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 traadv_fct ! acces to routine interp_4th_cpt USE trdtra ! trends manager: tracers USE diaptr ! poleward transport diagnostics USE diaar5 ! AR5 diagnostics ! USE iom ! I/O library USE in_out_manager ! I/O manager USE lib_mpp ! massively parallel library USE lbclnk ! ocean lateral boundary condition (or mpp link) 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 LOGICAL :: l_ptr ! flag to compute poleward transport LOGICAL :: l_hst ! flag to compute heat transport !! * Substitutions # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OCE 4.0 , NEMO Consortium (2018) !! $Id$ !! Software governed by the CeCILL license (see ./LICENSE) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE tra_adv_ubs( kt, kit000, cdtype, p2dt, pun, pvn, pwn, & & ptb, ptn, pta, kjpt, kn_ubs_v ) !!---------------------------------------------------------------------- !! *** 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 3rd order Upstream Biased Scheme (UBS) is based on an !! 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 FCT scheme, !! as the UBS have been found to be too diffusive. !! kn_ubs_v argument controles whether the FCT is based on !! a 2nd order centrered scheme (kn_ubs_v=2) or on a 4th order compact !! scheme (kn_ubs_v=4). !! !! ** Action : - update pta with the now advective tracer trends !! - send trends to trdtra module for further diagnostcs (l_trdtra=T) !! - htr_adv, str_adv : poleward advective heat and salt transport (ln_diaptr=T) !! !! 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 INTEGER , INTENT(in ) :: kn_ubs_v ! number of tracers REAL(wp) , INTENT(in ) :: p2dt ! 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 ! 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), DIMENSION(jpi,jpj,jpk) :: ztu, ztv, zltu, zltv, zti, ztw ! 3D workspace !!---------------------------------------------------------------------- ! 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. l_hst = .FALSE. l_ptr = .FALSE. IF( ( cdtype == 'TRA' .AND. l_trdtra ) .OR. ( cdtype == 'TRC' .AND. l_trdtrc ) ) l_trd = .TRUE. IF( cdtype == 'TRA' .AND. ln_diaptr ) 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. ! ztw (:,:, 1 ) = 0._wp ! surface & bottom value : set to zero for all tracers zltu(:,:,jpk) = 0._wp ; zltv(:,:,jpk) = 0._wp ztw (:,:,jpk) = 0._wp ; zti (:,:,jpk) = 0._wp ! ! ! =========== DO jn = 1, kjpt ! tracer loop ! ! =========== ! DO jk = 1, jpkm1 !== horizontal laplacian of before tracer ==! DO jj = 1, jpjm1 ! First derivative (masked gradient) DO ji = 1, fs_jpim1 ! vector opt. zeeu = e2_e1u(ji,jj) * e3u_n(ji,jj,jk) * umask(ji,jj,jk) zeev = e1_e2v(ji,jj) * e3v_n(ji,jj,jk) * 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._wp / ( 6._wp * e3t_n(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 CALL lbc_lnk( 'traadv_ubs', zltu, 'T', 1. ) ; CALL lbc_lnk( 'traadv_ubs', zltv, 'T', 1. ) ! Lateral boundary cond. (unchanged sgn) ! DO jk = 1, jpkm1 !== Horizontal advective fluxes ==! (UBS) DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. zfp_ui = pun(ji,jj,jk) + ABS( pun(ji,jj,jk) ) ! upstream transport (x2) 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 ! zltu(:,:,:) = pta(:,:,:,jn) ! store the initial trends before its update ! DO jk = 1, jpkm1 !== add the horizontal advective trend ==! 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) ) * r1_e1e2t(ji,jj) / e3t_n(ji,jj,jk) END DO END DO ! END DO ! zltu(:,:,:) = pta(:,:,:,jn) - zltu(:,:,:) ! Horizontal advective trend used in vertical 2nd order FCT case ! ! and/or in trend diagnostic (l_trd=T) ! 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( l_ptr ) CALL dia_ptr_hst( jn, 'adv', ztv(:,:,:) ) ! ! heati/salt transport IF( l_hst ) CALL dia_ar5_hst( jn, 'adv', ztu(:,:,:), ztv(:,:,:) ) ! ! ! !== vertical advective trend ==! ! SELECT CASE( kn_ubs_v ) ! select the vertical advection scheme ! CASE( 2 ) ! 2nd order FCT ! IF( l_trd ) zltv(:,:,:) = pta(:,:,:,jn) ! store pta if trend diag. ! ! !* upstream advection with initial mass fluxes & intermediate update ==! DO jk = 2, jpkm1 ! Interior value (w-masked) 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_wp * ( zfp_wk * ptb(ji,jj,jk,jn) + zfm_wk * ptb(ji,jj,jk-1,jn) ) * wmask(ji,jj,jk) END DO END DO END DO IF( ln_linssh ) THEN ! top ocean value (only in linear free surface as ztw has been w-masked) IF( ln_isfcav ) THEN ! top of the ice-shelf cavities and at the ocean surface DO jj = 1, jpj DO ji = 1, jpi ztw(ji,jj, mikt(ji,jj) ) = pwn(ji,jj,mikt(ji,jj)) * ptb(ji,jj,mikt(ji,jj),jn) ! linear free surface END DO END DO ELSE ! no cavities: only at the ocean surface ztw(:,:,1) = pwn(:,:,1) * ptb(:,:,1,jn) ENDIF ENDIF ! DO jk = 1, jpkm1 !* trend and after field with monotonic scheme DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ztak = - ( ztw(ji,jj,jk) - ztw(ji,jj,jk+1) ) * r1_e1e2t(ji,jj) / e3t_n(ji,jj,jk) pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztak zti(ji,jj,jk) = ( ptb(ji,jj,jk,jn) + p2dt * ( ztak + zltu(ji,jj,jk) ) ) * tmask(ji,jj,jk) END DO END DO END DO CALL lbc_lnk( 'traadv_ubs', zti, 'T', 1. ) ! Lateral boundary conditions on zti, zsi (unchanged sign) ! ! !* anti-diffusive flux : high order minus low order DO jk = 2, jpkm1 ! Interior value (w-masked) DO jj = 1, jpj DO ji = 1, jpi ztw(ji,jj,jk) = ( 0.5_wp * pwn(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji,jj,jk-1,jn) ) & & - ztw(ji,jj,jk) ) * wmask(ji,jj,jk) END DO END DO END DO ! ! top ocean value: high order == upstream ==>> zwz=0 IF( ln_linssh ) ztw(:,:, 1 ) = 0._wp ! only ocean surface as interior zwz values have been w-masked ! CALL nonosc_z( ptb(:,:,:,jn), ztw, zti, p2dt ) ! monotonicity algorithm ! CASE( 4 ) ! 4th order COMPACT CALL interp_4th_cpt( ptn(:,:,:,jn) , ztw ) ! 4th order compact interpolation of T at w-point DO jk = 2, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ztw(ji,jj,jk) = pwn(ji,jj,jk) * ztw(ji,jj,jk) * wmask(ji,jj,jk) END DO END DO END DO IF( ln_linssh ) ztw(:,:, 1 ) = pwn(:,:,1) * ptn(:,:,1,jn) !!gm ISF & 4th COMPACT doesn't work ! END SELECT ! DO jk = 1, jpkm1 ! final trend with corrected fluxes DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) - ( ztw(ji,jj,jk) - ztw(ji,jj,jk+1) ) * r1_e1e2t(ji,jj) / e3t_n(ji,jj,jk) END DO END DO END DO ! 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. zltv(ji,jj,jk) = pta(ji,jj,jk,jn) - zltv(ji,jj,jk) & & + ptn(ji,jj,jk,jn) * ( pwn(ji,jj,jk) - pwn(ji,jj,jk+1) ) & & * r1_e1e2t(ji,jj) / e3t_n(ji,jj,jk) END DO END DO END DO CALL trd_tra( kt, cdtype, jn, jptra_zad, zltv ) ENDIF ! END DO ! 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 ) :: p2dt ! 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 ! local scalars REAL(wp), DIMENSION(jpi,jpj,jpk) :: zbetup, zbetdo ! 3D workspace !!---------------------------------------------------------------------- ! 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(:,:,:) ) ! DO jk = 1, jpkm1 ! search maximum in neighbourhood 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(:,:,:) ) ! DO jk = 1, jpkm1 ! search minimum in neighbourhood 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(:,:,:) ! ! Positive and negative part of fluxes and beta terms ! --------------------------------------------------- DO jk = 1, jpkm1 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 = e1e2t(ji,jj) * e3t_n(ji,jj,jk) / p2dt 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 ! END SUBROUTINE nonosc_z !!====================================================================== END MODULE traadv_ubs