MODULE limthd_zdf_2 !!====================================================================== !! *** MODULE limthd_zdf_2 *** !! thermodynamic growth and decay of the ice !!====================================================================== !! History : 1.0 ! 01-04 (LIM) Original code !! 2.0 ! 02-08 (C. Ethe, G. Madec) F90 !!---------------------------------------------------------------------- #if defined key_lim2 !!---------------------------------------------------------------------- !! 'key_lim2' LIM 2.0 sea-ice model !!---------------------------------------------------------------------- !! lim_thd_zdf_2 : vertical accr./abl. and lateral ablation of sea ice !!---------------------------------------------------------------------- USE par_oce ! ocean parameters USE phycst ! ??? USE thd_ice_2 USE ice_2 USE limistate_2 USE cpl_oasis3, ONLY : lk_cpl USE in_out_manager USE lib_mpp ! MPP library USE wrk_nemo ! work arrays USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) IMPLICIT NONE PRIVATE PUBLIC lim_thd_zdf_2 ! called by lim_thd_2 REAL(wp) :: epsi20 = 1.e-20 , & ! constant values & epsi13 = 1.e-13 , & & zzero = 0.e0 , & & zone = 1.e0 !!---------------------------------------------------------------------- !! NEMO/LIM2 3.3 , UCL - NEMO Consortium (2010) !! $Id$ !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE lim_thd_zdf_2( kideb , kiut ) !!------------------------------------------------------------------ !! *** ROUTINE lim_thd_zdf_2 *** !! !! ** Purpose : This routine determines the time evolution of snow !! and sea-ice thicknesses, concentration and heat content !! due to the vertical and lateral thermodynamic accretion- !! ablation processes. One only treats the case of lat. abl. !! For lateral accretion, see routine lim_lat_accr !! !! ** Method : The representation of vertical growth and decay of !! the sea-ice model is based upon the diffusion of heat !! through the external and internal boundaries of a !! three-layer system (two layers of ice and one layer and !! one layer of snow, if present, on top of the ice). !! !! ** Action : - Calculation of some intermediates variables !! - Calculation of surface temperature !! - Calculation of available heat for surface ablation !! - Calculation of the changes in internal temperature !! of the three-layer system, due to vertical diffusion !! processes !! - Performs surface ablation and bottom accretion-ablation !! - Performs snow-ice formation !! - Performs lateral ablation !! !! References : Fichefet T. and M. Maqueda 1997, J. Geophys. Res., 102(C6), 12609-12646 !! Fichefet T. and M. Maqueda 1999, Clim. Dyn, 15(4), 251-268 !!------------------------------------------------------------------ INTEGER, INTENT(in) :: kideb ! Start point on which the the computation is applied INTEGER, INTENT(in) :: kiut ! End point on which the the computation is applied !! INTEGER :: ji ! dummy loop indices REAL(wp), POINTER, DIMENSION(:) :: zqcmlts ! energy due to surface melting REAL(wp), POINTER, DIMENSION(:) :: zqcmltb ! energy due to bottom melting REAL(wp), POINTER, DIMENSION(:) :: ztsmlt ! snow/ice surface melting temperature REAL(wp), POINTER, DIMENSION(:) :: ztbif ! int. temp. at the mid-point of the 1st layer of the snow/ice sys. REAL(wp), POINTER, DIMENSION(:) :: zksn ! effective conductivity of snow REAL(wp), POINTER, DIMENSION(:) :: zkic ! effective conductivity of ice REAL(wp), POINTER, DIMENSION(:) :: zksndh ! thermal cond. at the mid-point of the 1st layer of the snow/ice sys. REAL(wp), POINTER, DIMENSION(:) :: zfcsu ! conductive heat flux at the surface of the snow/ice system REAL(wp), POINTER, DIMENSION(:) :: zfcsudt ! = zfcsu * dt REAL(wp), POINTER, DIMENSION(:) :: zi0 ! frac. of the net SW rad. which is not absorbed at the surface REAL(wp), POINTER, DIMENSION(:) :: z1mi0 ! fraction of the net SW radiation absorbed at the surface REAL(wp), POINTER, DIMENSION(:) :: zqmax ! maximum energy stored in brine pockets REAL(wp), POINTER, DIMENSION(:) :: zrcpdt ! h_su*rho_su*cp_su/dt(h_su being the thick. of surf. layer) REAL(wp), POINTER, DIMENSION(:) :: zts_old ! previous surface temperature REAL(wp), POINTER, DIMENSION(:) :: zidsn , z1midsn , zidsnic ! temporary variables REAL(wp), POINTER, DIMENSION(:) :: zfnet ! net heat flux at the top surface( incl. conductive heat flux) REAL(wp), POINTER, DIMENSION(:) :: zsprecip ! snow accumulation REAL(wp), POINTER, DIMENSION(:) :: zhsnw_old ! previous snow thickness REAL(wp), POINTER, DIMENSION(:) :: zdhictop ! change in ice thickness due to top surf ablation/accretion REAL(wp), POINTER, DIMENSION(:) :: zdhicbot ! change in ice thickness due to bottom surf abl/acc REAL(wp), POINTER, DIMENSION(:) :: zqsup ! energy transmitted to ocean (coming from top surf abl/acc) REAL(wp), POINTER, DIMENSION(:) :: zqocea ! energy transmitted to ocean (coming from bottom sur abl/acc) REAL(wp), POINTER, DIMENSION(:) :: zfrl_old ! previous sea/ice fraction REAL(wp), POINTER, DIMENSION(:) :: zfrld_1d ! new sea/ice fraction REAL(wp), POINTER, DIMENSION(:) :: zep ! internal temperature of the 2nd layer of the snow/ice system REAL(wp), DIMENSION(3) :: & zplediag & ! principle diagonal, subdiag. and supdiag. of the , zsubdiag & ! tri-diagonal matrix coming from the computation , zsupdiag & ! of the temperatures inside the snow-ice system , zsmbr ! second member REAL(wp) :: & zhsu & ! thickness of surface layer , zhe & ! effective thickness for compu. of equ. thermal conductivity , zheshth & ! = zhe / thth , zghe & ! correction factor of the thermal conductivity , zumsb & ! parameter for numerical method to solve heat-diffusion eq. , zkhsn & ! conductivity at the snow layer , zkhic & ! conductivity at the ice layers , zkint & ! equivalent conductivity at the snow-ice interface , zkhsnint & ! = zkint*dt / (hsn*rhosn*cpsn) , zkhicint & ! = 2*zkint*dt / (hic*rhoic*cpic) , zpiv1, zpiv2 & ! temporary scalars used to solve the tri-diagonal system , zb2, zd2 & ! temporary scalars used to solve the tri-diagonal system , zb3, zd3 & ! temporary scalars used to solve the tri-diagonal system , ztint ! equivalent temperature at the snow-ice interface REAL(wp) :: & zexp & ! exponential function of the ice thickness , zfsab & ! part of solar radiation stored in brine pockets , zfts & ! value of energy balance function when the temp. equal surf. temp. , zdfts & ! value of derivative of ztfs when the temp. equal surf. temp. , zdts & ! surface temperature increment , zqsnw_mlt & ! energy needed to melt snow , zdhsmlt & ! change in snow thickness due to melt , zhsn & ! snow thickness (previous+accumulation-melt) , zqsn_mlt_rem & ! remaining heat coming from snow melting , zqice_top_mlt &! energy used to melt ice at top surface , zdhssub & ! change in snow thick. due to sublimation or evaporation , zdhisub & ! change in ice thick. due to sublimation or evaporation , zdhsn & ! snow ice thickness increment , zdtsn & ! snow internal temp. increment , zdtic & ! ice internal temp. increment , zqnes ! conductive energy due to ice melting in the first ice layer REAL(wp) :: & ztbot & ! temperature at the bottom surface , zfcbot & ! conductive heat flux at bottom surface , zqice_bot & ! energy used for bottom melting/growing , zqice_bot_mlt &! energy used for bottom melting , zqstbif_bot & ! part of energy stored in brine pockets used for bottom melting , zqstbif_old & ! temporary var. for zqstbif_bot , zdhicmlt & ! change in ice thickness due to bottom melting , zdhicm & ! change in ice thickness var. , zdhsnm & ! change in snow thickness var. , zhsnfi & ! snow thickness var. , zc1, zpc1 & ! temporary variables , zc2, zpc2 & ! temporary variables , zp1, zp2 & ! temporary variables , ztb2, ztb3 ! temporary variables REAL(wp) :: & zdrmh & ! change in snow/ice thick. after snow-ice formation , zhicnew & ! new ice thickness , zhsnnew & ! new snow thickness , zquot & , ztneq & ! temporary temp. variables , zqice & , zqicetot & ! total heat inside the snow/ice system , zdfrl & ! change in ice concentration , zdvsnvol & ! change in snow volume , zdrfrl1, zdrfrl2, zihsn, zidhb, zihic & ! temporary scalars , zihe, zihq, ziexp, ziqf, zihnf & ! temporary scalars , zibmlt, ziqr, zihgnew, zind, ztmp ! temporary scalars !!---------------------------------------------------------------------- CALL wrk_alloc( jpij, ztsmlt, ztbif , zksn , zkic , zksndh , zfcsu , zfcsudt , zi0 , z1mi0 , zqmax ) CALL wrk_alloc( jpij, zrcpdt, zts_old, zidsn , z1midsn , zidsnic, zfnet , zsprecip, zhsnw_old, zdhictop, zdhicbot ) CALL wrk_alloc( jpij, zqsup , zqocea , zfrl_old, zfrld_1d, zep , zqcmlts, zqcmltb ) !----------------------------------------------------------------------- ! 1. Boundaries conditions for snow/ice system internal temperature ! - If tbif_1d(ji,1) > rt0_snow, tbif_1d(ji,1) = rt0_snow ! - If tbif_1d(ji,2/3) > rt0_ice, tbif_1d(ji,2/3) = rt0_ice ! Computation of energies due to surface and bottom melting !----------------------------------------------------------------------- DO ji = kideb , kiut ! do nothing if the snow (ice) thickness falls below its minimum thickness zihsn = MAX( zzero , SIGN( zone , hsndif - h_snow_1d(ji) ) ) zihic = MAX( zzero , SIGN( zone , hicdif - h_ice_1d(ji) ) ) !--energy required to bring snow to its melting point (rt0_snow) zqcmlts(ji) = ( MAX ( zzero , rcpsn * h_snow_1d(ji) * ( tbif_1d(ji,1) - rt0_snow ) ) ) * ( 1.0 - zihsn ) !--energy required to bring ice to its melting point (rt0_ice) zqcmltb(ji) = ( MAX( zzero , rcpic * ( tbif_1d(ji,2) - rt0_ice ) * ( h_ice_1d(ji) / 2. ) ) & & + MAX( zzero , rcpic * ( tbif_1d(ji,3) - rt0_ice ) * ( h_ice_1d(ji) / 2. ) ) & & ) * ( 1.0 - zihic ) !--limitation of snow/ice system internal temperature tbif_1d(ji,1) = MIN( rt0_snow, tbif_1d(ji,1) ) tbif_1d(ji,2) = MIN( rt0_ice , tbif_1d(ji,2) ) tbif_1d(ji,3) = MIN( rt0_ice , tbif_1d(ji,3) ) END DO !------------------------------------------- ! 2. Calculate some intermediate variables. !------------------------------------------- ! initialisation of the thickness of surface layer zhsu = hnzst DO ji = kideb , kiut zind = MAX( zzero , SIGN( zone , zhsu - h_snow_1d(ji) ) ) zihsn = MAX( zzero , SIGN( zone , hsndif - h_snow_1d(ji) ) ) zihsn = MAX( zihsn , zind ) zihic = MAX( zzero , sign( zone , hicdif - h_ice_1d(ji) ) ) ! 2.1. Computation of surface melting temperature !---------------------------------------------------- zind = MAX( zzero , SIGN( zone , -h_snow_1d(ji) ) ) ztsmlt(ji) = ( 1.0 - zind ) * rt0_snow + zind * rt0_ice ! ! 2.2. Effective conductivity of snow and ice !----------------------------------------------- !---computation of the correction factor on the thermal conductivity !-- (Morales Maqueda, 1995 ; Fichefet and Morales Maqueda, 1997) zhe = ( rcdsn / ( rcdsn + rcdic ) ) * h_ice_1d(ji) & & + ( rcdic / ( rcdsn + rcdic ) ) * h_snow_1d(ji) zihe = MAX( zzero , SIGN( zone , 2.0 * zhe - thth ) ) zheshth = zhe / thth zghe = ( 1.0 - zihe ) * zheshth * ( 2.0 - zheshth ) & & + zihe * 0.5 * ( 1.5 + LOG( 2.0 * zheshth ) ) !---effective conductivities zksn(ji) = zghe * rcdsn zkic(ji) = zghe * rcdic ! ! 2.3. Computation of the conductive heat flux from the snow/ice ! system interior toward the top surface !------------------------------------------------------------------ !---Thermal conductivity at the mid-point of the first snow/ice system layer zksndh(ji) = ( ( 1.0 - zihsn ) * 2.0 * zksn(ji) + zihsn * 4.0 * zkic(ji) ) & & / ( ( 1.0 - zihsn ) * h_snow_1d(ji) & & + zihsn * ( ( 1.0 + 3.0 * zihic ) * h_ice_1d(ji) & & + 4.0 * zkic(ji)/zksn(ji) * h_snow_1d(ji) ) ) !---internal temperature at the mid-point of the first snow/ice system layer ztbif(ji) = ( 1.0 - zihsn ) * tbif_1d(ji,1) & & + zihsn * ( ( 1.0 - zihic ) * tbif_1d(ji,2) & & + zihic * tfu_1d(ji) ) !---conductive heat flux zfcsu(ji) = zksndh(ji) * ( ztbif(ji) - sist_1d(ji) ) END DO !-------------------------------------------------------------------- ! 3. Calculate : ! - fstbif_1d, part of solar radiation absorbing inside the ice ! assuming an exponential absorption (Grenfell and Maykut, 1977) ! - zqmax, maximum energy stored in brine pockets ! - qstbif_1d, total energy stored in brine pockets (updating) !------------------------------------------------------------------- DO ji = kideb , kiut zihsn = MAX( zzero , SIGN (zone , -h_snow_1d(ji) ) ) zihic = MAX( zzero , 1.0 - ( h_ice_1d(ji) / zhsu ) ) zind = MAX( zzero , SIGN (zone , hicdif - h_ice_1d(ji) ) ) !--Computation of the fraction of the net shortwave radiation which !--penetrates inside the ice cover ( See Forcat) zi0(ji) = zihsn * ( fr1_i0_1d(ji) + zihic * fr2_i0_1d(ji) ) zexp = MIN( zone , EXP( -1.5 * ( h_ice_1d(ji) - zhsu ) ) ) fstbif_1d(ji) = zi0(ji) * qsr_ice_1d(ji) * zexp !--Computation of maximum energy stored in brine pockets zqmax and update !--the total energy stored in brine pockets, if less than zqmax zqmax(ji) = MAX( zzero , 0.5 * xlic * ( h_ice_1d(ji) - hicmin ) ) zfsab = zi0(ji) * qsr_ice_1d(ji) * ( 1.0 - zexp ) zihq = ( 1.0 - zind ) * MAX(zzero, SIGN( zone , qstbif_1d(ji) - zqmax(ji) ) ) & & + zind * zone qstbif_1d(ji) = ( qstbif_1d(ji) + ( 1.0 - zihq ) * zfsab * rdt_ice ) * swiqst !--fraction of shortwave radiation absorbed at surface ziexp = zihq * zexp + ( 1.0 - zihq ) * ( swiqst + ( 1.0 - swiqst ) * zexp ) z1mi0(ji) = 1.0 - zi0(ji) * ziexp END DO IF( ltrcdm2dc_ice )THEN DO ji = kideb , kiut zihsn = MAX( zzero , SIGN (zone , -h_snow_1d(ji) ) ) zihic = MAX( zzero , 1.0 - ( h_ice_1d(ji) / zhsu ) ) zi0(ji) = zihsn * ( fr1_i0_1d(ji) + zihic * fr2_i0_1d(ji) ) zexp = MIN( zone , EXP( -1.5 * ( h_ice_1d(ji) - zhsu ) ) ) fstbif_daymean_1d(ji) = zi0(ji) * qsr_ice_mean_1d(ji) * zexp END DO ENDIF !-------------------------------------------------------------------------------- ! 4. Computation of the surface temperature : determined by considering the ! budget of a thin layer of thick. zhsu at the top surface (H. Grenier, 1995) ! and based on a surface energy balance : ! hsu * rcp * dT/dt = Fsr + Fnsr(T) + Fcs(T), ! where - Fsr is the net absorbed solar radiation, ! - Fnsr is the total non solar radiation (incoming and outgoing long-wave, ! sensible and latent heat fluxes) ! - Fcs the conductive heat flux at the top of surface !------------------------------------------------------------------------------ ! 4.1. Computation of intermediate values !--------------------------------------------- DO ji = kideb, kiut zrcpdt(ji) = ( rcpsn * MIN( h_snow_1d(ji) , zhsu ) & & + rcpic * MAX( zhsu - h_snow_1d(ji) , zzero ) ) / rdt_ice zts_old(ji) = sist_1d(ji) END DO ! 4.2. Computation of surface temperature by expanding the eq. of energy balance ! with Ts = Tp + DT. One obtain , F(Tp) + DT * DF(Tp) = 0 ! where - F(Tp) = Fsr + Fnsr(Tp) + Fcs(Tp) ! - DF(Tp)= (dFnsr(Tp)/dT) + (dFcs(Tp)/dT) - hsu*rcp/dt !--------------------------------------------------------------------------------- DO ji = kideb, kiut !---computation of the derivative of energy balance function zdfts = zksndh(ji) & ! contribution of the conductive heat flux & + zrcpdt(ji) & ! contribution of hsu * rcp / dt & - dqns_ice_1d (ji) ! contribution of the total non solar radiation !---computation of the energy balance function zfts = - z1mi0 (ji) * qsr_ice_1d(ji) & ! net absorbed solar radiation & - qns_ice_1d(ji) & ! total non solar radiation & - zfcsu (ji) ! conductive heat flux from the surface !---computation of surface temperature increment zdts = -zfts / zdfts !---computation of the new surface temperature sist_1d(ji) = sist_1d(ji) + zdts END DO !---------------------------------------------------------------------------- ! 5. Boundary condition at the top surface !-- IF Tsb < Tmelt, Fnet = Fcs (the net heat flux equal the conductive heat flux) ! Otherwise Tsb = Tmelt and Qnet(Tmelt) > 0 ! Fnet(Tmelt) is therefore the net surface flux needed for melting !---------------------------------------------------------------------------- ! 5.1. Limitation of surface temperature and update total non solar fluxes, ! latent heat flux and conductive flux at the top surface !---------------------------------------------------------------------- IF ( .NOT. lk_cpl ) THEN ! duplicate the loop for performances issues DO ji = kideb, kiut sist_1d(ji) = MIN( ztsmlt(ji) , sist_1d(ji) ) qns_ice_1d(ji) = qns_ice_1d(ji) + dqns_ice_1d(ji) * ( sist_1d(ji) - zts_old(ji) ) qla_ice_1d(ji) = qla_ice_1d(ji) + dqla_ice_1d(ji) * ( sist_1d(ji) - zts_old(ji) ) zfcsu(ji) = zksndh(ji) * ( ztbif(ji) - sist_1d(ji) ) END DO ELSE DO ji = kideb, kiut sist_1d(ji) = MIN( ztsmlt(ji) , sist_1d(ji) ) qla_ice_1d(ji) = -9999. ! default definition, not used as parsub = 0. in this case zfcsu(ji) = zksndh(ji) * ( ztbif(ji) - sist_1d(ji) ) END DO ENDIF ! 5.2. Calculate available heat for surface ablation. !--------------------------------------------------------------------- DO ji = kideb, kiut zfnet(ji) = qns_ice_1d(ji) + z1mi0(ji) * qsr_ice_1d(ji) + zfcsu(ji) zfnet(ji) = MAX( zzero , zfnet(ji) ) zfnet(ji) = zfnet(ji) * MAX( zzero , SIGN( zone , sist_1d(ji) - ztsmlt(ji) ) ) END DO !------------------------------------------------------------------------- ! 6. Calculate changes in internal temperature due to vertical diffusion ! processes. The evolution of this temperature is governed by the one- ! dimensionnal heat-diffusion equation. ! Given the temperature tbif(1/2/3), at time m we solve a set ! of finite difference equations to obtain new tempe. Each tempe is coupled ! to the temp. immediatly above and below by heat conduction terms. Thus ! we have a set of equations of the form A * T = B, where A is a tridiagonal ! matrix, T a vector whose components are the unknown new temp. !------------------------------------------------------------------------- !--parameter for the numerical methode use to solve the heat-diffusion equation !- implicit, explicit or Crank-Nicholson zumsb = 1.0 - sbeta DO ji = kideb, kiut zidsn(ji) = MAX ( zzero, SIGN( zone, hsndif - h_snow_1d(ji) ) ) z1midsn(ji) = 1.0 - zidsn(ji) zihic = MAX ( zzero, SIGN( zone, hicdif - h_ice_1d(ji) ) ) zidsnic(ji) = zidsn(ji) * zihic zfcsudt(ji) = zfcsu(ji) * rdt_ice END DO DO ji = kideb, kiut ! 6.1 Calculate intermediate variables. !---------------------------------------- !--conductivity at the snow surface zkhsn = 2.0 * zksn(ji) * rdt_ice / rcpsn !--conductivity at the ice surface zkhic = 4.0 * zkic(ji) * rdt_ice / MAX( h_ice_1d(ji) * h_ice_1d(ji) * rcpic , epsi20 ) !--conductivity at the snow/ice interface zkint = 4.0 * zksn(ji) * zkic(ji) & & / ( zksn(ji) * h_ice_1d(ji) + 2.0 * zkic(ji) * h_snow_1d(ji) * z1midsn(ji)) zkhsnint = zkint * rdt_ice / rcpsn zkhicint = zkint * 2.0 * rdt_ice / MAX( h_ice_1d(ji) * rcpic , epsi20 ) ! 6.2. Fulfill the linear system matrix. !----------------------------------------- !$$$ zplediag(1) = 1 + sbeta * z1midsn(ji) * ( zkhsn + zkhsnint ) zplediag(1) = zidsn(ji) + z1midsn(ji) * h_snow_1d(ji) & & + sbeta * z1midsn(ji) * zkhsnint zplediag(2) = 1 + sbeta * ( z1midsn(ji) * zkhicint + zkhic ) zplediag(3) = 1 + 3.0 * sbeta * zkhic zsubdiag(1) = 0.e0 zsubdiag(2) = -1.e0 * z1midsn(ji) * sbeta * zkhicint zsubdiag(3) = -1.e0 * sbeta * zkhic zsupdiag(1) = -1.e0 * z1midsn(ji) * sbeta * zkhsnint zsupdiag(2) = zsubdiag(3) zsupdiag(3) = 0.e0 ! 6.3. Fulfill the idependent term vector. !------------------------------------------- !$$$ zsmbr(1) = zidsn(ji) * sist_1d(ji) + z1midsn(ji) * & !$$$ & ( tbif_1d(ji,1) + zkhsn * sist_1d(ji) !$$$ & - zumsb * ( zkhsn * tbif_1d(ji,1) !$$$ & + zkhsnint * ( tbif_1d(ji,1) - tbif_1d(ji,2) ) ) ) zsmbr(1) = zidsn(ji) * sist_1d(ji) + z1midsn(ji) * & & ( h_snow_1d(ji) * tbif_1d(ji,1) - ( zfcsudt(ji) / rcpsn ) & & - zumsb * zkhsnint * ( tbif_1d(ji,1) - tbif_1d(ji,2) ) ) zsmbr(2) = tbif_1d(ji,2) & & - zidsn(ji) * ( 1.0 - zidsnic(ji) ) & & * ( zfcsudt(ji) / MAX( h_ice_1d(ji) * rcpic , epsi20 ) ) & & + zumsb * ( zkhicint * ( tbif_1d(ji,1) - tbif_1d(ji,2) ) & & - zkhic * ( tbif_1d(ji,2) - tbif_1d(ji,3) ) ) zsmbr(3) = tbif_1d(ji,3) & & + zkhic * ( 2.0 * tfu_1d(ji) & & + zumsb * ( tbif_1d(ji,2) - 3.0 * tbif_1d(ji,3) ) ) ! 6.4. Solve the system (Gauss elimination method). !---------------------------------------------------- zpiv1 = zsubdiag(2) / zplediag(1) zb2 = zplediag(2) - zpiv1 * zsupdiag(1) zd2 = zsmbr(2) - zpiv1 * zsmbr(1) zpiv2 = zsubdiag(3) / zb2 zb3 = zplediag(3) - zpiv2 * zsupdiag(2) zd3 = zsmbr(3) - zpiv2 * zd2 tbif_1d(ji,3) = zd3 / zb3 tbif_1d(ji,2) = ( zd2 - zsupdiag(2) * tbif_1d(ji,3) ) / zb2 tbif_1d(ji,1) = ( zsmbr(1) - zsupdiag(1) * tbif_1d(ji,2) ) / zplediag(1) !--- taking into account the particular case of zidsnic(ji) = 1 ztint = ( zkic(ji) * h_snow_1d(ji) * tfu_1d (ji) & & + zksn(ji) * h_ice_1d(ji) * sist_1d(ji) ) & & / ( zkic(ji) * h_snow_1d(ji) + zksn(ji) * h_ice_1d(ji) ) tbif_1d(ji,1) = ( 1.0 - zidsnic(ji) ) * tbif_1d(ji,1) & & + zidsnic(ji) * ( ztint + sist_1d(ji) ) / 2.0 tbif_1d(ji,2) = ( 1.0 - zidsnic(ji) ) * tbif_1d(ji,2) & & + zidsnic(ji) * ( 3.0 * ztint + tfu_1d(ji) ) / 4.0 tbif_1d(ji,3) = ( 1.0 - zidsnic(ji) ) * tbif_1d(ji,3) & & + zidsnic(ji) * ( ztint + 3.0 * tfu_1d(ji) ) / 4.0 END DO !---------------------------------------------------------------------- ! 9. Take into account surface ablation and bottom accretion-ablation.| !---------------------------------------------------------------------- !---Snow accumulation in one thermodynamic time step zsprecip(kideb:kiut) = sprecip_1d(kideb:kiut) * rdt_ice / rhosn DO ji = kideb, kiut ! 9.1. Surface ablation and update of snow thickness and qstbif_1d !-------------------------------------------------------------------- !-------------------------------------------------------------------------- !-- Melting snow processes : !-- Melt at the upper surface is computed from the difference between !-- the net heat flux (including the conductive heat flux) at the upper !-- surface and the pre-existing energy due to surface melting !------------------------------------------------------------------------------ !-- store the snow thickness zhsnw_old(ji) = h_snow_1d(ji) !--computation of the energy needed to melt snow zqsnw_mlt = zfnet(ji) * rdt_ice - zqcmlts(ji) !--change in snow thickness due to melt zdhsmlt = - zqsnw_mlt / xlsn !-- compute new snow thickness, taking into account the part of snow accumulation ! (as snow precipitation) and the part of snow lost due to melt zhsn = h_snow_1d(ji) + zsprecip(ji) + zdhsmlt h_snow_1d(ji) = MAX( zzero , zhsn ) !-- compute the volume of snow lost after surface melting and the associated mass dvsbq_1d(ji) = ( 1.0 - frld_1d(ji) ) * ( h_snow_1d(ji) - zhsnw_old(ji) - zsprecip(ji) ) dvsbq_1d(ji) = MIN( zzero , dvsbq_1d(ji) ) ztmp = rhosn * dvsbq_1d(ji) rdm_snw_1d(ji) = ztmp !--heat content of the water provided to the ocean (referenced to rt0) rdq_snw_1d(ji) = cpic * ztmp * ( rt0_snow - rt0 ) !-- If the snow is completely melted the remaining heat is used to melt ice zqsn_mlt_rem = MAX( zzero , -zhsn ) * xlsn zqice_top_mlt = zqsn_mlt_rem zqstbif_old = qstbif_1d(ji) !-------------------------------------------------------------------------- !-- Melting ice processes at the top surface : !-- The energy used to melt ice, zqice_top_mlt, is taken from the energy !-- stored in brine pockets qstbif_1d and the remaining energy coming !-- from the melting snow process zqsn_mlt_rem. !-- If qstbif_1d > zqsn_mlt_rem then, one uses only a zqsn_mlt_rem part !-- of qstbif_1d to melt ice, !-- zqice_top_mlt = zqice_top_mlt + zqsn_mlt_rem !-- qstbif_1d = qstbif_1d - zqsn_mlt_rem !-- Otherwise one uses all qstbif_1d to melt ice !-- zqice_top_mlt = zqice_top_mlt + qstbif_1d !-- qstbif_1d = 0 !------------------------------------------------------ ziqf = MAX ( zzero , SIGN( zone , qstbif_1d(ji) - zqsn_mlt_rem ) ) zqice_top_mlt = ziqf * ( zqice_top_mlt + zqsn_mlt_rem ) & & + ( 1.0 - ziqf ) * ( zqice_top_mlt + qstbif_1d(ji) ) qstbif_1d(ji) = ziqf * ( qstbif_1d(ji) - zqsn_mlt_rem ) & & + ( 1.0 - ziqf ) * ( qstbif_1d(ji) - qstbif_1d(ji) ) !-- The contribution of the energy stored in brine pockets qstbif_1d to melt !-- ice is taking into account only when qstbif_1d is less than zqmax. !-- Otherwise, only the remaining energy coming from the melting snow !-- process is used zihq = MAX ( zzero , SIGN( zone , qstbif_1d(ji) - zqmax(ji) ) ) zqice_top_mlt = zihq * zqice_top_mlt & & + ( 1.0 - zihq ) * zqsn_mlt_rem qstbif_1d(ji) = zihq * qstbif_1d(ji) & & + ( 1.0 - zihq ) * zqstbif_old !--change in ice thickness due to melt at the top surface zdhictop(ji) = -zqice_top_mlt / xlic !--compute the volume formed after surface melting dvsbq_1d(ji) = zdhictop(ji) * ( 1.0 - frld_1d(ji) ) !------------------------------------------------------------------------- !-- A small variation at the surface also occurs because of sublimation !-- associated with the latent flux. If qla_ice_1d is negative, snow condensates at ! the surface. Otherwise, snow evaporates !----------------------------------------------------------------------- !----change in snow and ice thicknesses due to sublimation or evaporation zdhssub = parsub * ( qla_ice_1d(ji) / ( rhosn * xsn ) ) * rdt_ice zhsn = h_snow_1d(ji) - zdhssub zdhisub = MAX( zzero , -zhsn ) * rhosn/rhoic zdhictop(ji) = zdhictop(ji) - zdhisub h_snow_1d(ji) = MAX( zzero , zhsn ) !------------------------------------------------- !-- Update Internal temperature and qstbif_1d. !------------------------------------------- zihsn = MAX( zzero , SIGN( zone, -h_snow_1d(ji) ) ) tbif_1d(ji,1) = ( 1.0 - zihsn ) * tbif_1d(ji,1) + zihsn * tfu_1d(ji) !--change in snow internal temperature if snow has increased zihnf = MAX( zzero , SIGN( zone , h_snow_1d(ji) - zhsnw_old(ji) ) ) zdhsn = 1.0 - zhsnw_old(ji) / MAX( h_snow_1d(ji) , epsi20 ) zdtsn = zdhsn * ( sist_1d(ji) - tbif_1d(ji,1) ) tbif_1d(ji,1) = tbif_1d(ji,1) + z1midsn(ji) * zihnf * zdtsn !--energy created due to ice melting in the first ice layer zqnes = ( rt0_ice - tbif_1d(ji,2) ) * rcpic * ( h_ice_1d(ji) / 2. ) !--change in first ice layer internal temperature ziqr = MAX( zzero , SIGN( zone , qstbif_1d(ji) - zqnes ) ) zdtic = qstbif_1d(ji) / ( rcpic * ( h_ice_1d(ji) / 2. ) ) tbif_1d(ji,2) = ziqr * rt0_ice + ( 1 - ziqr ) * ( tbif_1d(ji,2) + zdtic ) !--update qstbif_1d qstbif_1d(ji) = ziqr * ( qstbif_1d(ji) - zqnes ) * swiqst !-- 9.2. Calculate bottom accretion-ablation and update qstbif_1d. ! Growth and melting at bottom ice surface are governed by ! -xlic * Dh = (Fcb - Fbot ) * Dt ! where Fbot is the net downward heat flux from ice to the ocean ! and Fcb is the conductive heat flux at the bottom surface !--------------------------------------------------------------------------- ztbot = ( 1.0 - zidsnic(ji) ) * tbif_1d(ji,3) + zidsnic(ji) * sist_1d(ji) !---computes conductive heat flux at bottom surface zfcbot = 4.0 * zkic(ji) * ( tfu_1d(ji) - ztbot ) & & / ( h_ice_1d(ji) + zidsnic(ji) * ( 3. * h_ice_1d(ji) & & + 4.0 * zkic(ji)/zksn(ji) * h_snow_1d(ji) ) ) !---computation of net energy needed for bottom melting/growing zqice_bot = ( zfcbot - ( fbif_1d(ji) + qlbbq_1d(ji) ) ) * rdt_ice zqstbif_bot = qstbif_1d(ji) !---switch to know if bottom surface melts ( = 1 ) or grows ( = 0 )occurs zibmlt = MAX( zzero , SIGN( zone , -zqice_bot ) ) !--particular case of melting (in the same way as the top surface) zqice_bot_mlt = zqice_bot zqstbif_old = zqstbif_bot ziqf = MAX ( zzero , SIGN( zone , qstbif_1d(ji) + zqice_bot_mlt ) ) zqice_bot_mlt = ziqf * ( zqice_bot_mlt + zqice_bot_mlt ) & & + ( 1.0 - ziqf ) * ( zqice_bot_mlt + qstbif_1d(ji) ) qstbif_1d(ji) = ziqf * ( qstbif_1d(ji) + zqice_bot_mlt ) & & + ( 1.0 - ziqf ) * ( qstbif_1d(ji) - qstbif_1d(ji) ) !-- The contribution of the energy stored in brine pockets qstbif_1d to melt !-- ice is taking into account only when qstbif_1d is less than zqmax. zihq = MAX ( zzero , SIGN( zone , qstbif_1d(ji) - zqmax(ji) ) ) zqice_bot_mlt = zihq * zqice_bot_mlt & & + ( 1.0 - zihq ) * zqice_bot qstbif_1d(ji) = zihq * qstbif_1d(ji) & & + ( 1.0 - zihq ) * zqstbif_old !---treatment of the case of melting/growing zqice_bot = zibmlt * ( zqice_bot_mlt - zqcmltb(ji) ) & & + ( 1.0 - zibmlt ) * ( zqice_bot - zqcmltb(ji) ) qstbif_1d(ji) = zibmlt * qstbif_1d(ji) & & + ( 1.0 - zibmlt ) * zqstbif_bot !--computes change in ice thickness due to melt or growth zdhicbot(ji) = zqice_bot / xlic !--limitation of bottom melting if so : hmelt maximum melting at bottom zdhicmlt = MAX( hmelt , zdhicbot(ji) ) !-- output part due to bottom melting only IF( zdhicmlt < 0.e0 ) rdvomif_1d(ji) = ( 1.0 - frld_1d(ji) ) * zdhicmlt !--energy after bottom melting/growing zqsup(ji) = ( 1.0 - frld_1d(ji) ) * xlic * ( zdhicmlt - zdhicbot(ji) ) !-- compute the new thickness and the newly formed volume after bottom melting/growing zdhicbot(ji) = zdhicmlt dvbbq_1d(ji) = ( 1.0 - frld_1d(ji) ) * zdhicbot(ji) ! 9.3. Updating ice thickness after top surface ablation ! and bottom surface accretion/ablation !--------------------------------------------------------------- zhicnew = h_ice_1d(ji) + zdhictop(ji) + zdhicbot(ji) ! ! 9.4. Case of total ablation (ice is gone but snow may be left) !------------------------------------------------------------------- zhsn = h_snow_1d(ji) zihgnew = 1.0 - MAX( zzero , SIGN( zone , -zhicnew ) ) zihsn = MAX( zzero , SIGN( zone , -zhsn ) ) !---convert zdhicm = ( 1.0 - zihgnew ) * ( zhicnew - qstbif_1d(ji) / xlic ) zdhsnm = ( 1.0 - zihsn ) * zdhicm * rhoic / rhosn !---updating new ice thickness and computing the newly formed ice mass zhicnew = zihgnew * zhicnew ztmp = ( 1.0 - frld_1d(ji) ) * ( zhicnew - h_ice_1d(ji) ) * rhoic rdm_ice_1d(ji) = rdm_ice_1d(ji) + ztmp !---heat content of the water provided to the ocean (referenced to rt0) ! use of rt0_ice is OK for melting ice; in the case of freezing, tfu_1d should be used. ! This is done in 9.5 section (see below) rdq_ice_1d(ji) = cpic * ztmp * ( rt0_ice - rt0 ) !---updating new snow thickness and computing the newly formed snow mass zhsnfi = zhsn + zdhsnm h_snow_1d(ji) = MAX( zzero , zhsnfi ) ztmp = ( 1.0 - frld_1d(ji) ) * ( h_snow_1d(ji) - zhsn ) * rhosn rdm_snw_1d(ji) = rdm_snw_1d(ji) + ztmp !---updating the heat content of the water provided to the ocean (referenced to rt0) rdq_snw_1d(ji) = rdq_snw_1d(ji) + cpic * ztmp * ( rt0_snow - rt0 ) !--remaining energy in case of total ablation zqocea(ji) = - ( zihsn * xlic * zdhicm + xlsn * ( zhsnfi - h_snow_1d(ji) ) ) * ( 1.0 - frld_1d(ji) ) qstbif_1d(ji) = zihgnew * qstbif_1d(ji) ! ! 9.5. Update internal temperature and ice thickness. !------------------------------------------------------- ! sist_1d(ji) = zihgnew * sist_1d(ji) + ( 1.0 - zihgnew ) * tfu_1d(ji) zidhb = MAX( zzero , SIGN( zone , - zdhicbot(ji) ) ) zc1 = - zhicnew * 0.5 zpc1 = MIN( 0.5 * zone , - h_ice_1d(ji) * 0.5 - zdhictop(ji) ) zc2 = - zhicnew zpc2 = zidhb * zc2 + ( 1.0 - zidhb ) * ( - h_ice_1d(ji) - zdhictop(ji) ) zp1 = MAX( zpc1 , zc1 ) zp2 = MAX( zpc2 , zc1 ) zep(ji) = tbif_1d(ji,2) ztb2 = 2.0 * ( - zp1 * tbif_1d(ji,2) & & + ( zp1 - zp2 ) * tbif_1d(ji,3) & & + ( zp2 - zc1 ) * tfu_1d(ji) ) / MAX( zhicnew , epsi20 ) tbif_1d(ji,2) = zihgnew * ztb2 + ( 1.0 - zihgnew ) * tfu_1d(ji) !--- zp1 = MIN( zpc1 , zc1 ) zp2 = MIN( zpc2 , zc1 ) zp1 = MAX( zc2 , zp1 ) ztb3 = 2.0 * ( ( 1.0 - zidhb ) * ( ( zc1 - zp2 ) * tbif_1d(ji,3) & & + ( zp2 - zc2 ) * tfu_1d(ji) ) & & + zidhb * ( ( zc1 - zp1 ) * zep(ji) & & + ( zp1 - zc2 ) * tbif_1d(ji,3)) ) / MAX( zhicnew , epsi20 ) tbif_1d(ji,3) = zihgnew * ztb3 + ( 1.0 - zihgnew ) * tfu_1d(ji) h_ice_1d(ji) = zhicnew ! update the ice heat content given to the ocean in freezing case ! (part due to difference between rt0_ice and tfu_1d) ztmp = ( 1. - zidhb ) * rhoic * dvbbq_1d(ji) rdq_ice_1d(ji) = rdq_ice_1d(ji) + cpic * ztmp * ( tfu_1d(ji) - rt0_ice ) END DO !---------------------------------------------------------------------------- ! 10. Surface accretion. ! The change of ice thickness after snow/ice formation is such that ! the interface between snow and ice is located at the same height ! as the ocean surface. It is given by (Fichefet and Morales Maqueda 1999) ! D(h_ice) = (- D(hsn)/alph) = [rhosn*hsn - (rau0 - rhoic)*hic] ! / [alph*rhosn+rau0 - rhoic] !---------------------------------------------------------------------------- ! DO ji = kideb , kiut !-- Computation of the change of ice thickness after snow-ice formation zdrmh = ( rhosn * h_snow_1d(ji) + ( rhoic - rau0 ) * h_ice_1d(ji) ) & & / ( alphs * rhosn + rau0 - rhoic ) zdrmh = MAX( zzero , zdrmh ) !--New ice and snow thicknesses Fichefet and Morales Maqueda (1999) zhicnew = MAX( h_ice_1d(ji) , h_ice_1d(ji) + zdrmh ) zhsnnew = MIN( h_snow_1d(ji) , h_snow_1d(ji) - alphs * zdrmh ) !---Compute new ice temperatures. snow temperature remains unchanged ! Lepparanta (1983): zihic = 1.0 - MAX( zzero , SIGN( zone , -zhicnew ) ) zquot = ( 1.0 - zihic ) & & + zihic * MIN( zone , h_ice_1d(ji) / MAX( zhicnew , epsi20 ) ) ztneq = alphs * cnscg * tbif_1d(ji,1) & & + ( 1.0 - alphs * ( rhosn/rhoic ) ) * tfu_1d(ji) zep(ji) = tbif_1d(ji,2) tbif_1d(ji,2) = ztneq - zquot * zquot * ( ztneq - tbif_1d(ji,2) ) tbif_1d(ji,3) = 2.0 * ztneq & & + zquot * ( tbif_1d(ji,3) + zep(ji) - 2.0 * ztneq ) - tbif_1d(ji,2) !--- Lepparanta (1983) (latent heat released during white ice formation ! goes to the ocean -for lateral ablation-) qldif_1d(ji) = qldif_1d(ji) + zdrmh * ( 1.0 - alphs * ( rhosn/rhoic ) ) * xlic * ( 1.0 - frld_1d(ji) ) !-- Changes in ice volume and ice mass Lepparanta (1983): dvnbq_1d(ji) = ( 1.0 - frld_1d(ji) ) * ( zhicnew - h_ice_1d(ji) ) dmgwi_1d(ji) = dmgwi_1d(ji) + ( 1.0 -frld_1d(ji) ) * ( h_snow_1d(ji) - zhsnnew ) * rhosn !--- volume change of ice and snow (used for ocean-ice freshwater flux computation) ztmp = ( 1.0 - frld_1d(ji) ) * ( zhicnew - h_ice_1d (ji) ) * rhoic rdm_ice_1d(ji) = rdm_ice_1d(ji) + ztmp rdq_ice_1d(ji) = rdq_ice_1d(ji) + cpic * ztmp * ( tfu_1d(ji) - rt0 ) !!gm BUG ?? snow ==> only needed for nn_ice_embd == 0 (standard levitating sea-ice) ztmp = ( 1.0 - frld_1d(ji) ) * ( zhsnnew - h_snow_1d(ji) ) * rhosn rdm_snw_1d(ji) = rdm_snw_1d(ji) + ztmp rdq_snw_1d(ji) = rdq_snw_1d(ji) + cpic * ztmp * ( rt0_snow - rt0 ) !--- Actualize new snow and ice thickness. h_snow_1d(ji) = zhsnnew h_ice_1d (ji) = zhicnew END DO !---------------------------------------------------- ! 11. Lateral ablation (Changes in sea/ice fraction) !---------------------------------------------------- DO ji = kideb , kiut zfrl_old(ji) = frld_1d(ji) zihic = 1.0 - MAX( zzero , SIGN( zone , -h_ice_1d(ji) ) ) zihsn = 1.0 - MAX( zzero , SIGN( zone , -h_snow_1d(ji) ) ) !--In the case of total ablation (all the ice ice has melted) frld = 1 frld_1d(ji) = ( 1.0 - zihic ) + zihic * zfrl_old(ji) !--Part of solar radiation absorbing inside the ice and going !--through the ocean fscbq_1d(ji) = ( 1.0 - zfrl_old(ji) ) * ( 1.0 - thcm_1d(ji) ) * fstbif_1d(ji) !--Total remaining energy after bottom melting/growing qfvbq_1d(ji) = zqsup(ji) + ( 1.0 - zihic ) * zqocea(ji) !--Updating of total heat from the ocean qldif_1d(ji) = qldif_1d(ji) + qfvbq_1d(ji) + ( 1.0 - zihic ) * fscbq_1d(ji) * rdt_ice !--Computation of total heat inside the snow/ice system zqice = h_snow_1d(ji) * xlsn + h_ice_1d(ji) * xlic zqicetot = ( 1.0 - frld_1d(ji) ) * zqice !--The concentration of ice is reduced (frld increases) if the heat !--exchange between ice and ocean is positive ziqf = MAX( zzero , SIGN( zone , zqicetot - qldif_1d(ji) ) ) zdfrl = qldif_1d(ji) / MAX( epsi20 , zqice ) frld_1d(ji) = ( 1.0 - ziqf ) & & + ziqf * ( frld_1d(ji) + MAX( zzero , zdfrl ) ) fltbif_1d(ji) = ( ( 1.0 - zfrl_old(ji) ) * qstbif_1d(ji) - zqicetot ) / rdt_ice !-- Opening of leads: Hakkinen & Mellor, 1992. zdfrl = - ( zdhictop(ji) + zdhicbot(ji) ) * hakspl * ( 1.0 - zfrl_old(ji) ) & & / MAX( epsi13 , h_ice_1d(ji) + h_snow_1d(ji) * rhosn/rhoic ) zfrld_1d(ji) = frld_1d(ji) + MAX( zzero , zdfrl ) !--Limitation of sea-ice fraction <= 1 zfrld_1d(ji) = ziqf * MIN( 0.99 * zone , zfrld_1d(ji) ) + ( 1 - ziqf ) !---Update surface and internal temperature and snow/ice thicknesses. sist_1d(ji) = sist_1d(ji) + ( 1.0 - ziqf ) * ( tfu_1d(ji) - sist_1d(ji) ) tbif_1d(ji,1) = tbif_1d(ji,1) + ( 1.0 - ziqf ) * ( tfu_1d(ji) - tbif_1d(ji,1) ) tbif_1d(ji,2) = tbif_1d(ji,2) + ( 1.0 - ziqf ) * ( tfu_1d(ji) - tbif_1d(ji,2) ) tbif_1d(ji,3) = tbif_1d(ji,3) + ( 1.0 - ziqf ) * ( tfu_1d(ji) - tbif_1d(ji,3) ) !--variation of ice volume and ice mass dvlbq_1d(ji) = zihic * ( zfrl_old(ji) - frld_1d(ji) ) * h_ice_1d(ji) ztmp = dvlbq_1d(ji) * rhoic rdm_ice_1d(ji) = rdm_ice_1d(ji) + ztmp !!gm !!gm This should be split in two parts: !!gm 1- heat required to bring sea-ice to tfu : this part should be added to the heat flux taken from the ocean !!gm cpic * ztmp * 0.5 * ( tbif_1d(ji,2) + tbif_1d(ji,3) - 2.* rt0_ice ) !!gm 2- heat content of lateral ablation referenced to rt0 : this part only put in rdq_ice_1d !!gm cpic * ztmp * ( rt0_ice - rt0 ) !!gm Currently we put all the heat in rdq_ice_1d rdq_ice_1d(ji) = rdq_ice_1d(ji) + cpic * ztmp * 0.5 * ( tbif_1d(ji,2) + tbif_1d(ji,3) - 2.* rt0 ) ! !--variation of snow volume and snow mass zdvsnvol = zihsn * ( zfrl_old(ji) - frld_1d(ji) ) * h_snow_1d(ji) ztmp = zdvsnvol * rhosn rdm_snw_1d(ji) = rdm_snw_1d(ji) + ztmp !!gm !!gm This should be split in two parts: !!gm 1- heat required to bring snow to tfu : this part should be added to the heat flux taken from the ocean !!gm cpic * ztmp * ( tbif_1d(ji,1) - rt0_snow ) !!gm 2- heat content of lateral ablation referenced to rt0 : this part only put in rdq_snw_1d !!gm cpic * ztmp * ( rt0_snow - rt0 ) !!gm Currently we put all the heat in rdq_snw_1d rdq_snw_1d(ji) = rdq_snw_1d(ji) + cpic * ztmp * ( tbif_1d(ji,1) - rt0 ) h_snow_1d(ji) = ziqf * h_snow_1d(ji) zdrfrl1 = ziqf * ( 1.0 - frld_1d(ji) ) / MAX( epsi20 , 1.0 - zfrld_1d(ji) ) zdrfrl2 = ziqf * ( 1.0 - zfrl_old(ji) ) / MAX( epsi20 , 1.0 - zfrld_1d(ji) ) h_snow_1d (ji) = zdrfrl1 * h_snow_1d(ji) h_ice_1d (ji) = zdrfrl1 * h_ice_1d(ji) qstbif_1d(ji) = zdrfrl2 * qstbif_1d(ji) frld_1d(ji) = zfrld_1d(ji) ! END DO ! CALL wrk_dealloc( jpij, ztsmlt, ztbif , zksn , zkic , zksndh , zfcsu , zfcsudt , zi0 , z1mi0 , zqmax ) CALL wrk_dealloc( jpij, zrcpdt, zts_old, zidsn , z1midsn , zidsnic, zfnet , zsprecip, zhsnw_old, zdhictop, zdhicbot ) CALL wrk_dealloc( jpij, zqsup , zqocea , zfrl_old, zfrld_1d, zep , zqcmlts, zqcmltb ) ! END SUBROUTINE lim_thd_zdf_2 #else !!---------------------------------------------------------------------- !! Default Option NO sea-ice model !!---------------------------------------------------------------------- CONTAINS SUBROUTINE lim_thd_zdf_2 ! Empty routine END SUBROUTINE lim_thd_zdf_2 #endif !!====================================================================== END MODULE limthd_zdf_2