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dynhpg.F90 in NEMO/branches/2019/UKMO_MERGE_2019/src/OCE/DYN – NEMO

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source: NEMO/branches/2019/UKMO_MERGE_2019/src/OCE/DYN/dynhpg.F90 @ 14296

Last change on this file since 14296 was 12077, checked in by mathiot, 5 years ago
include ENHANCE-02_ISF_nemo in UKMO merge branch
Property svn:keywords set to `Id`
File size: 73.5 KB

Rev	Line
[3]	1	MODULE dynhpg
	2	!!======================================================================
	3	!! * MODULE dynhpg *
	4	!! Ocean dynamics: hydrostatic pressure gradient trend
	5	!!======================================================================
[2528]	6	!! History : OPA ! 1987-09 (P. Andrich, M.-A. Foujols) hpg_zco: Original code
	7	!! 5.0 ! 1991-11 (G. Madec)
	8	!! 7.0 ! 1996-01 (G. Madec) hpg_sco: Original code for s-coordinates
	9	!! 8.0 ! 1997-05 (G. Madec) split dynber into dynkeg and dynhpg
	10	!! 8.5 ! 2002-07 (G. Madec) F90: Free form and module
	11	!! 8.5 ! 2002-08 (A. Bozec) hpg_zps: Original code
	12	!! NEMO 1.0 ! 2005-10 (A. Beckmann, B.W. An) various s-coordinate options
[3764]	13	!! ! Original code for hpg_ctl, hpg_hel hpg_wdj, hpg_djc, hpg_rot
[2528]	14	!! - ! 2005-11 (G. Madec) style & small optimisation
	15	!! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase
[3294]	16	!! 3.4 ! 2011-11 (H. Liu) hpg_prj: Original code for s-coordinates
	17	!! ! (A. Coward) suppression of hel, wdj and rot options
[5120]	18	!! 3.6 ! 2014-11 (P. Mathiot) hpg_isf: original code for ice shelf cavity
[503]	19	!!----------------------------------------------------------------------
[3]	20
	21	!!----------------------------------------------------------------------
[455]	22	!! dyn_hpg : update the momentum trend with the now horizontal
[3]	23	!! gradient of the hydrostatic pressure
[2528]	24	!! dyn_hpg_init : initialisation and control of options
[455]	25	!! hpg_zco : z-coordinate scheme
	26	!! hpg_zps : z-coordinate plus partial steps (interpolation)
	27	!! hpg_sco : s-coordinate (standard jacobian formulation)
[5120]	28	!! hpg_isf : s-coordinate (sco formulation) adapted to ice shelf
[455]	29	!! hpg_djc : s-coordinate (Density Jacobian with Cubic polynomial)
[3294]	30	!! hpg_prj : s-coordinate (Pressure Jacobian with Cubic polynomial)
[3]	31	!!----------------------------------------------------------------------
	32	USE oce ! ocean dynamics and tracers
[12077]	33	USE isf_oce , ONLY : risfload ! ice shelf (risfload variable)
	34	USE isfload , ONLY : isf_load ! ice shelf (isf_load routine )
[4990]	35	USE sbc_oce ! surface variable (only for the flag with ice shelf)
[3]	36	USE dom_oce ! ocean space and time domain
[6152]	37	USE wet_dry ! wetting and drying
[3]	38	USE phycst ! physical constants
[4990]	39	USE trd_oce ! trends: ocean variables
	40	USE trddyn ! trend manager: dynamics
[11822]	41	USE zpshde ! partial step: hor. derivative (zps_hde routine)
[4990]	42	!
[2715]	43	USE in_out_manager ! I/O manager
[258]	44	USE prtctl ! Print control
[4990]	45	USE lbclnk ! lateral boundary condition
[2715]	46	USE lib_mpp ! MPP library
[4990]	47	USE eosbn2 ! compute density
[3294]	48	USE timing ! Timing
[6140]	49	USE iom
[3]	50
	51	IMPLICIT NONE
	52	PRIVATE
	53
[2528]	54	PUBLIC dyn_hpg ! routine called by step module
	55	PUBLIC dyn_hpg_init ! routine called by opa module
[3]	56
[9490]	57	! !!* Namelist namdyn_hpg : hydrostatic pressure gradient
	58	LOGICAL, PUBLIC :: ln_hpg_zco !: z-coordinate - full steps
	59	LOGICAL, PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation)
	60	LOGICAL, PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation)
	61	LOGICAL, PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial)
	62	LOGICAL, PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme)
	63	LOGICAL, PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf
[455]	64
[9490]	65	! !! Flag to control the type of hydrostatic pressure gradient
	66	INTEGER, PARAMETER :: np_ERROR =-10 ! error in specification of lateral diffusion
	67	INTEGER, PARAMETER :: np_zco = 0 ! z-coordinate - full steps
	68	INTEGER, PARAMETER :: np_zps = 1 ! z-coordinate - partial steps (interpolation)
	69	INTEGER, PARAMETER :: np_sco = 2 ! s-coordinate (standard jacobian formulation)
	70	INTEGER, PARAMETER :: np_djc = 3 ! s-coordinate (Density Jacobian with Cubic polynomial)
	71	INTEGER, PARAMETER :: np_prj = 4 ! s-coordinate (Pressure Jacobian scheme)
	72	INTEGER, PARAMETER :: np_isf = 5 ! s-coordinate similar to sco modify for isf
	73	!
	74	INTEGER, PUBLIC :: nhpg !: type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM)
[455]	75
[3]	76	!! * Substitutions
	77	# include "vectopt_loop_substitute.h90"
	78	!!----------------------------------------------------------------------
[9598]	79	!! NEMO/OCE 4.0 , NEMO Consortium (2018)
[2528]	80	!! $Id$
[10068]	81	!! Software governed by the CeCILL license (see ./LICENSE)
[3]	82	!!----------------------------------------------------------------------
	83	CONTAINS
	84
[10928]	85	SUBROUTINE dyn_hpg( kt, Kmm, puu, pvv, Krhs )
[3]	86	!!---------------------------------------------------------------------
	87	!! * ROUTINE dyn_hpg *
	88	!!
[3764]	89	!! ** Method : Call the hydrostatic pressure gradient routine
[503]	90	!! using the scheme defined in the namelist
[3764]	91	!!
[10928]	92	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
[4990]	93	!! - send trends to trd_dyn for futher diagnostics (l_trddyn=T)
[503]	94	!!----------------------------------------------------------------------
[10928]	95	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	96	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
	97	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
	98	!
[9019]	99	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: ztrdu, ztrdv
[455]	100	!!----------------------------------------------------------------------
[2528]	101	!
[9019]	102	IF( ln_timing ) CALL timing_start('dyn_hpg')
[2715]	103	!
[10928]	104	IF( l_trddyn ) THEN ! Temporary saving of puu(:,:,:,Krhs) and pvv(:,:,:,Krhs) trends (l_trddyn)
[9019]	105	ALLOCATE( ztrdu(jpi,jpj,jpk) , ztrdv(jpi,jpj,jpk) )
[10928]	106	ztrdu(:,:,:) = puu(:,:,:,Krhs)
	107	ztrdv(:,:,:) = pvv(:,:,:,Krhs)
[3764]	108	ENDIF
[2528]	109	!
[3294]	110	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
[10928]	111	CASE ( np_zco ) ; CALL hpg_zco ( kt, Kmm, puu, pvv, Krhs ) ! z-coordinate
	112	CASE ( np_zps ) ; CALL hpg_zps ( kt, Kmm, puu, pvv, Krhs ) ! z-coordinate plus partial steps (interpolation)
	113	CASE ( np_sco ) ; CALL hpg_sco ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate (standard jacobian formulation)
	114	CASE ( np_djc ) ; CALL hpg_djc ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate (Density Jacobian with Cubic polynomial)
	115	CASE ( np_prj ) ; CALL hpg_prj ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate (Pressure Jacobian scheme)
	116	CASE ( np_isf ) ; CALL hpg_isf ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate similar to sco modify for ice shelf
[455]	117	END SELECT
[2528]	118	!
[503]	119	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
[10928]	120	ztrdu(:,:,:) = puu(:,:,:,Krhs) - ztrdu(:,:,:)
	121	ztrdv(:,:,:) = pvv(:,:,:,Krhs) - ztrdv(:,:,:)
[10946]	122	CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt, Kmm )
[9019]	123	DEALLOCATE( ztrdu , ztrdv )
[3764]	124	ENDIF
[503]	125	!
[10928]	126	IF(ln_ctl) CALL prt_ctl( tab3d_1=puu(:,:,:,Krhs), clinfo1=' hpg - Ua: ', mask1=umask, &
	127	& tab3d_2=pvv(:,:,:,Krhs), clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
[503]	128	!
[9019]	129	IF( ln_timing ) CALL timing_stop('dyn_hpg')
[2715]	130	!
[455]	131	END SUBROUTINE dyn_hpg
	132
	133
[10928]	134	SUBROUTINE dyn_hpg_init( Kmm )
[455]	135	!!----------------------------------------------------------------------
[2528]	136	!! * ROUTINE dyn_hpg_init *
[455]	137	!!
	138	!! ** Purpose : initializations for the hydrostatic pressure gradient
	139	!! computation and consistency control
	140	!!
[1601]	141	!! ** Action : Read the namelist namdyn_hpg and check the consistency
[455]	142	!! with the type of vertical coordinate used (zco, zps, sco)
	143	!!----------------------------------------------------------------------
[10928]	144	INTEGER, INTENT( in ) :: Kmm ! ocean time level index
	145	!
[455]	146	INTEGER :: ioptio = 0 ! temporary integer
[4147]	147	INTEGER :: ios ! Local integer output status for namelist read
[1601]	148	!!
[6140]	149	INTEGER :: ji, jj, jk, ikt ! dummy loop indices ISF
	150	REAL(wp) :: znad
[9019]	151	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: zts_top, zrhd ! hypothesys on isf density
	152	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zrhdtop_isf ! density at bottom of ISF
	153	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: ziceload ! density at bottom of ISF
[6140]	154	!!
[3294]	155	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
[5930]	156	& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf
[455]	157	!!----------------------------------------------------------------------
[2528]	158	!
[4147]	159	REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient
	160	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
[11822]	161	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist' )
[6140]	162	!
[4147]	163	REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient
	164	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
[11822]	165	902 IF( ios > 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist' )
[4624]	166	IF(lwm) WRITE ( numond, namdyn_hpg )
[2528]	167	!
	168	IF(lwp) THEN ! Control print
[455]	169	WRITE(numout,*)
[2528]	170	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
	171	WRITE(numout,*) '~~~~~~~~~~~~'
[1601]	172	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
	173	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
	174	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
	175	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
[5120]	176	WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf
[1601]	177	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
[3294]	178	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
[455]	179	ENDIF
[2528]	180	!
[3294]	181	IF( ln_hpg_djc ) &
[9019]	182	& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method', &
	183	& ' currently disabled (bugs under investigation).' , &
	184	& ' Please select either ln_hpg_sco or ln_hpg_prj instead' )
	185	!
	186	IF( .NOT.ln_linssh .AND. .NOT.(ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) &
	187	& CALL ctl_stop('dyn_hpg_init : non-linear free surface requires either ', &
	188	& ' the standard jacobian formulation hpg_sco or ' , &
	189	& ' the pressure jacobian formulation hpg_prj' )
	190	!
	191	IF( ln_hpg_isf ) THEN
	192	IF( .NOT. ln_isfcav ) CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' )
	193	ELSE
	194	IF( ln_isfcav ) CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' )
	195	ENDIF
[2528]	196	!
[9490]	197	! ! Set nhpg from ln_hpg_... flags & consistency check
	198	nhpg = np_ERROR
	199	ioptio = 0
	200	IF( ln_hpg_zco ) THEN ; nhpg = np_zco ; ioptio = ioptio +1 ; ENDIF
	201	IF( ln_hpg_zps ) THEN ; nhpg = np_zps ; ioptio = ioptio +1 ; ENDIF
	202	IF( ln_hpg_sco ) THEN ; nhpg = np_sco ; ioptio = ioptio +1 ; ENDIF
	203	IF( ln_hpg_djc ) THEN ; nhpg = np_djc ; ioptio = ioptio +1 ; ENDIF
	204	IF( ln_hpg_prj ) THEN ; nhpg = np_prj ; ioptio = ioptio +1 ; ENDIF
	205	IF( ln_hpg_isf ) THEN ; nhpg = np_isf ; ioptio = ioptio +1 ; ENDIF
[2528]	206	!
[2715]	207	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
[5120]	208	!
[9490]	209	IF(lwp) THEN
	210	WRITE(numout,*)
	211	SELECT CASE( nhpg )
	212	CASE( np_zco ) ; WRITE(numout,*) ' ==>>> z-coord. - full steps '
	213	CASE( np_zps ) ; WRITE(numout,*) ' ==>>> z-coord. - partial steps (interpolation)'
	214	CASE( np_sco ) ; WRITE(numout,*) ' ==>>> s-coord. (standard jacobian formulation)'
	215	CASE( np_djc ) ; WRITE(numout,*) ' ==>>> s-coord. (Density Jacobian: Cubic polynomial)'
	216	CASE( np_prj ) ; WRITE(numout,*) ' ==>>> s-coord. (Pressure Jacobian: Cubic polynomial)'
	217	CASE( np_isf ) ; WRITE(numout,*) ' ==>>> s-coord. (standard jacobian formulation) for isf'
	218	END SELECT
	219	WRITE(numout,*)
	220	ENDIF
[9019]	221	!
[2528]	222	END SUBROUTINE dyn_hpg_init
[455]	223
	224
[10928]	225	SUBROUTINE hpg_zco( kt, Kmm, puu, pvv, Krhs )
[455]	226	!!---------------------------------------------------------------------
	227	!! * ROUTINE hpg_zco *
	228	!!
	229	!! ** Method : z-coordinate case, levels are horizontal surfaces.
	230	!! The now hydrostatic pressure gradient at a given level, jk,
	231	!! is computed by taking the vertical integral of the in-situ
	232	!! density gradient along the model level from the suface to that
	233	!! level: zhpi = grav .....
	234	!! zhpj = grav .....
[10928]	235	!! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)).
	236	!! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi
	237	!! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj
[3764]	238	!!
[10928]	239	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
[503]	240	!!----------------------------------------------------------------------
[10928]	241	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	242	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
	243	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[6140]	244	!
[503]	245	INTEGER :: ji, jj, jk ! dummy loop indices
	246	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
[9019]	247	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
[3]	248	!!----------------------------------------------------------------------
[3764]	249	!
[3]	250	IF( kt == nit000 ) THEN
	251	IF(lwp) WRITE(numout,*)
[455]	252	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
	253	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
[3]	254	ENDIF
	255
[3764]	256	zcoef0 = - grav * 0.5_wp ! Local constant initialization
	257
[455]	258	! Surface value
[3]	259	DO jj = 2, jpjm1
	260	DO ji = fs_2, fs_jpim1 ! vector opt.
[10928]	261	zcoef1 = zcoef0 * e3w(ji,jj,1,Kmm)
[455]	262	! hydrostatic pressure gradient
[6140]	263	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
	264	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
[3]	265	! add to the general momentum trend
[10928]	266	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1)
	267	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1)
[455]	268	END DO
	269	END DO
[3294]	270
[503]	271	!
[455]	272	! interior value (2=<jk=<jpkm1)
[3]	273	DO jk = 2, jpkm1
[455]	274	DO jj = 2, jpjm1
[3]	275	DO ji = fs_2, fs_jpim1 ! vector opt.
[10928]	276	zcoef1 = zcoef0 * e3w(ji,jj,jk,Kmm)
[455]	277	! hydrostatic pressure gradient
	278	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
[6140]	279	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
	280	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
[455]	281
	282	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
[6140]	283	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
	284	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
[3]	285	! add to the general momentum trend
[10928]	286	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk)
	287	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk)
[3]	288	END DO
	289	END DO
	290	END DO
[503]	291	!
[455]	292	END SUBROUTINE hpg_zco
[216]	293
[3]	294
[10928]	295	SUBROUTINE hpg_zps( kt, Kmm, puu, pvv, Krhs )
[3]	296	!!---------------------------------------------------------------------
[455]	297	!! * ROUTINE hpg_zps *
[3764]	298	!!
[455]	299	!! ** Method : z-coordinate plus partial steps case. blahblah...
[3764]	300	!!
[10928]	301	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
[3764]	302	!!----------------------------------------------------------------------
[10928]	303	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	304	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
	305	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[503]	306	!!
	307	INTEGER :: ji, jj, jk ! dummy loop indices
	308	INTEGER :: iku, ikv ! temporary integers
	309	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
[9019]	310	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
[11822]	311	REAL(wp), DIMENSION(jpi,jpj) :: zgtsu, zgtsv, zgru, zgrv
[3]	312	!!----------------------------------------------------------------------
[3294]	313	!
[3]	314	IF( kt == nit000 ) THEN
	315	IF(lwp) WRITE(numout,*)
[455]	316	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
[503]	317	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
[3]	318	ENDIF
	319
[11822]	320	! Partial steps: Compute NOW horizontal gradient of t, s, rd at the last ocean level
	321	CALL zps_hde( kt, Kmm, jpts, ts(:,:,:,:,Kmm), zgtsu, zgtsv, rhd, zgru , zgrv )
[3294]	322
[503]	323	! Local constant initialization
[2528]	324	zcoef0 = - grav * 0.5_wp
[3]	325
[2528]	326	! Surface value (also valid in partial step case)
[3]	327	DO jj = 2, jpjm1
	328	DO ji = fs_2, fs_jpim1 ! vector opt.
[10928]	329	zcoef1 = zcoef0 * e3w(ji,jj,1,Kmm)
[3]	330	! hydrostatic pressure gradient
[6140]	331	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
	332	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
[3]	333	! add to the general momentum trend
[10928]	334	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1)
	335	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1)
[3]	336	END DO
	337	END DO
	338
[503]	339	! interior value (2=<jk=<jpkm1)
[3]	340	DO jk = 2, jpkm1
	341	DO jj = 2, jpjm1
	342	DO ji = fs_2, fs_jpim1 ! vector opt.
[10928]	343	zcoef1 = zcoef0 * e3w(ji,jj,jk,Kmm)
[3]	344	! hydrostatic pressure gradient
	345	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
[455]	346	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
[6140]	347	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
[3]	348
	349	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
[455]	350	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
[6140]	351	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
[3]	352	! add to the general momentum trend
[10928]	353	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk)
	354	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk)
[455]	355	END DO
[3]	356	END DO
	357	END DO
	358
[11822]	359	! partial steps correction at the last level (use zgru & zgrv computed in zpshde.F90)
[3]	360	DO jj = 2, jpjm1
	361	DO ji = 2, jpim1
[2528]	362	iku = mbku(ji,jj)
	363	ikv = mbkv(ji,jj)
[10928]	364	zcoef2 = zcoef0 * MIN( e3w(ji,jj,iku,Kmm), e3w(ji+1,jj ,iku,Kmm) )
	365	zcoef3 = zcoef0 * MIN( e3w(ji,jj,ikv,Kmm), e3w(ji ,jj+1,ikv,Kmm) )
[2528]	366	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
[10928]	367	puu (ji,jj,iku,Krhs) = puu(ji,jj,iku,Krhs) - zhpi(ji,jj,iku) ! subtract old value
[2528]	368	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
[11822]	369	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + zgru(ji,jj) ) * r1_e1u(ji,jj)
[10928]	370	puu (ji,jj,iku,Krhs) = puu(ji,jj,iku,Krhs) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
[3]	371	ENDIF
[2528]	372	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
[10928]	373	pvv (ji,jj,ikv,Krhs) = pvv(ji,jj,ikv,Krhs) - zhpj(ji,jj,ikv) ! subtract old value
[2528]	374	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
[11822]	375	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + zgrv(ji,jj) ) * r1_e2v(ji,jj)
[10928]	376	pvv (ji,jj,ikv,Krhs) = pvv(ji,jj,ikv,Krhs) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
[3]	377	ENDIF
	378	END DO
	379	END DO
[503]	380	!
[455]	381	END SUBROUTINE hpg_zps
[216]	382
[6140]	383
[10928]	384	SUBROUTINE hpg_sco( kt, Kmm, puu, pvv, Krhs )
[3]	385	!!---------------------------------------------------------------------
[455]	386	!! * ROUTINE hpg_sco *
[3]	387	!!
[455]	388	!! ** Method : s-coordinate case. Jacobian scheme.
	389	!! The now hydrostatic pressure gradient at a given level, jk,
	390	!! is computed by taking the vertical integral of the in-situ
[3]	391	!! density gradient along the model level from the suface to that
[455]	392	!! level. s-coordinates (ln_sco): a corrective term is added
	393	!! to the horizontal pressure gradient :
	394	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
	395	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
[10928]	396	!! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)).
	397	!! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi
	398	!! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj
[3]	399	!!
[10928]	400	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
[503]	401	!!----------------------------------------------------------------------
[10928]	402	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	403	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
	404	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[503]	405	!!
[6152]	406	INTEGER :: ji, jj, jk, jii, jjj ! dummy loop indices
	407	REAL(wp) :: zcoef0, zuap, zvap, znad, ztmp ! temporary scalars
[7646]	408	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
[9019]	409	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
	410	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter
[5120]	411	!!----------------------------------------------------------------------
	412	!
[9039]	413	IF( ln_wd_il ) ALLOCATE(zcpx(jpi,jpj), zcpy(jpi,jpj))
[9023]	414	!
[5120]	415	IF( kt == nit000 ) THEN
	416	IF(lwp) WRITE(numout,*)
	417	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
	418	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
	419	ENDIF
[6140]	420	!
[5120]	421	zcoef0 = - grav * 0.5_wp
[6140]	422	IF ( ln_linssh ) THEN ; znad = 0._wp ! Fixed volume: density anomaly
	423	ELSE ; znad = 1._wp ! Variable volume: density
[5120]	424	ENDIF
[6140]	425	!
[9023]	426	IF( ln_wd_il ) THEN
	427	DO jj = 2, jpjm1
	428	DO ji = 2, jpim1
[10928]	429	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
[9023]	430	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
[10928]	431	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) &
[9023]	432	& > rn_wdmin1 + rn_wdmin2
[10928]	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) ) > &
[9023]	435	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
[6152]	436
[9023]	437	IF(ll_tmp1) THEN
	438	zcpx(ji,jj) = 1.0_wp
	439	ELSE IF(ll_tmp2) THEN
[10928]	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)) )
[9023]	443	ELSE
	444	zcpx(ji,jj) = 0._wp
	445	END IF
	446
[10928]	447	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
[9023]	448	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
[10928]	449	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) &
[9023]	450	& > rn_wdmin1 + rn_wdmin2
[10928]	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) ) > &
[9023]	453	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
[6152]	454
[9023]	455	IF(ll_tmp1) THEN
	456	zcpy(ji,jj) = 1.0_wp
	457	ELSE IF(ll_tmp2) THEN
[10928]	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)) )
[9023]	461	ELSE
	462	zcpy(ji,jj) = 0._wp
	463	END IF
	464	END DO
	465	END DO
[10425]	466	CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1., zcpy, 'V', 1. )
[9023]	467	END IF
	468
[5120]	469	! Surface value
	470	DO jj = 2, jpjm1
	471	DO ji = fs_2, fs_jpim1 ! vector opt.
	472	! hydrostatic pressure gradient along s-surfaces
[10928]	473	zhpi(ji,jj,1) = zcoef0 * ( e3w(ji+1,jj ,1,Kmm) * ( znad + rhd(ji+1,jj ,1) ) &
	474	& - e3w(ji ,jj ,1,Kmm) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e1u(ji,jj)
	475	zhpj(ji,jj,1) = zcoef0 * ( e3w(ji ,jj+1,1,Kmm) * ( znad + rhd(ji ,jj+1,1) ) &
	476	& - e3w(ji ,jj ,1,Kmm) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e2v(ji,jj)
[5120]	477	! s-coordinate pressure gradient correction
[6140]	478	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
[10928]	479	& * ( gde3w(ji+1,jj,1) - gde3w(ji,jj,1) ) * r1_e1u(ji,jj)
[6140]	480	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
[10928]	481	& * ( gde3w(ji,jj+1,1) - gde3w(ji,jj,1) ) * r1_e2v(ji,jj)
[9019]	482	!
[9023]	483	IF( ln_wd_il ) THEN
[9019]	484	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
	485	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
	486	zuap = zuap * zcpx(ji,jj)
	487	zvap = zvap * zcpy(ji,jj)
[6152]	488	ENDIF
[9019]	489	!
[5120]	490	! add to the general momentum trend
[10928]	491	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1) + zuap
	492	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1) + zvap
[5120]	493	END DO
	494	END DO
	495
	496	! interior value (2=<jk=<jpkm1)
	497	DO jk = 2, jpkm1
	498	DO jj = 2, jpjm1
	499	DO ji = fs_2, fs_jpim1 ! vector opt.
	500	! hydrostatic pressure gradient along s-surfaces
[6140]	501	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 * r1_e1u(ji,jj) &
[10928]	502	& * ( e3w(ji+1,jj,jk,Kmm) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) &
	503	& - e3w(ji ,jj,jk,Kmm) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) )
[6140]	504	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 * r1_e2v(ji,jj) &
[10928]	505	& * ( e3w(ji,jj+1,jk,Kmm) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) &
	506	& - e3w(ji,jj ,jk,Kmm) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) )
[5120]	507	! s-coordinate pressure gradient correction
[6140]	508	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
[10928]	509	& * ( gde3w(ji+1,jj ,jk) - gde3w(ji,jj,jk) ) * r1_e1u(ji,jj)
[6140]	510	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
[10928]	511	& * ( gde3w(ji ,jj+1,jk) - gde3w(ji,jj,jk) ) * r1_e2v(ji,jj)
[9019]	512	!
[9023]	513	IF( ln_wd_il ) THEN
[9019]	514	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
	515	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
	516	zuap = zuap * zcpx(ji,jj)
	517	zvap = zvap * zcpy(ji,jj)
[6152]	518	ENDIF
[9019]	519	!
[5120]	520	! add to the general momentum trend
[10928]	521	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk) + zuap
	522	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk) + zvap
[5120]	523	END DO
	524	END DO
	525	END DO
	526	!
[9039]	527	IF( ln_wd_il ) DEALLOCATE( zcpx , zcpy )
[5120]	528	!
	529	END SUBROUTINE hpg_sco
	530
[6140]	531
[10928]	532	SUBROUTINE hpg_isf( kt, Kmm, puu, pvv, Krhs )
[5120]	533	!!---------------------------------------------------------------------
[6140]	534	!! * ROUTINE hpg_isf *
[5120]	535	!!
	536	!! ** Method : s-coordinate case. Jacobian scheme.
	537	!! The now hydrostatic pressure gradient at a given level, jk,
	538	!! is computed by taking the vertical integral of the in-situ
	539	!! density gradient along the model level from the suface to that
	540	!! level. s-coordinates (ln_sco): a corrective term is added
	541	!! to the horizontal pressure gradient :
	542	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
	543	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
[10928]	544	!! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)).
	545	!! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi
	546	!! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj
[12068]	547	!! iceload is added
[5120]	548	!!
[10928]	549	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
[5120]	550	!!----------------------------------------------------------------------
[10928]	551	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	552	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
	553	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[5120]	554	!!
[6140]	555	INTEGER :: ji, jj, jk, ikt, iktp1i, iktp1j ! dummy loop indices
	556	REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars
[9019]	557	REAL(wp), DIMENSION(jpi,jpj,jpk ) :: zhpi, zhpj
	558	REAL(wp), DIMENSION(jpi,jpj,jpts) :: zts_top
	559	REAL(wp), DIMENSION(jpi,jpj) :: zrhdtop_oce
[3]	560	!!----------------------------------------------------------------------
[3294]	561	!
[9019]	562	zcoef0 = - grav * 0.5_wp ! Local constant initialization
[3294]	563	!
[9019]	564	znad=1._wp ! To use density and not density anomaly
	565	!
	566	! ! iniitialised to 0. zhpi zhpi
	567	zhpi(:,:,:) = 0._wp ; zhpj(:,:,:) = 0._wp
[6140]	568
[4990]	569	! compute rhd at the ice/oce interface (ocean side)
[6140]	570	! usefull to reduce residual current in the test case ISOMIP with no melting
[9019]	571	DO ji = 1, jpi
	572	DO jj = 1, jpj
	573	ikt = mikt(ji,jj)
[10928]	574	zts_top(ji,jj,1) = ts(ji,jj,ikt,1,Kmm)
	575	zts_top(ji,jj,2) = ts(ji,jj,ikt,2,Kmm)
[4990]	576	END DO
	577	END DO
[9019]	578	CALL eos( zts_top, risfdep, zrhdtop_oce )
[6140]	579
	580	!==================================================================================
	581	!===== Compute surface value =====================================================
	582	!==================================================================================
[455]	583	DO jj = 2, jpjm1
[3764]	584	DO ji = fs_2, fs_jpim1 ! vector opt.
[6140]	585	ikt = mikt(ji,jj)
	586	iktp1i = mikt(ji+1,jj)
	587	iktp1j = mikt(ji,jj+1)
[4990]	588	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
	589	! we assume ISF is in isostatic equilibrium
[10928]	590	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * e3w(ji+1,jj,iktp1i,Kmm) &
[6140]	591	& * ( 2._wp * znad + rhd(ji+1,jj,iktp1i) + zrhdtop_oce(ji+1,jj) ) &
[10928]	592	& - 0.5_wp * e3w(ji,jj,ikt,Kmm) &
[6140]	593	& * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) &
[12068]	594	& + ( risfload(ji+1,jj) - risfload(ji,jj)) )
[10928]	595	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * e3w(ji,jj+1,iktp1j,Kmm) &
[6140]	596	& * ( 2._wp * znad + rhd(ji,jj+1,iktp1j) + zrhdtop_oce(ji,jj+1) ) &
[10928]	597	& - 0.5_wp * e3w(ji,jj,ikt,Kmm) &
[6140]	598	& * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) &
[12068]	599	& + ( risfload(ji,jj+1) - risfload(ji,jj)) )
[4990]	600	! s-coordinate pressure gradient correction (=0 if z coordinate)
[6140]	601	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
[10928]	602	& * ( gde3w(ji+1,jj,1) - gde3w(ji,jj,1) ) * r1_e1u(ji,jj)
[6140]	603	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
[10928]	604	& * ( gde3w(ji,jj+1,1) - gde3w(ji,jj,1) ) * r1_e2v(ji,jj)
[455]	605	! add to the general momentum trend
[10928]	606	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
	607	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
[3764]	608	END DO
	609	END DO
[4990]	610	!==================================================================================
	611	!===== Compute interior value =====================================================
	612	!==================================================================================
[6140]	613	! interior value (2=<jk=<jpkm1)
	614	DO jk = 2, jpkm1
	615	DO jj = 2, jpjm1
	616	DO ji = fs_2, fs_jpim1 ! vector opt.
[455]	617	! hydrostatic pressure gradient along s-surfaces
[6140]	618	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
[10928]	619	& * ( e3w(ji+1,jj,jk,Kmm) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2znad ) wmask(ji+1,jj,jk) &
	620	& - e3w(ji ,jj,jk,Kmm) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2znad ) wmask(ji ,jj,jk) )
[6140]	621	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
[10928]	622	& * ( e3w(ji,jj+1,jk,Kmm) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2znad ) wmask(ji,jj+1,jk) &
	623	& - e3w(ji,jj ,jk,Kmm) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2znad ) wmask(ji,jj ,jk) )
[455]	624	! s-coordinate pressure gradient correction
[6140]	625	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
[10928]	626	& * ( gde3w(ji+1,jj ,jk) - gde3w(ji,jj,jk) ) / e1u(ji,jj)
[6140]	627	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
[10928]	628	& * ( gde3w(ji ,jj+1,jk) - gde3w(ji,jj,jk) ) / e2v(ji,jj)
[455]	629	! add to the general momentum trend
[10928]	630	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + (zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
	631	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + (zhpj(ji,jj,jk) + zvap) * vmask(ji,jj,jk)
[455]	632	END DO
	633	END DO
	634	END DO
[503]	635	!
[5120]	636	END SUBROUTINE hpg_isf
[455]	637
[4990]	638
[10928]	639	SUBROUTINE hpg_djc( kt, Kmm, puu, pvv, Krhs )
[455]	640	!!---------------------------------------------------------------------
	641	!! * ROUTINE hpg_djc *
	642	!!
	643	!! ** Method : Density Jacobian with Cubic polynomial scheme
[3764]	644	!!
[503]	645	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
[455]	646	!!----------------------------------------------------------------------
[10928]	647	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	648	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
	649	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[503]	650	!!
	651	INTEGER :: ji, jj, jk ! dummy loop indices
	652	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
	653	REAL(wp) :: z1_10, cffu, cffx ! " "
	654	REAL(wp) :: z1_12, cffv, cffy ! " "
[6152]	655	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
[9019]	656	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
	657	REAL(wp), DIMENSION(jpi,jpj,jpk) :: dzx, dzy, dzz, dzu, dzv, dzw
	658	REAL(wp), DIMENSION(jpi,jpj,jpk) :: drhox, drhoy, drhoz, drhou, drhov, drhow
	659	REAL(wp), DIMENSION(jpi,jpj,jpk) :: rho_i, rho_j, rho_k
	660	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter
[455]	661	!!----------------------------------------------------------------------
[3294]	662	!
[9023]	663	IF( ln_wd_il ) THEN
[9019]	664	ALLOCATE( zcpx(jpi,jpj) , zcpy(jpi,jpj) )
[9023]	665	DO jj = 2, jpjm1
	666	DO ji = 2, jpim1
[10928]	667	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
[9023]	668	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
[10928]	669	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) &
[9023]	670	& > rn_wdmin1 + rn_wdmin2
[10928]	671	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji+1,jj,Kmm) ) > 1.E-12 ) .AND. ( &
	672	& MAX( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
[9023]	673	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
	674	IF(ll_tmp1) THEN
	675	zcpx(ji,jj) = 1.0_wp
	676	ELSE IF(ll_tmp2) THEN
[10928]	677	! no worries about ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm) = 0, it won't happen ! here
	678	zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
	679	& / (ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm)) )
[9023]	680	ELSE
	681	zcpx(ji,jj) = 0._wp
	682	END IF
[6152]	683
[10928]	684	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
[9023]	685	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
[10928]	686	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) &
[9023]	687	& > rn_wdmin1 + rn_wdmin2
[10928]	688	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. ( &
	689	& MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
[9023]	690	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
[6152]	691
[9023]	692	IF(ll_tmp1) THEN
	693	zcpy(ji,jj) = 1.0_wp
	694	ELSE IF(ll_tmp2) THEN
[10928]	695	! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here
	696	zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
	697	& / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) )
[9023]	698	ELSE
	699	zcpy(ji,jj) = 0._wp
	700	END IF
	701	END DO
	702	END DO
[10425]	703	CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1., zcpy, 'V', 1. )
[9023]	704	END IF
[6152]	705
[455]	706	IF( kt == nit000 ) THEN
	707	IF(lwp) WRITE(numout,*)
	708	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
	709	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
[216]	710	ENDIF
	711
[503]	712	! Local constant initialization
[2528]	713	zcoef0 = - grav * 0.5_wp
	714	z1_10 = 1._wp / 10._wp
	715	z1_12 = 1._wp / 12._wp
[455]	716
	717	!----------------------------------------------------------------------------------------
	718	! compute and store in provisional arrays elementary vertical and horizontal differences
	719	!----------------------------------------------------------------------------------------
	720
	721	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
	722
	723	DO jk = 2, jpkm1
	724	DO jj = 2, jpjm1
	725	DO ji = fs_2, fs_jpim1 ! vector opt.
[6140]	726	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
[10928]	727	dzz (ji,jj,jk) = gde3w(ji ,jj ,jk) - gde3w(ji,jj,jk-1)
[6140]	728	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
[10928]	729	dzx (ji,jj,jk) = gde3w(ji+1,jj ,jk) - gde3w(ji,jj,jk )
[6140]	730	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
[10928]	731	dzy (ji,jj,jk) = gde3w(ji ,jj+1,jk) - gde3w(ji,jj,jk )
[455]	732	END DO
	733	END DO
	734	END DO
	735
	736	!-------------------------------------------------------------------------
	737	! compute harmonic averages using eq. 5.18
	738	!-------------------------------------------------------------------------
	739	zep = 1.e-15
	740
[503]	741	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
	742	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
[455]	743
	744	DO jk = 2, jpkm1
	745	DO jj = 2, jpjm1
	746	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	747	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
[455]	748
[2528]	749	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
	750	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
[3764]	751
[2528]	752	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
	753	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
[455]	754
	755	IF( cffw > zep) THEN
[2528]	756	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
	757	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
[455]	758	ELSE
[2528]	759	drhow(ji,jj,jk) = 0._wp
[455]	760	ENDIF
	761
[2528]	762	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
	763	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
[455]	764
	765	IF( cffu > zep ) THEN
[2528]	766	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
	767	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
[455]	768	ELSE
[2528]	769	drhou(ji,jj,jk ) = 0._wp
[455]	770	ENDIF
	771
	772	IF( cffx > zep ) THEN
[2528]	773	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
	774	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
[455]	775	ELSE
[2528]	776	dzu(ji,jj,jk) = 0._wp
[455]	777	ENDIF
	778
	779	IF( cffv > zep ) THEN
[2528]	780	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
	781	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
[455]	782	ELSE
[2528]	783	drhov(ji,jj,jk) = 0._wp
[455]	784	ENDIF
	785
	786	IF( cffy > zep ) THEN
[2528]	787	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
	788	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
[455]	789	ELSE
[2528]	790	dzv(ji,jj,jk) = 0._wp
[455]	791	ENDIF
	792
	793	END DO
	794	END DO
	795	END DO
	796
	797	!----------------------------------------------------------------------------------
	798	! apply boundary conditions at top and bottom using 5.36-5.37
	799	!----------------------------------------------------------------------------------
[2528]	800	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
	801	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
	802	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
[455]	803
[2528]	804	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
	805	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
	806	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
[455]	807
	808
	809	!--------------------------------------------------------------
	810	! Upper half of top-most grid box, compute and store
	811	!-------------------------------------------------------------
	812
[6140]	813	!!bug gm : e3w-gde3w = 0.5*e3w .... and gde3w(2)-gde3w(1)=e3w(2) .... to be verified
	814	! true if gde3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
[455]	815
	816	DO jj = 2, jpjm1
	817	DO ji = fs_2, fs_jpim1 ! vector opt.
[10928]	818	rho_k(ji,jj,1) = -grav * ( e3w(ji,jj,1,Kmm) - gde3w(ji,jj,1) ) &
[6140]	819	& * ( rhd(ji,jj,1) &
	820	& + 0.5_wp * ( rhd (ji,jj,2) - rhd (ji,jj,1) ) &
[10928]	821	& * ( e3w (ji,jj,1,Kmm) - gde3w(ji,jj,1) ) &
	822	& / ( gde3w(ji,jj,2) - gde3w(ji,jj,1) ) )
[455]	823	END DO
	824	END DO
	825
	826	!!bug gm : here also, simplification is possible
	827	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
	828
	829	DO jk = 2, jpkm1
	830	DO jj = 2, jpjm1
	831	DO ji = fs_2, fs_jpim1 ! vector opt.
	832
[6140]	833	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
[10928]	834	& * ( gde3w(ji,jj,jk) - gde3w(ji,jj,jk-1) ) &
[6140]	835	& - grav * z1_10 * ( &
	836	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
[10928]	837	& * ( gde3w(ji,jj,jk) - gde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
[6140]	838	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
	839	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
[455]	840	& )
	841
[6140]	842	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
[10928]	843	& * ( gde3w(ji+1,jj,jk) - gde3w(ji,jj,jk) ) &
[6140]	844	& - grav* z1_10 * ( &
	845	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
[10928]	846	& * ( gde3w(ji+1,jj,jk) - gde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
[6140]	847	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
	848	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
[455]	849	& )
	850
[6140]	851	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
[10928]	852	& * ( gde3w(ji,jj+1,jk) - gde3w(ji,jj,jk) ) &
[6140]	853	& - grav* z1_10 * ( &
	854	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
[10928]	855	& * ( gde3w(ji,jj+1,jk) - gde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
[6140]	856	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
	857	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
[455]	858	& )
	859
	860	END DO
	861	END DO
	862	END DO
[10425]	863	CALL lbc_lnk_multi( 'dynhpg', rho_k, 'W', 1., rho_i, 'U', 1., rho_j, 'V', 1. )
[455]	864
	865	! ---------------
	866	! Surface value
	867	! ---------------
	868	DO jj = 2, jpjm1
	869	DO ji = fs_2, fs_jpim1 ! vector opt.
[6140]	870	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) * r1_e1u(ji,jj)
	871	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) * r1_e2v(ji,jj)
[9023]	872	IF( ln_wd_il ) THEN
[6152]	873	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
	874	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
	875	ENDIF
[455]	876	! add to the general momentum trend
[10928]	877	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1)
	878	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1)
[455]	879	END DO
	880	END DO
	881
	882	! ----------------
	883	! interior value (2=<jk=<jpkm1)
	884	! ----------------
	885	DO jk = 2, jpkm1
[3764]	886	DO jj = 2, jpjm1
[455]	887	DO ji = fs_2, fs_jpim1 ! vector opt.
	888	! hydrostatic pressure gradient along s-surfaces
	889	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
	890	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
[6140]	891	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) * r1_e1u(ji,jj)
[455]	892	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
	893	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
[6140]	894	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) * r1_e2v(ji,jj)
[9023]	895	IF( ln_wd_il ) THEN
[6152]	896	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
	897	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
	898	ENDIF
[455]	899	! add to the general momentum trend
[10928]	900	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk)
	901	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk)
[455]	902	END DO
	903	END DO
	904	END DO
[503]	905	!
[9023]	906	IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy )
[2715]	907	!
[455]	908	END SUBROUTINE hpg_djc
	909
	910
[10928]	911	SUBROUTINE hpg_prj( kt, Kmm, puu, pvv, Krhs )
[455]	912	!!---------------------------------------------------------------------
[3294]	913	!! * ROUTINE hpg_prj *
[455]	914	!!
[3294]	915	!! ** Method : s-coordinate case.
	916	!! A Pressure-Jacobian horizontal pressure gradient method
	917	!! based on the constrained cubic-spline interpolation for
	918	!! all vertical coordinate systems
[455]	919	!!
[10928]	920	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
[455]	921	!!----------------------------------------------------------------------
[3294]	922	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
[10928]	923	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	924	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
	925	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[503]	926	!!
[3294]	927	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
[6140]	928	REAL(wp) :: zcoef0, znad ! local scalars
	929	!
[3294]	930	!! The local variables for the correction term
	931	INTEGER :: jk1, jis, jid, jjs, jjd
[6152]	932	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
[3294]	933	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
[3764]	934	REAL(wp) :: zrhdt1
[3294]	935	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
[9019]	936	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdept, zrhh
	937	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
	938	REAL(wp), DIMENSION(jpi,jpj) :: zsshu_n, zsshv_n
	939	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter
[455]	940	!!----------------------------------------------------------------------
[3294]	941	!
[455]	942	IF( kt == nit000 ) THEN
	943	IF(lwp) WRITE(numout,*)
[3294]	944	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
	945	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
[3]	946	ENDIF
	947
[3294]	948	! Local constant initialization
[3764]	949	zcoef0 = - grav
[6140]	950	znad = 1._wp
	951	IF( ln_linssh ) znad = 0._wp
[3]	952
[9023]	953	IF( ln_wd_il ) THEN
[9019]	954	ALLOCATE( zcpx(jpi,jpj) , zcpy(jpi,jpj) )
	955	DO jj = 2, jpjm1
[9023]	956	DO ji = 2, jpim1
[10928]	957	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
[9023]	958	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
[10928]	959	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) &
[9023]	960	& > rn_wdmin1 + rn_wdmin2
[10928]	961	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji+1,jj,Kmm) ) > 1.E-12 ) .AND. ( &
	962	& MAX( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
[9023]	963	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
[6152]	964
[9023]	965	IF(ll_tmp1) THEN
	966	zcpx(ji,jj) = 1.0_wp
	967	ELSE IF(ll_tmp2) THEN
[10928]	968	! no worries about ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm) = 0, it won't happen ! here
	969	zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
	970	& / (ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm)) )
[9023]	971
	972	zcpx(ji,jj) = max(min( zcpx(ji,jj) , 1.0_wp),0.0_wp)
	973	ELSE
	974	zcpx(ji,jj) = 0._wp
	975	END IF
[6152]	976
[10928]	977	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
[9023]	978	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
[10928]	979	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) &
[9023]	980	& > rn_wdmin1 + rn_wdmin2
[10928]	981	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. ( &
	982	& MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
[9023]	983	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
[6152]	984
[9023]	985	IF(ll_tmp1) THEN
	986	zcpy(ji,jj) = 1.0_wp
	987	ELSE IF(ll_tmp2) THEN
[10928]	988	! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here
	989	zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
	990	& / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) )
[9023]	991	zcpy(ji,jj) = max(min( zcpy(ji,jj) , 1.0_wp),0.0_wp)
	992
[9019]	993	ELSE
	994	zcpy(ji,jj) = 0._wp
	995	ENDIF
	996	END DO
	997	END DO
[10425]	998	CALL lbc_lnk_multi( 'dynhpg', zcpx, 'U', 1., zcpy, 'V', 1. )
[9019]	999	ENDIF
[6152]	1000
[3294]	1001	! Clean 3-D work arrays
	1002	zhpi(:,:,:) = 0._wp
	1003	zrhh(:,:,:) = rhd(:,:,:)
[3764]	1004
[3294]	1005	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
	1006	DO jj = 1, jpj
[3764]	1007	DO ji = 1, jpi
[7646]	1008	jk = mbkt(ji,jj)+1
[6140]	1009	IF( jk <= 0 ) THEN ; zrhh(ji,jj, : ) = 0._wp
	1010	ELSEIF( jk == 1 ) THEN ; zrhh(ji,jj,jk+1:jpk) = rhd(ji,jj,jk)
	1011	ELSEIF( jk < jpkm1 ) THEN
[3294]	1012	DO jkk = jk+1, jpk
[10928]	1013	zrhh(ji,jj,jkk) = interp1(gde3w(ji,jj,jkk ), gde3w(ji,jj,jkk-1), &
	1014	& gde3w(ji,jj,jkk-2), rhd (ji,jj,jkk-1), rhd(ji,jj,jkk-2))
[3764]	1015	END DO
[3294]	1016	ENDIF
	1017	END DO
	1018	END DO
[3]	1019
[3632]	1020	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
[4990]	1021	DO jj = 1, jpj
	1022	DO ji = 1, jpi
[10928]	1023	zdept(ji,jj,1) = 0.5_wp * e3w(ji,jj,1,Kmm) - ssh(ji,jj,Kmm) * znad
[4990]	1024	END DO
	1025	END DO
[455]	1026
[4990]	1027	DO jk = 2, jpk
	1028	DO jj = 1, jpj
	1029	DO ji = 1, jpi
[10928]	1030	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + e3w(ji,jj,jk,Kmm)
[4990]	1031	END DO
	1032	END DO
	1033	END DO
[455]	1034
[4990]	1035	fsp(:,:,:) = zrhh (:,:,:)
[3632]	1036	xsp(:,:,:) = zdept(:,:,:)
	1037
[3764]	1038	! Construct the vertical density profile with the
[3294]	1039	! constrained cubic spline interpolation
	1040	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
[6140]	1041	CALL cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
[3294]	1042
	1043	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
	1044	DO jj = 2, jpj
[3764]	1045	DO ji = 2, jpi
[6140]	1046	zrhdt1 = zrhh(ji,jj,1) - interp3( zdept(ji,jj,1), asp(ji,jj,1), bsp(ji,jj,1), &
[10928]	1047	& csp(ji,jj,1), dsp(ji,jj,1) ) * 0.25_wp * e3w(ji,jj,1,Kmm)
[3294]	1048
	1049	! assuming linear profile across the top half surface layer
[10928]	1050	zhpi(ji,jj,1) = 0.5_wp * e3w(ji,jj,1,Kmm) * zrhdt1
[3294]	1051	END DO
[455]	1052	END DO
	1053
[3294]	1054	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
[3764]	1055	DO jk = 2, jpkm1
	1056	DO jj = 2, jpj
[3294]	1057	DO ji = 2, jpi
[6140]	1058	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
	1059	& integ_spline( zdept(ji,jj,jk-1), zdept(ji,jj,jk), &
	1060	& asp (ji,jj,jk-1), bsp (ji,jj,jk-1), &
	1061	& csp (ji,jj,jk-1), dsp (ji,jj,jk-1) )
[3294]	1062	END DO
	1063	END DO
[455]	1064	END DO
	1065
[3294]	1066	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
[5224]	1067
	1068	! Prepare zsshu_n and zsshv_n
[3764]	1069	DO jj = 2, jpjm1
	1070	DO ji = 2, jpim1
[6140]	1071	!!gm BUG ? if it is ssh at u- & v-point then it should be:
[10928]	1072	! zsshu_n(ji,jj) = (e1e2t(ji,jj) * ssh(ji,jj,Kmm) + e1e2t(ji+1,jj) * ssh(ji+1,jj,Kmm)) * &
[6140]	1073	! & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
[10928]	1074	! zsshv_n(ji,jj) = (e1e2t(ji,jj) * ssh(ji,jj,Kmm) + e1e2t(ji,jj+1) * ssh(ji,jj+1,Kmm)) * &
[6140]	1075	! & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
	1076	!!gm not this:
[10928]	1077	zsshu_n(ji,jj) = (e1e2u(ji,jj) * ssh(ji,jj,Kmm) + e1e2u(ji+1, jj) * ssh(ji+1,jj,Kmm)) * &
[5836]	1078	& r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
[10928]	1079	zsshv_n(ji,jj) = (e1e2v(ji,jj) * ssh(ji,jj,Kmm) + e1e2v(ji+1, jj) * ssh(ji,jj+1,Kmm)) * &
[5836]	1080	& r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
[3294]	1081	END DO
[455]	1082	END DO
	1083
[10425]	1084	CALL lbc_lnk_multi ('dynhpg', zsshu_n, 'U', 1., zsshv_n, 'V', 1. )
[6152]	1085
[5224]	1086	DO jj = 2, jpjm1
	1087	DO ji = 2, jpim1
[10928]	1088	zu(ji,jj,1) = - ( e3u(ji,jj,1,Kmm) - zsshu_n(ji,jj) * znad)
	1089	zv(ji,jj,1) = - ( e3v(ji,jj,1,Kmm) - zsshv_n(ji,jj) * znad)
[5224]	1090	END DO
	1091	END DO
	1092
[3764]	1093	DO jk = 2, jpkm1
	1094	DO jj = 2, jpjm1
	1095	DO ji = 2, jpim1
[10928]	1096	zu(ji,jj,jk) = zu(ji,jj,jk-1) - e3u(ji,jj,jk,Kmm)
	1097	zv(ji,jj,jk) = zv(ji,jj,jk-1) - e3v(ji,jj,jk,Kmm)
[3294]	1098	END DO
	1099	END DO
[455]	1100	END DO
[3764]	1101
	1102	DO jk = 1, jpkm1
	1103	DO jj = 2, jpjm1
	1104	DO ji = 2, jpim1
[10928]	1105	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * e3u(ji,jj,jk,Kmm)
	1106	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * e3v(ji,jj,jk,Kmm)
[3294]	1107	END DO
	1108	END DO
	1109	END DO
[455]	1110
[3632]	1111	DO jk = 1, jpkm1
	1112	DO jj = 2, jpjm1
	1113	DO ji = 2, jpim1
[6140]	1114	zu(ji,jj,jk) = MIN( zu(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
	1115	zu(ji,jj,jk) = MAX( zu(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
	1116	zv(ji,jj,jk) = MIN( zv(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
	1117	zv(ji,jj,jk) = MAX( zv(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
[3632]	1118	END DO
	1119	END DO
	1120	END DO
	1121
	1122
[3764]	1123	DO jk = 1, jpkm1
	1124	DO jj = 2, jpjm1
	1125	DO ji = 2, jpim1
[3294]	1126	zpwes = 0._wp; zpwed = 0._wp
	1127	zpnss = 0._wp; zpnsd = 0._wp
	1128	zuijk = zu(ji,jj,jk)
	1129	zvijk = zv(ji,jj,jk)
	1130
	1131	!!!!! for u equation
	1132	IF( jk <= mbku(ji,jj) ) THEN
[3632]	1133	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
[3294]	1134	jis = ji + 1; jid = ji
	1135	ELSE
	1136	jis = ji; jid = ji +1
	1137	ENDIF
	1138
	1139	! integrate the pressure on the shallow side
[3764]	1140	jk1 = jk
[3632]	1141	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
[3294]	1142	IF( jk1 == mbku(ji,jj) ) THEN
[3632]	1143	zuijk = -zdept(jis,jj,jk1)
[3294]	1144	EXIT
	1145	ENDIF
[3632]	1146	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
[3764]	1147	zpwes = zpwes + &
[3632]	1148	integ_spline(zdept(jis,jj,jk1), zdeps, &
[3294]	1149	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
	1150	csp(jis,jj,jk1), dsp(jis,jj,jk1))
	1151	jk1 = jk1 + 1
	1152	END DO
[3764]	1153
[3294]	1154	! integrate the pressure on the deep side
[3764]	1155	jk1 = jk
[3632]	1156	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
[3294]	1157	IF( jk1 == 1 ) THEN
[10928]	1158	zdeps = zdept(jid,jj,1) + MIN(zuijk, ssh(jid,jj,Kmm)*znad)
[3632]	1159	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
	1160	bsp(jid,jj,1), csp(jid,jj,1), &
	1161	dsp(jid,jj,1)) * zdeps
	1162	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
[3294]	1163	EXIT
	1164	ENDIF
[3632]	1165	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
[3764]	1166	zpwed = zpwed + &
[3632]	1167	integ_spline(zdeps, zdept(jid,jj,jk1), &
[3294]	1168	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
	1169	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
	1170	jk1 = jk1 - 1
	1171	END DO
[3764]	1172
[3294]	1173	! update the momentum trends in u direction
	1174
[6140]	1175	zdpdx1 = zcoef0 * r1_e1u(ji,jj) * ( zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk) )
	1176	IF( .NOT.ln_linssh ) THEN
	1177	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * &
[10928]	1178	& ( REAL(jis-jid, wp) * (zpwes + zpwed) + (ssh(ji+1,jj,Kmm)-ssh(ji,jj,Kmm)) )
[3294]	1179	ELSE
[6140]	1180	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
[3294]	1181	ENDIF
[9023]	1182	IF( ln_wd_il ) THEN
	1183	zdpdx1 = zdpdx1 * zcpx(ji,jj) * wdrampu(ji,jj)
	1184	zdpdx2 = zdpdx2 * zcpx(ji,jj) * wdrampu(ji,jj)
[6152]	1185	ENDIF
[10928]	1186	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + (zdpdx1 + zdpdx2) * umask(ji,jj,jk)
[3294]	1187	ENDIF
[3764]	1188
[3294]	1189	!!!!! for v equation
	1190	IF( jk <= mbkv(ji,jj) ) THEN
[3632]	1191	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
[3294]	1192	jjs = jj + 1; jjd = jj
	1193	ELSE
	1194	jjs = jj ; jjd = jj + 1
	1195	ENDIF
	1196
	1197	! integrate the pressure on the shallow side
[3764]	1198	jk1 = jk
[3632]	1199	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
[3294]	1200	IF( jk1 == mbkv(ji,jj) ) THEN
[3632]	1201	zvijk = -zdept(ji,jjs,jk1)
[3294]	1202	EXIT
	1203	ENDIF
[3632]	1204	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
[3764]	1205	zpnss = zpnss + &
[3632]	1206	integ_spline(zdept(ji,jjs,jk1), zdeps, &
[3294]	1207	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
	1208	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
	1209	jk1 = jk1 + 1
	1210	END DO
[3764]	1211
[3294]	1212	! integrate the pressure on the deep side
[3764]	1213	jk1 = jk
[3632]	1214	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
[3294]	1215	IF( jk1 == 1 ) THEN
[10928]	1216	zdeps = zdept(ji,jjd,1) + MIN(zvijk, ssh(ji,jjd,Kmm)*znad)
[3632]	1217	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
	1218	bsp(ji,jjd,1), csp(ji,jjd,1), &
	1219	dsp(ji,jjd,1) ) * zdeps
	1220	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
[3294]	1221	EXIT
	1222	ENDIF
[3632]	1223	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
[3764]	1224	zpnsd = zpnsd + &
[3632]	1225	integ_spline(zdeps, zdept(ji,jjd,jk1), &
[3294]	1226	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
	1227	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
	1228	jk1 = jk1 - 1
	1229	END DO
	1230
[3764]	1231
[3294]	1232	! update the momentum trends in v direction
	1233
[6140]	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) * &
[10928]	1237	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (ssh(ji,jj+1,Kmm)-ssh(ji,jj,Kmm)) )
[3294]	1238	ELSE
[6140]	1239	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
[3294]	1240	ENDIF
[9023]	1241	IF( ln_wd_il ) THEN
	1242	zdpdy1 = zdpdy1 * zcpy(ji,jj) * wdrampv(ji,jj)
	1243	zdpdy2 = zdpdy2 * zcpy(ji,jj) * wdrampv(ji,jj)
[6152]	1244	ENDIF
	1245
[10928]	1246	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + (zdpdy1 + zdpdy2) * vmask(ji,jj,jk)
[3294]	1247	ENDIF
[6140]	1248	!
	1249	END DO
	1250	END DO
[455]	1251	END DO
[503]	1252	!
[9023]	1253	IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy )
[2715]	1254	!
[3294]	1255	END SUBROUTINE hpg_prj
[455]	1256
[4990]	1257
[6140]	1258	SUBROUTINE cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
[3294]	1259	!!----------------------------------------------------------------------
	1260	!! * ROUTINE cspline *
[3764]	1261	!!
[3294]	1262	!! ** Purpose : constrained cubic spline interpolation
[3764]	1263	!!
	1264	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
[4990]	1265	!!
[3294]	1266	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
	1267	!!----------------------------------------------------------------------
[6140]	1268	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: fsp, xsp ! value and coordinate
	1269	REAL(wp), DIMENSION(:,:,:), INTENT( out) :: asp, bsp, csp, dsp ! coefficients of the interpoated function
	1270	INTEGER , INTENT(in ) :: polynomial_type ! 1: cubic spline ; 2: Linear
[4990]	1271	!
[3294]	1272	INTEGER :: ji, jj, jk ! dummy loop indices
	1273	INTEGER :: jpi, jpj, jpkm1
	1274	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
	1275	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
	1276	REAL(wp) :: zdf(size(fsp,3))
	1277	!!----------------------------------------------------------------------
[6140]	1278	!
	1279	!!gm WHAT !!!!! THIS IS VERY DANGEROUS !!!!!
[3294]	1280	jpi = size(fsp,1)
	1281	jpj = size(fsp,2)
[7761]	1282	jpkm1 = MAX( 1, size(fsp,3) - 1 )
[6140]	1283	!
[3294]	1284	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
	1285	DO ji = 1, jpi
	1286	DO jj = 1, jpj
[3764]	1287	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
[3294]	1288	! DO jk = 2, jpkm1-1
[3764]	1289	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
	1290	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1291	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
	1292	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
	1293	!
	1294	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
[3764]	1295	!
[3294]	1296	! IF(zdf1 * zdf2 <= 0._wp) THEN
	1297	! zdf(jk) = 0._wp
	1298	! ELSE
	1299	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
	1300	! ENDIF
	1301	! END DO
[3764]	1302
[3294]	1303	!!Simply geometric average
	1304	DO jk = 2, jpkm1-1
[9019]	1305	zdf1 = (fsp(ji,jj,jk ) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk ) - xsp(ji,jj,jk-1))
	1306	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk )) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk ))
[3764]	1307
[3294]	1308	IF(zdf1 * zdf2 <= 0._wp) THEN
	1309	zdf(jk) = 0._wp
	1310	ELSE
	1311	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
	1312	ENDIF
	1313	END DO
[3764]	1314
[3294]	1315	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
[6140]	1316	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
[3294]	1317	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
[6140]	1318	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - 0.5_wp * zdf(jpkm1 - 1)
[3764]	1319
[3294]	1320	DO jk = 1, jpkm1 - 1
[3764]	1321	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1322	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
	1323	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
[3764]	1324	zddf1 = -2._wp * ztmp1 + ztmp2
[3294]	1325	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
[3764]	1326	zddf2 = 2._wp * ztmp1 - ztmp2
	1327
[3294]	1328	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
	1329	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
[3764]	1330	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
[3294]	1331	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
	1332	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
	1333	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
	1334	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
	1335	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
	1336	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
	1337	END DO
	1338	END DO
	1339	END DO
[3764]	1340
[6140]	1341	ELSEIF ( polynomial_type == 2 ) THEN ! Linear
[3294]	1342	DO ji = 1, jpi
	1343	DO jj = 1, jpj
	1344	DO jk = 1, jpkm1-1
[3764]	1345	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1346	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
[3764]	1347
[3294]	1348	dsp(ji,jj,jk) = 0._wp
	1349	csp(ji,jj,jk) = 0._wp
	1350	bsp(ji,jj,jk) = ztmp1 / zdxtmp
	1351	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
	1352	END DO
	1353	END DO
	1354	END DO
[9019]	1355	!
[3294]	1356	ELSE
[9019]	1357	CALL ctl_stop( 'invalid polynomial type in cspline' )
[3294]	1358	ENDIF
[9019]	1359	!
[3294]	1360	END SUBROUTINE cspline
	1361
	1362
[3764]	1363	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
[3294]	1364	!!----------------------------------------------------------------------
	1365	!! * ROUTINE interp1 *
[3764]	1366	!!
[3294]	1367	!! ** Purpose : 1-d linear interpolation
[3764]	1368	!!
[4990]	1369	!! ** Method : interpolation is straight forward
[3764]	1370	!! extrapolation is also permitted (no value limit)
[3294]	1371	!!----------------------------------------------------------------------
[3764]	1372	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
[3294]	1373	REAL(wp) :: f ! result of the interpolation (extrapolation)
	1374	REAL(wp) :: zdeltx
	1375	!!----------------------------------------------------------------------
[6140]	1376	!
[3294]	1377	zdeltx = xr - xl
[6140]	1378	IF( abs(zdeltx) <= 10._wp * EPSILON(x) ) THEN
	1379	f = 0.5_wp * (fl + fr)
[3294]	1380	ELSE
[6140]	1381	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
[3294]	1382	ENDIF
[6140]	1383	!
[3294]	1384	END FUNCTION interp1
	1385
[4990]	1386
[6140]	1387	FUNCTION interp2( x, a, b, c, d ) RESULT(f)
[3294]	1388	!!----------------------------------------------------------------------
	1389	!! * ROUTINE interp1 *
[3764]	1390	!!
[3294]	1391	!! ** Purpose : 1-d constrained cubic spline interpolation
[3764]	1392	!!
[3294]	1393	!! ** Method : cubic spline interpolation
	1394	!!
	1395	!!----------------------------------------------------------------------
[3764]	1396	REAL(wp), INTENT(in) :: x, a, b, c, d
[3294]	1397	REAL(wp) :: f ! value from the interpolation
	1398	!!----------------------------------------------------------------------
[6140]	1399	!
[3764]	1400	f = a + x* ( b + x * ( c + d * x ) )
[6140]	1401	!
[3294]	1402	END FUNCTION interp2
	1403
	1404
[6140]	1405	FUNCTION interp3( x, a, b, c, d ) RESULT(f)
[3294]	1406	!!----------------------------------------------------------------------
	1407	!! * ROUTINE interp1 *
[3764]	1408	!!
[9019]	1409	!! ** Purpose : Calculate the first order of derivative of
[3294]	1410	!! a cubic spline function y=a+bx+cx^2+d*x^3
[3764]	1411	!!
[3294]	1412	!! ** Method : f=dy/dx=b+2cx+3dx^2
	1413	!!
	1414	!!----------------------------------------------------------------------
[3764]	1415	REAL(wp), INTENT(in) :: x, a, b, c, d
[3294]	1416	REAL(wp) :: f ! value from the interpolation
	1417	!!----------------------------------------------------------------------
[6140]	1418	!
[3294]	1419	f = b + x * ( 2._wp * c + 3._wp * d * x)
[6140]	1420	!
[3294]	1421	END FUNCTION interp3
	1422
[3764]	1423
[6140]	1424	FUNCTION integ_spline( xl, xr, a, b, c, d ) RESULT(f)
[3294]	1425	!!----------------------------------------------------------------------
	1426	!! * ROUTINE interp1 *
[3764]	1427	!!
[3294]	1428	!! ** Purpose : 1-d constrained cubic spline integration
	1429	!!
[3764]	1430	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
	1431	!!
[3294]	1432	!!----------------------------------------------------------------------
[3764]	1433	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
	1434	REAL(wp) :: za1, za2, za3
[3294]	1435	REAL(wp) :: f ! integration result
	1436	!!----------------------------------------------------------------------
[6140]	1437	!
[3764]	1438	za1 = 0.5_wp * b
	1439	za2 = c / 3.0_wp
	1440	za3 = 0.25_wp * d
[6140]	1441	!
[3294]	1442	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
	1443	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
[6140]	1444	!
[3632]	1445	END FUNCTION integ_spline
[3294]	1446
[3]	1447	!!======================================================================
	1448	END MODULE dynhpg
[3632]	1449

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