jpjm1
	646	DO ji = fs_2, fs_jpim1 ! vector opt.
	647	iku=miku(ji,jj); ikv=mikv(ji,jj)
	648	DO jk = 2, jpkm1
[455]	649	! hydrostatic pressure gradient along s-surfaces
[4990]	650	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
	651	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) + zhpi(ji,jj,jk-1) &
	652	& + zcoef0 / e1u(ji,jj) &
	653	& * ( fse3w(ji+1,jj ,jk) * ( (rhd(ji+1,jj,jk ) + znad) &
	654	& + (rhd(ji+1,jj,jk-1) + znad) ) * tmask(ji+1,jj,jk-1) &
	655	& - fse3w(ji ,jj ,jk) * ( (rhd(ji ,jj,jk ) + znad) &
	656	& + (rhd(ji ,jj,jk-1) + znad) ) * tmask(ji ,jj,jk-1) )
[455]	657	! s-coordinate pressure gradient correction
[4990]	658	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
	659	zuap = - zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
	660	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) * umask(ji,jj,jk-1)
	661	ua(ji,jj,jk) = ua(ji,jj,jk) + ( zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
	662
	663	! hydrostatic pressure gradient along s-surfaces
	664	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
	665	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) + zhpj(ji,jj,jk-1) &
	666	& + zcoef0 / e2v(ji,jj) &
	667	& * ( fse3w(ji ,jj+1,jk) * ( (rhd(ji,jj+1,jk ) + znad) &
	668	& + (rhd(ji,jj+1,jk-1) + znad) ) * tmask(ji,jj+1,jk-1) &
	669	& - fse3w(ji ,jj ,jk) * ( (rhd(ji,jj ,jk ) + znad) &
	670	& + (rhd(ji,jj ,jk-1) + znad) ) * tmask(ji,jj ,jk-1) )
	671	! s-coordinate pressure gradient correction
	672	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
	673	zvap = - zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
	674	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) * vmask(ji,jj,jk-1)
[455]	675	! add to the general momentum trend
[4990]	676	va(ji,jj,jk) = va(ji,jj,jk) + ( zhpj(ji,jj,jk) + zvap ) * vmask(ji,jj,jk)
[455]	677	END DO
	678	END DO
	679	END DO
[4990]	680
	681	!==================================================================================
	682	!===== Compute bottom cell contribution (partial cell) ============================
	683	!==================================================================================
	684
	685	DO jj = 2, jpjm1
	686	DO ji = 2, jpim1
	687	iku = mbku(ji,jj)
	688	ikv = mbkv(ji,jj)
	689
	690	IF (iku .GT. 1) THEN
	691	! remove old value (interior case)
	692	zuap = -zcoef0 * ( rhd (ji+1,jj ,iku) + rhd (ji,jj,iku) + 2._wp * znad ) &
	693	& * ( fsde3w(ji+1,jj ,iku) - fsde3w(ji,jj,iku) ) / e1u(ji,jj)
	694	ua(ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) - zuap
	695	! put new value
	696	! -zpshpi to avoid double contribution of the partial step in the top layer
	697	zuap = -zcoef0 * ( aru(ji,jj) + 2._wp * znad ) * gzu(ji,jj) / e1u(ji,jj)
	698	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) + zcoef0 / e1u(ji,jj) * ge3ru(ji,jj) - zpshpi(ji,jj)
	699	ua(ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) + zuap
	700	END IF
	701	! v direction
	702	IF (ikv .GT. 1) THEN
	703	! remove old value (interior case)
	704	zvap = -zcoef0 * ( rhd (ji ,jj+1,ikv) + rhd (ji,jj,ikv) + 2._wp * znad ) &
	705	& * ( fsde3w(ji ,jj+1,ikv) - fsde3w(ji,jj,ikv) ) / e2v(ji,jj)
	706	va(ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) - zvap
	707	! put new value
	708	! -zpshpj to avoid double contribution of the partial step in the top layer
	709	zvap = -zcoef0 * ( arv(ji,jj) + 2._wp * znad ) * gzv(ji,jj) / e2v(ji,jj)
	710	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) + zcoef0 / e2v(ji,jj) * ge3rv(ji,jj) - zpshpj(ji,jj)
	711	va(ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) + zvap
	712	END IF
	713	END DO
	714	END DO
	715
	716	! set back to original density value into the ice shelf cell (maybe useless because it is masked)
	717	rhd = zrhd
[503]	718	!
[4990]	719	CALL wrk_dealloc( jpi,jpj,2, ztstop)
	720	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
	721	CALL wrk_dealloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
[3294]	722	!
[5120]	723	END SUBROUTINE hpg_isf
[455]	724
[4990]	725
[455]	726	SUBROUTINE hpg_djc( kt )
	727	!!---------------------------------------------------------------------
	728	!! * ROUTINE hpg_djc *
	729	!!
	730	!! ** Method : Density Jacobian with Cubic polynomial scheme
[3764]	731	!!
[503]	732	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
[455]	733	!!----------------------------------------------------------------------
[503]	734	INTEGER, INTENT(in) :: kt ! ocean time-step index
	735	!!
	736	INTEGER :: ji, jj, jk ! dummy loop indices
	737	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
	738	REAL(wp) :: z1_10, cffu, cffx ! " "
	739	REAL(wp) :: z1_12, cffv, cffy ! " "
[3764]	740	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3294]	741	REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw
	742	REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow
	743	REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k
[455]	744	!!----------------------------------------------------------------------
[3294]	745	!
[3764]	746	CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
	747	CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
	748	CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
[3294]	749	!
[455]	750
	751	IF( kt == nit000 ) THEN
	752	IF(lwp) WRITE(numout,*)
	753	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
	754	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
[216]	755	ENDIF
	756
[503]	757	! Local constant initialization
[2528]	758	zcoef0 = - grav * 0.5_wp
	759	z1_10 = 1._wp / 10._wp
	760	z1_12 = 1._wp / 12._wp
[455]	761
	762	!----------------------------------------------------------------------------------------
	763	! compute and store in provisional arrays elementary vertical and horizontal differences
	764	!----------------------------------------------------------------------------------------
	765
	766	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
	767
	768	DO jk = 2, jpkm1
	769	DO jj = 2, jpjm1
	770	DO ji = fs_2, fs_jpim1 ! vector opt.
	771	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
	772	dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1)
	773	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
	774	dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk )
	775	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
	776	dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk )
	777	END DO
	778	END DO
	779	END DO
	780
	781	!-------------------------------------------------------------------------
	782	! compute harmonic averages using eq. 5.18
	783	!-------------------------------------------------------------------------
	784	zep = 1.e-15
	785
[503]	786	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
	787	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
[455]	788
	789	DO jk = 2, jpkm1
	790	DO jj = 2, jpjm1
	791	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	792	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
[455]	793
[2528]	794	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
	795	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
[3764]	796
[2528]	797	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
	798	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
[455]	799
	800	IF( cffw > zep) THEN
[2528]	801	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
	802	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
[455]	803	ELSE
[2528]	804	drhow(ji,jj,jk) = 0._wp
[455]	805	ENDIF
	806
[2528]	807	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
	808	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
[455]	809
	810	IF( cffu > zep ) THEN
[2528]	811	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
	812	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
[455]	813	ELSE
[2528]	814	drhou(ji,jj,jk ) = 0._wp
[455]	815	ENDIF
	816
	817	IF( cffx > zep ) THEN
[2528]	818	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
	819	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
[455]	820	ELSE
[2528]	821	dzu(ji,jj,jk) = 0._wp
[455]	822	ENDIF
	823
	824	IF( cffv > zep ) THEN
[2528]	825	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
	826	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
[455]	827	ELSE
[2528]	828	drhov(ji,jj,jk) = 0._wp
[455]	829	ENDIF
	830
	831	IF( cffy > zep ) THEN
[2528]	832	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
	833	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
[455]	834	ELSE
[2528]	835	dzv(ji,jj,jk) = 0._wp
[455]	836	ENDIF
	837
	838	END DO
	839	END DO
	840	END DO
	841
	842	!----------------------------------------------------------------------------------
	843	! apply boundary conditions at top and bottom using 5.36-5.37
	844	!----------------------------------------------------------------------------------
[2528]	845	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
	846	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
	847	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
[455]	848
[2528]	849	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
	850	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
	851	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
[455]	852
	853
	854	!--------------------------------------------------------------
	855	! Upper half of top-most grid box, compute and store
	856	!-------------------------------------------------------------
	857
	858	!!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified
	859	! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
	860
	861	DO jj = 2, jpjm1
	862	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	863	rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) &
	864	& * ( rhd(ji,jj,1) &
	865	& + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) &
	866	& * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) &
[3764]	867	& / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) )
[455]	868	END DO
	869	END DO
	870
	871	!!bug gm : here also, simplification is possible
	872	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
	873
	874	DO jk = 2, jpkm1
	875	DO jj = 2, jpjm1
	876	DO ji = fs_2, fs_jpim1 ! vector opt.
	877
	878	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
	879	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) &
	880	& - grav * z1_10 * ( &
	881	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
	882	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
	883	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
	884	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
	885	& )
	886
	887	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
	888	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) &
	889	& - grav* z1_10 * ( &
	890	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
	891	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
	892	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
	893	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
	894	& )
	895
	896	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
	897	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) &
	898	& - grav* z1_10 * ( &
	899	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
	900	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
	901	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
	902	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
	903	& )
	904
	905	END DO
	906	END DO
	907	END DO
	908	CALL lbc_lnk(rho_k,'W',1.)
	909	CALL lbc_lnk(rho_i,'U',1.)
	910	CALL lbc_lnk(rho_j,'V',1.)
	911
	912
	913	! ---------------
	914	! Surface value
	915	! ---------------
	916	DO jj = 2, jpjm1
	917	DO ji = fs_2, fs_jpim1 ! vector opt.
	918	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj)
	919	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj)
	920	! add to the general momentum trend
	921	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
	922	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
	923	END DO
	924	END DO
	925
	926	! ----------------
	927	! interior value (2=<jk=<jpkm1)
	928	! ----------------
	929	DO jk = 2, jpkm1
[3764]	930	DO jj = 2, jpjm1
[455]	931	DO ji = fs_2, fs_jpim1 ! vector opt.
	932	! hydrostatic pressure gradient along s-surfaces
	933	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
	934	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
	935	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj)
	936	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
	937	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
	938	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj)
	939	! add to the general momentum trend
	940	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	941	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
	942	END DO
	943	END DO
	944	END DO
[503]	945	!
[3764]	946	CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
	947	CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
	948	CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
[2715]	949	!
[455]	950	END SUBROUTINE hpg_djc
	951
	952
[3294]	953	SUBROUTINE hpg_prj( kt )
[455]	954	!!---------------------------------------------------------------------
[3294]	955	!! * ROUTINE hpg_prj *
[455]	956	!!
[3294]	957	!! ** Method : s-coordinate case.
	958	!! A Pressure-Jacobian horizontal pressure gradient method
	959	!! based on the constrained cubic-spline interpolation for
	960	!! all vertical coordinate systems
[455]	961	!!
[3294]	962	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[455]	963	!!----------------------------------------------------------------------
[3294]	964	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
	965	INTEGER, INTENT(in) :: kt ! ocean time-step index
[503]	966	!!
[3294]	967	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
	968	REAL(wp) :: zcoef0, znad ! temporary scalars
[503]	969	!!
[3294]	970	!! The local variables for the correction term
	971	INTEGER :: jk1, jis, jid, jjs, jjd
	972	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
[3764]	973	REAL(wp) :: zrhdt1
[3294]	974	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
[3764]	975	REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh
[3294]	976	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
[5224]	977	REAL(wp), POINTER, DIMENSION(:,:) :: zsshu_n, zsshv_n
[455]	978	!!----------------------------------------------------------------------
[3294]	979	!
[3764]	980	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
	981	CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh )
[5224]	982	CALL wrk_alloc( jpi,jpj, zsshu_n, zsshv_n )
[3294]	983	!
[455]	984	IF( kt == nit000 ) THEN
	985	IF(lwp) WRITE(numout,*)
[3294]	986	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
	987	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
[3]	988	ENDIF
	989
[3294]	990	!!----------------------------------------------------------------------
	991	! Local constant initialization
[3764]	992	zcoef0 = - grav
[3294]	993	znad = 0.0_wp
	994	IF( lk_vvl ) znad = 1._wp
[3]	995
[3294]	996	! Clean 3-D work arrays
	997	zhpi(:,:,:) = 0._wp
	998	zrhh(:,:,:) = rhd(:,:,:)
[3764]	999
[3294]	1000	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
	1001	DO jj = 1, jpj
[3764]	1002	DO ji = 1, jpi
[3294]	1003	jk = mbathy(ji,jj)
	1004	IF( jk <= 0 ) THEN; zrhh(ji,jj,:) = 0._wp
	1005	ELSE IF(jk == 1) THEN; zrhh(ji,jj, jk+1:jpk) = rhd(ji,jj,jk)
	1006	ELSE IF(jk < jpkm1) THEN
	1007	DO jkk = jk+1, jpk
	1008	zrhh(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1), &
	1009	fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2))
[3764]	1010	END DO
[3294]	1011	ENDIF
	1012	END DO
	1013	END DO
[3]	1014
[3632]	1015	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
[4990]	1016	DO jj = 1, jpj
	1017	DO ji = 1, jpi
	1018	zdept(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) - sshn(ji,jj) * znad
	1019	END DO
	1020	END DO
[455]	1021
[4990]	1022	DO jk = 2, jpk
	1023	DO jj = 1, jpj
	1024	DO ji = 1, jpi
	1025	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + fse3w(ji,jj,jk)
	1026	END DO
	1027	END DO
	1028	END DO
[455]	1029
[4990]	1030	fsp(:,:,:) = zrhh (:,:,:)
[3632]	1031	xsp(:,:,:) = zdept(:,:,:)
	1032
[3764]	1033	! Construct the vertical density profile with the
[3294]	1034	! constrained cubic spline interpolation
	1035	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
[3764]	1036	CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type)
[3294]	1037
	1038	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
	1039	DO jj = 2, jpj
[3764]	1040	DO ji = 2, jpi
[3632]	1041	zrhdt1 = zrhh(ji,jj,1) - interp3(zdept(ji,jj,1),asp(ji,jj,1), &
[3294]	1042	bsp(ji,jj,1), csp(ji,jj,1), &
[3632]	1043	dsp(ji,jj,1) ) * 0.25_wp * fse3w(ji,jj,1)
[3294]	1044
	1045	! assuming linear profile across the top half surface layer
[3764]	1046	zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * zrhdt1
[3294]	1047	END DO
[455]	1048	END DO
	1049
[3294]	1050	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
[3764]	1051	DO jk = 2, jpkm1
	1052	DO jj = 2, jpj
[3294]	1053	DO ji = 2, jpi
	1054	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
[3632]	1055	integ_spline(zdept(ji,jj,jk-1), zdept(ji,jj,jk),&
[3294]	1056	asp(ji,jj,jk-1), bsp(ji,jj,jk-1), &
	1057	csp(ji,jj,jk-1), dsp(ji,jj,jk-1))
	1058	END DO
	1059	END DO
[455]	1060	END DO
	1061
[3294]	1062	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
[5224]	1063
	1064	! Prepare zsshu_n and zsshv_n
[3764]	1065	DO jj = 2, jpjm1
	1066	DO ji = 2, jpim1
[5224]	1067	zsshu_n(ji,jj) = (e12u(ji,jj) * sshn(ji,jj) + e12u(ji+1, jj) * sshn(ji+1,jj)) * &
	1068	& r1_e12u(ji,jj) * umask(ji,jj,1) * 0.5_wp
	1069	zsshv_n(ji,jj) = (e12v(ji,jj) * sshn(ji,jj) + e12v(ji+1, jj) * sshn(ji,jj+1)) * &
	1070	& r1_e12v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
[3294]	1071	END DO
[455]	1072	END DO
	1073
[5224]	1074	DO jj = 2, jpjm1
	1075	DO ji = 2, jpim1
	1076	zu(ji,jj,1) = - ( fse3u(ji,jj,1) - zsshu_n(ji,jj) * znad)
	1077	zv(ji,jj,1) = - ( fse3v(ji,jj,1) - zsshv_n(ji,jj) * znad)
	1078	END DO
	1079	END DO
	1080
[3764]	1081	DO jk = 2, jpkm1
	1082	DO jj = 2, jpjm1
	1083	DO ji = 2, jpim1
[3294]	1084	zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk)
	1085	zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk)
	1086	END DO
	1087	END DO
[455]	1088	END DO
[3764]	1089
	1090	DO jk = 1, jpkm1
	1091	DO jj = 2, jpjm1
	1092	DO ji = 2, jpim1
[3294]	1093	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk)
	1094	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk)
	1095	END DO
	1096	END DO
	1097	END DO
[455]	1098
[3632]	1099	DO jk = 1, jpkm1
	1100	DO jj = 2, jpjm1
	1101	DO ji = 2, jpim1
	1102	zu(ji,jj,jk) = min(zu(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
	1103	zu(ji,jj,jk) = max(zu(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
	1104	zv(ji,jj,jk) = min(zv(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
	1105	zv(ji,jj,jk) = max(zv(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
	1106	END DO
	1107	END DO
	1108	END DO
	1109
	1110
[3764]	1111	DO jk = 1, jpkm1
	1112	DO jj = 2, jpjm1
	1113	DO ji = 2, jpim1
[3294]	1114	zpwes = 0._wp; zpwed = 0._wp
	1115	zpnss = 0._wp; zpnsd = 0._wp
	1116	zuijk = zu(ji,jj,jk)
	1117	zvijk = zv(ji,jj,jk)
	1118
	1119	!!!!! for u equation
	1120	IF( jk <= mbku(ji,jj) ) THEN
[3632]	1121	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
[3294]	1122	jis = ji + 1; jid = ji
	1123	ELSE
	1124	jis = ji; jid = ji +1
	1125	ENDIF
	1126
	1127	! integrate the pressure on the shallow side
[3764]	1128	jk1 = jk
[3632]	1129	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
[3294]	1130	IF( jk1 == mbku(ji,jj) ) THEN
[3632]	1131	zuijk = -zdept(jis,jj,jk1)
[3294]	1132	EXIT
	1133	ENDIF
[3632]	1134	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
[3764]	1135	zpwes = zpwes + &
[3632]	1136	integ_spline(zdept(jis,jj,jk1), zdeps, &
[3294]	1137	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
	1138	csp(jis,jj,jk1), dsp(jis,jj,jk1))
	1139	jk1 = jk1 + 1
	1140	END DO
[3764]	1141
[3294]	1142	! integrate the pressure on the deep side
[3764]	1143	jk1 = jk
[3632]	1144	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
[3294]	1145	IF( jk1 == 1 ) THEN
[3632]	1146	zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad)
	1147	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
	1148	bsp(jid,jj,1), csp(jid,jj,1), &
	1149	dsp(jid,jj,1)) * zdeps
	1150	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
[3294]	1151	EXIT
	1152	ENDIF
[3632]	1153	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
[3764]	1154	zpwed = zpwed + &
[3632]	1155	integ_spline(zdeps, zdept(jid,jj,jk1), &
[3294]	1156	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
	1157	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
	1158	jk1 = jk1 - 1
	1159	END DO
[3764]	1160
[3294]	1161	! update the momentum trends in u direction
	1162
	1163	zdpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk))
	1164	IF( lk_vvl ) THEN
[3764]	1165	zdpdx2 = zcoef0 / e1u(ji,jj) * &
	1166	( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) )
[3294]	1167	ELSE
[3764]	1168	zdpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
[3294]	1169	ENDIF
	1170
	1171	ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * &
	1172	& umask(ji,jj,jk) * tmask(ji,jj,jk) * tmask(ji+1,jj,jk)
	1173	ENDIF
[3764]	1174
[3294]	1175	!!!!! for v equation
	1176	IF( jk <= mbkv(ji,jj) ) THEN
[3632]	1177	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
[3294]	1178	jjs = jj + 1; jjd = jj
	1179	ELSE
	1180	jjs = jj ; jjd = jj + 1
	1181	ENDIF
	1182
	1183	! integrate the pressure on the shallow side
[3764]	1184	jk1 = jk
[3632]	1185	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
[3294]	1186	IF( jk1 == mbkv(ji,jj) ) THEN
[3632]	1187	zvijk = -zdept(ji,jjs,jk1)
[3294]	1188	EXIT
	1189	ENDIF
[3632]	1190	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
[3764]	1191	zpnss = zpnss + &
[3632]	1192	integ_spline(zdept(ji,jjs,jk1), zdeps, &
[3294]	1193	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
	1194	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
	1195	jk1 = jk1 + 1
	1196	END DO
[3764]	1197
[3294]	1198	! integrate the pressure on the deep side
[3764]	1199	jk1 = jk
[3632]	1200	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
[3294]	1201	IF( jk1 == 1 ) THEN
[3632]	1202	zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad)
	1203	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
	1204	bsp(ji,jjd,1), csp(ji,jjd,1), &
	1205	dsp(ji,jjd,1) ) * zdeps
	1206	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
[3294]	1207	EXIT
	1208	ENDIF
[3632]	1209	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
[3764]	1210	zpnsd = zpnsd + &
[3632]	1211	integ_spline(zdeps, zdept(ji,jjd,jk1), &
[3294]	1212	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
	1213	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
	1214	jk1 = jk1 - 1
	1215	END DO
	1216
[3764]	1217
[3294]	1218	! update the momentum trends in v direction
	1219
	1220	zdpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk))
	1221	IF( lk_vvl ) THEN
	1222	zdpdy2 = zcoef0 / e2v(ji,jj) * &
[3764]	1223	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) )
[3294]	1224	ELSE
[3764]	1225	zdpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
[3294]	1226	ENDIF
	1227
	1228	va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2)*&
	1229	& vmask(ji,jj,jk)tmask(ji,jj,jk)tmask(ji,jj+1,jk)
	1230	ENDIF
	1231
[3764]	1232
[3294]	1233	END DO
	1234	END DO
[455]	1235	END DO
[503]	1236	!
[3764]	1237	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
	1238	CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh )
[5224]	1239	CALL wrk_dealloc( jpi,jpj, zsshu_n, zsshv_n )
[2715]	1240	!
[3294]	1241	END SUBROUTINE hpg_prj
[455]	1242
[4990]	1243
[3294]	1244	SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type)
	1245	!!----------------------------------------------------------------------
	1246	!! * ROUTINE cspline *
[3764]	1247	!!
[3294]	1248	!! ** Purpose : constrained cubic spline interpolation
[3764]	1249	!!
	1250	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
[4990]	1251	!!
[3294]	1252	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
	1253	!!----------------------------------------------------------------------
	1254	IMPLICIT NONE
	1255	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate
[3764]	1256	REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of
[3294]	1257	! the interpoated function
[3764]	1258	INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline
[3294]	1259	! 2: Linear
[4990]	1260	!
[3294]	1261	INTEGER :: ji, jj, jk ! dummy loop indices
	1262	INTEGER :: jpi, jpj, jpkm1
	1263	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
	1264	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
	1265	REAL(wp) :: zdf(size(fsp,3))
	1266	!!----------------------------------------------------------------------
	1267
	1268	jpi = size(fsp,1)
	1269	jpj = size(fsp,2)
	1270	jpkm1 = size(fsp,3) - 1
	1271
[3764]	1272
[3294]	1273	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
	1274	DO ji = 1, jpi
	1275	DO jj = 1, jpj
[3764]	1276	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
[3294]	1277	! DO jk = 2, jpkm1-1
[3764]	1278	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
	1279	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1280	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
	1281	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
	1282	!
	1283	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
[3764]	1284	!
[3294]	1285	! IF(zdf1 * zdf2 <= 0._wp) THEN
	1286	! zdf(jk) = 0._wp
	1287	! ELSE
	1288	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
	1289	! ENDIF
	1290	! END DO
[3764]	1291
[3294]	1292	!!Simply geometric average
	1293	DO jk = 2, jpkm1-1
	1294	zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1))
	1295	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk))
[3764]	1296
[3294]	1297	IF(zdf1 * zdf2 <= 0._wp) THEN
	1298	zdf(jk) = 0._wp
	1299	ELSE
	1300	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
	1301	ENDIF
	1302	END DO
[3764]	1303
[3294]	1304	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
	1305	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
	1306	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
	1307	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - &
	1308	& 0.5_wp * zdf(jpkm1 - 1)
[3764]	1309
[3294]	1310	DO jk = 1, jpkm1 - 1
[3764]	1311	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1312	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
	1313	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
[3764]	1314	zddf1 = -2._wp * ztmp1 + ztmp2
[3294]	1315	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
[3764]	1316	zddf2 = 2._wp * ztmp1 - ztmp2
	1317
[3294]	1318	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
	1319	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
[3764]	1320	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
[3294]	1321	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
	1322	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
	1323	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
	1324	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
	1325	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
	1326	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
	1327	END DO
	1328	END DO
	1329	END DO
[3764]	1330
[3294]	1331	ELSE IF (polynomial_type == 2) THEN ! Linear
	1332	DO ji = 1, jpi
	1333	DO jj = 1, jpj
	1334	DO jk = 1, jpkm1-1
[3764]	1335	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1336	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
[3764]	1337
[3294]	1338	dsp(ji,jj,jk) = 0._wp
	1339	csp(ji,jj,jk) = 0._wp
	1340	bsp(ji,jj,jk) = ztmp1 / zdxtmp
	1341	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
	1342	END DO
	1343	END DO
	1344	END DO
	1345
	1346	ELSE
	1347	CALL ctl_stop( 'invalid polynomial type in cspline' )
	1348	ENDIF
	1349
	1350	END SUBROUTINE cspline
	1351
	1352
[3764]	1353	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
[3294]	1354	!!----------------------------------------------------------------------
	1355	!! * ROUTINE interp1 *
[3764]	1356	!!
[3294]	1357	!! ** Purpose : 1-d linear interpolation
[3764]	1358	!!
[4990]	1359	!! ** Method : interpolation is straight forward
[3764]	1360	!! extrapolation is also permitted (no value limit)
[3294]	1361	!!----------------------------------------------------------------------
	1362	IMPLICIT NONE
[3764]	1363	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
[3294]	1364	REAL(wp) :: f ! result of the interpolation (extrapolation)
	1365	REAL(wp) :: zdeltx
	1366	!!----------------------------------------------------------------------
	1367
	1368	zdeltx = xr - xl
	1369	IF(abs(zdeltx) <= 10._wp * EPSILON(x)) THEN
	1370	f = 0.5_wp * (fl + fr)
	1371	ELSE
	1372	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
	1373	ENDIF
[3764]	1374
[3294]	1375	END FUNCTION interp1
	1376
[4990]	1377
[3764]	1378	FUNCTION interp2(x, a, b, c, d) RESULT(f)
[3294]	1379	!!----------------------------------------------------------------------
	1380	!! * ROUTINE interp1 *
[3764]	1381	!!
[3294]	1382	!! ** Purpose : 1-d constrained cubic spline interpolation
[3764]	1383	!!
[3294]	1384	!! ** Method : cubic spline interpolation
	1385	!!
	1386	!!----------------------------------------------------------------------
	1387	IMPLICIT NONE
[3764]	1388	REAL(wp), INTENT(in) :: x, a, b, c, d
[3294]	1389	REAL(wp) :: f ! value from the interpolation
	1390	!!----------------------------------------------------------------------
	1391
[3764]	1392	f = a + x* ( b + x * ( c + d * x ) )
[3294]	1393
	1394	END FUNCTION interp2
	1395
	1396
[3764]	1397	FUNCTION interp3(x, a, b, c, d) RESULT(f)
[3294]	1398	!!----------------------------------------------------------------------
	1399	!! * ROUTINE interp1 *
[3764]	1400	!!
[3294]	1401	!! ** Purpose : Calculate the first order of deriavtive of
	1402	!! a cubic spline function y=a+bx+cx^2+d*x^3
[3764]	1403	!!
[3294]	1404	!! ** Method : f=dy/dx=b+2cx+3dx^2
	1405	!!
	1406	!!----------------------------------------------------------------------
	1407	IMPLICIT NONE
[3764]	1408	REAL(wp), INTENT(in) :: x, a, b, c, d
[3294]	1409	REAL(wp) :: f ! value from the interpolation
	1410	!!----------------------------------------------------------------------
	1411
	1412	f = b + x * ( 2._wp * c + 3._wp * d * x)
	1413
	1414	END FUNCTION interp3
	1415
[3764]	1416
	1417	FUNCTION integ_spline(xl, xr, a, b, c, d) RESULT(f)
[3294]	1418	!!----------------------------------------------------------------------
	1419	!! * ROUTINE interp1 *
[3764]	1420	!!
[3294]	1421	!! ** Purpose : 1-d constrained cubic spline integration
	1422	!!
[3764]	1423	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
	1424	!!
[3294]	1425	!!----------------------------------------------------------------------
	1426	IMPLICIT NONE
[3764]	1427	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
	1428	REAL(wp) :: za1, za2, za3
[3294]	1429	REAL(wp) :: f ! integration result
	1430	!!----------------------------------------------------------------------
	1431
[3764]	1432	za1 = 0.5_wp * b
	1433	za2 = c / 3.0_wp
	1434	za3 = 0.25_wp * d
[3294]	1435
	1436	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
	1437	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
	1438
[3632]	1439	END FUNCTION integ_spline
[3294]	1440
[3]	1441	!!======================================================================
	1442	END MODULE dynhpg
[3632]	1443

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