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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 @ 13226

Last change on this file since 13226 was 13226, checked in by orioltp, 4 years ago
Merging dev_r12512_HPC-04_mcastril_Mixed_Precision_implementation into the trunk
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"
[1231]	43	!!----------------------------------------------------------------------
[9598]	44	!! NEMO/OCE 4.0 , NEMO Consortium (2018)
[1231]	45	!! $Id$
[10068]	46	!! Software governed by the CeCILL license (see ./LICENSE)
[1231]	47	!!----------------------------------------------------------------------
	48	CONTAINS
	49
[12377]	50	SUBROUTINE tra_adv_qck ( kt, kit000, cdtype, p2dt, pU, pV, pW, Kbb, Kmm, pt, kjpt, Krhs )
[1231]	51	!!----------------------------------------------------------------------
	52	!! * ROUTINE tra_adv_qck *
	53	!!
	54	!! ** Purpose : Compute the now trend due to the advection of tracers
	55	!! and add it to the general trend of passive tracer equations.
	56	!!
	57	!! ** Method : The advection is evaluated by a third order scheme
[1559]	58	!! For a positive velocity u : u(i)>0
	59	!! \|--FU--\|--FC--\|--FD--\|------\|
	60	!! i-1 i i+1 i+2
[1231]	61	!!
[1559]	62	!! For a negative velocity u : u(i)<0
	63	!! \|------\|--FD--\|--FC--\|--FU--\|
	64	!! i-1 i i+1 i+2
	65	!! where FU is the second upwind point
	66	!! FD is the first douwning point
	67	!! FC is the central point (or the first upwind point)
[1231]	68	!!
[1559]	69	!! Flux(i) = u(i) * { 0.5(FC+FD) -0.5C(i)(FD-FC) -((1-C(i))/6)(FU+FD-2FC) }
	70	!! with C(i)=\|u(i)\|dx(i)/dt (=Courant number)
[1231]	71	!!
	72	!! dt = 2*rdtra and the scalar values are tb and sb
	73	!!
[12377]	74	!! On the vertical, the simple centered scheme used pt(:,:,:,:,Kmm)
[1231]	75	!!
[1559]	76	!! The fluxes are bounded by the ULTIMATE limiter to
	77	!! guarantee the monotonicity of the solution and to
[1231]	78	!! prevent the appearance of spurious numerical oscillations
	79	!!
[12377]	80	!! ** Action : - update pt(:,:,:,:,Krhs) with the now advective tracer trends
[6140]	81	!! - send trends to trdtra module for further diagnostcs (l_trdtra=T)
[12377]	82	!! - poleward advective heat and salt transport (ln_diaptr=T)
[1231]	83	!!
	84	!! ** Reference : Leonard (1979, 1991)
	85	!!----------------------------------------------------------------------
[12377]	86	INTEGER , INTENT(in ) :: kt ! ocean time-step index
	87	INTEGER , INTENT(in ) :: Kbb, Kmm, Krhs ! ocean time level indices
	88	INTEGER , INTENT(in ) :: kit000 ! first time step index
	89	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	90	INTEGER , INTENT(in ) :: kjpt ! number of tracers
	91	REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
	92	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pU, pV, pW ! 3 ocean volume transport components
	93	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt,jpt), INTENT(inout) :: pt ! tracers and RHS of tracer equation
[1231]	94	!!----------------------------------------------------------------------
[3294]	95	!
	96	IF( kt == kit000 ) THEN
[1231]	97	IF(lwp) WRITE(numout,*)
[2528]	98	IF(lwp) WRITE(numout,*) 'tra_adv_qck : 3rd order quickest advection scheme on ', cdtype
[1231]	99	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~'
	100	IF(lwp) WRITE(numout,*)
	101	ENDIF
[5836]	102	!
[4990]	103	l_trd = .FALSE.
[7646]	104	l_ptr = .FALSE.
[12377]	105	IF( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. ( cdtype == 'TRC' .AND. l_trdtrc ) ) l_trd = .TRUE.
	106	IF( cdtype == 'TRA' .AND. ( iom_use( 'sophtadv' ) .OR. iom_use( 'sophtadv' ) ) ) l_ptr = .TRUE.
[4499]	107	!
[7646]	108	!
[6140]	109	! ! horizontal fluxes are computed with the QUICKEST + ULTIMATE scheme
[12377]	110	CALL tra_adv_qck_i( kt, cdtype, p2dt, pU, Kbb, Kmm, pt, kjpt, Krhs )
	111	CALL tra_adv_qck_j( kt, cdtype, p2dt, pV, Kbb, Kmm, pt, kjpt, Krhs )
[1231]	112
[6140]	113	! ! vertical fluxes are computed with the 2nd order centered scheme
[12377]	114	CALL tra_adv_cen2_k( kt, cdtype, pW, Kmm, pt, kjpt, Krhs )
[1231]	115	!
	116	END SUBROUTINE tra_adv_qck
	117
	118
[12377]	119	SUBROUTINE tra_adv_qck_i( kt, cdtype, p2dt, pU, Kbb, Kmm, pt, kjpt, Krhs )
[1231]	120	!!----------------------------------------------------------------------
	121	!!
	122	!!----------------------------------------------------------------------
[12377]	123	INTEGER , INTENT(in ) :: kt ! ocean time-step index
	124	INTEGER , INTENT(in ) :: Kbb, Kmm, Krhs ! ocean time level indices
	125	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	126	INTEGER , INTENT(in ) :: kjpt ! number of tracers
	127	REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
	128	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pU ! i-velocity components
	129	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt,jpt), INTENT(inout) :: pt ! active tracers and RHS of tracer equation
[2528]	130	!!
[5836]	131	INTEGER :: ji, jj, jk, jn ! dummy loop indices
[6140]	132	REAL(wp) :: ztra, zbtr, zdir, zdx, zmsk ! local scalars
[9019]	133	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwx, zfu, zfc, zfd
[1231]	134	!----------------------------------------------------------------------
[2715]	135	!
[2528]	136	! ! ===========
	137	DO jn = 1, kjpt ! tracer loop
	138	! ! ===========
[5836]	139	zfu(:,:,:) = 0._wp ; zfc(:,:,:) = 0._wp
	140	zfd(:,:,:) = 0._wp ; zwx(:,:,:) = 0._wp
	141	!
	142	!!gm why not using a SHIFT instruction...
[12377]	143	DO_3D_00_00( 1, jpkm1 )
	144	zfc(ji,jj,jk) = pt(ji-1,jj,jk,jn,Kbb) ! Upstream in the x-direction for the tracer
	145	zfd(ji,jj,jk) = pt(ji+1,jj,jk,jn,Kbb) ! Downstream in the x-direction for the tracer
	146	END_3D
[13226]	147	CALL lbc_lnk_multi( 'traadv_qck', zfc(:,:,:), 'T', 1.0_wp , zfd(:,:,:), 'T', 1.0_wp ) ! Lateral boundary conditions
[2528]	148
[1231]	149	!
	150	! Horizontal advective fluxes
	151	! ---------------------------
[12377]	152	DO_3D_00_00( 1, jpkm1 )
[13226]	153	zdir = 0.5 + SIGN( 0.5_wp, pU(ji,jj,jk) ) ! if pU > 0 : zdir = 1 otherwise zdir = 0
[12377]	154	zfu(ji,jj,jk) = zdir * zfc(ji,jj,jk ) + ( 1. - zdir ) * zfd(ji+1,jj,jk) ! FU in the x-direction for T
	155	END_3D
[1231]	156	!
[12377]	157	DO_3D_00_00( 1, jpkm1 )
[13226]	158	zdir = 0.5 + SIGN( 0.5_wp, pU(ji,jj,jk) ) ! if pU > 0 : zdir = 1 otherwise zdir = 0
[12377]	159	zdx = ( zdir * e1t(ji,jj) + ( 1. - zdir ) * e1t(ji+1,jj) ) * e2u(ji,jj) * e3u(ji,jj,jk,Kmm)
	160	zwx(ji,jj,jk) = ABS( pU(ji,jj,jk) ) * p2dt / zdx ! (0<zc_cfl<1 : Courant number on x-direction)
	161	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
	162	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
	163	END_3D
[2528]	164	!--- Lateral boundary conditions
[13226]	165	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]	166
[1231]	167	!--- QUICKEST scheme
[2528]	168	CALL quickest( zfu, zfd, zfc, zwx )
[1231]	169	!
[2528]	170	! Mask at the T-points in the x-direction (mask=0 or mask=1)
[12377]	171	DO_3D_00_00( 1, jpkm1 )
	172	zfu(ji,jj,jk) = tmask(ji-1,jj,jk) + tmask(ji,jj,jk) + tmask(ji+1,jj,jk) - 2.
	173	END_3D
[13226]	174	CALL lbc_lnk( 'traadv_qck', zfu(:,:,:), 'T', 1.0_wp ) ! Lateral boundary conditions
[2528]	175
[1231]	176	!
[2528]	177	! Tracer flux on the x-direction
	178	DO jk = 1, jpkm1
	179	!
[12377]	180	DO_2D_00_00
[13226]	181	zdir = 0.5 + SIGN( 0.5_wp, pU(ji,jj,jk) ) ! if pU > 0 : zdir = 1 otherwise zdir = 0
[12377]	182	!--- If the second ustream point is a land point
	183	!--- the flux is computed by the 1st order UPWIND scheme
	184	zmsk = zdir * zfu(ji,jj,jk) + ( 1. - zdir ) * zfu(ji+1,jj,jk)
	185	zwx(ji,jj,jk) = zmsk * zwx(ji,jj,jk) + ( 1. - zmsk ) * zfc(ji,jj,jk)
	186	zwx(ji,jj,jk) = zwx(ji,jj,jk) * pU(ji,jj,jk)
	187	END_2D
[3300]	188	END DO
	189	!
[13226]	190	CALL lbc_lnk( 'traadv_qck', zwx(:,:,:), 'T', 1.0_wp ) ! Lateral boundary conditions
[3300]	191	!
	192	! Computation of the trend
[12377]	193	DO_3D_00_00( 1, jpkm1 )
	194	zbtr = r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm)
	195	! horizontal advective trends
	196	ztra = - zbtr * ( zwx(ji,jj,jk) - zwx(ji-1,jj,jk) )
	197	!--- add it to the general tracer trends
	198	pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) + ztra
	199	END_3D
[6140]	200	! ! trend diagnostics
[12377]	201	IF( l_trd ) CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_xad, zwx, pU, pt(:,:,:,jn,Kmm) )
[2528]	202	!
	203	END DO
	204	!
[1559]	205	END SUBROUTINE tra_adv_qck_i
[1231]	206
	207
[12377]	208	SUBROUTINE tra_adv_qck_j( kt, cdtype, p2dt, pV, Kbb, Kmm, pt, kjpt, Krhs )
[1231]	209	!!----------------------------------------------------------------------
	210	!!
	211	!!----------------------------------------------------------------------
[12377]	212	INTEGER , INTENT(in ) :: kt ! ocean time-step index
	213	INTEGER , INTENT(in ) :: Kbb, Kmm, Krhs ! ocean time level indices
	214	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	215	INTEGER , INTENT(in ) :: kjpt ! number of tracers
	216	REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
	217	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pV ! j-velocity components
	218	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt,jpt), INTENT(inout) :: pt ! active tracers and RHS of tracer equation
[1559]	219	!!
[9019]	220	INTEGER :: ji, jj, jk, jn ! dummy loop indices
[6140]	221	REAL(wp) :: ztra, zbtr, zdir, zdx, zmsk ! local scalars
[9019]	222	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwy, zfu, zfc, zfd ! 3D workspace
[1231]	223	!----------------------------------------------------------------------
[2715]	224	!
[2528]	225	! ! ===========
	226	DO jn = 1, kjpt ! tracer loop
	227	! ! ===========
	228	zfu(:,:,:) = 0.0 ; zfc(:,:,:) = 0.0
	229	zfd(:,:,:) = 0.0 ; zwy(:,:,:) = 0.0
	230	!
	231	DO jk = 1, jpkm1
	232	!
	233	!--- Computation of the ustream and downstream value of the tracer and the mask
[12377]	234	DO_2D_00_00
	235	! Upstream in the x-direction for the tracer
	236	zfc(ji,jj,jk) = pt(ji,jj-1,jk,jn,Kbb)
	237	! Downstream in the x-direction for the tracer
	238	zfd(ji,jj,jk) = pt(ji,jj+1,jk,jn,Kbb)
	239	END_2D
[1559]	240	END DO
[13226]	241	CALL lbc_lnk_multi( 'traadv_qck', zfc(:,:,:), 'T', 1.0_wp , zfd(:,:,:), 'T', 1.0_wp ) ! Lateral boundary conditions
[2528]	242
	243
[1231]	244	!
	245	! Horizontal advective fluxes
	246	! ---------------------------
	247	!
[12377]	248	DO_3D_00_00( 1, jpkm1 )
[13226]	249	zdir = 0.5 + SIGN( 0.5_wp, pV(ji,jj,jk) ) ! if pU > 0 : zdir = 1 otherwise zdir = 0
[12377]	250	zfu(ji,jj,jk) = zdir * zfc(ji,jj,jk ) + ( 1. - zdir ) * zfd(ji,jj+1,jk) ! FU in the x-direction for T
	251	END_3D
[1231]	252	!
[12377]	253	DO_3D_00_00( 1, jpkm1 )
[13226]	254	zdir = 0.5 + SIGN( 0.5_wp, pV(ji,jj,jk) ) ! if pU > 0 : zdir = 1 otherwise zdir = 0
[12377]	255	zdx = ( zdir * e2t(ji,jj) + ( 1. - zdir ) * e2t(ji,jj+1) ) * e1v(ji,jj) * e3v(ji,jj,jk,Kmm)
	256	zwy(ji,jj,jk) = ABS( pV(ji,jj,jk) ) * p2dt / zdx ! (0<zc_cfl<1 : Courant number on x-direction)
	257	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
	258	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
	259	END_3D
[2528]	260
	261	!--- Lateral boundary conditions
[13226]	262	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]	263
[1231]	264	!--- QUICKEST scheme
[2528]	265	CALL quickest( zfu, zfd, zfc, zwy )
[1231]	266	!
[2528]	267	! Mask at the T-points in the x-direction (mask=0 or mask=1)
[12377]	268	DO_3D_00_00( 1, jpkm1 )
	269	zfu(ji,jj,jk) = tmask(ji,jj-1,jk) + tmask(ji,jj,jk) + tmask(ji,jj+1,jk) - 2.
	270	END_3D
[13226]	271	CALL lbc_lnk( 'traadv_qck', zfu(:,:,:), 'T', 1.0_wp ) !--- Lateral boundary conditions
[2528]	272	!
	273	! Tracer flux on the x-direction
	274	DO jk = 1, jpkm1
	275	!
[12377]	276	DO_2D_00_00
[13226]	277	zdir = 0.5 + SIGN( 0.5_wp, pV(ji,jj,jk) ) ! if pU > 0 : zdir = 1 otherwise zdir = 0
[12377]	278	!--- If the second ustream point is a land point
	279	!--- the flux is computed by the 1st order UPWIND scheme
	280	zmsk = zdir * zfu(ji,jj,jk) + ( 1. - zdir ) * zfu(ji,jj+1,jk)
	281	zwy(ji,jj,jk) = zmsk * zwy(ji,jj,jk) + ( 1. - zmsk ) * zfc(ji,jj,jk)
	282	zwy(ji,jj,jk) = zwy(ji,jj,jk) * pV(ji,jj,jk)
	283	END_2D
[3300]	284	END DO
	285	!
[13226]	286	CALL lbc_lnk( 'traadv_qck', zwy(:,:,:), 'T', 1.0_wp ) ! Lateral boundary conditions
[3300]	287	!
	288	! Computation of the trend
[12377]	289	DO_3D_00_00( 1, jpkm1 )
	290	zbtr = r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm)
	291	! horizontal advective trends
	292	ztra = - zbtr * ( zwy(ji,jj,jk) - zwy(ji,jj-1,jk) )
	293	!--- add it to the general tracer trends
	294	pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) + ztra
	295	END_3D
[6140]	296	! ! trend diagnostics
[12377]	297	IF( l_trd ) CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_yad, zwy, pV, pt(:,:,:,jn,Kmm) )
[2528]	298	! ! "Poleward" heat and salt transports (contribution of upstream fluxes)
[9019]	299	IF( l_ptr ) CALL dia_ptr_hst( jn, 'adv', zwy(:,:,:) )
[2528]	300	!
	301	END DO
	302	!
[1559]	303	END SUBROUTINE tra_adv_qck_j
[1231]	304
	305
[12377]	306	SUBROUTINE tra_adv_cen2_k( kt, cdtype, pW, Kmm, pt, kjpt, Krhs )
[1231]	307	!!----------------------------------------------------------------------
	308	!!
	309	!!----------------------------------------------------------------------
[12377]	310	INTEGER , INTENT(in ) :: kt ! ocean time-step index
	311	INTEGER , INTENT(in ) :: Kmm, Krhs ! ocean time level indices
	312	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	313	INTEGER , INTENT(in ) :: kjpt ! number of tracers
	314	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pW ! vertical velocity
	315	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt,jpt), INTENT(inout) :: pt ! active tracers and RHS of tracer equation
[2715]	316	!
[2528]	317	INTEGER :: ji, jj, jk, jn ! dummy loop indices
[9019]	318	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwz ! 3D workspace
[1559]	319	!!----------------------------------------------------------------------
[4990]	320	!
[6140]	321	zwz(:,:, 1 ) = 0._wp ! surface & bottom values set to zero for all tracers
	322	zwz(:,:,jpk) = 0._wp
[5836]	323	!
[2528]	324	! ! ===========
	325	DO jn = 1, kjpt ! tracer loop
	326	! ! ===========
	327	!
[12377]	328	DO_3D_00_00( 2, jpkm1 )
	329	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)
	330	END_3D
[6140]	331	IF( ln_linssh ) THEN !* top value (only in linear free surf. as zwz is multiplied by wmask)
[5836]	332	IF( ln_isfcav ) THEN ! ice-shelf cavities (top of the ocean)
[12377]	333	DO_2D_11_11
	334	zwz(ji,jj, mikt(ji,jj) ) = pW(ji,jj,mikt(ji,jj)) * pt(ji,jj,mikt(ji,jj),jn,Kmm) ! linear free surface
	335	END_2D
[6140]	336	ELSE ! no ocean cavities (only ocean surface)
[12377]	337	zwz(:,:,1) = pW(:,:,1) * pt(:,:,1,jn,Kmm)
[5836]	338	ENDIF
	339	ENDIF
[2528]	340	!
[12377]	341	DO_3D_00_00( 1, jpkm1 )
	342	pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) - ( zwz(ji,jj,jk) - zwz(ji,jj,jk+1) ) &
	343	& * r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm)
	344	END_3D
[6140]	345	! ! Send trends for diagnostic
[12377]	346	IF( l_trd ) CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_zad, zwz, pW, pt(:,:,:,jn,Kmm) )
[2528]	347	!
[1231]	348	END DO
	349	!
[1559]	350	END SUBROUTINE tra_adv_cen2_k
[1231]	351
	352
[2528]	353	SUBROUTINE quickest( pfu, pfd, pfc, puc )
[1231]	354	!!----------------------------------------------------------------------
	355	!!
[2528]	356	!! ** Purpose : Computation of advective flux with Quickest scheme
	357	!!
	358	!! ** Method :
[1231]	359	!!----------------------------------------------------------------------
[2528]	360	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pfu ! second upwind point
	361	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pfd ! first douwning point
	362	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pfc ! the central point (or the first upwind point)
	363	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: puc ! input as Courant number ; output as flux
	364	!!
	365	INTEGER :: ji, jj, jk ! dummy loop indices
	366	REAL(wp) :: zcoef1, zcoef2, zcoef3 ! local scalars
	367	REAL(wp) :: zc, zcurv, zfho ! - -
	368	!----------------------------------------------------------------------
[3294]	369	!
[12377]	370	DO_3D_11_11( 1, jpkm1 )
	371	zc = puc(ji,jj,jk) ! Courant number
	372	zcurv = pfd(ji,jj,jk) + pfu(ji,jj,jk) - 2. * pfc(ji,jj,jk)
	373	zcoef1 = 0.5 * ( pfc(ji,jj,jk) + pfd(ji,jj,jk) )
	374	zcoef2 = 0.5 * zc * ( pfd(ji,jj,jk) - pfc(ji,jj,jk) )
	375	zcoef3 = ( 1. - ( zc * zc ) ) * r1_6 * zcurv
	376	zfho = zcoef1 - zcoef2 - zcoef3 ! phi_f QUICKEST
	377	!
	378	zcoef1 = pfd(ji,jj,jk) - pfu(ji,jj,jk)
	379	zcoef2 = ABS( zcoef1 )
	380	zcoef3 = ABS( zcurv )
	381	IF( zcoef3 >= zcoef2 ) THEN
	382	zfho = pfc(ji,jj,jk)
	383	ELSE
	384	zcoef3 = pfu(ji,jj,jk) + ( ( pfc(ji,jj,jk) - pfu(ji,jj,jk) ) / MAX( zc, 1.e-9 ) ) ! phi_REF
	385	IF( zcoef1 >= 0. ) THEN
	386	zfho = MAX( pfc(ji,jj,jk), zfho )
	387	zfho = MIN( zfho, MIN( zcoef3, pfd(ji,jj,jk) ) )
	388	ELSE
	389	zfho = MIN( pfc(ji,jj,jk), zfho )
	390	zfho = MAX( zfho, MAX( zcoef3, pfd(ji,jj,jk) ) )
	391	ENDIF
	392	ENDIF
	393	puc(ji,jj,jk) = zfho
	394	END_3D
[1231]	395	!
	396	END SUBROUTINE quickest
	397
	398	!!======================================================================
	399	END MODULE traadv_qck

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