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dynhpg.F90 @ 15529

Last change on this file since 15529 was 15529, checked in by techene, 3 years ago
#2695 : isf+qco are now compatible
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File size: 75.8 KB

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[3]	1	MODULE dynhpg
	2	!!======================================================================
	3	!! * MODULE dynhpg *
	4	!! Ocean dynamics: hydrostatic pressure gradient trend
	5	!!======================================================================
[2528]	6	!! History : OPA ! 1987-09 (P. Andrich, M.-A. Foujols) hpg_zco: Original code
	7	!! 5.0 ! 1991-11 (G. Madec)
	8	!! 7.0 ! 1996-01 (G. Madec) hpg_sco: Original code for s-coordinates
	9	!! 8.0 ! 1997-05 (G. Madec) split dynber into dynkeg and dynhpg
	10	!! 8.5 ! 2002-07 (G. Madec) F90: Free form and module
	11	!! 8.5 ! 2002-08 (A. Bozec) hpg_zps: Original code
	12	!! NEMO 1.0 ! 2005-10 (A. Beckmann, B.W. An) various s-coordinate options
[3764]	13	!! ! Original code for hpg_ctl, hpg_hel hpg_wdj, hpg_djc, hpg_rot
[2528]	14	!! - ! 2005-11 (G. Madec) style & small optimisation
	15	!! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase
[3294]	16	!! 3.4 ! 2011-11 (H. Liu) hpg_prj: Original code for s-coordinates
	17	!! ! (A. Coward) suppression of hel, wdj and rot options
[5120]	18	!! 3.6 ! 2014-11 (P. Mathiot) hpg_isf: original code for ice shelf cavity
[14060]	19	!! 4.2 ! 2020-12 (M. Bell, A. Young) hpg_djc: revised djc scheme
[503]	20	!!----------------------------------------------------------------------
[3]	21
	22	!!----------------------------------------------------------------------
[455]	23	!! dyn_hpg : update the momentum trend with the now horizontal
[3]	24	!! gradient of the hydrostatic pressure
[2528]	25	!! dyn_hpg_init : initialisation and control of options
[455]	26	!! hpg_zco : z-coordinate scheme
	27	!! hpg_zps : z-coordinate plus partial steps (interpolation)
	28	!! hpg_sco : s-coordinate (standard jacobian formulation)
[5120]	29	!! hpg_isf : s-coordinate (sco formulation) adapted to ice shelf
[455]	30	!! hpg_djc : s-coordinate (Density Jacobian with Cubic polynomial)
[3294]	31	!! hpg_prj : s-coordinate (Pressure Jacobian with Cubic polynomial)
[3]	32	!!----------------------------------------------------------------------
	33	USE oce ! ocean dynamics and tracers
[12377]	34	USE isf_oce , ONLY : risfload ! ice shelf (risfload variable)
	35	USE isfload , ONLY : isf_load ! ice shelf (isf_load routine )
[4990]	36	USE sbc_oce ! surface variable (only for the flag with ice shelf)
[3]	37	USE dom_oce ! ocean space and time domain
[6152]	38	USE wet_dry ! wetting and drying
[3]	39	USE phycst ! physical constants
[4990]	40	USE trd_oce ! trends: ocean variables
	41	USE trddyn ! trend manager: dynamics
[11416]	42	USE zpshde ! partial step: hor. derivative (zps_hde routine)
[4990]	43	!
[2715]	44	USE in_out_manager ! I/O manager
[258]	45	USE prtctl ! Print control
[4990]	46	USE lbclnk ! lateral boundary condition
[2715]	47	USE lib_mpp ! MPP library
[4990]	48	USE eosbn2 ! compute density
[3294]	49	USE timing ! Timing
[6140]	50	USE iom
[3]	51
	52	IMPLICIT NONE
	53	PRIVATE
	54
[2528]	55	PUBLIC dyn_hpg ! routine called by step module
	56	PUBLIC dyn_hpg_init ! routine called by opa module
[3]	57
[9490]	58	! !!* Namelist namdyn_hpg : hydrostatic pressure gradient
	59	LOGICAL, PUBLIC :: ln_hpg_zco !: z-coordinate - full steps
	60	LOGICAL, PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation)
	61	LOGICAL, PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation)
	62	LOGICAL, PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial)
	63	LOGICAL, PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme)
	64	LOGICAL, PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf
[455]	65
[9490]	66	! !! Flag to control the type of hydrostatic pressure gradient
	67	INTEGER, PARAMETER :: np_ERROR =-10 ! error in specification of lateral diffusion
	68	INTEGER, PARAMETER :: np_zco = 0 ! z-coordinate - full steps
	69	INTEGER, PARAMETER :: np_zps = 1 ! z-coordinate - partial steps (interpolation)
	70	INTEGER, PARAMETER :: np_sco = 2 ! s-coordinate (standard jacobian formulation)
	71	INTEGER, PARAMETER :: np_djc = 3 ! s-coordinate (Density Jacobian with Cubic polynomial)
	72	INTEGER, PARAMETER :: np_prj = 4 ! s-coordinate (Pressure Jacobian scheme)
	73	INTEGER, PARAMETER :: np_isf = 5 ! s-coordinate similar to sco modify for isf
	74	!
[14060]	75	INTEGER, PUBLIC :: nhpg !: type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM)
	76	!
	77	LOGICAL :: ln_hpg_djc_vnh, ln_hpg_djc_vnv ! flag to specify hpg_djc boundary condition type
	78	REAL(wp), PUBLIC :: aco_bc_hor, bco_bc_hor, aco_bc_vrt, bco_bc_vrt !: coefficients for hpg_djc hor and vert boundary conditions
[455]	79
[3]	80	!! * Substitutions
[12377]	81	# include "do_loop_substitute.h90"
[13237]	82	# include "domzgr_substitute.h90"
	83
[3]	84	!!----------------------------------------------------------------------
[9598]	85	!! NEMO/OCE 4.0 , NEMO Consortium (2018)
[2528]	86	!! $Id$
[10068]	87	!! Software governed by the CeCILL license (see ./LICENSE)
[3]	88	!!----------------------------------------------------------------------
	89	CONTAINS
	90
[12377]	91	SUBROUTINE dyn_hpg( kt, Kmm, puu, pvv, Krhs )
[3]	92	!!---------------------------------------------------------------------
	93	!! * ROUTINE dyn_hpg *
	94	!!
[3764]	95	!! ** Method : Call the hydrostatic pressure gradient routine
[503]	96	!! using the scheme defined in the namelist
[3764]	97	!!
[12377]	98	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
[4990]	99	!! - send trends to trd_dyn for futher diagnostics (l_trddyn=T)
[503]	100	!!----------------------------------------------------------------------
[12377]	101	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	102	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
	103	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
	104	!
[9019]	105	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: ztrdu, ztrdv
[455]	106	!!----------------------------------------------------------------------
[2528]	107	!
[9019]	108	IF( ln_timing ) CALL timing_start('dyn_hpg')
[2715]	109	!
[12377]	110	IF( l_trddyn ) THEN ! Temporary saving of puu(:,:,:,Krhs) and pvv(:,:,:,Krhs) trends (l_trddyn)
[9019]	111	ALLOCATE( ztrdu(jpi,jpj,jpk) , ztrdv(jpi,jpj,jpk) )
[12377]	112	ztrdu(:,:,:) = puu(:,:,:,Krhs)
	113	ztrdv(:,:,:) = pvv(:,:,:,Krhs)
[3764]	114	ENDIF
[2528]	115	!
[3294]	116	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
[12377]	117	CASE ( np_zco ) ; CALL hpg_zco ( kt, Kmm, puu, pvv, Krhs ) ! z-coordinate
	118	CASE ( np_zps ) ; CALL hpg_zps ( kt, Kmm, puu, pvv, Krhs ) ! z-coordinate plus partial steps (interpolation)
	119	CASE ( np_sco ) ; CALL hpg_sco ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate (standard jacobian formulation)
	120	CASE ( np_djc ) ; CALL hpg_djc ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate (Density Jacobian with Cubic polynomial)
	121	CASE ( np_prj ) ; CALL hpg_prj ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate (Pressure Jacobian scheme)
	122	CASE ( np_isf ) ; CALL hpg_isf ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate similar to sco modify for ice shelf
[455]	123	END SELECT
[2528]	124	!
[503]	125	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
[12377]	126	ztrdu(:,:,:) = puu(:,:,:,Krhs) - ztrdu(:,:,:)
	127	ztrdv(:,:,:) = pvv(:,:,:,Krhs) - ztrdv(:,:,:)
	128	CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt, Kmm )
[9019]	129	DEALLOCATE( ztrdu , ztrdv )
[3764]	130	ENDIF
[503]	131	!
[12377]	132	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=puu(:,:,:,Krhs), clinfo1=' hpg - Ua: ', mask1=umask, &
	133	& tab3d_2=pvv(:,:,:,Krhs), clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
[503]	134	!
[9019]	135	IF( ln_timing ) CALL timing_stop('dyn_hpg')
[2715]	136	!
[455]	137	END SUBROUTINE dyn_hpg
	138
	139
[12377]	140	SUBROUTINE dyn_hpg_init( Kmm )
[455]	141	!!----------------------------------------------------------------------
[2528]	142	!! * ROUTINE dyn_hpg_init *
[455]	143	!!
	144	!! ** Purpose : initializations for the hydrostatic pressure gradient
	145	!! computation and consistency control
	146	!!
[1601]	147	!! ** Action : Read the namelist namdyn_hpg and check the consistency
[455]	148	!! with the type of vertical coordinate used (zco, zps, sco)
	149	!!----------------------------------------------------------------------
[12377]	150	INTEGER, INTENT( in ) :: Kmm ! ocean time level index
	151	!
[455]	152	INTEGER :: ioptio = 0 ! temporary integer
[4147]	153	INTEGER :: ios ! Local integer output status for namelist read
[1601]	154	!!
[6140]	155	INTEGER :: ji, jj, jk, ikt ! dummy loop indices ISF
[9019]	156	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: zts_top, zrhd ! hypothesys on isf density
	157	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zrhdtop_isf ! density at bottom of ISF
	158	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: ziceload ! density at bottom of ISF
[6140]	159	!!
[3294]	160	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
[14060]	161	& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf, &
	162	& ln_hpg_djc_vnh, ln_hpg_djc_vnv
[455]	163	!!----------------------------------------------------------------------
[2528]	164	!
[4147]	165	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
[11536]	166	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist' )
[6140]	167	!
[4147]	168	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
[11536]	169	902 IF( ios > 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist' )
[4624]	170	IF(lwm) WRITE ( numond, namdyn_hpg )
[2528]	171	!
	172	IF(lwp) THEN ! Control print
[455]	173	WRITE(numout,*)
[2528]	174	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
	175	WRITE(numout,*) '~~~~~~~~~~~~'
[1601]	176	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
	177	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
	178	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
	179	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
[5120]	180	WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf
[1601]	181	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
[3294]	182	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
[455]	183	ENDIF
[2528]	184	!
[14141]	185	IF( .NOT.ln_linssh .AND. (ln_hpg_zco.OR.ln_hpg_zps) ) &
	186	& CALL ctl_stop( 'dyn_hpg_init : non-linear free surface incompatible with hpg_zco or hpg_zps' )
	187	!
[14143]	188	IF( (.NOT.ln_hpg_isf .AND. ln_isfcav) .OR. (ln_hpg_isf .AND. .NOT.ln_isfcav) ) &
[14141]	189	& CALL ctl_stop( 'dyn_hpg_init : ln_hpg_isf=T requires ln_isfcav=T and vice versa' )
	190	!
[2528]	191	!
[9490]	192	! ! Set nhpg from ln_hpg_... flags & consistency check
	193	nhpg = np_ERROR
	194	ioptio = 0
	195	IF( ln_hpg_zco ) THEN ; nhpg = np_zco ; ioptio = ioptio +1 ; ENDIF
	196	IF( ln_hpg_zps ) THEN ; nhpg = np_zps ; ioptio = ioptio +1 ; ENDIF
	197	IF( ln_hpg_sco ) THEN ; nhpg = np_sco ; ioptio = ioptio +1 ; ENDIF
	198	IF( ln_hpg_djc ) THEN ; nhpg = np_djc ; ioptio = ioptio +1 ; ENDIF
	199	IF( ln_hpg_prj ) THEN ; nhpg = np_prj ; ioptio = ioptio +1 ; ENDIF
	200	IF( ln_hpg_isf ) THEN ; nhpg = np_isf ; ioptio = ioptio +1 ; ENDIF
[2528]	201	!
[2715]	202	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
[5120]	203	!
[9490]	204	IF(lwp) THEN
	205	WRITE(numout,*)
	206	SELECT CASE( nhpg )
	207	CASE( np_zco ) ; WRITE(numout,*) ' ==>>> z-coord. - full steps '
	208	CASE( np_zps ) ; WRITE(numout,*) ' ==>>> z-coord. - partial steps (interpolation)'
	209	CASE( np_sco ) ; WRITE(numout,*) ' ==>>> s-coord. (standard jacobian formulation)'
	210	CASE( np_djc ) ; WRITE(numout,*) ' ==>>> s-coord. (Density Jacobian: Cubic polynomial)'
	211	CASE( np_prj ) ; WRITE(numout,*) ' ==>>> s-coord. (Pressure Jacobian: Cubic polynomial)'
	212	CASE( np_isf ) ; WRITE(numout,*) ' ==>>> s-coord. (standard jacobian formulation) for isf'
	213	END SELECT
	214	WRITE(numout,*)
	215	ENDIF
[9019]	216	!
[14060]	217	IF ( ln_hpg_djc ) THEN
	218	IF (ln_hpg_djc_vnh) THEN ! Von Neumann boundary condition
	219	IF(lwp) WRITE(numout,*) ' horizontal bc: von Neumann '
	220	aco_bc_hor = 6.0_wp/5.0_wp
	221	bco_bc_hor = 7.0_wp/15.0_wp
	222	ELSE ! Linear extrapolation
	223	IF(lwp) WRITE(numout,*) ' horizontal bc: linear extrapolation'
	224	aco_bc_hor = 3.0_wp/2.0_wp
	225	bco_bc_hor = 1.0_wp/2.0_wp
	226	END IF
	227	IF (ln_hpg_djc_vnv) THEN ! Von Neumann boundary condition
	228	IF(lwp) WRITE(numout,*) ' vertical bc: von Neumann '
	229	aco_bc_vrt = 6.0_wp/5.0_wp
	230	bco_bc_vrt = 7.0_wp/15.0_wp
	231	ELSE ! Linear extrapolation
	232	IF(lwp) WRITE(numout,*) ' vertical bc: linear extrapolation'
	233	aco_bc_vrt = 3.0_wp/2.0_wp
	234	bco_bc_vrt = 1.0_wp/2.0_wp
	235	END IF
	236	END IF
[14141]	237	!
[2528]	238	END SUBROUTINE dyn_hpg_init
[455]	239
	240
[12377]	241	SUBROUTINE hpg_zco( kt, Kmm, puu, pvv, Krhs )
[455]	242	!!---------------------------------------------------------------------
	243	!! * ROUTINE hpg_zco *
	244	!!
	245	!! ** Method : z-coordinate case, levels are horizontal surfaces.
	246	!! The now hydrostatic pressure gradient at a given level, jk,
	247	!! is computed by taking the vertical integral of the in-situ
	248	!! density gradient along the model level from the suface to that
	249	!! level: zhpi = grav .....
	250	!! zhpj = grav .....
[12377]	251	!! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)).
	252	!! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi
	253	!! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj
[3764]	254	!!
[12377]	255	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
[503]	256	!!----------------------------------------------------------------------
[12377]	257	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	258	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
	259	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[6140]	260	!
[503]	261	INTEGER :: ji, jj, jk ! dummy loop indices
	262	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
[14834]	263	REAL(wp), DIMENSION(A2D(nn_hls)) :: zhpi, zhpj
[3]	264	!!----------------------------------------------------------------------
[3764]	265	!
[14834]	266	IF( .NOT. l_istiled .OR. ntile == 1 ) THEN ! Do only on the first tile
	267	IF( kt == nit000 ) THEN
	268	IF(lwp) WRITE(numout,*)
	269	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
	270	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
	271	ENDIF
[3]	272	ENDIF
[14064]	273	!
	274	zcoef0 = - grav * 0.5_wp ! Local constant initialization
	275	!
	276	DO_2D( 0, 0, 0, 0 ) ! Surface value
[12377]	277	zcoef1 = zcoef0 * e3w(ji,jj,1,Kmm)
[14064]	278	! ! hydrostatic pressure gradient
	279	zhpi(ji,jj) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
	280	zhpj(ji,jj) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
	281	! ! add to the general momentum trend
	282	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj)
	283	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj)
[12377]	284	END_2D
[503]	285	!
[14064]	286	DO_3D( 0, 0, 0, 0, 2, jpkm1 ) ! interior value (2=<jk=<jpkm1)
[12377]	287	zcoef1 = zcoef0 * e3w(ji,jj,jk,Kmm)
[14064]	288	! ! hydrostatic pressure gradient
	289	zhpi(ji,jj) = zhpi(ji,jj) + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
	290	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
[455]	291
[14064]	292	zhpj(ji,jj) = zhpj(ji,jj) + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
	293	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
	294	! ! add to the general momentum trend
	295	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj)
	296	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj)
[12377]	297	END_3D
[503]	298	!
[455]	299	END SUBROUTINE hpg_zco
[216]	300
[3]	301
[12377]	302	SUBROUTINE hpg_zps( kt, Kmm, puu, pvv, Krhs )
[3]	303	!!---------------------------------------------------------------------
[455]	304	!! * ROUTINE hpg_zps *
[3764]	305	!!
[455]	306	!! ** Method : z-coordinate plus partial steps case. blahblah...
[3764]	307	!!
[12377]	308	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
[3764]	309	!!----------------------------------------------------------------------
[12377]	310	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	311	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
	312	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[503]	313	!!
	314	INTEGER :: ji, jj, jk ! dummy loop indices
	315	INTEGER :: iku, ikv ! temporary integers
	316	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
[14834]	317	REAL(wp), DIMENSION(A2D(nn_hls),jpk ) :: zhpi, zhpj
	318	REAL(wp), DIMENSION(A2D(nn_hls),jpts) :: zgtsu, zgtsv
	319	REAL(wp), DIMENSION(A2D(nn_hls) ) :: zgru, zgrv
[3]	320	!!----------------------------------------------------------------------
[3294]	321	!
[14834]	322	IF( .NOT. l_istiled .OR. ntile == 1 ) THEN ! Do only on the first tile
	323	IF( kt == nit000 ) THEN
	324	IF(lwp) WRITE(numout,*)
	325	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
	326	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
	327	ENDIF
[3]	328	ENDIF
	329
[11416]	330	! Partial steps: Compute NOW horizontal gradient of t, s, rd at the last ocean level
[12377]	331	CALL zps_hde( kt, Kmm, jpts, ts(:,:,:,:,Kmm), zgtsu, zgtsv, rhd, zgru , zgrv )
[3294]	332
[503]	333	! Local constant initialization
[2528]	334	zcoef0 = - grav * 0.5_wp
[3]	335
[2528]	336	! Surface value (also valid in partial step case)
[13295]	337	DO_2D( 0, 0, 0, 0 )
[12377]	338	zcoef1 = zcoef0 * e3w(ji,jj,1,Kmm)
	339	! hydrostatic pressure gradient
	340	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
	341	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
	342	! add to the general momentum trend
	343	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1)
	344	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1)
	345	END_2D
[3]	346
[503]	347	! interior value (2=<jk=<jpkm1)
[13295]	348	DO_3D( 0, 0, 0, 0, 2, jpkm1 )
[12377]	349	zcoef1 = zcoef0 * e3w(ji,jj,jk,Kmm)
	350	! hydrostatic pressure gradient
	351	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
	352	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
	353	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
[3]	354
[12377]	355	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
	356	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
	357	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
	358	! add to the general momentum trend
	359	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk)
	360	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk)
	361	END_3D
[3]	362
[11416]	363	! partial steps correction at the last level (use zgru & zgrv computed in zpshde.F90)
[13295]	364	DO_2D( 0, 0, 0, 0 )
[12377]	365	iku = mbku(ji,jj)
	366	ikv = mbkv(ji,jj)
	367	zcoef2 = zcoef0 * MIN( e3w(ji,jj,iku,Kmm), e3w(ji+1,jj ,iku,Kmm) )
	368	zcoef3 = zcoef0 * MIN( e3w(ji,jj,ikv,Kmm), e3w(ji ,jj+1,ikv,Kmm) )
	369	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
	370	puu (ji,jj,iku,Krhs) = puu(ji,jj,iku,Krhs) - zhpi(ji,jj,iku) ! subtract old value
	371	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
	372	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + zgru(ji,jj) ) * r1_e1u(ji,jj)
	373	puu (ji,jj,iku,Krhs) = puu(ji,jj,iku,Krhs) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
	374	ENDIF
	375	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
	376	pvv (ji,jj,ikv,Krhs) = pvv(ji,jj,ikv,Krhs) - zhpj(ji,jj,ikv) ! subtract old value
	377	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
	378	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + zgrv(ji,jj) ) * r1_e2v(ji,jj)
	379	pvv (ji,jj,ikv,Krhs) = pvv(ji,jj,ikv,Krhs) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
	380	ENDIF
	381	END_2D
[503]	382	!
[455]	383	END SUBROUTINE hpg_zps
[216]	384
[6140]	385
[12377]	386	SUBROUTINE hpg_sco( kt, Kmm, puu, pvv, Krhs )
[3]	387	!!---------------------------------------------------------------------
[455]	388	!! * ROUTINE hpg_sco *
[3]	389	!!
[455]	390	!! ** Method : s-coordinate case. Jacobian scheme.
	391	!! The now hydrostatic pressure gradient at a given level, jk,
	392	!! is computed by taking the vertical integral of the in-situ
[3]	393	!! density gradient along the model level from the suface to that
[455]	394	!! level. s-coordinates (ln_sco): a corrective term is added
	395	!! to the horizontal pressure gradient :
	396	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
	397	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
[12377]	398	!! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)).
	399	!! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi
	400	!! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj
[3]	401	!!
[12377]	402	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
[503]	403	!!----------------------------------------------------------------------
[12377]	404	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	405	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
	406	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[503]	407	!!
[14064]	408	INTEGER :: ji, jj, jk, jii, jjj ! dummy loop indices
	409	REAL(wp) :: zcoef0, zuap, zvap, ztmp ! local scalars
	410	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
[14834]	411	REAL(wp), DIMENSION(A2D(nn_hls),jpk) :: zhpi, zhpj
[9019]	412	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter
[5120]	413	!!----------------------------------------------------------------------
	414	!
[14834]	415	IF( ln_wd_il ) ALLOCATE(zcpx(A2D(nn_hls)), zcpy(A2D(nn_hls)))
[9023]	416	!
[14834]	417	IF( .NOT. l_istiled .OR. ntile == 1 ) THEN ! Do only on the first tile
	418	IF( kt == nit000 ) THEN
	419	IF(lwp) WRITE(numout,*)
	420	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
	421	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OCE original scheme used'
	422	ENDIF
[5120]	423	ENDIF
[6140]	424	!
[5120]	425	zcoef0 = - grav * 0.5_wp
[6140]	426	!
[9023]	427	IF( ln_wd_il ) THEN
[13295]	428	DO_2D( 0, 0, 0, 0 )
[12377]	429	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
	430	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
	431	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) &
	432	& > rn_wdmin1 + rn_wdmin2
	433	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji+1,jj,Kmm) ) > 1.E-12 ) .AND. ( &
	434	& MAX( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
	435	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
[6152]	436
[12377]	437	IF(ll_tmp1) THEN
	438	zcpx(ji,jj) = 1.0_wp
	439	ELSE IF(ll_tmp2) THEN
	440	! no worries about ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm) = 0, it won't happen ! here
	441	zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
	442	& / (ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm)) )
	443	ELSE
	444	zcpx(ji,jj) = 0._wp
	445	END IF
	446
	447	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
	448	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
	449	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) &
	450	& > rn_wdmin1 + rn_wdmin2
	451	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. ( &
	452	& MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
	453	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
[6152]	454
[12377]	455	IF(ll_tmp1) THEN
	456	zcpy(ji,jj) = 1.0_wp
	457	ELSE IF(ll_tmp2) THEN
	458	! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here
	459	zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
	460	& / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) )
	461	ELSE
	462	zcpy(ji,jj) = 0._wp
	463	END IF
	464	END_2D
[9023]	465	END IF
[14064]	466	!
	467	DO_2D( 0, 0, 0, 0 ) ! Surface value
	468	! ! hydrostatic pressure gradient along s-surfaces
	469	zhpi(ji,jj,1) = zcoef0 * r1_e1u(ji,jj) &
	470	& * ( e3w(ji+1,jj ,1,Kmm) * rhd(ji+1,jj ,1) &
	471	& - e3w(ji ,jj ,1,Kmm) * rhd(ji ,jj ,1) )
	472	zhpj(ji,jj,1) = zcoef0 * r1_e2v(ji,jj) &
	473	& * ( e3w(ji ,jj+1,1,Kmm) * rhd(ji ,jj+1,1) &
	474	& - e3w(ji ,jj ,1,Kmm) * rhd(ji ,jj ,1) )
	475	! ! s-coordinate pressure gradient correction
	476	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) ) &
[12377]	477	& * ( gde3w(ji+1,jj,1) - gde3w(ji,jj,1) ) * r1_e1u(ji,jj)
[14064]	478	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) ) &
[12377]	479	& * ( gde3w(ji,jj+1,1) - gde3w(ji,jj,1) ) * r1_e2v(ji,jj)
	480	!
	481	IF( ln_wd_il ) THEN
	482	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
	483	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
	484	zuap = zuap * zcpx(ji,jj)
	485	zvap = zvap * zcpy(ji,jj)
	486	ENDIF
[14064]	487	! ! add to the general momentum trend
[12377]	488	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1) + zuap
	489	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1) + zvap
	490	END_2D
[14064]	491	!
	492	DO_3D( 0, 0, 0, 0, 2, jpkm1 ) ! interior value (2=<jk=<jpkm1)
	493	! ! hydrostatic pressure gradient along s-surfaces
	494	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 * r1_e1u(ji,jj) &
	495	& * ( e3w(ji+1,jj,jk,Kmm) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
	496	& - e3w(ji ,jj,jk,Kmm) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) )
	497	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 * r1_e2v(ji,jj) &
	498	& * ( e3w(ji,jj+1,jk,Kmm) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
	499	& - e3w(ji,jj ,jk,Kmm) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) )
	500	! ! s-coordinate pressure gradient correction
	501	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) ) &
[12377]	502	& * ( gde3w(ji+1,jj ,jk) - gde3w(ji,jj,jk) ) * r1_e1u(ji,jj)
[14064]	503	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) ) &
[12377]	504	& * ( gde3w(ji ,jj+1,jk) - gde3w(ji,jj,jk) ) * r1_e2v(ji,jj)
	505	!
	506	IF( ln_wd_il ) THEN
	507	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
	508	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
	509	zuap = zuap * zcpx(ji,jj)
	510	zvap = zvap * zcpy(ji,jj)
	511	ENDIF
	512	!
	513	! add to the general momentum trend
	514	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk) + zuap
	515	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk) + zvap
	516	END_3D
[5120]	517	!
[9039]	518	IF( ln_wd_il ) DEALLOCATE( zcpx , zcpy )
[5120]	519	!
	520	END SUBROUTINE hpg_sco
	521
[6140]	522
[12377]	523	SUBROUTINE hpg_isf( kt, Kmm, puu, pvv, Krhs )
[5120]	524	!!---------------------------------------------------------------------
[6140]	525	!! * ROUTINE hpg_isf *
[5120]	526	!!
	527	!! ** Method : s-coordinate case. Jacobian scheme.
	528	!! The now hydrostatic pressure gradient at a given level, jk,
	529	!! is computed by taking the vertical integral of the in-situ
	530	!! density gradient along the model level from the suface to that
	531	!! level. s-coordinates (ln_sco): a corrective term is added
	532	!! to the horizontal pressure gradient :
	533	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
	534	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
[12377]	535	!! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)).
	536	!! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi
	537	!! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj
	538	!! iceload is added
[5120]	539	!!
[12377]	540	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
[5120]	541	!!----------------------------------------------------------------------
[12377]	542	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	543	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
	544	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[5120]	545	!!
[14064]	546	INTEGER :: ji, jj, jk ! dummy loop indices
	547	INTEGER :: ikt , ikti1, iktj1 ! local integer
	548	REAL(wp) :: ze3w, ze3wi1, ze3wj1 ! local scalars
	549	REAL(wp) :: zcoef0, zuap, zvap ! - -
[14834]	550	REAL(wp), DIMENSION(A2D(nn_hls),jpk ) :: zhpi, zhpj
	551	REAL(wp), DIMENSION(A2D(nn_hls),jpts) :: zts_top
[15529]	552	REAL(wp), DIMENSION(A2D(nn_hls)) :: zrhd_top, zdep_top
[3]	553	!!----------------------------------------------------------------------
[3294]	554	!
[9019]	555	zcoef0 = - grav * 0.5_wp ! Local constant initialization
[3294]	556	!
[9019]	557	! ! iniitialised to 0. zhpi zhpi
	558	zhpi(:,:,:) = 0._wp ; zhpj(:,:,:) = 0._wp
[6140]	559
[4990]	560	! compute rhd at the ice/oce interface (ocean side)
[6140]	561	! usefull to reduce residual current in the test case ISOMIP with no melting
[14834]	562	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
	563	ikt = mikt(ji,jj)
	564	zts_top(ji,jj,1) = ts(ji,jj,ikt,1,Kmm)
	565	zts_top(ji,jj,2) = ts(ji,jj,ikt,2,Kmm)
[15529]	566	zdep_top(ji,jj) = MAX( risfdep(ji,jj) , gdept(ji,jj,1,Kmm) )
[14834]	567	END_2D
[15529]	568	CALL eos( zts_top, zdep_top, zrhd_top )
[6140]	569
[14064]	570	! !===========================!
	571	! !===== surface value =====!
	572	! !===========================!
[13295]	573	DO_2D( 0, 0, 0, 0 )
[14064]	574	ikt = mikt(ji ,jj ) ; ze3w = e3w(ji ,jj ,ikt ,Kmm)
	575	ikti1 = mikt(ji+1,jj ) ; ze3wi1 = e3w(ji+1,jj ,ikti1,Kmm)
	576	iktj1 = mikt(ji ,jj+1) ; ze3wj1 = e3w(ji ,jj+1,iktj1,Kmm)
	577	! ! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
	578	! ! we assume ISF is in isostatic equilibrium
	579	zhpi(ji,jj,1) = zcoef0 * r1_e1u(ji,jj) * ( risfload(ji+1,jj) - risfload(ji,jj) &
[15529]	580	& + 0.5_wp * ( ze3wi1 * ( rhd(ji+1,jj,ikti1) + zrhd_top(ji+1,jj) ) &
	581	& - ze3w * ( rhd(ji ,jj,ikt ) + zrhd_top(ji ,jj) ) ) )
[14064]	582	zhpj(ji,jj,1) = zcoef0 * r1_e2v(ji,jj) * ( risfload(ji,jj+1) - risfload(ji,jj) &
[15529]	583	& + 0.5_wp * ( ze3wj1 * ( rhd(ji,jj+1,iktj1) + zrhd_top(ji,jj+1) ) &
	584	& - ze3w * ( rhd(ji,jj ,ikt ) + zrhd_top(ji,jj ) ) ) )
[14064]	585	! ! s-coordinate pressure gradient correction (=0 if z coordinate)
	586	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) ) &
[12377]	587	& * ( gde3w(ji+1,jj,1) - gde3w(ji,jj,1) ) * r1_e1u(ji,jj)
[14064]	588	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) ) &
[12377]	589	& * ( gde3w(ji,jj+1,1) - gde3w(ji,jj,1) ) * r1_e2v(ji,jj)
[14064]	590	! ! add to the general momentum trend
[12377]	591	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
	592	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
	593	END_2D
[14064]	594	!
	595	! !=============================!
	596	! !===== interior values =====!
	597	! !=============================!
[13295]	598	DO_3D( 0, 0, 0, 0, 2, jpkm1 )
[14064]	599	ze3w = e3w(ji ,jj ,jk,Kmm)
	600	ze3wi1 = e3w(ji+1,jj ,jk,Kmm)
	601	ze3wj1 = e3w(ji ,jj+1,jk,Kmm)
	602	! ! hydrostatic pressure gradient along s-surfaces
[12377]	603	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
[14064]	604	& * ( ze3wi1 * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) * wmask(ji+1,jj,jk) &
	605	& - ze3w * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) * wmask(ji ,jj,jk) )
[12377]	606	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
[14064]	607	& * ( ze3wj1 * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) * wmask(ji,jj+1,jk) &
	608	& - ze3w * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) * wmask(ji,jj ,jk) )
	609	! ! s-coordinate pressure gradient correction
	610	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) ) &
[12377]	611	& * ( gde3w(ji+1,jj ,jk) - gde3w(ji,jj,jk) ) / e1u(ji,jj)
[14064]	612	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) ) &
[12377]	613	& * ( gde3w(ji ,jj+1,jk) - gde3w(ji,jj,jk) ) / e2v(ji,jj)
[14064]	614	! ! add to the general momentum trend
[12377]	615	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + (zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
	616	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + (zhpj(ji,jj,jk) + zvap) * vmask(ji,jj,jk)
	617	END_3D
[503]	618	!
[5120]	619	END SUBROUTINE hpg_isf
[455]	620
[4990]	621
[12377]	622	SUBROUTINE hpg_djc( kt, Kmm, puu, pvv, Krhs )
[455]	623	!!---------------------------------------------------------------------
	624	!! * ROUTINE hpg_djc *
	625	!!
	626	!! ** Method : Density Jacobian with Cubic polynomial scheme
[3764]	627	!!
[503]	628	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
[455]	629	!!----------------------------------------------------------------------
[12377]	630	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	631	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
	632	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[503]	633	!!
	634	INTEGER :: ji, jj, jk ! dummy loop indices
[14060]	635	INTEGER :: iktb, iktt ! jk indices at tracer points for top and bottom points
[503]	636	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
[14834]	637	REAL(wp) :: z_grav_10, z1_12, z1_cff
[14060]	638	REAL(wp) :: cffu, cffx ! " "
	639	REAL(wp) :: cffv, cffy ! " "
[6152]	640	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
[14834]	641	REAL(wp), DIMENSION(A2D(nn_hls),jpk) :: zhpi, zhpj
	642
	643	REAL(wp), DIMENSION(A2D(nn_hls),jpk) :: zdzx, zdzy, zdzz ! Primitive grid differences ('delta_xyz')
	644	REAL(wp), DIMENSION(A2D(nn_hls),jpk) :: zdz_i, zdz_j, zdz_k ! Harmonic average of primitive grid differences ('d_xyz')
	645	REAL(wp), DIMENSION(A2D(nn_hls),jpk) :: zdrhox, zdrhoy, zdrhoz ! Primitive rho differences ('delta_rho')
	646	REAL(wp), DIMENSION(A2D(nn_hls),jpk) :: zdrho_i, zdrho_j, zdrho_k ! Harmonic average of primitive rho differences ('d_rho')
	647	REAL(wp), DIMENSION(A2D(nn_hls),jpk) :: z_rho_i, z_rho_j, z_rho_k ! Face intergrals
	648	REAL(wp), DIMENSION(A2D(nn_hls)) :: zz_dz_i, zz_dz_j, zz_drho_i, zz_drho_j ! temporary arrays
[9019]	649	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter
[455]	650	!!----------------------------------------------------------------------
[3294]	651	!
[9023]	652	IF( ln_wd_il ) THEN
[14834]	653	ALLOCATE( zcpx(A2D(nn_hls)) , zcpy(A2D(nn_hls)) )
[13295]	654	DO_2D( 0, 0, 0, 0 )
[12377]	655	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
	656	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
	657	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) &
	658	& > rn_wdmin1 + rn_wdmin2
	659	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji+1,jj,Kmm) ) > 1.E-12 ) .AND. ( &
	660	& MAX( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
	661	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
	662	IF(ll_tmp1) THEN
	663	zcpx(ji,jj) = 1.0_wp
	664	ELSE IF(ll_tmp2) THEN
	665	! no worries about ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm) = 0, it won't happen ! here
	666	zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
	667	& / (ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm)) )
	668	ELSE
	669	zcpx(ji,jj) = 0._wp
	670	END IF
	671
	672	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
	673	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
	674	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) &
	675	& > rn_wdmin1 + rn_wdmin2
	676	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. ( &
	677	& MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
	678	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
[6152]	679
[12377]	680	IF(ll_tmp1) THEN
	681	zcpy(ji,jj) = 1.0_wp
	682	ELSE IF(ll_tmp2) THEN
	683	! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here
	684	zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
	685	& / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) )
	686	ELSE
	687	zcpy(ji,jj) = 0._wp
	688	END IF
	689	END_2D
[9023]	690	END IF
[6152]	691
[14834]	692	IF( .NOT. l_istiled .OR. ntile == 1 ) THEN ! Do only on the first tile
	693	IF( kt == nit000 ) THEN
	694	IF(lwp) WRITE(numout,*)
	695	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
	696	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
	697	ENDIF
[216]	698	ENDIF
	699
[503]	700	! Local constant initialization
[2528]	701	zcoef0 = - grav * 0.5_wp
[14060]	702	z_grav_10 = grav / 10._wp
	703	z1_12 = 1.0_wp / 12._wp
[455]	704
	705	!----------------------------------------------------------------------------------------
[14060]	706	! 1. compute and store elementary vertical differences in provisional arrays
[455]	707	!----------------------------------------------------------------------------------------
	708
[14060]	709	!!bug gm Not a true bug, but... zdzz=e3w for zdzx, zdzy verify what it is really
[455]	710
[14060]	711	DO_3D( 1, 1, 1, 1, 2, jpkm1 )
[14064]	712	zdrhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
[14060]	713	zdzz (ji,jj,jk) = - gde3w(ji ,jj ,jk) + gde3w(ji,jj,jk-1)
[12377]	714	END_3D
[455]	715
	716	!-------------------------------------------------------------------------
[14060]	717	! 2. compute harmonic averages for vertical differences using eq. 5.18
[455]	718	!-------------------------------------------------------------------------
	719	zep = 1.e-15
	720
[14060]	721	!! mb zdrho_k, zdz_k, zdrho_i, zdz_i, zdrho_j, zdz_j re-centred about the point (ji,jj,jk)
	722	zdrho_k(:,:,:) = 0._wp
	723	zdz_k (:,:,:) = 0._wp
[455]	724
[14834]	725	DO_3D( 1, 1, 1, 1, 2, jpk-2 )
	726	cffw = MAX( 2._wp * zdrhoz(ji,jj,jk) * zdrhoz(ji,jj,jk+1), 0._wp )
	727	z1_cff = zdrhoz(ji,jj,jk) + zdrhoz(ji,jj,jk+1)
	728	zdrho_k(ji,jj,jk) = cffw / SIGN( MAX( ABS(z1_cff), zep ), z1_cff )
[14060]	729	zdz_k(ji,jj,jk) = 2._wp * zdzz(ji,jj,jk) * zdzz(ji,jj,jk+1) &
	730	& / ( zdzz(ji,jj,jk) + zdzz(ji,jj,jk+1) )
	731	END_3D
[455]	732
[14060]	733	!----------------------------------------------------------------------------------
	734	! 3. apply boundary conditions at top and bottom using 5.36-5.37
	735	!----------------------------------------------------------------------------------
[3764]	736
[14060]	737	! mb for sea-ice shelves we will need to re-write this upper boundary condition in the same form as the lower boundary condition
[14834]	738	DO_2D( 1, 1, 1, 1 )
	739	zdrho_k(ji,jj,1) = aco_bc_vrt * ( rhd (ji,jj,2) - rhd (ji,jj,1) ) - bco_bc_vrt * zdrho_k(ji,jj,2)
	740	zdz_k (ji,jj,1) = aco_bc_vrt * (-gde3w(ji,jj,2) + gde3w(ji,jj,1) ) - bco_bc_vrt * zdz_k (ji,jj,2)
	741	END_2D
[455]	742
[14060]	743	DO_2D( 1, 1, 1, 1 )
	744	IF ( mbkt(ji,jj)>1 ) THEN
	745	iktb = mbkt(ji,jj)
[14064]	746	zdrho_k(ji,jj,iktb) = aco_bc_vrt * ( rhd(ji,jj,iktb) - rhd(ji,jj,iktb-1) ) - bco_bc_vrt * zdrho_k(ji,jj,iktb-1)
[14060]	747	zdz_k (ji,jj,iktb) = aco_bc_vrt * (-gde3w(ji,jj,iktb) + gde3w(ji,jj,iktb-1) ) - bco_bc_vrt * zdz_k (ji,jj,iktb-1)
	748	END IF
	749	END_2D
[455]	750
[14060]	751	!--------------------------------------------------------------
	752	! 4. Compute side face integrals
	753	!-------------------------------------------------------------
[455]	754
[14060]	755	!! ssh replaces e3w_n ; gde3w is a depth; the formulae involve heights
	756	!! rho_k stores grav * FX / rho_0
	757
	758	!--------------------------------------------------------------
	759	! 4. a) Upper half of top-most grid box, compute and store
	760	!-------------------------------------------------------------
[14118]	761	! *** AY note: ssh(ji,jj,Kmm) + gde3w(ji,jj,1) = e3w(ji,jj,1,Kmm)
[14060]	762	DO_2D( 0, 1, 0, 1)
	763	z_rho_k(ji,jj,1) = grav * ( ssh(ji,jj,Kmm) + gde3w(ji,jj,1) ) &
[14064]	764	& * ( rhd(ji,jj,1) &
	765	& + 0.5_wp * ( rhd (ji,jj,2) - rhd (ji,jj,1) ) &
[14060]	766	& * ( ssh (ji,jj,Kmm) + gde3w(ji,jj,1) ) &
	767	& / ( - gde3w(ji,jj,2) + gde3w(ji,jj,1) ) )
	768	END_2D
	769
	770	!--------------------------------------------------------------
	771	! 4. b) Interior faces, compute and store
	772	!-------------------------------------------------------------
	773
	774	DO_3D( 0, 1, 0, 1, 2, jpkm1 )
[14064]	775	z_rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
[14060]	776	& * ( - gde3w(ji,jj,jk) + gde3w(ji,jj,jk-1) ) &
	777	& + z_grav_10 * ( &
	778	& ( zdrho_k (ji,jj,jk) - zdrho_k (ji,jj,jk-1) ) &
	779	& * ( - gde3w(ji,jj,jk) + gde3w(ji,jj,jk-1) - z1_12 * ( zdz_k (ji,jj,jk) + zdz_k (ji,jj,jk-1) ) ) &
	780	& - ( zdz_k (ji,jj,jk) - zdz_k (ji,jj,jk-1) ) &
[14064]	781	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( zdrho_k(ji,jj,jk) + zdrho_k(ji,jj,jk-1) ) ) &
[14060]	782	& )
	783	END_3D
	784
	785	!----------------------------------------------------------------------------------------
	786	! 5. compute and store elementary horizontal differences in provisional arrays
	787	!----------------------------------------------------------------------------------------
[14834]	788	zdrhox(:,:,:) = 0._wp
	789	zdzx (:,:,:) = 0._wp
	790	zdrhoy(:,:,:) = 0._wp
	791	zdzy (:,:,:) = 0._wp
[14060]	792
[14834]	793	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 1, jpkm1 )
	794	zdrhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji ,jj ,jk)
	795	zdzx (ji,jj,jk) = gde3w(ji ,jj ,jk) - gde3w(ji+1,jj ,jk)
	796	zdrhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji ,jj ,jk)
	797	zdzy (ji,jj,jk) = gde3w(ji ,jj ,jk) - gde3w(ji ,jj+1,jk)
[14060]	798	END_3D
	799
[14834]	800	IF( nn_hls == 1 ) CALL lbc_lnk( 'dynhpg', zdrhox, 'U', -1._wp, zdzx, 'U', -1._wp, zdrhoy, 'V', -1._wp, zdzy, 'V', -1._wp )
[14060]	801
	802	!-------------------------------------------------------------------------
	803	! 6. compute harmonic averages using eq. 5.18
	804	!-------------------------------------------------------------------------
	805
	806	DO_3D( 0, 1, 0, 1, 1, jpkm1 )
[14834]	807	cffu = MAX( 2._wp * zdrhox(ji-1,jj,jk) * zdrhox(ji,jj,jk), 0._wp )
	808	z1_cff = zdrhox(ji-1,jj,jk) + zdrhox(ji,jj,jk)
	809	zdrho_i(ji,jj,jk) = cffu / SIGN( MAX( ABS(z1_cff), zep ), z1_cff )
[455]	810
[14834]	811	cffx = MAX( 2._wp * zdzx(ji-1,jj,jk) * zdzx(ji,jj,jk), 0._wp )
	812	z1_cff = zdzx(ji-1,jj,jk) + zdzx(ji,jj,jk)
	813	zdz_i(ji,jj,jk) = cffx / SIGN( MAX( ABS(z1_cff), zep ), z1_cff )
[455]	814
[14834]	815	cffv = MAX( 2._wp * zdrhoy(ji,jj-1,jk) * zdrhoy(ji,jj,jk), 0._wp )
	816	z1_cff = zdrhoy(ji,jj-1,jk) + zdrhoy(ji,jj,jk)
	817	zdrho_j(ji,jj,jk) = cffv / SIGN( MAX( ABS(z1_cff), zep ), z1_cff )
[455]	818
[14834]	819	cffy = MAX( 2._wp * zdzy(ji,jj-1,jk) * zdzy(ji,jj,jk), 0._wp )
	820	z1_cff = zdzy(ji,jj-1,jk) + zdzy(ji,jj,jk)
	821	zdz_j(ji,jj,jk) = cffy / SIGN( MAX( ABS(z1_cff), zep ), z1_cff )
[12377]	822	END_3D
[14060]	823
	824	!!! Note that zdzx, zdzy, zdzz, zdrhox, zdrhoy and zdrhoz should NOT be used beyond this point
[455]	825
	826	!----------------------------------------------------------------------------------
[14060]	827	! 6B. apply boundary conditions at side boundaries using 5.36-5.37
[455]	828	!----------------------------------------------------------------------------------
	829
[14060]	830	DO jk = 1, jpkm1
	831	zz_drho_i(:,:) = zdrho_i(:,:,jk)
	832	zz_dz_i (:,:) = zdz_i (:,:,jk)
	833	zz_drho_j(:,:) = zdrho_j(:,:,jk)
	834	zz_dz_j (:,:) = zdz_j (:,:,jk)
[14834]	835	! Walls coming from left: should check from 2 to jpi-1 (and jpj=2-jpj)
	836	DO_2D( 0, 0, 0, 1 )
	837	IF ( umask(ji,jj,jk) > 0.5_wp .AND. umask(ji-1,jj,jk) < 0.5_wp .AND. umask(ji+1,jj,jk) > 0.5_wp) THEN
	838	zz_drho_i(ji,jj) = aco_bc_hor * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) ) - bco_bc_hor * zdrho_i(ji+1,jj,jk)
	839	zz_dz_i (ji,jj) = aco_bc_hor * (-gde3w(ji+1,jj,jk) + gde3w(ji,jj,jk) ) - bco_bc_hor * zdz_i (ji+1,jj,jk)
[14060]	840	END IF
[14834]	841	END_2D
	842	! Walls coming from right: should check from 3 to jpi (and jpj=2-jpj)
	843	DO_2D( -1, 1, 0, 1 )
	844	IF ( umask(ji,jj,jk) < 0.5_wp .AND. umask(ji-1,jj,jk) > 0.5_wp .AND. umask(ji-2,jj,jk) > 0.5_wp) THEN
	845	zz_drho_i(ji,jj) = aco_bc_hor * ( rhd (ji,jj,jk) - rhd (ji-1,jj,jk) ) - bco_bc_hor * zdrho_i(ji-1,jj,jk)
	846	zz_dz_i (ji,jj) = aco_bc_hor * (-gde3w(ji,jj,jk) + gde3w(ji-1,jj,jk) ) - bco_bc_hor * zdz_i (ji-1,jj,jk)
[14060]	847	END IF
[14834]	848	END_2D
	849	! Walls coming from left: should check from 2 to jpj-1 (and jpi=2-jpi)
	850	DO_2D( 0, 1, 0, 0 )
	851	IF ( vmask(ji,jj,jk) > 0.5_wp .AND. vmask(ji,jj-1,jk) < 0.5_wp .AND. vmask(ji,jj+1,jk) > 0.5_wp) THEN
	852	zz_drho_j(ji,jj) = aco_bc_hor * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) ) - bco_bc_hor * zdrho_j(ji,jj+1,jk)
	853	zz_dz_j (ji,jj) = aco_bc_hor * (-gde3w(ji,jj+1,jk) + gde3w(ji,jj,jk) ) - bco_bc_hor * zdz_j (ji,jj+1,jk)
[14060]	854	END IF
	855	END_2D
[14834]	856	! Walls coming from right: should check from 3 to jpj (and jpi=2-jpi)
	857	DO_2D( 0, 1, -1, 1 )
	858	IF ( vmask(ji,jj,jk) < 0.5_wp .AND. vmask(ji,jj-1,jk) > 0.5_wp .AND. vmask(ji,jj-2,jk) > 0.5_wp) THEN
	859	zz_drho_j(ji,jj) = aco_bc_hor * ( rhd (ji,jj,jk) - rhd (ji,jj-1,jk) ) - bco_bc_hor * zdrho_j(ji,jj-1,jk)
	860	zz_dz_j (ji,jj) = aco_bc_hor * (-gde3w(ji,jj,jk) + gde3w(ji,jj-1,jk) ) - bco_bc_hor * zdz_j (ji,jj-1,jk)
	861	END IF
	862	END_2D
[14060]	863	zdrho_i(:,:,jk) = zz_drho_i(:,:)
	864	zdz_i (:,:,jk) = zz_dz_i (:,:)
	865	zdrho_j(:,:,jk) = zz_drho_j(:,:)
	866	zdz_j (:,:,jk) = zz_dz_j (:,:)
	867	END DO
[455]	868
	869	!--------------------------------------------------------------
[14060]	870	! 7. Calculate integrals on side faces
[455]	871	!-------------------------------------------------------------
	872
[14060]	873	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
	874	! two -ve signs cancel in next two lines (within zcoef0 and because gde3w is a depth not a height)
[14064]	875	z_rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
[14060]	876	& * ( gde3w(ji+1,jj,jk) - gde3w(ji,jj,jk) )
	877	IF ( umask(ji-1, jj, jk) > 0.5 .OR. umask(ji+1, jj, jk) > 0.5 ) THEN
	878	z_rho_i(ji,jj,jk) = z_rho_i(ji,jj,jk) - z_grav_10 * ( &
	879	& ( zdrho_i (ji+1,jj,jk) - zdrho_i (ji,jj,jk) ) &
	880	& * ( - gde3w(ji+1,jj,jk) + gde3w(ji,jj,jk) - z1_12 * ( zdz_i (ji+1,jj,jk) + zdz_i (ji,jj,jk) ) ) &
	881	& - ( zdz_i (ji+1,jj,jk) - zdz_i (ji,jj,jk) ) &
[14064]	882	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( zdrho_i(ji+1,jj,jk) + zdrho_i(ji,jj,jk) ) ) &
[14060]	883	& )
	884	END IF
	885
[14064]	886	z_rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
[14060]	887	& * ( gde3w(ji,jj+1,jk) - gde3w(ji,jj,jk) )
	888	IF ( vmask(ji, jj-1, jk) > 0.5 .OR. vmask(ji, jj+1, jk) > 0.5 ) THEN
	889	z_rho_j(ji,jj,jk) = z_rho_j(ji,jj,jk) - z_grav_10 * ( &
	890	& ( zdrho_j (ji,jj+1,jk) - zdrho_j (ji,jj,jk) ) &
	891	& * ( - gde3w(ji,jj+1,jk) + gde3w(ji,jj,jk) - z1_12 * ( zdz_j (ji,jj+1,jk) + zdz_j (ji,jj,jk) ) ) &
	892	& - ( zdz_j (ji,jj+1,jk) - zdz_j (ji,jj,jk) ) &
[14064]	893	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( zdrho_j(ji,jj+1,jk) + zdrho_j(ji,jj,jk) ) ) &
[14060]	894	& )
	895	END IF
	896	END_3D
[455]	897
[14060]	898	!--------------------------------------------------------------
	899	! 8. Integrate in the vertical
	900	!-------------------------------------------------------------
[14064]	901	!
[455]	902	! ---------------
	903	! Surface value
	904	! ---------------
[13295]	905	DO_2D( 0, 0, 0, 0 )
[14060]	906	zhpi(ji,jj,1) = ( z_rho_k(ji,jj,1) - z_rho_k(ji+1,jj ,1) - z_rho_i(ji,jj,1) ) * r1_e1u(ji,jj)
	907	zhpj(ji,jj,1) = ( z_rho_k(ji,jj,1) - z_rho_k(ji ,jj+1,1) - z_rho_j(ji,jj,1) ) * r1_e2v(ji,jj)
[12377]	908	IF( ln_wd_il ) THEN
	909	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
	910	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
	911	ENDIF
	912	! add to the general momentum trend
	913	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1)
	914	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1)
	915	END_2D
[455]	916
	917	! ----------------
	918	! interior value (2=<jk=<jpkm1)
	919	! ----------------
[13295]	920	DO_3D( 0, 0, 0, 0, 2, jpkm1 )
[12377]	921	! hydrostatic pressure gradient along s-surfaces
[14060]	922	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
	923	& + ( ( z_rho_k(ji,jj,jk) - z_rho_k(ji+1,jj,jk ) ) &
	924	& - ( z_rho_i(ji,jj,jk) - z_rho_i(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
	925	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
	926	& + ( ( z_rho_k(ji,jj,jk) - z_rho_k(ji,jj+1,jk ) ) &
	927	& -( z_rho_j(ji,jj,jk) - z_rho_j(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
[12377]	928	IF( ln_wd_il ) THEN
	929	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
	930	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
	931	ENDIF
	932	! add to the general momentum trend
	933	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk)
	934	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk)
	935	END_3D
[503]	936	!
[9023]	937	IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy )
[2715]	938	!
[455]	939	END SUBROUTINE hpg_djc
	940
	941
[12377]	942	SUBROUTINE hpg_prj( kt, Kmm, puu, pvv, Krhs )
[455]	943	!!---------------------------------------------------------------------
[3294]	944	!! * ROUTINE hpg_prj *
[455]	945	!!
[3294]	946	!! ** Method : s-coordinate case.
	947	!! A Pressure-Jacobian horizontal pressure gradient method
	948	!! based on the constrained cubic-spline interpolation for
	949	!! all vertical coordinate systems
[455]	950	!!
[12377]	951	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
[455]	952	!!----------------------------------------------------------------------
[3294]	953	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
[12377]	954	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	955	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
	956	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[503]	957	!!
[3294]	958	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
[6140]	959	REAL(wp) :: zcoef0, znad ! local scalars
	960	!
[3294]	961	!! The local variables for the correction term
	962	INTEGER :: jk1, jis, jid, jjs, jjd
[6152]	963	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
[3294]	964	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
[3764]	965	REAL(wp) :: zrhdt1
[3294]	966	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
[14834]	967	REAL(wp), DIMENSION(A2D(nn_hls)) :: zpgu, zpgv ! 2D workspace
	968	REAL(wp), DIMENSION(A2D(nn_hls)) :: zsshu_n, zsshv_n
	969	REAL(wp), DIMENSION(A2D(nn_hls),jpk) :: zdept, zrhh
	970	REAL(wp), DIMENSION(A2D(nn_hls),jpk) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
[9019]	971	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter
[455]	972	!!----------------------------------------------------------------------
[3294]	973	!
[14834]	974	IF( .NOT. l_istiled .OR. ntile == 1 ) THEN ! Do only on the first tile
	975	IF( kt == nit000 ) THEN
	976	IF(lwp) WRITE(numout,*)
	977	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
	978	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
	979	ENDIF
[3]	980	ENDIF
	981
[3294]	982	! Local constant initialization
[3764]	983	zcoef0 = - grav
[6140]	984	znad = 1._wp
[14064]	985	IF( ln_linssh ) znad = 1._wp
	986	!
	987	! ---------------
	988	! Surface pressure gradient to be removed
	989	! ---------------
	990	DO_2D( 0, 0, 0, 0 )
	991	zpgu(ji,jj) = - grav * ( ssh(ji+1,jj,Kmm) - ssh(ji,jj,Kmm) ) * r1_e1u(ji,jj)
	992	zpgv(ji,jj) = - grav * ( ssh(ji,jj+1,Kmm) - ssh(ji,jj,Kmm) ) * r1_e2v(ji,jj)
	993	END_2D
	994	!
[9023]	995	IF( ln_wd_il ) THEN
[14834]	996	ALLOCATE( zcpx(A2D(nn_hls)) , zcpy(A2D(nn_hls)) )
[13295]	997	DO_2D( 0, 0, 0, 0 )
[14834]	998	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
	999	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
	1000	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) > &
	1001	& rn_wdmin1 + rn_wdmin2
	1002	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji+1,jj,Kmm) ) > 1.E-12 ) .AND. &
	1003	& ( MAX( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
	1004	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
[6152]	1005
[14834]	1006	IF(ll_tmp1) THEN
	1007	zcpx(ji,jj) = 1.0_wp
	1008	ELSE IF(ll_tmp2) THEN
	1009	! no worries about ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm) = 0, it won't happen ! here
	1010	zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
	1011	& / (ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm)) )
	1012	zcpx(ji,jj) = MAX(MIN( zcpx(ji,jj) , 1.0_wp),0.0_wp)
	1013	ELSE
	1014	zcpx(ji,jj) = 0._wp
	1015	END IF
[6152]	1016
[14834]	1017	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
	1018	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
	1019	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) > &
	1020	& rn_wdmin1 + rn_wdmin2
	1021	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. &
	1022	& ( MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
	1023	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
[9023]	1024
[14834]	1025	IF(ll_tmp1) THEN
	1026	zcpy(ji,jj) = 1.0_wp
	1027	ELSE IF(ll_tmp2) THEN
	1028	! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here
	1029	zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
	1030	& / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) )
	1031	zcpy(ji,jj) = MAX(MIN( zcpy(ji,jj) , 1.0_wp),0.0_wp)
[12377]	1032	ELSE
	1033	zcpy(ji,jj) = 0._wp
	1034	ENDIF
	1035	END_2D
[9019]	1036	ENDIF
[6152]	1037
[3294]	1038	! Clean 3-D work arrays
	1039	zhpi(:,:,:) = 0._wp
[14834]	1040	zrhh(:,:,:) = rhd(A2D(nn_hls),:)
[3764]	1041
[3294]	1042	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
[13295]	1043	DO_2D( 1, 1, 1, 1 )
[14834]	1044	jk = mbkt(ji,jj)
	1045	IF( jk <= 1 ) THEN ; zrhh(ji,jj, : ) = 0._wp
	1046	ELSEIF( jk == 2 ) THEN ; zrhh(ji,jj,jk+1:jpk) = rhd(ji,jj,jk)
	1047	ELSEIF( jk < jpkm1 ) THEN
	1048	DO jkk = jk+1, jpk
	1049	zrhh(ji,jj,jkk) = interp1(gde3w(ji,jj,jkk ), gde3w(ji,jj,jkk-1), &
	1050	& gde3w(ji,jj,jkk-2), zrhh (ji,jj,jkk-1), zrhh(ji,jj,jkk-2))
	1051	END DO
	1052	ENDIF
[12377]	1053	END_2D
[3]	1054
[3632]	1055	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
[13295]	1056	DO_2D( 1, 1, 1, 1 )
[14064]	1057	zdept(ji,jj,1) = 0.5_wp * e3w(ji,jj,1,Kmm) - ssh(ji,jj,Kmm)
[12377]	1058	END_2D
[455]	1059
[13295]	1060	DO_3D( 1, 1, 1, 1, 2, jpk )
[12377]	1061	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + e3w(ji,jj,jk,Kmm)
	1062	END_3D
[455]	1063
[4990]	1064	fsp(:,:,:) = zrhh (:,:,:)
[3632]	1065	xsp(:,:,:) = zdept(:,:,:)
	1066
[3764]	1067	! Construct the vertical density profile with the
[3294]	1068	! constrained cubic spline interpolation
	1069	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
[6140]	1070	CALL cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
[3294]	1071
	1072	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
[13295]	1073	DO_2D( 0, 1, 0, 1 )
[14834]	1074	zrhdt1 = zrhh(ji,jj,1) - interp3( zdept(ji,jj,1), asp(ji,jj,1), bsp(ji,jj,1), &
	1075	& csp(ji,jj,1), dsp(ji,jj,1) ) * 0.25_wp * e3w(ji,jj,1,Kmm)
[3294]	1076
[14834]	1077	! assuming linear profile across the top half surface layer
	1078	zhpi(ji,jj,1) = 0.5_wp * e3w(ji,jj,1,Kmm) * zrhdt1
[12377]	1079	END_2D
[455]	1080
[3294]	1081	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
[13295]	1082	DO_3D( 0, 1, 0, 1, 2, jpkm1 )
[14834]	1083	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
	1084	& integ_spline( zdept(ji,jj,jk-1), zdept(ji,jj,jk), &
	1085	& asp (ji,jj,jk-1), bsp (ji,jj,jk-1), &
	1086	& csp (ji,jj,jk-1), dsp (ji,jj,jk-1) )
[12377]	1087	END_3D
[455]	1088
[3294]	1089	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
[5224]	1090
	1091	! Prepare zsshu_n and zsshv_n
[13295]	1092	DO_2D( 0, 0, 0, 0 )
[6140]	1093	!!gm BUG ? if it is ssh at u- & v-point then it should be:
[12377]	1094	! zsshu_n(ji,jj) = (e1e2t(ji,jj) * ssh(ji,jj,Kmm) + e1e2t(ji+1,jj) * ssh(ji+1,jj,Kmm)) * &
[6140]	1095	! & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
[12377]	1096	! zsshv_n(ji,jj) = (e1e2t(ji,jj) * ssh(ji,jj,Kmm) + e1e2t(ji,jj+1) * ssh(ji,jj+1,Kmm)) * &
[6140]	1097	! & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
	1098	!!gm not this:
[14834]	1099	zsshu_n(ji,jj) = (e1e2u(ji,jj) * ssh(ji,jj,Kmm) + e1e2u(ji+1, jj) * ssh(ji+1,jj,Kmm)) * &
	1100	& r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
	1101	zsshv_n(ji,jj) = (e1e2v(ji,jj) * ssh(ji,jj,Kmm) + e1e2v(ji+1, jj) * ssh(ji,jj+1,Kmm)) * &
	1102	& r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
[12377]	1103	END_2D
[455]	1104
[13295]	1105	DO_2D( 0, 0, 0, 0 )
[14834]	1106	zu(ji,jj,1) = - ( e3u(ji,jj,1,Kmm) - zsshu_n(ji,jj) )
	1107	zv(ji,jj,1) = - ( e3v(ji,jj,1,Kmm) - zsshv_n(ji,jj) )
[12377]	1108	END_2D
[5224]	1109
[13295]	1110	DO_3D( 0, 0, 0, 0, 2, jpkm1 )
[14834]	1111	zu(ji,jj,jk) = zu(ji,jj,jk-1) - e3u(ji,jj,jk,Kmm)
	1112	zv(ji,jj,jk) = zv(ji,jj,jk-1) - e3v(ji,jj,jk,Kmm)
[12377]	1113	END_3D
[3764]	1114
[13295]	1115	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[14834]	1116	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * e3u(ji,jj,jk,Kmm)
	1117	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * e3v(ji,jj,jk,Kmm)
[12377]	1118	END_3D
[455]	1119
[13295]	1120	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[14834]	1121	zu(ji,jj,jk) = MIN( zu(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
	1122	zu(ji,jj,jk) = MAX( zu(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
	1123	zv(ji,jj,jk) = MIN( zv(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
	1124	zv(ji,jj,jk) = MAX( zv(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
[12377]	1125	END_3D
[3632]	1126
	1127
[13295]	1128	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[14834]	1129	zpwes = 0._wp; zpwed = 0._wp
	1130	zpnss = 0._wp; zpnsd = 0._wp
	1131	zuijk = zu(ji,jj,jk)
	1132	zvijk = zv(ji,jj,jk)
[3294]	1133
[14834]	1134	!!!!! for u equation
	1135	IF( jk <= mbku(ji,jj) ) THEN
	1136	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
	1137	jis = ji + 1; jid = ji
	1138	ELSE
	1139	jis = ji; jid = ji +1
	1140	ENDIF
[3294]	1141
[14834]	1142	! integrate the pressure on the shallow side
	1143	jk1 = jk
	1144	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
	1145	IF( jk1 == mbku(ji,jj) ) THEN
	1146	zuijk = -zdept(jis,jj,jk1)
	1147	EXIT
	1148	ENDIF
	1149	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
	1150	zpwes = zpwes + &
	1151	integ_spline(zdept(jis,jj,jk1), zdeps, &
	1152	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
	1153	csp(jis,jj,jk1), dsp(jis,jj,jk1))
	1154	jk1 = jk1 + 1
	1155	END DO
[3764]	1156
[14834]	1157	! integrate the pressure on the deep side
	1158	jk1 = jk
	1159	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
	1160	IF( jk1 == 1 ) THEN
	1161	zdeps = zdept(jid,jj,1) + MIN(zuijk, ssh(jid,jj,Kmm)*znad)
	1162	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
	1163	bsp(jid,jj,1) , csp(jid,jj,1), &
	1164	dsp(jid,jj,1)) * zdeps
	1165	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
	1166	EXIT
	1167	ENDIF
	1168	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
	1169	zpwed = zpwed + &
	1170	integ_spline(zdeps, zdept(jid,jj,jk1), &
	1171	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
	1172	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
	1173	jk1 = jk1 - 1
	1174	END DO
[3764]	1175
[14834]	1176	! update the momentum trends in u direction
	1177	zdpdx1 = zcoef0 * r1_e1u(ji,jj) * ( zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk) )
	1178	IF( .NOT.ln_linssh ) THEN
	1179	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * &
	1180	& ( REAL(jis-jid, wp) * (zpwes + zpwed) + (ssh(ji+1,jj,Kmm)-ssh(ji,jj,Kmm)) )
	1181	ELSE
	1182	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
	1183	ENDIF
	1184	IF( ln_wd_il ) THEN
	1185	zdpdx1 = zdpdx1 * zcpx(ji,jj) * wdrampu(ji,jj)
	1186	zdpdx2 = zdpdx2 * zcpx(ji,jj) * wdrampu(ji,jj)
	1187	ENDIF
	1188	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + (zdpdx1 + zdpdx2 - zpgu(ji,jj)) * umask(ji,jj,jk)
[12377]	1189	ENDIF
[3764]	1190
[14834]	1191	!!!!! for v equation
	1192	IF( jk <= mbkv(ji,jj) ) THEN
	1193	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
	1194	jjs = jj + 1; jjd = jj
	1195	ELSE
	1196	jjs = jj ; jjd = jj + 1
	1197	ENDIF
[3294]	1198
[14834]	1199	! integrate the pressure on the shallow side
	1200	jk1 = jk
	1201	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
	1202	IF( jk1 == mbkv(ji,jj) ) THEN
	1203	zvijk = -zdept(ji,jjs,jk1)
	1204	EXIT
	1205	ENDIF
	1206	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
	1207	zpnss = zpnss + &
	1208	integ_spline(zdept(ji,jjs,jk1), zdeps, &
	1209	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
	1210	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
	1211	jk1 = jk1 + 1
	1212	END DO
[3764]	1213
[14834]	1214	! integrate the pressure on the deep side
	1215	jk1 = jk
	1216	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
	1217	IF( jk1 == 1 ) THEN
	1218	zdeps = zdept(ji,jjd,1) + MIN(zvijk, ssh(ji,jjd,Kmm)*znad)
	1219	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
	1220	bsp(ji,jjd,1) , csp(ji,jjd,1), &
	1221	dsp(ji,jjd,1) ) * zdeps
	1222	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
	1223	EXIT
	1224	ENDIF
	1225	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
	1226	zpnsd = zpnsd + &
	1227	integ_spline(zdeps, zdept(ji,jjd,jk1), &
	1228	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
	1229	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
	1230	jk1 = jk1 - 1
	1231	END DO
[3294]	1232
[14834]	1233	! update the momentum trends in v direction
	1234	zdpdy1 = zcoef0 * r1_e2v(ji,jj) * ( zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk) )
	1235	IF( .NOT.ln_linssh ) THEN
	1236	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * &
	1237	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (ssh(ji,jj+1,Kmm)-ssh(ji,jj,Kmm)) )
	1238	ELSE
	1239	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
	1240	ENDIF
	1241	IF( ln_wd_il ) THEN
	1242	zdpdy1 = zdpdy1 * zcpy(ji,jj) * wdrampv(ji,jj)
	1243	zdpdy2 = zdpdy2 * zcpy(ji,jj) * wdrampv(ji,jj)
	1244	ENDIF
[3764]	1245
[14834]	1246	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + (zdpdy1 + zdpdy2 - zpgv(ji,jj)) * vmask(ji,jj,jk)
[12377]	1247	ENDIF
	1248	!
	1249	END_3D
[503]	1250	!
[9023]	1251	IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy )
[2715]	1252	!
[3294]	1253	END SUBROUTINE hpg_prj
[455]	1254
[4990]	1255
[6140]	1256	SUBROUTINE cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
[3294]	1257	!!----------------------------------------------------------------------
	1258	!! * ROUTINE cspline *
[3764]	1259	!!
[3294]	1260	!! ** Purpose : constrained cubic spline interpolation
[3764]	1261	!!
	1262	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
[4990]	1263	!!
[3294]	1264	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
	1265	!!----------------------------------------------------------------------
[14834]	1266	REAL(wp), DIMENSION(A2D(nn_hls),jpk), INTENT(in ) :: fsp, xsp ! value and coordinate
	1267	REAL(wp), DIMENSION(A2D(nn_hls),jpk), INTENT( out) :: asp, bsp, csp, dsp ! coefficients of the interpoated function
	1268	INTEGER , INTENT(in ) :: polynomial_type ! 1: cubic spline ; 2: Linear
[4990]	1269	!
[3294]	1270	INTEGER :: ji, jj, jk ! dummy loop indices
	1271	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
	1272	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
[14834]	1273	REAL(wp) :: zdf(jpk)
[3294]	1274	!!----------------------------------------------------------------------
[6140]	1275	!
[3294]	1276	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
[14834]	1277	DO_2D( 1, 1, 1, 1 )
	1278	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
	1279	! DO jk = 2, jpkm1-1
	1280	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
	1281	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
	1282	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
	1283	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
	1284	!
	1285	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
	1286	!
	1287	! IF(zdf1 * zdf2 <= 0._wp) THEN
	1288	! zdf(jk) = 0._wp
	1289	! ELSE
	1290	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
	1291	! ENDIF
	1292	! END DO
[3764]	1293
[14834]	1294	!!Simply geometric average
	1295	DO jk = 2, jpk-2
	1296	zdf1 = (fsp(ji,jj,jk ) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk ) - xsp(ji,jj,jk-1))
	1297	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk )) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk ))
[3764]	1298
[14834]	1299	IF(zdf1 * zdf2 <= 0._wp) THEN
	1300	zdf(jk) = 0._wp
	1301	ELSE
	1302	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
	1303	ENDIF
	1304	END DO
[3764]	1305
[14834]	1306	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
	1307	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
	1308	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
	1309	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - 0.5_wp * zdf(jpk - 2)
[3764]	1310
[14834]	1311	DO jk = 1, jpk-2
	1312	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
	1313	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
	1314	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
	1315	zddf1 = -2._wp * ztmp1 + ztmp2
	1316	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
	1317	zddf2 = 2._wp * ztmp1 - ztmp2
[3764]	1318
[14834]	1319	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
	1320	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
	1321	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
	1322	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
	1323	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
	1324	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
	1325	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
	1326	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
	1327	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
[3294]	1328	END DO
[14834]	1329	END_2D
[3764]	1330
[6140]	1331	ELSEIF ( polynomial_type == 2 ) THEN ! Linear
[14834]	1332	DO_3D( 1, 1, 1, 1, 1, jpk-2 )
	1333	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
	1334	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
[3764]	1335
[14834]	1336	dsp(ji,jj,jk) = 0._wp
	1337	csp(ji,jj,jk) = 0._wp
	1338	bsp(ji,jj,jk) = ztmp1 / zdxtmp
	1339	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
	1340	END_3D
[9019]	1341	!
[3294]	1342	ELSE
[9019]	1343	CALL ctl_stop( 'invalid polynomial type in cspline' )
[3294]	1344	ENDIF
[9019]	1345	!
[3294]	1346	END SUBROUTINE cspline
	1347
	1348
[3764]	1349	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
[3294]	1350	!!----------------------------------------------------------------------
	1351	!! * ROUTINE interp1 *
[3764]	1352	!!
[3294]	1353	!! ** Purpose : 1-d linear interpolation
[3764]	1354	!!
[4990]	1355	!! ** Method : interpolation is straight forward
[3764]	1356	!! extrapolation is also permitted (no value limit)
[3294]	1357	!!----------------------------------------------------------------------
[3764]	1358	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
[3294]	1359	REAL(wp) :: f ! result of the interpolation (extrapolation)
	1360	REAL(wp) :: zdeltx
	1361	!!----------------------------------------------------------------------
[6140]	1362	!
[3294]	1363	zdeltx = xr - xl
[6140]	1364	IF( abs(zdeltx) <= 10._wp * EPSILON(x) ) THEN
	1365	f = 0.5_wp * (fl + fr)
[3294]	1366	ELSE
[6140]	1367	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
[3294]	1368	ENDIF
[6140]	1369	!
[3294]	1370	END FUNCTION interp1
	1371
[4990]	1372
[6140]	1373	FUNCTION interp2( x, a, b, c, d ) RESULT(f)
[3294]	1374	!!----------------------------------------------------------------------
	1375	!! * ROUTINE interp1 *
[3764]	1376	!!
[3294]	1377	!! ** Purpose : 1-d constrained cubic spline interpolation
[3764]	1378	!!
[3294]	1379	!! ** Method : cubic spline interpolation
	1380	!!
	1381	!!----------------------------------------------------------------------
[3764]	1382	REAL(wp), INTENT(in) :: x, a, b, c, d
[3294]	1383	REAL(wp) :: f ! value from the interpolation
	1384	!!----------------------------------------------------------------------
[6140]	1385	!
[3764]	1386	f = a + x* ( b + x * ( c + d * x ) )
[6140]	1387	!
[3294]	1388	END FUNCTION interp2
	1389
	1390
[6140]	1391	FUNCTION interp3( x, a, b, c, d ) RESULT(f)
[3294]	1392	!!----------------------------------------------------------------------
	1393	!! * ROUTINE interp1 *
[3764]	1394	!!
[9019]	1395	!! ** Purpose : Calculate the first order of derivative of
[3294]	1396	!! a cubic spline function y=a+bx+cx^2+d*x^3
[3764]	1397	!!
[3294]	1398	!! ** Method : f=dy/dx=b+2cx+3dx^2
	1399	!!
	1400	!!----------------------------------------------------------------------
[3764]	1401	REAL(wp), INTENT(in) :: x, a, b, c, d
[3294]	1402	REAL(wp) :: f ! value from the interpolation
	1403	!!----------------------------------------------------------------------
[6140]	1404	!
[3294]	1405	f = b + x * ( 2._wp * c + 3._wp * d * x)
[6140]	1406	!
[3294]	1407	END FUNCTION interp3
	1408
[3764]	1409
[6140]	1410	FUNCTION integ_spline( xl, xr, a, b, c, d ) RESULT(f)
[3294]	1411	!!----------------------------------------------------------------------
	1412	!! * ROUTINE interp1 *
[3764]	1413	!!
[3294]	1414	!! ** Purpose : 1-d constrained cubic spline integration
	1415	!!
[3764]	1416	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
	1417	!!
[3294]	1418	!!----------------------------------------------------------------------
[3764]	1419	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
	1420	REAL(wp) :: za1, za2, za3
[3294]	1421	REAL(wp) :: f ! integration result
	1422	!!----------------------------------------------------------------------
[6140]	1423	!
[3764]	1424	za1 = 0.5_wp * b
	1425	za2 = c / 3.0_wp
	1426	za3 = 0.25_wp * d
[6140]	1427	!
[3294]	1428	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
	1429	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
[6140]	1430	!
[3632]	1431	END FUNCTION integ_spline
[3294]	1432
[3]	1433	!!======================================================================
	1434	END MODULE dynhpg

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source: NEMO/trunk/src/OCE/DYN/dynhpg.F90 @ 15529

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