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dynhpg.F90 @ 8112

Last change on this file since 8112 was 8112, checked in by davestorkey, 7 years ago
UKMO/branch/dev_r5518_GO6_package_FVPS: FVPS implementation
File size: 71.6 KB

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[3]	1	MODULE dynhpg
	2	!!======================================================================
	3	!! * MODULE dynhpg *
	4	!! Ocean dynamics: hydrostatic pressure gradient trend
	5	!!======================================================================
[2528]	6	!! History : OPA ! 1987-09 (P. Andrich, M.-A. Foujols) hpg_zco: Original code
	7	!! 5.0 ! 1991-11 (G. Madec)
	8	!! 7.0 ! 1996-01 (G. Madec) hpg_sco: Original code for s-coordinates
	9	!! 8.0 ! 1997-05 (G. Madec) split dynber into dynkeg and dynhpg
	10	!! 8.5 ! 2002-07 (G. Madec) F90: Free form and module
	11	!! 8.5 ! 2002-08 (A. Bozec) hpg_zps: Original code
	12	!! NEMO 1.0 ! 2005-10 (A. Beckmann, B.W. An) various s-coordinate options
[3764]	13	!! ! Original code for hpg_ctl, hpg_hel hpg_wdj, hpg_djc, hpg_rot
[2528]	14	!! - ! 2005-11 (G. Madec) style & small optimisation
	15	!! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase
[3294]	16	!! 3.4 ! 2011-11 (H. Liu) hpg_prj: Original code for s-coordinates
	17	!! ! (A. Coward) suppression of hel, wdj and rot options
[5120]	18	!! 3.6 ! 2014-11 (P. Mathiot) hpg_isf: original code for ice shelf cavity
[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
[4990]	33	USE sbc_oce ! surface variable (only for the flag with ice shelf)
[3]	34	USE dom_oce ! ocean space and time domain
	35	USE phycst ! physical constants
[4990]	36	USE trd_oce ! trends: ocean variables
	37	USE trddyn ! trend manager: dynamics
	38	!
[2715]	39	USE in_out_manager ! I/O manager
[258]	40	USE prtctl ! Print control
[4990]	41	USE lbclnk ! lateral boundary condition
[2715]	42	USE lib_mpp ! MPP library
[4990]	43	USE eosbn2 ! compute density
[3294]	44	USE wrk_nemo ! Memory Allocation
	45	USE timing ! Timing
[8112]	46	USE iom
[3]	47
	48	IMPLICIT NONE
	49	PRIVATE
	50
[2528]	51	PUBLIC dyn_hpg ! routine called by step module
	52	PUBLIC dyn_hpg_init ! routine called by opa module
[3]	53
[4147]	54	! !!* Namelist namdyn_hpg : hydrostatic pressure gradient
	55	LOGICAL , PUBLIC :: ln_hpg_zco !: z-coordinate - full steps
	56	LOGICAL , PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation)
	57	LOGICAL , PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation)
	58	LOGICAL , PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial)
	59	LOGICAL , PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme)
[5120]	60	LOGICAL , PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf
[4147]	61	LOGICAL , PUBLIC :: ln_dynhpg_imp !: semi-implicite hpg flag
[455]	62
[3764]	63	INTEGER , PUBLIC :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM)
[455]	64
[3]	65	!! * Substitutions
	66	# include "domzgr_substitute.h90"
	67	# include "vectopt_loop_substitute.h90"
	68	!!----------------------------------------------------------------------
[2528]	69	!! NEMO/OPA 3.3 , NEMO Consortium (2010)
	70	!! $Id$
	71	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
[3]	72	!!----------------------------------------------------------------------
	73	CONTAINS
	74
	75	SUBROUTINE dyn_hpg( kt )
	76	!!---------------------------------------------------------------------
	77	!! * ROUTINE dyn_hpg *
	78	!!
[3764]	79	!! ** Method : Call the hydrostatic pressure gradient routine
[503]	80	!! using the scheme defined in the namelist
[3764]	81	!!
[455]	82	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[4990]	83	!! - send trends to trd_dyn for futher diagnostics (l_trddyn=T)
[503]	84	!!----------------------------------------------------------------------
	85	INTEGER, INTENT(in) :: kt ! ocean time-step index
[3294]	86	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdu, ztrdv
[455]	87	!!----------------------------------------------------------------------
[2528]	88	!
[3294]	89	IF( nn_timing == 1 ) CALL timing_start('dyn_hpg')
[2715]	90	!
[503]	91	IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn)
[3294]	92	CALL wrk_alloc( jpi,jpj,jpk, ztrdu, ztrdv )
[3764]	93	ztrdu(:,:,:) = ua(:,:,:)
	94	ztrdv(:,:,:) = va(:,:,:)
	95	ENDIF
[2528]	96	!
[3294]	97	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
[503]	98	CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate
	99	CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation)
	100	CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation)
[3294]	101	CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial)
	102	CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme)
[5120]	103	CASE ( 5 ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf
[455]	104	END SELECT
[2528]	105	!
[503]	106	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
[455]	107	ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:)
	108	ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:)
[4990]	109	CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt )
[3294]	110	CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv )
[3764]	111	ENDIF
[503]	112	!
	113	IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, &
	114	& tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
	115	!
[3294]	116	IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg')
[2715]	117	!
[455]	118	END SUBROUTINE dyn_hpg
	119
	120
[2528]	121	SUBROUTINE dyn_hpg_init
[455]	122	!!----------------------------------------------------------------------
[2528]	123	!! * ROUTINE dyn_hpg_init *
[455]	124	!!
	125	!! ** Purpose : initializations for the hydrostatic pressure gradient
	126	!! computation and consistency control
	127	!!
[1601]	128	!! ** Action : Read the namelist namdyn_hpg and check the consistency
[455]	129	!! with the type of vertical coordinate used (zco, zps, sco)
	130	!!----------------------------------------------------------------------
	131	INTEGER :: ioptio = 0 ! temporary integer
[4147]	132	INTEGER :: ios ! Local integer output status for namelist read
[1601]	133	!!
[3294]	134	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
[5120]	135	& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf, ln_dynhpg_imp
[455]	136	!!----------------------------------------------------------------------
[2528]	137	!
[4147]	138	REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient
	139	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
	140	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp )
	141
	142	REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient
	143	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
	144	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp )
[4624]	145	IF(lwm) WRITE ( numond, namdyn_hpg )
[2528]	146	!
	147	IF(lwp) THEN ! Control print
[455]	148	WRITE(numout,*)
[2528]	149	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
	150	WRITE(numout,*) '~~~~~~~~~~~~'
[1601]	151	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
	152	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
	153	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
	154	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
[5120]	155	WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf
[1601]	156	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
[3294]	157	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
[1601]	158	WRITE(numout,*) ' time stepping: centered (F) or semi-implicit (T) ln_dynhpg_imp = ', ln_dynhpg_imp
[455]	159	ENDIF
[2528]	160	!
[3294]	161	IF( ln_hpg_djc ) &
	162	& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method &
	163	& currently disabled (bugs under investigation). Please select &
	164	& either ln_hpg_sco or ln_hpg_prj instead')
[2528]	165	!
[5120]	166	IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) &
[3294]	167	& CALL ctl_stop('dyn_hpg_init : variable volume key_vvl requires:&
	168	& the standard jacobian formulation hpg_sco or &
	169	& the pressure jacobian formulation hpg_prj')
[5120]	170
	171	IF( ln_hpg_isf .AND. .NOT. ln_isfcav ) &
	172	& CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' )
	173	IF( .NOT. ln_hpg_isf .AND. ln_isfcav ) &
	174	& CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' )
[3294]	175	!
[503]	176	! ! Set nhpg from ln_hpg_... flags
[455]	177	IF( ln_hpg_zco ) nhpg = 0
	178	IF( ln_hpg_zps ) nhpg = 1
	179	IF( ln_hpg_sco ) nhpg = 2
[3294]	180	IF( ln_hpg_djc ) nhpg = 3
	181	IF( ln_hpg_prj ) nhpg = 4
[5120]	182	IF( ln_hpg_isf ) nhpg = 5
[2528]	183	!
[3294]	184	! ! Consistency check
[3764]	185	ioptio = 0
[455]	186	IF( ln_hpg_zco ) ioptio = ioptio + 1
	187	IF( ln_hpg_zps ) ioptio = ioptio + 1
	188	IF( ln_hpg_sco ) ioptio = ioptio + 1
	189	IF( ln_hpg_djc ) ioptio = ioptio + 1
[3294]	190	IF( ln_hpg_prj ) ioptio = ioptio + 1
[5120]	191	IF( ln_hpg_isf ) ioptio = ioptio + 1
[2715]	192	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
[5120]	193	!
	194	! initialisation of ice load
	195	riceload(:,:)=0.0
[503]	196	!
[2528]	197	END SUBROUTINE dyn_hpg_init
[455]	198
	199
	200	SUBROUTINE hpg_zco( kt )
	201	!!---------------------------------------------------------------------
	202	!! * ROUTINE hpg_zco *
	203	!!
	204	!! ** Method : z-coordinate case, levels are horizontal surfaces.
	205	!! The now hydrostatic pressure gradient at a given level, jk,
	206	!! is computed by taking the vertical integral of the in-situ
	207	!! density gradient along the model level from the suface to that
	208	!! level: zhpi = grav .....
	209	!! zhpj = grav .....
[3]	210	!! add it to the general momentum trend (ua,va).
[455]	211	!! ua = ua - 1/e1u * zhpi
	212	!! va = va - 1/e2v * zhpj
[3764]	213	!!
[3]	214	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[503]	215	!!----------------------------------------------------------------------
	216	INTEGER, INTENT(in) :: kt ! ocean time-step index
	217	!!
	218	INTEGER :: ji, jj, jk ! dummy loop indices
	219	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
[3764]	220	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3]	221	!!----------------------------------------------------------------------
[3764]	222	!
[3294]	223	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
	224	!
[3]	225	IF( kt == nit000 ) THEN
	226	IF(lwp) WRITE(numout,*)
[455]	227	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
	228	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
[3]	229	ENDIF
	230
[3764]	231	zcoef0 = - grav * 0.5_wp ! Local constant initialization
	232
[455]	233	! Surface value
[3]	234	DO jj = 2, jpjm1
	235	DO ji = fs_2, fs_jpim1 ! vector opt.
[455]	236	zcoef1 = zcoef0 * fse3w(ji,jj,1)
	237	! hydrostatic pressure gradient
	238	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
	239	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
[3]	240	! add to the general momentum trend
[455]	241	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
	242	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
	243	END DO
	244	END DO
[3294]	245
[503]	246	!
[455]	247	! interior value (2=<jk=<jpkm1)
[3]	248	DO jk = 2, jpkm1
[455]	249	DO jj = 2, jpjm1
[3]	250	DO ji = fs_2, fs_jpim1 ! vector opt.
[455]	251	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
	252	! hydrostatic pressure gradient
	253	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
	254	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
	255	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
	256
	257	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
	258	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
	259	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
[3]	260	! add to the general momentum trend
[455]	261	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	262	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
[3]	263	END DO
	264	END DO
	265	END DO
[503]	266	!
[3294]	267	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
	268	!
[455]	269	END SUBROUTINE hpg_zco
[216]	270
[3]	271
[455]	272	SUBROUTINE hpg_zps( kt )
[3]	273	!!---------------------------------------------------------------------
[455]	274	!! * ROUTINE hpg_zps *
[3764]	275	!!
[455]	276	!! ** Method : z-coordinate plus partial steps case. blahblah...
[3764]	277	!!
[3]	278	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[3764]	279	!!----------------------------------------------------------------------
[503]	280	INTEGER, INTENT(in) :: kt ! ocean time-step index
	281	!!
	282	INTEGER :: ji, jj, jk ! dummy loop indices
	283	INTEGER :: iku, ikv ! temporary integers
	284	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
[3764]	285	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3]	286	!!----------------------------------------------------------------------
[3294]	287	!
	288	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
	289	!
[3]	290	IF( kt == nit000 ) THEN
	291	IF(lwp) WRITE(numout,*)
[455]	292	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
[503]	293	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
[3]	294	ENDIF
	295
[3294]	296
[503]	297	! Local constant initialization
[2528]	298	zcoef0 = - grav * 0.5_wp
[3]	299
[2528]	300	! Surface value (also valid in partial step case)
[3]	301	DO jj = 2, jpjm1
	302	DO ji = fs_2, fs_jpim1 ! vector opt.
[170]	303	zcoef1 = zcoef0 * fse3w(ji,jj,1)
[3]	304	! hydrostatic pressure gradient
[455]	305	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
	306	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
[3]	307	! add to the general momentum trend
	308	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
	309	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
	310	END DO
	311	END DO
	312
[3294]	313
[503]	314	! interior value (2=<jk=<jpkm1)
[3]	315	DO jk = 2, jpkm1
	316	DO jj = 2, jpjm1
	317	DO ji = fs_2, fs_jpim1 ! vector opt.
[170]	318	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
[3]	319	! hydrostatic pressure gradient
	320	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
[455]	321	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
	322	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
[3]	323
	324	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
[455]	325	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
	326	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
[3]	327	! add to the general momentum trend
	328	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	329	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
[455]	330	END DO
[3]	331	END DO
	332	END DO
	333
[3294]	334
[2528]	335	! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
[3]	336	DO jj = 2, jpjm1
	337	DO ji = 2, jpim1
[2528]	338	iku = mbku(ji,jj)
	339	ikv = mbkv(ji,jj)
[3]	340	zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) )
	341	zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) )
[2528]	342	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
	343	ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value
	344	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
	345	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj)
	346	ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
[3]	347	ENDIF
[2528]	348	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
	349	va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value
	350	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
	351	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj)
	352	va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
[3]	353	ENDIF
	354	END DO
	355	END DO
[503]	356	!
[3294]	357	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
	358	!
[455]	359	END SUBROUTINE hpg_zps
[216]	360
[455]	361	SUBROUTINE hpg_sco( kt )
[3]	362	!!---------------------------------------------------------------------
[455]	363	!! * ROUTINE hpg_sco *
[3]	364	!!
[455]	365	!! ** Method : s-coordinate case. Jacobian scheme.
	366	!! The now hydrostatic pressure gradient at a given level, jk,
	367	!! is computed by taking the vertical integral of the in-situ
[3]	368	!! density gradient along the model level from the suface to that
[455]	369	!! level. s-coordinates (ln_sco): a corrective term is added
	370	!! to the horizontal pressure gradient :
	371	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
	372	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
[3]	373	!! add it to the general momentum trend (ua,va).
[455]	374	!! ua = ua - 1/e1u * zhpi
	375	!! va = va - 1/e2v * zhpj
[3]	376	!!
	377	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[503]	378	!!----------------------------------------------------------------------
	379	INTEGER, INTENT(in) :: kt ! ocean time-step index
	380	!!
[5120]	381	INTEGER :: ji, jj, jk ! dummy loop indices
[8112]	382	REAL(wp) :: zcoef0, zuap, zvap, znad, zvnum ! temporary scalars
	383	REAL(wp), POINTER, DIMENSION(:,:) :: zunum, zudenom ! temporary numerators for u and v velocities (for debugging)
	384	REAL(wp), POINTER, DIMENSION(:,:) :: zpb, zpt ! pressure at top and bottom of cells
	385	REAL(wp), POINTER, DIMENSION(:,:) :: zzb, zzt ! geopotential height (gz) at top and bottom of cells
	386	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj, zp3d, zz3d
[5120]	387	!!----------------------------------------------------------------------
	388	!
[8112]	389	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj, zp3d, zz3d )
	390	CALL wrk_alloc( jpi,jpj, zunum, zudenom, zpb, zpt, zzb, zzt )
[5120]	391	!
	392	IF( kt == nit000 ) THEN
	393	IF(lwp) WRITE(numout,*)
	394	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
	395	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
	396	ENDIF
	397
	398	! Local constant initialization
	399	zcoef0 = - grav * 0.5_wp
	400	! To use density and not density anomaly
	401	IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
	402	ELSE ; znad = 0._wp ! Fixed volume
	403	ENDIF
	404
[8112]	405	! set the pressure values to zero at the top of the model (the atmospheric surface pressure is included in the barotropic step ?)
	406	zpb(:,:) = 0._wp
	407	zzb(:,:) = grav * sshn(:,:) ! surface height had been incorrectly set to zero; corrected on 24 Apr 2017
	408
	409	if(lwp) write(numout,*) 'hpg_sco: grav is ',grav
	410
	411	DO jk = 1, jpkm1
	412
	413	zpt(:,:) = zpb(:,:)
	414	zzt(:,:) = zzb(:,:)
	415
	416	zp3d(:,:,jk) = zpt(:,:)
	417	zz3d(:,:,jk) = zzt(:,:)
	418
	419	! integrate the pressure from the top of the cell to the bottom of the cell; a factor rho_0 has been removed from the pressure
	420	! corrected to calculate for loops from 1 to jpj and 1 to jpi 25 Apr 2017
	421	DO jj = 1, jpj
	422	DO ji = 1, jpi ! vector opt.
	423	!!$ zpb(ji,jj) = zpt(ji,jj) + grav * fse3w_n(ji,jj,jk) * ( znad + rhd(ji,jj,jk) )
	424	zpb(ji,jj) = zpt(ji,jj) + grav * fse3t_n(ji,jj,jk) * ( znad + rhd(ji,jj,jk) )
	425	zzb(ji,jj) = grav * ( sshn(ji,jj) - fsdepw_n(ji,jj,jk+1) ) ! surface height had been set to zero; corrected on 24 Apr 2017
	426	END DO
[5120]	427	END DO
	428
[8112]	429	! calculate the Jacobian of the pressure forces
[5120]	430	DO jj = 2, jpjm1
	431	DO ji = fs_2, fs_jpim1 ! vector opt.
[8112]	432	zunum(ji, jj) = ( zpb(ji+1,jj) - zpt(ji , jj) )( zzb(ji , jj) - zzt(ji+1, jj) ) - ( zpb(ji , jj) - zpt(ji+1, jj) )( zzb(ji+1, jj) - zzt(ji , jj) )
	433	zudenom(ji, jj) = zpb(ji+1, jj) - zpt(ji , jj) + zpb(ji , jj) - zpt(ji+1, jj)
	434	zhpi(ji, jj, jk) = zunum(ji, jj) * r1_e1u(ji, jj) / zudenom(ji, jj)
	435	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	436
	437	zvnum = ( zpb(ji,jj+1) - zpt(ji, jj ) )( zzb(ji, jj ) - zzt(ji, jj+1) ) - ( zpb(ji, jj ) - zpt(ji, jj+1) )( zzb(ji, jj+1) - zzt(ji, jj ) )
	438	zhpj(ji, jj, jk) = zvnum * r1_e2v(ji, jj) / ( zpb(ji, jj+1) - zpt(ji, jj ) + zpb(ji, jj ) - zpt(ji, jj+1) )
	439	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
[5120]	440	END DO
	441	END DO
[8112]	442
	443	! temporary diagnostic outputs (to be used on just a few timesteps on a small configuration)
	444	!!$ DO jj = 1, jpj
	445	!!$ write(numout, *) 'fse3w_n, jk, jj = ', jk, jj, (fse3w_n(ji,jj,jk), ji = 1, jpi)
	446	!!$ write(numout, *) 'rhd, jk, jj = ', jk, jj, (rhd(ji,jj,jk), ji = 1, jpi)
	447	!!$ write(numout, *) 'gdepw_n, jk+1, jj = ', jk+1, jj, (gdepw_n(ji,jj,jk+1), ji = 1, jpim1)
	448	!!$ write(numout, *) 'r1_e1u, jk, jj = ', jk, jj, (r1_e1u(ji,jj), ji = 1, jpim1)
	449	!!$ write(numout, *) 'zpt, jk, jj = ', jk, jj, (zpt(ji,jj), ji = 1, jpi)
	450	!!$ write(numout, *) 'zpb, jk, jj = ', jk, jj, (zpb(ji,jj), ji = 1, jpi)
	451	!!$ write(numout, *) 'zzt, jk, jj = ', jk, jj, (zzt(ji,jj), ji = 1, jpi)
	452	!!$ write(numout, *) 'zzb, jk, jj = ', jk, jj, (zzb(ji,jj), ji = 1, jpi)
	453	!!$ write(numout, *) 'zunum, jk, jj = ', jk, jj, (zunum(ji,jj), ji = 1, jpi)
	454	!!$ write(numout, *) 'zudenom, jk, jj = ', jk, jj, (zudenom(ji,jj), ji = 1, jpi)
	455	!!$ write(numout, *) 'tmask, jk, jj = ', jk, jj, (tmask(ji,jj,jk), ji = 1, jpi)
	456	!!$ write(numout, *) 'umask, jk, jj = ', jk, jj, (umask(ji,jj,jk), ji = 1, jpi)
	457	!!$ write(numout, *) 'vmask, jk, jj = ', jk, jj, (vmask(ji,jj,jk), ji = 1, jpi)
	458	!!$
	459	!!$ write(numout, *) 'zhpi, jk, jj = ', jk, jj, (zhpi(ji,jj,jk), ji = 1, jpi)
	460	!!$ write(numout, *) 'zhpj, jk, jj = ', jk, jj, (zhpj(ji,jj,jk), ji = 1, jpi)
	461	!!$ END DO
	462
[5120]	463	END DO
	464	!
[8112]	465	CALL iom_put("pressure" , zp3d(:,:,:) )
	466	CALL iom_put("hpgdepth" , zz3d(:,:,:) )
	467	CALL iom_put("rho" , rhd(:,:,:) )
	468	CALL iom_put("hpgi", zhpi(:,:,:) )
	469	CALL iom_put("hpgj", zhpj(:,:,:) )
[5120]	470	!
[8112]	471	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj, zp3d, zz3d )
	472	CALL wrk_dealloc( jpi,jpj, zpb, zpt, zzb, zzt )
	473	!
[5120]	474	END SUBROUTINE hpg_sco
	475
	476	SUBROUTINE hpg_isf( kt )
	477	!!---------------------------------------------------------------------
	478	!! * ROUTINE hpg_sco *
	479	!!
	480	!! ** Method : s-coordinate case. Jacobian scheme.
	481	!! The now hydrostatic pressure gradient at a given level, jk,
	482	!! is computed by taking the vertical integral of the in-situ
	483	!! density gradient along the model level from the suface to that
	484	!! level. s-coordinates (ln_sco): a corrective term is added
	485	!! to the horizontal pressure gradient :
	486	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
	487	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
	488	!! add it to the general momentum trend (ua,va).
	489	!! ua = ua - 1/e1u * zhpi
	490	!! va = va - 1/e2v * zhpj
	491	!! iceload is added and partial cell case are added to the top and bottom
	492	!!
	493	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
	494	!!----------------------------------------------------------------------
	495	INTEGER, INTENT(in) :: kt ! ocean time-step index
	496	!!
[4990]	497	INTEGER :: ji, jj, jk, iku, ikv, ikt, iktp1i, iktp1j ! dummy loop indices
	498	REAL(wp) :: zcoef0, zuap, zvap, znad, ze3wu, ze3wv, zuapint, zvapint, zhpjint, zhpiint, zdzwt, zdzwtjp1, zdzwtip1 ! temporary scalars
	499	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj, zrhd
	500	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop
	501	REAL(wp), POINTER, DIMENSION(:,:) :: ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj
[3]	502	!!----------------------------------------------------------------------
[3294]	503	!
[4990]	504	CALL wrk_alloc( jpi,jpj, 2, ztstop)
	505	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
	506	CALL wrk_alloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
[3294]	507	!
[4990]	508	IF( kt == nit000 ) THEN
[3]	509	IF(lwp) WRITE(numout,*)
[5120]	510	IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf'
[455]	511	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
[3]	512	ENDIF
	513
[503]	514	! Local constant initialization
[2528]	515	zcoef0 = - grav * 0.5_wp
[592]	516	! To use density and not density anomaly
[4990]	517	! IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
	518	! ELSE ; znad = 0._wp ! Fixed volume
	519	! ENDIF
	520	znad=1._wp
	521	! iniitialised to 0. zhpi zhpi
	522	zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp
[455]	523
[4990]	524	!==================================================================================
	525	!=====Compute iceload and contribution of the half first wet layer =================
	526	!===================================================================================
	527
	528	! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude)
	529	ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp
	530
	531	! compute density of the water displaced by the ice shelf
	532	zrhd = rhd ! save rhd
	533	DO jk = 1, jpk
	534	zdept(:,:)=gdept_1d(jk)
	535	CALL eos(ztstop(:,:,:),zdept(:,:),rhd(:,:,jk))
	536	END DO
	537	WHERE ( tmask(:,:,:) == 1._wp)
	538	rhd(:,:,:) = zrhd(:,:,:) ! replace wet cell by the saved rhd
	539	END WHERE
	540
	541	! compute rhd at the ice/oce interface (ice shelf side)
	542	CALL eos(ztstop,risfdep,zrhdtop_isf)
	543
	544	! compute rhd at the ice/oce interface (ocean side)
	545	DO ji=1,jpi
	546	DO jj=1,jpj
	547	ikt=mikt(ji,jj)
	548	ztstop(ji,jj,1)=tsn(ji,jj,ikt,1)
	549	ztstop(ji,jj,2)=tsn(ji,jj,ikt,2)
	550	END DO
	551	END DO
	552	CALL eos(ztstop,risfdep,zrhdtop_oce)
	553	!
	554	! Surface value + ice shelf gradient
	555	! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v)
	556	ziceload = 0._wp
	557	DO jj = 1, jpj
	558	DO ji = 1, jpi ! vector opt.
	559	ikt=mikt(ji,jj)
	560	ziceload(ji,jj) = ziceload(ji,jj) + (znad + rhd(ji,jj,1) ) * fse3w(ji,jj,1) * (1._wp - tmask(ji,jj,1))
	561	DO jk=2,ikt-1
	562	ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + rhd(ji,jj,jk-1) + rhd(ji,jj,jk)) * fse3w(ji,jj,jk) &
	563	& * (1._wp - tmask(ji,jj,jk))
	564	END DO
	565	IF (ikt .GE. 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + rhd(ji,jj,ikt-1)) &
	566	& * ( risfdep(ji,jj) - gdept_1d(ikt-1) )
	567	END DO
	568	END DO
	569	riceload(:,:) = 0.0_wp ; riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5
	570	! compute zp from z=0 to first T wet point (correction due to zps not yet applied)
[455]	571	DO jj = 2, jpjm1
[3764]	572	DO ji = fs_2, fs_jpim1 ! vector opt.
[4990]	573	ikt=mikt(ji,jj) ; iktp1i=mikt(ji+1,jj); iktp1j=mikt(ji,jj+1)
	574	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
	575	! we assume ISF is in isostatic equilibrium
	576	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * fse3w(ji+1,jj ,iktp1i) &
	577	& * ( 2._wp * znad + rhd(ji+1,jj ,iktp1i) + zrhdtop_oce(ji+1,jj ) ) &
	578	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
	579	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
	580	& + ( ziceload(ji+1,jj) - ziceload(ji,jj)) )
	581	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * fse3w(ji ,jj+1,iktp1j) &
	582	& * ( 2._wp * znad + rhd(ji ,jj+1,iktp1j) + zrhdtop_oce(ji ,jj+1) ) &
	583	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
	584	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
	585	& + ( ziceload(ji,jj+1) - ziceload(ji,jj) ) )
	586	! s-coordinate pressure gradient correction (=0 if z coordinate)
[2528]	587	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
[455]	588	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
[2528]	589	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
[455]	590	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
	591	! add to the general momentum trend
[4990]	592	ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
	593	va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
[3764]	594	END DO
	595	END DO
[4990]	596	!==================================================================================
	597	!===== Compute partial cell contribution for the top cell =========================
	598	!==================================================================================
	599	DO jj = 2, jpjm1
	600	DO ji = fs_2, fs_jpim1 ! vector opt.
	601	iku = miku(ji,jj) ;
	602	zpshpi(ji,jj)=0.0_wp ; zpshpj(ji,jj)=0.0_wp
	603	ze3wu = (gdepw_0(ji+1,jj,iku+1) - gdept_0(ji+1,jj,iku)) - (gdepw_0(ji,jj,iku+1) - gdept_0(ji,jj,iku))
	604	! u direction
	605	IF ( iku .GT. 1 ) THEN
	606	! case iku
	607	zhpi(ji,jj,iku) = zcoef0 / e1u(ji,jj) * ze3wu &
	608	& * ( rhd (ji+1,jj,iku) + rhd (ji,jj,iku) &
	609	& + SIGN(1._wp,ze3wu) * grui(ji,jj) + 2._wp * znad )
	610	! corrective term ( = 0 if z coordinate )
	611	zuap = -zcoef0 * ( arui(ji,jj) + 2._wp * znad ) * gzui(ji,jj) / e1u(ji,jj)
	612	! zhpi will be added in interior loop
	613	ua(ji,jj,iku) = ua(ji,jj,iku) + zuap
	614	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
	615	IF (mbku(ji,jj) == iku + 1) zpshpi(ji,jj) = zhpi(ji,jj,iku)
[3764]	616
[4990]	617	! case iku + 1 (remove the zphi term added in the interior loop and compute the one corrected for zps)
	618	zhpiint = zcoef0 / e1u(ji,jj) &
	619	& * ( fse3w(ji+1,jj ,iku+1) * ( (rhd(ji+1,jj,iku+1) + znad) &
	620	& + (rhd(ji+1,jj,iku ) + znad) ) * tmask(ji+1,jj,iku) &
	621	& - fse3w(ji ,jj ,iku+1) * ( (rhd(ji ,jj,iku+1) + znad) &
	622	& + (rhd(ji ,jj,iku ) + znad) ) * tmask(ji ,jj,iku) )
	623	zhpi(ji,jj,iku+1) = zcoef0 / e1u(ji,jj) * ge3rui(ji,jj) - zhpiint
	624	END IF
	625
	626	! v direction
	627	ikv = mikv(ji,jj)
	628	ze3wv = (gdepw_0(ji,jj+1,ikv+1) - gdept_0(ji,jj+1,ikv)) - (gdepw_0(ji,jj,ikv+1) - gdept_0(ji,jj,ikv))
	629	IF ( ikv .GT. 1 ) THEN
	630	! case ikv
	631	zhpj(ji,jj,ikv) = zcoef0 / e2v(ji,jj) * ze3wv &
	632	& * ( rhd(ji,jj+1,ikv) + rhd (ji,jj,ikv) &
	633	& + SIGN(1._wp,ze3wv) * grvi(ji,jj) + 2._wp * znad )
	634	! corrective term ( = 0 if z coordinate )
	635	zvap = -zcoef0 * ( arvi(ji,jj) + 2._wp * znad ) * gzvi(ji,jj) / e2v(ji,jj)
	636	! zhpi will be added in interior loop
	637	va(ji,jj,ikv) = va(ji,jj,ikv) + zvap
	638	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
	639	IF (mbkv(ji,jj) == ikv + 1) zpshpj(ji,jj) = zhpj(ji,jj,ikv)
	640
	641	! case ikv + 1 (remove the zphj term added in the interior loop and compute the one corrected for zps)
	642	zhpjint = zcoef0 / e2v(ji,jj) &
	643	& * ( fse3w(ji ,jj+1,ikv+1) * ( (rhd(ji,jj+1,ikv+1) + znad) &
	644	& + (rhd(ji,jj+1,ikv ) + znad) ) * tmask(ji,jj+1,ikv) &
	645	& - fse3w(ji ,jj ,ikv+1) * ( (rhd(ji,jj ,ikv+1) + znad) &
	646	& + (rhd(ji,jj ,ikv ) + znad) ) * tmask(ji,jj ,ikv) )
	647	zhpj(ji,jj,ikv+1) = zcoef0 / e2v(ji,jj) * ge3rvi(ji,jj) - zhpjint
	648	END IF
	649	END DO
	650	END DO
	651
	652	!==================================================================================
	653	!===== Compute interior value =====================================================
	654	!==================================================================================
	655
	656	DO jj = 2, jpjm1
	657	DO ji = fs_2, fs_jpim1 ! vector opt.
	658	iku=miku(ji,jj); ikv=mikv(ji,jj)
	659	DO jk = 2, jpkm1
[455]	660	! hydrostatic pressure gradient along s-surfaces
[4990]	661	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
	662	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) + zhpi(ji,jj,jk-1) &
	663	& + zcoef0 / e1u(ji,jj) &
	664	& * ( fse3w(ji+1,jj ,jk) * ( (rhd(ji+1,jj,jk ) + znad) &
	665	& + (rhd(ji+1,jj,jk-1) + znad) ) * tmask(ji+1,jj,jk-1) &
	666	& - fse3w(ji ,jj ,jk) * ( (rhd(ji ,jj,jk ) + znad) &
	667	& + (rhd(ji ,jj,jk-1) + znad) ) * tmask(ji ,jj,jk-1) )
[455]	668	! s-coordinate pressure gradient correction
[4990]	669	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
	670	zuap = - zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
	671	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) * umask(ji,jj,jk-1)
	672	ua(ji,jj,jk) = ua(ji,jj,jk) + ( zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
	673
	674	! hydrostatic pressure gradient along s-surfaces
	675	! zhpi is masked for the first wet cell (contribution already done in the upper bloc)
	676	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) + zhpj(ji,jj,jk-1) &
	677	& + zcoef0 / e2v(ji,jj) &
	678	& * ( fse3w(ji ,jj+1,jk) * ( (rhd(ji,jj+1,jk ) + znad) &
	679	& + (rhd(ji,jj+1,jk-1) + znad) ) * tmask(ji,jj+1,jk-1) &
	680	& - fse3w(ji ,jj ,jk) * ( (rhd(ji,jj ,jk ) + znad) &
	681	& + (rhd(ji,jj ,jk-1) + znad) ) * tmask(ji,jj ,jk-1) )
	682	! s-coordinate pressure gradient correction
	683	! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
	684	zvap = - zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
	685	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) * vmask(ji,jj,jk-1)
[455]	686	! add to the general momentum trend
[4990]	687	va(ji,jj,jk) = va(ji,jj,jk) + ( zhpj(ji,jj,jk) + zvap ) * vmask(ji,jj,jk)
[455]	688	END DO
	689	END DO
	690	END DO
[4990]	691
	692	!==================================================================================
	693	!===== Compute bottom cell contribution (partial cell) ============================
	694	!==================================================================================
	695
	696	DO jj = 2, jpjm1
	697	DO ji = 2, jpim1
	698	iku = mbku(ji,jj)
	699	ikv = mbkv(ji,jj)
	700
	701	IF (iku .GT. 1) THEN
	702	! remove old value (interior case)
	703	zuap = -zcoef0 * ( rhd (ji+1,jj ,iku) + rhd (ji,jj,iku) + 2._wp * znad ) &
	704	& * ( fsde3w(ji+1,jj ,iku) - fsde3w(ji,jj,iku) ) / e1u(ji,jj)
	705	ua(ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) - zuap
	706	! put new value
	707	! -zpshpi to avoid double contribution of the partial step in the top layer
	708	zuap = -zcoef0 * ( aru(ji,jj) + 2._wp * znad ) * gzu(ji,jj) / e1u(ji,jj)
	709	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) + zcoef0 / e1u(ji,jj) * ge3ru(ji,jj) - zpshpi(ji,jj)
	710	ua(ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) + zuap
	711	END IF
	712	! v direction
	713	IF (ikv .GT. 1) THEN
	714	! remove old value (interior case)
	715	zvap = -zcoef0 * ( rhd (ji ,jj+1,ikv) + rhd (ji,jj,ikv) + 2._wp * znad ) &
	716	& * ( fsde3w(ji ,jj+1,ikv) - fsde3w(ji,jj,ikv) ) / e2v(ji,jj)
	717	va(ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) - zvap
	718	! put new value
	719	! -zpshpj to avoid double contribution of the partial step in the top layer
	720	zvap = -zcoef0 * ( arv(ji,jj) + 2._wp * znad ) * gzv(ji,jj) / e2v(ji,jj)
	721	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) + zcoef0 / e2v(ji,jj) * ge3rv(ji,jj) - zpshpj(ji,jj)
	722	va(ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) + zvap
	723	END IF
	724	END DO
	725	END DO
	726
	727	! set back to original density value into the ice shelf cell (maybe useless because it is masked)
	728	rhd = zrhd
[503]	729	!
[4990]	730	CALL wrk_dealloc( jpi,jpj,2, ztstop)
	731	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
	732	CALL wrk_dealloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
[3294]	733	!
[5120]	734	END SUBROUTINE hpg_isf
[455]	735
[4990]	736
[455]	737	SUBROUTINE hpg_djc( kt )
	738	!!---------------------------------------------------------------------
	739	!! * ROUTINE hpg_djc *
	740	!!
	741	!! ** Method : Density Jacobian with Cubic polynomial scheme
[3764]	742	!!
[503]	743	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
[455]	744	!!----------------------------------------------------------------------
[503]	745	INTEGER, INTENT(in) :: kt ! ocean time-step index
	746	!!
	747	INTEGER :: ji, jj, jk ! dummy loop indices
	748	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
	749	REAL(wp) :: z1_10, cffu, cffx ! " "
	750	REAL(wp) :: z1_12, cffv, cffy ! " "
[3764]	751	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3294]	752	REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw
	753	REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow
	754	REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k
[455]	755	!!----------------------------------------------------------------------
[3294]	756	!
[3764]	757	CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
	758	CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
	759	CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
[3294]	760	!
[455]	761
	762	IF( kt == nit000 ) THEN
	763	IF(lwp) WRITE(numout,*)
	764	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
	765	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
[216]	766	ENDIF
	767
[503]	768	! Local constant initialization
[2528]	769	zcoef0 = - grav * 0.5_wp
	770	z1_10 = 1._wp / 10._wp
	771	z1_12 = 1._wp / 12._wp
[455]	772
	773	!----------------------------------------------------------------------------------------
	774	! compute and store in provisional arrays elementary vertical and horizontal differences
	775	!----------------------------------------------------------------------------------------
	776
	777	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
	778
	779	DO jk = 2, jpkm1
	780	DO jj = 2, jpjm1
	781	DO ji = fs_2, fs_jpim1 ! vector opt.
	782	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
	783	dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1)
	784	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
	785	dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk )
	786	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
	787	dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk )
	788	END DO
	789	END DO
	790	END DO
	791
	792	!-------------------------------------------------------------------------
	793	! compute harmonic averages using eq. 5.18
	794	!-------------------------------------------------------------------------
	795	zep = 1.e-15
	796
[503]	797	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
	798	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
[455]	799
	800	DO jk = 2, jpkm1
	801	DO jj = 2, jpjm1
	802	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	803	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
[455]	804
[2528]	805	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
	806	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
[3764]	807
[2528]	808	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
	809	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
[455]	810
	811	IF( cffw > zep) THEN
[2528]	812	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
	813	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
[455]	814	ELSE
[2528]	815	drhow(ji,jj,jk) = 0._wp
[455]	816	ENDIF
	817
[2528]	818	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
	819	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
[455]	820
	821	IF( cffu > zep ) THEN
[2528]	822	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
	823	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
[455]	824	ELSE
[2528]	825	drhou(ji,jj,jk ) = 0._wp
[455]	826	ENDIF
	827
	828	IF( cffx > zep ) THEN
[2528]	829	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
	830	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
[455]	831	ELSE
[2528]	832	dzu(ji,jj,jk) = 0._wp
[455]	833	ENDIF
	834
	835	IF( cffv > zep ) THEN
[2528]	836	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
	837	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
[455]	838	ELSE
[2528]	839	drhov(ji,jj,jk) = 0._wp
[455]	840	ENDIF
	841
	842	IF( cffy > zep ) THEN
[2528]	843	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
	844	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
[455]	845	ELSE
[2528]	846	dzv(ji,jj,jk) = 0._wp
[455]	847	ENDIF
	848
	849	END DO
	850	END DO
	851	END DO
	852
	853	!----------------------------------------------------------------------------------
	854	! apply boundary conditions at top and bottom using 5.36-5.37
	855	!----------------------------------------------------------------------------------
[2528]	856	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
	857	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
	858	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
[455]	859
[2528]	860	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
	861	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
	862	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
[455]	863
	864
	865	!--------------------------------------------------------------
	866	! Upper half of top-most grid box, compute and store
	867	!-------------------------------------------------------------
	868
	869	!!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified
	870	! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
	871
	872	DO jj = 2, jpjm1
	873	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	874	rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) &
	875	& * ( rhd(ji,jj,1) &
	876	& + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) &
	877	& * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) &
[3764]	878	& / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) )
[455]	879	END DO
	880	END DO
	881
	882	!!bug gm : here also, simplification is possible
	883	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
	884
	885	DO jk = 2, jpkm1
	886	DO jj = 2, jpjm1
	887	DO ji = fs_2, fs_jpim1 ! vector opt.
	888
	889	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
	890	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) &
	891	& - grav * z1_10 * ( &
	892	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
	893	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
	894	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
	895	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
	896	& )
	897
	898	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
	899	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) &
	900	& - grav* z1_10 * ( &
	901	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
	902	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
	903	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
	904	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
	905	& )
	906
	907	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
	908	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) &
	909	& - grav* z1_10 * ( &
	910	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
	911	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
	912	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
	913	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
	914	& )
	915
	916	END DO
	917	END DO
	918	END DO
	919	CALL lbc_lnk(rho_k,'W',1.)
	920	CALL lbc_lnk(rho_i,'U',1.)
	921	CALL lbc_lnk(rho_j,'V',1.)
	922
	923
	924	! ---------------
	925	! Surface value
	926	! ---------------
	927	DO jj = 2, jpjm1
	928	DO ji = fs_2, fs_jpim1 ! vector opt.
	929	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj)
	930	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj)
	931	! add to the general momentum trend
	932	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
	933	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
	934	END DO
	935	END DO
	936
	937	! ----------------
	938	! interior value (2=<jk=<jpkm1)
	939	! ----------------
	940	DO jk = 2, jpkm1
[3764]	941	DO jj = 2, jpjm1
[455]	942	DO ji = fs_2, fs_jpim1 ! vector opt.
	943	! hydrostatic pressure gradient along s-surfaces
	944	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
	945	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
	946	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj)
	947	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
	948	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
	949	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj)
	950	! add to the general momentum trend
	951	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	952	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
	953	END DO
	954	END DO
	955	END DO
[503]	956	!
[3764]	957	CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
	958	CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
	959	CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
[2715]	960	!
[455]	961	END SUBROUTINE hpg_djc
	962
	963
[3294]	964	SUBROUTINE hpg_prj( kt )
[455]	965	!!---------------------------------------------------------------------
[3294]	966	!! * ROUTINE hpg_prj *
[455]	967	!!
[3294]	968	!! ** Method : s-coordinate case.
	969	!! A Pressure-Jacobian horizontal pressure gradient method
	970	!! based on the constrained cubic-spline interpolation for
	971	!! all vertical coordinate systems
[455]	972	!!
[3294]	973	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[455]	974	!!----------------------------------------------------------------------
[3294]	975	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
	976	INTEGER, INTENT(in) :: kt ! ocean time-step index
[503]	977	!!
[3294]	978	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
	979	REAL(wp) :: zcoef0, znad ! temporary scalars
[503]	980	!!
[3294]	981	!! The local variables for the correction term
	982	INTEGER :: jk1, jis, jid, jjs, jjd
	983	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
[3764]	984	REAL(wp) :: zrhdt1
[3294]	985	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
[3764]	986	REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh
[3294]	987	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
[5224]	988	REAL(wp), POINTER, DIMENSION(:,:) :: zsshu_n, zsshv_n
[455]	989	!!----------------------------------------------------------------------
[3294]	990	!
[3764]	991	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
	992	CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh )
[5224]	993	CALL wrk_alloc( jpi,jpj, zsshu_n, zsshv_n )
[3294]	994	!
[455]	995	IF( kt == nit000 ) THEN
	996	IF(lwp) WRITE(numout,*)
[3294]	997	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
	998	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
[3]	999	ENDIF
	1000
[3294]	1001	!!----------------------------------------------------------------------
	1002	! Local constant initialization
[3764]	1003	zcoef0 = - grav
[3294]	1004	znad = 0.0_wp
	1005	IF( lk_vvl ) znad = 1._wp
[3]	1006
[3294]	1007	! Clean 3-D work arrays
	1008	zhpi(:,:,:) = 0._wp
	1009	zrhh(:,:,:) = rhd(:,:,:)
[3764]	1010
[3294]	1011	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
	1012	DO jj = 1, jpj
[3764]	1013	DO ji = 1, jpi
[3294]	1014	jk = mbathy(ji,jj)
	1015	IF( jk <= 0 ) THEN; zrhh(ji,jj,:) = 0._wp
	1016	ELSE IF(jk == 1) THEN; zrhh(ji,jj, jk+1:jpk) = rhd(ji,jj,jk)
	1017	ELSE IF(jk < jpkm1) THEN
	1018	DO jkk = jk+1, jpk
	1019	zrhh(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1), &
	1020	fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2))
[3764]	1021	END DO
[3294]	1022	ENDIF
	1023	END DO
	1024	END DO
[3]	1025
[3632]	1026	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
[4990]	1027	DO jj = 1, jpj
	1028	DO ji = 1, jpi
	1029	zdept(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) - sshn(ji,jj) * znad
	1030	END DO
	1031	END DO
[455]	1032
[4990]	1033	DO jk = 2, jpk
	1034	DO jj = 1, jpj
	1035	DO ji = 1, jpi
	1036	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + fse3w(ji,jj,jk)
	1037	END DO
	1038	END DO
	1039	END DO
[455]	1040
[4990]	1041	fsp(:,:,:) = zrhh (:,:,:)
[3632]	1042	xsp(:,:,:) = zdept(:,:,:)
	1043
[3764]	1044	! Construct the vertical density profile with the
[3294]	1045	! constrained cubic spline interpolation
	1046	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
[3764]	1047	CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type)
[3294]	1048
	1049	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
	1050	DO jj = 2, jpj
[3764]	1051	DO ji = 2, jpi
[3632]	1052	zrhdt1 = zrhh(ji,jj,1) - interp3(zdept(ji,jj,1),asp(ji,jj,1), &
[3294]	1053	bsp(ji,jj,1), csp(ji,jj,1), &
[3632]	1054	dsp(ji,jj,1) ) * 0.25_wp * fse3w(ji,jj,1)
[3294]	1055
	1056	! assuming linear profile across the top half surface layer
[3764]	1057	zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * zrhdt1
[3294]	1058	END DO
[455]	1059	END DO
	1060
[3294]	1061	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
[3764]	1062	DO jk = 2, jpkm1
	1063	DO jj = 2, jpj
[3294]	1064	DO ji = 2, jpi
	1065	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
[3632]	1066	integ_spline(zdept(ji,jj,jk-1), zdept(ji,jj,jk),&
[3294]	1067	asp(ji,jj,jk-1), bsp(ji,jj,jk-1), &
	1068	csp(ji,jj,jk-1), dsp(ji,jj,jk-1))
	1069	END DO
	1070	END DO
[455]	1071	END DO
	1072
[3294]	1073	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
[5224]	1074
	1075	! Prepare zsshu_n and zsshv_n
[3764]	1076	DO jj = 2, jpjm1
	1077	DO ji = 2, jpim1
[5224]	1078	zsshu_n(ji,jj) = (e12u(ji,jj) * sshn(ji,jj) + e12u(ji+1, jj) * sshn(ji+1,jj)) * &
	1079	& r1_e12u(ji,jj) * umask(ji,jj,1) * 0.5_wp
	1080	zsshv_n(ji,jj) = (e12v(ji,jj) * sshn(ji,jj) + e12v(ji+1, jj) * sshn(ji,jj+1)) * &
	1081	& r1_e12v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
[3294]	1082	END DO
[455]	1083	END DO
	1084
[5224]	1085	DO jj = 2, jpjm1
	1086	DO ji = 2, jpim1
	1087	zu(ji,jj,1) = - ( fse3u(ji,jj,1) - zsshu_n(ji,jj) * znad)
	1088	zv(ji,jj,1) = - ( fse3v(ji,jj,1) - zsshv_n(ji,jj) * znad)
	1089	END DO
	1090	END DO
	1091
[3764]	1092	DO jk = 2, jpkm1
	1093	DO jj = 2, jpjm1
	1094	DO ji = 2, jpim1
[3294]	1095	zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk)
	1096	zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk)
	1097	END DO
	1098	END DO
[455]	1099	END DO
[3764]	1100
	1101	DO jk = 1, jpkm1
	1102	DO jj = 2, jpjm1
	1103	DO ji = 2, jpim1
[3294]	1104	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk)
	1105	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk)
	1106	END DO
	1107	END DO
	1108	END DO
[455]	1109
[3632]	1110	DO jk = 1, jpkm1
	1111	DO jj = 2, jpjm1
	1112	DO ji = 2, jpim1
	1113	zu(ji,jj,jk) = min(zu(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
	1114	zu(ji,jj,jk) = max(zu(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
	1115	zv(ji,jj,jk) = min(zv(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
	1116	zv(ji,jj,jk) = max(zv(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
	1117	END DO
	1118	END DO
	1119	END DO
	1120
	1121
[3764]	1122	DO jk = 1, jpkm1
	1123	DO jj = 2, jpjm1
	1124	DO ji = 2, jpim1
[3294]	1125	zpwes = 0._wp; zpwed = 0._wp
	1126	zpnss = 0._wp; zpnsd = 0._wp
	1127	zuijk = zu(ji,jj,jk)
	1128	zvijk = zv(ji,jj,jk)
	1129
	1130	!!!!! for u equation
	1131	IF( jk <= mbku(ji,jj) ) THEN
[3632]	1132	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
[3294]	1133	jis = ji + 1; jid = ji
	1134	ELSE
	1135	jis = ji; jid = ji +1
	1136	ENDIF
	1137
	1138	! integrate the pressure on the shallow side
[3764]	1139	jk1 = jk
[3632]	1140	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
[3294]	1141	IF( jk1 == mbku(ji,jj) ) THEN
[3632]	1142	zuijk = -zdept(jis,jj,jk1)
[3294]	1143	EXIT
	1144	ENDIF
[3632]	1145	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
[3764]	1146	zpwes = zpwes + &
[3632]	1147	integ_spline(zdept(jis,jj,jk1), zdeps, &
[3294]	1148	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
	1149	csp(jis,jj,jk1), dsp(jis,jj,jk1))
	1150	jk1 = jk1 + 1
	1151	END DO
[3764]	1152
[3294]	1153	! integrate the pressure on the deep side
[3764]	1154	jk1 = jk
[3632]	1155	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
[3294]	1156	IF( jk1 == 1 ) THEN
[3632]	1157	zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad)
	1158	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
	1159	bsp(jid,jj,1), csp(jid,jj,1), &
	1160	dsp(jid,jj,1)) * zdeps
	1161	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
[3294]	1162	EXIT
	1163	ENDIF
[3632]	1164	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
[3764]	1165	zpwed = zpwed + &
[3632]	1166	integ_spline(zdeps, zdept(jid,jj,jk1), &
[3294]	1167	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
	1168	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
	1169	jk1 = jk1 - 1
	1170	END DO
[3764]	1171
[3294]	1172	! update the momentum trends in u direction
	1173
	1174	zdpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk))
	1175	IF( lk_vvl ) THEN
[3764]	1176	zdpdx2 = zcoef0 / e1u(ji,jj) * &
	1177	( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) )
[3294]	1178	ELSE
[3764]	1179	zdpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
[3294]	1180	ENDIF
	1181
	1182	ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * &
	1183	& umask(ji,jj,jk) * tmask(ji,jj,jk) * tmask(ji+1,jj,jk)
	1184	ENDIF
[3764]	1185
[3294]	1186	!!!!! for v equation
	1187	IF( jk <= mbkv(ji,jj) ) THEN
[3632]	1188	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
[3294]	1189	jjs = jj + 1; jjd = jj
	1190	ELSE
	1191	jjs = jj ; jjd = jj + 1
	1192	ENDIF
	1193
	1194	! integrate the pressure on the shallow side
[3764]	1195	jk1 = jk
[3632]	1196	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
[3294]	1197	IF( jk1 == mbkv(ji,jj) ) THEN
[3632]	1198	zvijk = -zdept(ji,jjs,jk1)
[3294]	1199	EXIT
	1200	ENDIF
[3632]	1201	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
[3764]	1202	zpnss = zpnss + &
[3632]	1203	integ_spline(zdept(ji,jjs,jk1), zdeps, &
[3294]	1204	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
	1205	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
	1206	jk1 = jk1 + 1
	1207	END DO
[3764]	1208
[3294]	1209	! integrate the pressure on the deep side
[3764]	1210	jk1 = jk
[3632]	1211	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
[3294]	1212	IF( jk1 == 1 ) THEN
[3632]	1213	zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad)
	1214	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
	1215	bsp(ji,jjd,1), csp(ji,jjd,1), &
	1216	dsp(ji,jjd,1) ) * zdeps
	1217	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
[3294]	1218	EXIT
	1219	ENDIF
[3632]	1220	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
[3764]	1221	zpnsd = zpnsd + &
[3632]	1222	integ_spline(zdeps, zdept(ji,jjd,jk1), &
[3294]	1223	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
	1224	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
	1225	jk1 = jk1 - 1
	1226	END DO
	1227
[3764]	1228
[3294]	1229	! update the momentum trends in v direction
	1230
	1231	zdpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk))
	1232	IF( lk_vvl ) THEN
	1233	zdpdy2 = zcoef0 / e2v(ji,jj) * &
[3764]	1234	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) )
[3294]	1235	ELSE
[3764]	1236	zdpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
[3294]	1237	ENDIF
	1238
	1239	va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2)*&
	1240	& vmask(ji,jj,jk)tmask(ji,jj,jk)tmask(ji,jj+1,jk)
	1241	ENDIF
	1242
[3764]	1243
[3294]	1244	END DO
	1245	END DO
[455]	1246	END DO
[503]	1247	!
[3764]	1248	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
	1249	CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh )
[5224]	1250	CALL wrk_dealloc( jpi,jpj, zsshu_n, zsshv_n )
[2715]	1251	!
[3294]	1252	END SUBROUTINE hpg_prj
[455]	1253
[4990]	1254
[3294]	1255	SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type)
	1256	!!----------------------------------------------------------------------
	1257	!! * ROUTINE cspline *
[3764]	1258	!!
[3294]	1259	!! ** Purpose : constrained cubic spline interpolation
[3764]	1260	!!
	1261	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
[4990]	1262	!!
[3294]	1263	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
	1264	!!----------------------------------------------------------------------
	1265	IMPLICIT NONE
	1266	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate
[3764]	1267	REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of
[3294]	1268	! the interpoated function
[3764]	1269	INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline
[3294]	1270	! 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	!!----------------------------------------------------------------------
	1278
	1279	jpi = size(fsp,1)
	1280	jpj = size(fsp,2)
	1281	jpkm1 = size(fsp,3) - 1
	1282
[3764]	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
	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) ) / &
	1316	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
	1317	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
	1318	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - &
	1319	& 0.5_wp * zdf(jpkm1 - 1)
[3764]	1320
[3294]	1321	DO jk = 1, jpkm1 - 1
[3764]	1322	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1323	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
	1324	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
[3764]	1325	zddf1 = -2._wp * ztmp1 + ztmp2
[3294]	1326	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
[3764]	1327	zddf2 = 2._wp * ztmp1 - ztmp2
	1328
[3294]	1329	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
	1330	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
[3764]	1331	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
[3294]	1332	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
	1333	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
	1334	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
	1335	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
	1336	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
	1337	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
	1338	END DO
	1339	END DO
	1340	END DO
[3764]	1341
[3294]	1342	ELSE IF (polynomial_type == 2) THEN ! Linear
	1343	DO ji = 1, jpi
	1344	DO jj = 1, jpj
	1345	DO jk = 1, jpkm1-1
[3764]	1346	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1347	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
[3764]	1348
[3294]	1349	dsp(ji,jj,jk) = 0._wp
	1350	csp(ji,jj,jk) = 0._wp
	1351	bsp(ji,jj,jk) = ztmp1 / zdxtmp
	1352	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
	1353	END DO
	1354	END DO
	1355	END DO
	1356
	1357	ELSE
	1358	CALL ctl_stop( 'invalid polynomial type in cspline' )
	1359	ENDIF
	1360
	1361	END SUBROUTINE cspline
	1362
	1363
[3764]	1364	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
[3294]	1365	!!----------------------------------------------------------------------
	1366	!! * ROUTINE interp1 *
[3764]	1367	!!
[3294]	1368	!! ** Purpose : 1-d linear interpolation
[3764]	1369	!!
[4990]	1370	!! ** Method : interpolation is straight forward
[3764]	1371	!! extrapolation is also permitted (no value limit)
[3294]	1372	!!----------------------------------------------------------------------
	1373	IMPLICIT NONE
[3764]	1374	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
[3294]	1375	REAL(wp) :: f ! result of the interpolation (extrapolation)
	1376	REAL(wp) :: zdeltx
	1377	!!----------------------------------------------------------------------
	1378
	1379	zdeltx = xr - xl
	1380	IF(abs(zdeltx) <= 10._wp * EPSILON(x)) THEN
	1381	f = 0.5_wp * (fl + fr)
	1382	ELSE
	1383	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
	1384	ENDIF
[3764]	1385
[3294]	1386	END FUNCTION interp1
	1387
[4990]	1388
[3764]	1389	FUNCTION interp2(x, a, b, c, d) RESULT(f)
[3294]	1390	!!----------------------------------------------------------------------
	1391	!! * ROUTINE interp1 *
[3764]	1392	!!
[3294]	1393	!! ** Purpose : 1-d constrained cubic spline interpolation
[3764]	1394	!!
[3294]	1395	!! ** Method : cubic spline interpolation
	1396	!!
	1397	!!----------------------------------------------------------------------
	1398	IMPLICIT NONE
[3764]	1399	REAL(wp), INTENT(in) :: x, a, b, c, d
[3294]	1400	REAL(wp) :: f ! value from the interpolation
	1401	!!----------------------------------------------------------------------
	1402
[3764]	1403	f = a + x* ( b + x * ( c + d * x ) )
[3294]	1404
	1405	END FUNCTION interp2
	1406
	1407
[3764]	1408	FUNCTION interp3(x, a, b, c, d) RESULT(f)
[3294]	1409	!!----------------------------------------------------------------------
	1410	!! * ROUTINE interp1 *
[3764]	1411	!!
[3294]	1412	!! ** Purpose : Calculate the first order of deriavtive of
	1413	!! a cubic spline function y=a+bx+cx^2+d*x^3
[3764]	1414	!!
[3294]	1415	!! ** Method : f=dy/dx=b+2cx+3dx^2
	1416	!!
	1417	!!----------------------------------------------------------------------
	1418	IMPLICIT NONE
[3764]	1419	REAL(wp), INTENT(in) :: x, a, b, c, d
[3294]	1420	REAL(wp) :: f ! value from the interpolation
	1421	!!----------------------------------------------------------------------
	1422
	1423	f = b + x * ( 2._wp * c + 3._wp * d * x)
	1424
	1425	END FUNCTION interp3
	1426
[3764]	1427
	1428	FUNCTION integ_spline(xl, xr, a, b, c, d) RESULT(f)
[3294]	1429	!!----------------------------------------------------------------------
	1430	!! * ROUTINE interp1 *
[3764]	1431	!!
[3294]	1432	!! ** Purpose : 1-d constrained cubic spline integration
	1433	!!
[3764]	1434	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
	1435	!!
[3294]	1436	!!----------------------------------------------------------------------
	1437	IMPLICIT NONE
[3764]	1438	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
	1439	REAL(wp) :: za1, za2, za3
[3294]	1440	REAL(wp) :: f ! integration result
	1441	!!----------------------------------------------------------------------
	1442
[3764]	1443	za1 = 0.5_wp * b
	1444	za2 = c / 3.0_wp
	1445	za3 = 0.25_wp * d
[3294]	1446
	1447	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
	1448	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
	1449
[3632]	1450	END FUNCTION integ_spline
[3294]	1451
[3]	1452	!!======================================================================
	1453	END MODULE dynhpg
[3632]	1454

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