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dynhpg.F90 in NEMO/branches/2020/dev_r14116_HPC-04_mcastril_Mixed_Precision_implementation_final/src/OCE/DYN – NEMO

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source: NEMO/branches/2020/dev_r14116_HPC-04_mcastril_Mixed_Precision_implementation_final/src/OCE/DYN/dynhpg.F90 @ 14219

Last change on this file since 14219 was 14219, checked in by mcastril, 4 years ago
Add Mixed Precision support by Oriol Tintó
Property svn:keywords set to `Id`
File size: 75.2 KB

Rev	Line
[3]	1	MODULE dynhpg
	2	!!======================================================================
	3	!! * MODULE dynhpg *
	4	!! Ocean dynamics: hydrostatic pressure gradient trend
	5	!!======================================================================
[2528]	6	!! History : OPA ! 1987-09 (P. Andrich, M.-A. Foujols) hpg_zco: Original code
	7	!! 5.0 ! 1991-11 (G. Madec)
	8	!! 7.0 ! 1996-01 (G. Madec) hpg_sco: Original code for s-coordinates
	9	!! 8.0 ! 1997-05 (G. Madec) split dynber into dynkeg and dynhpg
	10	!! 8.5 ! 2002-07 (G. Madec) F90: Free form and module
	11	!! 8.5 ! 2002-08 (A. Bozec) hpg_zps: Original code
	12	!! NEMO 1.0 ! 2005-10 (A. Beckmann, B.W. An) various s-coordinate options
[3764]	13	!! ! Original code for hpg_ctl, hpg_hel hpg_wdj, hpg_djc, hpg_rot
[2528]	14	!! - ! 2005-11 (G. Madec) style & small optimisation
	15	!! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase
[3294]	16	!! 3.4 ! 2011-11 (H. Liu) hpg_prj: Original code for s-coordinates
	17	!! ! (A. Coward) suppression of hel, wdj and rot options
[5120]	18	!! 3.6 ! 2014-11 (P. Mathiot) hpg_isf: original code for ice shelf cavity
[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"
[14219]	83	# include "single_precision_substitute.h90"
[13237]	84
[3]	85	!!----------------------------------------------------------------------
[9598]	86	!! NEMO/OCE 4.0 , NEMO Consortium (2018)
[2528]	87	!! $Id$
[10068]	88	!! Software governed by the CeCILL license (see ./LICENSE)
[3]	89	!!----------------------------------------------------------------------
	90	CONTAINS
	91
[12377]	92	SUBROUTINE dyn_hpg( kt, Kmm, puu, pvv, Krhs )
[3]	93	!!---------------------------------------------------------------------
	94	!! * ROUTINE dyn_hpg *
	95	!!
[3764]	96	!! ** Method : Call the hydrostatic pressure gradient routine
[503]	97	!! using the scheme defined in the namelist
[3764]	98	!!
[12377]	99	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
[4990]	100	!! - send trends to trd_dyn for futher diagnostics (l_trddyn=T)
[503]	101	!!----------------------------------------------------------------------
[12377]	102	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	103	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
[14219]	104	REAL(dp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[12377]	105	!
[14219]	106	REAL(dp), ALLOCATABLE, DIMENSION(:,:,:) :: ztrdu, ztrdv
[455]	107	!!----------------------------------------------------------------------
[2528]	108	!
[9019]	109	IF( ln_timing ) CALL timing_start('dyn_hpg')
[2715]	110	!
[12377]	111	IF( l_trddyn ) THEN ! Temporary saving of puu(:,:,:,Krhs) and pvv(:,:,:,Krhs) trends (l_trddyn)
[9019]	112	ALLOCATE( ztrdu(jpi,jpj,jpk) , ztrdv(jpi,jpj,jpk) )
[12377]	113	ztrdu(:,:,:) = puu(:,:,:,Krhs)
	114	ztrdv(:,:,:) = pvv(:,:,:,Krhs)
[3764]	115	ENDIF
[2528]	116	!
[3294]	117	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
[12377]	118	CASE ( np_zco ) ; CALL hpg_zco ( kt, Kmm, puu, pvv, Krhs ) ! z-coordinate
	119	CASE ( np_zps ) ; CALL hpg_zps ( kt, Kmm, puu, pvv, Krhs ) ! z-coordinate plus partial steps (interpolation)
	120	CASE ( np_sco ) ; CALL hpg_sco ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate (standard jacobian formulation)
	121	CASE ( np_djc ) ; CALL hpg_djc ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate (Density Jacobian with Cubic polynomial)
	122	CASE ( np_prj ) ; CALL hpg_prj ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate (Pressure Jacobian scheme)
	123	CASE ( np_isf ) ; CALL hpg_isf ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate similar to sco modify for ice shelf
[455]	124	END SELECT
[2528]	125	!
[503]	126	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
[12377]	127	ztrdu(:,:,:) = puu(:,:,:,Krhs) - ztrdu(:,:,:)
	128	ztrdv(:,:,:) = pvv(:,:,:,Krhs) - ztrdv(:,:,:)
	129	CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt, Kmm )
[9019]	130	DEALLOCATE( ztrdu , ztrdv )
[3764]	131	ENDIF
[503]	132	!
[14219]	133	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=CASTWP(puu(:,:,:,Krhs)), clinfo1=' hpg - Ua: ', mask1=umask, &
	134	& tab3d_2=CASTWP(pvv(:,:,:,Krhs)), clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
[503]	135	!
[9019]	136	IF( ln_timing ) CALL timing_stop('dyn_hpg')
[2715]	137	!
[455]	138	END SUBROUTINE dyn_hpg
	139
	140
[12377]	141	SUBROUTINE dyn_hpg_init( Kmm )
[455]	142	!!----------------------------------------------------------------------
[2528]	143	!! * ROUTINE dyn_hpg_init *
[455]	144	!!
	145	!! ** Purpose : initializations for the hydrostatic pressure gradient
	146	!! computation and consistency control
	147	!!
[1601]	148	!! ** Action : Read the namelist namdyn_hpg and check the consistency
[455]	149	!! with the type of vertical coordinate used (zco, zps, sco)
	150	!!----------------------------------------------------------------------
[12377]	151	INTEGER, INTENT( in ) :: Kmm ! ocean time level index
	152	!
[455]	153	INTEGER :: ioptio = 0 ! temporary integer
[4147]	154	INTEGER :: ios ! Local integer output status for namelist read
[1601]	155	!!
[6140]	156	INTEGER :: ji, jj, jk, ikt ! dummy loop indices ISF
[9019]	157	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: zts_top, zrhd ! hypothesys on isf density
	158	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zrhdtop_isf ! density at bottom of ISF
	159	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: ziceload ! density at bottom of ISF
[6140]	160	!!
[3294]	161	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
[14060]	162	& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf, &
	163	& ln_hpg_djc_vnh, ln_hpg_djc_vnv
[455]	164	!!----------------------------------------------------------------------
[2528]	165	!
[4147]	166	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
[11536]	167	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist' )
[6140]	168	!
[4147]	169	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
[11536]	170	902 IF( ios > 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist' )
[4624]	171	IF(lwm) WRITE ( numond, namdyn_hpg )
[2528]	172	!
	173	IF(lwp) THEN ! Control print
[455]	174	WRITE(numout,*)
[2528]	175	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
	176	WRITE(numout,*) '~~~~~~~~~~~~'
[1601]	177	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
	178	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
	179	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
	180	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
[5120]	181	WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf
[1601]	182	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
[3294]	183	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
[455]	184	ENDIF
[2528]	185	!
[14200]	186	IF( .NOT.ln_linssh .AND. (ln_hpg_zco.OR.ln_hpg_zps) ) &
	187	& CALL ctl_stop( 'dyn_hpg_init : non-linear free surface incompatible with hpg_zco or hpg_zps' )
	188	!
	189	IF( (.NOT.ln_hpg_isf .AND. ln_isfcav) .OR. (ln_hpg_isf .AND. .NOT.ln_isfcav) ) &
	190	& CALL ctl_stop( 'dyn_hpg_init : ln_hpg_isf=T requires ln_isfcav=T and vice versa' )
	191	!
	192	#if defined key_qco
[9019]	193	IF( ln_hpg_isf ) THEN
[14200]	194	CALL ctl_stop( 'dyn_hpg_init : key_qco and ln_hpg_isf not yet compatible' )
[9019]	195	ENDIF
[14200]	196	#endif
[2528]	197	!
[9490]	198	! ! Set nhpg from ln_hpg_... flags & consistency check
	199	nhpg = np_ERROR
	200	ioptio = 0
	201	IF( ln_hpg_zco ) THEN ; nhpg = np_zco ; ioptio = ioptio +1 ; ENDIF
	202	IF( ln_hpg_zps ) THEN ; nhpg = np_zps ; ioptio = ioptio +1 ; ENDIF
	203	IF( ln_hpg_sco ) THEN ; nhpg = np_sco ; ioptio = ioptio +1 ; ENDIF
	204	IF( ln_hpg_djc ) THEN ; nhpg = np_djc ; ioptio = ioptio +1 ; ENDIF
	205	IF( ln_hpg_prj ) THEN ; nhpg = np_prj ; ioptio = ioptio +1 ; ENDIF
	206	IF( ln_hpg_isf ) THEN ; nhpg = np_isf ; ioptio = ioptio +1 ; ENDIF
[2528]	207	!
[2715]	208	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
[5120]	209	!
[9490]	210	IF(lwp) THEN
	211	WRITE(numout,*)
	212	SELECT CASE( nhpg )
	213	CASE( np_zco ) ; WRITE(numout,*) ' ==>>> z-coord. - full steps '
	214	CASE( np_zps ) ; WRITE(numout,*) ' ==>>> z-coord. - partial steps (interpolation)'
	215	CASE( np_sco ) ; WRITE(numout,*) ' ==>>> s-coord. (standard jacobian formulation)'
	216	CASE( np_djc ) ; WRITE(numout,*) ' ==>>> s-coord. (Density Jacobian: Cubic polynomial)'
	217	CASE( np_prj ) ; WRITE(numout,*) ' ==>>> s-coord. (Pressure Jacobian: Cubic polynomial)'
	218	CASE( np_isf ) ; WRITE(numout,*) ' ==>>> s-coord. (standard jacobian formulation) for isf'
	219	END SELECT
	220	WRITE(numout,*)
	221	ENDIF
[9019]	222	!
[14060]	223	IF ( ln_hpg_djc ) THEN
	224	IF (ln_hpg_djc_vnh) THEN ! Von Neumann boundary condition
	225	IF(lwp) WRITE(numout,*) ' horizontal bc: von Neumann '
	226	aco_bc_hor = 6.0_wp/5.0_wp
	227	bco_bc_hor = 7.0_wp/15.0_wp
	228	ELSE ! Linear extrapolation
	229	IF(lwp) WRITE(numout,*) ' horizontal bc: linear extrapolation'
	230	aco_bc_hor = 3.0_wp/2.0_wp
	231	bco_bc_hor = 1.0_wp/2.0_wp
	232	END IF
	233	IF (ln_hpg_djc_vnv) THEN ! Von Neumann boundary condition
	234	IF(lwp) WRITE(numout,*) ' vertical bc: von Neumann '
	235	aco_bc_vrt = 6.0_wp/5.0_wp
	236	bco_bc_vrt = 7.0_wp/15.0_wp
	237	ELSE ! Linear extrapolation
	238	IF(lwp) WRITE(numout,*) ' vertical bc: linear extrapolation'
	239	aco_bc_vrt = 3.0_wp/2.0_wp
	240	bco_bc_vrt = 1.0_wp/2.0_wp
	241	END IF
	242	END IF
[14200]	243	!
[2528]	244	END SUBROUTINE dyn_hpg_init
[455]	245
	246
[12377]	247	SUBROUTINE hpg_zco( kt, Kmm, puu, pvv, Krhs )
[455]	248	!!---------------------------------------------------------------------
	249	!! * ROUTINE hpg_zco *
	250	!!
	251	!! ** Method : z-coordinate case, levels are horizontal surfaces.
	252	!! The now hydrostatic pressure gradient at a given level, jk,
	253	!! is computed by taking the vertical integral of the in-situ
	254	!! density gradient along the model level from the suface to that
	255	!! level: zhpi = grav .....
	256	!! zhpj = grav .....
[12377]	257	!! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)).
	258	!! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi
	259	!! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj
[3764]	260	!!
[12377]	261	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
[503]	262	!!----------------------------------------------------------------------
[12377]	263	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	264	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
[14219]	265	REAL(dp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[6140]	266	!
[503]	267	INTEGER :: ji, jj, jk ! dummy loop indices
	268	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
[14064]	269	REAL(wp), DIMENSION(jpi,jpj) :: zhpi, zhpj
[3]	270	!!----------------------------------------------------------------------
[3764]	271	!
[3]	272	IF( kt == nit000 ) THEN
	273	IF(lwp) WRITE(numout,*)
[455]	274	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
	275	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
[3]	276	ENDIF
[14064]	277	!
	278	zcoef0 = - grav * 0.5_wp ! Local constant initialization
	279	!
	280	DO_2D( 0, 0, 0, 0 ) ! Surface value
[12377]	281	zcoef1 = zcoef0 * e3w(ji,jj,1,Kmm)
[14064]	282	! ! hydrostatic pressure gradient
	283	zhpi(ji,jj) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
	284	zhpj(ji,jj) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
	285	! ! add to the general momentum trend
	286	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj)
	287	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj)
[12377]	288	END_2D
[503]	289	!
[14064]	290	DO_3D( 0, 0, 0, 0, 2, jpkm1 ) ! interior value (2=<jk=<jpkm1)
[12377]	291	zcoef1 = zcoef0 * e3w(ji,jj,jk,Kmm)
[14064]	292	! ! hydrostatic pressure gradient
	293	zhpi(ji,jj) = zhpi(ji,jj) + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
	294	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
[455]	295
[14064]	296	zhpj(ji,jj) = zhpj(ji,jj) + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
	297	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
	298	! ! add to the general momentum trend
	299	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj)
	300	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj)
[12377]	301	END_3D
[503]	302	!
[455]	303	END SUBROUTINE hpg_zco
[216]	304
[3]	305
[12377]	306	SUBROUTINE hpg_zps( kt, Kmm, puu, pvv, Krhs )
[3]	307	!!---------------------------------------------------------------------
[455]	308	!! * ROUTINE hpg_zps *
[3764]	309	!!
[455]	310	!! ** Method : z-coordinate plus partial steps case. blahblah...
[3764]	311	!!
[12377]	312	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
[3764]	313	!!----------------------------------------------------------------------
[12377]	314	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	315	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
[14219]	316	REAL(dp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[503]	317	!!
	318	INTEGER :: ji, jj, jk ! dummy loop indices
	319	INTEGER :: iku, ikv ! temporary integers
	320	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
[13982]	321	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
	322	REAL(wp), DIMENSION(jpi,jpj,jpts) :: zgtsu, zgtsv
	323	REAL(wp), DIMENSION(jpi,jpj) :: zgru, zgrv
[3]	324	!!----------------------------------------------------------------------
[3294]	325	!
[3]	326	IF( kt == nit000 ) THEN
	327	IF(lwp) WRITE(numout,*)
[455]	328	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
[503]	329	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
[3]	330	ENDIF
	331
[11416]	332	! Partial steps: Compute NOW horizontal gradient of t, s, rd at the last ocean level
[12377]	333	CALL zps_hde( kt, Kmm, jpts, ts(:,:,:,:,Kmm), zgtsu, zgtsv, rhd, zgru , zgrv )
[3294]	334
[503]	335	! Local constant initialization
[2528]	336	zcoef0 = - grav * 0.5_wp
[3]	337
[2528]	338	! Surface value (also valid in partial step case)
[13295]	339	DO_2D( 0, 0, 0, 0 )
[12377]	340	zcoef1 = zcoef0 * e3w(ji,jj,1,Kmm)
	341	! hydrostatic pressure gradient
	342	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
	343	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
	344	! add to the general momentum trend
	345	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1)
	346	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1)
	347	END_2D
[3]	348
[503]	349	! interior value (2=<jk=<jpkm1)
[13295]	350	DO_3D( 0, 0, 0, 0, 2, jpkm1 )
[12377]	351	zcoef1 = zcoef0 * e3w(ji,jj,jk,Kmm)
	352	! hydrostatic pressure gradient
	353	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
	354	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
	355	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
[3]	356
[12377]	357	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
	358	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
	359	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
	360	! add to the general momentum trend
	361	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk)
	362	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk)
	363	END_3D
[3]	364
[11416]	365	! partial steps correction at the last level (use zgru & zgrv computed in zpshde.F90)
[13295]	366	DO_2D( 0, 0, 0, 0 )
[12377]	367	iku = mbku(ji,jj)
	368	ikv = mbkv(ji,jj)
	369	zcoef2 = zcoef0 * MIN( e3w(ji,jj,iku,Kmm), e3w(ji+1,jj ,iku,Kmm) )
	370	zcoef3 = zcoef0 * MIN( e3w(ji,jj,ikv,Kmm), e3w(ji ,jj+1,ikv,Kmm) )
	371	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
	372	puu (ji,jj,iku,Krhs) = puu(ji,jj,iku,Krhs) - zhpi(ji,jj,iku) ! subtract old value
	373	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
	374	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + zgru(ji,jj) ) * r1_e1u(ji,jj)
	375	puu (ji,jj,iku,Krhs) = puu(ji,jj,iku,Krhs) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
	376	ENDIF
	377	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
	378	pvv (ji,jj,ikv,Krhs) = pvv(ji,jj,ikv,Krhs) - zhpj(ji,jj,ikv) ! subtract old value
	379	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
	380	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + zgrv(ji,jj) ) * r1_e2v(ji,jj)
	381	pvv (ji,jj,ikv,Krhs) = pvv(ji,jj,ikv,Krhs) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
	382	ENDIF
	383	END_2D
[503]	384	!
[455]	385	END SUBROUTINE hpg_zps
[216]	386
[6140]	387
[12377]	388	SUBROUTINE hpg_sco( kt, Kmm, puu, pvv, Krhs )
[3]	389	!!---------------------------------------------------------------------
[455]	390	!! * ROUTINE hpg_sco *
[3]	391	!!
[455]	392	!! ** Method : s-coordinate case. Jacobian scheme.
	393	!! The now hydrostatic pressure gradient at a given level, jk,
	394	!! is computed by taking the vertical integral of the in-situ
[3]	395	!! density gradient along the model level from the suface to that
[455]	396	!! level. s-coordinates (ln_sco): a corrective term is added
	397	!! to the horizontal pressure gradient :
	398	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
	399	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
[12377]	400	!! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)).
	401	!! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi
	402	!! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj
[3]	403	!!
[12377]	404	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
[503]	405	!!----------------------------------------------------------------------
[12377]	406	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	407	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
[14219]	408	REAL(dp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[503]	409	!!
[14064]	410	INTEGER :: ji, jj, jk, jii, jjj ! dummy loop indices
	411	REAL(wp) :: zcoef0, zuap, zvap, ztmp ! local scalars
	412	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
[9019]	413	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
	414	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter
[5120]	415	!!----------------------------------------------------------------------
	416	!
[9039]	417	IF( ln_wd_il ) ALLOCATE(zcpx(jpi,jpj), zcpy(jpi,jpj))
[9023]	418	!
[5120]	419	IF( kt == nit000 ) THEN
	420	IF(lwp) WRITE(numout,*)
	421	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
	422	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
	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
[13226]	465	CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1.0_wp, zcpy, 'V', 1.0_wp )
[9023]	466	END IF
[14064]	467	!
	468	DO_2D( 0, 0, 0, 0 ) ! Surface value
	469	! ! hydrostatic pressure gradient along s-surfaces
	470	zhpi(ji,jj,1) = zcoef0 * r1_e1u(ji,jj) &
	471	& * ( e3w(ji+1,jj ,1,Kmm) * rhd(ji+1,jj ,1) &
	472	& - e3w(ji ,jj ,1,Kmm) * rhd(ji ,jj ,1) )
	473	zhpj(ji,jj,1) = zcoef0 * r1_e2v(ji,jj) &
	474	& * ( e3w(ji ,jj+1,1,Kmm) * rhd(ji ,jj+1,1) &
	475	& - e3w(ji ,jj ,1,Kmm) * rhd(ji ,jj ,1) )
	476	! ! s-coordinate pressure gradient correction
	477	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) ) &
[12377]	478	& * ( gde3w(ji+1,jj,1) - gde3w(ji,jj,1) ) * r1_e1u(ji,jj)
[14064]	479	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) ) &
[12377]	480	& * ( gde3w(ji,jj+1,1) - gde3w(ji,jj,1) ) * r1_e2v(ji,jj)
	481	!
	482	IF( ln_wd_il ) THEN
	483	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
	484	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
	485	zuap = zuap * zcpx(ji,jj)
	486	zvap = zvap * zcpy(ji,jj)
	487	ENDIF
[14064]	488	! ! add to the general momentum trend
[12377]	489	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1) + zuap
	490	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1) + zvap
	491	END_2D
[14064]	492	!
	493	DO_3D( 0, 0, 0, 0, 2, jpkm1 ) ! interior value (2=<jk=<jpkm1)
	494	! ! hydrostatic pressure gradient along s-surfaces
	495	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 * r1_e1u(ji,jj) &
	496	& * ( e3w(ji+1,jj,jk,Kmm) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
	497	& - e3w(ji ,jj,jk,Kmm) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) )
	498	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 * r1_e2v(ji,jj) &
	499	& * ( e3w(ji,jj+1,jk,Kmm) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
	500	& - e3w(ji,jj ,jk,Kmm) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) )
	501	! ! s-coordinate pressure gradient correction
	502	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) ) &
[12377]	503	& * ( gde3w(ji+1,jj ,jk) - gde3w(ji,jj,jk) ) * r1_e1u(ji,jj)
[14064]	504	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) ) &
[12377]	505	& * ( gde3w(ji ,jj+1,jk) - gde3w(ji,jj,jk) ) * r1_e2v(ji,jj)
	506	!
	507	IF( ln_wd_il ) THEN
	508	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
	509	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
	510	zuap = zuap * zcpx(ji,jj)
	511	zvap = zvap * zcpy(ji,jj)
	512	ENDIF
	513	!
	514	! add to the general momentum trend
	515	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk) + zuap
	516	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk) + zvap
	517	END_3D
[5120]	518	!
[9039]	519	IF( ln_wd_il ) DEALLOCATE( zcpx , zcpy )
[5120]	520	!
	521	END SUBROUTINE hpg_sco
	522
[6140]	523
[12377]	524	SUBROUTINE hpg_isf( kt, Kmm, puu, pvv, Krhs )
[5120]	525	!!---------------------------------------------------------------------
[6140]	526	!! * ROUTINE hpg_isf *
[5120]	527	!!
	528	!! ** Method : s-coordinate case. Jacobian scheme.
	529	!! The now hydrostatic pressure gradient at a given level, jk,
	530	!! is computed by taking the vertical integral of the in-situ
	531	!! density gradient along the model level from the suface to that
	532	!! level. s-coordinates (ln_sco): a corrective term is added
	533	!! to the horizontal pressure gradient :
	534	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
	535	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
[12377]	536	!! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)).
	537	!! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi
	538	!! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj
	539	!! iceload is added
[5120]	540	!!
[12377]	541	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
[5120]	542	!!----------------------------------------------------------------------
[12377]	543	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	544	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
[14219]	545	REAL(dp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[5120]	546	!!
[14064]	547	INTEGER :: ji, jj, jk ! dummy loop indices
	548	INTEGER :: ikt , ikti1, iktj1 ! local integer
	549	REAL(wp) :: ze3w, ze3wi1, ze3wj1 ! local scalars
	550	REAL(wp) :: zcoef0, zuap, zvap ! - -
[9019]	551	REAL(wp), DIMENSION(jpi,jpj,jpk ) :: zhpi, zhpj
	552	REAL(wp), DIMENSION(jpi,jpj,jpts) :: zts_top
	553	REAL(wp), DIMENSION(jpi,jpj) :: zrhdtop_oce
[3]	554	!!----------------------------------------------------------------------
[3294]	555	!
[9019]	556	zcoef0 = - grav * 0.5_wp ! Local constant initialization
[3294]	557	!
[9019]	558	! ! iniitialised to 0. zhpi zhpi
	559	zhpi(:,:,:) = 0._wp ; zhpj(:,:,:) = 0._wp
[6140]	560
[4990]	561	! compute rhd at the ice/oce interface (ocean side)
[6140]	562	! usefull to reduce residual current in the test case ISOMIP with no melting
[9019]	563	DO ji = 1, jpi
	564	DO jj = 1, jpj
	565	ikt = mikt(ji,jj)
[12377]	566	zts_top(ji,jj,1) = ts(ji,jj,ikt,1,Kmm)
	567	zts_top(ji,jj,2) = ts(ji,jj,ikt,2,Kmm)
[4990]	568	END DO
	569	END DO
[9019]	570	CALL eos( zts_top, risfdep, zrhdtop_oce )
[6140]	571
[14064]	572	! !===========================!
	573	! !===== surface value =====!
	574	! !===========================!
[13295]	575	DO_2D( 0, 0, 0, 0 )
[14064]	576	ikt = mikt(ji ,jj ) ; ze3w = e3w(ji ,jj ,ikt ,Kmm)
	577	ikti1 = mikt(ji+1,jj ) ; ze3wi1 = e3w(ji+1,jj ,ikti1,Kmm)
	578	iktj1 = mikt(ji ,jj+1) ; ze3wj1 = e3w(ji ,jj+1,iktj1,Kmm)
	579	! ! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
	580	! ! we assume ISF is in isostatic equilibrium
	581	zhpi(ji,jj,1) = zcoef0 * r1_e1u(ji,jj) * ( risfload(ji+1,jj) - risfload(ji,jj) &
	582	& + 0.5_wp * ( ze3wi1 * ( rhd(ji+1,jj,ikti1) + zrhdtop_oce(ji+1,jj) ) &
	583	& - ze3w * ( rhd(ji ,jj,ikt ) + zrhdtop_oce(ji ,jj) ) ) )
	584	zhpj(ji,jj,1) = zcoef0 * r1_e2v(ji,jj) * ( risfload(ji,jj+1) - risfload(ji,jj) &
	585	& + 0.5_wp * ( ze3wj1 * ( rhd(ji,jj+1,iktj1) + zrhdtop_oce(ji,jj+1) ) &
	586	& - ze3w * ( rhd(ji,jj ,ikt ) + zrhdtop_oce(ji,jj ) ) ) )
	587	! ! s-coordinate pressure gradient correction (=0 if z coordinate)
	588	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) ) &
[12377]	589	& * ( gde3w(ji+1,jj,1) - gde3w(ji,jj,1) ) * r1_e1u(ji,jj)
[14064]	590	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) ) &
[12377]	591	& * ( gde3w(ji,jj+1,1) - gde3w(ji,jj,1) ) * r1_e2v(ji,jj)
[14064]	592	! ! add to the general momentum trend
[12377]	593	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
	594	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
	595	END_2D
[14064]	596	!
	597	! !=============================!
	598	! !===== interior values =====!
	599	! !=============================!
[13295]	600	DO_3D( 0, 0, 0, 0, 2, jpkm1 )
[14064]	601	ze3w = e3w(ji ,jj ,jk,Kmm)
	602	ze3wi1 = e3w(ji+1,jj ,jk,Kmm)
	603	ze3wj1 = e3w(ji ,jj+1,jk,Kmm)
	604	! ! hydrostatic pressure gradient along s-surfaces
[12377]	605	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
[14064]	606	& * ( ze3wi1 * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) * wmask(ji+1,jj,jk) &
	607	& - ze3w * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) * wmask(ji ,jj,jk) )
[12377]	608	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
[14064]	609	& * ( ze3wj1 * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) * wmask(ji,jj+1,jk) &
	610	& - ze3w * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) * wmask(ji,jj ,jk) )
	611	! ! s-coordinate pressure gradient correction
	612	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) ) &
[12377]	613	& * ( gde3w(ji+1,jj ,jk) - gde3w(ji,jj,jk) ) / e1u(ji,jj)
[14064]	614	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) ) &
[12377]	615	& * ( gde3w(ji ,jj+1,jk) - gde3w(ji,jj,jk) ) / e2v(ji,jj)
[14064]	616	! ! add to the general momentum trend
[12377]	617	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + (zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
	618	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + (zhpj(ji,jj,jk) + zvap) * vmask(ji,jj,jk)
	619	END_3D
[503]	620	!
[5120]	621	END SUBROUTINE hpg_isf
[455]	622
[4990]	623
[12377]	624	SUBROUTINE hpg_djc( kt, Kmm, puu, pvv, Krhs )
[455]	625	!!---------------------------------------------------------------------
	626	!! * ROUTINE hpg_djc *
	627	!!
	628	!! ** Method : Density Jacobian with Cubic polynomial scheme
[3764]	629	!!
[503]	630	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
[455]	631	!!----------------------------------------------------------------------
[12377]	632	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	633	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
[14219]	634	REAL(dp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[503]	635	!!
	636	INTEGER :: ji, jj, jk ! dummy loop indices
[14060]	637	INTEGER :: iktb, iktt ! jk indices at tracer points for top and bottom points
[503]	638	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
[14060]	639	REAL(wp) :: z_grav_10, z1_12
	640	REAL(wp) :: cffu, cffx ! " "
	641	REAL(wp) :: cffv, cffy ! " "
[6152]	642	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
[9019]	643	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
[14060]	644
	645	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdzx, zdzy, zdzz ! Primitive grid differences ('delta_xyz')
	646	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdz_i, zdz_j, zdz_k ! Harmonic average of primitive grid differences ('d_xyz')
	647	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdrhox, zdrhoy, zdrhoz ! Primitive rho differences ('delta_rho')
	648	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdrho_i, zdrho_j, zdrho_k ! Harmonic average of primitive rho differences ('d_rho')
	649	REAL(wp), DIMENSION(jpi,jpj,jpk) :: z_rho_i, z_rho_j, z_rho_k ! Face intergrals
	650	REAL(wp), DIMENSION(jpi,jpj) :: zz_dz_i, zz_dz_j, zz_drho_i, zz_drho_j ! temporary arrays
[9019]	651	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter
[455]	652	!!----------------------------------------------------------------------
[3294]	653	!
[9023]	654	IF( ln_wd_il ) THEN
[9019]	655	ALLOCATE( zcpx(jpi,jpj) , zcpy(jpi,jpj) )
[13295]	656	DO_2D( 0, 0, 0, 0 )
[12377]	657	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
	658	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
	659	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) &
	660	& > rn_wdmin1 + rn_wdmin2
	661	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji+1,jj,Kmm) ) > 1.E-12 ) .AND. ( &
	662	& MAX( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
	663	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
	664	IF(ll_tmp1) THEN
	665	zcpx(ji,jj) = 1.0_wp
	666	ELSE IF(ll_tmp2) THEN
	667	! no worries about ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm) = 0, it won't happen ! here
	668	zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
	669	& / (ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm)) )
	670	ELSE
	671	zcpx(ji,jj) = 0._wp
	672	END IF
	673
	674	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
	675	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
	676	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) &
	677	& > rn_wdmin1 + rn_wdmin2
	678	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. ( &
	679	& MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
	680	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
[6152]	681
[12377]	682	IF(ll_tmp1) THEN
	683	zcpy(ji,jj) = 1.0_wp
	684	ELSE IF(ll_tmp2) THEN
	685	! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here
	686	zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
	687	& / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) )
	688	ELSE
	689	zcpy(ji,jj) = 0._wp
	690	END IF
	691	END_2D
[13226]	692	CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1.0_wp, zcpy, 'V', 1.0_wp )
[9023]	693	END IF
[6152]	694
[455]	695	IF( kt == nit000 ) THEN
	696	IF(lwp) WRITE(numout,*)
	697	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
	698	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
[216]	699	ENDIF
	700
[503]	701	! Local constant initialization
[2528]	702	zcoef0 = - grav * 0.5_wp
[14060]	703	z_grav_10 = grav / 10._wp
	704	z1_12 = 1.0_wp / 12._wp
[455]	705
	706	!----------------------------------------------------------------------------------------
[14060]	707	! 1. compute and store elementary vertical differences in provisional arrays
[455]	708	!----------------------------------------------------------------------------------------
	709
[14060]	710	!!bug gm Not a true bug, but... zdzz=e3w for zdzx, zdzy verify what it is really
[455]	711
[14060]	712	DO_3D( 1, 1, 1, 1, 2, jpkm1 )
[14064]	713	zdrhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
[14060]	714	zdzz (ji,jj,jk) = - gde3w(ji ,jj ,jk) + gde3w(ji,jj,jk-1)
[12377]	715	END_3D
[455]	716
	717	!-------------------------------------------------------------------------
[14060]	718	! 2. compute harmonic averages for vertical differences using eq. 5.18
[455]	719	!-------------------------------------------------------------------------
	720	zep = 1.e-15
	721
[14060]	722	!! mb zdrho_k, zdz_k, zdrho_i, zdz_i, zdrho_j, zdz_j re-centred about the point (ji,jj,jk)
	723	zdrho_k(:,:,:) = 0._wp
	724	zdz_k (:,:,:) = 0._wp
[455]	725
[14060]	726	DO_3D( 1, 1, 1, 1, 2, jpk-2 )
	727	cffw = 2._wp * zdrhoz(ji ,jj ,jk) * zdrhoz(ji,jj,jk+1)
	728	IF( cffw > zep) THEN
	729	zdrho_k(ji,jj,jk) = cffw / ( zdrhoz(ji,jj,jk) + zdrhoz(ji,jj,jk+1) )
	730	ENDIF
	731	zdz_k(ji,jj,jk) = 2._wp * zdzz(ji,jj,jk) * zdzz(ji,jj,jk+1) &
	732	& / ( zdzz(ji,jj,jk) + zdzz(ji,jj,jk+1) )
	733	END_3D
[455]	734
[14060]	735	!----------------------------------------------------------------------------------
	736	! 3. apply boundary conditions at top and bottom using 5.36-5.37
	737	!----------------------------------------------------------------------------------
[3764]	738
[14060]	739	! mb for sea-ice shelves we will need to re-write this upper boundary condition in the same form as the lower boundary condition
[14064]	740	zdrho_k(:,:,1) = aco_bc_vrt * ( rhd (:,:,2) - rhd (:,:,1) ) - bco_bc_vrt * zdrho_k(:,:,2)
[14060]	741	zdz_k (:,:,1) = aco_bc_vrt * (-gde3w(:,:,2) + gde3w(:,:,1) ) - bco_bc_vrt * zdz_k (:,:,2)
[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	!-------------------------------------------------------------
[14200]	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	!----------------------------------------------------------------------------------------
	788
	789	DO_3D( 1, 0, 1, 0, 1, jpkm1 )
[14064]	790	zdrhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
[14060]	791	zdzx (ji,jj,jk) = - gde3w(ji+1,jj ,jk) + gde3w(ji,jj,jk )
[14064]	792	zdrhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
[14060]	793	zdzy (ji,jj,jk) = - gde3w(ji ,jj+1,jk) + gde3w(ji,jj,jk )
	794	END_3D
	795
[14219]	796	CALL lbc_lnk_multi( 'dynhpg', zdrhox, 'U', 1._wp, zdzx, 'U', 1._wp, zdrhoy, 'V', 1._wp, zdzy, 'V', 1._wp )
[14060]	797
	798	!-------------------------------------------------------------------------
	799	! 6. compute harmonic averages using eq. 5.18
	800	!-------------------------------------------------------------------------
	801
	802	DO_3D( 0, 1, 0, 1, 1, jpkm1 )
	803	cffu = 2._wp * zdrhox(ji-1,jj ,jk) * zdrhox(ji,jj,jk )
[12377]	804	IF( cffu > zep ) THEN
[14060]	805	zdrho_i(ji,jj,jk) = cffu / ( zdrhox(ji-1,jj,jk) + zdrhox(ji,jj,jk) )
[12377]	806	ELSE
[14060]	807	zdrho_i(ji,jj,jk ) = 0._wp
[12377]	808	ENDIF
[455]	809
[14060]	810	cffx = 2._wp * zdzx (ji-1,jj ,jk) * zdzx (ji,jj,jk )
[12377]	811	IF( cffx > zep ) THEN
[14060]	812	zdz_i(ji,jj,jk) = cffx / ( zdzx(ji-1,jj,jk) + zdzx(ji,jj,jk) )
[12377]	813	ELSE
[14060]	814	zdz_i(ji,jj,jk) = 0._wp
[12377]	815	ENDIF
[455]	816
[14060]	817	cffv = 2._wp * zdrhoy(ji ,jj-1,jk) * zdrhoy(ji,jj,jk )
[12377]	818	IF( cffv > zep ) THEN
[14060]	819	zdrho_j(ji,jj,jk) = cffv / ( zdrhoy(ji,jj-1,jk) + zdrhoy(ji,jj,jk) )
[12377]	820	ELSE
[14060]	821	zdrho_j(ji,jj,jk) = 0._wp
[12377]	822	ENDIF
[455]	823
[14060]	824	cffy = 2._wp * zdzy (ji ,jj-1,jk) * zdzy (ji,jj,jk )
[12377]	825	IF( cffy > zep ) THEN
[14060]	826	zdz_j(ji,jj,jk) = cffy / ( zdzy(ji,jj-1,jk) + zdzy(ji,jj,jk) )
[12377]	827	ELSE
[14060]	828	zdz_j(ji,jj,jk) = 0._wp
[12377]	829	ENDIF
	830	END_3D
[14060]	831
	832	!!! Note that zdzx, zdzy, zdzz, zdrhox, zdrhoy and zdrhoz should NOT be used beyond this point
[455]	833
	834	!----------------------------------------------------------------------------------
[14060]	835	! 6B. apply boundary conditions at side boundaries using 5.36-5.37
[455]	836	!----------------------------------------------------------------------------------
	837
[14060]	838	DO jk = 1, jpkm1
	839	zz_drho_i(:,:) = zdrho_i(:,:,jk)
	840	zz_dz_i (:,:) = zdz_i (:,:,jk)
	841	zz_drho_j(:,:) = zdrho_j(:,:,jk)
	842	zz_dz_j (:,:) = zdz_j (:,:,jk)
	843	DO_2D( 0, 1, 0, 1)
	844	! Walls coming from left: should check from 2 to jpi-1 (and jpj=2-jpj)
	845	IF (ji < jpi) THEN
	846	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
[14064]	847	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)
[14060]	848	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)
	849	END IF
	850	END IF
	851	! Walls coming from right: should check from 3 to jpi (and jpj=2-jpj)
	852	IF (ji > 2) THEN
	853	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
[14064]	854	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)
[14060]	855	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)
	856	END IF
	857	END IF
	858	! Walls coming from left: should check from 2 to jpj-1 (and jpi=2-jpi)
	859	IF (jj < jpj) THEN
	860	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
[14064]	861	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)
[14060]	862	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)
	863	END IF
	864	END IF
	865	! Walls coming from right: should check from 3 to jpj (and jpi=2-jpi)
	866	IF (jj > 2) THEN
	867	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
[14064]	868	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)
[14060]	869	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)
	870	END IF
	871	END IF
	872	END_2D
	873	zdrho_i(:,:,jk) = zz_drho_i(:,:)
	874	zdz_i (:,:,jk) = zz_dz_i (:,:)
	875	zdrho_j(:,:,jk) = zz_drho_j(:,:)
	876	zdz_j (:,:,jk) = zz_dz_j (:,:)
	877	END DO
[455]	878
	879	!--------------------------------------------------------------
[14060]	880	! 7. Calculate integrals on side faces
[455]	881	!-------------------------------------------------------------
	882
[14060]	883	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
	884	! two -ve signs cancel in next two lines (within zcoef0 and because gde3w is a depth not a height)
[14064]	885	z_rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
[14060]	886	& * ( gde3w(ji+1,jj,jk) - gde3w(ji,jj,jk) )
	887	IF ( umask(ji-1, jj, jk) > 0.5 .OR. umask(ji+1, jj, jk) > 0.5 ) THEN
	888	z_rho_i(ji,jj,jk) = z_rho_i(ji,jj,jk) - z_grav_10 * ( &
	889	& ( zdrho_i (ji+1,jj,jk) - zdrho_i (ji,jj,jk) ) &
	890	& * ( - gde3w(ji+1,jj,jk) + gde3w(ji,jj,jk) - z1_12 * ( zdz_i (ji+1,jj,jk) + zdz_i (ji,jj,jk) ) ) &
	891	& - ( zdz_i (ji+1,jj,jk) - zdz_i (ji,jj,jk) ) &
[14064]	892	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( zdrho_i(ji+1,jj,jk) + zdrho_i(ji,jj,jk) ) ) &
[14060]	893	& )
	894	END IF
	895
[14064]	896	z_rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
[14060]	897	& * ( gde3w(ji,jj+1,jk) - gde3w(ji,jj,jk) )
	898	IF ( vmask(ji, jj-1, jk) > 0.5 .OR. vmask(ji, jj+1, jk) > 0.5 ) THEN
	899	z_rho_j(ji,jj,jk) = z_rho_j(ji,jj,jk) - z_grav_10 * ( &
	900	& ( zdrho_j (ji,jj+1,jk) - zdrho_j (ji,jj,jk) ) &
	901	& * ( - gde3w(ji,jj+1,jk) + gde3w(ji,jj,jk) - z1_12 * ( zdz_j (ji,jj+1,jk) + zdz_j (ji,jj,jk) ) ) &
	902	& - ( zdz_j (ji,jj+1,jk) - zdz_j (ji,jj,jk) ) &
[14064]	903	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( zdrho_j(ji,jj+1,jk) + zdrho_j(ji,jj,jk) ) ) &
[14060]	904	& )
	905	END IF
	906	END_3D
[455]	907
[14060]	908	!--------------------------------------------------------------
	909	! 8. Integrate in the vertical
	910	!-------------------------------------------------------------
[14064]	911	!
[455]	912	! ---------------
	913	! Surface value
	914	! ---------------
[13295]	915	DO_2D( 0, 0, 0, 0 )
[14060]	916	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)
	917	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]	918	IF( ln_wd_il ) THEN
	919	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
	920	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
	921	ENDIF
	922	! add to the general momentum trend
	923	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1)
	924	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1)
	925	END_2D
[455]	926
	927	! ----------------
	928	! interior value (2=<jk=<jpkm1)
	929	! ----------------
[13295]	930	DO_3D( 0, 0, 0, 0, 2, jpkm1 )
[12377]	931	! hydrostatic pressure gradient along s-surfaces
[14060]	932	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
	933	& + ( ( z_rho_k(ji,jj,jk) - z_rho_k(ji+1,jj,jk ) ) &
	934	& - ( z_rho_i(ji,jj,jk) - z_rho_i(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
	935	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
	936	& + ( ( z_rho_k(ji,jj,jk) - z_rho_k(ji,jj+1,jk ) ) &
	937	& -( z_rho_j(ji,jj,jk) - z_rho_j(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
[12377]	938	IF( ln_wd_il ) THEN
	939	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
	940	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
	941	ENDIF
	942	! add to the general momentum trend
	943	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk)
	944	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk)
	945	END_3D
[503]	946	!
[9023]	947	IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy )
[2715]	948	!
[455]	949	END SUBROUTINE hpg_djc
	950
	951
[12377]	952	SUBROUTINE hpg_prj( kt, Kmm, puu, pvv, Krhs )
[455]	953	!!---------------------------------------------------------------------
[3294]	954	!! * ROUTINE hpg_prj *
[455]	955	!!
[3294]	956	!! ** Method : s-coordinate case.
	957	!! A Pressure-Jacobian horizontal pressure gradient method
	958	!! based on the constrained cubic-spline interpolation for
	959	!! all vertical coordinate systems
[455]	960	!!
[12377]	961	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
[455]	962	!!----------------------------------------------------------------------
[3294]	963	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
[12377]	964	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	965	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
[14219]	966	REAL(dp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[503]	967	!!
[3294]	968	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
[6140]	969	REAL(wp) :: zcoef0, znad ! local scalars
	970	!
[3294]	971	!! The local variables for the correction term
	972	INTEGER :: jk1, jis, jid, jjs, jjd
[6152]	973	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
[3294]	974	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
[3764]	975	REAL(wp) :: zrhdt1
[3294]	976	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
[14064]	977	REAL(wp), DIMENSION(jpi,jpj) :: zpgu, zpgv ! 2D workspace
	978	REAL(wp), DIMENSION(jpi,jpj) :: zsshu_n, zsshv_n
[9019]	979	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdept, zrhh
	980	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
	981	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter
[455]	982	!!----------------------------------------------------------------------
[3294]	983	!
[455]	984	IF( kt == nit000 ) THEN
	985	IF(lwp) WRITE(numout,*)
[3294]	986	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
	987	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
[3]	988	ENDIF
	989
[3294]	990	! Local constant initialization
[3764]	991	zcoef0 = - grav
[6140]	992	znad = 1._wp
[14219]	993	IF( ln_linssh ) znad = 0._wp
	994
[9023]	995	IF( ln_wd_il ) THEN
[9019]	996	ALLOCATE( zcpx(jpi,jpj) , zcpy(jpi,jpj) )
[13295]	997	DO_2D( 0, 0, 0, 0 )
[12377]	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
[12377]	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
	1013	zcpx(ji,jj) = max(min( zcpx(ji,jj) , 1.0_wp),0.0_wp)
	1014	ELSE
	1015	zcpx(ji,jj) = 0._wp
	1016	END IF
	1017
	1018	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
	1019	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
	1020	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) &
	1021	& > rn_wdmin1 + rn_wdmin2
	1022	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. ( &
	1023	& MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
	1024	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
[6152]	1025
[12377]	1026	IF(ll_tmp1) THEN
	1027	zcpy(ji,jj) = 1.0_wp
	1028	ELSE IF(ll_tmp2) THEN
	1029	! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here
	1030	zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
	1031	& / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) )
	1032	zcpy(ji,jj) = max(min( zcpy(ji,jj) , 1.0_wp),0.0_wp)
[9023]	1033
[12377]	1034	ELSE
	1035	zcpy(ji,jj) = 0._wp
	1036	ENDIF
	1037	END_2D
[13226]	1038	CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1.0_wp, zcpy, 'V', 1.0_wp )
[9019]	1039	ENDIF
[6152]	1040
[3294]	1041	! Clean 3-D work arrays
	1042	zhpi(:,:,:) = 0._wp
	1043	zrhh(:,:,:) = rhd(:,:,:)
[3764]	1044
[3294]	1045	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
[13295]	1046	DO_2D( 1, 1, 1, 1 )
[13288]	1047	jk = mbkt(ji,jj)
	1048	IF( jk <= 1 ) THEN ; zrhh(ji,jj, : ) = 0._wp
	1049	ELSEIF( jk == 2 ) THEN ; zrhh(ji,jj,jk+1:jpk) = rhd(ji,jj,jk)
[12377]	1050	ELSEIF( jk < jpkm1 ) THEN
	1051	DO jkk = jk+1, jpk
[14219]	1052	zrhh(ji,jj,jkk) = interp1(CASTWP(gde3w(ji,jj,jkk )), CASTWP(gde3w(ji,jj,jkk-1)), &
	1053	& CASTWP(gde3w(ji,jj,jkk-2)), zrhh (ji,jj,jkk-1), zrhh(ji,jj,jkk-2))
	1054
[12377]	1055	END DO
	1056	ENDIF
	1057	END_2D
[3]	1058
[3632]	1059	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
[13295]	1060	DO_2D( 1, 1, 1, 1 )
[14064]	1061	zdept(ji,jj,1) = 0.5_wp * e3w(ji,jj,1,Kmm) - ssh(ji,jj,Kmm)
[12377]	1062	END_2D
[455]	1063
[13295]	1064	DO_3D( 1, 1, 1, 1, 2, jpk )
[12377]	1065	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + e3w(ji,jj,jk,Kmm)
	1066	END_3D
[455]	1067
[4990]	1068	fsp(:,:,:) = zrhh (:,:,:)
[3632]	1069	xsp(:,:,:) = zdept(:,:,:)
	1070
[3764]	1071	! Construct the vertical density profile with the
[3294]	1072	! constrained cubic spline interpolation
	1073	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
[6140]	1074	CALL cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
[3294]	1075
	1076	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
[13295]	1077	DO_2D( 0, 1, 0, 1 )
[12377]	1078	zrhdt1 = zrhh(ji,jj,1) - interp3( zdept(ji,jj,1), asp(ji,jj,1), bsp(ji,jj,1), &
	1079	& csp(ji,jj,1), dsp(ji,jj,1) ) * 0.25_wp * e3w(ji,jj,1,Kmm)
[3294]	1080
[12377]	1081	! assuming linear profile across the top half surface layer
	1082	zhpi(ji,jj,1) = 0.5_wp * e3w(ji,jj,1,Kmm) * zrhdt1
	1083	END_2D
[455]	1084
[3294]	1085	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
[13295]	1086	DO_3D( 0, 1, 0, 1, 2, jpkm1 )
[12377]	1087	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
	1088	& integ_spline( zdept(ji,jj,jk-1), zdept(ji,jj,jk), &
	1089	& asp (ji,jj,jk-1), bsp (ji,jj,jk-1), &
	1090	& csp (ji,jj,jk-1), dsp (ji,jj,jk-1) )
	1091	END_3D
[455]	1092
[3294]	1093	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
[5224]	1094
	1095	! Prepare zsshu_n and zsshv_n
[13295]	1096	DO_2D( 0, 0, 0, 0 )
[6140]	1097	!!gm BUG ? if it is ssh at u- & v-point then it should be:
[12377]	1098	! zsshu_n(ji,jj) = (e1e2t(ji,jj) * ssh(ji,jj,Kmm) + e1e2t(ji+1,jj) * ssh(ji+1,jj,Kmm)) * &
[6140]	1099	! & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
[12377]	1100	! zsshv_n(ji,jj) = (e1e2t(ji,jj) * ssh(ji,jj,Kmm) + e1e2t(ji,jj+1) * ssh(ji,jj+1,Kmm)) * &
[6140]	1101	! & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
	1102	!!gm not this:
[12377]	1103	zsshu_n(ji,jj) = (e1e2u(ji,jj) * ssh(ji,jj,Kmm) + e1e2u(ji+1, jj) * ssh(ji+1,jj,Kmm)) * &
	1104	& r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
	1105	zsshv_n(ji,jj) = (e1e2v(ji,jj) * ssh(ji,jj,Kmm) + e1e2v(ji+1, jj) * ssh(ji,jj+1,Kmm)) * &
	1106	& r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
	1107	END_2D
[455]	1108
[13226]	1109	CALL lbc_lnk_multi ('dynhpg', zsshu_n, 'U', 1.0_wp, zsshv_n, 'V', 1.0_wp )
[6152]	1110
[13295]	1111	DO_2D( 0, 0, 0, 0 )
[14064]	1112	zu(ji,jj,1) = - ( e3u(ji,jj,1,Kmm) - zsshu_n(ji,jj) )
	1113	zv(ji,jj,1) = - ( e3v(ji,jj,1,Kmm) - zsshv_n(ji,jj) )
[12377]	1114	END_2D
[5224]	1115
[13295]	1116	DO_3D( 0, 0, 0, 0, 2, jpkm1 )
[12377]	1117	zu(ji,jj,jk) = zu(ji,jj,jk-1) - e3u(ji,jj,jk,Kmm)
	1118	zv(ji,jj,jk) = zv(ji,jj,jk-1) - e3v(ji,jj,jk,Kmm)
	1119	END_3D
[3764]	1120
[13295]	1121	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[12377]	1122	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * e3u(ji,jj,jk,Kmm)
	1123	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * e3v(ji,jj,jk,Kmm)
	1124	END_3D
[455]	1125
[13295]	1126	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[12377]	1127	zu(ji,jj,jk) = MIN( zu(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
	1128	zu(ji,jj,jk) = MAX( zu(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
	1129	zv(ji,jj,jk) = MIN( zv(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
	1130	zv(ji,jj,jk) = MAX( zv(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
	1131	END_3D
[3632]	1132
	1133
[13295]	1134	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[12377]	1135	zpwes = 0._wp; zpwed = 0._wp
	1136	zpnss = 0._wp; zpnsd = 0._wp
	1137	zuijk = zu(ji,jj,jk)
	1138	zvijk = zv(ji,jj,jk)
[3294]	1139
[12377]	1140	!!!!! for u equation
	1141	IF( jk <= mbku(ji,jj) ) THEN
	1142	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
	1143	jis = ji + 1; jid = ji
	1144	ELSE
	1145	jis = ji; jid = ji +1
	1146	ENDIF
[3294]	1147
[12377]	1148	! integrate the pressure on the shallow side
	1149	jk1 = jk
	1150	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
	1151	IF( jk1 == mbku(ji,jj) ) THEN
	1152	zuijk = -zdept(jis,jj,jk1)
	1153	EXIT
	1154	ENDIF
	1155	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
	1156	zpwes = zpwes + &
	1157	integ_spline(zdept(jis,jj,jk1), zdeps, &
	1158	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
	1159	csp(jis,jj,jk1), dsp(jis,jj,jk1))
	1160	jk1 = jk1 + 1
	1161	END DO
[3764]	1162
[12377]	1163	! integrate the pressure on the deep side
	1164	jk1 = jk
	1165	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
	1166	IF( jk1 == 1 ) THEN
	1167	zdeps = zdept(jid,jj,1) + MIN(zuijk, ssh(jid,jj,Kmm)*znad)
	1168	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
	1169	bsp(jid,jj,1), csp(jid,jj,1), &
	1170	dsp(jid,jj,1)) * zdeps
	1171	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
	1172	EXIT
	1173	ENDIF
	1174	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
	1175	zpwed = zpwed + &
	1176	integ_spline(zdeps, zdept(jid,jj,jk1), &
	1177	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
	1178	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
	1179	jk1 = jk1 - 1
	1180	END DO
[3764]	1181
[12377]	1182	! update the momentum trends in u direction
[3294]	1183
[12377]	1184	zdpdx1 = zcoef0 * r1_e1u(ji,jj) * ( zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk) )
	1185	IF( .NOT.ln_linssh ) THEN
	1186	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * &
	1187	& ( REAL(jis-jid, wp) * (zpwes + zpwed) + (ssh(ji+1,jj,Kmm)-ssh(ji,jj,Kmm)) )
	1188	ELSE
	1189	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
	1190	ENDIF
	1191	IF( ln_wd_il ) THEN
	1192	zdpdx1 = zdpdx1 * zcpx(ji,jj) * wdrampu(ji,jj)
	1193	zdpdx2 = zdpdx2 * zcpx(ji,jj) * wdrampu(ji,jj)
	1194	ENDIF
[14064]	1195	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + (zdpdx1 + zdpdx2 - zpgu(ji,jj)) * umask(ji,jj,jk)
[12377]	1196	ENDIF
[3764]	1197
[12377]	1198	!!!!! for v equation
	1199	IF( jk <= mbkv(ji,jj) ) THEN
	1200	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
	1201	jjs = jj + 1; jjd = jj
	1202	ELSE
	1203	jjs = jj ; jjd = jj + 1
	1204	ENDIF
[3294]	1205
[12377]	1206	! integrate the pressure on the shallow side
	1207	jk1 = jk
	1208	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
	1209	IF( jk1 == mbkv(ji,jj) ) THEN
	1210	zvijk = -zdept(ji,jjs,jk1)
	1211	EXIT
	1212	ENDIF
	1213	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
	1214	zpnss = zpnss + &
	1215	integ_spline(zdept(ji,jjs,jk1), zdeps, &
	1216	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
	1217	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
	1218	jk1 = jk1 + 1
	1219	END DO
[3764]	1220
[12377]	1221	! integrate the pressure on the deep side
	1222	jk1 = jk
	1223	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
	1224	IF( jk1 == 1 ) THEN
	1225	zdeps = zdept(ji,jjd,1) + MIN(zvijk, ssh(ji,jjd,Kmm)*znad)
	1226	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
	1227	bsp(ji,jjd,1), csp(ji,jjd,1), &
	1228	dsp(ji,jjd,1) ) * zdeps
	1229	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
	1230	EXIT
	1231	ENDIF
	1232	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
	1233	zpnsd = zpnsd + &
	1234	integ_spline(zdeps, zdept(ji,jjd,jk1), &
	1235	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
	1236	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
	1237	jk1 = jk1 - 1
	1238	END DO
[3294]	1239
[3764]	1240
[12377]	1241	! update the momentum trends in v direction
[3294]	1242
[12377]	1243	zdpdy1 = zcoef0 * r1_e2v(ji,jj) * ( zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk) )
	1244	IF( .NOT.ln_linssh ) THEN
	1245	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * &
	1246	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (ssh(ji,jj+1,Kmm)-ssh(ji,jj,Kmm)) )
	1247	ELSE
	1248	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
	1249	ENDIF
	1250	IF( ln_wd_il ) THEN
	1251	zdpdy1 = zdpdy1 * zcpy(ji,jj) * wdrampv(ji,jj)
	1252	zdpdy2 = zdpdy2 * zcpy(ji,jj) * wdrampv(ji,jj)
	1253	ENDIF
[6152]	1254
[14064]	1255	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + (zdpdy1 + zdpdy2 - zpgv(ji,jj)) * vmask(ji,jj,jk)
[12377]	1256	ENDIF
	1257	!
	1258	END_3D
[503]	1259	!
[9023]	1260	IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy )
[2715]	1261	!
[3294]	1262	END SUBROUTINE hpg_prj
[455]	1263
[4990]	1264
[6140]	1265	SUBROUTINE cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
[3294]	1266	!!----------------------------------------------------------------------
	1267	!! * ROUTINE cspline *
[3764]	1268	!!
[3294]	1269	!! ** Purpose : constrained cubic spline interpolation
[3764]	1270	!!
	1271	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
[4990]	1272	!!
[3294]	1273	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
	1274	!!----------------------------------------------------------------------
[6140]	1275	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: fsp, xsp ! value and coordinate
	1276	REAL(wp), DIMENSION(:,:,:), INTENT( out) :: asp, bsp, csp, dsp ! coefficients of the interpoated function
	1277	INTEGER , INTENT(in ) :: polynomial_type ! 1: cubic spline ; 2: Linear
[4990]	1278	!
[3294]	1279	INTEGER :: ji, jj, jk ! dummy loop indices
	1280	INTEGER :: jpi, jpj, jpkm1
	1281	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
	1282	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
	1283	REAL(wp) :: zdf(size(fsp,3))
	1284	!!----------------------------------------------------------------------
[6140]	1285	!
	1286	!!gm WHAT !!!!! THIS IS VERY DANGEROUS !!!!!
[3294]	1287	jpi = size(fsp,1)
	1288	jpj = size(fsp,2)
[7761]	1289	jpkm1 = MAX( 1, size(fsp,3) - 1 )
[6140]	1290	!
[3294]	1291	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
	1292	DO ji = 1, jpi
	1293	DO jj = 1, jpj
[3764]	1294	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
[3294]	1295	! DO jk = 2, jpkm1-1
[3764]	1296	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
	1297	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1298	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
	1299	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
	1300	!
	1301	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
[3764]	1302	!
[3294]	1303	! IF(zdf1 * zdf2 <= 0._wp) THEN
	1304	! zdf(jk) = 0._wp
	1305	! ELSE
	1306	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
	1307	! ENDIF
	1308	! END DO
[3764]	1309
[3294]	1310	!!Simply geometric average
	1311	DO jk = 2, jpkm1-1
[9019]	1312	zdf1 = (fsp(ji,jj,jk ) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk ) - xsp(ji,jj,jk-1))
	1313	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk )) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk ))
[3764]	1314
[3294]	1315	IF(zdf1 * zdf2 <= 0._wp) THEN
	1316	zdf(jk) = 0._wp
	1317	ELSE
	1318	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
	1319	ENDIF
	1320	END DO
[3764]	1321
[3294]	1322	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
[6140]	1323	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
[3294]	1324	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
[6140]	1325	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - 0.5_wp * zdf(jpkm1 - 1)
[3764]	1326
[3294]	1327	DO jk = 1, jpkm1 - 1
[3764]	1328	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1329	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
	1330	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
[3764]	1331	zddf1 = -2._wp * ztmp1 + ztmp2
[3294]	1332	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
[3764]	1333	zddf2 = 2._wp * ztmp1 - ztmp2
	1334
[3294]	1335	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
	1336	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
[3764]	1337	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
[3294]	1338	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
	1339	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
	1340	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
	1341	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
	1342	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
	1343	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
	1344	END DO
	1345	END DO
	1346	END DO
[3764]	1347
[6140]	1348	ELSEIF ( polynomial_type == 2 ) THEN ! Linear
[3294]	1349	DO ji = 1, jpi
	1350	DO jj = 1, jpj
	1351	DO jk = 1, jpkm1-1
[3764]	1352	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1353	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
[3764]	1354
[3294]	1355	dsp(ji,jj,jk) = 0._wp
	1356	csp(ji,jj,jk) = 0._wp
	1357	bsp(ji,jj,jk) = ztmp1 / zdxtmp
	1358	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
	1359	END DO
	1360	END DO
	1361	END DO
[9019]	1362	!
[3294]	1363	ELSE
[9019]	1364	CALL ctl_stop( 'invalid polynomial type in cspline' )
[3294]	1365	ENDIF
[9019]	1366	!
[3294]	1367	END SUBROUTINE cspline
	1368
	1369
[3764]	1370	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
[3294]	1371	!!----------------------------------------------------------------------
	1372	!! * ROUTINE interp1 *
[3764]	1373	!!
[3294]	1374	!! ** Purpose : 1-d linear interpolation
[3764]	1375	!!
[4990]	1376	!! ** Method : interpolation is straight forward
[3764]	1377	!! extrapolation is also permitted (no value limit)
[3294]	1378	!!----------------------------------------------------------------------
[3764]	1379	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
[3294]	1380	REAL(wp) :: f ! result of the interpolation (extrapolation)
	1381	REAL(wp) :: zdeltx
	1382	!!----------------------------------------------------------------------
[6140]	1383	!
[3294]	1384	zdeltx = xr - xl
[6140]	1385	IF( abs(zdeltx) <= 10._wp * EPSILON(x) ) THEN
	1386	f = 0.5_wp * (fl + fr)
[3294]	1387	ELSE
[6140]	1388	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
[3294]	1389	ENDIF
[6140]	1390	!
[3294]	1391	END FUNCTION interp1
	1392
[4990]	1393
[6140]	1394	FUNCTION interp2( x, a, b, c, d ) RESULT(f)
[3294]	1395	!!----------------------------------------------------------------------
	1396	!! * ROUTINE interp1 *
[3764]	1397	!!
[3294]	1398	!! ** Purpose : 1-d constrained cubic spline interpolation
[3764]	1399	!!
[3294]	1400	!! ** Method : cubic spline interpolation
	1401	!!
	1402	!!----------------------------------------------------------------------
[3764]	1403	REAL(wp), INTENT(in) :: x, a, b, c, d
[3294]	1404	REAL(wp) :: f ! value from the interpolation
	1405	!!----------------------------------------------------------------------
[6140]	1406	!
[3764]	1407	f = a + x* ( b + x * ( c + d * x ) )
[6140]	1408	!
[3294]	1409	END FUNCTION interp2
	1410
	1411
[6140]	1412	FUNCTION interp3( x, a, b, c, d ) RESULT(f)
[3294]	1413	!!----------------------------------------------------------------------
	1414	!! * ROUTINE interp1 *
[3764]	1415	!!
[9019]	1416	!! ** Purpose : Calculate the first order of derivative of
[3294]	1417	!! a cubic spline function y=a+bx+cx^2+d*x^3
[3764]	1418	!!
[3294]	1419	!! ** Method : f=dy/dx=b+2cx+3dx^2
	1420	!!
	1421	!!----------------------------------------------------------------------
[3764]	1422	REAL(wp), INTENT(in) :: x, a, b, c, d
[3294]	1423	REAL(wp) :: f ! value from the interpolation
	1424	!!----------------------------------------------------------------------
[6140]	1425	!
[3294]	1426	f = b + x * ( 2._wp * c + 3._wp * d * x)
[6140]	1427	!
[3294]	1428	END FUNCTION interp3
	1429
[3764]	1430
[6140]	1431	FUNCTION integ_spline( xl, xr, a, b, c, d ) RESULT(f)
[3294]	1432	!!----------------------------------------------------------------------
	1433	!! * ROUTINE interp1 *
[3764]	1434	!!
[3294]	1435	!! ** Purpose : 1-d constrained cubic spline integration
	1436	!!
[3764]	1437	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
	1438	!!
[3294]	1439	!!----------------------------------------------------------------------
[3764]	1440	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
	1441	REAL(wp) :: za1, za2, za3
[3294]	1442	REAL(wp) :: f ! integration result
	1443	!!----------------------------------------------------------------------
[6140]	1444	!
[3764]	1445	za1 = 0.5_wp * b
	1446	za2 = c / 3.0_wp
	1447	za3 = 0.25_wp * d
[6140]	1448	!
[3294]	1449	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
	1450	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
[6140]	1451	!
[3632]	1452	END FUNCTION integ_spline
[3294]	1453
[3]	1454	!!======================================================================
	1455	END MODULE dynhpg

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