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dynhpg.F90 @ 14338

Last change on this file since 14338 was 14338, checked in by smasson, 3 years ago
dev_r14312_MPI_Interface: simplification of lbclnk and lbcnfd and their generic interfaces, #2598
Property svn:keywords set to `Id`
File size: 75.4 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"
	83
[3]	84	!!----------------------------------------------------------------------
[9598]	85	!! NEMO/OCE 4.0 , NEMO Consortium (2018)
[2528]	86	!! $Id$
[10068]	87	!! Software governed by the CeCILL license (see ./LICENSE)
[3]	88	!!----------------------------------------------------------------------
	89	CONTAINS
	90
[12377]	91	SUBROUTINE dyn_hpg( kt, Kmm, puu, pvv, Krhs )
[3]	92	!!---------------------------------------------------------------------
	93	!! * ROUTINE dyn_hpg *
	94	!!
[3764]	95	!! ** Method : Call the hydrostatic pressure gradient routine
[503]	96	!! using the scheme defined in the namelist
[3764]	97	!!
[12377]	98	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
[4990]	99	!! - send trends to trd_dyn for futher diagnostics (l_trddyn=T)
[503]	100	!!----------------------------------------------------------------------
[12377]	101	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	102	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
	103	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
	104	!
[9019]	105	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: ztrdu, ztrdv
[455]	106	!!----------------------------------------------------------------------
[2528]	107	!
[9019]	108	IF( ln_timing ) CALL timing_start('dyn_hpg')
[2715]	109	!
[12377]	110	IF( l_trddyn ) THEN ! Temporary saving of puu(:,:,:,Krhs) and pvv(:,:,:,Krhs) trends (l_trddyn)
[9019]	111	ALLOCATE( ztrdu(jpi,jpj,jpk) , ztrdv(jpi,jpj,jpk) )
[12377]	112	ztrdu(:,:,:) = puu(:,:,:,Krhs)
	113	ztrdv(:,:,:) = pvv(:,:,:,Krhs)
[3764]	114	ENDIF
[2528]	115	!
[3294]	116	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
[12377]	117	CASE ( np_zco ) ; CALL hpg_zco ( kt, Kmm, puu, pvv, Krhs ) ! z-coordinate
	118	CASE ( np_zps ) ; CALL hpg_zps ( kt, Kmm, puu, pvv, Krhs ) ! z-coordinate plus partial steps (interpolation)
	119	CASE ( np_sco ) ; CALL hpg_sco ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate (standard jacobian formulation)
	120	CASE ( np_djc ) ; CALL hpg_djc ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate (Density Jacobian with Cubic polynomial)
	121	CASE ( np_prj ) ; CALL hpg_prj ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate (Pressure Jacobian scheme)
	122	CASE ( np_isf ) ; CALL hpg_isf ( kt, Kmm, puu, pvv, Krhs ) ! s-coordinate similar to sco modify for ice shelf
[455]	123	END SELECT
[2528]	124	!
[503]	125	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
[12377]	126	ztrdu(:,:,:) = puu(:,:,:,Krhs) - ztrdu(:,:,:)
	127	ztrdv(:,:,:) = pvv(:,:,:,Krhs) - ztrdv(:,:,:)
	128	CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt, Kmm )
[9019]	129	DEALLOCATE( ztrdu , ztrdv )
[3764]	130	ENDIF
[503]	131	!
[12377]	132	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=puu(:,:,:,Krhs), clinfo1=' hpg - Ua: ', mask1=umask, &
	133	& tab3d_2=pvv(:,:,:,Krhs), clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
[503]	134	!
[9019]	135	IF( ln_timing ) CALL timing_stop('dyn_hpg')
[2715]	136	!
[455]	137	END SUBROUTINE dyn_hpg
	138
	139
[12377]	140	SUBROUTINE dyn_hpg_init( Kmm )
[455]	141	!!----------------------------------------------------------------------
[2528]	142	!! * ROUTINE dyn_hpg_init *
[455]	143	!!
	144	!! ** Purpose : initializations for the hydrostatic pressure gradient
	145	!! computation and consistency control
	146	!!
[1601]	147	!! ** Action : Read the namelist namdyn_hpg and check the consistency
[455]	148	!! with the type of vertical coordinate used (zco, zps, sco)
	149	!!----------------------------------------------------------------------
[12377]	150	INTEGER, INTENT( in ) :: Kmm ! ocean time level index
	151	!
[455]	152	INTEGER :: ioptio = 0 ! temporary integer
[4147]	153	INTEGER :: ios ! Local integer output status for namelist read
[1601]	154	!!
[6140]	155	INTEGER :: ji, jj, jk, ikt ! dummy loop indices ISF
[9019]	156	REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: zts_top, zrhd ! hypothesys on isf density
	157	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zrhdtop_isf ! density at bottom of ISF
	158	REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: ziceload ! density at bottom of ISF
[6140]	159	!!
[3294]	160	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
[14060]	161	& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf, &
	162	& ln_hpg_djc_vnh, ln_hpg_djc_vnv
[455]	163	!!----------------------------------------------------------------------
[2528]	164	!
[4147]	165	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
[11536]	166	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist' )
[6140]	167	!
[4147]	168	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
[11536]	169	902 IF( ios > 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist' )
[4624]	170	IF(lwm) WRITE ( numond, namdyn_hpg )
[2528]	171	!
	172	IF(lwp) THEN ! Control print
[455]	173	WRITE(numout,*)
[2528]	174	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
	175	WRITE(numout,*) '~~~~~~~~~~~~'
[1601]	176	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
	177	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
	178	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
	179	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
[5120]	180	WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf
[1601]	181	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
[3294]	182	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
[455]	183	ENDIF
[2528]	184	!
[14141]	185	IF( .NOT.ln_linssh .AND. (ln_hpg_zco.OR.ln_hpg_zps) ) &
	186	& CALL ctl_stop( 'dyn_hpg_init : non-linear free surface incompatible with hpg_zco or hpg_zps' )
	187	!
[14143]	188	IF( (.NOT.ln_hpg_isf .AND. ln_isfcav) .OR. (ln_hpg_isf .AND. .NOT.ln_isfcav) ) &
[14141]	189	& CALL ctl_stop( 'dyn_hpg_init : ln_hpg_isf=T requires ln_isfcav=T and vice versa' )
	190	!
	191	#if defined key_qco
[9019]	192	IF( ln_hpg_isf ) THEN
[14141]	193	CALL ctl_stop( 'dyn_hpg_init : key_qco and ln_hpg_isf not yet compatible' )
[9019]	194	ENDIF
[14141]	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	!
[14060]	222	IF ( ln_hpg_djc ) THEN
	223	IF (ln_hpg_djc_vnh) THEN ! Von Neumann boundary condition
	224	IF(lwp) WRITE(numout,*) ' horizontal bc: von Neumann '
	225	aco_bc_hor = 6.0_wp/5.0_wp
	226	bco_bc_hor = 7.0_wp/15.0_wp
	227	ELSE ! Linear extrapolation
	228	IF(lwp) WRITE(numout,*) ' horizontal bc: linear extrapolation'
	229	aco_bc_hor = 3.0_wp/2.0_wp
	230	bco_bc_hor = 1.0_wp/2.0_wp
	231	END IF
	232	IF (ln_hpg_djc_vnv) THEN ! Von Neumann boundary condition
	233	IF(lwp) WRITE(numout,*) ' vertical bc: von Neumann '
	234	aco_bc_vrt = 6.0_wp/5.0_wp
	235	bco_bc_vrt = 7.0_wp/15.0_wp
	236	ELSE ! Linear extrapolation
	237	IF(lwp) WRITE(numout,*) ' vertical bc: linear extrapolation'
	238	aco_bc_vrt = 3.0_wp/2.0_wp
	239	bco_bc_vrt = 1.0_wp/2.0_wp
	240	END IF
	241	END IF
[14141]	242	!
[2528]	243	END SUBROUTINE dyn_hpg_init
[455]	244
	245
[12377]	246	SUBROUTINE hpg_zco( kt, Kmm, puu, pvv, Krhs )
[455]	247	!!---------------------------------------------------------------------
	248	!! * ROUTINE hpg_zco *
	249	!!
	250	!! ** Method : z-coordinate case, levels are horizontal surfaces.
	251	!! The now hydrostatic pressure gradient at a given level, jk,
	252	!! is computed by taking the vertical integral of the in-situ
	253	!! density gradient along the model level from the suface to that
	254	!! level: zhpi = grav .....
	255	!! zhpj = grav .....
[12377]	256	!! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)).
	257	!! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi
	258	!! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj
[3764]	259	!!
[12377]	260	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
[503]	261	!!----------------------------------------------------------------------
[12377]	262	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	263	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
	264	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[6140]	265	!
[503]	266	INTEGER :: ji, jj, jk ! dummy loop indices
	267	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
[14064]	268	REAL(wp), DIMENSION(jpi,jpj) :: zhpi, zhpj
[3]	269	!!----------------------------------------------------------------------
[3764]	270	!
[3]	271	IF( kt == nit000 ) THEN
	272	IF(lwp) WRITE(numout,*)
[455]	273	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
	274	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
[3]	275	ENDIF
[14064]	276	!
	277	zcoef0 = - grav * 0.5_wp ! Local constant initialization
	278	!
	279	DO_2D( 0, 0, 0, 0 ) ! Surface value
[12377]	280	zcoef1 = zcoef0 * e3w(ji,jj,1,Kmm)
[14064]	281	! ! hydrostatic pressure gradient
	282	zhpi(ji,jj) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
	283	zhpj(ji,jj) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
	284	! ! add to the general momentum trend
	285	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj)
	286	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj)
[12377]	287	END_2D
[503]	288	!
[14064]	289	DO_3D( 0, 0, 0, 0, 2, jpkm1 ) ! interior value (2=<jk=<jpkm1)
[12377]	290	zcoef1 = zcoef0 * e3w(ji,jj,jk,Kmm)
[14064]	291	! ! hydrostatic pressure gradient
	292	zhpi(ji,jj) = zhpi(ji,jj) + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
	293	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
[455]	294
[14064]	295	zhpj(ji,jj) = zhpj(ji,jj) + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
	296	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
	297	! ! add to the general momentum trend
	298	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj)
	299	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj)
[12377]	300	END_3D
[503]	301	!
[455]	302	END SUBROUTINE hpg_zco
[216]	303
[3]	304
[12377]	305	SUBROUTINE hpg_zps( kt, Kmm, puu, pvv, Krhs )
[3]	306	!!---------------------------------------------------------------------
[455]	307	!! * ROUTINE hpg_zps *
[3764]	308	!!
[455]	309	!! ** Method : z-coordinate plus partial steps case. blahblah...
[3764]	310	!!
[12377]	311	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
[3764]	312	!!----------------------------------------------------------------------
[12377]	313	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	314	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
	315	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[503]	316	!!
	317	INTEGER :: ji, jj, jk ! dummy loop indices
	318	INTEGER :: iku, ikv ! temporary integers
	319	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
[13982]	320	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
	321	REAL(wp), DIMENSION(jpi,jpj,jpts) :: zgtsu, zgtsv
	322	REAL(wp), DIMENSION(jpi,jpj) :: zgru, zgrv
[3]	323	!!----------------------------------------------------------------------
[3294]	324	!
[3]	325	IF( kt == nit000 ) THEN
	326	IF(lwp) WRITE(numout,*)
[455]	327	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
[503]	328	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
[3]	329	ENDIF
	330
[11416]	331	! Partial steps: Compute NOW horizontal gradient of t, s, rd at the last ocean level
[12377]	332	CALL zps_hde( kt, Kmm, jpts, ts(:,:,:,:,Kmm), zgtsu, zgtsv, rhd, zgru , zgrv )
[3294]	333
[503]	334	! Local constant initialization
[2528]	335	zcoef0 = - grav * 0.5_wp
[3]	336
[2528]	337	! Surface value (also valid in partial step case)
[13295]	338	DO_2D( 0, 0, 0, 0 )
[12377]	339	zcoef1 = zcoef0 * e3w(ji,jj,1,Kmm)
	340	! hydrostatic pressure gradient
	341	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
	342	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
	343	! add to the general momentum trend
	344	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1)
	345	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1)
	346	END_2D
[3]	347
[503]	348	! interior value (2=<jk=<jpkm1)
[13295]	349	DO_3D( 0, 0, 0, 0, 2, jpkm1 )
[12377]	350	zcoef1 = zcoef0 * e3w(ji,jj,jk,Kmm)
	351	! hydrostatic pressure gradient
	352	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
	353	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
	354	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
[3]	355
[12377]	356	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
	357	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
	358	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
	359	! add to the general momentum trend
	360	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk)
	361	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk)
	362	END_3D
[3]	363
[11416]	364	! partial steps correction at the last level (use zgru & zgrv computed in zpshde.F90)
[13295]	365	DO_2D( 0, 0, 0, 0 )
[12377]	366	iku = mbku(ji,jj)
	367	ikv = mbkv(ji,jj)
	368	zcoef2 = zcoef0 * MIN( e3w(ji,jj,iku,Kmm), e3w(ji+1,jj ,iku,Kmm) )
	369	zcoef3 = zcoef0 * MIN( e3w(ji,jj,ikv,Kmm), e3w(ji ,jj+1,ikv,Kmm) )
	370	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
	371	puu (ji,jj,iku,Krhs) = puu(ji,jj,iku,Krhs) - zhpi(ji,jj,iku) ! subtract old value
	372	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
	373	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + zgru(ji,jj) ) * r1_e1u(ji,jj)
	374	puu (ji,jj,iku,Krhs) = puu(ji,jj,iku,Krhs) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
	375	ENDIF
	376	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
	377	pvv (ji,jj,ikv,Krhs) = pvv(ji,jj,ikv,Krhs) - zhpj(ji,jj,ikv) ! subtract old value
	378	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
	379	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + zgrv(ji,jj) ) * r1_e2v(ji,jj)
	380	pvv (ji,jj,ikv,Krhs) = pvv(ji,jj,ikv,Krhs) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
	381	ENDIF
	382	END_2D
[503]	383	!
[455]	384	END SUBROUTINE hpg_zps
[216]	385
[6140]	386
[12377]	387	SUBROUTINE hpg_sco( kt, Kmm, puu, pvv, Krhs )
[3]	388	!!---------------------------------------------------------------------
[455]	389	!! * ROUTINE hpg_sco *
[3]	390	!!
[455]	391	!! ** Method : s-coordinate case. Jacobian scheme.
	392	!! The now hydrostatic pressure gradient at a given level, jk,
	393	!! is computed by taking the vertical integral of the in-situ
[3]	394	!! density gradient along the model level from the suface to that
[455]	395	!! level. s-coordinates (ln_sco): a corrective term is added
	396	!! to the horizontal pressure gradient :
	397	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
	398	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
[12377]	399	!! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)).
	400	!! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi
	401	!! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj
[3]	402	!!
[12377]	403	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
[503]	404	!!----------------------------------------------------------------------
[12377]	405	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	406	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
	407	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[503]	408	!!
[14064]	409	INTEGER :: ji, jj, jk, jii, jjj ! dummy loop indices
	410	REAL(wp) :: zcoef0, zuap, zvap, ztmp ! local scalars
	411	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
[9019]	412	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
	413	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter
[5120]	414	!!----------------------------------------------------------------------
	415	!
[9039]	416	IF( ln_wd_il ) ALLOCATE(zcpx(jpi,jpj), zcpy(jpi,jpj))
[9023]	417	!
[5120]	418	IF( kt == nit000 ) THEN
	419	IF(lwp) WRITE(numout,*)
	420	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
[14227]	421	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OCE original scheme used'
[5120]	422	ENDIF
[6140]	423	!
[5120]	424	zcoef0 = - grav * 0.5_wp
[6140]	425	!
[9023]	426	IF( ln_wd_il ) THEN
[13295]	427	DO_2D( 0, 0, 0, 0 )
[12377]	428	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
	429	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
	430	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) &
	431	& > rn_wdmin1 + rn_wdmin2
	432	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji+1,jj,Kmm) ) > 1.E-12 ) .AND. ( &
	433	& MAX( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
	434	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
[6152]	435
[12377]	436	IF(ll_tmp1) THEN
	437	zcpx(ji,jj) = 1.0_wp
	438	ELSE IF(ll_tmp2) THEN
	439	! no worries about ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm) = 0, it won't happen ! here
	440	zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
	441	& / (ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm)) )
	442	ELSE
	443	zcpx(ji,jj) = 0._wp
	444	END IF
	445
	446	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
	447	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
	448	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) &
	449	& > rn_wdmin1 + rn_wdmin2
	450	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. ( &
	451	& MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
	452	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
[6152]	453
[12377]	454	IF(ll_tmp1) THEN
	455	zcpy(ji,jj) = 1.0_wp
	456	ELSE IF(ll_tmp2) THEN
	457	! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here
	458	zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
	459	& / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) )
	460	ELSE
	461	zcpy(ji,jj) = 0._wp
	462	END IF
	463	END_2D
[14338]	464	CALL lbc_lnk( 'dynhpg', zcpx, 'U', 1.0_wp, zcpy, 'V', 1.0_wp )
[9023]	465	END IF
[14064]	466	!
	467	DO_2D( 0, 0, 0, 0 ) ! Surface value
	468	! ! hydrostatic pressure gradient along s-surfaces
	469	zhpi(ji,jj,1) = zcoef0 * r1_e1u(ji,jj) &
	470	& * ( e3w(ji+1,jj ,1,Kmm) * rhd(ji+1,jj ,1) &
	471	& - e3w(ji ,jj ,1,Kmm) * rhd(ji ,jj ,1) )
	472	zhpj(ji,jj,1) = zcoef0 * r1_e2v(ji,jj) &
	473	& * ( e3w(ji ,jj+1,1,Kmm) * rhd(ji ,jj+1,1) &
	474	& - e3w(ji ,jj ,1,Kmm) * rhd(ji ,jj ,1) )
	475	! ! s-coordinate pressure gradient correction
	476	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) ) &
[12377]	477	& * ( gde3w(ji+1,jj,1) - gde3w(ji,jj,1) ) * r1_e1u(ji,jj)
[14064]	478	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) ) &
[12377]	479	& * ( gde3w(ji,jj+1,1) - gde3w(ji,jj,1) ) * r1_e2v(ji,jj)
	480	!
	481	IF( ln_wd_il ) THEN
	482	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
	483	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
	484	zuap = zuap * zcpx(ji,jj)
	485	zvap = zvap * zcpy(ji,jj)
	486	ENDIF
[14064]	487	! ! add to the general momentum trend
[12377]	488	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1) + zuap
	489	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1) + zvap
	490	END_2D
[14064]	491	!
	492	DO_3D( 0, 0, 0, 0, 2, jpkm1 ) ! interior value (2=<jk=<jpkm1)
	493	! ! hydrostatic pressure gradient along s-surfaces
	494	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 * r1_e1u(ji,jj) &
	495	& * ( e3w(ji+1,jj,jk,Kmm) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
	496	& - e3w(ji ,jj,jk,Kmm) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) )
	497	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 * r1_e2v(ji,jj) &
	498	& * ( e3w(ji,jj+1,jk,Kmm) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
	499	& - e3w(ji,jj ,jk,Kmm) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) )
	500	! ! s-coordinate pressure gradient correction
	501	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) ) &
[12377]	502	& * ( gde3w(ji+1,jj ,jk) - gde3w(ji,jj,jk) ) * r1_e1u(ji,jj)
[14064]	503	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) ) &
[12377]	504	& * ( gde3w(ji ,jj+1,jk) - gde3w(ji,jj,jk) ) * r1_e2v(ji,jj)
	505	!
	506	IF( ln_wd_il ) THEN
	507	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
	508	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
	509	zuap = zuap * zcpx(ji,jj)
	510	zvap = zvap * zcpy(ji,jj)
	511	ENDIF
	512	!
	513	! add to the general momentum trend
	514	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk) + zuap
	515	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk) + zvap
	516	END_3D
[5120]	517	!
[9039]	518	IF( ln_wd_il ) DEALLOCATE( zcpx , zcpy )
[5120]	519	!
	520	END SUBROUTINE hpg_sco
	521
[6140]	522
[12377]	523	SUBROUTINE hpg_isf( kt, Kmm, puu, pvv, Krhs )
[5120]	524	!!---------------------------------------------------------------------
[6140]	525	!! * ROUTINE hpg_isf *
[5120]	526	!!
	527	!! ** Method : s-coordinate case. Jacobian scheme.
	528	!! The now hydrostatic pressure gradient at a given level, jk,
	529	!! is computed by taking the vertical integral of the in-situ
	530	!! density gradient along the model level from the suface to that
	531	!! level. s-coordinates (ln_sco): a corrective term is added
	532	!! to the horizontal pressure gradient :
	533	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
	534	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
[12377]	535	!! add it to the general momentum trend (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)).
	536	!! puu(:,:,:,Krhs) = puu(:,:,:,Krhs) - 1/e1u * zhpi
	537	!! pvv(:,:,:,Krhs) = pvv(:,:,:,Krhs) - 1/e2v * zhpj
	538	!! iceload is added
[5120]	539	!!
[12377]	540	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
[5120]	541	!!----------------------------------------------------------------------
[12377]	542	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	543	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
	544	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[5120]	545	!!
[14064]	546	INTEGER :: ji, jj, jk ! dummy loop indices
	547	INTEGER :: ikt , ikti1, iktj1 ! local integer
	548	REAL(wp) :: ze3w, ze3wi1, ze3wj1 ! local scalars
	549	REAL(wp) :: zcoef0, zuap, zvap ! - -
[9019]	550	REAL(wp), DIMENSION(jpi,jpj,jpk ) :: zhpi, zhpj
	551	REAL(wp), DIMENSION(jpi,jpj,jpts) :: zts_top
	552	REAL(wp), DIMENSION(jpi,jpj) :: zrhdtop_oce
[3]	553	!!----------------------------------------------------------------------
[3294]	554	!
[9019]	555	zcoef0 = - grav * 0.5_wp ! Local constant initialization
[3294]	556	!
[9019]	557	! ! iniitialised to 0. zhpi zhpi
	558	zhpi(:,:,:) = 0._wp ; zhpj(:,:,:) = 0._wp
[6140]	559
[4990]	560	! compute rhd at the ice/oce interface (ocean side)
[6140]	561	! usefull to reduce residual current in the test case ISOMIP with no melting
[9019]	562	DO ji = 1, jpi
	563	DO jj = 1, jpj
	564	ikt = mikt(ji,jj)
[12377]	565	zts_top(ji,jj,1) = ts(ji,jj,ikt,1,Kmm)
	566	zts_top(ji,jj,2) = ts(ji,jj,ikt,2,Kmm)
[4990]	567	END DO
	568	END DO
[9019]	569	CALL eos( zts_top, risfdep, zrhdtop_oce )
[6140]	570
[14064]	571	! !===========================!
	572	! !===== surface value =====!
	573	! !===========================!
[13295]	574	DO_2D( 0, 0, 0, 0 )
[14064]	575	ikt = mikt(ji ,jj ) ; ze3w = e3w(ji ,jj ,ikt ,Kmm)
	576	ikti1 = mikt(ji+1,jj ) ; ze3wi1 = e3w(ji+1,jj ,ikti1,Kmm)
	577	iktj1 = mikt(ji ,jj+1) ; ze3wj1 = e3w(ji ,jj+1,iktj1,Kmm)
	578	! ! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
	579	! ! we assume ISF is in isostatic equilibrium
	580	zhpi(ji,jj,1) = zcoef0 * r1_e1u(ji,jj) * ( risfload(ji+1,jj) - risfload(ji,jj) &
	581	& + 0.5_wp * ( ze3wi1 * ( rhd(ji+1,jj,ikti1) + zrhdtop_oce(ji+1,jj) ) &
	582	& - ze3w * ( rhd(ji ,jj,ikt ) + zrhdtop_oce(ji ,jj) ) ) )
	583	zhpj(ji,jj,1) = zcoef0 * r1_e2v(ji,jj) * ( risfload(ji,jj+1) - risfload(ji,jj) &
	584	& + 0.5_wp * ( ze3wj1 * ( rhd(ji,jj+1,iktj1) + zrhdtop_oce(ji,jj+1) ) &
	585	& - ze3w * ( rhd(ji,jj ,ikt ) + zrhdtop_oce(ji,jj ) ) ) )
	586	! ! s-coordinate pressure gradient correction (=0 if z coordinate)
	587	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) ) &
[12377]	588	& * ( gde3w(ji+1,jj,1) - gde3w(ji,jj,1) ) * r1_e1u(ji,jj)
[14064]	589	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) ) &
[12377]	590	& * ( gde3w(ji,jj+1,1) - gde3w(ji,jj,1) ) * r1_e2v(ji,jj)
[14064]	591	! ! add to the general momentum trend
[12377]	592	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
	593	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
	594	END_2D
[14064]	595	!
	596	! !=============================!
	597	! !===== interior values =====!
	598	! !=============================!
[13295]	599	DO_3D( 0, 0, 0, 0, 2, jpkm1 )
[14064]	600	ze3w = e3w(ji ,jj ,jk,Kmm)
	601	ze3wi1 = e3w(ji+1,jj ,jk,Kmm)
	602	ze3wj1 = e3w(ji ,jj+1,jk,Kmm)
	603	! ! hydrostatic pressure gradient along s-surfaces
[12377]	604	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
[14064]	605	& * ( ze3wi1 * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) * wmask(ji+1,jj,jk) &
	606	& - ze3w * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) * wmask(ji ,jj,jk) )
[12377]	607	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
[14064]	608	& * ( ze3wj1 * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) * wmask(ji,jj+1,jk) &
	609	& - ze3w * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) * wmask(ji,jj ,jk) )
	610	! ! s-coordinate pressure gradient correction
	611	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) ) &
[12377]	612	& * ( gde3w(ji+1,jj ,jk) - gde3w(ji,jj,jk) ) / e1u(ji,jj)
[14064]	613	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) ) &
[12377]	614	& * ( gde3w(ji ,jj+1,jk) - gde3w(ji,jj,jk) ) / e2v(ji,jj)
[14064]	615	! ! add to the general momentum trend
[12377]	616	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + (zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
	617	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + (zhpj(ji,jj,jk) + zvap) * vmask(ji,jj,jk)
	618	END_3D
[503]	619	!
[5120]	620	END SUBROUTINE hpg_isf
[455]	621
[4990]	622
[12377]	623	SUBROUTINE hpg_djc( kt, Kmm, puu, pvv, Krhs )
[455]	624	!!---------------------------------------------------------------------
	625	!! * ROUTINE hpg_djc *
	626	!!
	627	!! ** Method : Density Jacobian with Cubic polynomial scheme
[3764]	628	!!
[503]	629	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
[455]	630	!!----------------------------------------------------------------------
[12377]	631	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	632	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
	633	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[503]	634	!!
	635	INTEGER :: ji, jj, jk ! dummy loop indices
[14060]	636	INTEGER :: iktb, iktt ! jk indices at tracer points for top and bottom points
[503]	637	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
[14060]	638	REAL(wp) :: z_grav_10, z1_12
	639	REAL(wp) :: cffu, cffx ! " "
	640	REAL(wp) :: cffv, cffy ! " "
[6152]	641	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
[9019]	642	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zhpj
[14060]	643
	644	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdzx, zdzy, zdzz ! Primitive grid differences ('delta_xyz')
	645	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdz_i, zdz_j, zdz_k ! Harmonic average of primitive grid differences ('d_xyz')
	646	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdrhox, zdrhoy, zdrhoz ! Primitive rho differences ('delta_rho')
	647	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdrho_i, zdrho_j, zdrho_k ! Harmonic average of primitive rho differences ('d_rho')
	648	REAL(wp), DIMENSION(jpi,jpj,jpk) :: z_rho_i, z_rho_j, z_rho_k ! Face intergrals
	649	REAL(wp), DIMENSION(jpi,jpj) :: zz_dz_i, zz_dz_j, zz_drho_i, zz_drho_j ! temporary arrays
[9019]	650	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter
[455]	651	!!----------------------------------------------------------------------
[3294]	652	!
[9023]	653	IF( ln_wd_il ) THEN
[9019]	654	ALLOCATE( zcpx(jpi,jpj) , zcpy(jpi,jpj) )
[13295]	655	DO_2D( 0, 0, 0, 0 )
[12377]	656	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
	657	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
	658	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) &
	659	& > rn_wdmin1 + rn_wdmin2
	660	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji+1,jj,Kmm) ) > 1.E-12 ) .AND. ( &
	661	& MAX( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
	662	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
	663	IF(ll_tmp1) THEN
	664	zcpx(ji,jj) = 1.0_wp
	665	ELSE IF(ll_tmp2) THEN
	666	! no worries about ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm) = 0, it won't happen ! here
	667	zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
	668	& / (ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm)) )
	669	ELSE
	670	zcpx(ji,jj) = 0._wp
	671	END IF
	672
	673	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
	674	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
	675	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) &
	676	& > rn_wdmin1 + rn_wdmin2
	677	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. ( &
	678	& MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
	679	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
[6152]	680
[12377]	681	IF(ll_tmp1) THEN
	682	zcpy(ji,jj) = 1.0_wp
	683	ELSE IF(ll_tmp2) THEN
	684	! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here
	685	zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
	686	& / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) )
	687	ELSE
	688	zcpy(ji,jj) = 0._wp
	689	END IF
	690	END_2D
[14338]	691	CALL lbc_lnk( 'dynhpg', zcpx, 'U', 1.0_wp, zcpy, 'V', 1.0_wp )
[9023]	692	END IF
[6152]	693
[455]	694	IF( kt == nit000 ) THEN
	695	IF(lwp) WRITE(numout,*)
	696	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
	697	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
[216]	698	ENDIF
	699
[503]	700	! Local constant initialization
[2528]	701	zcoef0 = - grav * 0.5_wp
[14060]	702	z_grav_10 = grav / 10._wp
	703	z1_12 = 1.0_wp / 12._wp
[455]	704
	705	!----------------------------------------------------------------------------------------
[14060]	706	! 1. compute and store elementary vertical differences in provisional arrays
[455]	707	!----------------------------------------------------------------------------------------
	708
[14060]	709	!!bug gm Not a true bug, but... zdzz=e3w for zdzx, zdzy verify what it is really
[455]	710
[14060]	711	DO_3D( 1, 1, 1, 1, 2, jpkm1 )
[14064]	712	zdrhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
[14060]	713	zdzz (ji,jj,jk) = - gde3w(ji ,jj ,jk) + gde3w(ji,jj,jk-1)
[12377]	714	END_3D
[455]	715
	716	!-------------------------------------------------------------------------
[14060]	717	! 2. compute harmonic averages for vertical differences using eq. 5.18
[455]	718	!-------------------------------------------------------------------------
	719	zep = 1.e-15
	720
[14060]	721	!! mb zdrho_k, zdz_k, zdrho_i, zdz_i, zdrho_j, zdz_j re-centred about the point (ji,jj,jk)
	722	zdrho_k(:,:,:) = 0._wp
	723	zdz_k (:,:,:) = 0._wp
[455]	724
[14060]	725	DO_3D( 1, 1, 1, 1, 2, jpk-2 )
	726	cffw = 2._wp * zdrhoz(ji ,jj ,jk) * zdrhoz(ji,jj,jk+1)
	727	IF( cffw > zep) THEN
	728	zdrho_k(ji,jj,jk) = cffw / ( zdrhoz(ji,jj,jk) + zdrhoz(ji,jj,jk+1) )
	729	ENDIF
	730	zdz_k(ji,jj,jk) = 2._wp * zdzz(ji,jj,jk) * zdzz(ji,jj,jk+1) &
	731	& / ( zdzz(ji,jj,jk) + zdzz(ji,jj,jk+1) )
	732	END_3D
[455]	733
[14060]	734	!----------------------------------------------------------------------------------
	735	! 3. apply boundary conditions at top and bottom using 5.36-5.37
	736	!----------------------------------------------------------------------------------
[3764]	737
[14060]	738	! 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]	739	zdrho_k(:,:,1) = aco_bc_vrt * ( rhd (:,:,2) - rhd (:,:,1) ) - bco_bc_vrt * zdrho_k(:,:,2)
[14060]	740	zdz_k (:,:,1) = aco_bc_vrt * (-gde3w(:,:,2) + gde3w(:,:,1) ) - bco_bc_vrt * zdz_k (:,:,2)
[455]	741
[14060]	742	DO_2D( 1, 1, 1, 1 )
	743	IF ( mbkt(ji,jj)>1 ) THEN
	744	iktb = mbkt(ji,jj)
[14064]	745	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]	746	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)
	747	END IF
	748	END_2D
[455]	749
[14060]	750	!--------------------------------------------------------------
	751	! 4. Compute side face integrals
	752	!-------------------------------------------------------------
[455]	753
[14060]	754	!! ssh replaces e3w_n ; gde3w is a depth; the formulae involve heights
	755	!! rho_k stores grav * FX / rho_0
	756
	757	!--------------------------------------------------------------
	758	! 4. a) Upper half of top-most grid box, compute and store
	759	!-------------------------------------------------------------
[14118]	760	! *** AY note: ssh(ji,jj,Kmm) + gde3w(ji,jj,1) = e3w(ji,jj,1,Kmm)
[14060]	761	DO_2D( 0, 1, 0, 1)
	762	z_rho_k(ji,jj,1) = grav * ( ssh(ji,jj,Kmm) + gde3w(ji,jj,1) ) &
[14064]	763	& * ( rhd(ji,jj,1) &
	764	& + 0.5_wp * ( rhd (ji,jj,2) - rhd (ji,jj,1) ) &
[14060]	765	& * ( ssh (ji,jj,Kmm) + gde3w(ji,jj,1) ) &
	766	& / ( - gde3w(ji,jj,2) + gde3w(ji,jj,1) ) )
	767	END_2D
	768
	769	!--------------------------------------------------------------
	770	! 4. b) Interior faces, compute and store
	771	!-------------------------------------------------------------
	772
	773	DO_3D( 0, 1, 0, 1, 2, jpkm1 )
[14064]	774	z_rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
[14060]	775	& * ( - gde3w(ji,jj,jk) + gde3w(ji,jj,jk-1) ) &
	776	& + z_grav_10 * ( &
	777	& ( zdrho_k (ji,jj,jk) - zdrho_k (ji,jj,jk-1) ) &
	778	& * ( - gde3w(ji,jj,jk) + gde3w(ji,jj,jk-1) - z1_12 * ( zdz_k (ji,jj,jk) + zdz_k (ji,jj,jk-1) ) ) &
	779	& - ( zdz_k (ji,jj,jk) - zdz_k (ji,jj,jk-1) ) &
[14064]	780	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( zdrho_k(ji,jj,jk) + zdrho_k(ji,jj,jk-1) ) ) &
[14060]	781	& )
	782	END_3D
	783
	784	!----------------------------------------------------------------------------------------
	785	! 5. compute and store elementary horizontal differences in provisional arrays
	786	!----------------------------------------------------------------------------------------
	787
	788	DO_3D( 1, 0, 1, 0, 1, jpkm1 )
[14064]	789	zdrhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
[14060]	790	zdzx (ji,jj,jk) = - gde3w(ji+1,jj ,jk) + gde3w(ji,jj,jk )
[14064]	791	zdrhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
[14060]	792	zdzy (ji,jj,jk) = - gde3w(ji ,jj+1,jk) + gde3w(ji,jj,jk )
	793	END_3D
	794
[14338]	795	CALL lbc_lnk( 'dynhpg', zdrhox, 'U', 1., zdzx, 'U', 1., zdrhoy, 'V', 1., zdzy, 'V', 1. )
[14060]	796
	797	!-------------------------------------------------------------------------
	798	! 6. compute harmonic averages using eq. 5.18
	799	!-------------------------------------------------------------------------
	800
	801	DO_3D( 0, 1, 0, 1, 1, jpkm1 )
	802	cffu = 2._wp * zdrhox(ji-1,jj ,jk) * zdrhox(ji,jj,jk )
[12377]	803	IF( cffu > zep ) THEN
[14060]	804	zdrho_i(ji,jj,jk) = cffu / ( zdrhox(ji-1,jj,jk) + zdrhox(ji,jj,jk) )
[12377]	805	ELSE
[14060]	806	zdrho_i(ji,jj,jk ) = 0._wp
[12377]	807	ENDIF
[455]	808
[14060]	809	cffx = 2._wp * zdzx (ji-1,jj ,jk) * zdzx (ji,jj,jk )
[12377]	810	IF( cffx > zep ) THEN
[14060]	811	zdz_i(ji,jj,jk) = cffx / ( zdzx(ji-1,jj,jk) + zdzx(ji,jj,jk) )
[12377]	812	ELSE
[14060]	813	zdz_i(ji,jj,jk) = 0._wp
[12377]	814	ENDIF
[455]	815
[14060]	816	cffv = 2._wp * zdrhoy(ji ,jj-1,jk) * zdrhoy(ji,jj,jk )
[12377]	817	IF( cffv > zep ) THEN
[14060]	818	zdrho_j(ji,jj,jk) = cffv / ( zdrhoy(ji,jj-1,jk) + zdrhoy(ji,jj,jk) )
[12377]	819	ELSE
[14060]	820	zdrho_j(ji,jj,jk) = 0._wp
[12377]	821	ENDIF
[455]	822
[14060]	823	cffy = 2._wp * zdzy (ji ,jj-1,jk) * zdzy (ji,jj,jk )
[12377]	824	IF( cffy > zep ) THEN
[14060]	825	zdz_j(ji,jj,jk) = cffy / ( zdzy(ji,jj-1,jk) + zdzy(ji,jj,jk) )
[12377]	826	ELSE
[14060]	827	zdz_j(ji,jj,jk) = 0._wp
[12377]	828	ENDIF
	829	END_3D
[14060]	830
	831	!!! Note that zdzx, zdzy, zdzz, zdrhox, zdrhoy and zdrhoz should NOT be used beyond this point
[455]	832
	833	!----------------------------------------------------------------------------------
[14060]	834	! 6B. apply boundary conditions at side boundaries using 5.36-5.37
[455]	835	!----------------------------------------------------------------------------------
	836
[14060]	837	DO jk = 1, jpkm1
	838	zz_drho_i(:,:) = zdrho_i(:,:,jk)
	839	zz_dz_i (:,:) = zdz_i (:,:,jk)
	840	zz_drho_j(:,:) = zdrho_j(:,:,jk)
	841	zz_dz_j (:,:) = zdz_j (:,:,jk)
	842	DO_2D( 0, 1, 0, 1)
	843	! Walls coming from left: should check from 2 to jpi-1 (and jpj=2-jpj)
	844	IF (ji < jpi) THEN
	845	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]	846	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]	847	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)
	848	END IF
	849	END IF
	850	! Walls coming from right: should check from 3 to jpi (and jpj=2-jpj)
	851	IF (ji > 2) THEN
	852	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]	853	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]	854	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)
	855	END IF
	856	END IF
	857	! Walls coming from left: should check from 2 to jpj-1 (and jpi=2-jpi)
	858	IF (jj < jpj) THEN
	859	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]	860	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]	861	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)
	862	END IF
	863	END IF
	864	! Walls coming from right: should check from 3 to jpj (and jpi=2-jpi)
	865	IF (jj > 2) THEN
	866	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]	867	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]	868	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)
	869	END IF
	870	END IF
	871	END_2D
	872	zdrho_i(:,:,jk) = zz_drho_i(:,:)
	873	zdz_i (:,:,jk) = zz_dz_i (:,:)
	874	zdrho_j(:,:,jk) = zz_drho_j(:,:)
	875	zdz_j (:,:,jk) = zz_dz_j (:,:)
	876	END DO
[455]	877
	878	!--------------------------------------------------------------
[14060]	879	! 7. Calculate integrals on side faces
[455]	880	!-------------------------------------------------------------
	881
[14060]	882	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
	883	! two -ve signs cancel in next two lines (within zcoef0 and because gde3w is a depth not a height)
[14064]	884	z_rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
[14060]	885	& * ( gde3w(ji+1,jj,jk) - gde3w(ji,jj,jk) )
	886	IF ( umask(ji-1, jj, jk) > 0.5 .OR. umask(ji+1, jj, jk) > 0.5 ) THEN
	887	z_rho_i(ji,jj,jk) = z_rho_i(ji,jj,jk) - z_grav_10 * ( &
	888	& ( zdrho_i (ji+1,jj,jk) - zdrho_i (ji,jj,jk) ) &
	889	& * ( - gde3w(ji+1,jj,jk) + gde3w(ji,jj,jk) - z1_12 * ( zdz_i (ji+1,jj,jk) + zdz_i (ji,jj,jk) ) ) &
	890	& - ( zdz_i (ji+1,jj,jk) - zdz_i (ji,jj,jk) ) &
[14064]	891	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( zdrho_i(ji+1,jj,jk) + zdrho_i(ji,jj,jk) ) ) &
[14060]	892	& )
	893	END IF
	894
[14064]	895	z_rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
[14060]	896	& * ( gde3w(ji,jj+1,jk) - gde3w(ji,jj,jk) )
	897	IF ( vmask(ji, jj-1, jk) > 0.5 .OR. vmask(ji, jj+1, jk) > 0.5 ) THEN
	898	z_rho_j(ji,jj,jk) = z_rho_j(ji,jj,jk) - z_grav_10 * ( &
	899	& ( zdrho_j (ji,jj+1,jk) - zdrho_j (ji,jj,jk) ) &
	900	& * ( - gde3w(ji,jj+1,jk) + gde3w(ji,jj,jk) - z1_12 * ( zdz_j (ji,jj+1,jk) + zdz_j (ji,jj,jk) ) ) &
	901	& - ( zdz_j (ji,jj+1,jk) - zdz_j (ji,jj,jk) ) &
[14064]	902	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( zdrho_j(ji,jj+1,jk) + zdrho_j(ji,jj,jk) ) ) &
[14060]	903	& )
	904	END IF
	905	END_3D
[455]	906
[14060]	907	!--------------------------------------------------------------
	908	! 8. Integrate in the vertical
	909	!-------------------------------------------------------------
[14064]	910	!
[455]	911	! ---------------
	912	! Surface value
	913	! ---------------
[13295]	914	DO_2D( 0, 0, 0, 0 )
[14060]	915	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)
	916	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]	917	IF( ln_wd_il ) THEN
	918	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
	919	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
	920	ENDIF
	921	! add to the general momentum trend
	922	puu(ji,jj,1,Krhs) = puu(ji,jj,1,Krhs) + zhpi(ji,jj,1)
	923	pvv(ji,jj,1,Krhs) = pvv(ji,jj,1,Krhs) + zhpj(ji,jj,1)
	924	END_2D
[455]	925
	926	! ----------------
	927	! interior value (2=<jk=<jpkm1)
	928	! ----------------
[13295]	929	DO_3D( 0, 0, 0, 0, 2, jpkm1 )
[12377]	930	! hydrostatic pressure gradient along s-surfaces
[14060]	931	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
	932	& + ( ( z_rho_k(ji,jj,jk) - z_rho_k(ji+1,jj,jk ) ) &
	933	& - ( z_rho_i(ji,jj,jk) - z_rho_i(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
	934	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
	935	& + ( ( z_rho_k(ji,jj,jk) - z_rho_k(ji,jj+1,jk ) ) &
	936	& -( z_rho_j(ji,jj,jk) - z_rho_j(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
[12377]	937	IF( ln_wd_il ) THEN
	938	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
	939	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
	940	ENDIF
	941	! add to the general momentum trend
	942	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + zhpi(ji,jj,jk)
	943	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + zhpj(ji,jj,jk)
	944	END_3D
[503]	945	!
[9023]	946	IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy )
[2715]	947	!
[455]	948	END SUBROUTINE hpg_djc
	949
	950
[12377]	951	SUBROUTINE hpg_prj( kt, Kmm, puu, pvv, Krhs )
[455]	952	!!---------------------------------------------------------------------
[3294]	953	!! * ROUTINE hpg_prj *
[455]	954	!!
[3294]	955	!! ** Method : s-coordinate case.
	956	!! A Pressure-Jacobian horizontal pressure gradient method
	957	!! based on the constrained cubic-spline interpolation for
	958	!! all vertical coordinate systems
[455]	959	!!
[12377]	960	!! ** Action : - Update (puu(:,:,:,Krhs),pvv(:,:,:,Krhs)) with the now hydrastatic pressure trend
[455]	961	!!----------------------------------------------------------------------
[3294]	962	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
[12377]	963	INTEGER , INTENT( in ) :: kt ! ocean time-step index
	964	INTEGER , INTENT( in ) :: Kmm, Krhs ! ocean time level indices
	965	REAL(wp), DIMENSION(jpi,jpj,jpk,jpt), INTENT(inout) :: puu, pvv ! ocean velocities and RHS of momentum equation
[503]	966	!!
[3294]	967	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
[6140]	968	REAL(wp) :: zcoef0, znad ! local scalars
	969	!
[3294]	970	!! The local variables for the correction term
	971	INTEGER :: jk1, jis, jid, jjs, jjd
[6152]	972	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
[3294]	973	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
[3764]	974	REAL(wp) :: zrhdt1
[3294]	975	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
[14064]	976	REAL(wp), DIMENSION(jpi,jpj) :: zpgu, zpgv ! 2D workspace
	977	REAL(wp), DIMENSION(jpi,jpj) :: zsshu_n, zsshv_n
[9019]	978	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zdept, zrhh
	979	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
	980	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: zcpx, zcpy !W/D pressure filter
[455]	981	!!----------------------------------------------------------------------
[3294]	982	!
[455]	983	IF( kt == nit000 ) THEN
	984	IF(lwp) WRITE(numout,*)
[3294]	985	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
	986	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
[3]	987	ENDIF
	988
[3294]	989	! Local constant initialization
[3764]	990	zcoef0 = - grav
[6140]	991	znad = 1._wp
[14064]	992	IF( ln_linssh ) znad = 1._wp
	993	!
	994	! ---------------
	995	! Surface pressure gradient to be removed
	996	! ---------------
	997	DO_2D( 0, 0, 0, 0 )
	998	zpgu(ji,jj) = - grav * ( ssh(ji+1,jj,Kmm) - ssh(ji,jj,Kmm) ) * r1_e1u(ji,jj)
	999	zpgv(ji,jj) = - grav * ( ssh(ji,jj+1,Kmm) - ssh(ji,jj,Kmm) ) * r1_e2v(ji,jj)
	1000	END_2D
	1001	!
[9023]	1002	IF( ln_wd_il ) THEN
[9019]	1003	ALLOCATE( zcpx(jpi,jpj) , zcpy(jpi,jpj) )
[13295]	1004	DO_2D( 0, 0, 0, 0 )
[12377]	1005	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
	1006	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) .AND. &
	1007	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) ) &
	1008	& > rn_wdmin1 + rn_wdmin2
	1009	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji+1,jj,Kmm) ) > 1.E-12 ) .AND. ( &
	1010	& MAX( ssh(ji,jj,Kmm) , ssh(ji+1,jj,Kmm) ) > &
	1011	& MAX( -ht_0(ji,jj) , -ht_0(ji+1,jj) ) + rn_wdmin1 + rn_wdmin2 )
[6152]	1012
[12377]	1013	IF(ll_tmp1) THEN
	1014	zcpx(ji,jj) = 1.0_wp
	1015	ELSE IF(ll_tmp2) THEN
	1016	! no worries about ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm) = 0, it won't happen ! here
	1017	zcpx(ji,jj) = ABS( (ssh(ji+1,jj,Kmm) + ht_0(ji+1,jj) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
	1018	& / (ssh(ji+1,jj,Kmm) - ssh(ji ,jj,Kmm)) )
	1019
	1020	zcpx(ji,jj) = max(min( zcpx(ji,jj) , 1.0_wp),0.0_wp)
	1021	ELSE
	1022	zcpx(ji,jj) = 0._wp
	1023	END IF
	1024
	1025	ll_tmp1 = MIN( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
	1026	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) .AND. &
	1027	& MAX( ssh(ji,jj,Kmm) + ht_0(ji,jj), ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) ) &
	1028	& > rn_wdmin1 + rn_wdmin2
	1029	ll_tmp2 = ( ABS( ssh(ji,jj,Kmm) - ssh(ji,jj+1,Kmm) ) > 1.E-12 ) .AND. ( &
	1030	& MAX( ssh(ji,jj,Kmm) , ssh(ji,jj+1,Kmm) ) > &
	1031	& MAX( -ht_0(ji,jj) , -ht_0(ji,jj+1) ) + rn_wdmin1 + rn_wdmin2 )
[6152]	1032
[12377]	1033	IF(ll_tmp1) THEN
	1034	zcpy(ji,jj) = 1.0_wp
	1035	ELSE IF(ll_tmp2) THEN
	1036	! no worries about ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm) = 0, it won't happen ! here
	1037	zcpy(ji,jj) = ABS( (ssh(ji,jj+1,Kmm) + ht_0(ji,jj+1) - ssh(ji,jj,Kmm) - ht_0(ji,jj)) &
	1038	& / (ssh(ji,jj+1,Kmm) - ssh(ji,jj ,Kmm)) )
	1039	zcpy(ji,jj) = max(min( zcpy(ji,jj) , 1.0_wp),0.0_wp)
[9023]	1040
[12377]	1041	ELSE
	1042	zcpy(ji,jj) = 0._wp
	1043	ENDIF
	1044	END_2D
[14338]	1045	CALL lbc_lnk( 'dynhpg', zcpx, 'U', 1.0_wp, zcpy, 'V', 1.0_wp )
[9019]	1046	ENDIF
[6152]	1047
[3294]	1048	! Clean 3-D work arrays
	1049	zhpi(:,:,:) = 0._wp
	1050	zrhh(:,:,:) = rhd(:,:,:)
[3764]	1051
[3294]	1052	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
[13295]	1053	DO_2D( 1, 1, 1, 1 )
[13288]	1054	jk = mbkt(ji,jj)
	1055	IF( jk <= 1 ) THEN ; zrhh(ji,jj, : ) = 0._wp
	1056	ELSEIF( jk == 2 ) THEN ; zrhh(ji,jj,jk+1:jpk) = rhd(ji,jj,jk)
[12377]	1057	ELSEIF( jk < jpkm1 ) THEN
	1058	DO jkk = jk+1, jpk
	1059	zrhh(ji,jj,jkk) = interp1(gde3w(ji,jj,jkk ), gde3w(ji,jj,jkk-1), &
[13288]	1060	& gde3w(ji,jj,jkk-2), zrhh (ji,jj,jkk-1), zrhh(ji,jj,jkk-2))
[12377]	1061	END DO
	1062	ENDIF
	1063	END_2D
[3]	1064
[3632]	1065	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
[13295]	1066	DO_2D( 1, 1, 1, 1 )
[14064]	1067	zdept(ji,jj,1) = 0.5_wp * e3w(ji,jj,1,Kmm) - ssh(ji,jj,Kmm)
[12377]	1068	END_2D
[455]	1069
[13295]	1070	DO_3D( 1, 1, 1, 1, 2, jpk )
[12377]	1071	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + e3w(ji,jj,jk,Kmm)
	1072	END_3D
[455]	1073
[4990]	1074	fsp(:,:,:) = zrhh (:,:,:)
[3632]	1075	xsp(:,:,:) = zdept(:,:,:)
	1076
[3764]	1077	! Construct the vertical density profile with the
[3294]	1078	! constrained cubic spline interpolation
	1079	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
[6140]	1080	CALL cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
[3294]	1081
	1082	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
[13295]	1083	DO_2D( 0, 1, 0, 1 )
[12377]	1084	zrhdt1 = zrhh(ji,jj,1) - interp3( zdept(ji,jj,1), asp(ji,jj,1), bsp(ji,jj,1), &
	1085	& csp(ji,jj,1), dsp(ji,jj,1) ) * 0.25_wp * e3w(ji,jj,1,Kmm)
[3294]	1086
[12377]	1087	! assuming linear profile across the top half surface layer
	1088	zhpi(ji,jj,1) = 0.5_wp * e3w(ji,jj,1,Kmm) * zrhdt1
	1089	END_2D
[455]	1090
[3294]	1091	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
[13295]	1092	DO_3D( 0, 1, 0, 1, 2, jpkm1 )
[12377]	1093	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
	1094	& integ_spline( zdept(ji,jj,jk-1), zdept(ji,jj,jk), &
	1095	& asp (ji,jj,jk-1), bsp (ji,jj,jk-1), &
	1096	& csp (ji,jj,jk-1), dsp (ji,jj,jk-1) )
	1097	END_3D
[455]	1098
[3294]	1099	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
[5224]	1100
	1101	! Prepare zsshu_n and zsshv_n
[13295]	1102	DO_2D( 0, 0, 0, 0 )
[6140]	1103	!!gm BUG ? if it is ssh at u- & v-point then it should be:
[12377]	1104	! zsshu_n(ji,jj) = (e1e2t(ji,jj) * ssh(ji,jj,Kmm) + e1e2t(ji+1,jj) * ssh(ji+1,jj,Kmm)) * &
[6140]	1105	! & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
[12377]	1106	! zsshv_n(ji,jj) = (e1e2t(ji,jj) * ssh(ji,jj,Kmm) + e1e2t(ji,jj+1) * ssh(ji,jj+1,Kmm)) * &
[6140]	1107	! & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
	1108	!!gm not this:
[12377]	1109	zsshu_n(ji,jj) = (e1e2u(ji,jj) * ssh(ji,jj,Kmm) + e1e2u(ji+1, jj) * ssh(ji+1,jj,Kmm)) * &
	1110	& r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
	1111	zsshv_n(ji,jj) = (e1e2v(ji,jj) * ssh(ji,jj,Kmm) + e1e2v(ji+1, jj) * ssh(ji,jj+1,Kmm)) * &
	1112	& r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
	1113	END_2D
[455]	1114
[14338]	1115	CALL lbc_lnk ('dynhpg', zsshu_n, 'U', 1.0_wp, zsshv_n, 'V', 1.0_wp )
[6152]	1116
[13295]	1117	DO_2D( 0, 0, 0, 0 )
[14064]	1118	zu(ji,jj,1) = - ( e3u(ji,jj,1,Kmm) - zsshu_n(ji,jj) )
	1119	zv(ji,jj,1) = - ( e3v(ji,jj,1,Kmm) - zsshv_n(ji,jj) )
[12377]	1120	END_2D
[5224]	1121
[13295]	1122	DO_3D( 0, 0, 0, 0, 2, jpkm1 )
[12377]	1123	zu(ji,jj,jk) = zu(ji,jj,jk-1) - e3u(ji,jj,jk,Kmm)
	1124	zv(ji,jj,jk) = zv(ji,jj,jk-1) - e3v(ji,jj,jk,Kmm)
	1125	END_3D
[3764]	1126
[13295]	1127	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[12377]	1128	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * e3u(ji,jj,jk,Kmm)
	1129	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * e3v(ji,jj,jk,Kmm)
	1130	END_3D
[455]	1131
[13295]	1132	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[12377]	1133	zu(ji,jj,jk) = MIN( zu(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
	1134	zu(ji,jj,jk) = MAX( zu(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
	1135	zv(ji,jj,jk) = MIN( zv(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
	1136	zv(ji,jj,jk) = MAX( zv(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
	1137	END_3D
[3632]	1138
	1139
[13295]	1140	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[12377]	1141	zpwes = 0._wp; zpwed = 0._wp
	1142	zpnss = 0._wp; zpnsd = 0._wp
	1143	zuijk = zu(ji,jj,jk)
	1144	zvijk = zv(ji,jj,jk)
[3294]	1145
[12377]	1146	!!!!! for u equation
	1147	IF( jk <= mbku(ji,jj) ) THEN
	1148	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
	1149	jis = ji + 1; jid = ji
	1150	ELSE
	1151	jis = ji; jid = ji +1
	1152	ENDIF
[3294]	1153
[12377]	1154	! integrate the pressure on the shallow side
	1155	jk1 = jk
	1156	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
	1157	IF( jk1 == mbku(ji,jj) ) THEN
	1158	zuijk = -zdept(jis,jj,jk1)
	1159	EXIT
	1160	ENDIF
	1161	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
	1162	zpwes = zpwes + &
	1163	integ_spline(zdept(jis,jj,jk1), zdeps, &
	1164	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
	1165	csp(jis,jj,jk1), dsp(jis,jj,jk1))
	1166	jk1 = jk1 + 1
	1167	END DO
[3764]	1168
[12377]	1169	! integrate the pressure on the deep side
	1170	jk1 = jk
	1171	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
	1172	IF( jk1 == 1 ) THEN
	1173	zdeps = zdept(jid,jj,1) + MIN(zuijk, ssh(jid,jj,Kmm)*znad)
	1174	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
	1175	bsp(jid,jj,1), csp(jid,jj,1), &
	1176	dsp(jid,jj,1)) * zdeps
	1177	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
	1178	EXIT
	1179	ENDIF
	1180	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
	1181	zpwed = zpwed + &
	1182	integ_spline(zdeps, zdept(jid,jj,jk1), &
	1183	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
	1184	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
	1185	jk1 = jk1 - 1
	1186	END DO
[3764]	1187
[12377]	1188	! update the momentum trends in u direction
[3294]	1189
[12377]	1190	zdpdx1 = zcoef0 * r1_e1u(ji,jj) * ( zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk) )
	1191	IF( .NOT.ln_linssh ) THEN
	1192	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * &
	1193	& ( REAL(jis-jid, wp) * (zpwes + zpwed) + (ssh(ji+1,jj,Kmm)-ssh(ji,jj,Kmm)) )
	1194	ELSE
	1195	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
	1196	ENDIF
	1197	IF( ln_wd_il ) THEN
	1198	zdpdx1 = zdpdx1 * zcpx(ji,jj) * wdrampu(ji,jj)
	1199	zdpdx2 = zdpdx2 * zcpx(ji,jj) * wdrampu(ji,jj)
	1200	ENDIF
[14064]	1201	puu(ji,jj,jk,Krhs) = puu(ji,jj,jk,Krhs) + (zdpdx1 + zdpdx2 - zpgu(ji,jj)) * umask(ji,jj,jk)
[12377]	1202	ENDIF
[3764]	1203
[12377]	1204	!!!!! for v equation
	1205	IF( jk <= mbkv(ji,jj) ) THEN
	1206	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
	1207	jjs = jj + 1; jjd = jj
	1208	ELSE
	1209	jjs = jj ; jjd = jj + 1
	1210	ENDIF
[3294]	1211
[12377]	1212	! integrate the pressure on the shallow side
	1213	jk1 = jk
	1214	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
	1215	IF( jk1 == mbkv(ji,jj) ) THEN
	1216	zvijk = -zdept(ji,jjs,jk1)
	1217	EXIT
	1218	ENDIF
	1219	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
	1220	zpnss = zpnss + &
	1221	integ_spline(zdept(ji,jjs,jk1), zdeps, &
	1222	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
	1223	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
	1224	jk1 = jk1 + 1
	1225	END DO
[3764]	1226
[12377]	1227	! integrate the pressure on the deep side
	1228	jk1 = jk
	1229	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
	1230	IF( jk1 == 1 ) THEN
	1231	zdeps = zdept(ji,jjd,1) + MIN(zvijk, ssh(ji,jjd,Kmm)*znad)
	1232	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
	1233	bsp(ji,jjd,1), csp(ji,jjd,1), &
	1234	dsp(ji,jjd,1) ) * zdeps
	1235	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
	1236	EXIT
	1237	ENDIF
	1238	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
	1239	zpnsd = zpnsd + &
	1240	integ_spline(zdeps, zdept(ji,jjd,jk1), &
	1241	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
	1242	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
	1243	jk1 = jk1 - 1
	1244	END DO
[3294]	1245
[3764]	1246
[12377]	1247	! update the momentum trends in v direction
[3294]	1248
[12377]	1249	zdpdy1 = zcoef0 * r1_e2v(ji,jj) * ( zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk) )
	1250	IF( .NOT.ln_linssh ) THEN
	1251	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * &
	1252	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (ssh(ji,jj+1,Kmm)-ssh(ji,jj,Kmm)) )
	1253	ELSE
	1254	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
	1255	ENDIF
	1256	IF( ln_wd_il ) THEN
	1257	zdpdy1 = zdpdy1 * zcpy(ji,jj) * wdrampv(ji,jj)
	1258	zdpdy2 = zdpdy2 * zcpy(ji,jj) * wdrampv(ji,jj)
	1259	ENDIF
[6152]	1260
[14064]	1261	pvv(ji,jj,jk,Krhs) = pvv(ji,jj,jk,Krhs) + (zdpdy1 + zdpdy2 - zpgv(ji,jj)) * vmask(ji,jj,jk)
[12377]	1262	ENDIF
	1263	!
	1264	END_3D
[503]	1265	!
[9023]	1266	IF( ln_wd_il ) DEALLOCATE( zcpx, zcpy )
[2715]	1267	!
[3294]	1268	END SUBROUTINE hpg_prj
[455]	1269
[4990]	1270
[6140]	1271	SUBROUTINE cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
[3294]	1272	!!----------------------------------------------------------------------
	1273	!! * ROUTINE cspline *
[3764]	1274	!!
[3294]	1275	!! ** Purpose : constrained cubic spline interpolation
[3764]	1276	!!
	1277	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
[4990]	1278	!!
[3294]	1279	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
	1280	!!----------------------------------------------------------------------
[6140]	1281	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: fsp, xsp ! value and coordinate
	1282	REAL(wp), DIMENSION(:,:,:), INTENT( out) :: asp, bsp, csp, dsp ! coefficients of the interpoated function
	1283	INTEGER , INTENT(in ) :: polynomial_type ! 1: cubic spline ; 2: Linear
[4990]	1284	!
[3294]	1285	INTEGER :: ji, jj, jk ! dummy loop indices
	1286	INTEGER :: jpi, jpj, jpkm1
	1287	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
	1288	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
	1289	REAL(wp) :: zdf(size(fsp,3))
	1290	!!----------------------------------------------------------------------
[6140]	1291	!
	1292	!!gm WHAT !!!!! THIS IS VERY DANGEROUS !!!!!
[3294]	1293	jpi = size(fsp,1)
	1294	jpj = size(fsp,2)
[7761]	1295	jpkm1 = MAX( 1, size(fsp,3) - 1 )
[6140]	1296	!
[3294]	1297	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
	1298	DO ji = 1, jpi
	1299	DO jj = 1, jpj
[3764]	1300	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
[3294]	1301	! DO jk = 2, jpkm1-1
[3764]	1302	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
	1303	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1304	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
	1305	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
	1306	!
	1307	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
[3764]	1308	!
[3294]	1309	! IF(zdf1 * zdf2 <= 0._wp) THEN
	1310	! zdf(jk) = 0._wp
	1311	! ELSE
	1312	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
	1313	! ENDIF
	1314	! END DO
[3764]	1315
[3294]	1316	!!Simply geometric average
	1317	DO jk = 2, jpkm1-1
[9019]	1318	zdf1 = (fsp(ji,jj,jk ) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk ) - xsp(ji,jj,jk-1))
	1319	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk )) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk ))
[3764]	1320
[3294]	1321	IF(zdf1 * zdf2 <= 0._wp) THEN
	1322	zdf(jk) = 0._wp
	1323	ELSE
	1324	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
	1325	ENDIF
	1326	END DO
[3764]	1327
[3294]	1328	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
[6140]	1329	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
[3294]	1330	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
[6140]	1331	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - 0.5_wp * zdf(jpkm1 - 1)
[3764]	1332
[3294]	1333	DO jk = 1, jpkm1 - 1
[3764]	1334	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1335	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
	1336	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
[3764]	1337	zddf1 = -2._wp * ztmp1 + ztmp2
[3294]	1338	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
[3764]	1339	zddf2 = 2._wp * ztmp1 - ztmp2
	1340
[3294]	1341	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
	1342	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
[3764]	1343	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
[3294]	1344	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
	1345	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
	1346	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
	1347	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
	1348	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
	1349	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
	1350	END DO
	1351	END DO
	1352	END DO
[3764]	1353
[6140]	1354	ELSEIF ( polynomial_type == 2 ) THEN ! Linear
[3294]	1355	DO ji = 1, jpi
	1356	DO jj = 1, jpj
	1357	DO jk = 1, jpkm1-1
[3764]	1358	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1359	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
[3764]	1360
[3294]	1361	dsp(ji,jj,jk) = 0._wp
	1362	csp(ji,jj,jk) = 0._wp
	1363	bsp(ji,jj,jk) = ztmp1 / zdxtmp
	1364	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
	1365	END DO
	1366	END DO
	1367	END DO
[9019]	1368	!
[3294]	1369	ELSE
[9019]	1370	CALL ctl_stop( 'invalid polynomial type in cspline' )
[3294]	1371	ENDIF
[9019]	1372	!
[3294]	1373	END SUBROUTINE cspline
	1374
	1375
[3764]	1376	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
[3294]	1377	!!----------------------------------------------------------------------
	1378	!! * ROUTINE interp1 *
[3764]	1379	!!
[3294]	1380	!! ** Purpose : 1-d linear interpolation
[3764]	1381	!!
[4990]	1382	!! ** Method : interpolation is straight forward
[3764]	1383	!! extrapolation is also permitted (no value limit)
[3294]	1384	!!----------------------------------------------------------------------
[3764]	1385	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
[3294]	1386	REAL(wp) :: f ! result of the interpolation (extrapolation)
	1387	REAL(wp) :: zdeltx
	1388	!!----------------------------------------------------------------------
[6140]	1389	!
[3294]	1390	zdeltx = xr - xl
[6140]	1391	IF( abs(zdeltx) <= 10._wp * EPSILON(x) ) THEN
	1392	f = 0.5_wp * (fl + fr)
[3294]	1393	ELSE
[6140]	1394	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
[3294]	1395	ENDIF
[6140]	1396	!
[3294]	1397	END FUNCTION interp1
	1398
[4990]	1399
[6140]	1400	FUNCTION interp2( x, a, b, c, d ) RESULT(f)
[3294]	1401	!!----------------------------------------------------------------------
	1402	!! * ROUTINE interp1 *
[3764]	1403	!!
[3294]	1404	!! ** Purpose : 1-d constrained cubic spline interpolation
[3764]	1405	!!
[3294]	1406	!! ** Method : cubic spline interpolation
	1407	!!
	1408	!!----------------------------------------------------------------------
[3764]	1409	REAL(wp), INTENT(in) :: x, a, b, c, d
[3294]	1410	REAL(wp) :: f ! value from the interpolation
	1411	!!----------------------------------------------------------------------
[6140]	1412	!
[3764]	1413	f = a + x* ( b + x * ( c + d * x ) )
[6140]	1414	!
[3294]	1415	END FUNCTION interp2
	1416
	1417
[6140]	1418	FUNCTION interp3( x, a, b, c, d ) RESULT(f)
[3294]	1419	!!----------------------------------------------------------------------
	1420	!! * ROUTINE interp1 *
[3764]	1421	!!
[9019]	1422	!! ** Purpose : Calculate the first order of derivative of
[3294]	1423	!! a cubic spline function y=a+bx+cx^2+d*x^3
[3764]	1424	!!
[3294]	1425	!! ** Method : f=dy/dx=b+2cx+3dx^2
	1426	!!
	1427	!!----------------------------------------------------------------------
[3764]	1428	REAL(wp), INTENT(in) :: x, a, b, c, d
[3294]	1429	REAL(wp) :: f ! value from the interpolation
	1430	!!----------------------------------------------------------------------
[6140]	1431	!
[3294]	1432	f = b + x * ( 2._wp * c + 3._wp * d * x)
[6140]	1433	!
[3294]	1434	END FUNCTION interp3
	1435
[3764]	1436
[6140]	1437	FUNCTION integ_spline( xl, xr, a, b, c, d ) RESULT(f)
[3294]	1438	!!----------------------------------------------------------------------
	1439	!! * ROUTINE interp1 *
[3764]	1440	!!
[3294]	1441	!! ** Purpose : 1-d constrained cubic spline integration
	1442	!!
[3764]	1443	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
	1444	!!
[3294]	1445	!!----------------------------------------------------------------------
[3764]	1446	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
	1447	REAL(wp) :: za1, za2, za3
[3294]	1448	REAL(wp) :: f ! integration result
	1449	!!----------------------------------------------------------------------
[6140]	1450	!
[3764]	1451	za1 = 0.5_wp * b
	1452	za2 = c / 3.0_wp
	1453	za3 = 0.25_wp * d
[6140]	1454	!
[3294]	1455	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
	1456	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
[6140]	1457	!
[3632]	1458	END FUNCTION integ_spline
[3294]	1459
[3]	1460	!!======================================================================
	1461	END MODULE dynhpg

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source: NEMO/branches/2021/dev_r14312_MPI_Interface/src/OCE/DYN/dynhpg.F90 @ 14338

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