MODULE icethd_do !!====================================================================== !! *** MODULE icethd_do *** !! sea-ice: sea ice growth in the leads (open water) !!====================================================================== !! History : ! 2005-12 (M. Vancoppenolle) Original code !! 4.0 ! 2018 (many people) SI3 [aka Sea Ice cube] !!---------------------------------------------------------------------- #if defined key_si3 !!---------------------------------------------------------------------- !! 'key_si3' SI3 sea-ice model !!---------------------------------------------------------------------- !! ice_thd_do : ice growth in open water (=lateral accretion of ice) !! ice_thd_do_init : initialization !!---------------------------------------------------------------------- USE dom_oce ! ocean space and time domain USE phycst ! physical constants USE sbc_oce , ONLY : sss_m USE sbc_ice , ONLY : utau_ice, vtau_ice USE ice1D ! sea-ice: thermodynamics variables USE ice ! sea-ice: variables USE icetab ! sea-ice: 2D <==> 1D USE icectl ! sea-ice: conservation USE icethd_ent ! sea-ice: thermodynamics, enthalpy USE icevar ! sea-ice: operations USE icethd_sal ! sea-ice: salinity profiles ! USE in_out_manager ! I/O manager USE lib_mpp ! MPP library USE lib_fortran ! fortran utilities (glob_sum + no signed zero) USE lbclnk ! lateral boundary conditions (or mpp links) IMPLICIT NONE PRIVATE PUBLIC ice_thd_do ! called by ice_thd PUBLIC ice_thd_do_init ! called by ice_stp ! !!** namelist (namthd_do) ** REAL(wp) :: rn_hinew ! thickness for new ice formation (m) LOGICAL :: ln_frazil ! use of frazil ice collection as function of wind (T) or not (F) REAL(wp) :: rn_maxfraz ! maximum portion of frazil ice collecting at the ice bottom REAL(wp) :: rn_vfraz ! threshold drift speed for collection of bottom frazil ice REAL(wp) :: rn_Cfraz ! squeezing coefficient for collection of bottom frazil ice !! * Substitutions # include "do_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/ICE 4.0 , NEMO Consortium (2018) !! $Id$ !! Software governed by the CeCILL license (see ./LICENSE) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE ice_thd_do !!------------------------------------------------------------------- !! *** ROUTINE ice_thd_do *** !! !! ** Purpose : Computation of the evolution of the ice thickness and !! concentration as a function of the heat balance in the leads !! !! ** Method : Ice is formed in the open water when ocean looses heat !! (heat budget of open water is negative) following !! !! (dA/dt)acc = F[ (1-A)/(1-a) ] * [ Bl / (Li*h0) ] !! where - h0 is the thickness of ice created in the lead !! - a is a minimum fraction for leads !! - F is a monotonic non-increasing function defined as: !! F(X)=( 1 - X**exld )**(1.0/exld) !! - exld is the exponent closure rate (=2 default val.) !! !! ** Action : - Adjustment of snow and ice thicknesses and heat !! content in brine pockets !! - Updating ice internal temperature !! - Computation of variation of ice volume and mass !! - Computation of a_i after lateral accretion and !! update h_s_1d, h_i_1d !!------------------------------------------------------------------------ INTEGER :: ji, jj, jk, jl ! dummy loop indices INTEGER :: iter ! - - REAL(wp) :: ztmelts, zfrazb, zweight, zde ! local scalars REAL(wp) :: zgamafr, zvfrx, zvgx, ztaux, ztwogp, zf ! - - REAL(wp) :: ztenagm, zvfry, zvgy, ztauy, zvrel2, zfp, zsqcd , zhicrit ! - - ! REAL(wp) :: zQm ! enthalpy exchanged with the ocean (J/m2, >0 towards ocean) REAL(wp) :: zEi ! sea ice specific enthalpy (J/kg) REAL(wp) :: zEw ! seawater specific enthalpy (J/kg) REAL(wp) :: zfmdt ! mass flux x time step (kg/m2, >0 towards ocean) ! REAL(wp) :: zv_newfra ! INTEGER , DIMENSION(jpij) :: jcat ! indexes of categories where new ice grows REAL(wp), DIMENSION(jpij) :: zswinew ! switch for new ice or not ! REAL(wp), DIMENSION(jpij) :: zv_newice ! volume of accreted ice REAL(wp), DIMENSION(jpij) :: za_newice ! fractional area of accreted ice REAL(wp), DIMENSION(jpij) :: zh_newice ! thickness of accreted ice REAL(wp), DIMENSION(jpij) :: ze_newice ! heat content of accreted ice REAL(wp), DIMENSION(jpij) :: zs_newice ! salinity of accreted ice REAL(wp), DIMENSION(jpij) :: zo_newice ! age of accreted ice REAL(wp), DIMENSION(jpij) :: zdv_res ! residual volume in case of excessive heat budget REAL(wp), DIMENSION(jpij) :: zda_res ! residual area in case of excessive heat budget REAL(wp), DIMENSION(jpij) :: zv_frazb ! accretion of frazil ice at the ice bottom REAL(wp), DIMENSION(jpij) :: zvrel_1d ! relative ice / frazil velocity (1D vector) ! REAL(wp), DIMENSION(jpij,jpl) :: zv_b ! old volume of ice in category jl REAL(wp), DIMENSION(jpij,jpl) :: za_b ! old area of ice in category jl ! REAL(wp), DIMENSION(jpij,nlay_i,jpl) :: ze_i_2d !: 1-D version of e_i ! REAL(wp), DIMENSION(jpi,jpj) :: zvrel ! relative ice / frazil velocity ! REAL(wp) :: zcai = 1.4e-3_wp ! ice-air drag (clem: should be dependent on coupling/forcing used) !!-----------------------------------------------------------------------! IF( ln_icediachk ) CALL ice_cons_hsm( 0, 'icethd_do', rdiag_v, rdiag_s, rdiag_t, rdiag_fv, rdiag_fs, rdiag_ft ) IF( ln_icediachk ) CALL ice_cons2D ( 0, 'icethd_do', diag_v, diag_s, diag_t, diag_fv, diag_fs, diag_ft ) at_i(:,:) = SUM( a_i, dim=3 ) !------------------------------------------------------------------------------! ! 1) Collection thickness of ice formed in leads and polynyas !------------------------------------------------------------------------------! ! ht_i_new is the thickness of new ice formed in open water ! ht_i_new can be either prescribed (ln_frazil=F) or computed (ln_frazil=T) ! Frazil ice forms in open water, is transported by wind ! accumulates at the edge of the consolidated ice edge ! where it forms aggregates of a specific thickness called ! collection thickness. zvrel(:,:) = 0._wp ! Default new ice thickness WHERE( qlead(:,:) < 0._wp .AND. tau_icebfr(:,:) == 0._wp ) ; ht_i_new(:,:) = rn_hinew ! if cooling and no landfast ELSEWHERE ; ht_i_new(:,:) = 0._wp END WHERE IF( ln_frazil ) THEN ! ht_i_new(:,:) = 0._wp ! ! Physical constants zhicrit = 0.04 ! frazil ice thickness ztwogp = 2. * rho0 / ( grav * 0.3 * ( rho0 - rhoi ) ) ! reduced grav zsqcd = 1.0 / SQRT( 1.3 * zcai ) ! 1/SQRT(airdensity*drag) zgamafr = 0.03 ! DO_2D_00_00 IF ( qlead(ji,jj) < 0._wp .AND. tau_icebfr(ji,jj) == 0._wp ) THEN ! activated if cooling and no landfast ! -- Wind stress -- ! ztaux = ( utau_ice(ji-1,jj ) * umask(ji-1,jj ,1) & & + utau_ice(ji ,jj ) * umask(ji ,jj ,1) ) * 0.5_wp ztauy = ( vtau_ice(ji ,jj-1) * vmask(ji ,jj-1,1) & & + vtau_ice(ji ,jj ) * vmask(ji ,jj ,1) ) * 0.5_wp ! Square root of wind stress ztenagm = SQRT( SQRT( ztaux * ztaux + ztauy * ztauy ) ) ! -- Frazil ice velocity -- ! rswitch = MAX( 0._wp, SIGN( 1._wp , ztenagm - epsi10 ) ) zvfrx = rswitch * zgamafr * zsqcd * ztaux / MAX( ztenagm, epsi10 ) zvfry = rswitch * zgamafr * zsqcd * ztauy / MAX( ztenagm, epsi10 ) ! -- Pack ice velocity -- ! zvgx = ( u_ice(ji-1,jj ) * umask(ji-1,jj ,1) + u_ice(ji,jj) * umask(ji,jj,1) ) * 0.5_wp zvgy = ( v_ice(ji ,jj-1) * vmask(ji ,jj-1,1) + v_ice(ji,jj) * vmask(ji,jj,1) ) * 0.5_wp ! -- Relative frazil/pack ice velocity -- ! rswitch = MAX( 0._wp, SIGN( 1._wp , at_i(ji,jj) - epsi10 ) ) zvrel2 = MAX( ( zvfrx - zvgx ) * ( zvfrx - zvgx ) & & + ( zvfry - zvgy ) * ( zvfry - zvgy ) , 0.15 * 0.15 ) * rswitch zvrel(ji,jj) = SQRT( zvrel2 ) ! -- new ice thickness (iterative loop) -- ! ht_i_new(ji,jj) = zhicrit + ( zhicrit + 0.1 ) & & / ( ( zhicrit + 0.1 ) * ( zhicrit + 0.1 ) - zhicrit * zhicrit ) * ztwogp * zvrel2 iter = 1 DO WHILE ( iter < 20 ) zf = ( ht_i_new(ji,jj) - zhicrit ) * ( ht_i_new(ji,jj) * ht_i_new(ji,jj) - zhicrit * zhicrit ) - & & ht_i_new(ji,jj) * zhicrit * ztwogp * zvrel2 zfp = ( ht_i_new(ji,jj) - zhicrit ) * ( 3.0 * ht_i_new(ji,jj) + zhicrit ) - zhicrit * ztwogp * zvrel2 ht_i_new(ji,jj) = ht_i_new(ji,jj) - zf / MAX( zfp, epsi20 ) iter = iter + 1 END DO ! ! bound ht_i_new (though I don't see why it should be necessary) ht_i_new(ji,jj) = MAX( 0.01_wp, MIN( ht_i_new(ji,jj), hi_max(jpl) ) ) ! ENDIF ! END_2D ! CALL lbc_lnk_multi( 'icethd_do', zvrel, 'T', 1., ht_i_new, 'T', 1. ) ENDIF !------------------------------------------------------------------------------! ! 2) Compute thickness, salinity, enthalpy, age, area and volume of new ice !------------------------------------------------------------------------------! ! This occurs if open water energy budget is negative (cooling) and there is no landfast ice ! Identify grid points where new ice forms npti = 0 ; nptidx(:) = 0 DO_2D_11_11 IF ( qlead(ji,jj) < 0._wp .AND. tau_icebfr(ji,jj) == 0._wp ) THEN npti = npti + 1 nptidx( npti ) = (jj - 1) * jpi + ji ENDIF END_2D ! Move from 2-D to 1-D vectors IF ( npti > 0 ) THEN CALL tab_2d_1d( npti, nptidx(1:npti), at_i_1d(1:npti) , at_i ) CALL tab_3d_2d( npti, nptidx(1:npti), a_i_2d (1:npti,1:jpl), a_i (:,:,:) ) CALL tab_3d_2d( npti, nptidx(1:npti), v_i_2d (1:npti,1:jpl), v_i (:,:,:) ) CALL tab_3d_2d( npti, nptidx(1:npti), sv_i_2d(1:npti,1:jpl), sv_i(:,:,:) ) DO jl = 1, jpl DO jk = 1, nlay_i CALL tab_2d_1d( npti, nptidx(1:npti), ze_i_2d(1:npti,jk,jl), e_i(:,:,jk,jl) ) END DO END DO CALL tab_2d_1d( npti, nptidx(1:npti), qlead_1d (1:npti) , qlead ) CALL tab_2d_1d( npti, nptidx(1:npti), t_bo_1d (1:npti) , t_bo ) CALL tab_2d_1d( npti, nptidx(1:npti), sfx_opw_1d(1:npti) , sfx_opw ) CALL tab_2d_1d( npti, nptidx(1:npti), wfx_opw_1d(1:npti) , wfx_opw ) CALL tab_2d_1d( npti, nptidx(1:npti), zh_newice (1:npti) , ht_i_new ) CALL tab_2d_1d( npti, nptidx(1:npti), zvrel_1d (1:npti) , zvrel ) CALL tab_2d_1d( npti, nptidx(1:npti), hfx_thd_1d(1:npti) , hfx_thd ) CALL tab_2d_1d( npti, nptidx(1:npti), hfx_opw_1d(1:npti) , hfx_opw ) CALL tab_2d_1d( npti, nptidx(1:npti), rn_amax_1d(1:npti) , rn_amax_2d ) CALL tab_2d_1d( npti, nptidx(1:npti), sss_1d (1:npti) , sss_m ) ! Convert units for ice internal energy DO jl = 1, jpl DO jk = 1, nlay_i WHERE( v_i_2d(1:npti,jl) > 0._wp ) ze_i_2d(1:npti,jk,jl) = ze_i_2d(1:npti,jk,jl) / v_i_2d(1:npti,jl) * REAL( nlay_i ) ELSEWHERE ze_i_2d(1:npti,jk,jl) = 0._wp END WHERE END DO END DO ! Keep old ice areas and volume in memory zv_b(1:npti,:) = v_i_2d(1:npti,:) za_b(1:npti,:) = a_i_2d(1:npti,:) ! --- Salinity of new ice --- ! SELECT CASE ( nn_icesal ) CASE ( 1 ) ! Sice = constant zs_newice(1:npti) = rn_icesal CASE ( 2 ) ! Sice = F(z,t) [Vancoppenolle et al (2005)] DO ji = 1, npti zs_newice(ji) = MIN( 4.606 + 0.91 / zh_newice(ji) , rn_simax , 0.5 * sss_1d(ji) ) END DO CASE ( 3 ) ! Sice = F(z) [multiyear ice] zs_newice(1:npti) = 2.3 END SELECT ! --- Heat content of new ice --- ! ! We assume that new ice is formed at the seawater freezing point DO ji = 1, npti ztmelts = - rTmlt * zs_newice(ji) ! Melting point (C) ze_newice(ji) = rhoi * ( rcpi * ( ztmelts - ( t_bo_1d(ji) - rt0 ) ) & & + rLfus * ( 1.0 - ztmelts / MIN( t_bo_1d(ji) - rt0, -epsi10 ) ) & & - rcp * ztmelts ) END DO ! --- Age of new ice --- ! zo_newice(1:npti) = 0._wp ! --- Volume of new ice --- ! DO ji = 1, npti zEi = - ze_newice(ji) * r1_rhoi ! specific enthalpy of forming ice [J/kg] zEw = rcp * ( t_bo_1d(ji) - rt0 ) ! specific enthalpy of seawater at t_bo_1d [J/kg] ! clem: we suppose we are already at the freezing point (condition qlead<0 is satisfyied) zdE = zEi - zEw ! specific enthalpy difference [J/kg] zfmdt = - qlead_1d(ji) / zdE ! Fm.dt [kg/m2] (<0) ! clem: we use qlead instead of zqld (icethd) because we suppose we are at the freezing point zv_newice(ji) = - zfmdt * r1_rhoi zQm = zfmdt * zEw ! heat to the ocean >0 associated with mass flux ! Contribution to heat flux to the ocean [W.m-2], >0 hfx_thd_1d(ji) = hfx_thd_1d(ji) + zfmdt * zEw * r1_Dt_ice ! Total heat flux used in this process [W.m-2] hfx_opw_1d(ji) = hfx_opw_1d(ji) - zfmdt * zdE * r1_Dt_ice ! mass flux wfx_opw_1d(ji) = wfx_opw_1d(ji) - zv_newice(ji) * rhoi * r1_Dt_ice ! salt flux sfx_opw_1d(ji) = sfx_opw_1d(ji) - zv_newice(ji) * rhoi * zs_newice(ji) * r1_Dt_ice END DO zv_frazb(1:npti) = 0._wp IF( ln_frazil ) THEN ! A fraction zfrazb of frazil ice is accreted at the ice bottom DO ji = 1, npti rswitch = 1._wp - MAX( 0._wp, SIGN( 1._wp , - at_i_1d(ji) ) ) zfrazb = rswitch * ( TANH( rn_Cfraz * ( zvrel_1d(ji) - rn_vfraz ) ) + 1.0 ) * 0.5 * rn_maxfraz zv_frazb(ji) = zfrazb * zv_newice(ji) zv_newice(ji) = ( 1.0 - zfrazb ) * zv_newice(ji) END DO END IF ! --- Area of new ice --- ! DO ji = 1, npti za_newice(ji) = zv_newice(ji) / zh_newice(ji) END DO !------------------------------------------------------------------------------! ! 3) Redistribute new ice area and volume into ice categories ! !------------------------------------------------------------------------------! ! --- lateral ice growth --- ! ! If lateral ice growth gives an ice concentration > amax, then ! we keep the excessive volume in memory and attribute it later to bottom accretion DO ji = 1, npti IF ( za_newice(ji) > MAX( 0._wp, rn_amax_1d(ji) - at_i_1d(ji) ) ) THEN ! max is for roundoff error zda_res(ji) = za_newice(ji) - MAX( 0._wp, rn_amax_1d(ji) - at_i_1d(ji) ) zdv_res(ji) = zda_res (ji) * zh_newice(ji) za_newice(ji) = MAX( 0._wp, za_newice(ji) - zda_res (ji) ) zv_newice(ji) = MAX( 0._wp, zv_newice(ji) - zdv_res (ji) ) ELSE zda_res(ji) = 0._wp zdv_res(ji) = 0._wp ENDIF END DO ! find which category to fill DO jl = 1, jpl DO ji = 1, npti IF( zh_newice(ji) > hi_max(jl-1) .AND. zh_newice(ji) <= hi_max(jl) ) THEN a_i_2d(ji,jl) = a_i_2d(ji,jl) + za_newice(ji) v_i_2d(ji,jl) = v_i_2d(ji,jl) + zv_newice(ji) jcat(ji) = jl ENDIF END DO END DO at_i_1d(1:npti) = SUM( a_i_2d(1:npti,:), dim=2 ) ! Heat content DO ji = 1, npti jl = jcat(ji) ! categroy in which new ice is put zswinew (ji) = MAX( 0._wp , SIGN( 1._wp , - za_b(ji,jl) ) ) ! 0 if old ice END DO DO jk = 1, nlay_i DO ji = 1, npti jl = jcat(ji) rswitch = MAX( 0._wp, SIGN( 1._wp , v_i_2d(ji,jl) - epsi20 ) ) ze_i_2d(ji,jk,jl) = zswinew(ji) * ze_newice(ji) + & & ( 1.0 - zswinew(ji) ) * ( ze_newice(ji) * zv_newice(ji) + ze_i_2d(ji,jk,jl) * zv_b(ji,jl) ) & & * rswitch / MAX( v_i_2d(ji,jl), epsi20 ) END DO END DO ! --- bottom ice growth + ice enthalpy remapping --- ! DO jl = 1, jpl ! for remapping h_i_old (1:npti,0:nlay_i+1) = 0._wp eh_i_old(1:npti,0:nlay_i+1) = 0._wp DO jk = 1, nlay_i DO ji = 1, npti h_i_old (ji,jk) = v_i_2d(ji,jl) * r1_nlay_i eh_i_old(ji,jk) = ze_i_2d(ji,jk,jl) * h_i_old(ji,jk) END DO END DO ! new volumes including lateral/bottom accretion + residual DO ji = 1, npti rswitch = MAX( 0._wp, SIGN( 1._wp , at_i_1d(ji) - epsi20 ) ) zv_newfra = rswitch * ( zdv_res(ji) + zv_frazb(ji) ) * a_i_2d(ji,jl) / MAX( at_i_1d(ji) , epsi20 ) a_i_2d(ji,jl) = rswitch * a_i_2d(ji,jl) v_i_2d(ji,jl) = v_i_2d(ji,jl) + zv_newfra ! for remapping h_i_old (ji,nlay_i+1) = zv_newfra eh_i_old(ji,nlay_i+1) = ze_newice(ji) * zv_newfra END DO ! --- Ice enthalpy remapping --- ! CALL ice_thd_ent( ze_i_2d(1:npti,:,jl) ) END DO ! --- Update salinity --- ! DO jl = 1, jpl DO ji = 1, npti sv_i_2d(ji,jl) = sv_i_2d(ji,jl) + zs_newice(ji) * ( v_i_2d(ji,jl) - zv_b(ji,jl) ) END DO END DO ! Change units for e_i DO jl = 1, jpl DO jk = 1, nlay_i ze_i_2d(1:npti,jk,jl) = ze_i_2d(1:npti,jk,jl) * v_i_2d(1:npti,jl) * r1_nlay_i END DO END DO ! Move 2D vectors to 1D vectors CALL tab_2d_3d( npti, nptidx(1:npti), a_i_2d (1:npti,1:jpl), a_i (:,:,:) ) CALL tab_2d_3d( npti, nptidx(1:npti), v_i_2d (1:npti,1:jpl), v_i (:,:,:) ) CALL tab_2d_3d( npti, nptidx(1:npti), sv_i_2d(1:npti,1:jpl), sv_i(:,:,:) ) DO jl = 1, jpl DO jk = 1, nlay_i CALL tab_1d_2d( npti, nptidx(1:npti), ze_i_2d(1:npti,jk,jl), e_i(:,:,jk,jl) ) END DO END DO CALL tab_1d_2d( npti, nptidx(1:npti), sfx_opw_1d(1:npti), sfx_opw ) CALL tab_1d_2d( npti, nptidx(1:npti), wfx_opw_1d(1:npti), wfx_opw ) CALL tab_1d_2d( npti, nptidx(1:npti), hfx_thd_1d(1:npti), hfx_thd ) CALL tab_1d_2d( npti, nptidx(1:npti), hfx_opw_1d(1:npti), hfx_opw ) ! ENDIF ! npti > 0 ! IF( ln_icediachk ) CALL ice_cons_hsm(1, 'icethd_do', rdiag_v, rdiag_s, rdiag_t, rdiag_fv, rdiag_fs, rdiag_ft) IF( ln_icediachk ) CALL ice_cons2D (1, 'icethd_do', diag_v, diag_s, diag_t, diag_fv, diag_fs, diag_ft) ! END SUBROUTINE ice_thd_do SUBROUTINE ice_thd_do_init !!----------------------------------------------------------------------- !! *** ROUTINE ice_thd_do_init *** !! !! ** Purpose : Physical constants and parameters associated with !! ice growth in the leads !! !! ** Method : Read the namthd_do namelist and check the parameters !! called at the first timestep (nit000) !! !! ** input : Namelist namthd_do !!------------------------------------------------------------------- INTEGER :: ios ! Local integer !! NAMELIST/namthd_do/ rn_hinew, ln_frazil, rn_maxfraz, rn_vfraz, rn_Cfraz !!------------------------------------------------------------------- ! READ ( numnam_ice_ref, namthd_do, IOSTAT = ios, ERR = 901) 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namthd_do in reference namelist' ) READ ( numnam_ice_cfg, namthd_do, IOSTAT = ios, ERR = 902 ) 902 IF( ios > 0 ) CALL ctl_nam ( ios , 'namthd_do in configuration namelist' ) IF(lwm) WRITE( numoni, namthd_do ) ! IF(lwp) THEN ! control print WRITE(numout,*) WRITE(numout,*) 'ice_thd_do_init: Ice growth in open water' WRITE(numout,*) '~~~~~~~~~~~~~~~' WRITE(numout,*) ' Namelist namthd_do:' WRITE(numout,*) ' ice thickness for lateral accretion rn_hinew = ', rn_hinew WRITE(numout,*) ' Frazil ice thickness as a function of wind or not ln_frazil = ', ln_frazil WRITE(numout,*) ' Maximum proportion of frazil ice collecting at bottom rn_maxfraz = ', rn_maxfraz WRITE(numout,*) ' Threshold relative drift speed for collection of frazil rn_vfraz = ', rn_vfraz WRITE(numout,*) ' Squeezing coefficient for collection of frazil rn_Cfraz = ', rn_Cfraz ENDIF ! IF ( rn_hinew < rn_himin ) CALL ctl_stop( 'ice_thd_do_init : rn_hinew should be >= rn_himin' ) ! END SUBROUTINE ice_thd_do_init #else !!---------------------------------------------------------------------- !! Default option NO SI3 sea-ice model !!---------------------------------------------------------------------- #endif !!====================================================================== END MODULE icethd_do