MODULE limthd_lac !!====================================================================== !! *** MODULE limthd_lac *** !! lateral thermodynamic growth of the ice !!====================================================================== !! History : LIM ! 2005-12 (M. Vancoppenolle) Original code !! - ! 2006-01 (M. Vancoppenolle) add ITD !! 3.0 ! 2007-07 (M. Vancoppenolle) Mass and energy conservation tested !! 4.0 ! 2011-02 (G. Madec) dynamical allocation !!---------------------------------------------------------------------- #if defined key_lim3 !!---------------------------------------------------------------------- !! 'key_lim3' LIM3 sea-ice model !!---------------------------------------------------------------------- !! lim_lat_acr : lateral accretion of ice !!---------------------------------------------------------------------- USE par_oce ! ocean parameters USE dom_oce ! domain variables USE phycst ! physical constants USE sbc_oce ! Surface boundary condition: ocean fields USE sbc_ice ! Surface boundary condition: ice fields USE thd_ice ! LIM thermodynamics USE dom_ice ! LIM domain USE ice ! LIM variables USE limtab ! LIM 2D <==> 1D USE limcons ! LIM conservation USE in_out_manager ! I/O manager USE lib_mpp ! MPP library USE wrk_nemo ! work arrays USE lbclnk ! ocean lateral boundary conditions (or mpp link) USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) USE limthd_ent USE limvar IMPLICIT NONE PRIVATE PUBLIC lim_thd_lac ! called by lim_thd !!---------------------------------------------------------------------- !! NEMO/LIM3 4.0 , UCL - NEMO Consortium (2011) !! $Id$ !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE lim_thd_lac !!------------------------------------------------------------------- !! *** ROUTINE lim_thd_lac *** !! !! ** Purpose : Computation of the evolution of the ice thickness and !! concentration as a function of the heat balance in the leads. !! It is only used for lateral accretion !! !! ** Method : Ice is formed in the open water when ocean lose heat !! (heat budget of open water Bl is negative) . !! Computation of the increase of 1-A (ice concentration) fol- !! lowing the law : !! (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 frldb after lateral accretion and !! update ht_s_1d, ht_i_1d and tbif_1d(:,:) !!------------------------------------------------------------------------ INTEGER :: ji,jj,jk,jl ! dummy loop indices INTEGER :: nbpac ! local integers INTEGER :: ii, ij, iter ! - - REAL(wp) :: ztmelts, zdv, zfrazb, zweight, zde ! local scalars REAL(wp) :: zgamafr, zvfrx, zvgx, ztaux, ztwogp, zf ! - - REAL(wp) :: ztenagm, zvfry, zvgy, ztauy, zvrel2, zfp, zsqcd , zhicrit ! - - CHARACTER (len = 15) :: fieldid 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 , POINTER, DIMENSION(:) :: jcat ! indexes of categories where new ice grows REAL(wp), POINTER, DIMENSION(:) :: zswinew ! switch for new ice or not REAL(wp), POINTER, DIMENSION(:) :: zv_newice ! volume of accreted ice REAL(wp), POINTER, DIMENSION(:) :: za_newice ! fractional area of accreted ice REAL(wp), POINTER, DIMENSION(:) :: zh_newice ! thickness of accreted ice REAL(wp), POINTER, DIMENSION(:) :: ze_newice ! heat content of accreted ice REAL(wp), POINTER, DIMENSION(:) :: zs_newice ! salinity of accreted ice REAL(wp), POINTER, DIMENSION(:) :: zo_newice ! age of accreted ice REAL(wp), POINTER, DIMENSION(:) :: zdv_res ! residual volume in case of excessive heat budget REAL(wp), POINTER, DIMENSION(:) :: zda_res ! residual area in case of excessive heat budget REAL(wp), POINTER, DIMENSION(:) :: zat_i_1d ! total ice fraction REAL(wp), POINTER, DIMENSION(:) :: zv_frazb ! accretion of frazil ice at the ice bottom REAL(wp), POINTER, DIMENSION(:) :: zvrel_1d ! relative ice / frazil velocity (1D vector) REAL(wp), POINTER, DIMENSION(:,:) :: zv_b ! old volume of ice in category jl REAL(wp), POINTER, DIMENSION(:,:) :: za_b ! old area of ice in category jl REAL(wp), POINTER, DIMENSION(:,:) :: za_i_1d ! 1-D version of a_i REAL(wp), POINTER, DIMENSION(:,:) :: zv_i_1d ! 1-D version of v_i REAL(wp), POINTER, DIMENSION(:,:) :: zsmv_i_1d ! 1-D version of smv_i REAL(wp), POINTER, DIMENSION(:,:,:) :: ze_i_1d !: 1-D version of e_i REAL(wp), POINTER, DIMENSION(:,:) :: zvrel ! relative ice / frazil velocity REAL(wp) :: zcai = 1.4e-3_wp ! ice-air drag (clem: should be dependent on coupling/forcing used) !!-----------------------------------------------------------------------! CALL wrk_alloc( jpij, jcat ) ! integer CALL wrk_alloc( jpij, zswinew, zv_newice, za_newice, zh_newice, ze_newice, zs_newice, zo_newice ) CALL wrk_alloc( jpij, zdv_res, zda_res, zat_i_1d, zv_frazb, zvrel_1d ) CALL wrk_alloc( jpij,jpl, zv_b, za_b, za_i_1d, zv_i_1d, zsmv_i_1d ) CALL wrk_alloc( jpij,nlay_i,jpl, ze_i_1d ) CALL wrk_alloc( jpi,jpj, zvrel ) CALL lim_var_agg(1) CALL lim_var_glo2eqv !------------------------------------------------------------------------------| ! 2) Convert units for ice internal energy !------------------------------------------------------------------------------| DO jl = 1, jpl DO jk = 1, nlay_i DO jj = 1, jpj DO ji = 1, jpi !Energy of melting q(S,T) [J.m-3] rswitch = MAX( 0._wp , SIGN( 1._wp , v_i(ji,jj,jl) - epsi20 ) ) !0 if no ice e_i(ji,jj,jk,jl) = rswitch * e_i(ji,jj,jk,jl) / MAX( v_i(ji,jj,jl), epsi20 ) * REAL( nlay_i, wp ) END DO END DO END DO END DO !------------------------------------------------------------------------------! ! 3) Collection thickness of ice formed in leads and polynyas !------------------------------------------------------------------------------! ! hicol is the thickness of new ice formed in open water ! hicol can be either prescribed (frazswi = 0) or computed (frazswi = 1) ! 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. ! Note : the following algorithm currently breaks vectorization ! zvrel(:,:) = 0._wp ! Default new ice thickness WHERE( qlead(:,:) < 0._wp ) ; hicol = rn_hnewice ELSEWHERE ; hicol = 0._wp END WHERE IF( ln_frazil ) THEN !-------------------- ! Physical constants !-------------------- hicol(:,:) = 0._wp zhicrit = 0.04 ! frazil ice thickness ztwogp = 2. * rau0 / ( grav * 0.3 * ( rau0 - rhoic ) ) ! reduced grav zsqcd = 1.0 / SQRT( 1.3 * zcai ) ! 1/SQRT(airdensity*drag) zgamafr = 0.03 DO jj = 2, jpj DO ji = 2, jpi IF ( qlead(ji,jj) < 0._wp ) THEN !------------- ! Wind stress !------------- ! C-grid wind stress components 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 !------------------- ! C-grid ice velocity rswitch = MAX( 0._wp, SIGN( 1._wp , at_i(ji,jj) ) ) zvgx = rswitch * ( u_ice(ji-1,jj ) * umask(ji-1,jj ,1) + u_ice(ji,jj) * umask(ji,jj,1) ) * 0.5_wp zvgy = rswitch * ( 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 !----------------------------------- ! absolute relative velocity zvrel2 = MAX( ( zvfrx - zvgx ) * ( zvfrx - zvgx ) & & + ( zvfry - zvgy ) * ( zvfry - zvgy ) , 0.15 * 0.15 ) zvrel(ji,jj) = SQRT( zvrel2 ) !--------------------- ! Iterative procedure !--------------------- hicol(ji,jj) = zhicrit + ( zhicrit + 0.1 ) & & / ( ( zhicrit + 0.1 ) * ( zhicrit + 0.1 ) - zhicrit * zhicrit ) * ztwogp * zvrel2 iter = 1 DO WHILE ( iter < 20 ) zf = ( hicol(ji,jj) - zhicrit ) * ( hicol(ji,jj) * hicol(ji,jj) - zhicrit * zhicrit ) - & & hicol(ji,jj) * zhicrit * ztwogp * zvrel2 zfp = ( hicol(ji,jj) - zhicrit ) * ( 3.0 * hicol(ji,jj) + zhicrit ) - zhicrit * ztwogp * zvrel2 hicol(ji,jj) = hicol(ji,jj) - zf/zfp iter = iter + 1 END DO ENDIF ! end of selection of pixels where ice forms END DO END DO ! CALL lbc_lnk( zvrel(:,:), 'T', 1. ) CALL lbc_lnk( hicol(:,:), 'T', 1. ) ENDIF ! End of computation of frazil ice collection thickness !------------------------------------------------------------------------------! ! 4) Identify grid points where new ice forms !------------------------------------------------------------------------------! !------------------------------------- ! Select points for new ice formation !------------------------------------- ! This occurs if open water energy budget is negative nbpac = 0 npac(:) = 0 ! DO jj = 1, jpj DO ji = 1, jpi IF ( qlead(ji,jj) < 0._wp ) THEN nbpac = nbpac + 1 npac( nbpac ) = (jj - 1) * jpi + ji ENDIF END DO END DO ! debug point to follow jiindex_1d = 0 IF( ln_icectl ) THEN DO ji = mi0(iiceprt), mi1(iiceprt) DO jj = mj0(jiceprt), mj1(jiceprt) IF ( qlead(ji,jj) < 0._wp ) THEN jiindex_1d = (jj - 1) * jpi + ji ENDIF END DO END DO ENDIF IF( ln_icectl ) WRITE(numout,*) 'lim_thd_lac : nbpac = ', nbpac !------------------------------ ! Move from 2-D to 1-D vectors !------------------------------ ! If ocean gains heat do nothing. Otherwise compute new ice formation IF ( nbpac > 0 ) THEN CALL tab_2d_1d( nbpac, zat_i_1d (1:nbpac) , at_i , jpi, jpj, npac(1:nbpac) ) DO jl = 1, jpl CALL tab_2d_1d( nbpac, za_i_1d (1:nbpac,jl), a_i (:,:,jl), jpi, jpj, npac(1:nbpac) ) CALL tab_2d_1d( nbpac, zv_i_1d (1:nbpac,jl), v_i (:,:,jl), jpi, jpj, npac(1:nbpac) ) CALL tab_2d_1d( nbpac, zsmv_i_1d(1:nbpac,jl), smv_i(:,:,jl), jpi, jpj, npac(1:nbpac) ) DO jk = 1, nlay_i CALL tab_2d_1d( nbpac, ze_i_1d(1:nbpac,jk,jl), e_i(:,:,jk,jl) , jpi, jpj, npac(1:nbpac) ) END DO END DO CALL tab_2d_1d( nbpac, qlead_1d (1:nbpac) , qlead , jpi, jpj, npac(1:nbpac) ) CALL tab_2d_1d( nbpac, t_bo_1d (1:nbpac) , t_bo , jpi, jpj, npac(1:nbpac) ) CALL tab_2d_1d( nbpac, sfx_opw_1d(1:nbpac) , sfx_opw , jpi, jpj, npac(1:nbpac) ) CALL tab_2d_1d( nbpac, wfx_opw_1d(1:nbpac) , wfx_opw , jpi, jpj, npac(1:nbpac) ) CALL tab_2d_1d( nbpac, hicol_1d (1:nbpac) , hicol , jpi, jpj, npac(1:nbpac) ) CALL tab_2d_1d( nbpac, zvrel_1d (1:nbpac) , zvrel , jpi, jpj, npac(1:nbpac) ) CALL tab_2d_1d( nbpac, hfx_thd_1d(1:nbpac) , hfx_thd , jpi, jpj, npac(1:nbpac) ) CALL tab_2d_1d( nbpac, hfx_opw_1d(1:nbpac) , hfx_opw , jpi, jpj, npac(1:nbpac) ) CALL tab_2d_1d( nbpac, rn_amax_1d(1:nbpac) , rn_amax_2d, jpi, jpj, npac(1:nbpac) ) !------------------------------------------------------------------------------! ! 5) Compute thickness, salinity, enthalpy, age, area and volume of new ice !------------------------------------------------------------------------------! !----------------------------------------- ! Keep old ice areas and volume in memory !----------------------------------------- zv_b(1:nbpac,:) = zv_i_1d(1:nbpac,:) za_b(1:nbpac,:) = za_i_1d(1:nbpac,:) !---------------------- ! Thickness of new ice !---------------------- zh_newice(1:nbpac) = hicol_1d(1:nbpac) !---------------------- ! Salinity of new ice !---------------------- SELECT CASE ( nn_icesal ) CASE ( 1 ) ! Sice = constant zs_newice(1:nbpac) = rn_icesal CASE ( 2 ) ! Sice = F(z,t) [Vancoppenolle et al (2005)] DO ji = 1, nbpac ii = MOD( npac(ji) - 1 , jpi ) + 1 ij = ( npac(ji) - 1 ) / jpi + 1 zs_newice(ji) = MIN( 4.606 + 0.91 / zh_newice(ji) , rn_simax , 0.5 * sss_m(ii,ij) ) END DO CASE ( 3 ) ! Sice = F(z) [multiyear ice] zs_newice(1:nbpac) = 2.3 END SELECT !------------------------- ! Heat content of new ice !------------------------- ! We assume that new ice is formed at the seawater freezing point DO ji = 1, nbpac ztmelts = - tmut * zs_newice(ji) + rt0 ! Melting point (K) ze_newice(ji) = rhoic * ( cpic * ( ztmelts - t_bo_1d(ji) ) & & + lfus * ( 1.0 - ( ztmelts - rt0 ) / MIN( t_bo_1d(ji) - rt0, -epsi10 ) ) & & - rcp * ( ztmelts - rt0 ) ) END DO !---------------- ! Age of new ice !---------------- DO ji = 1, nbpac zo_newice(ji) = 0._wp END DO !------------------- ! Volume of new ice !------------------- DO ji = 1, nbpac zEi = - ze_newice(ji) * r1_rhoic ! 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 (limthd) because we suppose we are at the freezing point zv_newice(ji) = - zfmdt * r1_rhoic 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_rdtice ! Total heat flux used in this process [W.m-2] hfx_opw_1d(ji) = hfx_opw_1d(ji) - zfmdt * zdE * r1_rdtice ! mass flux wfx_opw_1d(ji) = wfx_opw_1d(ji) - zv_newice(ji) * rhoic * r1_rdtice ! salt flux sfx_opw_1d(ji) = sfx_opw_1d(ji) - zv_newice(ji) * rhoic * zs_newice(ji) * r1_rdtice END DO zv_frazb(:) = 0._wp IF( ln_frazil ) THEN ! A fraction zfrazb of frazil ice is accreted at the ice bottom DO ji = 1, nbpac rswitch = 1._wp - MAX( 0._wp, SIGN( 1._wp , - zat_i_1d(ji) ) ) zfrazb = rswitch * ( TANH( rn_Cfrazb * ( zvrel_1d(ji) - rn_vfrazb ) ) + 1.0 ) * 0.5 * rn_maxfrazb 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, nbpac za_newice(ji) = zv_newice(ji) / zh_newice(ji) END DO !------------------------------------------------------------------------------! ! 6) Redistribute new ice area and volume into ice categories ! !------------------------------------------------------------------------------! !------------------------ ! 6.1) lateral ice growth !------------------------ ! If lateral ice growth gives an ice concentration gt 1, then ! we keep the excessive volume in memory and attribute it later to bottom accretion DO ji = 1, nbpac IF ( za_newice(ji) > ( rn_amax_1d(ji) - zat_i_1d(ji) ) ) THEN zda_res(ji) = za_newice(ji) - ( rn_amax_1d(ji) - zat_i_1d(ji) ) zdv_res(ji) = zda_res (ji) * zh_newice(ji) za_newice(ji) = za_newice(ji) - zda_res (ji) zv_newice(ji) = 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 zat_i_1d(:) = 0._wp DO jl = 1, jpl DO ji = 1, nbpac IF( zh_newice(ji) > hi_max(jl-1) .AND. zh_newice(ji) <= hi_max(jl) ) THEN za_i_1d (ji,jl) = za_i_1d (ji,jl) + za_newice(ji) zv_i_1d (ji,jl) = zv_i_1d (ji,jl) + zv_newice(ji) jcat (ji) = jl ENDIF zat_i_1d(ji) = zat_i_1d(ji) + za_i_1d (ji,jl) END DO END DO ! Heat content DO ji = 1, nbpac 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, nbpac jl = jcat(ji) rswitch = MAX( 0._wp, SIGN( 1._wp , zv_i_1d(ji,jl) - epsi20 ) ) ze_i_1d(ji,jk,jl) = zswinew(ji) * ze_newice(ji) + & & ( 1.0 - zswinew(ji) ) * ( ze_newice(ji) * zv_newice(ji) + ze_i_1d(ji,jk,jl) * zv_b(ji,jl) ) & & * rswitch / MAX( zv_i_1d(ji,jl), epsi20 ) END DO END DO !------------------------------------------------ ! 6.2) bottom ice growth + ice enthalpy remapping !------------------------------------------------ DO jl = 1, jpl ! for remapping h_i_old (1:nbpac,0:nlay_i+1) = 0._wp qh_i_old(1:nbpac,0:nlay_i+1) = 0._wp DO jk = 1, nlay_i DO ji = 1, nbpac h_i_old (ji,jk) = zv_i_1d(ji,jl) * r1_nlay_i qh_i_old(ji,jk) = ze_i_1d(ji,jk,jl) * h_i_old(ji,jk) END DO END DO ! new volumes including lateral/bottom accretion + residual DO ji = 1, nbpac rswitch = MAX( 0._wp, SIGN( 1._wp , zat_i_1d(ji) - epsi20 ) ) zv_newfra = rswitch * ( zdv_res(ji) + zv_frazb(ji) ) * za_i_1d(ji,jl) / MAX( zat_i_1d(ji) , epsi20 ) za_i_1d(ji,jl) = rswitch * za_i_1d(ji,jl) zv_i_1d(ji,jl) = zv_i_1d(ji,jl) + zv_newfra ! for remapping h_i_old (ji,nlay_i+1) = zv_newfra qh_i_old(ji,nlay_i+1) = ze_newice(ji) * zv_newfra ENDDO ! --- Ice enthalpy remapping --- ! CALL lim_thd_ent( 1, nbpac, ze_i_1d(1:nbpac,:,jl) ) ENDDO !----------------- ! Update salinity !----------------- DO jl = 1, jpl DO ji = 1, nbpac zdv = zv_i_1d(ji,jl) - zv_b(ji,jl) zsmv_i_1d(ji,jl) = zsmv_i_1d(ji,jl) + zdv * zs_newice(ji) END DO END DO !------------------------------------------------------------------------------! ! 7) Change 2D vectors to 1D vectors !------------------------------------------------------------------------------! DO jl = 1, jpl CALL tab_1d_2d( nbpac, a_i (:,:,jl), npac(1:nbpac), za_i_1d (1:nbpac,jl), jpi, jpj ) CALL tab_1d_2d( nbpac, v_i (:,:,jl), npac(1:nbpac), zv_i_1d (1:nbpac,jl), jpi, jpj ) CALL tab_1d_2d( nbpac, smv_i (:,:,jl), npac(1:nbpac), zsmv_i_1d(1:nbpac,jl) , jpi, jpj ) DO jk = 1, nlay_i CALL tab_1d_2d( nbpac, e_i(:,:,jk,jl), npac(1:nbpac), ze_i_1d(1:nbpac,jk,jl), jpi, jpj ) END DO END DO CALL tab_1d_2d( nbpac, sfx_opw, npac(1:nbpac), sfx_opw_1d(1:nbpac), jpi, jpj ) CALL tab_1d_2d( nbpac, wfx_opw, npac(1:nbpac), wfx_opw_1d(1:nbpac), jpi, jpj ) CALL tab_1d_2d( nbpac, hfx_thd, npac(1:nbpac), hfx_thd_1d(1:nbpac), jpi, jpj ) CALL tab_1d_2d( nbpac, hfx_opw, npac(1:nbpac), hfx_opw_1d(1:nbpac), jpi, jpj ) ! ENDIF ! nbpac > 0 !------------------------------------------------------------------------------! ! 8) Change units for e_i !------------------------------------------------------------------------------! DO jl = 1, jpl DO jk = 1, nlay_i DO jj = 1, jpj DO ji = 1, jpi ! heat content in J/m2 e_i(ji,jj,jk,jl) = e_i(ji,jj,jk,jl) * v_i(ji,jj,jl) * r1_nlay_i END DO END DO END DO END DO ! CALL wrk_dealloc( jpij, jcat ) ! integer CALL wrk_dealloc( jpij, zswinew, zv_newice, za_newice, zh_newice, ze_newice, zs_newice, zo_newice ) CALL wrk_dealloc( jpij, zdv_res, zda_res, zat_i_1d, zv_frazb, zvrel_1d ) CALL wrk_dealloc( jpij,jpl, zv_b, za_b, za_i_1d, zv_i_1d, zsmv_i_1d ) CALL wrk_dealloc( jpij,nlay_i,jpl, ze_i_1d ) CALL wrk_dealloc( jpi,jpj, zvrel ) ! END SUBROUTINE lim_thd_lac #else !!---------------------------------------------------------------------- !! Default option NO LIM3 sea-ice model !!---------------------------------------------------------------------- CONTAINS SUBROUTINE lim_thd_lac ! Empty routine END SUBROUTINE lim_thd_lac #endif !!====================================================================== END MODULE limthd_lac