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traadv_fct.F90 in NEMO/branches/2020/dev_r13648_ASINTER-04_laurent_bulk_ice/src/OCE/TRA – NEMO

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source: NEMO/branches/2020/dev_r13648_ASINTER-04_laurent_bulk_ice/src/OCE/TRA/traadv_fct.F90 @ 14017

Last change on this file since 14017 was 14017, checked in by laurent, 4 years ago
Keep up with trunk revision 13999
Property svn:keywords set to `Id`
File size: 36.5 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
[14017]	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
[14017]	26	USE iom !
[3625]	27	USE lib_mpp ! MPP library
[14017]	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
[14017]	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 *
[14017]	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)
[14017]	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
[14017]	83	! TEMP: [tiling] This can be A2D(nn_hls) if using XIOS (subdomain support)
	84	! NOTE: [tiling-comms-merge] These were changed to INTENT(inout) but they are not modified, so it is reverted
[12377]	85	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pU, pV, pW ! 3 ocean volume flux components
	86	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt,jpt), INTENT(inout) :: pt ! tracers and RHS of tracer equation
[2715]	87	!
[14017]	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 ! - -
[14017]	92	REAL(wp), DIMENSION(A2D(nn_hls),jpk) :: zwi, zwx, zwy, zwz, ztu, ztv, zltu, zltv, ztw
[9019]	93	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ztrdx, ztrdy, ztrdz, zptry
[11407]	94	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: zwinf, zwdia, zwsup
	95	LOGICAL :: ll_zAimp ! flag to apply adaptive implicit vertical advection
[3]	96	!!----------------------------------------------------------------------
[3294]	97	!
[14017]	98	IF( ntile == 0 .OR. ntile == 1 ) THEN ! Do only on the first tile
	99	IF( kt == kit000 ) THEN
	100	IF(lwp) WRITE(numout,*)
	101	IF(lwp) WRITE(numout,*) 'tra_adv_fct : FCT advection scheme on ', cdtype
	102	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~'
	103	ENDIF
	104	! NOTE: [tiling-comms-merge] Bug fix- move array zeroing out of this IF block
	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
[14017]	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
[14017]	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	!
[14017]	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
[14017]	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
[14017]	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 ==!
[14017]	156	! !* upstream tracer flux in the i and j direction
	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 )
[14017]	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
[14017]	183	!
	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
[14017]	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 ;
[14017]	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
[14017]	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)
[14017]	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
[14017]	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
[13226]	242	CALL lbc_lnk_multi( 'traadv_fct', zltu, 'T', 1.0_wp , zltv, 'T', 1.0_wp ) ! Lateral boundary cond. (unchanged sgn)
[5770]	243	!
[14017]	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)
[14017]	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
[14017]	251	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]	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
[14017]	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
[14017]	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)
[5770]	261	!
[14017]	262	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)
	263	!
[13497]	264	DO_3D( 0, 0, 0, 0, 1, jpkm1 ) ! Horizontal advective fluxes
[12377]	265	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)
	266	zC2t_v = pt(ji,jj,jk,jn,Kmm) + pt(ji ,jj+1,jk,jn,Kmm)
	267	! ! C4 interpolation of T at u- & v-points (x2)
	268	zC4t_u = zC2t_u + r1_6 * ( ztu(ji-1,jj ,jk) - ztu(ji+1,jj ,jk) )
	269	zC4t_v = zC2t_v + r1_6 * ( ztv(ji ,jj-1,jk) - ztv(ji ,jj+1,jk) )
[14017]	270	! ! C4 minus upstream advective fluxes
[12377]	271	zwx(ji,jj,jk) = 0.5_wp * pU(ji,jj,jk) * zC4t_u - zwx(ji,jj,jk)
	272	zwy(ji,jj,jk) = 0.5_wp * pV(ji,jj,jk) * zC4t_v - zwy(ji,jj,jk)
	273	END_3D
[14017]	274	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]	275	!
	276	END SELECT
[14017]	277	!
[6140]	278	SELECT CASE( kn_fct_v ) !* vertical anti-diffusive fluxes (w-masked interior values)
[5770]	279	!
[6140]	280	CASE( 2 ) !- 2nd order centered
[14017]	281	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, jpkm1 )
[12377]	282	zwz(ji,jj,jk) = ( pW(ji,jj,jk) * 0.5_wp * ( pt(ji,jj,jk,jn,Kmm) + pt(ji,jj,jk-1,jn,Kmm) ) &
	283	& - zwz(ji,jj,jk) ) * wmask(ji,jj,jk)
	284	END_3D
[5770]	285	!
[6140]	286	CASE( 4 ) !- 4th order COMPACT
[12377]	287	CALL interp_4th_cpt( pt(:,:,:,jn,Kmm) , ztw ) ! zwt = COMPACT interpolation of T at w-point
[14017]	288	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, jpkm1 )
[12377]	289	zwz(ji,jj,jk) = ( pW(ji,jj,jk) * ztw(ji,jj,jk) - zwz(ji,jj,jk) ) * wmask(ji,jj,jk)
	290	END_3D
[5770]	291	!
	292	END SELECT
[6140]	293	IF( ln_linssh ) THEN ! top ocean value: high order = upstream ==>> zwz=0
[7753]	294	zwz(:,:,1) = 0._wp ! only ocean surface as interior zwz values have been w-masked
[6140]	295	ENDIF
[14017]	296	!
	297	IF (nn_hls.EQ.1) THEN
	298	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 )
	299	ELSE
	300	CALL lbc_lnk( 'traadv_fct', zwi, 'T', 1.0_wp)
	301	END IF
	302	!
	303	IF (nn_hls.EQ.1) THEN
	304	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 )
	305	ELSE
	306	CALL lbc_lnk( 'traadv_fct', zwi, 'T', 1.0_wp)
	307	END IF
	308	!
[11407]	309	IF ( ll_zAimp ) THEN
[14017]	310	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 1, jpkm1 ) !* trend and after field with monotonic scheme
[13497]	311	! ! total intermediate advective trends
[12377]	312	ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) &
	313	& + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) &
	314	& + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj)
[14017]	315	ztw(ji,jj,jk) = zwi(ji,jj,jk) + p2dt * ztra / e3t(ji,jj,jk,Krhs) * tmask(ji,jj,jk)
[12377]	316	END_3D
[11407]	317	!
[11411]	318	CALL tridia_solver( zwdia, zwsup, zwinf, ztw, ztw , 0 )
[11407]	319	!
[14017]	320	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, jpkm1 ) ! Interior value ( multiplied by wmask)
[12377]	321	zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) )
	322	zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) )
[14017]	323	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]	324	END_3D
[11407]	325	END IF
[11411]	326	!
[5770]	327	! !== monotonicity algorithm ==!
	328	!
[12377]	329	CALL nonosc( Kmm, pt(:,:,:,jn,Kbb), zwx, zwy, zwz, zwi, p2dt )
[6140]	330	!
[5770]	331	! !== final trend with corrected fluxes ==!
	332	!
[13295]	333	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[12377]	334	ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) &
	335	& + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) &
	336	& + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj)
	337	pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) + ztra / e3t(ji,jj,jk,Kmm)
	338	zwi(ji,jj,jk) = zwi(ji,jj,jk) + p2dt * ztra / e3t(ji,jj,jk,Krhs) * tmask(ji,jj,jk)
	339	END_3D
[5770]	340	!
[11407]	341	IF ( ll_zAimp ) THEN
	342	!
[11411]	343	ztw(:,:,1) = 0._wp ; ztw(:,:,jpk) = 0._wp
[13497]	344	DO_3D( 0, 0, 0, 0, 2, jpkm1 ) ! Interior value ( multiplied by wmask)
[12377]	345	zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) )
	346	zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) )
	347	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)
	348	zwz(ji,jj,jk) = zwz(ji,jj,jk) + ztw(ji,jj,jk) ! Update vertical fluxes for trend diagnostic
	349	END_3D
[13295]	350	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[12377]	351	pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) - ( ztw(ji,jj,jk) - ztw(ji ,jj ,jk+1) ) &
	352	& * r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm)
	353	END_3D
[14017]	354	END IF
	355	! NOTE: [tiling-comms-merge] I tested this
	356	! NOT TESTED - NEED l_trd OR l_hst TRUE
[9019]	357	IF( l_trd .OR. l_hst ) THEN ! trend diagnostics // heat/salt transport
[14017]	358	ztrdx(:,:,:) = ztrdx(:,:,:) + zwx(:,:,:) ! <<< add anti-diffusive fluxes
[9019]	359	ztrdy(:,:,:) = ztrdy(:,:,:) + zwy(:,:,:) ! to upstream fluxes
	360	ztrdz(:,:,:) = ztrdz(:,:,:) + zwz(:,:,:) !
[5770]	361	!
[9019]	362	IF( l_trd ) THEN ! trend diagnostics
[12377]	363	CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_xad, ztrdx, pU, pt(:,:,:,jn,Kmm) )
	364	CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_yad, ztrdy, pV, pt(:,:,:,jn,Kmm) )
	365	CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_zad, ztrdz, pW, pt(:,:,:,jn,Kmm) )
[9019]	366	ENDIF
	367	! ! heat/salt transport
	368	IF( l_hst ) CALL dia_ar5_hst( jn, 'adv', ztrdx(:,:,:), ztrdy(:,:,:) )
[5770]	369	!
[9019]	370	ENDIF
[14017]	371	! NOTE: [tiling-comms-merge] I tested this
	372	! NOT TESTED - NEED l_ptr TRUE
[9019]	373	IF( l_ptr ) THEN ! "Poleward" transports
	374	zptry(:,:,:) = zptry(:,:,:) + zwy(:,:,:) ! <<< add anti-diffusive fluxes
[7646]	375	CALL dia_ptr_hst( jn, 'adv', zptry(:,:,:) )
[2528]	376	ENDIF
[503]	377	!
[6140]	378	END DO ! end of tracer loop
[503]	379	!
[11407]	380	IF ( ll_zAimp ) THEN
	381	DEALLOCATE( zwdia, zwinf, zwsup )
	382	ENDIF
[14017]	383	IF( l_trd .OR. l_hst ) THEN
[10024]	384	DEALLOCATE( ztrdx, ztrdy, ztrdz )
	385	ENDIF
[14017]	386	IF( l_ptr ) THEN
[10024]	387	DEALLOCATE( zptry )
	388	ENDIF
	389	!
[5770]	390	END SUBROUTINE tra_adv_fct
[3]	391
[5737]	392
[12377]	393	SUBROUTINE nonosc( Kmm, pbef, paa, pbb, pcc, paft, p2dt )
[3]	394	!!---------------------------------------------------------------------
	395	!! * ROUTINE nonosc *
	396	!!
[14017]	397	!! ** Purpose : compute monotonic tracer fluxes from the upstream
	398	!! scheme and the before field by a nonoscillatory algorithm
	399	!!
[3]	400	!! ** Method : ... ???
	401	!! warning : pbef and paft must be masked, but the boundaries
	402	!! conditions on the fluxes are not necessary zalezak (1979)
	403	!! drange (1995) multi-dimensional forward-in-time and upstream-
	404	!! in-space based differencing for fluid
	405	!!----------------------------------------------------------------------
[14017]	406	INTEGER , INTENT(in ) :: Kmm ! time level index
	407	REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
	408	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pbef ! before field
	409	REAL(wp), DIMENSION(A2D(nn_hls) ,jpk), INTENT(in ) :: paft ! after field
	410	REAL(wp), DIMENSION(A2D(nn_hls) ,jpk), INTENT(inout) :: paa, pbb, pcc ! monotonic fluxes in the 3 directions
[2715]	411	!
[4990]	412	INTEGER :: ji, jj, jk ! dummy loop indices
	413	INTEGER :: ikm1 ! local integer
[13226]	414	REAL(dp) :: zpos, zneg, zbt, za, zb, zc, zbig, zrtrn ! local scalars
	415	REAL(dp) :: zau, zbu, zcu, zav, zbv, zcv, zup, zdo ! - -
[14017]	416	REAL(dp), DIMENSION(A2D(nn_hls),jpk) :: zbetup, zbetdo, zbup, zbdo
[3]	417	!!----------------------------------------------------------------------
[3294]	418	!
[13226]	419	zbig = 1.e+40_dp
	420	zrtrn = 1.e-15_dp
	421	zbetup(:,:,:) = 0._dp ; zbetdo(:,:,:) = 0._dp
[785]	422
[3]	423	! Search local extrema
	424	! --------------------
[785]	425	! max/min of pbef & paft with large negative/positive value (-/+zbig) inside land
[14017]	426	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpk )
	427	zbup(ji,jj,jk) = MAX( pbef(ji,jj,jk) * tmask(ji,jj,jk) - zbig * ( 1._wp - tmask(ji,jj,jk) ), &
	428	& paft(ji,jj,jk) * tmask(ji,jj,jk) - zbig * ( 1._wp - tmask(ji,jj,jk) ) )
	429	zbdo(ji,jj,jk) = MIN( pbef(ji,jj,jk) * tmask(ji,jj,jk) + zbig * ( 1._wp - tmask(ji,jj,jk) ), &
	430	& paft(ji,jj,jk) * tmask(ji,jj,jk) + zbig * ( 1._wp - tmask(ji,jj,jk) ) )
	431	END_3D
[785]	432
[5120]	433	DO jk = 1, jpkm1
	434	ikm1 = MAX(jk-1,1)
[14017]	435	DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
[5120]	436
[12377]	437	! search maximum in neighbourhood
	438	zup = MAX( zbup(ji ,jj ,jk ), &
	439	& zbup(ji-1,jj ,jk ), zbup(ji+1,jj ,jk ), &
	440	& zbup(ji ,jj-1,jk ), zbup(ji ,jj+1,jk ), &
	441	& zbup(ji ,jj ,ikm1), zbup(ji ,jj ,jk+1) )
[3]	442
[12377]	443	! search minimum in neighbourhood
	444	zdo = MIN( zbdo(ji ,jj ,jk ), &
	445	& zbdo(ji-1,jj ,jk ), zbdo(ji+1,jj ,jk ), &
	446	& zbdo(ji ,jj-1,jk ), zbdo(ji ,jj+1,jk ), &
	447	& zbdo(ji ,jj ,ikm1), zbdo(ji ,jj ,jk+1) )
[3]	448
[12377]	449	! positive part of the flux
	450	zpos = MAX( 0., paa(ji-1,jj ,jk ) ) - MIN( 0., paa(ji ,jj ,jk ) ) &
	451	& + MAX( 0., pbb(ji ,jj-1,jk ) ) - MIN( 0., pbb(ji ,jj ,jk ) ) &
	452	& + MAX( 0., pcc(ji ,jj ,jk+1) ) - MIN( 0., pcc(ji ,jj ,jk ) )
[785]	453
[12377]	454	! negative part of the flux
	455	zneg = MAX( 0., paa(ji ,jj ,jk ) ) - MIN( 0., paa(ji-1,jj ,jk ) ) &
	456	& + MAX( 0., pbb(ji ,jj ,jk ) ) - MIN( 0., pbb(ji ,jj-1,jk ) ) &
	457	& + MAX( 0., pcc(ji ,jj ,jk ) ) - MIN( 0., pcc(ji ,jj ,jk+1) )
[785]	458
[12377]	459	! up & down beta terms
	460	zbt = e1e2t(ji,jj) * e3t(ji,jj,jk,Kmm) / p2dt
	461	zbetup(ji,jj,jk) = ( zup - paft(ji,jj,jk) ) / ( zpos + zrtrn ) * zbt
	462	zbetdo(ji,jj,jk) = ( paft(ji,jj,jk) - zdo ) / ( zneg + zrtrn ) * zbt
	463	END_2D
[3]	464	END DO
[14017]	465	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]	466
[237]	467	! 3. monotonic flux in the i & j direction (paa & pbb)
	468	! ----------------------------------------
[14017]	469	DO_3D( 1, 0, 1, 0, 1, jpkm1 )
[12377]	470	zau = MIN( 1._wp, zbetdo(ji,jj,jk), zbetup(ji+1,jj,jk) )
	471	zbu = MIN( 1._wp, zbetup(ji,jj,jk), zbetdo(ji+1,jj,jk) )
[13226]	472	zcu = ( 0.5 + SIGN( 0.5_wp , paa(ji,jj,jk) ) )
[12377]	473	paa(ji,jj,jk) = paa(ji,jj,jk) * ( zcu * zau + ( 1._wp - zcu) * zbu )
[3]	474
[12377]	475	zav = MIN( 1._wp, zbetdo(ji,jj,jk), zbetup(ji,jj+1,jk) )
	476	zbv = MIN( 1._wp, zbetup(ji,jj,jk), zbetdo(ji,jj+1,jk) )
[13226]	477	zcv = ( 0.5 + SIGN( 0.5_wp , pbb(ji,jj,jk) ) )
[12377]	478	pbb(ji,jj,jk) = pbb(ji,jj,jk) * ( zcv * zav + ( 1._wp - zcv) * zbv )
[3]	479
[13497]	480	! monotonic flux in the k direction, i.e. pcc
	481	! -------------------------------------------
[12377]	482	za = MIN( 1., zbetdo(ji,jj,jk+1), zbetup(ji,jj,jk) )
	483	zb = MIN( 1., zbetup(ji,jj,jk+1), zbetdo(ji,jj,jk) )
[13226]	484	zc = ( 0.5 + SIGN( 0.5_wp , pcc(ji,jj,jk+1) ) )
[12377]	485	pcc(ji,jj,jk+1) = pcc(ji,jj,jk+1) * ( zc * za + ( 1._wp - zc) * zb )
	486	END_3D
[503]	487	!
[3]	488	END SUBROUTINE nonosc
	489
[5770]	490
[7646]	491	SUBROUTINE interp_4th_cpt_org( pt_in, pt_out )
[5770]	492	!!----------------------------------------------------------------------
[7646]	493	!! * ROUTINE interp_4th_cpt_org *
[14017]	494	!!
[5770]	495	!! ** Purpose : Compute the interpolation of tracer at w-point
	496	!!
	497	!! ** Method : 4th order compact interpolation
	498	!!----------------------------------------------------------------------
	499	REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pt_in ! now tracer fields
	500	REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT( out) :: pt_out ! now tracer field interpolated at w-pts
	501	!
	502	INTEGER :: ji, jj, jk ! dummy loop integers
	503	REAL(wp),DIMENSION(jpi,jpj,jpk) :: zwd, zwi, zws, zwrm, zwt
	504	!!----------------------------------------------------------------------
[14017]	505
[13497]	506	DO_3D( 1, 1, 1, 1, 3, jpkm1 ) !== build the three diagonal matrix ==!
[12377]	507	zwd (ji,jj,jk) = 4._wp
	508	zwi (ji,jj,jk) = 1._wp
	509	zws (ji,jj,jk) = 1._wp
	510	zwrm(ji,jj,jk) = 3._wp * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) )
	511	!
	512	IF( tmask(ji,jj,jk+1) == 0._wp) THEN ! Switch to second order centered at bottom
[5770]	513	zwd (ji,jj,jk) = 1._wp
	514	zwi (ji,jj,jk) = 0._wp
	515	zws (ji,jj,jk) = 0._wp
[14017]	516	zwrm(ji,jj,jk) = 0.5 * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) )
[12377]	517	ENDIF
	518	END_3D
[5770]	519	!
[13497]	520	jk = 2 ! Switch to second order centered at top
[13295]	521	DO_2D( 1, 1, 1, 1 )
[12377]	522	zwd (ji,jj,jk) = 1._wp
	523	zwi (ji,jj,jk) = 0._wp
	524	zws (ji,jj,jk) = 0._wp
	525	zwrm(ji,jj,jk) = 0.5 * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) )
	526	END_2D
	527	!
[5770]	528	! !== tridiagonal solve ==!
[13497]	529	DO_2D( 1, 1, 1, 1 ) ! first recurrence
[12377]	530	zwt(ji,jj,2) = zwd(ji,jj,2)
	531	END_2D
[13295]	532	DO_3D( 1, 1, 1, 1, 3, jpkm1 )
[12377]	533	zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1)
	534	END_3D
[5770]	535	!
[13497]	536	DO_2D( 1, 1, 1, 1 ) ! second recurrence: Zk = Yk - Ik / Tk-1 Zk-1
[12377]	537	pt_out(ji,jj,2) = zwrm(ji,jj,2)
	538	END_2D
[13295]	539	DO_3D( 1, 1, 1, 1, 3, jpkm1 )
[14017]	540	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]	541	END_3D
[5770]	542
[13497]	543	DO_2D( 1, 1, 1, 1 ) ! third recurrence: Xk = (Zk - Sk Xk+1 ) / Tk
[12377]	544	pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1)
	545	END_2D
[13295]	546	DO_3DS( 1, 1, 1, 1, jpk-2, 2, -1 )
[12377]	547	pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - zws(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk)
	548	END_3D
[14017]	549	!
[7646]	550	END SUBROUTINE interp_4th_cpt_org
	551
[14017]	552
[7646]	553	SUBROUTINE interp_4th_cpt( pt_in, pt_out )
	554	!!----------------------------------------------------------------------
	555	!! * ROUTINE interp_4th_cpt *
[14017]	556	!!
[7646]	557	!! ** Purpose : Compute the interpolation of tracer at w-point
	558	!!
	559	!! ** Method : 4th order compact interpolation
	560	!!----------------------------------------------------------------------
	561	REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pt_in ! field at t-point
[14017]	562	REAL(wp),DIMENSION(A2D(nn_hls) ,jpk), INTENT( out) :: pt_out ! field interpolated at w-point
[7646]	563	!
	564	INTEGER :: ji, jj, jk ! dummy loop integers
	565	INTEGER :: ikt, ikb ! local integers
[14017]	566	REAL(wp),DIMENSION(A2D(nn_hls),jpk) :: zwd, zwi, zws, zwrm, zwt
[7646]	567	!!----------------------------------------------------------------------
	568	!
	569	! !== build the three diagonal matrix & the RHS ==!
	570	!
[14017]	571	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 3, jpkm1 ) ! interior (from jk=3 to jpk-1)
[12377]	572	zwd (ji,jj,jk) = 3._wp * wmask(ji,jj,jk) + 1._wp ! diagonal
	573	zwi (ji,jj,jk) = wmask(ji,jj,jk) ! lower diagonal
	574	zws (ji,jj,jk) = wmask(ji,jj,jk) ! upper diagonal
	575	zwrm(ji,jj,jk) = 3._wp * wmask(ji,jj,jk) & ! RHS
	576	& * ( pt_in(ji,jj,jk) + pt_in(ji,jj,jk-1) )
	577	END_3D
[7646]	578	!
	579	!!gm
	580	! SELECT CASE( kbc ) !* boundary condition
	581	! CASE( np_NH ) ! Neumann homogeneous at top & bottom
	582	! CASE( np_CEN2 ) ! 2nd order centered at top & bottom
	583	! END SELECT
[14017]	584	!!gm
[7646]	585	!
[9901]	586	IF ( ln_isfcav ) THEN ! set level two values which may not be set in ISF case
	587	zwd(:,:,2) = 1._wp ; zwi(:,:,2) = 0._wp ; zws(:,:,2) = 0._wp ; zwrm(:,:,2) = 0._wp
	588	END IF
	589	!
[14017]	590	DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2nd order centered at top & bottom
[12377]	591	ikt = mikt(ji,jj) + 1 ! w-point below the 1st wet point
	592	ikb = MAX(mbkt(ji,jj), 2) ! - above the last wet point
	593	!
	594	zwd (ji,jj,ikt) = 1._wp ! top
	595	zwi (ji,jj,ikt) = 0._wp
	596	zws (ji,jj,ikt) = 0._wp
	597	zwrm(ji,jj,ikt) = 0.5_wp * ( pt_in(ji,jj,ikt-1) + pt_in(ji,jj,ikt) )
	598	!
	599	zwd (ji,jj,ikb) = 1._wp ! bottom
	600	zwi (ji,jj,ikb) = 0._wp
	601	zws (ji,jj,ikb) = 0._wp
[14017]	602	zwrm(ji,jj,ikb) = 0.5_wp * ( pt_in(ji,jj,ikb-1) + pt_in(ji,jj,ikb) )
[12377]	603	END_2D
[7646]	604	!
	605	! !== tridiagonal solver ==!
	606	!
[14017]	607	DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) !* 1st recurrence: Tk = Dk - Ik Sk-1 / Tk-1
[12377]	608	zwt(ji,jj,2) = zwd(ji,jj,2)
	609	END_2D
[14017]	610	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 3, jpkm1 )
[12377]	611	zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1)
	612	END_3D
[7646]	613	!
[14017]	614	DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) !* 2nd recurrence: Zk = Yk - Ik / Tk-1 Zk-1
[12377]	615	pt_out(ji,jj,2) = zwrm(ji,jj,2)
	616	END_2D
[14017]	617	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 3, jpkm1 )
	618	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]	619	END_3D
[7646]	620
[14017]	621	DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) !* 3d recurrence: Xk = (Zk - Sk Xk+1 ) / Tk
[12377]	622	pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1)
	623	END_2D
[14017]	624	DO_3DS( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, jpk-2, 2, -1 )
[12377]	625	pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - zws(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk)
	626	END_3D
[14017]	627	!
[5770]	628	END SUBROUTINE interp_4th_cpt
[7646]	629
	630
	631	SUBROUTINE tridia_solver( pD, pU, pL, pRHS, pt_out , klev )
	632	!!----------------------------------------------------------------------
	633	!! * ROUTINE tridia_solver *
[14017]	634	!!
[7646]	635	!! ** Purpose : solve a symmetric 3diagonal system
	636	!!
	637	!! ** Method : solve M.t_out = RHS(t) where M is a tri diagonal matrix ( jpk*jpk )
[14017]	638	!!
[7646]	639	!! ( D_1 U_1 0 0 0 )( t_1 ) ( RHS_1 )
	640	!! ( L_2 D_2 U_2 0 0 )( t_2 ) ( RHS_2 )
	641	!! ( 0 L_3 D_3 U_3 0 )( t_3 ) = ( RHS_3 )
	642	!! ( ... )( ... ) ( ... )
	643	!! ( 0 0 0 L_k D_k )( t_k ) ( RHS_k )
[14017]	644	!!
[7646]	645	!! M is decomposed in the product of an upper and lower triangular matrix.
[14017]	646	!! The tri-diagonals matrix is given as input 3D arrays: pD, pU, pL
[7646]	647	!! (i.e. the Diagonal, the Upper diagonal, and the Lower diagonal).
	648	!! The solution is pta.
	649	!! The 3d array zwt is used as a work space array.
	650	!!----------------------------------------------------------------------
[14017]	651	REAL(wp),DIMENSION(A2D(nn_hls),jpk), INTENT(in ) :: pD, pU, PL ! 3-diagonal matrix
	652	REAL(wp),DIMENSION(A2D(nn_hls),jpk), INTENT(in ) :: pRHS ! Right-Hand-Side
	653	REAL(wp),DIMENSION(A2D(nn_hls),jpk), INTENT( out) :: pt_out !!gm field at level=F(klev)
	654	INTEGER , INTENT(in ) :: klev ! =1 pt_out at w-level
	655	! ! =0 pt at t-level
[7646]	656	INTEGER :: ji, jj, jk ! dummy loop integers
	657	INTEGER :: kstart ! local indices
[14017]	658	REAL(wp),DIMENSION(A2D(nn_hls),jpk) :: zwt ! 3D work array
[7646]	659	!!----------------------------------------------------------------------
	660	!
	661	kstart = 1 + klev
	662	!
[14017]	663	DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) !* 1st recurrence: Tk = Dk - Ik Sk-1 / Tk-1
[12377]	664	zwt(ji,jj,kstart) = pD(ji,jj,kstart)
	665	END_2D
[14017]	666	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, kstart+1, jpkm1 )
[12377]	667	zwt(ji,jj,jk) = pD(ji,jj,jk) - pL(ji,jj,jk) * pU(ji,jj,jk-1) /zwt(ji,jj,jk-1)
	668	END_3D
[7646]	669	!
[14017]	670	DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) !* 2nd recurrence: Zk = Yk - Ik / Tk-1 Zk-1
[12377]	671	pt_out(ji,jj,kstart) = pRHS(ji,jj,kstart)
	672	END_2D
[14017]	673	DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, kstart+1, jpkm1 )
	674	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]	675	END_3D
[7646]	676
[14017]	677	DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) !* 3d recurrence: Xk = (Zk - Sk Xk+1 ) / Tk
[12377]	678	pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1)
	679	END_2D
[14017]	680	DO_3DS( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, jpk-2, kstart, -1 )
[12377]	681	pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - pU(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk)
	682	END_3D
[7646]	683	!
	684	END SUBROUTINE tridia_solver
	685
[3]	686	!!======================================================================
[5770]	687	END MODULE traadv_fct

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