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traadv_fct.F90 in branches/2016/dev_CNRS_2016/NEMOGCM/NEMO/OPA_SRC/TRA – NEMO

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source: branches/2016/dev_CNRS_2016/NEMOGCM/NEMO/OPA_SRC/TRA/traadv_fct.F90 @ 7277

Last change on this file since 7277 was 7277, checked in by flavoni, 8 years ago
update 2016 branch with simplif-2
Property svn:keywords set to `Id`
File size: 47.7 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	!! tra_adv_fct_zts: update the tracer trend with a 3D advective trends using a 2nd order FCT scheme
	12	!! with sub-time-stepping in the vertical direction
	13	!! nonosc : compute monotonic tracer fluxes by a non-oscillatory algorithm
	14	!! interp_4th_cpt : 4th order compact scheme for the vertical component of the advection
[3]	15	!!----------------------------------------------------------------------
[3625]	16	USE oce ! ocean dynamics and active tracers
	17	USE dom_oce ! ocean space and time domain
[4990]	18	USE trc_oce ! share passive tracers/Ocean variables
	19	USE trd_oce ! trends: ocean variables
[3625]	20	USE trdtra ! tracers trends
[4990]	21	USE diaptr ! poleward transport diagnostics
	22	!
[5770]	23	USE in_out_manager ! I/O manager
[3625]	24	USE lib_mpp ! MPP library
	25	USE lbclnk ! ocean lateral boundary condition (or mpp link)
[5770]	26	USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined)
[3625]	27	USE wrk_nemo ! Memory Allocation
	28	USE timing ! Timing
[3]	29
	30	IMPLICIT NONE
	31	PRIVATE
	32
[5770]	33	PUBLIC tra_adv_fct ! routine called by traadv.F90
	34	PUBLIC tra_adv_fct_zts ! routine called by traadv.F90
	35	PUBLIC interp_4th_cpt ! routine called by traadv_cen.F90
[3]	36
[5770]	37	LOGICAL :: l_trd ! flag to compute trends
	38	REAL(wp) :: r1_6 = 1._wp / 6._wp ! =1/6
[2528]	39
[7277]	40	! ! tridiag solver associated indices:
	41	INTEGER, PARAMETER :: np_NH = 0 ! Neumann homogeneous boundary condition
	42	INTEGER, PARAMETER :: np_CEN2 = 1 ! 2nd order centered boundary condition
	43
[3]	44	!! * Substitutions
	45	# include "vectopt_loop_substitute.h90"
	46	!!----------------------------------------------------------------------
[5770]	47	!! NEMO/OPA 3.7 , NEMO Consortium (2014)
[1152]	48	!! $Id$
[2528]	49	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
[3]	50	!!----------------------------------------------------------------------
	51	CONTAINS
	52
[5770]	53	SUBROUTINE tra_adv_fct( kt, kit000, cdtype, p2dt, pun, pvn, pwn, &
	54	& ptb, ptn, pta, kjpt, kn_fct_h, kn_fct_v )
[3]	55	!!----------------------------------------------------------------------
[5770]	56	!! * ROUTINE tra_adv_fct *
[3]	57	!!
[6140]	58	!! ** Purpose : Compute the now trend due to total advection of tracers
	59	!! and add it to the general trend of tracer equations
[3]	60	!!
[5770]	61	!! ** Method : - 2nd or 4th FCT scheme on the horizontal direction
	62	!! (choice through the value of kn_fct)
[6140]	63	!! - on the vertical the 4th order is a compact scheme
[5770]	64	!! - corrected flux (monotonic correction)
[3]	65	!!
[6140]	66	!! ** Action : - update pta with the now advective tracer trends
	67	!! - send trends to trdtra module for further diagnostcs (l_trdtra=T)
	68	!! - htr_adv, str_adv : poleward advective heat and salt transport (ln_diaptr=T)
[503]	69	!!----------------------------------------------------------------------
[2528]	70	INTEGER , INTENT(in ) :: kt ! ocean time-step index
[3294]	71	INTEGER , INTENT(in ) :: kit000 ! first time step index
[2528]	72	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	73	INTEGER , INTENT(in ) :: kjpt ! number of tracers
[5770]	74	INTEGER , INTENT(in ) :: kn_fct_h ! order of the FCT scheme (=2 or 4)
	75	INTEGER , INTENT(in ) :: kn_fct_v ! order of the FCT scheme (=2 or 4)
[6140]	76	REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
[2528]	77	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pun, pvn, pwn ! 3 ocean velocity components
	78	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb, ptn ! before and now tracer fields
	79	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend
[2715]	80	!
[5770]	81	INTEGER :: ji, jj, jk, jn ! dummy loop indices
[6140]	82	REAL(wp) :: ztra ! local scalar
[5770]	83	REAL(wp) :: zfp_ui, zfp_vj, zfp_wk, zC2t_u, zC4t_u ! - -
	84	REAL(wp) :: zfm_ui, zfm_vj, zfm_wk, zC2t_v, zC4t_v ! - -
	85	REAL(wp), POINTER, DIMENSION(:,:,:) :: zwi, zwx, zwy, zwz, ztu, ztv, zltu, zltv, ztw
	86	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdx, ztrdy, ztrdz
[3]	87	!!----------------------------------------------------------------------
[3294]	88	!
[5770]	89	IF( nn_timing == 1 ) CALL timing_start('tra_adv_fct')
[3294]	90	!
[5770]	91	CALL wrk_alloc( jpi,jpj,jpk, zwi, zwx, zwy, zwz, ztu, ztv, zltu, zltv, ztw )
[3294]	92	!
	93	IF( kt == kit000 ) THEN
[2528]	94	IF(lwp) WRITE(numout,*)
[5770]	95	IF(lwp) WRITE(numout,*) 'tra_adv_fct : FCT advection scheme on ', cdtype
[2528]	96	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~'
[3]	97	ENDIF
[2528]	98	!
[5770]	99	l_trd = .FALSE.
	100	IF( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. ( cdtype == 'TRC' .AND. l_trdtrc ) ) l_trd = .TRUE.
	101	!
[2528]	102	IF( l_trd ) THEN
[3294]	103	CALL wrk_alloc( jpi, jpj, jpk, ztrdx, ztrdy, ztrdz )
[5770]	104	ztrdx(:,:,:) = 0._wp ; ztrdy(:,:,:) = 0._wp ; ztrdz(:,:,:) = 0._wp
[3294]	105	ENDIF
[2528]	106	!
[6140]	107	! ! surface & bottom value : flux set to zero one for all
	108	zwz(:,:, 1 ) = 0._wp
[5770]	109	zwx(:,:,jpk) = 0._wp ; zwy(:,:,jpk) = 0._wp ; zwz(:,:,jpk) = 0._wp
[2528]	110	!
[5770]	111	zwi(:,:,:) = 0._wp
[6140]	112	!
	113	DO jn = 1, kjpt !== loop over the tracers ==!
[5770]	114	!
	115	! !== upstream advection with initial mass fluxes & intermediate update ==!
	116	! !* upstream tracer flux in the i and j direction
[2528]	117	DO jk = 1, jpkm1
	118	DO jj = 1, jpjm1
	119	DO ji = 1, fs_jpim1 ! vector opt.
	120	! upstream scheme
	121	zfp_ui = pun(ji,jj,jk) + ABS( pun(ji,jj,jk) )
	122	zfm_ui = pun(ji,jj,jk) - ABS( pun(ji,jj,jk) )
	123	zfp_vj = pvn(ji,jj,jk) + ABS( pvn(ji,jj,jk) )
	124	zfm_vj = pvn(ji,jj,jk) - ABS( pvn(ji,jj,jk) )
	125	zwx(ji,jj,jk) = 0.5 * ( zfp_ui * ptb(ji,jj,jk,jn) + zfm_ui * ptb(ji+1,jj ,jk,jn) )
	126	zwy(ji,jj,jk) = 0.5 * ( zfp_vj * ptb(ji,jj,jk,jn) + zfm_vj * ptb(ji ,jj+1,jk,jn) )
	127	END DO
[3]	128	END DO
	129	END DO
[5770]	130	! !* upstream tracer flux in the k direction *!
[6140]	131	DO jk = 2, jpkm1 ! Interior value ( multiplied by wmask)
[4990]	132	DO jj = 1, jpj
	133	DO ji = 1, jpi
[2528]	134	zfp_wk = pwn(ji,jj,jk) + ABS( pwn(ji,jj,jk) )
	135	zfm_wk = pwn(ji,jj,jk) - ABS( pwn(ji,jj,jk) )
[5120]	136	zwz(ji,jj,jk) = 0.5 * ( zfp_wk * ptb(ji,jj,jk,jn) + zfm_wk * ptb(ji,jj,jk-1,jn) ) * wmask(ji,jj,jk)
[2528]	137	END DO
[3]	138	END DO
	139	END DO
[6140]	140	IF( ln_linssh ) THEN ! top ocean value (only in linear free surface as zwz has been w-masked)
[5770]	141	IF( ln_isfcav ) THEN ! top of the ice-shelf cavities and at the ocean surface
[5120]	142	DO jj = 1, jpj
	143	DO ji = 1, jpi
	144	zwz(ji,jj, mikt(ji,jj) ) = pwn(ji,jj,mikt(ji,jj)) * ptb(ji,jj,mikt(ji,jj),jn) ! linear free surface
	145	END DO
	146	END DO
[5770]	147	ELSE ! no cavities: only at the ocean surface
	148	zwz(:,:,1) = pwn(:,:,1) * ptb(:,:,1,jn)
	149	ENDIF
[5120]	150	ENDIF
[5770]	151	!
	152	DO jk = 1, jpkm1 !* trend and after field with monotonic scheme
[216]	153	DO jj = 2, jpjm1
	154	DO ji = fs_2, fs_jpim1 ! vector opt.
[7277]	155	! ! total intermediate advective trends
[5770]	156	ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) &
	157	& + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) &
[7277]	158	& + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj)
	159	! ! update and guess with monotonic sheme
	160	pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra / e3t_n(ji,jj,jk) * tmask(ji,jj,jk)
	161	zwi(ji,jj,jk) = ( e3t_b(ji,jj,jk) * ptb(ji,jj,jk,jn) + p2dt * ztra ) / e3t_a(ji,jj,jk) * tmask(ji,jj,jk)
[216]	162	END DO
	163	END DO
	164	END DO
[5770]	165	CALL lbc_lnk( zwi, 'T', 1. ) ! Lateral boundary conditions on zwi (unchanged sign)
	166	!
	167	IF( l_trd ) THEN ! trend diagnostics (contribution of upstream fluxes)
[7277]	168	ztrdx(:,:,:) = zwx(:,:,:) ; ztrdy(:,:,:) = zwy(:,:,:) ; ztrdz(:,:,:) = zwz(:,:,:)
[2528]	169	END IF
[5770]	170	! ! "Poleward" heat and salt transports (contribution of upstream fluxes)
[5147]	171	IF( cdtype == 'TRA' .AND. ln_diaptr ) THEN
	172	IF( jn == jp_tem ) htr_adv(:) = ptr_sj( zwy(:,:,:) )
	173	IF( jn == jp_sal ) str_adv(:) = ptr_sj( zwy(:,:,:) )
[2528]	174	ENDIF
[5770]	175	!
	176	! !== anti-diffusive flux : high order minus low order ==!
	177	!
[6140]	178	SELECT CASE( kn_fct_h ) !* horizontal anti-diffusive fluxes
[5770]	179	!
[6140]	180	CASE( 2 ) !- 2nd order centered
[5770]	181	DO jk = 1, jpkm1
	182	DO jj = 1, jpjm1
	183	DO ji = 1, fs_jpim1 ! vector opt.
	184	zwx(ji,jj,jk) = 0.5_wp * pun(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji+1,jj,jk,jn) ) - zwx(ji,jj,jk)
	185	zwy(ji,jj,jk) = 0.5_wp * pvn(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji,jj+1,jk,jn) ) - zwy(ji,jj,jk)
	186	END DO
[503]	187	END DO
	188	END DO
[5770]	189	!
[6140]	190	CASE( 4 ) !- 4th order centered
	191	zltu(:,:,jpk) = 0._wp ! Bottom value : flux set to zero
[5770]	192	zltv(:,:,jpk) = 0._wp
[6140]	193	DO jk = 1, jpkm1 ! Laplacian
	194	DO jj = 1, jpjm1 ! 1st derivative (gradient)
[5770]	195	DO ji = 1, fs_jpim1 ! vector opt.
	196	ztu(ji,jj,jk) = ( ptn(ji+1,jj ,jk,jn) - ptn(ji,jj,jk,jn) ) * umask(ji,jj,jk)
	197	ztv(ji,jj,jk) = ( ptn(ji ,jj+1,jk,jn) - ptn(ji,jj,jk,jn) ) * vmask(ji,jj,jk)
	198	END DO
[503]	199	END DO
[6140]	200	DO jj = 2, jpjm1 ! 2nd derivative * 1/ 6
[5770]	201	DO ji = fs_2, fs_jpim1 ! vector opt.
	202	zltu(ji,jj,jk) = ( ztu(ji,jj,jk) + ztu(ji-1,jj,jk) ) * r1_6
	203	zltv(ji,jj,jk) = ( ztv(ji,jj,jk) + ztv(ji,jj-1,jk) ) * r1_6
	204	END DO
	205	END DO
[503]	206	END DO
[5770]	207	CALL lbc_lnk( zltu, 'T', 1. ) ; CALL lbc_lnk( zltv, 'T', 1. ) ! Lateral boundary cond. (unchanged sgn)
	208	!
[6140]	209	DO jk = 1, jpkm1 ! Horizontal advective fluxes
[5770]	210	DO jj = 1, jpjm1
	211	DO ji = 1, fs_jpim1 ! vector opt.
	212	zC2t_u = ptn(ji,jj,jk,jn) + ptn(ji+1,jj ,jk,jn) ! 2 x C2 interpolation of T at u- & v-points
	213	zC2t_v = ptn(ji,jj,jk,jn) + ptn(ji ,jj+1,jk,jn)
	214	! ! C4 minus upstream advective fluxes
	215	zwx(ji,jj,jk) = 0.5_wp * pun(ji,jj,jk) * ( zC2t_u + zltu(ji,jj,jk) - zltu(ji+1,jj,jk) ) - zwx(ji,jj,jk)
	216	zwy(ji,jj,jk) = 0.5_wp * pvn(ji,jj,jk) * ( zC2t_v + zltv(ji,jj,jk) - zltv(ji,jj+1,jk) ) - zwy(ji,jj,jk)
	217	END DO
[5120]	218	END DO
[5770]	219	END DO
	220	!
[6140]	221	CASE( 41 ) !- 4th order centered ==>> !!gm coding attempt need to be tested
	222	ztu(:,:,jpk) = 0._wp ! Bottom value : flux set to zero
[5770]	223	ztv(:,:,jpk) = 0._wp
[6140]	224	DO jk = 1, jpkm1 ! 1st derivative (gradient)
	225	DO jj = 1, jpjm1
[5770]	226	DO ji = 1, fs_jpim1 ! vector opt.
	227	ztu(ji,jj,jk) = ( ptn(ji+1,jj ,jk,jn) - ptn(ji,jj,jk,jn) ) * umask(ji,jj,jk)
	228	ztv(ji,jj,jk) = ( ptn(ji ,jj+1,jk,jn) - ptn(ji,jj,jk,jn) ) * vmask(ji,jj,jk)
	229	END DO
	230	END DO
[5120]	231	END DO
[5770]	232	CALL lbc_lnk( ztu, 'U', -1. ) ; CALL lbc_lnk( ztv, 'V', -1. ) ! Lateral boundary cond. (unchanged sgn)
	233	!
[6140]	234	DO jk = 1, jpkm1 ! Horizontal advective fluxes
[5770]	235	DO jj = 2, jpjm1
	236	DO ji = 2, fs_jpim1 ! vector opt.
	237	zC2t_u = ptn(ji,jj,jk,jn) + ptn(ji+1,jj ,jk,jn) ! 2 x C2 interpolation of T at u- & v-points (x2)
	238	zC2t_v = ptn(ji,jj,jk,jn) + ptn(ji ,jj+1,jk,jn)
	239	! ! C4 interpolation of T at u- & v-points (x2)
	240	zC4t_u = zC2t_u + r1_6 * ( ztu(ji-1,jj ,jk) - ztu(ji+1,jj ,jk) )
	241	zC4t_v = zC2t_v + r1_6 * ( ztv(ji ,jj-1,jk) - ztv(ji ,jj+1,jk) )
	242	! ! C4 minus upstream advective fluxes
	243	zwx(ji,jj,jk) = 0.5_wp * pun(ji,jj,jk) * zC4t_u - zwx(ji,jj,jk)
	244	zwy(ji,jj,jk) = 0.5_wp * pvn(ji,jj,jk) * zC4t_v - zwy(ji,jj,jk)
	245	END DO
	246	END DO
	247	END DO
	248	!
	249	END SELECT
[6140]	250	!
	251	SELECT CASE( kn_fct_v ) !* vertical anti-diffusive fluxes (w-masked interior values)
[5770]	252	!
[6140]	253	CASE( 2 ) !- 2nd order centered
[5770]	254	DO jk = 2, jpkm1
	255	DO jj = 2, jpjm1
	256	DO ji = fs_2, fs_jpim1
[6140]	257	zwz(ji,jj,jk) = ( pwn(ji,jj,jk) * 0.5_wp * ( ptn(ji,jj,jk,jn) + ptn(ji,jj,jk-1,jn) ) &
	258	& - zwz(ji,jj,jk) ) * wmask(ji,jj,jk)
[5770]	259	END DO
	260	END DO
	261	END DO
	262	!
[6140]	263	CASE( 4 ) !- 4th order COMPACT
	264	CALL interp_4th_cpt( ptn(:,:,:,jn) , ztw ) ! zwt = COMPACT interpolation of T at w-point
[5770]	265	DO jk = 2, jpkm1
	266	DO jj = 2, jpjm1
	267	DO ji = fs_2, fs_jpim1
	268	zwz(ji,jj,jk) = ( pwn(ji,jj,jk) * ztw(ji,jj,jk) - zwz(ji,jj,jk) ) * wmask(ji,jj,jk)
	269	END DO
	270	END DO
	271	END DO
	272	!
	273	END SELECT
[6140]	274	IF( ln_linssh ) THEN ! top ocean value: high order = upstream ==>> zwz=0
	275	zwz(:,:,1) = 0._wp ! only ocean surface as interior zwz values have been w-masked
	276	ENDIF
[5770]	277	!
[2528]	278	CALL lbc_lnk( zwx, 'U', -1. ) ; CALL lbc_lnk( zwy, 'V', -1. ) ! Lateral bondary conditions
	279	CALL lbc_lnk( zwz, 'W', 1. )
[6140]	280	!
[5770]	281	! !== monotonicity algorithm ==!
	282	!
[2528]	283	CALL nonosc( ptb(:,:,:,jn), zwx, zwy, zwz, zwi, p2dt )
[6140]	284	!
[5770]	285	! !== final trend with corrected fluxes ==!
	286	!
[216]	287	DO jk = 1, jpkm1
	288	DO jj = 2, jpjm1
[2528]	289	DO ji = fs_2, fs_jpim1 ! vector opt.
[5770]	290	pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) &
	291	& + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) &
	292	& + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) &
[6140]	293	& * r1_e1e2t(ji,jj) / e3t_n(ji,jj,jk)
[216]	294	END DO
	295	END DO
	296	END DO
[5770]	297	!
[6140]	298	IF( l_trd ) THEN ! trend diagnostics (contribution of upstream fluxes)
[2528]	299	ztrdx(:,:,:) = ztrdx(:,:,:) + zwx(:,:,:) ! <<< Add to previously computed
	300	ztrdy(:,:,:) = ztrdy(:,:,:) + zwy(:,:,:) ! <<< Add to previously computed
	301	ztrdz(:,:,:) = ztrdz(:,:,:) + zwz(:,:,:) ! <<< Add to previously computed
[5770]	302	!
	303	CALL trd_tra( kt, cdtype, jn, jptra_xad, ztrdx, pun, ptn(:,:,:,jn) )
	304	CALL trd_tra( kt, cdtype, jn, jptra_yad, ztrdy, pvn, ptn(:,:,:,jn) )
	305	CALL trd_tra( kt, cdtype, jn, jptra_zad, ztrdz, pwn, ptn(:,:,:,jn) )
	306	!
	307	CALL wrk_dealloc( jpi,jpj,jpk, ztrdx, ztrdy, ztrdz )
[2528]	308	END IF
[6140]	309	! ! "Poleward" heat and salt transports (contribution of upstream fluxes)
[5147]	310	IF( cdtype == 'TRA' .AND. ln_diaptr ) THEN
[6140]	311	IF( jn == jp_tem ) htr_adv(:) = htr_adv(:) + ptr_sj( zwy(:,:,:) )
	312	IF( jn == jp_sal ) str_adv(:) = str_adv(:) + ptr_sj( zwy(:,:,:) )
[2528]	313	ENDIF
[503]	314	!
[6140]	315	END DO ! end of tracer loop
[503]	316	!
[5770]	317	CALL wrk_dealloc( jpi,jpj,jpk, zwi, zwx, zwy, zwz, ztu, ztv, zltu, zltv, ztw )
[2528]	318	!
[5770]	319	IF( nn_timing == 1 ) CALL timing_stop('tra_adv_fct')
[2715]	320	!
[5770]	321	END SUBROUTINE tra_adv_fct
[3]	322
[5737]	323
[5770]	324	SUBROUTINE tra_adv_fct_zts( kt, kit000, cdtype, p2dt, pun, pvn, pwn, &
	325	& ptb, ptn, pta, kjpt, kn_fct_zts )
[4990]	326	!!----------------------------------------------------------------------
[5770]	327	!! * ROUTINE tra_adv_fct_zts *
[4990]	328	!!
	329	!! ** Purpose : Compute the now trend due to total advection of
	330	!! tracers and add it to the general trend of tracer equations
	331	!!
	332	!! ** Method : TVD ZTS scheme, i.e. 2nd order centered scheme with
	333	!! corrected flux (monotonic correction). This version use sub-
	334	!! timestepping for the vertical advection which increases stability
	335	!! when vertical metrics are small.
	336	!! note: - this advection scheme needs a leap-frog time scheme
	337	!!
	338	!! ** Action : - update (pta) with the now advective tracer trends
	339	!! - save the trends
	340	!!----------------------------------------------------------------------
	341	INTEGER , INTENT(in ) :: kt ! ocean time-step index
	342	INTEGER , INTENT(in ) :: kit000 ! first time step index
	343	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	344	INTEGER , INTENT(in ) :: kjpt ! number of tracers
[5770]	345	INTEGER , INTENT(in ) :: kn_fct_zts ! number of number of vertical sub-timesteps
[6140]	346	REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
[4990]	347	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pun, pvn, pwn ! 3 ocean velocity components
	348	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb, ptn ! before and now tracer fields
	349	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend
	350	!
	351	REAL(wp), DIMENSION( jpk ) :: zts ! length of sub-timestep for vertical advection
[6140]	352	REAL(wp) :: zr_p2dt ! reciprocal of tracer timestep
[4990]	353	INTEGER :: ji, jj, jk, jl, jn ! dummy loop indices
	354	INTEGER :: jtb, jtn, jta ! sub timestep pointers for leap-frog/euler forward steps
	355	INTEGER :: jtaken ! toggle for collecting appropriate fluxes from sub timesteps
	356	REAL(wp) :: z_rzts ! Fractional length of Euler forward sub-timestep for vertical advection
[6140]	357	REAL(wp) :: ztra ! local scalar
[4990]	358	REAL(wp) :: zfp_ui, zfp_vj, zfp_wk ! - -
	359	REAL(wp) :: zfm_ui, zfm_vj, zfm_wk ! - -
[5770]	360	REAL(wp), POINTER, DIMENSION(:,: ) :: zwx_sav , zwy_sav
	361	REAL(wp), POINTER, DIMENSION(:,:,:) :: zwi, zwx, zwy, zwz, zhdiv, zwzts, zwz_sav
	362	REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdx, ztrdy, ztrdz
	363	REAL(wp), POINTER, DIMENSION(:,:,:,:) :: ztrs
[4990]	364	!!----------------------------------------------------------------------
	365	!
[5770]	366	IF( nn_timing == 1 ) CALL timing_start('tra_adv_fct_zts')
[4990]	367	!
[5770]	368	CALL wrk_alloc( jpi,jpj, zwx_sav, zwy_sav )
[7277]	369	CALL wrk_alloc( jpi,jpj,jpk, zwx, zwy, zwz, zwi, zhdiv, zwzts, zwz_sav )
[5770]	370	CALL wrk_alloc( jpi,jpj,jpk,kjpt+1, ztrs )
[4990]	371	!
	372	IF( kt == kit000 ) THEN
	373	IF(lwp) WRITE(numout,*)
[5770]	374	IF(lwp) WRITE(numout,*) 'tra_adv_fct_zts : 2nd order FCT scheme with ', kn_fct_zts, ' vertical sub-timestep on ', cdtype
[4990]	375	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~'
	376	ENDIF
	377	!
	378	l_trd = .FALSE.
[5770]	379	IF( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. ( cdtype == 'TRC' .AND. l_trdtrc ) ) l_trd = .TRUE.
[4990]	380	!
	381	IF( l_trd ) THEN
[5770]	382	CALL wrk_alloc( jpi,jpj,jpk, ztrdx, ztrdy, ztrdz )
[4990]	383	ztrdx(:,:,:) = 0._wp ; ztrdy(:,:,:) = 0._wp ; ztrdz(:,:,:) = 0._wp
	384	ENDIF
	385	!
	386	zwi(:,:,:) = 0._wp
[5770]	387	z_rzts = 1._wp / REAL( kn_fct_zts, wp )
[6140]	388	zr_p2dt = 1._wp / p2dt
[4990]	389	!
[6140]	390	! surface & Bottom value : flux set to zero for all tracers
	391	zwz(:,:, 1 ) = 0._wp
	392	zwx(:,:,jpk) = 0._wp ; zwz(:,:,jpk) = 0._wp
	393	zwy(:,:,jpk) = 0._wp ; zwi(:,:,jpk) = 0._wp
	394	!
[4990]	395	! ! ===========
	396	DO jn = 1, kjpt ! tracer loop
	397	! ! ===========
[6140]	398	!
	399	! Upstream advection with initial mass fluxes & intermediate update
	400	DO jk = 1, jpkm1 ! upstream tracer flux in the i and j direction
[4990]	401	DO jj = 1, jpjm1
	402	DO ji = 1, fs_jpim1 ! vector opt.
	403	! upstream scheme
	404	zfp_ui = pun(ji,jj,jk) + ABS( pun(ji,jj,jk) )
	405	zfm_ui = pun(ji,jj,jk) - ABS( pun(ji,jj,jk) )
	406	zfp_vj = pvn(ji,jj,jk) + ABS( pvn(ji,jj,jk) )
	407	zfm_vj = pvn(ji,jj,jk) - ABS( pvn(ji,jj,jk) )
	408	zwx(ji,jj,jk) = 0.5_wp * ( zfp_ui * ptb(ji,jj,jk,jn) + zfm_ui * ptb(ji+1,jj ,jk,jn) )
	409	zwy(ji,jj,jk) = 0.5_wp * ( zfp_vj * ptb(ji,jj,jk,jn) + zfm_vj * ptb(ji ,jj+1,jk,jn) )
	410	END DO
	411	END DO
	412	END DO
[6140]	413	! ! upstream tracer flux in the k direction
	414	DO jk = 2, jpkm1 ! Interior value
[4990]	415	DO jj = 1, jpj
	416	DO ji = 1, jpi
	417	zfp_wk = pwn(ji,jj,jk) + ABS( pwn(ji,jj,jk) )
	418	zfm_wk = pwn(ji,jj,jk) - ABS( pwn(ji,jj,jk) )
[5770]	419	zwz(ji,jj,jk) = 0.5_wp * ( zfp_wk * ptb(ji,jj,jk,jn) + zfm_wk * ptb(ji,jj,jk-1,jn) ) * wmask(ji,jj,jk)
[4990]	420	END DO
	421	END DO
	422	END DO
[6140]	423	IF( ln_linssh ) THEN ! top value : linear free surface case only (as zwz is multiplied by wmask)
	424	IF( ln_isfcav ) THEN ! ice-shelf cavities: top value
[5120]	425	DO jj = 1, jpj
	426	DO ji = 1, jpi
[5770]	427	zwz(ji,jj, mikt(ji,jj) ) = pwn(ji,jj,mikt(ji,jj)) * ptb(ji,jj,mikt(ji,jj),jn)
[5120]	428	END DO
[5770]	429	END DO
[6140]	430	ELSE ! no cavities, surface value
[5770]	431	zwz(:,:,1) = pwn(:,:,1) * ptb(:,:,1,jn)
	432	ENDIF
[5120]	433	ENDIF
[5770]	434	!
	435	DO jk = 1, jpkm1 ! total advective trend
[4990]	436	DO jj = 2, jpjm1
	437	DO ji = fs_2, fs_jpim1 ! vector opt.
[6140]	438	! ! total intermediate advective trends
[5770]	439	ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) &
	440	& + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) &
[7277]	441	& + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj)
[6140]	442	! ! update and guess with monotonic sheme
[7277]	443	pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra / e3t_n(ji,jj,jk) * tmask(ji,jj,jk)
	444	zwi(ji,jj,jk) = ( e3t_b(ji,jj,jk) * ptb(ji,jj,jk,jn) + p2dt * ztra ) / e3t_a(ji,jj,jk) * tmask(ji,jj,jk)
[4990]	445	END DO
	446	END DO
	447	END DO
[5770]	448	!
	449	CALL lbc_lnk( zwi, 'T', 1. ) ! Lateral boundary conditions on zwi (unchanged sign)
	450	!
	451	IF( l_trd ) THEN ! trend diagnostics (contribution of upstream fluxes)
[4990]	452	ztrdx(:,:,:) = zwx(:,:,:) ; ztrdy(:,:,:) = zwy(:,:,:) ; ztrdz(:,:,:) = zwz(:,:,:)
	453	END IF
[5770]	454	! ! "Poleward" heat and salt transports (contribution of upstream fluxes)
[5147]	455	IF( cdtype == 'TRA' .AND. ln_diaptr ) THEN
	456	IF( jn == jp_tem ) htr_adv(:) = ptr_sj( zwy(:,:,:) )
	457	IF( jn == jp_sal ) str_adv(:) = ptr_sj( zwy(:,:,:) )
[4990]	458	ENDIF
	459
[5770]	460	! 3. anti-diffusive flux : high order minus low order
	461	! ---------------------------------------------------
[4990]	462
[5770]	463	DO jk = 1, jpkm1 !* horizontal anti-diffusive fluxes
	464	!
[4990]	465	DO jj = 1, jpjm1
	466	DO ji = 1, fs_jpim1 ! vector opt.
	467	zwx_sav(ji,jj) = zwx(ji,jj,jk)
	468	zwy_sav(ji,jj) = zwy(ji,jj,jk)
[5770]	469	!
[4990]	470	zwx(ji,jj,jk) = 0.5_wp * pun(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji+1,jj,jk,jn) )
	471	zwy(ji,jj,jk) = 0.5_wp * pvn(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji,jj+1,jk,jn) )
	472	END DO
	473	END DO
[5770]	474	!
	475	DO jj = 2, jpjm1 ! partial horizontal divergence
[4990]	476	DO ji = fs_2, fs_jpim1
	477	zhdiv(ji,jj,jk) = ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk) &
	478	& + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk) )
	479	END DO
	480	END DO
[5770]	481	!
[4990]	482	DO jj = 1, jpjm1
	483	DO ji = 1, fs_jpim1 ! vector opt.
[5770]	484	zwx(ji,jj,jk) = zwx(ji,jj,jk) - zwx_sav(ji,jj)
	485	zwy(ji,jj,jk) = zwy(ji,jj,jk) - zwy_sav(ji,jj)
[4990]	486	END DO
	487	END DO
	488	END DO
[6140]	489	!
[5770]	490	! !* vertical anti-diffusive flux
	491	zwz_sav(:,:,:) = zwz(:,:,:)
	492	ztrs (:,:,:,1) = ptb(:,:,:,jn)
[7277]	493	ztrs (:,:,1,2) = ptb(:,:,1,jn)
	494	ztrs (:,:,1,3) = ptb(:,:,1,jn)
[5770]	495	zwzts (:,:,:) = 0._wp
[4990]	496	!
[5770]	497	DO jl = 1, kn_fct_zts ! Start of sub timestepping loop
	498	!
	499	IF( jl == 1 ) THEN ! Euler forward to kick things off
	500	jtb = 1 ; jtn = 1 ; jta = 2
[6140]	501	zts(:) = p2dt * z_rzts
[5770]	502	jtaken = MOD( kn_fct_zts + 1 , 2) ! Toggle to collect every second flux
	503	! ! starting at jl =1 if kn_fct_zts is odd;
	504	! ! starting at jl =2 otherwise
	505	ELSEIF( jl == 2 ) THEN ! First leapfrog step
	506	jtb = 1 ; jtn = 2 ; jta = 3
[6140]	507	zts(:) = 2._wp * p2dt * z_rzts
[5770]	508	ELSE ! Shuffle pointers for subsequent leapfrog steps
	509	jtb = MOD(jtb,3) + 1
	510	jtn = MOD(jtn,3) + 1
	511	jta = MOD(jta,3) + 1
[4990]	512	ENDIF
[5770]	513	DO jk = 2, jpkm1 ! interior value
[4990]	514	DO jj = 2, jpjm1
	515	DO ji = fs_2, fs_jpim1
[5770]	516	zwz(ji,jj,jk) = 0.5_wp * pwn(ji,jj,jk) * ( ztrs(ji,jj,jk,jtn) + ztrs(ji,jj,jk-1,jtn) ) * wmask(ji,jj,jk)
	517	IF( jtaken == 0 ) zwzts(ji,jj,jk) = zwzts(ji,jj,jk) + zwz(ji,jj,jk) * zts(jk) ! Accumulate time-weighted vertcal flux
[4990]	518	END DO
	519	END DO
	520	END DO
[6140]	521	IF( ln_linssh ) THEN ! top value (only in linear free surface case)
[5770]	522	IF( ln_isfcav ) THEN ! ice-shelf cavities
	523	DO jj = 1, jpj
	524	DO ji = 1, jpi
	525	zwz(ji,jj, mikt(ji,jj) ) = pwn(ji,jj,mikt(ji,jj)) * ptb(ji,jj,mikt(ji,jj),jn) ! linear free surface
	526	END DO
	527	END DO
[6140]	528	ELSE ! no ocean cavities
[5770]	529	zwz(:,:,1) = pwn(:,:,1) * ptb(:,:,1,jn)
	530	ENDIF
	531	ENDIF
	532	!
[4990]	533	jtaken = MOD( jtaken + 1 , 2 )
[5770]	534	!
	535	DO jk = 2, jpkm1 ! total advective trends
[4990]	536	DO jj = 2, jpjm1
	537	DO ji = fs_2, fs_jpim1
[5770]	538	ztrs(ji,jj,jk,jta) = ztrs(ji,jj,jk,jtb) &
	539	& - zts(jk) * ( zhdiv(ji,jj,jk) + zwz(ji,jj,jk) - zwz(ji,jj,jk+1) ) &
[6140]	540	& * r1_e1e2t(ji,jj) / e3t_n(ji,jj,jk)
[4990]	541	END DO
	542	END DO
	543	END DO
[5770]	544	!
[4990]	545	END DO
	546
	547	DO jk = 2, jpkm1 ! Anti-diffusive vertical flux using average flux from the sub-timestepping
	548	DO jj = 2, jpjm1
	549	DO ji = fs_2, fs_jpim1
[6140]	550	zwz(ji,jj,jk) = ( zwzts(ji,jj,jk) * zr_p2dt - zwz_sav(ji,jj,jk) ) * wmask(ji,jj,jk)
[4990]	551	END DO
	552	END DO
	553	END DO
	554	CALL lbc_lnk( zwx, 'U', -1. ) ; CALL lbc_lnk( zwy, 'V', -1. ) ! Lateral bondary conditions
	555	CALL lbc_lnk( zwz, 'W', 1. )
	556
	557	! 4. monotonicity algorithm
	558	! -------------------------
	559	CALL nonosc( ptb(:,:,:,jn), zwx, zwy, zwz, zwi, p2dt )
	560
	561
	562	! 5. final trend with corrected fluxes
	563	! ------------------------------------
	564	DO jk = 1, jpkm1
	565	DO jj = 2, jpjm1
	566	DO ji = fs_2, fs_jpim1 ! vector opt.
[5770]	567	pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ( zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) &
	568	& + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) &
[6140]	569	& * r1_e1e2t(ji,jj) / e3t_n(ji,jj,jk)
[4990]	570	END DO
	571	END DO
	572	END DO
	573
	574	! ! trend diagnostics (contribution of upstream fluxes)
	575	IF( l_trd ) THEN
	576	ztrdx(:,:,:) = ztrdx(:,:,:) + zwx(:,:,:) ! <<< Add to previously computed
	577	ztrdy(:,:,:) = ztrdy(:,:,:) + zwy(:,:,:) ! <<< Add to previously computed
	578	ztrdz(:,:,:) = ztrdz(:,:,:) + zwz(:,:,:) ! <<< Add to previously computed
[5770]	579	!
[4990]	580	CALL trd_tra( kt, cdtype, jn, jptra_xad, ztrdx, pun, ptn(:,:,:,jn) )
	581	CALL trd_tra( kt, cdtype, jn, jptra_yad, ztrdy, pvn, ptn(:,:,:,jn) )
	582	CALL trd_tra( kt, cdtype, jn, jptra_zad, ztrdz, pwn, ptn(:,:,:,jn) )
[5770]	583	!
	584	CALL wrk_dealloc( jpi,jpj,jpk, ztrdx, ztrdy, ztrdz )
[4990]	585	END IF
	586	! ! "Poleward" heat and salt transports (contribution of upstream fluxes)
[5147]	587	IF( cdtype == 'TRA' .AND. ln_diaptr ) THEN
	588	IF( jn == jp_tem ) htr_adv(:) = ptr_sj( zwy(:,:,:) ) + htr_adv(:)
	589	IF( jn == jp_sal ) str_adv(:) = ptr_sj( zwy(:,:,:) ) + str_adv(:)
[4990]	590	ENDIF
	591	!
	592	END DO
	593	!
[5770]	594	CALL wrk_alloc( jpi,jpj, zwx_sav, zwy_sav )
	595	CALL wrk_alloc( jpi,jpj, jpk, zwx, zwy, zwz, zwi, zhdiv, zwzts, zwz_sav )
	596	CALL wrk_alloc( jpi,jpj,jpk,kjpt+1, ztrs )
[4990]	597	!
[5770]	598	IF( nn_timing == 1 ) CALL timing_stop('tra_adv_fct_zts')
[4990]	599	!
[5770]	600	END SUBROUTINE tra_adv_fct_zts
[4990]	601
[5737]	602
[2528]	603	SUBROUTINE nonosc( pbef, paa, pbb, pcc, paft, p2dt )
[3]	604	!!---------------------------------------------------------------------
	605	!! * ROUTINE nonosc *
	606	!!
	607	!! ** Purpose : compute monotonic tracer fluxes from the upstream
	608	!! scheme and the before field by a nonoscillatory algorithm
	609	!!
	610	!! ** Method : ... ???
	611	!! warning : pbef and paft must be masked, but the boundaries
	612	!! conditions on the fluxes are not necessary zalezak (1979)
	613	!! drange (1995) multi-dimensional forward-in-time and upstream-
	614	!! in-space based differencing for fluid
	615	!!----------------------------------------------------------------------
[6140]	616	REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
[2528]	617	REAL(wp), DIMENSION (jpi,jpj,jpk), INTENT(in ) :: pbef, paft ! before & after field
	618	REAL(wp), DIMENSION (jpi,jpj,jpk), INTENT(inout) :: paa, pbb, pcc ! monotonic fluxes in the 3 directions
[2715]	619	!
[4990]	620	INTEGER :: ji, jj, jk ! dummy loop indices
	621	INTEGER :: ikm1 ! local integer
[6140]	622	REAL(wp) :: zpos, zneg, zbt, za, zb, zc, zbig, zrtrn ! local scalars
[2715]	623	REAL(wp) :: zau, zbu, zcu, zav, zbv, zcv, zup, zdo ! - -
[3294]	624	REAL(wp), POINTER, DIMENSION(:,:,:) :: zbetup, zbetdo, zbup, zbdo
[3]	625	!!----------------------------------------------------------------------
[3294]	626	!
	627	IF( nn_timing == 1 ) CALL timing_start('nonosc')
	628	!
	629	CALL wrk_alloc( jpi, jpj, jpk, zbetup, zbetdo, zbup, zbdo )
	630	!
[2715]	631	zbig = 1.e+40_wp
	632	zrtrn = 1.e-15_wp
[4990]	633	zbetup(:,:,:) = 0._wp ; zbetdo(:,:,:) = 0._wp
[785]	634
[3]	635	! Search local extrema
	636	! --------------------
[785]	637	! max/min of pbef & paft with large negative/positive value (-/+zbig) inside land
[4990]	638	zbup = MAX( pbef * tmask - zbig * ( 1._wp - tmask ), &
	639	& paft * tmask - zbig * ( 1._wp - tmask ) )
	640	zbdo = MIN( pbef * tmask + zbig * ( 1._wp - tmask ), &
	641	& paft * tmask + zbig * ( 1._wp - tmask ) )
[785]	642
[5120]	643	DO jk = 1, jpkm1
	644	ikm1 = MAX(jk-1,1)
	645	DO jj = 2, jpjm1
	646	DO ji = fs_2, fs_jpim1 ! vector opt.
	647
[785]	648	! search maximum in neighbourhood
	649	zup = MAX( zbup(ji ,jj ,jk ), &
	650	& zbup(ji-1,jj ,jk ), zbup(ji+1,jj ,jk ), &
	651	& zbup(ji ,jj-1,jk ), zbup(ji ,jj+1,jk ), &
	652	& zbup(ji ,jj ,ikm1), zbup(ji ,jj ,jk+1) )
[3]	653
[785]	654	! search minimum in neighbourhood
	655	zdo = MIN( zbdo(ji ,jj ,jk ), &
	656	& zbdo(ji-1,jj ,jk ), zbdo(ji+1,jj ,jk ), &
	657	& zbdo(ji ,jj-1,jk ), zbdo(ji ,jj+1,jk ), &
	658	& zbdo(ji ,jj ,ikm1), zbdo(ji ,jj ,jk+1) )
[3]	659
[785]	660	! positive part of the flux
[3]	661	zpos = MAX( 0., paa(ji-1,jj ,jk ) ) - MIN( 0., paa(ji ,jj ,jk ) ) &
	662	& + MAX( 0., pbb(ji ,jj-1,jk ) ) - MIN( 0., pbb(ji ,jj ,jk ) ) &
	663	& + MAX( 0., pcc(ji ,jj ,jk+1) ) - MIN( 0., pcc(ji ,jj ,jk ) )
[785]	664
	665	! negative part of the flux
[3]	666	zneg = MAX( 0., paa(ji ,jj ,jk ) ) - MIN( 0., paa(ji-1,jj ,jk ) ) &
	667	& + MAX( 0., pbb(ji ,jj ,jk ) ) - MIN( 0., pbb(ji ,jj-1,jk ) ) &
	668	& + MAX( 0., pcc(ji ,jj ,jk ) ) - MIN( 0., pcc(ji ,jj ,jk+1) )
[785]	669
[3]	670	! up & down beta terms
[6140]	671	zbt = e1e2t(ji,jj) * e3t_n(ji,jj,jk) / p2dt
[785]	672	zbetup(ji,jj,jk) = ( zup - paft(ji,jj,jk) ) / ( zpos + zrtrn ) * zbt
	673	zbetdo(ji,jj,jk) = ( paft(ji,jj,jk) - zdo ) / ( zneg + zrtrn ) * zbt
[3]	674	END DO
	675	END DO
	676	END DO
[2528]	677	CALL lbc_lnk( zbetup, 'T', 1. ) ; CALL lbc_lnk( zbetdo, 'T', 1. ) ! lateral boundary cond. (unchanged sign)
[3]	678
[237]	679	! 3. monotonic flux in the i & j direction (paa & pbb)
	680	! ----------------------------------------
[3]	681	DO jk = 1, jpkm1
	682	DO jj = 2, jpjm1
	683	DO ji = fs_2, fs_jpim1 ! vector opt.
[4990]	684	zau = MIN( 1._wp, zbetdo(ji,jj,jk), zbetup(ji+1,jj,jk) )
	685	zbu = MIN( 1._wp, zbetup(ji,jj,jk), zbetdo(ji+1,jj,jk) )
[785]	686	zcu = ( 0.5 + SIGN( 0.5 , paa(ji,jj,jk) ) )
[4990]	687	paa(ji,jj,jk) = paa(ji,jj,jk) * ( zcu * zau + ( 1._wp - zcu) * zbu )
[3]	688
[4990]	689	zav = MIN( 1._wp, zbetdo(ji,jj,jk), zbetup(ji,jj+1,jk) )
	690	zbv = MIN( 1._wp, zbetup(ji,jj,jk), zbetdo(ji,jj+1,jk) )
[785]	691	zcv = ( 0.5 + SIGN( 0.5 , pbb(ji,jj,jk) ) )
[4990]	692	pbb(ji,jj,jk) = pbb(ji,jj,jk) * ( zcv * zav + ( 1._wp - zcv) * zbv )
[3]	693
	694	! monotonic flux in the k direction, i.e. pcc
	695	! -------------------------------------------
[785]	696	za = MIN( 1., zbetdo(ji,jj,jk+1), zbetup(ji,jj,jk) )
	697	zb = MIN( 1., zbetup(ji,jj,jk+1), zbetdo(ji,jj,jk) )
	698	zc = ( 0.5 + SIGN( 0.5 , pcc(ji,jj,jk+1) ) )
[4990]	699	pcc(ji,jj,jk+1) = pcc(ji,jj,jk+1) * ( zc * za + ( 1._wp - zc) * zb )
[3]	700	END DO
	701	END DO
	702	END DO
[2528]	703	CALL lbc_lnk( paa, 'U', -1. ) ; CALL lbc_lnk( pbb, 'V', -1. ) ! lateral boundary condition (changed sign)
[503]	704	!
[3294]	705	CALL wrk_dealloc( jpi, jpj, jpk, zbetup, zbetdo, zbup, zbdo )
[2715]	706	!
[3294]	707	IF( nn_timing == 1 ) CALL timing_stop('nonosc')
	708	!
[3]	709	END SUBROUTINE nonosc
	710
[5770]	711
[7277]	712	SUBROUTINE interp_4th_cpt_org( pt_in, pt_out )
[5770]	713	!!----------------------------------------------------------------------
[7277]	714	!! * ROUTINE interp_4th_cpt_org *
[5770]	715	!!
	716	!! ** Purpose : Compute the interpolation of tracer at w-point
	717	!!
	718	!! ** Method : 4th order compact interpolation
	719	!!----------------------------------------------------------------------
	720	REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pt_in ! now tracer fields
	721	REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT( out) :: pt_out ! now tracer field interpolated at w-pts
	722	!
	723	INTEGER :: ji, jj, jk ! dummy loop integers
	724	REAL(wp),DIMENSION(jpi,jpj,jpk) :: zwd, zwi, zws, zwrm, zwt
	725	!!----------------------------------------------------------------------
	726
	727	DO jk = 3, jpkm1 !== build the three diagonal matrix ==!
	728	DO jj = 1, jpj
	729	DO ji = 1, jpi
	730	zwd (ji,jj,jk) = 4._wp
	731	zwi (ji,jj,jk) = 1._wp
	732	zws (ji,jj,jk) = 1._wp
	733	zwrm(ji,jj,jk) = 3._wp * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) )
	734	!
	735	IF( tmask(ji,jj,jk+1) == 0._wp) THEN ! Switch to second order centered at bottom
	736	zwd (ji,jj,jk) = 1._wp
	737	zwi (ji,jj,jk) = 0._wp
	738	zws (ji,jj,jk) = 0._wp
	739	zwrm(ji,jj,jk) = 0.5 * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) )
	740	ENDIF
	741	END DO
	742	END DO
	743	END DO
	744	!
[7277]	745	jk = 2 ! Switch to second order centered at top
	746	DO jj = 1, jpj
	747	DO ji = 1, jpi
[5770]	748	zwd (ji,jj,jk) = 1._wp
	749	zwi (ji,jj,jk) = 0._wp
	750	zws (ji,jj,jk) = 0._wp
	751	zwrm(ji,jj,jk) = 0.5 * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) )
	752	END DO
	753	END DO
	754	!
	755	! !== tridiagonal solve ==!
	756	DO jj = 1, jpj ! first recurrence
	757	DO ji = 1, jpi
	758	zwt(ji,jj,2) = zwd(ji,jj,2)
	759	END DO
	760	END DO
	761	DO jk = 3, jpkm1
	762	DO jj = 1, jpj
	763	DO ji = 1, jpi
	764	zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1)
	765	END DO
	766	END DO
	767	END DO
	768	!
	769	DO jj = 1, jpj ! second recurrence: Zk = Yk - Ik / Tk-1 Zk-1
	770	DO ji = 1, jpi
	771	pt_out(ji,jj,2) = zwrm(ji,jj,2)
	772	END DO
	773	END DO
	774	DO jk = 3, jpkm1
	775	DO jj = 1, jpj
	776	DO ji = 1, jpi
	777	pt_out(ji,jj,jk) = zwrm(ji,jj,jk) - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1)
	778	END DO
	779	END DO
	780	END DO
	781
	782	DO jj = 1, jpj ! third recurrence: Xk = (Zk - Sk Xk+1 ) / Tk
	783	DO ji = 1, jpi
	784	pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1)
	785	END DO
	786	END DO
	787	DO jk = jpk-2, 2, -1
	788	DO jj = 1, jpj
	789	DO ji = 1, jpi
	790	pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - zws(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk)
	791	END DO
	792	END DO
	793	END DO
	794	!
[7277]	795	END SUBROUTINE interp_4th_cpt_org
	796
	797
	798	SUBROUTINE interp_4th_cpt( pt_in, pt_out )
	799	!!----------------------------------------------------------------------
	800	!! * ROUTINE interp_4th_cpt *
	801	!!
	802	!! ** Purpose : Compute the interpolation of tracer at w-point
	803	!!
	804	!! ** Method : 4th order compact interpolation
	805	!!----------------------------------------------------------------------
	806	REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pt_in ! field at t-point
	807	REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT( out) :: pt_out ! field interpolated at w-point
	808	!
	809	INTEGER :: ji, jj, jk ! dummy loop integers
	810	INTEGER :: ikt, ikb ! local integers
	811	REAL(wp),DIMENSION(jpi,jpj,jpk) :: zwd, zwi, zws, zwrm, zwt
	812	!!----------------------------------------------------------------------
	813	!
	814	! !== build the three diagonal matrix & the RHS ==!
	815	!
	816	DO jk = 3, jpkm1 ! interior (from jk=3 to jpk-1)
	817	DO jj = 2, jpjm1
	818	DO ji = fs_2, fs_jpim1
	819	zwd (ji,jj,jk) = 3._wp * wmask(ji,jj,jk) + 1._wp ! diagonal
	820	zwi (ji,jj,jk) = wmask(ji,jj,jk) ! lower diagonal
	821	zws (ji,jj,jk) = wmask(ji,jj,jk) ! upper diagonal
	822	zwrm(ji,jj,jk) = 3._wp * wmask(ji,jj,jk) & ! RHS
	823	& * ( pt_in(ji,jj,jk) + pt_in(ji,jj,jk-1) )
	824	END DO
	825	END DO
	826	END DO
	827	!
	828	!!gm
	829	! SELECT CASE( kbc ) !* boundary condition
	830	! CASE( np_NH ) ! Neumann homogeneous at top & bottom
	831	! CASE( np_CEN2 ) ! 2nd order centered at top & bottom
	832	! END SELECT
	833	!!gm
	834	!
	835	DO jj = 2, jpjm1 ! 2nd order centered at top & bottom
	836	DO ji = fs_2, fs_jpim1
	837	ikt = mikt(ji,jj) + 1 ! w-point below the 1st wet point
	838	ikb = mbkt(ji,jj) ! - above the last wet point
	839	!
	840	zwd (ji,jj,ikt) = 1._wp ! top
	841	zwi (ji,jj,ikt) = 0._wp
	842	zws (ji,jj,ikt) = 0._wp
	843	zwrm(ji,jj,ikt) = 0.5_wp * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) )
	844	!
	845	zwd (ji,jj,ikb) = 1._wp ! bottom
	846	zwi (ji,jj,ikb) = 0._wp
	847	zws (ji,jj,ikb) = 0._wp
	848	zwrm(ji,jj,ikb) = 0.5_wp * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) )
	849	END DO
	850	END DO
	851	!
	852	! !== tridiagonal solver ==!
	853	!
	854	DO jj = 2, jpjm1 !* 1st recurrence: Tk = Dk - Ik Sk-1 / Tk-1
	855	DO ji = fs_2, fs_jpim1
	856	zwt(ji,jj,2) = zwd(ji,jj,2)
	857	END DO
	858	END DO
	859	DO jk = 3, jpkm1
	860	DO jj = 2, jpjm1
	861	DO ji = fs_2, fs_jpim1
	862	zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1)
	863	END DO
	864	END DO
	865	END DO
	866	!
	867	DO jj = 2, jpjm1 !* 2nd recurrence: Zk = Yk - Ik / Tk-1 Zk-1
	868	DO ji = fs_2, fs_jpim1
	869	pt_out(ji,jj,2) = zwrm(ji,jj,2)
	870	END DO
	871	END DO
	872	DO jk = 3, jpkm1
	873	DO jj = 2, jpjm1
	874	DO ji = fs_2, fs_jpim1
	875	pt_out(ji,jj,jk) = zwrm(ji,jj,jk) - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1)
	876	END DO
	877	END DO
	878	END DO
	879
	880	DO jj = 2, jpjm1 !* 3d recurrence: Xk = (Zk - Sk Xk+1 ) / Tk
	881	DO ji = fs_2, fs_jpim1
	882	pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1)
	883	END DO
	884	END DO
	885	DO jk = jpk-2, 2, -1
	886	DO jj = 2, jpjm1
	887	DO ji = fs_2, fs_jpim1
	888	pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - zws(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk)
	889	END DO
	890	END DO
	891	END DO
	892	!
[5770]	893	END SUBROUTINE interp_4th_cpt
[7277]	894
	895
	896	SUBROUTINE tridia_solver( pD, pU, pL, pRHS, pt_out , klev )
	897	!!----------------------------------------------------------------------
	898	!! * ROUTINE tridia_solver *
	899	!!
	900	!! ** Purpose : solve a symmetric 3diagonal system
	901	!!
	902	!! ** Method : solve M.t_out = RHS(t) where M is a tri diagonal matrix ( jpk*jpk )
	903	!!
	904	!! ( D_1 U_1 0 0 0 )( t_1 ) ( RHS_1 )
	905	!! ( L_2 D_2 U_2 0 0 )( t_2 ) ( RHS_2 )
	906	!! ( 0 L_3 D_3 U_3 0 )( t_3 ) = ( RHS_3 )
	907	!! ( ... )( ... ) ( ... )
	908	!! ( 0 0 0 L_k D_k )( t_k ) ( RHS_k )
	909	!!
	910	!! M is decomposed in the product of an upper and lower triangular matrix.
	911	!! The tri-diagonals matrix is given as input 3D arrays: pD, pU, pL
	912	!! (i.e. the Diagonal, the Upper diagonal, and the Lower diagonal).
	913	!! The solution is pta.
	914	!! The 3d array zwt is used as a work space array.
	915	!!----------------------------------------------------------------------
	916	REAL(wp),DIMENSION(:,:,:), INTENT(in ) :: pD, pU, PL ! 3-diagonal matrix
	917	REAL(wp),DIMENSION(:,:,:), INTENT(in ) :: pRHS ! Right-Hand-Side
	918	REAL(wp),DIMENSION(:,:,:), INTENT( out) :: pt_out !!gm field at level=F(klev)
	919	INTEGER , INTENT(in ) :: klev ! =1 pt_out at w-level
	920	! ! =0 pt at t-level
	921	INTEGER :: ji, jj, jk ! dummy loop integers
	922	INTEGER :: kstart ! local indices
	923	REAL(wp),DIMENSION(jpi,jpj,jpk) :: zwt ! 3D work array
	924	!!----------------------------------------------------------------------
	925	!
	926	kstart = 1 + klev
	927	!
	928	DO jj = 2, jpjm1 !* 1st recurrence: Tk = Dk - Ik Sk-1 / Tk-1
	929	DO ji = fs_2, fs_jpim1
	930	zwt(ji,jj,kstart) = pD(ji,jj,kstart)
	931	END DO
	932	END DO
	933	DO jk = kstart+1, jpkm1
	934	DO jj = 2, jpjm1
	935	DO ji = fs_2, fs_jpim1
	936	zwt(ji,jj,jk) = pD(ji,jj,jk) - pL(ji,jj,jk) * pU(ji,jj,jk-1) /zwt(ji,jj,jk-1)
	937	END DO
	938	END DO
	939	END DO
	940	!
	941	DO jj = 2, jpjm1 !* 2nd recurrence: Zk = Yk - Ik / Tk-1 Zk-1
	942	DO ji = fs_2, fs_jpim1
	943	pt_out(ji,jj,kstart) = pRHS(ji,jj,kstart)
	944	END DO
	945	END DO
	946	DO jk = kstart+1, jpkm1
	947	DO jj = 2, jpjm1
	948	DO ji = fs_2, fs_jpim1
	949	pt_out(ji,jj,jk) = pRHS(ji,jj,jk) - pL(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1)
	950	END DO
	951	END DO
	952	END DO
	953
	954	DO jj = 2, jpjm1 !* 3d recurrence: Xk = (Zk - Sk Xk+1 ) / Tk
	955	DO ji = fs_2, fs_jpim1
	956	pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1)
	957	END DO
	958	END DO
	959	DO jk = jpk-2, kstart, -1
	960	DO jj = 2, jpjm1
	961	DO ji = fs_2, fs_jpim1
	962	pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - pU(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk)
	963	END DO
	964	END DO
	965	END DO
	966	!
	967	END SUBROUTINE tridia_solver
	968
[3]	969	!!======================================================================
[5770]	970	END MODULE traadv_fct

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