MODULE traadv_tvd !!============================================================================== !! *** MODULE traadv_tvd *** !! Ocean active tracers: horizontal & vertical advective trend !!============================================================================== !! History : ! 95-12 (L. Mortier) Original code !! ! 00-01 (H. Loukos) adapted to ORCA !! ! 00-10 (MA Foujols E.Kestenare) include file not routine !! ! 00-12 (E. Kestenare M. Levy) fix bug in trtrd indexes !! ! 01-07 (E. Durand G. Madec) adaptation to ORCA config !! 8.5 ! 02-06 (G. Madec) F90: Free form and module !! 9.0 ! 04-01 (A. de Miranda, G. Madec, J.M. Molines ): advective bbl !! 9.0 ! 08-04 (S. Cravatte) add the i-, j- & k- trends computation !! " " ! 05-11 (V. Garnier) Surface pressure gradient organization !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! 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 oce ! ocean dynamics and active tracers 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 step.F90 !! * Substitutions # include "domzgr_substitute.h90" # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! OPA 9.0 , LOCEAN-IPSL (2006) !! $Header$ !! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE tra_adv_tvd( kt, pun, pvn, pwn ) !!---------------------------------------------------------------------- !! *** 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 (ta,sa) with the now advective tracer trends !! - save the trends in (ztrdt,ztrds) ('key_trdtra') !!---------------------------------------------------------------------- USE oce , ztrdt => ua ! use ua as workspace USE oce , ztrds => va ! use va as workspace !! INTEGER , INTENT(in) :: kt ! ocean time-step index REAL(wp), INTENT(in), DIMENSION(jpi,jpj,jpk) :: pun ! ocean velocity u-component REAL(wp), INTENT(in), DIMENSION(jpi,jpj,jpk) :: pvn ! ocean velocity v-component REAL(wp), INTENT(in), DIMENSION(jpi,jpj,jpk) :: pwn ! ocean velocity w-component !! INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: & ! temporary scalar ztai, ztaj, ztak, & ! " " zsai, zsaj, zsak, & ! " " z_hdivn_x, z_hdivn_y, z_hdivn REAL(wp) :: & z2dtt, zbtr, zeu, zev, & ! temporary scalar zew, z2, zbtr1, & ! temporary scalar zfp_ui, zfp_vj, zfp_wk, & ! " " zfm_ui, zfm_vj, zfm_wk ! " " REAL(wp), DIMENSION (jpi,jpj,jpk) :: zti, ztu, ztv, ztw ! temporary workspace REAL(wp), DIMENSION (jpi,jpj,jpk) :: zsi, zsu, zsv, zsw ! " " !!---------------------------------------------------------------------- zti(:,:,:) = 0.e0 ; zsi(:,:,:) = 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. ELSE ; z2 = 2. ENDIF ! 1. Bottom value : flux set to zero ! --------------- ztu(:,:,jpk) = 0.e0 ; zsu(:,:,jpk) = 0.e0 ztv(:,:,jpk) = 0.e0 ; zsv(:,:,jpk) = 0.e0 ztw(:,:,jpk) = 0.e0 ; zsw(:,:,jpk) = 0.e0 zti(:,:,jpk) = 0.e0 ; zsi(:,:,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. zeu = 0.5 * e2u(ji,jj) * fse3u(ji,jj,jk) * pun(ji,jj,jk) zev = 0.5 * e1v(ji,jj) * fse3v(ji,jj,jk) * pvn(ji,jj,jk) ! upstream scheme zfp_ui = zeu + ABS( zeu ) zfm_ui = zeu - ABS( zeu ) zfp_vj = zev + ABS( zev ) zfm_vj = zev - ABS( zev ) ztu(ji,jj,jk) = zfp_ui * tb(ji,jj,jk) + zfm_ui * tb(ji+1,jj ,jk) ztv(ji,jj,jk) = zfp_vj * tb(ji,jj,jk) + zfm_vj * tb(ji ,jj+1,jk) zsu(ji,jj,jk) = zfp_ui * sb(ji,jj,jk) + zfm_ui * sb(ji+1,jj ,jk) zsv(ji,jj,jk) = zfp_vj * sb(ji,jj,jk) + zfm_vj * sb(ji ,jj+1,jk) END DO END DO END DO ! upstream tracer flux in the k direction ! Surface value IF( lk_dynspg_rl ) THEN ! rigid lid : flux set to zero ztw(:,:,1) = 0.e0 zsw(:,:,1) = 0.e0 ELSE ! free surface DO jj = 1, jpj DO ji = 1, jpi zew = e1t(ji,jj) * e2t(ji,jj) * pwn(ji,jj,1) ztw(ji,jj,1) = zew * tb(ji,jj,1) zsw(ji,jj,1) = zew * sb(ji,jj,1) END DO END DO ENDIF ! Interior value DO jk = 2, jpkm1 DO jj = 1, jpj DO ji = 1, jpi zew = 0.5 * e1t(ji,jj) * e2t(ji,jj) * pwn(ji,jj,jk) zfp_wk = zew + ABS( zew ) zfm_wk = zew - ABS( zew ) ztw(ji,jj,jk) = zfp_wk * tb(ji,jj,jk) + zfm_wk * tb(ji,jj,jk-1) zsw(ji,jj,jk) = zfp_wk * sb(ji,jj,jk) + zfm_wk * sb(ji,jj,jk-1) END DO END DO END DO ! total advective 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) ) ! i- j- horizontal & k- vertical advective trends ztai = - ( ztu(ji,jj,jk) - ztu(ji-1,jj ,jk ) ) * zbtr ztaj = - ( ztv(ji,jj,jk) - ztv(ji ,jj-1,jk ) ) * zbtr ztak = - ( ztw(ji,jj,jk) - ztw(ji ,jj ,jk+1) ) * zbtr zsai = - ( zsu(ji,jj,jk) - zsu(ji-1,jj ,jk ) ) * zbtr zsaj = - ( zsv(ji,jj,jk) - zsv(ji ,jj-1,jk ) ) * zbtr zsak = - ( zsw(ji,jj,jk) - zsw(ji ,jj ,jk+1) ) * zbtr ! total intermediate advective trends zti(ji,jj,jk) = ztai + ztaj + ztak zsi(ji,jj,jk) = zsai + zsaj + zsak END DO END DO END DO ! Save the intermediate i / j / k advective trends for diagnostics ! ------------------------------------------------------------------- ! Warning : We should use zun instead of un in the computations below, but we ! also use hdivn which is computed with un, vn (check ???). So we use un, vn ! for consistency. Results are therefore approximate with key_trabbl_adv. IF( l_trdtra ) THEN ztrdt(:,:,:) = 0.e0 ; ztrds(:,:,:) = 0.e0 ! ! T/S ZONAL advection trends 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) ) ztrdt(ji,jj,jk) = - ( ztu(ji,jj,jk) - ztu(ji-1,jj,jk) ) * zbtr ztrds(ji,jj,jk) = - ( zsu(ji,jj,jk) - zsu(ji-1,jj,jk) ) * zbtr END DO END DO END DO CALL trd_mod(ztrdt, ztrds, jptra_trd_xad, 'TRA', kt) ! save the trends ! ! T/S MERIDIONAL advection trends 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) ) ztrdt(ji,jj,jk) = - ( ztv(ji,jj,jk) - ztv(ji,jj-1,jk) ) * zbtr ztrds(ji,jj,jk) = - ( zsv(ji,jj,jk) - zsv(ji,jj-1,jk) ) * zbtr END DO END DO END DO CALL trd_mod(ztrdt, ztrds, jptra_trd_yad, 'TRA', kt) ! save the trends ! ! T/S VERTICAL advection trends 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) ) ztrdt(ji,jj,jk) = - ( ztw(ji,jj,jk) - ztw(ji,jj,jk+1) ) * zbtr ztrds(ji,jj,jk) = - ( zsw(ji,jj,jk) - zsw(ji,jj,jk+1) ) * zbtr END DO END DO END DO CALL trd_mod(ztrdt, ztrds, jptra_trd_zad, 'TRA', kt) ! save the trends ! ENDIF ! update and guess with monotonic sheme DO jk = 1, jpkm1 z2dtt = z2 * rdttra(jk) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ta(ji,jj,jk) = ta(ji,jj,jk) + zti(ji,jj,jk) sa(ji,jj,jk) = sa(ji,jj,jk) + zsi(ji,jj,jk) zti (ji,jj,jk) = ( tb(ji,jj,jk) + z2dtt * zti(ji,jj,jk) ) * tmask(ji,jj,jk) zsi (ji,jj,jk) = ( sb(ji,jj,jk) + z2dtt * zsi(ji,jj,jk) ) * tmask(ji,jj,jk) END DO END DO END DO ! Lateral boundary conditions on zti, zsi (unchanged sign) CALL lbc_lnk( zti, 'T', 1. ) CALL lbc_lnk( zsi, 'T', 1. ) ! 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. zeu = 0.5 * e2u(ji,jj) * fse3u(ji,jj,jk) * pun(ji,jj,jk) zev = 0.5 * e1v(ji,jj) * fse3v(ji,jj,jk) * pvn(ji,jj,jk) ztu(ji,jj,jk) = zeu * ( tn(ji,jj,jk) + tn(ji+1,jj,jk) ) - ztu(ji,jj,jk) zsu(ji,jj,jk) = zeu * ( sn(ji,jj,jk) + sn(ji+1,jj,jk) ) - zsu(ji,jj,jk) ztv(ji,jj,jk) = zev * ( tn(ji,jj,jk) + tn(ji,jj+1,jk) ) - ztv(ji,jj,jk) zsv(ji,jj,jk) = zev * ( sn(ji,jj,jk) + sn(ji,jj+1,jk) ) - zsv(ji,jj,jk) END DO END DO END DO ! antidiffusive flux on k ! Surface value ztw(:,:,1) = 0.e0 zsw(:,:,1) = 0.e0 ! Interior value DO jk = 2, jpkm1 DO jj = 1, jpj DO ji = 1, jpi zew = 0.5 * e1t(ji,jj) * e2t(ji,jj) * pwn(ji,jj,jk) ztw(ji,jj,jk) = zew * ( tn(ji,jj,jk) + tn(ji,jj,jk-1) ) - ztw(ji,jj,jk) zsw(ji,jj,jk) = zew * ( sn(ji,jj,jk) + sn(ji,jj,jk-1) ) - zsw(ji,jj,jk) END DO END DO END DO ! Lateral bondary conditions CALL lbc_lnk( ztu, 'U', -1. ) ; CALL lbc_lnk( zsu, 'U', -1. ) CALL lbc_lnk( ztv, 'V', -1. ) ; CALL lbc_lnk( zsv, 'V', -1. ) CALL lbc_lnk( ztw, 'W', 1. ) ; CALL lbc_lnk( zsw, 'W', 1. ) ! 4. monotonicity algorithm ! ------------------------- CALL nonosc( tb, ztu, ztv, ztw, zti, z2 ) CALL nonosc( sb, zsu, zsv, zsw, zsi, z2 ) ! 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) ) ! i- j- horizontal & k- vertical advective trends ztai = - ( ztu(ji,jj,jk) - ztu(ji-1,jj ,jk )) * zbtr ztaj = - ( ztv(ji,jj,jk) - ztv(ji ,jj-1,jk )) * zbtr ztak = - ( ztw(ji,jj,jk) - ztw(ji ,jj ,jk+1)) * zbtr zsai = - ( zsu(ji,jj,jk) - zsu(ji-1,jj ,jk )) * zbtr zsaj = - ( zsv(ji,jj,jk) - zsv(ji ,jj-1,jk )) * zbtr zsak = - ( zsw(ji,jj,jk) - zsw(ji ,jj ,jk+1)) * zbtr ! add them to the general tracer trends ta(ji,jj,jk) = ta(ji,jj,jk) + ztai + ztaj + ztak sa(ji,jj,jk) = sa(ji,jj,jk) + zsai + zsaj + zsak END DO END DO END DO ! Save the advective trends for diagnostics ! -------------------------------------------- IF( l_trdtra ) THEN ztrdt(:,:,:) = 0.e0 ; ztrds(:,:,:) = 0.e0 ! ! T/S ZONAL advection trends DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. !-- Compute zonal divergence by splitting hdivn (see divcur.F90) ! N.B. This computation is not valid along OBCs (if any) zbtr = 1. / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) ) z_hdivn_x = ( e2u(ji ,jj) * fse3u(ji ,jj,jk) * pun(ji ,jj,jk) & & - e2u(ji-1,jj) * fse3u(ji-1,jj,jk) * pun(ji-1,jj,jk) ) * zbtr !-- Compute T/S zonal advection trends ztrdt(ji,jj,jk) = - ( ztu(ji,jj,jk) - ztu(ji-1,jj,jk) ) * zbtr + tn(ji,jj,jk) * z_hdivn_x ztrds(ji,jj,jk) = - ( zsu(ji,jj,jk) - zsu(ji-1,jj,jk) ) * zbtr + sn(ji,jj,jk) * z_hdivn_x END DO END DO END DO CALL trd_mod(ztrdt, ztrds, jptra_trd_xad, 'TRA', kt, cnbpas='bis') ! <<< ADD TO PREVIOUSLY COMPUTED ! ! T/S MERIDIONAL advection trends DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. !-- Compute merid. divergence by splitting hdivn (see divcur.F90) ! N.B. This computation is not valid along OBCs (if any) zbtr = 1. / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) ) z_hdivn_y = ( e1v(ji, jj) * fse3v(ji,jj ,jk) * pvn(ji,jj ,jk) & & - e1v(ji,jj-1) * fse3v(ji,jj-1,jk) * pvn(ji,jj-1,jk) ) * zbtr !-- Compute T/S meridional advection trends ztrdt(ji,jj,jk) = - ( ztv(ji,jj,jk) - ztv(ji,jj-1,jk) ) * zbtr + tn(ji,jj,jk) * z_hdivn_y ztrds(ji,jj,jk) = - ( zsv(ji,jj,jk) - zsv(ji,jj-1,jk) ) * zbtr + sn(ji,jj,jk) * z_hdivn_y END DO END DO END DO CALL trd_mod(ztrdt, ztrds, jptra_trd_yad, 'TRA', kt, cnbpas='bis') ! <<< ADD TO PREVIOUSLY COMPUTED ! ! T/S VERTICAL advection trends DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zbtr1 = 1. / ( e1t(ji,jj) * e2t(ji,jj) ) #if defined key_zco zbtr = zbtr1 z_hdivn_x = e2u(ji,jj)*pun(ji,jj,jk) - e2u(ji-1,jj)*pun(ji-1,jj,jk) z_hdivn_y = e1v(ji,jj)*pvn(ji,jj,jk) - e1v(ji,jj-1)*pvn(ji,jj-1,jk) #else zbtr = zbtr1 / fse3t(ji,jj,jk) z_hdivn_x = e2u(ji,jj)*fse3u(ji,jj,jk)*pun(ji,jj,jk) - e2u(ji-1,jj)*fse3u(ji-1,jj,jk)*pun(ji-1,jj,jk) z_hdivn_y = e1v(ji,jj)*fse3v(ji,jj,jk)*pvn(ji,jj,jk) - e1v(ji,jj-1)*fse3v(ji,jj-1,jk)*pvn(ji,jj-1,jk) #endif z_hdivn = (z_hdivn_x + z_hdivn_y) * zbtr zbtr = zbtr1 / fse3t(ji,jj,jk) ztrdt(ji,jj,jk) = - ( ztw(ji,jj,jk) - ztw(ji,jj,jk+1) ) * zbtr - tn(ji,jj,jk) * z_hdivn ztrds(ji,jj,jk) = - ( zsw(ji,jj,jk) - zsw(ji,jj,jk+1) ) * zbtr - sn(ji,jj,jk) * z_hdivn END DO END DO END DO CALL trd_mod(ztrdt, ztrds, jptra_trd_zad, 'TRA', kt, cnbpas='bis') ! <<< ADD TO PREVIOUSLY COMPUTED ! ENDIF IF(ln_ctl) CALL prt_ctl( tab3d_1=ta, clinfo1=' tvd adv - Ta: ', mask1=tmask, & & tab3d_2=sa, clinfo2= ' Sa: ', mask2=tmask, clinfo3='tra' ) ! "zonal" mean advective heat and salt transport IF( ln_diaptr .AND. ( MOD( kt, nf_ptr ) == 0 ) ) THEN pht_adv(:) = ptr_vj( ztv(:,:,:) ) pst_adv(:) = ptr_vj( zsv(:,:,:) ) ENDIF ! 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), DIMENSION (jpi,jpj,jpk), INTENT( inout ) :: & pbef, & ! before field paft, & ! after field paa, & ! monotonic flux in the i direction pbb, & ! monotonic flux in the j direction pcc ! monotonic flux in the k direction !! 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 ! 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