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traadv_qck.F90 in branches/dev_r2586_dynamic_mem/NEMOGCM/NEMO/OPA_SRC/TRA – NEMO

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source: branches/dev_r2586_dynamic_mem/NEMOGCM/NEMO/OPA_SRC/TRA/traadv_qck.F90 @ 2598

Last change on this file since 2598 was 2590, checked in by trackstand2, 13 years ago
Merge branch 'dynamic_memory' into master-svn-dyn
Property svn:keywords set to `Id`
File size: 24.1 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
[1231]	28
	29	IMPLICIT NONE
	30	PRIVATE
	31
[1559]	32	PUBLIC tra_adv_qck ! routine called by step.F90
[1231]	33
[2528]	34	LOGICAL :: l_trd ! flag to compute trends
	35	REAL(wp) :: r1_6 = 1./ 6. ! 1/6 ratio
[1559]	36
[1231]	37	!! * Substitutions
	38	# include "domzgr_substitute.h90"
	39	# include "vectopt_loop_substitute.h90"
	40	!!----------------------------------------------------------------------
[2528]	41	!! NEMO/OPA 3.3 , NEMO Consortium (2010)
[1231]	42	!! $Id$
[2528]	43	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
[1231]	44	!!----------------------------------------------------------------------
	45	CONTAINS
	46
[2528]	47	SUBROUTINE tra_adv_qck ( kt, cdtype, p2dt, pun, pvn, pwn, &
	48	& ptb, ptn, pta, kjpt )
[1231]	49	!!----------------------------------------------------------------------
	50	!! * ROUTINE tra_adv_qck *
	51	!!
	52	!! ** Purpose : Compute the now trend due to the advection of tracers
	53	!! and add it to the general trend of passive tracer equations.
	54	!!
	55	!! ** Method : The advection is evaluated by a third order scheme
[1559]	56	!! For a positive velocity u : u(i)>0
	57	!! \|--FU--\|--FC--\|--FD--\|------\|
	58	!! i-1 i i+1 i+2
[1231]	59	!!
[1559]	60	!! For a negative velocity u : u(i)<0
	61	!! \|------\|--FD--\|--FC--\|--FU--\|
	62	!! i-1 i i+1 i+2
	63	!! where FU is the second upwind point
	64	!! FD is the first douwning point
	65	!! FC is the central point (or the first upwind point)
[1231]	66	!!
[1559]	67	!! Flux(i) = u(i) * { 0.5(FC+FD) -0.5C(i)(FD-FC) -((1-C(i))/6)(FU+FD-2FC) }
	68	!! with C(i)=\|u(i)\|dx(i)/dt (=Courant number)
[1231]	69	!!
	70	!! dt = 2*rdtra and the scalar values are tb and sb
	71	!!
[2528]	72	!! On the vertical, the simple centered scheme used ptn
[1231]	73	!!
[1559]	74	!! The fluxes are bounded by the ULTIMATE limiter to
	75	!! guarantee the monotonicity of the solution and to
[1231]	76	!! prevent the appearance of spurious numerical oscillations
	77	!!
[2528]	78	!! ** Action : - update (pta) with the now advective tracer trends
	79	!! - save the trends
[1231]	80	!!
	81	!! ** Reference : Leonard (1979, 1991)
	82	!!----------------------------------------------------------------------
[2528]	83	INTEGER , INTENT(in ) :: kt ! ocean time-step index
	84	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	85	INTEGER , INTENT(in ) :: kjpt ! number of tracers
	86	REAL(wp), DIMENSION( jpk ), INTENT(in ) :: p2dt ! vertical profile of tracer time-step
	87	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pun, pvn, pwn ! 3 ocean velocity components
	88	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb, ptn ! before and now tracer fields
	89	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend
[1231]	90	!!----------------------------------------------------------------------
	91
[2528]	92	IF( kt == nit000 ) THEN
[1231]	93	IF(lwp) WRITE(numout,*)
[2528]	94	IF(lwp) WRITE(numout,*) 'tra_adv_qck : 3rd order quickest advection scheme on ', cdtype
[1231]	95	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~'
	96	IF(lwp) WRITE(numout,*)
[2528]	97	!
	98	l_trd = .FALSE.
	99	IF( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. ( cdtype == 'TRC' .AND. l_trdtrc ) ) l_trd = .TRUE.
[1231]	100	ENDIF
	101
	102	! I. The horizontal fluxes are computed with the QUICKEST + ULTIMATE scheme
[2528]	103	CALL tra_adv_qck_i( kt, cdtype, p2dt, pun, ptb, ptn, pta, kjpt )
	104	CALL tra_adv_qck_j( kt, cdtype, p2dt, pvn, ptb, ptn, pta, kjpt )
[1231]	105
	106	! II. The vertical fluxes are computed with the 2nd order centered scheme
[2528]	107	CALL tra_adv_cen2_k( kt, cdtype, pwn, ptn, pta, kjpt )
[1231]	108	!
	109	END SUBROUTINE tra_adv_qck
	110
	111
[2528]	112	SUBROUTINE tra_adv_qck_i( kt, cdtype, p2dt, pun, &
	113	& ptb, ptn, pta, kjpt )
[1231]	114	!!----------------------------------------------------------------------
	115	!!
	116	!!----------------------------------------------------------------------
[2528]	117	USE oce , zwx => ua ! use ua as workspace
[2590]	118	USE wrk_nemo, ONLY: wrk_use, wrk_release
	119	USE wrk_nemo, ONLY: zfu => wrk_3d_1, zfc => wrk_3d_2, zfd => wrk_3d_3
[2528]	120	!!
	121	INTEGER , INTENT(in ) :: kt ! ocean time-step index
	122	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	123	INTEGER , INTENT(in ) :: kjpt ! number of tracers
	124	REAL(wp), DIMENSION( jpk ), INTENT(in ) :: p2dt ! vertical profile of tracer time-step
	125	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pun ! i-velocity components
	126	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb, ptn ! before and now tracer fields
	127	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend
	128	!!
	129	INTEGER :: ji, jj, jk, jn ! dummy loop indices
	130	REAL(wp) :: ztra, zbtr ! local scalars
	131	REAL(wp) :: zdir, zdx, zdt, zmsk ! local scalars
[1231]	132	!----------------------------------------------------------------------
[2590]	133	!
	134	IF(.not. wrk_use(3, 1,2,3))THEN
	135	CALL ctl_stop('tra_adv_qck_i: ERROR: requested workspace arrays unavailable')
	136	RETURN
	137	END IF
[2528]	138	! ! ===========
	139	DO jn = 1, kjpt ! tracer loop
	140	! ! ===========
	141	zfu(:,:,:) = 0.0 ; zfc(:,:,:) = 0.0
	142	zfd(:,:,:) = 0.0 ; zwx(:,:,:) = 0.0
	143	!
	144	DO jk = 1, jpkm1
	145	!
	146	!--- Computation of the ustream and downstream value of the tracer and the mask
	147	DO jj = 2, jpjm1
	148	DO ji = fs_2, fs_jpim1 ! vector opt.
	149	! Upstream in the x-direction for the tracer
	150	zfc(ji,jj,jk) = ptb(ji-1,jj,jk,jn)
	151	! Downstream in the x-direction for the tracer
	152	zfd(ji,jj,jk) = ptb(ji+1,jj,jk,jn)
	153	END DO
[1559]	154	END DO
	155	END DO
[2528]	156	CALL lbc_lnk( zfc(:,:,:), 'T', 1. ) ; CALL lbc_lnk( zfd(:,:,:), 'T', 1. ) ! Lateral boundary conditions
	157
[1231]	158	!
	159	! Horizontal advective fluxes
	160	! ---------------------------
	161	!
[2528]	162	DO jk = 1, jpkm1
	163	DO jj = 2, jpjm1
	164	DO ji = fs_2, fs_jpim1 ! vector opt.
	165	zdir = 0.5 + SIGN( 0.5, pun(ji,jj,jk) ) ! if pun > 0 : zdir = 1 otherwise zdir = 0
	166	zfu(ji,jj,jk) = zdir * zfc(ji,jj,jk ) + ( 1. - zdir ) * zfd(ji+1,jj,jk) ! FU in the x-direction for T
	167	END DO
	168	END DO
[1559]	169	END DO
[1231]	170	!
[2528]	171	DO jk = 1, jpkm1
	172	zdt = p2dt(jk)
	173	DO jj = 2, jpjm1
	174	DO ji = fs_2, fs_jpim1 ! vector opt.
	175	zdir = 0.5 + SIGN( 0.5, pun(ji,jj,jk) ) ! if pun > 0 : zdir = 1 otherwise zdir = 0
	176	zdx = ( zdir * e1t(ji,jj) + ( 1. - zdir ) * e1t(ji+1,jj) ) * e2u(ji,jj) * fse3u(ji,jj,jk)
	177	zwx(ji,jj,jk) = ABS( pun(ji,jj,jk) ) * zdt / zdx ! (0<zc_cfl<1 : Courant number on x-direction)
	178	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
	179	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
	180	END DO
	181	END DO
	182	END DO
	183	!--- Lateral boundary conditions
	184	CALL lbc_lnk( zfu(:,:,:), 'T', 1. ) ; CALL lbc_lnk( zfd(:,:,:), 'T', 1. )
	185	CALL lbc_lnk( zfc(:,:,:), 'T', 1. ) ; CALL lbc_lnk( zwx(:,:,:), 'T', 1. )
	186
[1231]	187	!--- QUICKEST scheme
[2528]	188	CALL quickest( zfu, zfd, zfc, zwx )
[1231]	189	!
[2528]	190	! Mask at the T-points in the x-direction (mask=0 or mask=1)
	191	DO jk = 1, jpkm1
	192	DO jj = 2, jpjm1
	193	DO ji = fs_2, fs_jpim1 ! vector opt.
	194	zfu(ji,jj,jk) = tmask(ji-1,jj,jk) + tmask(ji,jj,jk) + tmask(ji+1,jj,jk) - 2.
	195	ENDDO
[1231]	196	END DO
	197	END DO
[2528]	198	CALL lbc_lnk( zfu(:,:,:), 'T', 1. ) ! Lateral boundary conditions
	199
[1231]	200	!
[2528]	201	! Tracer flux on the x-direction
	202	DO jk = 1, jpkm1
	203	!
[1231]	204	DO jj = 2, jpjm1
[2528]	205	DO ji = fs_2, fs_jpim1 ! vector opt.
	206	zdir = 0.5 + SIGN( 0.5, pun(ji,jj,jk) ) ! if pun > 0 : zdir = 1 otherwise zdir = 0
	207	!--- If the second ustream point is a land point
	208	!--- the flux is computed by the 1st order UPWIND scheme
	209	zmsk = zdir * zfu(ji,jj,jk) + ( 1. - zdir ) * zfu(ji+1,jj,jk)
	210	zwx(ji,jj,jk) = zmsk * zwx(ji,jj,jk) + ( 1. - zmsk ) * zfc(ji,jj,jk)
	211	zwx(ji,jj,jk) = zwx(ji,jj,jk) * pun(ji,jj,jk)
[1231]	212	END DO
	213	END DO
[2528]	214	!
	215	! Computation of the trend
	216	DO jj = 2, jpjm1
	217	DO ji = fs_2, fs_jpim1 ! vector opt.
	218	zbtr = 1. / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) )
	219	! horizontal advective trends
	220	ztra = - zbtr * ( zwx(ji,jj,jk) - zwx(ji-1,jj,jk) )
	221	!--- add it to the general tracer trends
	222	pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra
	223	END DO
	224	END DO
	225	!
[1231]	226	END DO
[2528]	227	! ! trend diagnostics (contribution of upstream fluxes)
	228	IF( l_trd ) CALL trd_tra( kt, cdtype, jn, jptra_trd_xad, zwx, pun, ptn(:,:,:,jn) )
	229	!
	230	END DO
	231	!
[2590]	232	IF(.not. wrk_release(3, 1,2,3))THEN
	233	CALL ctl_stop('tra_adv_qck_i: ERROR: failed to release workspace arrays')
	234	END IF
	235	!
[1559]	236	END SUBROUTINE tra_adv_qck_i
[1231]	237
	238
[2528]	239	SUBROUTINE tra_adv_qck_j( kt, cdtype, p2dt, pvn, &
	240	& ptb, ptn, pta, kjpt )
[1231]	241	!!----------------------------------------------------------------------
	242	!!
	243	!!----------------------------------------------------------------------
[2528]	244	USE oce , zwy => ua ! use ua as workspace
[2590]	245	USE wrk_nemo, ONLY: wrk_use, wrk_release
	246	USE wrk_nemo, ONLY: zfu => wrk_3d_1, zfc => wrk_3d_2, zfd => wrk_3d_3
[1559]	247	!!
[2528]	248	INTEGER , INTENT(in ) :: kt ! ocean time-step index
	249	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	250	INTEGER , INTENT(in ) :: kjpt ! number of tracers
	251	REAL(wp), DIMENSION( jpk ), INTENT(in ) :: p2dt ! vertical profile of tracer time-step
	252	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pvn ! j-velocity components
	253	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb, ptn ! before and now tracer fields
	254	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend
	255	!!
	256	INTEGER :: ji, jj, jk, jn ! dummy loop indices
	257	REAL(wp) :: ztra, zbtr ! local scalars
	258	REAL(wp) :: zdir, zdx, zdt, zmsk ! local scalars
[1231]	259	!----------------------------------------------------------------------
[2590]	260	!
	261	IF(.not. wrk_use(3, 1,2,3))THEN
	262	CALL ctl_stop('tra_adv_qck_j: ERROR: requested workspace arrays unavailable')
	263	RETURN
	264	END IF
[2528]	265	! ! ===========
	266	DO jn = 1, kjpt ! tracer loop
	267	! ! ===========
	268	zfu(:,:,:) = 0.0 ; zfc(:,:,:) = 0.0
	269	zfd(:,:,:) = 0.0 ; zwy(:,:,:) = 0.0
	270	!
	271	DO jk = 1, jpkm1
	272	!
	273	!--- Computation of the ustream and downstream value of the tracer and the mask
	274	DO jj = 2, jpjm1
	275	DO ji = fs_2, fs_jpim1 ! vector opt.
	276	! Upstream in the x-direction for the tracer
	277	zfc(ji,jj,jk) = ptb(ji,jj-1,jk,jn)
	278	! Downstream in the x-direction for the tracer
	279	zfd(ji,jj,jk) = ptb(ji,jj+1,jk,jn)
	280	END DO
[1559]	281	END DO
	282	END DO
[2528]	283	CALL lbc_lnk( zfc(:,:,:), 'T', 1. ) ; CALL lbc_lnk( zfd(:,:,:), 'T', 1. ) ! Lateral boundary conditions
	284
	285
[1231]	286	!
	287	! Horizontal advective fluxes
	288	! ---------------------------
	289	!
[2528]	290	DO jk = 1, jpkm1
	291	DO jj = 2, jpjm1
	292	DO ji = fs_2, fs_jpim1 ! vector opt.
	293	zdir = 0.5 + SIGN( 0.5, pvn(ji,jj,jk) ) ! if pun > 0 : zdir = 1 otherwise zdir = 0
	294	zfu(ji,jj,jk) = zdir * zfc(ji,jj,jk ) + ( 1. - zdir ) * zfd(ji,jj+1,jk) ! FU in the x-direction for T
	295	END DO
[1559]	296	END DO
	297	END DO
[1231]	298	!
[2528]	299	DO jk = 1, jpkm1
	300	zdt = p2dt(jk)
	301	DO jj = 2, jpjm1
	302	DO ji = fs_2, fs_jpim1 ! vector opt.
	303	zdir = 0.5 + SIGN( 0.5, pvn(ji,jj,jk) ) ! if pun > 0 : zdir = 1 otherwise zdir = 0
	304	zdx = ( zdir * e2t(ji,jj) + ( 1. - zdir ) * e2t(ji,jj+1) ) * e1v(ji,jj) * fse3v(ji,jj,jk)
	305	zwy(ji,jj,jk) = ABS( pvn(ji,jj,jk) ) * zdt / zdx ! (0<zc_cfl<1 : Courant number on x-direction)
	306	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
	307	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
	308	END DO
	309	END DO
	310	END DO
	311
	312	!--- Lateral boundary conditions
	313	CALL lbc_lnk( zfu(:,:,:), 'T', 1. ) ; CALL lbc_lnk( zfd(:,:,:), 'T', 1. )
	314	CALL lbc_lnk( zfc(:,:,:), 'T', 1. ) ; CALL lbc_lnk( zwy(:,:,:), 'T', 1. )
	315
[1231]	316	!--- QUICKEST scheme
[2528]	317	CALL quickest( zfu, zfd, zfc, zwy )
[1231]	318	!
[2528]	319	! Mask at the T-points in the x-direction (mask=0 or mask=1)
	320	DO jk = 1, jpkm1
	321	DO jj = 2, jpjm1
	322	DO ji = fs_2, fs_jpim1 ! vector opt.
	323	zfu(ji,jj,jk) = tmask(ji,jj-1,jk) + tmask(ji,jj,jk) + tmask(ji,jj+1,jk) - 2.
	324	END DO
[1231]	325	END DO
	326	END DO
[2528]	327	!--- Lateral boundary conditions
	328	CALL lbc_lnk( zfu(:,:,:), 'T', 1. )
	329	!
	330	! Tracer flux on the x-direction
	331	DO jk = 1, jpkm1
	332	!
[1231]	333	DO jj = 2, jpjm1
[2528]	334	DO ji = fs_2, fs_jpim1 ! vector opt.
	335	zdir = 0.5 + SIGN( 0.5, pvn(ji,jj,jk) ) ! if pun > 0 : zdir = 1 otherwise zdir = 0
	336	!--- If the second ustream point is a land point
	337	!--- the flux is computed by the 1st order UPWIND scheme
	338	zmsk = zdir * zfu(ji,jj,jk) + ( 1. - zdir ) * zfu(ji,jj+1,jk)
	339	zwy(ji,jj,jk) = zmsk * zwy(ji,jj,jk) + ( 1. - zmsk ) * zfc(ji,jj,jk)
	340	zwy(ji,jj,jk) = zwy(ji,jj,jk) * pvn(ji,jj,jk)
[1231]	341	END DO
	342	END DO
[2528]	343	!
	344	! Computation of the trend
	345	DO jj = 2, jpjm1
	346	DO ji = fs_2, fs_jpim1 ! vector opt.
	347	zbtr = 1. / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) )
	348	! horizontal advective trends
	349	ztra = - zbtr * ( zwy(ji,jj,jk) - zwy(ji,jj-1,jk) )
	350	!--- add it to the general tracer trends
	351	pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra
[1231]	352	END DO
	353	END DO
[2528]	354	!
	355	END DO
	356	! ! trend diagnostics (contribution of upstream fluxes)
	357	IF( l_trd ) CALL trd_tra( kt, cdtype, jn, jptra_trd_yad, zwy, pvn, ptn(:,:,:,jn) )
	358	! ! "Poleward" heat and salt transports (contribution of upstream fluxes)
	359	IF( cdtype == 'TRA' .AND. ln_diaptr .AND. ( MOD( kt, nn_fptr ) == 0 ) ) THEN
	360	IF( jn == jp_tem ) htr_adv(:) = ptr_vj( zwy(:,:,:) )
	361	IF( jn == jp_sal ) str_adv(:) = ptr_vj( zwy(:,:,:) )
[1231]	362	ENDIF
[2528]	363	!
	364	END DO
	365	!
[2590]	366	IF(.not. wrk_release(3, 1,2,3))THEN
	367	CALL ctl_stop('tra_adv_qck_j: ERROR: failed to release workspace arrays')
	368	END IF
	369	!
[1559]	370	END SUBROUTINE tra_adv_qck_j
[1231]	371
	372
[2528]	373	SUBROUTINE tra_adv_cen2_k( kt, cdtype, pwn, &
	374	& ptn, pta, kjpt )
[1231]	375	!!----------------------------------------------------------------------
	376	!!
	377	!!----------------------------------------------------------------------
[2528]	378	USE oce , zwz => ua ! use ua as workspace
[1559]	379	!!
[2528]	380	INTEGER , INTENT(in ) :: kt ! ocean time-step index
	381	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	382	INTEGER , INTENT(in ) :: kjpt ! number of tracers
	383	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pwn ! vertical velocity
	384	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptn ! before and now tracer fields
	385	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend
	386	!!
	387	INTEGER :: ji, jj, jk, jn ! dummy loop indices
	388	REAL(wp) :: zbtr , ztra ! temporary scalars
[1559]	389	!!----------------------------------------------------------------------
[2528]	390
	391	! ! ===========
	392	DO jn = 1, kjpt ! tracer loop
	393	! ! ===========
	394	! 1. Bottom value : flux set to zero
	395	zwz(:,:,jpk) = 0.e0 ! Bottom value : flux set to zero
	396	!
	397	! ! Surface value
	398	IF( lk_vvl ) THEN ; zwz(:,:, 1 ) = 0.e0 ! Variable volume : flux set to zero
	399	ELSE ; zwz(:,:, 1 ) = pwn(:,:,1) * ptn(:,:,1,jn) ! Constant volume : advective flux through the surface
	400	ENDIF
	401	!
	402	DO jk = 2, jpkm1 ! Interior point: second order centered tracer flux at w-point
	403	DO jj = 2, jpjm1
	404	DO ji = fs_2, fs_jpim1 ! vector opt.
	405	zwz(ji,jj,jk) = 0.5 * pwn(ji,jj,jk) * ( ptn(ji,jj,jk-1,jn) + ptn(ji,jj,jk,jn) )
	406	END DO
[1231]	407	END DO
	408	END DO
[2528]	409	!
	410	DO jk = 1, jpkm1 !== Tracer flux divergence added to the general trend ==!
	411	DO jj = 2, jpjm1
	412	DO ji = fs_2, fs_jpim1 ! vector opt.
	413	zbtr = 1. / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) )
	414	! k- vertical advective trends
	415	ztra = - zbtr * ( zwz(ji,jj,jk) - zwz(ji,jj,jk+1) )
	416	! added to the general tracer trends
	417	pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra
	418	END DO
[1231]	419	END DO
	420	END DO
[2528]	421	! ! Save the vertical advective trends for diagnostic
	422	IF( l_trd ) CALL trd_tra( kt, cdtype, jn, jptra_trd_zad, zwz, pwn, ptn(:,:,:,jn) )
	423	!
[1231]	424	END DO
	425	!
[1559]	426	END SUBROUTINE tra_adv_cen2_k
[1231]	427
	428
[2528]	429	SUBROUTINE quickest( pfu, pfd, pfc, puc )
[1231]	430	!!----------------------------------------------------------------------
	431	!!
[2528]	432	!! ** Purpose : Computation of advective flux with Quickest scheme
	433	!!
	434	!! ** Method :
[1231]	435	!!----------------------------------------------------------------------
[2528]	436	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pfu ! second upwind point
	437	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pfd ! first douwning point
	438	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pfc ! the central point (or the first upwind point)
	439	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: puc ! input as Courant number ; output as flux
	440	!!
	441	INTEGER :: ji, jj, jk ! dummy loop indices
	442	REAL(wp) :: zcoef1, zcoef2, zcoef3 ! local scalars
	443	REAL(wp) :: zc, zcurv, zfho ! - -
	444	!----------------------------------------------------------------------
	445
	446	DO jk = 1, jpkm1
	447	DO jj = 1, jpj
	448	DO ji = 1, jpi
	449	zc = puc(ji,jj,jk) ! Courant number
	450	zcurv = pfd(ji,jj,jk) + pfu(ji,jj,jk) - 2. * pfc(ji,jj,jk)
	451	zcoef1 = 0.5 * ( pfc(ji,jj,jk) + pfd(ji,jj,jk) )
	452	zcoef2 = 0.5 * zc * ( pfd(ji,jj,jk) - pfc(ji,jj,jk) )
	453	zcoef3 = ( 1. - ( zc * zc ) ) * r1_6 * zcurv
	454	zfho = zcoef1 - zcoef2 - zcoef3 ! phi_f QUICKEST
	455	!
	456	zcoef1 = pfd(ji,jj,jk) - pfu(ji,jj,jk)
	457	zcoef2 = ABS( zcoef1 )
	458	zcoef3 = ABS( zcurv )
	459	IF( zcoef3 >= zcoef2 ) THEN
	460	zfho = pfc(ji,jj,jk)
	461	ELSE
	462	zcoef3 = pfu(ji,jj,jk) + ( ( pfc(ji,jj,jk) - pfu(ji,jj,jk) ) / MAX( zc, 1.e-9 ) ) ! phi_REF
	463	IF( zcoef1 >= 0. ) THEN
	464	zfho = MAX( pfc(ji,jj,jk), zfho )
	465	zfho = MIN( zfho, MIN( zcoef3, pfd(ji,jj,jk) ) )
	466	ELSE
	467	zfho = MIN( pfc(ji,jj,jk), zfho )
	468	zfho = MAX( zfho, MAX( zcoef3, pfd(ji,jj,jk) ) )
	469	ENDIF
	470	ENDIF
	471	puc(ji,jj,jk) = zfho
	472	END DO
	473	END DO
	474	END DO
[1231]	475	!
	476	END SUBROUTINE quickest
	477
	478	!!======================================================================
	479	END MODULE traadv_qck

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