MODULE limitd_me !!====================================================================== !! *** MODULE limitd_me *** !! LIM-3 : Mechanical impact on ice thickness distribution !!====================================================================== !! History : LIM ! 2006-02 (M. Vancoppenolle) Original code !! 3.2 ! 2009-07 (M. Vancoppenolle, Y. Aksenov, G. Madec) bug correction in smsw & sfx_mec !! 4.0 ! 2011-02 (G. Madec) dynamical allocation !!---------------------------------------------------------------------- #if defined key_lim3 !!---------------------------------------------------------------------- !! 'key_lim3' LIM-3 sea-ice model !!---------------------------------------------------------------------- USE par_oce ! ocean parameters USE dom_oce ! ocean domain USE phycst ! physical constants (ocean directory) USE sbc_oce ! surface boundary condition: ocean fields USE thd_ice ! LIM thermodynamics USE ice ! LIM variables USE par_ice ! LIM parameters USE dom_ice ! LIM domain USE limthd_lac ! LIM USE limvar ! LIM USE limcons ! LIM USE in_out_manager ! I/O manager USE lbclnk ! lateral boundary condition - MPP exchanges USE lib_mpp ! MPP library USE wrk_nemo ! work arrays USE prtctl ! Print control ! Check budget (Rousset) USE iom ! I/O manager USE lib_fortran ! glob_sum USE limdiahsb USE timing ! Timing IMPLICIT NONE PRIVATE PUBLIC lim_itd_me ! called by ice_stp PUBLIC lim_itd_me_icestrength PUBLIC lim_itd_me_init PUBLIC lim_itd_me_zapsmall PUBLIC lim_itd_me_alloc ! called by iceini.F90 REAL(wp) :: epsi20 = 1.e-20_wp ! constant values REAL(wp) :: epsi10 = 1.e-10_wp ! constant values REAL(wp) :: epsi06 = 1.e-06_wp ! constant values !----------------------------------------------------------------------- ! Variables shared among ridging subroutines !----------------------------------------------------------------------- REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: asum ! sum of total ice and open water area REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: aksum ! ratio of area removed to area ridged REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: athorn ! participation function; fraction of ridging/ ! ! closing associated w/ category n REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: hrmin ! minimum ridge thickness REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: hrmax ! maximum ridge thickness REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: hraft ! thickness of rafted ice REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: krdg ! mean ridge thickness/thickness of ridging ice REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: aridge ! participating ice ridging REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: araft ! participating ice rafting REAL(wp), PARAMETER :: krdgmin = 1.1_wp ! min ridge thickness multiplier REAL(wp), PARAMETER :: kraft = 2.0_wp ! rafting multipliyer REAL(wp), PARAMETER :: kamax = 1.0_wp ! max of ice area authorized (clem: scheme is not stable if kamax <= 0.99) REAL(wp) :: Cp ! ! !----------------------------------------------------------------------- ! Ridging diagnostic arrays for history files !----------------------------------------------------------------------- REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: dardg1dt ! rate of fractional area loss by ridging ice (1/s) REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: dardg2dt ! rate of fractional area gain by new ridges (1/s) REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: dvirdgdt ! rate of ice volume ridged (m/s) REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: opening ! rate of opening due to divergence/shear (1/s) ! !!---------------------------------------------------------------------- !! NEMO/LIM3 3.3 , UCL - NEMO Consortium (2010) !! $Id$ !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS INTEGER FUNCTION lim_itd_me_alloc() !!---------------------------------------------------------------------! !! *** ROUTINE lim_itd_me_alloc *** !!---------------------------------------------------------------------! ALLOCATE( & !* Variables shared among ridging subroutines & asum (jpi,jpj) , athorn(jpi,jpj,0:jpl) , & & aksum(jpi,jpj) , & ! & hrmin(jpi,jpj,jpl) , hraft(jpi,jpj,jpl) , aridge(jpi,jpj,jpl) , & & hrmax(jpi,jpj,jpl) , krdg (jpi,jpj,jpl) , araft (jpi,jpj,jpl) , & ! !* Ridging diagnostic arrays for history files & dardg1dt(jpi,jpj) , dardg2dt(jpi,jpj) , & & dvirdgdt(jpi,jpj) , opening(jpi,jpj) , STAT=lim_itd_me_alloc ) ! IF( lim_itd_me_alloc /= 0 ) CALL ctl_warn( 'lim_itd_me_alloc: failed to allocate arrays' ) ! END FUNCTION lim_itd_me_alloc SUBROUTINE lim_itd_me !!---------------------------------------------------------------------! !! *** ROUTINE lim_itd_me *** !! !! ** Purpose : computes the mechanical redistribution of ice thickness !! !! ** Method : Steps : !! 1) Thickness categories boundaries, ice / o.w. concentrations !! Ridge preparation !! 2) Dynamical inputs (closing rate, divu_adv, opning) !! 3) Ridging iteration !! 4) Ridging diagnostics !! 5) Heat, salt and freshwater fluxes !! 6) Compute increments of tate variables and come back to old values !! !! References : Flato, G. M., and W. D. Hibler III, 1995, JGR, 100, 18,611-18,626. !! Hibler, W. D. III, 1980, MWR, 108, 1943-1973, 1980. !! Rothrock, D. A., 1975: JGR, 80, 4514-4519. !! Thorndike et al., 1975, JGR, 80, 4501-4513. !! Bitz et al., JGR, 2001 !! Amundrud and Melling, JGR 2005 !! Babko et al., JGR 2002 !! !! This routine is based on CICE code and authors William H. Lipscomb, !! and Elizabeth C. Hunke, LANL are gratefully acknowledged !!--------------------------------------------------------------------! INTEGER :: ji, jj, jk, jl ! dummy loop index INTEGER :: niter, nitermax = 20 ! local integer LOGICAL :: asum_error ! flag for asum .ne. 1 INTEGER :: iterate_ridging ! if true, repeat the ridging REAL(wp) :: w1, tmpfac ! local scalar CHARACTER (len = 15) :: fieldid REAL(wp), POINTER, DIMENSION(:,:) :: closing_net ! net rate at which area is removed (1/s) ! (ridging ice area - area of new ridges) / dt REAL(wp), POINTER, DIMENSION(:,:) :: divu_adv ! divu as implied by transport scheme (1/s) REAL(wp), POINTER, DIMENSION(:,:) :: opning ! rate of opening due to divergence/shear REAL(wp), POINTER, DIMENSION(:,:) :: closing_gross ! rate at which area removed, not counting area of new ridges REAL(wp), POINTER, DIMENSION(:,:) :: msnow_mlt ! mass of snow added to ocean (kg m-2) REAL(wp), POINTER, DIMENSION(:,:) :: esnow_mlt ! energy needed to melt snow in ocean (J m-2) REAL(wp), POINTER, DIMENSION(:,:) :: vt_i_init, vt_i_final ! ice volume summed over categories REAL(wp) :: zchk_v_i, zchk_smv, zchk_fs, zchk_fw, zchk_v_i_b, zchk_smv_b, zchk_fs_b, zchk_fw_b ! Check conservation (C Rousset) REAL(wp) :: zchk_vmin, zchk_amin, zchk_amax ! Check errors (C Rousset) ! mass and salt flux (clem) REAL(wp), POINTER, DIMENSION(:,:,:) :: zviold, zvsold, zsmvold ! old ice volume... !!----------------------------------------------------------------------------- IF( nn_timing == 1 ) CALL timing_start('limitd_me') CALL wrk_alloc( jpi, jpj, closing_net, divu_adv, opning, closing_gross, msnow_mlt, esnow_mlt, vt_i_init, vt_i_final ) CALL wrk_alloc( jpi, jpj, jpl, zviold, zvsold, zsmvold ) ! clem IF( numit == nstart ) CALL lim_itd_me_init ! Initialization (first time-step only) IF(ln_ctl) THEN CALL prt_ctl(tab2d_1=ato_i , clinfo1=' lim_itd_me: ato_i : ', tab2d_2=at_i , clinfo2=' at_i : ') CALL prt_ctl(tab2d_1=divu_i, clinfo1=' lim_itd_me: divu_i : ', tab2d_2=delta_i, clinfo2=' delta_i : ') ENDIF IF( ln_limdyn ) THEN ! Start ridging and rafting ! ! ------------------------------- !- check conservation (C Rousset) IF (ln_limdiahsb) THEN zchk_v_i_b = glob_sum( SUM( v_i(:,:,:), dim=3 ) * area(:,:) * tms(:,:) ) zchk_smv_b = glob_sum( SUM( smv_i(:,:,:), dim=3 ) * area(:,:) * tms(:,:) ) zchk_fw_b = glob_sum( rdm_ice(:,:) * area(:,:) * tms(:,:) ) zchk_fs_b = glob_sum( ( sfx_bri(:,:) + sfx_thd(:,:) + sfx_res(:,:) + sfx_mec(:,:) ) * area(:,:) * tms(:,:) ) ENDIF !- check conservation (C Rousset) ! ------------------------------- ! mass and salt flux init (clem) zviold(:,:,:) = v_i(:,:,:) zvsold(:,:,:) = v_s(:,:,:) zsmvold(:,:,:) = smv_i(:,:,:) !-----------------------------------------------------------------------------! ! 1) Thickness categories boundaries, ice / o.w. concentrations, init_ons !-----------------------------------------------------------------------------! Cp = 0.5 * grav * (rau0-rhoic) * rhoic / rau0 ! proport const for PE ! CALL lim_itd_me_ridgeprep ! prepare ridging ! IF( con_i) CALL lim_column_sum( jpl, v_i, vt_i_init ) ! conservation check DO jj = 1, jpj ! Initialize arrays. DO ji = 1, jpi msnow_mlt(ji,jj) = 0._wp esnow_mlt(ji,jj) = 0._wp dardg1dt (ji,jj) = 0._wp dardg2dt (ji,jj) = 0._wp dvirdgdt (ji,jj) = 0._wp opening (ji,jj) = 0._wp !-----------------------------------------------------------------------------! ! 2) Dynamical inputs (closing rate, divu_adv, opning) !-----------------------------------------------------------------------------! ! ! 2.1 closing_net !----------------- ! Compute the net rate of closing due to convergence ! and shear, based on Flato and Hibler (1995). ! ! The energy dissipation rate is equal to the net closing rate ! times the ice strength. ! ! NOTE: The NET closing rate is equal to the rate that open water ! area is removed, plus the rate at which ice area is removed by ! ridging, minus the rate at which area is added in new ridges. ! The GROSS closing rate is equal to the first two terms (open ! water closing and thin ice ridging) without the third term ! (thick, newly ridged ice). closing_net(ji,jj) = Cs * 0.5 * ( Delta_i(ji,jj) - ABS( divu_i(ji,jj) ) ) - MIN( divu_i(ji,jj), 0._wp ) ! 2.2 divu_adv !-------------- ! Compute divu_adv, the divergence rate given by the transport/ ! advection scheme, which may not be equal to divu as computed ! from the velocity field. ! ! If divu_adv < 0, make sure the closing rate is large enough ! to give asum = 1.0 after ridging. divu_adv(ji,jj) = ( kamax - asum(ji,jj) ) * r1_rdtice ! asum found in ridgeprep IF( divu_adv(ji,jj) < 0._wp ) closing_net(ji,jj) = MAX( closing_net(ji,jj), -divu_adv(ji,jj) ) ! 2.3 opning !------------ ! Compute the (non-negative) opening rate that will give asum = 1.0 after ridging. opning(ji,jj) = closing_net(ji,jj) + divu_adv(ji,jj) END DO END DO !-----------------------------------------------------------------------------! ! 3) Ridging iteration !-----------------------------------------------------------------------------! niter = 1 ! iteration counter iterate_ridging = 1 DO WHILE ( iterate_ridging > 0 .AND. niter < nitermax ) DO jj = 1, jpj DO ji = 1, jpi ! 3.2 closing_gross !-----------------------------------------------------------------------------! ! Based on the ITD of ridging and ridged ice, convert the net ! closing rate to a gross closing rate. ! NOTE: 0 < aksum <= 1 closing_gross(ji,jj) = closing_net(ji,jj) / aksum(ji,jj) ! correction to closing rate and opening if closing rate is excessive !--------------------------------------------------------------------- ! Reduce the closing rate if more than 100% of the open water ! would be removed. Reduce the opening rate proportionately. IF ( ato_i(ji,jj) .GT. epsi10 .AND. athorn(ji,jj,0) .GT. 0.0 ) THEN w1 = athorn(ji,jj,0) * closing_gross(ji,jj) * rdt_ice IF ( w1 .GT. ato_i(ji,jj)) THEN tmpfac = ato_i(ji,jj) / w1 closing_gross(ji,jj) = closing_gross(ji,jj) * tmpfac opning(ji,jj) = opning(ji,jj) * tmpfac ENDIF !w1 ENDIF !at0i and athorn END DO ! ji END DO ! jj ! correction to closing rate / opening if excessive ice removal !--------------------------------------------------------------- ! Reduce the closing rate if more than 100% of any ice category ! would be removed. Reduce the opening rate proportionately. DO jl = 1, jpl DO jj = 1, jpj DO ji = 1, jpi IF ( a_i(ji,jj,jl) > epsi10 .AND. athorn(ji,jj,jl) > 0._wp )THEN w1 = athorn(ji,jj,jl) * closing_gross(ji,jj) * rdt_ice IF ( w1 > a_i(ji,jj,jl) ) THEN tmpfac = a_i(ji,jj,jl) / w1 closing_gross(ji,jj) = closing_gross(ji,jj) * tmpfac opning (ji,jj) = opning (ji,jj) * tmpfac ENDIF ENDIF END DO !ji END DO ! jj END DO !jl ! 3.3 Redistribute area, volume, and energy. !-----------------------------------------------------------------------------! CALL lim_itd_me_ridgeshift( opning, closing_gross, msnow_mlt, esnow_mlt ) ! 3.4 Compute total area of ice plus open water after ridging. !-----------------------------------------------------------------------------! CALL lim_itd_me_asumr ! 3.5 Do we keep on iterating ??? !-----------------------------------------------------------------------------! ! Check whether asum = 1. If not (because the closing and opening ! rates were reduced above), ridge again with new rates. iterate_ridging = 0 DO jj = 1, jpj DO ji = 1, jpi IF (ABS(asum(ji,jj) - kamax ) .LT. epsi10) THEN closing_net(ji,jj) = 0._wp opning (ji,jj) = 0._wp ELSE iterate_ridging = 1 divu_adv (ji,jj) = ( kamax - asum(ji,jj) ) * r1_rdtice closing_net(ji,jj) = MAX( 0._wp, -divu_adv(ji,jj) ) opning (ji,jj) = MAX( 0._wp, divu_adv(ji,jj) ) ENDIF END DO END DO IF( lk_mpp ) CALL mpp_max( iterate_ridging ) ! Repeat if necessary. ! NOTE: If strength smoothing is turned on, the ridging must be ! iterated globally because of the boundary update in the ! smoothing. niter = niter + 1 IF( iterate_ridging == 1 ) THEN IF( niter > nitermax ) THEN WRITE(numout,*) ' ALERTE : non-converging ridging scheme ' WRITE(numout,*) ' niter, iterate_ridging ', niter, iterate_ridging ENDIF CALL lim_itd_me_ridgeprep ENDIF END DO !! on the do while over iter !-----------------------------------------------------------------------------! ! 4) Ridging diagnostics !-----------------------------------------------------------------------------! ! Convert ridging rate diagnostics to correct units. ! Update fresh water and heat fluxes due to snow melt. asum_error = .false. DO jj = 1, jpj DO ji = 1, jpi IF(ABS(asum(ji,jj) - kamax) > epsi10 ) asum_error = .true. dardg1dt(ji,jj) = dardg1dt(ji,jj) * r1_rdtice dardg2dt(ji,jj) = dardg2dt(ji,jj) * r1_rdtice dvirdgdt(ji,jj) = dvirdgdt(ji,jj) * r1_rdtice opening (ji,jj) = opening (ji,jj) * r1_rdtice !-----------------------------------------------------------------------------! ! 5) Heat, salt and freshwater fluxes !-----------------------------------------------------------------------------! fmmec(ji,jj) = fmmec(ji,jj) + msnow_mlt(ji,jj) * r1_rdtice ! fresh water source for ocean fhmec(ji,jj) = fhmec(ji,jj) + esnow_mlt(ji,jj) * r1_rdtice ! heat sink for ocean END DO END DO ! Check if there is a ridging error DO jj = 1, jpj DO ji = 1, jpi IF( ABS( asum(ji,jj) - kamax) > epsi10 ) THEN ! there is a bug WRITE(numout,*) ' ' WRITE(numout,*) ' ALERTE : Ridging error: total area = ', asum(ji,jj) WRITE(numout,*) ' limitd_me ' WRITE(numout,*) ' POINT : ', ji, jj WRITE(numout,*) ' jpl, a_i, athorn ' WRITE(numout,*) 0, ato_i(ji,jj), athorn(ji,jj,0) DO jl = 1, jpl WRITE(numout,*) jl, a_i(ji,jj,jl), athorn(ji,jj,jl) END DO ENDIF ! asum END DO !ji END DO !jj ! Conservation check IF ( con_i ) THEN CALL lim_column_sum (jpl, v_i, vt_i_final) fieldid = ' v_i : limitd_me ' CALL lim_cons_check (vt_i_init, vt_i_final, 1.0e-6, fieldid) ENDIF !-----------------------------------------------------------------------------! ! 6) Updating state variables and trend terms (done in limupdate) !-----------------------------------------------------------------------------! CALL lim_var_glo2eqv CALL lim_itd_me_zapsmall !-------------------------------- ! Update mass/salt fluxes (clem) !-------------------------------- DO jl = 1, jpl DO jj = 1, jpj DO ji = 1, jpi diag_dyn_gr(ji,jj) = diag_dyn_gr(ji,jj) + ( v_i(ji,jj,jl) - zviold(ji,jj,jl) ) * r1_rdtice rdm_ice(ji,jj) = rdm_ice(ji,jj) + ( v_i(ji,jj,jl) - zviold(ji,jj,jl) ) * rhoic rdm_snw(ji,jj) = rdm_snw(ji,jj) + ( v_s(ji,jj,jl) - zvsold(ji,jj,jl) ) * rhosn sfx_mec(ji,jj) = sfx_mec(ji,jj) - ( smv_i(ji,jj,jl) - zsmvold(ji,jj,jl) ) * rhoic * r1_rdtice END DO END DO END DO IF(ln_ctl) THEN ! Control print CALL prt_ctl_info(' ') CALL prt_ctl_info(' - Cell values : ') CALL prt_ctl_info(' ~~~~~~~~~~~~~ ') CALL prt_ctl(tab2d_1=area , clinfo1=' lim_itd_me : cell area :') CALL prt_ctl(tab2d_1=at_i , clinfo1=' lim_itd_me : at_i :') CALL prt_ctl(tab2d_1=vt_i , clinfo1=' lim_itd_me : vt_i :') CALL prt_ctl(tab2d_1=vt_s , clinfo1=' lim_itd_me : vt_s :') DO jl = 1, jpl CALL prt_ctl_info(' ') CALL prt_ctl_info(' - Category : ', ivar1=jl) CALL prt_ctl_info(' ~~~~~~~~~~') CALL prt_ctl(tab2d_1=a_i (:,:,jl) , clinfo1= ' lim_itd_me : a_i : ') CALL prt_ctl(tab2d_1=ht_i (:,:,jl) , clinfo1= ' lim_itd_me : ht_i : ') CALL prt_ctl(tab2d_1=ht_s (:,:,jl) , clinfo1= ' lim_itd_me : ht_s : ') CALL prt_ctl(tab2d_1=v_i (:,:,jl) , clinfo1= ' lim_itd_me : v_i : ') CALL prt_ctl(tab2d_1=v_s (:,:,jl) , clinfo1= ' lim_itd_me : v_s : ') CALL prt_ctl(tab2d_1=e_s (:,:,1,jl) , clinfo1= ' lim_itd_me : e_s : ') CALL prt_ctl(tab2d_1=t_su (:,:,jl) , clinfo1= ' lim_itd_me : t_su : ') CALL prt_ctl(tab2d_1=t_s (:,:,1,jl) , clinfo1= ' lim_itd_me : t_snow : ') CALL prt_ctl(tab2d_1=sm_i (:,:,jl) , clinfo1= ' lim_itd_me : sm_i : ') CALL prt_ctl(tab2d_1=smv_i (:,:,jl) , clinfo1= ' lim_itd_me : smv_i : ') DO jk = 1, nlay_i CALL prt_ctl_info(' ') CALL prt_ctl_info(' - Layer : ', ivar1=jk) CALL prt_ctl_info(' ~~~~~~~') CALL prt_ctl(tab2d_1=t_i(:,:,jk,jl) , clinfo1= ' lim_itd_me : t_i : ') CALL prt_ctl(tab2d_1=e_i(:,:,jk,jl) , clinfo1= ' lim_itd_me : e_i : ') END DO END DO ENDIF ! ------------------------------- !- check conservation (C Rousset) IF (ln_limdiahsb) THEN zchk_fs = glob_sum( ( sfx_bri(:,:) + sfx_thd(:,:) + sfx_res(:,:) + sfx_mec(:,:) ) * area(:,:) * tms(:,:) ) - zchk_fs_b zchk_fw = glob_sum( rdm_ice(:,:) * area(:,:) * tms(:,:) ) - zchk_fw_b zchk_v_i = ( glob_sum( SUM( v_i(:,:,:), dim=3 ) * area(:,:) * tms(:,:) ) - zchk_v_i_b - ( zchk_fw / rhoic ) ) * r1_rdtice zchk_smv = ( glob_sum( SUM( smv_i(:,:,:), dim=3 ) * area(:,:) * tms(:,:) ) - zchk_smv_b ) * r1_rdtice + ( zchk_fs / rhoic ) zchk_vmin = glob_min(v_i) zchk_amax = glob_max(SUM(a_i,dim=3)) zchk_amin = glob_min(a_i) IF(lwp) THEN IF ( ABS( zchk_v_i ) > 1.e-5 ) WRITE(numout,*) 'violation volume [m3/day] (limitd_me) = ',(zchk_v_i * rday) IF ( ABS( zchk_smv ) > 1.e-4 ) WRITE(numout,*) 'violation saline [psu*m3/day] (limitd_me) = ',(zchk_smv * rday) IF ( zchk_vmin < 0. ) WRITE(numout,*) 'violation v_i<0 [mm] (limitd_me) = ',(zchk_vmin * 1.e-3) IF ( zchk_amax > kamax+epsi10 ) WRITE(numout,*) 'violation a_i>amax (limitd_me) = ',zchk_amax IF ( zchk_amin < 0. ) WRITE(numout,*) 'violation a_i<0 (limitd_me) = ',zchk_amin ENDIF ENDIF !- check conservation (C Rousset) ! ------------------------------- ENDIF ! ln_limdyn=.true. ! CALL wrk_dealloc( jpi, jpj, closing_net, divu_adv, opning, closing_gross, msnow_mlt, esnow_mlt, vt_i_init, vt_i_final ) ! CALL wrk_dealloc( jpi, jpj, jpl, zviold, zvsold, zsmvold ) ! clem ! IF( nn_timing == 1 ) CALL timing_stop('limitd_me') END SUBROUTINE lim_itd_me SUBROUTINE lim_itd_me_icestrength( kstrngth ) !!---------------------------------------------------------------------- !! *** ROUTINE lim_itd_me_icestrength *** !! !! ** Purpose : computes ice strength used in dynamics routines of ice thickness !! !! ** Method : Compute the strength of the ice pack, defined as the energy (J m-2) !! dissipated per unit area removed from the ice pack under compression, !! and assumed proportional to the change in potential energy caused !! by ridging. Note that only Hibler's formulation is stable and that !! ice strength has to be smoothed !! !! ** Inputs / Ouputs : kstrngth (what kind of ice strength we are using) !!---------------------------------------------------------------------- INTEGER, INTENT(in) :: kstrngth ! = 1 for Rothrock formulation, 0 for Hibler (1979) INTEGER :: ji,jj, jl ! dummy loop indices INTEGER :: ksmooth ! smoothing the resistance to deformation INTEGER :: numts_rm ! number of time steps for the P smoothing REAL(wp) :: hi, zw1, zp, zdummy, zzc, z1_3 ! local scalars REAL(wp), POINTER, DIMENSION(:,:) :: zworka ! temporary array used here !!---------------------------------------------------------------------- CALL wrk_alloc( jpi, jpj, zworka ) !------------------------------------------------------------------------------! ! 1) Initialize !------------------------------------------------------------------------------! strength(:,:) = 0._wp !------------------------------------------------------------------------------! ! 2) Compute thickness distribution of ridging and ridged ice !------------------------------------------------------------------------------! CALL lim_itd_me_ridgeprep !------------------------------------------------------------------------------! ! 3) Rothrock(1975)'s method !------------------------------------------------------------------------------! IF( kstrngth == 1 ) THEN z1_3 = 1._wp / 3._wp DO jl = 1, jpl DO jj= 1, jpj DO ji = 1, jpi ! IF( a_i(ji,jj,jl) > epsi10 .AND. athorn(ji,jj,jl) > 0._wp ) THEN hi = v_i(ji,jj,jl) / a_i(ji,jj,jl) !---------------------------- ! PE loss from deforming ice !---------------------------- strength(ji,jj) = strength(ji,jj) - athorn(ji,jj,jl) * hi * hi !-------------------------- ! PE gain from rafting ice !-------------------------- strength(ji,jj) = strength(ji,jj) + 2._wp * araft(ji,jj,jl) * hi * hi !---------------------------- ! PE gain from ridging ice !---------------------------- strength(ji,jj) = strength(ji,jj) + aridge(ji,jj,jl)/krdg(ji,jj,jl) & * z1_3 * (hrmax(ji,jj,jl)**3 - hrmin(ji,jj,jl)**3) / ( hrmax(ji,jj,jl)-hrmin(ji,jj,jl) ) !!gm Optimization: (a**3-b**3)/(a-b) = a*a+ab+b*b ==> less costly operations even if a**3 is replaced by a*a*a... ENDIF ! aicen > epsi10 ! END DO ! ji END DO !jj END DO !jl zzc = Cf * Cp ! where Cp = (g/2)*(rhow-rhoi)*(rhoi/rhow) and Cf accounts for frictional dissipation strength(:,:) = zzc * strength(:,:) / aksum(:,:) ksmooth = 1 !------------------------------------------------------------------------------! ! 4) Hibler (1979)' method !------------------------------------------------------------------------------! ELSE ! kstrngth ne 1: Hibler (1979) form ! strength(:,:) = Pstar * vt_i(:,:) * EXP( - C_rhg * ( 1._wp - at_i(:,:) ) ) ! ksmooth = 1 ! ENDIF ! kstrngth ! !------------------------------------------------------------------------------! ! 5) Impact of brine volume !------------------------------------------------------------------------------! ! CAN BE REMOVED ! IF ( brinstren_swi == 1 ) THEN DO jj = 1, jpj DO ji = 1, jpi IF ( bv_i(ji,jj) .GT. 0.0 ) THEN zdummy = MIN ( bv_i(ji,jj), 0.10 ) * MIN( bv_i(ji,jj), 0.10 ) ELSE zdummy = 0.0 ENDIF strength(ji,jj) = strength(ji,jj) * exp(-5.88*SQRT(MAX(bv_i(ji,jj),0.0))) END DO ! j END DO ! i ENDIF ! !------------------------------------------------------------------------------! ! 6) Smoothing ice strength !------------------------------------------------------------------------------! ! !------------------- ! Spatial smoothing !------------------- IF ( ksmooth == 1 ) THEN CALL lbc_lnk( strength, 'T', 1. ) DO jj = 2, jpj - 1 DO ji = 2, jpi - 1 IF ( ( asum(ji,jj) - ato_i(ji,jj) ) .GT. epsi10) THEN ! ice is ! present zworka(ji,jj) = 4.0 * strength(ji,jj) & & + strength(ji-1,jj) * tms(ji-1,jj) & & + strength(ji+1,jj) * tms(ji+1,jj) & & + strength(ji,jj-1) * tms(ji,jj-1) & & + strength(ji,jj+1) * tms(ji,jj+1) zw1 = 4.0 + tms(ji-1,jj) + tms(ji+1,jj) + tms(ji,jj-1) + tms(ji,jj+1) zworka(ji,jj) = zworka(ji,jj) / zw1 ELSE zworka(ji,jj) = 0._wp ENDIF END DO END DO DO jj = 2, jpj - 1 DO ji = 2, jpi - 1 strength(ji,jj) = zworka(ji,jj) END DO END DO CALL lbc_lnk( strength, 'T', 1. ) ENDIF ! ksmooth !-------------------- ! Temporal smoothing !-------------------- IF ( numit == nit000 + nn_fsbc - 1 ) THEN strp1(:,:) = 0.0 strp2(:,:) = 0.0 ENDIF IF ( ksmooth == 2 ) THEN CALL lbc_lnk( strength, 'T', 1. ) DO jj = 1, jpj - 1 DO ji = 1, jpi - 1 IF ( ( asum(ji,jj) - ato_i(ji,jj) ) .GT. epsi10) THEN ! ice is present numts_rm = 1 ! number of time steps for the running mean IF ( strp1(ji,jj) .GT. 0.0 ) numts_rm = numts_rm + 1 IF ( strp2(ji,jj) .GT. 0.0 ) numts_rm = numts_rm + 1 zp = ( strength(ji,jj) + strp1(ji,jj) + strp2(ji,jj) ) / numts_rm strp2(ji,jj) = strp1(ji,jj) strp1(ji,jj) = strength(ji,jj) strength(ji,jj) = zp ENDIF END DO END DO ENDIF ! ksmooth CALL lbc_lnk( strength, 'T', 1. ) ! Boundary conditions CALL wrk_dealloc( jpi, jpj, zworka ) ! END SUBROUTINE lim_itd_me_icestrength SUBROUTINE lim_itd_me_ridgeprep !!---------------------------------------------------------------------! !! *** ROUTINE lim_itd_me_ridgeprep *** !! !! ** Purpose : preparation for ridging and strength calculations !! !! ** Method : Compute the thickness distribution of the ice and open water !! participating in ridging and of the resulting ridges. !!---------------------------------------------------------------------! INTEGER :: ji,jj, jl ! dummy loop indices INTEGER :: krdg_index ! REAL(wp) :: Gstari, astari, hi, hrmean, zdummy ! local scalar REAL(wp), POINTER, DIMENSION(:,:) :: zworka ! temporary array used here REAL(wp), POINTER, DIMENSION(:,:,:) :: Gsum ! Gsum(n) = sum of areas in categories 0 to n !------------------------------------------------------------------------------! CALL wrk_alloc( jpi,jpj, zworka ) CALL wrk_alloc( jpi,jpj,jpl+2, Gsum, kkstart = -1 ) Gstari = 1.0/Gstar astari = 1.0/astar aksum(:,:) = 0.0 athorn(:,:,:) = 0.0 aridge(:,:,:) = 0.0 araft (:,:,:) = 0.0 hrmin(:,:,:) = 0.0 hrmax(:,:,:) = 0.0 hraft(:,:,:) = 0.0 krdg (:,:,:) = 1.0 ! ! Zero out categories with very small areas CALL lim_itd_me_zapsmall !------------------------------------------------------------------------------! ! 1) Participation function !------------------------------------------------------------------------------! ! Compute total area of ice plus open water. CALL lim_itd_me_asumr ! This is in general not equal to one ! because of divergence during transport ! Compute cumulative thickness distribution function ! Compute the cumulative thickness distribution function Gsum, ! where Gsum(n) is the fractional area in categories 0 to n. ! initial value (in h = 0) equals open water area Gsum(:,:,-1) = 0._wp DO jj = 1, jpj DO ji = 1, jpi IF( ato_i(ji,jj) > epsi10 ) THEN ; Gsum(ji,jj,0) = ato_i(ji,jj) ELSE ; Gsum(ji,jj,0) = 0._wp ENDIF END DO END DO ! for each value of h, you have to add ice concentration then DO jl = 1, jpl DO jj = 1, jpj DO ji = 1, jpi IF( a_i(ji,jj,jl) .GT. epsi10 ) THEN ; Gsum(ji,jj,jl) = Gsum(ji,jj,jl-1) + a_i(ji,jj,jl) ELSE ; Gsum(ji,jj,jl) = Gsum(ji,jj,jl-1) ENDIF END DO END DO END DO ! Normalize the cumulative distribution to 1 zworka(:,:) = 1._wp / Gsum(:,:,jpl) DO jl = 0, jpl Gsum(:,:,jl) = Gsum(:,:,jl) * zworka(:,:) END DO ! 1.3 Compute participation function a(h) = b(h).g(h) (athorn) !-------------------------------------------------------------------------------------------------- ! Compute the participation function athorn; this is analogous to ! a(h) = b(h)g(h) as defined in Thorndike et al. (1975). ! area lost from category n due to ridging/closing ! athorn(n) = total area lost due to ridging/closing ! assume b(h) = (2/Gstar) * (1 - G(h)/Gstar). ! ! The expressions for athorn are found by integrating b(h)g(h) between ! the category boundaries. !----------------------------------------------------------------- krdg_index = 1 IF( krdg_index == 0 ) THEN !--- Linear formulation (Thorndike et al., 1975) DO jl = 0, ice_cat_bounds(1,2) ! only undeformed ice participates DO jj = 1, jpj DO ji = 1, jpi IF( Gsum(ji,jj,jl) < Gstar) THEN athorn(ji,jj,jl) = Gstari * (Gsum(ji,jj,jl)-Gsum(ji,jj,jl-1)) * & (2.0 - (Gsum(ji,jj,jl-1)+Gsum(ji,jj,jl))*Gstari) ELSEIF (Gsum(ji,jj,jl-1) < Gstar) THEN athorn(ji,jj,jl) = Gstari * (Gstar-Gsum(ji,jj,jl-1)) * & (2.0 - (Gsum(ji,jj,jl-1)+Gstar)*Gstari) ELSE athorn(ji,jj,jl) = 0.0 ENDIF END DO ! ji END DO ! jj END DO ! jl ELSE !--- Exponential, more stable formulation (Lipscomb et al, 2007) ! zdummy = 1._wp / ( 1._wp - EXP(-astari) ) ! precompute exponential terms using Gsum as a work array DO jl = -1, jpl Gsum(:,:,jl) = EXP( -Gsum(:,:,jl) * astari ) * zdummy END DO !jl DO jl = 0, ice_cat_bounds(1,2) athorn(:,:,jl) = Gsum(:,:,jl-1) - Gsum(:,:,jl) END DO ! ENDIF ! krdg_index IF( raftswi == 1 ) THEN ! Ridging and rafting ice participation functions ! DO jl = 1, jpl DO jj = 1, jpj DO ji = 1, jpi IF ( athorn(ji,jj,jl) .GT. 0._wp ) THEN !!gm TANH( -X ) = - TANH( X ) so can be computed only 1 time.... aridge(ji,jj,jl) = ( TANH ( Craft * ( ht_i(ji,jj,jl) - hparmeter ) ) + 1.0 ) * 0.5 * athorn(ji,jj,jl) araft (ji,jj,jl) = ( TANH ( -Craft * ( ht_i(ji,jj,jl) - hparmeter ) ) + 1.0 ) * 0.5 * athorn(ji,jj,jl) IF ( araft(ji,jj,jl) < epsi06 ) araft(ji,jj,jl) = 0._wp aridge(ji,jj,jl) = MAX( athorn(ji,jj,jl) - araft(ji,jj,jl), 0.0 ) ENDIF ! athorn END DO ! ji END DO ! jj END DO ! jl ELSE ! raftswi = 0 ! DO jl = 1, jpl aridge(:,:,jl) = athorn(:,:,jl) END DO ! ENDIF IF ( raftswi == 1 ) THEN IF( MAXVAL(aridge + araft - athorn(:,:,1:jpl)) .GT. epsi10 ) THEN DO jl = 1, jpl DO jj = 1, jpj DO ji = 1, jpi IF ( aridge(ji,jj,jl) + araft(ji,jj,jl) - athorn(ji,jj,jl) .GT. epsi10 ) THEN WRITE(numout,*) ' ALERTE 96 : wrong participation function ... ' WRITE(numout,*) ' ji, jj, jl : ', ji, jj, jl WRITE(numout,*) ' lat, lon : ', gphit(ji,jj), glamt(ji,jj) WRITE(numout,*) ' aridge : ', aridge(ji,jj,1:jpl) WRITE(numout,*) ' araft : ', araft(ji,jj,1:jpl) WRITE(numout,*) ' athorn : ', athorn(ji,jj,1:jpl) ENDIF END DO END DO END DO ENDIF ENDIF !----------------------------------------------------------------- ! 2) Transfer function !----------------------------------------------------------------- ! Compute max and min ridged ice thickness for each ridging category. ! Assume ridged ice is uniformly distributed between hrmin and hrmax. ! ! This parameterization is a modified version of Hibler (1980). ! The mean ridging thickness, hrmean, is proportional to hi^(0.5) ! and for very thick ridging ice must be >= krdgmin*hi ! ! The minimum ridging thickness, hrmin, is equal to 2*hi ! (i.e., rafting) and for very thick ridging ice is ! constrained by hrmin <= (hrmean + hi)/2. ! ! The maximum ridging thickness, hrmax, is determined by ! hrmean and hrmin. ! ! These modifications have the effect of reducing the ice strength ! (relative to the Hibler formulation) when very thick ice is ! ridging. ! ! aksum = net area removed/ total area removed ! where total area removed = area of ice that ridges ! net area removed = total area removed - area of new ridges !----------------------------------------------------------------- ! Transfer function DO jl = 1, jpl !all categories have a specific transfer function DO jj = 1, jpj DO ji = 1, jpi IF (a_i(ji,jj,jl) .GT. epsi10 .AND. athorn(ji,jj,jl) .GT. 0.0 ) THEN hi = v_i(ji,jj,jl) / a_i(ji,jj,jl) hrmean = MAX(SQRT(Hstar*hi), hi*krdgmin) hrmin(ji,jj,jl) = MIN(2.0*hi, 0.5*(hrmean + hi)) hrmax(ji,jj,jl) = 2.0*hrmean - hrmin(ji,jj,jl) hraft(ji,jj,jl) = kraft*hi krdg(ji,jj,jl) = hrmean / hi ELSE hraft(ji,jj,jl) = 0.0 hrmin(ji,jj,jl) = 0.0 hrmax(ji,jj,jl) = 0.0 krdg (ji,jj,jl) = 1.0 ENDIF END DO ! ji END DO ! jj END DO ! jl ! Normalization factor : aksum, ensures mass conservation aksum(:,:) = athorn(:,:,0) DO jl = 1, jpl aksum(:,:) = aksum(:,:) + aridge(:,:,jl) * ( 1._wp - 1._wp / krdg(:,:,jl) ) & & + araft (:,:,jl) * ( 1._wp - 1._wp / kraft ) END DO ! CALL wrk_dealloc( jpi,jpj, zworka ) CALL wrk_dealloc( jpi,jpj,jpl+2, Gsum, kkstart = -1 ) ! END SUBROUTINE lim_itd_me_ridgeprep SUBROUTINE lim_itd_me_ridgeshift( opning, closing_gross, msnow_mlt, esnow_mlt ) !!---------------------------------------------------------------------- !! *** ROUTINE lim_itd_me_icestrength *** !! !! ** Purpose : shift ridging ice among thickness categories of ice thickness !! !! ** Method : Remove area, volume, and energy from each ridging category !! and add to thicker ice categories. !!---------------------------------------------------------------------- REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: opning ! rate of opening due to divergence/shear REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: closing_gross ! rate at which area removed, excluding area of new ridges REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: msnow_mlt ! mass of snow added to ocean (kg m-2) REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: esnow_mlt ! energy needed to melt snow in ocean (J m-2) ! CHARACTER (len=80) :: fieldid ! field identifier LOGICAL, PARAMETER :: l_conservation_check = .true. ! if true, check conservation (useful for debugging) ! LOGICAL :: neg_ato_i ! flag for ato_i(i,j) < -puny LOGICAL :: large_afrac ! flag for afrac > 1 LOGICAL :: large_afrft ! flag for afrac > 1 INTEGER :: ji, jj, jl, jl1, jl2, jk ! dummy loop indices INTEGER :: ij ! horizontal index, combines i and j loops INTEGER :: icells ! number of cells with aicen > puny REAL(wp) :: zindb, zsrdg2 ! local scalar REAL(wp) :: hL, hR, farea, zdummy, zdummy0, ztmelts ! left and right limits of integration INTEGER , POINTER, DIMENSION(:) :: indxi, indxj ! compressed indices REAL(wp), POINTER, DIMENSION(:,:) :: vice_init, vice_final ! ice volume summed over categories REAL(wp), POINTER, DIMENSION(:,:) :: eice_init, eice_final ! ice energy summed over layers REAL(wp), POINTER, DIMENSION(:,:,:) :: aicen_init, vicen_init ! ice area & volume before ridging REAL(wp), POINTER, DIMENSION(:,:,:) :: vsnon_init, esnon_init ! snow volume & energy before ridging REAL(wp), POINTER, DIMENSION(:,:,:) :: smv_i_init, oa_i_init ! ice salinity & age before ridging REAL(wp), POINTER, DIMENSION(:,:,:,:) :: eicen_init ! ice energy before ridging REAL(wp), POINTER, DIMENSION(:,:) :: afrac , fvol ! fraction of category area ridged & new ridge volume going to n2 REAL(wp), POINTER, DIMENSION(:,:) :: ardg1 , ardg2 ! area of ice ridged & new ridges REAL(wp), POINTER, DIMENSION(:,:) :: vsrdg , esrdg ! snow volume & energy of ridging ice REAL(wp), POINTER, DIMENSION(:,:) :: oirdg1, oirdg2 ! areal age content of ridged & rifging ice REAL(wp), POINTER, DIMENSION(:,:) :: dhr , dhr2 ! hrmax - hrmin & hrmax^2 - hrmin^2 REAL(wp), POINTER, DIMENSION(:,:) :: vrdg1 ! volume of ice ridged REAL(wp), POINTER, DIMENSION(:,:) :: vrdg2 ! volume of new ridges REAL(wp), POINTER, DIMENSION(:,:) :: vsw ! volume of seawater trapped into ridges REAL(wp), POINTER, DIMENSION(:,:) :: srdg1 ! sal*volume of ice ridged REAL(wp), POINTER, DIMENSION(:,:) :: srdg2 ! sal*volume of new ridges REAL(wp), POINTER, DIMENSION(:,:) :: smsw ! sal*volume of water trapped into ridges REAL(wp), POINTER, DIMENSION(:,:) :: afrft ! fraction of category area rafted REAL(wp), POINTER, DIMENSION(:,:) :: arft1 , arft2 ! area of ice rafted and new rafted zone REAL(wp), POINTER, DIMENSION(:,:) :: virft , vsrft ! ice & snow volume of rafting ice REAL(wp), POINTER, DIMENSION(:,:) :: esrft , smrft ! snow energy & salinity of rafting ice REAL(wp), POINTER, DIMENSION(:,:) :: oirft1, oirft2 ! areal age content of rafted ice & rafting ice REAL(wp), POINTER, DIMENSION(:,:,:) :: eirft ! ice energy of rafting ice REAL(wp), POINTER, DIMENSION(:,:,:) :: erdg1 ! enth*volume of ice ridged REAL(wp), POINTER, DIMENSION(:,:,:) :: erdg2 ! enth*volume of new ridges REAL(wp), POINTER, DIMENSION(:,:,:) :: ersw ! enth of water trapped into ridges !!---------------------------------------------------------------------- CALL wrk_alloc( (jpi+1)*(jpj+1), indxi, indxj ) CALL wrk_alloc( jpi, jpj, vice_init, vice_final, eice_init, eice_final ) CALL wrk_alloc( jpi, jpj, afrac, fvol , ardg1, ardg2, vsrdg, esrdg, oirdg1, oirdg2, dhr, dhr2 ) CALL wrk_alloc( jpi, jpj, vrdg1, vrdg2, vsw , srdg1, srdg2, smsw ) CALL wrk_alloc( jpi, jpj, afrft, arft1, arft2, virft, vsrft, esrft, smrft, oirft1, oirft2 ) CALL wrk_alloc( jpi, jpj, jpl, aicen_init, vicen_init, vsnon_init, esnon_init, smv_i_init, oa_i_init ) CALL wrk_alloc( jpi, jpj, jkmax, eirft, erdg1, erdg2, ersw ) CALL wrk_alloc( jpi, jpj, jkmax, jpl, eicen_init ) ! Conservation check eice_init(:,:) = 0._wp IF( con_i ) THEN CALL lim_column_sum (jpl, v_i, vice_init ) CALL lim_column_sum_energy (jpl, nlay_i, e_i, eice_init ) DO ji = mi0(jiindx), mi1(jiindx) DO jj = mj0(jjindx), mj1(jjindx) WRITE(numout,*) ' vice_init : ', vice_init(ji,jj) WRITE(numout,*) ' eice_init : ', eice_init(ji,jj) END DO END DO ENDIF !------------------------------------------------------------------------------- ! 1) Compute change in open water area due to closing and opening. !------------------------------------------------------------------------------- neg_ato_i = .false. DO jj = 1, jpj DO ji = 1, jpi ato_i(ji,jj) = ato_i(ji,jj) - athorn(ji,jj,0) * closing_gross(ji,jj) * rdt_ice & & + opning(ji,jj) * rdt_ice IF( ato_i(ji,jj) < -epsi10 ) THEN neg_ato_i = .TRUE. ELSEIF( ato_i(ji,jj) < 0._wp ) THEN ! roundoff error ato_i(ji,jj) = 0._wp ENDIF END DO !jj END DO !ji ! if negative open water area alert it IF( neg_ato_i ) THEN ! there is a bug DO jj = 1, jpj DO ji = 1, jpi IF( ato_i(ji,jj) < -epsi10 ) THEN WRITE(numout,*) '' WRITE(numout,*) 'Ridging error: ato_i < 0' WRITE(numout,*) 'ato_i : ', ato_i(ji,jj) ENDIF ! ato_i < -epsi10 END DO END DO ENDIF !----------------------------------------------------------------- ! 2) Save initial state variables !----------------------------------------------------------------- DO jl = 1, jpl aicen_init(:,:,jl) = a_i(:,:,jl) vicen_init(:,:,jl) = v_i(:,:,jl) vsnon_init(:,:,jl) = v_s(:,:,jl) ! smv_i_init(:,:,jl) = smv_i(:,:,jl) oa_i_init (:,:,jl) = oa_i (:,:,jl) END DO !jl esnon_init(:,:,:) = e_s(:,:,1,:) DO jl = 1, jpl DO jk = 1, nlay_i eicen_init(:,:,jk,jl) = e_i(:,:,jk,jl) END DO END DO ! !----------------------------------------------------------------- ! 3) Pump everything from ice which is being ridged / rafted !----------------------------------------------------------------- ! Compute the area, volume, and energy of ice ridging in each ! category, along with the area of the resulting ridge. DO jl1 = 1, jpl !jl1 describes the ridging category !------------------------------------------------ ! 3.1) Identify grid cells with nonzero ridging !------------------------------------------------ icells = 0 DO jj = 1, jpj DO ji = 1, jpi IF( aicen_init(ji,jj,jl1) > epsi10 .AND. athorn(ji,jj,jl1) > 0._wp & & .AND. closing_gross(ji,jj) > 0._wp ) THEN icells = icells + 1 indxi(icells) = ji indxj(icells) = jj ENDIF ! test on a_icen_init END DO ! ji END DO ! jj large_afrac = .false. large_afrft = .false. !CDIR NODEP DO ij = 1, icells ji = indxi(ij) jj = indxj(ij) !-------------------------------------------------------------------- ! 3.2) Compute area of ridging ice (ardg1) and of new ridge (ardg2) !-------------------------------------------------------------------- ardg1(ji,jj) = aridge(ji,jj,jl1)*closing_gross(ji,jj)*rdt_ice arft1(ji,jj) = araft (ji,jj,jl1)*closing_gross(ji,jj)*rdt_ice ardg2(ji,jj) = ardg1(ji,jj) / krdg(ji,jj,jl1) arft2(ji,jj) = arft1(ji,jj) / kraft oirdg1(ji,jj)= aridge(ji,jj,jl1)*closing_gross(ji,jj)*rdt_ice oirft1(ji,jj)= araft (ji,jj,jl1)*closing_gross(ji,jj)*rdt_ice oirdg2(ji,jj)= oirdg1(ji,jj) / krdg(ji,jj,jl1) oirft2(ji,jj)= oirft1(ji,jj) / kraft !--------------------------------------------------------------- ! 3.3) Compute ridging /rafting fractions, make sure afrac <=1 !--------------------------------------------------------------- afrac(ji,jj) = ardg1(ji,jj) / aicen_init(ji,jj,jl1) !ridging afrft(ji,jj) = arft1(ji,jj) / aicen_init(ji,jj,jl1) !rafting IF (afrac(ji,jj) > kamax + epsi10) THEN !riging large_afrac = .true. ELSEIF (afrac(ji,jj) > kamax) THEN ! roundoff error afrac(ji,jj) = kamax ENDIF IF (afrft(ji,jj) > kamax + epsi10) THEN !rafting large_afrft = .true. ELSEIF (afrft(ji,jj) > kamax) THEN ! roundoff error afrft(ji,jj) = kamax ENDIF !-------------------------------------------------------------------------- ! 3.4) Subtract area, volume, and energy from ridging ! / rafting category n1. !-------------------------------------------------------------------------- vrdg1(ji,jj) = vicen_init(ji,jj,jl1) * afrac(ji,jj) / ( 1._wp + ridge_por ) vrdg2(ji,jj) = vrdg1(ji,jj) * ( 1. + ridge_por ) vsw (ji,jj) = vrdg1(ji,jj) * ridge_por vsrdg(ji,jj) = vsnon_init(ji,jj,jl1) * afrac(ji,jj) esrdg(ji,jj) = esnon_init(ji,jj,jl1) * afrac(ji,jj) srdg1(ji,jj) = smv_i_init(ji,jj,jl1) * afrac(ji,jj) / ( 1._wp + ridge_por ) srdg2(ji,jj) = smv_i_init(ji,jj,jl1) * afrac(ji,jj) ! rafting volumes, heat contents ... virft(ji,jj) = vicen_init(ji,jj,jl1) * afrft(ji,jj) vsrft(ji,jj) = vsnon_init(ji,jj,jl1) * afrft(ji,jj) esrft(ji,jj) = esnon_init(ji,jj,jl1) * afrft(ji,jj) smrft(ji,jj) = smv_i_init(ji,jj,jl1) * afrft(ji,jj) ! substract everything a_i(ji,jj,jl1) = a_i(ji,jj,jl1) - ardg1(ji,jj) - arft1(ji,jj) v_i(ji,jj,jl1) = v_i(ji,jj,jl1) - vrdg1(ji,jj) - virft(ji,jj) v_s(ji,jj,jl1) = v_s(ji,jj,jl1) - vsrdg(ji,jj) - vsrft(ji,jj) e_s(ji,jj,1,jl1) = e_s(ji,jj,1,jl1) - esrdg(ji,jj) - esrft(ji,jj) oa_i(ji,jj,jl1) = oa_i(ji,jj,jl1) - oirdg1(ji,jj) - oirft1(ji,jj) smv_i(ji,jj,jl1) = smv_i(ji,jj,jl1) - srdg1(ji,jj) - smrft(ji,jj) !----------------------------------------------------------------- ! 3.5) Compute properties of new ridges !----------------------------------------------------------------- !------------- ! Salinity !------------- smsw(ji,jj) = sss_m(ji,jj) * vsw(ji,jj) * rhoic / rau0 ! salt content of seawater frozen in voids zsrdg2 = srdg1(ji,jj) + smsw(ji,jj) ! salt content of new ridge srdg2(ji,jj) = MIN( s_i_max * vrdg2(ji,jj) , zsrdg2 ) ! impose a maximum salinity ! ! excess of salt is flushed into the ocean !sfx_mec(ji,jj) = sfx_mec(ji,jj) + ( zsrdg2 - srdg2(ji,jj) ) * rhoic * r1_rdtice !rdm_ice(ji,jj) = rdm_ice(ji,jj) + vsw(ji,jj) * rhoic ! gurvan: increase in ice volume du to seawater frozen in voids !------------------------------------ ! 3.6 Increment ridging diagnostics !------------------------------------ ! jl1 looping 1-jpl ! ij looping 1-icells dardg1dt (ji,jj) = dardg1dt(ji,jj) + ardg1(ji,jj) + arft1(ji,jj) dardg2dt (ji,jj) = dardg2dt(ji,jj) + ardg2(ji,jj) + arft2(ji,jj) opening (ji,jj) = opening (ji,jj) + opning(ji,jj) * rdt_ice IF( con_i ) vice_init(ji,jj) = vice_init(ji,jj) + vrdg2(ji,jj) - vrdg1(ji,jj) !------------------------------------------ ! 3.7 Put the snow somewhere in the ocean !------------------------------------------ ! Place part of the snow lost by ridging into the ocean. ! Note that esnow_mlt < 0; the ocean must cool to melt snow. ! If the ocean temp = Tf already, new ice must grow. ! During the next time step, thermo_rates will determine whether ! the ocean cools or new ice grows. ! jl1 looping 1-jpl ! ij looping 1-icells msnow_mlt(ji,jj) = msnow_mlt(ji,jj) + rhosn*vsrdg(ji,jj)*(1.0-fsnowrdg) & ! rafting included & + rhosn*vsrft(ji,jj)*(1.0-fsnowrft) esnow_mlt(ji,jj) = esnow_mlt(ji,jj) + esrdg(ji,jj)*(1.0-fsnowrdg) & !rafting included & + esrft(ji,jj)*(1.0-fsnowrft) !----------------------------------------------------------------- ! 3.8 Compute quantities used to apportion ice among categories ! in the n2 loop below !----------------------------------------------------------------- ! jl1 looping 1-jpl ! ij looping 1-icells dhr (ji,jj) = hrmax(ji,jj,jl1) - hrmin(ji,jj,jl1) dhr2(ji,jj) = hrmax(ji,jj,jl1) * hrmax(ji,jj,jl1) - hrmin(ji,jj,jl1) * hrmin(ji,jj,jl1) END DO ! ij !-------------------------------------------------------------------- ! 3.9 Compute ridging ice enthalpy, remove it from ridging ice and ! compute ridged ice enthalpy !-------------------------------------------------------------------- DO jk = 1, nlay_i !CDIR NODEP DO ij = 1, icells ji = indxi(ij) jj = indxj(ij) ! heat content of ridged ice erdg1(ji,jj,jk) = eicen_init(ji,jj,jk,jl1) * afrac(ji,jj) / ( 1._wp + ridge_por ) eirft(ji,jj,jk) = eicen_init(ji,jj,jk,jl1) * afrft(ji,jj) e_i (ji,jj,jk,jl1) = e_i(ji,jj,jk,jl1) - erdg1(ji,jj,jk) - eirft(ji,jj,jk) ! sea water heat content ztmelts = - tmut * sss_m(ji,jj) + rtt ! heat content per unit volume zdummy0 = - rcp * ( sst_m(ji,jj) + rt0 - rtt ) * vsw(ji,jj) ! corrected sea water salinity zindb = MAX( 0._wp , SIGN( 1._wp , vsw(ji,jj) - epsi20 ) ) zdummy = zindb * ( srdg1(ji,jj) - srdg2(ji,jj) ) / MAX( ridge_por * vsw(ji,jj), epsi20 ) ztmelts = - tmut * zdummy + rtt ersw(ji,jj,jk) = - rcp * ( ztmelts - rtt ) * vsw(ji,jj) ! heat flux fheat_mec(ji,jj) = fheat_mec(ji,jj) + ( ersw(ji,jj,jk) - zdummy0 ) * r1_rdtice ! Correct dimensions to avoid big values ersw(ji,jj,jk) = ersw(ji,jj,jk) * 1.e-09 ! Mutliply by ice volume, and divide by number of layers to get heat content in 10^9 J ersw (ji,jj,jk) = ersw(ji,jj,jk) * area(ji,jj) * vsw(ji,jj) / REAL( nlay_i ) erdg2(ji,jj,jk) = erdg1(ji,jj,jk) + ersw(ji,jj,jk) END DO ! ij END DO !jk IF( con_i ) THEN DO jk = 1, nlay_i !CDIR NODEP DO ij = 1, icells ji = indxi(ij) jj = indxj(ij) eice_init(ji,jj) = eice_init(ji,jj) + erdg2(ji,jj,jk) - erdg1(ji,jj,jk) END DO ! ij END DO !jk ENDIF IF( large_afrac ) THEN ! there is a bug !CDIR NODEP DO ij = 1, icells ji = indxi(ij) jj = indxj(ij) IF( afrac(ji,jj) > kamax + epsi10 ) THEN WRITE(numout,*) '' WRITE(numout,*) ' ardg > a_i' WRITE(numout,*) ' ardg, aicen_init : ', ardg1(ji,jj), aicen_init(ji,jj,jl1) ENDIF END DO ENDIF IF( large_afrft ) THEN ! there is a bug !CDIR NODEP DO ij = 1, icells ji = indxi(ij) jj = indxj(ij) IF( afrft(ji,jj) > kamax + epsi10 ) THEN WRITE(numout,*) '' WRITE(numout,*) ' arft > a_i' WRITE(numout,*) ' arft, aicen_init : ', arft1(ji,jj), aicen_init(ji,jj,jl1) ENDIF END DO ENDIF !------------------------------------------------------------------------------- ! 4) Add area, volume, and energy of new ridge to each category jl2 !------------------------------------------------------------------------------- ! jl1 looping 1-jpl DO jl2 = ice_cat_bounds(1,1), ice_cat_bounds(1,2) ! over categories to which ridged ice is transferred !CDIR NODEP DO ij = 1, icells ji = indxi(ij) jj = indxj(ij) ! Compute the fraction of ridged ice area and volume going to ! thickness category jl2. ! Transfer area, volume, and energy accordingly. IF( hrmin(ji,jj,jl1) >= hi_max(jl2) .OR. & hrmax(ji,jj,jl1) <= hi_max(jl2-1) ) THEN hL = 0._wp hR = 0._wp ELSE hL = MAX( hrmin(ji,jj,jl1), hi_max(jl2-1) ) hR = MIN( hrmax(ji,jj,jl1), hi_max(jl2) ) ENDIF ! fraction of ridged ice area and volume going to n2 farea = ( hR - hL ) / dhr(ji,jj) fvol(ji,jj) = ( hR*hR - hL*hL ) / dhr2(ji,jj) a_i (ji,jj ,jl2) = a_i (ji,jj ,jl2) + ardg2 (ji,jj) * farea v_i (ji,jj ,jl2) = v_i (ji,jj ,jl2) + vrdg2 (ji,jj) * fvol(ji,jj) v_s (ji,jj ,jl2) = v_s (ji,jj ,jl2) + vsrdg (ji,jj) * fvol(ji,jj) * fsnowrdg e_s (ji,jj,1,jl2) = e_s (ji,jj,1,jl2) + esrdg (ji,jj) * fvol(ji,jj) * fsnowrdg smv_i(ji,jj ,jl2) = smv_i(ji,jj ,jl2) + srdg2 (ji,jj) * fvol(ji,jj) oa_i (ji,jj ,jl2) = oa_i (ji,jj ,jl2) + oirdg2(ji,jj) * farea END DO ! ij ! Transfer ice energy to category jl2 by ridging DO jk = 1, nlay_i !CDIR NODEP DO ij = 1, icells ji = indxi(ij) jj = indxj(ij) e_i(ji,jj,jk,jl2) = e_i(ji,jj,jk,jl2) + fvol(ji,jj)*erdg2(ji,jj,jk) END DO END DO ! END DO ! jl2 (new ridges) DO jl2 = ice_cat_bounds(1,1), ice_cat_bounds(1,2) !CDIR NODEP DO ij = 1, icells ji = indxi(ij) jj = indxj(ij) ! Compute the fraction of rafted ice area and volume going to ! thickness category jl2, transfer area, volume, and energy accordingly. ! IF( hraft(ji,jj,jl1) <= hi_max(jl2) .AND. & hraft(ji,jj,jl1) > hi_max(jl2-1) ) THEN a_i (ji,jj ,jl2) = a_i (ji,jj ,jl2) + arft2 (ji,jj) v_i (ji,jj ,jl2) = v_i (ji,jj ,jl2) + virft (ji,jj) v_s (ji,jj ,jl2) = v_s (ji,jj ,jl2) + vsrft (ji,jj) * fsnowrft e_s (ji,jj,1,jl2) = e_s (ji,jj,1,jl2) + esrft (ji,jj) * fsnowrft smv_i(ji,jj ,jl2) = smv_i(ji,jj ,jl2) + smrft (ji,jj) oa_i (ji,jj ,jl2) = oa_i (ji,jj ,jl2) + oirft2(ji,jj) ENDIF ! hraft ! END DO ! ij ! Transfer rafted ice energy to category jl2 DO jk = 1, nlay_i !CDIR NODEP DO ij = 1, icells ji = indxi(ij) jj = indxj(ij) IF( hraft(ji,jj,jl1) <= hi_max(jl2) .AND. & hraft(ji,jj,jl1) > hi_max(jl2-1) ) THEN e_i(ji,jj,jk,jl2) = e_i(ji,jj,jk,jl2) + eirft(ji,jj,jk) ENDIF END DO ! ij END DO !jk END DO ! jl2 END DO ! jl1 (deforming categories) ! Conservation check IF ( con_i ) THEN CALL lim_column_sum (jpl, v_i, vice_final) fieldid = ' v_i : limitd_me ' CALL lim_cons_check (vice_init, vice_final, 1.0e-6, fieldid) CALL lim_column_sum_energy (jpl, nlay_i, e_i, eice_final ) fieldid = ' e_i : limitd_me ' CALL lim_cons_check (eice_init, eice_final, 1.0e-2, fieldid) DO ji = mi0(jiindx), mi1(jiindx) DO jj = mj0(jjindx), mj1(jjindx) WRITE(numout,*) ' vice_init : ', vice_init (ji,jj) WRITE(numout,*) ' vice_final : ', vice_final(ji,jj) WRITE(numout,*) ' eice_init : ', eice_init (ji,jj) WRITE(numout,*) ' eice_final : ', eice_final(ji,jj) END DO END DO ENDIF ! CALL wrk_dealloc( (jpi+1)*(jpj+1), indxi, indxj ) CALL wrk_dealloc( jpi, jpj, vice_init, vice_final, eice_init, eice_final ) CALL wrk_dealloc( jpi, jpj, afrac, fvol , ardg1, ardg2, vsrdg, esrdg, oirdg1, oirdg2, dhr, dhr2 ) CALL wrk_dealloc( jpi, jpj, vrdg1, vrdg2, vsw , srdg1, srdg2, smsw ) CALL wrk_dealloc( jpi, jpj, afrft, arft1, arft2, virft, vsrft, esrft, smrft, oirft1, oirft2 ) CALL wrk_dealloc( jpi, jpj, jpl, aicen_init, vicen_init, vsnon_init, esnon_init, smv_i_init, oa_i_init ) CALL wrk_dealloc( jpi, jpj, jkmax, eirft, erdg1, erdg2, ersw ) CALL wrk_dealloc( jpi, jpj, jkmax, jpl, eicen_init ) ! END SUBROUTINE lim_itd_me_ridgeshift SUBROUTINE lim_itd_me_asumr !!----------------------------------------------------------------------------- !! *** ROUTINE lim_itd_me_asumr *** !! !! ** Purpose : finds total fractional area !! !! ** Method : Find the total area of ice plus open water in each grid cell. !! This is similar to the aggregate_area subroutine except that the !! total area can be greater than 1, so the open water area is !! included in the sum instead of being computed as a residual. !!----------------------------------------------------------------------------- INTEGER :: jl ! dummy loop index !!----------------------------------------------------------------------------- ! asum(:,:) = ato_i(:,:) ! open water DO jl = 1, jpl ! ice categories asum(:,:) = asum(:,:) + a_i(:,:,jl) END DO ! END SUBROUTINE lim_itd_me_asumr SUBROUTINE lim_itd_me_init !!------------------------------------------------------------------- !! *** ROUTINE lim_itd_me_init *** !! !! ** Purpose : Physical constants and parameters linked !! to the mechanical ice redistribution !! !! ** Method : Read the namiceitdme namelist !! and check the parameters values !! called at the first timestep (nit000) !! !! ** input : Namelist namiceitdme !!------------------------------------------------------------------- NAMELIST/namiceitdme/ ridge_scheme_swi, Cs, Cf, fsnowrdg, fsnowrft,& Gstar, astar, & Hstar, raftswi, hparmeter, Craft, ridge_por, & sal_max_ridge, partfun_swi, transfun_swi, & brinstren_swi !!------------------------------------------------------------------- ! REWIND( numnam_ice ) ! read namiceitdme namelist READ ( numnam_ice , namiceitdme) ! IF (lwp) THEN ! control print WRITE(numout,*) WRITE(numout,*)' lim_itd_me_init : ice parameters for mechanical ice redistribution ' WRITE(numout,*)' ~~~~~~~~~~~~~~~' WRITE(numout,*)' Switch choosing the ice redistribution scheme ridge_scheme_swi', ridge_scheme_swi WRITE(numout,*)' Fraction of shear energy contributing to ridging Cs ', Cs WRITE(numout,*)' Ratio of ridging work to PotEner change in ridging Cf ', Cf WRITE(numout,*)' Fraction of snow volume conserved during ridging fsnowrdg ', fsnowrdg WRITE(numout,*)' Fraction of snow volume conserved during ridging fsnowrft ', fsnowrft WRITE(numout,*)' Fraction of total ice coverage contributing to ridging Gstar ', Gstar WRITE(numout,*)' Equivalent to G* for an exponential part function astar ', astar WRITE(numout,*)' Quantity playing a role in max ridged ice thickness Hstar ', Hstar WRITE(numout,*)' Rafting of ice sheets or not raftswi ', raftswi WRITE(numout,*)' Parmeter thickness (threshold between ridge-raft) hparmeter ', hparmeter WRITE(numout,*)' Rafting hyperbolic tangent coefficient Craft ', Craft WRITE(numout,*)' Initial porosity of ridges ridge_por ', ridge_por WRITE(numout,*)' Maximum salinity of ridging ice sal_max_ridge ', sal_max_ridge WRITE(numout,*)' Switch for part. function (0) linear (1) exponential partfun_swi ', partfun_swi WRITE(numout,*)' Switch for tran. function (0) linear (1) exponential transfun_swi ', transfun_swi WRITE(numout,*)' Switch for including brine volume in ice strength comp. brinstren_swi ', brinstren_swi ENDIF ! END SUBROUTINE lim_itd_me_init SUBROUTINE lim_itd_me_zapsmall !!------------------------------------------------------------------- !! *** ROUTINE lim_itd_me_zapsmall *** !! !! ** Purpose : Remove too small sea ice areas and correct salt fluxes !! !! history : !! author: William H. Lipscomb, LANL !! Nov 2003: Modified by Julie Schramm to conserve volume and energy !! Sept 2004: Modified by William Lipscomb; replaced normalize_state with !! additions to local freshwater, salt, and heat fluxes !! 9.0, LIM3.0 - 02-2006 (M. Vancoppenolle) original code !!------------------------------------------------------------------- INTEGER :: ji, jj, jl, jk ! dummy loop indices INTEGER :: icells ! number of cells with ice to zap REAL(wp), POINTER, DIMENSION(:,:) :: zmask ! 2D workspace REAL(wp) :: zmask_glo !!gm REAL(wp) :: xtmp ! temporary variable !!------------------------------------------------------------------- CALL wrk_alloc( jpi, jpj, zmask ) DO jl = 1, jpl !----------------------------------------------------------------- ! Count categories to be zapped. ! Abort model in case of negative area. !----------------------------------------------------------------- icells = 0 zmask(:,:) = 0._wp DO jj = 1, jpj DO ji = 1, jpi IF( ( a_i(ji,jj,jl) >= -epsi10 .AND. a_i(ji,jj,jl) < 0._wp ) .OR. & & ( a_i(ji,jj,jl) > 0._wp .AND. a_i(ji,jj,jl) <= epsi10 ) .OR. & & ( v_i(ji,jj,jl) == 0._wp .AND. a_i(ji,jj,jl) > 0._wp ) .OR. & & ( v_i(ji,jj,jl) > 0._wp .AND. v_i(ji,jj,jl) <= epsi10 ) ) zmask(ji,jj) = 1._wp END DO END DO !zmask_glo = glob_sum(zmask) !IF( ln_nicep .AND. lwp ) WRITE(numout,*) zmask_glo, ' cells of ice zapped in the ocean ' !----------------------------------------------------------------- ! Zap ice energy and use ocean heat to melt ice !----------------------------------------------------------------- DO jk = 1, nlay_i DO jj = 1 , jpj DO ji = 1 , jpi !!gm xtmp = e_i(ji,jj,jk,jl) / area(ji,jj) * r1_rdtice !!gm xtmp = xtmp * unit_fac ! fheat_res(ji,jj) = fheat_res(ji,jj) - xtmp e_i(ji,jj,jk,jl) = e_i(ji,jj,jk,jl) * ( 1._wp - zmask(ji,jj) ) END DO END DO END DO DO jj = 1 , jpj DO ji = 1 , jpi !----------------------------------------------------------------- ! Zap snow energy and use ocean heat to melt snow !----------------------------------------------------------------- ! xtmp = esnon(i,j,n) / dt ! < 0 ! fhnet(i,j) = fhnet(i,j) + xtmp ! fhnet_hist(i,j) = fhnet_hist(i,j) + xtmp ! xtmp is greater than 0 ! fluxes are positive to the ocean ! here the flux has to be negative for the ocean !!gm xtmp = ( rhosn*cpic*( rtt-t_s(ji,jj,1,jl) ) + rhosn*lfus ) * r1_rdtice ! fheat_res(ji,jj) = fheat_res(ji,jj) - xtmp !!gm xtmp = ( rhosn*cpic*( rtt-t_s(ji,jj,1,jl) ) + rhosn*lfus ) * r1_rdtice !RB ??????? t_s(ji,jj,1,jl) = rtt * zmask(ji,jj) + t_s(ji,jj,1,jl) * ( 1._wp - zmask(ji,jj) ) !----------------------------------------------------------------- ! zap ice and snow volume, add water and salt to ocean !----------------------------------------------------------------- ! xtmp = (rhoi*vicen(i,j,n) + rhos*vsnon(i,j,n)) / dt ! sfx_res(ji,jj) = sfx_res(ji,jj) + ( sss_m(ji,jj) ) & ! * rhosn * v_s(ji,jj,jl) * r1_rdtice ! sfx_res(ji,jj) = sfx_res(ji,jj) + ( sss_m(ji,jj) - sm_i(ji,jj,jl) ) & ! * rhoic * v_i(ji,jj,jl) * r1_rdtice ! sfx (i,j) = sfx (i,j) + xtmp ato_i(ji,jj) = a_i (ji,jj,jl) * zmask(ji,jj) + ato_i(ji,jj) a_i (ji,jj,jl) = a_i (ji,jj,jl) * ( 1._wp - zmask(ji,jj) ) v_i (ji,jj,jl) = v_i (ji,jj,jl) * ( 1._wp - zmask(ji,jj) ) v_s (ji,jj,jl) = v_s (ji,jj,jl) * ( 1._wp - zmask(ji,jj) ) t_su (ji,jj,jl) = t_su (ji,jj,jl) * ( 1._wp - zmask(ji,jj) ) + t_bo(ji,jj) * zmask(ji,jj) oa_i (ji,jj,jl) = oa_i (ji,jj,jl) * ( 1._wp - zmask(ji,jj) ) smv_i(ji,jj,jl) = smv_i(ji,jj,jl) * ( 1._wp - zmask(ji,jj) ) ! END DO END DO ! END DO ! jl ! CALL wrk_dealloc( jpi, jpj, zmask ) ! END SUBROUTINE lim_itd_me_zapsmall #else !!---------------------------------------------------------------------- !! Default option Empty module NO LIM-3 sea-ice model !!---------------------------------------------------------------------- CONTAINS SUBROUTINE lim_itd_me ! Empty routines END SUBROUTINE lim_itd_me SUBROUTINE lim_itd_me_icestrength END SUBROUTINE lim_itd_me_icestrength SUBROUTINE lim_itd_me_sort END SUBROUTINE lim_itd_me_sort SUBROUTINE lim_itd_me_init END SUBROUTINE lim_itd_me_init SUBROUTINE lim_itd_me_zapsmall END SUBROUTINE lim_itd_me_zapsmall #endif !!====================================================================== END MODULE limitd_me