MODULE dynzdf_imp_atsk !!============================================================================== !! *** MODULE dynzdf_imp_atsk *** !! Ocean dynamics: vertical component(s) of the momentum mixing trend !!============================================================================== !!---------------------------------------------------------------------- !! dyn_zdf_imp_tsk : update the momentum trend with the vertical !! diffusion using an implicit time-stepping and !! j-k-i loops. !!---------------------------------------------------------------------- !! * Modules used USE oce ! ocean dynamics and tracers USE dom_oce ! ocean space and time domain USE phycst ! physical constants USE zdf_oce ! ocean vertical physics USE in_out_manager ! I/O manager USE taumod ! surface ocean stress USE trdmod ! ocean dynamics trends USE trdmod_oce ! ocean variables trends IMPLICIT NONE PRIVATE !! * Routine accessibility PUBLIC dyn_zdf_imp_tsk ! called by step.F90 !! * Substitutions # include "domzgr_substitute.h90" # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! OPA 9.0 , LODYC-IPSL (2003) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE dyn_zdf_imp_tsk( kt ) !!---------------------------------------------------------------------- !! *** ROUTINE dyn_zdf_imp_tsk *** !! !! ** Purpose : Compute the trend due to the vert. momentum diffusion !! and the surface forcing, and add it to the general trend of !! the momentum equations. !! !! ** Method : The vertical momentum mixing trend is given by : !! dz( avmu dz(u) ) = 1/e3u dk+1( avmu/e3uw dk(ua) ) !! backward time stepping !! Surface boundary conditions: wind stress input !! Bottom boundary conditions : bottom stress (cf zdfbfr.F) !! Add this trend to the general trend ua : !! ua = ua + dz( avmu dz(u) ) !! !! ** Action : - Update (ua,va) arrays with the after vertical diffusive !! mixing trend. !! - Save the trends in (ztdua,ztdva) ('l_trddyn') !! !! History : !! 8.5 ! 02-08 (G. Madec) auto-tasking option !! 9.0 ! 04-08 (C. Talandier) New trends organization !!--------------------------------------------------------------------- !! * Modules used USE oce, ONLY : ztdua => ta, & ! use ta as 3D workspace ztdva => sa ! use sa as 3D workspace !! * Arguments INTEGER, INTENT( in ) :: kt ! ocean time-step index !! * Local declarations INTEGER :: ji, jj, jk ! dummy loop indices INTEGER :: & ikst, ikenm2, ikstp1, & ! temporary integers ikbu, ikbum1, ikbv, ikbvm1 ! " " REAL(wp) :: & zrau0r, z2dt, zua, zva, & !temporary scalars z2dtf, zcoef, zzws REAL(wp), DIMENSION(jpi,jpk) :: & zwx, zwy, zwz, & ! workspace zwd, zws, zwi, zwt REAL(wp), DIMENSION(jpi,jpj) :: & ztsx, ztsy, ztbx, ztby ! temporary workspace arrays !!---------------------------------------------------------------------- IF( kt == nit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'dyn_zdf_imp_tsk : vertical momentum diffusion implicit operator' IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~~~ auto-task case (j-k-i loop)' ENDIF ! 0. Local constant initialization ! -------------------------------- zrau0r = 1. / rau0 ! inverse of the reference density z2dt = 2. * rdt ! Leap-frog environnement ztsx(:,:) = 0.e0 ztsy(:,:) = 0.e0 ztbx(:,:) = 0.e0 ztby(:,:) = 0.e0 ! Euler time stepping when starting from rest IF( neuler == 0 .AND. kt == nit000 ) z2dt = rdt ! Save ua and va trends IF( l_trddyn ) THEN ztdua(:,:,:) = ua(:,:,:) ztdva(:,:,:) = va(:,:,:) ENDIF ! ! =============== DO jj = 2, jpjm1 ! Vertical slab ! ! =============== ! 1. Vertical diffusion on u ! --------------------------- ! Matrix and second member construction ! bottom boundary condition: only zws must be masked as avmu can take ! non zero value at the ocean bottom depending on the bottom friction ! used (see zdfmix.F) DO jk = 1, jpkm1 DO ji = 2, jpim1 zcoef = - z2dt / fse3u(ji,jj,jk) zwi(ji,jk) = zcoef * avmu(ji,jj,jk ) / fse3uw(ji,jj,jk ) zzws = zcoef * avmu(ji,jj,jk+1) / fse3uw(ji,jj,jk+1) zws(ji,jk) = zzws * umask(ji,jj,jk+1) zwd(ji,jk) = 1. - zwi(ji,jk) - zzws zwy(ji,jk) = ub(ji,jj,jk) + z2dt * ua(ji,jj,jk) END DO END DO ! Surface boudary conditions DO ji = 2, jpim1 z2dtf = z2dt / ( fse3u(ji,jj,1)*rau0 ) zwi(ji,1) = 0. zwd(ji,1) = 1. - zws(ji,1) zwy(ji,1) = zwy(ji,1) + z2dtf * taux(ji,jj) END DO ! Matrix inversion starting from the first level ikst = 1 !!---------------------------------------------------------------------- !! ZDF.MATRIXSOLVER !! ******************** !!---------------------------------------------------------------------- !! Matrix inversion ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) ! ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) ! ( ... )( ... ) ( ... ) ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) ! ! m is decomposed in the product of an upper and lower triangular ! matrix ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi ! The second member is in 2d array zwy ! The solution is in 2d array zwx ! The 2d arry zwt and zwz are work space arrays ! ! N.B. the starting vertical index (ikst) is equal to 1 except for ! the resolution of tke matrix where surface tke value is prescribed ! so that ikstrt=2. !!---------------------------------------------------------------------- ikstp1 = ikst + 1 ikenm2 = jpk - 2 DO ji = 2, jpim1 zwt(ji,ikst) = zwd(ji,ikst) END DO DO jk = ikstp1, jpkm1 DO ji = 2, jpim1 zwt(ji,jk) = zwd(ji,jk) - zwi(ji,jk) * zws(ji,jk-1) / zwt(ji,jk-1) END DO END DO DO ji = 2, jpim1 zwz(ji,ikst) = zwy(ji,ikst) END DO DO jk = ikstp1, jpkm1 DO ji = 2, jpim1 zwz(ji,jk) = zwy(ji,jk) - zwi(ji,jk) / zwt(ji,jk-1) * zwz(ji,jk-1) END DO END DO DO ji = 2, jpim1 zwx(ji,jpkm1) = zwz(ji,jpkm1) / zwt(ji,jpkm1) END DO DO jk = ikenm2, ikst, -1 DO ji = 2, jpim1 zwx(ji,jk) =( zwz(ji,jk) - zws(ji,jk) * zwx(ji,jk+1) ) / zwt(ji,jk) END DO END DO ! Normalization to obtain the general momentum trend ua DO jk = 1, jpkm1 DO ji = 2, jpim1 ua(ji,jj,jk) = ( zwx(ji,jk) - ub(ji,jj,jk) ) / z2dt END DO END DO ! diagnose surface and bottom momentum fluxes ! for trends diagnostics DO ji = 2, jpim1 ! save the surface forcing momentum fluxes ztsx(ji,jj) = taux(ji,jj) / ( fse3u(ji,jj,1)*rau0 ) ! save bottom friction momentum fluxes ikbu = MIN( mbathy(ji+1,jj), mbathy(ji,jj) ) ikbum1 = MAX( ikbu-1, 1 ) ztbx(ji,jj) = - avmu(ji,jj,ikbu) * zwx(ji,ikbum1) & / ( fse3u(ji,jj,ikbum1)*fse3uw(ji,jj,ikbu) ) ! subtract surface forcing and bottom friction trend from vertical ! diffusive momentum trend ztdua(ji,jj,1 ) = ztdua(ji,jj,1 ) - ztsx(ji,jj) ztdua(ji,jj,ikbum1) = ztdua(ji,jj,ikbum1) - ztbx(ji,jj) END DO ! 2. Vertical diffusion on v ! --------------------------- ! Matrix and second member construction ! bottom boundary condition: only zws must be masked as avmv can take ! non zero value at the ocean bottom depending on the bottom friction ! used (see zdfmix.F) DO jk = 1, jpkm1 DO ji = 2, jpim1 zcoef = -z2dt/fse3v(ji,jj,jk) zwi(ji,jk) = zcoef * avmv(ji,jj,jk ) / fse3vw(ji,jj,jk ) zzws = zcoef * avmv(ji,jj,jk+1) / fse3vw(ji,jj,jk+1) zws(ji,jk) = zzws * vmask(ji,jj,jk+1) zwd(ji,jk) = 1. - zwi(ji,jk) - zzws zwy(ji,jk) = vb(ji,jj,jk) + z2dt * va(ji,jj,jk) END DO END DO ! Surface boudary conditions DO ji = 2, jpim1 z2dtf = z2dt / ( fse3v(ji,jj,1)*rau0 ) zwi(ji,1) = 0.e0 zwd(ji,1) = 1. - zws(ji,1) zwy(ji,1) = zwy(ji,1) + z2dtf * tauy(ji,jj) END DO ! Matrix inversion starting from the first level ikst = 1 !!---------------------------------------------------------------------- !! ZDF.MATRIXSOLVER !! ******************** !!---------------------------------------------------------------------- !! Matrix inversion ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) ! ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) ! ( ... )( ... ) ( ... ) ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) ! ! m is decomposed in the product of an upper and lower triangular ! matrix ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi ! The second member is in 2d array zwy ! The solution is in 2d array zwx ! The 2d arry zwt and zwz are work space arrays ! ! N.B. the starting vertical index (ikst) is equal to 1 except for ! the resolution of tke matrix where surface tke value is prescribed ! so that ikstrt=2. !!---------------------------------------------------------------------- ikstp1 = ikst + 1 ikenm2 = jpk - 2 DO ji = 2, jpim1 zwt(ji,ikst) = zwd(ji,ikst) END DO DO jk = ikstp1, jpkm1 DO ji = 2, jpim1 zwt(ji,jk) = zwd(ji,jk) - zwi(ji,jk) * zws(ji,jk-1) / zwt(ji,jk-1) END DO END DO DO ji = 2, jpim1 zwz(ji,ikst) = zwy(ji,ikst) END DO DO jk = ikstp1, jpkm1 DO ji = 2, jpim1 zwz(ji,jk) = zwy(ji,jk) - zwi(ji,jk) / zwt(ji,jk-1) * zwz(ji,jk-1) END DO END DO DO ji = 2, jpim1 zwx(ji,jpkm1) = zwz(ji,jpkm1) / zwt(ji,jpkm1) END DO DO jk = ikenm2, ikst, -1 DO ji = 2, jpim1 zwx(ji,jk) =( zwz(ji,jk) - zws(ji,jk) * zwx(ji,jk+1) ) / zwt(ji,jk) END DO END DO ! Normalization to obtain the general momentum trend va DO jk = 1, jpkm1 DO ji = 2, jpim1 va(ji,jj,jk) = ( zwx(ji,jk) - vb(ji,jj,jk) ) / z2dt END DO END DO ! diagnose surface and bottom momentum fluxes ! for trends diagnostics DO ji = 2, jpim1 ! save the surface forcing momentum fluxes ztsy(ji,jj) = tauy(ji,jj) / ( fse3v(ji,jj,1)*rau0 ) ! save bottom friction momentum fluxes ikbv = MIN( mbathy(ji,jj+1), mbathy(ji,jj) ) ikbvm1 = MAX( ikbv-1, 1 ) ztby(ji,jj) = - avmv(ji,jj,ikbv) * zwx(ji,ikbvm1) & / ( fse3v(ji,jj,ikbvm1)*fse3vw(ji,jj,ikbv) ) ! subtract surface forcing and bottom friction trend from vertical ! diffusive momentum trend ztdva(ji,jj,1 ) = ztdva(ji,jj,1 ) - ztsy(ji,jj) ztdva(ji,jj,ikbvm1) = ztdva(ji,jj,ikbvm1) - ztby(ji,jj) END DO ! ! =============== END DO ! End of slab ! ! =============== ! save the vertical diffusion trends for diagnostic ! momentum trends IF( l_trddyn ) THEN ztdua(:,:,:) = ua(:,:,:) - ztdua(:,:,:) ztdva(:,:,:) = va(:,:,:) - ztdva(:,:,:) CALL trd_mod(ztdua, ztdva, jpdtdzdf, 'DYN', kt) ztdua(:,:,:) = 0.e0 ztdva(:,:,:) = 0.e0 ztdua(:,:,1) = ztsx(:,:) ztdva(:,:,1) = ztsy(:,:) CALL trd_mod(ztdua , ztdva , jpdtdswf, 'DYN', kt) ztdua(:,:,:) = 0.e0 ztdva(:,:,:) = 0.e0 ztdua(:,:,1) = ztbx(:,:) ztdva(:,:,1) = ztby(:,:) CALL trd_mod(ztdua , ztdva , jpdtdbfr, 'DYN', kt) ENDIF IF(l_ctl) THEN ! print sum trends (used for debugging) zua = SUM( ua(2:nictl,2:njctl,1:jpkm1) * umask(2:nictl,2:njctl,1:jpkm1) ) zva = SUM( va(2:nictl,2:njctl,1:jpkm1) * vmask(2:nictl,2:njctl,1:jpkm1) ) WRITE(numout,*) ' zdf - Ua: ', zua-u_ctl, ' Va: ', zva-v_ctl u_ctl = zua ; v_ctl = zva ENDIF END SUBROUTINE dyn_zdf_imp_tsk !!============================================================================== END MODULE dynzdf_imp_atsk