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 !! tra_adv_fct_zts: update the tracer trend with a 3D advective trends using a 2nd 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 in_out_manager ! I/O manager 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) USE wrk_nemo ! Memory Allocation USE timing ! Timing IMPLICIT NONE PRIVATE PUBLIC tra_adv_fct ! routine called by traadv.F90 PUBLIC tra_adv_fct_zts ! routine called by traadv.F90 PUBLIC interp_4th_cpt ! routine called by traadv_cen.F90 LOGICAL :: l_trd ! flag to compute trends REAL(wp) :: r1_6 = 1._wp / 6._wp ! =1/6 !! * Substitutions # include "domzgr_substitute.h90" # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OPA 3.7 , NEMO Consortium (2014) !! $Id$ !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE tra_adv_fct( kt, kit000, cdtype, p2dt, pun, pvn, pwn, & & ptb, ptn, pta, kjpt, 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) !! - 4th order compact scheme on the vertical !! - corrected flux (monotonic correction) !! !! ** Action : - update (pta) with the now advective tracer trends !! - send the trends for further diagnostics !!---------------------------------------------------------------------- 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 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), 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 REAL(wp) :: z2dtt, 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), POINTER, DIMENSION(:,:,:) :: zwi, zwx, zwy, zwz, ztu, ztv, zltu, zltv, ztw REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdx, ztrdy, ztrdz !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('tra_adv_fct') ! CALL wrk_alloc( jpi,jpj,jpk, zwi, zwx, zwy, zwz, ztu, ztv, zltu, zltv, ztw ) ! 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. 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 ! ! ! surface & bottom value : flux set to zero one for all IF( lk_vvl ) zwz(:,:, 1 ) = 0._wp ! except at the surface in linear free surface case zwx(:,:,jpk) = 0._wp ; zwy(:,:,jpk) = 0._wp ; zwz(:,:,jpk) = 0._wp ! zwi(:,:,:) = 0._wp ! ! =========== DO jn = 1, kjpt ! tracer loop ! ! =========== ! ! !== 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 *! DO jk = 2, jpkm1 ! Interior value ( multiplied by wmask) 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 ! IF(.NOT.lk_vvl ) 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 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 ! no cavities: only at the ocean surface zwz(:,:,1) = pwn(:,:,1) * ptb(:,:,1,jn) ENDIF ENDIF ! DO jk = 1, jpkm1 !* trend and after field with monotonic scheme 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) * fse3t_n(ji,jj,jk) ) ! update and guess with monotonic sheme !!gm why tmask added in the two following lines ??? the mask is done in tranxt ! pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra * tmask(ji,jj,jk) zwi(ji,jj,jk) = ( ptb(ji,jj,jk,jn) + z2dtt * ztra ) * tmask(ji,jj,jk) END DO END DO END DO CALL lbc_lnk( zwi, 'T', 1. ) ! Lateral boundary conditions on zwi (unchanged sign) ! IF( l_trd ) 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( cdtype == 'TRA' .AND. ln_diaptr ) THEN IF( jn == jp_tem ) htr_adv(:) = ptr_sj( zwy(:,:,:) ) IF( jn == jp_sal ) str_adv(:) = ptr_sj( zwy(:,:,:) ) ENDIF ! ! ! !== anti-diffusive flux : high order minus low order ==! ! SELECT CASE( kn_fct_h ) !* horizontal anti-diffusive fluxes ! CASE( 2 ) ! 2nd order centered DO jk = 1, jpkm1 DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. zwx(ji,jj,jk) = 0.5_wp * 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_wp * 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 ! 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 jj = 1, jpjm1 ! First derivative (gradient) DO ji = 1, fs_jpim1 ! vector opt. ztu(ji,jj,jk) = ( ptn(ji+1,jj ,jk,jn) - ptn(ji,jj,jk,jn) ) * umask(ji,jj,jk) ztv(ji,jj,jk) = ( ptn(ji ,jj+1,jk,jn) - ptn(ji,jj,jk,jn) ) * vmask(ji,jj,jk) END DO END DO DO jj = 2, jpjm1 ! DO ji = fs_2, fs_jpim1 ! vector opt. 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 DO END DO END DO ! CALL lbc_lnk( zltu, 'T', 1. ) ; CALL lbc_lnk( zltv, 'T', 1. ) ! Lateral boundary cond. (unchanged sgn) ! DO jk = 1, jpkm1 ! Horizontal advective fluxes DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. zC2t_u = ptn(ji,jj,jk,jn) + ptn(ji+1,jj ,jk,jn) ! 2 x C2 interpolation of T at u- & v-points zC2t_v = ptn(ji,jj,jk,jn) + ptn(ji ,jj+1,jk,jn) ! ! C4 minus upstream advective fluxes zwx(ji,jj,jk) = 0.5_wp * pun(ji,jj,jk) * ( zC2t_u + zltu(ji,jj,jk) - zltu(ji+1,jj,jk) ) - zwx(ji,jj,jk) zwy(ji,jj,jk) = 0.5_wp * pvn(ji,jj,jk) * ( zC2t_v + zltv(ji,jj,jk) - zltv(ji,jj+1,jk) ) - zwy(ji,jj,jk) END DO END DO END DO ! 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 jk = 1, jpkm1 ! gradient DO jj = 1, jpjm1 ! First derivative (gradient) DO ji = 1, fs_jpim1 ! vector opt. ztu(ji,jj,jk) = ( ptn(ji+1,jj ,jk,jn) - ptn(ji,jj,jk,jn) ) * umask(ji,jj,jk) ztv(ji,jj,jk) = ( ptn(ji ,jj+1,jk,jn) - ptn(ji,jj,jk,jn) ) * vmask(ji,jj,jk) END DO END DO END DO CALL lbc_lnk( ztu, 'U', -1. ) ; CALL lbc_lnk( ztv, 'V', -1. ) ! Lateral boundary cond. (unchanged sgn) ! DO jk = 1, jpkm1 ! Horizontal advective fluxes DO jj = 2, jpjm1 DO ji = 2, fs_jpim1 ! vector opt. zC2t_u = ptn(ji,jj,jk,jn) + ptn(ji+1,jj ,jk,jn) ! 2 x C2 interpolation of T at u- & v-points (x2) zC2t_v = ptn(ji,jj,jk,jn) + ptn(ji ,jj+1,jk,jn) ! ! 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 * pun(ji,jj,jk) * zC4t_u - zwx(ji,jj,jk) zwy(ji,jj,jk) = 0.5_wp * pvn(ji,jj,jk) * zC4t_v - zwy(ji,jj,jk) END DO END DO END DO ! END SELECT ! !* vertical anti-diffusive fluxes SELECT CASE( kn_fct_v ) ! Interior values (w-masked) ! CASE( 2 ) ! 2nd order centered DO jk = 2, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 zwz(ji,jj,jk) = ( 0.5_wp * pwn(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji,jj,jk-1,jn) ) & - zwz(ji,jj,jk) ) * wmask(ji,jj,jk) END DO END DO END DO ! CASE( 4 ) ! 4th order COMPACT ! CALL interp_4th_cpt( ptn(:,:,:,jn) , ztw ) ! COMPACT interpolation of T at w-point ! DO jk = 2, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 zwz(ji,jj,jk) = ( pwn(ji,jj,jk) * ztw(ji,jj,jk) - zwz(ji,jj,jk) ) * wmask(ji,jj,jk) END DO END DO END DO ! END SELECT ! ! top ocean value: high order = upstream ==>> zwz=0 zwz(:,:, 1 ) = 0._wp ! only ocean surface as interior zwz values have been w-masked ! CALL lbc_lnk( zwx, 'U', -1. ) ; CALL lbc_lnk( zwy, 'V', -1. ) ! Lateral bondary conditions CALL lbc_lnk( zwz, 'W', 1. ) ! !== monotonicity algorithm ==! ! CALL nonosc( ptb(:,:,:,jn), zwx, zwy, zwz, zwi, p2dt ) ! !== final trend with corrected fluxes ==! ! DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) - ( 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) * fse3t(ji,jj,jk) ) END DO END DO END DO ! IF( l_trd ) THEN ! trend diagnostics (contribution of upstream fluxes) 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) ) ! CALL wrk_dealloc( jpi,jpj,jpk, ztrdx, ztrdy, ztrdz ) END IF ! ! "Poleward" heat and salt transports (contribution of upstream fluxes) IF( cdtype == 'TRA' .AND. ln_diaptr ) THEN IF( jn == jp_tem ) htr_adv(:) = ptr_sj( zwy(:,:,:) ) + htr_adv(:) IF( jn == jp_sal ) str_adv(:) = ptr_sj( zwy(:,:,:) ) + str_adv(:) ENDIF ! END DO ! CALL wrk_dealloc( jpi,jpj,jpk, zwi, zwx, zwy, zwz, ztu, ztv, zltu, zltv, ztw ) ! IF( nn_timing == 1 ) CALL timing_stop('tra_adv_fct') ! END SUBROUTINE tra_adv_fct SUBROUTINE tra_adv_fct_zts( kt, kit000, cdtype, p2dt, pun, pvn, pwn, & & ptb, ptn, pta, kjpt, kn_fct_zts ) !!---------------------------------------------------------------------- !! *** ROUTINE tra_adv_fct_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 !!---------------------------------------------------------------------- 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 INTEGER , INTENT(in ) :: kn_fct_zts ! number of number of vertical sub-timesteps 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 :: 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, 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, zwx, zwy, zwz, zhdiv, zwzts, zwz_sav REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdx, ztrdy, ztrdz REAL(wp), POINTER, DIMENSION(:,:,:,:) :: ztrs !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('tra_adv_fct_zts') ! CALL wrk_alloc( jpi,jpj, zwx_sav, zwy_sav ) CALL wrk_alloc( jpi,jpj, jpk, zwx, zwy, zwz, zwi, zhdiv, zwzts, zwz_sav ) CALL wrk_alloc( jpi,jpj,jpk,kjpt+1, ztrs ) ! IF( kt == kit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'tra_adv_fct_zts : 2nd order FCT scheme with ', kn_fct_zts, ' vertical sub-timestep 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 ! zwi(:,:,:) = 0._wp z_rzts = 1._wp / REAL( kn_fct_zts, 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 DO jk = 2, jpkm1 ! Interior value 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) ) * wmask(ji,jj,jk) END DO END DO END DO ! ! top value IF( lk_vvl ) THEN ! variable volume: only k=1 as zwz is multiplied by wmask zwz(:,:, 1 ) = 0._wp ELSE ! linear free surface IF( ln_isfcav ) THEN ! ice-shelf cavities 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) END DO END DO ELSE ! standard case zwz(:,:,1) = pwn(:,:,1) * ptb(:,:,1,jn) ENDIF ENDIF ! DO jk = 1, jpkm1 ! total advective trend 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) * fse3t_n(ji,jj,jk) ) ! update and guess with monotonic sheme pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra zwi(ji,jj,jk) = ( ptb(ji,jj,jk,jn) + z2dtt * ztra ) * tmask(ji,jj,jk) END DO END DO END DO ! CALL lbc_lnk( zwi, 'T', 1. ) ! Lateral boundary conditions on zwi (unchanged sign) ! IF( l_trd ) 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( cdtype == 'TRA' .AND. ln_diaptr ) THEN IF( jn == jp_tem ) htr_adv(:) = ptr_sj( zwy(:,:,:) ) IF( jn == jp_sal ) str_adv(:) = ptr_sj( zwy(:,:,:) ) ENDIF ! 3. anti-diffusive flux : high order minus low order ! --------------------------------------------------- DO jk = 1, jpkm1 !* horizontal anti-diffusive fluxes ! 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 ! !* vertical anti-diffusive flux zwz_sav(:,:,:) = zwz(:,:,:) ztrs (:,:,:,1) = ptb(:,:,:,jn) zwzts (:,:,:) = 0._wp IF( lk_vvl ) zwz(:,:, 1 ) = 0._wp ! surface value set to zero in vvl case ! DO jl = 1, kn_fct_zts ! 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( kn_fct_zts + 1 , 2) ! Toggle to collect every second flux ! ! starting at jl =1 if kn_fct_zts 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) ) * wmask(ji,jj,jk) 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 IF(.NOT.lk_vvl ) THEN ! top value (only in linear free surface case) IF( ln_isfcav ) THEN ! ice-shelf cavities 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 ! standard case zwz(:,:,1) = pwn(:,:,1) * ptb(:,:,1,jn) ENDIF ENDIF ! jtaken = MOD( jtaken + 1 , 2 ) ! DO jk = 2, jpkm1 ! total advective trends DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ztrs(ji,jj,jk,jta) = ztrs(ji,jj,jk,jtb) & & - zts(jk) * ( zhdiv(ji,jj,jk) + zwz(ji,jj,jk) - zwz(ji,jj,jk+1) ) & & / ( e1e2t(ji,jj) * fse3t(ji,jj,jk) ) 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) ) * wmask(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. pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ( zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) & & + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) & & / ( e1e2t(ji,jj) * fse3t_n(ji,jj,jk) ) 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) ) ! CALL wrk_dealloc( jpi,jpj,jpk, ztrdx, ztrdy, ztrdz ) END IF ! ! "Poleward" heat and salt transports (contribution of upstream fluxes) IF( cdtype == 'TRA' .AND. ln_diaptr ) THEN IF( jn == jp_tem ) htr_adv(:) = ptr_sj( zwy(:,:,:) ) + htr_adv(:) IF( jn == jp_sal ) str_adv(:) = ptr_sj( zwy(:,:,:) ) + str_adv(:) ENDIF ! END DO ! CALL wrk_alloc( jpi,jpj, zwx_sav, zwy_sav ) CALL wrk_alloc( jpi,jpj, jpk, zwx, zwy, zwz, zwi, zhdiv, zwzts, zwz_sav ) CALL wrk_alloc( jpi,jpj,jpk,kjpt+1, ztrs ) ! IF( nn_timing == 1 ) CALL timing_stop('tra_adv_fct_zts') ! END SUBROUTINE tra_adv_fct_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 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 ! 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 jk = 3, jpkm1 !== build the three diagonal matrix ==! DO jj = 1, jpj DO ji = 1, jpi 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 DO END DO END DO ! jk=2 ! Switch to second order centered at top DO jj=1,jpj DO ji=1,jpi 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 DO END DO ! ! !== tridiagonal solve ==! DO jj = 1, jpj ! first recurrence DO ji = 1, jpi zwt(ji,jj,2) = zwd(ji,jj,2) END DO END DO DO jk = 3, jpkm1 DO jj = 1, jpj DO ji = 1, jpi zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1) END DO END DO END DO ! DO jj = 1, jpj ! second recurrence: Zk = Yk - Ik / Tk-1 Zk-1 DO ji = 1, jpi pt_out(ji,jj,2) = zwrm(ji,jj,2) END DO END DO DO jk = 3, jpkm1 DO jj = 1, jpj DO ji = 1, jpi 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 DO END DO END DO DO jj = 1, jpj ! third recurrence: Xk = (Zk - Sk Xk+1 ) / Tk DO ji = 1, jpi pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1) END DO END DO DO jk = jpk-2, 2, -1 DO jj = 1, jpj DO ji = 1, jpi 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 DO END DO END DO ! END SUBROUTINE interp_4th_cpt !!====================================================================== END MODULE traadv_fct