MODULE dynzdf_imp !!====================================================================== !! *** MODULE dynzdf_imp *** !! Ocean dynamics: vertical component(s) of the momentum mixing trend, implicit scheme !!====================================================================== !! History : OPA ! 1990-10 (B. Blanke) Original code !! 8.0 ! 1997-05 (G. Madec) vertical component of isopycnal !! NEMO 0.5 ! 2002-08 (G. Madec) F90: Free form and module !! 3.3 ! 2010-04 (M. Leclair, G. Madec) Forcing averaged over 2 time steps !! 3.4 ! 2012-01 (H. Liu) Semi-implicit bottom friction !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! dyn_zdf_imp : compute the vertical diffusion using a implicit scheme !! together with the Leap-Frog time integration. !!---------------------------------------------------------------------- USE oce ! ocean dynamics and tracers USE phycst ! physical constants USE dom_oce ! ocean space and time domain USE domvvl ! variable volume USE sbc_oce ! surface boundary condition: ocean USE dynadv , ONLY: ln_dynadv_vec ! Momentum advection form USE zdf_oce ! ocean vertical physics USE zdfbfr ! Bottom friction setup ! USE in_out_manager ! I/O manager USE lib_mpp ! MPP library USE wrk_nemo ! Memory Allocation USE timing ! Timing IMPLICIT NONE PRIVATE PUBLIC dyn_zdf_imp ! 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/OPA 3.3 , NEMO Consortium (2010) !! $Id$ !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE dyn_zdf_imp( kt, p2dt ) !!---------------------------------------------------------------------- !! *** ROUTINE dyn_zdf_imp *** !! !! ** 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[ avmu / 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 zdfbfr.F) !! !! ** Action : (ua,va) after velocity !!--------------------------------------------------------------------- INTEGER , INTENT(in) :: kt ! ocean time-step index REAL(wp), INTENT(in) :: p2dt ! vertical profile of tracer time-step ! INTEGER :: ji, jj, jk ! dummy loop indices INTEGER :: ikbu, ikbv ! local integers REAL(wp) :: zzwi, ze3ua ! local scalars REAL(wp) :: zzws, ze3va ! - - REAL(wp), POINTER, DIMENSION(:,:,:) :: zwi, zwd, zws !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('dyn_zdf_imp') ! CALL wrk_alloc( jpi,jpj,jpk, zwi, zwd, zws ) ! IF( kt == nit000 ) THEN 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 ! ! !== Time step dynamics ==! ! IF( ln_dynadv_vec .OR. ln_linssh ) THEN ! applied on velocity DO jk = 1, jpkm1 ua(:,:,jk) = ( ub(:,:,jk) + p2dt * ua(:,:,jk) ) * umask(:,:,jk) va(:,:,jk) = ( vb(:,:,jk) + p2dt * va(:,:,jk) ) * vmask(:,:,jk) END DO ELSE ! applied on thickness weighted velocity DO jk = 1, jpkm1 ua(:,:,jk) = ( e3u_b(:,:,jk) * ub(:,:,jk) & & + p2dt * e3u_n(:,:,jk) * ua(:,:,jk) ) / e3u_a(:,:,jk) * umask(:,:,jk) va(:,:,jk) = ( e3v_b(:,:,jk) * vb(:,:,jk) & & + p2dt * e3v_n(:,:,jk) * va(:,:,jk) ) / e3v_a(:,:,jk) * vmask(:,:,jk) 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_bfrimp ) THEN DO jj = 2, jpjm1 DO ji = 2, jpim1 ikbu = mbku(ji,jj) ! ocean bottom level at u- and v-points ikbv = mbkv(ji,jj) ! (deepest ocean u- and v-points) avmu(ji,jj,ikbu+1) = -bfrua(ji,jj) * e3uw_n(ji,jj,ikbu+1) avmv(ji,jj,ikbv+1) = -bfrva(ji,jj) * e3vw_n(ji,jj,ikbv+1) END DO END DO IF ( ln_isfcav ) THEN DO jj = 2, jpjm1 DO ji = 2, jpim1 ikbu = miku(ji,jj) ! ocean top level at u- and v-points ikbv = mikv(ji,jj) ! (first wet ocean u- and v-points) IF( ikbu >= 2 ) avmu(ji,jj,ikbu) = -tfrua(ji,jj) * e3uw_n(ji,jj,ikbu) IF( ikbv >= 2 ) avmv(ji,jj,ikbv) = -tfrva(ji,jj) * e3vw_n(ji,jj,ikbv) END DO END DO END IF ENDIF ! ! 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_bfrimp .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. ikbu = mbku(ji,jj) ! ocean bottom level at u- and v-points ikbv = mbkv(ji,jj) ! (deepest ocean u- and v-points) ze3ua = ( 1._wp - r_vvl ) * e3u_n(ji,jj,ikbu) + r_vvl * e3u_a(ji,jj,ikbu) ze3va = ( 1._wp - r_vvl ) * e3v_n(ji,jj,ikbv) + r_vvl * e3v_a(ji,jj,ikbv) ua(ji,jj,ikbu) = ua(ji,jj,ikbu) + p2dt * bfrua(ji,jj) * ua_b(ji,jj) / ze3ua va(ji,jj,ikbv) = va(ji,jj,ikbv) + p2dt * bfrva(ji,jj) * va_b(ji,jj) / ze3va END DO END DO IF( ln_isfcav ) THEN ! Ocean cavities (ISF) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ikbu = miku(ji,jj) ! top ocean level at u- and v-points ikbv = mikv(ji,jj) ! (first wet ocean u- and v-points) ze3ua = ( 1._wp - r_vvl ) * e3u_n(ji,jj,ikbu) + r_vvl * e3u_a(ji,jj,ikbu) ze3va = ( 1._wp - r_vvl ) * e3v_n(ji,jj,ikbv) + r_vvl * e3v_a(ji,jj,ikbv) ua(ji,jj,ikbu) = ua(ji,jj,ikbu) + p2dt * tfrua(ji,jj) * ua_b(ji,jj) / ze3ua va(ji,jj,ikbv) = va(ji,jj,ikbv) + p2dt * tfrva(ji,jj) * va_b(ji,jj) / ze3va END DO END DO END IF ENDIF ! ! !== Vertical diffusion on u ==! ! ! Matrix and second member construction ! bottom boundary condition: both zwi and zws must be masked as avmu can take ! non zero value at the ocean bottom depending on the bottom friction used. ! DO jk = 1, jpkm1 ! Matrix 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 T-point zzwi = - p2dt * avmu(ji,jj,jk ) / ( ze3ua * e3uw_n(ji,jj,jk ) ) zzws = - p2dt * avmu(ji,jj,jk+1) / ( ze3ua * e3uw_n(ji,jj,jk+1) ) zwi(ji,jj,jk) = zzwi * wumask(ji,jj,jk ) zws(ji,jj,jk) = zzws * wumask(ji,jj,jk+1) zwd(ji,jj,jk) = 1._wp - zzwi - zzws END DO END DO END DO 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 ! 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) + p2dt * 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 and second member construction ! bottom boundary condition: both zwi and zws must be masked as avmv can take ! non zero value at the ocean bottom depending on the bottom friction used ! DO jk = 1, jpkm1 ! Matrix 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 T-point zzwi = - p2dt * avmv (ji,jj,jk ) / ( ze3va * e3vw_n(ji,jj,jk ) ) zzws = - p2dt * avmv (ji,jj,jk+1) / ( ze3va * e3vw_n(ji,jj,jk+1) ) zwi(ji,jj,jk) = zzwi * wvmask(ji,jj,jk ) zws(ji,jj,jk) = zzws * wvmask(ji,jj,jk+1) zwd(ji,jj,jk) = 1._wp - zzwi - zzws END DO END DO END DO 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 ! 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) + p2dt * 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 ! J. Chanut: Lines below are useless ? !! restore bottom layer avmu(v) !!gm I almost sure it is !!!! IF( ln_bfrimp ) THEN DO jj = 2, jpjm1 DO ji = 2, jpim1 ikbu = mbku(ji,jj) ! ocean bottom level at u- and v-points ikbv = mbkv(ji,jj) ! (deepest ocean u- and v-points) avmu(ji,jj,ikbu+1) = 0._wp avmv(ji,jj,ikbv+1) = 0._wp END DO END DO IF (ln_isfcav) THEN DO jj = 2, jpjm1 DO ji = 2, jpim1 ikbu = miku(ji,jj) ! ocean top level at u- and v-points ikbv = mikv(ji,jj) ! (first wet ocean u- and v-points) IF( ikbu > 1 ) avmu(ji,jj,ikbu) = 0._wp IF( ikbv > 1 ) avmv(ji,jj,ikbv) = 0._wp END DO END DO ENDIF ENDIF ! CALL wrk_dealloc( jpi,jpj,jpk, zwi, zwd, zws) ! IF( nn_timing == 1 ) CALL timing_stop('dyn_zdf_imp') ! END SUBROUTINE dyn_zdf_imp !!============================================================================== END MODULE dynzdf_imp