MODULE traadv_fct_lf !!============================================================================== !! *** 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-lf : 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 - loop fusion version !! nonosc_lf : compute monotonic tracer fluxes by a non-oscillatory algorithm - loop fusion version !!---------------------------------------------------------------------- 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) USE traadv_fct IMPLICIT NONE PRIVATE PUBLIC tra_adv_fct_lf ! called by traadv.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" #define search_in_neighbour(out,OP,vec,ji,jj,jk) \ out = OP(vec(ji,jj,jk),vec(ji-1,jj,jk),vec(ji+1,jj,jk),vec(ji,jj-1,jk),vec(ji,jj+1,jk),vec(ji,jj,MAX(jk-1,1)),vec(ji,jj,jk+1)) #define pos_part_of_flux(ji,jj,jk,out) \ out = MAX(0.,paa_in(ji-1,jj,jk)) - MIN(0.,paa_in(ji,jj,jk)) \ + MAX(0.,pbb_in(ji,jj-1,jk)) - MIN(0.,pbb_in(ji,jj,jk)) \ + MAX(0.,pcc_in(ji,jj,jk+1)) - MIN(0.,pcc_in(ji,jj,jk)) #define neg_part_of_flux(ji,jj,jk,out) \ out = MAX( 0.,paa_in(ji,jj,jk) ) - MIN( 0., paa_in(ji-1,jj,jk)) \ + MAX( 0.,pbb_in(ji,jj,jk) ) - MIN( 0., pbb_in(ji,jj-1,jk)) \ + MAX( 0.,pcc_in(ji,jj,jk) ) - MIN( 0., pcc_in(ji,jj,jk+1)) #define beta_terms(bt,betup,betdo,up,pos,do,neg,ji,jj,jk) \ bt = e1e2t(ji,jj) * e3t(ji,jj,jk,Kmm) / p2dt ; \ betup = ( up - paft(ji,jj,jk) ) / ( pos + zrtrn ) * bt ; \ betdo = ( paft(ji,jj,jk) - do ) / ( neg + zrtrn ) * bt #define monotonic_flux(a,b,c,betup_p1,betdo_p1,vec,vec_in,jk) \ a = MIN( 1._wp, zbetdo, betup_p1 ) ; \ b = MIN( 1._wp, zbetup, betdo_p1 ) ; \ c = ( 0.5_wp + SIGN( 0.5_wp , vec_in(ji,jj,jk) ) ) ; \ vec(ji,jj,jk) = vec_in(ji,jj,jk) * ( c * a + ( 1._wp - c) * b ) #define monotonic_flux_k(a,b,c,betup_p1,betdo_p1,vec,vec_in,jk) \ a = MIN( 1._wp, betdo_p1, zbetup ) ; \ b = MIN( 1._wp, betup_p1, zbetdo ) ; \ c = ( 0.5 + SIGN( 0.5_wp , vec_in(ji,jj,jk+1) ) ) ; \ vec(ji,jj,jk+1) = vec_in(ji,jj,jk+1) * ( c * a + ( 1._wp - c) * b ) !!---------------------------------------------------------------------- !! NEMO/OCE 4.0 , NEMO Consortium (2018) !! $Id: traadv_fct.F90 13660 2020-10-22 10:47:32Z francesca $ !! Software governed by the CeCILL license (see ./LICENSE) !!---------------------------------------------------------------------- CONTAINS 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(inout) :: 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, zwx_im1, zfp_ui, zfp_ui_m1, zfp_vj, zfp_vj_m1, zfp_wk, zC2t_u, zC4t_u ! - - REAL(wp) :: zwy, zwy_jm1, zfm_ui, zfm_ui_m1, zfm_vj, zfm_vj_m1, zfm_wk, zC2t_v, zC4t_v ! - - REAL(wp) :: ztu_im1, ztu_ip1, ztv_jm1, ztv_jp1, zltu_ip1, zltv_jp1, zltu, zltv REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwi, zwx_3d, zwy_3d, zwz, ztw, zltu_3d, zltv_3d, ztu, ztv 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 !! -- init to 0 zwi(:,:,:) = 0._wp 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 i and j direction ! !* 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 ! DO jk = 1, jpkm1 DO jj = 1, jpj-1 zfp_ui = pU(1,jj,jk) + ABS( pU(1,jj,jk) ) zfm_ui = pU(1,jj,jk) - ABS( pU(1,jj,jk) ) zwx = 0.5 * ( zfp_ui * pt(1,jj,jk,jn,Kbb) + zfm_ui * pt(2,jj ,jk,jn,Kbb) ) zwx_3d(1,jj,jk) = zwx zfp_vj = pV(1,jj,jk) + ABS( pV(1,jj,jk) ) zfm_vj = pV(1,jj,jk) - ABS( pV(1,jj,jk) ) zwy = 0.5 * ( zfp_vj * pt(1,jj,jk,jn,Kbb) + zfm_vj * pt(1 ,jj+1,jk,jn,Kbb) ) zwy_3d(1,jj,jk) = zwy END DO DO ji = 1, jpi-1 zfp_ui = pU(ji,1,jk) + ABS( pU(ji,1,jk) ) zfm_ui = pU(ji,1,jk) - ABS( pU(ji,1,jk) ) zwx = 0.5 * ( zfp_ui * pt(ji,1,jk,jn,Kbb) + zfm_ui * pt(ji+1,1 ,jk,jn,Kbb) ) zwx_3d(ji,1,jk) = zwx zfp_vj = pV(ji,1,jk) + ABS( pV(ji,1,jk) ) zfm_vj = pV(ji,1,jk) - ABS( pV(ji,1,jk) ) zwy = 0.5 * ( zfp_vj * pt(ji,1,jk,jn,Kbb) + zfm_vj * pt(ji ,2,jk,jn,Kbb) ) zwy_3d(ji,1,jk) = zwy END DO DO_2D( 1, 1, 1, 1 ) zfp_ui = pU(ji,jj,jk) + ABS( pU(ji,jj,jk) ) zfm_ui = pU(ji,jj,jk) - ABS( pU(ji,jj,jk) ) zwx = 0.5 * ( zfp_ui * pt(ji,jj,jk,jn,Kbb) + zfm_ui * pt(ji+1,jj ,jk,jn,Kbb) ) zwx_3d(ji,jj,jk) = zwx zfp_ui_m1 = pU(ji-1,jj,jk) + ABS( pU(ji-1,jj,jk) ) zfm_ui_m1 = pU(ji-1,jj,jk) - ABS( pU(ji-1,jj,jk) ) zwx_im1 = 0.5 * ( zfp_ui_m1 * pt(ji-1,jj,jk,jn,Kbb) + zfm_ui_m1 * pt(ji,jj ,jk,jn,Kbb) ) zfp_vj = pV(ji,jj,jk) + ABS( pV(ji,jj,jk) ) zfm_vj = pV(ji,jj,jk) - ABS( pV(ji,jj,jk) ) zwy = 0.5 * ( zfp_vj * pt(ji,jj,jk,jn,Kbb) + zfm_vj * pt(ji ,jj+1,jk,jn,Kbb) ) zwy_3d(ji,jj,jk) = zwy zfp_vj_m1 = pV(ji,jj-1,jk) + ABS( pV(ji,jj-1,jk) ) zfm_vj_m1 = pV(ji,jj-1,jk) - ABS( pV(ji,jj-1,jk) ) zwy_jm1 = 0.5 * ( zfp_vj_m1 * pt(ji,jj-1,jk,jn,Kbb) + zfm_vj_m1 * pt(ji,jj,jk,jn,Kbb) ) ! ! total intermediate advective trends ztra = - ( zwx - zwx_im1 + zwy - 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 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_3d(ji,jj,jk) = ( ztu(ji,jj,jk) + ztu(ji-1,jj,jk) ) * r1_6 zltv_3d(ji,jj,jk) = ( ztv(ji,jj,jk) + ztv(ji,jj-1,jk) ) * r1_6 END_2D END DO CALL lbc_lnk_multi( 'traadv_fct', zltu_3d, 'T', 1.0_wp , zltv_3d, 'T', 1.0_wp ) ! 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 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) ) - 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) ) - zwy_3d(ji,jj,jk) END_3D ! CALL lbc_lnk_multi( 'traadv_fct', zwx_3d, 'U', -1.0_wp , zwy_3d, 'V', -1.0_wp ) ! Lateral boundary cond. (unchanged sgn) 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_multi( '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 ==! ! #if defined key_agrif CALL nonosc( Kmm, pt(:,:,:,jn,Kbb), zwx_3d, zwy_3d, zwz, zwi, p2dt ) #else CALL nonosc_lf( Kmm, pt(:,:,:,jn,Kbb), zwx_3d, zwy_3d, zwz, zwi, p2dt ) #endif ! ! !== 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 IF( l_ptr ) THEN DEALLOCATE( zptry ) ENDIF ! END SUBROUTINE tra_adv_fct_lf SUBROUTINE nonosc_lf( 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, paft ! before & after field REAL(wp), DIMENSION (jpi,jpj,jpk), INTENT(inout) :: paa, pbb, pcc ! monotonic fluxes in the 3 directions REAL(wp), DIMENSION (jpi,jpj,jpk) :: paa_in, pbb_in, pcc_in ! monotonic fluxes in the 3 directions ! REAL(dp), DIMENSION (jpi,jpj,jpk) :: zbup, zbdo ! 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) :: zbetup, zbetdo REAL(dp) :: zbt_ip1, zpos_ip1, zneg_ip1, zup_ip1, zdo_ip1, zbetup_ip1, zbetdo_ip1 REAL(dp) :: zbt_jp1, zpos_jp1, zneg_jp1, zup_jp1, zdo_jp1, zbetup_jp1, zbetdo_jp1 REAL(dp) :: zbt_kp1, zpos_kp1, zneg_kp1, zup_kp1, zdo_kp1, zbetup_kp1, zbetdo_kp1 !!---------------------------------------------------------------------- ! zbig = 1.e+40_dp zrtrn = 1.e-15_dp paa_in(:,:,:) = paa(:,:,:) pbb_in(:,:,:) = pbb(:,:,:) pcc_in(:,:,:) = pcc(:,:,:) ! 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_3D( 1, 0, 1, 0, 1, jpk-2 ) ! search maximum in neighbourhood search_in_neighbour(zup,MAX,zbup,ji,jj,jk) search_in_neighbour(zup_ip1,MAX,zbup,ji+1,jj,jk) search_in_neighbour(zup_jp1,MAX,zbup,ji,jj+1,jk) search_in_neighbour(zup_kp1,MAX,zbup,ji,jj,jk+1) ! search minimum in neighbourhood search_in_neighbour(zdo,MIN,zbdo,ji,jj,jk) search_in_neighbour(zdo_ip1,MIN,zbdo,ji+1,jj,jk) search_in_neighbour(zdo_jp1,MIN,zbdo,ji,jj+1,jk) search_in_neighbour(zdo_kp1,MIN,zbdo,ji,jj,jk+1) ! positive part of the flux pos_part_of_flux(ji,jj,jk,zpos) pos_part_of_flux(ji+1,jj,jk,zpos_ip1) pos_part_of_flux(ji,jj+1,jk,zpos_jp1) pos_part_of_flux(ji,jj,jk+1,zpos_kp1) ! negative part of the flux neg_part_of_flux(ji,jj,jk,zneg) neg_part_of_flux(ji+1,jj,jk,zneg_ip1) neg_part_of_flux(ji,jj+1,jk,zneg_jp1) neg_part_of_flux(ji,jj,jk+1,zneg_kp1) ! up & down beta terms beta_terms(zbt,zbetup,zbetdo,zup,zpos,zdo,zneg,ji,jj,jk) beta_terms(zbt_ip1,zbetup_ip1,zbetdo_ip1,zup_ip1,zpos_ip1,zdo_ip1,zneg_ip1,ji+1,jj,jk) beta_terms(zbt_jp1,zbetup_jp1,zbetdo_jp1,zup_jp1,zpos_jp1,zdo_jp1,zneg_jp1,ji,jj+1,jk) beta_terms(zbt_kp1,zbetup_kp1,zbetdo_kp1,zup_kp1,zpos_kp1,zdo_kp1,zneg_kp1,ji,jj,jk+1) ! 3. monotonic flux in the i & j (paa & pbb) ! ---------------------------------------- monotonic_flux(zau,zbu,zcu,zbetup_ip1,zbetdo_ip1,paa,paa_in,jk) monotonic_flux(zav,zbv,zcv,zbetup_jp1,zbetdo_jp1,pbb,pbb_in,jk) ! monotonic flux in the k direction, i.e. pcc ! ------------------------------------------- monotonic_flux_k(za,zb,zc,zbetup_kp1,zbetdo_kp1,pcc,pcc_in,jk) END_3D ! DO_2D( 1, 0, 1, 0 ) ! search maximum in neighbourhood search_in_neighbour(zup,MAX,zbup,ji,jj,jpk-1) search_in_neighbour(zup_ip1,MAX,zbup,ji+1,jj,jpk-1) search_in_neighbour(zup_jp1,MAX,zbup,ji,jj+1,jpk-1) ! search minimum in neighbourhood search_in_neighbour(zdo,MIN,zbdo,ji,jj,jk) search_in_neighbour(zdo_ip1,MIN,zbdo,ji+1,jj,jpk-1) search_in_neighbour(zdo_jp1,MIN,zbdo,ji,jj+1,jpk-1) ! positive part of the flux pos_part_of_flux(ji,jj,jpk-1,zpos) pos_part_of_flux(ji+1,jj,jpk-1,zpos_ip1) pos_part_of_flux(ji,jj+1,jpk-1,zpos_jp1) ! negative part of the flux neg_part_of_flux(ji,jj,jpk-1,zneg) neg_part_of_flux(ji+1,jj,jpk-1,zneg_ip1) neg_part_of_flux(ji,jj+1,jpk-1,zneg_jp1) ! up & down beta terms beta_terms(zbt,zbetup,zbetdo,zup,zpos,zdo,zneg,ji,jj,jpk-1) beta_terms(zbt_ip1,zbetup_ip1,zbetdo_ip1,zup_ip1,zpos_ip1,zdo_ip1,zneg_ip1,ji+1,jj,jpk-1) beta_terms(zbt_jp1,zbetup_jp1,zbetdo_jp1,zup_jp1,zpos_jp1,zdo_jp1,zneg_jp1,ji,jj+1,jpk-1) zbetup_kp1 = 0._dp zbetdo_kp1 = 0._dp ! 3. monotonic flux in the i & j direction (paa & pbb) ! ---------------------------------------- monotonic_flux(zau,zbu,zcu,zbetup_ip1,zbetdo_ip1,paa,paa_in,jpk-1) monotonic_flux(zav,zbv,zcv,zbetup_jp1,zbetdo_jp1,pbb,pbb_in,jpk-1) ! monotonic flux in the k direction, i.e. pcc ! ------------------------------------------- monotonic_flux_k(za,zb,zc,zbetup_kp1,zbetdo_kp1,pcc,pcc_in,jpk-1) END_2D END SUBROUTINE nonosc_lf END MODULE traadv_fct_lf