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traadv_qck.F90 in trunk/NEMOGCM/NEMO/OPA_SRC/TRA – NEMO

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source: trunk/NEMOGCM/NEMO/OPA_SRC/TRA/traadv_qck.F90 @ 3558

Last change on this file since 3558 was 3558, checked in by rblod, 11 years ago
Fix issues when using key_nosignedzeo, see ticket #996
Property svn:keywords set to `Id`
File size: 24.2 KB

Rev	Line
[1231]	1	MODULE traadv_qck
	2	!!==============================================================================
	3	!! * MODULE traadv_qck *
[2528]	4	!! Ocean tracers: horizontal & vertical advective trend
[1231]	5	!!==============================================================================
[1559]	6	!! History : 3.0 ! 2008-07 (G. Reffray) Original code
[2528]	7	!! 3.3 ! 2010-05 (C.Ethe, G. Madec) merge TRC-TRA + switch from velocity to transport
[1231]	8	!!----------------------------------------------------------------------
	9
	10	!!----------------------------------------------------------------------
[2528]	11	!! tra_adv_qck : update the tracer trend with the horizontal advection
	12	!! trends using a 3rd order finite difference scheme
	13	!! tra_adv_qck_i : apply QUICK scheme in i-direction
	14	!! tra_adv_qck_j : apply QUICK scheme in j-direction
[1559]	15	!! tra_adv_cen2_k : 2nd centered scheme for the vertical advection
[1231]	16	!!----------------------------------------------------------------------
	17	USE oce ! ocean dynamics and active tracers
	18	USE dom_oce ! ocean space and time domain
[2528]	19	USE trdmod_oce ! ocean space and time domain
	20	USE trdtra ! ocean tracers trends
[1231]	21	USE trabbl ! advective term in the BBL
	22	USE lib_mpp ! distribued memory computing
	23	USE lbclnk ! ocean lateral boundary condition (or mpp link)
	24	USE dynspg_oce ! surface pressure gradient variables
	25	USE in_out_manager ! I/O manager
	26	USE diaptr ! poleward transport diagnostics
[2528]	27	USE trc_oce ! share passive tracers/Ocean variables
[3294]	28	USE wrk_nemo ! Memory Allocation
	29	USE timing ! Timing
[3558]	30	USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined)
[1231]	31
	32	IMPLICIT NONE
	33	PRIVATE
	34
[1559]	35	PUBLIC tra_adv_qck ! routine called by step.F90
[1231]	36
[2528]	37	LOGICAL :: l_trd ! flag to compute trends
	38	REAL(wp) :: r1_6 = 1./ 6. ! 1/6 ratio
[1559]	39
[1231]	40	!! * Substitutions
	41	# include "domzgr_substitute.h90"
	42	# include "vectopt_loop_substitute.h90"
	43	!!----------------------------------------------------------------------
[2528]	44	!! NEMO/OPA 3.3 , NEMO Consortium (2010)
[1231]	45	!! $Id$
[2528]	46	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
[1231]	47	!!----------------------------------------------------------------------
	48	CONTAINS
	49
[3294]	50	SUBROUTINE tra_adv_qck ( kt, kit000, cdtype, p2dt, pun, pvn, pwn, &
[2528]	51	& ptb, ptn, pta, kjpt )
[1231]	52	!!----------------------------------------------------------------------
	53	!! * ROUTINE tra_adv_qck *
	54	!!
	55	!! ** Purpose : Compute the now trend due to the advection of tracers
	56	!! and add it to the general trend of passive tracer equations.
	57	!!
	58	!! ** Method : The advection is evaluated by a third order scheme
[1559]	59	!! For a positive velocity u : u(i)>0
	60	!! \|--FU--\|--FC--\|--FD--\|------\|
	61	!! i-1 i i+1 i+2
[1231]	62	!!
[1559]	63	!! For a negative velocity u : u(i)<0
	64	!! \|------\|--FD--\|--FC--\|--FU--\|
	65	!! i-1 i i+1 i+2
	66	!! where FU is the second upwind point
	67	!! FD is the first douwning point
	68	!! FC is the central point (or the first upwind point)
[1231]	69	!!
[1559]	70	!! Flux(i) = u(i) * { 0.5(FC+FD) -0.5C(i)(FD-FC) -((1-C(i))/6)(FU+FD-2FC) }
	71	!! with C(i)=\|u(i)\|dx(i)/dt (=Courant number)
[1231]	72	!!
	73	!! dt = 2*rdtra and the scalar values are tb and sb
	74	!!
[2528]	75	!! On the vertical, the simple centered scheme used ptn
[1231]	76	!!
[1559]	77	!! The fluxes are bounded by the ULTIMATE limiter to
	78	!! guarantee the monotonicity of the solution and to
[1231]	79	!! prevent the appearance of spurious numerical oscillations
	80	!!
[2528]	81	!! ** Action : - update (pta) with the now advective tracer trends
	82	!! - save the trends
[1231]	83	!!
	84	!! ** Reference : Leonard (1979, 1991)
	85	!!----------------------------------------------------------------------
[2528]	86	INTEGER , INTENT(in ) :: kt ! ocean time-step index
[3294]	87	INTEGER , INTENT(in ) :: kit000 ! first time step index
[2528]	88	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	89	INTEGER , INTENT(in ) :: kjpt ! number of tracers
	90	REAL(wp), DIMENSION( jpk ), INTENT(in ) :: p2dt ! vertical profile of tracer time-step
	91	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pun, pvn, pwn ! 3 ocean velocity components
	92	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb, ptn ! before and now tracer fields
	93	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend
[1231]	94	!!----------------------------------------------------------------------
	95
[3294]	96	!
	97	IF( nn_timing == 1 ) CALL timing_start('tra_adv_qck')
	98	!
	99	IF( kt == kit000 ) THEN
[1231]	100	IF(lwp) WRITE(numout,*)
[2528]	101	IF(lwp) WRITE(numout,*) 'tra_adv_qck : 3rd order quickest advection scheme on ', cdtype
[1231]	102	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~'
	103	IF(lwp) WRITE(numout,*)
[2528]	104	!
	105	l_trd = .FALSE.
	106	IF( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. ( cdtype == 'TRC' .AND. l_trdtrc ) ) l_trd = .TRUE.
[1231]	107	ENDIF
	108
	109	! I. The horizontal fluxes are computed with the QUICKEST + ULTIMATE scheme
[2528]	110	CALL tra_adv_qck_i( kt, cdtype, p2dt, pun, ptb, ptn, pta, kjpt )
	111	CALL tra_adv_qck_j( kt, cdtype, p2dt, pvn, ptb, ptn, pta, kjpt )
[1231]	112
	113	! II. The vertical fluxes are computed with the 2nd order centered scheme
[2528]	114	CALL tra_adv_cen2_k( kt, cdtype, pwn, ptn, pta, kjpt )
[1231]	115	!
[3294]	116	IF( nn_timing == 1 ) CALL timing_stop('tra_adv_qck')
	117	!
[1231]	118	END SUBROUTINE tra_adv_qck
	119
	120
[2528]	121	SUBROUTINE tra_adv_qck_i( kt, cdtype, p2dt, pun, &
	122	& ptb, ptn, pta, kjpt )
[1231]	123	!!----------------------------------------------------------------------
	124	!!
	125	!!----------------------------------------------------------------------
[2715]	126	USE oce , ONLY: zwx => ua ! ua used as workspace
	127	!
	128	INTEGER , INTENT(in ) :: kt ! ocean time-step index
	129	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	130	INTEGER , INTENT(in ) :: kjpt ! number of tracers
	131	REAL(wp), DIMENSION( jpk ), INTENT(in ) :: p2dt ! vertical profile of tracer time-step
	132	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pun ! i-velocity components
	133	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb, ptn ! before and now tracer fields
	134	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend
[2528]	135	!!
[2715]	136	INTEGER :: ji, jj, jk, jn ! dummy loop indices
	137	REAL(wp) :: ztra, zbtr, zdir, zdx, zdt, zmsk ! local scalars
[3294]	138	REAL(wp), POINTER, DIMENSION(:,:,:) :: zfu, zfc, zfd
[1231]	139	!----------------------------------------------------------------------
[2715]	140	!
[3294]	141	CALL wrk_alloc( jpi, jpj, jpk, zfu, zfc, zfd )
[2528]	142	! ! ===========
	143	DO jn = 1, kjpt ! tracer loop
	144	! ! ===========
	145	zfu(:,:,:) = 0.0 ; zfc(:,:,:) = 0.0
	146	zfd(:,:,:) = 0.0 ; zwx(:,:,:) = 0.0
	147	!
	148	DO jk = 1, jpkm1
	149	!
	150	!--- Computation of the ustream and downstream value of the tracer and the mask
	151	DO jj = 2, jpjm1
	152	DO ji = fs_2, fs_jpim1 ! vector opt.
	153	! Upstream in the x-direction for the tracer
	154	zfc(ji,jj,jk) = ptb(ji-1,jj,jk,jn)
	155	! Downstream in the x-direction for the tracer
	156	zfd(ji,jj,jk) = ptb(ji+1,jj,jk,jn)
	157	END DO
[1559]	158	END DO
	159	END DO
[2528]	160	CALL lbc_lnk( zfc(:,:,:), 'T', 1. ) ; CALL lbc_lnk( zfd(:,:,:), 'T', 1. ) ! Lateral boundary conditions
	161
[1231]	162	!
	163	! Horizontal advective fluxes
	164	! ---------------------------
	165	!
[2528]	166	DO jk = 1, jpkm1
	167	DO jj = 2, jpjm1
	168	DO ji = fs_2, fs_jpim1 ! vector opt.
	169	zdir = 0.5 + SIGN( 0.5, pun(ji,jj,jk) ) ! if pun > 0 : zdir = 1 otherwise zdir = 0
	170	zfu(ji,jj,jk) = zdir * zfc(ji,jj,jk ) + ( 1. - zdir ) * zfd(ji+1,jj,jk) ! FU in the x-direction for T
	171	END DO
	172	END DO
[1559]	173	END DO
[1231]	174	!
[2528]	175	DO jk = 1, jpkm1
	176	zdt = p2dt(jk)
	177	DO jj = 2, jpjm1
	178	DO ji = fs_2, fs_jpim1 ! vector opt.
	179	zdir = 0.5 + SIGN( 0.5, pun(ji,jj,jk) ) ! if pun > 0 : zdir = 1 otherwise zdir = 0
[3301]	180	zdx = ( zdir * e1t(ji,jj) + ( 1. - zdir ) * e1t(ji+1,jj) ) * e2u(ji,jj) * fse3u(ji,jj,jk)
[2528]	181	zwx(ji,jj,jk) = ABS( pun(ji,jj,jk) ) * zdt / zdx ! (0<zc_cfl<1 : Courant number on x-direction)
	182	zfc(ji,jj,jk) = zdir * ptb(ji ,jj,jk,jn) + ( 1. - zdir ) * ptb(ji+1,jj,jk,jn) ! FC in the x-direction for T
	183	zfd(ji,jj,jk) = zdir * ptb(ji+1,jj,jk,jn) + ( 1. - zdir ) * ptb(ji ,jj,jk,jn) ! FD in the x-direction for T
	184	END DO
	185	END DO
	186	END DO
	187	!--- Lateral boundary conditions
	188	CALL lbc_lnk( zfu(:,:,:), 'T', 1. ) ; CALL lbc_lnk( zfd(:,:,:), 'T', 1. )
	189	CALL lbc_lnk( zfc(:,:,:), 'T', 1. ) ; CALL lbc_lnk( zwx(:,:,:), 'T', 1. )
	190
[1231]	191	!--- QUICKEST scheme
[2528]	192	CALL quickest( zfu, zfd, zfc, zwx )
[1231]	193	!
[2528]	194	! Mask at the T-points in the x-direction (mask=0 or mask=1)
	195	DO jk = 1, jpkm1
	196	DO jj = 2, jpjm1
	197	DO ji = fs_2, fs_jpim1 ! vector opt.
	198	zfu(ji,jj,jk) = tmask(ji-1,jj,jk) + tmask(ji,jj,jk) + tmask(ji+1,jj,jk) - 2.
[2715]	199	END DO
[1231]	200	END DO
	201	END DO
[2528]	202	CALL lbc_lnk( zfu(:,:,:), 'T', 1. ) ! Lateral boundary conditions
	203
[1231]	204	!
[2528]	205	! Tracer flux on the x-direction
	206	DO jk = 1, jpkm1
	207	!
[1231]	208	DO jj = 2, jpjm1
[2528]	209	DO ji = fs_2, fs_jpim1 ! vector opt.
	210	zdir = 0.5 + SIGN( 0.5, pun(ji,jj,jk) ) ! if pun > 0 : zdir = 1 otherwise zdir = 0
	211	!--- If the second ustream point is a land point
	212	!--- the flux is computed by the 1st order UPWIND scheme
	213	zmsk = zdir * zfu(ji,jj,jk) + ( 1. - zdir ) * zfu(ji+1,jj,jk)
	214	zwx(ji,jj,jk) = zmsk * zwx(ji,jj,jk) + ( 1. - zmsk ) * zfc(ji,jj,jk)
	215	zwx(ji,jj,jk) = zwx(ji,jj,jk) * pun(ji,jj,jk)
[1231]	216	END DO
	217	END DO
[3300]	218	END DO
	219	!
	220	CALL lbc_lnk( zwx(:,:,:), 'T', 1. ) ! Lateral boundary conditions
	221	!
	222	! Computation of the trend
	223	DO jk = 1, jpkm1
[2528]	224	DO jj = 2, jpjm1
	225	DO ji = fs_2, fs_jpim1 ! vector opt.
	226	zbtr = 1. / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) )
	227	! horizontal advective trends
	228	ztra = - zbtr * ( zwx(ji,jj,jk) - zwx(ji-1,jj,jk) )
	229	!--- add it to the general tracer trends
	230	pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra
	231	END DO
	232	END DO
[1231]	233	END DO
[2528]	234	! ! trend diagnostics (contribution of upstream fluxes)
	235	IF( l_trd ) CALL trd_tra( kt, cdtype, jn, jptra_trd_xad, zwx, pun, ptn(:,:,:,jn) )
	236	!
	237	END DO
	238	!
[3294]	239	CALL wrk_dealloc( jpi, jpj, jpk, zfu, zfc, zfd )
[2715]	240	!
[1559]	241	END SUBROUTINE tra_adv_qck_i
[1231]	242
	243
[2528]	244	SUBROUTINE tra_adv_qck_j( kt, cdtype, p2dt, pvn, &
	245	& ptb, ptn, pta, kjpt )
[1231]	246	!!----------------------------------------------------------------------
	247	!!
	248	!!----------------------------------------------------------------------
[2715]	249	USE oce , ONLY: zwy => ua ! ua used as workspace
	250	!
	251	INTEGER , INTENT(in ) :: kt ! ocean time-step index
	252	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	253	INTEGER , INTENT(in ) :: kjpt ! number of tracers
	254	REAL(wp), DIMENSION( jpk ), INTENT(in ) :: p2dt ! vertical profile of tracer time-step
	255	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pvn ! j-velocity components
	256	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb, ptn ! before and now tracer fields
	257	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend
[1559]	258	!!
[2715]	259	INTEGER :: ji, jj, jk, jn ! dummy loop indices
	260	REAL(wp) :: ztra, zbtr, zdir, zdx, zdt, zmsk ! local scalars
[3294]	261	REAL(wp), POINTER, DIMENSION(:,:,:) :: zfu, zfc, zfd
[1231]	262	!----------------------------------------------------------------------
[2715]	263	!
[3294]	264	CALL wrk_alloc( jpi, jpj, jpk, zfu, zfc, zfd )
	265	!
[2528]	266	! ! ===========
	267	DO jn = 1, kjpt ! tracer loop
	268	! ! ===========
	269	zfu(:,:,:) = 0.0 ; zfc(:,:,:) = 0.0
	270	zfd(:,:,:) = 0.0 ; zwy(:,:,:) = 0.0
	271	!
	272	DO jk = 1, jpkm1
	273	!
	274	!--- Computation of the ustream and downstream value of the tracer and the mask
	275	DO jj = 2, jpjm1
	276	DO ji = fs_2, fs_jpim1 ! vector opt.
	277	! Upstream in the x-direction for the tracer
	278	zfc(ji,jj,jk) = ptb(ji,jj-1,jk,jn)
	279	! Downstream in the x-direction for the tracer
	280	zfd(ji,jj,jk) = ptb(ji,jj+1,jk,jn)
	281	END DO
[1559]	282	END DO
	283	END DO
[2528]	284	CALL lbc_lnk( zfc(:,:,:), 'T', 1. ) ; CALL lbc_lnk( zfd(:,:,:), 'T', 1. ) ! Lateral boundary conditions
	285
	286
[1231]	287	!
	288	! Horizontal advective fluxes
	289	! ---------------------------
	290	!
[2528]	291	DO jk = 1, jpkm1
	292	DO jj = 2, jpjm1
	293	DO ji = fs_2, fs_jpim1 ! vector opt.
	294	zdir = 0.5 + SIGN( 0.5, pvn(ji,jj,jk) ) ! if pun > 0 : zdir = 1 otherwise zdir = 0
	295	zfu(ji,jj,jk) = zdir * zfc(ji,jj,jk ) + ( 1. - zdir ) * zfd(ji,jj+1,jk) ! FU in the x-direction for T
	296	END DO
[1559]	297	END DO
	298	END DO
[1231]	299	!
[2528]	300	DO jk = 1, jpkm1
	301	zdt = p2dt(jk)
	302	DO jj = 2, jpjm1
	303	DO ji = fs_2, fs_jpim1 ! vector opt.
	304	zdir = 0.5 + SIGN( 0.5, pvn(ji,jj,jk) ) ! if pun > 0 : zdir = 1 otherwise zdir = 0
[3301]	305	zdx = ( zdir * e2t(ji,jj) + ( 1. - zdir ) * e2t(ji,jj+1) ) * e1v(ji,jj) * fse3v(ji,jj,jk)
[2528]	306	zwy(ji,jj,jk) = ABS( pvn(ji,jj,jk) ) * zdt / zdx ! (0<zc_cfl<1 : Courant number on x-direction)
	307	zfc(ji,jj,jk) = zdir * ptb(ji,jj ,jk,jn) + ( 1. - zdir ) * ptb(ji,jj+1,jk,jn) ! FC in the x-direction for T
	308	zfd(ji,jj,jk) = zdir * ptb(ji,jj+1,jk,jn) + ( 1. - zdir ) * ptb(ji,jj ,jk,jn) ! FD in the x-direction for T
	309	END DO
	310	END DO
	311	END DO
	312
	313	!--- Lateral boundary conditions
	314	CALL lbc_lnk( zfu(:,:,:), 'T', 1. ) ; CALL lbc_lnk( zfd(:,:,:), 'T', 1. )
	315	CALL lbc_lnk( zfc(:,:,:), 'T', 1. ) ; CALL lbc_lnk( zwy(:,:,:), 'T', 1. )
	316
[1231]	317	!--- QUICKEST scheme
[2528]	318	CALL quickest( zfu, zfd, zfc, zwy )
[1231]	319	!
[2528]	320	! Mask at the T-points in the x-direction (mask=0 or mask=1)
	321	DO jk = 1, jpkm1
	322	DO jj = 2, jpjm1
	323	DO ji = fs_2, fs_jpim1 ! vector opt.
	324	zfu(ji,jj,jk) = tmask(ji,jj-1,jk) + tmask(ji,jj,jk) + tmask(ji,jj+1,jk) - 2.
	325	END DO
[1231]	326	END DO
	327	END DO
[2528]	328	!--- Lateral boundary conditions
	329	CALL lbc_lnk( zfu(:,:,:), 'T', 1. )
	330	!
	331	! Tracer flux on the x-direction
	332	DO jk = 1, jpkm1
	333	!
[1231]	334	DO jj = 2, jpjm1
[2528]	335	DO ji = fs_2, fs_jpim1 ! vector opt.
	336	zdir = 0.5 + SIGN( 0.5, pvn(ji,jj,jk) ) ! if pun > 0 : zdir = 1 otherwise zdir = 0
	337	!--- If the second ustream point is a land point
	338	!--- the flux is computed by the 1st order UPWIND scheme
	339	zmsk = zdir * zfu(ji,jj,jk) + ( 1. - zdir ) * zfu(ji,jj+1,jk)
	340	zwy(ji,jj,jk) = zmsk * zwy(ji,jj,jk) + ( 1. - zmsk ) * zfc(ji,jj,jk)
	341	zwy(ji,jj,jk) = zwy(ji,jj,jk) * pvn(ji,jj,jk)
[1231]	342	END DO
	343	END DO
[3300]	344	END DO
	345	!
	346	CALL lbc_lnk( zwy(:,:,:), 'T', 1. ) ! Lateral boundary conditions
	347	!
	348	! Computation of the trend
	349	DO jk = 1, jpkm1
[2528]	350	DO jj = 2, jpjm1
	351	DO ji = fs_2, fs_jpim1 ! vector opt.
	352	zbtr = 1. / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) )
	353	! horizontal advective trends
	354	ztra = - zbtr * ( zwy(ji,jj,jk) - zwy(ji,jj-1,jk) )
	355	!--- add it to the general tracer trends
	356	pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra
[1231]	357	END DO
	358	END DO
[2528]	359	END DO
	360	! ! trend diagnostics (contribution of upstream fluxes)
	361	IF( l_trd ) CALL trd_tra( kt, cdtype, jn, jptra_trd_yad, zwy, pvn, ptn(:,:,:,jn) )
	362	! ! "Poleward" heat and salt transports (contribution of upstream fluxes)
	363	IF( cdtype == 'TRA' .AND. ln_diaptr .AND. ( MOD( kt, nn_fptr ) == 0 ) ) THEN
	364	IF( jn == jp_tem ) htr_adv(:) = ptr_vj( zwy(:,:,:) )
	365	IF( jn == jp_sal ) str_adv(:) = ptr_vj( zwy(:,:,:) )
[1231]	366	ENDIF
[2528]	367	!
	368	END DO
	369	!
[3294]	370	CALL wrk_dealloc( jpi, jpj, jpk, zfu, zfc, zfd )
[2715]	371	!
[1559]	372	END SUBROUTINE tra_adv_qck_j
[1231]	373
	374
[2528]	375	SUBROUTINE tra_adv_cen2_k( kt, cdtype, pwn, &
	376	& ptn, pta, kjpt )
[1231]	377	!!----------------------------------------------------------------------
	378	!!
	379	!!----------------------------------------------------------------------
[2715]	380	USE oce, ONLY: zwz => ua ! ua used as workspace
	381	!
	382	INTEGER , INTENT(in ) :: kt ! ocean time-step index
	383	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	384	INTEGER , INTENT(in ) :: kjpt ! number of tracers
	385	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pwn ! vertical velocity
	386	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptn ! before and now tracer fields
	387	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend
	388	!
[2528]	389	INTEGER :: ji, jj, jk, jn ! dummy loop indices
[2715]	390	REAL(wp) :: zbtr , ztra ! local scalars
[1559]	391	!!----------------------------------------------------------------------
[2528]	392
	393	! ! ===========
	394	DO jn = 1, kjpt ! tracer loop
	395	! ! ===========
	396	! 1. Bottom value : flux set to zero
	397	zwz(:,:,jpk) = 0.e0 ! Bottom value : flux set to zero
	398	!
	399	! ! Surface value
	400	IF( lk_vvl ) THEN ; zwz(:,:, 1 ) = 0.e0 ! Variable volume : flux set to zero
	401	ELSE ; zwz(:,:, 1 ) = pwn(:,:,1) * ptn(:,:,1,jn) ! Constant volume : advective flux through the surface
	402	ENDIF
	403	!
	404	DO jk = 2, jpkm1 ! Interior point: second order centered tracer flux at w-point
	405	DO jj = 2, jpjm1
	406	DO ji = fs_2, fs_jpim1 ! vector opt.
	407	zwz(ji,jj,jk) = 0.5 * pwn(ji,jj,jk) * ( ptn(ji,jj,jk-1,jn) + ptn(ji,jj,jk,jn) )
	408	END DO
[1231]	409	END DO
	410	END DO
[2528]	411	!
	412	DO jk = 1, jpkm1 !== Tracer flux divergence added to the general trend ==!
	413	DO jj = 2, jpjm1
	414	DO ji = fs_2, fs_jpim1 ! vector opt.
	415	zbtr = 1. / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) )
	416	! k- vertical advective trends
	417	ztra = - zbtr * ( zwz(ji,jj,jk) - zwz(ji,jj,jk+1) )
	418	! added to the general tracer trends
	419	pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra
	420	END DO
[1231]	421	END DO
	422	END DO
[2528]	423	! ! Save the vertical advective trends for diagnostic
	424	IF( l_trd ) CALL trd_tra( kt, cdtype, jn, jptra_trd_zad, zwz, pwn, ptn(:,:,:,jn) )
	425	!
[1231]	426	END DO
	427	!
[1559]	428	END SUBROUTINE tra_adv_cen2_k
[1231]	429
	430
[2528]	431	SUBROUTINE quickest( pfu, pfd, pfc, puc )
[1231]	432	!!----------------------------------------------------------------------
	433	!!
[2528]	434	!! ** Purpose : Computation of advective flux with Quickest scheme
	435	!!
	436	!! ** Method :
[1231]	437	!!----------------------------------------------------------------------
[2528]	438	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pfu ! second upwind point
	439	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pfd ! first douwning point
	440	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pfc ! the central point (or the first upwind point)
	441	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: puc ! input as Courant number ; output as flux
	442	!!
	443	INTEGER :: ji, jj, jk ! dummy loop indices
	444	REAL(wp) :: zcoef1, zcoef2, zcoef3 ! local scalars
	445	REAL(wp) :: zc, zcurv, zfho ! - -
	446	!----------------------------------------------------------------------
[3294]	447	!
	448	IF( nn_timing == 1 ) CALL timing_start('quickest')
	449	!
[2528]	450	DO jk = 1, jpkm1
	451	DO jj = 1, jpj
	452	DO ji = 1, jpi
	453	zc = puc(ji,jj,jk) ! Courant number
	454	zcurv = pfd(ji,jj,jk) + pfu(ji,jj,jk) - 2. * pfc(ji,jj,jk)
	455	zcoef1 = 0.5 * ( pfc(ji,jj,jk) + pfd(ji,jj,jk) )
	456	zcoef2 = 0.5 * zc * ( pfd(ji,jj,jk) - pfc(ji,jj,jk) )
	457	zcoef3 = ( 1. - ( zc * zc ) ) * r1_6 * zcurv
	458	zfho = zcoef1 - zcoef2 - zcoef3 ! phi_f QUICKEST
	459	!
	460	zcoef1 = pfd(ji,jj,jk) - pfu(ji,jj,jk)
	461	zcoef2 = ABS( zcoef1 )
	462	zcoef3 = ABS( zcurv )
	463	IF( zcoef3 >= zcoef2 ) THEN
	464	zfho = pfc(ji,jj,jk)
	465	ELSE
	466	zcoef3 = pfu(ji,jj,jk) + ( ( pfc(ji,jj,jk) - pfu(ji,jj,jk) ) / MAX( zc, 1.e-9 ) ) ! phi_REF
	467	IF( zcoef1 >= 0. ) THEN
	468	zfho = MAX( pfc(ji,jj,jk), zfho )
	469	zfho = MIN( zfho, MIN( zcoef3, pfd(ji,jj,jk) ) )
	470	ELSE
	471	zfho = MIN( pfc(ji,jj,jk), zfho )
	472	zfho = MAX( zfho, MAX( zcoef3, pfd(ji,jj,jk) ) )
	473	ENDIF
	474	ENDIF
	475	puc(ji,jj,jk) = zfho
	476	END DO
	477	END DO
	478	END DO
[1231]	479	!
[3294]	480	IF( nn_timing == 1 ) CALL timing_stop('quickest')
	481	!
[1231]	482	END SUBROUTINE quickest
	483
	484	!!======================================================================
	485	END MODULE traadv_qck

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