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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 @ 11989

Last change on this file since 11989 was 11989, checked in by cetlod, 4 years ago
cmip6 diag : finalisation of CMIP6 diags implementation
Property svn:keywords set to `Id`
File size: 23.2 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
[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
[11989]	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
	42	# include "vectopt_loop_substitute.h90"
	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
[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	!!
[6140]	81	!! ** Action : - update pta with the now advective tracer trends
	82	!! - send trends to trdtra module for further diagnostcs (l_trdtra=T)
[11989]	83	!! - poleward advective heat and salt transport (ln_diaptr=T)
[1231]	84	!!
	85	!! ** Reference : Leonard (1979, 1991)
	86	!!----------------------------------------------------------------------
[2528]	87	INTEGER , INTENT(in ) :: kt ! ocean time-step index
[3294]	88	INTEGER , INTENT(in ) :: kit000 ! first time step index
[2528]	89	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	90	INTEGER , INTENT(in ) :: kjpt ! number of tracers
[6140]	91	REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
[2528]	92	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pun, pvn, pwn ! 3 ocean velocity components
	93	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb, ptn ! before and now tracer fields
	94	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend
[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.
[11989]	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
[2528]	111	CALL tra_adv_qck_i( kt, cdtype, p2dt, pun, ptb, ptn, pta, kjpt )
	112	CALL tra_adv_qck_j( kt, cdtype, p2dt, pvn, ptb, ptn, pta, kjpt )
[1231]	113
[6140]	114	! ! vertical fluxes are computed with the 2nd order centered scheme
[2528]	115	CALL tra_adv_cen2_k( kt, cdtype, pwn, ptn, pta, kjpt )
[1231]	116	!
	117	END SUBROUTINE tra_adv_qck
	118
	119
[2528]	120	SUBROUTINE tra_adv_qck_i( kt, cdtype, p2dt, pun, &
	121	& ptb, ptn, pta, kjpt )
[1231]	122	!!----------------------------------------------------------------------
	123	!!
	124	!!----------------------------------------------------------------------
[2715]	125	INTEGER , INTENT(in ) :: kt ! ocean time-step index
	126	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	127	INTEGER , INTENT(in ) :: kjpt ! number of tracers
[6140]	128	REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
[2715]	129	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pun ! i-velocity components
	130	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb, ptn ! before and now tracer fields
	131	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend
[2528]	132	!!
[5836]	133	INTEGER :: ji, jj, jk, jn ! dummy loop indices
[6140]	134	REAL(wp) :: ztra, zbtr, zdir, zdx, zmsk ! local scalars
[9019]	135	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwx, zfu, zfc, zfd
[1231]	136	!----------------------------------------------------------------------
[2715]	137	!
[2528]	138	! ! ===========
	139	DO jn = 1, kjpt ! tracer loop
	140	! ! ===========
[5836]	141	zfu(:,:,:) = 0._wp ; zfc(:,:,:) = 0._wp
	142	zfd(:,:,:) = 0._wp ; zwx(:,:,:) = 0._wp
	143	!
	144	!!gm why not using a SHIFT instruction...
	145	DO jk = 1, jpkm1 !--- Computation of the ustream and downstream value of the tracer and the mask
[2528]	146	DO jj = 2, jpjm1
	147	DO ji = fs_2, fs_jpim1 ! vector opt.
[5836]	148	zfc(ji,jj,jk) = ptb(ji-1,jj,jk,jn) ! Upstream in the x-direction for the tracer
	149	zfd(ji,jj,jk) = ptb(ji+1,jj,jk,jn) ! Downstream in the x-direction for the tracer
[2528]	150	END DO
[1559]	151	END DO
	152	END DO
[10425]	153	CALL lbc_lnk_multi( 'traadv_qck', zfc(:,:,:), 'T', 1. , zfd(:,:,:), 'T', 1. ) ! Lateral boundary conditions
[2528]	154
[1231]	155	!
	156	! Horizontal advective fluxes
	157	! ---------------------------
[2528]	158	DO jk = 1, jpkm1
	159	DO jj = 2, jpjm1
	160	DO ji = fs_2, fs_jpim1 ! vector opt.
	161	zdir = 0.5 + SIGN( 0.5, pun(ji,jj,jk) ) ! if pun > 0 : zdir = 1 otherwise zdir = 0
	162	zfu(ji,jj,jk) = zdir * zfc(ji,jj,jk ) + ( 1. - zdir ) * zfd(ji+1,jj,jk) ! FU in the x-direction for T
	163	END DO
	164	END DO
[1559]	165	END DO
[1231]	166	!
[2528]	167	DO jk = 1, jpkm1
	168	DO jj = 2, jpjm1
	169	DO ji = fs_2, fs_jpim1 ! vector opt.
	170	zdir = 0.5 + SIGN( 0.5, pun(ji,jj,jk) ) ! if pun > 0 : zdir = 1 otherwise zdir = 0
[6140]	171	zdx = ( zdir * e1t(ji,jj) + ( 1. - zdir ) * e1t(ji+1,jj) ) * e2u(ji,jj) * e3u_n(ji,jj,jk)
	172	zwx(ji,jj,jk) = ABS( pun(ji,jj,jk) ) * p2dt / zdx ! (0<zc_cfl<1 : Courant number on x-direction)
[2528]	173	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
	174	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
	175	END DO
	176	END DO
	177	END DO
	178	!--- Lateral boundary conditions
[10425]	179	CALL lbc_lnk_multi( 'traadv_qck', zfu(:,:,:), 'T', 1. , zfd(:,:,:), 'T', 1., zfc(:,:,:), 'T', 1., zwx(:,:,:), 'T', 1. )
[2528]	180
[1231]	181	!--- QUICKEST scheme
[2528]	182	CALL quickest( zfu, zfd, zfc, zwx )
[1231]	183	!
[2528]	184	! Mask at the T-points in the x-direction (mask=0 or mask=1)
	185	DO jk = 1, jpkm1
	186	DO jj = 2, jpjm1
	187	DO ji = fs_2, fs_jpim1 ! vector opt.
	188	zfu(ji,jj,jk) = tmask(ji-1,jj,jk) + tmask(ji,jj,jk) + tmask(ji+1,jj,jk) - 2.
[2715]	189	END DO
[1231]	190	END DO
	191	END DO
[10425]	192	CALL lbc_lnk( 'traadv_qck', zfu(:,:,:), 'T', 1. ) ! Lateral boundary conditions
[2528]	193
[1231]	194	!
[2528]	195	! Tracer flux on the x-direction
	196	DO jk = 1, jpkm1
	197	!
[1231]	198	DO jj = 2, jpjm1
[2528]	199	DO ji = fs_2, fs_jpim1 ! vector opt.
	200	zdir = 0.5 + SIGN( 0.5, pun(ji,jj,jk) ) ! if pun > 0 : zdir = 1 otherwise zdir = 0
	201	!--- If the second ustream point is a land point
	202	!--- the flux is computed by the 1st order UPWIND scheme
	203	zmsk = zdir * zfu(ji,jj,jk) + ( 1. - zdir ) * zfu(ji+1,jj,jk)
	204	zwx(ji,jj,jk) = zmsk * zwx(ji,jj,jk) + ( 1. - zmsk ) * zfc(ji,jj,jk)
	205	zwx(ji,jj,jk) = zwx(ji,jj,jk) * pun(ji,jj,jk)
[1231]	206	END DO
	207	END DO
[3300]	208	END DO
	209	!
[10425]	210	CALL lbc_lnk( 'traadv_qck', zwx(:,:,:), 'T', 1. ) ! Lateral boundary conditions
[3300]	211	!
	212	! Computation of the trend
	213	DO jk = 1, jpkm1
[2528]	214	DO jj = 2, jpjm1
	215	DO ji = fs_2, fs_jpim1 ! vector opt.
[6140]	216	zbtr = r1_e1e2t(ji,jj) / e3t_n(ji,jj,jk)
[2528]	217	! horizontal advective trends
	218	ztra = - zbtr * ( zwx(ji,jj,jk) - zwx(ji-1,jj,jk) )
	219	!--- add it to the general tracer trends
	220	pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra
	221	END DO
	222	END DO
[1231]	223	END DO
[6140]	224	! ! trend diagnostics
[9019]	225	IF( l_trd ) CALL trd_tra( kt, cdtype, jn, jptra_xad, zwx, pun, ptn(:,:,:,jn) )
[2528]	226	!
	227	END DO
	228	!
[1559]	229	END SUBROUTINE tra_adv_qck_i
[1231]	230
	231
[2528]	232	SUBROUTINE tra_adv_qck_j( kt, cdtype, p2dt, pvn, &
	233	& ptb, ptn, pta, kjpt )
[1231]	234	!!----------------------------------------------------------------------
	235	!!
	236	!!----------------------------------------------------------------------
[2715]	237	INTEGER , INTENT(in ) :: kt ! ocean time-step index
	238	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	239	INTEGER , INTENT(in ) :: kjpt ! number of tracers
[6140]	240	REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
[2715]	241	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pvn ! j-velocity components
	242	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb, ptn ! before and now tracer fields
	243	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend
[1559]	244	!!
[9019]	245	INTEGER :: ji, jj, jk, jn ! dummy loop indices
[6140]	246	REAL(wp) :: ztra, zbtr, zdir, zdx, zmsk ! local scalars
[9019]	247	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwy, zfu, zfc, zfd ! 3D workspace
[1231]	248	!----------------------------------------------------------------------
[2715]	249	!
[2528]	250	! ! ===========
	251	DO jn = 1, kjpt ! tracer loop
	252	! ! ===========
	253	zfu(:,:,:) = 0.0 ; zfc(:,:,:) = 0.0
	254	zfd(:,:,:) = 0.0 ; zwy(:,:,:) = 0.0
	255	!
	256	DO jk = 1, jpkm1
	257	!
	258	!--- Computation of the ustream and downstream value of the tracer and the mask
	259	DO jj = 2, jpjm1
	260	DO ji = fs_2, fs_jpim1 ! vector opt.
	261	! Upstream in the x-direction for the tracer
	262	zfc(ji,jj,jk) = ptb(ji,jj-1,jk,jn)
	263	! Downstream in the x-direction for the tracer
	264	zfd(ji,jj,jk) = ptb(ji,jj+1,jk,jn)
	265	END DO
[1559]	266	END DO
	267	END DO
[10425]	268	CALL lbc_lnk_multi( 'traadv_qck', zfc(:,:,:), 'T', 1. , zfd(:,:,:), 'T', 1. ) ! Lateral boundary conditions
[2528]	269
	270
[1231]	271	!
	272	! Horizontal advective fluxes
	273	! ---------------------------
	274	!
[2528]	275	DO jk = 1, jpkm1
	276	DO jj = 2, jpjm1
	277	DO ji = fs_2, fs_jpim1 ! vector opt.
	278	zdir = 0.5 + SIGN( 0.5, pvn(ji,jj,jk) ) ! if pun > 0 : zdir = 1 otherwise zdir = 0
	279	zfu(ji,jj,jk) = zdir * zfc(ji,jj,jk ) + ( 1. - zdir ) * zfd(ji,jj+1,jk) ! FU in the x-direction for T
	280	END DO
[1559]	281	END DO
	282	END DO
[1231]	283	!
[2528]	284	DO jk = 1, jpkm1
	285	DO jj = 2, jpjm1
	286	DO ji = fs_2, fs_jpim1 ! vector opt.
	287	zdir = 0.5 + SIGN( 0.5, pvn(ji,jj,jk) ) ! if pun > 0 : zdir = 1 otherwise zdir = 0
[6140]	288	zdx = ( zdir * e2t(ji,jj) + ( 1. - zdir ) * e2t(ji,jj+1) ) * e1v(ji,jj) * e3v_n(ji,jj,jk)
	289	zwy(ji,jj,jk) = ABS( pvn(ji,jj,jk) ) * p2dt / zdx ! (0<zc_cfl<1 : Courant number on x-direction)
[2528]	290	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
	291	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
	292	END DO
	293	END DO
	294	END DO
	295
	296	!--- Lateral boundary conditions
[10425]	297	CALL lbc_lnk_multi( 'traadv_qck', zfu(:,:,:), 'T', 1. , zfd(:,:,:), 'T', 1., zfc(:,:,:), 'T', 1., zwy(:,:,:), 'T', 1. )
[2528]	298
[1231]	299	!--- QUICKEST scheme
[2528]	300	CALL quickest( zfu, zfd, zfc, zwy )
[1231]	301	!
[2528]	302	! Mask at the T-points in the x-direction (mask=0 or mask=1)
	303	DO jk = 1, jpkm1
	304	DO jj = 2, jpjm1
	305	DO ji = fs_2, fs_jpim1 ! vector opt.
	306	zfu(ji,jj,jk) = tmask(ji,jj-1,jk) + tmask(ji,jj,jk) + tmask(ji,jj+1,jk) - 2.
	307	END DO
[1231]	308	END DO
	309	END DO
[10425]	310	CALL lbc_lnk( 'traadv_qck', zfu(:,:,:), 'T', 1. ) !--- Lateral boundary conditions
[2528]	311	!
	312	! Tracer flux on the x-direction
	313	DO jk = 1, jpkm1
	314	!
[1231]	315	DO jj = 2, jpjm1
[2528]	316	DO ji = fs_2, fs_jpim1 ! vector opt.
	317	zdir = 0.5 + SIGN( 0.5, pvn(ji,jj,jk) ) ! if pun > 0 : zdir = 1 otherwise zdir = 0
	318	!--- If the second ustream point is a land point
	319	!--- the flux is computed by the 1st order UPWIND scheme
	320	zmsk = zdir * zfu(ji,jj,jk) + ( 1. - zdir ) * zfu(ji,jj+1,jk)
	321	zwy(ji,jj,jk) = zmsk * zwy(ji,jj,jk) + ( 1. - zmsk ) * zfc(ji,jj,jk)
	322	zwy(ji,jj,jk) = zwy(ji,jj,jk) * pvn(ji,jj,jk)
[1231]	323	END DO
	324	END DO
[3300]	325	END DO
	326	!
[10425]	327	CALL lbc_lnk( 'traadv_qck', zwy(:,:,:), 'T', 1. ) ! Lateral boundary conditions
[3300]	328	!
	329	! Computation of the trend
	330	DO jk = 1, jpkm1
[2528]	331	DO jj = 2, jpjm1
	332	DO ji = fs_2, fs_jpim1 ! vector opt.
[6140]	333	zbtr = r1_e1e2t(ji,jj) / e3t_n(ji,jj,jk)
[2528]	334	! horizontal advective trends
	335	ztra = - zbtr * ( zwy(ji,jj,jk) - zwy(ji,jj-1,jk) )
	336	!--- add it to the general tracer trends
	337	pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra
[1231]	338	END DO
	339	END DO
[2528]	340	END DO
[6140]	341	! ! trend diagnostics
[9019]	342	IF( l_trd ) CALL trd_tra( kt, cdtype, jn, jptra_yad, zwy, pvn, ptn(:,:,:,jn) )
[2528]	343	! ! "Poleward" heat and salt transports (contribution of upstream fluxes)
[9019]	344	IF( l_ptr ) CALL dia_ptr_hst( jn, 'adv', zwy(:,:,:) )
[2528]	345	!
	346	END DO
	347	!
[1559]	348	END SUBROUTINE tra_adv_qck_j
[1231]	349
	350
[2528]	351	SUBROUTINE tra_adv_cen2_k( kt, cdtype, pwn, &
	352	& ptn, pta, kjpt )
[1231]	353	!!----------------------------------------------------------------------
	354	!!
	355	!!----------------------------------------------------------------------
[2715]	356	INTEGER , INTENT(in ) :: kt ! ocean time-step index
	357	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	358	INTEGER , INTENT(in ) :: kjpt ! number of tracers
	359	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pwn ! vertical velocity
	360	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptn ! before and now tracer fields
	361	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend
	362	!
[2528]	363	INTEGER :: ji, jj, jk, jn ! dummy loop indices
[9019]	364	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwz ! 3D workspace
[1559]	365	!!----------------------------------------------------------------------
[4990]	366	!
[6140]	367	zwz(:,:, 1 ) = 0._wp ! surface & bottom values set to zero for all tracers
	368	zwz(:,:,jpk) = 0._wp
[5836]	369	!
[2528]	370	! ! ===========
	371	DO jn = 1, kjpt ! tracer loop
	372	! ! ===========
	373	!
[5836]	374	DO jk = 2, jpkm1 !* Interior point (w-masked 2nd order centered flux)
[2528]	375	DO jj = 2, jpjm1
	376	DO ji = fs_2, fs_jpim1 ! vector opt.
[5836]	377	zwz(ji,jj,jk) = 0.5 * pwn(ji,jj,jk) * ( ptn(ji,jj,jk-1,jn) + ptn(ji,jj,jk,jn) ) * wmask(ji,jj,jk)
[2528]	378	END DO
[1231]	379	END DO
	380	END DO
[6140]	381	IF( ln_linssh ) THEN !* top value (only in linear free surf. as zwz is multiplied by wmask)
[5836]	382	IF( ln_isfcav ) THEN ! ice-shelf cavities (top of the ocean)
	383	DO jj = 1, jpj
	384	DO ji = 1, jpi
	385	zwz(ji,jj, mikt(ji,jj) ) = pwn(ji,jj,mikt(ji,jj)) * ptn(ji,jj,mikt(ji,jj),jn) ! linear free surface
	386	END DO
	387	END DO
[6140]	388	ELSE ! no ocean cavities (only ocean surface)
[5836]	389	zwz(:,:,1) = pwn(:,:,1) * ptn(:,:,1,jn)
	390	ENDIF
	391	ENDIF
[2528]	392	!
	393	DO jk = 1, jpkm1 !== Tracer flux divergence added to the general trend ==!
	394	DO jj = 2, jpjm1
	395	DO ji = fs_2, fs_jpim1 ! vector opt.
[5836]	396	pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) - ( zwz(ji,jj,jk) - zwz(ji,jj,jk+1) ) &
[6140]	397	& * r1_e1e2t(ji,jj) / e3t_n(ji,jj,jk)
[2528]	398	END DO
[1231]	399	END DO
	400	END DO
[6140]	401	! ! Send trends for diagnostic
[4990]	402	IF( l_trd ) CALL trd_tra( kt, cdtype, jn, jptra_zad, zwz, pwn, ptn(:,:,:,jn) )
[2528]	403	!
[1231]	404	END DO
	405	!
[1559]	406	END SUBROUTINE tra_adv_cen2_k
[1231]	407
	408
[2528]	409	SUBROUTINE quickest( pfu, pfd, pfc, puc )
[1231]	410	!!----------------------------------------------------------------------
	411	!!
[2528]	412	!! ** Purpose : Computation of advective flux with Quickest scheme
	413	!!
	414	!! ** Method :
[1231]	415	!!----------------------------------------------------------------------
[2528]	416	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pfu ! second upwind point
	417	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pfd ! first douwning point
	418	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pfc ! the central point (or the first upwind point)
	419	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: puc ! input as Courant number ; output as flux
	420	!!
	421	INTEGER :: ji, jj, jk ! dummy loop indices
	422	REAL(wp) :: zcoef1, zcoef2, zcoef3 ! local scalars
	423	REAL(wp) :: zc, zcurv, zfho ! - -
	424	!----------------------------------------------------------------------
[3294]	425	!
[2528]	426	DO jk = 1, jpkm1
	427	DO jj = 1, jpj
	428	DO ji = 1, jpi
	429	zc = puc(ji,jj,jk) ! Courant number
	430	zcurv = pfd(ji,jj,jk) + pfu(ji,jj,jk) - 2. * pfc(ji,jj,jk)
	431	zcoef1 = 0.5 * ( pfc(ji,jj,jk) + pfd(ji,jj,jk) )
	432	zcoef2 = 0.5 * zc * ( pfd(ji,jj,jk) - pfc(ji,jj,jk) )
	433	zcoef3 = ( 1. - ( zc * zc ) ) * r1_6 * zcurv
	434	zfho = zcoef1 - zcoef2 - zcoef3 ! phi_f QUICKEST
	435	!
	436	zcoef1 = pfd(ji,jj,jk) - pfu(ji,jj,jk)
	437	zcoef2 = ABS( zcoef1 )
	438	zcoef3 = ABS( zcurv )
	439	IF( zcoef3 >= zcoef2 ) THEN
	440	zfho = pfc(ji,jj,jk)
	441	ELSE
	442	zcoef3 = pfu(ji,jj,jk) + ( ( pfc(ji,jj,jk) - pfu(ji,jj,jk) ) / MAX( zc, 1.e-9 ) ) ! phi_REF
	443	IF( zcoef1 >= 0. ) THEN
	444	zfho = MAX( pfc(ji,jj,jk), zfho )
	445	zfho = MIN( zfho, MIN( zcoef3, pfd(ji,jj,jk) ) )
	446	ELSE
	447	zfho = MIN( pfc(ji,jj,jk), zfho )
	448	zfho = MAX( zfho, MAX( zcoef3, pfd(ji,jj,jk) ) )
	449	ENDIF
	450	ENDIF
	451	puc(ji,jj,jk) = zfho
	452	END DO
	453	END DO
	454	END DO
[1231]	455	!
	456	END SUBROUTINE quickest
	457
	458	!!======================================================================
	459	END MODULE traadv_qck

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