| 1 | MODULE icethd_dh |
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| 2 | !!====================================================================== |
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| 3 | !! *** MODULE icethd_dh *** |
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| 4 | !! seaice : thermodynamic growth and melt |
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| 5 | !!====================================================================== |
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| 6 | !! History : ! 2003-05 (M. Vancoppenolle) Original code in 1D |
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| 7 | !! ! 2005-06 (M. Vancoppenolle) 3D version |
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| 8 | !! 4.0 ! 2018 (many people) SI3 [aka Sea Ice cube] |
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| 9 | !!---------------------------------------------------------------------- |
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| 10 | #if defined key_si3 |
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| 11 | !!---------------------------------------------------------------------- |
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| 12 | !! 'key_si3' SI3 sea-ice model |
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| 13 | !!---------------------------------------------------------------------- |
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| 14 | !! ice_thd_dh : vertical sea-ice growth and melt |
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| 15 | !!---------------------------------------------------------------------- |
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| 16 | USE dom_oce ! ocean space and time domain |
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| 17 | USE phycst ! physical constants |
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| 18 | USE ice ! sea-ice: variables |
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| 19 | USE ice1D ! sea-ice: thermodynamics variables |
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| 20 | USE icethd_sal ! sea-ice: salinity profiles |
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| 21 | USE icevar ! for CALL ice_var_snwblow |
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| 22 | ! |
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| 23 | USE in_out_manager ! I/O manager |
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| 24 | USE lib_mpp ! MPP library |
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| 25 | USE lib_fortran ! fortran utilities (glob_sum + no signed zero) |
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| 26 | |
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| 27 | IMPLICIT NONE |
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| 28 | PRIVATE |
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| 29 | |
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| 30 | PUBLIC ice_thd_dh ! called by ice_thd |
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| 31 | |
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| 32 | !!---------------------------------------------------------------------- |
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| 33 | !! NEMO/ICE 4.0 , NEMO Consortium (2018) |
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| 34 | !! $Id$ |
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| 35 | !! Software governed by the CeCILL license (see ./LICENSE) |
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| 36 | !!---------------------------------------------------------------------- |
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| 37 | CONTAINS |
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| 38 | |
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| 39 | SUBROUTINE ice_thd_dh |
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| 40 | !!------------------------------------------------------------------ |
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| 41 | !! *** ROUTINE ice_thd_dh *** |
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| 42 | !! |
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| 43 | !! ** Purpose : compute ice and snow thickness changes due to growth/melting |
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| 44 | !! |
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| 45 | !! ** Method : Ice/Snow surface melting arises from imbalance in surface fluxes |
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| 46 | !! Bottom accretion/ablation arises from flux budget |
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| 47 | !! Snow thickness can increase by precipitation and decrease by sublimation |
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| 48 | !! If snow load excesses Archmiede limit, snow-ice is formed by |
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| 49 | !! the flooding of sea-water in the snow |
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| 50 | !! |
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| 51 | !! - Compute available flux of heat for surface ablation |
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| 52 | !! - Compute snow and sea ice enthalpies |
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| 53 | !! - Surface ablation and sublimation |
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| 54 | !! - Bottom accretion/ablation |
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| 55 | !! - Snow ice formation |
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| 56 | !! |
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| 57 | !! ** Note : h=max(0,h+dh) are often used to ensure positivity of h. |
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| 58 | !! very small negative values can occur otherwise (e.g. -1.e-20) |
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| 59 | !! |
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| 60 | !! References : Bitz and Lipscomb, 1999, J. Geophys. Res. |
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| 61 | !! Fichefet T. and M. Maqueda 1997, J. Geophys. Res., 102(C6), 12609-12646 |
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| 62 | !! Vancoppenolle, Fichefet and Bitz, 2005, Geophys. Res. Let. |
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| 63 | !! Vancoppenolle et al.,2009, Ocean Modelling |
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| 64 | !!------------------------------------------------------------------ |
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| 65 | INTEGER :: ji, jk ! dummy loop indices |
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| 66 | INTEGER :: iter ! local integer |
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| 67 | |
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| 68 | REAL(wp) :: ztmelts ! local scalar |
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| 69 | REAL(wp) :: zdum |
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| 70 | REAL(wp) :: zfracs ! fractionation coefficient for bottom salt entrapment |
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| 71 | REAL(wp) :: zswi1 ! switch for computation of bottom salinity |
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| 72 | REAL(wp) :: zswi12 ! switch for computation of bottom salinity |
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| 73 | REAL(wp) :: zswi2 ! switch for computation of bottom salinity |
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| 74 | REAL(wp) :: zgrr ! bottom growth rate |
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| 75 | REAL(wp) :: zt_i_new ! bottom formation temperature |
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| 76 | REAL(wp) :: z1_rho ! 1/(rhos+rau0-rhoi) |
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| 77 | |
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| 78 | REAL(wp) :: zQm ! enthalpy exchanged with the ocean (J/m2), >0 towards the ocean |
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| 79 | REAL(wp) :: zEi ! specific enthalpy of sea ice (J/kg) |
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| 80 | REAL(wp) :: zEw ! specific enthalpy of exchanged water (J/kg) |
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| 81 | REAL(wp) :: zdE ! specific enthalpy difference (J/kg) |
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| 82 | REAL(wp) :: zfmdt ! exchange mass flux x time step (J/m2), >0 towards the ocean |
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| 83 | |
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| 84 | REAL(wp), DIMENSION(jpij) :: zq_top ! heat for surface ablation (J.m-2) |
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| 85 | REAL(wp), DIMENSION(jpij) :: zq_bot ! heat for bottom ablation (J.m-2) |
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| 86 | REAL(wp), DIMENSION(jpij) :: zq_rema ! remaining heat at the end of the routine (J.m-2) |
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| 87 | REAL(wp), DIMENSION(jpij) :: zf_tt ! Heat budget to determine melting or freezing(W.m-2) |
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| 88 | REAL(wp), DIMENSION(jpij) :: zevap_rema ! remaining mass flux from sublimation (kg.m-2) |
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| 89 | REAL(wp), DIMENSION(jpij) :: zdeltah |
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| 90 | REAL(wp), DIMENSION(jpij) :: zsnw ! distribution of snow after wind blowing |
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| 91 | |
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| 92 | INTEGER , DIMENSION(jpij,nlay_i) :: icount ! number of layers vanishing by melting |
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| 93 | REAL(wp), DIMENSION(jpij,0:nlay_i+1) :: zh_i ! ice layer thickness (m) |
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| 94 | REAL(wp), DIMENSION(jpij,0:nlay_s ) :: zh_s ! snw layer thickness (m) |
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| 95 | REAL(wp), DIMENSION(jpij,0:nlay_s ) :: ze_s ! snw layer enthalpy (J.m-3) |
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| 96 | |
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| 97 | REAL(wp) :: zswitch_sal |
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| 98 | |
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| 99 | INTEGER :: num_iter_max ! Heat conservation |
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| 100 | !!------------------------------------------------------------------ |
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| 101 | |
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| 102 | ! Discriminate between time varying salinity and constant |
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| 103 | SELECT CASE( nn_icesal ) ! varying salinity or not |
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| 104 | CASE( 1 , 3 ) ; zswitch_sal = 0._wp ! prescribed salinity profile |
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| 105 | CASE( 2 ) ; zswitch_sal = 1._wp ! varying salinity profile |
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| 106 | END SELECT |
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| 107 | |
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| 108 | ! initialize ice layer thicknesses and enthalpies |
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| 109 | eh_i_old(1:npti,0:nlay_i+1) = 0._wp |
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| 110 | h_i_old (1:npti,0:nlay_i+1) = 0._wp |
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| 111 | zh_i (1:npti,0:nlay_i+1) = 0._wp |
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| 112 | DO jk = 1, nlay_i |
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| 113 | DO ji = 1, npti |
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| 114 | eh_i_old(ji,jk) = h_i_1d(ji) * r1_nlay_i * e_i_1d(ji,jk) |
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| 115 | h_i_old (ji,jk) = h_i_1d(ji) * r1_nlay_i |
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| 116 | zh_i (ji,jk) = h_i_1d(ji) * r1_nlay_i |
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| 117 | END DO |
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| 118 | END DO |
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| 119 | ! |
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| 120 | ! initialize snw layer thicknesses and enthalpies |
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| 121 | zh_s(1:npti,0) = 0._wp |
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| 122 | ze_s(1:npti,0) = 0._wp |
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| 123 | DO jk = 1, nlay_s |
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| 124 | DO ji = 1, npti |
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| 125 | zh_s(ji,jk) = h_s_1d(ji) * r1_nlay_s |
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| 126 | ze_s(ji,jk) = e_s_1d(ji,jk) |
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| 127 | END DO |
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| 128 | END DO |
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| 129 | ! |
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| 130 | ! ! ============================================== ! |
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| 131 | ! ! Available heat for surface and bottom ablation ! |
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| 132 | ! ! ============================================== ! |
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| 133 | ! |
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| 134 | IF( ln_cndflx .AND. .NOT.ln_cndemulate ) THEN |
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| 135 | ! |
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| 136 | DO ji = 1, npti |
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| 137 | zq_top(ji) = MAX( 0._wp, qml_ice_1d(ji) * rdt_ice ) |
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| 138 | END DO |
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| 139 | ! |
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| 140 | ELSE |
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| 141 | ! |
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| 142 | DO ji = 1, npti |
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| 143 | zdum = qns_ice_1d(ji) + qsr_ice_1d(ji) - qtr_ice_top_1d(ji) - qcn_ice_top_1d(ji) |
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| 144 | qml_ice_1d(ji) = zdum * MAX( 0._wp , SIGN( 1._wp, t_su_1d(ji) - rt0 ) ) |
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| 145 | zq_top(ji) = MAX( 0._wp, qml_ice_1d(ji) * rdt_ice ) |
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| 146 | END DO |
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| 147 | ! |
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| 148 | ENDIF |
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| 149 | ! |
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| 150 | DO ji = 1, npti |
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| 151 | zf_tt(ji) = qcn_ice_bot_1d(ji) + qsb_ice_bot_1d(ji) + fhld_1d(ji) + qtr_ice_bot_1d(ji) * frq_m_1d(ji) |
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| 152 | zq_bot(ji) = MAX( 0._wp, zf_tt(ji) * rdt_ice ) |
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| 153 | END DO |
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| 154 | |
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| 155 | ! ! ============ ! |
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| 156 | ! ! Snow ! |
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| 157 | ! ! ============ ! |
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| 158 | ! |
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| 159 | ! Internal melting |
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| 160 | ! ---------------- |
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| 161 | ! IF snow temperature is above freezing point, THEN snow melts (should not happen but sometimes it does) |
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| 162 | DO jk = 1, nlay_s |
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| 163 | DO ji = 1, npti |
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| 164 | IF( t_s_1d(ji,jk) > rt0 ) THEN |
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| 165 | hfx_res_1d (ji) = hfx_res_1d (ji) - ze_s(ji,jk) * zh_s(ji,jk) * a_i_1d(ji) * r1_rdtice ! heat flux to the ocean [W.m-2], < 0 |
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| 166 | wfx_snw_sum_1d(ji) = wfx_snw_sum_1d(ji) + rhos * zh_s(ji,jk) * a_i_1d(ji) * r1_rdtice ! mass flux |
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| 167 | ! updates |
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| 168 | dh_s_mlt(ji) = dh_s_mlt(ji) - zh_s(ji,jk) |
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| 169 | h_s_1d (ji) = MAX( 0._wp, h_s_1d (ji) - zh_s(ji,jk) ) |
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| 170 | zh_s (ji,jk) = 0._wp |
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| 171 | ze_s (ji,jk) = 0._wp |
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| 172 | END IF |
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| 173 | END DO |
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| 174 | END DO |
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| 175 | |
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| 176 | ! Snow precipitation |
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| 177 | !------------------- |
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| 178 | CALL ice_var_snwblow( 1._wp - at_i_1d(1:npti), zsnw(1:npti) ) ! snow distribution over ice after wind blowing |
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| 179 | |
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| 180 | DO ji = 1, npti |
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| 181 | IF( sprecip_1d(ji) > 0._wp ) THEN |
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| 182 | zh_s(ji,0) = zsnw(ji) * sprecip_1d(ji) * rdt_ice * r1_rhos / at_i_1d(ji) ! thickness of precip |
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| 183 | ze_s(ji,0) = MAX( 0._wp, - qprec_ice_1d(ji) ) ! enthalpy of the precip (>0, J.m-3) |
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| 184 | ! |
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| 185 | hfx_spr_1d(ji) = hfx_spr_1d(ji) + ze_s(ji,0) * zh_s(ji,0) * a_i_1d(ji) * r1_rdtice ! heat flux from snow precip (>0, W.m-2) |
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| 186 | wfx_spr_1d(ji) = wfx_spr_1d(ji) - rhos * zh_s(ji,0) * a_i_1d(ji) * r1_rdtice ! mass flux, <0 |
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| 187 | ! |
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| 188 | ! update thickness |
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| 189 | h_s_1d(ji) = h_s_1d(ji) + zh_s(ji,0) |
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| 190 | ENDIF |
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| 191 | END DO |
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| 192 | |
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| 193 | ! Snow melting |
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| 194 | ! ------------ |
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| 195 | ! If heat still available (zq_top > 0) |
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| 196 | ! then all snw precip has been melted and we need to melt more snow |
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| 197 | DO jk = 0, nlay_s |
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| 198 | DO ji = 1, npti |
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| 199 | IF( zh_s(ji,jk) > 0._wp .AND. zq_top(ji) > 0._wp ) THEN |
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| 200 | ! |
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| 201 | rswitch = MAX( 0._wp , SIGN( 1._wp , ze_s(ji,jk) - epsi20 ) ) |
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| 202 | zdum = - rswitch * zq_top(ji) / MAX( ze_s(ji,jk), epsi20 ) ! thickness change |
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| 203 | zdum = MAX( zdum , - zh_s(ji,jk) ) ! bound melting |
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| 204 | |
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| 205 | hfx_snw_1d (ji) = hfx_snw_1d (ji) - ze_s(ji,jk) * zdum * a_i_1d(ji) * r1_rdtice ! heat used to melt snow(W.m-2, >0) |
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| 206 | wfx_snw_sum_1d(ji) = wfx_snw_sum_1d(ji) - rhos * zdum * a_i_1d(ji) * r1_rdtice ! snow melting only = water into the ocean |
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| 207 | |
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| 208 | ! updates available heat + thickness |
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| 209 | dh_s_mlt(ji) = dh_s_mlt(ji) + zdum |
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| 210 | zq_top (ji) = MAX( 0._wp , zq_top (ji) + zdum * ze_s(ji,jk) ) |
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| 211 | h_s_1d (ji) = MAX( 0._wp , h_s_1d (ji) + zdum ) |
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| 212 | zh_s (ji,jk) = MAX( 0._wp , zh_s (ji,jk) + zdum ) |
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| 213 | !!$ IF( zh_s(ji,jk) == 0._wp ) ze_s(ji,jk) = 0._wp |
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| 214 | ! |
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| 215 | ENDIF |
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| 216 | END DO |
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| 217 | END DO |
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| 218 | |
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| 219 | ! Snow sublimation |
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| 220 | !----------------- |
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| 221 | ! qla_ice is always >=0 (upwards), heat goes to the atmosphere, therefore snow sublimates |
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| 222 | ! comment: not counted in mass/heat exchange in iceupdate.F90 since this is an exchange with atm. (not ocean) |
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| 223 | zdeltah (1:npti) = 0._wp ! total snow thickness that sublimates, < 0 |
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| 224 | zevap_rema(1:npti) = 0._wp |
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| 225 | DO ji = 1, npti |
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| 226 | zdeltah (ji) = MAX( - evap_ice_1d(ji) * r1_rhos * rdt_ice, - h_s_1d(ji) ) ! amount of snw that sublimates, < 0 |
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| 227 | zevap_rema(ji) = evap_ice_1d(ji) * rdt_ice + zdeltah(ji) * rhos ! remaining evap in kg.m-2 (used for ice sublimation later on) |
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| 228 | END DO |
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| 229 | |
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| 230 | DO jk = 0, nlay_s |
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| 231 | DO ji = 1, npti |
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| 232 | zdum = MAX( -zh_s(ji,jk), zdeltah(ji) ) ! snow layer thickness that sublimates, < 0 |
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| 233 | ! |
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| 234 | hfx_sub_1d (ji) = hfx_sub_1d (ji) + ze_s(ji,jk) * zdum * a_i_1d(ji) * r1_rdtice ! Heat flux of snw that sublimates [W.m-2], < 0 |
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| 235 | wfx_snw_sub_1d(ji) = wfx_snw_sub_1d(ji) - rhos * zdum * a_i_1d(ji) * r1_rdtice ! Mass flux by sublimation |
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| 236 | |
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| 237 | ! update thickness |
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| 238 | h_s_1d(ji) = MAX( 0._wp , h_s_1d(ji) + zdum ) |
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| 239 | zh_s (ji,jk) = MAX( 0._wp , zh_s (ji,jk) + zdum ) |
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| 240 | !!$ IF( zh_s(ji,jk) == 0._wp ) ze_s(ji,jk) = 0._wp |
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| 241 | |
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| 242 | ! update sublimation left |
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| 243 | zdeltah(ji) = MIN( zdeltah(ji) - zdum, 0._wp ) |
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| 244 | END DO |
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| 245 | END DO |
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| 246 | |
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| 247 | ! |
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| 248 | ! ! ============ ! |
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| 249 | ! ! Ice ! |
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| 250 | ! ! ============ ! |
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| 251 | |
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| 252 | ! Surface ice melting |
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| 253 | !-------------------- |
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| 254 | DO jk = 1, nlay_i |
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| 255 | DO ji = 1, npti |
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| 256 | ztmelts = - rTmlt * sz_i_1d(ji,jk) ! Melting point of layer k [C] |
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| 257 | |
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| 258 | IF( t_i_1d(ji,jk) >= (ztmelts+rt0) ) THEN !-- Internal melting |
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| 259 | |
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| 260 | zEi = - e_i_1d(ji,jk) * r1_rhoi ! Specific enthalpy of layer k [J/kg, <0] |
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| 261 | zdE = 0._wp ! Specific enthalpy difference (J/kg, <0) |
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| 262 | ! set up at 0 since no energy is needed to melt water...(it is already melted) |
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| 263 | zdum = MIN( 0._wp , - zh_i(ji,jk) ) ! internal melting occurs when the internal temperature is above freezing |
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| 264 | ! this should normally not happen, but sometimes, heat diffusion leads to this |
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| 265 | zfmdt = - zdum * rhoi ! Recompute mass flux [kg/m2, >0] |
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| 266 | ! |
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| 267 | dh_i_itm(ji) = dh_i_itm(ji) + zdum ! Cumulate internal melting |
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| 268 | ! |
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| 269 | hfx_res_1d(ji) = hfx_res_1d(ji) + zEi * zfmdt * a_i_1d(ji) * r1_rdtice ! Heat flux to the ocean [W.m-2], <0 |
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| 270 | ! ice enthalpy zEi is "sent" to the ocean |
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| 271 | wfx_res_1d(ji) = wfx_res_1d(ji) - rhoi * zdum * a_i_1d(ji) * r1_rdtice ! Mass flux |
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| 272 | sfx_res_1d(ji) = sfx_res_1d(ji) - rhoi * zdum * s_i_1d(ji) * a_i_1d(ji) * r1_rdtice ! Salt flux |
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| 273 | ! using s_i_1d and not sz_i_1d(jk) is ok |
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| 274 | ELSE !-- Surface melting |
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| 275 | |
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| 276 | zEi = - e_i_1d(ji,jk) * r1_rhoi ! Specific enthalpy of layer k [J/kg, <0] |
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| 277 | zEw = rcp * ztmelts ! Specific enthalpy of resulting meltwater [J/kg, <0] |
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| 278 | zdE = zEi - zEw ! Specific enthalpy difference < 0 |
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| 279 | |
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| 280 | zfmdt = - zq_top(ji) / zdE ! Mass flux to the ocean [kg/m2, >0] |
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| 281 | |
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| 282 | zdum = - zfmdt * r1_rhoi ! Melt of layer jk [m, <0] |
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| 283 | |
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| 284 | zdum = MIN( 0._wp , MAX( zdum , - zh_i(ji,jk) ) ) ! Melt of layer jk cannot exceed the layer thickness [m, <0] |
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| 285 | |
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| 286 | zq_top(ji) = MAX( 0._wp , zq_top(ji) - zdum * rhoi * zdE ) ! update available heat |
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| 287 | |
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| 288 | dh_i_sum(ji) = dh_i_sum(ji) + zdum ! Cumulate surface melt |
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| 289 | |
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| 290 | zfmdt = - rhoi * zdum ! Recompute mass flux [kg/m2, >0] |
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| 291 | |
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| 292 | zQm = zfmdt * zEw ! Energy of the melt water sent to the ocean [J/m2, <0] |
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| 293 | |
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| 294 | hfx_thd_1d(ji) = hfx_thd_1d(ji) + zEw * zfmdt * a_i_1d(ji) * r1_rdtice ! Heat flux [W.m-2], < 0 |
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| 295 | hfx_sum_1d(ji) = hfx_sum_1d(ji) - zdE * zfmdt * a_i_1d(ji) * r1_rdtice ! Heat flux used in this process [W.m-2], > 0 |
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| 296 | wfx_sum_1d(ji) = wfx_sum_1d(ji) - rhoi * zdum * a_i_1d(ji) * r1_rdtice ! Mass flux |
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| 297 | sfx_sum_1d(ji) = sfx_sum_1d(ji) - rhoi * zdum * s_i_1d(ji) * a_i_1d(ji) * r1_rdtice ! Salt flux >0 |
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| 298 | ! using s_i_1d and not sz_i_1d(jk) is ok) |
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| 299 | END IF |
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| 300 | ! update thickness |
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| 301 | zh_i(ji,jk) = MAX( 0._wp, zh_i(ji,jk) + zdum ) |
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| 302 | h_i_1d(ji) = MAX( 0._wp, h_i_1d(ji) + zdum ) |
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| 303 | ! |
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| 304 | ! update heat content (J.m-2) and layer thickness |
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| 305 | eh_i_old(ji,jk) = eh_i_old(ji,jk) + zdum * e_i_1d(ji,jk) |
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| 306 | h_i_old (ji,jk) = h_i_old (ji,jk) + zdum |
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| 307 | ! |
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| 308 | ! |
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| 309 | ! Ice sublimation |
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| 310 | ! --------------- |
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| 311 | zdum = MAX( - zh_i(ji,jk) , - zevap_rema(ji) * r1_rhoi ) |
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| 312 | ! |
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| 313 | hfx_sub_1d(ji) = hfx_sub_1d(ji) + e_i_1d(ji,jk) * zdum * a_i_1d(ji) * r1_rdtice ! Heat flux [W.m-2], < 0 |
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| 314 | wfx_ice_sub_1d(ji) = wfx_ice_sub_1d(ji) - rhoi * zdum * a_i_1d(ji) * r1_rdtice ! Mass flux > 0 |
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| 315 | sfx_sub_1d(ji) = sfx_sub_1d(ji) - rhoi * zdum * s_i_1d(ji) * a_i_1d(ji) * r1_rdtice ! Salt flux >0 |
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| 316 | ! clem: flux is sent to the ocean for simplicity |
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| 317 | ! but salt should remain in the ice except |
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| 318 | ! if all ice is melted. => must be corrected |
|---|
| 319 | ! update remaining mass flux and thickness |
|---|
| 320 | zevap_rema(ji) = zevap_rema(ji) + zdum * rhoi |
|---|
| 321 | zh_i(ji,jk) = MAX( 0._wp, zh_i(ji,jk) + zdum ) |
|---|
| 322 | h_i_1d(ji) = MAX( 0._wp, h_i_1d(ji) + zdum ) |
|---|
| 323 | dh_i_sub(ji) = dh_i_sub(ji) + zdum |
|---|
| 324 | |
|---|
| 325 | ! update heat content (J.m-2) and layer thickness |
|---|
| 326 | eh_i_old(ji,jk) = eh_i_old(ji,jk) + zdum * e_i_1d(ji,jk) |
|---|
| 327 | h_i_old (ji,jk) = h_i_old (ji,jk) + zdum |
|---|
| 328 | |
|---|
| 329 | ! record which layers have disappeared (for bottom melting) |
|---|
| 330 | ! => icount=0 : no layer has vanished |
|---|
| 331 | ! => icount=5 : 5 layers have vanished |
|---|
| 332 | rswitch = MAX( 0._wp , SIGN( 1._wp , - zh_i(ji,jk) ) ) |
|---|
| 333 | icount(ji,jk) = NINT( rswitch ) |
|---|
| 334 | |
|---|
| 335 | END DO |
|---|
| 336 | END DO |
|---|
| 337 | |
|---|
| 338 | ! remaining "potential" evap is sent to ocean |
|---|
| 339 | DO ji = 1, npti |
|---|
| 340 | wfx_err_sub_1d(ji) = wfx_err_sub_1d(ji) - zevap_rema(ji) * a_i_1d(ji) * r1_rdtice ! <=0 (net evap for the ocean in kg.m-2.s-1) |
|---|
| 341 | END DO |
|---|
| 342 | |
|---|
| 343 | |
|---|
| 344 | ! Ice Basal growth |
|---|
| 345 | !------------------ |
|---|
| 346 | ! Basal growth is driven by heat imbalance at the ice-ocean interface, |
|---|
| 347 | ! between the inner conductive flux (qcn_ice_bot), from the open water heat flux |
|---|
| 348 | ! (fhld) and the sensible ice-ocean flux (qsb_ice_bot). |
|---|
| 349 | ! qcn_ice_bot is positive downwards. qsb_ice_bot and fhld are positive to the ice |
|---|
| 350 | |
|---|
| 351 | ! If salinity varies in time, an iterative procedure is required, because |
|---|
| 352 | ! the involved quantities are inter-dependent. |
|---|
| 353 | ! Basal growth (dh_i_bog) depends upon new ice specific enthalpy (zEi), |
|---|
| 354 | ! which depends on forming ice salinity (s_i_new), which depends on dh/dt (dh_i_bog) |
|---|
| 355 | ! -> need for an iterative procedure, which converges quickly |
|---|
| 356 | |
|---|
| 357 | num_iter_max = 1 |
|---|
| 358 | IF( nn_icesal == 2 ) num_iter_max = 5 ! salinity varying in time |
|---|
| 359 | |
|---|
| 360 | DO ji = 1, npti |
|---|
| 361 | IF( zf_tt(ji) < 0._wp ) THEN |
|---|
| 362 | DO iter = 1, num_iter_max ! iterations |
|---|
| 363 | |
|---|
| 364 | ! New bottom ice salinity (Cox & Weeks, JGR88 ) |
|---|
| 365 | !--- zswi1 if dh/dt < 2.0e-8 |
|---|
| 366 | !--- zswi12 if 2.0e-8 < dh/dt < 3.6e-7 |
|---|
| 367 | !--- zswi2 if dh/dt > 3.6e-7 |
|---|
| 368 | zgrr = MIN( 1.0e-3, MAX ( dh_i_bog(ji) * r1_rdtice , epsi10 ) ) |
|---|
| 369 | zswi2 = MAX( 0._wp , SIGN( 1._wp , zgrr - 3.6e-7 ) ) |
|---|
| 370 | zswi12 = MAX( 0._wp , SIGN( 1._wp , zgrr - 2.0e-8 ) ) * ( 1.0 - zswi2 ) |
|---|
| 371 | zswi1 = 1. - zswi2 * zswi12 |
|---|
| 372 | zfracs = MIN( zswi1 * 0.12 + zswi12 * ( 0.8925 + 0.0568 * LOG( 100.0 * zgrr ) ) & |
|---|
| 373 | & + zswi2 * 0.26 / ( 0.26 + 0.74 * EXP ( - 724300.0 * zgrr ) ) , 0.5 ) |
|---|
| 374 | |
|---|
| 375 | s_i_new(ji) = zswitch_sal * zfracs * sss_1d(ji) + ( 1. - zswitch_sal ) * s_i_1d(ji) ! New ice salinity |
|---|
| 376 | |
|---|
| 377 | ztmelts = - rTmlt * s_i_new(ji) ! New ice melting point (C) |
|---|
| 378 | |
|---|
| 379 | zt_i_new = zswitch_sal * t_bo_1d(ji) + ( 1. - zswitch_sal) * t_i_1d(ji, nlay_i) |
|---|
| 380 | |
|---|
| 381 | zEi = rcpi * ( zt_i_new - (ztmelts+rt0) ) & ! Specific enthalpy of forming ice (J/kg, <0) |
|---|
| 382 | & - rLfus * ( 1.0 - ztmelts / ( MIN( zt_i_new - rt0, -epsi10 ) ) ) + rcp * ztmelts |
|---|
| 383 | |
|---|
| 384 | zEw = rcp * ( t_bo_1d(ji) - rt0 ) ! Specific enthalpy of seawater (J/kg, < 0) |
|---|
| 385 | |
|---|
| 386 | zdE = zEi - zEw ! Specific enthalpy difference (J/kg, <0) |
|---|
| 387 | |
|---|
| 388 | dh_i_bog(ji) = rdt_ice * MAX( 0._wp , zf_tt(ji) / ( zdE * rhoi ) ) |
|---|
| 389 | |
|---|
| 390 | END DO |
|---|
| 391 | ! Contribution to Energy and Salt Fluxes |
|---|
| 392 | zfmdt = - rhoi * dh_i_bog(ji) ! Mass flux x time step (kg/m2, < 0) |
|---|
| 393 | |
|---|
| 394 | hfx_thd_1d(ji) = hfx_thd_1d(ji) + zEw * zfmdt * a_i_1d(ji) * r1_rdtice ! Heat flux to the ocean [W.m-2], >0 |
|---|
| 395 | hfx_bog_1d(ji) = hfx_bog_1d(ji) - zdE * zfmdt * a_i_1d(ji) * r1_rdtice ! Heat flux used in this process [W.m-2], <0 |
|---|
| 396 | wfx_bog_1d(ji) = wfx_bog_1d(ji) - rhoi * dh_i_bog(ji) * a_i_1d(ji) * r1_rdtice ! Mass flux, <0 |
|---|
| 397 | sfx_bog_1d(ji) = sfx_bog_1d(ji) - rhoi * dh_i_bog(ji) * s_i_new(ji) * a_i_1d(ji) * r1_rdtice ! Salt flux, <0 |
|---|
| 398 | |
|---|
| 399 | ! update thickness |
|---|
| 400 | zh_i(ji,nlay_i+1) = zh_i(ji,nlay_i+1) + dh_i_bog(ji) |
|---|
| 401 | h_i_1d(ji) = h_i_1d(ji) + dh_i_bog(ji) |
|---|
| 402 | |
|---|
| 403 | ! update heat content (J.m-2) and layer thickness |
|---|
| 404 | eh_i_old(ji,nlay_i+1) = eh_i_old(ji,nlay_i+1) + dh_i_bog(ji) * (-zEi * rhoi) |
|---|
| 405 | h_i_old (ji,nlay_i+1) = h_i_old (ji,nlay_i+1) + dh_i_bog(ji) |
|---|
| 406 | |
|---|
| 407 | ENDIF |
|---|
| 408 | |
|---|
| 409 | END DO |
|---|
| 410 | |
|---|
| 411 | ! Ice Basal melt |
|---|
| 412 | !--------------- |
|---|
| 413 | DO jk = nlay_i, 1, -1 |
|---|
| 414 | DO ji = 1, npti |
|---|
| 415 | IF( zf_tt(ji) > 0._wp .AND. jk > icount(ji,jk) ) THEN ! do not calculate where layer has already disappeared by surface melting |
|---|
| 416 | |
|---|
| 417 | ztmelts = - rTmlt * sz_i_1d(ji,jk) ! Melting point of layer jk (C) |
|---|
| 418 | |
|---|
| 419 | IF( t_i_1d(ji,jk) >= (ztmelts+rt0) ) THEN !-- Internal melting |
|---|
| 420 | |
|---|
| 421 | zEi = - e_i_1d(ji,jk) * r1_rhoi ! Specific enthalpy of melting ice (J/kg, <0) |
|---|
| 422 | zdE = 0._wp ! Specific enthalpy difference (J/kg, <0) |
|---|
| 423 | ! set up at 0 since no energy is needed to melt water...(it is already melted) |
|---|
| 424 | zdum = MIN( 0._wp , - zh_i(ji,jk) ) ! internal melting occurs when the internal temperature is above freezing |
|---|
| 425 | ! this should normally not happen, but sometimes, heat diffusion leads to this |
|---|
| 426 | dh_i_itm (ji) = dh_i_itm(ji) + zdum |
|---|
| 427 | ! |
|---|
| 428 | zfmdt = - zdum * rhoi ! Mass flux x time step > 0 |
|---|
| 429 | ! |
|---|
| 430 | hfx_res_1d(ji) = hfx_res_1d(ji) + zEi * zfmdt * a_i_1d(ji) * r1_rdtice ! Heat flux to the ocean [W.m-2], <0 |
|---|
| 431 | ! ice enthalpy zEi is "sent" to the ocean |
|---|
| 432 | wfx_res_1d(ji) = wfx_res_1d(ji) - rhoi * zdum * a_i_1d(ji) * r1_rdtice ! Mass flux |
|---|
| 433 | sfx_res_1d(ji) = sfx_res_1d(ji) - rhoi * zdum * s_i_1d(ji) * a_i_1d(ji) * r1_rdtice ! Salt flux |
|---|
| 434 | ! using s_i_1d and not sz_i_1d(jk) is ok |
|---|
| 435 | ELSE !-- Basal melting |
|---|
| 436 | |
|---|
| 437 | zEi = - e_i_1d(ji,jk) * r1_rhoi ! Specific enthalpy of melting ice (J/kg, <0) |
|---|
| 438 | zEw = rcp * ztmelts ! Specific enthalpy of meltwater (J/kg, <0) |
|---|
| 439 | zdE = zEi - zEw ! Specific enthalpy difference (J/kg, <0) |
|---|
| 440 | |
|---|
| 441 | zfmdt = - zq_bot(ji) / zdE ! Mass flux x time step (kg/m2, >0) |
|---|
| 442 | |
|---|
| 443 | zdum = - zfmdt * r1_rhoi ! Gross thickness change |
|---|
| 444 | |
|---|
| 445 | zdum = MIN( 0._wp , MAX( zdum, - zh_i(ji,jk) ) ) ! bound thickness change |
|---|
| 446 | |
|---|
| 447 | zq_bot(ji) = MAX( 0._wp , zq_bot(ji) - zdum * rhoi * zdE ) ! update available heat. MAX is necessary for roundup errors |
|---|
| 448 | |
|---|
| 449 | dh_i_bom(ji) = dh_i_bom(ji) + zdum ! Update basal melt |
|---|
| 450 | |
|---|
| 451 | zfmdt = - zdum * rhoi ! Mass flux x time step > 0 |
|---|
| 452 | |
|---|
| 453 | zQm = zfmdt * zEw ! Heat exchanged with ocean |
|---|
| 454 | |
|---|
| 455 | hfx_thd_1d(ji) = hfx_thd_1d(ji) + zEw * zfmdt * a_i_1d(ji) * r1_rdtice ! Heat flux to the ocean [W.m-2], <0 |
|---|
| 456 | hfx_bom_1d(ji) = hfx_bom_1d(ji) - zdE * zfmdt * a_i_1d(ji) * r1_rdtice ! Heat used in this process [W.m-2], >0 |
|---|
| 457 | wfx_bom_1d(ji) = wfx_bom_1d(ji) - rhoi * zdum * a_i_1d(ji) * r1_rdtice ! Mass flux |
|---|
| 458 | sfx_bom_1d(ji) = sfx_bom_1d(ji) - rhoi * zdum * s_i_1d(ji) * a_i_1d(ji) * r1_rdtice ! Salt flux |
|---|
| 459 | ! using s_i_1d and not sz_i_1d(jk) is ok |
|---|
| 460 | ENDIF |
|---|
| 461 | ! update thickness |
|---|
| 462 | zh_i(ji,jk) = MAX( 0._wp, zh_i(ji,jk) + zdum ) |
|---|
| 463 | h_i_1d(ji) = MAX( 0._wp, h_i_1d(ji) + zdum ) |
|---|
| 464 | ! |
|---|
| 465 | ! update heat content (J.m-2) and layer thickness |
|---|
| 466 | eh_i_old(ji,jk) = eh_i_old(ji,jk) + zdum * e_i_1d(ji,jk) |
|---|
| 467 | h_i_old (ji,jk) = h_i_old (ji,jk) + zdum |
|---|
| 468 | ENDIF |
|---|
| 469 | END DO |
|---|
| 470 | END DO |
|---|
| 471 | |
|---|
| 472 | ! Remove snow if ice has melted entirely |
|---|
| 473 | ! -------------------------------------- |
|---|
| 474 | DO jk = 0, nlay_s |
|---|
| 475 | DO ji = 1,npti |
|---|
| 476 | IF( h_i_1d(ji) == 0._wp ) THEN |
|---|
| 477 | ! mass & energy loss to the ocean |
|---|
| 478 | hfx_res_1d(ji) = hfx_res_1d(ji) - ze_s(ji,jk) * zh_s(ji,jk) * a_i_1d(ji) * r1_rdtice ! heat flux to the ocean [W.m-2], < 0 |
|---|
| 479 | wfx_res_1d(ji) = wfx_res_1d(ji) + rhos * zh_s(ji,jk) * a_i_1d(ji) * r1_rdtice ! mass flux |
|---|
| 480 | |
|---|
| 481 | ! update thickness and energy |
|---|
| 482 | h_s_1d(ji) = 0._wp |
|---|
| 483 | ze_s (ji,jk) = 0._wp |
|---|
| 484 | zh_s (ji,jk) = 0._wp |
|---|
| 485 | ENDIF |
|---|
| 486 | END DO |
|---|
| 487 | END DO |
|---|
| 488 | |
|---|
| 489 | ! Snow-Ice formation |
|---|
| 490 | ! ------------------ |
|---|
| 491 | ! When snow load exceeds Archimede's limit, snow-ice interface goes down under sea-level, |
|---|
| 492 | ! flooding of seawater transforms snow into ice. Thickness that is transformed is dh_snowice (positive for the ice) |
|---|
| 493 | z1_rho = 1._wp / ( rhos+rau0-rhoi ) |
|---|
| 494 | zdeltah(1:npti) = 0._wp |
|---|
| 495 | DO ji = 1, npti |
|---|
| 496 | ! |
|---|
| 497 | dh_snowice(ji) = MAX( 0._wp , ( rhos * h_s_1d(ji) + (rhoi-rau0) * h_i_1d(ji) ) * z1_rho ) |
|---|
| 498 | |
|---|
| 499 | h_i_1d(ji) = h_i_1d(ji) + dh_snowice(ji) |
|---|
| 500 | h_s_1d(ji) = h_s_1d(ji) - dh_snowice(ji) |
|---|
| 501 | |
|---|
| 502 | ! Contribution to energy flux to the ocean [J/m2], >0 (if sst<0) |
|---|
| 503 | zfmdt = ( rhos - rhoi ) * dh_snowice(ji) ! <0 |
|---|
| 504 | zEw = rcp * sst_1d(ji) |
|---|
| 505 | zQm = zfmdt * zEw |
|---|
| 506 | |
|---|
| 507 | hfx_thd_1d(ji) = hfx_thd_1d(ji) + zEw * zfmdt * a_i_1d(ji) * r1_rdtice ! Heat flux |
|---|
| 508 | sfx_sni_1d(ji) = sfx_sni_1d(ji) + sss_1d(ji) * zfmdt * a_i_1d(ji) * r1_rdtice ! Salt flux |
|---|
| 509 | |
|---|
| 510 | ! Case constant salinity in time: virtual salt flux to keep salinity constant |
|---|
| 511 | IF( nn_icesal /= 2 ) THEN |
|---|
| 512 | sfx_bri_1d(ji) = sfx_bri_1d(ji) - sss_1d(ji) * zfmdt * a_i_1d(ji) * r1_rdtice & ! put back sss_m into the ocean |
|---|
| 513 | & - s_i_1d(ji) * dh_snowice(ji) * rhoi * a_i_1d(ji) * r1_rdtice ! and get rn_icesal from the ocean |
|---|
| 514 | ENDIF |
|---|
| 515 | |
|---|
| 516 | ! Mass flux: All snow is thrown in the ocean, and seawater is taken to replace the volume |
|---|
| 517 | wfx_sni_1d (ji) = wfx_sni_1d (ji) - dh_snowice(ji) * rhoi * a_i_1d(ji) * r1_rdtice |
|---|
| 518 | wfx_snw_sni_1d(ji) = wfx_snw_sni_1d(ji) + dh_snowice(ji) * rhos * a_i_1d(ji) * r1_rdtice |
|---|
| 519 | |
|---|
| 520 | ! update thickness |
|---|
| 521 | zh_i(ji,0) = zh_i(ji,0) + dh_snowice(ji) |
|---|
| 522 | zdeltah(ji) = dh_snowice(ji) |
|---|
| 523 | |
|---|
| 524 | ! update heat content (J.m-2) and layer thickness |
|---|
| 525 | h_i_old (ji,0) = h_i_old (ji,0) + dh_snowice(ji) |
|---|
| 526 | eh_i_old(ji,0) = eh_i_old(ji,0) + zfmdt * zEw ! 1st part (sea water enthalpy) |
|---|
| 527 | |
|---|
| 528 | END DO |
|---|
| 529 | ! |
|---|
| 530 | DO jk = nlay_s, 0, -1 ! flooding of snow starts from the base |
|---|
| 531 | DO ji = 1, npti |
|---|
| 532 | zdum = MIN( zdeltah(ji), zh_s(ji,jk) ) ! amount of snw that floods, > 0 |
|---|
| 533 | zh_s(ji,jk) = MAX( 0._wp, zh_s(ji,jk) - zdum ) ! remove some snow thickness |
|---|
| 534 | eh_i_old(ji,0) = eh_i_old(ji,0) + zdum * ze_s(ji,jk) ! 2nd part (snow enthalpy) |
|---|
| 535 | ! update dh_snowice |
|---|
| 536 | zdeltah(ji) = MAX( 0._wp, zdeltah(ji) - zdum ) |
|---|
| 537 | END DO |
|---|
| 538 | END DO |
|---|
| 539 | ! |
|---|
| 540 | ! |
|---|
| 541 | !!$ ! --- Update snow diags --- ! |
|---|
| 542 | !!$ !!clem: this is wrong. dh_s_tot is not used anyway |
|---|
| 543 | !!$ DO ji = 1, npti |
|---|
| 544 | !!$ dh_s_tot(ji) = dh_s_tot(ji) + dh_s_mlt(ji) + zdeltah(ji) + zdh_s_sub(ji) - dh_snowice(ji) |
|---|
| 545 | !!$ END DO |
|---|
| 546 | ! |
|---|
| 547 | ! |
|---|
| 548 | ! Remapping of snw enthalpy on a regular grid |
|---|
| 549 | !-------------------------------------------- |
|---|
| 550 | CALL snw_ent( zh_s, ze_s, e_s_1d ) |
|---|
| 551 | |
|---|
| 552 | ! recalculate t_s_1d from e_s_1d |
|---|
| 553 | DO jk = 1, nlay_s |
|---|
| 554 | DO ji = 1,npti |
|---|
| 555 | IF( h_s_1d(ji) > 0._wp ) THEN |
|---|
| 556 | t_s_1d(ji,jk) = rt0 + ( - e_s_1d(ji,jk) * r1_rhos * r1_rcpi + rLfus * r1_rcpi ) |
|---|
| 557 | ELSE |
|---|
| 558 | t_s_1d(ji,jk) = rt0 |
|---|
| 559 | ENDIF |
|---|
| 560 | END DO |
|---|
| 561 | END DO |
|---|
| 562 | |
|---|
| 563 | ! Note: remapping of ice enthalpy is done in icethd.F90 |
|---|
| 564 | |
|---|
| 565 | ! --- ensure that a_i = 0 & h_s = 0 where h_i = 0 --- |
|---|
| 566 | WHERE( h_i_1d(1:npti) == 0._wp ) |
|---|
| 567 | a_i_1d (1:npti) = 0._wp |
|---|
| 568 | h_s_1d (1:npti) = 0._wp |
|---|
| 569 | t_su_1d(1:npti) = rt0 |
|---|
| 570 | END WHERE |
|---|
| 571 | |
|---|
| 572 | END SUBROUTINE ice_thd_dh |
|---|
| 573 | |
|---|
| 574 | SUBROUTINE snw_ent( ph_old, pe_old, pe_new ) |
|---|
| 575 | !!------------------------------------------------------------------- |
|---|
| 576 | !! *** ROUTINE snw_ent *** |
|---|
| 577 | !! |
|---|
| 578 | !! ** Purpose : |
|---|
| 579 | !! This routine computes new vertical grids in the snow, |
|---|
| 580 | !! and consistently redistributes temperatures. |
|---|
| 581 | !! Redistribution is made so as to ensure to energy conservation |
|---|
| 582 | !! |
|---|
| 583 | !! |
|---|
| 584 | !! ** Method : linear conservative remapping |
|---|
| 585 | !! |
|---|
| 586 | !! ** Steps : 1) cumulative integrals of old enthalpies/thicknesses |
|---|
| 587 | !! 2) linear remapping on the new layers |
|---|
| 588 | !! |
|---|
| 589 | !! ------------ cum0(0) ------------- cum1(0) |
|---|
| 590 | !! NEW ------------- |
|---|
| 591 | !! ------------ cum0(1) ==> ------------- |
|---|
| 592 | !! ... ------------- |
|---|
| 593 | !! ------------ ------------- |
|---|
| 594 | !! ------------ cum0(nlay_s+1) ------------- cum1(nlay_s) |
|---|
| 595 | !! |
|---|
| 596 | !! |
|---|
| 597 | !! References : Bitz & Lipscomb, JGR 99; Vancoppenolle et al., GRL, 2005 |
|---|
| 598 | !!------------------------------------------------------------------- |
|---|
| 599 | REAL(wp), DIMENSION(jpij,0:nlay_s), INTENT(in ) :: ph_old ! old thicknesses (m) |
|---|
| 600 | REAL(wp), DIMENSION(jpij,0:nlay_s), INTENT(in ) :: pe_old ! old enthlapies (J.m-3) |
|---|
| 601 | REAL(wp), DIMENSION(jpij,1:nlay_s), INTENT(inout) :: pe_new ! new enthlapies (J.m-3, remapped) |
|---|
| 602 | ! |
|---|
| 603 | INTEGER :: ji ! dummy loop indices |
|---|
| 604 | INTEGER :: jk0, jk1 ! old/new layer indices |
|---|
| 605 | ! |
|---|
| 606 | REAL(wp), DIMENSION(jpij,0:nlay_s+1) :: zeh_cum0, zh_cum0 ! old cumulative enthlapies and layers interfaces |
|---|
| 607 | REAL(wp), DIMENSION(jpij,0:nlay_s) :: zeh_cum1, zh_cum1 ! new cumulative enthlapies and layers interfaces |
|---|
| 608 | REAL(wp), DIMENSION(jpij) :: zhnew ! new layers thicknesses |
|---|
| 609 | !!------------------------------------------------------------------- |
|---|
| 610 | |
|---|
| 611 | !-------------------------------------------------------------------------- |
|---|
| 612 | ! 1) Cumulative integral of old enthalpy * thickness and layers interfaces |
|---|
| 613 | !-------------------------------------------------------------------------- |
|---|
| 614 | zeh_cum0(1:npti,0) = 0._wp |
|---|
| 615 | zh_cum0 (1:npti,0) = 0._wp |
|---|
| 616 | DO jk0 = 1, nlay_s+1 |
|---|
| 617 | DO ji = 1, npti |
|---|
| 618 | zeh_cum0(ji,jk0) = zeh_cum0(ji,jk0-1) + pe_old(ji,jk0-1) * ph_old(ji,jk0-1) |
|---|
| 619 | zh_cum0 (ji,jk0) = zh_cum0 (ji,jk0-1) + ph_old(ji,jk0-1) |
|---|
| 620 | END DO |
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| 621 | END DO |
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| 622 | |
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| 623 | !------------------------------------ |
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| 624 | ! 2) Interpolation on the new layers |
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| 625 | !------------------------------------ |
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| 626 | ! new layer thickesses |
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| 627 | DO ji = 1, npti |
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| 628 | zhnew(ji) = SUM( ph_old(ji,0:nlay_s) ) * r1_nlay_s |
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| 629 | END DO |
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| 630 | |
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| 631 | ! new layers interfaces |
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| 632 | zh_cum1(1:npti,0) = 0._wp |
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| 633 | DO jk1 = 1, nlay_s |
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| 634 | DO ji = 1, npti |
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| 635 | zh_cum1(ji,jk1) = zh_cum1(ji,jk1-1) + zhnew(ji) |
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| 636 | END DO |
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| 637 | END DO |
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| 638 | |
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| 639 | zeh_cum1(1:npti,0:nlay_s) = 0._wp |
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| 640 | ! new cumulative q*h => linear interpolation |
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| 641 | DO jk0 = 1, nlay_s+1 |
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| 642 | DO jk1 = 1, nlay_s-1 |
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| 643 | DO ji = 1, npti |
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| 644 | IF( zh_cum1(ji,jk1) <= zh_cum0(ji,jk0) .AND. zh_cum1(ji,jk1) > zh_cum0(ji,jk0-1) ) THEN |
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| 645 | zeh_cum1(ji,jk1) = ( zeh_cum0(ji,jk0-1) * ( zh_cum0(ji,jk0) - zh_cum1(ji,jk1 ) ) + & |
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| 646 | & zeh_cum0(ji,jk0 ) * ( zh_cum1(ji,jk1) - zh_cum0(ji,jk0-1) ) ) & |
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| 647 | & / ( zh_cum0(ji,jk0) - zh_cum0(ji,jk0-1) ) |
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| 648 | ENDIF |
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| 649 | END DO |
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| 650 | END DO |
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| 651 | END DO |
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| 652 | ! to ensure that total heat content is strictly conserved, set: |
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| 653 | zeh_cum1(1:npti,nlay_s) = zeh_cum0(1:npti,nlay_s+1) |
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| 654 | |
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| 655 | ! new enthalpies |
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| 656 | DO jk1 = 1, nlay_s |
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| 657 | DO ji = 1, npti |
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| 658 | rswitch = MAX( 0._wp , SIGN( 1._wp , zhnew(ji) - epsi20 ) ) |
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| 659 | pe_new(ji,jk1) = rswitch * ( zeh_cum1(ji,jk1) - zeh_cum1(ji,jk1-1) ) / MAX( zhnew(ji), epsi20 ) |
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| 660 | END DO |
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| 661 | END DO |
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| 662 | |
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| 663 | END SUBROUTINE snw_ent |
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| 664 | |
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| 665 | |
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| 666 | #else |
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| 667 | !!---------------------------------------------------------------------- |
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| 668 | !! Default option NO SI3 sea-ice model |
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| 669 | !!---------------------------------------------------------------------- |
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| 670 | #endif |
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| 671 | |
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| 672 | !!====================================================================== |
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| 673 | END MODULE icethd_dh |
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