MODULE traadv_ubs !!============================================================================== !! *** MODULE traadv_ubs *** !! Ocean active tracers: horizontal & vertical advective trend !!============================================================================== !! History : 1.0 ! 2006-08 (L. Debreu, R. Benshila) Original code !! 3.3 ! 2010-05 (C. Ethe, G. Madec) merge TRC-TRA + switch from velocity to transport !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! tra_adv_ubs : update the tracer trend with the horizontal !! advection trends using a third order biaised scheme !!---------------------------------------------------------------------- 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 ! trends manager: tracers USE dynspg_oce ! choice/control of key cpp for surface pressure gradient USE diaptr ! poleward transport diagnostics ! USE lib_mpp ! I/O library USE lbclnk ! ocean lateral boundary condition (or mpp link) USE in_out_manager ! I/O manager 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_ubs ! routine called by traadv module LOGICAL :: l_trd ! flag to compute trends or not !! * 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_ubs ( kt, kit000, cdtype, p2dt, pun, pvn, pwn, & & ptb, ptn, pta, kjpt ) !!---------------------------------------------------------------------- !! *** ROUTINE tra_adv_ubs *** !! !! ** Purpose : Compute the now trend due to the advection of tracers !! and add it to the general trend of passive tracer equations. !! !! ** Method : The upstream biased scheme (UBS) is based on a 3rd order !! upstream-biased parabolic interpolation (Shchepetkin and McWilliams 2005) !! It is only used in the horizontal direction. !! For example the i-component of the advective fluxes are given by : !! ! e2u e3u un ( mi(Tn) - zltu(i ) ) if un(i) >= 0 !! ztu = ! or !! ! e2u e3u un ( mi(Tn) - zltu(i+1) ) if un(i) < 0 !! where zltu is the second derivative of the before temperature field: !! zltu = 1/e3t di[ e2u e3u / e1u di[Tb] ] !! This results in a dissipatively dominant (i.e. hyper-diffusive) !! truncation error. The overall performance of the advection scheme !! is similar to that reported in (Farrow and Stevens, 1995). !! For stability reasons, the first term of the fluxes which corresponds !! to a second order centered scheme is evaluated using the now velocity !! (centered in time) while the second term which is the diffusive part !! of the scheme, is evaluated using the before velocity (forward in time). !! Note that UBS is not positive. Do not use it on passive tracers. !! On the vertical, the advection is evaluated using a TVD scheme, !! as the UBS have been found to be too diffusive. !! !! ** Action : - update (pta) with the now advective tracer trends !! !! Reference : Shchepetkin, A. F., J. C. McWilliams, 2005, Ocean Modelling, 9, 347-404. !! Farrow, D.E., Stevens, D.P., 1995, J. Phys. Ocean. 25, 1731Ð1741. !!---------------------------------------------------------------------- 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 transport 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) :: ztra, zbtr, zcoef, z2dtt ! local scalars REAL(wp) :: zfp_ui, zfm_ui, zcenut, ztak, zfp_wk, zfm_wk ! - - REAL(wp) :: zfp_vj, zfm_vj, zcenvt, zeeu, zeev, z_hdivn ! - - REAL(wp), POINTER, DIMENSION(:,:,:) :: ztu, ztv, zltu, zltv, zti, ztw !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('tra_adv_ubs') ! CALL wrk_alloc( jpi, jpj, jpk, ztu, ztv, zltu, zltv, zti, ztw ) ! IF( kt == kit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'tra_adv_ubs : horizontal UBS 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. ! ! ! =========== DO jn = 1, kjpt ! tracer loop ! ! =========== ! 1. Bottom value : flux set to zero ! ---------------------------------- zltu(:,:,jpk) = 0.e0 ; zltv(:,:,jpk) = 0.e0 ! DO jk = 1, jpkm1 ! Horizontal slab ! ! Laplacian DO jj = 1, jpjm1 ! First derivative (gradient) DO ji = 1, fs_jpim1 ! vector opt. zeeu = e2u(ji,jj) * fse3u(ji,jj,jk) / e1u(ji,jj) * umask(ji,jj,jk) zeev = e1v(ji,jj) * fse3v(ji,jj,jk) / e2v(ji,jj) * vmask(ji,jj,jk) ztu(ji,jj,jk) = zeeu * ( ptb(ji+1,jj ,jk,jn) - ptb(ji,jj,jk,jn) ) ztv(ji,jj,jk) = zeev * ( ptb(ji ,jj+1,jk,jn) - ptb(ji,jj,jk,jn) ) END DO END DO DO jj = 2, jpjm1 ! Second derivative (divergence) DO ji = fs_2, fs_jpim1 ! vector opt. zcoef = 1. / ( 6. * fse3t(ji,jj,jk) ) zltu(ji,jj,jk) = ( ztu(ji,jj,jk) - ztu(ji-1,jj,jk) ) * zcoef zltv(ji,jj,jk) = ( ztv(ji,jj,jk) - ztv(ji,jj-1,jk) ) * zcoef END DO END DO ! END DO ! End of slab CALL lbc_lnk( zltu, 'T', 1. ) ; CALL lbc_lnk( zltv, 'T', 1. ) ! Lateral boundary cond. (unchanged sgn) ! ! Horizontal advective fluxes DO jk = 1, jpkm1 ! Horizontal slab DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. ! upstream transport (x2) 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) ) ! 2nd order centered advective fluxes (x2) zcenut = pun(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji+1,jj ,jk,jn) ) zcenvt = pvn(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji ,jj+1,jk,jn) ) ! UBS advective fluxes ztu(ji,jj,jk) = 0.5 * ( zcenut - zfp_ui * zltu(ji,jj,jk) - zfm_ui * zltu(ji+1,jj,jk) ) ztv(ji,jj,jk) = 0.5 * ( zcenvt - zfp_vj * zltv(ji,jj,jk) - zfm_vj * zltv(ji,jj+1,jk) ) END DO END DO END DO ! End of slab zltu(:,:,:) = pta(:,:,:,jn) ! store pta trends DO jk = 1, jpkm1 ! Horizontal advective trends DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) & & - ( ztu(ji,jj,jk) - ztu(ji-1,jj ,jk) & & + ztv(ji,jj,jk) - ztv(ji ,jj-1,jk) ) / ( e1e2t(ji,jj) * fse3t(ji,jj,jk) ) END DO END DO ! END DO ! End of slab ! Horizontal trend used in tra_adv_ztvd subroutine zltu(:,:,:) = pta(:,:,:,jn) - zltu(:,:,:) ! IF( l_trd ) THEN ! trend diagnostics CALL trd_tra( kt, cdtype, jn, jptra_xad, ztu, pun, ptn(:,:,:,jn) ) CALL trd_tra( kt, cdtype, jn, jptra_yad, ztv, pvn, ptn(:,:,:,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( ztv(:,:,:) ) IF( jn == jp_sal ) str_adv(:) = ptr_sj( ztv(:,:,:) ) ENDIF ! TVD scheme for the vertical direction ! ---------------------- IF( l_trd ) zltv(:,:,:) = pta(:,:,:,jn) ! store pta if trend diag. ! Bottom value : flux set to zero ztw(:,:,jpk) = 0.e0 ; zti(:,:,jpk) = 0.e0 ! Surface value IF( lk_vvl ) THEN ; ztw(:,:,1) = 0.e0 ! variable volume : flux set to zero ELSE ; ztw(:,:,1) = pwn(:,:,1) * ptb(:,:,1,jn) ! free constant surface ENDIF ! upstream advection with initial mass fluxes & intermediate update ! ------------------------------------------------------------------- ! Interior value DO jk = 2, jpkm1 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,jn) + zfm_wk * ptb(ji,jj,jk-1,jn) ) END DO END DO END DO ! update and guess with monotonic sheme DO jk = 1, jpkm1 z2dtt = p2dt(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) ) ztak = - ( ztw(ji,jj,jk) - ztw(ji,jj,jk+1) ) * zbtr pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztak zti(ji,jj,jk) = ( ptb(ji,jj,jk,jn) + z2dtt * ( ztak + zltu(ji,jj,jk) ) ) * tmask(ji,jj,jk) END DO END DO END DO ! CALL lbc_lnk( zti, 'T', 1. ) ! Lateral boundary conditions on zti, zsi (unchanged sign) ! antidiffusive flux : high order minus low order 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,jn) + ptn(ji,jj,jk-1,jn) ) - ztw(ji,jj,jk) END DO END DO END DO ! CALL nonosc_z( ptb(:,:,:,jn), ztw, zti, p2dt ) ! monotonicity algorithm ! 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) ) ! k- vertical advective trends ztra = - zbtr * ( ztw(ji,jj,jk) - ztw(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 ! Save the final vertical advective trends IF( l_trd ) THEN ! vertical advective trend diagnostics DO jk = 1, jpkm1 ! (compute -w.dk[ptn]= -dk[w.ptn] + ptn.dk[w]) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zbtr = 1.e0 / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) ) z_hdivn = ( pwn(ji,jj,jk) - pwn(ji,jj,jk+1) ) * zbtr zltv(ji,jj,jk) = pta(ji,jj,jk,jn) - zltv(ji,jj,jk) + ptn(ji,jj,jk,jn) * z_hdivn END DO END DO END DO CALL trd_tra( kt, cdtype, jn, jptra_zad, zltv ) ENDIF ! END DO ! CALL wrk_dealloc( jpi, jpj, jpk, ztu, ztv, zltu, zltv, zti, ztw ) ! IF( nn_timing == 1 ) CALL timing_stop('tra_adv_ubs') ! END SUBROUTINE tra_adv_ubs SUBROUTINE nonosc_z( pbef, pcc, paft, p2dt ) !!--------------------------------------------------------------------- !! *** ROUTINE nonosc_z *** !! !! ** 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 ), DIMENSION(jpk) :: p2dt ! vertical profile of tracer time-step REAL(wp), DIMENSION (jpi,jpj,jpk) :: pbef ! before field REAL(wp), INTENT(inout), DIMENSION (jpi,jpj,jpk) :: paft ! after field REAL(wp), INTENT(inout), DIMENSION (jpi,jpj,jpk) :: pcc ! monotonic flux in the k direction ! 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), POINTER, DIMENSION(:,:,:) :: zbetup, zbetdo !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('nonosc_z') ! CALL wrk_alloc( jpi, jpj, jpk, zbetup, zbetdo ) ! zbig = 1.e+40_wp zrtrn = 1.e-15_wp zbetup(:,:,:) = 0._wp ; zbetdo(:,:,:) = 0._wp ! 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 ,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 ,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 = p2dt(jk) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ! positive & negative part of the flux zpos = MAX( 0., pcc(ji ,jj ,jk+1) ) - MIN( 0., pcc(ji ,jj ,jk ) ) zneg = 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 ! 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 ! CALL wrk_dealloc( jpi, jpj, jpk, zbetup, zbetdo ) ! IF( nn_timing == 1 ) CALL timing_stop('nonosc_z') ! END SUBROUTINE nonosc_z !!====================================================================== END MODULE traadv_ubs