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dynhpg.F90 in branches/2014/dev_r4704_NOC5_MPP_BDY_UPDATE/NEMOGCM/NEMO/OPA_SRC/DYN – NEMO

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source: branches/2014/dev_r4704_NOC5_MPP_BDY_UPDATE/NEMOGCM/NEMO/OPA_SRC/DYN/dynhpg.F90 @ 6225

Last change on this file since 6225 was 6225, checked in by jamesharle, 8 years ago
Update MPP_BDY_UPDATE branch to be consistent with head of trunk
Property svn:keywords set to `Id`
File size: 70.7 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
[6225]	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)
[6225]	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
[6225]	33	USE sbc_oce ! surface variable (only for the flag with ice shelf)
[3]	34	USE dom_oce ! ocean space and time domain
[6225]	35	USE wet_dry ! wetting and drying
[3]	36	USE phycst ! physical constants
[6225]	37	USE trd_oce ! trends: ocean variables
	38	USE trddyn ! trend manager: dynamics
	39	!jc USE zpshde ! partial step: hor. derivative (zps_hde routine)
	40	!
[2715]	41	USE in_out_manager ! I/O manager
[258]	42	USE prtctl ! Print control
[6225]	43	USE lbclnk ! lateral boundary condition
[2715]	44	USE lib_mpp ! MPP library
[6225]	45	USE eosbn2 ! compute density
[3294]	46	USE wrk_nemo ! Memory Allocation
	47	USE timing ! Timing
[6225]	48	USE iom
[3]	49
	50	IMPLICIT NONE
	51	PRIVATE
	52
[2528]	53	PUBLIC dyn_hpg ! routine called by step module
	54	PUBLIC dyn_hpg_init ! routine called by opa module
[3]	55
[6225]	56	! !!* Namelist namdyn_hpg : hydrostatic pressure gradient
	57	LOGICAL , PUBLIC :: ln_hpg_zco !: z-coordinate - full steps
	58	LOGICAL , PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation)
	59	LOGICAL , PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation)
	60	LOGICAL , PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial)
	61	LOGICAL , PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme)
	62	LOGICAL , PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf
[455]	63
[3764]	64	INTEGER , PUBLIC :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM)
[455]	65
[3]	66	!! * Substitutions
	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
[6225]	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)
[6225]	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(:,:,:)
[6225]	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	!!
[6225]	134	INTEGER :: ji, jj, jk, ikt ! dummy loop indices ISF
	135	REAL(wp) :: znad
	136	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop, zrhd ! hypothesys on isf density
	137	REAL(wp), POINTER, DIMENSION(:,:) :: zrhdtop_isf ! density at bottom of ISF
	138	REAL(wp), POINTER, DIMENSION(:,:) :: ziceload ! density at bottom of ISF
	139	!!
[3294]	140	NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, &
[6225]	141	& ln_hpg_djc, ln_hpg_prj, ln_hpg_isf
[455]	142	!!----------------------------------------------------------------------
[2528]	143	!
[4147]	144	REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient
	145	READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901)
[6225]	146	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp )
	147	!
[4147]	148	REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient
	149	READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 )
[6225]	150	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp )
[4624]	151	IF(lwm) WRITE ( numond, namdyn_hpg )
[2528]	152	!
	153	IF(lwp) THEN ! Control print
[455]	154	WRITE(numout,*)
[2528]	155	WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation'
	156	WRITE(numout,*) '~~~~~~~~~~~~'
[1601]	157	WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme'
	158	WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco
	159	WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps
	160	WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco
[6225]	161	WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf
[1601]	162	WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc
[3294]	163	WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj
[455]	164	ENDIF
[2528]	165	!
[3294]	166	IF( ln_hpg_djc ) &
	167	& CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method &
	168	& currently disabled (bugs under investigation). Please select &
	169	& either ln_hpg_sco or ln_hpg_prj instead')
[2528]	170	!
[6225]	171	IF( .NOT.ln_linssh .AND. .NOT.(ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) &
	172	& CALL ctl_stop('dyn_hpg_init : non-linear free surface requires either ', &
	173	& ' the standard jacobian formulation hpg_sco or ' , &
	174	& ' the pressure jacobian formulation hpg_prj' )
	175
	176	IF( ln_hpg_isf .AND. .NOT. ln_isfcav ) &
	177	& CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' )
	178	IF( .NOT. ln_hpg_isf .AND. ln_isfcav ) &
	179	& CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' )
[3294]	180	!
[503]	181	! ! Set nhpg from ln_hpg_... flags
[455]	182	IF( ln_hpg_zco ) nhpg = 0
	183	IF( ln_hpg_zps ) nhpg = 1
	184	IF( ln_hpg_sco ) nhpg = 2
[3294]	185	IF( ln_hpg_djc ) nhpg = 3
	186	IF( ln_hpg_prj ) nhpg = 4
[6225]	187	IF( ln_hpg_isf ) nhpg = 5
[2528]	188	!
[3294]	189	! ! Consistency check
[3764]	190	ioptio = 0
[455]	191	IF( ln_hpg_zco ) ioptio = ioptio + 1
	192	IF( ln_hpg_zps ) ioptio = ioptio + 1
	193	IF( ln_hpg_sco ) ioptio = ioptio + 1
	194	IF( ln_hpg_djc ) ioptio = ioptio + 1
[3294]	195	IF( ln_hpg_prj ) ioptio = ioptio + 1
[6225]	196	IF( ln_hpg_isf ) ioptio = ioptio + 1
[2715]	197	IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' )
[6225]	198	!
	199	! initialisation of ice shelf load
	200	IF ( .NOT. ln_isfcav ) riceload(:,:)=0.0
	201	IF ( ln_isfcav ) THEN
	202	CALL wrk_alloc( jpi,jpj, 2, ztstop)
	203	CALL wrk_alloc( jpi,jpj,jpk, zrhd )
	204	CALL wrk_alloc( jpi,jpj, zrhdtop_isf, ziceload)
	205	!
	206	IF(lwp) WRITE(numout,*)
	207	IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf'
	208	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~'
	209
	210	! To use density and not density anomaly
	211	znad=1._wp
	212
	213	! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude)
	214	ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp
	215
	216	! compute density of the water displaced by the ice shelf
	217	DO jk = 1, jpk
	218	CALL eos(ztstop(:,:,:),gdept_n(:,:,jk),zrhd(:,:,jk))
	219	END DO
	220
	221	! compute rhd at the ice/oce interface (ice shelf side)
	222	CALL eos(ztstop,risfdep,zrhdtop_isf)
	223
	224	! Surface value + ice shelf gradient
	225	! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v)
	226	! divided by 2 later
	227	ziceload = 0._wp
	228	DO jj = 1, jpj
	229	DO ji = 1, jpi
	230	ikt=mikt(ji,jj)
	231	ziceload(ji,jj) = ziceload(ji,jj) + (znad + zrhd(ji,jj,1) ) * e3w_n(ji,jj,1) * (1._wp - tmask(ji,jj,1))
	232	DO jk=2,ikt-1
	233	ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhd(ji,jj,jk-1) + zrhd(ji,jj,jk)) * e3w_n(ji,jj,jk) &
	234	& * (1._wp - tmask(ji,jj,jk))
	235	END DO
	236	IF (ikt >= 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + zrhd(ji,jj,ikt-1)) &
	237	& * ( risfdep(ji,jj) - gdept_1d(ikt-1) )
	238	END DO
	239	END DO
	240	riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5
	241
	242	CALL wrk_dealloc( jpi,jpj, 2, ztstop)
	243	CALL wrk_dealloc( jpi,jpj,jpk, zrhd )
	244	CALL wrk_dealloc( jpi,jpj, zrhdtop_isf, ziceload)
	245	END IF
[503]	246	!
[2528]	247	END SUBROUTINE dyn_hpg_init
[455]	248
	249
	250	SUBROUTINE hpg_zco( kt )
	251	!!---------------------------------------------------------------------
	252	!! * ROUTINE hpg_zco *
	253	!!
	254	!! ** Method : z-coordinate case, levels are horizontal surfaces.
	255	!! The now hydrostatic pressure gradient at a given level, jk,
	256	!! is computed by taking the vertical integral of the in-situ
	257	!! density gradient along the model level from the suface to that
	258	!! level: zhpi = grav .....
	259	!! zhpj = grav .....
[3]	260	!! add it to the general momentum trend (ua,va).
[455]	261	!! ua = ua - 1/e1u * zhpi
	262	!! va = va - 1/e2v * zhpj
[3764]	263	!!
[3]	264	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[503]	265	!!----------------------------------------------------------------------
	266	INTEGER, INTENT(in) :: kt ! ocean time-step index
[6225]	267	!
[503]	268	INTEGER :: ji, jj, jk ! dummy loop indices
	269	REAL(wp) :: zcoef0, zcoef1 ! temporary scalars
[3764]	270	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3]	271	!!----------------------------------------------------------------------
[3764]	272	!
[6225]	273	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
[3294]	274	!
[3]	275	IF( kt == nit000 ) THEN
	276	IF(lwp) WRITE(numout,*)
[455]	277	IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend'
	278	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case '
[3]	279	ENDIF
	280
[3764]	281	zcoef0 = - grav * 0.5_wp ! Local constant initialization
	282
[455]	283	! Surface value
[3]	284	DO jj = 2, jpjm1
	285	DO ji = fs_2, fs_jpim1 ! vector opt.
[6225]	286	zcoef1 = zcoef0 * e3w_n(ji,jj,1)
[455]	287	! hydrostatic pressure gradient
[6225]	288	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
	289	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
[3]	290	! add to the general momentum trend
[455]	291	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
	292	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
	293	END DO
	294	END DO
[3294]	295
[503]	296	!
[455]	297	! interior value (2=<jk=<jpkm1)
[3]	298	DO jk = 2, jpkm1
[455]	299	DO jj = 2, jpjm1
[3]	300	DO ji = fs_2, fs_jpim1 ! vector opt.
[6225]	301	zcoef1 = zcoef0 * e3w_n(ji,jj,jk)
[455]	302	! hydrostatic pressure gradient
	303	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
[6225]	304	& + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) &
	305	& - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
[455]	306
	307	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
[6225]	308	& + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) &
	309	& - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
[3]	310	! add to the general momentum trend
[455]	311	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	312	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
[3]	313	END DO
	314	END DO
	315	END DO
[503]	316	!
[6225]	317	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
[3294]	318	!
[455]	319	END SUBROUTINE hpg_zco
[216]	320
[3]	321
[455]	322	SUBROUTINE hpg_zps( kt )
[3]	323	!!---------------------------------------------------------------------
[455]	324	!! * ROUTINE hpg_zps *
[3764]	325	!!
[455]	326	!! ** Method : z-coordinate plus partial steps case. blahblah...
[3764]	327	!!
[3]	328	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[3764]	329	!!----------------------------------------------------------------------
[503]	330	INTEGER, INTENT(in) :: kt ! ocean time-step index
	331	!!
	332	INTEGER :: ji, jj, jk ! dummy loop indices
	333	INTEGER :: iku, ikv ! temporary integers
	334	REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars
[3764]	335	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3]	336	!!----------------------------------------------------------------------
[3294]	337	!
[6225]	338	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
[3294]	339	!
[3]	340	IF( kt == nit000 ) THEN
	341	IF(lwp) WRITE(numout,*)
[455]	342	IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend'
[503]	343	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization'
[3]	344	ENDIF
	345
[6225]	346	! Partial steps: bottom before horizontal gradient of t, s, rd at the last ocean level
	347	!jc CALL zps_hde ( kt, jpts, tsn, gtsu, gtsv, rhd, gru , grv )
[3294]	348
[503]	349	! Local constant initialization
[2528]	350	zcoef0 = - grav * 0.5_wp
[3]	351
[2528]	352	! Surface value (also valid in partial step case)
[3]	353	DO jj = 2, jpjm1
	354	DO ji = fs_2, fs_jpim1 ! vector opt.
[6225]	355	zcoef1 = zcoef0 * e3w_n(ji,jj,1)
[3]	356	! hydrostatic pressure gradient
[6225]	357	zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) * r1_e1u(ji,jj)
	358	zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) * r1_e2v(ji,jj)
[3]	359	! add to the general momentum trend
	360	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
	361	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
	362	END DO
	363	END DO
	364
[503]	365	! interior value (2=<jk=<jpkm1)
[3]	366	DO jk = 2, jpkm1
	367	DO jj = 2, jpjm1
	368	DO ji = fs_2, fs_jpim1 ! vector opt.
[6225]	369	zcoef1 = zcoef0 * e3w_n(ji,jj,jk)
[3]	370	! hydrostatic pressure gradient
	371	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
[455]	372	& + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) &
[6225]	373	& - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) * r1_e1u(ji,jj)
[3]	374
	375	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
[455]	376	& + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) &
[6225]	377	& - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) * r1_e2v(ji,jj)
[3]	378	! add to the general momentum trend
	379	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	380	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
[455]	381	END DO
[3]	382	END DO
	383	END DO
	384
[2528]	385	! partial steps correction at the last level (use gru & grv computed in zpshde.F90)
[3]	386	DO jj = 2, jpjm1
	387	DO ji = 2, jpim1
[2528]	388	iku = mbku(ji,jj)
	389	ikv = mbkv(ji,jj)
[6225]	390	zcoef2 = zcoef0 * MIN( e3w_n(ji,jj,iku), e3w_n(ji+1,jj ,iku) )
	391	zcoef3 = zcoef0 * MIN( e3w_n(ji,jj,ikv), e3w_n(ji ,jj+1,ikv) )
[2528]	392	IF( iku > 1 ) THEN ! on i-direction (level 2 or more)
	393	ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value
	394	zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one
[6225]	395	& + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) * r1_e1u(ji,jj)
[2528]	396	ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend
[3]	397	ENDIF
[2528]	398	IF( ikv > 1 ) THEN ! on j-direction (level 2 or more)
	399	va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value
	400	zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one
[6225]	401	& + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) * r1_e2v(ji,jj)
[2528]	402	va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend
[3]	403	ENDIF
	404	END DO
	405	END DO
[503]	406	!
[6225]	407	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
[3294]	408	!
[455]	409	END SUBROUTINE hpg_zps
[216]	410
[3]	411
[455]	412	SUBROUTINE hpg_sco( kt )
[3]	413	!!---------------------------------------------------------------------
[455]	414	!! * ROUTINE hpg_sco *
[3]	415	!!
[455]	416	!! ** Method : s-coordinate case. Jacobian scheme.
	417	!! The now hydrostatic pressure gradient at a given level, jk,
	418	!! is computed by taking the vertical integral of the in-situ
[3]	419	!! density gradient along the model level from the suface to that
[455]	420	!! level. s-coordinates (ln_sco): a corrective term is added
	421	!! to the horizontal pressure gradient :
	422	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
	423	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
[3]	424	!! add it to the general momentum trend (ua,va).
[455]	425	!! ua = ua - 1/e1u * zhpi
	426	!! va = va - 1/e2v * zhpj
[3]	427	!!
	428	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[503]	429	!!----------------------------------------------------------------------
	430	INTEGER, INTENT(in) :: kt ! ocean time-step index
	431	!!
[6225]	432	INTEGER :: ji, jj, jk, jii, jjj ! dummy loop indices
	433	REAL(wp) :: zcoef0, zuap, zvap, znad, ztmp ! temporary scalars
	434	LOGICAL :: ll_tmp1, ll_tmp2, ll_tmp3 ! local logical variables
[3764]	435	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[6225]	436	REAL(wp), POINTER, DIMENSION(:,:) :: zcpx, zcpy !W/D pressure filter
[3]	437	!!----------------------------------------------------------------------
[3294]	438	!
	439	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj )
[6225]	440	IF(ln_wd) CALL wrk_alloc( jpi,jpj, zcpx, zcpy )
[3294]	441	!
[3]	442	IF( kt == nit000 ) THEN
	443	IF(lwp) WRITE(numout,*)
[455]	444	IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend'
	445	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used'
[3]	446	ENDIF
[6225]	447	!
[2528]	448	zcoef0 = - grav * 0.5_wp
[6225]	449	IF ( ln_linssh ) THEN ; znad = 0._wp ! Fixed volume: density anomaly
	450	ELSE ; znad = 1._wp ! Variable volume: density
[592]	451	ENDIF
[6225]	452	!
	453	IF(ln_wd) THEN
	454	DO jj = 2, jpjm1
	455	DO ji = 2, jpim1
	456	ll_tmp1 = MIN(sshn(ji,jj), sshn(ji+1,jj)) > MAX(-bathy(ji,jj), -bathy(ji+1,jj))
	457	ll_tmp2 = MAX(sshn(ji,jj) + bathy(ji,jj), sshn(ji+1,jj) + bathy(ji+1,jj)) > rn_wdmin1 + rn_wdmin2
	458	ll_tmp3 = MAX(sshn(ji,jj), sshn(ji+1,jj)) > MAX(-bathy(ji,jj), -bathy(ji+1,jj)) + &
	459	& rn_wdmin1 + rn_wdmin2
[455]	460
[6225]	461	IF(ll_tmp1.AND.ll_tmp2) THEN
	462	zcpx(ji,jj) = 1.0_wp
	463	wduflt(ji,jj) = 1.0_wp
	464	ELSE IF(ll_tmp3) THEN
	465	! no worries about sshn(ji+1,jj)-sshn(ji,jj) = 0, it won't happen ! here
	466	zcpx(ji,jj) = ABS((sshn(ji+1,jj) + bathy(ji+1,jj) - sshn(ji,jj) - bathy(ji,jj)) / &
	467	& (sshn(ji+1,jj) - sshn(ji,jj)))
	468	wduflt(ji,jj) = 1.0_wp
	469	ELSE
	470	zcpx(ji,jj) = 0._wp
	471	wduflt(ji,jj) = 0.0_wp
	472	END IF
	473
	474	ll_tmp1 = MIN(sshn(ji,jj), sshn(ji,jj+1)) > MAX(-bathy(ji,jj), -bathy(ji,jj+1))
	475	ll_tmp2 = MAX(sshn(ji,jj) + bathy(ji,jj), sshn(ji,jj+1) + bathy(ji,jj+1)) > rn_wdmin1 + rn_wdmin2
	476	ll_tmp3 = MAX(sshn(ji,jj), sshn(ji,jj+1)) > MAX(-bathy(ji,jj), -bathy(ji,jj+1)) + &
	477	& rn_wdmin1 + rn_wdmin2
	478
	479	IF(ll_tmp1.AND.ll_tmp2) THEN
	480	zcpy(ji,jj) = 1.0_wp
	481	wdvflt(ji,jj) = 1.0_wp
	482	ELSE IF(ll_tmp3) THEN
	483	! no worries about sshn(ji,jj+1)-sshn(ji,jj) = 0, it won't happen ! here
	484	zcpy(ji,jj) = ABS((sshn(ji,jj+1) + bathy(ji,jj+1) - sshn(ji,jj) - bathy(ji,jj)) / &
	485	& (sshn(ji,jj+1) - sshn(ji,jj)))
	486	wdvflt(ji,jj) = 1.0_wp
	487	ELSE
	488	zcpy(ji,jj) = 0._wp
	489	wdvflt(ji,jj) = 0.0_wp
	490	END IF
	491	END DO
	492	END DO
	493	CALL lbc_lnk( zcpx, 'U', 1._wp ) ; CALL lbc_lnk( zcpy, 'V', 1._wp )
	494	ENDIF
	495
	496
[503]	497	! Surface value
[455]	498	DO jj = 2, jpjm1
[3764]	499	DO ji = fs_2, fs_jpim1 ! vector opt.
[455]	500	! hydrostatic pressure gradient along s-surfaces
[6225]	501	zhpi(ji,jj,1) = zcoef0 * ( e3w_n(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) &
	502	& - e3w_n(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e1u(ji,jj)
	503	zhpj(ji,jj,1) = zcoef0 * ( e3w_n(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) &
	504	& - e3w_n(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) * r1_e2v(ji,jj)
[455]	505	! s-coordinate pressure gradient correction
[6225]	506	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
	507	& * ( gde3w_n(ji+1,jj,1) - gde3w_n(ji,jj,1) ) * r1_e1u(ji,jj)
	508	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
	509	& * ( gde3w_n(ji,jj+1,1) - gde3w_n(ji,jj,1) ) * r1_e2v(ji,jj)
	510
	511
	512	IF(ln_wd) THEN
	513
	514	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
	515	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
	516	zuap = zuap * zcpx(ji,jj)
	517	zvap = zvap * zcpy(ji,jj)
	518	ENDIF
	519
[455]	520	! add to the general momentum trend
	521	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap
	522	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap
[3764]	523	END DO
	524	END DO
	525
[503]	526	! interior value (2=<jk=<jpkm1)
[3764]	527	DO jk = 2, jpkm1
	528	DO jj = 2, jpjm1
	529	DO ji = fs_2, fs_jpim1 ! vector opt.
[455]	530	! hydrostatic pressure gradient along s-surfaces
[6225]	531	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 * r1_e1u(ji,jj) &
	532	& * ( e3w_n(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) &
	533	& - e3w_n(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) )
	534	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 * r1_e2v(ji,jj) &
	535	& * ( e3w_n(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) &
	536	& - e3w_n(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) )
[455]	537	! s-coordinate pressure gradient correction
[6225]	538	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
	539	& * ( gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk) ) * r1_e1u(ji,jj)
	540	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
	541	& * ( gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk) ) * r1_e2v(ji,jj)
	542
	543	IF(ln_wd) THEN
	544	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
	545	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
	546	zuap = zuap * zcpx(ji,jj)
	547	zvap = zvap * zcpy(ji,jj)
	548	ENDIF
	549
[455]	550	! add to the general momentum trend
	551	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap
	552	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap
	553	END DO
	554	END DO
	555	END DO
[503]	556	!
[3294]	557	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj )
[6225]	558	IF(ln_wd) CALL wrk_dealloc( jpi,jpj, zcpx, zcpy )
[3294]	559	!
[455]	560	END SUBROUTINE hpg_sco
	561
[6225]	562
	563	SUBROUTINE hpg_isf( kt )
	564	!!---------------------------------------------------------------------
	565	!! * ROUTINE hpg_isf *
	566	!!
	567	!! ** Method : s-coordinate case. Jacobian scheme.
	568	!! The now hydrostatic pressure gradient at a given level, jk,
	569	!! is computed by taking the vertical integral of the in-situ
	570	!! density gradient along the model level from the suface to that
	571	!! level. s-coordinates (ln_sco): a corrective term is added
	572	!! to the horizontal pressure gradient :
	573	!! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ]
	574	!! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ]
	575	!! add it to the general momentum trend (ua,va).
	576	!! ua = ua - 1/e1u * zhpi
	577	!! va = va - 1/e2v * zhpj
	578	!! iceload is added and partial cell case are added to the top and bottom
	579	!!
	580	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
	581	!!----------------------------------------------------------------------
	582	INTEGER, INTENT(in) :: kt ! ocean time-step index
	583	!!
	584	INTEGER :: ji, jj, jk, ikt, iktp1i, iktp1j ! dummy loop indices
	585	REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars
	586	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
	587	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop
	588	REAL(wp), POINTER, DIMENSION(:,:) :: zrhdtop_oce
	589	!!----------------------------------------------------------------------
	590	!
	591	CALL wrk_alloc( jpi,jpj, 2, ztstop)
	592	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj)
	593	CALL wrk_alloc( jpi,jpj, zrhdtop_oce )
	594	!
	595	! Local constant initialization
	596	zcoef0 = - grav * 0.5_wp
	597
	598	! To use density and not density anomaly
	599	znad=1._wp
	600
	601	! iniitialised to 0. zhpi zhpi
	602	zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp
	603
	604	! compute rhd at the ice/oce interface (ocean side)
	605	! usefull to reduce residual current in the test case ISOMIP with no melting
	606	DO ji=1,jpi
	607	DO jj=1,jpj
	608	ikt=mikt(ji,jj)
	609	ztstop(ji,jj,1)=tsn(ji,jj,ikt,1)
	610	ztstop(ji,jj,2)=tsn(ji,jj,ikt,2)
	611	END DO
	612	END DO
	613	CALL eos( ztstop, risfdep, zrhdtop_oce )
	614
	615	!==================================================================================
	616	!===== Compute surface value =====================================================
	617	!==================================================================================
	618	DO jj = 2, jpjm1
	619	DO ji = fs_2, fs_jpim1 ! vector opt.
	620	ikt = mikt(ji,jj)
	621	iktp1i = mikt(ji+1,jj)
	622	iktp1j = mikt(ji,jj+1)
	623	! hydrostatic pressure gradient along s-surfaces and ice shelf pressure
	624	! we assume ISF is in isostatic equilibrium
	625	zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * e3w_n(ji+1,jj,iktp1i) &
	626	& * ( 2._wp * znad + rhd(ji+1,jj,iktp1i) + zrhdtop_oce(ji+1,jj) ) &
	627	& - 0.5_wp * e3w_n(ji,jj,ikt) &
	628	& * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) &
	629	& + ( riceload(ji+1,jj) - riceload(ji,jj)) )
	630	zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * e3w_n(ji,jj+1,iktp1j) &
	631	& * ( 2._wp * znad + rhd(ji,jj+1,iktp1j) + zrhdtop_oce(ji,jj+1) ) &
	632	& - 0.5_wp * e3w_n(ji,jj,ikt) &
	633	& * ( 2._wp * znad + rhd(ji,jj,ikt) + zrhdtop_oce(ji,jj) ) &
	634	& + ( riceload(ji,jj+1) - riceload(ji,jj)) )
	635	! s-coordinate pressure gradient correction (=0 if z coordinate)
	636	zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) &
	637	& * ( gde3w_n(ji+1,jj,1) - gde3w_n(ji,jj,1) ) * r1_e1u(ji,jj)
	638	zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) &
	639	& * ( gde3w_n(ji,jj+1,1) - gde3w_n(ji,jj,1) ) * r1_e2v(ji,jj)
	640	! add to the general momentum trend
	641	ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1)
	642	va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1)
	643	END DO
	644	END DO
	645	!==================================================================================
	646	!===== Compute interior value =====================================================
	647	!==================================================================================
	648	! interior value (2=<jk=<jpkm1)
	649	DO jk = 2, jpkm1
	650	DO jj = 2, jpjm1
	651	DO ji = fs_2, fs_jpim1 ! vector opt.
	652	! hydrostatic pressure gradient along s-surfaces
	653	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) &
	654	& * ( e3w_n(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2znad ) wmask(ji+1,jj,jk) &
	655	& - e3w_n(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2znad ) wmask(ji ,jj,jk) )
	656	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) &
	657	& * ( e3w_n(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2znad ) wmask(ji,jj+1,jk) &
	658	& - e3w_n(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2znad ) wmask(ji,jj ,jk) )
	659	! s-coordinate pressure gradient correction
	660	zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
	661	& * ( gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk) ) / e1u(ji,jj)
	662	zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) &
	663	& * ( gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk) ) / e2v(ji,jj)
	664	! add to the general momentum trend
	665	ua(ji,jj,jk) = ua(ji,jj,jk) + (zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk)
	666	va(ji,jj,jk) = va(ji,jj,jk) + (zhpj(ji,jj,jk) + zvap) * vmask(ji,jj,jk)
	667	END DO
	668	END DO
	669	END DO
	670	!
	671	CALL wrk_dealloc( jpi,jpj,2 , ztstop)
	672	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj)
	673	CALL wrk_dealloc( jpi,jpj , zrhdtop_oce )
	674	!
	675	END SUBROUTINE hpg_isf
	676
	677
[455]	678	SUBROUTINE hpg_djc( kt )
	679	!!---------------------------------------------------------------------
	680	!! * ROUTINE hpg_djc *
	681	!!
	682	!! ** Method : Density Jacobian with Cubic polynomial scheme
[3764]	683	!!
[503]	684	!! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003
[455]	685	!!----------------------------------------------------------------------
[503]	686	INTEGER, INTENT(in) :: kt ! ocean time-step index
	687	!!
	688	INTEGER :: ji, jj, jk ! dummy loop indices
	689	REAL(wp) :: zcoef0, zep, cffw ! temporary scalars
	690	REAL(wp) :: z1_10, cffu, cffx ! " "
	691	REAL(wp) :: z1_12, cffv, cffy ! " "
[6225]	692	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
[3764]	693	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj
[3294]	694	REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw
	695	REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow
	696	REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k
[6225]	697	REAL(wp), POINTER, DIMENSION(:,:) :: zcpx, zcpy !W/D pressure filter
[455]	698	!!----------------------------------------------------------------------
[3294]	699	!
[3764]	700	CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
	701	CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
	702	CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
[6225]	703	IF(ln_wd) CALL wrk_alloc( jpi,jpj, zcpx, zcpy )
[3294]	704	!
[6225]	705	!
	706	IF(ln_wd) THEN
	707	DO jj = 2, jpjm1
	708	DO ji = 2, jpim1
	709	ll_tmp1 = MIN(sshn(ji,jj), sshn(ji+1,jj)) > MAX(-bathy(ji,jj), -bathy(ji+1,jj)) &
	710	& .and. MAX(sshn(ji,jj) + bathy(ji,jj), sshn(ji+1,jj) + bathy(ji+1,jj)) &
	711	& > rn_wdmin1 + rn_wdmin2
	712	ll_tmp2 = MAX(sshn(ji,jj), sshn(ji+1,jj)) > MAX(-bathy(ji,jj), -bathy(ji+1,jj)) +&
	713	& rn_wdmin1 + rn_wdmin2
[455]	714
[6225]	715	IF(ll_tmp1) THEN
	716	zcpx(ji,jj) = 1.0_wp
	717	ELSE IF(ll_tmp2) THEN
	718	! no worries about sshn(ji+1,jj)-sshn(ji,jj) = 0, it won't happen ! here
	719	zcpx(ji,jj) = ABS((sshn(ji+1,jj) + bathy(ji+1,jj) - sshn(ji,jj) - bathy(ji,jj)) /&
	720	& (sshn(ji+1,jj) - sshn(ji,jj)))
	721	ELSE
	722	zcpx(ji,jj) = 0._wp
	723	END IF
	724
	725	ll_tmp1 = MIN(sshn(ji,jj), sshn(ji,jj+1)) > MAX(-bathy(ji,jj), -bathy(ji,jj+1)) &
	726	& .and. MAX(sshn(ji,jj) + bathy(ji,jj), sshn(ji,jj+1) + bathy(ji,jj+1)) &
	727	& > rn_wdmin1 + rn_wdmin2
	728	ll_tmp2 = MAX(sshn(ji,jj), sshn(ji,jj+1)) > MAX(-bathy(ji,jj), -bathy(ji,jj+1)) +&
	729	& rn_wdmin1 + rn_wdmin2
	730
	731	IF(ll_tmp1) THEN
	732	zcpy(ji,jj) = 1.0_wp
	733	ELSE IF(ll_tmp2) THEN
	734	! no worries about sshn(ji,jj+1)-sshn(ji,jj) = 0, it won't happen ! here
	735	zcpy(ji,jj) = ABS((sshn(ji,jj+1) + bathy(ji,jj+1) - sshn(ji,jj) - bathy(ji,jj)) /&
	736	& (sshn(ji,jj+1) - sshn(ji,jj)))
	737	ELSE
	738	zcpy(ji,jj) = 0._wp
	739	END IF
	740	END DO
	741	END DO
	742	CALL lbc_lnk( zcpx, 'U', 1._wp ) ; CALL lbc_lnk( zcpy, 'V', 1._wp )
	743	ENDIF
	744
	745
[455]	746	IF( kt == nit000 ) THEN
	747	IF(lwp) WRITE(numout,*)
	748	IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend'
	749	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme'
[216]	750	ENDIF
	751
[503]	752	! Local constant initialization
[2528]	753	zcoef0 = - grav * 0.5_wp
	754	z1_10 = 1._wp / 10._wp
	755	z1_12 = 1._wp / 12._wp
[455]	756
	757	!----------------------------------------------------------------------------------------
	758	! compute and store in provisional arrays elementary vertical and horizontal differences
	759	!----------------------------------------------------------------------------------------
	760
	761	!!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really
	762
	763	DO jk = 2, jpkm1
	764	DO jj = 2, jpjm1
	765	DO ji = fs_2, fs_jpim1 ! vector opt.
[6225]	766	drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1)
	767	dzz (ji,jj,jk) = gde3w_n(ji ,jj ,jk) - gde3w_n(ji,jj,jk-1)
	768	drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk )
	769	dzx (ji,jj,jk) = gde3w_n(ji+1,jj ,jk) - gde3w_n(ji,jj,jk )
	770	drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk )
	771	dzy (ji,jj,jk) = gde3w_n(ji ,jj+1,jk) - gde3w_n(ji,jj,jk )
[455]	772	END DO
	773	END DO
	774	END DO
	775
	776	!-------------------------------------------------------------------------
	777	! compute harmonic averages using eq. 5.18
	778	!-------------------------------------------------------------------------
	779	zep = 1.e-15
	780
[503]	781	!!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2)
	782	!!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj
[455]	783
	784	DO jk = 2, jpkm1
	785	DO jj = 2, jpjm1
	786	DO ji = fs_2, fs_jpim1 ! vector opt.
[2528]	787	cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1)
[455]	788
[2528]	789	cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk )
	790	cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk )
[3764]	791
[2528]	792	cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk )
	793	cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk )
[455]	794
	795	IF( cffw > zep) THEN
[2528]	796	drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) &
	797	& / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) )
[455]	798	ELSE
[2528]	799	drhow(ji,jj,jk) = 0._wp
[455]	800	ENDIF
	801
[2528]	802	dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) &
	803	& / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) )
[455]	804
	805	IF( cffu > zep ) THEN
[2528]	806	drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) &
	807	& / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) )
[455]	808	ELSE
[2528]	809	drhou(ji,jj,jk ) = 0._wp
[455]	810	ENDIF
	811
	812	IF( cffx > zep ) THEN
[2528]	813	dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) &
	814	& / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) )
[455]	815	ELSE
[2528]	816	dzu(ji,jj,jk) = 0._wp
[455]	817	ENDIF
	818
	819	IF( cffv > zep ) THEN
[2528]	820	drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) &
	821	& / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) )
[455]	822	ELSE
[2528]	823	drhov(ji,jj,jk) = 0._wp
[455]	824	ENDIF
	825
	826	IF( cffy > zep ) THEN
[2528]	827	dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) &
	828	& / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) )
[455]	829	ELSE
[2528]	830	dzv(ji,jj,jk) = 0._wp
[455]	831	ENDIF
	832
	833	END DO
	834	END DO
	835	END DO
	836
	837	!----------------------------------------------------------------------------------
	838	! apply boundary conditions at top and bottom using 5.36-5.37
	839	!----------------------------------------------------------------------------------
[2528]	840	drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 )
	841	drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 )
	842	drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 )
[455]	843
[2528]	844	drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1)
	845	drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1)
	846	drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1)
[455]	847
	848
	849	!--------------------------------------------------------------
	850	! Upper half of top-most grid box, compute and store
	851	!-------------------------------------------------------------
	852
[6225]	853	!!bug gm : e3w-gde3w = 0.5*e3w .... and gde3w(2)-gde3w(1)=e3w(2) .... to be verified
	854	! true if gde3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be
[455]	855
	856	DO jj = 2, jpjm1
	857	DO ji = fs_2, fs_jpim1 ! vector opt.
[6225]	858	rho_k(ji,jj,1) = -grav * ( e3w_n(ji,jj,1) - gde3w_n(ji,jj,1) ) &
	859	& * ( rhd(ji,jj,1) &
	860	& + 0.5_wp * ( rhd (ji,jj,2) - rhd (ji,jj,1) ) &
	861	& * ( e3w_n (ji,jj,1) - gde3w_n(ji,jj,1) ) &
	862	& / ( gde3w_n(ji,jj,2) - gde3w_n(ji,jj,1) ) )
[455]	863	END DO
	864	END DO
	865
	866	!!bug gm : here also, simplification is possible
	867	!!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop
	868
	869	DO jk = 2, jpkm1
	870	DO jj = 2, jpjm1
	871	DO ji = fs_2, fs_jpim1 ! vector opt.
	872
[6225]	873	rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) &
	874	& * ( gde3w_n(ji,jj,jk) - gde3w_n(ji,jj,jk-1) ) &
	875	& - grav * z1_10 * ( &
	876	& ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) &
	877	& * ( gde3w_n(ji,jj,jk) - gde3w_n(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) &
	878	& - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) &
	879	& * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) &
[455]	880	& )
	881
[6225]	882	rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) &
	883	& * ( gde3w_n(ji+1,jj,jk) - gde3w_n(ji,jj,jk) ) &
	884	& - grav* z1_10 * ( &
	885	& ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) &
	886	& * ( gde3w_n(ji+1,jj,jk) - gde3w_n(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) &
	887	& - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) &
	888	& * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) &
[455]	889	& )
	890
[6225]	891	rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) &
	892	& * ( gde3w_n(ji,jj+1,jk) - gde3w_n(ji,jj,jk) ) &
	893	& - grav* z1_10 * ( &
	894	& ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) &
	895	& * ( gde3w_n(ji,jj+1,jk) - gde3w_n(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) &
	896	& - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) &
	897	& * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) &
[455]	898	& )
	899
	900	END DO
	901	END DO
	902	END DO
	903	CALL lbc_lnk(rho_k,'W',1.)
	904	CALL lbc_lnk(rho_i,'U',1.)
	905	CALL lbc_lnk(rho_j,'V',1.)
	906
	907
	908	! ---------------
	909	! Surface value
	910	! ---------------
	911	DO jj = 2, jpjm1
	912	DO ji = fs_2, fs_jpim1 ! vector opt.
[6225]	913	zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) * r1_e1u(ji,jj)
	914	zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) * r1_e2v(ji,jj)
	915	IF(ln_wd) THEN
	916	zhpi(ji,jj,1) = zhpi(ji,jj,1) * zcpx(ji,jj)
	917	zhpj(ji,jj,1) = zhpj(ji,jj,1) * zcpy(ji,jj)
	918	ENDIF
[455]	919	! add to the general momentum trend
	920	ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1)
	921	va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1)
	922	END DO
	923	END DO
	924
	925	! ----------------
	926	! interior value (2=<jk=<jpkm1)
	927	! ----------------
	928	DO jk = 2, jpkm1
[3764]	929	DO jj = 2, jpjm1
[455]	930	DO ji = fs_2, fs_jpim1 ! vector opt.
	931	! hydrostatic pressure gradient along s-surfaces
	932	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) &
	933	& + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) &
[6225]	934	& - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) * r1_e1u(ji,jj)
[455]	935	zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) &
	936	& + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) &
[6225]	937	& -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) * r1_e2v(ji,jj)
	938	IF(ln_wd) THEN
	939	zhpi(ji,jj,jk) = zhpi(ji,jj,jk) * zcpx(ji,jj)
	940	zhpj(ji,jj,jk) = zhpj(ji,jj,jk) * zcpy(ji,jj)
	941	ENDIF
[455]	942	! add to the general momentum trend
	943	ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk)
	944	va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk)
	945	END DO
	946	END DO
	947	END DO
[503]	948	!
[3764]	949	CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw )
	950	CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow )
	951	CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj )
[6225]	952	IF(ln_wd) CALL wrk_dealloc( jpi,jpj, zcpx, zcpy )
[2715]	953	!
[455]	954	END SUBROUTINE hpg_djc
	955
	956
[3294]	957	SUBROUTINE hpg_prj( kt )
[455]	958	!!---------------------------------------------------------------------
[3294]	959	!! * ROUTINE hpg_prj *
[455]	960	!!
[3294]	961	!! ** Method : s-coordinate case.
	962	!! A Pressure-Jacobian horizontal pressure gradient method
	963	!! based on the constrained cubic-spline interpolation for
	964	!! all vertical coordinate systems
[455]	965	!!
[3294]	966	!! ** Action : - Update (ua,va) with the now hydrastatic pressure trend
[455]	967	!!----------------------------------------------------------------------
[3294]	968	INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear
	969	INTEGER, INTENT(in) :: kt ! ocean time-step index
[503]	970	!!
[3294]	971	INTEGER :: ji, jj, jk, jkk ! dummy loop indices
[6225]	972	REAL(wp) :: zcoef0, znad ! local scalars
	973	!
[3294]	974	!! The local variables for the correction term
	975	INTEGER :: jk1, jis, jid, jjs, jjd
[6225]	976	LOGICAL :: ll_tmp1, ll_tmp2 ! local logical variables
[3294]	977	REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps
[3764]	978	REAL(wp) :: zrhdt1
[3294]	979	REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2
[3764]	980	REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh
[3294]	981	REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp
[6225]	982	REAL(wp), POINTER, DIMENSION(:,:) :: zsshu_n, zsshv_n
	983	REAL(wp), POINTER, DIMENSION(:,:) :: zcpx, zcpy !W/D pressure filter
[455]	984	!!----------------------------------------------------------------------
[3294]	985	!
[6225]	986	CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
	987	CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh )
	988	CALL wrk_alloc( jpi,jpj, zsshu_n, zsshv_n )
	989	IF(ln_wd) CALL wrk_alloc( jpi,jpj, zcpx, zcpy )
[3294]	990	!
[455]	991	IF( kt == nit000 ) THEN
	992	IF(lwp) WRITE(numout,*)
[3294]	993	IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend'
	994	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian'
[3]	995	ENDIF
	996
[3294]	997	! Local constant initialization
[3764]	998	zcoef0 = - grav
[6225]	999	znad = 1._wp
	1000	IF( ln_linssh ) znad = 0._wp
[3]	1001
[6225]	1002	IF(ln_wd) THEN
	1003	DO jj = 2, jpjm1
	1004	DO ji = 2, jpim1
	1005	ll_tmp1 = MIN(sshn(ji,jj), sshn(ji+1,jj)) > MAX(-bathy(ji,jj), -bathy(ji+1,jj)) &
	1006	& .and. MAX(sshn(ji,jj) + bathy(ji,jj), sshn(ji+1,jj) + bathy(ji+1,jj)) &
	1007	& > rn_wdmin1 + rn_wdmin2
	1008	ll_tmp2 = MAX(sshn(ji,jj), sshn(ji+1,jj)) > MAX(-bathy(ji,jj), -bathy(ji+1,jj)) +&
	1009	& rn_wdmin1 + rn_wdmin2
	1010
	1011	IF(ll_tmp1) THEN
	1012	zcpx(ji,jj) = 1.0_wp
	1013	ELSE IF(ll_tmp2) THEN
	1014	! no worries about sshn(ji+1,jj)-sshn(ji,jj) = 0, it won't happen ! here
	1015	zcpx(ji,jj) = ABS((sshn(ji+1,jj) + bathy(ji+1,jj) - sshn(ji,jj) - bathy(ji,jj)) /&
	1016	& (sshn(ji+1,jj) - sshn(ji,jj)))
	1017	ELSE
	1018	zcpx(ji,jj) = 0._wp
	1019	END IF
	1020
	1021	ll_tmp1 = MIN(sshn(ji,jj), sshn(ji,jj+1)) > MAX(-bathy(ji,jj), -bathy(ji,jj+1)) &
	1022	& .and. MAX(sshn(ji,jj) + bathy(ji,jj), sshn(ji,jj+1) + bathy(ji,jj+1)) &
	1023	& > rn_wdmin1 + rn_wdmin2
	1024	ll_tmp2 = MAX(sshn(ji,jj), sshn(ji,jj+1)) > MAX(-bathy(ji,jj), -bathy(ji,jj+1)) +&
	1025	& rn_wdmin1 + rn_wdmin2
	1026
	1027	IF(ll_tmp1.OR.ll_tmp2) THEN
	1028	zcpy(ji,jj) = 1.0_wp
	1029	ELSE IF(ll_tmp2) THEN
	1030	! no worries about sshn(ji,jj+1)-sshn(ji,jj) = 0, it won't happen ! here
	1031	zcpy(ji,jj) = ABS((sshn(ji,jj+1) + bathy(ji,jj+1) - sshn(ji,jj) - bathy(ji,jj)) /&
	1032	& (sshn(ji,jj+1) - sshn(ji,jj)))
	1033	ELSE
	1034	zcpy(ji,jj) = 0._wp
	1035	END IF
	1036	END DO
	1037	END DO
	1038	CALL lbc_lnk( zcpx, 'U', 1._wp ) ; CALL lbc_lnk( zcpy, 'V', 1._wp )
	1039	ENDIF
	1040
[3294]	1041	! Clean 3-D work arrays
	1042	zhpi(:,:,:) = 0._wp
	1043	zrhh(:,:,:) = rhd(:,:,:)
[3764]	1044
[3294]	1045	! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate
	1046	DO jj = 1, jpj
[3764]	1047	DO ji = 1, jpi
[3294]	1048	jk = mbathy(ji,jj)
[6225]	1049	IF( jk <= 0 ) THEN ; zrhh(ji,jj, : ) = 0._wp
	1050	ELSEIF( jk == 1 ) THEN ; zrhh(ji,jj,jk+1:jpk) = rhd(ji,jj,jk)
	1051	ELSEIF( jk < jpkm1 ) THEN
[3294]	1052	DO jkk = jk+1, jpk
[6225]	1053	zrhh(ji,jj,jkk) = interp1(gde3w_n(ji,jj,jkk ), gde3w_n(ji,jj,jkk-1), &
	1054	& gde3w_n(ji,jj,jkk-2), rhd (ji,jj,jkk-1), rhd(ji,jj,jkk-2))
[3764]	1055	END DO
[3294]	1056	ENDIF
	1057	END DO
	1058	END DO
[3]	1059
[3632]	1060	! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)"
[6225]	1061	DO jj = 1, jpj
	1062	DO ji = 1, jpi
	1063	zdept(ji,jj,1) = 0.5_wp * e3w_n(ji,jj,1) - sshn(ji,jj) * znad
	1064	END DO
	1065	END DO
[455]	1066
[6225]	1067	DO jk = 2, jpk
	1068	DO jj = 1, jpj
	1069	DO ji = 1, jpi
	1070	zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + e3w_n(ji,jj,jk)
	1071	END DO
	1072	END DO
	1073	END DO
[455]	1074
[6225]	1075	fsp(:,:,:) = zrhh (:,:,:)
[3632]	1076	xsp(:,:,:) = zdept(:,:,:)
	1077
[3764]	1078	! Construct the vertical density profile with the
[3294]	1079	! constrained cubic spline interpolation
	1080	! rho(z) = asp + bspz + cspz^2 + dsp*z^3
[6225]	1081	CALL cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
[3294]	1082
	1083	! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)"
	1084	DO jj = 2, jpj
[3764]	1085	DO ji = 2, jpi
[6225]	1086	zrhdt1 = zrhh(ji,jj,1) - interp3( zdept(ji,jj,1), asp(ji,jj,1), bsp(ji,jj,1), &
	1087	& csp(ji,jj,1), dsp(ji,jj,1) ) * 0.25_wp * e3w_n(ji,jj,1)
[3294]	1088
	1089	! assuming linear profile across the top half surface layer
[6225]	1090	zhpi(ji,jj,1) = 0.5_wp * e3w_n(ji,jj,1) * zrhdt1
[3294]	1091	END DO
[455]	1092	END DO
	1093
[3294]	1094	! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)"
[3764]	1095	DO jk = 2, jpkm1
	1096	DO jj = 2, jpj
[3294]	1097	DO ji = 2, jpi
[6225]	1098	zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + &
	1099	& integ_spline( zdept(ji,jj,jk-1), zdept(ji,jj,jk), &
	1100	& asp (ji,jj,jk-1), bsp (ji,jj,jk-1), &
	1101	& csp (ji,jj,jk-1), dsp (ji,jj,jk-1) )
[3294]	1102	END DO
	1103	END DO
[455]	1104	END DO
	1105
[3294]	1106	! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1)
[6225]	1107
	1108	! Prepare zsshu_n and zsshv_n
[3764]	1109	DO jj = 2, jpjm1
	1110	DO ji = 2, jpim1
[6225]	1111	!!gm BUG ? if it is ssh at u- & v-point then it should be:
	1112	! zsshu_n(ji,jj) = (e1e2t(ji,jj) * sshn(ji,jj) + e1e2t(ji+1,jj) * sshn(ji+1,jj)) * &
	1113	! & r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
	1114	! zsshv_n(ji,jj) = (e1e2t(ji,jj) * sshn(ji,jj) + e1e2t(ji,jj+1) * sshn(ji,jj+1)) * &
	1115	! & r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
	1116	!!gm not this:
	1117	zsshu_n(ji,jj) = (e1e2u(ji,jj) * sshn(ji,jj) + e1e2u(ji+1, jj) * sshn(ji+1,jj)) * &
	1118	& r1_e1e2u(ji,jj) * umask(ji,jj,1) * 0.5_wp
	1119	zsshv_n(ji,jj) = (e1e2v(ji,jj) * sshn(ji,jj) + e1e2v(ji+1, jj) * sshn(ji,jj+1)) * &
	1120	& r1_e1e2v(ji,jj) * vmask(ji,jj,1) * 0.5_wp
[3294]	1121	END DO
[455]	1122	END DO
	1123
[6225]	1124	CALL lbc_lnk (zsshu_n, 'U', 1.)
	1125	CALL lbc_lnk (zsshv_n, 'V', 1.)
	1126
	1127	DO jj = 2, jpjm1
	1128	DO ji = 2, jpim1
	1129	zu(ji,jj,1) = - ( e3u_n(ji,jj,1) - zsshu_n(ji,jj) * znad)
	1130	zv(ji,jj,1) = - ( e3v_n(ji,jj,1) - zsshv_n(ji,jj) * znad)
	1131	END DO
	1132	END DO
	1133
[3764]	1134	DO jk = 2, jpkm1
	1135	DO jj = 2, jpjm1
	1136	DO ji = 2, jpim1
[6225]	1137	zu(ji,jj,jk) = zu(ji,jj,jk-1) - e3u_n(ji,jj,jk)
	1138	zv(ji,jj,jk) = zv(ji,jj,jk-1) - e3v_n(ji,jj,jk)
[3294]	1139	END DO
	1140	END DO
[455]	1141	END DO
[3764]	1142
	1143	DO jk = 1, jpkm1
	1144	DO jj = 2, jpjm1
	1145	DO ji = 2, jpim1
[6225]	1146	zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * e3u_n(ji,jj,jk)
	1147	zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * e3v_n(ji,jj,jk)
[3294]	1148	END DO
	1149	END DO
	1150	END DO
[455]	1151
[3632]	1152	DO jk = 1, jpkm1
	1153	DO jj = 2, jpjm1
	1154	DO ji = 2, jpim1
[6225]	1155	zu(ji,jj,jk) = MIN( zu(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
	1156	zu(ji,jj,jk) = MAX( zu(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji+1,jj,jk) ) )
	1157	zv(ji,jj,jk) = MIN( zv(ji,jj,jk) , MAX( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
	1158	zv(ji,jj,jk) = MAX( zv(ji,jj,jk) , MIN( -zdept(ji,jj,jk) , -zdept(ji,jj+1,jk) ) )
[3632]	1159	END DO
	1160	END DO
	1161	END DO
	1162
	1163
[3764]	1164	DO jk = 1, jpkm1
	1165	DO jj = 2, jpjm1
	1166	DO ji = 2, jpim1
[3294]	1167	zpwes = 0._wp; zpwed = 0._wp
	1168	zpnss = 0._wp; zpnsd = 0._wp
	1169	zuijk = zu(ji,jj,jk)
	1170	zvijk = zv(ji,jj,jk)
	1171
	1172	!!!!! for u equation
	1173	IF( jk <= mbku(ji,jj) ) THEN
[3632]	1174	IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN
[3294]	1175	jis = ji + 1; jid = ji
	1176	ELSE
	1177	jis = ji; jid = ji +1
	1178	ENDIF
	1179
	1180	! integrate the pressure on the shallow side
[3764]	1181	jk1 = jk
[3632]	1182	DO WHILE ( -zdept(jis,jj,jk1) > zuijk )
[3294]	1183	IF( jk1 == mbku(ji,jj) ) THEN
[3632]	1184	zuijk = -zdept(jis,jj,jk1)
[3294]	1185	EXIT
	1186	ENDIF
[3632]	1187	zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk)
[3764]	1188	zpwes = zpwes + &
[3632]	1189	integ_spline(zdept(jis,jj,jk1), zdeps, &
[3294]	1190	asp(jis,jj,jk1), bsp(jis,jj,jk1), &
	1191	csp(jis,jj,jk1), dsp(jis,jj,jk1))
	1192	jk1 = jk1 + 1
	1193	END DO
[3764]	1194
[3294]	1195	! integrate the pressure on the deep side
[3764]	1196	jk1 = jk
[3632]	1197	DO WHILE ( -zdept(jid,jj,jk1) < zuijk )
[3294]	1198	IF( jk1 == 1 ) THEN
[3632]	1199	zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad)
	1200	zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), &
	1201	bsp(jid,jj,1), csp(jid,jj,1), &
	1202	dsp(jid,jj,1)) * zdeps
	1203	zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps
[3294]	1204	EXIT
	1205	ENDIF
[3632]	1206	zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk)
[3764]	1207	zpwed = zpwed + &
[3632]	1208	integ_spline(zdeps, zdept(jid,jj,jk1), &
[3294]	1209	asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), &
	1210	csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) )
	1211	jk1 = jk1 - 1
	1212	END DO
[3764]	1213
[3294]	1214	! update the momentum trends in u direction
	1215
[6225]	1216	zdpdx1 = zcoef0 * r1_e1u(ji,jj) * ( zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk) )
	1217	IF( .NOT.ln_linssh ) THEN
	1218	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * &
	1219	& ( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) )
[3294]	1220	ELSE
[6225]	1221	zdpdx2 = zcoef0 * r1_e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed)
[3294]	1222	ENDIF
[6225]	1223	IF(ln_wd) THEN
	1224	zdpdx1 = zdpdx1 * zcpx(ji,jj)
	1225	zdpdx2 = zdpdx2 * zcpx(ji,jj)
	1226	ENDIF
	1227	ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * umask(ji,jj,jk)
[3294]	1228	ENDIF
[3764]	1229
[3294]	1230	!!!!! for v equation
	1231	IF( jk <= mbkv(ji,jj) ) THEN
[3632]	1232	IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN
[3294]	1233	jjs = jj + 1; jjd = jj
	1234	ELSE
	1235	jjs = jj ; jjd = jj + 1
	1236	ENDIF
	1237
	1238	! integrate the pressure on the shallow side
[3764]	1239	jk1 = jk
[3632]	1240	DO WHILE ( -zdept(ji,jjs,jk1) > zvijk )
[3294]	1241	IF( jk1 == mbkv(ji,jj) ) THEN
[3632]	1242	zvijk = -zdept(ji,jjs,jk1)
[3294]	1243	EXIT
	1244	ENDIF
[3632]	1245	zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk)
[3764]	1246	zpnss = zpnss + &
[3632]	1247	integ_spline(zdept(ji,jjs,jk1), zdeps, &
[3294]	1248	asp(ji,jjs,jk1), bsp(ji,jjs,jk1), &
	1249	csp(ji,jjs,jk1), dsp(ji,jjs,jk1) )
	1250	jk1 = jk1 + 1
	1251	END DO
[3764]	1252
[3294]	1253	! integrate the pressure on the deep side
[3764]	1254	jk1 = jk
[3632]	1255	DO WHILE ( -zdept(ji,jjd,jk1) < zvijk )
[3294]	1256	IF( jk1 == 1 ) THEN
[3632]	1257	zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad)
	1258	zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), &
	1259	bsp(ji,jjd,1), csp(ji,jjd,1), &
	1260	dsp(ji,jjd,1) ) * zdeps
	1261	zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps
[3294]	1262	EXIT
	1263	ENDIF
[3632]	1264	zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk)
[3764]	1265	zpnsd = zpnsd + &
[3632]	1266	integ_spline(zdeps, zdept(ji,jjd,jk1), &
[3294]	1267	asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), &
	1268	csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) )
	1269	jk1 = jk1 - 1
	1270	END DO
	1271
[3764]	1272
[3294]	1273	! update the momentum trends in v direction
	1274
[6225]	1275	zdpdy1 = zcoef0 * r1_e2v(ji,jj) * ( zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk) )
	1276	IF( .NOT.ln_linssh ) THEN
	1277	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * &
	1278	( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) )
[3294]	1279	ELSE
[6225]	1280	zdpdy2 = zcoef0 * r1_e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd )
[3294]	1281	ENDIF
[6225]	1282	IF(ln_wd) THEN
	1283	zdpdy1 = zdpdy1 * zcpy(ji,jj)
	1284	zdpdy2 = zdpdy2 * zcpy(ji,jj)
	1285	ENDIF
[3294]	1286
[6225]	1287	va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2) * vmask(ji,jj,jk)
[3294]	1288	ENDIF
[6225]	1289	!
	1290	END DO
	1291	END DO
[455]	1292	END DO
[503]	1293	!
[6225]	1294	CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp )
	1295	CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh )
	1296	CALL wrk_dealloc( jpi,jpj, zsshu_n, zsshv_n )
	1297	IF(ln_wd) CALL wrk_dealloc( jpi,jpj, zcpx, zcpy )
[2715]	1298	!
[3294]	1299	END SUBROUTINE hpg_prj
[455]	1300
[6225]	1301
	1302	SUBROUTINE cspline( fsp, xsp, asp, bsp, csp, dsp, polynomial_type )
[3294]	1303	!!----------------------------------------------------------------------
	1304	!! * ROUTINE cspline *
[3764]	1305	!!
[3294]	1306	!! ** Purpose : constrained cubic spline interpolation
[3764]	1307	!!
	1308	!! ** Method : f(x) = asp + bspx + cspx^2 + dsp*x^3
[6225]	1309	!!
[3294]	1310	!! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation
	1311	!!----------------------------------------------------------------------
[6225]	1312	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: fsp, xsp ! value and coordinate
	1313	REAL(wp), DIMENSION(:,:,:), INTENT( out) :: asp, bsp, csp, dsp ! coefficients of the interpoated function
	1314	INTEGER , INTENT(in ) :: polynomial_type ! 1: cubic spline ; 2: Linear
	1315	!
[3294]	1316	INTEGER :: ji, jj, jk ! dummy loop indices
	1317	INTEGER :: jpi, jpj, jpkm1
	1318	REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp
	1319	REAL(wp) :: zdxtmp1, zdxtmp2, zalpha
	1320	REAL(wp) :: zdf(size(fsp,3))
	1321	!!----------------------------------------------------------------------
[6225]	1322	!
	1323	!!gm WHAT !!!!! THIS IS VERY DANGEROUS !!!!!
[3294]	1324	jpi = size(fsp,1)
	1325	jpj = size(fsp,2)
	1326	jpkm1 = size(fsp,3) - 1
[6225]	1327	!
[3294]	1328	IF (polynomial_type == 1) THEN ! Constrained Cubic Spline
	1329	DO ji = 1, jpi
	1330	DO jj = 1, jpj
[3764]	1331	!!Fritsch&Butland's method, 1984 (preferred, but more computation)
[3294]	1332	! DO jk = 2, jpkm1-1
[3764]	1333	! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1)
	1334	! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1335	! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1
	1336	! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2
	1337	!
	1338	! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp
[3764]	1339	!
[3294]	1340	! IF(zdf1 * zdf2 <= 0._wp) THEN
	1341	! zdf(jk) = 0._wp
	1342	! ELSE
	1343	! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 )
	1344	! ENDIF
	1345	! END DO
[3764]	1346
[3294]	1347	!!Simply geometric average
	1348	DO jk = 2, jpkm1-1
	1349	zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1))
	1350	zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk))
[3764]	1351
[3294]	1352	IF(zdf1 * zdf2 <= 0._wp) THEN
	1353	zdf(jk) = 0._wp
	1354	ELSE
	1355	zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2)
	1356	ENDIF
	1357	END DO
[3764]	1358
[3294]	1359	zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / &
[6225]	1360	& ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2)
[3294]	1361	zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / &
[6225]	1362	& ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - 0.5_wp * zdf(jpkm1 - 1)
[3764]	1363
[3294]	1364	DO jk = 1, jpkm1 - 1
[3764]	1365	zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1366	ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp
	1367	ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp
[3764]	1368	zddf1 = -2._wp * ztmp1 + ztmp2
[3294]	1369	ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp
[3764]	1370	zddf2 = 2._wp * ztmp1 - ztmp2
	1371
[3294]	1372	dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp
	1373	csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp
[3764]	1374	bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - &
[3294]	1375	& csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - &
	1376	& dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - &
	1377	& xsp(ji,jj,jk+1) * xsp(ji,jj,jk))
	1378	asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + &
	1379	& (xsp(ji,jj,jk) * (csp(ji,jj,jk) + &
	1380	& dsp(ji,jj,jk) * xsp(ji,jj,jk))))
	1381	END DO
	1382	END DO
	1383	END DO
[3764]	1384
[6225]	1385	ELSEIF ( polynomial_type == 2 ) THEN ! Linear
[3294]	1386	DO ji = 1, jpi
	1387	DO jj = 1, jpj
	1388	DO jk = 1, jpkm1-1
[3764]	1389	zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk)
[3294]	1390	ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk)
[3764]	1391
[3294]	1392	dsp(ji,jj,jk) = 0._wp
	1393	csp(ji,jj,jk) = 0._wp
	1394	bsp(ji,jj,jk) = ztmp1 / zdxtmp
	1395	asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk)
	1396	END DO
	1397	END DO
	1398	END DO
	1399
	1400	ELSE
	1401	CALL ctl_stop( 'invalid polynomial type in cspline' )
	1402	ENDIF
	1403
	1404	END SUBROUTINE cspline
	1405
	1406
[3764]	1407	FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f)
[3294]	1408	!!----------------------------------------------------------------------
	1409	!! * ROUTINE interp1 *
[3764]	1410	!!
[3294]	1411	!! ** Purpose : 1-d linear interpolation
[3764]	1412	!!
[6225]	1413	!! ** Method : interpolation is straight forward
[3764]	1414	!! extrapolation is also permitted (no value limit)
[3294]	1415	!!----------------------------------------------------------------------
[3764]	1416	REAL(wp), INTENT(in) :: x, xl, xr, fl, fr
[3294]	1417	REAL(wp) :: f ! result of the interpolation (extrapolation)
	1418	REAL(wp) :: zdeltx
	1419	!!----------------------------------------------------------------------
[6225]	1420	!
[3294]	1421	zdeltx = xr - xl
[6225]	1422	IF( abs(zdeltx) <= 10._wp * EPSILON(x) ) THEN
	1423	f = 0.5_wp * (fl + fr)
[3294]	1424	ELSE
[6225]	1425	f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx
[3294]	1426	ENDIF
[6225]	1427	!
[3294]	1428	END FUNCTION interp1
	1429
[6225]	1430
	1431	FUNCTION interp2( x, a, b, c, d ) RESULT(f)
[3294]	1432	!!----------------------------------------------------------------------
	1433	!! * ROUTINE interp1 *
[3764]	1434	!!
[3294]	1435	!! ** Purpose : 1-d constrained cubic spline interpolation
[3764]	1436	!!
[3294]	1437	!! ** Method : cubic spline interpolation
	1438	!!
	1439	!!----------------------------------------------------------------------
[3764]	1440	REAL(wp), INTENT(in) :: x, a, b, c, d
[3294]	1441	REAL(wp) :: f ! value from the interpolation
	1442	!!----------------------------------------------------------------------
[6225]	1443	!
[3764]	1444	f = a + x* ( b + x * ( c + d * x ) )
[6225]	1445	!
[3294]	1446	END FUNCTION interp2
	1447
	1448
[6225]	1449	FUNCTION interp3( x, a, b, c, d ) RESULT(f)
[3294]	1450	!!----------------------------------------------------------------------
	1451	!! * ROUTINE interp1 *
[3764]	1452	!!
[3294]	1453	!! ** Purpose : Calculate the first order of deriavtive of
	1454	!! a cubic spline function y=a+bx+cx^2+d*x^3
[3764]	1455	!!
[3294]	1456	!! ** Method : f=dy/dx=b+2cx+3dx^2
	1457	!!
	1458	!!----------------------------------------------------------------------
[3764]	1459	REAL(wp), INTENT(in) :: x, a, b, c, d
[3294]	1460	REAL(wp) :: f ! value from the interpolation
	1461	!!----------------------------------------------------------------------
[6225]	1462	!
[3294]	1463	f = b + x * ( 2._wp * c + 3._wp * d * x)
[6225]	1464	!
[3294]	1465	END FUNCTION interp3
	1466
[3764]	1467
[6225]	1468	FUNCTION integ_spline( xl, xr, a, b, c, d ) RESULT(f)
[3294]	1469	!!----------------------------------------------------------------------
	1470	!! * ROUTINE interp1 *
[3764]	1471	!!
[3294]	1472	!! ** Purpose : 1-d constrained cubic spline integration
	1473	!!
[3764]	1474	!! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr
	1475	!!
[3294]	1476	!!----------------------------------------------------------------------
[3764]	1477	REAL(wp), INTENT(in) :: xl, xr, a, b, c, d
	1478	REAL(wp) :: za1, za2, za3
[3294]	1479	REAL(wp) :: f ! integration result
	1480	!!----------------------------------------------------------------------
[6225]	1481	!
[3764]	1482	za1 = 0.5_wp * b
	1483	za2 = c / 3.0_wp
	1484	za3 = 0.25_wp * d
[6225]	1485	!
[3294]	1486	f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - &
	1487	& xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) )
[6225]	1488	!
[3632]	1489	END FUNCTION integ_spline
[3294]	1490
[3]	1491	!!======================================================================
	1492	END MODULE dynhpg
[3632]	1493

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