MODULE traadv_tvd !!============================================================================== !! *** MODULE traadv_tvd *** !! Ocean tracers: horizontal & vertical advective trend !!============================================================================== !! History : OPA ! 1995-12 (L. Mortier) Original code !! ! 2000-01 (H. Loukos) adapted to ORCA !! ! 2000-10 (MA Foujols E.Kestenare) include file not routine !! ! 2000-12 (E. Kestenare M. Levy) fix bug in trtrd indexes !! ! 2001-07 (E. Durand G. Madec) adaptation to ORCA config !! 8.5 ! 2002-06 (G. Madec) F90: Free form and module !! NEMO 1.0 ! 2004-01 (A. de Miranda, G. Madec, J.M. Molines ): advective bbl !! 2.0 ! 2008-04 (S. Cravatte) add the i-, j- & k- trends computation !! - ! 2009-11 (V. Garnier) Surface pressure gradient organization !! 3.3 ! 2010-05 (C. Ethe, G. Madec) merge TRC-TRA + switch from velocity to transport !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! tra_adv_tvd : update the tracer trend with the 3D advection trends using a TVD scheme !! nonosc : compute monotonic tracer fluxes by a non-oscillatory algorithm !!---------------------------------------------------------------------- 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 dynspg_oce ! choice/control of key cpp for surface pressure gradient USE diaptr ! poleward transport diagnostics USE phycst ! USE lib_mpp ! MPP library USE lbclnk ! ocean lateral boundary condition (or mpp link) USE in_out_manager ! I/O manager USE wrk_nemo ! Memory Allocation USE timing ! Timing USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) USE iom IMPLICIT NONE PRIVATE PUBLIC tra_adv_tvd ! routine called by traadv.F90 PUBLIC tra_adv_tvd_zts ! routine called by traadv.F90 LOGICAL :: l_trd ! flag to compute trends LOGICAL :: l_trans ! flag to output vertically integrated transports !! * Substitutions # include "domzgr_substitute.h90" # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OPA 3.3 , NEMO Consortium (2010) !! $Id: traadv_tvd.F90 4990 2014-12-15 16:42:49Z timgraham $ !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE tra_adv_tvd ( kt, kit000, cdtype, p2dt, pun, pvn, pwn, & & ptb, ptn, pta, kjpt ) !!---------------------------------------------------------------------- !! *** ROUTINE tra_adv_tvd *** !! !! ** Purpose : Compute the now trend due to total advection of !! tracers and add it to the general trend of tracer equations !! !! ** Method : TVD scheme, i.e. 2nd order centered scheme with !! corrected flux (monotonic correction) !! note: - this advection scheme needs a leap-frog time scheme !! !! ** Action : - update (pta) with the now advective tracer trends !! - save the trends !!---------------------------------------------------------------------- USE oce , ONLY: zwx => ua , zwy => va ! (ua,va) used as workspace ! INTEGER , INTENT(in ) :: kt ! ocean time-step index 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 REAL(wp), DIMENSION( jpk ), INTENT(in ) :: p2dt ! vertical profile of tracer time-step REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pun, pvn, pwn ! 3 ocean velocity components REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb, ptn ! before and now tracer fields REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend ! INTEGER :: ji, jj, jk, jn ! dummy loop indices INTEGER :: ik REAL(wp) :: z2dtt, zbtr, ztra ! local scalar REAL(wp) :: zfp_ui, zfp_vj, zfp_wk ! - - REAL(wp) :: zfm_ui, zfm_vj, zfm_wk ! - - REAL(wp), POINTER, DIMENSION(:,:,:) :: zwi, zwz REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdx, ztrdy, ztrdz, zptry REAL(wp), POINTER, DIMENSION(:,:) :: z2d !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('tra_adv_tvd') ! CALL wrk_alloc( jpi, jpj, jpk, zwi, zwz ) ! IF( kt == kit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'tra_adv_tvd : TVD advection scheme on ', cdtype IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' ! ENDIF l_trd = .FALSE. l_trans = .FALSE. IF( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. ( cdtype == 'TRC' .AND. l_trdtrc ) ) l_trd = .TRUE. IF( cdtype == 'TRA' .AND. (iom_use("uadv_heattr") .OR. iom_use("vadv_heattr") ) ) l_trans = .TRUE. ! IF( l_trd .OR. l_trans ) THEN CALL wrk_alloc( jpi, jpj, jpk, ztrdx, ztrdy, ztrdz ) ztrdx(:,:,:) = 0.e0 ; ztrdy(:,:,:) = 0.e0 ; ztrdz(:,:,:) = 0.e0 CALL wrk_alloc( jpi, jpj, z2d ) ENDIF ! IF( cdtype == 'TRA' .AND. ln_diaptr ) THEN CALL wrk_alloc( jpi, jpj, jpk, zptry ) zptry(:,:,:) = 0._wp ENDIF ! zwi(:,:,:) = 0.e0 ; ! ! ! =========== DO jn = 1, kjpt ! tracer loop ! ! =========== ! 1. Bottom and k=1 value : flux set to zero ! ---------------------------------- zwx(:,:,jpk) = 0.e0 ; zwz(:,:,jpk) = 0.e0 zwy(:,:,jpk) = 0.e0 ; zwi(:,:,jpk) = 0.e0 zwz(:,:,1 ) = 0._wp ! 2. upstream advection with initial mass fluxes & intermediate update ! -------------------------------------------------------------------- ! upstream tracer flux in the i and j direction DO jk = 1, jpkm1 DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. ! upstream scheme zfp_ui = pun(ji,jj,jk) + ABS( pun(ji,jj,jk) ) zfm_ui = pun(ji,jj,jk) - ABS( pun(ji,jj,jk) ) zfp_vj = pvn(ji,jj,jk) + ABS( pvn(ji,jj,jk) ) zfm_vj = pvn(ji,jj,jk) - ABS( pvn(ji,jj,jk) ) zwx(ji,jj,jk) = 0.5 * ( zfp_ui * ptb(ji,jj,jk,jn) + zfm_ui * ptb(ji+1,jj ,jk,jn) ) zwy(ji,jj,jk) = 0.5 * ( zfp_vj * ptb(ji,jj,jk,jn) + zfm_vj * ptb(ji ,jj+1,jk,jn) ) END DO END DO END DO ! upstream tracer flux in the k direction ! Interior value DO jk = 2, jpkm1 DO jj = 1, jpj DO ji = 1, jpi zfp_wk = pwn(ji,jj,jk) + ABS( pwn(ji,jj,jk) ) zfm_wk = pwn(ji,jj,jk) - ABS( pwn(ji,jj,jk) ) zwz(ji,jj,jk) = 0.5 * ( zfp_wk * ptb(ji,jj,jk,jn) + zfm_wk * ptb(ji,jj,jk-1,jn) ) * wmask(ji,jj,jk) END DO END DO END DO ! Surface value IF( lk_vvl ) THEN IF ( ln_isfcav ) THEN DO jj = 1, jpj DO ji = 1, jpi zwz(ji,jj, mikt(ji,jj) ) = 0.e0 ! volume variable END DO END DO ELSE zwz(:,:,1) = 0.e0 ! volume variable END IF ELSE IF ( ln_isfcav ) THEN DO jj = 1, jpj DO ji = 1, jpi zwz(ji,jj, mikt(ji,jj) ) = pwn(ji,jj,mikt(ji,jj)) * ptb(ji,jj,mikt(ji,jj),jn) ! linear free surface END DO END DO ELSE zwz(:,:,1) = pwn(:,:,1) * ptb(:,:,1,jn) ! linear free surface END IF ENDIF ! total advective trend DO jk = 1, jpkm1 z2dtt = p2dt(jk) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ! 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) ) / e1e2t(ji,jj) ! update and guess with monotonic sheme pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra / fse3t_n(ji,jj,jk) * tmask(ji,jj,jk) zwi(ji,jj,jk) = ( fse3t_b(ji,jj,jk) * ptb(ji,jj,jk,jn) + z2dtt * ztra ) / fse3t_a(ji,jj,jk) * tmask(ji,jj,jk) END DO END DO END DO ! ! Lateral boundary conditions on zwi (unchanged sign) CALL lbc_lnk( zwi, 'T', 1. ) ! ! trend diagnostics (contribution of upstream fluxes) IF( l_trd .OR. l_trans ) THEN ! store intermediate advective trends ztrdx(:,:,:) = zwx(:,:,:) ; ztrdy(:,:,:) = zwy(:,:,:) ; ztrdz(:,:,:) = zwz(:,:,:) END IF ! ! "Poleward" heat and salt transports (contribution of upstream fluxes) IF( cdtype == 'TRA' .AND. ln_diaptr ) zptry(:,:,:) = zwy(:,:,:) ! 3. antidiffusive flux : high order minus low order ! -------------------------------------------------- ! antidiffusive flux on i and j DO jk = 1, jpkm1 DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. zwx(ji,jj,jk) = 0.5 * pun(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji+1,jj,jk,jn) ) - zwx(ji,jj,jk) zwy(ji,jj,jk) = 0.5 * pvn(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji,jj+1,jk,jn) ) - zwy(ji,jj,jk) END DO END DO END DO ! antidiffusive flux on k ! Interior value DO jk = 2, jpkm1 DO jj = 1, jpj DO ji = 1, jpi zwz(ji,jj,jk) = 0.5 * pwn(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji,jj,jk-1,jn) ) - zwz(ji,jj,jk) END DO END DO END DO ! surface value IF ( ln_isfcav ) THEN DO jj = 1, jpj DO ji = 1, jpi zwz(ji,jj,mikt(ji,jj)) = 0.e0 END DO END DO ELSE zwz(:,:,1) = 0.e0 END IF CALL lbc_lnk( zwx, 'U', -1. ) ; CALL lbc_lnk( zwy, 'V', -1. ) ! Lateral bondary conditions CALL lbc_lnk( zwz, 'W', 1. ) ! 4. monotonicity algorithm ! ------------------------- CALL nonosc( ptb(:,:,:,jn), zwx, zwy, zwz, zwi, p2dt ) ! 5. final trend with corrected fluxes ! ------------------------------------ DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zbtr = 1. / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) ) ! total advective trends ztra = - zbtr * ( 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) ) ! add them to the general tracer trends pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra * tmask(ji,jj,jk) END DO END DO END DO ! ! trend diagnostics (contribution of upstream fluxes) IF( l_trd .OR. l_trans ) THEN ztrdx(:,:,:) = ztrdx(:,:,:) + zwx(:,:,:) ! <<< Add to previously computed ztrdy(:,:,:) = ztrdy(:,:,:) + zwy(:,:,:) ! <<< Add to previously computed ztrdz(:,:,:) = ztrdz(:,:,:) + zwz(:,:,:) ! <<< Add to previously computed ENDIF IF( l_trd ) THEN CALL trd_tra( kt, cdtype, jn, jptra_xad, ztrdx, pun, ptn(:,:,:,jn) ) CALL trd_tra( kt, cdtype, jn, jptra_yad, ztrdy, pvn, ptn(:,:,:,jn) ) CALL trd_tra( kt, cdtype, jn, jptra_zad, ztrdz, pwn, ptn(:,:,:,jn) ) END IF IF( l_trans .AND. jn==jp_tem ) THEN z2d(:,:) = 0._wp DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. z2d(ji,jj) = z2d(ji,jj) + ztrdx(ji,jj,jk) END DO END DO END DO CALL lbc_lnk( z2d, 'U', -1. ) CALL iom_put( "uadv_heattr", rau0_rcp * z2d ) ! heat transport in i-direction ! z2d(:,:) = 0._wp DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. z2d(ji,jj) = z2d(ji,jj) + ztrdy(ji,jj,jk) END DO END DO END DO CALL lbc_lnk( z2d, 'V', -1. ) CALL iom_put( "vadv_heattr", rau0_rcp * z2d ) ! heat transport in j-direction ENDIF ! "Poleward" heat and salt transports (contribution of upstream fluxes) IF( cdtype == 'TRA' .AND. ln_diaptr ) THEN zptry(:,:,:) = zptry(:,:,:) + zwy(:,:,:) ! <<< Add to previously computed CALL dia_ptr_ohst_components( jn, 'adv', zptry(:,:,:) ) ENDIF ! END DO ! CALL wrk_dealloc( jpi, jpj, jpk, zwi, zwz ) IF( l_trd .OR. l_trans ) THEN CALL wrk_dealloc( jpi, jpj, jpk, ztrdx, ztrdy, ztrdz ) CALL wrk_dealloc( jpi, jpj, z2d ) ENDIF IF( cdtype == 'TRA' .AND. ln_diaptr ) CALL wrk_dealloc( jpi, jpj, jpk, zptry ) ! IF( nn_timing == 1 ) CALL timing_stop('tra_adv_tvd') ! END SUBROUTINE tra_adv_tvd SUBROUTINE tra_adv_tvd_zts ( kt, kit000, cdtype, p2dt, pun, pvn, pwn, & & ptb, ptn, pta, kjpt ) !!---------------------------------------------------------------------- !! *** ROUTINE tra_adv_tvd_zts *** !! !! ** Purpose : Compute the now trend due to total advection of !! tracers and add it to the general trend of tracer equations !! !! ** Method : TVD ZTS scheme, i.e. 2nd order centered scheme with !! corrected flux (monotonic correction). This version use sub- !! timestepping for the vertical advection which increases stability !! when vertical metrics are small. !! note: - this advection scheme needs a leap-frog time scheme !! !! ** Action : - update (pta) with the now advective tracer trends !! - save the trends !!---------------------------------------------------------------------- USE oce , ONLY: zwx => ua , zwy => va ! (ua,va) used as workspace ! INTEGER , INTENT(in ) :: kt ! ocean time-step index 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 REAL(wp), DIMENSION( jpk ), INTENT(in ) :: p2dt ! vertical profile of tracer time-step REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pun, pvn, pwn ! 3 ocean velocity components REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb, ptn ! before and now tracer fields REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend ! REAL(wp), DIMENSION( jpk ) :: zts ! length of sub-timestep for vertical advection REAL(wp), DIMENSION( jpk ) :: zr_p2dt ! reciprocal of tracer timestep INTEGER :: ji, jj, jk, jl, jn ! dummy loop indices INTEGER :: jnzts = 5 ! number of sub-timesteps for vertical advection INTEGER :: jtb, jtn, jta ! sub timestep pointers for leap-frog/euler forward steps INTEGER :: jtaken ! toggle for collecting appropriate fluxes from sub timesteps REAL(wp) :: z_rzts ! Fractional length of Euler forward sub-timestep for vertical advection REAL(wp) :: z2dtt, zbtr, ztra ! local scalar REAL(wp) :: zfp_ui, zfp_vj, zfp_wk ! - - REAL(wp) :: zfm_ui, zfm_vj, zfm_wk ! - - REAL(wp), POINTER, DIMENSION(:,: ) :: zwx_sav , zwy_sav REAL(wp), POINTER, DIMENSION(:,:,:) :: zwi, zwz, zhdiv, zwz_sav, zwzts REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdx, ztrdy, ztrdz REAL(wp), POINTER, DIMENSION(:,:,:) :: zptry REAL(wp), POINTER, DIMENSION(:,:,:,:) :: ztrs !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('tra_adv_tvd_zts') ! CALL wrk_alloc( jpi, jpj, zwx_sav, zwy_sav ) CALL wrk_alloc( jpi, jpj, jpk, zwi, zwz , zhdiv, zwz_sav, zwzts ) CALL wrk_alloc( jpi, jpj, jpk, kjpt+1, ztrs ) ! IF( kt == kit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'tra_adv_tvd_zts : TVD ZTS advection scheme on ', cdtype IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' ENDIF ! l_trd = .FALSE. IF( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. ( cdtype == 'TRC' .AND. l_trdtrc ) ) l_trd = .TRUE. ! IF( l_trd ) THEN CALL wrk_alloc( jpi, jpj, jpk, ztrdx, ztrdy, ztrdz ) ztrdx(:,:,:) = 0._wp ; ztrdy(:,:,:) = 0._wp ; ztrdz(:,:,:) = 0._wp ENDIF ! IF( cdtype == 'TRA' .AND. ln_diaptr ) THEN CALL wrk_alloc( jpi, jpj,jpk, zptry ) zptry(:,:,:) = 0._wp ENDIF ! zwi(:,:,:) = 0._wp z_rzts = 1._wp / REAL( jnzts, wp ) zr_p2dt(:) = 1._wp / p2dt(:) ! ! ! =========== DO jn = 1, kjpt ! tracer loop ! ! =========== ! 1. Bottom value : flux set to zero ! ---------------------------------- zwx(:,:,jpk) = 0._wp ; zwz(:,:,jpk) = 0._wp zwy(:,:,jpk) = 0._wp ; zwi(:,:,jpk) = 0._wp ! 2. upstream advection with initial mass fluxes & intermediate update ! -------------------------------------------------------------------- ! upstream tracer flux in the i and j direction DO jk = 1, jpkm1 DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. ! upstream scheme zfp_ui = pun(ji,jj,jk) + ABS( pun(ji,jj,jk) ) zfm_ui = pun(ji,jj,jk) - ABS( pun(ji,jj,jk) ) zfp_vj = pvn(ji,jj,jk) + ABS( pvn(ji,jj,jk) ) zfm_vj = pvn(ji,jj,jk) - ABS( pvn(ji,jj,jk) ) zwx(ji,jj,jk) = 0.5_wp * ( zfp_ui * ptb(ji,jj,jk,jn) + zfm_ui * ptb(ji+1,jj ,jk,jn) ) zwy(ji,jj,jk) = 0.5_wp * ( zfp_vj * ptb(ji,jj,jk,jn) + zfm_vj * ptb(ji ,jj+1,jk,jn) ) END DO END DO END DO ! upstream tracer flux in the k direction ! Interior value DO jk = 2, jpkm1 DO jj = 1, jpj DO ji = 1, jpi zfp_wk = pwn(ji,jj,jk) + ABS( pwn(ji,jj,jk) ) zfm_wk = pwn(ji,jj,jk) - ABS( pwn(ji,jj,jk) ) zwz(ji,jj,jk) = 0.5_wp * ( zfp_wk * ptb(ji,jj,jk,jn) + zfm_wk * ptb(ji,jj,jk-1,jn) ) END DO END DO END DO ! Surface value IF( lk_vvl ) THEN IF ( ln_isfcav ) THEN DO jj = 1, jpj DO ji = 1, jpi zwz(ji,jj, mikt(ji,jj) ) = 0.e0 ! volume variable + isf END DO END DO ELSE zwz(:,:,1) = 0.e0 ! volume variable + no isf END IF ELSE IF ( ln_isfcav ) THEN DO jj = 1, jpj DO ji = 1, jpi zwz(ji,jj, mikt(ji,jj) ) = pwn(ji,jj,mikt(ji,jj)) * ptb(ji,jj,mikt(ji,jj),jn) ! linear free surface + isf END DO END DO ELSE zwz(:,:,1) = pwn(:,:,1) * ptb(:,:,1,jn) ! linear free surface + no isf END IF ENDIF ! total advective trend DO jk = 1, jpkm1 z2dtt = p2dt(jk) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ! 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) ) / e1e2t(ji,jj) ! update and guess with monotonic sheme pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra / fse3t_n(ji,jj,jk) * tmask(ji,jj,jk) zwi(ji,jj,jk) = ( fse3t_b(ji,jj,jk) * ptb(ji,jj,jk,jn) + z2dtt * ztra ) / fse3t_a(ji,jj,jk) * tmask(ji,jj,jk) END DO END DO END DO ! ! Lateral boundary conditions on zwi (unchanged sign) CALL lbc_lnk( zwi, 'T', 1. ) ! ! trend diagnostics (contribution of upstream fluxes) IF( l_trd ) THEN ! store intermediate advective trends ztrdx(:,:,:) = zwx(:,:,:) ; ztrdy(:,:,:) = zwy(:,:,:) ; ztrdz(:,:,:) = zwz(:,:,:) END IF ! ! "Poleward" heat and salt transports (contribution of upstream fluxes) IF( cdtype == 'TRA' .AND. ln_diaptr ) zptry(:,:,:) = zwy(:,:,:) ! 3. antidiffusive flux : high order minus low order ! -------------------------------------------------- ! antidiffusive flux on i and j ! DO jk = 1, jpkm1 ! DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. zwx_sav(ji,jj) = zwx(ji,jj,jk) zwy_sav(ji,jj) = zwy(ji,jj,jk) zwx(ji,jj,jk) = 0.5_wp * pun(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji+1,jj,jk,jn) ) zwy(ji,jj,jk) = 0.5_wp * pvn(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji,jj+1,jk,jn) ) END DO END DO DO jj = 2, jpjm1 ! partial horizontal divergence DO ji = fs_2, fs_jpim1 zhdiv(ji,jj,jk) = ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk) & & + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk) ) END DO END DO DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. zwx(ji,jj,jk) = zwx(ji,jj,jk) - zwx_sav(ji,jj) zwy(ji,jj,jk) = zwy(ji,jj,jk) - zwy_sav(ji,jj) END DO END DO END DO ! antidiffusive flux on k zwz(:,:,1) = 0._wp ! Surface value zwz_sav(:,:,:) = zwz(:,:,:) ! ztrs(:,:,:,1) = ptb(:,:,:,jn) zwzts(:,:,:) = 0._wp DO jl = 1, jnzts ! Start of sub timestepping loop IF( jl == 1 ) THEN ! Euler forward to kick things off jtb = 1 ; jtn = 1 ; jta = 2 zts(:) = p2dt(:) * z_rzts jtaken = MOD( jnzts + 1 , 2) ! Toggle to collect every second flux ! starting at jl =1 if jnzts is odd; ! starting at jl =2 otherwise ELSEIF( jl == 2 ) THEN ! First leapfrog step jtb = 1 ; jtn = 2 ; jta = 3 zts(:) = 2._wp * p2dt(:) * z_rzts ELSE ! Shuffle pointers for subsequent leapfrog steps jtb = MOD(jtb,3) + 1 jtn = MOD(jtn,3) + 1 jta = MOD(jta,3) + 1 ENDIF DO jk = 2, jpkm1 ! Interior value DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 zwz(ji,jj,jk) = 0.5_wp * pwn(ji,jj,jk) * ( ztrs(ji,jj,jk,jtn) + ztrs(ji,jj,jk-1,jtn) ) IF( jtaken == 0 ) zwzts(ji,jj,jk) = zwzts(ji,jj,jk) + zwz(ji,jj,jk)*zts(jk) ! Accumulate time-weighted vertcal flux END DO END DO END DO jtaken = MOD( jtaken + 1 , 2 ) DO jk = 2, jpkm1 ! Interior value DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 zbtr = 1._wp / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) ) ! total advective trends ztra = - zbtr * ( zhdiv(ji,jj,jk) + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) ztrs(ji,jj,jk,jta) = ztrs(ji,jj,jk,jtb) + zts(jk) * ztra END DO END DO END DO END DO DO jk = 2, jpkm1 ! Anti-diffusive vertical flux using average flux from the sub-timestepping DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 zwz(ji,jj,jk) = zwzts(ji,jj,jk) * zr_p2dt(jk) - zwz_sav(ji,jj,jk) END DO END DO END DO CALL lbc_lnk( zwx, 'U', -1. ) ; CALL lbc_lnk( zwy, 'V', -1. ) ! Lateral bondary conditions CALL lbc_lnk( zwz, 'W', 1. ) ! 4. monotonicity algorithm ! ------------------------- CALL nonosc( ptb(:,:,:,jn), zwx, zwy, zwz, zwi, p2dt ) ! 5. final trend with corrected fluxes ! ------------------------------------ DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zbtr = 1. / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) ) ! total advective trends ztra = - zbtr * ( 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) ) ! add them to the general tracer trends pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra END DO END DO END DO ! ! trend diagnostics (contribution of upstream fluxes) IF( l_trd ) THEN ztrdx(:,:,:) = ztrdx(:,:,:) + zwx(:,:,:) ! <<< Add to previously computed ztrdy(:,:,:) = ztrdy(:,:,:) + zwy(:,:,:) ! <<< Add to previously computed ztrdz(:,:,:) = ztrdz(:,:,:) + zwz(:,:,:) ! <<< Add to previously computed CALL trd_tra( kt, cdtype, jn, jptra_xad, ztrdx, pun, ptn(:,:,:,jn) ) CALL trd_tra( kt, cdtype, jn, jptra_yad, ztrdy, pvn, ptn(:,:,:,jn) ) CALL trd_tra( kt, cdtype, jn, jptra_zad, ztrdz, pwn, ptn(:,:,:,jn) ) END IF ! ! "Poleward" heat and salt transports (contribution of upstream fluxes) IF( cdtype == 'TRA' .AND. ln_diaptr ) THEN zptry(:,:,:) = zptry(:,:,:) + zwy(:,:,:) CALL dia_ptr_ohst_components( jn, 'adv', zptry(:,:,:) ) ENDIF ! END DO ! CALL wrk_dealloc( jpi, jpj, jpk, zwi, zwz, zhdiv, zwz_sav, zwzts ) CALL wrk_dealloc( jpi, jpj, jpk, kjpt+1, ztrs ) CALL wrk_dealloc( jpi, jpj, zwx_sav, zwy_sav ) IF( l_trd ) CALL wrk_dealloc( jpi, jpj, jpk, ztrdx, ztrdy, ztrdz ) IF( cdtype == 'TRA' .AND. ln_diaptr ) CALL wrk_dealloc( jpi, jpj, jpk, zptry ) ! IF( nn_timing == 1 ) CALL timing_stop('tra_adv_tvd_zts') ! END SUBROUTINE tra_adv_tvd_zts SUBROUTINE nonosc( 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 !!---------------------------------------------------------------------- REAL(wp), DIMENSION(jpk) , INTENT(in ) :: p2dt ! vertical profile of tracer time-step REAL(wp), DIMENSION (jpi,jpj,jpk), INTENT(in ) :: pbef, paft ! before & after field REAL(wp), DIMENSION (jpi,jpj,jpk), INTENT(inout) :: paa, pbb, pcc ! monotonic fluxes in the 3 directions ! INTEGER :: ji, jj, jk ! dummy loop indices INTEGER :: ikm1 ! local integer REAL(wp) :: zpos, zneg, zbt, za, zb, zc, zbig, zrtrn, z2dtt ! local scalars REAL(wp) :: zau, zbu, zcu, zav, zbv, zcv, zup, zdo ! - - REAL(wp), POINTER, DIMENSION(:,:,:) :: zbetup, zbetdo, zbup, zbdo !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('nonosc') ! CALL wrk_alloc( jpi, jpj, jpk, zbetup, zbetdo, zbup, zbdo ) ! zbig = 1.e+40_wp zrtrn = 1.e-15_wp zbetup(:,:,:) = 0._wp ; zbetdo(:,:,:) = 0._wp ! Search local extrema ! -------------------- ! max/min of pbef & paft with large negative/positive value (-/+zbig) inside land zbup = MAX( pbef * tmask - zbig * ( 1._wp - tmask ), & & paft * tmask - zbig * ( 1._wp - tmask ) ) zbdo = MIN( pbef * tmask + zbig * ( 1._wp - tmask ), & & paft * tmask + zbig * ( 1._wp - tmask ) ) DO jk = 1, jpkm1 ikm1 = MAX(jk-1,1) z2dtt = p2dt(jk) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ! 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 = e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) / z2dtt 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 DO END DO END DO CALL lbc_lnk( zbetup, 'T', 1. ) ; CALL lbc_lnk( zbetdo, 'T', 1. ) ! lateral boundary cond. (unchanged sign) ! 3. monotonic flux in the i & j direction (paa & pbb) ! ---------------------------------------- DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. 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 , 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 , 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 , pcc(ji,jj,jk+1) ) ) pcc(ji,jj,jk+1) = pcc(ji,jj,jk+1) * ( zc * za + ( 1._wp - zc) * zb ) END DO END DO END DO CALL lbc_lnk( paa, 'U', -1. ) ; CALL lbc_lnk( pbb, 'V', -1. ) ! lateral boundary condition (changed sign) ! CALL wrk_dealloc( jpi, jpj, jpk, zbetup, zbetdo, zbup, zbdo ) ! IF( nn_timing == 1 ) CALL timing_stop('nonosc') ! END SUBROUTINE nonosc !!====================================================================== END MODULE traadv_tvd