MODULE traadv_tvd !!============================================================================== !! *** MODULE traadv_tvd *** !! Ocean active tracers: horizontal & vertical advective trend !!============================================================================== !! History : 7.0 ! 1995-12 (L. Mortier) Original code !! 8.0 ! 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 !! - ! 2008-04 (S. Cravatte) add the i-, j- & k- trends computation !! - ! 2005-11 (V. Garnier) Surface pressure gradient organization !! 2.4 ! 2008-01 (G. Madec) merge TRC-TRA + switch from velocity to transport !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! tra_adv_tvd : update the tracer trend with the horizontal and !! vertical advection trends using a TVD scheme !! nonosc : compute monotonic tracer fluxes by a nonoscillatory algorithm !!---------------------------------------------------------------------- USE dom_oce ! ocean space and time domain USE trdmod ! ocean active tracers trends USE trdmod_oce ! ocean variables trends USE in_out_manager ! I/O manager USE dynspg_oce ! choice/control of key cpp for surface pressure gradient USE trabbl ! Advective term of BBL USE lib_mpp ! USE lbclnk ! ocean lateral boundary condition (or mpp link) USE diaptr ! poleward transport diagnostics USE prtctl ! Print control IMPLICIT NONE PRIVATE PUBLIC tra_adv_tvd ! routine called by traadv.F90 !! * Substitutions # include "domzgr_substitute.h90" # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OPA 2.4 , LOCEAN-IPSL (2008) !! $Id$ !! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE tra_adv_tvd( kt, cdtype, ktra, pun, pvn, pwn, & & ptb, ptn, pta ) !!---------------------------------------------------------------------- !! *** 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 in (ztrdt,ztrds) ('key_trdtra') !!---------------------------------------------------------------------- INTEGER , INTENT(in ) :: kt ! ocean time-step index CHARACTER(len=3), INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) INTEGER , INTENT(in ) :: ktra ! tracer index REAL(wp) , INTENT(in ), DIMENSION(jpi,jpj,jpk) :: pun, pvn, pwn ! 3 ocean velocity components REAL(wp) , INTENT(inout), DIMENSION(jpi,jpj,jpk) :: ptb, ptn ! before and now tracer fields REAL(wp) , INTENT(inout), DIMENSION(jpi,jpj,jpk) :: pta ! tracer trend !! INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: z2dtt, zbtr, z2, zzti ! temporary scalar REAL(wp) :: zfp_ui, zfp_vj, zfp_wk ! " " REAL(wp) :: zfm_ui, zfm_vj, zfm_wk ! " " REAL(wp), DIMENSION (jpi,jpj,jpk) :: zti, ztu, ztv, ztw ! 3D workspace !!---------------------------------------------------------------------- zti(:,:,:) = 0.e0 IF( kt == nit000 .AND. lwp ) THEN WRITE(numout,*) WRITE(numout,*) 'tra_adv_tvd : TVD advection scheme' WRITE(numout,*) '~~~~~~~~~~~' ENDIF IF( neuler == 0 .AND. kt == nit000 ) THEN ; z2 = 1. ! euler time-stepping ELSE ; z2 = 2. ! leap-frog time-stepping ENDIF ! 1. Bottom value : flux set to zero ! --------------- ztu(:,:,jpk) = 0.e0 ; ztv(:,:,jpk) = 0.e0 ztw(:,:,jpk) = 0.e0 ; zti(:,:,jpk) = 0.e0 ! 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. 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) ) ztu(ji,jj,jk) = 0.5 * ( zfp_ui * ptb(ji,jj,jk) + zfm_ui * ptb(ji+1,jj ,jk) ) ztv(ji,jj,jk) = 0.5 * ( zfp_vj * ptb(ji,jj,jk) + zfm_vj * ptb(ji ,jj+1,jk) ) END DO END DO END DO ! ! upstream tracer flux in the k direction ! ! Surface value IF( lk_dynspg_rl .OR. lk_vvl ) THEN ; ztw(:,:,1) = 0.e0 ! rigid lid or non-linear fs ELSE ; ztw(:,:,1) = pwn(:,:,1) * ptb(:,:,1) ! free surface ENDIF ! 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) ) ztw(ji,jj,jk) = 0.5 * ( zfp_wk * ptb(ji,jj,jk) + zfm_wk * ptb(ji,jj,jk-1) ) END DO END DO END DO ! ! upstream advective trend DO jk = 1, jpkm1 z2dtt = z2 * rdttra(jk) 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 intermediate advective trends zzti = - ( ztu(ji,jj,jk) - ztu(ji-1,jj ,jk ) & & + ztv(ji,jj,jk) - ztv(ji ,jj-1,jk ) & & + ztw(ji,jj,jk) - ztw(ji ,jj ,jk+1) ) * zbtr ! update and guess with monotonic sheme pta(ji,jj,jk) = pta(ji,jj,jk) + zzti zti(ji,jj,jk) = ( ptb(ji,jj,jk) + z2dtt * zzti ) * tmask(ji,jj,jk) END DO END DO END DO ! CALL lbc_lnk( zti, 'T', 1. ) ! Lateral boundary conditions on zti (unchanged sign) ! ! trend diagnostics (contribution of upstream fluxes) IF( l_trdtra ) THEN CALL trd_tra_adv( kt, ktra, jpt_trd_xad, cdtype, ztu, pun, ptn ) CALL trd_tra_adv( kt, ktra, jpt_trd_yad, cdtype, ztv, pvn, ptn ) CALL trd_tra_adv( kt, ktra, jpt_trd_zad, cdtype, ztw, pwn, ptn ) ENDIF ! ! "Poleward" heat and salt transports (contribution of upstream fluxes) IF( cdtype == 'TRA' .AND. ln_diaptr .AND. ( MOD( kt, nf_ptr ) == 0 ) ) THEN IF( ktra == jp_tem) pht_adv(:) = ptr_vj( ztv(:,:,:) ) IF( ktra == jp_sal) pst_adv(:) = ptr_vj( ztv(:,:,:) ) ENDIF ! 3. antidiffusive flux : high order minus low order ! -------------------------------------------------- ! ! anti-diffusive flux on i and j DO jk = 1, jpkm1 DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. ztu(ji,jj,jk) = 0.5 * pun(ji,jj,jk) * ( ptn(ji,jj,jk) + ptn(ji+1,jj,jk) ) - ztu(ji,jj,jk) ztv(ji,jj,jk) = 0.5 * pvn(ji,jj,jk) * ( ptn(ji,jj,jk) + ptn(ji,jj+1,jk) ) - ztv(ji,jj,jk) END DO END DO END DO ! ! antidiffusive flux on k ztw(:,:,1) = 0.e0 ! Surface value ! DO jk = 2, jpkm1 ! Interior value DO jj = 1, jpj DO ji = 1, jpi ztw(ji,jj,jk) = 0.5 * pwn(ji,jj,jk) * ( ptn(ji,jj,jk) + ptn(ji,jj,jk-1) ) - ztw(ji,jj,jk) END DO END DO END DO ! CALL lbc_lnk( ztu, 'U', -1. ) ! Lateral bondary conditions on upstream fluxes CALL lbc_lnk( ztv, 'V', -1. ) CALL lbc_lnk( ztw, 'W', 1. ) ! ! monotonicity algorithm CALL nonosc( ptb, ztu, ztv, ztw, zti, z2 ) ! 4. final trend with anti-diffusive 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) ) ! anti-diffusive trends added to the general tracer trends pta(ji,jj,jk) = pta(ji,jj,jk) - ( ztu(ji,jj,jk) - ztu(ji-1,jj ,jk ) & & + ztv(ji,jj,jk) - ztv(ji ,jj-1,jk ) & & + ztw(ji,jj,jk) - ztw(ji ,jj ,jk+1) ) * zbtr END DO END DO END DO IF( l_trdtra ) THEN ! trend diagnostic (contribution of anti-diffusive fluxes) CALL trd_tra_adv( kt, ktra, jpt_trd_xad, cdtype, ztu, pun, ptn, cnbpas='bis' ) ! <<< Add to iad trend CALL trd_tra_adv( kt, ktra, jpt_trd_yad, cdtype, ztv, pvn, ptn, cnbpas='bis' ) ! <<< Add to jad trend CALL trd_tra_adv( kt, ktra, jpt_trd_zad, cdtype, ztw, pwn, ptn, cnbpas='bis' ) ! <<< Add to zad trend ENDIF ! ! "Poleward" heat and salt transports (contribution of anti-diffusive fluxes) IF( cdtype == 'TRA' .AND. ln_diaptr .AND. ( MOD( kt, nf_ptr ) == 0 ) ) THEN IF( ktra == jp_tem) pht_adv(:) = pht_adv(:) + ptr_vj( ztv(:,:,:) ) IF( ktra == jp_sal) pst_adv(:) = pst_adv(:) + ptr_vj( ztv(:,:,:) ) ENDIF ! ! control print IF(ln_ctl) CALL prt_ctl( tab3d_1=pta, clinfo1=' tvd - adv: ', mask1=tmask, clinfo3=cdtype ) ! END SUBROUTINE tra_adv_tvd SUBROUTINE nonosc( pbef, paa, pbb, pcc, paft, prdt ) !!--------------------------------------------------------------------- !! *** 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), INTENT(in ) :: prdt ! ??? REAL(wp), INTENT(inout), DIMENSION (jpi,jpj,jpk) :: pbef, paft ! before & after field REAL(wp), INTENT(inout), DIMENSION (jpi,jpj,jpk) :: paa, pbb, pcc ! monotonic flux in the 3 directions !! INTEGER :: ji, jj, jk ! dummy loop indices INTEGER :: ikm1 REAL(wp), DIMENSION (jpi,jpj,jpk) :: zbetup, zbetdo REAL(wp) :: zpos, zneg, zbt, za, zb, zc, zbig, zrtrn, z2dtt !!---------------------------------------------------------------------- zbig = 1.e+40 zrtrn = 1.e-15 zbetup(:,:,:) = 0.e0 ; zbetdo(:,:,:) = 0.e0 !!gm optimisation : add the optimal version I wrote 1 year ago ! Search local extrema ! -------------------- ! large negative value (-zbig) inside land pbef(:,:,:) = pbef(:,:,:) * tmask(:,:,:) - zbig * ( 1.e0 - tmask(:,:,:) ) paft(:,:,:) = paft(:,:,:) * tmask(:,:,:) - zbig * ( 1.e0 - tmask(:,:,:) ) ! search maximum in neighbourhood DO jk = 1, jpkm1 ikm1 = MAX(jk-1,1) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zbetup(ji,jj,jk) = MAX( pbef(ji ,jj ,jk ), paft(ji ,jj ,jk ), & & pbef(ji-1,jj ,jk ), pbef(ji+1,jj ,jk ), & & paft(ji-1,jj ,jk ), paft(ji+1,jj ,jk ), & & pbef(ji ,jj-1,jk ), pbef(ji ,jj+1,jk ), & & paft(ji ,jj-1,jk ), paft(ji ,jj+1,jk ), & & pbef(ji ,jj ,ikm1), pbef(ji ,jj ,jk+1), & & paft(ji ,jj ,ikm1), paft(ji ,jj ,jk+1) ) END DO END DO END DO ! large positive value (+zbig) inside land pbef(:,:,:) = pbef(:,:,:) * tmask(:,:,:) + zbig * ( 1.e0 - tmask(:,:,:) ) paft(:,:,:) = paft(:,:,:) * tmask(:,:,:) + zbig * ( 1.e0 - tmask(:,:,:) ) ! search minimum in neighbourhood DO jk = 1, jpkm1 ikm1 = MAX(jk-1,1) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zbetdo(ji,jj,jk) = MIN( pbef(ji ,jj ,jk ), paft(ji ,jj ,jk ), & & pbef(ji-1,jj ,jk ), pbef(ji+1,jj ,jk ), & & paft(ji-1,jj ,jk ), paft(ji+1,jj ,jk ), & & pbef(ji ,jj-1,jk ), pbef(ji ,jj+1,jk ), & & paft(ji ,jj-1,jk ), paft(ji ,jj+1,jk ), & & pbef(ji ,jj ,ikm1), pbef(ji ,jj ,jk+1), & & paft(ji ,jj ,ikm1), paft(ji ,jj ,jk+1) ) END DO END DO END DO ! restore masked values to zero pbef(:,:,:) = pbef(:,:,:) * tmask(:,:,:) paft(:,:,:) = paft(:,:,:) * tmask(:,:,:) ! 2. Positive and negative part of fluxes and beta terms ! ------------------------------------------------------ DO jk = 1, jpkm1 z2dtt = prdt * rdttra(jk) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ! positive & negative 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 ) ) 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) = ( zbetup(ji,jj,jk) - paft(ji,jj,jk) ) / (zpos+zrtrn) * zbt zbetdo(ji,jj,jk) = ( paft(ji,jj,jk) - zbetdo(ji,jj,jk) ) / (zneg+zrtrn) * zbt END DO END DO END DO ! lateral boundary condition on zbetup & zbetdo (unchanged sign) CALL lbc_lnk( zbetup, 'T', 1. ) CALL lbc_lnk( zbetdo, 'T', 1. ) ! 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. za = MIN( 1.e0, zbetdo(ji,jj,jk), zbetup(ji+1,jj,jk) ) zb = MIN( 1.e0, zbetup(ji,jj,jk), zbetdo(ji+1,jj,jk) ) zc = 0.5 * ( 1.e0 + SIGN( 1.e0, paa(ji,jj,jk) ) ) paa(ji,jj,jk) = paa(ji,jj,jk) * ( zc * za + ( 1.e0 - zc) * zb ) za = MIN( 1.e0, zbetdo(ji,jj,jk), zbetup(ji,jj+1,jk) ) zb = MIN( 1.e0, zbetup(ji,jj,jk), zbetdo(ji,jj+1,jk) ) zc = 0.5 * ( 1.e0 + SIGN( 1.e0, pbb(ji,jj,jk) ) ) pbb(ji,jj,jk) = pbb(ji,jj,jk) * ( zc * za + ( 1.e0 - zc) * zb ) END DO END DO END DO ! monotonic flux in the k direction, i.e. pcc ! ------------------------------------------- DO jk = 2, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. za = MIN( 1., zbetdo(ji,jj,jk), zbetup(ji,jj,jk-1) ) zb = MIN( 1., zbetup(ji,jj,jk), zbetdo(ji,jj,jk-1) ) zc = 0.5 * ( 1.e0 + SIGN( 1.e0, pcc(ji,jj,jk) ) ) pcc(ji,jj,jk) = pcc(ji,jj,jk) * ( zc * za + ( 1.e0 - zc) * zb ) END DO END DO END DO ! lateral boundary condition on paa, pbb, pcc CALL lbc_lnk( paa, 'U', -1. ) ! changed sign CALL lbc_lnk( pbb, 'V', -1. ) ! changed sign CALL lbc_lnk( pcc, 'W', 1. ) ! NO changed sign ! END SUBROUTINE nonosc !!====================================================================== END MODULE traadv_tvd