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traadv_qck.F90 in NEMO/branches/2020/tickets_icb_1900/src/OCE/TRA – NEMO

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source: NEMO/branches/2020/tickets_icb_1900/src/OCE/TRA/traadv_qck.F90 @ 14012

Last change on this file since 14012 was 14012, checked in by mathiot, 4 years ago
ticket 1900: upgrade branch to 13991 before the next upgrade
Property svn:keywords set to `Id`
File size: 21.9 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
[14012]	93	! TEMP: [tiling] This can be A2D(nn_hls) if using XIOS (subdomain support)
	94	! NOTE: [tiling-comms-merge] These were changed to INTENT(inout) but they are not modified, so it is reverted
[12377]	95	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pU, pV, pW ! 3 ocean volume transport components
	96	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt,jpt), INTENT(inout) :: pt ! tracers and RHS of tracer equation
[1231]	97	!!----------------------------------------------------------------------
[3294]	98	!
[14012]	99	IF( ntile == 0 .OR. ntile == 1 ) THEN ! Do only on the first tile
	100	IF( kt == kit000 ) THEN
	101	IF(lwp) WRITE(numout,*)
	102	IF(lwp) WRITE(numout,*) 'tra_adv_qck : 3rd order quickest advection scheme on ', cdtype
	103	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~'
	104	IF(lwp) WRITE(numout,*)
	105	ENDIF
	106	!
	107	l_trd = .FALSE.
	108	l_ptr = .FALSE.
	109	IF( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. ( cdtype == 'TRC' .AND. l_trdtrc ) ) l_trd = .TRUE.
	110	IF( cdtype == 'TRA' .AND. ( iom_use( 'sophtadv' ) .OR. iom_use( 'sophtadv' ) ) ) l_ptr = .TRUE.
[1231]	111	ENDIF
[5836]	112	!
[6140]	113	! ! horizontal fluxes are computed with the QUICKEST + ULTIMATE scheme
[12377]	114	CALL tra_adv_qck_i( kt, cdtype, p2dt, pU, Kbb, Kmm, pt, kjpt, Krhs )
	115	CALL tra_adv_qck_j( kt, cdtype, p2dt, pV, Kbb, Kmm, pt, kjpt, Krhs )
[1231]	116
[6140]	117	! ! vertical fluxes are computed with the 2nd order centered scheme
[12377]	118	CALL tra_adv_cen2_k( kt, cdtype, pW, Kmm, pt, kjpt, Krhs )
[1231]	119	!
	120	END SUBROUTINE tra_adv_qck
	121
	122
[12377]	123	SUBROUTINE tra_adv_qck_i( kt, cdtype, p2dt, pU, Kbb, Kmm, pt, kjpt, Krhs )
[1231]	124	!!----------------------------------------------------------------------
	125	!!
	126	!!----------------------------------------------------------------------
[12377]	127	INTEGER , INTENT(in ) :: kt ! ocean time-step index
	128	INTEGER , INTENT(in ) :: Kbb, Kmm, Krhs ! ocean time level indices
	129	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	130	INTEGER , INTENT(in ) :: kjpt ! number of tracers
	131	REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
[14012]	132	! TEMP: [tiling] This can be A2D(nn_hls) if using XIOS (subdomain support)
[12377]	133	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pU ! i-velocity components
	134	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt,jpt), INTENT(inout) :: pt ! active tracers and RHS of tracer equation
[2528]	135	!!
[5836]	136	INTEGER :: ji, jj, jk, jn ! dummy loop indices
[6140]	137	REAL(wp) :: ztra, zbtr, zdir, zdx, zmsk ! local scalars
[14012]	138	REAL(wp), DIMENSION(A2D(nn_hls),jpk) :: zwx, zfu, zfc, zfd
[1231]	139	!----------------------------------------------------------------------
[2715]	140	!
[2528]	141	! ! ===========
	142	DO jn = 1, kjpt ! tracer loop
	143	! ! ===========
[5836]	144	zfu(:,:,:) = 0._wp ; zfc(:,:,:) = 0._wp
	145	zfd(:,:,:) = 0._wp ; zwx(:,:,:) = 0._wp
	146	!
	147	!!gm why not using a SHIFT instruction...
[14012]	148	DO_3D( 0, 0, nn_hls-1, nn_hls-1, 1, jpkm1 ) !--- Computation of the ustream and downstream value of the tracer and the mask
[12377]	149	zfc(ji,jj,jk) = pt(ji-1,jj,jk,jn,Kbb) ! Upstream in the x-direction for the tracer
	150	zfd(ji,jj,jk) = pt(ji+1,jj,jk,jn,Kbb) ! Downstream in the x-direction for the tracer
	151	END_3D
[14012]	152	IF (nn_hls.EQ.1) CALL lbc_lnk_multi( 'traadv_qck', zfc(:,:,:), 'T', 1.0_wp , zfd(:,:,:), 'T', 1.0_wp ) ! Lateral boundary conditions
[2528]	153
[1231]	154	!
	155	! Horizontal advective fluxes
	156	! ---------------------------
[14012]	157	DO_3D( 0, 0, nn_hls-1, 0, 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	zfu(ji,jj,jk) = zdir * zfc(ji,jj,jk ) + ( 1. - zdir ) * zfd(ji+1,jj,jk) ! FU in the x-direction for T
	160	END_3D
[1231]	161	!
[14012]	162	DO_3D( 0, 0, nn_hls-1, 0, 1, jpkm1 )
[13226]	163	zdir = 0.5 + SIGN( 0.5_wp, pU(ji,jj,jk) ) ! if pU > 0 : zdir = 1 otherwise zdir = 0
[12377]	164	zdx = ( zdir * e1t(ji,jj) + ( 1. - zdir ) * e1t(ji+1,jj) ) * e2u(ji,jj) * e3u(ji,jj,jk,Kmm)
	165	zwx(ji,jj,jk) = ABS( pU(ji,jj,jk) ) * p2dt / zdx ! (0<zc_cfl<1 : Courant number on x-direction)
	166	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
	167	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
	168	END_3D
[2528]	169	!--- Lateral boundary conditions
[14012]	170	IF (nn_hls.EQ.1) 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]	171
[1231]	172	!--- QUICKEST scheme
[2528]	173	CALL quickest( zfu, zfd, zfc, zwx )
[1231]	174	!
[2528]	175	! Mask at the T-points in the x-direction (mask=0 or mask=1)
[14012]	176	DO_3D( 0, 0, nn_hls-1, nn_hls-1, 1, jpkm1 )
[12377]	177	zfu(ji,jj,jk) = tmask(ji-1,jj,jk) + tmask(ji,jj,jk) + tmask(ji+1,jj,jk) - 2.
	178	END_3D
[14012]	179	IF (nn_hls.EQ.1) CALL lbc_lnk( 'traadv_qck', zfu(:,:,:), 'T', 1.0_wp ) ! Lateral boundary conditions
[2528]	180
[1231]	181	!
[2528]	182	! Tracer flux on the x-direction
[14012]	183	DO_3D( 0, 0, 1, 0, 1, jpkm1 )
	184	zdir = 0.5 + SIGN( 0.5_wp, pU(ji,jj,jk) ) ! if pU > 0 : zdir = 1 otherwise zdir = 0
	185	!--- If the second ustream point is a land point
	186	!--- the flux is computed by the 1st order UPWIND scheme
	187	zmsk = zdir * zfu(ji,jj,jk) + ( 1. - zdir ) * zfu(ji+1,jj,jk)
	188	zwx(ji,jj,jk) = zmsk * zwx(ji,jj,jk) + ( 1. - zmsk ) * zfc(ji,jj,jk)
	189	zwx(ji,jj,jk) = zwx(ji,jj,jk) * pU(ji,jj,jk)
	190	END_3D
[3300]	191	!
	192	! Computation of the trend
[13899]	193	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[12377]	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
[14012]	217	! TEMP: [tiling] This can be A2D(nn_hls) if using XIOS (subdomain support)
[12377]	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
[14012]	223	REAL(wp), DIMENSION(A2D(nn_hls),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
[14012]	235	DO_2D( nn_hls-1, nn_hls-1, 0, 0 )
[12377]	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
[14012]	242	IF (nn_hls.EQ.1) CALL lbc_lnk_multi( 'traadv_qck', zfc(:,:,:), 'T', 1.0_wp , zfd(:,:,:), 'T', 1.0_wp ) ! Lateral boundary conditions
[2528]	243
[1231]	244	!
	245	! Horizontal advective fluxes
	246	! ---------------------------
	247	!
[14012]	248	DO_3D( nn_hls-1, 0, 0, 0, 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	!
[14012]	253	DO_3D( nn_hls-1, 0, 0, 0, 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
[14012]	262	IF (nn_hls.EQ.1) 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)
[14012]	268	DO_3D( nn_hls-1, nn_hls-1, 0, 0, 1, jpkm1 )
[12377]	269	zfu(ji,jj,jk) = tmask(ji,jj-1,jk) + tmask(ji,jj,jk) + tmask(ji,jj+1,jk) - 2.
	270	END_3D
[14012]	271	IF (nn_hls.EQ.1) CALL lbc_lnk( 'traadv_qck', zfu(:,:,:), 'T', 1.0_wp ) !--- Lateral boundary conditions
[2528]	272	!
	273	! Tracer flux on the x-direction
[14012]	274	DO_3D( 1, 0, 0, 0, 1, jpkm1 )
	275	zdir = 0.5 + SIGN( 0.5_wp, pV(ji,jj,jk) ) ! if pU > 0 : zdir = 1 otherwise zdir = 0
	276	!--- If the second ustream point is a land point
	277	!--- the flux is computed by the 1st order UPWIND scheme
	278	zmsk = zdir * zfu(ji,jj,jk) + ( 1. - zdir ) * zfu(ji,jj+1,jk)
	279	zwy(ji,jj,jk) = zmsk * zwy(ji,jj,jk) + ( 1. - zmsk ) * zfc(ji,jj,jk)
	280	zwy(ji,jj,jk) = zwy(ji,jj,jk) * pV(ji,jj,jk)
	281	END_3D
[3300]	282	!
	283	! Computation of the trend
[13899]	284	DO_3D( 0, 0, 0, 0, 1, jpkm1 )
[12377]	285	zbtr = r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm)
	286	! horizontal advective trends
	287	ztra = - zbtr * ( zwy(ji,jj,jk) - zwy(ji,jj-1,jk) )
	288	!--- add it to the general tracer trends
	289	pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) + ztra
	290	END_3D
[6140]	291	! ! trend diagnostics
[12377]	292	IF( l_trd ) CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_yad, zwy, pV, pt(:,:,:,jn,Kmm) )
[2528]	293	! ! "Poleward" heat and salt transports (contribution of upstream fluxes)
[9019]	294	IF( l_ptr ) CALL dia_ptr_hst( jn, 'adv', zwy(:,:,:) )
[2528]	295	!
	296	END DO
	297	!
[1559]	298	END SUBROUTINE tra_adv_qck_j
[1231]	299
	300
[12377]	301	SUBROUTINE tra_adv_cen2_k( kt, cdtype, pW, Kmm, pt, kjpt, Krhs )
[1231]	302	!!----------------------------------------------------------------------
	303	!!
	304	!!----------------------------------------------------------------------
[12377]	305	INTEGER , INTENT(in ) :: kt ! ocean time-step index
	306	INTEGER , INTENT(in ) :: Kmm, Krhs ! ocean time level indices
	307	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	308	INTEGER , INTENT(in ) :: kjpt ! number of tracers
[14012]	309	! TEMP: [tiling] This can be A2D(nn_hls) if using XIOS (subdomain support)
	310	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pW ! vertical velocity
[12377]	311	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt,jpt), INTENT(inout) :: pt ! active tracers and RHS of tracer equation
[2715]	312	!
[2528]	313	INTEGER :: ji, jj, jk, jn ! dummy loop indices
[14012]	314	REAL(wp), DIMENSION(A2D(nn_hls),jpk) :: zwz ! 3D workspace
[1559]	315	!!----------------------------------------------------------------------
[4990]	316	!
[6140]	317	zwz(:,:, 1 ) = 0._wp ! surface & bottom values set to zero for all tracers
	318	zwz(:,:,jpk) = 0._wp
[5836]	319	!
[2528]	320	! ! ===========
	321	DO jn = 1, kjpt ! tracer loop
	322	! ! ===========
	323	!
[13899]	324	DO_3D( 0, 0, 0, 0, 2, jpkm1 ) !* Interior point (w-masked 2nd order centered flux)
[12377]	325	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)
	326	END_3D
[6140]	327	IF( ln_linssh ) THEN !* top value (only in linear free surf. as zwz is multiplied by wmask)
[5836]	328	IF( ln_isfcav ) THEN ! ice-shelf cavities (top of the ocean)
[14012]	329	DO_2D( 0, 0, 0, 0 )
[12377]	330	zwz(ji,jj, mikt(ji,jj) ) = pW(ji,jj,mikt(ji,jj)) * pt(ji,jj,mikt(ji,jj),jn,Kmm) ! linear free surface
	331	END_2D
[6140]	332	ELSE ! no ocean cavities (only ocean surface)
[14012]	333	DO_2D( 0, 0, 0, 0 )
	334	zwz(ji,jj,1) = pW(ji,jj,1) * pt(ji,jj,1,jn,Kmm)
	335	END_2D
[5836]	336	ENDIF
	337	ENDIF
[2528]	338	!
[13899]	339	DO_3D( 0, 0, 0, 0, 1, jpkm1 ) !== Tracer flux divergence added to the general trend ==!
[12377]	340	pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) - ( zwz(ji,jj,jk) - zwz(ji,jj,jk+1) ) &
	341	& * r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm)
	342	END_3D
[6140]	343	! ! Send trends for diagnostic
[12377]	344	IF( l_trd ) CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_zad, zwz, pW, pt(:,:,:,jn,Kmm) )
[2528]	345	!
[1231]	346	END DO
	347	!
[1559]	348	END SUBROUTINE tra_adv_cen2_k
[1231]	349
	350
[2528]	351	SUBROUTINE quickest( pfu, pfd, pfc, puc )
[1231]	352	!!----------------------------------------------------------------------
	353	!!
[2528]	354	!! ** Purpose : Computation of advective flux with Quickest scheme
	355	!!
	356	!! ** Method :
[1231]	357	!!----------------------------------------------------------------------
[14012]	358	REAL(wp), DIMENSION(A2D(nn_hls),jpk), INTENT(in ) :: pfu ! second upwind point
	359	REAL(wp), DIMENSION(A2D(nn_hls),jpk), INTENT(in ) :: pfd ! first douwning point
	360	REAL(wp), DIMENSION(A2D(nn_hls),jpk), INTENT(in ) :: pfc ! the central point (or the first upwind point)
	361	REAL(wp), DIMENSION(A2D(nn_hls),jpk), INTENT(inout) :: puc ! input as Courant number ; output as flux
[2528]	362	!!
	363	INTEGER :: ji, jj, jk ! dummy loop indices
	364	REAL(wp) :: zcoef1, zcoef2, zcoef3 ! local scalars
	365	REAL(wp) :: zc, zcurv, zfho ! - -
	366	!----------------------------------------------------------------------
[3294]	367	!
[14012]	368	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
[12377]	369	zc = puc(ji,jj,jk) ! Courant number
	370	zcurv = pfd(ji,jj,jk) + pfu(ji,jj,jk) - 2. * pfc(ji,jj,jk)
	371	zcoef1 = 0.5 * ( pfc(ji,jj,jk) + pfd(ji,jj,jk) )
	372	zcoef2 = 0.5 * zc * ( pfd(ji,jj,jk) - pfc(ji,jj,jk) )
	373	zcoef3 = ( 1. - ( zc * zc ) ) * r1_6 * zcurv
	374	zfho = zcoef1 - zcoef2 - zcoef3 ! phi_f QUICKEST
	375	!
	376	zcoef1 = pfd(ji,jj,jk) - pfu(ji,jj,jk)
	377	zcoef2 = ABS( zcoef1 )
	378	zcoef3 = ABS( zcurv )
	379	IF( zcoef3 >= zcoef2 ) THEN
	380	zfho = pfc(ji,jj,jk)
	381	ELSE
	382	zcoef3 = pfu(ji,jj,jk) + ( ( pfc(ji,jj,jk) - pfu(ji,jj,jk) ) / MAX( zc, 1.e-9 ) ) ! phi_REF
	383	IF( zcoef1 >= 0. ) THEN
	384	zfho = MAX( pfc(ji,jj,jk), zfho )
	385	zfho = MIN( zfho, MIN( zcoef3, pfd(ji,jj,jk) ) )
	386	ELSE
	387	zfho = MIN( pfc(ji,jj,jk), zfho )
	388	zfho = MAX( zfho, MAX( zcoef3, pfd(ji,jj,jk) ) )
	389	ENDIF
	390	ENDIF
	391	puc(ji,jj,jk) = zfho
	392	END_3D
[1231]	393	!
	394	END SUBROUTINE quickest
	395
	396	!!======================================================================
	397	END MODULE traadv_qck

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