MODULE dynzad !!====================================================================== !! *** MODULE dynzad *** !! Ocean dynamics : vertical advection trend !!====================================================================== !! History : OPA ! 1991-01 (G. Madec) Original code !! 7.0 ! 1991-11 (G. Madec) !! 7.5 ! 1996-01 (G. Madec) statement function for e3 !! NEMO 0.5 ! 2002-07 (G. Madec) Free form, F90 !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! dyn_zad : vertical advection momentum trend !!---------------------------------------------------------------------- USE oce ! ocean dynamics and tracers USE dom_oce ! ocean space and time domain USE sbc_oce ! surface boundary condition: ocean 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 wrk_nemo ! Memory Allocation USE timing ! Timing IMPLICIT NONE PRIVATE PUBLIC dyn_zad ! routine called by dynadv.F90 PUBLIC dyn_zad_zts ! routine called by dynadv.F90 !! * Substitutions # include "domzgr_substitute.h90" # 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_zad ( kt ) !!---------------------------------------------------------------------- !! *** ROUTINE dynzad *** !! !! ** Purpose : Compute the now vertical momentum advection trend and !! add it to the general trend of momentum equation. !! !! ** Method : The now vertical advection of momentum is given by: !! w dz(u) = ua + 1/(e1u*e2u*e3u) mk+1[ mi(e1t*e2t*wn) dk(un) ] !! w dz(v) = va + 1/(e1v*e2v*e3v) mk+1[ mj(e1t*e2t*wn) dk(vn) ] !! Add this trend to the general trend (ua,va): !! (ua,va) = (ua,va) + w dz(u,v) !! !! ** Action : - Update (ua,va) with the vert. momentum adv. trends !! - Send the trends to trddyn for diagnostics (l_trddyn=T) !!---------------------------------------------------------------------- INTEGER, INTENT(in) :: kt ! ocean time-step inedx ! INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: zua, zva ! temporary scalars REAL(wp), POINTER, DIMENSION(:,:,:) :: zwuw , zwvw REAL(wp), POINTER, DIMENSION(:,: ) :: zww REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdu, ztrdv !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('dyn_zad') ! CALL wrk_alloc( jpi,jpj, zww ) CALL wrk_alloc( jpi,jpj,jpk, zwuw , zwvw ) ! IF( kt == nit000 ) THEN IF(lwp)WRITE(numout,*) IF(lwp)WRITE(numout,*) 'dyn_zad : arakawa advection scheme' ENDIF IF( l_trddyn ) THEN ! Save ua and va trends CALL wrk_alloc( jpi, jpj, jpk, ztrdu, ztrdv ) ztrdu(:,:,:) = ua(:,:,:) ztrdv(:,:,:) = va(:,:,:) ENDIF DO jk = 2, jpkm1 ! Vertical momentum advection at level w and u- and v- vertical DO jj = 2, jpj ! vertical fluxes DO ji = fs_2, jpi ! vector opt. zww(ji,jj) = 0.25_wp * e1t(ji,jj) * e2t(ji,jj) * wn(ji,jj,jk) END DO END DO DO jj = 2, jpjm1 ! vertical momentum advection at w-point DO ji = fs_2, fs_jpim1 ! vector opt. zwuw(ji,jj,jk) = ( zww(ji+1,jj ) + zww(ji,jj) ) * ( un(ji,jj,jk-1)-un(ji,jj,jk) ) zwvw(ji,jj,jk) = ( zww(ji ,jj+1) + zww(ji,jj) ) * ( vn(ji,jj,jk-1)-vn(ji,jj,jk) ) END DO END DO END DO ! ! Surface and bottom advective fluxes set to zero IF ( ln_isfcav ) THEN DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zwuw(ji,jj, 1:miku(ji,jj) ) = 0._wp zwvw(ji,jj, 1:mikv(ji,jj) ) = 0._wp zwuw(ji,jj,jpk) = 0._wp zwvw(ji,jj,jpk) = 0._wp END DO END DO ELSE DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zwuw(ji,jj, 1 ) = 0._wp zwvw(ji,jj, 1 ) = 0._wp zwuw(ji,jj,jpk) = 0._wp zwvw(ji,jj,jpk) = 0._wp END DO END DO END IF DO jk = 1, jpkm1 ! Vertical momentum advection at u- and v-points DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ! ! vertical momentum advective trends zua = - ( zwuw(ji,jj,jk) + zwuw(ji,jj,jk+1) ) / ( e1u(ji,jj) * e2u(ji,jj) * fse3u(ji,jj,jk) ) zva = - ( zwvw(ji,jj,jk) + zwvw(ji,jj,jk+1) ) / ( e1v(ji,jj) * e2v(ji,jj) * fse3v(ji,jj,jk) ) ! ! add the trends to the general momentum trends ua(ji,jj,jk) = ua(ji,jj,jk) + zua va(ji,jj,jk) = va(ji,jj,jk) + zva END DO END DO END DO IF( l_trddyn ) THEN ! save the vertical advection trends for diagnostic ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:) ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:) CALL trd_dyn( ztrdu, ztrdv, jpdyn_zad, kt ) CALL wrk_dealloc( jpi, jpj, jpk, ztrdu, ztrdv ) ENDIF ! ! Control print IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' zad - Ua: ', mask1=umask, & & tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) ! CALL wrk_dealloc( jpi,jpj, zww ) CALL wrk_dealloc( jpi,jpj,jpk, zwuw , zwvw ) ! IF( nn_timing == 1 ) CALL timing_stop('dyn_zad') ! END SUBROUTINE dyn_zad SUBROUTINE dyn_zad_zts ( kt ) !!---------------------------------------------------------------------- !! *** ROUTINE dynzad_zts *** !! !! ** Purpose : Compute the now vertical momentum advection trend and !! add it to the general trend of momentum equation. This version !! uses sub-timesteps for improved numerical stability with small !! vertical grid sizes. This is especially relevant when using !! embedded ice with thin surface boxes. !! !! ** Method : The now vertical advection of momentum is given by: !! w dz(u) = ua + 1/(e1u*e2u*e3u) mk+1[ mi(e1t*e2t*wn) dk(un) ] !! w dz(v) = va + 1/(e1v*e2v*e3v) mk+1[ mj(e1t*e2t*wn) dk(vn) ] !! Add this trend to the general trend (ua,va): !! (ua,va) = (ua,va) + w dz(u,v) !! !! ** Action : - Update (ua,va) with the vert. momentum adv. trends !! - Save the trends in (ztrdu,ztrdv) ('key_trddyn') !!---------------------------------------------------------------------- INTEGER, INTENT(in) :: kt ! ocean time-step inedx ! INTEGER :: ji, jj, jk, jl ! dummy loop indices INTEGER :: jnzts = 5 ! number of sub-timesteps for vertical advection INTEGER :: jtb, jtn, jta ! sub timestep pointers for leap-frog/euler forward steps REAL(wp) :: zua, zva ! temporary scalars REAL(wp) :: zr_rdt ! temporary scalar REAL(wp) :: z2dtzts ! length of Euler forward sub-timestep for vertical advection REAL(wp) :: zts ! length of sub-timestep for vertical advection REAL(wp), POINTER, DIMENSION(:,:,:) :: zwuw , zwvw, zww REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdu, ztrdv REAL(wp), POINTER, DIMENSION(:,:,:,:) :: zus , zvs !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('dyn_zad_zts') ! CALL wrk_alloc( jpi,jpj,jpk, zwuw , zwvw, zww ) CALL wrk_alloc( jpi,jpj,jpk,3, zus, zvs ) ! IF( kt == nit000 ) THEN IF(lwp)WRITE(numout,*) IF(lwp)WRITE(numout,*) 'dyn_zad_zts : arakawa advection scheme with sub-timesteps' ENDIF IF( l_trddyn ) THEN ! Save ua and va trends CALL wrk_alloc( jpi, jpj, jpk, ztrdu, ztrdv ) ztrdu(:,:,:) = ua(:,:,:) ztrdv(:,:,:) = va(:,:,:) ENDIF IF( neuler == 0 .AND. kt == nit000 ) THEN z2dtzts = rdt / REAL( jnzts, wp ) ! = rdt (restart with Euler time stepping) ELSE z2dtzts = 2._wp * rdt / REAL( jnzts, wp ) ! = 2 rdt (leapfrog) ENDIF DO jk = 2, jpkm1 ! Calculate and store vertical fluxes DO jj = 2, jpj DO ji = fs_2, jpi ! vector opt. zww(ji,jj,jk) = 0.25_wp * e1t(ji,jj) * e2t(ji,jj) * wn(ji,jj,jk) END DO END DO END DO ! ! Surface and bottom advective fluxes set to zero DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zwuw(ji,jj, 1 ) = 0._wp zwvw(ji,jj, 1 ) = 0._wp zwuw(ji,jj,jpk) = 0._wp zwvw(ji,jj,jpk) = 0._wp END DO END DO ! Start with before values and use sub timestepping to reach after values zus(:,:,:,1) = ub(:,:,:) zvs(:,:,:,1) = vb(:,:,:) DO jl = 1, jnzts ! Start of sub timestepping loop IF( jl == 1 ) THEN ! Euler forward to kick things off jtb = 1 ; jtn = 1 ; jta = 2 zts = z2dtzts ELSEIF( jl == 2 ) THEN ! First leapfrog step jtb = 1 ; jtn = 2 ; jta = 3 zts = 2._wp * z2dtzts ELSE ! Shuffle pointers for subsequent leapfrog steps jtb = MOD(jtb,3) + 1 jtn = MOD(jtn,3) + 1 jta = MOD(jta,3) + 1 ENDIF DO jk = 2, jpkm1 ! Vertical momentum advection at level w and u- and v- vertical DO jj = 2, jpjm1 ! vertical momentum advection at w-point DO ji = fs_2, fs_jpim1 ! vector opt. zwuw(ji,jj,jk) = ( zww(ji+1,jj ,jk) + zww(ji,jj,jk) ) * ( zus(ji,jj,jk-1,jtn)-zus(ji,jj,jk,jtn) ) !* wumask(ji,jj,jk) zwvw(ji,jj,jk) = ( zww(ji ,jj+1,jk) + zww(ji,jj,jk) ) * ( zvs(ji,jj,jk-1,jtn)-zvs(ji,jj,jk,jtn) ) !* wvmask(ji,jj,jk) END DO END DO END DO DO jk = 1, jpkm1 ! Vertical momentum advection at u- and v-points DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ! ! vertical momentum advective trends zua = - ( zwuw(ji,jj,jk) + zwuw(ji,jj,jk+1) ) / ( e1u(ji,jj) * e2u(ji,jj) * fse3u(ji,jj,jk) ) zva = - ( zwvw(ji,jj,jk) + zwvw(ji,jj,jk+1) ) / ( e1v(ji,jj) * e2v(ji,jj) * fse3v(ji,jj,jk) ) zus(ji,jj,jk,jta) = zus(ji,jj,jk,jtb) + zua * zts zvs(ji,jj,jk,jta) = zvs(ji,jj,jk,jtb) + zva * zts END DO END DO END DO END DO ! End of sub timestepping loop zr_rdt = 1._wp / ( REAL( jnzts, wp ) * z2dtzts ) DO jk = 1, jpkm1 ! Recover trends over the outer timestep DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ! ! vertical momentum advective trends ! ! add the trends to the general momentum trends ua(ji,jj,jk) = ua(ji,jj,jk) + ( zus(ji,jj,jk,jta) - ub(ji,jj,jk)) * zr_rdt va(ji,jj,jk) = va(ji,jj,jk) + ( zvs(ji,jj,jk,jta) - vb(ji,jj,jk)) * zr_rdt END DO END DO END DO IF( l_trddyn ) THEN ! save the vertical advection trends for diagnostic ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:) ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:) CALL trd_dyn( ztrdu, ztrdv, jpdyn_zad, kt ) CALL wrk_dealloc( jpi, jpj, jpk, ztrdu, ztrdv ) ENDIF ! ! Control print IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' zad - Ua: ', mask1=umask, & & tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) ! CALL wrk_dealloc( jpi,jpj,jpk, zwuw , zwvw, zww ) CALL wrk_dealloc( jpi,jpj,jpk,3, zus, zvs ) ! IF( nn_timing == 1 ) CALL timing_stop('dyn_zad_zts') ! END SUBROUTINE dyn_zad_zts !!====================================================================== END MODULE dynzad