MODULE dynzdf !!============================================================================== !! *** MODULE dynzdf *** !! Ocean dynamics : vertical component of the momentum mixing trend !!============================================================================== !! History : 1.0 ! 2005-11 (G. Madec) Original code !! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase !! 4.0 ! 2017-06 (G. Madec) remove the explicit time-stepping option + avm at t-point !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! dyn_zdf : compute the after velocity through implicit calculation of vertical mixing !!---------------------------------------------------------------------- USE oce ! ocean dynamics and tracers variables USE phycst ! physical constants USE dom_oce ! ocean space and time domain variables USE sbc_oce ! surface boundary condition: ocean USE zdf_oce ! ocean vertical physics variables USE zdfdrg ! vertical physics: top/bottom drag coef. USE dynadv ,ONLY: ln_dynadv_vec ! dynamics: advection form USE dynldf_iso,ONLY: akzu, akzv ! dynamics: vertical component of rotated lateral mixing USE ldfdyn ! lateral diffusion: eddy viscosity coef. and type of operator USE trd_oce ! trends: ocean variables USE trddyn ! trend manager: dynamics ! USE in_out_manager ! I/O manager USE lib_mpp ! MPP library USE prtctl ! Print control USE timing ! Timing IMPLICIT NONE PRIVATE PUBLIC dyn_zdf ! routine called by step.F90 REAL(wp) :: r_vvl ! non-linear free surface indicator: =0 if ln_linssh=T, =1 otherwise !! * Substitutions # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OCE 4.0 , NEMO Consortium (2018) !! $Id$ !! Software governed by the CeCILL license (see ./LICENSE) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE dyn_zdf( kt ) !!---------------------------------------------------------------------- !! *** ROUTINE dyn_zdf *** !! !! ** Purpose : compute the trend due to the vert. momentum diffusion !! together with the Leap-Frog time stepping using an !! implicit scheme. !! !! ** Method : - Leap-Frog time stepping on all trends but the vertical mixing !! ua = ub + 2*dt * ua vector form or linear free surf. !! ua = ( e3u_b*ub + 2*dt * e3u_n*ua ) / e3u_a otherwise !! - update the after velocity with the implicit vertical mixing. !! This requires to solver the following system: !! ua = ua + 1/e3u_a dk+1[ mi(avm) / e3uw_a dk[ua] ] !! with the following surface/top/bottom boundary condition: !! surface: wind stress input (averaged over kt-1/2 & kt+1/2) !! top & bottom : top stress (iceshelf-ocean) & bottom stress (cf zdfdrg.F90) !! !! ** Action : (ua,va) after velocity !!--------------------------------------------------------------------- INTEGER, INTENT(in) :: kt ! ocean time-step index ! INTEGER :: ji, jj, jk ! dummy loop indices INTEGER :: iku, ikv ! local integers REAL(wp) :: zzwi, ze3ua, zdt ! local scalars REAL(wp) :: zzws, ze3va ! - - REAL(wp) :: z1_e3ua, z1_e3va ! - - REAL(wp) :: zWu , zWv ! - - REAL(wp) :: zWui, zWvi ! - - REAL(wp) :: zWus, zWvs ! - - REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwi, zwd, zws ! 3D workspace REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ztrdu, ztrdv ! - - !!--------------------------------------------------------------------- ! IF( ln_timing ) CALL timing_start('dyn_zdf') ! IF( kt == nit000 ) THEN !* initialization IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'dyn_zdf_imp : vertical momentum diffusion implicit operator' IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ ' ! If( ln_linssh ) THEN ; r_vvl = 0._wp ! non-linear free surface indicator ELSE ; r_vvl = 1._wp ENDIF ENDIF ! !* set time step IF( neuler == 0 .AND. kt == nit000 ) THEN ; r2dt = rdt ! = rdt (restart with Euler time stepping) ELSEIF( kt <= nit000 + 1 ) THEN ; r2dt = 2. * rdt ! = 2 rdt (leapfrog) ENDIF ! ! !* explicit top/bottom drag case IF( .NOT.ln_drgimp ) CALL zdf_drg_exp( kt, ub, vb, ua, va ) ! add top/bottom friction trend to (ua,va) ! ! IF( l_trddyn ) THEN !* temporary save of ta and sa trends ALLOCATE( ztrdu(jpi,jpj,jpk), ztrdv(jpi,jpj,jpk) ) ztrdu(:,:,:) = ua(:,:,:) ztrdv(:,:,:) = va(:,:,:) ENDIF ! ! !== RHS: Leap-Frog time stepping on all trends but the vertical mixing ==! (put in ua,va) ! ! ! time stepping except vertical diffusion IF( ln_dynadv_vec .OR. ln_linssh ) THEN ! applied on velocity DO jk = 1, jpkm1 ua(:,:,jk) = ( ub(:,:,jk) + r2dt * ua(:,:,jk) ) * umask(:,:,jk) va(:,:,jk) = ( vb(:,:,jk) + r2dt * va(:,:,jk) ) * vmask(:,:,jk) END DO ELSE ! applied on thickness weighted velocity DO jk = 1, jpkm1 ua(:,:,jk) = ( e3u_b(:,:,jk) * ub(:,:,jk) & & + r2dt * e3u_n(:,:,jk) * ua(:,:,jk) ) / e3u_a(:,:,jk) * umask(:,:,jk) va(:,:,jk) = ( e3v_b(:,:,jk) * vb(:,:,jk) & & + r2dt * e3v_n(:,:,jk) * va(:,:,jk) ) / e3v_a(:,:,jk) * vmask(:,:,jk) END DO ENDIF ! ! add top/bottom friction ! With split-explicit free surface, barotropic stress is treated explicitly Update velocities at the bottom. ! J. Chanut: The bottom stress is computed considering after barotropic velocities, which does ! not lead to the effective stress seen over the whole barotropic loop. ! G. Madec : in linear free surface, e3u_a = e3u_n = e3u_0, so systematic use of e3u_a IF( ln_drgimp .AND. ln_dynspg_ts ) THEN DO jk = 1, jpkm1 ! remove barotropic velocities ua(:,:,jk) = ( ua(:,:,jk) - ua_b(:,:) ) * umask(:,:,jk) va(:,:,jk) = ( va(:,:,jk) - va_b(:,:) ) * vmask(:,:,jk) END DO DO jj = 2, jpjm1 ! Add bottom/top stress due to barotropic component only DO ji = fs_2, fs_jpim1 ! vector opt. iku = mbku(ji,jj) ! ocean bottom level at u- and v-points ikv = mbkv(ji,jj) ! (deepest ocean u- and v-points) ze3ua = ( 1._wp - r_vvl ) * e3u_n(ji,jj,iku) + r_vvl * e3u_a(ji,jj,iku) ze3va = ( 1._wp - r_vvl ) * e3v_n(ji,jj,ikv) + r_vvl * e3v_a(ji,jj,ikv) ua(ji,jj,iku) = ua(ji,jj,iku) + r2dt * 0.5*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) * ua_b(ji,jj) / ze3ua va(ji,jj,ikv) = va(ji,jj,ikv) + r2dt * 0.5*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) * va_b(ji,jj) / ze3va END DO END DO IF( ln_isfcav.OR.ln_drgice_imp ) THEN ! Ocean cavities (ISF) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. iku = miku(ji,jj) ! top ocean level at u- and v-points ikv = mikv(ji,jj) ! (first wet ocean u- and v-points) ze3ua = ( 1._wp - r_vvl ) * e3u_n(ji,jj,iku) + r_vvl * e3u_a(ji,jj,iku) ze3va = ( 1._wp - r_vvl ) * e3v_n(ji,jj,ikv) + r_vvl * e3v_a(ji,jj,ikv) ua(ji,jj,iku) = ua(ji,jj,iku) + r2dt * 0.5*( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) * ua_b(ji,jj) / ze3ua va(ji,jj,ikv) = va(ji,jj,ikv) + r2dt * 0.5*( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) * va_b(ji,jj) / ze3va END DO END DO END IF ENDIF ! ! !== Vertical diffusion on u ==! ! ! !* Matrix construction zdt = r2dt * 0.5 IF( ln_zad_Aimp ) THEN !! SELECT CASE( nldf_dyn ) CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu) DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ze3ua = ( 1._wp - r_vvl ) * e3u_n(ji,jj,jk) + r_vvl * e3u_a(ji,jj,jk) ! after scale factor at U-point zzwi = - zdt * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) + akzu(ji,jj,jk ) ) & & / ( ze3ua * e3uw_n(ji,jj,jk ) ) * wumask(ji,jj,jk ) zzws = - zdt * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) + akzu(ji,jj,jk+1) ) & & / ( ze3ua * e3uw_n(ji,jj,jk+1) ) * wumask(ji,jj,jk+1) zWui = ( wi(ji,jj,jk ) + wi(ji+1,jj,jk ) ) / ze3ua zWus = ( wi(ji,jj,jk+1) + wi(ji+1,jj,jk+1) ) / ze3ua zwi(ji,jj,jk) = zzwi + zdt * MIN( zWui, 0._wp ) zws(ji,jj,jk) = zzws - zdt * MAX( zWus, 0._wp ) zwd(ji,jj,jk) = 1._wp - zzwi - zzws + zdt * ( MAX( zWui, 0._wp ) - MIN( zWus, 0._wp ) ) END DO END DO END DO CASE DEFAULT ! iso-level lateral mixing DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ze3ua = ( 1._wp - r_vvl ) * e3u_n(ji,jj,jk) + r_vvl * e3u_a(ji,jj,jk) ! after scale factor at U-point zzwi = - zdt * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) ) / ( ze3ua * e3uw_n(ji,jj,jk ) ) * wumask(ji,jj,jk ) zzws = - zdt * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) ) / ( ze3ua * e3uw_n(ji,jj,jk+1) ) * wumask(ji,jj,jk+1) zWui = ( wi(ji,jj,jk ) + wi(ji+1,jj,jk ) ) / ze3ua zWus = ( wi(ji,jj,jk+1) + wi(ji+1,jj,jk+1) ) / ze3ua zwi(ji,jj,jk) = zzwi + zdt * MIN( zWui, 0._wp ) zws(ji,jj,jk) = zzws - zdt * MAX( zWus, 0._wp ) zwd(ji,jj,jk) = 1._wp - zzwi - zzws + zdt * ( MAX( zWui, 0._wp ) - MIN( zWus, 0._wp ) ) END DO END DO END DO END SELECT DO jj = 2, jpjm1 !* Surface boundary conditions DO ji = fs_2, fs_jpim1 ! vector opt. zwi(ji,jj,1) = 0._wp ze3ua = ( 1._wp - r_vvl ) * e3u_n(ji,jj,1) + r_vvl * e3u_a(ji,jj,1) zzws = - zdt * ( avm(ji+1,jj,2) + avm(ji ,jj,2) ) / ( ze3ua * e3uw_n(ji,jj,2) ) * wumask(ji,jj,2) zWus = ( wi(ji ,jj,2) + wi(ji+1,jj,2) ) / ze3ua zws(ji,jj,1 ) = zzws - zdt * MAX( zWus, 0._wp ) zwd(ji,jj,1 ) = 1._wp - zzws - zdt * ( MIN( zWus, 0._wp ) ) END DO END DO ELSE SELECT CASE( nldf_dyn ) CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu) DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ze3ua = ( 1._wp - r_vvl ) * e3u_n(ji,jj,jk) + r_vvl * e3u_a(ji,jj,jk) ! after scale factor at U-point zzwi = - zdt * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) + akzu(ji,jj,jk ) ) & & / ( ze3ua * e3uw_n(ji,jj,jk ) ) * wumask(ji,jj,jk ) zzws = - zdt * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) + akzu(ji,jj,jk+1) ) & & / ( ze3ua * e3uw_n(ji,jj,jk+1) ) * wumask(ji,jj,jk+1) zwi(ji,jj,jk) = zzwi zws(ji,jj,jk) = zzws zwd(ji,jj,jk) = 1._wp - zzwi - zzws END DO END DO END DO CASE DEFAULT ! iso-level lateral mixing DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ze3ua = ( 1._wp - r_vvl ) * e3u_n(ji,jj,jk) + r_vvl * e3u_a(ji,jj,jk) ! after scale factor at U-point zzwi = - zdt * ( avm(ji+1,jj,jk ) + avm(ji,jj,jk ) ) / ( ze3ua * e3uw_n(ji,jj,jk ) ) * wumask(ji,jj,jk ) zzws = - zdt * ( avm(ji+1,jj,jk+1) + avm(ji,jj,jk+1) ) / ( ze3ua * e3uw_n(ji,jj,jk+1) ) * wumask(ji,jj,jk+1) zwi(ji,jj,jk) = zzwi zws(ji,jj,jk) = zzws zwd(ji,jj,jk) = 1._wp - zzwi - zzws END DO END DO END DO END SELECT DO jj = 2, jpjm1 !* Surface boundary conditions DO ji = fs_2, fs_jpim1 ! vector opt. zwi(ji,jj,1) = 0._wp zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) END DO END DO ENDIF ! ! ! !== Apply semi-implicit bottom friction ==! ! ! Only needed for semi-implicit bottom friction setup. The explicit ! bottom friction has been included in "u(v)a" which act as the R.H.S ! column vector of the tri-diagonal matrix equation ! IF ( ln_drgimp ) THEN ! implicit bottom friction DO jj = 2, jpjm1 DO ji = 2, jpim1 iku = mbku(ji,jj) ! ocean bottom level at u- and v-points ze3ua = ( 1._wp - r_vvl ) * e3u_n(ji,jj,iku) + r_vvl * e3u_a(ji,jj,iku) ! after scale factor at T-point zwd(ji,jj,iku) = zwd(ji,jj,iku) - r2dt * 0.5*( rCdU_bot(ji+1,jj)+rCdU_bot(ji,jj) ) / ze3ua END DO END DO IF ( ln_isfcav.OR.ln_drgice_imp ) THEN ! top friction (always implicit) DO jj = 2, jpjm1 DO ji = 2, jpim1 !!gm top Cd is masked (=0 outside cavities) no need of test on mik>=2 ==>> it has been suppressed iku = miku(ji,jj) ! ocean top level at u- and v-points ze3ua = ( 1._wp - r_vvl ) * e3u_n(ji,jj,iku) + r_vvl * e3u_a(ji,jj,iku) ! after scale factor at T-point zwd(ji,jj,iku) = zwd(ji,jj,iku) - r2dt * 0.5*( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) / ze3ua END DO END DO END IF ENDIF ! ! Matrix inversion starting from the first level !----------------------------------------------------------------------- ! 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 a lower triangular matrix ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi ! The solution (the after velocity) is in ua !----------------------------------------------------------------------- ! DO jk = 2, jpkm1 !== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) == DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zwd(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwd(ji,jj,jk-1) END DO END DO END DO ! DO jj = 2, jpjm1 !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 ==! DO ji = fs_2, fs_jpim1 ! vector opt. ze3ua = ( 1._wp - r_vvl ) * e3u_n(ji,jj,1) + r_vvl * e3u_a(ji,jj,1) ua(ji,jj,1) = ua(ji,jj,1) + r2dt * 0.5_wp * ( utau_b(ji,jj) + utau(ji,jj) ) & & / ( ze3ua * rau0 ) * umask(ji,jj,1) END DO END DO DO jk = 2, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ua(ji,jj,jk) = ua(ji,jj,jk) - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * ua(ji,jj,jk-1) END DO END DO END DO ! DO jj = 2, jpjm1 !== thrid recurrence : SOLk = ( Lk - Uk * Ek+1 ) / Dk ==! DO ji = fs_2, fs_jpim1 ! vector opt. ua(ji,jj,jpkm1) = ua(ji,jj,jpkm1) / zwd(ji,jj,jpkm1) END DO END DO DO jk = jpk-2, 1, -1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ua(ji,jj,jk) = ( ua(ji,jj,jk) - zws(ji,jj,jk) * ua(ji,jj,jk+1) ) / zwd(ji,jj,jk) END DO END DO END DO ! ! !== Vertical diffusion on v ==! ! ! !* Matrix construction zdt = r2dt * 0.5 IF( ln_zad_Aimp ) THEN !! SELECT CASE( nldf_dyn ) CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzv) DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ze3va = ( 1._wp - r_vvl ) * e3v_n(ji,jj,jk) + r_vvl * e3v_a(ji,jj,jk) ! after scale factor at V-point zzwi = - zdt * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) + akzv(ji,jj,jk ) ) & & / ( ze3va * e3vw_n(ji,jj,jk ) ) * wvmask(ji,jj,jk ) zzws = - zdt * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) + akzv(ji,jj,jk+1) ) & & / ( ze3va * e3vw_n(ji,jj,jk+1) ) * wvmask(ji,jj,jk+1) zWvi = ( wi(ji,jj,jk ) + wi(ji,jj+1,jk ) ) / ze3va zWvs = ( wi(ji,jj,jk+1) + wi(ji,jj+1,jk+1) ) / ze3va zwi(ji,jj,jk) = zzwi + zdt * MIN( zWvi, 0._wp ) zws(ji,jj,jk) = zzws - zdt * MAX( zWvs, 0._wp ) zwd(ji,jj,jk) = 1._wp - zzwi - zzws - zdt * ( - MAX( zWvi, 0._wp ) + MIN( zWvs, 0._wp ) ) END DO END DO END DO CASE DEFAULT ! iso-level lateral mixing DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ze3va = ( 1._wp - r_vvl ) * e3v_n(ji,jj,jk) + r_vvl * e3v_a(ji,jj,jk) ! after scale factor at V-point zzwi = - zdt * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) ) / ( ze3va * e3vw_n(ji,jj,jk ) ) * wvmask(ji,jj,jk ) zzws = - zdt * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) ) / ( ze3va * e3vw_n(ji,jj,jk+1) ) * wvmask(ji,jj,jk+1) zWvi = ( wi(ji,jj,jk ) + wi(ji,jj+1,jk ) ) / ze3va zWvs = ( wi(ji,jj,jk+1) + wi(ji,jj+1,jk+1) ) / ze3va zwi(ji,jj,jk) = zzwi + zdt * MIN( zWvi, 0._wp ) zws(ji,jj,jk) = zzws - zdt * MAX( zWvs, 0._wp ) zwd(ji,jj,jk) = 1._wp - zzwi - zzws - zdt * ( - MAX( zWvi, 0._wp ) + MIN( zWvs, 0._wp ) ) END DO END DO END DO END SELECT DO jj = 2, jpjm1 !* Surface boundary conditions DO ji = fs_2, fs_jpim1 ! vector opt. zwi(ji,jj,1) = 0._wp ze3va = ( 1._wp - r_vvl ) * e3v_n(ji,jj,1) + r_vvl * e3v_a(ji,jj,1) zzws = - zdt * ( avm(ji,jj+1,2) + avm(ji,jj,2) ) / ( ze3va * e3vw_n(ji,jj,2) ) * wvmask(ji,jj,2) zWvs = ( wi(ji,jj ,2) + wi(ji,jj+1,2) ) / ze3va zws(ji,jj,1 ) = zzws - zdt * MAX( zWvs, 0._wp ) zwd(ji,jj,1 ) = 1._wp - zzws - zdt * ( MIN( zWvs, 0._wp ) ) END DO END DO ELSE SELECT CASE( nldf_dyn ) CASE( np_lap_i ) ! rotated lateral mixing: add its vertical mixing (akzu) DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ze3va = ( 1._wp - r_vvl ) * e3v_n(ji,jj,jk) + r_vvl * e3v_a(ji,jj,jk) ! after scale factor at V-point zzwi = - zdt * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) + akzv(ji,jj,jk ) ) & & / ( ze3va * e3vw_n(ji,jj,jk ) ) * wvmask(ji,jj,jk ) zzws = - zdt * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) + akzv(ji,jj,jk+1) ) & & / ( ze3va * e3vw_n(ji,jj,jk+1) ) * wvmask(ji,jj,jk+1) zwi(ji,jj,jk) = zzwi zws(ji,jj,jk) = zzws zwd(ji,jj,jk) = 1._wp - zzwi - zzws END DO END DO END DO CASE DEFAULT ! iso-level lateral mixing DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ze3va = ( 1._wp - r_vvl ) * e3v_n(ji,jj,jk) + r_vvl * e3v_a(ji,jj,jk) ! after scale factor at V-point zzwi = - zdt * ( avm(ji,jj+1,jk ) + avm(ji,jj,jk ) ) / ( ze3va * e3vw_n(ji,jj,jk ) ) * wvmask(ji,jj,jk ) zzws = - zdt * ( avm(ji,jj+1,jk+1) + avm(ji,jj,jk+1) ) / ( ze3va * e3vw_n(ji,jj,jk+1) ) * wvmask(ji,jj,jk+1) zwi(ji,jj,jk) = zzwi zws(ji,jj,jk) = zzws zwd(ji,jj,jk) = 1._wp - zzwi - zzws END DO END DO END DO END SELECT DO jj = 2, jpjm1 !* Surface boundary conditions DO ji = fs_2, fs_jpim1 ! vector opt. zwi(ji,jj,1) = 0._wp zwd(ji,jj,1) = 1._wp - zws(ji,jj,1) END DO END DO ENDIF ! ! !== Apply semi-implicit top/bottom friction ==! ! ! Only needed for semi-implicit bottom friction setup. The explicit ! bottom friction has been included in "u(v)a" which act as the R.H.S ! column vector of the tri-diagonal matrix equation ! IF( ln_drgimp ) THEN DO jj = 2, jpjm1 DO ji = 2, jpim1 ikv = mbkv(ji,jj) ! (deepest ocean u- and v-points) ze3va = ( 1._wp - r_vvl ) * e3v_n(ji,jj,ikv) + r_vvl * e3v_a(ji,jj,ikv) ! after scale factor at T-point zwd(ji,jj,ikv) = zwd(ji,jj,ikv) - r2dt * 0.5*( rCdU_bot(ji,jj+1)+rCdU_bot(ji,jj) ) / ze3va END DO END DO IF ( ln_isfcav.OR.ln_drgice_imp ) THEN DO jj = 2, jpjm1 DO ji = 2, jpim1 ikv = mikv(ji,jj) ! (first wet ocean u- and v-points) ze3va = ( 1._wp - r_vvl ) * e3v_n(ji,jj,ikv) + r_vvl * e3v_a(ji,jj,ikv) ! after scale factor at T-point zwd(ji,jj,iku) = zwd(ji,jj,iku) - r2dt * 0.5*( rCdU_top(ji+1,jj)+rCdU_top(ji,jj) ) / ze3va END DO END DO ENDIF ENDIF ! 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 solution (after velocity) is in 2d array va !----------------------------------------------------------------------- ! DO jk = 2, jpkm1 !== First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) == DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zwd(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwd(ji,jj,jk-1) END DO END DO END DO ! DO jj = 2, jpjm1 !== second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 ==! DO ji = fs_2, fs_jpim1 ! vector opt. ze3va = ( 1._wp - r_vvl ) * e3v_n(ji,jj,1) + r_vvl * e3v_a(ji,jj,1) va(ji,jj,1) = va(ji,jj,1) + r2dt * 0.5_wp * ( vtau_b(ji,jj) + vtau(ji,jj) ) & & / ( ze3va * rau0 ) * vmask(ji,jj,1) END DO END DO DO jk = 2, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. va(ji,jj,jk) = va(ji,jj,jk) - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * va(ji,jj,jk-1) END DO END DO END DO ! DO jj = 2, jpjm1 !== third recurrence : SOLk = ( Lk - Uk * SOLk+1 ) / Dk ==! DO ji = fs_2, fs_jpim1 ! vector opt. va(ji,jj,jpkm1) = va(ji,jj,jpkm1) / zwd(ji,jj,jpkm1) END DO END DO DO jk = jpk-2, 1, -1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 va(ji,jj,jk) = ( va(ji,jj,jk) - zws(ji,jj,jk) * va(ji,jj,jk+1) ) / zwd(ji,jj,jk) END DO END DO END DO ! IF( l_trddyn ) THEN ! save the vertical diffusive trends for further diagnostics ztrdu(:,:,:) = ( ua(:,:,:) - ub(:,:,:) ) / r2dt - ztrdu(:,:,:) ztrdv(:,:,:) = ( va(:,:,:) - vb(:,:,:) ) / r2dt - ztrdv(:,:,:) CALL trd_dyn( ztrdu, ztrdv, jpdyn_zdf, kt ) DEALLOCATE( ztrdu, ztrdv ) ENDIF ! ! print mean trends (used for debugging) IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' zdf - Ua: ', mask1=umask, & & tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) ! IF( ln_timing ) CALL timing_stop('dyn_zdf') ! END SUBROUTINE dyn_zdf !!============================================================================== END MODULE dynzdf