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MODULE traadv_mus
!!======================================================================
!! *** MODULE traadv_mus ***
!! Ocean tracers: horizontal & vertical advective trend
!!======================================================================
!! History : ! 2000-06 (A.Estublier) for passive tracers
!! ! 2001-08 (E.Durand, G.Madec) adapted for T & S
!! NEMO 1.0 ! 2002-06 (G. Madec) F90: Free form and module
!! 3.2 ! 2010-05 (C. Ethe, G. Madec) merge TRC-TRA + switch from velocity to transport
!! 3.4 ! 2012-06 (P. Oddo, M. Vichi) include the upstream where needed
!! 3.7 ! 2015-09 (G. Madec) add the ice-shelf cavities boundary condition
!! 4.5 ! 2022-06 (S. Techene, G, Madec) refactorization to reduce local memory usage
!!----------------------------------------------------------------------
!!----------------------------------------------------------------------
!! tra_adv_mus : update the tracer trend with the horizontal
!! and vertical advection trends using MUSCL scheme
!!----------------------------------------------------------------------
USE oce ! ocean dynamics and active tracers
USE trc_oce ! share passive tracers/Ocean variables
USE dom_oce ! ocean space and time domain
USE trd_oce ! trends: ocean variables
USE trdtra ! tracers trends manager
USE sbcrnf ! river runoffs
USE diaptr ! poleward transport diagnostics
USE diaar5 ! AR5 diagnostics
!
USE iom ! XIOS library
USE in_out_manager ! I/O manager
USE lib_mpp ! distribued memory computing
USE lbclnk ! ocean lateral boundary condition (or mpp link)
USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined)
IMPLICIT NONE
PRIVATE
PUBLIC tra_adv_mus ! routine called by traadv.F90
PUBLIC tra_adv_mus_hls1 ! routine called by traadv.F90
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: upsmsk !: mixed upstream/centered scheme near some straits
! ! and in closed seas (orca 2 and 1 configurations)
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: xind !: mixed upstream/centered index
LOGICAL :: l_trd ! flag to compute trends
LOGICAL :: l_ptr ! flag to compute poleward transport
LOGICAL :: l_hst ! flag to compute heat/salt transport
!! * Substitutions
# include "do_loop_substitute.h90"
# include "domzgr_substitute.h90"
!!----------------------------------------------------------------------
!! NEMO/OCE 4.0 , NEMO Consortium (2018)
!! $Id: traadv_mus.F90 15512 2021-11-15 17:22:03Z techene $
!! Software governed by the CeCILL license (see ./LICENSE)
!!----------------------------------------------------------------------
CONTAINS
SUBROUTINE tra_adv_mus( kt, kit000, cdtype, p2dt, pU, pV, pW, &
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& Kbb, Kmm, pt, kjpt, Krhs, ld_msc_ups )
!!----------------------------------------------------------------------
!! *** ROUTINE tra_adv_mus ***
!!
!! ** Purpose : Compute the now trend due to total advection of tracers
!! using a MUSCL scheme (Monotone Upstream-centered Scheme for
!! Conservation Laws) and add it to the general tracer trend.
!!
!! ** Method : MUSCL scheme plus centered scheme at ocean boundaries
!! ld_msc_ups=T :
!!
!! ** Action : - update pt(:,:,:,:,Krhs) with the now advective tracer trends
!! - send trends to trdtra module for further diagnostcs (l_trdtra=T)
!! - poleward advective heat and salt transport (ln_diaptr=T)
!!
!! References : Estubier, A., and M. Levy, Notes Techn. Pole de Modelisation
!! IPSL, Sept. 2000 (http://www.lodyc.jussieu.fr/opa)
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: kt ! ocean time-step index
INTEGER , INTENT(in ) :: Kbb, Kmm, Krhs ! ocean time level indices
INTEGER , INTENT(in ) :: kit000 ! first time step index
CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
INTEGER , INTENT(in ) :: kjpt ! number of tracers
LOGICAL , INTENT(in ) :: ld_msc_ups ! use upstream scheme within muscl
REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
! TEMP: [tiling] This can be A2D(nn_hls) after all lbc_lnks removed in the nn_hls = 2 case in tra_adv_fct
REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pU, pV, pW ! 3 ocean volume flux components
REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt,jpt), INTENT(inout) :: pt ! tracers and RHS of tracer equation
!
INTEGER :: ji, jj, jk, jn ! dummy loop indices
INTEGER :: ierr ! local integer
INTEGER :: ik
REAL(wp) :: zu, z0u, zzslpx, zzwx, zw , zalpha ! local scalars
REAL(wp) :: zv, z0v, zzslpy, zzwy, z0w ! - -
REAL(wp) :: zdzt_kp2, zslpz_kp1, zfW_kp1
REAL(wp), DIMENSION(A2D(2)) :: zdxt, zslpx, zwx ! 2D workspace
REAL(wp), DIMENSION(A2D(2)) :: zdyt, zslpy, zwy ! - -
!!----------------------------------------------------------------------
!
IF( .NOT. l_istiled .OR. ntile == 1 ) THEN ! Do only on the first tile
IF( kt == kit000 ) THEN
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) 'tra_adv : MUSCL advection scheme on ', cdtype
IF(lwp) WRITE(numout,*) ' : mixed up-stream ', ld_msc_ups
IF(lwp) WRITE(numout,*) '~~~~~~~'
IF(lwp) WRITE(numout,*)
!
! Upstream / MUSCL scheme indicator
!
ALLOCATE( xind(jpi,jpj,jpk), STAT=ierr )
xind(:,:,:) = 1._wp ! set equal to 1 where up-stream is not needed
IF( ld_msc_ups ) THEN ! define the upstream indicator (if asked)
DO jk = 1, jpkm1
xind(:,:,jk) = 1._wp & ! =>1 where up-stream is not needed
& - rnfmsk(:,:) * rnfmsk_z(jk) * tmask(:,:,jk) ! =>0 near runoff mouths (& closed sea outflows)
END DO
ENDIF
!
ENDIF
!
l_trd = .FALSE.
l_hst = .FALSE.
l_ptr = .FALSE.
IF( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. ( cdtype == 'TRC' .AND. l_trdtrc ) ) l_trd = .TRUE.
IF( l_diaptr .AND. cdtype == 'TRA' .AND. ( iom_use( 'sophtadv' ) .OR. iom_use( 'sophtadv' ) ) ) l_ptr = .TRUE.
IF( l_iom .AND. cdtype == 'TRA' .AND. ( iom_use("uadv_heattr") .OR. iom_use("vadv_heattr") .OR. &
& iom_use("uadv_salttr") .OR. iom_use("vadv_salttr") ) ) l_hst = .TRUE.
ENDIF
!
!
DO jn = 1, kjpt !== loop over the tracers ==!
!
DO jk = 1, jpkm1
! !* Horizontal advective fluxes
!
! !-- first guess of the slopes
DO_2D( 2, 1, 2, 1 )
zdxt(ji,jj) = ( pt(ji+1,jj ,jk,jn,Kbb) - pt(ji,jj,jk,jn,Kbb) ) * umask(ji,jj,jk)
zdyt(ji,jj) = ( pt(ji ,jj+1,jk,jn,Kbb) - pt(ji,jj,jk,jn,Kbb) ) * vmask(ji,jj,jk)
END_2D
! !-- Slopes of tracer
DO_2D( 1, 1, 1, 1 )
! ! 1/2 Slopes at T-point (set to 0 if adjectent slopes are of opposite sign)
zzslpx = ( zdxt(ji,jj) + zdxt(ji-1,jj ) ) &
& * ( 0.25_wp + SIGN( 0.25_wp, zdxt(ji,jj) * zdxt(ji-1,jj ) ) )
zzslpy = ( zdyt(ji,jj) + zdyt(ji ,jj-1) ) &
& * ( 0.25_wp + SIGN( 0.25_wp, zdyt(ji,jj) * zdyt(ji ,jj-1) ) )
! ! Slopes limitation
zslpx(ji,jj) = SIGN( 1.0_wp, zzslpx ) * MIN( ABS( zzslpx ), &
& 2._wp*ABS( zdxt (ji-1,jj) ), &
& 2._wp*ABS( zdxt (ji ,jj) ) )
zslpy(ji,jj) = SIGN( 1.0_wp, zzslpy ) * MIN( ABS( zzslpy ), &
& 2._wp*ABS( zdyt (ji,jj-1) ), &
& 2._wp*ABS( zdyt (ji,jj ) ) )
END_2D
!!gm + !!st ticket ? comparaison pommes et carrottes ABS(zzslpx) et 2._wp*ABS( zdxt (ji-1,jj) )
!
DO_2D( 1, 0, 1, 0 ) !-- MUSCL horizontal advective fluxes
z0u = SIGN( 0.5_wp, pU(ji,jj,jk) )
zalpha = 0.5_wp - z0u
zu = z0u - 0.5_wp * pU(ji,jj,jk) * p2dt * r1_e1e2u(ji,jj) / e3u(ji,jj,jk,Kmm)
zzwx = pt(ji+1,jj,jk,jn,Kbb) + xind(ji,jj,jk) * zu * zslpx(ji+1,jj)
zzwy = pt(ji ,jj,jk,jn,Kbb) + xind(ji,jj,jk) * zu * zslpx(ji ,jj)
zwx(ji,jj) = pU(ji,jj,jk) * ( zalpha * zzwx + (1._wp-zalpha) * zzwy )
!
z0v = SIGN( 0.5_wp, pV(ji,jj,jk) )
zalpha = 0.5_wp - z0v
zv = z0v - 0.5_wp * pV(ji,jj,jk) * p2dt * r1_e1e2v(ji,jj) / e3v(ji,jj,jk,Kmm)
zzwx = pt(ji,jj+1,jk,jn,Kbb) + xind(ji,jj,jk) * zv * zslpy(ji,jj+1)
zzwy = pt(ji,jj ,jk,jn,Kbb) + xind(ji,jj,jk) * zv * zslpy(ji,jj )
zwy(ji,jj) = pV(ji,jj,jk) * ( zalpha * zzwx + (1._wp-zalpha) * zzwy )
END_2D
!
DO_2D( 0, 0, 0, 0 ) !-- Tracer advective trend
pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) - ( zwx(ji,jj) - zwx(ji-1,jj ) &
& + zwy(ji,jj) - zwy(ji ,jj-1) ) &
& * r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm)
END_2D
END DO
!!gm + !!st to be done with the whole rewritting of trd
!! trd routine arguments MUST be changed adding jk and zwx, zwy in 2D
!!
!! ! ! trend diagnostics
!! IF( l_trd ) THEN
!! CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jk, jptra_xad, zwx(:,:), pU, pt(:,:,:,jn,Kbb) )
!! CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jk, jptra_yad, zwy(:,:), pV, pt(:,:,:,jn,Kbb) )
!! END IF
!! ! ! "Poleward" heat and salt transports
!! IF( l_ptr ) CALL dia_ptr_hst( jn, jk, 'adv', zwy(:,:) )
!! ! ! heat transport
!! IF( l_hst ) CALL dia_ar5_hst( jn, jk, 'adv', zwx(:,:), zwy(:,:) )
!
! !* Vertical advective fluxes
!
#define zdzt_kp1 zdxt
#define zslpz zslpx
#define zfW zwx
zfW (A2D(0)) = 0._wp ! anciennement zwx at jk = 1
! ! anciennement zwx at jk = 2
DO_2D( 0, 0, 0, 0 )
zdzt_kp1(ji,jj) = tmask(ji,jj,2) * ( pt(ji,jj,1,jn,Kbb) - pt(ji,jj,2,jn,Kbb) )
END_2D
zslpz (A2D(0)) = 0._wp ! anciennement zslpx at jk = 1
!
IF( ln_linssh ) THEN !-- linear ssh : non zero top values
DO_2D( 0, 0, 0, 0 ) ! at the ocean surface
zfW(ji,jj) = pW(ji,jj,1) * pt(ji,jj,1,jn,Kbb) ! surface flux
END_2D
IF( ln_isfcav ) THEN ! ice-shelf cavities (top of the ocean)
DO_2D( 0, 0, 0, 0 ) ! update pt(Krhs) under the ice-shelf
ik = mikt(ji,jj) ! the flux at ik-1 is zero ( inside ice-shelf )
IF( ik > 1 ) THEN
pt(ji,jj,ik,jn,Krhs) = pt(ji,jj,ik,jn,Krhs) - pW(ji,jj,ik) * pt(ji,jj,ik,jn,Kbb) &
& * r1_e1e2t(ji,jj) / e3t(ji,jj,ik,Kmm)
ENDIF
END_2D
ENDIF
ENDIF
!
! wmask usage for computing zw and zwk is needed in isf case and linear ssh
!
!
DO jk = 1, jpkm1
IF( jk < jpkm1 ) THEN
DO_2D( 0, 0, 0, 0 )
! !-- Slopes of tracer
! ! masked vertical gradient at jk+2
zdzt_kp2 = ( pt(ji,jj,jk+1,jn,Kbb) - pt(ji,jj,jk+2,jn,Kbb) ) * tmask(ji,jj,jk+2) !!st wmask(ji,jj,jk+2)
! ! vertical slope at jk+1
zslpz_kp1 = ( zdzt_kp1(ji,jj) + zdzt_kp2 ) &
& * ( 0.25_wp + SIGN( 0.25_wp, zdzt_kp1(ji,jj) * zdzt_kp2 ) )
! ! slope limitation
zslpz_kp1 = SIGN( 1.0_wp, zslpz_kp1 ) * MIN( ABS( zslpz_kp1 ), &
& 2.*ABS( zdzt_kp2 ), &
& 2.*ABS( zdzt_kp1(ji,jj) ) )
! !-- vertical advective flux at jk+1
! ! caution: zfW_kp1 is masked for ice-shelf cavities
! ! since top fluxes already added to pt(Krhs) before the vertical loop
z0w = SIGN( 0.5_wp, pW(ji,jj,jk+1) )
zalpha = 0.5_wp + z0w
zw = z0w - 0.5_wp * pW(ji,jj,jk+1) * p2dt * r1_e1e2t(ji,jj) / e3w(ji,jj,jk+1,Kmm)
zzwx = pt(ji,jj,jk+1,jn,Kbb) + xind(ji,jj,jk) * zw * zslpz_kp1
zzwy = pt(ji,jj,jk ,jn,Kbb) + xind(ji,jj,jk) * zw * zslpz(ji,jj)
zfW_kp1 = pW(ji,jj,jk+1) * ( zalpha * zzwx + (1.-zalpha) * zzwy ) * wmask(ji,jj,jk)!!st * wmask(ji,jj,jk+1)
! !-- vertical advective trend at jk
pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) - ( zfW(ji,jj) - zfW_kp1 ) &
& * r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm)
! ! updates for next level
zdzt_kp1(ji,jj) = zdzt_kp2
zslpz (ji,jj) = zslpz_kp1
zfW (ji,jj) = zfW_kp1
END_2D
ELSE
DO_2D( 0, 0, 0, 0 ) !-- vertical advective trend at jpkm1
pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) - zfW(ji,jj) &
& * r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm)
END_2D
ENDIF
END DO ! end of jk loop
!
!!gm + !!st idem see above
!! ! ! send trends for diagnostic
!! IF( l_trd ) CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_zad, zwx, pW, pt(:,:,:,jn,Kbb) )
!
END DO ! end of tracer loop
!
END SUBROUTINE tra_adv_mus
SUBROUTINE tra_adv_mus_hls1( kt, kit000, cdtype, p2dt, pU, pV, pW, &
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& Kbb, Kmm, pt, kjpt, Krhs, ld_msc_ups )
!!----------------------------------------------------------------------
!! *** ROUTINE tra_adv_mus ***
!!
!! ** Purpose : Compute the now trend due to total advection of tracers
!! using a MUSCL scheme (Monotone Upstream-centered Scheme for
!! Conservation Laws) and add it to the general tracer trend.
!!
!! ** Method : MUSCL scheme plus centered scheme at ocean boundaries
!! ld_msc_ups=T :
!!
!! ** Action : - update pt(:,:,:,:,Krhs) with the now advective tracer trends
!! - send trends to trdtra module for further diagnostcs (l_trdtra=T)
!! - poleward advective heat and salt transport (ln_diaptr=T)
!!
!! References : Estubier, A., and M. Levy, Notes Techn. Pole de Modelisation
!! IPSL, Sept. 2000 (http://www.lodyc.jussieu.fr/opa)
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: kt ! ocean time-step index
INTEGER , INTENT(in ) :: Kbb, Kmm, Krhs ! ocean time level indices
INTEGER , INTENT(in ) :: kit000 ! first time step index
CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
INTEGER , INTENT(in ) :: kjpt ! number of tracers
LOGICAL , INTENT(in ) :: ld_msc_ups ! use upstream scheme within muscl
REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
! TEMP: [tiling] This can be A2D(nn_hls) after all lbc_lnks removed in the nn_hls = 2 case in tra_adv_fct
REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pU, pV, pW ! 3 ocean volume flux components
REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt,jpt), INTENT(inout) :: pt ! tracers and RHS of tracer equation
!
INTEGER :: ji, jj, jk, jn ! dummy loop indices
INTEGER :: ierr ! local integer
REAL(wp) :: zu, z0u, zzwx, zw , zalpha ! local scalars
REAL(wp) :: zv, z0v, zzwy, z0w ! - -
REAL(wp), DIMENSION(A2D(nn_hls),jpk) :: zwx, zslpx ! 3D workspace
REAL(wp), DIMENSION(A2D(nn_hls),jpk) :: zwy, zslpy ! - -
!!----------------------------------------------------------------------
!
IF( .NOT. l_istiled .OR. ntile == 1 ) THEN ! Do only on the first tile
IF( kt == kit000 ) THEN
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) 'tra_adv : MUSCL advection scheme on ', cdtype
IF(lwp) WRITE(numout,*) ' : mixed up-stream ', ld_msc_ups
IF(lwp) WRITE(numout,*) '~~~~~~~'
IF(lwp) WRITE(numout,*)
!
! Upstream / MUSCL scheme indicator
!
ALLOCATE( xind(jpi,jpj,jpk), STAT=ierr )
xind(:,:,:) = 1._wp ! set equal to 1 where up-stream is not needed
!
IF( ld_msc_ups ) THEN ! define the upstream indicator (if asked)
ALLOCATE( upsmsk(jpi,jpj), STAT=ierr )
upsmsk(:,:) = 0._wp ! not upstream by default
!
DO jk = 1, jpkm1
xind(:,:,jk) = 1._wp & ! =>1 where up-stream is not needed
& - MAX ( rnfmsk(:,:) * rnfmsk_z(jk), & ! =>0 near runoff mouths (& closed sea outflows)
& upsmsk(:,:) ) * tmask(:,:,jk) ! =>0 in some user defined area
END DO
ENDIF
!
ENDIF
!
l_trd = .FALSE.
l_hst = .FALSE.
l_ptr = .FALSE.
IF( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. ( cdtype == 'TRC' .AND. l_trdtrc ) ) l_trd = .TRUE.
IF( l_diaptr .AND. cdtype == 'TRA' .AND. ( iom_use( 'sophtadv' ) .OR. iom_use( 'sophtadv' ) ) ) l_ptr = .TRUE.
IF( l_iom .AND. cdtype == 'TRA' .AND. ( iom_use("uadv_heattr") .OR. iom_use("vadv_heattr") .OR. &
& iom_use("uadv_salttr") .OR. iom_use("vadv_salttr") ) ) l_hst = .TRUE.
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ENDIF
!
DO jn = 1, kjpt !== loop over the tracers ==!
!
! !* Horizontal advective fluxes
!
! !-- first guess of the slopes
zwx(:,:,jpk) = 0._wp ! bottom values
zwy(:,:,jpk) = 0._wp
DO_3D( nn_hls, nn_hls-1, nn_hls, nn_hls-1, 1, jpkm1 )
zwx(ji,jj,jk) = umask(ji,jj,jk) * ( pt(ji+1,jj,jk,jn,Kbb) - pt(ji,jj,jk,jn,Kbb) )
zwy(ji,jj,jk) = vmask(ji,jj,jk) * ( pt(ji,jj+1,jk,jn,Kbb) - pt(ji,jj,jk,jn,Kbb) )
END_3D
! !-- Slopes of tracer
zslpx(:,:,jpk) = 0._wp ! bottom values
zslpy(:,:,jpk) = 0._wp
DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 1, jpkm1 )
zslpx(ji,jj,jk) = ( zwx(ji,jj,jk) + zwx(ji-1,jj ,jk) ) &
& * ( 0.25 + SIGN( 0.25_wp, zwx(ji,jj,jk) * zwx(ji-1,jj ,jk) ) )
zslpy(ji,jj,jk) = ( zwy(ji,jj,jk) + zwy(ji ,jj-1,jk) ) &
& * ( 0.25 + SIGN( 0.25_wp, zwy(ji,jj,jk) * zwy(ji ,jj-1,jk) ) )
END_3D
!
DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 1, jpkm1 ) !-- Slopes limitation
zslpx(ji,jj,jk) = SIGN( 1.0_wp, zslpx(ji,jj,jk) ) * MIN( ABS( zslpx(ji ,jj,jk) ), &
& 2.*ABS( zwx (ji-1,jj,jk) ), &
& 2.*ABS( zwx (ji ,jj,jk) ) )
zslpy(ji,jj,jk) = SIGN( 1.0_wp, zslpy(ji,jj,jk) ) * MIN( ABS( zslpy(ji,jj ,jk) ), &
& 2.*ABS( zwy (ji,jj-1,jk) ), &
& 2.*ABS( zwy (ji,jj ,jk) ) )
END_3D
! NOTE [ comm_cleanup ] : need to change sign to ensure halo 1 - halo 2 compatibility
IF ( nn_hls==1 ) CALL lbc_lnk( 'traadv_mus', zslpx, 'T', -1.0_wp , zslpy, 'T', -1.0_wp ) ! lateral boundary conditions (changed sign)
!
DO_3D( 1, 0, 1, 0, 1, jpkm1 ) !-- MUSCL horizontal advective fluxes
! MUSCL fluxes
z0u = SIGN( 0.5_wp, pU(ji,jj,jk) )
zalpha = 0.5 - z0u
zu = z0u - 0.5 * pU(ji,jj,jk) * p2dt * r1_e1e2u(ji,jj) / e3u(ji,jj,jk,Kmm)
zzwx = pt(ji+1,jj,jk,jn,Kbb) + xind(ji,jj,jk) * zu * zslpx(ji+1,jj,jk)
zzwy = pt(ji ,jj,jk,jn,Kbb) + xind(ji,jj,jk) * zu * zslpx(ji ,jj,jk)
zwx(ji,jj,jk) = pU(ji,jj,jk) * ( zalpha * zzwx + (1.-zalpha) * zzwy )
!
z0v = SIGN( 0.5_wp, pV(ji,jj,jk) )
zalpha = 0.5 - z0v
zv = z0v - 0.5 * pV(ji,jj,jk) * p2dt * r1_e1e2v(ji,jj) / e3v(ji,jj,jk,Kmm)
zzwx = pt(ji,jj+1,jk,jn,Kbb) + xind(ji,jj,jk) * zv * zslpy(ji,jj+1,jk)
zzwy = pt(ji,jj ,jk,jn,Kbb) + xind(ji,jj,jk) * zv * zslpy(ji,jj ,jk)
zwy(ji,jj,jk) = pV(ji,jj,jk) * ( zalpha * zzwx + (1.-zalpha) * zzwy )
END_3D
!
DO_3D( 0, 0, 0, 0, 1, jpkm1 ) !-- Tracer advective trend
pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) &
& + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) ) &
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& * r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm)
END_3D
! ! trend diagnostics
IF( l_trd ) THEN
CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_xad, zwx, pU, pt(:,:,:,jn,Kbb) )
CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_yad, zwy, pV, pt(:,:,:,jn,Kbb) )
END IF
! ! "Poleward" heat and salt transports
IF( l_ptr ) CALL dia_ptr_hst( jn, 'adv', zwy(:,:,:) )
! ! heat transport
IF( l_hst ) CALL dia_ar5_hst( jn, 'adv', zwx(:,:,:), zwy(:,:,:) )
!
! !* Vertical advective fluxes
!
! !-- first guess of the slopes
zwx(:,:, 1 ) = 0._wp ! surface & bottom boundary conditions
zwx(:,:,jpk) = 0._wp
DO_3D( 0, 0, 0, 0, 2, jpkm1 ) ! interior values
zwx(ji,jj,jk) = tmask(ji,jj,jk) * ( pt(ji,jj,jk-1,jn,Kbb) - pt(ji,jj,jk,jn,Kbb) )
END_3D
! !-- Slopes of tracer
zslpx(:,:,1) = 0._wp ! surface values
DO_3D( 0, 0, 0, 0, 2, jpkm1 )
zslpx(ji,jj,jk) = ( zwx(ji,jj,jk) + zwx(ji,jj,jk+1) ) &
& * ( 0.25 + SIGN( 0.25_wp, zwx(ji,jj,jk) * zwx(ji,jj,jk+1) ) )
END_3D
DO_3D( 0, 0, 0, 0, 2, jpkm1 ) !-- Slopes limitation
zslpx(ji,jj,jk) = SIGN( 1.0_wp, zslpx(ji,jj,jk) ) * MIN( ABS( zslpx(ji,jj,jk ) ), &
& 2.*ABS( zwx (ji,jj,jk+1) ), &
& 2.*ABS( zwx (ji,jj,jk ) ) )
END_3D
DO_3D( 0, 0, 0, 0, 1, jpk-2 ) !-- vertical advective flux
z0w = SIGN( 0.5_wp, pW(ji,jj,jk+1) )
zalpha = 0.5 + z0w
zw = z0w - 0.5 * pW(ji,jj,jk+1) * p2dt * r1_e1e2t(ji,jj) / e3w(ji,jj,jk+1,Kmm)
zzwx = pt(ji,jj,jk+1,jn,Kbb) + xind(ji,jj,jk) * zw * zslpx(ji,jj,jk+1)
zzwy = pt(ji,jj,jk ,jn,Kbb) + xind(ji,jj,jk) * zw * zslpx(ji,jj,jk )
zwx(ji,jj,jk+1) = pW(ji,jj,jk+1) * ( zalpha * zzwx + (1.-zalpha) * zzwy ) * wmask(ji,jj,jk)
END_3D
IF( ln_linssh ) THEN ! top values, linear free surface only
IF( ln_isfcav ) THEN ! ice-shelf cavities (top of the ocean)
DO_2D( 0, 0, 0, 0 )
zwx(ji,jj, mikt(ji,jj) ) = pW(ji,jj,mikt(ji,jj)) * pt(ji,jj,mikt(ji,jj),jn,Kbb)
END_2D
ELSE ! no cavities: only at the ocean surface
DO_2D( 0, 0, 0, 0 )
zwx(ji,jj,1) = pW(ji,jj,1) * pt(ji,jj,1,jn,Kbb)
END_2D
ENDIF
ENDIF
!
DO_3D( 0, 0, 0, 0, 1, jpkm1 ) !-- vertical advective trend
pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) - ( zwx(ji,jj,jk) - zwx(ji,jj,jk+1) ) &
& * r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm)
END_3D
! ! send trends for diagnostic
IF( l_trd ) CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_zad, zwx, pW, pt(:,:,:,jn,Kbb) )
!
END DO ! end of tracer loop
!
END SUBROUTINE tra_adv_mus_hls1
!!======================================================================
END MODULE traadv_mus