MODULE traadv_muscl2 !!====================================================================== !! *** MODULE traadv_muscl2 *** !! Ocean tracers: horizontal & vertical advective trend !!====================================================================== !! History : 1.0 ! 2002-06 (G. Madec) from traadv_muscl !! 3.2 ! 2010-05 (C. Ethe, G. Madec) merge TRC-TRA + switch from velocity to transport !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! tra_adv_muscl2 : update the tracer trend with the horizontal !! and vertical advection trends using MUSCL2 scheme !!---------------------------------------------------------------------- USE oce ! ocean dynamics and active tracers USE trc_oce ! share passive tracers/Ocean variables USE dom_oce ! ocean space and time domain USE trd_oce ! trends: ocean variables USE trdtra ! trends manager: tracers USE in_out_manager ! I/O manager USE dynspg_oce ! choice/control of key cpp for surface pressure gradient USE diaptr ! poleward transport diagnostics ! USE lib_mpp ! distribued memory computing USE lbclnk ! ocean lateral boundary condition (or mpp link) USE wrk_nemo ! Memory Allocation USE timing ! Timing USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) IMPLICIT NONE PRIVATE PUBLIC tra_adv_muscl2 ! routine called by step.F90 !! * Substitutions # include "domzgr_substitute.h90" # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OPA 3.3 , NEMO Consortium (2010) !! $Id$ !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE tra_adv_muscl2( kt, kit000, cdtype, p2dt, pun, pvn, pwn, & & ptb, ptn, pta, kjpt ) !!---------------------------------------------------------------------- !! *** ROUTINE tra_adv_muscl2 *** !! !! ** Purpose : Compute the now trend due to total advection of T and !! S using a MUSCL scheme (Monotone Upstream-centered Scheme for !! Conservation Laws) and add it to the general tracer trend. !! !! ** Method : MUSCL scheme plus centered scheme at ocean boundaries !! !! ** Action : - update (pta) with the now advective tracer trends !! - save trends !! !! References : Estubier, A., and M. Levy, Notes Techn. Pole de Modelisation !! IPSL, Sept. 2000 (http://www.lodyc.jussieu.fr/opa) !!---------------------------------------------------------------------- INTEGER , INTENT(in ) :: kt ! ocean time-step index INTEGER , INTENT(in ) :: 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 & 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) :: zu, z0u, zzwx, zw ! local scalars REAL(wp) :: zv, z0v, zzwy, z0w ! - - REAL(wp) :: ztra, zbtr, zdt, zalpha ! - - REAL(wp), POINTER, DIMENSION(:,:,:) :: zslpx, zslpy , zwx, zwy !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('tra_adv_muscl2') ! CALL wrk_alloc( jpi, jpj, jpk, zslpx, zslpy, zwx, zwy ) ! IF( kt == kit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'tra_adv_muscl2 : MUSCL2 advection scheme on ', cdtype IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~~' ENDIF ! ! ! =========== DO jn = 1, kjpt ! tracer loop ! ! =========== ! I. Horizontal advective fluxes ! ------------------------------ ! first guess of the slopes zwx(:,:,jpk) = 0.e0 ; zwy(:,:,jpk) = 0.e0 ! bottom values ! interior values DO jk = 1, jpkm1 DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. zwx(ji,jj,jk) = umask(ji,jj,jk) * ( ptb(ji+1,jj,jk,jn) - ptb(ji,jj,jk,jn) ) zwy(ji,jj,jk) = vmask(ji,jj,jk) * ( ptb(ji,jj+1,jk,jn) - ptb(ji,jj,jk,jn) ) END DO END DO END DO ! CALL lbc_lnk( zwx, 'U', -1. ) ! lateral boundary conditions on zwx, zwy (changed sign) CALL lbc_lnk( zwy, 'V', -1. ) ! !-- Slopes of tracer zslpx(:,:,jpk) = 0.e0 ; zslpy(:,:,jpk) = 0.e0 ! bottom values DO jk = 1, jpkm1 ! interior values DO jj = 2, jpj DO ji = fs_2, jpi ! vector opt. zslpx(ji,jj,jk) = ( zwx(ji,jj,jk) + zwx(ji-1,jj ,jk) ) & & * ( 0.25 + SIGN( 0.25, zwx(ji,jj,jk) * zwx(ji-1,jj ,jk) ) ) zslpy(ji,jj,jk) = ( zwy(ji,jj,jk) + zwy(ji ,jj-1,jk) ) & & * ( 0.25 + SIGN( 0.25, zwy(ji,jj,jk) * zwy(ji ,jj-1,jk) ) ) END DO END DO END DO ! DO jk = 1, jpkm1 ! Slopes limitation DO jj = 2, jpj DO ji = fs_2, jpi ! vector opt. zslpx(ji,jj,jk) = SIGN( 1., zslpx(ji,jj,jk) ) * MIN( ABS( zslpx(ji ,jj,jk) ), & & 2.*ABS( zwx (ji-1,jj,jk) ), & & 2.*ABS( zwx (ji ,jj,jk) ) ) zslpy(ji,jj,jk) = SIGN( 1., zslpy(ji,jj,jk) ) * MIN( ABS( zslpy(ji,jj ,jk) ), & & 2.*ABS( zwy (ji,jj-1,jk) ), & & 2.*ABS( zwy (ji,jj ,jk) ) ) END DO END DO END DO ! interior values ! !-- MUSCL horizontal advective fluxes DO jk = 1, jpkm1 ! interior values zdt = p2dt(jk) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ! MUSCL fluxes z0u = SIGN( 0.5, pun(ji,jj,jk) ) zalpha = 0.5 - z0u zu = z0u - 0.5 * pun(ji,jj,jk) * zdt / ( e1u(ji,jj) * e2u(ji,jj) * fse3u(ji,jj,jk) ) zzwx = ptb(ji+1,jj,jk,jn) + zu * zslpx(ji+1,jj,jk) zzwy = ptb(ji ,jj,jk,jn) + zu * zslpx(ji ,jj,jk) zwx(ji,jj,jk) = pun(ji,jj,jk) * ( zalpha * zzwx + (1.-zalpha) * zzwy ) ! z0v = SIGN( 0.5, pvn(ji,jj,jk) ) zalpha = 0.5 - z0v zv = z0v - 0.5 * pvn(ji,jj,jk) * zdt / ( e1v(ji,jj) * e2v(ji,jj) * fse3v(ji,jj,jk) ) zzwx = ptb(ji,jj+1,jk,jn) + zv * zslpy(ji,jj+1,jk) zzwy = ptb(ji,jj ,jk,jn) + zv * zslpy(ji,jj ,jk) zwy(ji,jj,jk) = pvn(ji,jj,jk) * ( zalpha * zzwx + (1.-zalpha) * zzwy ) END DO END DO END DO !! centered scheme at lateral b.C. if off-shore velocity DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. IF( umask(ji,jj,jk) == 0. ) THEN IF( pun(ji+1,jj,jk) > 0. .AND. ji /= jpi ) THEN zwx(ji+1,jj,jk) = 0.5 * pun(ji+1,jj,jk) * ( ptn(ji+1,jj,jk,jn) + ptn(ji+2,jj,jk,jn) ) ENDIF IF( pun(ji-1,jj,jk) < 0. ) THEN zwx(ji-1,jj,jk) = 0.5 * pun(ji-1,jj,jk) * ( ptn(ji-1,jj,jk,jn) + ptn(ji,jj,jk,jn) ) ENDIF ENDIF IF( vmask(ji,jj,jk) == 0. ) THEN IF( pvn(ji,jj+1,jk) > 0. .AND. jj /= jpj ) THEN zwy(ji,jj+1,jk) = 0.5 * pvn(ji,jj+1,jk) * ( ptn(ji,jj+1,jk,jn) + ptn(ji,jj+2,jk,jn) ) ENDIF IF( pvn(ji,jj-1,jk) < 0. ) THEN zwy(ji,jj-1,jk) = 0.5 * pvn(ji,jj-1,jk) * ( ptn(ji,jj-1,jk,jn) + ptn(ji,jj,jk,jn) ) ENDIF ENDIF END DO END DO END DO CALL lbc_lnk( zwx, 'U', -1. ) ; CALL lbc_lnk( zwy, 'V', -1. ) ! lateral boundary condition (changed sign) ! Tracer flux divergence at t-point added to the general trend 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) ) ! horizontal advective trends ztra = - zbtr * ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) & & + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) ) ! added 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( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. & &( cdtype == 'TRC' .AND. l_trdtrc ) ) THEN CALL trd_tra( kt, cdtype, jn, jptra_xad, zwx, pun, ptb(:,:,:,jn) ) CALL trd_tra( kt, cdtype, jn, jptra_yad, zwy, pvn, ptb(:,:,:,jn) ) 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 ! II. Vertical advective fluxes ! ----------------------------- ! !-- first guess of the slopes zwx (:,:, 1 ) = 0.e0 ; zwx (:,:,jpk) = 0.e0 ! surface & bottom boundary conditions DO jk = 2, jpkm1 ! interior values zwx(:,:,jk) = tmask(:,:,jk) * ( ptb(:,:,jk-1,jn) - ptb(:,:,jk,jn) ) END DO ! !-- Slopes of tracer zslpx(:,:,1) = 0.e0 ! surface values DO jk = 2, jpkm1 ! interior value DO jj = 1, jpj DO ji = 1, jpi zslpx(ji,jj,jk) = ( zwx(ji,jj,jk) + zwx(ji,jj,jk+1) ) & & * ( 0.25 + SIGN( 0.25, zwx(ji,jj,jk) * zwx(ji,jj,jk+1) ) ) END DO END DO END DO ! !-- Slopes limitation DO jk = 2, jpkm1 ! interior values DO jj = 1, jpj DO ji = 1, jpi zslpx(ji,jj,jk) = SIGN( 1., zslpx(ji,jj,jk) ) * MIN( ABS( zslpx(ji,jj,jk ) ), & & 2.*ABS( zwx (ji,jj,jk+1) ), & & 2.*ABS( zwx (ji,jj,jk ) ) ) END DO END DO END DO ! !-- vertical advective flux ! ! surface values (bottom already set to zero) IF( lk_vvl ) THEN ; zwx(:,:, 1 ) = 0.e0 ! variable volume ELSE ; zwx(:,:, 1 ) = pwn(:,:,1) * ptb(:,:,1,jn) ! linear free surface ENDIF ! DO jk = 1, jpkm1 ! interior values zdt = p2dt(jk) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zbtr = 1. / ( e1t(ji,jj) * e2t(ji,jj) * fse3w(ji,jj,jk+1) ) z0w = SIGN( 0.5, pwn(ji,jj,jk+1) ) zalpha = 0.5 + z0w zw = z0w - 0.5 * pwn(ji,jj,jk+1) * zdt * zbtr zzwx = ptb(ji,jj,jk+1,jn) + zw * zslpx(ji,jj,jk+1) zzwy = ptb(ji,jj,jk ,jn) + zw * zslpx(ji,jj,jk ) zwx(ji,jj,jk+1) = pwn(ji,jj,jk+1) * ( zalpha * zzwx + (1.-zalpha) * zzwy ) END DO END DO END DO ! DO jk = 2, jpkm1 ! centered near the bottom DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. IF( tmask(ji,jj,jk+1) == 0. ) THEN IF( pwn(ji,jj,jk) > 0. ) THEN zwx(ji,jj,jk) = 0.5 * pwn(ji,jj,jk) * ( ptn(ji,jj,jk-1,jn) + ptn(ji,jj,jk,jn) ) ENDIF ENDIF END DO END DO END DO ! DO jk = 1, jpkm1 ! Compute & add the vertical advective trend DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zbtr = 1. / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) ) ! vertical advective trends ztra = - zbtr * ( zwx(ji,jj,jk) - zwx(ji,jj,jk+1) ) ! added 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( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. & &( cdtype == 'TRC' .AND. l_trdtrc ) ) & CALL trd_tra( kt, cdtype, jn, jptra_zad, zwx, pwn, ptb(:,:,:,jn) ) ! END DO ! CALL wrk_dealloc( jpi, jpj, jpk, zslpx, zslpy, zwx, zwy ) ! IF( nn_timing == 1 ) CALL timing_stop('tra_adv_muscl2') ! END SUBROUTINE tra_adv_muscl2 !!====================================================================== END MODULE traadv_muscl2