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

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source: branches/UKMO/restart_datestamp/NEMOGCM/NEMO/OPA_SRC/DYN/dynhpg.F90 @ 5420

Last change on this file since 5420 was 5420, checked in by davestorkey, 9 years ago
Remove keyword updating from UKMO restart_datestamp branch.
File size: 64.3 KB

Rev	Line
[3]	1	MODULE dynhpg
	2	!!======================================================================
	3	!! * MODULE dynhpg *
	4	!! Ocean dynamics: hydrostatic pressure gradient trend
	5	!!======================================================================
[2528]	6	!! History : OPA ! 1987-09 (P. Andrich, M.-A. Foujols) hpg_zco: Original code
	7	!! 5.0 ! 1991-11 (G. Madec)
	8	!! 7.0 ! 1996-01 (G. Madec) hpg_sco: Original code for s-coordinates
	9	!! 8.0 ! 1997-05 (G. Madec) split dynber into dynkeg and dynhpg
	10	!! 8.5 ! 2002-07 (G. Madec) F90: Free form and module
	11	!! 8.5 ! 2002-08 (A. Bozec) hpg_zps: Original code
	12	!! NEMO 1.0 ! 2005-10 (A. Beckmann, B.W. An) various s-coordinate options
[3764]	13	!! ! Original code for hpg_ctl, hpg_hel hpg_wdj, hpg_djc, hpg_rot
[2528]	14	!! - ! 2005-11 (G. Madec) style & small optimisation
	15	!! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase
[3294]	16	!! 3.4 ! 2011-11 (H. Liu) hpg_prj: Original code for s-coordinates
	17	!! ! (A. Coward) suppression of hel, wdj and rot options
[503]	18	!!----------------------------------------------------------------------
[3]	19
	20	!!----------------------------------------------------------------------
[455]	21	!! dyn_hpg : update the momentum trend with the now horizontal
[3]	22	!! gradient of the hydrostatic pressure
[2528]	23	!! dyn_hpg_init : initialisation and control of options
[455]	24	!! hpg_zco : z-coordinate scheme
	25	!! hpg_zps : z-coordinate plus partial steps (interpolation)
	26	!! hpg_sco : s-coordinate (standard jacobian formulation)
	27	!! hpg_djc : s-coordinate (Density Jacobian with Cubic polynomial)
[3294]	28	!! hpg_prj : s-coordinate (Pressure Jacobian with Cubic polynomial)
[3]	29	!!----------------------------------------------------------------------
	30	USE oce ! ocean dynamics and tracers
[4990]	31	USE sbc_oce ! surface variable (only for the flag with ice shelf)
[3]	32	USE dom_oce ! ocean space and time domain
	33	USE phycst ! physical constants
[4990]	34	USE trd_oce ! trends: ocean variables
	35	USE trddyn ! trend manager: dynamics
	36	!
[2715]	37	USE in_out_manager ! I/O manager
[258]	38	USE prtctl ! Print control
[4990]	39	USE lbclnk ! lateral boundary condition
[2715]	40	USE lib_mpp ! MPP library
[4990]	41	USE eosbn2 ! compute density
[3294]	42	USE wrk_nemo ! Memory Allocation
	43	USE timing ! Timing
[3]	44
	45	IMPLICIT NONE
	46	PRIVATE
	47
[2528]	48	PUBLIC dyn_hpg ! routine called by step module
	49	PUBLIC dyn_hpg_init ! routine called by opa module
[3]	50
[4147]	51	! !!* Namelist namdyn_hpg : hydrostatic pressure gradient
	52	LOGICAL , PUBLIC :: ln_hpg_zco !: z-coordinate - full steps
	53	LOGICAL , PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation)
	54	LOGICAL , PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation)
	55	LOGICAL , PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial)
	56	LOGICAL , PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme)
	57	LOGICAL , PUBLIC :: ln_dynhpg_imp !: semi-implicite hpg flag
[455]	58
[3764]	59	INTEGER , PUBLIC :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM)
[455]	60
[3]	61	!! * Substitutions
	62	# include "domzgr_substitute.h90"
	63	# include "vectopt_loop_substitute.h90"
	64	!!----------------------------------------------------------------------
[2528]	65	!! NEMO/OPA 3.3 , NEMO Consortium (2010)
	66	!! $Id$
	67	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
[3]	68	!!----------------------------------------------------------------------
	69	CONTAINS
	70
	71	SUBROUTINE dyn_hpg( kt )
	72	!!---------------------------------------------------------------------
	73	!! * ROUTINE dyn_hpg *
	74	!!
[3764]	75	!! ** Method : Call the hydrostatic pressure gradient routine
[503]	76	!! using the scheme defined in the namelist
[3764]	77	!!
[455]	78	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[4990]	79	!! - send trends to trd_dyn for futher diagnostics (l_trddyn=T)
[503]	80	!!----------------------------------------------------------------------
	81	INTEGER, INTENT(in) :: kt ! ocean time-step index
[3294]	82	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdu, ztrdv
[455]	83	!!----------------------------------------------------------------------
[2528]	84	!
[3294]	85	IF( nn_timing == 1 ) CALL timing_start('dyn_hpg')
[2715]	86	!
[503]	87	IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn)
[3294]	88	CALL wrk_alloc( jpi,jpj,jpk, ztrdu, ztrdv )
[3764]	89	ztrdu(:,:,:) = ua(:,:,:)
	90	ztrdv(:,:,:) = va(:,:,:)
	91	ENDIF
[2528]	92	!
[3294]	93	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
[503]	94	CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate
	95	CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation)
	96	CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation)
[3294]	97	CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial)
	98	CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme)
[455]	99	END SELECT
[2528]	100	!
[503]	101	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
[455]	102	ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:)
	103	ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:)
[4990]	104	CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt )
[3294]	105	CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv )
[3764]	106	ENDIF
[503]	107	!
	108	IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, &
	109	& tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
	110	!
[3294]	111	IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg')
[2715]	112	!
[455]	113	END SUBROUTINE dyn_hpg
	114
	115
[2528]	116	SUBROUTINE dyn_hpg_init
[455]	117	!!----------------------------------------------------------------------
[2528]	118	!! * ROUTINE dyn_hpg_init *
[455]	119	!!
	120	!! ** Purpose : initializations for the hydrostatic pressure gradient
	121	!! computation and consistency control
	122	!!
[1601]	123	!! ** Action : Read the namelist namdyn_hpg and check the consistency
[455]	124	!! with the type of vertical coordinate used (zco, zps, sco)
	125	!!----------------------------------------------------------------------
	126	INTEGER :: ioptio = 0 ! temporary integer
[4147]	127	INTEGER :: ios ! Local integer output status for namelist read
[1601]	128	!!
[3294]	129	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
	130	& ln_hpg_djc, ln_hpg_prj, ln_dynhpg_imp
[455]	131	!!----------------------------------------------------------------------
[2528]	132	!
[4147]	133	REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient
	134	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
	135	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp )
	136
	137	REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient
	138	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
	139	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp )
[4624]	140	IF(lwm) WRITE ( numond, namdyn_hpg )
[2528]	141	!
	142	IF(lwp) THEN ! Control print
[455]	143	WRITE(numout,*)
[2528]	144	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
	145	WRITE(numout,*) '~~~~~~~~~~~~'
[1601]	146	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
	147	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
	148	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
	149	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
	150	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
[3294]	151	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
[1601]	152	WRITE(numout,*) ' time stepping: centered (F) or semi-implicit (T) ln_dynhpg_imp = ', ln_dynhpg_imp
[455]	153	ENDIF
[2528]	154	!
[3294]	155	IF( ln_hpg_djc ) &
	156	& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method &
	157	& currently disabled (bugs under investigation). Please select &
	158	& either ln_hpg_sco or ln_hpg_prj instead')
[2528]	159	!
[3294]	160	IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj) ) &
	161	& CALL ctl_stop('dyn_hpg_init : variable volume key_vvl requires:&
	162	& the standard jacobian formulation hpg_sco or &
	163	& the pressure jacobian formulation hpg_prj')
	164	!
[503]	165	! ! Set nhpg from ln_hpg_... flags
[455]	166	IF( ln_hpg_zco ) nhpg = 0
	167	IF( ln_hpg_zps ) nhpg = 1
	168	IF( ln_hpg_sco ) nhpg = 2
[3294]	169	IF( ln_hpg_djc ) nhpg = 3
	170	IF( ln_hpg_prj ) nhpg = 4
[2528]	171	!
[3294]	172	! ! Consistency check
[3764]	173	ioptio = 0
[455]	174	IF( ln_hpg_zco ) ioptio = ioptio + 1
	175	IF( ln_hpg_zps ) ioptio = ioptio + 1
	176	IF( ln_hpg_sco ) ioptio = ioptio + 1
	177	IF( ln_hpg_djc ) ioptio = ioptio + 1
[3294]	178	IF( ln_hpg_prj ) ioptio = ioptio + 1
[2715]	179	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
[4990]	180	IF( (ln_hpg_zco .OR. ln_hpg_zps .OR. ln_hpg_djc .OR. ln_hpg_prj ) .AND. nn_isf .NE. 0 ) &
	181	& CALL ctl_stop( 'Only hpg_sco has been corrected to work with ice shelf cavity.' )
[503]	182	!
[2528]	183	END SUBROUTINE dyn_hpg_init
[455]	184
	185
	186	SUBROUTINE hpg_zco( kt )
	187	!!---------------------------------------------------------------------
	188	!! * ROUTINE hpg_zco *
	189	!!
	190	!! ** Method : z-coordinate case, levels are horizontal surfaces.
	191	!! The now hydrostatic pressure gradient at a given level, jk,
	192	!! is computed by taking the vertical integral of the in-situ
	193	!! density gradient along the model level from the suface to that
	194	!! level: zhpi = grav .....
	195	!! zhpj = grav .....
[3]	196	!! add it to the general momentum trend (ua,va).
[455]	197	!! ua = ua - 1/e1u * zhpi
	198	!! va = va - 1/e2v * zhpj
[3764]	199	!!
[3]	200	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[503]	201	!!----------------------------------------------------------------------
	202	INTEGER, INTENT(in) :: kt ! ocean time-step index
	203	!!
	204	INTEGER :: ji, jj, jk ! dummy loop indices
	205	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
[3764]	206	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3]	207	!!----------------------------------------------------------------------
[3764]	208	!
[3294]	209	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
	210	!
[3]	211	IF( kt == nit000 ) THEN
	212	IF(lwp) WRITE(numout,*)
[455]	213	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
	214	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
[3]	215	ENDIF
	216
[3764]	217	zcoef0 = - grav * 0.5_wp ! Local constant initialization
	218
[455]	219	! Surface value
[3]	220	DO jj = 2, jpjm1
	221	DO ji = fs_2, fs_jpim1 ! vector opt.
[455]	222	zcoef1 = zcoef0 * fse3w(ji,jj,1)
	223	! hydrostatic pressure gradient
	224	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
	225	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
[3]	226	! add to the general momentum trend
[455]	227	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
	228	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
	229	END DO
	230	END DO
[3294]	231
[503]	232	!
[455]	233	! interior value (2=<jk=<jpkm1)
[3]	234	DO jk = 2, jpkm1
[455]	235	DO jj = 2, jpjm1
[3]	236	DO ji = fs_2, fs_jpim1 ! vector opt.
[455]	237	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
	238	! hydrostatic pressure gradient
	239	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
	240	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
	241	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
	242
	243	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
	244	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
	245	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
[3]	246	! add to the general momentum trend
[455]	247	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	248	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
[3]	249	END DO
	250	END DO
	251	END DO
[503]	252	!
[3294]	253	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
	254	!
[455]	255	END SUBROUTINE hpg_zco
[216]	256
[3]	257
[455]	258	SUBROUTINE hpg_zps( kt )
[3]	259	!!---------------------------------------------------------------------
[455]	260	!! * ROUTINE hpg_zps *
[3764]	261	!!
[455]	262	!! ** Method : z-coordinate plus partial steps case. blahblah...
[3764]	263	!!
[3]	264	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[3764]	265	!!----------------------------------------------------------------------
[503]	266	INTEGER, INTENT(in) :: kt ! ocean time-step index
	267	!!
	268	INTEGER :: ji, jj, jk ! dummy loop indices
	269	INTEGER :: iku, ikv ! temporary integers
	270	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
[3764]	271	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3]	272	!!----------------------------------------------------------------------
[3294]	273	!
	274	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
	275	!
[3]	276	IF( kt == nit000 ) THEN
	277	IF(lwp) WRITE(numout,*)
[455]	278	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
[503]	279	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
[3]	280	ENDIF
	281
[3294]	282
[503]	283	! Local constant initialization
[2528]	284	zcoef0 = - grav * 0.5_wp
[3]	285
[2528]	286	! Surface value (also valid in partial step case)
[3]	287	DO jj = 2, jpjm1
	288	DO ji = fs_2, fs_jpim1 ! vector opt.
[170]	289	zcoef1 = zcoef0 * fse3w(ji,jj,1)
[3]	290	! hydrostatic pressure gradient
[455]	291	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
	292	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
[3]	293	! add to the general momentum trend
	294	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
	295	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
	296	END DO
	297	END DO
	298
[3294]	299
[503]	300	! interior value (2=<jk=<jpkm1)
[3]	301	DO jk = 2, jpkm1
	302	DO jj = 2, jpjm1
	303	DO ji = fs_2, fs_jpim1 ! vector opt.
[170]	304	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
[3]	305	! hydrostatic pressure gradient
	306	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
[455]	307	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
	308	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
[3]	309
	310	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
[455]	311	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
	312	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
[3]	313	! add to the general momentum trend
	314	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	315	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
[455]	316	END DO
[3]	317	END DO
	318	END DO
	319
[3294]	320
[2528]	321	! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
[3]	322	DO jj = 2, jpjm1
	323	DO ji = 2, jpim1
[2528]	324	iku = mbku(ji,jj)
	325	ikv = mbkv(ji,jj)
[3]	326	zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) )
	327	zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) )
[2528]	328	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
	329	ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value
	330	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
	331	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj)
	332	ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
[3]	333	ENDIF
[2528]	334	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
	335	va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value
	336	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
	337	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj)
	338	va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
[3]	339	ENDIF
	340	END DO
	341	END DO
[503]	342	!
[3294]	343	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
	344	!
[455]	345	END SUBROUTINE hpg_zps
[216]	346
[3]	347
[455]	348	SUBROUTINE hpg_sco( kt )
[3]	349	!!---------------------------------------------------------------------
[455]	350	!! * ROUTINE hpg_sco *
[3]	351	!!
[455]	352	!! ** Method : s-coordinate case. Jacobian scheme.
	353	!! The now hydrostatic pressure gradient at a given level, jk,
	354	!! is computed by taking the vertical integral of the in-situ
[3]	355	!! density gradient along the model level from the suface to that
[455]	356	!! level. s-coordinates (ln_sco): a corrective term is added
	357	!! to the horizontal pressure gradient :
	358	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
	359	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
[3]	360	!! add it to the general momentum trend (ua,va).
[455]	361	!! ua = ua - 1/e1u * zhpi
	362	!! va = va - 1/e2v * zhpj
[3]	363	!!
	364	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[503]	365	!!----------------------------------------------------------------------
	366	INTEGER, INTENT(in) :: kt ! ocean time-step index
	367	!!
[4990]	368	INTEGER :: ji, jj, jk, iku, ikv, ikt, iktp1i, iktp1j ! dummy loop indices
	369	REAL(wp) :: zcoef0, zuap, zvap, znad, ze3wu, ze3wv, zuapint, zvapint, zhpjint, zhpiint, zdzwt, zdzwtjp1, zdzwtip1 ! temporary scalars
	370	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj, zrhd
	371	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop
	372	REAL(wp), POINTER, DIMENSION(:,:) :: ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj
[3]	373	!!----------------------------------------------------------------------
[3294]	374	!
[4990]	375	CALL wrk_alloc( jpi,jpj, 2, ztstop)
	376	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
	377	CALL wrk_alloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
[3294]	378	!
[4990]	379	IF( kt == nit000 ) THEN
[3]	380	IF(lwp) WRITE(numout,*)
[455]	381	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
	382	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
[3]	383	ENDIF
	384
[503]	385	! Local constant initialization
[2528]	386	zcoef0 = - grav * 0.5_wp
[592]	387	! To use density and not density anomaly
[4990]	388	! IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
	389	! ELSE ; znad = 0._wp ! Fixed volume
	390	! ENDIF
	391	znad=1._wp
	392	! iniitialised to 0. zhpi zhpi
	393	zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp
[455]	394
[4990]	395	!==================================================================================
	396	!=====Compute iceload and contribution of the half first wet layer =================
	397	!===================================================================================
	398
	399	! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude)
	400	ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp
	401
	402	! compute density of the water displaced by the ice shelf
	403	zrhd = rhd ! save rhd
	404	DO jk = 1, jpk
	405	zdept(:,:)=gdept_1d(jk)
	406	CALL eos(ztstop(:,:,:),zdept(:,:),rhd(:,:,jk))
	407	END DO
	408	WHERE ( tmask(:,:,:) == 1._wp)
	409	rhd(:,:,:) = zrhd(:,:,:) ! replace wet cell by the saved rhd
	410	END WHERE
	411
	412	! compute rhd at the ice/oce interface (ice shelf side)
	413	CALL eos(ztstop,risfdep,zrhdtop_isf)
	414
	415	! compute rhd at the ice/oce interface (ocean side)
	416	DO ji=1,jpi
	417	DO jj=1,jpj
	418	ikt=mikt(ji,jj)
	419	ztstop(ji,jj,1)=tsn(ji,jj,ikt,1)
	420	ztstop(ji,jj,2)=tsn(ji,jj,ikt,2)
	421	END DO
	422	END DO
	423	CALL eos(ztstop,risfdep,zrhdtop_oce)
	424	!
	425	! Surface value + ice shelf gradient
	426	! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v)
	427	ziceload = 0._wp
	428	DO jj = 1, jpj
	429	DO ji = 1, jpi ! vector opt.
	430	ikt=mikt(ji,jj)
	431	ziceload(ji,jj) = ziceload(ji,jj) + (znad + rhd(ji,jj,1) ) * fse3w(ji,jj,1) * (1._wp - tmask(ji,jj,1))
	432	DO jk=2,ikt-1
	433	ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + rhd(ji,jj,jk-1) + rhd(ji,jj,jk)) * fse3w(ji,jj,jk) &
	434	& * (1._wp - tmask(ji,jj,jk))
	435	END DO
	436	IF (ikt .GE. 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + rhd(ji,jj,ikt-1)) &
	437	& * ( risfdep(ji,jj) - gdept_1d(ikt-1) )
	438	END DO
	439	END DO
	440	riceload(:,:) = 0.0_wp ; riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5
	441	! compute zp from z=0 to first T wet point (correction due to zps not yet applied)
[455]	442	DO jj = 2, jpjm1
[3764]	443	DO ji = fs_2, fs_jpim1 ! vector opt.
[4990]	444	ikt=mikt(ji,jj) ; iktp1i=mikt(ji+1,jj); iktp1j=mikt(ji,jj+1)
	445	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
	446	! we assume ISF is in isostatic equilibrium
	447	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * fse3w(ji+1,jj ,iktp1i) &
	448	& * ( 2._wp * znad + rhd(ji+1,jj ,iktp1i) + zrhdtop_oce(ji+1,jj ) ) &
	449	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
	450	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
	451	& + ( ziceload(ji+1,jj) - ziceload(ji,jj)) )
	452	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * fse3w(ji ,jj+1,iktp1j) &
	453	& * ( 2._wp * znad + rhd(ji ,jj+1,iktp1j) + zrhdtop_oce(ji ,jj+1) ) &
	454	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
	455	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
	456	& + ( ziceload(ji,jj+1) - ziceload(ji,jj) ) )
	457	! s-coordinate pressure gradient correction (=0 if z coordinate)
[2528]	458	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
[455]	459	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
[2528]	460	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
[455]	461	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
	462	! add to the general momentum trend
[4990]	463	ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
	464	va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
[3764]	465	END DO
	466	END DO
[4990]	467	!==================================================================================
	468	!===== Compute partial cell contribution for the top cell =========================
	469	!==================================================================================
	470	DO jj = 2, jpjm1
	471	DO ji = fs_2, fs_jpim1 ! vector opt.
	472	iku = miku(ji,jj) ;
	473	zpshpi(ji,jj)=0.0_wp ; zpshpj(ji,jj)=0.0_wp
	474	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))
	475	! u direction
	476	IF ( iku .GT. 1 ) THEN
	477	! case iku
	478	zhpi(ji,jj,iku) = zcoef0 / e1u(ji,jj) * ze3wu &
	479	& * ( rhd (ji+1,jj,iku) + rhd (ji,jj,iku) &
	480	& + SIGN(1._wp,ze3wu) * grui(ji,jj) + 2._wp * znad )
	481	! corrective term ( = 0 if z coordinate )
	482	zuap = -zcoef0 * ( arui(ji,jj) + 2._wp * znad ) * gzui(ji,jj) / e1u(ji,jj)
	483	! zhpi will be added in interior loop
	484	ua(ji,jj,iku) = ua(ji,jj,iku) + zuap
	485	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
	486	IF (mbku(ji,jj) == iku + 1) zpshpi(ji,jj) = zhpi(ji,jj,iku)
[3764]	487
[4990]	488	! case iku + 1 (remove the zphi term added in the interior loop and compute the one corrected for zps)
	489	zhpiint = zcoef0 / e1u(ji,jj) &
	490	& * ( fse3w(ji+1,jj ,iku+1) * ( (rhd(ji+1,jj,iku+1) + znad) &
	491	& + (rhd(ji+1,jj,iku ) + znad) ) * tmask(ji+1,jj,iku) &
	492	& - fse3w(ji ,jj ,iku+1) * ( (rhd(ji ,jj,iku+1) + znad) &
	493	& + (rhd(ji ,jj,iku ) + znad) ) * tmask(ji ,jj,iku) )
	494	zhpi(ji,jj,iku+1) = zcoef0 / e1u(ji,jj) * ge3rui(ji,jj) - zhpiint
	495	END IF
	496
	497	! v direction
	498	ikv = mikv(ji,jj)
	499	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))
	500	IF ( ikv .GT. 1 ) THEN
	501	! case ikv
	502	zhpj(ji,jj,ikv) = zcoef0 / e2v(ji,jj) * ze3wv &
	503	& * ( rhd(ji,jj+1,ikv) + rhd (ji,jj,ikv) &
	504	& + SIGN(1._wp,ze3wv) * grvi(ji,jj) + 2._wp * znad )
	505	! corrective term ( = 0 if z coordinate )
	506	zvap = -zcoef0 * ( arvi(ji,jj) + 2._wp * znad ) * gzvi(ji,jj) / e2v(ji,jj)
	507	! zhpi will be added in interior loop
	508	va(ji,jj,ikv) = va(ji,jj,ikv) + zvap
	509	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
	510	IF (mbkv(ji,jj) == ikv + 1) zpshpj(ji,jj) = zhpj(ji,jj,ikv)
	511
	512	! case ikv + 1 (remove the zphj term added in the interior loop and compute the one corrected for zps)
	513	zhpjint = zcoef0 / e2v(ji,jj) &
	514	& * ( fse3w(ji ,jj+1,ikv+1) * ( (rhd(ji,jj+1,ikv+1) + znad) &
	515	& + (rhd(ji,jj+1,ikv ) + znad) ) * tmask(ji,jj+1,ikv) &
	516	& - fse3w(ji ,jj ,ikv+1) * ( (rhd(ji,jj ,ikv+1) + znad) &
	517	& + (rhd(ji,jj ,ikv ) + znad) ) * tmask(ji,jj ,ikv) )
	518	zhpj(ji,jj,ikv+1) = zcoef0 / e2v(ji,jj) * ge3rvi(ji,jj) - zhpjint
	519	END IF
	520	END DO
	521	END DO
	522
	523	!==================================================================================
	524	!===== Compute interior value =====================================================
	525	!==================================================================================
	526
	527	DO jj = 2, jpjm1
	528	DO ji = fs_2, fs_jpim1 ! vector opt.
	529	iku=miku(ji,jj); ikv=mikv(ji,jj)
	530	DO jk = 2, jpkm1
[455]	531	! hydrostatic pressure gradient along s-surfaces
[4990]	532	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
	533	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) + zhpi(ji,jj,jk-1) &
	534	& + zcoef0 / e1u(ji,jj) &
	535	& * ( fse3w(ji+1,jj ,jk) * ( (rhd(ji+1,jj,jk ) + znad) &
	536	& + (rhd(ji+1,jj,jk-1) + znad) ) * tmask(ji+1,jj,jk-1) &
	537	& - fse3w(ji ,jj ,jk) * ( (rhd(ji ,jj,jk ) + znad) &
	538	& + (rhd(ji ,jj,jk-1) + znad) ) * tmask(ji ,jj,jk-1) )
[455]	539	! s-coordinate pressure gradient correction
[4990]	540	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
	541	zuap = - zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
	542	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) * umask(ji,jj,jk-1)
	543	ua(ji,jj,jk) = ua(ji,jj,jk) + ( zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
	544
	545	! hydrostatic pressure gradient along s-surfaces
	546	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
	547	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) + zhpj(ji,jj,jk-1) &
	548	& + zcoef0 / e2v(ji,jj) &
	549	& * ( fse3w(ji ,jj+1,jk) * ( (rhd(ji,jj+1,jk ) + znad) &
	550	& + (rhd(ji,jj+1,jk-1) + znad) ) * tmask(ji,jj+1,jk-1) &
	551	& - fse3w(ji ,jj ,jk) * ( (rhd(ji,jj ,jk ) + znad) &
	552	& + (rhd(ji,jj ,jk-1) + znad) ) * tmask(ji,jj ,jk-1) )
	553	! s-coordinate pressure gradient correction
	554	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
	555	zvap = - zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
	556	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) * vmask(ji,jj,jk-1)
[455]	557	! add to the general momentum trend
[4990]	558	va(ji,jj,jk) = va(ji,jj,jk) + ( zhpj(ji,jj,jk) + zvap ) * vmask(ji,jj,jk)
[455]	559	END DO
	560	END DO
	561	END DO
[4990]	562
	563	!==================================================================================
	564	!===== Compute bottom cell contribution (partial cell) ============================
	565	!==================================================================================
	566
	567	# if defined key_vectopt_loop
	568	jj = 1
	569	DO ji = jpi+2, jpij-jpi-1 ! vector opt. (forced unrolling)
	570	# else
	571	DO jj = 2, jpjm1
	572	DO ji = 2, jpim1
	573	# endif
	574	iku = mbku(ji,jj)
	575	ikv = mbkv(ji,jj)
	576
	577	IF (iku .GT. 1) THEN
	578	! remove old value (interior case)
	579	zuap = -zcoef0 * ( rhd (ji+1,jj ,iku) + rhd (ji,jj,iku) + 2._wp * znad ) &
	580	& * ( fsde3w(ji+1,jj ,iku) - fsde3w(ji,jj,iku) ) / e1u(ji,jj)
	581	ua(ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) - zuap
	582	! put new value
	583	! -zpshpi to avoid double contribution of the partial step in the top layer
	584	zuap = -zcoef0 * ( aru(ji,jj) + 2._wp * znad ) * gzu(ji,jj) / e1u(ji,jj)
	585	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) + zcoef0 / e1u(ji,jj) * ge3ru(ji,jj) - zpshpi(ji,jj)
	586	ua(ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) + zuap
	587	END IF
	588	! v direction
	589	IF (ikv .GT. 1) THEN
	590	! remove old value (interior case)
	591	zvap = -zcoef0 * ( rhd (ji ,jj+1,ikv) + rhd (ji,jj,ikv) + 2._wp * znad ) &
	592	& * ( fsde3w(ji ,jj+1,ikv) - fsde3w(ji,jj,ikv) ) / e2v(ji,jj)
	593	va(ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) - zvap
	594	! put new value
	595	! -zpshpj to avoid double contribution of the partial step in the top layer
	596	zvap = -zcoef0 * ( arv(ji,jj) + 2._wp * znad ) * gzv(ji,jj) / e2v(ji,jj)
	597	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) + zcoef0 / e2v(ji,jj) * ge3rv(ji,jj) - zpshpj(ji,jj)
	598	va(ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) + zvap
	599	END IF
	600	# if ! defined key_vectopt_loop
	601	END DO
	602	# endif
	603	END DO
	604
	605	! set back to original density value into the ice shelf cell (maybe useless because it is masked)
	606	rhd = zrhd
[503]	607	!
[4990]	608	CALL wrk_dealloc( jpi,jpj,2, ztstop)
	609	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
	610	CALL wrk_dealloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
[3294]	611	!
[455]	612	END SUBROUTINE hpg_sco
	613
[4990]	614
[455]	615	SUBROUTINE hpg_djc( kt )
	616	!!---------------------------------------------------------------------
	617	!! * ROUTINE hpg_djc *
	618	!!
	619	!! ** Method : Density Jacobian with Cubic polynomial scheme
[3764]	620	!!
[503]	621	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
[455]	622	!!----------------------------------------------------------------------
[503]	623	INTEGER, INTENT(in) :: kt ! ocean time-step index
	624	!!
	625	INTEGER :: ji, jj, jk ! dummy loop indices
	626	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
	627	REAL(wp) :: z1_10, cffu, cffx ! " "
	628	REAL(wp) :: z1_12, cffv, cffy ! " "
[3764]	629	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3294]	630	REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw
	631	REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow
	632	REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k
[455]	633	!!----------------------------------------------------------------------
[3294]	634	!
[3764]	635	CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
	636	CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
	637	CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
[3294]	638	!
[455]	639
	640	IF( kt == nit000 ) THEN
	641	IF(lwp) WRITE(numout,*)
	642	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
	643	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
[216]	644	ENDIF
	645
[503]	646	! Local constant initialization
[2528]	647	zcoef0 = - grav * 0.5_wp
	648	z1_10 = 1._wp / 10._wp
	649	z1_12 = 1._wp / 12._wp
[455]	650
	651	!----------------------------------------------------------------------------------------
	652	! compute and store in provisional arrays elementary vertical and horizontal differences
	653	!----------------------------------------------------------------------------------------
	654
	655	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
	656
	657	DO jk = 2, jpkm1
	658	DO jj = 2, jpjm1
	659	DO ji = fs_2, fs_jpim1 ! vector opt.
	660	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
	661	dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1)
	662	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
	663	dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk )
	664	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
	665	dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk )
	666	END DO
	667	END DO
	668	END DO
	669
	670	!-------------------------------------------------------------------------
	671	! compute harmonic averages using eq. 5.18
	672	!-------------------------------------------------------------------------
	673	zep = 1.e-15
	674
[503]	675	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
	676	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
[455]	677
	678	DO jk = 2, jpkm1
	679	DO jj = 2, jpjm1
	680	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	681	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
[455]	682
[2528]	683	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
	684	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
[3764]	685
[2528]	686	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
	687	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
[455]	688
	689	IF( cffw > zep) THEN
[2528]	690	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
	691	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
[455]	692	ELSE
[2528]	693	drhow(ji,jj,jk) = 0._wp
[455]	694	ENDIF
	695
[2528]	696	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
	697	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
[455]	698
	699	IF( cffu > zep ) THEN
[2528]	700	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
	701	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
[455]	702	ELSE
[2528]	703	drhou(ji,jj,jk ) = 0._wp
[455]	704	ENDIF
	705
	706	IF( cffx > zep ) THEN
[2528]	707	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
	708	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
[455]	709	ELSE
[2528]	710	dzu(ji,jj,jk) = 0._wp
[455]	711	ENDIF
	712
	713	IF( cffv > zep ) THEN
[2528]	714	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
	715	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
[455]	716	ELSE
[2528]	717	drhov(ji,jj,jk) = 0._wp
[455]	718	ENDIF
	719
	720	IF( cffy > zep ) THEN
[2528]	721	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
	722	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
[455]	723	ELSE
[2528]	724	dzv(ji,jj,jk) = 0._wp
[455]	725	ENDIF
	726
	727	END DO
	728	END DO
	729	END DO
	730
	731	!----------------------------------------------------------------------------------
	732	! apply boundary conditions at top and bottom using 5.36-5.37
	733	!----------------------------------------------------------------------------------
[2528]	734	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
	735	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
	736	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
[455]	737
[2528]	738	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
	739	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
	740	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
[455]	741
	742
	743	!--------------------------------------------------------------
	744	! Upper half of top-most grid box, compute and store
	745	!-------------------------------------------------------------
	746
	747	!!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified
	748	! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
	749
	750	DO jj = 2, jpjm1
	751	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	752	rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) &
	753	& * ( rhd(ji,jj,1) &
	754	& + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) &
	755	& * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) &
[3764]	756	& / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) )
[455]	757	END DO
	758	END DO
	759
	760	!!bug gm : here also, simplification is possible
	761	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
	762
	763	DO jk = 2, jpkm1
	764	DO jj = 2, jpjm1
	765	DO ji = fs_2, fs_jpim1 ! vector opt.
	766
	767	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
	768	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) &
	769	& - grav * z1_10 * ( &
	770	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
	771	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
	772	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
	773	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
	774	& )
	775
	776	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
	777	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) &
	778	& - grav* z1_10 * ( &
	779	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
	780	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
	781	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
	782	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
	783	& )
	784
	785	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
	786	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) &
	787	& - grav* z1_10 * ( &
	788	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
	789	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
	790	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
	791	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
	792	& )
	793
	794	END DO
	795	END DO
	796	END DO
	797	CALL lbc_lnk(rho_k,'W',1.)
	798	CALL lbc_lnk(rho_i,'U',1.)
	799	CALL lbc_lnk(rho_j,'V',1.)
	800
	801
	802	! ---------------
	803	! Surface value
	804	! ---------------
	805	DO jj = 2, jpjm1
	806	DO ji = fs_2, fs_jpim1 ! vector opt.
	807	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj)
	808	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj)
	809	! add to the general momentum trend
	810	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
	811	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
	812	END DO
	813	END DO
	814
	815	! ----------------
	816	! interior value (2=<jk=<jpkm1)
	817	! ----------------
	818	DO jk = 2, jpkm1
[3764]	819	DO jj = 2, jpjm1
[455]	820	DO ji = fs_2, fs_jpim1 ! vector opt.
	821	! hydrostatic pressure gradient along s-surfaces
	822	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
	823	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
	824	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj)
	825	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
	826	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
	827	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj)
	828	! add to the general momentum trend
	829	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	830	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
	831	END DO
	832	END DO
	833	END DO
[503]	834	!
[3764]	835	CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
	836	CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
	837	CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
[2715]	838	!
[455]	839	END SUBROUTINE hpg_djc
	840
	841
[3294]	842	SUBROUTINE hpg_prj( kt )
[455]	843	!!---------------------------------------------------------------------
[3294]	844	!! * ROUTINE hpg_prj *
[455]	845	!!
[3294]	846	!! ** Method : s-coordinate case.
	847	!! A Pressure-Jacobian horizontal pressure gradient method
	848	!! based on the constrained cubic-spline interpolation for
	849	!! all vertical coordinate systems
[455]	850	!!
[3294]	851	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[455]	852	!!----------------------------------------------------------------------
[3294]	853	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
	854	INTEGER, INTENT(in) :: kt ! ocean time-step index
[503]	855	!!
[3294]	856	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
	857	REAL(wp) :: zcoef0, znad ! temporary scalars
[503]	858	!!
[3294]	859	!! The local variables for the correction term
	860	INTEGER :: jk1, jis, jid, jjs, jjd
	861	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
[3764]	862	REAL(wp) :: zrhdt1
[3294]	863	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
[3764]	864	REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh
[3294]	865	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
[455]	866	!!----------------------------------------------------------------------
[3294]	867	!
[3764]	868	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
	869	CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh )
[3294]	870	!
[455]	871	IF( kt == nit000 ) THEN
	872	IF(lwp) WRITE(numout,*)
[3294]	873	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
	874	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
[3]	875	ENDIF
	876
[3294]	877	!!----------------------------------------------------------------------
	878	! Local constant initialization
[3764]	879	zcoef0 = - grav
[3294]	880	znad = 0.0_wp
	881	IF( lk_vvl ) znad = 1._wp
[3]	882
[3294]	883	! Clean 3-D work arrays
	884	zhpi(:,:,:) = 0._wp
	885	zrhh(:,:,:) = rhd(:,:,:)
[3764]	886
[3294]	887	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
	888	DO jj = 1, jpj
[3764]	889	DO ji = 1, jpi
[3294]	890	jk = mbathy(ji,jj)
	891	IF( jk <= 0 ) THEN; zrhh(ji,jj,:) = 0._wp
	892	ELSE IF(jk == 1) THEN; zrhh(ji,jj, jk+1:jpk) = rhd(ji,jj,jk)
	893	ELSE IF(jk < jpkm1) THEN
	894	DO jkk = jk+1, jpk
	895	zrhh(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1), &
	896	fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2))
[3764]	897	END DO
[3294]	898	ENDIF
	899	END DO
	900	END DO
[3]	901
[3632]	902	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
[4990]	903	DO jj = 1, jpj
	904	DO ji = 1, jpi
	905	zdept(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) - sshn(ji,jj) * znad
	906	END DO
	907	END DO
[455]	908
[4990]	909	DO jk = 2, jpk
	910	DO jj = 1, jpj
	911	DO ji = 1, jpi
	912	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + fse3w(ji,jj,jk)
	913	END DO
	914	END DO
	915	END DO
[455]	916
[4990]	917	fsp(:,:,:) = zrhh (:,:,:)
[3632]	918	xsp(:,:,:) = zdept(:,:,:)
	919
[3764]	920	! Construct the vertical density profile with the
[3294]	921	! constrained cubic spline interpolation
	922	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
[3764]	923	CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type)
[3294]	924
	925	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
	926	DO jj = 2, jpj
[3764]	927	DO ji = 2, jpi
[3632]	928	zrhdt1 = zrhh(ji,jj,1) - interp3(zdept(ji,jj,1),asp(ji,jj,1), &
[3294]	929	bsp(ji,jj,1), csp(ji,jj,1), &
[3632]	930	dsp(ji,jj,1) ) * 0.25_wp * fse3w(ji,jj,1)
[3294]	931
	932	! assuming linear profile across the top half surface layer
[3764]	933	zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * zrhdt1
[3294]	934	END DO
[455]	935	END DO
	936
[3294]	937	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
[3764]	938	DO jk = 2, jpkm1
	939	DO jj = 2, jpj
[3294]	940	DO ji = 2, jpi
	941	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
[3632]	942	integ_spline(zdept(ji,jj,jk-1), zdept(ji,jj,jk),&
[3294]	943	asp(ji,jj,jk-1), bsp(ji,jj,jk-1), &
	944	csp(ji,jj,jk-1), dsp(ji,jj,jk-1))
	945	END DO
	946	END DO
[455]	947	END DO
	948
[3294]	949	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
[3764]	950	DO jj = 2, jpjm1
	951	DO ji = 2, jpim1
[4292]	952	zu(ji,jj,1) = - ( fse3u(ji,jj,1) - sshn(ji,jj) * znad) ! probable bug: changed from sshu_n for ztilde compilation
	953	zv(ji,jj,1) = - ( fse3v(ji,jj,1) - sshn(ji,jj) * znad) ! probable bug: changed from sshv_n for ztilde compilation
[3294]	954	END DO
[455]	955	END DO
	956
[3764]	957	DO jk = 2, jpkm1
	958	DO jj = 2, jpjm1
	959	DO ji = 2, jpim1
[3294]	960	zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk)
	961	zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk)
	962	END DO
	963	END DO
[455]	964	END DO
[3764]	965
	966	DO jk = 1, jpkm1
	967	DO jj = 2, jpjm1
	968	DO ji = 2, jpim1
[3294]	969	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk)
	970	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk)
	971	END DO
	972	END DO
	973	END DO
[455]	974
[3632]	975	DO jk = 1, jpkm1
	976	DO jj = 2, jpjm1
	977	DO ji = 2, jpim1
	978	zu(ji,jj,jk) = min(zu(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
	979	zu(ji,jj,jk) = max(zu(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
	980	zv(ji,jj,jk) = min(zv(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
	981	zv(ji,jj,jk) = max(zv(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
	982	END DO
	983	END DO
	984	END DO
	985
	986
[3764]	987	DO jk = 1, jpkm1
	988	DO jj = 2, jpjm1
	989	DO ji = 2, jpim1
[3294]	990	zpwes = 0._wp; zpwed = 0._wp
	991	zpnss = 0._wp; zpnsd = 0._wp
	992	zuijk = zu(ji,jj,jk)
	993	zvijk = zv(ji,jj,jk)
	994
	995	!!!!! for u equation
	996	IF( jk <= mbku(ji,jj) ) THEN
[3632]	997	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
[3294]	998	jis = ji + 1; jid = ji
	999	ELSE
	1000	jis = ji; jid = ji +1
	1001	ENDIF
	1002
	1003	! integrate the pressure on the shallow side
[3764]	1004	jk1 = jk
[3632]	1005	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
[3294]	1006	IF( jk1 == mbku(ji,jj) ) THEN
[3632]	1007	zuijk = -zdept(jis,jj,jk1)
[3294]	1008	EXIT
	1009	ENDIF
[3632]	1010	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
[3764]	1011	zpwes = zpwes + &
[3632]	1012	integ_spline(zdept(jis,jj,jk1), zdeps, &
[3294]	1013	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
	1014	csp(jis,jj,jk1), dsp(jis,jj,jk1))
	1015	jk1 = jk1 + 1
	1016	END DO
[3764]	1017
[3294]	1018	! integrate the pressure on the deep side
[3764]	1019	jk1 = jk
[3632]	1020	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
[3294]	1021	IF( jk1 == 1 ) THEN
[3632]	1022	zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad)
	1023	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
	1024	bsp(jid,jj,1), csp(jid,jj,1), &
	1025	dsp(jid,jj,1)) * zdeps
	1026	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
[3294]	1027	EXIT
	1028	ENDIF
[3632]	1029	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
[3764]	1030	zpwed = zpwed + &
[3632]	1031	integ_spline(zdeps, zdept(jid,jj,jk1), &
[3294]	1032	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
	1033	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
	1034	jk1 = jk1 - 1
	1035	END DO
[3764]	1036
[3294]	1037	! update the momentum trends in u direction
	1038
	1039	zdpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk))
	1040	IF( lk_vvl ) THEN
[3764]	1041	zdpdx2 = zcoef0 / e1u(ji,jj) * &
	1042	( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) )
[3294]	1043	ELSE
[3764]	1044	zdpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
[3294]	1045	ENDIF
	1046
	1047	ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * &
	1048	& umask(ji,jj,jk) * tmask(ji,jj,jk) * tmask(ji+1,jj,jk)
	1049	ENDIF
[3764]	1050
[3294]	1051	!!!!! for v equation
	1052	IF( jk <= mbkv(ji,jj) ) THEN
[3632]	1053	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
[3294]	1054	jjs = jj + 1; jjd = jj
	1055	ELSE
	1056	jjs = jj ; jjd = jj + 1
	1057	ENDIF
	1058
	1059	! integrate the pressure on the shallow side
[3764]	1060	jk1 = jk
[3632]	1061	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
[3294]	1062	IF( jk1 == mbkv(ji,jj) ) THEN
[3632]	1063	zvijk = -zdept(ji,jjs,jk1)
[3294]	1064	EXIT
	1065	ENDIF
[3632]	1066	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
[3764]	1067	zpnss = zpnss + &
[3632]	1068	integ_spline(zdept(ji,jjs,jk1), zdeps, &
[3294]	1069	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
	1070	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
	1071	jk1 = jk1 + 1
	1072	END DO
[3764]	1073
[3294]	1074	! integrate the pressure on the deep side
[3764]	1075	jk1 = jk
[3632]	1076	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
[3294]	1077	IF( jk1 == 1 ) THEN
[3632]	1078	zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad)
	1079	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
	1080	bsp(ji,jjd,1), csp(ji,jjd,1), &
	1081	dsp(ji,jjd,1) ) * zdeps
	1082	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
[3294]	1083	EXIT
	1084	ENDIF
[3632]	1085	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
[3764]	1086	zpnsd = zpnsd + &
[3632]	1087	integ_spline(zdeps, zdept(ji,jjd,jk1), &
[3294]	1088	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
	1089	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
	1090	jk1 = jk1 - 1
	1091	END DO
	1092
[3764]	1093
[3294]	1094	! update the momentum trends in v direction
	1095
	1096	zdpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk))
	1097	IF( lk_vvl ) THEN
	1098	zdpdy2 = zcoef0 / e2v(ji,jj) * &
[3764]	1099	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) )
[3294]	1100	ELSE
[3764]	1101	zdpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
[3294]	1102	ENDIF
	1103
	1104	va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2)*&
	1105	& vmask(ji,jj,jk)tmask(ji,jj,jk)tmask(ji,jj+1,jk)
	1106	ENDIF
	1107
[3764]	1108
[3294]	1109	END DO
	1110	END DO
[455]	1111	END DO
[503]	1112	!
[3764]	1113	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
	1114	CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh )
[2715]	1115	!
[3294]	1116	END SUBROUTINE hpg_prj
[455]	1117
[4990]	1118
[3294]	1119	SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type)
	1120	!!----------------------------------------------------------------------
	1121	!! * ROUTINE cspline *
[3764]	1122	!!
[3294]	1123	!! ** Purpose : constrained cubic spline interpolation
[3764]	1124	!!
	1125	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
[4990]	1126	!!
[3294]	1127	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
	1128	!!----------------------------------------------------------------------
	1129	IMPLICIT NONE
	1130	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate
[3764]	1131	REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of
[3294]	1132	! the interpoated function
[3764]	1133	INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline
[3294]	1134	! 2: Linear
[4990]	1135	!
[3294]	1136	INTEGER :: ji, jj, jk ! dummy loop indices
	1137	INTEGER :: jpi, jpj, jpkm1
	1138	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
	1139	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
	1140	REAL(wp) :: zdf(size(fsp,3))
	1141	!!----------------------------------------------------------------------
	1142
	1143	jpi = size(fsp,1)
	1144	jpj = size(fsp,2)
	1145	jpkm1 = size(fsp,3) - 1
	1146
[3764]	1147
[3294]	1148	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
	1149	DO ji = 1, jpi
	1150	DO jj = 1, jpj
[3764]	1151	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
[3294]	1152	! DO jk = 2, jpkm1-1
[3764]	1153	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
	1154	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1155	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
	1156	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
	1157	!
	1158	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
[3764]	1159	!
[3294]	1160	! IF(zdf1 * zdf2 <= 0._wp) THEN
	1161	! zdf(jk) = 0._wp
	1162	! ELSE
	1163	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
	1164	! ENDIF
	1165	! END DO
[3764]	1166
[3294]	1167	!!Simply geometric average
	1168	DO jk = 2, jpkm1-1
	1169	zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1))
	1170	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk))
[3764]	1171
[3294]	1172	IF(zdf1 * zdf2 <= 0._wp) THEN
	1173	zdf(jk) = 0._wp
	1174	ELSE
	1175	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
	1176	ENDIF
	1177	END DO
[3764]	1178
[3294]	1179	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
	1180	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
	1181	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
	1182	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - &
	1183	& 0.5_wp * zdf(jpkm1 - 1)
[3764]	1184
[3294]	1185	DO jk = 1, jpkm1 - 1
[3764]	1186	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1187	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
	1188	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
[3764]	1189	zddf1 = -2._wp * ztmp1 + ztmp2
[3294]	1190	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
[3764]	1191	zddf2 = 2._wp * ztmp1 - ztmp2
	1192
[3294]	1193	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
	1194	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
[3764]	1195	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
[3294]	1196	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
	1197	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
	1198	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
	1199	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
	1200	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
	1201	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
	1202	END DO
	1203	END DO
	1204	END DO
[3764]	1205
[3294]	1206	ELSE IF (polynomial_type == 2) THEN ! Linear
	1207	DO ji = 1, jpi
	1208	DO jj = 1, jpj
	1209	DO jk = 1, jpkm1-1
[3764]	1210	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1211	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
[3764]	1212
[3294]	1213	dsp(ji,jj,jk) = 0._wp
	1214	csp(ji,jj,jk) = 0._wp
	1215	bsp(ji,jj,jk) = ztmp1 / zdxtmp
	1216	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
	1217	END DO
	1218	END DO
	1219	END DO
	1220
	1221	ELSE
	1222	CALL ctl_stop( 'invalid polynomial type in cspline' )
	1223	ENDIF
	1224
	1225	END SUBROUTINE cspline
	1226
	1227
[3764]	1228	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
[3294]	1229	!!----------------------------------------------------------------------
	1230	!! * ROUTINE interp1 *
[3764]	1231	!!
[3294]	1232	!! ** Purpose : 1-d linear interpolation
[3764]	1233	!!
[4990]	1234	!! ** Method : interpolation is straight forward
[3764]	1235	!! extrapolation is also permitted (no value limit)
[3294]	1236	!!----------------------------------------------------------------------
	1237	IMPLICIT NONE
[3764]	1238	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
[3294]	1239	REAL(wp) :: f ! result of the interpolation (extrapolation)
	1240	REAL(wp) :: zdeltx
	1241	!!----------------------------------------------------------------------
	1242
	1243	zdeltx = xr - xl
	1244	IF(abs(zdeltx) <= 10._wp * EPSILON(x)) THEN
	1245	f = 0.5_wp * (fl + fr)
	1246	ELSE
	1247	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
	1248	ENDIF
[3764]	1249
[3294]	1250	END FUNCTION interp1
	1251
[4990]	1252
[3764]	1253	FUNCTION interp2(x, a, b, c, d) RESULT(f)
[3294]	1254	!!----------------------------------------------------------------------
	1255	!! * ROUTINE interp1 *
[3764]	1256	!!
[3294]	1257	!! ** Purpose : 1-d constrained cubic spline interpolation
[3764]	1258	!!
[3294]	1259	!! ** Method : cubic spline interpolation
	1260	!!
	1261	!!----------------------------------------------------------------------
	1262	IMPLICIT NONE
[3764]	1263	REAL(wp), INTENT(in) :: x, a, b, c, d
[3294]	1264	REAL(wp) :: f ! value from the interpolation
	1265	!!----------------------------------------------------------------------
	1266
[3764]	1267	f = a + x* ( b + x * ( c + d * x ) )
[3294]	1268
	1269	END FUNCTION interp2
	1270
	1271
[3764]	1272	FUNCTION interp3(x, a, b, c, d) RESULT(f)
[3294]	1273	!!----------------------------------------------------------------------
	1274	!! * ROUTINE interp1 *
[3764]	1275	!!
[3294]	1276	!! ** Purpose : Calculate the first order of deriavtive of
	1277	!! a cubic spline function y=a+bx+cx^2+d*x^3
[3764]	1278	!!
[3294]	1279	!! ** Method : f=dy/dx=b+2cx+3dx^2
	1280	!!
	1281	!!----------------------------------------------------------------------
	1282	IMPLICIT NONE
[3764]	1283	REAL(wp), INTENT(in) :: x, a, b, c, d
[3294]	1284	REAL(wp) :: f ! value from the interpolation
	1285	!!----------------------------------------------------------------------
	1286
	1287	f = b + x * ( 2._wp * c + 3._wp * d * x)
	1288
	1289	END FUNCTION interp3
	1290
[3764]	1291
	1292	FUNCTION integ_spline(xl, xr, a, b, c, d) RESULT(f)
[3294]	1293	!!----------------------------------------------------------------------
	1294	!! * ROUTINE interp1 *
[3764]	1295	!!
[3294]	1296	!! ** Purpose : 1-d constrained cubic spline integration
	1297	!!
[3764]	1298	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
	1299	!!
[3294]	1300	!!----------------------------------------------------------------------
	1301	IMPLICIT NONE
[3764]	1302	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
	1303	REAL(wp) :: za1, za2, za3
[3294]	1304	REAL(wp) :: f ! integration result
	1305	!!----------------------------------------------------------------------
	1306
[3764]	1307	za1 = 0.5_wp * b
	1308	za2 = c / 3.0_wp
	1309	za3 = 0.25_wp * d
[3294]	1310
	1311	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
	1312	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
	1313
[3632]	1314	END FUNCTION integ_spline
[3294]	1315
[3]	1316	!!======================================================================
	1317	END MODULE dynhpg
[3632]	1318

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