MODULE traadv_tvd !!============================================================================== !! *** MODULE traadv_tvd *** !! Ocean active tracers: horizontal & vertical advective trend !!============================================================================== !!---------------------------------------------------------------------- !! 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 !!---------------------------------------------------------------------- !! * Modules used USE oce ! ocean dynamics and active tracers USE dom_oce ! ocean space and time domain USE trdtra_oce ! ocean active tracer trends USE in_out_manager ! I/O manager USE dynspg_fsc ! surface pressure gradient USE dynspg_fsc_atsk ! autotasked 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 IMPLICIT NONE PRIVATE !! * Accessibility PUBLIC tra_adv_tvd ! routine called by step.F90 !! * Substitutions # include "domzgr_substitute.h90" # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! OPA 9.0 , LODYC-IPSL (2003) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE tra_adv_tvd( kt ) !!---------------------------------------------------------------------- !! *** 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 (ttrdh,strdh) ('key_trdtra') !! !! 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 !!---------------------------------------------------------------------- !! * Modules used #if defined key_trabbl_adv USE oce , zun => ua, & ! use ua as workspace & zvn => va ! use va as workspace REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwn #else USE oce , zun => un, & ! When no bbl, zun == un zvn => vn, & ! zvn == vn zwn => wn ! zwn == wn #endif !! * Arguments INTEGER, INTENT( in ) :: kt ! ocean time-step !! * Local declarations INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: zta, zsa ! temporary scalar REAL(wp), DIMENSION (jpi,jpj,jpk) :: & zti, ztu, ztv, ztw, & ! temporary workspace zsi, zsu, zsv, zsw ! " " REAL(wp) :: & z2dtt, zbtr, zeu, zev, zew, z2, & ! temporary scalar zfp_ui, zfp_vj, zfp_wk, & ! " " zfm_ui, zfm_vj, zfm_wk ! " " !!---------------------------------------------------------------------- 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 #if defined key_trabbl_adv ! Advective Bottom boundary layer: add the velocity ! ------------------------------------------------- zun(:,:,:) = un (:,:,:) - u_bbl(:,:,:) zvn(:,:,:) = vn (:,:,:) - v_bbl(:,:,:) zwn(:,:,:) = wn (:,:,:) + w_bbl(:,:,:) #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) * zun(ji,jj,jk) zev = 0.5 * e1v(ji,jj) * fse3v(ji,jj,jk) * zvn(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_fsc .OR. lk_dynspg_fsc_tsk ) THEN ! free surface-constant volume DO jj = 1, jpj DO ji = 1, jpi zew = e1t(ji,jj) * e2t(ji,jj) * zwn(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 ELSE ! rigid lid : flux set to zero ztw(:,:,1) = 0.e0 zsw(:,:,1) = 0.e0 ENDIF ! Interior value DO jk = 2, jpkm1 DO jj = 1, jpj DO ji = 1, jpi zew = 0.5 * e1t(ji,jj) * e2t(ji,jj) * zwn(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) ) zti(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 zsi(ji,jj,jk) = - ( zsu(ji,jj,jk) - zsu(ji-1,jj ,jk ) & & + zsv(ji,jj,jk) - zsv(ji ,jj-1,jk ) & & + zsw(ji,jj,jk) - zsw(ji ,jj ,jk+1) ) * zbtr END DO END DO END DO ! 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) * zun(ji,jj,jk) zev = 0.5 * e1v(ji,jj) * fse3v(ji,jj,jk) * zvn(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. zsw(:,:,1) = 0. ! Interior value DO jk = 2, jpkm1 DO jj = 1, jpj DO ji = 1, jpi zew = 0.5 * e1t(ji,jj) * e2t(ji,jj) * zwn(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) ) ta(ji,jj,jk) = ta(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 sa(ji,jj,jk) = sa(ji,jj,jk) & & - ( zsu(ji,jj,jk) - zsu(ji-1,jj ,jk ) & & + zsv(ji,jj,jk) - zsv(ji ,jj-1,jk ) & & + zsw(ji,jj,jk) - zsw(ji ,jj ,jk+1) ) * zbtr END DO END DO END DO IF(l_ctl) THEN zta = SUM( ta(2:nictl,2:njctl,1:jpkm1) * tmask(2:nictl,2:njctl,1:jpkm1) ) zsa = SUM( sa(2:nictl,2:njctl,1:jpkm1) * tmask(2:nictl,2:njctl,1:jpkm1) ) WRITE(numout,*) ' zad - Ta: ', zta-t_ctl, ' Sa: ', zsa-s_ctl, ' tvd' t_ctl = zta ; s_ctl = zsa ENDIF ! "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 !! !! History : !! ! 97-04 (L. Mortier) Original code !! ! 00-02 (H. Loukos) rewritting for opa8 !! ! 00-10 (M.A Foujols, E. Kestenare) lateral b.c. !! ! 01-03 (E. Kestenare) add key_passivetrc !! ! 01-07 (E. Durand G. Madec) adapted for T & S !! 8.5 ! 02-06 (G. Madec) F90: Free form and module !!---------------------------------------------------------------------- !! * Arguments 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 !! * Local declarations 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 ! Search local extrema ! -------------------- ! large negative value (-zbig) inside land WHERE( tmask(:,:,:) == 0. ) pbef(:,:,:) = -zbig paft(:,:,:) = -zbig ENDWHERE ! 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 WHERE( tmask(:,:,:) == 0. ) pbef(:,:,:) = +zbig paft(:,:,:) = +zbig ENDWHERE ! 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 direction, i.e. paa ! ---------------------------------------------- DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zc = paa(ji,jj,jk) IF( zc >= 0. ) THEN za = MIN( 1., zbetdo(ji,jj,jk), zbetup(ji+1,jj,jk) ) paa(ji,jj,jk) = za * zc ELSE zb = MIN( 1., zbetup(ji,jj,jk), zbetdo(ji+1,jj,jk) ) paa(ji,jj,jk) = zb * zc ENDIF END DO END DO END DO ! lateral boundary condition on paa (changed sign) CALL lbc_lnk( paa, 'U', -1. ) ! 4. monotonic flux in the j direction, i.e. pbb ! ---------------------------------------------- DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zc = pbb(ji,jj,jk) IF( zc >= 0. ) THEN za = MIN( 1., zbetdo(ji,jj,jk), zbetup(ji,jj+1,jk) ) pbb(ji,jj,jk) = za * zc ELSE zb = MIN( 1., zbetup(ji,jj,jk), zbetdo(ji,jj+1,jk) ) pbb(ji,jj,jk) = zb * zc ENDIF END DO END DO END DO ! lateral boundary condition on pbb (changed sign) CALL lbc_lnk( pbb, 'V', -1. ) ! 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. zc = pcc(ji,jj,jk) IF( zc >= 0. ) THEN za = MIN( 1., zbetdo(ji,jj,jk), zbetup(ji,jj,jk-1) ) pcc(ji,jj,jk) = za * zc ELSE zb = MIN( 1., zbetup(ji,jj,jk), zbetdo(ji,jj,jk-1) ) pcc(ji,jj,jk) = zb * zc ENDIF END DO END DO END DO ! lateral boundary condition on pcc (unchanged sign) CALL lbc_lnk( pcc, 'W', 1. ) END SUBROUTINE nonosc !!====================================================================== END MODULE traadv_tvd