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traadv_fct.F90 in NEMO/branches/2020/dev_r14116_HPC-04_mcastril_Mixed_Precision_implementation_final/src/OCE/TRA – NEMO

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source: NEMO/branches/2020/dev_r14116_HPC-04_mcastril_Mixed_Precision_implementation_final/src/OCE/TRA/traadv_fct.F90 @ 14762

Last change on this file since 14762 was 14649, checked in by sparonuz, 3 years ago
Corrected variables/function names spelled with wrong camelcase mask
Property svn:keywords set to `Id`
File size: 35.9 KB

Rev	Line
[5770]	1	MODULE traadv_fct
[3]	2	!!==============================================================================
[5770]	3	!! * MODULE traadv_fct *
	4	!! Ocean tracers: horizontal & vertical advective trend (2nd/4th order Flux Corrected Transport method)
[3]	5	!!==============================================================================
[5770]	6	!! History : 3.7 ! 2015-09 (L. Debreu, G. Madec) original code (inspired from traadv_tvd.F90)
[503]	7	!!----------------------------------------------------------------------
[3]	8
	9	!!----------------------------------------------------------------------
[5770]	10	!! tra_adv_fct : update the tracer trend with a 3D advective trends using a 2nd or 4th order FCT scheme
	11	!! with sub-time-stepping in the vertical direction
[14072]	12	!! nonosc : compute monotonic tracer fluxes by a non-oscillatory algorithm
[5770]	13	!! interp_4th_cpt : 4th order compact scheme for the vertical component of the advection
[3]	14	!!----------------------------------------------------------------------
[3625]	15	USE oce ! ocean dynamics and active tracers
	16	USE dom_oce ! ocean space and time domain
[4990]	17	USE trc_oce ! share passive tracers/Ocean variables
	18	USE trd_oce ! trends: ocean variables
[3625]	19	USE trdtra ! tracers trends
[4990]	20	USE diaptr ! poleward transport diagnostics
[7646]	21	USE diaar5 ! AR5 diagnostics
[12489]	22	USE phycst , ONLY : rho0_rcp
[11407]	23	USE zdf_oce , ONLY : ln_zad_Aimp
[4990]	24	!
[5770]	25	USE in_out_manager ! I/O manager
[14072]	26	USE iom !
[3625]	27	USE lib_mpp ! MPP library
[14072]	28	USE lbclnk ! ocean lateral boundary condition (or mpp link)
	29	USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined)
[3]	30
	31	IMPLICIT NONE
	32	PRIVATE
	33
[9019]	34	PUBLIC tra_adv_fct ! called by traadv.F90
	35	PUBLIC interp_4th_cpt ! called by traadv_cen.F90
[13982]	36	PUBLIC tridia_solver ! called by traadv_fct_lf.F90
	37	PUBLIC nonosc ! called by traadv_fct_lf.F90 - key_agrif
[3]	38
[5770]	39	LOGICAL :: l_trd ! flag to compute trends
[7646]	40	LOGICAL :: l_ptr ! flag to compute poleward transport
	41	LOGICAL :: l_hst ! flag to compute heat/salt transport
[5770]	42	REAL(wp) :: r1_6 = 1._wp / 6._wp ! =1/6
[2528]	43
[7646]	44	! ! tridiag solver associated indices:
	45	INTEGER, PARAMETER :: np_NH = 0 ! Neumann homogeneous boundary condition
	46	INTEGER, PARAMETER :: np_CEN2 = 1 ! 2nd order centered boundary condition
	47
[3]	48	!! * Substitutions
[12377]	49	# include "do_loop_substitute.h90"
[13237]	50	# include "domzgr_substitute.h90"
[14219]	51	# include "single_precision_substitute.h90"
[3]	52	!!----------------------------------------------------------------------
[9598]	53	!! NEMO/OCE 4.0 , NEMO Consortium (2018)
[1152]	54	!! $Id$
[10068]	55	!! Software governed by the CeCILL license (see ./LICENSE)
[3]	56	!!----------------------------------------------------------------------
	57	CONTAINS
	58
[12377]	59	SUBROUTINE tra_adv_fct( kt, kit000, cdtype, p2dt, pU, pV, pW, &
	60	& Kbb, Kmm, pt, kjpt, Krhs, kn_fct_h, kn_fct_v )
[3]	61	!!----------------------------------------------------------------------
[5770]	62	!! * ROUTINE tra_adv_fct *
[14072]	63	!!
[6140]	64	!! ** Purpose : Compute the now trend due to total advection of tracers
	65	!! and add it to the general trend of tracer equations
[3]	66	!!
[5770]	67	!! ** Method : - 2nd or 4th FCT scheme on the horizontal direction
	68	!! (choice through the value of kn_fct)
[14072]	69	!! - on the vertical the 4th order is a compact scheme
	70	!! - corrected flux (monotonic correction)
[3]	71	!!
[12377]	72	!! ** Action : - update pt(:,:,:,:,Krhs) with the now advective tracer trends
[9019]	73	!! - send trends to trdtra module for further diagnostics (l_trdtra=T)
[12377]	74	!! - poleward advective heat and salt transport (ln_diaptr=T)
[503]	75	!!----------------------------------------------------------------------
[12377]	76	INTEGER , INTENT(in ) :: kt ! ocean time-step index
	77	INTEGER , INTENT(in ) :: Kbb, Kmm, Krhs ! ocean time level indices
	78	INTEGER , INTENT(in ) :: kit000 ! first time step index
	79	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	80	INTEGER , INTENT(in ) :: kjpt ! number of tracers
	81	INTEGER , INTENT(in ) :: kn_fct_h ! order of the FCT scheme (=2 or 4)
	82	INTEGER , INTENT(in ) :: kn_fct_v ! order of the FCT scheme (=2 or 4)
	83	REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
[13982]	84	! TEMP: [tiling] This can be A2D(nn_hls) if using XIOS (subdomain support)
[12377]	85	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pU, pV, pW ! 3 ocean volume flux components
[14219]	86	REAL(dp), DIMENSION(jpi,jpj,jpk,kjpt,jpt), INTENT(inout) :: pt ! tracers and RHS of tracer equation
[2715]	87	!
[13982]	88	INTEGER :: ji, jj, jk, jn ! dummy loop indices
[6140]	89	REAL(wp) :: ztra ! local scalar
[5770]	90	REAL(wp) :: zfp_ui, zfp_vj, zfp_wk, zC2t_u, zC4t_u ! - -
	91	REAL(wp) :: zfm_ui, zfm_vj, zfm_wk, zC2t_v, zC4t_v ! - -
[14644]	92	REAL(dp), DIMENSION(A2D(nn_hls),jpk) :: zwx, zwy, zwz
	93	REAL(wp), DIMENSION(A2D(nn_hls),jpk) :: zwi, ztu, ztv, zltu, zltv, ztw
[9019]	94	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ztrdx, ztrdy, ztrdz, zptry
[11407]	95	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: zwinf, zwdia, zwsup
	96	LOGICAL :: ll_zAimp ! flag to apply adaptive implicit vertical advection
[3]	97	!!----------------------------------------------------------------------
[3294]	98	!
[13982]	99	IF( ntile == 0 .OR. ntile == 1 ) THEN ! Do only on the first tile
	100	IF( kt == kit000 ) THEN
	101	IF(lwp) WRITE(numout,*)
	102	IF(lwp) WRITE(numout,*) 'tra_adv_fct : FCT advection scheme on ', cdtype
	103	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~'
	104	ENDIF
	105	!
	106	l_trd = .FALSE. ! set local switches
	107	l_hst = .FALSE.
	108	l_ptr = .FALSE.
	109	ll_zAimp = .FALSE.
	110	IF( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. ( cdtype =='TRC' .AND. l_trdtrc ) ) l_trd = .TRUE.
	111	IF( cdtype == 'TRA' .AND. ( iom_use( 'sophtadv' ) .OR. iom_use( 'sophtadv' ) ) ) l_ptr = .TRUE.
	112	IF( cdtype == 'TRA' .AND. ( iom_use("uadv_heattr") .OR. iom_use("vadv_heattr") .OR. &
	113	& iom_use("uadv_salttr") .OR. iom_use("vadv_salttr") ) ) l_hst = .TRUE.
	114	!
[3]	115	ENDIF
[13982]	116
[13226]	117	!! -- init to 0
	118	zwi(:,:,:) = 0._wp
	119	zwx(:,:,:) = 0._wp
	120	zwy(:,:,:) = 0._wp
	121	zwz(:,:,:) = 0._wp
	122	ztu(:,:,:) = 0._wp
	123	ztv(:,:,:) = 0._wp
	124	zltu(:,:,:) = 0._wp
	125	zltv(:,:,:) = 0._wp
	126	ztw(:,:,:) = 0._wp
[2528]	127	!
[7646]	128	IF( l_trd .OR. l_hst ) THEN
[13982]	129	ALLOCATE( ztrdx(A2D(nn_hls),jpk), ztrdy(A2D(nn_hls),jpk), ztrdz(A2D(nn_hls),jpk) )
[7753]	130	ztrdx(:,:,:) = 0._wp ; ztrdy(:,:,:) = 0._wp ; ztrdz(:,:,:) = 0._wp
[3294]	131	ENDIF
[2528]	132	!
[13982]	133	IF( l_ptr ) THEN
	134	ALLOCATE( zptry(A2D(nn_hls),jpk) )
[7753]	135	zptry(:,:,:) = 0._wp
[7646]	136	ENDIF
[2528]	137	!
[11407]	138	! If adaptive vertical advection, check if it is needed on this PE at this time
	139	IF( ln_zad_Aimp ) THEN
[13982]	140	IF( MAXVAL( ABS( wi(A2D(nn_hls),:) ) ) > 0._wp ) ll_zAimp = .TRUE.
[11407]	141	END IF
	142	! If active adaptive vertical advection, build tridiagonal matrix
	143	IF( ll_zAimp ) THEN
[13982]	144	ALLOCATE(zwdia(A2D(nn_hls),jpk), zwinf(A2D(nn_hls),jpk), zwsup(A2D(nn_hls),jpk))
	145	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 1, jpkm1 )
[13237]	146	zwdia(ji,jj,jk) = 1._wp + p2dt * ( MAX( wi(ji,jj,jk) , 0._wp ) - MIN( wi(ji,jj,jk+1) , 0._wp ) ) &
	147	& / e3t(ji,jj,jk,Krhs)
[12377]	148	zwinf(ji,jj,jk) = p2dt * MIN( wi(ji,jj,jk ) , 0._wp ) / e3t(ji,jj,jk,Krhs)
	149	zwsup(ji,jj,jk) = -p2dt * MAX( wi(ji,jj,jk+1) , 0._wp ) / e3t(ji,jj,jk,Krhs)
	150	END_3D
[11407]	151	END IF
	152	!
[6140]	153	DO jn = 1, kjpt !== loop over the tracers ==!
[5770]	154	!
	155	! !== upstream advection with initial mass fluxes & intermediate update ==!
[14072]	156	! !* upstream tracer flux in the i and j direction
[13982]	157	DO_3D( nn_hls, nn_hls-1, nn_hls, nn_hls-1, 1, jpkm1 )
[12377]	158	! upstream scheme
	159	zfp_ui = pU(ji,jj,jk) + ABS( pU(ji,jj,jk) )
	160	zfm_ui = pU(ji,jj,jk) - ABS( pU(ji,jj,jk) )
	161	zfp_vj = pV(ji,jj,jk) + ABS( pV(ji,jj,jk) )
	162	zfm_vj = pV(ji,jj,jk) - ABS( pV(ji,jj,jk) )
	163	zwx(ji,jj,jk) = 0.5 * ( zfp_ui * pt(ji,jj,jk,jn,Kbb) + zfm_ui * pt(ji+1,jj ,jk,jn,Kbb) )
	164	zwy(ji,jj,jk) = 0.5 * ( zfp_vj * pt(ji,jj,jk,jn,Kbb) + zfm_vj * pt(ji ,jj+1,jk,jn,Kbb) )
	165	END_3D
[13497]	166	! !* upstream tracer flux in the k direction *!
	167	DO_3D( 1, 1, 1, 1, 2, jpkm1 ) ! Interior value ( multiplied by wmask)
[12377]	168	zfp_wk = pW(ji,jj,jk) + ABS( pW(ji,jj,jk) )
	169	zfm_wk = pW(ji,jj,jk) - ABS( pW(ji,jj,jk) )
	170	zwz(ji,jj,jk) = 0.5 * ( zfp_wk * pt(ji,jj,jk,jn,Kbb) + zfm_wk * pt(ji,jj,jk-1,jn,Kbb) ) * wmask(ji,jj,jk)
	171	END_3D
[13497]	172	IF( ln_linssh ) THEN ! top ocean value (only in linear free surface as zwz has been w-masked)
	173	IF( ln_isfcav ) THEN ! top of the ice-shelf cavities and at the ocean surface
[13295]	174	DO_2D( 1, 1, 1, 1 )
[14072]	175	zwz(ji,jj, mikt(ji,jj) ) = pW(ji,jj,mikt(ji,jj)) * pt(ji,jj,mikt(ji,jj),jn,Kbb) ! linear free surface
[12377]	176	END_2D
[13497]	177	ELSE ! no cavities: only at the ocean surface
[13295]	178	DO_2D( 1, 1, 1, 1 )
[13286]	179	zwz(ji,jj,1) = pW(ji,jj,1) * pt(ji,jj,1,jn,Kbb)
	180	END_2D
[5770]	181	ENDIF
[5120]	182	ENDIF
[14072]	183	!
[13982]	184	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 1, jpkm1 ) !* trend and after field with monotonic scheme
[13497]	185	! ! total intermediate advective trends
[12377]	186	ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) &
	187	& + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) &
	188	& + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj)
[13497]	189	! ! update and guess with monotonic sheme
[13237]	190	pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) + ztra &
	191	& / e3t(ji,jj,jk,Kmm ) * tmask(ji,jj,jk)
	192	zwi(ji,jj,jk) = ( e3t(ji,jj,jk,Kbb) * pt(ji,jj,jk,jn,Kbb) + p2dt * ztra ) &
	193	& / e3t(ji,jj,jk,Krhs) * tmask(ji,jj,jk)
[12377]	194	END_3D
[14072]	195
[11407]	196	IF ( ll_zAimp ) THEN
	197	CALL tridia_solver( zwdia, zwsup, zwinf, zwi, zwi , 0 )
	198	!
[11411]	199	ztw(:,:,1) = 0._wp ; ztw(:,:,jpk) = 0._wp ;
[13982]	200	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, jpkm1 ) ! Interior value ( multiplied by wmask)
[12377]	201	zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) )
	202	zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) )
	203	ztw(ji,jj,jk) = 0.5 * e1e2t(ji,jj) * ( zfp_wk * zwi(ji,jj,jk) + zfm_wk * zwi(ji,jj,jk-1) ) * wmask(ji,jj,jk)
	204	zwz(ji,jj,jk) = zwz(ji,jj,jk) + ztw(ji,jj,jk) ! update vertical fluxes
	205	END_3D
[13295]	206	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[12377]	207	pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) - ( ztw(ji,jj,jk) - ztw(ji ,jj ,jk+1) ) &
	208	& * r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm)
	209	END_3D
[11407]	210	!
	211	END IF
[13982]	212	!
[7646]	213	IF( l_trd .OR. l_hst ) THEN ! trend diagnostics (contribution of upstream fluxes)
[7753]	214	ztrdx(:,:,:) = zwx(:,:,:) ; ztrdy(:,:,:) = zwy(:,:,:) ; ztrdz(:,:,:) = zwz(:,:,:)
[2528]	215	END IF
[5770]	216	! ! "Poleward" heat and salt transports (contribution of upstream fluxes)
[14072]	217	IF( l_ptr ) zptry(:,:,:) = zwy(:,:,:)
[5770]	218	!
	219	! !== anti-diffusive flux : high order minus low order ==!
	220	!
[6140]	221	SELECT CASE( kn_fct_h ) !* horizontal anti-diffusive fluxes
[5770]	222	!
[6140]	223	CASE( 2 ) !- 2nd order centered
[13982]	224	DO_3D( nn_hls, nn_hls-1, nn_hls, nn_hls-1, 1, jpkm1 )
[12377]	225	zwx(ji,jj,jk) = 0.5_wp * pU(ji,jj,jk) * ( pt(ji,jj,jk,jn,Kmm) + pt(ji+1,jj,jk,jn,Kmm) ) - zwx(ji,jj,jk)
	226	zwy(ji,jj,jk) = 0.5_wp * pV(ji,jj,jk) * ( pt(ji,jj,jk,jn,Kmm) + pt(ji,jj+1,jk,jn,Kmm) ) - zwy(ji,jj,jk)
	227	END_3D
[5770]	228	!
[6140]	229	CASE( 4 ) !- 4th order centered
[7753]	230	zltu(:,:,jpk) = 0._wp ! Bottom value : flux set to zero
	231	zltv(:,:,jpk) = 0._wp
[6140]	232	DO jk = 1, jpkm1 ! Laplacian
[13497]	233	DO_2D( 1, 0, 1, 0 ) ! 1st derivative (gradient)
[12377]	234	ztu(ji,jj,jk) = ( pt(ji+1,jj ,jk,jn,Kmm) - pt(ji,jj,jk,jn,Kmm) ) * umask(ji,jj,jk)
	235	ztv(ji,jj,jk) = ( pt(ji ,jj+1,jk,jn,Kmm) - pt(ji,jj,jk,jn,Kmm) ) * vmask(ji,jj,jk)
	236	END_2D
[13497]	237	DO_2D( 0, 0, 0, 0 ) ! 2nd derivative * 1/ 6
[12377]	238	zltu(ji,jj,jk) = ( ztu(ji,jj,jk) + ztu(ji-1,jj,jk) ) * r1_6
	239	zltv(ji,jj,jk) = ( ztv(ji,jj,jk) + ztv(ji,jj-1,jk) ) * r1_6
	240	END_2D
[503]	241	END DO
[14644]	242	CALL lbc_lnk( 'traadv_fct', zltu, 'T', 1.0_wp , zltv, 'T', 1.0_wp ) ! Lateral boundary cond. (unchanged sgn)
[5770]	243	!
[13982]	244	DO_3D( 1, 0, 1, 0, 1, jpkm1 )
[12377]	245	zC2t_u = pt(ji,jj,jk,jn,Kmm) + pt(ji+1,jj ,jk,jn,Kmm) ! 2 x C2 interpolation of T at u- & v-points
	246	zC2t_v = pt(ji,jj,jk,jn,Kmm) + pt(ji ,jj+1,jk,jn,Kmm)
[13982]	247	! ! C4 minus upstream advective fluxes
[12377]	248	zwx(ji,jj,jk) = 0.5_wp * pU(ji,jj,jk) * ( zC2t_u + zltu(ji,jj,jk) - zltu(ji+1,jj,jk) ) - zwx(ji,jj,jk)
	249	zwy(ji,jj,jk) = 0.5_wp * pV(ji,jj,jk) * ( zC2t_v + zltv(ji,jj,jk) - zltv(ji,jj+1,jk) ) - zwy(ji,jj,jk)
	250	END_3D
[14644]	251	IF (nn_hls.EQ.2) CALL lbc_lnk( 'traadv_fct', zwx, 'U', -1.0_wp, zwy, 'V', -1.0_wp ) ! Lateral boundary cond. (unchanged sgn)
[5770]	252	!
[6140]	253	CASE( 41 ) !- 4th order centered ==>> !!gm coding attempt need to be tested
[7753]	254	ztu(:,:,jpk) = 0._wp ! Bottom value : flux set to zero
	255	ztv(:,:,jpk) = 0._wp
[13982]	256	DO_3D( nn_hls, nn_hls-1, nn_hls, nn_hls-1, 1, jpkm1 ) ! 1st derivative (gradient)
[12377]	257	ztu(ji,jj,jk) = ( pt(ji+1,jj ,jk,jn,Kmm) - pt(ji,jj,jk,jn,Kmm) ) * umask(ji,jj,jk)
	258	ztv(ji,jj,jk) = ( pt(ji ,jj+1,jk,jn,Kmm) - pt(ji,jj,jk,jn,Kmm) ) * vmask(ji,jj,jk)
	259	END_3D
[14644]	260	IF (nn_hls.EQ.1) CALL lbc_lnk( 'traadv_fct', ztu, 'U', -1.0_wp , ztv, 'V', -1.0_wp ) ! Lateral boundary cond. (unchanged sgn)
[5770]	261	!
[13497]	262	DO_3D( 0, 0, 0, 0, 1, jpkm1 ) ! Horizontal advective fluxes
[12377]	263	zC2t_u = pt(ji,jj,jk,jn,Kmm) + pt(ji+1,jj ,jk,jn,Kmm) ! 2 x C2 interpolation of T at u- & v-points (x2)
	264	zC2t_v = pt(ji,jj,jk,jn,Kmm) + pt(ji ,jj+1,jk,jn,Kmm)
	265	! ! C4 interpolation of T at u- & v-points (x2)
	266	zC4t_u = zC2t_u + r1_6 * ( ztu(ji-1,jj ,jk) - ztu(ji+1,jj ,jk) )
	267	zC4t_v = zC2t_v + r1_6 * ( ztv(ji ,jj-1,jk) - ztv(ji ,jj+1,jk) )
[14072]	268	! ! C4 minus upstream advective fluxes
[12377]	269	zwx(ji,jj,jk) = 0.5_wp * pU(ji,jj,jk) * zC4t_u - zwx(ji,jj,jk)
	270	zwy(ji,jj,jk) = 0.5_wp * pV(ji,jj,jk) * zC4t_v - zwy(ji,jj,jk)
	271	END_3D
[14644]	272	IF (nn_hls.EQ.2) CALL lbc_lnk( 'traadv_fct', zwx, 'U', -1.0_wp , zwy, 'V', -1.0_wp ) ! Lateral boundary cond. (unchanged sgn)
[5770]	273	!
	274	END SELECT
[14072]	275	!
[6140]	276	SELECT CASE( kn_fct_v ) !* vertical anti-diffusive fluxes (w-masked interior values)
[5770]	277	!
[6140]	278	CASE( 2 ) !- 2nd order centered
[13982]	279	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, jpkm1 )
[12377]	280	zwz(ji,jj,jk) = ( pW(ji,jj,jk) * 0.5_wp * ( pt(ji,jj,jk,jn,Kmm) + pt(ji,jj,jk-1,jn,Kmm) ) &
	281	& - zwz(ji,jj,jk) ) * wmask(ji,jj,jk)
	282	END_3D
[5770]	283	!
[6140]	284	CASE( 4 ) !- 4th order COMPACT
[14219]	285	CALL interp_4th_cpt( CASTWP(pt(:,:,:,jn,Kmm)) , ztw ) ! zwt = COMPACT interpolation of T at w-point
[13982]	286	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, jpkm1 )
[12377]	287	zwz(ji,jj,jk) = ( pW(ji,jj,jk) * ztw(ji,jj,jk) - zwz(ji,jj,jk) ) * wmask(ji,jj,jk)
	288	END_3D
[5770]	289	!
	290	END SELECT
[6140]	291	IF( ln_linssh ) THEN ! top ocean value: high order = upstream ==>> zwz=0
[7753]	292	zwz(:,:,1) = 0._wp ! only ocean surface as interior zwz values have been w-masked
[6140]	293	ENDIF
[13982]	294	!
	295	IF (nn_hls.EQ.1) THEN
[14648]	296	CALL lbc_lnk( 'traadv_fct', zwi, 'T', 1.0_wp )
	297	CALL lbc_lnk( 'traadv_fct', zwx, 'U', -1.0_wp , zwy, 'V', -1.0_wp, zwz, 'T', 1.0_wp )
[13982]	298	ELSE
	299	CALL lbc_lnk( 'traadv_fct', zwi, 'T', 1.0_wp)
	300	END IF
	301	!
[11407]	302	IF ( ll_zAimp ) THEN
[13982]	303	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 1, jpkm1 ) !* trend and after field with monotonic scheme
[13497]	304	! ! total intermediate advective trends
[12377]	305	ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) &
	306	& + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) &
	307	& + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj)
[13982]	308	ztw(ji,jj,jk) = zwi(ji,jj,jk) + p2dt * ztra / e3t(ji,jj,jk,Krhs) * tmask(ji,jj,jk)
[12377]	309	END_3D
[11407]	310	!
[11411]	311	CALL tridia_solver( zwdia, zwsup, zwinf, ztw, ztw , 0 )
[11407]	312	!
[13982]	313	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, jpkm1 ) ! Interior value ( multiplied by wmask)
[12377]	314	zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) )
	315	zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) )
[13982]	316	zwz(ji,jj,jk) = zwz(ji,jj,jk) + 0.5 * e1e2t(ji,jj) * ( zfp_wk * ztw(ji,jj,jk) + zfm_wk * ztw(ji,jj,jk-1) ) * wmask(ji,jj,jk)
[12377]	317	END_3D
[11407]	318	END IF
[11411]	319	!
[5770]	320	! !== monotonicity algorithm ==!
	321	!
[14219]	322	CALL nonosc( Kmm, CASTWP(pt(:,:,:,jn,Kbb)), zwx, zwy, zwz, zwi, p2dt )
[6140]	323	!
[5770]	324	! !== final trend with corrected fluxes ==!
	325	!
[13295]	326	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[12377]	327	ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) &
	328	& + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) &
	329	& + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj)
	330	pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) + ztra / e3t(ji,jj,jk,Kmm)
	331	zwi(ji,jj,jk) = zwi(ji,jj,jk) + p2dt * ztra / e3t(ji,jj,jk,Krhs) * tmask(ji,jj,jk)
	332	END_3D
[5770]	333	!
[11407]	334	IF ( ll_zAimp ) THEN
	335	!
[11411]	336	ztw(:,:,1) = 0._wp ; ztw(:,:,jpk) = 0._wp
[13497]	337	DO_3D( 0, 0, 0, 0, 2, jpkm1 ) ! Interior value ( multiplied by wmask)
[12377]	338	zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) )
	339	zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) )
	340	ztw(ji,jj,jk) = - 0.5 * e1e2t(ji,jj) * ( zfp_wk * zwi(ji,jj,jk) + zfm_wk * zwi(ji,jj,jk-1) ) * wmask(ji,jj,jk)
	341	zwz(ji,jj,jk) = zwz(ji,jj,jk) + ztw(ji,jj,jk) ! Update vertical fluxes for trend diagnostic
	342	END_3D
[13295]	343	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[12377]	344	pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) - ( ztw(ji,jj,jk) - ztw(ji ,jj ,jk+1) ) &
	345	& * r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm)
	346	END_3D
[13982]	347	END IF
[9019]	348	IF( l_trd .OR. l_hst ) THEN ! trend diagnostics // heat/salt transport
[13982]	349	ztrdx(:,:,:) = ztrdx(:,:,:) + zwx(:,:,:) ! <<< add anti-diffusive fluxes
[9019]	350	ztrdy(:,:,:) = ztrdy(:,:,:) + zwy(:,:,:) ! to upstream fluxes
	351	ztrdz(:,:,:) = ztrdz(:,:,:) + zwz(:,:,:) !
[5770]	352	!
[9019]	353	IF( l_trd ) THEN ! trend diagnostics
[14219]	354	CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_xad, ztrdx, pU, CASTWP(pt(:,:,:,jn,Kmm)) )
	355	CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_yad, ztrdy, pV, CASTWP(pt(:,:,:,jn,Kmm)) )
	356	CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_zad, ztrdz, pW, CASTWP(pt(:,:,:,jn,Kmm)) )
[9019]	357	ENDIF
	358	! ! heat/salt transport
	359	IF( l_hst ) CALL dia_ar5_hst( jn, 'adv', ztrdx(:,:,:), ztrdy(:,:,:) )
[5770]	360	!
[9019]	361	ENDIF
	362	IF( l_ptr ) THEN ! "Poleward" transports
	363	zptry(:,:,:) = zptry(:,:,:) + zwy(:,:,:) ! <<< add anti-diffusive fluxes
[7646]	364	CALL dia_ptr_hst( jn, 'adv', zptry(:,:,:) )
[2528]	365	ENDIF
[503]	366	!
[6140]	367	END DO ! end of tracer loop
[503]	368	!
[11407]	369	IF ( ll_zAimp ) THEN
	370	DEALLOCATE( zwdia, zwinf, zwsup )
	371	ENDIF
[13982]	372	IF( l_trd .OR. l_hst ) THEN
[10024]	373	DEALLOCATE( ztrdx, ztrdy, ztrdz )
	374	ENDIF
[14072]	375	IF( l_ptr ) THEN
[10024]	376	DEALLOCATE( zptry )
	377	ENDIF
	378	!
[5770]	379	END SUBROUTINE tra_adv_fct
[3]	380
[5737]	381
[12377]	382	SUBROUTINE nonosc( Kmm, pbef, paa, pbb, pcc, paft, p2dt )
[3]	383	!!---------------------------------------------------------------------
	384	!! * ROUTINE nonosc *
	385	!!
[14072]	386	!! ** Purpose : compute monotonic tracer fluxes from the upstream
	387	!! scheme and the before field by a nonoscillatory algorithm
	388	!!
[3]	389	!! ** Method : ... ???
	390	!! warning : pbef and paft must be masked, but the boundaries
	391	!! conditions on the fluxes are not necessary zalezak (1979)
	392	!! drange (1995) multi-dimensional forward-in-time and upstream-
	393	!! in-space based differencing for fluid
	394	!!----------------------------------------------------------------------
[13982]	395	INTEGER , INTENT(in ) :: Kmm ! time level index
	396	REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
	397	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pbef ! before field
	398	REAL(wp), DIMENSION(A2D(nn_hls) ,jpk), INTENT(in ) :: paft ! after field
[14219]	399	REAL(dp), DIMENSION(A2D(nn_hls) ,jpk), INTENT(inout) :: paa, pbb, pcc ! monotonic fluxes in the 3 directions
[2715]	400	!
[4990]	401	INTEGER :: ji, jj, jk ! dummy loop indices
	402	INTEGER :: ikm1 ! local integer
[13226]	403	REAL(dp) :: zpos, zneg, zbt, za, zb, zc, zbig, zrtrn ! local scalars
	404	REAL(dp) :: zau, zbu, zcu, zav, zbv, zcv, zup, zdo ! - -
[13982]	405	REAL(dp), DIMENSION(A2D(nn_hls),jpk) :: zbetup, zbetdo, zbup, zbdo
[3]	406	!!----------------------------------------------------------------------
[3294]	407	!
[13226]	408	zbig = 1.e+40_dp
	409	zrtrn = 1.e-15_dp
	410	zbetup(:,:,:) = 0._dp ; zbetdo(:,:,:) = 0._dp
[785]	411
[3]	412	! Search local extrema
	413	! --------------------
[785]	414	! max/min of pbef & paft with large negative/positive value (-/+zbig) inside land
[13982]	415	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpk )
	416	zbup(ji,jj,jk) = MAX( pbef(ji,jj,jk) * tmask(ji,jj,jk) - zbig * ( 1._wp - tmask(ji,jj,jk) ), &
	417	& paft(ji,jj,jk) * tmask(ji,jj,jk) - zbig * ( 1._wp - tmask(ji,jj,jk) ) )
	418	zbdo(ji,jj,jk) = MIN( pbef(ji,jj,jk) * tmask(ji,jj,jk) + zbig * ( 1._wp - tmask(ji,jj,jk) ), &
	419	& paft(ji,jj,jk) * tmask(ji,jj,jk) + zbig * ( 1._wp - tmask(ji,jj,jk) ) )
	420	END_3D
[785]	421
[5120]	422	DO jk = 1, jpkm1
	423	ikm1 = MAX(jk-1,1)
[13982]	424	DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
[5120]	425
[12377]	426	! search maximum in neighbourhood
	427	zup = MAX( zbup(ji ,jj ,jk ), &
	428	& zbup(ji-1,jj ,jk ), zbup(ji+1,jj ,jk ), &
	429	& zbup(ji ,jj-1,jk ), zbup(ji ,jj+1,jk ), &
	430	& zbup(ji ,jj ,ikm1), zbup(ji ,jj ,jk+1) )
[3]	431
[12377]	432	! search minimum in neighbourhood
	433	zdo = MIN( zbdo(ji ,jj ,jk ), &
	434	& zbdo(ji-1,jj ,jk ), zbdo(ji+1,jj ,jk ), &
	435	& zbdo(ji ,jj-1,jk ), zbdo(ji ,jj+1,jk ), &
	436	& zbdo(ji ,jj ,ikm1), zbdo(ji ,jj ,jk+1) )
[3]	437
[12377]	438	! positive part of the flux
	439	zpos = MAX( 0., paa(ji-1,jj ,jk ) ) - MIN( 0., paa(ji ,jj ,jk ) ) &
	440	& + MAX( 0., pbb(ji ,jj-1,jk ) ) - MIN( 0., pbb(ji ,jj ,jk ) ) &
	441	& + MAX( 0., pcc(ji ,jj ,jk+1) ) - MIN( 0., pcc(ji ,jj ,jk ) )
[785]	442
[12377]	443	! negative part of the flux
	444	zneg = MAX( 0., paa(ji ,jj ,jk ) ) - MIN( 0., paa(ji-1,jj ,jk ) ) &
	445	& + MAX( 0., pbb(ji ,jj ,jk ) ) - MIN( 0., pbb(ji ,jj-1,jk ) ) &
	446	& + MAX( 0., pcc(ji ,jj ,jk ) ) - MIN( 0., pcc(ji ,jj ,jk+1) )
[785]	447
[12377]	448	! up & down beta terms
	449	zbt = e1e2t(ji,jj) * e3t(ji,jj,jk,Kmm) / p2dt
	450	zbetup(ji,jj,jk) = ( zup - paft(ji,jj,jk) ) / ( zpos + zrtrn ) * zbt
	451	zbetdo(ji,jj,jk) = ( paft(ji,jj,jk) - zdo ) / ( zneg + zrtrn ) * zbt
	452	END_2D
[3]	453	END DO
[14644]	454	IF (nn_hls.EQ.1) CALL lbc_lnk( 'traadv_fct', zbetup, 'T', 1.0_wp , zbetdo, 'T', 1.0_wp ) ! lateral boundary cond. (unchanged sign)
[3]	455
[237]	456	! 3. monotonic flux in the i & j direction (paa & pbb)
	457	! ----------------------------------------
[13982]	458	DO_3D( 1, 0, 1, 0, 1, jpkm1 )
[12377]	459	zau = MIN( 1._wp, zbetdo(ji,jj,jk), zbetup(ji+1,jj,jk) )
	460	zbu = MIN( 1._wp, zbetup(ji,jj,jk), zbetdo(ji+1,jj,jk) )
[14495]	461	zcu = ( 0.5 + SIGN( 0.5_wp , CASTWP(paa(ji,jj,jk)) ) )
[12377]	462	paa(ji,jj,jk) = paa(ji,jj,jk) * ( zcu * zau + ( 1._wp - zcu) * zbu )
[3]	463
[12377]	464	zav = MIN( 1._wp, zbetdo(ji,jj,jk), zbetup(ji,jj+1,jk) )
	465	zbv = MIN( 1._wp, zbetup(ji,jj,jk), zbetdo(ji,jj+1,jk) )
[14495]	466	zcv = ( 0.5 + SIGN( 0.5_wp , CASTWP(pbb(ji,jj,jk)) ) )
[12377]	467	pbb(ji,jj,jk) = pbb(ji,jj,jk) * ( zcv * zav + ( 1._wp - zcv) * zbv )
[3]	468
[13497]	469	! monotonic flux in the k direction, i.e. pcc
	470	! -------------------------------------------
[12377]	471	za = MIN( 1., zbetdo(ji,jj,jk+1), zbetup(ji,jj,jk) )
	472	zb = MIN( 1., zbetup(ji,jj,jk+1), zbetdo(ji,jj,jk) )
[14495]	473	zc = ( 0.5 + SIGN( 0.5_wp , CASTWP(pcc(ji,jj,jk+1)) ) )
[12377]	474	pcc(ji,jj,jk+1) = pcc(ji,jj,jk+1) * ( zc * za + ( 1._wp - zc) * zb )
	475	END_3D
[503]	476	!
[3]	477	END SUBROUTINE nonosc
	478
[5770]	479
[7646]	480	SUBROUTINE interp_4th_cpt_org( pt_in, pt_out )
[5770]	481	!!----------------------------------------------------------------------
[7646]	482	!! * ROUTINE interp_4th_cpt_org *
[14072]	483	!!
[5770]	484	!! ** Purpose : Compute the interpolation of tracer at w-point
	485	!!
	486	!! ** Method : 4th order compact interpolation
	487	!!----------------------------------------------------------------------
	488	REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pt_in ! now tracer fields
	489	REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT( out) :: pt_out ! now tracer field interpolated at w-pts
	490	!
	491	INTEGER :: ji, jj, jk ! dummy loop integers
	492	REAL(wp),DIMENSION(jpi,jpj,jpk) :: zwd, zwi, zws, zwrm, zwt
	493	!!----------------------------------------------------------------------
[14072]	494
[13497]	495	DO_3D( 1, 1, 1, 1, 3, jpkm1 ) !== build the three diagonal matrix ==!
[12377]	496	zwd (ji,jj,jk) = 4._wp
	497	zwi (ji,jj,jk) = 1._wp
	498	zws (ji,jj,jk) = 1._wp
	499	zwrm(ji,jj,jk) = 3._wp * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) )
	500	!
	501	IF( tmask(ji,jj,jk+1) == 0._wp) THEN ! Switch to second order centered at bottom
[5770]	502	zwd (ji,jj,jk) = 1._wp
	503	zwi (ji,jj,jk) = 0._wp
	504	zws (ji,jj,jk) = 0._wp
[14072]	505	zwrm(ji,jj,jk) = 0.5 * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) )
[12377]	506	ENDIF
	507	END_3D
[5770]	508	!
[13497]	509	jk = 2 ! Switch to second order centered at top
[13295]	510	DO_2D( 1, 1, 1, 1 )
[12377]	511	zwd (ji,jj,jk) = 1._wp
	512	zwi (ji,jj,jk) = 0._wp
	513	zws (ji,jj,jk) = 0._wp
	514	zwrm(ji,jj,jk) = 0.5 * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) )
	515	END_2D
	516	!
[5770]	517	! !== tridiagonal solve ==!
[13497]	518	DO_2D( 1, 1, 1, 1 ) ! first recurrence
[12377]	519	zwt(ji,jj,2) = zwd(ji,jj,2)
	520	END_2D
[13295]	521	DO_3D( 1, 1, 1, 1, 3, jpkm1 )
[12377]	522	zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1)
	523	END_3D
[5770]	524	!
[13497]	525	DO_2D( 1, 1, 1, 1 ) ! second recurrence: Zk = Yk - Ik / Tk-1 Zk-1
[12377]	526	pt_out(ji,jj,2) = zwrm(ji,jj,2)
	527	END_2D
[13295]	528	DO_3D( 1, 1, 1, 1, 3, jpkm1 )
[14072]	529	pt_out(ji,jj,jk) = zwrm(ji,jj,jk) - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1)
[12377]	530	END_3D
[5770]	531
[13497]	532	DO_2D( 1, 1, 1, 1 ) ! third recurrence: Xk = (Zk - Sk Xk+1 ) / Tk
[12377]	533	pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1)
	534	END_2D
[13295]	535	DO_3DS( 1, 1, 1, 1, jpk-2, 2, -1 )
[12377]	536	pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - zws(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk)
	537	END_3D
[14072]	538	!
[7646]	539	END SUBROUTINE interp_4th_cpt_org
	540
[14072]	541
[7646]	542	SUBROUTINE interp_4th_cpt( pt_in, pt_out )
	543	!!----------------------------------------------------------------------
	544	!! * ROUTINE interp_4th_cpt *
[14072]	545	!!
[7646]	546	!! ** Purpose : Compute the interpolation of tracer at w-point
	547	!!
	548	!! ** Method : 4th order compact interpolation
	549	!!----------------------------------------------------------------------
	550	REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pt_in ! field at t-point
[13982]	551	REAL(wp),DIMENSION(A2D(nn_hls) ,jpk), INTENT( out) :: pt_out ! field interpolated at w-point
[7646]	552	!
	553	INTEGER :: ji, jj, jk ! dummy loop integers
	554	INTEGER :: ikt, ikb ! local integers
[13982]	555	REAL(wp),DIMENSION(A2D(nn_hls),jpk) :: zwd, zwi, zws, zwrm, zwt
[7646]	556	!!----------------------------------------------------------------------
	557	!
	558	! !== build the three diagonal matrix & the RHS ==!
	559	!
[13982]	560	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 3, jpkm1 ) ! interior (from jk=3 to jpk-1)
[12377]	561	zwd (ji,jj,jk) = 3._wp * wmask(ji,jj,jk) + 1._wp ! diagonal
	562	zwi (ji,jj,jk) = wmask(ji,jj,jk) ! lower diagonal
	563	zws (ji,jj,jk) = wmask(ji,jj,jk) ! upper diagonal
	564	zwrm(ji,jj,jk) = 3._wp * wmask(ji,jj,jk) & ! RHS
	565	& * ( pt_in(ji,jj,jk) + pt_in(ji,jj,jk-1) )
	566	END_3D
[7646]	567	!
	568	!!gm
	569	! SELECT CASE( kbc ) !* boundary condition
	570	! CASE( np_NH ) ! Neumann homogeneous at top & bottom
	571	! CASE( np_CEN2 ) ! 2nd order centered at top & bottom
	572	! END SELECT
[14072]	573	!!gm
[7646]	574	!
[9901]	575	IF ( ln_isfcav ) THEN ! set level two values which may not be set in ISF case
	576	zwd(:,:,2) = 1._wp ; zwi(:,:,2) = 0._wp ; zws(:,:,2) = 0._wp ; zwrm(:,:,2) = 0._wp
	577	END IF
	578	!
[13982]	579	DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2nd order centered at top & bottom
[12377]	580	ikt = mikt(ji,jj) + 1 ! w-point below the 1st wet point
	581	ikb = MAX(mbkt(ji,jj), 2) ! - above the last wet point
	582	!
	583	zwd (ji,jj,ikt) = 1._wp ! top
	584	zwi (ji,jj,ikt) = 0._wp
	585	zws (ji,jj,ikt) = 0._wp
	586	zwrm(ji,jj,ikt) = 0.5_wp * ( pt_in(ji,jj,ikt-1) + pt_in(ji,jj,ikt) )
	587	!
	588	zwd (ji,jj,ikb) = 1._wp ! bottom
	589	zwi (ji,jj,ikb) = 0._wp
	590	zws (ji,jj,ikb) = 0._wp
[14072]	591	zwrm(ji,jj,ikb) = 0.5_wp * ( pt_in(ji,jj,ikb-1) + pt_in(ji,jj,ikb) )
[12377]	592	END_2D
[7646]	593	!
	594	! !== tridiagonal solver ==!
	595	!
[13982]	596	DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) !* 1st recurrence: Tk = Dk - Ik Sk-1 / Tk-1
[12377]	597	zwt(ji,jj,2) = zwd(ji,jj,2)
	598	END_2D
[13982]	599	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 3, jpkm1 )
[12377]	600	zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1)
	601	END_3D
[7646]	602	!
[13982]	603	DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) !* 2nd recurrence: Zk = Yk - Ik / Tk-1 Zk-1
[12377]	604	pt_out(ji,jj,2) = zwrm(ji,jj,2)
	605	END_2D
[13982]	606	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 3, jpkm1 )
[14072]	607	pt_out(ji,jj,jk) = zwrm(ji,jj,jk) - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1)
[12377]	608	END_3D
[7646]	609
[13982]	610	DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) !* 3d recurrence: Xk = (Zk - Sk Xk+1 ) / Tk
[12377]	611	pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1)
	612	END_2D
[13982]	613	DO_3DS( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, jpk-2, 2, -1 )
[12377]	614	pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - zws(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk)
	615	END_3D
[14072]	616	!
[5770]	617	END SUBROUTINE interp_4th_cpt
[7646]	618
	619
	620	SUBROUTINE tridia_solver( pD, pU, pL, pRHS, pt_out , klev )
	621	!!----------------------------------------------------------------------
	622	!! * ROUTINE tridia_solver *
[14072]	623	!!
[7646]	624	!! ** Purpose : solve a symmetric 3diagonal system
	625	!!
	626	!! ** Method : solve M.t_out = RHS(t) where M is a tri diagonal matrix ( jpk*jpk )
[14072]	627	!!
[7646]	628	!! ( D_1 U_1 0 0 0 )( t_1 ) ( RHS_1 )
	629	!! ( L_2 D_2 U_2 0 0 )( t_2 ) ( RHS_2 )
	630	!! ( 0 L_3 D_3 U_3 0 )( t_3 ) = ( RHS_3 )
	631	!! ( ... )( ... ) ( ... )
	632	!! ( 0 0 0 L_k D_k )( t_k ) ( RHS_k )
[14072]	633	!!
[7646]	634	!! M is decomposed in the product of an upper and lower triangular matrix.
[14072]	635	!! The tri-diagonals matrix is given as input 3D arrays: pD, pU, pL
[7646]	636	!! (i.e. the Diagonal, the Upper diagonal, and the Lower diagonal).
	637	!! The solution is pta.
	638	!! The 3d array zwt is used as a work space array.
	639	!!----------------------------------------------------------------------
[14649]	640	REAL(wp),DIMENSION(A2D(nn_hls),jpk), INTENT(in ) :: pD, pU, pL ! 3-diagonal matrix
[13982]	641	REAL(wp),DIMENSION(A2D(nn_hls),jpk), INTENT(in ) :: pRHS ! Right-Hand-Side
	642	REAL(wp),DIMENSION(A2D(nn_hls),jpk), INTENT( out) :: pt_out !!gm field at level=F(klev)
	643	INTEGER , INTENT(in ) :: klev ! =1 pt_out at w-level
	644	! ! =0 pt at t-level
[7646]	645	INTEGER :: ji, jj, jk ! dummy loop integers
	646	INTEGER :: kstart ! local indices
[13982]	647	REAL(wp),DIMENSION(A2D(nn_hls),jpk) :: zwt ! 3D work array
[7646]	648	!!----------------------------------------------------------------------
	649	!
	650	kstart = 1 + klev
	651	!
[13982]	652	DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) !* 1st recurrence: Tk = Dk - Ik Sk-1 / Tk-1
[12377]	653	zwt(ji,jj,kstart) = pD(ji,jj,kstart)
	654	END_2D
[13982]	655	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, kstart+1, jpkm1 )
[12377]	656	zwt(ji,jj,jk) = pD(ji,jj,jk) - pL(ji,jj,jk) * pU(ji,jj,jk-1) /zwt(ji,jj,jk-1)
	657	END_3D
[7646]	658	!
[13982]	659	DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) !* 2nd recurrence: Zk = Yk - Ik / Tk-1 Zk-1
[12377]	660	pt_out(ji,jj,kstart) = pRHS(ji,jj,kstart)
	661	END_2D
[13982]	662	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, kstart+1, jpkm1 )
[14072]	663	pt_out(ji,jj,jk) = pRHS(ji,jj,jk) - pL(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1)
[12377]	664	END_3D
[7646]	665
[13982]	666	DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) !* 3d recurrence: Xk = (Zk - Sk Xk+1 ) / Tk
[12377]	667	pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1)
	668	END_2D
[13982]	669	DO_3DS( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, jpk-2, kstart, -1 )
[12377]	670	pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - pU(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk)
	671	END_3D
[7646]	672	!
	673	END SUBROUTINE tridia_solver
	674
[3]	675	!!======================================================================
[5770]	676	END MODULE traadv_fct

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