MODULE limhdf !!====================================================================== !! *** MODULE limhdf *** !! LIM ice model : horizontal diffusion of sea-ice quantities !!====================================================================== !! History : LIM ! 2000-01 (LIM) Original code !! - ! 2001-05 (G. Madec, R. Hordoir) opa norm !! 1.0 ! 2002-08 (C. Ethe) F90, free form !! 3.0 ! 2015-08 (O. Tintó and M. Castrillo) added lim_hdf (multiple) !!---------------------------------------------------------------------- #if defined key_lim3 !!---------------------------------------------------------------------- !! 'key_lim3' LIM3 sea-ice model !!---------------------------------------------------------------------- !! lim_hdf : diffusion trend on sea-ice variable !! lim_hdf_init : initialisation of diffusion trend on sea-ice variable !!---------------------------------------------------------------------- USE dom_oce ! ocean domain USE ice ! LIM-3: ice variables USE lbclnk ! lateral boundary condition - MPP exchanges USE lib_mpp ! MPP library USE wrk_nemo ! work arrays USE prtctl ! Print control USE in_out_manager ! I/O manager USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) IMPLICIT NONE PRIVATE PUBLIC lim_hdf ! called by lim_trp PUBLIC lim_hdf_init ! called by sbc_lim_init LOGICAL :: linit = .TRUE. ! initialization flag (set to flase after the 1st call) INTEGER :: nn_convfrq !: convergence check frequency of the Crant-Nicholson scheme REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: efact ! metric coefficient !! * Substitution # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/LIM3 4.0 , UCL - NEMO Consortium (2010) !! $Id: limhdf.F90 4990 2014-12-15 16:42:49Z timgraham $ !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE lim_hdf( ptab , ihdf_vars , jpl , nlay_i ) !!------------------------------------------------------------------- !! *** ROUTINE lim_hdf *** !! !! ** purpose : Compute and add the diffusive trend on sea-ice variables !! !! ** method : Second order diffusive operator evaluated using a !! Cranck-Nicholson time Scheme. !! !! ** Action : update ptab with the diffusive contribution !!------------------------------------------------------------------- INTEGER :: jpl, nlay_i, isize, ihdf_vars REAL(wp), DIMENSION(:,:,:), INTENT( inout ),TARGET :: ptab ! Field on which the diffusion is applied ! INTEGER :: ji, jj, jk, jl , jm ! dummy loop indices INTEGER :: iter, ierr ! local integers REAL(wp) :: zrlxint ! local scalars REAL(wp), POINTER , DIMENSION ( : ) :: zconv ! local scalars REAL(wp), POINTER , DIMENSION(:,:,:) :: zrlx,zdiv0, ztab0 REAL(wp), POINTER , DIMENSION(:,:) :: zflu, zflv, zdiv CHARACTER(lc) :: charout ! local character REAL(wp), PARAMETER :: zrelax = 0.5_wp ! relaxation constant for iterative procedure REAL(wp), PARAMETER :: zalfa = 0.5_wp ! =1.0/0.5/0.0 = implicit/Cranck-Nicholson/explicit INTEGER , PARAMETER :: its = 100 ! Maximum number of iteration !!------------------------------------------------------------------- TYPE(arrayptr) , ALLOCATABLE, DIMENSION(:) :: pt2d_array, zrlx_array CHARACTER(len=1) , ALLOCATABLE, DIMENSION(:) :: type_array ! define the nature of ptab array grid-points ! ! = T , U , V , F , W and I points REAL(wp) , ALLOCATABLE, DIMENSION(:) :: psgn_array ! =-1 the sign change across the north fold boundary !!--------------------------------------------------------------------- ! !== Initialisation ==! ! +1 open water diffusion isize = jpl*(ihdf_vars+nlay_i)+1 ALLOCATE( zconv (isize) ) ALLOCATE( pt2d_array(isize) , zrlx_array(isize) ) ALLOCATE( type_array(isize) ) ALLOCATE( psgn_array(isize) ) CALL wrk_alloc( jpi, jpj, isize, zrlx, zdiv0, ztab0 ) CALL wrk_alloc( jpi, jpj, zflu, zflv, zdiv ) DO jk= 1 , isize pt2d_array(jk)%pt2d=>ptab(:,:,jk) zrlx_array(jk)%pt2d=>zrlx(:,:,jk) type_array(jk)='T' psgn_array(jk)=1. END DO ! IF( linit ) THEN ! Metric coefficient (compute at the first call and saved in efact) ALLOCATE( efact(jpi,jpj) , STAT=ierr ) IF( lk_mpp ) CALL mpp_sum( ierr ) IF( ierr /= 0 ) CALL ctl_stop( 'STOP', 'lim_hdf : unable to allocate arrays' ) DO jj = 2, jpjm1 DO ji = fs_2 , fs_jpim1 ! vector opt. efact(ji,jj) = ( e2u(ji,jj) + e2u(ji-1,jj) + e1v(ji,jj) + e1v(ji,jj-1) ) * r1_e12t(ji,jj) END DO END DO linit = .FALSE. ENDIF ! ! Time integration parameters ! zflu (jpi,: ) = 0._wp zflv (jpi,: ) = 0._wp DO jk=1 , isize ztab0(:, : , jk ) = ptab(:,:,jk) ! Arrays initialization zdiv0(:, 1 , jk ) = 0._wp zdiv0(:,jpj, jk ) = 0._wp zdiv0(1, :, jk ) = 0._wp zdiv0(jpi,:, jk ) = 0._wp END DO zconv = 1._wp !== horizontal diffusion using a Crant-Nicholson scheme ==! iter = 0 ! DO WHILE( MAXVAL(zconv(:)) > ( 2._wp * 1.e-04 ) .AND. iter <= its ) ! Sub-time step loop ! iter = iter + 1 ! incrementation of the sub-time step number ! DO jk = 1 , isize jl = (jk-1) /( ihdf_vars+nlay_i)+1 IF (zconv(jk) > ( 2._wp * 1.e-04 )) THEN DO jj = 1, jpjm1 ! diffusive fluxes in U- and V- direction DO ji = 1 , fs_jpim1 ! vector opt. zflu(ji,jj) = pahu3D(ji,jj,jl) * e2u(ji,jj) * r1_e1u(ji,jj) * ( ptab(ji+1,jj,jk) - ptab(ji,jj,jk) ) zflv(ji,jj) = pahv3D(ji,jj,jl) * e1v(ji,jj) * r1_e2v(ji,jj) * ( ptab(ji,jj+1,jk) - ptab(ji,jj,jk) ) END DO END DO ! DO jj= 2, jpjm1 ! diffusive trend : divergence of the fluxes DO ji = fs_2 , fs_jpim1 ! vector opt. zdiv(ji,jj) = ( zflu(ji,jj) - zflu(ji-1,jj) + zflv(ji,jj) - zflv(ji,jj-1) ) * r1_e12t(ji,jj) END DO END DO ! IF( iter == 1 ) zdiv0(:,:,jk) = zdiv(:,:) ! save the 1st evaluation of the diffusive trend in zdiv0 ! DO jj = 2, jpjm1 ! iterative evaluation DO ji = fs_2 , fs_jpim1 ! vector opt. zrlxint = ( ztab0(ji,jj,jk) & & + rdt_ice * ( zalfa * ( zdiv(ji,jj) + efact(ji,jj) * ptab(ji,jj,jk) ) & & + ( 1.0 - zalfa ) * zdiv0(ji,jj,jk) ) & & ) / ( 1.0 + zalfa * rdt_ice * efact(ji,jj) ) zrlx(ji,jj,jk) = ptab(ji,jj,jk) + zrelax * ( zrlxint - ptab(ji,jj,jk) ) END DO END DO END IF END DO CALL lbc_lnk_multi( zrlx_array, type_array , psgn_array , isize ) ! Multiple interchange of all the variables ! IF ( MOD( iter-1 , nn_convfrq ) == 0 ) THEN !Convergence test every nn_convfrq iterations (perf. optimization ) DO jk=1,isize zconv(jk) = 0._wp ! convergence test DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 zconv(jk) = MAX( zconv(jk), ABS( zrlx(ji,jj,jk) - ptab(ji,jj,jk) ) ) END DO END DO END DO IF( lk_mpp ) CALL mpp_max_multiple( zconv , isize ) ! max over the global domain for all the variables ENDIF ! DO jk=1,isize ptab(:,:,jk) = zrlx(:,:,jk) END DO ! END DO ! end of sub-time step loop ! ----------------------- !!! final step (clem) !!! DO jk = 1, isize jl = (jk-1) /( ihdf_vars+nlay_i)+1 DO jj = 1, jpjm1 ! diffusive fluxes in U- and V- direction DO ji = 1 , fs_jpim1 ! vector opt. zflu(ji,jj) = pahu3D(ji,jj,jl) * e2u(ji,jj) * r1_e1u(ji,jj) * ( ptab(ji+1,jj,jk) - ptab(ji,jj,jk) ) zflv(ji,jj) = pahv3D(ji,jj,jl) * e1v(ji,jj) * r1_e2v(ji,jj) * ( ptab(ji,jj+1,jk) - ptab(ji,jj,jk) ) END DO END DO ! DO jj= 2, jpjm1 ! diffusive trend : divergence of the fluxes DO ji = fs_2 , fs_jpim1 ! vector opt. zdiv(ji,jj) = ( zflu(ji,jj) - zflu(ji-1,jj) + zflv(ji,jj) - zflv(ji,jj-1) ) * r1_e12t(ji,jj) ptab(ji,jj,jk) = ztab0(ji,jj,jk) + 0.5 * ( zdiv(ji,jj) + zdiv0(ji,jj,jk) ) END DO END DO END DO CALL lbc_lnk_multi( pt2d_array, type_array , psgn_array , isize ) ! Multiple interchange of all the variables !!! final step (clem) !!! ! ----------------------- ! IF(ln_ctl) THEN ! DO jk = 1 , isize ! zrlx(:,:,jk) = ptab(:,:,jk) - ztab0(:,:,jk) ! WRITE(charout,FMT="('lim_hdf : zconv =',D23.16, ' iter =',I4)") zconv, iter ! CALL prt_ctl( tab2d_1=zrlx(:,:,jk), clinfo1=charout ) ! END DO ! ENDIF ! CALL wrk_dealloc( jpi, jpj, isize, zrlx, zdiv0, ztab0 ) CALL wrk_dealloc( jpi, jpj, zflu, zflv, zdiv ) DEALLOCATE( zconv ) DEALLOCATE( pt2d_array , zrlx_array ) DEALLOCATE( type_array ) DEALLOCATE( psgn_array ) ! END SUBROUTINE lim_hdf SUBROUTINE lim_hdf_init !!------------------------------------------------------------------- !! *** ROUTINE lim_hdf_init *** !! !! ** Purpose : Initialisation of horizontal diffusion of sea-ice !! !! ** Method : Read the namicehdf namelist !! !! ** input : Namelist namicehdf !!------------------------------------------------------------------- INTEGER :: ios ! Local integer output status for namelist read NAMELIST/namicehdf/ nn_ahi0, rn_ahi0_ref, nn_convfrq INTEGER :: ji, jj REAL(wp) :: za00, zd_max !!------------------------------------------------------------------- ! REWIND( numnam_ice_ref ) ! Namelist namicehdf in reference namelist : Ice horizontal diffusion READ ( numnam_ice_ref, namicehdf, IOSTAT = ios, ERR = 901) 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namicehdf in reference namelist', lwp ) REWIND( numnam_ice_cfg ) ! Namelist namicehdf in configuration namelist : Ice horizontal diffusion READ ( numnam_ice_cfg, namicehdf, IOSTAT = ios, ERR = 902 ) 902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namicehdf in configuration namelist', lwp ) IF(lwm) WRITE ( numoni, namicehdf ) ! IF(lwp) THEN ! control print WRITE(numout,*) WRITE(numout,*) 'lim_hdf_init : Ice horizontal diffusion' WRITE(numout,*) '~~~~~~~~~~~' WRITE(numout,*) ' horizontal diffusivity calculation nn_ahi0 = ', nn_ahi0 WRITE(numout,*) ' horizontal diffusivity coeff. (orca2 grid) rn_ahi0_ref = ', rn_ahi0_ref WRITE(numout,*) ' convergence check frequency of the Crant-Nicholson scheme nn_convfrq = ', nn_convfrq ENDIF ! ! Diffusion coefficients SELECT CASE( nn_ahi0 ) CASE( -1 ) ahiu(:,:) = 0._wp ahiv(:,:) = 0._wp IF(lwp) WRITE(numout,*) '' IF(lwp) WRITE(numout,*) ' No sea-ice diffusion applied' CASE( 0 ) ahiu(:,:) = rn_ahi0_ref ahiv(:,:) = rn_ahi0_ref IF(lwp) WRITE(numout,*) '' IF(lwp) WRITE(numout,*) ' laplacian operator: ahim constant = rn_ahi0_ref' CASE( 1 ) zd_max = MAX( MAXVAL( e1t(:,:) ), MAXVAL( e2t(:,:) ) ) IF( lk_mpp ) CALL mpp_max( zd_max ) ! max over the global domain ahiu(:,:) = rn_ahi0_ref * zd_max * 1.e-05_wp ! 1.e05 = 100km = max grid space at 60deg latitude in orca2 ! (60deg = min latitude for ice cover) ahiv(:,:) = rn_ahi0_ref * zd_max * 1.e-05_wp IF(lwp) WRITE(numout,*) '' IF(lwp) WRITE(numout,*) ' laplacian operator: ahim proportional to max of e1 e2 over the domain (', zd_max, ')' IF(lwp) WRITE(numout,*) ' value for ahim = ', rn_ahi0_ref * zd_max * 1.e-05_wp CASE( 2 ) zd_max = MAX( MAXVAL( e1t(:,:) ), MAXVAL( e2t(:,:) ) ) IF( lk_mpp ) CALL mpp_max( zd_max ) ! max over the global domain za00 = rn_ahi0_ref * 1.e-05_wp ! 1.e05 = 100km = max grid space at 60deg latitude in orca2 ! (60deg = min latitude for ice cover) DO jj = 1, jpj DO ji = 1, jpi ahiu(ji,jj) = za00 * MAX( e1t(ji,jj), e2t(ji,jj) ) * umask(ji,jj,1) ahiv(ji,jj) = za00 * MAX( e1f(ji,jj), e2f(ji,jj) ) * vmask(ji,jj,1) END DO END DO ! IF(lwp) WRITE(numout,*) '' IF(lwp) WRITE(numout,*) ' laplacian operator: ahim proportional to e1' IF(lwp) WRITE(numout,*) ' maximum grid-spacing = ', zd_max, ' maximum value for ahim = ', za00*zd_max END SELECT ! END SUBROUTINE lim_hdf_init #else !!---------------------------------------------------------------------- !! Default option Dummy module NO LIM sea-ice model !!---------------------------------------------------------------------- #endif !!====================================================================== END MODULE limhdf