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dynhpg.F90 in branches/2014/dev_r4650_UKMO2_ice_shelves/NEMOGCM/NEMO/OPA_SRC/DYN – NEMO

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source: branches/2014/dev_r4650_UKMO2_ice_shelves/NEMOGCM/NEMO/OPA_SRC/DYN/dynhpg.F90 @ 4726

Last change on this file since 4726 was 4726, checked in by mathiot, 10 years ago
ISF branch: change name of 2 variables (icedep => risfdep and lmask => ssmask), cosmetic changes and add ldfslp key
Property svn:keywords set to `Id`
File size: 63.2 KB

Rev	Line
[3]	1	MODULE dynhpg
	2	!!======================================================================
	3	!! * MODULE dynhpg *
	4	!! Ocean dynamics: hydrostatic pressure gradient trend
	5	!!======================================================================
[2528]	6	!! History : OPA ! 1987-09 (P. Andrich, M.-A. Foujols) hpg_zco: Original code
	7	!! 5.0 ! 1991-11 (G. Madec)
	8	!! 7.0 ! 1996-01 (G. Madec) hpg_sco: Original code for s-coordinates
	9	!! 8.0 ! 1997-05 (G. Madec) split dynber into dynkeg and dynhpg
	10	!! 8.5 ! 2002-07 (G. Madec) F90: Free form and module
	11	!! 8.5 ! 2002-08 (A. Bozec) hpg_zps: Original code
	12	!! NEMO 1.0 ! 2005-10 (A. Beckmann, B.W. An) various s-coordinate options
[3764]	13	!! ! Original code for hpg_ctl, hpg_hel hpg_wdj, hpg_djc, hpg_rot
[2528]	14	!! - ! 2005-11 (G. Madec) style & small optimisation
	15	!! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase
[3294]	16	!! 3.4 ! 2011-11 (H. Liu) hpg_prj: Original code for s-coordinates
	17	!! ! (A. Coward) suppression of hel, wdj and rot options
[503]	18	!!----------------------------------------------------------------------
[3]	19
	20	!!----------------------------------------------------------------------
[455]	21	!! dyn_hpg : update the momentum trend with the now horizontal
[3]	22	!! gradient of the hydrostatic pressure
[2528]	23	!! dyn_hpg_init : initialisation and control of options
[455]	24	!! hpg_zco : z-coordinate scheme
	25	!! hpg_zps : z-coordinate plus partial steps (interpolation)
	26	!! hpg_sco : s-coordinate (standard jacobian formulation)
	27	!! hpg_djc : s-coordinate (Density Jacobian with Cubic polynomial)
[3294]	28	!! hpg_prj : s-coordinate (Pressure Jacobian with Cubic polynomial)
[3]	29	!!----------------------------------------------------------------------
	30	USE oce ! ocean dynamics and tracers
[4724]	31	USE sbc_oce ! surface variable (only for the flag with ice shelf)
[3]	32	USE dom_oce ! ocean space and time domain
	33	USE phycst ! physical constants
[3764]	34	USE trdmod ! ocean dynamics trends
[216]	35	USE trdmod_oce ! ocean variables trends
[2715]	36	USE in_out_manager ! I/O manager
[258]	37	USE prtctl ! Print control
[3764]	38	USE lbclnk ! lateral boundary condition
[2715]	39	USE lib_mpp ! MPP library
[4666]	40	USE eosbn2 ! compute density
[3294]	41	USE wrk_nemo ! Memory Allocation
	42	USE timing ! Timing
[3]	43
	44	IMPLICIT NONE
	45	PRIVATE
	46
[2528]	47	PUBLIC dyn_hpg ! routine called by step module
	48	PUBLIC dyn_hpg_init ! routine called by opa module
[3]	49
[4147]	50	! !!* Namelist namdyn_hpg : hydrostatic pressure gradient
	51	LOGICAL , PUBLIC :: ln_hpg_zco !: z-coordinate - full steps
	52	LOGICAL , PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation)
	53	LOGICAL , PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation)
	54	LOGICAL , PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial)
	55	LOGICAL , PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme)
	56	LOGICAL , PUBLIC :: ln_dynhpg_imp !: semi-implicite hpg flag
[455]	57
[3764]	58	INTEGER , PUBLIC :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM)
[455]	59
[3]	60	!! * Substitutions
	61	# include "domzgr_substitute.h90"
	62	# include "vectopt_loop_substitute.h90"
	63	!!----------------------------------------------------------------------
[2528]	64	!! NEMO/OPA 3.3 , NEMO Consortium (2010)
	65	!! $Id$
	66	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
[3]	67	!!----------------------------------------------------------------------
	68	CONTAINS
	69
	70	SUBROUTINE dyn_hpg( kt )
	71	!!---------------------------------------------------------------------
	72	!! * ROUTINE dyn_hpg *
	73	!!
[3764]	74	!! ** Method : Call the hydrostatic pressure gradient routine
[503]	75	!! using the scheme defined in the namelist
[3764]	76	!!
[455]	77	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
	78	!! - Save the trend (l_trddyn=T)
[503]	79	!!----------------------------------------------------------------------
	80	INTEGER, INTENT(in) :: kt ! ocean time-step index
[3294]	81	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdu, ztrdv
[455]	82	!!----------------------------------------------------------------------
[2528]	83	!
[3294]	84	IF( nn_timing == 1 ) CALL timing_start('dyn_hpg')
[2715]	85	!
[503]	86	IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn)
[3294]	87	CALL wrk_alloc( jpi,jpj,jpk, ztrdu, ztrdv )
[3764]	88	ztrdu(:,:,:) = ua(:,:,:)
	89	ztrdv(:,:,:) = va(:,:,:)
	90	ENDIF
[2528]	91	!
[3294]	92	SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation
[503]	93	CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate
	94	CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation)
	95	CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation)
[3294]	96	CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial)
	97	CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme)
[455]	98	END SELECT
[2528]	99	!
[503]	100	IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics
[455]	101	ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:)
	102	ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:)
[503]	103	CALL trd_mod( ztrdu, ztrdv, jpdyn_trd_hpg, 'DYN', kt )
[3294]	104	CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv )
[3764]	105	ENDIF
[503]	106	!
	107	IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, &
	108	& tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' )
	109	!
[3294]	110	IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg')
[2715]	111	!
[455]	112	END SUBROUTINE dyn_hpg
	113
	114
[2528]	115	SUBROUTINE dyn_hpg_init
[455]	116	!!----------------------------------------------------------------------
[2528]	117	!! * ROUTINE dyn_hpg_init *
[455]	118	!!
	119	!! ** Purpose : initializations for the hydrostatic pressure gradient
	120	!! computation and consistency control
	121	!!
[1601]	122	!! ** Action : Read the namelist namdyn_hpg and check the consistency
[455]	123	!! with the type of vertical coordinate used (zco, zps, sco)
	124	!!----------------------------------------------------------------------
	125	INTEGER :: ioptio = 0 ! temporary integer
[4147]	126	INTEGER :: ios ! Local integer output status for namelist read
[1601]	127	!!
[3294]	128	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
	129	& ln_hpg_djc, ln_hpg_prj, ln_dynhpg_imp
[455]	130	!!----------------------------------------------------------------------
[2528]	131	!
[4147]	132	REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient
	133	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
	134	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp )
	135
	136	REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient
	137	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
	138	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp )
[4666]	139	WRITE ( numond, namdyn_hpg )
[2528]	140	!
	141	IF(lwp) THEN ! Control print
[455]	142	WRITE(numout,*)
[2528]	143	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
	144	WRITE(numout,*) '~~~~~~~~~~~~'
[1601]	145	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
	146	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
	147	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
	148	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
	149	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
[3294]	150	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
[1601]	151	WRITE(numout,*) ' time stepping: centered (F) or semi-implicit (T) ln_dynhpg_imp = ', ln_dynhpg_imp
[455]	152	ENDIF
[2528]	153	!
[3294]	154	IF( ln_hpg_djc ) &
	155	& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method &
	156	& currently disabled (bugs under investigation). Please select &
	157	& either ln_hpg_sco or ln_hpg_prj instead')
[2528]	158	!
[3294]	159	IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj) ) &
	160	& CALL ctl_stop('dyn_hpg_init : variable volume key_vvl requires:&
	161	& the standard jacobian formulation hpg_sco or &
	162	& the pressure jacobian formulation hpg_prj')
	163	!
[503]	164	! ! Set nhpg from ln_hpg_... flags
[455]	165	IF( ln_hpg_zco ) nhpg = 0
	166	IF( ln_hpg_zps ) nhpg = 1
	167	IF( ln_hpg_sco ) nhpg = 2
[3294]	168	IF( ln_hpg_djc ) nhpg = 3
	169	IF( ln_hpg_prj ) nhpg = 4
[2528]	170	!
[3294]	171	! ! Consistency check
[3764]	172	ioptio = 0
[455]	173	IF( ln_hpg_zco ) ioptio = ioptio + 1
	174	IF( ln_hpg_zps ) ioptio = ioptio + 1
	175	IF( ln_hpg_sco ) ioptio = ioptio + 1
	176	IF( ln_hpg_djc ) ioptio = ioptio + 1
[3294]	177	IF( ln_hpg_prj ) ioptio = ioptio + 1
[2715]	178	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
[4724]	179	IF( (ln_hpg_zco .OR. ln_hpg_zps .OR. ln_hpg_djc .OR. ln_hpg_prj ) .AND. nn_isf .NE. 0 ) CALL ctl_stop( 'Only hpg_sco has been corrected to work with ice shelf cavity. Comparison in a GYRE simulation with bump in the middle show similar result than hpg_zps' )
[503]	180	!
[2528]	181	END SUBROUTINE dyn_hpg_init
[455]	182
	183
	184	SUBROUTINE hpg_zco( kt )
	185	!!---------------------------------------------------------------------
	186	!! * ROUTINE hpg_zco *
	187	!!
	188	!! ** Method : z-coordinate case, levels are horizontal surfaces.
	189	!! The now hydrostatic pressure gradient at a given level, jk,
	190	!! is computed by taking the vertical integral of the in-situ
	191	!! density gradient along the model level from the suface to that
	192	!! level: zhpi = grav .....
	193	!! zhpj = grav .....
[3]	194	!! add it to the general momentum trend (ua,va).
[455]	195	!! ua = ua - 1/e1u * zhpi
	196	!! va = va - 1/e2v * zhpj
[3764]	197	!!
[3]	198	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[503]	199	!!----------------------------------------------------------------------
	200	INTEGER, INTENT(in) :: kt ! ocean time-step index
	201	!!
	202	INTEGER :: ji, jj, jk ! dummy loop indices
	203	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
[3764]	204	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3]	205	!!----------------------------------------------------------------------
[3764]	206	!
[3294]	207	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
	208	!
[3]	209	IF( kt == nit000 ) THEN
	210	IF(lwp) WRITE(numout,*)
[455]	211	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
	212	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
[3]	213	ENDIF
	214
[3764]	215	zcoef0 = - grav * 0.5_wp ! Local constant initialization
	216
[455]	217	! Surface value
[3]	218	DO jj = 2, jpjm1
	219	DO ji = fs_2, fs_jpim1 ! vector opt.
[455]	220	zcoef1 = zcoef0 * fse3w(ji,jj,1)
	221	! hydrostatic pressure gradient
	222	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
	223	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
[3]	224	! add to the general momentum trend
[455]	225	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
	226	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
	227	END DO
	228	END DO
[3294]	229
[503]	230	!
[455]	231	! interior value (2=<jk=<jpkm1)
[3]	232	DO jk = 2, jpkm1
[455]	233	DO jj = 2, jpjm1
[3]	234	DO ji = fs_2, fs_jpim1 ! vector opt.
[455]	235	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
	236	! hydrostatic pressure gradient
	237	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
	238	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
	239	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
	240
	241	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
	242	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
	243	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
[3]	244	! add to the general momentum trend
[455]	245	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	246	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
[3]	247	END DO
	248	END DO
	249	END DO
[503]	250	!
[3294]	251	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
	252	!
[455]	253	END SUBROUTINE hpg_zco
[216]	254
[3]	255
[455]	256	SUBROUTINE hpg_zps( kt )
[3]	257	!!---------------------------------------------------------------------
[455]	258	!! * ROUTINE hpg_zps *
[3764]	259	!!
[455]	260	!! ** Method : z-coordinate plus partial steps case. blahblah...
[3764]	261	!!
[3]	262	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[3764]	263	!!----------------------------------------------------------------------
[503]	264	INTEGER, INTENT(in) :: kt ! ocean time-step index
	265	!!
	266	INTEGER :: ji, jj, jk ! dummy loop indices
	267	INTEGER :: iku, ikv ! temporary integers
	268	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
[3764]	269	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3]	270	!!----------------------------------------------------------------------
[3294]	271	!
	272	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
	273	!
[3]	274	IF( kt == nit000 ) THEN
	275	IF(lwp) WRITE(numout,*)
[455]	276	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
[503]	277	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
[3]	278	ENDIF
	279
[3294]	280
[503]	281	! Local constant initialization
[2528]	282	zcoef0 = - grav * 0.5_wp
[3]	283
[2528]	284	! Surface value (also valid in partial step case)
[3]	285	DO jj = 2, jpjm1
	286	DO ji = fs_2, fs_jpim1 ! vector opt.
[170]	287	zcoef1 = zcoef0 * fse3w(ji,jj,1)
[3]	288	! hydrostatic pressure gradient
[455]	289	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj)
	290	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj)
[3]	291	! add to the general momentum trend
	292	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
	293	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
	294	END DO
	295	END DO
	296
[3294]	297
[503]	298	! interior value (2=<jk=<jpkm1)
[3]	299	DO jk = 2, jpkm1
	300	DO jj = 2, jpjm1
	301	DO ji = fs_2, fs_jpim1 ! vector opt.
[170]	302	zcoef1 = zcoef0 * fse3w(ji,jj,jk)
[3]	303	! hydrostatic pressure gradient
	304	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
[455]	305	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
	306	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj)
[3]	307
	308	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
[455]	309	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
	310	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj)
[3]	311	! add to the general momentum trend
	312	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	313	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
[455]	314	END DO
[3]	315	END DO
	316	END DO
	317
[3294]	318
[2528]	319	! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
[3]	320	# if defined key_vectopt_loop
	321	jj = 1
	322	DO ji = jpi+2, jpij-jpi-1 ! vector opt. (forced unrolling)
	323	# else
	324	DO jj = 2, jpjm1
	325	DO ji = 2, jpim1
	326	# endif
[2528]	327	iku = mbku(ji,jj)
	328	ikv = mbkv(ji,jj)
[3]	329	zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) )
	330	zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) )
[2528]	331	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
	332	ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value
	333	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
	334	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj)
	335	ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
[3]	336	ENDIF
[2528]	337	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
	338	va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value
	339	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
	340	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj)
	341	va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
[3]	342	ENDIF
	343	# if ! defined key_vectopt_loop
	344	END DO
	345	# endif
	346	END DO
[503]	347	!
[3294]	348	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
	349	!
[455]	350	END SUBROUTINE hpg_zps
[216]	351
[3]	352
[455]	353	SUBROUTINE hpg_sco( kt )
[3]	354	!!---------------------------------------------------------------------
[455]	355	!! * ROUTINE hpg_sco *
[3]	356	!!
[455]	357	!! ** Method : s-coordinate case. Jacobian scheme.
	358	!! The now hydrostatic pressure gradient at a given level, jk,
	359	!! is computed by taking the vertical integral of the in-situ
[3]	360	!! density gradient along the model level from the suface to that
[455]	361	!! level. s-coordinates (ln_sco): a corrective term is added
	362	!! to the horizontal pressure gradient :
	363	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
	364	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
[3]	365	!! add it to the general momentum trend (ua,va).
[455]	366	!! ua = ua - 1/e1u * zhpi
	367	!! va = va - 1/e2v * zhpj
[3]	368	!!
	369	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[503]	370	!!----------------------------------------------------------------------
	371	INTEGER, INTENT(in) :: kt ! ocean time-step index
	372	!!
[4666]	373	INTEGER :: ji, jj, jk, iku, ikv, ikt, iktp1i, iktp1j ! dummy loop indices
	374	REAL(wp) :: zcoef0, zuap, zvap, znad, ze3wu, ze3wv, zuapint, zvapint, zhpjint, zhpiint, zdzwt, zdzwtjp1, zdzwtip1 ! temporary scalars
	375	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj, zrhd
	376	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop
	377	REAL(wp), POINTER, DIMENSION(:,:) :: ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj
[3]	378	!!----------------------------------------------------------------------
[3294]	379	!
[4666]	380	CALL wrk_alloc( jpi,jpj, 2, ztstop)
	381	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
	382	CALL wrk_alloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
[3294]	383	!
[4666]	384	IF( kt == nit000 ) THEN
[3]	385	IF(lwp) WRITE(numout,*)
[455]	386	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
	387	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
[3]	388	ENDIF
	389
[503]	390	! Local constant initialization
[2528]	391	zcoef0 = - grav * 0.5_wp
[592]	392	! To use density and not density anomaly
[4666]	393	! IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume
	394	! ELSE ; znad = 0._wp ! Fixed volume
	395	! ENDIF
	396	znad=1._wp
	397	! iniitialised to 0. zhpi zhpi
	398	zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp
[4724]	399
	400	! assume density of water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude)
[4666]	401	ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp
[4724]	402	zrhd = rhd ! save rhd
[4666]	403	DO jk = 1, jpk
	404	zdept(:,:)=gdept_1d(jk)
	405	CALL eos(ztstop(:,:,:),zdept(:,:),rhd(:,:,jk))
	406	END DO
	407	WHERE ( tmask(:,:,:) == 1._wp)
[4724]	408	rhd(:,:,:) = zrhd(:,:,:) ! replace wet cell by the saved rhd
[4666]	409	END WHERE
	410
[4724]	411	! compute rhd at the ice/oce interface (ice shelf side)
[4726]	412	CALL eos(ztstop,risfdep,zrhdtop_isf)
[4666]	413
[4724]	414	! compute rhd at the ice/oce interface (ocean side)
[4666]	415	DO ji=1,jpi
	416	DO jj=1,jpj
	417	ikt=mikt(ji,jj)
	418	ztstop(ji,jj,1)=tsn(ji,jj,ikt,1)
	419	ztstop(ji,jj,2)=tsn(ji,jj,ikt,2)
	420	END DO
	421	END DO
[4726]	422	CALL eos(ztstop,risfdep,zrhdtop_oce)
[4666]	423	!
	424	! Surface value + ice shelf gradient
[4724]	425	! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v)
[4666]	426	ziceload = 0._wp
	427	DO jj = 1, jpj
	428	DO ji = 1, jpi ! vector opt.
	429	ikt=mikt(ji,jj)
	430	ziceload(ji,jj) = ziceload(ji,jj) + (znad + rhd(ji,jj,1) ) * fse3w(ji,jj,1) * (1._wp - tmask(ji,jj,1))
	431	DO jk=2,ikt-1
	432	ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + rhd(ji,jj,jk-1) + rhd(ji,jj,jk)) * fse3w(ji,jj,jk) &
	433	& * (1._wp - tmask(ji,jj,jk))
	434	END DO
	435	IF (ikt .GE. 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + rhd(ji,jj,ikt-1)) &
	436	& * ( fsdepw(ji,jj,ikt) - gdept_1d(ikt-1) )
	437	END DO
	438	END DO
[4724]	439	riceload(:,:) = 0.0_wp ; riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5
	440	! compute zp from z=0 to first T wet point (correction due to zps not yet applied)
[455]	441	DO jj = 2, jpjm1
[3764]	442	DO ji = fs_2, fs_jpim1 ! vector opt.
[4666]	443	ikt=mikt(ji,jj) ; iktp1i=mikt(ji+1,jj); iktp1j=mikt(ji,jj+1)
	444	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
[4724]	445	! we assume ISF is in isostatic equilibrium
[4666]	446	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * fse3w(ji+1,jj ,iktp1i) &
	447	& * ( 2._wp * znad + rhd(ji+1,jj ,iktp1i) + zrhdtop_oce(ji+1,jj ) ) &
	448	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
	449	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
	450	& + ( ziceload(ji+1,jj) - ziceload(ji,jj)) )
	451	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * fse3w(ji ,jj+1,iktp1j) &
	452	& * ( 2._wp * znad + rhd(ji ,jj+1,iktp1j) + zrhdtop_oce(ji ,jj+1) ) &
	453	& - 0.5_wp * fse3w(ji ,jj ,ikt ) &
	454	& * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) &
	455	& + ( ziceload(ji,jj+1) - ziceload(ji,jj) ) )
[4724]	456	! s-coordinate pressure gradient correction (=0 if z coordinate)
[2528]	457	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
[455]	458	& * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj)
[2528]	459	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
[455]	460	& * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj)
	461	! add to the general momentum trend
[4666]	462	ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
	463	va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
[3764]	464	END DO
	465	END DO
[4666]	466	!
	467	DO jj = 2, jpjm1
	468	DO ji = fs_2, fs_jpim1 ! vector opt.
	469	iku = miku(ji,jj) ;
	470	zpshpi(ji,jj)=0.0_wp ; zpshpj(ji,jj)=0.0_wp
	471	ze3wu = fse3w(ji+1,jj,iku+1)-fse3w(ji,jj,iku+1)
	472	! u direction
	473	IF ( iku .GT. 1 ) THEN
	474	! case iku
	475	zhpi(ji,jj,iku) = zcoef0 / e1u(ji,jj) * ze3wu &
	476	& * ( rhd (ji+1,jj,iku) + rhd (ji,jj,iku) &
	477	& + SIGN(1._wp,ze3wu) * grui(ji,jj) + 2._wp * znad )
[4724]	478	! corrective term ( = 0 if z coordinate )
[4666]	479	zuap = -zcoef0 * ( arui(ji,jj) + 2._wp * znad ) * gzui(ji,jj) / e1u(ji,jj)
	480	! zhpi will be added in interior loop and zuapint will be removed in the interior loop
	481	ua(ji,jj,iku) = ua(ji,jj,iku) + zuap
[4724]	482	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
	483	IF (mbku(ji,jj) == iku + 1) zpshpi(ji,jj) = zhpi(ji,jj,iku)
[3764]	484
[4666]	485	! zhpi will be added in interior loop and zuapint will be removed in the interior loop
	486	! case iku + 1 (remove the zphi term added in the interior loop)
	487	zhpiint = zcoef0 / e1u(ji,jj) &
	488	& * ( fse3w(ji+1,jj ,iku+1) * ( (rhd(ji+1,jj,iku+1) + znad) &
	489	& + (rhd(ji+1,jj,iku ) + znad) ) * tmask(ji+1,jj,iku) &
	490	& - fse3w(ji ,jj ,iku+1) * ( (rhd(ji ,jj,iku+1) + znad) &
	491	& + (rhd(ji ,jj,iku ) + znad) ) * tmask(ji ,jj,iku) )
	492	zhpi(ji,jj,iku+1) = zcoef0 / e1u(ji,jj) * ge3rui(ji,jj) - zhpiint
	493	END IF
	494	! v direction
	495	ikv = mikv(ji,jj)
	496	ze3wv = fse3w(ji,jj+1,ikv+1)-fse3w(ji,jj,ikv+1)
	497	IF ( ikv .GT. 1 ) THEN
	498	! case ikv
	499	zhpj(ji,jj,ikv) = zcoef0 / e2v(ji,jj) * ze3wv &
	500	& * ( rhd(ji,jj+1,ikv) + rhd (ji,jj,ikv) &
	501	& + SIGN(1._wp,ze3wv) * grvi(ji,jj) + 2._wp * znad )
[4724]	502	! corrective term ( = 0 if z coordinate )
[4666]	503	zvap = -zcoef0 * ( arvi(ji,jj) + 2._wp * znad ) * gzvi(ji,jj) / e2v(ji,jj)
	504	! zhpi will be added in interior loop and zvapint will be removed in the interior loop
	505	va(ji,jj,ikv) = va(ji,jj,ikv) + zvap
[4724]	506	! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure
[4666]	507	IF (mbkv(ji,jj) == ikv + 1) zpshpj(ji,jj) = zhpj(ji,jj,ikv)
	508	! zhpi will be added in interior loop and zvapint will be removed in the interior loop
	509	! case ikv + 1 (remove the zphj term added in the interior loop)
	510	zhpjint = zcoef0 / e2v(ji,jj) &
	511	& * ( fse3w(ji ,jj+1,ikv+1) * ( (rhd(ji,jj+1,ikv+1) + znad) &
	512	& + (rhd(ji,jj+1,ikv ) + znad) ) * tmask(ji,jj+1,ikv) &
	513	& - fse3w(ji ,jj ,ikv+1) * ( (rhd(ji,jj ,ikv+1) + znad) &
	514	& + (rhd(ji,jj ,ikv ) + znad) ) * tmask(ji,jj ,ikv) )
	515	zhpj(ji,jj,ikv+1) = zcoef0 / e2v(ji,jj) * ge3rvi(ji,jj) - zhpjint
	516	END IF
	517	END DO
	518	END DO
	519
[503]	520	! interior value (2=<jk=<jpkm1)
[4666]	521	DO jj = 2, jpjm1
	522	DO ji = fs_2, fs_jpim1 ! vector opt.
	523	iku=miku(ji,jj); ikv=mikv(ji,jj)
	524	DO jk = 2, jpkm1
[455]	525	! hydrostatic pressure gradient along s-surfaces
	526	! s-coordinate pressure gradient correction
[4666]	527	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) + zhpi(ji,jj,jk-1) &
	528	& + zcoef0 / e1u(ji,jj) &
	529	& * ( fse3w(ji+1,jj ,jk) * ( (rhd(ji+1,jj,jk ) + znad) &
	530	& + (rhd(ji+1,jj,jk-1) + znad) ) * tmask(ji+1,jj,jk-1) &
	531	& - fse3w(ji ,jj ,jk) * ( (rhd(ji ,jj,jk ) + znad) &
	532	& + (rhd(ji ,jj,jk-1) + znad) ) * tmask(ji ,jj,jk-1) )
[4724]	533	!corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
[4666]	534	zuap = - zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
	535	& * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) * umask(ji,jj,jk-1)
	536	ua(ji,jj,jk) = ua(ji,jj,jk) + ( zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
	537
	538	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) + zhpj(ji,jj,jk-1) &
	539	& + zcoef0 / e2v(ji,jj) &
	540	& * ( fse3w(ji ,jj+1,jk) * ( (rhd(ji,jj+1,jk ) + znad) &
	541	& + (rhd(ji,jj+1,jk-1) + znad) ) * tmask(ji,jj+1,jk-1) &
	542	& - fse3w(ji ,jj ,jk) * ( (rhd(ji,jj ,jk ) + znad) &
	543	& + (rhd(ji,jj ,jk-1) + znad) ) * tmask(ji,jj ,jk-1) )
[4724]	544	!corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc)
[4666]	545	zvap = - zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
	546	& * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) * vmask(ji,jj,jk-1)
[455]	547	! add to the general momentum trend
[4666]	548	va(ji,jj,jk) = va(ji,jj,jk) + ( zhpj(ji,jj,jk) + zvap ) * vmask(ji,jj,jk)
[455]	549	END DO
	550	END DO
	551	END DO
[4666]	552
	553	! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
	554	# if defined key_vectopt_loop
	555	jj = 1
	556	DO ji = jpi+2, jpij-jpi-1 ! vector opt. (forced unrolling)
	557	# else
	558	DO jj = 2, jpjm1
	559	DO ji = 2, jpim1
	560	# endif
	561	iku = mbku(ji,jj)
	562	ikv = mbkv(ji,jj)
	563
	564	IF (iku .GT. 1) THEN
	565	! remove old value (interior case)
	566	zuap = -zcoef0 * ( rhd (ji+1,jj ,iku) + rhd (ji,jj,iku) + 2._wp * znad ) &
	567	& * ( fsde3w(ji+1,jj ,iku) - fsde3w(ji,jj,iku) ) / e1u(ji,jj)
	568	ua(ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) - zuap
	569	! put new value
[4724]	570	! -zpshpi to avoid double contribution of the partial step in the top layer
[4666]	571	zuap = -zcoef0 * ( aru(ji,jj) + 2._wp * znad ) * gzu(ji,jj) / e1u(ji,jj)
	572	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) + zcoef0 / e1u(ji,jj) * ge3ru(ji,jj) - zpshpi(ji,jj)
	573	ua(ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) + zuap
	574	END IF
	575	! v direction
	576	IF (ikv .GT. 1) THEN
	577	! remove old value (interior case)
	578	zvap = -zcoef0 * ( rhd (ji ,jj+1,ikv) + rhd (ji,jj,ikv) + 2._wp * znad ) &
	579	& * ( fsde3w(ji ,jj+1,ikv) - fsde3w(ji,jj,ikv) ) / e2v(ji,jj)
	580	va(ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) - zvap
	581	! put new value
[4724]	582	! -zpshpj to avoid double contribution of the partial step in the top layer
[4666]	583	zvap = -zcoef0 * ( arv(ji,jj) + 2._wp * znad ) * gzv(ji,jj) / e2v(ji,jj)
	584	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) + zcoef0 / e2v(ji,jj) * ge3rv(ji,jj) - zpshpj(ji,jj)
	585	va(ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) + zvap
	586	END IF
	587	# if ! defined key_vectopt_loop
	588	END DO
	589	# endif
	590	END DO
	591
	592
	593	rhd = zrhd
[503]	594	!
[4666]	595	CALL wrk_dealloc( jpi,jpj,2, ztstop)
	596	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj, zrhd)
	597	CALL wrk_dealloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj)
[3294]	598	!
[455]	599	END SUBROUTINE hpg_sco
	600
	601	SUBROUTINE hpg_djc( kt )
	602	!!---------------------------------------------------------------------
	603	!! * ROUTINE hpg_djc *
	604	!!
	605	!! ** Method : Density Jacobian with Cubic polynomial scheme
[3764]	606	!!
[503]	607	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
[455]	608	!!----------------------------------------------------------------------
[503]	609	INTEGER, INTENT(in) :: kt ! ocean time-step index
	610	!!
	611	INTEGER :: ji, jj, jk ! dummy loop indices
	612	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
	613	REAL(wp) :: z1_10, cffu, cffx ! " "
	614	REAL(wp) :: z1_12, cffv, cffy ! " "
[3764]	615	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3294]	616	REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw
	617	REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow
	618	REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k
[455]	619	!!----------------------------------------------------------------------
[3294]	620	!
[3764]	621	CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
	622	CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
	623	CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
[3294]	624	!
[455]	625
	626	IF( kt == nit000 ) THEN
	627	IF(lwp) WRITE(numout,*)
	628	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
	629	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
[216]	630	ENDIF
	631
[503]	632	! Local constant initialization
[2528]	633	zcoef0 = - grav * 0.5_wp
	634	z1_10 = 1._wp / 10._wp
	635	z1_12 = 1._wp / 12._wp
[455]	636
	637	!----------------------------------------------------------------------------------------
	638	! compute and store in provisional arrays elementary vertical and horizontal differences
	639	!----------------------------------------------------------------------------------------
	640
	641	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
	642
	643	DO jk = 2, jpkm1
	644	DO jj = 2, jpjm1
	645	DO ji = fs_2, fs_jpim1 ! vector opt.
	646	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
	647	dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1)
	648	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
	649	dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk )
	650	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
	651	dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk )
	652	END DO
	653	END DO
	654	END DO
	655
	656	!-------------------------------------------------------------------------
	657	! compute harmonic averages using eq. 5.18
	658	!-------------------------------------------------------------------------
	659	zep = 1.e-15
	660
[503]	661	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
	662	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
[455]	663
	664	DO jk = 2, jpkm1
	665	DO jj = 2, jpjm1
	666	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	667	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
[455]	668
[2528]	669	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
	670	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
[3764]	671
[2528]	672	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
	673	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
[455]	674
	675	IF( cffw > zep) THEN
[2528]	676	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
	677	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
[455]	678	ELSE
[2528]	679	drhow(ji,jj,jk) = 0._wp
[455]	680	ENDIF
	681
[2528]	682	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
	683	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
[455]	684
	685	IF( cffu > zep ) THEN
[2528]	686	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
	687	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
[455]	688	ELSE
[2528]	689	drhou(ji,jj,jk ) = 0._wp
[455]	690	ENDIF
	691
	692	IF( cffx > zep ) THEN
[2528]	693	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
	694	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
[455]	695	ELSE
[2528]	696	dzu(ji,jj,jk) = 0._wp
[455]	697	ENDIF
	698
	699	IF( cffv > zep ) THEN
[2528]	700	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
	701	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
[455]	702	ELSE
[2528]	703	drhov(ji,jj,jk) = 0._wp
[455]	704	ENDIF
	705
	706	IF( cffy > zep ) THEN
[2528]	707	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
	708	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
[455]	709	ELSE
[2528]	710	dzv(ji,jj,jk) = 0._wp
[455]	711	ENDIF
	712
	713	END DO
	714	END DO
	715	END DO
	716
	717	!----------------------------------------------------------------------------------
	718	! apply boundary conditions at top and bottom using 5.36-5.37
	719	!----------------------------------------------------------------------------------
[2528]	720	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
	721	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
	722	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
[455]	723
[2528]	724	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
	725	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
	726	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
[455]	727
	728
	729	!--------------------------------------------------------------
	730	! Upper half of top-most grid box, compute and store
	731	!-------------------------------------------------------------
	732
	733	!!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified
	734	! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
	735
	736	DO jj = 2, jpjm1
	737	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	738	rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) &
	739	& * ( rhd(ji,jj,1) &
	740	& + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) &
	741	& * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) &
[3764]	742	& / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) )
[455]	743	END DO
	744	END DO
	745
	746	!!bug gm : here also, simplification is possible
	747	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
	748
	749	DO jk = 2, jpkm1
	750	DO jj = 2, jpjm1
	751	DO ji = fs_2, fs_jpim1 ! vector opt.
	752
	753	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
	754	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) &
	755	& - grav * z1_10 * ( &
	756	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
	757	& * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
	758	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
	759	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
	760	& )
	761
	762	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
	763	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) &
	764	& - grav* z1_10 * ( &
	765	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
	766	& * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
	767	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
	768	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
	769	& )
	770
	771	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
	772	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) &
	773	& - grav* z1_10 * ( &
	774	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
	775	& * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
	776	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
	777	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
	778	& )
	779
	780	END DO
	781	END DO
	782	END DO
	783	CALL lbc_lnk(rho_k,'W',1.)
	784	CALL lbc_lnk(rho_i,'U',1.)
	785	CALL lbc_lnk(rho_j,'V',1.)
	786
	787
	788	! ---------------
	789	! Surface value
	790	! ---------------
	791	DO jj = 2, jpjm1
	792	DO ji = fs_2, fs_jpim1 ! vector opt.
	793	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj)
	794	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj)
	795	! add to the general momentum trend
	796	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
	797	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
	798	END DO
	799	END DO
	800
	801	! ----------------
	802	! interior value (2=<jk=<jpkm1)
	803	! ----------------
	804	DO jk = 2, jpkm1
[3764]	805	DO jj = 2, jpjm1
[455]	806	DO ji = fs_2, fs_jpim1 ! vector opt.
	807	! hydrostatic pressure gradient along s-surfaces
	808	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
	809	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
	810	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj)
	811	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
	812	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
	813	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj)
	814	! add to the general momentum trend
	815	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	816	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
	817	END DO
	818	END DO
	819	END DO
[503]	820	!
[3764]	821	CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
	822	CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
	823	CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
[2715]	824	!
[455]	825	END SUBROUTINE hpg_djc
	826
	827
[3294]	828	SUBROUTINE hpg_prj( kt )
[455]	829	!!---------------------------------------------------------------------
[3294]	830	!! * ROUTINE hpg_prj *
[455]	831	!!
[3294]	832	!! ** Method : s-coordinate case.
	833	!! A Pressure-Jacobian horizontal pressure gradient method
	834	!! based on the constrained cubic-spline interpolation for
	835	!! all vertical coordinate systems
[455]	836	!!
[3294]	837	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
	838	!! - Save the trend (l_trddyn=T)
	839	!!
[455]	840	!!----------------------------------------------------------------------
[3294]	841	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
	842	INTEGER, INTENT(in) :: kt ! ocean time-step index
[503]	843	!!
[3294]	844	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
	845	REAL(wp) :: zcoef0, znad ! temporary scalars
[503]	846	!!
[3294]	847	!! The local variables for the correction term
	848	INTEGER :: jk1, jis, jid, jjs, jjd
	849	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
[3764]	850	REAL(wp) :: zrhdt1
[3294]	851	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
[3764]	852	REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh
[3294]	853	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
[455]	854	!!----------------------------------------------------------------------
[3294]	855	!
[3764]	856	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
	857	CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh )
[3294]	858	!
[455]	859	IF( kt == nit000 ) THEN
	860	IF(lwp) WRITE(numout,*)
[3294]	861	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
	862	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
[3]	863	ENDIF
	864
[3294]	865	!!----------------------------------------------------------------------
	866	! Local constant initialization
[3764]	867	zcoef0 = - grav
[3294]	868	znad = 0.0_wp
	869	IF( lk_vvl ) znad = 1._wp
[3]	870
[3294]	871	! Clean 3-D work arrays
	872	zhpi(:,:,:) = 0._wp
	873	zrhh(:,:,:) = rhd(:,:,:)
[3764]	874
[3294]	875	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
	876	DO jj = 1, jpj
[3764]	877	DO ji = 1, jpi
[3294]	878	jk = mbathy(ji,jj)
	879	IF( jk <= 0 ) THEN; zrhh(ji,jj,:) = 0._wp
	880	ELSE IF(jk == 1) THEN; zrhh(ji,jj, jk+1:jpk) = rhd(ji,jj,jk)
	881	ELSE IF(jk < jpkm1) THEN
	882	DO jkk = jk+1, jpk
	883	zrhh(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1), &
	884	fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2))
[3764]	885	END DO
[3294]	886	ENDIF
	887	END DO
	888	END DO
[3]	889
[3632]	890	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
	891	DO jj = 1, jpj; DO ji = 1, jpi
	892	zdept(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) - sshn(ji,jj) * znad
	893	END DO ; END DO
[455]	894
[3632]	895	DO jk = 2, jpk; DO jj = 1, jpj; DO ji = 1, jpi
	896	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + fse3w(ji,jj,jk)
	897	END DO ; END DO ; END DO
[455]	898
[3632]	899	fsp(:,:,:) = zrhh(:,:,:)
	900	xsp(:,:,:) = zdept(:,:,:)
	901
[3764]	902	! Construct the vertical density profile with the
[3294]	903	! constrained cubic spline interpolation
	904	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
[3764]	905	CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type)
[3294]	906
	907	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
	908	DO jj = 2, jpj
[3764]	909	DO ji = 2, jpi
[3632]	910	zrhdt1 = zrhh(ji,jj,1) - interp3(zdept(ji,jj,1),asp(ji,jj,1), &
[3294]	911	bsp(ji,jj,1), csp(ji,jj,1), &
[3632]	912	dsp(ji,jj,1) ) * 0.25_wp * fse3w(ji,jj,1)
[3294]	913
	914	! assuming linear profile across the top half surface layer
[3764]	915	zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * zrhdt1
[3294]	916	END DO
[455]	917	END DO
	918
[3294]	919	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
[3764]	920	DO jk = 2, jpkm1
	921	DO jj = 2, jpj
[3294]	922	DO ji = 2, jpi
	923	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
[3632]	924	integ_spline(zdept(ji,jj,jk-1), zdept(ji,jj,jk),&
[3294]	925	asp(ji,jj,jk-1), bsp(ji,jj,jk-1), &
	926	csp(ji,jj,jk-1), dsp(ji,jj,jk-1))
	927	END DO
	928	END DO
[455]	929	END DO
	930
[3294]	931	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
[3764]	932	DO jj = 2, jpjm1
	933	DO ji = 2, jpim1
[4292]	934	zu(ji,jj,1) = - ( fse3u(ji,jj,1) - sshn(ji,jj) * znad) ! probable bug: changed from sshu_n for ztilde compilation
	935	zv(ji,jj,1) = - ( fse3v(ji,jj,1) - sshn(ji,jj) * znad) ! probable bug: changed from sshv_n for ztilde compilation
[3294]	936	END DO
[455]	937	END DO
	938
[3764]	939	DO jk = 2, jpkm1
	940	DO jj = 2, jpjm1
	941	DO ji = 2, jpim1
[3294]	942	zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk)
	943	zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk)
	944	END DO
	945	END DO
[455]	946	END DO
[3764]	947
	948	DO jk = 1, jpkm1
	949	DO jj = 2, jpjm1
	950	DO ji = 2, jpim1
[3294]	951	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk)
	952	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk)
	953	END DO
	954	END DO
	955	END DO
[455]	956
[3632]	957	DO jk = 1, jpkm1
	958	DO jj = 2, jpjm1
	959	DO ji = 2, jpim1
	960	zu(ji,jj,jk) = min(zu(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
	961	zu(ji,jj,jk) = max(zu(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk)))
	962	zv(ji,jj,jk) = min(zv(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
	963	zv(ji,jj,jk) = max(zv(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk)))
	964	END DO
	965	END DO
	966	END DO
	967
	968
[3764]	969	DO jk = 1, jpkm1
	970	DO jj = 2, jpjm1
	971	DO ji = 2, jpim1
[3294]	972	zpwes = 0._wp; zpwed = 0._wp
	973	zpnss = 0._wp; zpnsd = 0._wp
	974	zuijk = zu(ji,jj,jk)
	975	zvijk = zv(ji,jj,jk)
	976
	977	!!!!! for u equation
	978	IF( jk <= mbku(ji,jj) ) THEN
[3632]	979	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
[3294]	980	jis = ji + 1; jid = ji
	981	ELSE
	982	jis = ji; jid = ji +1
	983	ENDIF
	984
	985	! integrate the pressure on the shallow side
[3764]	986	jk1 = jk
[3632]	987	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
[3294]	988	IF( jk1 == mbku(ji,jj) ) THEN
[3632]	989	zuijk = -zdept(jis,jj,jk1)
[3294]	990	EXIT
	991	ENDIF
[3632]	992	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
[3764]	993	zpwes = zpwes + &
[3632]	994	integ_spline(zdept(jis,jj,jk1), zdeps, &
[3294]	995	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
	996	csp(jis,jj,jk1), dsp(jis,jj,jk1))
	997	jk1 = jk1 + 1
	998	END DO
[3764]	999
[3294]	1000	! integrate the pressure on the deep side
[3764]	1001	jk1 = jk
[3632]	1002	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
[3294]	1003	IF( jk1 == 1 ) THEN
[3632]	1004	zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad)
	1005	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
	1006	bsp(jid,jj,1), csp(jid,jj,1), &
	1007	dsp(jid,jj,1)) * zdeps
	1008	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
[3294]	1009	EXIT
	1010	ENDIF
[3632]	1011	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
[3764]	1012	zpwed = zpwed + &
[3632]	1013	integ_spline(zdeps, zdept(jid,jj,jk1), &
[3294]	1014	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
	1015	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
	1016	jk1 = jk1 - 1
	1017	END DO
[3764]	1018
[3294]	1019	! update the momentum trends in u direction
	1020
	1021	zdpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk))
	1022	IF( lk_vvl ) THEN
[3764]	1023	zdpdx2 = zcoef0 / e1u(ji,jj) * &
	1024	( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) )
[3294]	1025	ELSE
[3764]	1026	zdpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
[3294]	1027	ENDIF
	1028
	1029	ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * &
	1030	& umask(ji,jj,jk) * tmask(ji,jj,jk) * tmask(ji+1,jj,jk)
	1031	ENDIF
[3764]	1032
[3294]	1033	!!!!! for v equation
	1034	IF( jk <= mbkv(ji,jj) ) THEN
[3632]	1035	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
[3294]	1036	jjs = jj + 1; jjd = jj
	1037	ELSE
	1038	jjs = jj ; jjd = jj + 1
	1039	ENDIF
	1040
	1041	! integrate the pressure on the shallow side
[3764]	1042	jk1 = jk
[3632]	1043	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
[3294]	1044	IF( jk1 == mbkv(ji,jj) ) THEN
[3632]	1045	zvijk = -zdept(ji,jjs,jk1)
[3294]	1046	EXIT
	1047	ENDIF
[3632]	1048	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
[3764]	1049	zpnss = zpnss + &
[3632]	1050	integ_spline(zdept(ji,jjs,jk1), zdeps, &
[3294]	1051	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
	1052	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
	1053	jk1 = jk1 + 1
	1054	END DO
[3764]	1055
[3294]	1056	! integrate the pressure on the deep side
[3764]	1057	jk1 = jk
[3632]	1058	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
[3294]	1059	IF( jk1 == 1 ) THEN
[3632]	1060	zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad)
	1061	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
	1062	bsp(ji,jjd,1), csp(ji,jjd,1), &
	1063	dsp(ji,jjd,1) ) * zdeps
	1064	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
[3294]	1065	EXIT
	1066	ENDIF
[3632]	1067	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
[3764]	1068	zpnsd = zpnsd + &
[3632]	1069	integ_spline(zdeps, zdept(ji,jjd,jk1), &
[3294]	1070	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
	1071	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
	1072	jk1 = jk1 - 1
	1073	END DO
	1074
[3764]	1075
[3294]	1076	! update the momentum trends in v direction
	1077
	1078	zdpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk))
	1079	IF( lk_vvl ) THEN
	1080	zdpdy2 = zcoef0 / e2v(ji,jj) * &
[3764]	1081	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) )
[3294]	1082	ELSE
[3764]	1083	zdpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
[3294]	1084	ENDIF
	1085
	1086	va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2)*&
	1087	& vmask(ji,jj,jk)tmask(ji,jj,jk)tmask(ji,jj+1,jk)
	1088	ENDIF
	1089
[3764]	1090
[3294]	1091	END DO
	1092	END DO
[455]	1093	END DO
[503]	1094	!
[3764]	1095	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
	1096	CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh )
[2715]	1097	!
[3294]	1098	END SUBROUTINE hpg_prj
[455]	1099
[3294]	1100	SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type)
	1101	!!----------------------------------------------------------------------
	1102	!! * ROUTINE cspline *
[3764]	1103	!!
[3294]	1104	!! ** Purpose : constrained cubic spline interpolation
[3764]	1105	!!
	1106	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
[3294]	1107	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
	1108	!!
	1109	!!----------------------------------------------------------------------
	1110	IMPLICIT NONE
	1111	REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate
[3764]	1112	REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of
[3294]	1113	! the interpoated function
[3764]	1114	INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline
[3294]	1115	! 2: Linear
	1116
[3764]	1117	! Local Variables
[3294]	1118	INTEGER :: ji, jj, jk ! dummy loop indices
	1119	INTEGER :: jpi, jpj, jpkm1
	1120	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
	1121	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
	1122	REAL(wp) :: zdf(size(fsp,3))
	1123	!!----------------------------------------------------------------------
	1124
	1125	jpi = size(fsp,1)
	1126	jpj = size(fsp,2)
	1127	jpkm1 = size(fsp,3) - 1
	1128
[3764]	1129
[3294]	1130	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
	1131	DO ji = 1, jpi
	1132	DO jj = 1, jpj
[3764]	1133	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
[3294]	1134	! DO jk = 2, jpkm1-1
[3764]	1135	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
	1136	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1137	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
	1138	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
	1139	!
	1140	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
[3764]	1141	!
[3294]	1142	! IF(zdf1 * zdf2 <= 0._wp) THEN
	1143	! zdf(jk) = 0._wp
	1144	! ELSE
	1145	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
	1146	! ENDIF
	1147	! END DO
[3764]	1148
[3294]	1149	!!Simply geometric average
	1150	DO jk = 2, jpkm1-1
	1151	zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1))
	1152	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk))
[3764]	1153
[3294]	1154	IF(zdf1 * zdf2 <= 0._wp) THEN
	1155	zdf(jk) = 0._wp
	1156	ELSE
	1157	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
	1158	ENDIF
	1159	END DO
[3764]	1160
[3294]	1161	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
	1162	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
	1163	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
	1164	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - &
	1165	& 0.5_wp * zdf(jpkm1 - 1)
[3764]	1166
[3294]	1167	DO jk = 1, jpkm1 - 1
[3764]	1168	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1169	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
	1170	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
[3764]	1171	zddf1 = -2._wp * ztmp1 + ztmp2
[3294]	1172	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
[3764]	1173	zddf2 = 2._wp * ztmp1 - ztmp2
	1174
[3294]	1175	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
	1176	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
[3764]	1177	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
[3294]	1178	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
	1179	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
	1180	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
	1181	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
	1182	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
	1183	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
	1184	END DO
	1185	END DO
	1186	END DO
[3764]	1187
[3294]	1188	ELSE IF (polynomial_type == 2) THEN ! Linear
	1189	DO ji = 1, jpi
	1190	DO jj = 1, jpj
	1191	DO jk = 1, jpkm1-1
[3764]	1192	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1193	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
[3764]	1194
[3294]	1195	dsp(ji,jj,jk) = 0._wp
	1196	csp(ji,jj,jk) = 0._wp
	1197	bsp(ji,jj,jk) = ztmp1 / zdxtmp
	1198	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
	1199	END DO
	1200	END DO
	1201	END DO
	1202
	1203	ELSE
	1204	CALL ctl_stop( 'invalid polynomial type in cspline' )
	1205	ENDIF
	1206
[3764]	1207
[3294]	1208	END SUBROUTINE cspline
	1209
	1210
[3764]	1211	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
[3294]	1212	!!----------------------------------------------------------------------
	1213	!! * ROUTINE interp1 *
[3764]	1214	!!
[3294]	1215	!! ** Purpose : 1-d linear interpolation
[3764]	1216	!!
	1217	!! ** Method :
[3294]	1218	!! interpolation is straight forward
[3764]	1219	!! extrapolation is also permitted (no value limit)
[3294]	1220	!!
	1221	!!----------------------------------------------------------------------
	1222	IMPLICIT NONE
[3764]	1223	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
[3294]	1224	REAL(wp) :: f ! result of the interpolation (extrapolation)
	1225	REAL(wp) :: zdeltx
	1226	!!----------------------------------------------------------------------
	1227
	1228	zdeltx = xr - xl
	1229	IF(abs(zdeltx) <= 10._wp * EPSILON(x)) THEN
	1230	f = 0.5_wp * (fl + fr)
	1231	ELSE
	1232	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
	1233	ENDIF
[3764]	1234
[3294]	1235	END FUNCTION interp1
	1236
[3764]	1237	FUNCTION interp2(x, a, b, c, d) RESULT(f)
[3294]	1238	!!----------------------------------------------------------------------
	1239	!! * ROUTINE interp1 *
[3764]	1240	!!
[3294]	1241	!! ** Purpose : 1-d constrained cubic spline interpolation
[3764]	1242	!!
[3294]	1243	!! ** Method : cubic spline interpolation
	1244	!!
	1245	!!----------------------------------------------------------------------
	1246	IMPLICIT NONE
[3764]	1247	REAL(wp), INTENT(in) :: x, a, b, c, d
[3294]	1248	REAL(wp) :: f ! value from the interpolation
	1249	!!----------------------------------------------------------------------
	1250
[3764]	1251	f = a + x* ( b + x * ( c + d * x ) )
[3294]	1252
	1253	END FUNCTION interp2
	1254
	1255
[3764]	1256	FUNCTION interp3(x, a, b, c, d) RESULT(f)
[3294]	1257	!!----------------------------------------------------------------------
	1258	!! * ROUTINE interp1 *
[3764]	1259	!!
[3294]	1260	!! ** Purpose : Calculate the first order of deriavtive of
	1261	!! a cubic spline function y=a+bx+cx^2+d*x^3
[3764]	1262	!!
[3294]	1263	!! ** Method : f=dy/dx=b+2cx+3dx^2
	1264	!!
	1265	!!----------------------------------------------------------------------
	1266	IMPLICIT NONE
[3764]	1267	REAL(wp), INTENT(in) :: x, a, b, c, d
[3294]	1268	REAL(wp) :: f ! value from the interpolation
	1269	!!----------------------------------------------------------------------
	1270
	1271	f = b + x * ( 2._wp * c + 3._wp * d * x)
	1272
	1273	END FUNCTION interp3
	1274
[3764]	1275
	1276	FUNCTION integ_spline(xl, xr, a, b, c, d) RESULT(f)
[3294]	1277	!!----------------------------------------------------------------------
	1278	!! * ROUTINE interp1 *
[3764]	1279	!!
[3294]	1280	!! ** Purpose : 1-d constrained cubic spline integration
	1281	!!
[3764]	1282	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
	1283	!!
[3294]	1284	!!----------------------------------------------------------------------
	1285	IMPLICIT NONE
[3764]	1286	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
	1287	REAL(wp) :: za1, za2, za3
[3294]	1288	REAL(wp) :: f ! integration result
	1289	!!----------------------------------------------------------------------
	1290
[3764]	1291	za1 = 0.5_wp * b
	1292	za2 = c / 3.0_wp
	1293	za3 = 0.25_wp * d
[3294]	1294
	1295	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
	1296	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
	1297
[3632]	1298	END FUNCTION integ_spline
[3294]	1299
	1300
[3]	1301	!!======================================================================
	1302	END MODULE dynhpg
[3632]	1303

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