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

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source: NEMO/trunk/src/OCE/TRA/traadv_qck.F90 @ 13286

Last change on this file since 13286 was 13237, checked in by smasson, 4 years ago
trunk: Mid-year merge, merge back KERNEL-06_techene_e3
Property svn:keywords set to `Id`
File size: 21.1 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
[4990]	19	USE trc_oce ! share passive tracers/Ocean variables
	20	USE trd_oce ! trends: ocean variables
	21	USE trdtra ! trends manager: tracers
	22	USE diaptr ! poleward transport diagnostics
[12377]	23	USE iom
[4990]	24	!
[9124]	25	USE in_out_manager ! I/O manager
[1231]	26	USE lib_mpp ! distribued memory computing
	27	USE lbclnk ! ocean lateral boundary condition (or mpp link)
[3625]	28	USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined)
[1231]	29
	30	IMPLICIT NONE
	31	PRIVATE
	32
[1559]	33	PUBLIC tra_adv_qck ! routine called by step.F90
[1231]	34
[2528]	35	REAL(wp) :: r1_6 = 1./ 6. ! 1/6 ratio
[1559]	36
[7646]	37	LOGICAL :: l_trd ! flag to compute trends
	38	LOGICAL :: l_ptr ! flag to compute poleward transport
	39
	40
[1231]	41	!! * Substitutions
[12377]	42	# include "do_loop_substitute.h90"
[13237]	43	# include "domzgr_substitute.h90"
[1231]	44	!!----------------------------------------------------------------------
[9598]	45	!! NEMO/OCE 4.0 , NEMO Consortium (2018)
[1231]	46	!! $Id$
[10068]	47	!! Software governed by the CeCILL license (see ./LICENSE)
[1231]	48	!!----------------------------------------------------------------------
	49	CONTAINS
	50
[12377]	51	SUBROUTINE tra_adv_qck ( kt, kit000, cdtype, p2dt, pU, pV, pW, Kbb, Kmm, pt, kjpt, Krhs )
[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	!!
[12377]	75	!! On the vertical, the simple centered scheme used pt(:,:,:,:,Kmm)
[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	!!
[12377]	81	!! ** Action : - update pt(:,:,:,:,Krhs) with the now advective tracer trends
[6140]	82	!! - send trends to trdtra module for further diagnostcs (l_trdtra=T)
[12377]	83	!! - poleward advective heat and salt transport (ln_diaptr=T)
[1231]	84	!!
	85	!! ** Reference : Leonard (1979, 1991)
	86	!!----------------------------------------------------------------------
[12377]	87	INTEGER , INTENT(in ) :: kt ! ocean time-step index
	88	INTEGER , INTENT(in ) :: Kbb, Kmm, Krhs ! ocean time level indices
	89	INTEGER , INTENT(in ) :: kit000 ! first time step index
	90	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	91	INTEGER , INTENT(in ) :: kjpt ! number of tracers
	92	REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
	93	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pU, pV, pW ! 3 ocean volume transport components
	94	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt,jpt), INTENT(inout) :: pt ! tracers and RHS of tracer equation
[1231]	95	!!----------------------------------------------------------------------
[3294]	96	!
	97	IF( kt == kit000 ) THEN
[1231]	98	IF(lwp) WRITE(numout,*)
[2528]	99	IF(lwp) WRITE(numout,*) 'tra_adv_qck : 3rd order quickest advection scheme on ', cdtype
[1231]	100	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~'
	101	IF(lwp) WRITE(numout,*)
	102	ENDIF
[5836]	103	!
[4990]	104	l_trd = .FALSE.
[7646]	105	l_ptr = .FALSE.
[12377]	106	IF( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. ( cdtype == 'TRC' .AND. l_trdtrc ) ) l_trd = .TRUE.
	107	IF( cdtype == 'TRA' .AND. ( iom_use( 'sophtadv' ) .OR. iom_use( 'sophtadv' ) ) ) l_ptr = .TRUE.
[4499]	108	!
[7646]	109	!
[6140]	110	! ! horizontal fluxes are computed with the QUICKEST + ULTIMATE scheme
[12377]	111	CALL tra_adv_qck_i( kt, cdtype, p2dt, pU, Kbb, Kmm, pt, kjpt, Krhs )
	112	CALL tra_adv_qck_j( kt, cdtype, p2dt, pV, Kbb, Kmm, pt, kjpt, Krhs )
[1231]	113
[6140]	114	! ! vertical fluxes are computed with the 2nd order centered scheme
[12377]	115	CALL tra_adv_cen2_k( kt, cdtype, pW, Kmm, pt, kjpt, Krhs )
[1231]	116	!
	117	END SUBROUTINE tra_adv_qck
	118
	119
[12377]	120	SUBROUTINE tra_adv_qck_i( kt, cdtype, p2dt, pU, Kbb, Kmm, pt, kjpt, Krhs )
[1231]	121	!!----------------------------------------------------------------------
	122	!!
	123	!!----------------------------------------------------------------------
[12377]	124	INTEGER , INTENT(in ) :: kt ! ocean time-step index
	125	INTEGER , INTENT(in ) :: Kbb, Kmm, Krhs ! ocean time level indices
	126	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	127	INTEGER , INTENT(in ) :: kjpt ! number of tracers
	128	REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
	129	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pU ! i-velocity components
	130	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt,jpt), INTENT(inout) :: pt ! active tracers and RHS of tracer equation
[2528]	131	!!
[5836]	132	INTEGER :: ji, jj, jk, jn ! dummy loop indices
[6140]	133	REAL(wp) :: ztra, zbtr, zdir, zdx, zmsk ! local scalars
[9019]	134	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwx, zfu, zfc, zfd
[1231]	135	!----------------------------------------------------------------------
[2715]	136	!
[2528]	137	! ! ===========
	138	DO jn = 1, kjpt ! tracer loop
	139	! ! ===========
[5836]	140	zfu(:,:,:) = 0._wp ; zfc(:,:,:) = 0._wp
	141	zfd(:,:,:) = 0._wp ; zwx(:,:,:) = 0._wp
	142	!
	143	!!gm why not using a SHIFT instruction...
[12377]	144	DO_3D_00_00( 1, jpkm1 )
	145	zfc(ji,jj,jk) = pt(ji-1,jj,jk,jn,Kbb) ! Upstream in the x-direction for the tracer
	146	zfd(ji,jj,jk) = pt(ji+1,jj,jk,jn,Kbb) ! Downstream in the x-direction for the tracer
	147	END_3D
[13226]	148	CALL lbc_lnk_multi( 'traadv_qck', zfc(:,:,:), 'T', 1.0_wp , zfd(:,:,:), 'T', 1.0_wp ) ! Lateral boundary conditions
[2528]	149
[1231]	150	!
	151	! Horizontal advective fluxes
	152	! ---------------------------
[12377]	153	DO_3D_00_00( 1, jpkm1 )
[13226]	154	zdir = 0.5 + SIGN( 0.5_wp, pU(ji,jj,jk) ) ! if pU > 0 : zdir = 1 otherwise zdir = 0
[12377]	155	zfu(ji,jj,jk) = zdir * zfc(ji,jj,jk ) + ( 1. - zdir ) * zfd(ji+1,jj,jk) ! FU in the x-direction for T
	156	END_3D
[1231]	157	!
[12377]	158	DO_3D_00_00( 1, jpkm1 )
[13226]	159	zdir = 0.5 + SIGN( 0.5_wp, pU(ji,jj,jk) ) ! if pU > 0 : zdir = 1 otherwise zdir = 0
[12377]	160	zdx = ( zdir * e1t(ji,jj) + ( 1. - zdir ) * e1t(ji+1,jj) ) * e2u(ji,jj) * e3u(ji,jj,jk,Kmm)
	161	zwx(ji,jj,jk) = ABS( pU(ji,jj,jk) ) * p2dt / zdx ! (0<zc_cfl<1 : Courant number on x-direction)
	162	zfc(ji,jj,jk) = zdir * pt(ji ,jj,jk,jn,Kbb) + ( 1. - zdir ) * pt(ji+1,jj,jk,jn,Kbb) ! FC in the x-direction for T
	163	zfd(ji,jj,jk) = zdir * pt(ji+1,jj,jk,jn,Kbb) + ( 1. - zdir ) * pt(ji ,jj,jk,jn,Kbb) ! FD in the x-direction for T
	164	END_3D
[2528]	165	!--- Lateral boundary conditions
[13226]	166	CALL lbc_lnk_multi( 'traadv_qck', zfu(:,:,:), 'T', 1.0_wp , zfd(:,:,:), 'T', 1.0_wp, zfc(:,:,:), 'T', 1.0_wp, zwx(:,:,:), 'T', 1.0_wp )
[2528]	167
[1231]	168	!--- QUICKEST scheme
[2528]	169	CALL quickest( zfu, zfd, zfc, zwx )
[1231]	170	!
[2528]	171	! Mask at the T-points in the x-direction (mask=0 or mask=1)
[12377]	172	DO_3D_00_00( 1, jpkm1 )
	173	zfu(ji,jj,jk) = tmask(ji-1,jj,jk) + tmask(ji,jj,jk) + tmask(ji+1,jj,jk) - 2.
	174	END_3D
[13226]	175	CALL lbc_lnk( 'traadv_qck', zfu(:,:,:), 'T', 1.0_wp ) ! Lateral boundary conditions
[2528]	176
[1231]	177	!
[2528]	178	! Tracer flux on the x-direction
	179	DO jk = 1, jpkm1
	180	!
[12377]	181	DO_2D_00_00
[13226]	182	zdir = 0.5 + SIGN( 0.5_wp, pU(ji,jj,jk) ) ! if pU > 0 : zdir = 1 otherwise zdir = 0
[12377]	183	!--- If the second ustream point is a land point
	184	!--- the flux is computed by the 1st order UPWIND scheme
	185	zmsk = zdir * zfu(ji,jj,jk) + ( 1. - zdir ) * zfu(ji+1,jj,jk)
	186	zwx(ji,jj,jk) = zmsk * zwx(ji,jj,jk) + ( 1. - zmsk ) * zfc(ji,jj,jk)
	187	zwx(ji,jj,jk) = zwx(ji,jj,jk) * pU(ji,jj,jk)
	188	END_2D
[3300]	189	END DO
	190	!
[13226]	191	CALL lbc_lnk( 'traadv_qck', zwx(:,:,:), 'T', 1.0_wp ) ! Lateral boundary conditions
[3300]	192	!
	193	! Computation of the trend
[12377]	194	DO_3D_00_00( 1, jpkm1 )
	195	zbtr = r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm)
	196	! horizontal advective trends
	197	ztra = - zbtr * ( zwx(ji,jj,jk) - zwx(ji-1,jj,jk) )
	198	!--- add it to the general tracer trends
	199	pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) + ztra
	200	END_3D
[6140]	201	! ! trend diagnostics
[12377]	202	IF( l_trd ) CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_xad, zwx, pU, pt(:,:,:,jn,Kmm) )
[2528]	203	!
	204	END DO
	205	!
[1559]	206	END SUBROUTINE tra_adv_qck_i
[1231]	207
	208
[12377]	209	SUBROUTINE tra_adv_qck_j( kt, cdtype, p2dt, pV, Kbb, Kmm, pt, kjpt, Krhs )
[1231]	210	!!----------------------------------------------------------------------
	211	!!
	212	!!----------------------------------------------------------------------
[12377]	213	INTEGER , INTENT(in ) :: kt ! ocean time-step index
	214	INTEGER , INTENT(in ) :: Kbb, Kmm, Krhs ! ocean time level indices
	215	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	216	INTEGER , INTENT(in ) :: kjpt ! number of tracers
	217	REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
	218	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pV ! j-velocity components
	219	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt,jpt), INTENT(inout) :: pt ! active tracers and RHS of tracer equation
[1559]	220	!!
[9019]	221	INTEGER :: ji, jj, jk, jn ! dummy loop indices
[6140]	222	REAL(wp) :: ztra, zbtr, zdir, zdx, zmsk ! local scalars
[9019]	223	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwy, zfu, zfc, zfd ! 3D workspace
[1231]	224	!----------------------------------------------------------------------
[2715]	225	!
[2528]	226	! ! ===========
	227	DO jn = 1, kjpt ! tracer loop
	228	! ! ===========
	229	zfu(:,:,:) = 0.0 ; zfc(:,:,:) = 0.0
	230	zfd(:,:,:) = 0.0 ; zwy(:,:,:) = 0.0
	231	!
	232	DO jk = 1, jpkm1
	233	!
	234	!--- Computation of the ustream and downstream value of the tracer and the mask
[12377]	235	DO_2D_00_00
	236	! Upstream in the x-direction for the tracer
	237	zfc(ji,jj,jk) = pt(ji,jj-1,jk,jn,Kbb)
	238	! Downstream in the x-direction for the tracer
	239	zfd(ji,jj,jk) = pt(ji,jj+1,jk,jn,Kbb)
	240	END_2D
[1559]	241	END DO
[13226]	242	CALL lbc_lnk_multi( 'traadv_qck', zfc(:,:,:), 'T', 1.0_wp , zfd(:,:,:), 'T', 1.0_wp ) ! Lateral boundary conditions
[2528]	243
	244
[1231]	245	!
	246	! Horizontal advective fluxes
	247	! ---------------------------
	248	!
[12377]	249	DO_3D_00_00( 1, jpkm1 )
[13226]	250	zdir = 0.5 + SIGN( 0.5_wp, pV(ji,jj,jk) ) ! if pU > 0 : zdir = 1 otherwise zdir = 0
[12377]	251	zfu(ji,jj,jk) = zdir * zfc(ji,jj,jk ) + ( 1. - zdir ) * zfd(ji,jj+1,jk) ! FU in the x-direction for T
	252	END_3D
[1231]	253	!
[12377]	254	DO_3D_00_00( 1, jpkm1 )
[13226]	255	zdir = 0.5 + SIGN( 0.5_wp, pV(ji,jj,jk) ) ! if pU > 0 : zdir = 1 otherwise zdir = 0
[12377]	256	zdx = ( zdir * e2t(ji,jj) + ( 1. - zdir ) * e2t(ji,jj+1) ) * e1v(ji,jj) * e3v(ji,jj,jk,Kmm)
	257	zwy(ji,jj,jk) = ABS( pV(ji,jj,jk) ) * p2dt / zdx ! (0<zc_cfl<1 : Courant number on x-direction)
	258	zfc(ji,jj,jk) = zdir * pt(ji,jj ,jk,jn,Kbb) + ( 1. - zdir ) * pt(ji,jj+1,jk,jn,Kbb) ! FC in the x-direction for T
	259	zfd(ji,jj,jk) = zdir * pt(ji,jj+1,jk,jn,Kbb) + ( 1. - zdir ) * pt(ji,jj ,jk,jn,Kbb) ! FD in the x-direction for T
	260	END_3D
[2528]	261
	262	!--- Lateral boundary conditions
[13226]	263	CALL lbc_lnk_multi( 'traadv_qck', zfu(:,:,:), 'T', 1.0_wp , zfd(:,:,:), 'T', 1.0_wp, zfc(:,:,:), 'T', 1.0_wp, zwy(:,:,:), 'T', 1.0_wp )
[2528]	264
[1231]	265	!--- QUICKEST scheme
[2528]	266	CALL quickest( zfu, zfd, zfc, zwy )
[1231]	267	!
[2528]	268	! Mask at the T-points in the x-direction (mask=0 or mask=1)
[12377]	269	DO_3D_00_00( 1, jpkm1 )
	270	zfu(ji,jj,jk) = tmask(ji,jj-1,jk) + tmask(ji,jj,jk) + tmask(ji,jj+1,jk) - 2.
	271	END_3D
[13226]	272	CALL lbc_lnk( 'traadv_qck', zfu(:,:,:), 'T', 1.0_wp ) !--- Lateral boundary conditions
[2528]	273	!
	274	! Tracer flux on the x-direction
	275	DO jk = 1, jpkm1
	276	!
[12377]	277	DO_2D_00_00
[13226]	278	zdir = 0.5 + SIGN( 0.5_wp, pV(ji,jj,jk) ) ! if pU > 0 : zdir = 1 otherwise zdir = 0
[12377]	279	!--- If the second ustream point is a land point
	280	!--- the flux is computed by the 1st order UPWIND scheme
	281	zmsk = zdir * zfu(ji,jj,jk) + ( 1. - zdir ) * zfu(ji,jj+1,jk)
	282	zwy(ji,jj,jk) = zmsk * zwy(ji,jj,jk) + ( 1. - zmsk ) * zfc(ji,jj,jk)
	283	zwy(ji,jj,jk) = zwy(ji,jj,jk) * pV(ji,jj,jk)
	284	END_2D
[3300]	285	END DO
	286	!
[13226]	287	CALL lbc_lnk( 'traadv_qck', zwy(:,:,:), 'T', 1.0_wp ) ! Lateral boundary conditions
[3300]	288	!
	289	! Computation of the trend
[12377]	290	DO_3D_00_00( 1, jpkm1 )
	291	zbtr = r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm)
	292	! horizontal advective trends
	293	ztra = - zbtr * ( zwy(ji,jj,jk) - zwy(ji,jj-1,jk) )
	294	!--- add it to the general tracer trends
	295	pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) + ztra
	296	END_3D
[6140]	297	! ! trend diagnostics
[12377]	298	IF( l_trd ) CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_yad, zwy, pV, pt(:,:,:,jn,Kmm) )
[2528]	299	! ! "Poleward" heat and salt transports (contribution of upstream fluxes)
[9019]	300	IF( l_ptr ) CALL dia_ptr_hst( jn, 'adv', zwy(:,:,:) )
[2528]	301	!
	302	END DO
	303	!
[1559]	304	END SUBROUTINE tra_adv_qck_j
[1231]	305
	306
[12377]	307	SUBROUTINE tra_adv_cen2_k( kt, cdtype, pW, Kmm, pt, kjpt, Krhs )
[1231]	308	!!----------------------------------------------------------------------
	309	!!
	310	!!----------------------------------------------------------------------
[12377]	311	INTEGER , INTENT(in ) :: kt ! ocean time-step index
	312	INTEGER , INTENT(in ) :: Kmm, Krhs ! ocean time level indices
	313	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	314	INTEGER , INTENT(in ) :: kjpt ! number of tracers
	315	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pW ! vertical velocity
	316	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt,jpt), INTENT(inout) :: pt ! active tracers and RHS of tracer equation
[2715]	317	!
[2528]	318	INTEGER :: ji, jj, jk, jn ! dummy loop indices
[9019]	319	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwz ! 3D workspace
[1559]	320	!!----------------------------------------------------------------------
[4990]	321	!
[6140]	322	zwz(:,:, 1 ) = 0._wp ! surface & bottom values set to zero for all tracers
	323	zwz(:,:,jpk) = 0._wp
[5836]	324	!
[2528]	325	! ! ===========
	326	DO jn = 1, kjpt ! tracer loop
	327	! ! ===========
	328	!
[12377]	329	DO_3D_00_00( 2, jpkm1 )
	330	zwz(ji,jj,jk) = 0.5 * pW(ji,jj,jk) * ( pt(ji,jj,jk-1,jn,Kmm) + pt(ji,jj,jk,jn,Kmm) ) * wmask(ji,jj,jk)
	331	END_3D
[6140]	332	IF( ln_linssh ) THEN !* top value (only in linear free surf. as zwz is multiplied by wmask)
[5836]	333	IF( ln_isfcav ) THEN ! ice-shelf cavities (top of the ocean)
[12377]	334	DO_2D_11_11
	335	zwz(ji,jj, mikt(ji,jj) ) = pW(ji,jj,mikt(ji,jj)) * pt(ji,jj,mikt(ji,jj),jn,Kmm) ! linear free surface
	336	END_2D
[6140]	337	ELSE ! no ocean cavities (only ocean surface)
[12377]	338	zwz(:,:,1) = pW(:,:,1) * pt(:,:,1,jn,Kmm)
[5836]	339	ENDIF
	340	ENDIF
[2528]	341	!
[12377]	342	DO_3D_00_00( 1, jpkm1 )
	343	pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) - ( zwz(ji,jj,jk) - zwz(ji,jj,jk+1) ) &
	344	& * r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm)
	345	END_3D
[6140]	346	! ! Send trends for diagnostic
[12377]	347	IF( l_trd ) CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_zad, zwz, pW, pt(:,:,:,jn,Kmm) )
[2528]	348	!
[1231]	349	END DO
	350	!
[1559]	351	END SUBROUTINE tra_adv_cen2_k
[1231]	352
	353
[2528]	354	SUBROUTINE quickest( pfu, pfd, pfc, puc )
[1231]	355	!!----------------------------------------------------------------------
	356	!!
[2528]	357	!! ** Purpose : Computation of advective flux with Quickest scheme
	358	!!
	359	!! ** Method :
[1231]	360	!!----------------------------------------------------------------------
[2528]	361	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pfu ! second upwind point
	362	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pfd ! first douwning point
	363	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pfc ! the central point (or the first upwind point)
	364	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: puc ! input as Courant number ; output as flux
	365	!!
	366	INTEGER :: ji, jj, jk ! dummy loop indices
	367	REAL(wp) :: zcoef1, zcoef2, zcoef3 ! local scalars
	368	REAL(wp) :: zc, zcurv, zfho ! - -
	369	!----------------------------------------------------------------------
[3294]	370	!
[12377]	371	DO_3D_11_11( 1, jpkm1 )
	372	zc = puc(ji,jj,jk) ! Courant number
	373	zcurv = pfd(ji,jj,jk) + pfu(ji,jj,jk) - 2. * pfc(ji,jj,jk)
	374	zcoef1 = 0.5 * ( pfc(ji,jj,jk) + pfd(ji,jj,jk) )
	375	zcoef2 = 0.5 * zc * ( pfd(ji,jj,jk) - pfc(ji,jj,jk) )
	376	zcoef3 = ( 1. - ( zc * zc ) ) * r1_6 * zcurv
	377	zfho = zcoef1 - zcoef2 - zcoef3 ! phi_f QUICKEST
	378	!
	379	zcoef1 = pfd(ji,jj,jk) - pfu(ji,jj,jk)
	380	zcoef2 = ABS( zcoef1 )
	381	zcoef3 = ABS( zcurv )
	382	IF( zcoef3 >= zcoef2 ) THEN
	383	zfho = pfc(ji,jj,jk)
	384	ELSE
	385	zcoef3 = pfu(ji,jj,jk) + ( ( pfc(ji,jj,jk) - pfu(ji,jj,jk) ) / MAX( zc, 1.e-9 ) ) ! phi_REF
	386	IF( zcoef1 >= 0. ) THEN
	387	zfho = MAX( pfc(ji,jj,jk), zfho )
	388	zfho = MIN( zfho, MIN( zcoef3, pfd(ji,jj,jk) ) )
	389	ELSE
	390	zfho = MIN( pfc(ji,jj,jk), zfho )
	391	zfho = MAX( zfho, MAX( zcoef3, pfd(ji,jj,jk) ) )
	392	ENDIF
	393	ENDIF
	394	puc(ji,jj,jk) = zfho
	395	END_3D
[1231]	396	!
	397	END SUBROUTINE quickest
	398
	399	!!======================================================================
	400	END MODULE traadv_qck

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