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MODULE traadv_fct
!!==============================================================================
!! *** MODULE traadv_fct ***
!! Ocean tracers: horizontal & vertical advective trend (2nd/4th order Flux Corrected Transport method)
!!==============================================================================
!! History : 3.7 ! 2015-09 (L. Debreu, G. Madec) original code (inspired from traadv_tvd.F90)
!!----------------------------------------------------------------------
!!----------------------------------------------------------------------
!! tra_adv_fct : update the tracer trend with a 3D advective trends using a 2nd or 4th order FCT scheme
!! with sub-time-stepping in the vertical direction
!! nonosc : compute monotonic tracer fluxes by a non-oscillatory algorithm
!! interp_4th_cpt : 4th order compact scheme for the vertical component of the advection
!!----------------------------------------------------------------------
USE oce ! ocean dynamics and active tracers
USE dom_oce ! ocean space and time domain
USE trc_oce ! share passive tracers/Ocean variables
USE trd_oce ! trends: ocean variables
USE trdtra ! tracers trends
USE diaptr ! poleward transport diagnostics
USE diaar5 ! AR5 diagnostics
USE phycst , ONLY : rho0_rcp
USE zdf_oce , ONLY : ln_zad_Aimp
!
USE in_out_manager ! I/O manager
USE iom !
USE lib_mpp ! MPP library
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_fct ! called by traadv.F90
PUBLIC interp_4th_cpt ! called by traadv_cen.F90
LOGICAL :: l_trd ! flag to compute trends
LOGICAL :: l_ptr ! flag to compute poleward transport
LOGICAL :: l_hst ! flag to compute heat/salt transport
REAL(wp) :: r1_6 = 1._wp / 6._wp ! =1/6
! ! tridiag solver associated indices:
INTEGER, PARAMETER :: np_NH = 0 ! Neumann homogeneous boundary condition
INTEGER, PARAMETER :: np_CEN2 = 1 ! 2nd order centered boundary condition
!! * Substitutions
# include "do_loop_substitute.h90"
# include "domzgr_substitute.h90"
!!----------------------------------------------------------------------
!! NEMO/OCE 4.0 , NEMO Consortium (2018)
!! $Id: traadv_fct.F90 14857 2021-05-12 16:47:25Z hadcv $
!! Software governed by the CeCILL license (see ./LICENSE)
!!----------------------------------------------------------------------
CONTAINS
SUBROUTINE tra_adv_fct( kt, kit000, cdtype, p2dt, pU, pV, pW, &
& Kbb, Kmm, pt, kjpt, Krhs, kn_fct_h, kn_fct_v )
!!----------------------------------------------------------------------
!! *** ROUTINE tra_adv_fct ***
!!
!! ** Purpose : Compute the now trend due to total advection of tracers
!! and add it to the general trend of tracer equations
!!
!! ** Method : - 2nd or 4th FCT scheme on the horizontal direction
!! (choice through the value of kn_fct)
!! - on the vertical the 4th order is a compact scheme
!! - corrected flux (monotonic correction)
!!
!! ** Action : - update pt(:,:,:,:,Krhs) with the now advective tracer trends
!! - send trends to trdtra module for further diagnostics (l_trdtra=T)
!! - poleward advective heat and salt transport (ln_diaptr=T)
!!----------------------------------------------------------------------
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
INTEGER , INTENT(in ) :: kn_fct_h ! order of the FCT scheme (=2 or 4)
INTEGER , INTENT(in ) :: kn_fct_v ! order of the FCT scheme (=2 or 4)
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
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
REAL(wp) :: ztra ! local scalar
REAL(wp) :: zfp_ui, zfp_vj, zfp_wk, zC2t_u, zC4t_u ! - -
REAL(wp) :: zfm_ui, zfm_vj, zfm_wk, zC2t_v, zC4t_v ! - -
REAL(wp), DIMENSION(A2D(nn_hls),jpk) :: zwi, zwx, zwy, zwz, ztu, ztv, zltu, zltv, ztw
REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ztrdx, ztrdy, ztrdz, zptry
REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: zwinf, zwdia, zwsup
LOGICAL :: ll_zAimp ! flag to apply adaptive implicit vertical advection
!!----------------------------------------------------------------------
!
#if defined key_loop_fusion
CALL tra_adv_fct_lf ( kt, nit000, cdtype, p2dt, pU, pV, pW, Kbb, Kmm, pt, kjpt, Krhs, kn_fct_h, kn_fct_v )
#else
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_fct : FCT advection scheme on ', cdtype
IF(lwp) WRITE(numout,*) '~~~~~~~~~~~'
ENDIF
!
l_trd = .FALSE. ! set local switches
l_hst = .FALSE.
l_ptr = .FALSE.
ll_zAimp = .FALSE.
IF( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. ( cdtype =='TRC' .AND. l_trdtrc ) ) l_trd = .TRUE.
IF( cdtype == 'TRA' .AND. ( iom_use( 'sophtadv' ) .OR. iom_use( 'sophtadv' ) ) ) l_ptr = .TRUE.
IF( 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
!! -- init to 0
zwi(:,:,:) = 0._wp
zwx(:,:,:) = 0._wp
zwy(:,:,:) = 0._wp
zwz(:,:,:) = 0._wp
ztu(:,:,:) = 0._wp
ztv(:,:,:) = 0._wp
zltu(:,:,:) = 0._wp
zltv(:,:,:) = 0._wp
ztw(:,:,:) = 0._wp
!
IF( l_trd .OR. l_hst ) THEN
ALLOCATE( ztrdx(A2D(nn_hls),jpk), ztrdy(A2D(nn_hls),jpk), ztrdz(A2D(nn_hls),jpk) )
ztrdx(:,:,:) = 0._wp ; ztrdy(:,:,:) = 0._wp ; ztrdz(:,:,:) = 0._wp
ENDIF
!
IF( l_ptr ) THEN
ALLOCATE( zptry(A2D(nn_hls),jpk) )
zptry(:,:,:) = 0._wp
ENDIF
!
! If adaptive vertical advection, check if it is needed on this PE at this time
IF( ln_zad_Aimp ) THEN
IF( MAXVAL( ABS( wi(A2D(1),:) ) ) > 0._wp ) ll_zAimp = .TRUE.
END IF
! If active adaptive vertical advection, build tridiagonal matrix
IF( ll_zAimp ) THEN
ALLOCATE(zwdia(A2D(nn_hls),jpk), zwinf(A2D(nn_hls),jpk), zwsup(A2D(nn_hls),jpk))
DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 1, jpkm1 )
zwdia(ji,jj,jk) = 1._wp + p2dt * ( MAX( wi(ji,jj,jk) , 0._wp ) - MIN( wi(ji,jj,jk+1) , 0._wp ) ) &
& / e3t(ji,jj,jk,Krhs)
zwinf(ji,jj,jk) = p2dt * MIN( wi(ji,jj,jk ) , 0._wp ) / e3t(ji,jj,jk,Krhs)
zwsup(ji,jj,jk) = -p2dt * MAX( wi(ji,jj,jk+1) , 0._wp ) / e3t(ji,jj,jk,Krhs)
END_3D
END IF
!
DO jn = 1, kjpt !== loop over the tracers ==!
!
! !== upstream advection with initial mass fluxes & intermediate update ==!
! !* upstream tracer flux in the i and j direction
DO_3D( nn_hls, nn_hls-1, nn_hls, nn_hls-1, 1, jpkm1 )
! upstream scheme
zfp_ui = pU(ji,jj,jk) + ABS( pU(ji,jj,jk) )
zfm_ui = pU(ji,jj,jk) - ABS( pU(ji,jj,jk) )
zfp_vj = pV(ji,jj,jk) + ABS( pV(ji,jj,jk) )
zfm_vj = pV(ji,jj,jk) - ABS( pV(ji,jj,jk) )
zwx(ji,jj,jk) = 0.5 * ( zfp_ui * pt(ji,jj,jk,jn,Kbb) + zfm_ui * pt(ji+1,jj ,jk,jn,Kbb) )
zwy(ji,jj,jk) = 0.5 * ( zfp_vj * pt(ji,jj,jk,jn,Kbb) + zfm_vj * pt(ji ,jj+1,jk,jn,Kbb) )
END_3D
! !* upstream tracer flux in the k direction *!
DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, jpkm1 ) ! Interior value ( multiplied by wmask)
zfp_wk = pW(ji,jj,jk) + ABS( pW(ji,jj,jk) )
zfm_wk = pW(ji,jj,jk) - ABS( pW(ji,jj,jk) )
zwz(ji,jj,jk) = 0.5 * ( zfp_wk * pt(ji,jj,jk,jn,Kbb) + zfm_wk * pt(ji,jj,jk-1,jn,Kbb) ) * wmask(ji,jj,jk)
END_3D
IF( ln_linssh ) THEN ! top ocean value (only in linear free surface as zwz has been w-masked)
IF( ln_isfcav ) THEN ! top of the ice-shelf cavities and at the ocean surface
DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
zwz(ji,jj, mikt(ji,jj) ) = pW(ji,jj,mikt(ji,jj)) * pt(ji,jj,mikt(ji,jj),jn,Kbb) ! linear free surface
END_2D
ELSE ! no cavities: only at the ocean surface
DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
zwz(ji,jj,1) = pW(ji,jj,1) * pt(ji,jj,1,jn,Kbb)
END_2D
ENDIF
ENDIF
!
DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 1, jpkm1 ) !* trend and after field with monotonic scheme
! ! total intermediate advective trends
ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) &
& + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) &
& + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj)
! ! update and guess with monotonic sheme
pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) + ztra &
& / e3t(ji,jj,jk,Kmm ) * tmask(ji,jj,jk)
zwi(ji,jj,jk) = ( e3t(ji,jj,jk,Kbb) * pt(ji,jj,jk,jn,Kbb) + p2dt * ztra ) &
& / e3t(ji,jj,jk,Krhs) * tmask(ji,jj,jk)
END_3D
IF ( ll_zAimp ) THEN
CALL tridia_solver( zwdia, zwsup, zwinf, zwi, zwi , 0 )
!
ztw(:,:,1) = 0._wp ; ztw(:,:,jpk) = 0._wp ;
DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, jpkm1 ) ! Interior value ( multiplied by wmask)
zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) )
zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) )
ztw(ji,jj,jk) = 0.5 * e1e2t(ji,jj) * ( zfp_wk * zwi(ji,jj,jk) + zfm_wk * zwi(ji,jj,jk-1) ) * wmask(ji,jj,jk)
zwz(ji,jj,jk) = zwz(ji,jj,jk) + ztw(ji,jj,jk) ! update vertical fluxes
END_3D
DO_3D( 0, 0, 0, 0, 1, jpkm1 )
pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) - ( ztw(ji,jj,jk) - ztw(ji ,jj ,jk+1) ) &
& * r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm)
END_3D
!
END IF
!
IF( l_trd .OR. l_hst ) THEN ! trend diagnostics (contribution of upstream fluxes)
ztrdx(:,:,:) = zwx(:,:,:) ; ztrdy(:,:,:) = zwy(:,:,:) ; ztrdz(:,:,:) = zwz(:,:,:)
END IF
! ! "Poleward" heat and salt transports (contribution of upstream fluxes)
IF( l_ptr ) zptry(:,:,:) = zwy(:,:,:)
!
! !== anti-diffusive flux : high order minus low order ==!
!
SELECT CASE( kn_fct_h ) !* horizontal anti-diffusive fluxes
!
CASE( 2 ) !- 2nd order centered
DO_3D( nn_hls, nn_hls-1, nn_hls, nn_hls-1, 1, jpkm1 )
zwx(ji,jj,jk) = 0.5_wp * pU(ji,jj,jk) * ( pt(ji,jj,jk,jn,Kmm) + pt(ji+1,jj,jk,jn,Kmm) ) - zwx(ji,jj,jk)
zwy(ji,jj,jk) = 0.5_wp * pV(ji,jj,jk) * ( pt(ji,jj,jk,jn,Kmm) + pt(ji,jj+1,jk,jn,Kmm) ) - zwy(ji,jj,jk)
END_3D
!
CASE( 4 ) !- 4th order centered
zltu(:,:,jpk) = 0._wp ! Bottom value : flux set to zero
zltv(:,:,jpk) = 0._wp
DO jk = 1, jpkm1 ! Laplacian
DO_2D( 1, 0, 1, 0 ) ! 1st derivative (gradient)
ztu(ji,jj,jk) = ( pt(ji+1,jj ,jk,jn,Kmm) - pt(ji,jj,jk,jn,Kmm) ) * umask(ji,jj,jk)
ztv(ji,jj,jk) = ( pt(ji ,jj+1,jk,jn,Kmm) - pt(ji,jj,jk,jn,Kmm) ) * vmask(ji,jj,jk)
END_2D
DO_2D( 0, 0, 0, 0 ) ! 2nd derivative * 1/ 6
zltu(ji,jj,jk) = ( ztu(ji,jj,jk) + ztu(ji-1,jj,jk) ) * r1_6
zltv(ji,jj,jk) = ( ztv(ji,jj,jk) + ztv(ji,jj-1,jk) ) * r1_6
END_2D
END DO
! NOTE [ comm_cleanup ] : need to change sign to ensure halo 1 - halo 2 compatibility
CALL lbc_lnk( 'traadv_fct', zltu, 'T', -1.0_wp , zltv, 'T', -1.0_wp, ld4only= .TRUE. ) ! Lateral boundary cond. (unchanged sgn)
!
DO_3D( nn_hls, nn_hls-1, nn_hls, nn_hls-1, 1, jpkm1 )
zC2t_u = pt(ji,jj,jk,jn,Kmm) + pt(ji+1,jj ,jk,jn,Kmm) ! 2 x C2 interpolation of T at u- & v-points
zC2t_v = pt(ji,jj,jk,jn,Kmm) + pt(ji ,jj+1,jk,jn,Kmm)
! ! C4 minus upstream advective fluxes
! round brackets added to fix the order of floating point operations
! needed to ensure halo 1 - halo 2 compatibility
zwx(ji,jj,jk) = 0.5_wp * pU(ji,jj,jk) * ( zC2t_u + ( zltu(ji,jj,jk) - zltu(ji+1,jj,jk) &
& ) & ! bracket for halo 1 - halo 2 compatibility
& ) - zwx(ji,jj,jk)
zwy(ji,jj,jk) = 0.5_wp * pV(ji,jj,jk) * ( zC2t_v + ( zltv(ji,jj,jk) - zltv(ji,jj+1,jk) &
& ) & ! bracket for halo 1 - halo 2 compatibility
& ) - zwy(ji,jj,jk)
END_3D
!
CASE( 41 ) !- 4th order centered ==>> !!gm coding attempt need to be tested
ztu(:,:,jpk) = 0._wp ! Bottom value : flux set to zero
ztv(:,:,jpk) = 0._wp
DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 1, jpkm1 ) ! 1st derivative (gradient)
ztu(ji,jj,jk) = ( pt(ji+1,jj ,jk,jn,Kmm) - pt(ji,jj,jk,jn,Kmm) ) * umask(ji,jj,jk)
ztv(ji,jj,jk) = ( pt(ji ,jj+1,jk,jn,Kmm) - pt(ji,jj,jk,jn,Kmm) ) * vmask(ji,jj,jk)
END_3D
IF (nn_hls==1) CALL lbc_lnk( 'traadv_fct', ztu, 'U', -1.0_wp , ztv, 'V', -1.0_wp, ld4only= .TRUE. ) ! Lateral boundary cond. (unchanged sgn)
!
DO_3D( 0, 0, 0, 0, 1, jpkm1 ) ! Horizontal advective fluxes
zC2t_u = pt(ji,jj,jk,jn,Kmm) + pt(ji+1,jj ,jk,jn,Kmm) ! 2 x C2 interpolation of T at u- & v-points (x2)
zC2t_v = pt(ji,jj,jk,jn,Kmm) + pt(ji ,jj+1,jk,jn,Kmm)
! ! C4 interpolation of T at u- & v-points (x2)
zC4t_u = zC2t_u + r1_6 * ( ztu(ji-1,jj ,jk) - ztu(ji+1,jj ,jk) )
zC4t_v = zC2t_v + r1_6 * ( ztv(ji ,jj-1,jk) - ztv(ji ,jj+1,jk) )
! ! C4 minus upstream advective fluxes
zwx(ji,jj,jk) = 0.5_wp * pU(ji,jj,jk) * zC4t_u - zwx(ji,jj,jk)
zwy(ji,jj,jk) = 0.5_wp * pV(ji,jj,jk) * zC4t_v - zwy(ji,jj,jk)
END_3D
IF (nn_hls==2) CALL lbc_lnk( 'traadv_fct', zwx, 'U', -1.0_wp , zwy, 'V', -1.0_wp ) ! Lateral boundary cond. (unchanged sgn)
!
END SELECT
!
SELECT CASE( kn_fct_v ) !* vertical anti-diffusive fluxes (w-masked interior values)
!
CASE( 2 ) !- 2nd order centered
DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, jpkm1 )
zwz(ji,jj,jk) = ( pW(ji,jj,jk) * 0.5_wp * ( pt(ji,jj,jk,jn,Kmm) + pt(ji,jj,jk-1,jn,Kmm) ) &
& - zwz(ji,jj,jk) ) * wmask(ji,jj,jk)
END_3D
!
CASE( 4 ) !- 4th order COMPACT
CALL interp_4th_cpt( pt(:,:,:,jn,Kmm) , ztw ) ! zwt = COMPACT interpolation of T at w-point
DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, jpkm1 )
zwz(ji,jj,jk) = ( pW(ji,jj,jk) * ztw(ji,jj,jk) - zwz(ji,jj,jk) ) * wmask(ji,jj,jk)
END_3D
!
END SELECT
IF( ln_linssh ) THEN ! top ocean value: high order = upstream ==>> zwz=0
zwz(:,:,1) = 0._wp ! only ocean surface as interior zwz values have been w-masked
ENDIF
!
IF (nn_hls==1) THEN
CALL lbc_lnk( 'traadv_fct', zwi, 'T', 1.0_wp, zwx, 'U', -1.0_wp , zwy, 'V', -1.0_wp, zwz, 'T', 1.0_wp )
ELSE
CALL lbc_lnk( 'traadv_fct', zwi, 'T', 1.0_wp)
END IF
!
IF ( ll_zAimp ) THEN
DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 1, jpkm1 ) !* trend and after field with monotonic scheme
! ! total intermediate advective trends
ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) &
& + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) &
& + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj)
ztw(ji,jj,jk) = zwi(ji,jj,jk) + p2dt * ztra / e3t(ji,jj,jk,Krhs) * tmask(ji,jj,jk)
END_3D
!
CALL tridia_solver( zwdia, zwsup, zwinf, ztw, ztw , 0 )
!
DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 2, jpkm1 ) ! Interior value ( multiplied by wmask)
zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) )
zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) )
zwz(ji,jj,jk) = zwz(ji,jj,jk) + 0.5 * e1e2t(ji,jj) * ( zfp_wk * ztw(ji,jj,jk) + zfm_wk * ztw(ji,jj,jk-1) ) * wmask(ji,jj,jk)
END_3D
END IF
!
! !== monotonicity algorithm ==!
!
CALL nonosc( Kmm, pt(:,:,:,jn,Kbb), zwx, zwy, zwz, zwi, p2dt )
!
! !== final trend with corrected fluxes ==!
!
DO_3D( 0, 0, 0, 0, 1, jpkm1 )
ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) &
& + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) &
& + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj)
pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) + ztra / e3t(ji,jj,jk,Kmm)
zwi(ji,jj,jk) = zwi(ji,jj,jk) + p2dt * ztra / e3t(ji,jj,jk,Krhs) * tmask(ji,jj,jk)
END_3D
!
IF ( ll_zAimp ) THEN
!
ztw(:,:,1) = 0._wp ; ztw(:,:,jpk) = 0._wp
DO_3D( 0, 0, 0, 0, 2, jpkm1 ) ! Interior value ( multiplied by wmask)
zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) )
zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) )
ztw(ji,jj,jk) = - 0.5 * e1e2t(ji,jj) * ( zfp_wk * zwi(ji,jj,jk) + zfm_wk * zwi(ji,jj,jk-1) ) * wmask(ji,jj,jk)
zwz(ji,jj,jk) = zwz(ji,jj,jk) + ztw(ji,jj,jk) ! Update vertical fluxes for trend diagnostic
END_3D
DO_3D( 0, 0, 0, 0, 1, jpkm1 )
pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) - ( ztw(ji,jj,jk) - ztw(ji ,jj ,jk+1) ) &
& * r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm)
END_3D
END IF
IF( l_trd .OR. l_hst ) THEN ! trend diagnostics // heat/salt transport
ztrdx(:,:,:) = ztrdx(:,:,:) + zwx(:,:,:) ! <<< add anti-diffusive fluxes
ztrdy(:,:,:) = ztrdy(:,:,:) + zwy(:,:,:) ! to upstream fluxes
ztrdz(:,:,:) = ztrdz(:,:,:) + zwz(:,:,:) !
!
IF( l_trd ) THEN ! trend diagnostics
CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_xad, ztrdx, pU, pt(:,:,:,jn,Kmm) )
CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_yad, ztrdy, pV, pt(:,:,:,jn,Kmm) )
CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_zad, ztrdz, pW, pt(:,:,:,jn,Kmm) )
ENDIF
! ! heat/salt transport
IF( l_hst ) CALL dia_ar5_hst( jn, 'adv', ztrdx(:,:,:), ztrdy(:,:,:) )
!
ENDIF
IF( l_ptr ) THEN ! "Poleward" transports
zptry(:,:,:) = zptry(:,:,:) + zwy(:,:,:) ! <<< add anti-diffusive fluxes
CALL dia_ptr_hst( jn, 'adv', zptry(:,:,:) )
ENDIF
!
END DO ! end of tracer loop
!
IF ( ll_zAimp ) THEN
DEALLOCATE( zwdia, zwinf, zwsup )
ENDIF
IF( l_trd .OR. l_hst ) THEN
DEALLOCATE( ztrdx, ztrdy, ztrdz )
ENDIF
IF( l_ptr ) THEN
DEALLOCATE( zptry )
ENDIF
!
#endif
END SUBROUTINE tra_adv_fct
SUBROUTINE nonosc( Kmm, pbef, paa, pbb, pcc, paft, p2dt )
!!---------------------------------------------------------------------
!! *** ROUTINE nonosc ***
!!
!! ** Purpose : compute monotonic tracer fluxes from the upstream
!! scheme and the before field by a nonoscillatory algorithm
!!
!! ** Method : ... ???
!! warning : pbef and paft must be masked, but the boundaries
!! conditions on the fluxes are not necessary zalezak (1979)
!! drange (1995) multi-dimensional forward-in-time and upstream-
!! in-space based differencing for fluid
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: Kmm ! time level index
REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pbef ! before field
REAL(wp), DIMENSION(A2D(nn_hls) ,jpk), INTENT(in ) :: paft ! after field
REAL(wp), DIMENSION(A2D(nn_hls) ,jpk), INTENT(inout) :: paa, pbb, pcc ! monotonic fluxes in the 3 directions
!
INTEGER :: ji, jj, jk ! dummy loop indices
INTEGER :: ikm1 ! local integer
REAL(dp) :: zpos, zneg, zbt, za, zb, zc, zbig, zrtrn ! local scalars
REAL(dp) :: zau, zbu, zcu, zav, zbv, zcv, zup, zdo ! - -
REAL(dp), DIMENSION(A2D(nn_hls),jpk) :: zbetup, zbetdo, zbup, zbdo
!!----------------------------------------------------------------------
!
zbig = 1.e+40_dp
zrtrn = 1.e-15_dp
zbetup(:,:,:) = 0._dp ; zbetdo(:,:,:) = 0._dp
! Search local extrema
! --------------------
! max/min of pbef & paft with large negative/positive value (-/+zbig) inside land
DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpk )
zbup(ji,jj,jk) = MAX( pbef(ji,jj,jk) * tmask(ji,jj,jk) - zbig * ( 1._wp - tmask(ji,jj,jk) ), &
& paft(ji,jj,jk) * tmask(ji,jj,jk) - zbig * ( 1._wp - tmask(ji,jj,jk) ) )
zbdo(ji,jj,jk) = MIN( pbef(ji,jj,jk) * tmask(ji,jj,jk) + zbig * ( 1._wp - tmask(ji,jj,jk) ), &
& paft(ji,jj,jk) * tmask(ji,jj,jk) + zbig * ( 1._wp - tmask(ji,jj,jk) ) )
END_3D
DO jk = 1, jpkm1
ikm1 = MAX(jk-1,1)
DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )
! search maximum in neighbourhood
zup = MAX( zbup(ji ,jj ,jk ), &
& zbup(ji-1,jj ,jk ), zbup(ji+1,jj ,jk ), &
& zbup(ji ,jj-1,jk ), zbup(ji ,jj+1,jk ), &
& zbup(ji ,jj ,ikm1), zbup(ji ,jj ,jk+1) )
! search minimum in neighbourhood
zdo = MIN( zbdo(ji ,jj ,jk ), &
& zbdo(ji-1,jj ,jk ), zbdo(ji+1,jj ,jk ), &
& zbdo(ji ,jj-1,jk ), zbdo(ji ,jj+1,jk ), &
& zbdo(ji ,jj ,ikm1), zbdo(ji ,jj ,jk+1) )
! positive part of the flux
zpos = MAX( 0., paa(ji-1,jj ,jk ) ) - MIN( 0., paa(ji ,jj ,jk ) ) &
& + MAX( 0., pbb(ji ,jj-1,jk ) ) - MIN( 0., pbb(ji ,jj ,jk ) ) &
& + MAX( 0., pcc(ji ,jj ,jk+1) ) - MIN( 0., pcc(ji ,jj ,jk ) )
! negative part of the flux
zneg = MAX( 0., paa(ji ,jj ,jk ) ) - MIN( 0., paa(ji-1,jj ,jk ) ) &
& + MAX( 0., pbb(ji ,jj ,jk ) ) - MIN( 0., pbb(ji ,jj-1,jk ) ) &
& + MAX( 0., pcc(ji ,jj ,jk ) ) - MIN( 0., pcc(ji ,jj ,jk+1) )
! up & down beta terms
zbt = e1e2t(ji,jj) * e3t(ji,jj,jk,Kmm) / p2dt
zbetup(ji,jj,jk) = ( zup - paft(ji,jj,jk) ) / ( zpos + zrtrn ) * zbt
zbetdo(ji,jj,jk) = ( paft(ji,jj,jk) - zdo ) / ( zneg + zrtrn ) * zbt
END_2D
END DO
IF (nn_hls==1) CALL lbc_lnk( 'traadv_fct', zbetup, 'T', 1.0_wp , zbetdo, 'T', 1.0_wp, ld4only= .TRUE. ) ! lateral boundary cond. (unchanged sign)
! 3. monotonic flux in the i & j direction (paa & pbb)
! ----------------------------------------
DO_3D( 1, 0, 1, 0, 1, jpkm1 )
zau = MIN( 1._wp, zbetdo(ji,jj,jk), zbetup(ji+1,jj,jk) )
zbu = MIN( 1._wp, zbetup(ji,jj,jk), zbetdo(ji+1,jj,jk) )
zcu = ( 0.5 + SIGN( 0.5_wp , paa(ji,jj,jk) ) )
paa(ji,jj,jk) = paa(ji,jj,jk) * ( zcu * zau + ( 1._wp - zcu) * zbu )
zav = MIN( 1._wp, zbetdo(ji,jj,jk), zbetup(ji,jj+1,jk) )
zbv = MIN( 1._wp, zbetup(ji,jj,jk), zbetdo(ji,jj+1,jk) )
zcv = ( 0.5 + SIGN( 0.5_wp , pbb(ji,jj,jk) ) )
pbb(ji,jj,jk) = pbb(ji,jj,jk) * ( zcv * zav + ( 1._wp - zcv) * zbv )
! monotonic flux in the k direction, i.e. pcc
! -------------------------------------------
za = MIN( 1., zbetdo(ji,jj,jk+1), zbetup(ji,jj,jk) )
zb = MIN( 1., zbetup(ji,jj,jk+1), zbetdo(ji,jj,jk) )
zc = ( 0.5 + SIGN( 0.5_wp , pcc(ji,jj,jk+1) ) )
pcc(ji,jj,jk+1) = pcc(ji,jj,jk+1) * ( zc * za + ( 1._wp - zc) * zb )
END_3D
!
END SUBROUTINE nonosc
SUBROUTINE interp_4th_cpt_org( pt_in, pt_out )
!!----------------------------------------------------------------------
!! *** ROUTINE interp_4th_cpt_org ***
!!
!! ** Purpose : Compute the interpolation of tracer at w-point
!!
!! ** Method : 4th order compact interpolation
!!----------------------------------------------------------------------
REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pt_in ! now tracer fields
REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT( out) :: pt_out ! now tracer field interpolated at w-pts
!
INTEGER :: ji, jj, jk ! dummy loop integers
REAL(wp),DIMENSION(jpi,jpj,jpk) :: zwd, zwi, zws, zwrm, zwt
!!----------------------------------------------------------------------
DO_3D( 1, 1, 1, 1, 3, jpkm1 ) !== build the three diagonal matrix ==!
zwd (ji,jj,jk) = 4._wp
zwi (ji,jj,jk) = 1._wp
zws (ji,jj,jk) = 1._wp
zwrm(ji,jj,jk) = 3._wp * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) )
!
IF( tmask(ji,jj,jk+1) == 0._wp) THEN ! Switch to second order centered at bottom
zwd (ji,jj,jk) = 1._wp
zwi (ji,jj,jk) = 0._wp
zws (ji,jj,jk) = 0._wp
zwrm(ji,jj,jk) = 0.5 * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) )
ENDIF
END_3D
!
jk = 2 ! Switch to second order centered at top
DO_2D( 1, 1, 1, 1 )
zwd (ji,jj,jk) = 1._wp
zwi (ji,jj,jk) = 0._wp
zws (ji,jj,jk) = 0._wp
zwrm(ji,jj,jk) = 0.5 * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) )
END_2D
!
! !== tridiagonal solve ==!
DO_2D( 1, 1, 1, 1 ) ! first recurrence
zwt(ji,jj,2) = zwd(ji,jj,2)
END_2D
DO_3D( 1, 1, 1, 1, 3, jpkm1 )
zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1)
END_3D
!
DO_2D( 1, 1, 1, 1 ) ! second recurrence: Zk = Yk - Ik / Tk-1 Zk-1
pt_out(ji,jj,2) = zwrm(ji,jj,2)
END_2D
DO_3D( 1, 1, 1, 1, 3, jpkm1 )
pt_out(ji,jj,jk) = zwrm(ji,jj,jk) - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1)
END_3D
DO_2D( 1, 1, 1, 1 ) ! third recurrence: Xk = (Zk - Sk Xk+1 ) / Tk
pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1)
END_2D
DO_3DS( 1, 1, 1, 1, jpk-2, 2, -1 )
pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - zws(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk)
END_3D
!
END SUBROUTINE interp_4th_cpt_org
SUBROUTINE interp_4th_cpt( pt_in, pt_out )
!!----------------------------------------------------------------------
!! *** ROUTINE interp_4th_cpt ***
!!
!! ** Purpose : Compute the interpolation of tracer at w-point
!!
!! ** Method : 4th order compact interpolation
!!----------------------------------------------------------------------
REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pt_in ! field at t-point
REAL(wp),DIMENSION(A2D(nn_hls) ,jpk), INTENT( out) :: pt_out ! field interpolated at w-point
!
INTEGER :: ji, jj, jk ! dummy loop integers
INTEGER :: ikt, ikb ! local integers
REAL(wp),DIMENSION(A2D(nn_hls),jpk) :: zwd, zwi, zws, zwrm, zwt
!!----------------------------------------------------------------------
!
! !== build the three diagonal matrix & the RHS ==!
!
DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 3, jpkm1 ) ! interior (from jk=3 to jpk-1)
zwd (ji,jj,jk) = 3._wp * wmask(ji,jj,jk) + 1._wp ! diagonal
zwi (ji,jj,jk) = wmask(ji,jj,jk) ! lower diagonal
zws (ji,jj,jk) = wmask(ji,jj,jk) ! upper diagonal
zwrm(ji,jj,jk) = 3._wp * wmask(ji,jj,jk) & ! RHS
& * ( pt_in(ji,jj,jk) + pt_in(ji,jj,jk-1) )
END_3D
!
!!gm
! SELECT CASE( kbc ) !* boundary condition
! CASE( np_NH ) ! Neumann homogeneous at top & bottom
! CASE( np_CEN2 ) ! 2nd order centered at top & bottom
! END SELECT
!!gm
!
IF ( ln_isfcav ) THEN ! set level two values which may not be set in ISF case
zwd(:,:,2) = 1._wp ; zwi(:,:,2) = 0._wp ; zws(:,:,2) = 0._wp ; zwrm(:,:,2) = 0._wp
END IF
!
DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) ! 2nd order centered at top & bottom
ikt = mikt(ji,jj) + 1 ! w-point below the 1st wet point
ikb = MAX(mbkt(ji,jj), 2) ! - above the last wet point
!
zwd (ji,jj,ikt) = 1._wp ! top
zwi (ji,jj,ikt) = 0._wp
zws (ji,jj,ikt) = 0._wp
zwrm(ji,jj,ikt) = 0.5_wp * ( pt_in(ji,jj,ikt-1) + pt_in(ji,jj,ikt) )
!
zwd (ji,jj,ikb) = 1._wp ! bottom
zwi (ji,jj,ikb) = 0._wp
zws (ji,jj,ikb) = 0._wp
zwrm(ji,jj,ikb) = 0.5_wp * ( pt_in(ji,jj,ikb-1) + pt_in(ji,jj,ikb) )
END_2D
!
! !== tridiagonal solver ==!
!
DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) !* 1st recurrence: Tk = Dk - Ik Sk-1 / Tk-1
zwt(ji,jj,2) = zwd(ji,jj,2)
END_2D
DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 3, jpkm1 )
zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1)
END_3D
!
DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) !* 2nd recurrence: Zk = Yk - Ik / Tk-1 Zk-1
pt_out(ji,jj,2) = zwrm(ji,jj,2)
END_2D
DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, 3, jpkm1 )
pt_out(ji,jj,jk) = zwrm(ji,jj,jk) - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1)
END_3D
DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) !* 3d recurrence: Xk = (Zk - Sk Xk+1 ) / Tk
pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1)
END_2D
DO_3DS( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, jpk-2, 2, -1 )
pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - zws(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk)
END_3D
!
END SUBROUTINE interp_4th_cpt
SUBROUTINE tridia_solver( pD, pU, pL, pRHS, pt_out , klev )
!!----------------------------------------------------------------------
!! *** ROUTINE tridia_solver ***
!!
!! ** Purpose : solve a symmetric 3diagonal system
!!
!! ** Method : solve M.t_out = RHS(t) where M is a tri diagonal matrix ( jpk*jpk )
!!
!! ( D_1 U_1 0 0 0 )( t_1 ) ( RHS_1 )
!! ( L_2 D_2 U_2 0 0 )( t_2 ) ( RHS_2 )
!! ( 0 L_3 D_3 U_3 0 )( t_3 ) = ( RHS_3 )
!! ( ... )( ... ) ( ... )
!! ( 0 0 0 L_k D_k )( t_k ) ( RHS_k )
!!
!! M is decomposed in the product of an upper and lower triangular matrix.
!! The tri-diagonals matrix is given as input 3D arrays: pD, pU, pL
!! (i.e. the Diagonal, the Upper diagonal, and the Lower diagonal).
!! The solution is pta.
!! The 3d array zwt is used as a work space array.
!!----------------------------------------------------------------------
REAL(wp),DIMENSION(A2D(nn_hls),jpk), INTENT(in ) :: pD, pU, PL ! 3-diagonal matrix
REAL(wp),DIMENSION(A2D(nn_hls),jpk), INTENT(in ) :: pRHS ! Right-Hand-Side
REAL(wp),DIMENSION(A2D(nn_hls),jpk), INTENT( out) :: pt_out !!gm field at level=F(klev)
INTEGER , INTENT(in ) :: klev ! =1 pt_out at w-level
! ! =0 pt at t-level
INTEGER :: ji, jj, jk ! dummy loop integers
INTEGER :: kstart ! local indices
REAL(wp),DIMENSION(A2D(nn_hls),jpk) :: zwt ! 3D work array
!!----------------------------------------------------------------------
!
kstart = 1 + klev
!
DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) !* 1st recurrence: Tk = Dk - Ik Sk-1 / Tk-1
zwt(ji,jj,kstart) = pD(ji,jj,kstart)
END_2D
DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, kstart+1, jpkm1 )
zwt(ji,jj,jk) = pD(ji,jj,jk) - pL(ji,jj,jk) * pU(ji,jj,jk-1) /zwt(ji,jj,jk-1)
END_3D
!
DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) !* 2nd recurrence: Zk = Yk - Ik / Tk-1 Zk-1
pt_out(ji,jj,kstart) = pRHS(ji,jj,kstart)
END_2D
DO_3D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, kstart+1, jpkm1 )
pt_out(ji,jj,jk) = pRHS(ji,jj,jk) - pL(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1)
END_3D
DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 ) !* 3d recurrence: Xk = (Zk - Sk Xk+1 ) / Tk
pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1)
END_2D
DO_3DS( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1, jpk-2, kstart, -1 )
pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - pU(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk)
END_3D
!
END SUBROUTINE tridia_solver
#if defined key_loop_fusion
#define tracer_flux_i(out,zfp,zfm,ji,jj,jk) \
zfp = pU(ji,jj,jk) + ABS( pU(ji,jj,jk) ) ; \
zfm = pU(ji,jj,jk) - ABS( pU(ji,jj,jk) ) ; \
out = 0.5 * ( zfp * pt(ji,jj,jk,jn,Kbb) + zfm * pt(ji+1,jj,jk,jn,Kbb) )
#define tracer_flux_j(out,zfp,zfm,ji,jj,jk) \
zfp = pV(ji,jj,jk) + ABS( pV(ji,jj,jk) ) ; \
zfm = pV(ji,jj,jk) - ABS( pV(ji,jj,jk) ) ; \
out = 0.5 * ( zfp * pt(ji,jj,jk,jn,Kbb) + zfm * pt(ji,jj+1,jk,jn,Kbb) )
SUBROUTINE tra_adv_fct_lf( kt, kit000, cdtype, p2dt, pU, pV, pW, &
& Kbb, Kmm, pt, kjpt, Krhs, kn_fct_h, kn_fct_v )
!!----------------------------------------------------------------------
!! *** ROUTINE tra_adv_fct ***
!!
!! ** Purpose : Compute the now trend due to total advection of tracers
!! and add it to the general trend of tracer equations
!!
!! ** Method : - 2nd or 4th FCT scheme on the horizontal direction
!! (choice through the value of kn_fct)
!! - on the vertical the 4th order is a compact scheme
!! - corrected flux (monotonic correction)
!!
!! ** Action : - update pt(:,:,:,:,Krhs) with the now advective tracer trends
!! - send trends to trdtra module for further diagnostics (l_trdtra=T)
!! - poleward advective heat and salt transport (ln_diaptr=T)
!!----------------------------------------------------------------------
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
INTEGER , INTENT(in ) :: kn_fct_h ! order of the FCT scheme (=2 or 4)
INTEGER , INTENT(in ) :: kn_fct_v ! order of the FCT scheme (=2 or 4)
REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
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
REAL(wp) :: ztra ! local scalar
REAL(wp) :: zwx_im1, zfp_ui, zfp_ui_m1, zfp_vj, zfp_vj_m1, zfp_wk, zC2t_u, zC4t_u ! - -
REAL(wp) :: zwy_jm1, zfm_ui, zfm_ui_m1, zfm_vj, zfm_vj_m1, zfm_wk, zC2t_v, zC4t_v ! - -
REAL(wp) :: ztu, ztv, ztu_im1, ztu_ip1, ztv_jm1, ztv_jp1
REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwi, zwx_3d, zwy_3d, zwz, ztw, zltu_3d, zltv_3d
REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ztrdx, ztrdy, ztrdz, zptry
REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: zwinf, zwdia, zwsup
LOGICAL :: ll_zAimp ! flag to apply adaptive implicit vertical advection
!!----------------------------------------------------------------------
!
IF( kt == kit000 ) THEN
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) 'tra_adv_fct_lf : FCT advection scheme on ', cdtype
IF(lwp) WRITE(numout,*) '~~~~~~~~~~~'
ENDIF
!! -- init to 0
zwx_3d(:,:,:) = 0._wp
zwy_3d(:,:,:) = 0._wp
zwz(:,:,:) = 0._wp
zwi(:,:,:) = 0._wp
!
l_trd = .FALSE. ! set local switches
l_hst = .FALSE.
l_ptr = .FALSE.
ll_zAimp = .FALSE.
IF( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. ( cdtype =='TRC' .AND. l_trdtrc ) ) l_trd = .TRUE.
IF( cdtype == 'TRA' .AND. ( iom_use( 'sophtadv' ) .OR. iom_use( 'sophtadv' ) ) ) l_ptr = .TRUE.
IF( 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.
!
IF( l_trd .OR. l_hst ) THEN
ALLOCATE( ztrdx(jpi,jpj,jpk), ztrdy(jpi,jpj,jpk), ztrdz(jpi,jpj,jpk) )
ztrdx(:,:,:) = 0._wp ; ztrdy(:,:,:) = 0._wp ; ztrdz(:,:,:) = 0._wp
ENDIF
!
IF( l_ptr ) THEN
ALLOCATE( zptry(jpi,jpj,jpk) )
zptry(:,:,:) = 0._wp
ENDIF
!
! If adaptive vertical advection, check if it is needed on this PE at this time
IF( ln_zad_Aimp ) THEN
IF( MAXVAL( ABS( wi(:,:,:) ) ) > 0._wp ) ll_zAimp = .TRUE.
END IF
! If active adaptive vertical advection, build tridiagonal matrix
IF( ll_zAimp ) THEN
ALLOCATE(zwdia(jpi,jpj,jpk), zwinf(jpi,jpj,jpk),zwsup(jpi,jpj,jpk))
DO_3D( 1, 1, 1, 1, 1, jpkm1 )
zwdia(ji,jj,jk) = 1._wp + p2dt * ( MAX( wi(ji,jj,jk) , 0._wp ) - MIN( wi(ji,jj,jk+1) , 0._wp ) ) &
& / e3t(ji,jj,jk,Krhs)
zwinf(ji,jj,jk) = p2dt * MIN( wi(ji,jj,jk ) , 0._wp ) / e3t(ji,jj,jk,Krhs)
zwsup(ji,jj,jk) = -p2dt * MAX( wi(ji,jj,jk+1) , 0._wp ) / e3t(ji,jj,jk,Krhs)
END_3D
END IF
!
DO jn = 1, kjpt !== loop over the tracers ==!
!
! !== upstream advection with initial mass fluxes & intermediate update ==!
! !* upstream tracer flux in the k direction *!
DO_3D( 1, 1, 1, 1, 2, jpkm1 ) ! Interior value ( multiplied by wmask)
zfp_wk = pW(ji,jj,jk) + ABS( pW(ji,jj,jk) )
zfm_wk = pW(ji,jj,jk) - ABS( pW(ji,jj,jk) )
zwz(ji,jj,jk) = 0.5 * ( zfp_wk * pt(ji,jj,jk,jn,Kbb) + zfm_wk * pt(ji,jj,jk-1,jn,Kbb) ) * wmask(ji,jj,jk)
END_3D
IF( ln_linssh ) THEN ! top ocean value (only in linear free surface as zwz has been w-masked)
IF( ln_isfcav ) THEN ! top of the ice-shelf cavities and at the ocean surface
DO_2D( 1, 1, 1, 1 )
zwz(ji,jj, mikt(ji,jj) ) = pW(ji,jj,mikt(ji,jj)) * pt(ji,jj,mikt(ji,jj),jn,Kbb) ! linear free surface
END_2D
ELSE ! no cavities: only at the ocean surface
DO_2D( 1, 1, 1, 1 )
zwz(ji,jj,1) = pW(ji,jj,1) * pt(ji,jj,1,jn,Kbb)
END_2D
ENDIF
ENDIF
!
! !* upstream tracer flux in the i and j direction
DO jk = 1, jpkm1
DO jj = 1, jpj-1
tracer_flux_i(zwx_3d(1,jj,jk),zfp_ui,zfm_ui,1,jj,jk)
tracer_flux_j(zwy_3d(1,jj,jk),zfp_vj,zfm_vj,1,jj,jk)
END DO
DO ji = 1, jpi-1
tracer_flux_i(zwx_3d(ji,1,jk),zfp_ui,zfm_ui,ji,1,jk)
tracer_flux_j(zwy_3d(ji,1,jk),zfp_vj,zfm_vj,ji,1,jk)
END DO
DO_2D( 1, 1, 1, 1 )
tracer_flux_i(zwx_3d(ji,jj,jk),zfp_ui,zfm_ui,ji,jj,jk)
tracer_flux_i(zwx_im1,zfp_ui_m1,zfm_ui_m1,ji-1,jj,jk)
tracer_flux_j(zwy_3d(ji,jj,jk),zfp_vj,zfm_vj,ji,jj,jk)
tracer_flux_j(zwy_jm1,zfp_vj_m1,zfm_vj_m1,ji,jj-1,jk)
ztra = - ( zwx_3d(ji,jj,jk) - zwx_im1 + zwy_3d(ji,jj,jk) - zwy_jm1 + zwz(ji,jj,jk) - zwz(ji,jj,jk+1) ) * r1_e1e2t(ji,jj)
! ! update and guess with monotonic sheme
pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) + ztra &
& / e3t(ji,jj,jk,Kmm ) * tmask(ji,jj,jk)
zwi(ji,jj,jk) = ( e3t(ji,jj,jk,Kbb) * pt(ji,jj,jk,jn,Kbb) + p2dt * ztra ) &
& / e3t(ji,jj,jk,Krhs) * tmask(ji,jj,jk)
END_2D
END DO
IF ( ll_zAimp ) THEN
CALL tridia_solver( zwdia, zwsup, zwinf, zwi, zwi , 0 )
!
ztw(:,:,1) = 0._wp ; ztw(:,:,jpk) = 0._wp ;
DO_3D( 1, 1, 1, 1, 2, jpkm1 ) ! Interior value ( multiplied by wmask)
zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) )
zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) )
ztw(ji,jj,jk) = 0.5 * e1e2t(ji,jj) * ( zfp_wk * zwi(ji,jj,jk) + zfm_wk * zwi(ji,jj,jk-1) ) * wmask(ji,jj,jk)
zwz(ji,jj,jk) = zwz(ji,jj,jk) + ztw(ji,jj,jk) ! update vertical fluxes
END_3D
DO_3D( 0, 0, 0, 0, 1, jpkm1 )
pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) - ( ztw(ji,jj,jk) - ztw(ji ,jj ,jk+1) ) &
& * r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm)
END_3D
!
END IF
!
IF( l_trd .OR. l_hst ) THEN ! trend diagnostics (contribution of upstream fluxes)
ztrdx(:,:,:) = zwx_3d(:,:,:) ; ztrdy(:,:,:) = zwy_3d(:,:,:) ; ztrdz(:,:,:) = zwz(:,:,:)
END IF
! ! "Poleward" heat and salt transports (contribution of upstream fluxes)
IF( l_ptr ) zptry(:,:,:) = zwy_3d(:,:,:)
!
! !== anti-diffusive flux : high order minus low order ==!
!
SELECT CASE( kn_fct_h ) !* horizontal anti-diffusive fluxes
!
CASE( 2 ) !- 2nd order centered
DO_3D( 2, 1, 2, 1, 1, jpkm1 )
zwx_3d(ji,jj,jk) = 0.5_wp * pU(ji,jj,jk) * ( pt(ji,jj,jk,jn,Kmm) + pt(ji+1,jj,jk,jn,Kmm) ) - zwx_3d(ji,jj,jk)
zwy_3d(ji,jj,jk) = 0.5_wp * pV(ji,jj,jk) * ( pt(ji,jj,jk,jn,Kmm) + pt(ji,jj+1,jk,jn,Kmm) ) - zwy_3d(ji,jj,jk)
END_3D
!
CASE( 4 ) !- 4th order centered
zltu_3d(:,:,jpk) = 0._wp ! Bottom value : flux set to zero
zltv_3d(:,:,jpk) = 0._wp
! ! Laplacian
DO_3D( 0, 0, 0, 0, 1, jpkm1 ) ! 2nd derivative * 1/ 6
! ! 1st derivative (gradient)
ztu = ( pt(ji+1,jj,jk,jn,Kmm) - pt(ji,jj,jk,jn,Kmm) ) * umask(ji,jj,jk)
ztu_im1 = ( pt(ji,jj,jk,jn,Kmm) - pt(ji-1,jj,jk,jn,Kmm) ) * umask(ji-1,jj,jk)
ztv = ( pt(ji,jj+1,jk,jn,Kmm) - pt(ji,jj,jk,jn,Kmm) ) * vmask(ji,jj,jk)
ztv_jm1 = ( pt(ji,jj,jk,jn,Kmm) - pt(ji,jj-1,jk,jn,Kmm) ) * vmask(ji,jj-1,jk)
! ! 2nd derivative * 1/ 6
zltu_3d(ji,jj,jk) = ( ztu + ztu_im1 ) * r1_6
zltv_3d(ji,jj,jk) = ( ztv + ztv_jm1 ) * r1_6
END_2D
END DO
! NOTE [ comm_cleanup ] : need to change sign to ensure halo 1 - halo 2 compatibility
CALL lbc_lnk( 'traadv_fct', zltu_3d, 'T', -1.0_wp , zltv_3d, 'T', -1.0_wp ) ! Lateral boundary cond. (unchanged sgn)
!
DO_3D( 2, 1, 2, 1, 1, jpkm1 )
zC2t_u = pt(ji,jj,jk,jn,Kmm) + pt(ji+1,jj ,jk,jn,Kmm) ! 2 x C2 interpolation of T at u- & v-points
zC2t_v = pt(ji,jj,jk,jn,Kmm) + pt(ji ,jj+1,jk,jn,Kmm)
! ! C4 minus upstream advective fluxes
! round brackets added to fix the order of floating point operations
! needed to ensure halo 1 - halo 2 compatibility
zwx_3d(ji,jj,jk) = 0.5_wp * pU(ji,jj,jk) * ( zC2t_u + ( zltu_3d(ji,jj,jk) - zltu_3d(ji+1,jj,jk) &
& ) & ! bracket for halo 1 - halo 2 compatibility
& ) - zwx_3d(ji,jj,jk)
zwy_3d(ji,jj,jk) = 0.5_wp * pV(ji,jj,jk) * ( zC2t_v + ( zltv_3d(ji,jj,jk) - zltv_3d(ji,jj+1,jk) &
& ) & ! bracket for halo 1 - halo 2 compatibility
& ) - zwy_3d(ji,jj,jk)
END_3D
!
CASE( 41 ) !- 4th order centered ==>> !!gm coding attempt need to be tested
DO_3D( 0, 0, 0, 0, 1, jpkm1 ) ! Horizontal advective fluxes
ztu_im1 = ( pt(ji ,jj ,jk,jn,Kmm) - pt(ji-1,jj,jk,jn,Kmm) ) * umask(ji-1,jj,jk)
ztu_ip1 = ( pt(ji+2,jj ,jk,jn,Kmm) - pt(ji+1,jj,jk,jn,Kmm) ) * umask(ji+1,jj,jk)
ztv_jm1 = ( pt(ji,jj ,jk,jn,Kmm) - pt(ji,jj-1,jk,jn,Kmm) ) * vmask(ji,jj-1,jk)
ztv_jp1 = ( pt(ji,jj+2,jk,jn,Kmm) - pt(ji,jj+1,jk,jn,Kmm) ) * vmask(ji,jj+1,jk)
zC2t_u = pt(ji,jj,jk,jn,Kmm) + pt(ji+1,jj ,jk,jn,Kmm) ! 2 x C2 interpolation of T at u- & v-points (x2)
zC2t_v = pt(ji,jj,jk,jn,Kmm) + pt(ji ,jj+1,jk,jn,Kmm)
! ! C4 interpolation of T at u- & v-points (x2)
zC4t_u = zC2t_u + r1_6 * ( ztu_im1 - ztu_ip1 )
zC4t_v = zC2t_v + r1_6 * ( ztv_jm1 - ztv_jp1 )
! ! C4 minus upstream advective fluxes
zwx_3d(ji,jj,jk) = 0.5_wp * pU(ji,jj,jk) * zC4t_u - zwx_3d(ji,jj,jk)
zwy_3d(ji,jj,jk) = 0.5_wp * pV(ji,jj,jk) * zC4t_v - zwy_3d(ji,jj,jk)
END_3D
CALL lbc_lnk( 'traadv_fct', zwx_3d, 'U', -1.0_wp , zwy_3d, 'V', -1.0_wp ) ! Lateral boundary cond. (unchanged sgn)
!
END SELECT
!
SELECT CASE( kn_fct_v ) !* vertical anti-diffusive fluxes (w-masked interior values)
!
CASE( 2 ) !- 2nd order centered
DO_3D( 1, 1, 1, 1, 2, jpkm1 )
zwz(ji,jj,jk) = ( pW(ji,jj,jk) * 0.5_wp * ( pt(ji,jj,jk,jn,Kmm) + pt(ji,jj,jk-1,jn,Kmm) ) &
& - zwz(ji,jj,jk) ) * wmask(ji,jj,jk)
END_3D
!
CASE( 4 ) !- 4th order COMPACT
CALL interp_4th_cpt( pt(:,:,:,jn,Kmm) , ztw ) ! zwt = COMPACT interpolation of T at w-point
DO_3D( 1, 1, 1, 1, 2, jpkm1 )
zwz(ji,jj,jk) = ( pW(ji,jj,jk) * ztw(ji,jj,jk) - zwz(ji,jj,jk) ) * wmask(ji,jj,jk)
END_3D
!
END SELECT
IF( ln_linssh ) THEN ! top ocean value: high order = upstream ==>> zwz=0
zwz(:,:,1) = 0._wp ! only ocean surface as interior zwz values have been w-masked
ENDIF
!
CALL lbc_lnk( 'traadv_fct', zwi, 'T', 1.0_wp)
!
IF ( ll_zAimp ) THEN
DO_3D( 1, 1, 1, 1, 1, jpkm1 ) !* trend and after field with monotonic scheme
! ! total intermediate advective trends
ztra = - ( zwx_3d(ji,jj,jk) - zwx_3d(ji-1,jj ,jk ) &
& + zwy_3d(ji,jj,jk) - zwy_3d(ji ,jj-1,jk ) &
& + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj)
ztw(ji,jj,jk) = zwi(ji,jj,jk) + p2dt * ztra / e3t(ji,jj,jk,Krhs) * tmask(ji,jj,jk)
END_3D
!
CALL tridia_solver( zwdia, zwsup, zwinf, ztw, ztw , 0 )
!
DO_3D( 1, 1, 1, 1, 2, jpkm1 ) ! Interior value ( multiplied by wmask)
zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) )
zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) )
zwz(ji,jj,jk) = zwz(ji,jj,jk) + 0.5 * e1e2t(ji,jj) * ( zfp_wk * ztw(ji,jj,jk) + zfm_wk * ztw(ji,jj,jk-1) ) * wmask(ji,jj,jk)
END_3D
END IF
!
! !== monotonicity algorithm ==!
!
CALL nonosc( Kmm, pt(:,:,:,jn,Kbb), zwx_3d, zwy_3d, zwz, zwi, p2dt )
!
! !== final trend with corrected fluxes ==!
!
DO_3D( 0, 0, 0, 0, 1, jpkm1 )
ztra = - ( zwx_3d(ji,jj,jk) - zwx_3d(ji-1,jj ,jk ) &
& + zwy_3d(ji,jj,jk) - zwy_3d(ji ,jj-1,jk ) &
& + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj)
pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) + ztra / e3t(ji,jj,jk,Kmm)
zwi(ji,jj,jk) = zwi(ji,jj,jk) + p2dt * ztra / e3t(ji,jj,jk,Krhs) * tmask(ji,jj,jk)
END_3D
!
IF ( ll_zAimp ) THEN
!
ztw(:,:,1) = 0._wp ; ztw(:,:,jpk) = 0._wp
DO_3D( 0, 0, 0, 0, 2, jpkm1 ) ! Interior value ( multiplied by wmask)
zfp_wk = wi(ji,jj,jk) + ABS( wi(ji,jj,jk) )
zfm_wk = wi(ji,jj,jk) - ABS( wi(ji,jj,jk) )
ztw(ji,jj,jk) = - 0.5 * e1e2t(ji,jj) * ( zfp_wk * zwi(ji,jj,jk) + zfm_wk * zwi(ji,jj,jk-1) ) * wmask(ji,jj,jk)
zwz(ji,jj,jk) = zwz(ji,jj,jk) + ztw(ji,jj,jk) ! Update vertical fluxes for trend diagnostic
END_3D
DO_3D( 0, 0, 0, 0, 1, jpkm1 )
pt(ji,jj,jk,jn,Krhs) = pt(ji,jj,jk,jn,Krhs) - ( ztw(ji,jj,jk) - ztw(ji ,jj ,jk+1) ) &
& * r1_e1e2t(ji,jj) / e3t(ji,jj,jk,Kmm)
END_3D
END IF
! NOT TESTED - NEED l_trd OR l_hst TRUE
IF( l_trd .OR. l_hst ) THEN ! trend diagnostics // heat/salt transport
ztrdx(:,:,:) = ztrdx(:,:,:) + zwx_3d(:,:,:) ! <<< add anti-diffusive fluxes
ztrdy(:,:,:) = ztrdy(:,:,:) + zwy_3d(:,:,:) ! to upstream fluxes
ztrdz(:,:,:) = ztrdz(:,:,:) + zwz(:,:,:) !
!
IF( l_trd ) THEN ! trend diagnostics
CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_xad, ztrdx, pU, pt(:,:,:,jn,Kmm) )
CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_yad, ztrdy, pV, pt(:,:,:,jn,Kmm) )
CALL trd_tra( kt, Kmm, Krhs, cdtype, jn, jptra_zad, ztrdz, pW, pt(:,:,:,jn,Kmm) )
ENDIF
! ! heat/salt transport
IF( l_hst ) CALL dia_ar5_hst( jn, 'adv', ztrdx(:,:,:), ztrdy(:,:,:) )
!
ENDIF
! NOT TESTED - NEED l_ptr TRUE
IF( l_ptr ) THEN ! "Poleward" transports
zptry(:,:,:) = zptry(:,:,:) + zwy_3d(:,:,:) ! <<< add anti-diffusive fluxes
CALL dia_ptr_hst( jn, 'adv', zptry(:,:,:) )
ENDIF
!
END DO ! end of tracer loop
!
IF ( ll_zAimp ) THEN
DEALLOCATE( zwdia, zwinf, zwsup )
ENDIF
IF( l_trd .OR. l_hst ) THEN
DEALLOCATE( ztrdx, ztrdy, ztrdz )
ENDIF