MODULE iceadv_prather !!====================================================================== !! *** MODULE iceadv_prather *** !! LIM sea-ice model : sea-ice advection => Prather scheme !!====================================================================== !! History : LIM ! 2008-03 (M. Vancoppenolle) LIM-3 from LIM-2 code !! 3.2 ! 2009-06 (F. Dupont) correct a error in the North fold b.c. !! 4.0 ! 2011-02 (G. Madec) dynamical allocation !!-------------------------------------------------------------------- #if defined key_lim3 !!---------------------------------------------------------------------- !! 'key_lim3' LIM3 sea-ice model !!---------------------------------------------------------------------- !! ice_adv_prather : advection of sea ice using Prather scheme !!---------------------------------------------------------------------- USE dom_oce ! ocean domain USE ice ! sea-ice variables USE sbc_oce , ONLY : nn_fsbc ! frequency of sea-ice call ! USE lbclnk ! lateral boundary condition - MPP exchanges USE in_out_manager ! I/O manager USE prtctl ! Print control USE lib_mpp ! MPP library USE lib_fortran ! to use key_nosignedzero IMPLICIT NONE PRIVATE PUBLIC ice_adv_prather ! called by iceadv !! * Substitutions # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/ICE 4.0 , NEMO Consortium (2017) !! $Id: iceadv.F90 6746 2016-06-27 17:20:57Z clem $ !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE ice_adv_prather( kt, pu_ice, pv_ice, & & pato_i, pv_i, pv_s, psmv_i, poa_i, pa_i, pa_ip, pv_ip, pe_s, pe_i ) !!---------------------------------------------------------------------- !! ** routine ice_adv_prather ** !! !! ** purpose : Computes and adds the advection trend to sea-ice !! !! ** method : Uses Prather second order scheme that advects tracers !! but also their quadratic forms. The method preserves !! tracer structures by conserving second order moments. !! !! Reference: Prather, 1986, JGR, 91, D6. 6671-6681. !!---------------------------------------------------------------------- INTEGER , INTENT(in ) :: kt ! time step REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pu_ice ! ice i-velocity REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pv_ice ! ice j-velocity REAL(wp), DIMENSION(:,:) , INTENT(inout) :: pato_i ! open water area REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i ! ice volume REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_s ! snw volume REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: psmv_i ! salt content REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: poa_i ! age content REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_i ! ice concentration REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_ip ! melt pond fraction REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_ip ! melt pond volume REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s ! snw heat content REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_i ! ice heat content ! INTEGER :: jk, jl, jt ! dummy loop indices INTEGER :: initad ! number of sub-timestep for the advection REAL(wp) :: zcfl , zusnit ! - - REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zarea REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: z0opw REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: z0ice, z0snw, z0ai, z0es , z0smi , z0oi REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: z0ap , z0vp REAL(wp), ALLOCATABLE, DIMENSION(:,:,:,:) :: z0ei !!---------------------------------------------------------------------- ! IF( kt == nit000 .AND. lwp ) THEN WRITE(numout,*) WRITE(numout,*) 'ice_adv_prather: Prather advection scheme' WRITE(numout,*) '~~~~~~~~~~~~~~~' ENDIF ! ALLOCATE( zarea(jpi,jpj) , z0opw(jpi,jpj, 1 ) , & & z0ice(jpi,jpj,jpl) , z0snw(jpi,jpj,jpl) , z0ai(jpi,jpj,jpl) , z0es(jpi,jpj,jpl) , & & z0smi(jpi,jpj,jpl) , z0oi (jpi,jpj,jpl) , z0ap(jpi,jpj,jpl) , z0vp(jpi,jpj,jpl) , & & z0ei (jpi,jpj,nlay_i,jpl) ) ! ! --- If ice drift field is too fast, use an appropriate time step for advection (CFL test for stability) --- ! zcfl = MAXVAL( ABS( pu_ice(:,:) ) * rdt_ice * r1_e1u(:,:) ) zcfl = MAX( zcfl, MAXVAL( ABS( pv_ice(:,:) ) * rdt_ice * r1_e2v(:,:) ) ) IF( lk_mpp ) CALL mpp_max( zcfl ) IF( zcfl > 0.5 ) THEN ; initad = 2 ; zusnit = 0.5_wp ELSE ; initad = 1 ; zusnit = 1.0_wp ENDIF zarea(:,:) = e1e2t(:,:) !------------------------- ! transported fields !------------------------- z0opw(:,:,1) = pato_i(:,:) * e1e2t(:,:) ! Open water area DO jl = 1, jpl z0snw(:,:,jl) = pv_s (:,:, jl) * e1e2t(:,:) ! Snow volume z0ice(:,:,jl) = pv_i (:,:, jl) * e1e2t(:,:) ! Ice volume z0ai (:,:,jl) = pa_i (:,:, jl) * e1e2t(:,:) ! Ice area z0smi(:,:,jl) = psmv_i(:,:, jl) * e1e2t(:,:) ! Salt content z0oi (:,:,jl) = poa_i (:,:, jl) * e1e2t(:,:) ! Age content z0es (:,:,jl) = pe_s (:,:,1,jl) * e1e2t(:,:) ! Snow heat content DO jk = 1, nlay_i z0ei(:,:,jk,jl) = pe_i(:,:,jk,jl) * e1e2t(:,:) ! Ice heat content END DO IF ( nn_pnd_scheme > 0 ) THEN z0ap(:,:,jl) = pa_ip(:,:,jl) * e1e2t(:,:) ! Melt pond fraction z0vp(:,:,jl) = pv_ip(:,:,jl) * e1e2t(:,:) ! Melt pond volume ENDIF END DO ! !--------------------------------------------! IF( MOD( ( kt - 1) / nn_fsbc , 2 ) == 0 ) THEN !== odd ice time step: adv_x then adv_y ==! ! !--------------------------------------------! DO jt = 1, initad CALL adv_x( zusnit, pu_ice, 1._wp, zarea, z0opw (:,:,1), sxopw(:,:), & !--- ice open water area & sxxopw(:,:) , syopw(:,:), syyopw(:,:), sxyopw(:,:) ) CALL adv_y( zusnit, pv_ice, 0._wp, zarea, z0opw (:,:,1), sxopw(:,:), & & sxxopw(:,:) , syopw(:,:), syyopw(:,:), sxyopw(:,:) ) DO jl = 1, jpl CALL adv_x( zusnit, pu_ice, 1._wp, zarea, z0ice (:,:,jl), sxice(:,:,jl), & !--- ice volume --- & sxxice(:,:,jl), syice(:,:,jl), syyice(:,:,jl), sxyice(:,:,jl) ) CALL adv_y( zusnit, pv_ice, 0._wp, zarea, z0ice (:,:,jl), sxice(:,:,jl), & & sxxice(:,:,jl), syice(:,:,jl), syyice(:,:,jl), sxyice(:,:,jl) ) CALL adv_x( zusnit, pu_ice, 1._wp, zarea, z0snw (:,:,jl), sxsn (:,:,jl), & !--- snow volume --- & sxxsn (:,:,jl), sysn (:,:,jl), syysn (:,:,jl), sxysn (:,:,jl) ) CALL adv_y( zusnit, pv_ice, 0._wp, zarea, z0snw (:,:,jl), sxsn (:,:,jl), & & sxxsn (:,:,jl), sysn (:,:,jl), syysn (:,:,jl), sxysn (:,:,jl) ) CALL adv_x( zusnit, pu_ice, 1._wp, zarea, z0smi (:,:,jl), sxsal(:,:,jl), & !--- ice salinity --- & sxxsal(:,:,jl), sysal(:,:,jl), syysal(:,:,jl), sxysal(:,:,jl) ) CALL adv_y( zusnit, pv_ice, 0._wp, zarea, z0smi (:,:,jl), sxsal(:,:,jl), & & sxxsal(:,:,jl), sysal(:,:,jl), syysal(:,:,jl), sxysal(:,:,jl) ) CALL adv_x( zusnit, pu_ice, 1._wp, zarea, z0oi (:,:,jl), sxage(:,:,jl), & !--- ice age --- & sxxage(:,:,jl), syage(:,:,jl), syyage(:,:,jl), sxyage(:,:,jl) ) CALL adv_y( zusnit, pv_ice, 0._wp, zarea, z0oi (:,:,jl), sxage(:,:,jl), & & sxxage(:,:,jl), syage(:,:,jl), syyage(:,:,jl), sxyage(:,:,jl) ) CALL adv_x( zusnit, pu_ice, 1._wp, zarea, z0ai (:,:,jl), sxa (:,:,jl), & !--- ice concentrations --- & sxxa (:,:,jl), sya (:,:,jl), syya (:,:,jl), sxya (:,:,jl) ) CALL adv_y( zusnit, pv_ice, 0._wp, zarea, z0ai (:,:,jl), sxa (:,:,jl), & & sxxa (:,:,jl), sya (:,:,jl), syya (:,:,jl), sxya (:,:,jl) ) CALL adv_x( zusnit, pu_ice, 1._wp, zarea, z0es (:,:,jl), sxc0 (:,:,jl), & !--- snow heat contents --- & sxxc0 (:,:,jl), syc0 (:,:,jl), syyc0 (:,:,jl), sxyc0 (:,:,jl) ) CALL adv_y( zusnit, pv_ice, 0._wp, zarea, z0es (:,:,jl), sxc0 (:,:,jl), & & sxxc0 (:,:,jl), syc0 (:,:,jl), syyc0 (:,:,jl), sxyc0 (:,:,jl) ) DO jk = 1, nlay_i !--- ice heat contents --- CALL adv_x( zusnit, pu_ice, 1._wp, zarea, z0ei(:,:,jk,jl), sxe (:,:,jk,jl), & & sxxe(:,:,jk,jl), sye (:,:,jk,jl), & & syye(:,:,jk,jl), sxye(:,:,jk,jl) ) CALL adv_y( zusnit, pv_ice, 0._wp, zarea, z0ei(:,:,jk,jl), sxe (:,:,jk,jl), & & sxxe(:,:,jk,jl), sye (:,:,jk,jl), & & syye(:,:,jk,jl), sxye(:,:,jk,jl) ) END DO IF ( nn_pnd_scheme > 0 ) THEN CALL adv_x( zusnit, pu_ice, 1._wp, zarea, z0ap (:,:,jl), sxap (:,:,jl), & !--- melt pond fraction -- & sxxap (:,:,jl), syap (:,:,jl), syyap (:,:,jl), sxyap (:,:,jl) ) CALL adv_y( zusnit, pv_ice, 0._wp, zarea, z0ap (:,:,jl), sxap (:,:,jl), & & sxxap (:,:,jl), syap (:,:,jl), syyap (:,:,jl), sxyap (:,:,jl) ) CALL adv_x( zusnit, pu_ice, 1._wp, zarea, z0vp (:,:,jl), sxvp (:,:,jl), & !--- melt pond volume -- & sxxvp (:,:,jl), syvp (:,:,jl), syyvp (:,:,jl), sxyvp (:,:,jl) ) CALL adv_y( zusnit, pv_ice, 0._wp, zarea, z0vp (:,:,jl), sxvp (:,:,jl), & & sxxvp (:,:,jl), syvp (:,:,jl), syyvp (:,:,jl), sxyvp (:,:,jl) ) ENDIF END DO END DO ! !--------------------------------------------! ELSE !== even ice time step: adv_y then adv_x ==! ! !--------------------------------------------! DO jt = 1, initad CALL adv_y( zusnit, pv_ice, 1._wp, zarea, z0opw (:,:,1), sxopw(:,:), & !--- ice open water area & sxxopw(:,:) , syopw(:,:), syyopw(:,:), sxyopw(:,:) ) CALL adv_x( zusnit, pu_ice, 0._wp, zarea, z0opw (:,:,1), sxopw(:,:), & & sxxopw(:,:) , syopw(:,:), syyopw(:,:), sxyopw(:,:) ) DO jl = 1, jpl CALL adv_y( zusnit, pv_ice, 1._wp, zarea, z0ice (:,:,jl), sxice(:,:,jl), & !--- ice volume --- & sxxice(:,:,jl), syice(:,:,jl), syyice(:,:,jl), sxyice(:,:,jl) ) CALL adv_x( zusnit, pu_ice, 0._wp, zarea, z0ice (:,:,jl), sxice(:,:,jl), & & sxxice(:,:,jl), syice(:,:,jl), syyice(:,:,jl), sxyice(:,:,jl) ) CALL adv_y( zusnit, pv_ice, 1._wp, zarea, z0snw (:,:,jl), sxsn (:,:,jl), & !--- snow volume --- & sxxsn (:,:,jl), sysn (:,:,jl), syysn (:,:,jl), sxysn (:,:,jl) ) CALL adv_x( zusnit, pu_ice, 0._wp, zarea, z0snw (:,:,jl), sxsn (:,:,jl), & & sxxsn (:,:,jl), sysn (:,:,jl), syysn (:,:,jl), sxysn (:,:,jl) ) CALL adv_y( zusnit, pv_ice, 1._wp, zarea, z0smi (:,:,jl), sxsal(:,:,jl), & !--- ice salinity --- & sxxsal(:,:,jl), sysal(:,:,jl), syysal(:,:,jl), sxysal(:,:,jl) ) CALL adv_x( zusnit, pu_ice, 0._wp, zarea, z0smi (:,:,jl), sxsal(:,:,jl), & & sxxsal(:,:,jl), sysal(:,:,jl), syysal(:,:,jl), sxysal(:,:,jl) ) CALL adv_y( zusnit, pv_ice, 1._wp, zarea, z0oi (:,:,jl), sxage(:,:,jl), & !--- ice age --- & sxxage(:,:,jl), syage(:,:,jl), syyage(:,:,jl), sxyage(:,:,jl) ) CALL adv_x( zusnit, pu_ice, 0._wp, zarea, z0oi (:,:,jl), sxage(:,:,jl), & & sxxage(:,:,jl), syage(:,:,jl), syyage(:,:,jl), sxyage(:,:,jl) ) CALL adv_y( zusnit, pv_ice, 1._wp, zarea, z0ai (:,:,jl), sxa (:,:,jl), & !--- ice concentrations --- & sxxa (:,:,jl), sya (:,:,jl), syya (:,:,jl), sxya (:,:,jl) ) CALL adv_x( zusnit, pu_ice, 0._wp, zarea, z0ai (:,:,jl), sxa (:,:,jl), & & sxxa (:,:,jl), sya (:,:,jl), syya (:,:,jl), sxya (:,:,jl) ) CALL adv_y( zusnit, pv_ice, 1._wp, zarea, z0es (:,:,jl), sxc0 (:,:,jl), & !--- snow heat contents --- & sxxc0 (:,:,jl), syc0 (:,:,jl), syyc0 (:,:,jl), sxyc0 (:,:,jl) ) CALL adv_x( zusnit, pu_ice, 0._wp, zarea, z0es (:,:,jl), sxc0 (:,:,jl), & & sxxc0 (:,:,jl), syc0 (:,:,jl), syyc0 (:,:,jl), sxyc0 (:,:,jl) ) DO jk = 1, nlay_i !--- ice heat contents --- CALL adv_y( zusnit, pv_ice, 1._wp, zarea, z0ei(:,:,jk,jl), sxe (:,:,jk,jl), & & sxxe(:,:,jk,jl), sye (:,:,jk,jl), & & syye(:,:,jk,jl), sxye(:,:,jk,jl) ) CALL adv_x( zusnit, pu_ice, 0._wp, zarea, z0ei(:,:,jk,jl), sxe (:,:,jk,jl), & & sxxe(:,:,jk,jl), sye (:,:,jk,jl), & & syye(:,:,jk,jl), sxye(:,:,jk,jl) ) END DO IF ( nn_pnd_scheme > 0 ) THEN CALL adv_y( zusnit, pv_ice, 1._wp, zarea, z0ap (:,:,jl), sxap (:,:,jl), & !--- melt pond fraction --- & sxxap (:,:,jl), syap (:,:,jl), syyap (:,:,jl), sxyap (:,:,jl) ) CALL adv_x( zusnit, pu_ice, 0._wp, zarea, z0ap (:,:,jl), sxap (:,:,jl), & & sxxap (:,:,jl), syap (:,:,jl), syyap (:,:,jl), sxyap (:,:,jl) ) CALL adv_y( zusnit, pv_ice, 1._wp, zarea, z0vp (:,:,jl), sxvp (:,:,jl), & !--- melt pond volume --- & sxxvp (:,:,jl), syvp (:,:,jl), syyvp (:,:,jl), sxyvp (:,:,jl) ) CALL adv_x( zusnit, pu_ice, 0._wp, zarea, z0vp (:,:,jl), sxvp (:,:,jl), & & sxxvp (:,:,jl), syvp (:,:,jl), syyvp (:,:,jl), sxyvp (:,:,jl) ) ENDIF END DO END DO ENDIF !------------------------------------------- ! Recover the properties from their contents !------------------------------------------- pato_i(:,:) = z0opw(:,:,1) * r1_e1e2t(:,:) DO jl = 1, jpl pv_i (:,:, jl) = z0ice(:,:,jl) * r1_e1e2t(:,:) pv_s (:,:, jl) = z0snw(:,:,jl) * r1_e1e2t(:,:) psmv_i(:,:, jl) = z0smi(:,:,jl) * r1_e1e2t(:,:) poa_i (:,:, jl) = z0oi (:,:,jl) * r1_e1e2t(:,:) pa_i (:,:, jl) = z0ai (:,:,jl) * r1_e1e2t(:,:) pe_s (:,:,1,jl) = z0es (:,:,jl) * r1_e1e2t(:,:) DO jk = 1, nlay_i pe_i(:,:,jk,jl) = z0ei(:,:,jk,jl) * r1_e1e2t(:,:) END DO ! MV MP 2016 IF ( nn_pnd_scheme > 0 ) THEN pa_ip (:,:,jl) = z0ap (:,:,jl) * r1_e1e2t(:,:) pv_ip (:,:,jl) = z0vp (:,:,jl) * r1_e1e2t(:,:) ENDIF ! END MV MP 2016 END DO ! DEALLOCATE( zarea , z0opw , z0ice, z0snw , z0ai , z0es , z0smi , z0oi , z0ap , z0vp , z0ei ) ! END SUBROUTINE ice_adv_prather SUBROUTINE adv_x( pdf, put , pcrh, psm , ps0 , & & psx, psxx, psy , psyy, psxy ) !!---------------------------------------------------------------------- !! ** routine adv_x ** !! !! ** purpose : Computes and adds the advection trend to sea-ice !! variable on x axis !!---------------------------------------------------------------------- REAL(wp) , INTENT(in ) :: pdf ! reduction factor for the time step REAL(wp) , INTENT(in ) :: pcrh ! call adv_x then adv_y (=1) or the opposite (=0) REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: put ! i-direction ice velocity at U-point [m/s] REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: psm ! area REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: ps0 ! field to be advected REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: psx , psy ! 1st moments REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: psxx, psyy, psxy ! 2nd moments !! INTEGER :: ji, jj ! dummy loop indices REAL(wp) :: zs1max, zrdt, zslpmax, ztemp ! local scalars REAL(wp) :: zs1new, zalf , zalfq , zbt ! - - REAL(wp) :: zs2new, zalf1, zalf1q, zbt1 ! - - REAL(wp), DIMENSION(jpi,jpj) :: zf0 , zfx , zfy , zbet ! 2D workspace REAL(wp), DIMENSION(jpi,jpj) :: zfm , zfxx , zfyy , zfxy ! - - REAL(wp), DIMENSION(jpi,jpj) :: zalg, zalg1, zalg1q ! - - !----------------------------------------------------------------------- ! Limitation of moments. zrdt = rdt_ice * pdf ! If ice drift field is too fast, use an appropriate time step for advection. DO jj = 1, jpj DO ji = 1, jpi zslpmax = MAX( 0._wp, ps0(ji,jj) ) zs1max = 1.5 * zslpmax zs1new = MIN( zs1max, MAX( -zs1max, psx(ji,jj) ) ) zs2new = MIN( 2.0 * zslpmax - 0.3334 * ABS( zs1new ), & & MAX( ABS( zs1new ) - zslpmax, psxx(ji,jj) ) ) rswitch = ( 1.0 - MAX( 0._wp, SIGN( 1._wp, -zslpmax) ) ) * tmask(ji,jj,1) ! Case of empty boxes & Apply mask ps0 (ji,jj) = zslpmax psx (ji,jj) = zs1new * rswitch psxx(ji,jj) = zs2new * rswitch psy (ji,jj) = psy (ji,jj) * rswitch psyy(ji,jj) = psyy(ji,jj) * rswitch psxy(ji,jj) = MIN( zslpmax, MAX( -zslpmax, psxy(ji,jj) ) ) * rswitch END DO END DO ! Initialize volumes of boxes (=area if adv_x first called, =psm otherwise) psm (:,:) = MAX( pcrh * e1e2t(:,:) + ( 1.0 - pcrh ) * psm(:,:) , epsi20 ) ! Calculate fluxes and moments between boxes i<-->i+1 DO jj = 1, jpj ! Flux from i to i+1 WHEN u GT 0 DO ji = 1, jpi zbet(ji,jj) = MAX( 0._wp, SIGN( 1._wp, put(ji,jj) ) ) zalf = MAX( 0._wp, put(ji,jj) ) * zrdt * e2u(ji,jj) / psm(ji,jj) zalfq = zalf * zalf zalf1 = 1.0 - zalf zalf1q = zalf1 * zalf1 ! zfm (ji,jj) = zalf * psm (ji,jj) zf0 (ji,jj) = zalf * ( ps0 (ji,jj) + zalf1 * ( psx(ji,jj) + (zalf1 - zalf) * psxx(ji,jj) ) ) zfx (ji,jj) = zalfq * ( psx (ji,jj) + 3.0 * zalf1 * psxx(ji,jj) ) zfxx(ji,jj) = zalf * psxx(ji,jj) * zalfq zfy (ji,jj) = zalf * ( psy (ji,jj) + zalf1 * psxy(ji,jj) ) zfxy(ji,jj) = zalfq * psxy(ji,jj) zfyy(ji,jj) = zalf * psyy(ji,jj) ! Readjust moments remaining in the box. psm (ji,jj) = psm (ji,jj) - zfm(ji,jj) ps0 (ji,jj) = ps0 (ji,jj) - zf0(ji,jj) psx (ji,jj) = zalf1q * ( psx(ji,jj) - 3.0 * zalf * psxx(ji,jj) ) psxx(ji,jj) = zalf1 * zalf1q * psxx(ji,jj) psy (ji,jj) = psy (ji,jj) - zfy(ji,jj) psyy(ji,jj) = psyy(ji,jj) - zfyy(ji,jj) psxy(ji,jj) = zalf1q * psxy(ji,jj) END DO END DO DO jj = 1, jpjm1 ! Flux from i+1 to i when u LT 0. DO ji = 1, fs_jpim1 zalf = MAX( 0._wp, -put(ji,jj) ) * zrdt * e2u(ji,jj) / psm(ji+1,jj) zalg (ji,jj) = zalf zalfq = zalf * zalf zalf1 = 1.0 - zalf zalg1 (ji,jj) = zalf1 zalf1q = zalf1 * zalf1 zalg1q(ji,jj) = zalf1q ! zfm (ji,jj) = zfm (ji,jj) + zalf * psm (ji+1,jj) zf0 (ji,jj) = zf0 (ji,jj) + zalf * ( ps0 (ji+1,jj) - zalf1 * ( psx(ji+1,jj) - (zalf1 - zalf ) * psxx(ji+1,jj) ) ) zfx (ji,jj) = zfx (ji,jj) + zalfq * ( psx (ji+1,jj) - 3.0 * zalf1 * psxx(ji+1,jj) ) zfxx (ji,jj) = zfxx(ji,jj) + zalf * psxx(ji+1,jj) * zalfq zfy (ji,jj) = zfy (ji,jj) + zalf * ( psy (ji+1,jj) - zalf1 * psxy(ji+1,jj) ) zfxy (ji,jj) = zfxy(ji,jj) + zalfq * psxy(ji+1,jj) zfyy (ji,jj) = zfyy(ji,jj) + zalf * psyy(ji+1,jj) END DO END DO DO jj = 2, jpjm1 ! Readjust moments remaining in the box. DO ji = fs_2, fs_jpim1 zbt = zbet(ji-1,jj) zbt1 = 1.0 - zbet(ji-1,jj) ! psm (ji,jj) = zbt * psm(ji,jj) + zbt1 * ( psm(ji,jj) - zfm(ji-1,jj) ) ps0 (ji,jj) = zbt * ps0(ji,jj) + zbt1 * ( ps0(ji,jj) - zf0(ji-1,jj) ) psx (ji,jj) = zalg1q(ji-1,jj) * ( psx(ji,jj) + 3.0 * zalg(ji-1,jj) * psxx(ji,jj) ) psxx(ji,jj) = zalg1 (ji-1,jj) * zalg1q(ji-1,jj) * psxx(ji,jj) psy (ji,jj) = zbt * psy (ji,jj) + zbt1 * ( psy (ji,jj) - zfy (ji-1,jj) ) psyy(ji,jj) = zbt * psyy(ji,jj) + zbt1 * ( psyy(ji,jj) - zfyy(ji-1,jj) ) psxy(ji,jj) = zalg1q(ji-1,jj) * psxy(ji,jj) END DO END DO ! Put the temporary moments into appropriate neighboring boxes. DO jj = 2, jpjm1 ! Flux from i to i+1 IF u GT 0. DO ji = fs_2, fs_jpim1 zbt = zbet(ji-1,jj) zbt1 = 1.0 - zbet(ji-1,jj) psm(ji,jj) = zbt * ( psm(ji,jj) + zfm(ji-1,jj) ) + zbt1 * psm(ji,jj) zalf = zbt * zfm(ji-1,jj) / psm(ji,jj) zalf1 = 1.0 - zalf ztemp = zalf * ps0(ji,jj) - zalf1 * zf0(ji-1,jj) ! ps0 (ji,jj) = zbt * ( ps0(ji,jj) + zf0(ji-1,jj) ) + zbt1 * ps0(ji,jj) psx (ji,jj) = zbt * ( zalf * zfx(ji-1,jj) + zalf1 * psx(ji,jj) + 3.0 * ztemp ) + zbt1 * psx(ji,jj) psxx(ji,jj) = zbt * ( zalf * zalf * zfxx(ji-1,jj) + zalf1 * zalf1 * psxx(ji,jj) & & + 5.0 * ( zalf * zalf1 * ( psx (ji,jj) - zfx(ji-1,jj) ) - ( zalf1 - zalf ) * ztemp ) ) & & + zbt1 * psxx(ji,jj) psxy(ji,jj) = zbt * ( zalf * zfxy(ji-1,jj) + zalf1 * psxy(ji,jj) & & + 3.0 * (- zalf1*zfy(ji-1,jj) + zalf * psy(ji,jj) ) ) & & + zbt1 * psxy(ji,jj) psy (ji,jj) = zbt * ( psy (ji,jj) + zfy (ji-1,jj) ) + zbt1 * psy (ji,jj) psyy(ji,jj) = zbt * ( psyy(ji,jj) + zfyy(ji-1,jj) ) + zbt1 * psyy(ji,jj) END DO END DO DO jj = 2, jpjm1 ! Flux from i+1 to i IF u LT 0. DO ji = fs_2, fs_jpim1 zbt = zbet(ji,jj) zbt1 = 1.0 - zbet(ji,jj) psm(ji,jj) = zbt * psm(ji,jj) + zbt1 * ( psm(ji,jj) + zfm(ji,jj) ) zalf = zbt1 * zfm(ji,jj) / psm(ji,jj) zalf1 = 1.0 - zalf ztemp = - zalf * ps0(ji,jj) + zalf1 * zf0(ji,jj) ! ps0(ji,jj) = zbt * ps0 (ji,jj) + zbt1 * ( ps0(ji,jj) + zf0(ji,jj) ) psx(ji,jj) = zbt * psx (ji,jj) + zbt1 * ( zalf * zfx(ji,jj) + zalf1 * psx(ji,jj) + 3.0 * ztemp ) psxx(ji,jj) = zbt * psxx(ji,jj) + zbt1 * ( zalf * zalf * zfxx(ji,jj) + zalf1 * zalf1 * psxx(ji,jj) & & + 5.0 *( zalf * zalf1 * ( - psx(ji,jj) + zfx(ji,jj) ) & & + ( zalf1 - zalf ) * ztemp ) ) psxy(ji,jj) = zbt * psxy(ji,jj) + zbt1 * ( zalf * zfxy(ji,jj) + zalf1 * psxy(ji,jj) & & + 3.0 * ( zalf1 * zfy(ji,jj) - zalf * psy(ji,jj) ) ) psy(ji,jj) = zbt * psy (ji,jj) + zbt1 * ( psy (ji,jj) + zfy (ji,jj) ) psyy(ji,jj) = zbt * psyy(ji,jj) + zbt1 * ( psyy(ji,jj) + zfyy(ji,jj) ) END DO END DO !-- Lateral boundary conditions CALL lbc_lnk_multi( psm , 'T', 1., ps0 , 'T', 1. & & , psx , 'T', -1., psy , 'T', -1. & ! caution gradient ==> the sign changes & , psxx, 'T', 1., psyy, 'T', 1. & & , psxy, 'T', 1. ) IF(ln_ctl) THEN CALL prt_ctl(tab2d_1=psm , clinfo1=' adv_x: psm :', tab2d_2=ps0 , clinfo2=' ps0 : ') CALL prt_ctl(tab2d_1=psx , clinfo1=' adv_x: psx :', tab2d_2=psxx, clinfo2=' psxx : ') CALL prt_ctl(tab2d_1=psy , clinfo1=' adv_x: psy :', tab2d_2=psyy, clinfo2=' psyy : ') CALL prt_ctl(tab2d_1=psxy , clinfo1=' adv_x: psxy :') ENDIF ! END SUBROUTINE adv_x SUBROUTINE adv_y( pdf, pvt , pcrh, psm , ps0 , & & psx, psxx, psy , psyy, psxy ) !!--------------------------------------------------------------------- !! ** routine adv_y ** !! !! ** purpose : Computes and adds the advection trend to sea-ice !! variable on y axis !!--------------------------------------------------------------------- REAL(wp) , INTENT(in ) :: pdf ! reduction factor for the time step REAL(wp) , INTENT(in ) :: pcrh ! call adv_x then adv_y (=1) or the opposite (=0) REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pvt ! j-direction ice velocity at V-point [m/s] REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: psm ! area REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: ps0 ! field to be advected REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: psx , psy ! 1st moments REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: psxx, psyy, psxy ! 2nd moments !! INTEGER :: ji, jj ! dummy loop indices REAL(wp) :: zs1max, zrdt, zslpmax, ztemp ! temporary scalars REAL(wp) :: zs1new, zalf , zalfq , zbt ! - - REAL(wp) :: zs2new, zalf1, zalf1q, zbt1 ! - - REAL(wp), DIMENSION(jpi,jpj) :: zf0, zfx , zfy , zbet ! 2D workspace REAL(wp), DIMENSION(jpi,jpj) :: zfm, zfxx, zfyy, zfxy ! - - REAL(wp), DIMENSION(jpi,jpj) :: zalg, zalg1, zalg1q ! - - !--------------------------------------------------------------------- ! Limitation of moments. zrdt = rdt_ice * pdf ! If ice drift field is too fast, use an appropriate time step for advection. DO jj = 1, jpj DO ji = 1, jpi zslpmax = MAX( 0._wp, ps0(ji,jj) ) zs1max = 1.5 * zslpmax zs1new = MIN( zs1max, MAX( -zs1max, psy(ji,jj) ) ) zs2new = MIN( ( 2.0 * zslpmax - 0.3334 * ABS( zs1new ) ), & & MAX( ABS( zs1new )-zslpmax, psyy(ji,jj) ) ) rswitch = ( 1.0 - MAX( 0._wp, SIGN( 1._wp, -zslpmax) ) ) * tmask(ji,jj,1) ! Case of empty boxes & Apply mask ! ps0 (ji,jj) = zslpmax psx (ji,jj) = psx (ji,jj) * rswitch psxx(ji,jj) = psxx(ji,jj) * rswitch psy (ji,jj) = zs1new * rswitch psyy(ji,jj) = zs2new * rswitch psxy(ji,jj) = MIN( zslpmax, MAX( -zslpmax, psxy(ji,jj) ) ) * rswitch END DO END DO ! Initialize volumes of boxes (=area if adv_x first called, =psm otherwise) psm(:,:) = MAX( pcrh * e1e2t(:,:) + ( 1.0 - pcrh ) * psm(:,:) , epsi20 ) ! Calculate fluxes and moments between boxes j<-->j+1 DO jj = 1, jpj ! Flux from j to j+1 WHEN v GT 0 DO ji = 1, jpi zbet(ji,jj) = MAX( 0._wp, SIGN( 1._wp, pvt(ji,jj) ) ) zalf = MAX( 0._wp, pvt(ji,jj) ) * zrdt * e1v(ji,jj) / psm(ji,jj) zalfq = zalf * zalf zalf1 = 1.0 - zalf zalf1q = zalf1 * zalf1 ! zfm (ji,jj) = zalf * psm(ji,jj) zf0 (ji,jj) = zalf * ( ps0(ji,jj) + zalf1 * ( psy(ji,jj) + (zalf1-zalf) * psyy(ji,jj) ) ) zfy (ji,jj) = zalfq *( psy(ji,jj) + 3.0*zalf1*psyy(ji,jj) ) zfyy(ji,jj) = zalf * zalfq * psyy(ji,jj) zfx (ji,jj) = zalf * ( psx(ji,jj) + zalf1 * psxy(ji,jj) ) zfxy(ji,jj) = zalfq * psxy(ji,jj) zfxx(ji,jj) = zalf * psxx(ji,jj) ! ! Readjust moments remaining in the box. psm (ji,jj) = psm (ji,jj) - zfm(ji,jj) ps0 (ji,jj) = ps0 (ji,jj) - zf0(ji,jj) psy (ji,jj) = zalf1q * ( psy(ji,jj) -3.0 * zalf * psyy(ji,jj) ) psyy(ji,jj) = zalf1 * zalf1q * psyy(ji,jj) psx (ji,jj) = psx (ji,jj) - zfx(ji,jj) psxx(ji,jj) = psxx(ji,jj) - zfxx(ji,jj) psxy(ji,jj) = zalf1q * psxy(ji,jj) END DO END DO ! DO jj = 1, jpjm1 ! Flux from j+1 to j when v LT 0. DO ji = 1, jpi zalf = ( MAX(0._wp, -pvt(ji,jj) ) * zrdt * e1v(ji,jj) ) / psm(ji,jj+1) zalg (ji,jj) = zalf zalfq = zalf * zalf zalf1 = 1.0 - zalf zalg1 (ji,jj) = zalf1 zalf1q = zalf1 * zalf1 zalg1q(ji,jj) = zalf1q ! zfm (ji,jj) = zfm (ji,jj) + zalf * psm (ji,jj+1) zf0 (ji,jj) = zf0 (ji,jj) + zalf * ( ps0 (ji,jj+1) - zalf1 * (psy(ji,jj+1) - (zalf1 - zalf ) * psyy(ji,jj+1) ) ) zfy (ji,jj) = zfy (ji,jj) + zalfq * ( psy (ji,jj+1) - 3.0 * zalf1 * psyy(ji,jj+1) ) zfyy (ji,jj) = zfyy(ji,jj) + zalf * psyy(ji,jj+1) * zalfq zfx (ji,jj) = zfx (ji,jj) + zalf * ( psx (ji,jj+1) - zalf1 * psxy(ji,jj+1) ) zfxy (ji,jj) = zfxy(ji,jj) + zalfq * psxy(ji,jj+1) zfxx (ji,jj) = zfxx(ji,jj) + zalf * psxx(ji,jj+1) END DO END DO ! Readjust moments remaining in the box. DO jj = 2, jpj DO ji = 1, jpi zbt = zbet(ji,jj-1) zbt1 = ( 1.0 - zbet(ji,jj-1) ) ! psm (ji,jj) = zbt * psm(ji,jj) + zbt1 * ( psm(ji,jj) - zfm(ji,jj-1) ) ps0 (ji,jj) = zbt * ps0(ji,jj) + zbt1 * ( ps0(ji,jj) - zf0(ji,jj-1) ) psy (ji,jj) = zalg1q(ji,jj-1) * ( psy(ji,jj) + 3.0 * zalg(ji,jj-1) * psyy(ji,jj) ) psyy(ji,jj) = zalg1 (ji,jj-1) * zalg1q(ji,jj-1) * psyy(ji,jj) psx (ji,jj) = zbt * psx (ji,jj) + zbt1 * ( psx (ji,jj) - zfx (ji,jj-1) ) psxx(ji,jj) = zbt * psxx(ji,jj) + zbt1 * ( psxx(ji,jj) - zfxx(ji,jj-1) ) psxy(ji,jj) = zalg1q(ji,jj-1) * psxy(ji,jj) END DO END DO ! Put the temporary moments into appropriate neighboring boxes. DO jj = 2, jpjm1 ! Flux from j to j+1 IF v GT 0. DO ji = 1, jpi zbt = zbet(ji,jj-1) zbt1 = ( 1.0 - zbet(ji,jj-1) ) psm(ji,jj) = zbt * ( psm(ji,jj) + zfm(ji,jj-1) ) + zbt1 * psm(ji,jj) zalf = zbt * zfm(ji,jj-1) / psm(ji,jj) zalf1 = 1.0 - zalf ztemp = zalf * ps0(ji,jj) - zalf1 * zf0(ji,jj-1) ! ps0(ji,jj) = zbt * ( ps0(ji,jj) + zf0(ji,jj-1) ) + zbt1 * ps0(ji,jj) psy(ji,jj) = zbt * ( zalf * zfy(ji,jj-1) + zalf1 * psy(ji,jj) + 3.0 * ztemp ) & & + zbt1 * psy(ji,jj) psyy(ji,jj) = zbt * ( zalf * zalf * zfyy(ji,jj-1) + zalf1 * zalf1 * psyy(ji,jj) & & + 5.0 * ( zalf * zalf1 * ( psy(ji,jj) - zfy(ji,jj-1) ) - ( zalf1 - zalf ) * ztemp ) ) & & + zbt1 * psyy(ji,jj) psxy(ji,jj) = zbt * ( zalf * zfxy(ji,jj-1) + zalf1 * psxy(ji,jj) & & + 3.0 * (- zalf1 * zfx(ji,jj-1) + zalf * psx(ji,jj) ) ) & & + zbt1 * psxy(ji,jj) psx (ji,jj) = zbt * ( psx (ji,jj) + zfx (ji,jj-1) ) + zbt1 * psx (ji,jj) psxx(ji,jj) = zbt * ( psxx(ji,jj) + zfxx(ji,jj-1) ) + zbt1 * psxx(ji,jj) END DO END DO DO jj = 2, jpjm1 ! Flux from j+1 to j IF v LT 0. DO ji = 1, jpi zbt = zbet(ji,jj) zbt1 = ( 1.0 - zbet(ji,jj) ) psm(ji,jj) = zbt * psm(ji,jj) + zbt1 * ( psm(ji,jj) + zfm(ji,jj) ) zalf = zbt1 * zfm(ji,jj) / psm(ji,jj) zalf1 = 1.0 - zalf ztemp = - zalf * ps0 (ji,jj) + zalf1 * zf0(ji,jj) ps0 (ji,jj) = zbt * ps0 (ji,jj) + zbt1 * ( ps0(ji,jj) + zf0(ji,jj) ) psy (ji,jj) = zbt * psy (ji,jj) + zbt1 * ( zalf * zfy(ji,jj) + zalf1 * psy(ji,jj) + 3.0 * ztemp ) psyy(ji,jj) = zbt * psyy(ji,jj) + zbt1 * ( zalf * zalf * zfyy(ji,jj) + zalf1 * zalf1 * psyy(ji,jj) & & + 5.0 *( zalf *zalf1 *( -psy(ji,jj) + zfy(ji,jj) ) & & + ( zalf1 - zalf ) * ztemp ) ) psxy(ji,jj) = zbt * psxy(ji,jj) + zbt1 * ( zalf * zfxy(ji,jj) + zalf1 * psxy(ji,jj) & & + 3.0 * ( zalf1 * zfx(ji,jj) - zalf * psx(ji,jj) ) ) psx (ji,jj) = zbt * psx (ji,jj) + zbt1 * ( psx (ji,jj) + zfx (ji,jj) ) psxx(ji,jj) = zbt * psxx(ji,jj) + zbt1 * ( psxx(ji,jj) + zfxx(ji,jj) ) END DO END DO !-- Lateral boundary conditions CALL lbc_lnk_multi( psm , 'T', 1., ps0 , 'T', 1. & & , psx , 'T', -1., psy , 'T', -1. & ! caution gradient ==> the sign changes & , psxx, 'T', 1., psyy, 'T', 1. & & , psxy, 'T', 1. ) IF(ln_ctl) THEN CALL prt_ctl(tab2d_1=psm , clinfo1=' adv_y: psm :', tab2d_2=ps0 , clinfo2=' ps0 : ') CALL prt_ctl(tab2d_1=psx , clinfo1=' adv_y: psx :', tab2d_2=psxx, clinfo2=' psxx : ') CALL prt_ctl(tab2d_1=psy , clinfo1=' adv_y: psy :', tab2d_2=psyy, clinfo2=' psyy : ') CALL prt_ctl(tab2d_1=psxy , clinfo1=' adv_y: psxy :') ENDIF ! END SUBROUTINE adv_y #else !!---------------------------------------------------------------------- !! Default option Dummy module NO LIM sea-ice model !!---------------------------------------------------------------------- #endif !!====================================================================== END MODULE iceadv_prather