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traadv_fct.F90 in NEMO/trunk/src/OCE/TRA – NEMO

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source: NEMO/trunk/src/OCE/TRA/traadv_fct.F90 @ 14197

Last change on this file since 14197 was 14189, checked in by hadcv, 4 years ago
#2365: Remove comments from initial merge
Property svn:keywords set to `Id`
File size: 36.2 KB

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[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"
[3]	51	!!----------------------------------------------------------------------
[9598]	52	!! NEMO/OCE 4.0 , NEMO Consortium (2018)
[1152]	53	!! $Id$
[10068]	54	!! Software governed by the CeCILL license (see ./LICENSE)
[3]	55	!!----------------------------------------------------------------------
	56	CONTAINS
	57
[12377]	58	SUBROUTINE tra_adv_fct( kt, kit000, cdtype, p2dt, pU, pV, pW, &
	59	& Kbb, Kmm, pt, kjpt, Krhs, kn_fct_h, kn_fct_v )
[3]	60	!!----------------------------------------------------------------------
[5770]	61	!! * ROUTINE tra_adv_fct *
[14072]	62	!!
[6140]	63	!! ** Purpose : Compute the now trend due to total advection of tracers
	64	!! and add it to the general trend of tracer equations
[3]	65	!!
[5770]	66	!! ** Method : - 2nd or 4th FCT scheme on the horizontal direction
	67	!! (choice through the value of kn_fct)
[14072]	68	!! - on the vertical the 4th order is a compact scheme
	69	!! - corrected flux (monotonic correction)
[3]	70	!!
[12377]	71	!! ** Action : - update pt(:,:,:,:,Krhs) with the now advective tracer trends
[9019]	72	!! - send trends to trdtra module for further diagnostics (l_trdtra=T)
[12377]	73	!! - poleward advective heat and salt transport (ln_diaptr=T)
[503]	74	!!----------------------------------------------------------------------
[12377]	75	INTEGER , INTENT(in ) :: kt ! ocean time-step index
	76	INTEGER , INTENT(in ) :: Kbb, Kmm, Krhs ! ocean time level indices
	77	INTEGER , INTENT(in ) :: kit000 ! first time step index
	78	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	79	INTEGER , INTENT(in ) :: kjpt ! number of tracers
	80	INTEGER , INTENT(in ) :: kn_fct_h ! order of the FCT scheme (=2 or 4)
	81	INTEGER , INTENT(in ) :: kn_fct_v ! order of the FCT scheme (=2 or 4)
	82	REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
[13982]	83	! TEMP: [tiling] This can be A2D(nn_hls) if using XIOS (subdomain support)
[12377]	84	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pU, pV, pW ! 3 ocean volume flux components
	85	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt,jpt), INTENT(inout) :: pt ! tracers and RHS of tracer equation
[2715]	86	!
[13982]	87	INTEGER :: ji, jj, jk, jn ! dummy loop indices
[6140]	88	REAL(wp) :: ztra ! local scalar
[5770]	89	REAL(wp) :: zfp_ui, zfp_vj, zfp_wk, zC2t_u, zC4t_u ! - -
	90	REAL(wp) :: zfm_ui, zfm_vj, zfm_wk, zC2t_v, zC4t_v ! - -
[13982]	91	REAL(wp), DIMENSION(A2D(nn_hls),jpk) :: zwi, zwx, zwy, zwz, ztu, ztv, zltu, zltv, ztw
[9019]	92	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ztrdx, ztrdy, ztrdz, zptry
[11407]	93	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: zwinf, zwdia, zwsup
	94	LOGICAL :: ll_zAimp ! flag to apply adaptive implicit vertical advection
[3]	95	!!----------------------------------------------------------------------
[3294]	96	!
[13982]	97	IF( ntile == 0 .OR. ntile == 1 ) THEN ! Do only on the first tile
	98	IF( kt == kit000 ) THEN
	99	IF(lwp) WRITE(numout,*)
	100	IF(lwp) WRITE(numout,*) 'tra_adv_fct : FCT advection scheme on ', cdtype
	101	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~'
	102	ENDIF
	103	!
	104	l_trd = .FALSE. ! set local switches
	105	l_hst = .FALSE.
	106	l_ptr = .FALSE.
	107	ll_zAimp = .FALSE.
	108	IF( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. ( cdtype =='TRC' .AND. l_trdtrc ) ) l_trd = .TRUE.
	109	IF( cdtype == 'TRA' .AND. ( iom_use( 'sophtadv' ) .OR. iom_use( 'sophtadv' ) ) ) l_ptr = .TRUE.
	110	IF( cdtype == 'TRA' .AND. ( iom_use("uadv_heattr") .OR. iom_use("vadv_heattr") .OR. &
	111	& iom_use("uadv_salttr") .OR. iom_use("vadv_salttr") ) ) l_hst = .TRUE.
	112	!
[3]	113	ENDIF
[13982]	114
[13226]	115	!! -- init to 0
	116	zwi(:,:,:) = 0._wp
	117	zwx(:,:,:) = 0._wp
	118	zwy(:,:,:) = 0._wp
	119	zwz(:,:,:) = 0._wp
	120	ztu(:,:,:) = 0._wp
	121	ztv(:,:,:) = 0._wp
	122	zltu(:,:,:) = 0._wp
	123	zltv(:,:,:) = 0._wp
	124	ztw(:,:,:) = 0._wp
[2528]	125	!
[7646]	126	IF( l_trd .OR. l_hst ) THEN
[13982]	127	ALLOCATE( ztrdx(A2D(nn_hls),jpk), ztrdy(A2D(nn_hls),jpk), ztrdz(A2D(nn_hls),jpk) )
[7753]	128	ztrdx(:,:,:) = 0._wp ; ztrdy(:,:,:) = 0._wp ; ztrdz(:,:,:) = 0._wp
[3294]	129	ENDIF
[2528]	130	!
[13982]	131	IF( l_ptr ) THEN
	132	ALLOCATE( zptry(A2D(nn_hls),jpk) )
[7753]	133	zptry(:,:,:) = 0._wp
[7646]	134	ENDIF
[2528]	135	!
[11407]	136	! If adaptive vertical advection, check if it is needed on this PE at this time
	137	IF( ln_zad_Aimp ) THEN
[13982]	138	IF( MAXVAL( ABS( wi(A2D(nn_hls),:) ) ) > 0._wp ) ll_zAimp = .TRUE.
[11407]	139	END IF
	140	! If active adaptive vertical advection, build tridiagonal matrix
	141	IF( ll_zAimp ) THEN
[13982]	142	ALLOCATE(zwdia(A2D(nn_hls),jpk), zwinf(A2D(nn_hls),jpk), zwsup(A2D(nn_hls),jpk))
	143	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 1, jpkm1 )
[13237]	144	zwdia(ji,jj,jk) = 1._wp + p2dt * ( MAX( wi(ji,jj,jk) , 0._wp ) - MIN( wi(ji,jj,jk+1) , 0._wp ) ) &
	145	& / e3t(ji,jj,jk,Krhs)
[12377]	146	zwinf(ji,jj,jk) = p2dt * MIN( wi(ji,jj,jk ) , 0._wp ) / e3t(ji,jj,jk,Krhs)
	147	zwsup(ji,jj,jk) = -p2dt * MAX( wi(ji,jj,jk+1) , 0._wp ) / e3t(ji,jj,jk,Krhs)
	148	END_3D
[11407]	149	END IF
	150	!
[6140]	151	DO jn = 1, kjpt !== loop over the tracers ==!
[5770]	152	!
	153	! !== upstream advection with initial mass fluxes & intermediate update ==!
[14072]	154	! !* upstream tracer flux in the i and j direction
[13982]	155	DO_3D( nn_hls, nn_hls-1, nn_hls, nn_hls-1, 1, jpkm1 )
[12377]	156	! upstream scheme
	157	zfp_ui = pU(ji,jj,jk) + ABS( pU(ji,jj,jk) )
	158	zfm_ui = pU(ji,jj,jk) - ABS( pU(ji,jj,jk) )
	159	zfp_vj = pV(ji,jj,jk) + ABS( pV(ji,jj,jk) )
	160	zfm_vj = pV(ji,jj,jk) - ABS( pV(ji,jj,jk) )
	161	zwx(ji,jj,jk) = 0.5 * ( zfp_ui * pt(ji,jj,jk,jn,Kbb) + zfm_ui * pt(ji+1,jj ,jk,jn,Kbb) )
	162	zwy(ji,jj,jk) = 0.5 * ( zfp_vj * pt(ji,jj,jk,jn,Kbb) + zfm_vj * pt(ji ,jj+1,jk,jn,Kbb) )
	163	END_3D
[13497]	164	! !* upstream tracer flux in the k direction *!
	165	DO_3D( 1, 1, 1, 1, 2, jpkm1 ) ! Interior value ( multiplied by wmask)
[12377]	166	zfp_wk = pW(ji,jj,jk) + ABS( pW(ji,jj,jk) )
	167	zfm_wk = pW(ji,jj,jk) - ABS( pW(ji,jj,jk) )
	168	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)
	169	END_3D
[13497]	170	IF( ln_linssh ) THEN ! top ocean value (only in linear free surface as zwz has been w-masked)
	171	IF( ln_isfcav ) THEN ! top of the ice-shelf cavities and at the ocean surface
[13295]	172	DO_2D( 1, 1, 1, 1 )
[14072]	173	zwz(ji,jj, mikt(ji,jj) ) = pW(ji,jj,mikt(ji,jj)) * pt(ji,jj,mikt(ji,jj),jn,Kbb) ! linear free surface
[12377]	174	END_2D
[13497]	175	ELSE ! no cavities: only at the ocean surface
[13295]	176	DO_2D( 1, 1, 1, 1 )
[13286]	177	zwz(ji,jj,1) = pW(ji,jj,1) * pt(ji,jj,1,jn,Kbb)
	178	END_2D
[5770]	179	ENDIF
[5120]	180	ENDIF
[14072]	181	!
[13982]	182	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 1, jpkm1 ) !* trend and after field with monotonic scheme
[13497]	183	! ! total intermediate advective trends
[12377]	184	ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) &
	185	& + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) &
	186	& + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj)
[13497]	187	! ! update and guess with monotonic sheme
[13237]	188	pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) + ztra &
	189	& / e3t(ji,jj,jk,Kmm ) * tmask(ji,jj,jk)
	190	zwi(ji,jj,jk) = ( e3t(ji,jj,jk,Kbb) * pt(ji,jj,jk,jn,Kbb) + p2dt * ztra ) &
	191	& / e3t(ji,jj,jk,Krhs) * tmask(ji,jj,jk)
[12377]	192	END_3D
[14072]	193
[11407]	194	IF ( ll_zAimp ) THEN
	195	CALL tridia_solver( zwdia, zwsup, zwinf, zwi, zwi , 0 )
	196	!
[11411]	197	ztw(:,:,1) = 0._wp ; ztw(:,:,jpk) = 0._wp ;
[13982]	198	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, jpkm1 ) ! Interior value ( multiplied by wmask)
[12377]	199	zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) )
	200	zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) )
	201	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)
	202	zwz(ji,jj,jk) = zwz(ji,jj,jk) + ztw(ji,jj,jk) ! update vertical fluxes
	203	END_3D
[13295]	204	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[12377]	205	pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) - ( ztw(ji,jj,jk) - ztw(ji ,jj ,jk+1) ) &
	206	& * r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm)
	207	END_3D
[11407]	208	!
	209	END IF
[13982]	210	!
[7646]	211	IF( l_trd .OR. l_hst ) THEN ! trend diagnostics (contribution of upstream fluxes)
[7753]	212	ztrdx(:,:,:) = zwx(:,:,:) ; ztrdy(:,:,:) = zwy(:,:,:) ; ztrdz(:,:,:) = zwz(:,:,:)
[2528]	213	END IF
[5770]	214	! ! "Poleward" heat and salt transports (contribution of upstream fluxes)
[14072]	215	IF( l_ptr ) zptry(:,:,:) = zwy(:,:,:)
[5770]	216	!
	217	! !== anti-diffusive flux : high order minus low order ==!
	218	!
[6140]	219	SELECT CASE( kn_fct_h ) !* horizontal anti-diffusive fluxes
[5770]	220	!
[6140]	221	CASE( 2 ) !- 2nd order centered
[13982]	222	DO_3D( nn_hls, nn_hls-1, nn_hls, nn_hls-1, 1, jpkm1 )
[12377]	223	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)
	224	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)
	225	END_3D
[5770]	226	!
[6140]	227	CASE( 4 ) !- 4th order centered
[7753]	228	zltu(:,:,jpk) = 0._wp ! Bottom value : flux set to zero
	229	zltv(:,:,jpk) = 0._wp
[6140]	230	DO jk = 1, jpkm1 ! Laplacian
[13497]	231	DO_2D( 1, 0, 1, 0 ) ! 1st derivative (gradient)
[12377]	232	ztu(ji,jj,jk) = ( pt(ji+1,jj ,jk,jn,Kmm) - pt(ji,jj,jk,jn,Kmm) ) * umask(ji,jj,jk)
	233	ztv(ji,jj,jk) = ( pt(ji ,jj+1,jk,jn,Kmm) - pt(ji,jj,jk,jn,Kmm) ) * vmask(ji,jj,jk)
	234	END_2D
[13497]	235	DO_2D( 0, 0, 0, 0 ) ! 2nd derivative * 1/ 6
[12377]	236	zltu(ji,jj,jk) = ( ztu(ji,jj,jk) + ztu(ji-1,jj,jk) ) * r1_6
	237	zltv(ji,jj,jk) = ( ztv(ji,jj,jk) + ztv(ji,jj-1,jk) ) * r1_6
	238	END_2D
[503]	239	END DO
[13226]	240	CALL lbc_lnk_multi( 'traadv_fct', zltu, 'T', 1.0_wp , zltv, 'T', 1.0_wp ) ! Lateral boundary cond. (unchanged sgn)
[5770]	241	!
[13982]	242	DO_3D( 1, 0, 1, 0, 1, jpkm1 )
[12377]	243	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
	244	zC2t_v = pt(ji,jj,jk,jn,Kmm) + pt(ji ,jj+1,jk,jn,Kmm)
[13982]	245	! ! C4 minus upstream advective fluxes
[12377]	246	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)
	247	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)
	248	END_3D
[13982]	249	IF (nn_hls.EQ.2) CALL lbc_lnk_multi( 'traadv_fct', zwx, 'U', -1.0_wp, zwy, 'V', -1.0_wp ) ! Lateral boundary cond. (unchanged sgn)
[5770]	250	!
[6140]	251	CASE( 41 ) !- 4th order centered ==>> !!gm coding attempt need to be tested
[7753]	252	ztu(:,:,jpk) = 0._wp ! Bottom value : flux set to zero
	253	ztv(:,:,jpk) = 0._wp
[13982]	254	DO_3D( nn_hls, nn_hls-1, nn_hls, nn_hls-1, 1, jpkm1 ) ! 1st derivative (gradient)
[12377]	255	ztu(ji,jj,jk) = ( pt(ji+1,jj ,jk,jn,Kmm) - pt(ji,jj,jk,jn,Kmm) ) * umask(ji,jj,jk)
	256	ztv(ji,jj,jk) = ( pt(ji ,jj+1,jk,jn,Kmm) - pt(ji,jj,jk,jn,Kmm) ) * vmask(ji,jj,jk)
	257	END_3D
[13982]	258	IF (nn_hls.EQ.1) CALL lbc_lnk_multi( 'traadv_fct', ztu, 'U', -1.0_wp , ztv, 'V', -1.0_wp ) ! Lateral boundary cond. (unchanged sgn)
[5770]	259	!
[13982]	260	IF (nn_hls.EQ.1) CALL lbc_lnk_multi( 'traadv_fct', ztu, 'U', -1.0_wp , ztv, 'V', -1.0_wp ) ! Lateral boundary cond. (unchanged sgn)
	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
[13982]	272	IF (nn_hls.EQ.2) CALL lbc_lnk_multi( '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
[12377]	285	CALL interp_4th_cpt( 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
	296	CALL lbc_lnk_multi( 'traadv_fct', zwi, 'T', 1.0_wp, zwx, 'U', -1.0_wp , zwy, 'V', -1.0_wp, zwz, 'T', 1.0_wp )
	297	ELSE
	298	CALL lbc_lnk( 'traadv_fct', zwi, 'T', 1.0_wp)
	299	END IF
	300	!
	301	IF (nn_hls.EQ.1) THEN
	302	CALL lbc_lnk_multi( 'traadv_fct', zwi, 'T', 1.0_wp, zwx, 'U', -1.0_wp , zwy, 'V', -1.0_wp, zwz, 'T', 1.0_wp )
	303	ELSE
	304	CALL lbc_lnk( 'traadv_fct', zwi, 'T', 1.0_wp)
	305	END IF
	306	!
[11407]	307	IF ( ll_zAimp ) THEN
[13982]	308	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 1, jpkm1 ) !* trend and after field with monotonic scheme
[13497]	309	! ! total intermediate advective trends
[12377]	310	ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) &
	311	& + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) &
	312	& + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj)
[13982]	313	ztw(ji,jj,jk) = zwi(ji,jj,jk) + p2dt * ztra / e3t(ji,jj,jk,Krhs) * tmask(ji,jj,jk)
[12377]	314	END_3D
[11407]	315	!
[11411]	316	CALL tridia_solver( zwdia, zwsup, zwinf, ztw, ztw , 0 )
[11407]	317	!
[13982]	318	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, jpkm1 ) ! Interior value ( multiplied by wmask)
[12377]	319	zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) )
	320	zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) )
[13982]	321	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]	322	END_3D
[11407]	323	END IF
[11411]	324	!
[5770]	325	! !== monotonicity algorithm ==!
	326	!
[12377]	327	CALL nonosc( Kmm, pt(:,:,:,jn,Kbb), zwx, zwy, zwz, zwi, p2dt )
[6140]	328	!
[5770]	329	! !== final trend with corrected fluxes ==!
	330	!
[13295]	331	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[12377]	332	ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) &
	333	& + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) &
	334	& + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj)
	335	pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) + ztra / e3t(ji,jj,jk,Kmm)
	336	zwi(ji,jj,jk) = zwi(ji,jj,jk) + p2dt * ztra / e3t(ji,jj,jk,Krhs) * tmask(ji,jj,jk)
	337	END_3D
[5770]	338	!
[11407]	339	IF ( ll_zAimp ) THEN
	340	!
[11411]	341	ztw(:,:,1) = 0._wp ; ztw(:,:,jpk) = 0._wp
[13497]	342	DO_3D( 0, 0, 0, 0, 2, jpkm1 ) ! Interior value ( multiplied by wmask)
[12377]	343	zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) )
	344	zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) )
	345	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)
	346	zwz(ji,jj,jk) = zwz(ji,jj,jk) + ztw(ji,jj,jk) ! Update vertical fluxes for trend diagnostic
	347	END_3D
[13295]	348	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[12377]	349	pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) - ( ztw(ji,jj,jk) - ztw(ji ,jj ,jk+1) ) &
	350	& * r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm)
	351	END_3D
[13982]	352	END IF
[9019]	353	IF( l_trd .OR. l_hst ) THEN ! trend diagnostics // heat/salt transport
[13982]	354	ztrdx(:,:,:) = ztrdx(:,:,:) + zwx(:,:,:) ! <<< add anti-diffusive fluxes
[9019]	355	ztrdy(:,:,:) = ztrdy(:,:,:) + zwy(:,:,:) ! to upstream fluxes
	356	ztrdz(:,:,:) = ztrdz(:,:,:) + zwz(:,:,:) !
[5770]	357	!
[9019]	358	IF( l_trd ) THEN ! trend diagnostics
[12377]	359	CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_xad, ztrdx, pU, pt(:,:,:,jn,Kmm) )
	360	CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_yad, ztrdy, pV, pt(:,:,:,jn,Kmm) )
	361	CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_zad, ztrdz, pW, pt(:,:,:,jn,Kmm) )
[9019]	362	ENDIF
	363	! ! heat/salt transport
	364	IF( l_hst ) CALL dia_ar5_hst( jn, 'adv', ztrdx(:,:,:), ztrdy(:,:,:) )
[5770]	365	!
[9019]	366	ENDIF
	367	IF( l_ptr ) THEN ! "Poleward" transports
	368	zptry(:,:,:) = zptry(:,:,:) + zwy(:,:,:) ! <<< add anti-diffusive fluxes
[7646]	369	CALL dia_ptr_hst( jn, 'adv', zptry(:,:,:) )
[2528]	370	ENDIF
[503]	371	!
[6140]	372	END DO ! end of tracer loop
[503]	373	!
[11407]	374	IF ( ll_zAimp ) THEN
	375	DEALLOCATE( zwdia, zwinf, zwsup )
	376	ENDIF
[13982]	377	IF( l_trd .OR. l_hst ) THEN
[10024]	378	DEALLOCATE( ztrdx, ztrdy, ztrdz )
	379	ENDIF
[14072]	380	IF( l_ptr ) THEN
[10024]	381	DEALLOCATE( zptry )
	382	ENDIF
	383	!
[5770]	384	END SUBROUTINE tra_adv_fct
[3]	385
[5737]	386
[12377]	387	SUBROUTINE nonosc( Kmm, pbef, paa, pbb, pcc, paft, p2dt )
[3]	388	!!---------------------------------------------------------------------
	389	!! * ROUTINE nonosc *
	390	!!
[14072]	391	!! ** Purpose : compute monotonic tracer fluxes from the upstream
	392	!! scheme and the before field by a nonoscillatory algorithm
	393	!!
[3]	394	!! ** Method : ... ???
	395	!! warning : pbef and paft must be masked, but the boundaries
	396	!! conditions on the fluxes are not necessary zalezak (1979)
	397	!! drange (1995) multi-dimensional forward-in-time and upstream-
	398	!! in-space based differencing for fluid
	399	!!----------------------------------------------------------------------
[13982]	400	INTEGER , INTENT(in ) :: Kmm ! time level index
	401	REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
	402	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pbef ! before field
	403	REAL(wp), DIMENSION(A2D(nn_hls) ,jpk), INTENT(in ) :: paft ! after field
	404	REAL(wp), DIMENSION(A2D(nn_hls) ,jpk), INTENT(inout) :: paa, pbb, pcc ! monotonic fluxes in the 3 directions
[2715]	405	!
[4990]	406	INTEGER :: ji, jj, jk ! dummy loop indices
	407	INTEGER :: ikm1 ! local integer
[13226]	408	REAL(dp) :: zpos, zneg, zbt, za, zb, zc, zbig, zrtrn ! local scalars
	409	REAL(dp) :: zau, zbu, zcu, zav, zbv, zcv, zup, zdo ! - -
[13982]	410	REAL(dp), DIMENSION(A2D(nn_hls),jpk) :: zbetup, zbetdo, zbup, zbdo
[3]	411	!!----------------------------------------------------------------------
[3294]	412	!
[13226]	413	zbig = 1.e+40_dp
	414	zrtrn = 1.e-15_dp
	415	zbetup(:,:,:) = 0._dp ; zbetdo(:,:,:) = 0._dp
[785]	416
[3]	417	! Search local extrema
	418	! --------------------
[785]	419	! max/min of pbef & paft with large negative/positive value (-/+zbig) inside land
[13982]	420	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpk )
	421	zbup(ji,jj,jk) = MAX( pbef(ji,jj,jk) * tmask(ji,jj,jk) - zbig * ( 1._wp - tmask(ji,jj,jk) ), &
	422	& paft(ji,jj,jk) * tmask(ji,jj,jk) - zbig * ( 1._wp - tmask(ji,jj,jk) ) )
	423	zbdo(ji,jj,jk) = MIN( pbef(ji,jj,jk) * tmask(ji,jj,jk) + zbig * ( 1._wp - tmask(ji,jj,jk) ), &
	424	& paft(ji,jj,jk) * tmask(ji,jj,jk) + zbig * ( 1._wp - tmask(ji,jj,jk) ) )
	425	END_3D
[785]	426
[5120]	427	DO jk = 1, jpkm1
	428	ikm1 = MAX(jk-1,1)
[13982]	429	DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
[5120]	430
[12377]	431	! search maximum in neighbourhood
	432	zup = MAX( zbup(ji ,jj ,jk ), &
	433	& zbup(ji-1,jj ,jk ), zbup(ji+1,jj ,jk ), &
	434	& zbup(ji ,jj-1,jk ), zbup(ji ,jj+1,jk ), &
	435	& zbup(ji ,jj ,ikm1), zbup(ji ,jj ,jk+1) )
[3]	436
[12377]	437	! search minimum in neighbourhood
	438	zdo = MIN( zbdo(ji ,jj ,jk ), &
	439	& zbdo(ji-1,jj ,jk ), zbdo(ji+1,jj ,jk ), &
	440	& zbdo(ji ,jj-1,jk ), zbdo(ji ,jj+1,jk ), &
	441	& zbdo(ji ,jj ,ikm1), zbdo(ji ,jj ,jk+1) )
[3]	442
[12377]	443	! positive part of the flux
	444	zpos = MAX( 0., paa(ji-1,jj ,jk ) ) - MIN( 0., paa(ji ,jj ,jk ) ) &
	445	& + MAX( 0., pbb(ji ,jj-1,jk ) ) - MIN( 0., pbb(ji ,jj ,jk ) ) &
	446	& + MAX( 0., pcc(ji ,jj ,jk+1) ) - MIN( 0., pcc(ji ,jj ,jk ) )
[785]	447
[12377]	448	! negative part of the flux
	449	zneg = MAX( 0., paa(ji ,jj ,jk ) ) - MIN( 0., paa(ji-1,jj ,jk ) ) &
	450	& + MAX( 0., pbb(ji ,jj ,jk ) ) - MIN( 0., pbb(ji ,jj-1,jk ) ) &
	451	& + MAX( 0., pcc(ji ,jj ,jk ) ) - MIN( 0., pcc(ji ,jj ,jk+1) )
[785]	452
[12377]	453	! up & down beta terms
	454	zbt = e1e2t(ji,jj) * e3t(ji,jj,jk,Kmm) / p2dt
	455	zbetup(ji,jj,jk) = ( zup - paft(ji,jj,jk) ) / ( zpos + zrtrn ) * zbt
	456	zbetdo(ji,jj,jk) = ( paft(ji,jj,jk) - zdo ) / ( zneg + zrtrn ) * zbt
	457	END_2D
[3]	458	END DO
[13982]	459	IF (nn_hls.EQ.1) CALL lbc_lnk_multi( 'traadv_fct', zbetup, 'T', 1.0_wp , zbetdo, 'T', 1.0_wp ) ! lateral boundary cond. (unchanged sign)
[3]	460
[237]	461	! 3. monotonic flux in the i & j direction (paa & pbb)
	462	! ----------------------------------------
[13982]	463	DO_3D( 1, 0, 1, 0, 1, jpkm1 )
[12377]	464	zau = MIN( 1._wp, zbetdo(ji,jj,jk), zbetup(ji+1,jj,jk) )
	465	zbu = MIN( 1._wp, zbetup(ji,jj,jk), zbetdo(ji+1,jj,jk) )
[13226]	466	zcu = ( 0.5 + SIGN( 0.5_wp , paa(ji,jj,jk) ) )
[12377]	467	paa(ji,jj,jk) = paa(ji,jj,jk) * ( zcu * zau + ( 1._wp - zcu) * zbu )
[3]	468
[12377]	469	zav = MIN( 1._wp, zbetdo(ji,jj,jk), zbetup(ji,jj+1,jk) )
	470	zbv = MIN( 1._wp, zbetup(ji,jj,jk), zbetdo(ji,jj+1,jk) )
[13226]	471	zcv = ( 0.5 + SIGN( 0.5_wp , pbb(ji,jj,jk) ) )
[12377]	472	pbb(ji,jj,jk) = pbb(ji,jj,jk) * ( zcv * zav + ( 1._wp - zcv) * zbv )
[3]	473
[13497]	474	! monotonic flux in the k direction, i.e. pcc
	475	! -------------------------------------------
[12377]	476	za = MIN( 1., zbetdo(ji,jj,jk+1), zbetup(ji,jj,jk) )
	477	zb = MIN( 1., zbetup(ji,jj,jk+1), zbetdo(ji,jj,jk) )
[13226]	478	zc = ( 0.5 + SIGN( 0.5_wp , pcc(ji,jj,jk+1) ) )
[12377]	479	pcc(ji,jj,jk+1) = pcc(ji,jj,jk+1) * ( zc * za + ( 1._wp - zc) * zb )
	480	END_3D
[503]	481	!
[3]	482	END SUBROUTINE nonosc
	483
[5770]	484
[7646]	485	SUBROUTINE interp_4th_cpt_org( pt_in, pt_out )
[5770]	486	!!----------------------------------------------------------------------
[7646]	487	!! * ROUTINE interp_4th_cpt_org *
[14072]	488	!!
[5770]	489	!! ** Purpose : Compute the interpolation of tracer at w-point
	490	!!
	491	!! ** Method : 4th order compact interpolation
	492	!!----------------------------------------------------------------------
	493	REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pt_in ! now tracer fields
	494	REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT( out) :: pt_out ! now tracer field interpolated at w-pts
	495	!
	496	INTEGER :: ji, jj, jk ! dummy loop integers
	497	REAL(wp),DIMENSION(jpi,jpj,jpk) :: zwd, zwi, zws, zwrm, zwt
	498	!!----------------------------------------------------------------------
[14072]	499
[13497]	500	DO_3D( 1, 1, 1, 1, 3, jpkm1 ) !== build the three diagonal matrix ==!
[12377]	501	zwd (ji,jj,jk) = 4._wp
	502	zwi (ji,jj,jk) = 1._wp
	503	zws (ji,jj,jk) = 1._wp
	504	zwrm(ji,jj,jk) = 3._wp * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) )
	505	!
	506	IF( tmask(ji,jj,jk+1) == 0._wp) THEN ! Switch to second order centered at bottom
[5770]	507	zwd (ji,jj,jk) = 1._wp
	508	zwi (ji,jj,jk) = 0._wp
	509	zws (ji,jj,jk) = 0._wp
[14072]	510	zwrm(ji,jj,jk) = 0.5 * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) )
[12377]	511	ENDIF
	512	END_3D
[5770]	513	!
[13497]	514	jk = 2 ! Switch to second order centered at top
[13295]	515	DO_2D( 1, 1, 1, 1 )
[12377]	516	zwd (ji,jj,jk) = 1._wp
	517	zwi (ji,jj,jk) = 0._wp
	518	zws (ji,jj,jk) = 0._wp
	519	zwrm(ji,jj,jk) = 0.5 * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) )
	520	END_2D
	521	!
[5770]	522	! !== tridiagonal solve ==!
[13497]	523	DO_2D( 1, 1, 1, 1 ) ! first recurrence
[12377]	524	zwt(ji,jj,2) = zwd(ji,jj,2)
	525	END_2D
[13295]	526	DO_3D( 1, 1, 1, 1, 3, jpkm1 )
[12377]	527	zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1)
	528	END_3D
[5770]	529	!
[13497]	530	DO_2D( 1, 1, 1, 1 ) ! second recurrence: Zk = Yk - Ik / Tk-1 Zk-1
[12377]	531	pt_out(ji,jj,2) = zwrm(ji,jj,2)
	532	END_2D
[13295]	533	DO_3D( 1, 1, 1, 1, 3, jpkm1 )
[14072]	534	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]	535	END_3D
[5770]	536
[13497]	537	DO_2D( 1, 1, 1, 1 ) ! third recurrence: Xk = (Zk - Sk Xk+1 ) / Tk
[12377]	538	pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1)
	539	END_2D
[13295]	540	DO_3DS( 1, 1, 1, 1, jpk-2, 2, -1 )
[12377]	541	pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - zws(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk)
	542	END_3D
[14072]	543	!
[7646]	544	END SUBROUTINE interp_4th_cpt_org
	545
[14072]	546
[7646]	547	SUBROUTINE interp_4th_cpt( pt_in, pt_out )
	548	!!----------------------------------------------------------------------
	549	!! * ROUTINE interp_4th_cpt *
[14072]	550	!!
[7646]	551	!! ** Purpose : Compute the interpolation of tracer at w-point
	552	!!
	553	!! ** Method : 4th order compact interpolation
	554	!!----------------------------------------------------------------------
	555	REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pt_in ! field at t-point
[13982]	556	REAL(wp),DIMENSION(A2D(nn_hls) ,jpk), INTENT( out) :: pt_out ! field interpolated at w-point
[7646]	557	!
	558	INTEGER :: ji, jj, jk ! dummy loop integers
	559	INTEGER :: ikt, ikb ! local integers
[13982]	560	REAL(wp),DIMENSION(A2D(nn_hls),jpk) :: zwd, zwi, zws, zwrm, zwt
[7646]	561	!!----------------------------------------------------------------------
	562	!
	563	! !== build the three diagonal matrix & the RHS ==!
	564	!
[13982]	565	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 3, jpkm1 ) ! interior (from jk=3 to jpk-1)
[12377]	566	zwd (ji,jj,jk) = 3._wp * wmask(ji,jj,jk) + 1._wp ! diagonal
	567	zwi (ji,jj,jk) = wmask(ji,jj,jk) ! lower diagonal
	568	zws (ji,jj,jk) = wmask(ji,jj,jk) ! upper diagonal
	569	zwrm(ji,jj,jk) = 3._wp * wmask(ji,jj,jk) & ! RHS
	570	& * ( pt_in(ji,jj,jk) + pt_in(ji,jj,jk-1) )
	571	END_3D
[7646]	572	!
	573	!!gm
	574	! SELECT CASE( kbc ) !* boundary condition
	575	! CASE( np_NH ) ! Neumann homogeneous at top & bottom
	576	! CASE( np_CEN2 ) ! 2nd order centered at top & bottom
	577	! END SELECT
[14072]	578	!!gm
[7646]	579	!
[9901]	580	IF ( ln_isfcav ) THEN ! set level two values which may not be set in ISF case
	581	zwd(:,:,2) = 1._wp ; zwi(:,:,2) = 0._wp ; zws(:,:,2) = 0._wp ; zwrm(:,:,2) = 0._wp
	582	END IF
	583	!
[13982]	584	DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2nd order centered at top & bottom
[12377]	585	ikt = mikt(ji,jj) + 1 ! w-point below the 1st wet point
	586	ikb = MAX(mbkt(ji,jj), 2) ! - above the last wet point
	587	!
	588	zwd (ji,jj,ikt) = 1._wp ! top
	589	zwi (ji,jj,ikt) = 0._wp
	590	zws (ji,jj,ikt) = 0._wp
	591	zwrm(ji,jj,ikt) = 0.5_wp * ( pt_in(ji,jj,ikt-1) + pt_in(ji,jj,ikt) )
	592	!
	593	zwd (ji,jj,ikb) = 1._wp ! bottom
	594	zwi (ji,jj,ikb) = 0._wp
	595	zws (ji,jj,ikb) = 0._wp
[14072]	596	zwrm(ji,jj,ikb) = 0.5_wp * ( pt_in(ji,jj,ikb-1) + pt_in(ji,jj,ikb) )
[12377]	597	END_2D
[7646]	598	!
	599	! !== tridiagonal solver ==!
	600	!
[13982]	601	DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) !* 1st recurrence: Tk = Dk - Ik Sk-1 / Tk-1
[12377]	602	zwt(ji,jj,2) = zwd(ji,jj,2)
	603	END_2D
[13982]	604	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 3, jpkm1 )
[12377]	605	zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1)
	606	END_3D
[7646]	607	!
[13982]	608	DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) !* 2nd recurrence: Zk = Yk - Ik / Tk-1 Zk-1
[12377]	609	pt_out(ji,jj,2) = zwrm(ji,jj,2)
	610	END_2D
[13982]	611	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 3, jpkm1 )
[14072]	612	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]	613	END_3D
[7646]	614
[13982]	615	DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) !* 3d recurrence: Xk = (Zk - Sk Xk+1 ) / Tk
[12377]	616	pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1)
	617	END_2D
[13982]	618	DO_3DS( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, jpk-2, 2, -1 )
[12377]	619	pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - zws(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk)
	620	END_3D
[14072]	621	!
[5770]	622	END SUBROUTINE interp_4th_cpt
[7646]	623
	624
	625	SUBROUTINE tridia_solver( pD, pU, pL, pRHS, pt_out , klev )
	626	!!----------------------------------------------------------------------
	627	!! * ROUTINE tridia_solver *
[14072]	628	!!
[7646]	629	!! ** Purpose : solve a symmetric 3diagonal system
	630	!!
	631	!! ** Method : solve M.t_out = RHS(t) where M is a tri diagonal matrix ( jpk*jpk )
[14072]	632	!!
[7646]	633	!! ( D_1 U_1 0 0 0 )( t_1 ) ( RHS_1 )
	634	!! ( L_2 D_2 U_2 0 0 )( t_2 ) ( RHS_2 )
	635	!! ( 0 L_3 D_3 U_3 0 )( t_3 ) = ( RHS_3 )
	636	!! ( ... )( ... ) ( ... )
	637	!! ( 0 0 0 L_k D_k )( t_k ) ( RHS_k )
[14072]	638	!!
[7646]	639	!! M is decomposed in the product of an upper and lower triangular matrix.
[14072]	640	!! The tri-diagonals matrix is given as input 3D arrays: pD, pU, pL
[7646]	641	!! (i.e. the Diagonal, the Upper diagonal, and the Lower diagonal).
	642	!! The solution is pta.
	643	!! The 3d array zwt is used as a work space array.
	644	!!----------------------------------------------------------------------
[13982]	645	REAL(wp),DIMENSION(A2D(nn_hls),jpk), INTENT(in ) :: pD, pU, PL ! 3-diagonal matrix
	646	REAL(wp),DIMENSION(A2D(nn_hls),jpk), INTENT(in ) :: pRHS ! Right-Hand-Side
	647	REAL(wp),DIMENSION(A2D(nn_hls),jpk), INTENT( out) :: pt_out !!gm field at level=F(klev)
	648	INTEGER , INTENT(in ) :: klev ! =1 pt_out at w-level
	649	! ! =0 pt at t-level
[7646]	650	INTEGER :: ji, jj, jk ! dummy loop integers
	651	INTEGER :: kstart ! local indices
[13982]	652	REAL(wp),DIMENSION(A2D(nn_hls),jpk) :: zwt ! 3D work array
[7646]	653	!!----------------------------------------------------------------------
	654	!
	655	kstart = 1 + klev
	656	!
[13982]	657	DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) !* 1st recurrence: Tk = Dk - Ik Sk-1 / Tk-1
[12377]	658	zwt(ji,jj,kstart) = pD(ji,jj,kstart)
	659	END_2D
[13982]	660	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, kstart+1, jpkm1 )
[12377]	661	zwt(ji,jj,jk) = pD(ji,jj,jk) - pL(ji,jj,jk) * pU(ji,jj,jk-1) /zwt(ji,jj,jk-1)
	662	END_3D
[7646]	663	!
[13982]	664	DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) !* 2nd recurrence: Zk = Yk - Ik / Tk-1 Zk-1
[12377]	665	pt_out(ji,jj,kstart) = pRHS(ji,jj,kstart)
	666	END_2D
[13982]	667	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, kstart+1, jpkm1 )
[14072]	668	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]	669	END_3D
[7646]	670
[13982]	671	DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) !* 3d recurrence: Xk = (Zk - Sk Xk+1 ) / Tk
[12377]	672	pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1)
	673	END_2D
[13982]	674	DO_3DS( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, jpk-2, kstart, -1 )
[12377]	675	pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - pU(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk)
	676	END_3D
[7646]	677	!
	678	END SUBROUTINE tridia_solver
	679
[3]	680	!!======================================================================
[5770]	681	END MODULE traadv_fct

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