| 1 | MODULE icethd_zdf |
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| 2 | !!====================================================================== |
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| 3 | !! *** MODULE icethd_zdf *** |
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| 4 | !! sea-ice: vertical heat diffusion in sea ice (computation of temperatures) |
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| 5 | !!====================================================================== |
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| 6 | !! History : LIM ! 02-2003 (M. Vancoppenolle) original 1D code |
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| 7 | !! ! 06-2005 (M. Vancoppenolle) 3d version |
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| 8 | !! ! 11-2006 (X Fettweis) Vectorization by Xavier |
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| 9 | !! ! 04-2007 (M. Vancoppenolle) Energy conservation |
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| 10 | !! 4.0 ! 2011-02 (G. Madec) dynamical allocation |
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| 11 | !! - ! 2012-05 (C. Rousset) add penetration solar flux |
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| 12 | !!---------------------------------------------------------------------- |
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| 13 | #if defined key_lim3 |
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| 14 | !!---------------------------------------------------------------------- |
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| 15 | !! 'key_lim3' ESIM sea-ice model |
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| 16 | !!---------------------------------------------------------------------- |
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| 17 | USE dom_oce ! ocean space and time domain |
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| 18 | USE phycst ! physical constants (ocean directory) |
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| 19 | USE ice ! sea-ice: variables |
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| 20 | USE ice1D ! sea-ice: thermodynamics variables |
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| 21 | ! |
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| 22 | USE in_out_manager ! I/O manager |
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| 23 | USE lib_mpp ! MPP library |
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| 24 | USE lib_fortran ! fortran utilities (glob_sum + no signed zero) |
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| 25 | |
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| 26 | IMPLICIT NONE |
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| 27 | PRIVATE |
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| 28 | |
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| 29 | PUBLIC ice_thd_zdf ! called by icethd |
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| 30 | PUBLIC ice_thd_zdf_init ! called by icestp |
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| 31 | |
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| 32 | !!** namelist (namthd_zdf) ** |
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| 33 | LOGICAL :: ln_zdf_BL99 ! Heat diffusion follows Bitz and Lipscomb (1999) |
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| 34 | LOGICAL :: ln_cndi_U64 ! thermal conductivity: Untersteiner (1964) |
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| 35 | LOGICAL :: ln_cndi_P07 ! thermal conductivity: Pringle et al (2007) |
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| 36 | REAL(wp) :: rn_kappa_i ! coef. for the extinction of radiation Grenfell et al. (2006) [1/m] |
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| 37 | REAL(wp), PUBLIC :: rn_cnd_s ! thermal conductivity of the snow [W/m/K] |
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| 38 | |
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| 39 | INTEGER :: nice_zdf ! Choice of the type of vertical heat diffusion formulation |
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| 40 | ! ! associated indices: |
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| 41 | INTEGER, PARAMETER :: np_BL99 = 1 ! Bitz and Lipscomb (1999) |
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| 42 | |
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| 43 | INTEGER , PARAMETER :: np_zdf_jules_OFF = 0 ! compute all temperatures from qsr and qns |
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| 44 | INTEGER , PARAMETER :: np_zdf_jules_SND = 1 ! compute conductive heat flux and surface temperature from qsr and qns |
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| 45 | INTEGER , PARAMETER :: np_zdf_jules_RCV = 2 ! compute snow and inner ice temperatures from qcnd |
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| 46 | |
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| 47 | !!---------------------------------------------------------------------- |
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| 48 | !! NEMO/ICE 4.0 , NEMO Consortium (2017) |
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| 49 | !! $Id: icethd_zdf.F90 8420 2017-08-08 12:18:46Z clem $ |
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| 50 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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| 51 | !!---------------------------------------------------------------------- |
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| 52 | CONTAINS |
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| 53 | |
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| 54 | SUBROUTINE ice_thd_zdf |
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| 55 | |
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| 56 | !! |
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| 57 | !!------------------------------------------------------------------- |
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| 58 | !! *** ROUTINE ice_thd_zdf *** |
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| 59 | !! ** Purpose : |
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| 60 | !! This chooses between the appropriate routine for the |
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| 61 | !! computation of vertical diffusion |
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| 62 | !! |
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| 63 | !!------------------------------------------------------------------- |
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| 64 | !! |
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| 65 | |
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| 66 | SELECT CASE ( nice_zdf ) ! Choose the vertical heat diffusion solver |
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| 67 | |
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| 68 | !------------- |
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| 69 | CASE( np_BL99 ) ! BL99 solver |
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| 70 | !------------- |
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| 71 | |
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| 72 | IF ( nice_jules == np_jules_OFF ) THEN ! No Jules coupler |
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| 73 | |
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| 74 | CALL ice_thd_zdf_BL99 ( np_zdf_jules_OFF ) |
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| 75 | |
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| 76 | ENDIF |
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| 77 | |
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| 78 | IF ( nice_jules == np_jules_EMULE ) THEN ! Jules coupler is emulated |
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| 79 | |
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| 80 | CALL ice_thd_zdf_BL99 ( np_zdf_jules_SND ) |
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| 81 | CALL ice_thd_zdf_BL99 ( np_zdf_jules_RCV ) |
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| 82 | |
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| 83 | ENDIF |
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| 84 | |
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| 85 | IF ( nice_jules == np_jules_ACTIVE ) THEN ! Jules coupler is emulated |
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| 86 | |
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| 87 | CALL ice_thd_zdf_BL99 ( np_zdf_jules_RCV ) |
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| 88 | |
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| 89 | ENDIF |
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| 90 | |
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| 91 | END SELECT |
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| 92 | |
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| 93 | END SUBROUTINE ice_thd_zdf |
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| 94 | |
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| 95 | |
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| 96 | |
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| 97 | SUBROUTINE ice_thd_zdf_BL99(k_jules) |
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| 98 | !!------------------------------------------------------------------- |
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| 99 | !! *** ROUTINE ice_thd_zdf_BL99 *** |
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| 100 | !! ** Purpose : |
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| 101 | !! This routine determines the time evolution of snow and sea-ice |
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| 102 | !! temperature profiles, using the original Bitz and Lipscomb (1999) algorithm |
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| 103 | !! |
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| 104 | !! ** Method : |
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| 105 | !! This is done by solving the heat equation diffusion with |
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| 106 | !! a Neumann boundary condition at the surface and a Dirichlet one |
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| 107 | !! at the bottom. Solar radiation is partially absorbed into the ice. |
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| 108 | !! The specific heat and thermal conductivities depend on ice salinity |
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| 109 | !! and temperature to take into account brine pocket melting. The |
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| 110 | !! numerical |
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| 111 | !! scheme is an iterative Crank-Nicolson on a non-uniform multilayer grid |
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| 112 | !! in the ice and snow system. |
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| 113 | !! |
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| 114 | !! The successive steps of this routine are |
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| 115 | !! 1. initialization of ice-snow layers thicknesses |
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| 116 | !! 2. Internal absorbed and transmitted radiation |
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| 117 | !! Then iterative procedure begins |
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| 118 | !! 3. Thermal conductivity |
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| 119 | !! 4. Kappa factors |
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| 120 | !! 5. specific heat in the ice |
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| 121 | !! 6. eta factors |
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| 122 | !! 7. surface flux computation |
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| 123 | !! 8. tridiagonal system terms |
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| 124 | !! 9. solving the tridiagonal system with Gauss elimination |
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| 125 | !! Iterative procedure ends according to a criterion on evolution |
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| 126 | !! of temperature |
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| 127 | !! 10. Fluxes at the interfaces |
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| 128 | !! |
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| 129 | !! ** Inputs / Ouputs : (global commons) |
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| 130 | !! surface temperature : t_su_1d |
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| 131 | !! ice/snow temperatures : t_i_1d, t_s_1d |
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| 132 | !! ice salinities : sz_i_1d |
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| 133 | !! number of layers in the ice/snow: nlay_i, nlay_s |
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| 134 | !! total ice/snow thickness : h_i_1d, h_s_1d |
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| 135 | !!------------------------------------------------------------------- |
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| 136 | INTEGER, INTENT(in) :: k_jules ! Jules coupling (0=OFF, 1=RECEIVE, 2=SEND) |
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| 137 | |
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| 138 | INTEGER :: ji, jk ! spatial loop index |
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| 139 | INTEGER :: jm ! current reference number of equation |
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| 140 | INTEGER :: jm_mint, jm_maxt |
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| 141 | INTEGER :: iconv ! number of iterations in iterative procedure |
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| 142 | INTEGER :: iconv_max = 50 ! max number of iterations in iterative procedure |
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| 143 | |
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| 144 | INTEGER, DIMENSION(jpij) :: jm_min ! reference number of top equation |
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| 145 | INTEGER, DIMENSION(jpij) :: jm_max ! reference number of bottom equation |
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| 146 | |
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| 147 | REAL(wp) :: zg1s = 2._wp ! for the tridiagonal system |
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| 148 | REAL(wp) :: zg1 = 2._wp ! |
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| 149 | REAL(wp) :: zgamma = 18009._wp ! for specific heat |
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| 150 | REAL(wp) :: zbeta = 0.117_wp ! for thermal conductivity (could be 0.13) |
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| 151 | REAL(wp) :: zraext_s = 10._wp ! extinction coefficient of radiation in the snow |
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| 152 | REAL(wp) :: zkimin = 0.10_wp ! minimum ice thermal conductivity |
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| 153 | REAL(wp) :: ztsu_err = 1.e-5_wp ! range around which t_su is considered at 0C |
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| 154 | REAL(wp) :: zdti_bnd = 1.e-4_wp ! maximal authorized error on temperature |
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| 155 | REAL(wp) :: ztmelt_i ! ice melting temperature |
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| 156 | REAL(wp) :: zdti_max ! current maximal error on temperature |
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| 157 | REAL(wp) :: zcpi ! Ice specific heat |
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| 158 | REAL(wp) :: zhfx_err, zdq ! diag errors on heat |
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| 159 | REAL(wp) :: zfac ! dummy factor |
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| 160 | |
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| 161 | REAL(wp), DIMENSION(jpij) :: isnow ! switch for presence (1) or absence (0) of snow |
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| 162 | REAL(wp), DIMENSION(jpij) :: ztsub ! surface temperature at previous iteration |
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| 163 | REAL(wp), DIMENSION(jpij) :: zh_i, z1_h_i ! ice layer thickness |
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| 164 | REAL(wp), DIMENSION(jpij) :: zh_s, z1_h_s ! snow layer thickness |
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| 165 | REAL(wp), DIMENSION(jpij) :: zqns_ice_b ! solar radiation absorbed at the surface |
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| 166 | REAL(wp), DIMENSION(jpij) :: zfnet ! surface flux function |
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| 167 | REAL(wp), DIMENSION(jpij) :: zdqns_ice_b ! derivative of the surface flux function |
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| 168 | |
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| 169 | REAL(wp), DIMENSION(jpij ) :: ztsuold ! Old surface temperature in the ice |
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| 170 | REAL(wp), DIMENSION(jpij,nlay_i) :: ztiold ! Old temperature in the ice |
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| 171 | REAL(wp), DIMENSION(jpij,nlay_s) :: ztsold ! Old temperature in the snow |
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| 172 | REAL(wp), DIMENSION(jpij,nlay_i) :: ztib ! Temporary temperature in the ice to check the convergence |
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| 173 | REAL(wp), DIMENSION(jpij,nlay_s) :: ztsb ! Temporary temperature in the snow to check the convergence |
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| 174 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: ztcond_i ! Ice thermal conductivity |
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| 175 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: zradtr_i ! Radiation transmitted through the ice |
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| 176 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: zradab_i ! Radiation absorbed in the ice |
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| 177 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: zkappa_i ! Kappa factor in the ice |
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| 178 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: zeta_i ! Eta factor in the ice |
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| 179 | REAL(wp), DIMENSION(jpij,0:nlay_s) :: zradtr_s ! Radiation transmited through the snow |
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| 180 | REAL(wp), DIMENSION(jpij,0:nlay_s) :: zradab_s ! Radiation absorbed in the snow |
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| 181 | REAL(wp), DIMENSION(jpij,0:nlay_s) :: zkappa_s ! Kappa factor in the snow |
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| 182 | REAL(wp), DIMENSION(jpij,0:nlay_s) :: zeta_s ! Eta factor in the snow |
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| 183 | REAL(wp), DIMENSION(jpij,nlay_i+3) :: zindterm ! 'Ind'ependent term |
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| 184 | REAL(wp), DIMENSION(jpij,nlay_i+3) :: zindtbis ! Temporary 'ind'ependent term |
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| 185 | REAL(wp), DIMENSION(jpij,nlay_i+3) :: zdiagbis ! Temporary 'dia'gonal term |
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| 186 | REAL(wp), DIMENSION(jpij,nlay_i+3,3) :: ztrid ! Tridiagonal system terms |
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| 187 | REAL(wp), DIMENSION(jpij) :: zq_ini ! diag errors on heat |
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| 188 | REAL(wp), DIMENSION(jpij) :: zghe ! G(he), th. conduct enhancement factor, mono-cat |
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| 189 | |
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| 190 | REAL(wp) :: zfr1, zfr2, zfrqsr_tr_i ! dummy factor |
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| 191 | |
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| 192 | ! Mono-category |
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| 193 | REAL(wp) :: zepsilon ! determines thres. above which computation of G(h) is done |
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| 194 | REAL(wp) :: zhe ! dummy factor |
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| 195 | REAL(wp) :: zcnd_i ! mean sea ice thermal conductivity |
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| 196 | !!------------------------------------------------------------------ |
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| 197 | |
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| 198 | ! --- diag error on heat diffusion - PART 1 --- ! |
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| 199 | DO ji = 1, npti |
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| 200 | zq_ini(ji) = ( SUM( e_i_1d(ji,1:nlay_i) ) * h_i_1d(ji) * r1_nlay_i + & |
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| 201 | & SUM( e_s_1d(ji,1:nlay_s) ) * h_s_1d(ji) * r1_nlay_s ) |
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| 202 | END DO |
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| 203 | |
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| 204 | !------------------ |
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| 205 | ! 1) Initialization |
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| 206 | !------------------ |
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| 207 | DO ji = 1, npti |
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| 208 | isnow(ji)= 1._wp - MAX( 0._wp , SIGN(1._wp, - h_s_1d(ji) ) ) ! is there snow or not |
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| 209 | ! layer thickness |
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| 210 | zh_i(ji) = h_i_1d(ji) * r1_nlay_i |
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| 211 | zh_s(ji) = h_s_1d(ji) * r1_nlay_s |
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| 212 | END DO |
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| 213 | ! |
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| 214 | WHERE( zh_i(1:npti) >= epsi10 ) ; z1_h_i(1:npti) = 1._wp / zh_i(1:npti) |
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| 215 | ELSEWHERE ; z1_h_i(1:npti) = 0._wp |
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| 216 | END WHERE |
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| 217 | |
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| 218 | WHERE( zh_s(1:npti) >= epsi10 ) ; z1_h_s(1:npti) = 1._wp / zh_s(1:npti) |
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| 219 | ELSEWHERE ; z1_h_s(1:npti) = 0._wp |
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| 220 | END WHERE |
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| 221 | |
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| 222 | ! Store initial temperatures and non solar heat fluxes |
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| 223 | IF ( k_jules == np_zdf_jules_OFF .OR. k_jules == np_zdf_jules_SND ) THEN ! OFF or SND mode |
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| 224 | |
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| 225 | ztsub (1:npti) = t_su_1d(1:npti) ! surface temperature at iteration n-1 |
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| 226 | ztsuold(1:npti) = t_su_1d(1:npti) ! surface temperature initial value |
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| 227 | zdqns_ice_b(1:npti) = dqns_ice_1d(1:npti) ! derivative of incoming nonsolar flux |
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| 228 | zqns_ice_b (1:npti) = qns_ice_1d(1:npti) ! store previous qns_ice_1d value |
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| 229 | |
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| 230 | t_su_1d(1:npti) = MIN( t_su_1d(1:npti), rt0 - ztsu_err ) ! required to leave the choice between melting or not |
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| 231 | |
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| 232 | ENDIF |
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| 233 | |
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| 234 | ztsold (1:npti,:) = t_s_1d(1:npti,:) ! Old snow temperature |
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| 235 | ztiold (1:npti,:) = t_i_1d(1:npti,:) ! Old ice temperature |
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| 236 | |
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| 237 | !------------- |
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| 238 | ! 2) Radiation |
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| 239 | !------------- |
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| 240 | ! --- Transmission/absorption of solar radiation in the ice --- ! |
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| 241 | ! zfr1 = ( 0.18 * ( 1.0 - 0.81 ) + 0.35 * 0.81 ) ! standard value |
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| 242 | ! zfr2 = ( 0.82 * ( 1.0 - 0.81 ) + 0.65 * 0.81 ) ! zfr2 such that zfr1 + zfr2 to equal 1 |
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| 243 | |
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| 244 | ! DO ji = 1, npti |
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| 245 | |
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| 246 | ! zfac = MAX( 0._wp , 1._wp - ( h_i_1d(ji) * 10._wp ) ) |
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| 247 | |
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| 248 | ! zfrqsr_tr_i = zfr1 + zfac * zfr2 ! below 10 cm, linearly increase zfrqsr_tr_i until 1 at zero thickness |
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| 249 | ! IF ( h_s_1d(ji) >= 0.0_wp ) zfrqsr_tr_i = 0._wp ! snow fully opaque |
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| 250 | |
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| 251 | ! qsr_ice_tr_1d(ji) = zfrqsr_tr_i * qsr_ice_1d(ji) ! transmitted solar radiation |
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| 252 | |
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| 253 | ! zfsw(ji) = qsr_ice_1d(ji) - qsr_ice_tr_1d(ji) |
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| 254 | ! zftrice(ji) = qsr_ice_tr_1d(ji) |
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| 255 | ! i0(ji) = zfrqsr_tr_i |
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| 256 | |
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| 257 | ! END DO |
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| 258 | |
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| 259 | zradtr_s(1:npti,0) = qsr_ice_tr_1d(1:npti) |
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| 260 | DO jk = 1, nlay_s |
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| 261 | DO ji = 1, npti |
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| 262 | ! ! radiation transmitted below the layer-th snow layer |
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| 263 | zradtr_s(ji,jk) = zradtr_s(ji,0) * EXP( - zraext_s * zh_s(ji) * REAL(jk) ) |
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| 264 | ! ! radiation absorbed by the layer-th snow layer |
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| 265 | zradab_s(ji,jk) = zradtr_s(ji,jk-1) - zradtr_s(ji,jk) |
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| 266 | END DO |
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| 267 | END DO |
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| 268 | |
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| 269 | zradtr_i(1:npti,0) = zradtr_s(1:npti,nlay_s) * isnow(1:npti) + qsr_ice_tr_1d(1:npti) * ( 1._wp - isnow(1:npti) ) |
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| 270 | DO jk = 1, nlay_i |
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| 271 | DO ji = 1, npti |
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| 272 | ! ! radiation transmitted below the layer-th ice layer |
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| 273 | zradtr_i(ji,jk) = zradtr_i(ji,0) * EXP( - rn_kappa_i * zh_i(ji) * REAL(jk) ) |
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| 274 | ! ! radiation absorbed by the layer-th ice layer |
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| 275 | zradab_i(ji,jk) = zradtr_i(ji,jk-1) - zradtr_i(ji,jk) |
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| 276 | END DO |
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| 277 | END DO |
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| 278 | |
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| 279 | ftr_ice_1d(1:npti) = zradtr_i(1:npti,nlay_i) ! record radiation transmitted below the ice |
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| 280 | ! |
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| 281 | iconv = 0 ! number of iterations |
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| 282 | zdti_max = 1000._wp ! maximal value of error on all points |
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| 283 | ! !============================! |
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| 284 | DO WHILE ( zdti_max > zdti_bnd .AND. iconv < iconv_max ) ! Iterative procedure begins ! |
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| 285 | ! !============================! |
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| 286 | iconv = iconv + 1 |
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| 287 | ! |
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| 288 | ztib(1:npti,:) = t_i_1d(1:npti,:) |
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| 289 | ztsb(1:npti,:) = t_s_1d(1:npti,:) |
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| 290 | ! |
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| 291 | !-------------------------------- |
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| 292 | ! 3) Sea ice thermal conductivity |
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| 293 | !-------------------------------- |
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| 294 | IF( ln_cndi_U64 ) THEN !-- Untersteiner (1964) formula: k = k0 + beta.S/T |
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| 295 | ! |
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| 296 | DO ji = 1, npti |
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| 297 | ztcond_i(ji,0) = rcdic + zbeta * sz_i_1d(ji,1) / MIN( -epsi10, t_i_1d(ji,1) - rt0 ) |
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| 298 | ztcond_i(ji,nlay_i) = rcdic + zbeta * sz_i_1d(ji,nlay_i) / MIN( -epsi10, t_bo_1d(ji) - rt0 ) |
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| 299 | END DO |
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| 300 | DO jk = 1, nlay_i-1 |
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| 301 | DO ji = 1, npti |
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| 302 | ztcond_i(ji,jk) = rcdic + zbeta * 0.5_wp * ( sz_i_1d(ji,jk) + sz_i_1d(ji,jk+1) ) / & |
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| 303 | & MIN( -epsi10, 0.5_wp * (t_i_1d(ji,jk) + t_i_1d(ji,jk+1)) - rt0 ) |
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| 304 | END DO |
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| 305 | END DO |
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| 306 | ! |
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| 307 | ELSEIF( ln_cndi_P07 ) THEN !-- Pringle et al formula: k = k0 + beta1.S/T - beta2.T |
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| 308 | ! |
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| 309 | DO ji = 1, npti |
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| 310 | ztcond_i(ji,0) = rcdic + 0.09_wp * sz_i_1d(ji,1) / MIN( -epsi10, t_i_1d(ji,1) - rt0 ) & |
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| 311 | & - 0.011_wp * ( t_i_1d(ji,1) - rt0 ) |
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| 312 | ztcond_i(ji,nlay_i) = rcdic + 0.09_wp * sz_i_1d(ji,nlay_i) / MIN( -epsi10, t_bo_1d(ji) - rt0 ) & |
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| 313 | & - 0.011_wp * ( t_bo_1d(ji) - rt0 ) |
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| 314 | END DO |
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| 315 | DO jk = 1, nlay_i-1 |
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| 316 | DO ji = 1, npti |
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| 317 | ztcond_i(ji,jk) = rcdic + 0.09_wp * 0.5_wp * ( sz_i_1d(ji,jk) + sz_i_1d(ji,jk+1) ) / & |
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| 318 | & MIN( -epsi10, 0.5_wp * (t_i_1d(ji,jk) + t_i_1d(ji,jk+1)) - rt0 ) & |
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| 319 | & - 0.011_wp * ( 0.5_wp * (t_i_1d(ji,jk) + t_i_1d(ji,jk+1)) - rt0 ) |
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| 320 | END DO |
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| 321 | END DO |
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| 322 | ! |
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| 323 | ENDIF |
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| 324 | ztcond_i(1:npti,:) = MAX( zkimin, ztcond_i(1:npti,:) ) |
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| 325 | ! |
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| 326 | !--- G(he) : enhancement of thermal conductivity in mono-category case |
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| 327 | ! Computation of effective thermal conductivity G(h) |
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| 328 | ! Used in mono-category case only to simulate an ITD implicitly |
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| 329 | ! Fichefet and Morales Maqueda, JGR 1997 |
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| 330 | zghe(1:npti) = 1._wp |
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| 331 | ! |
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| 332 | SELECT CASE ( nn_monocat ) |
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| 333 | |
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| 334 | CASE ( 1 , 3 ) |
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| 335 | |
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| 336 | zepsilon = 0.1_wp |
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| 337 | DO ji = 1, npti |
|---|
| 338 | zcnd_i = SUM( ztcond_i(ji,:) ) / REAL( nlay_i+1, wp ) ! Mean sea ice thermal conductivity |
|---|
| 339 | zhe = ( rn_cnd_s * h_i_1d(ji) + zcnd_i * h_s_1d(ji) ) / ( rn_cnd_s + zcnd_i ) ! Effective thickness he (zhe) |
|---|
| 340 | IF( zhe >= zepsilon * 0.5_wp * EXP(1._wp) ) THEN |
|---|
| 341 | zghe(ji) = MIN( 2._wp, 0.5_wp * ( 1._wp + LOG( 2._wp * zhe / zepsilon ) ) ) ! G(he) |
|---|
| 342 | ENDIF |
|---|
| 343 | END DO |
|---|
| 344 | |
|---|
| 345 | END SELECT |
|---|
| 346 | ! |
|---|
| 347 | !----------------- |
|---|
| 348 | ! 4) kappa factors |
|---|
| 349 | !----------------- |
|---|
| 350 | !--- Snow |
|---|
| 351 | DO jk = 0, nlay_s-1 |
|---|
| 352 | DO ji = 1, npti |
|---|
| 353 | zkappa_s(ji,jk) = zghe(ji) * rn_cnd_s * z1_h_s(ji) |
|---|
| 354 | END DO |
|---|
| 355 | END DO |
|---|
| 356 | DO ji = 1, npti ! Snow-ice interface |
|---|
| 357 | zfac = 0.5_wp * ( ztcond_i(ji,0) * zh_s(ji) + rn_cnd_s * zh_i(ji) ) |
|---|
| 358 | IF( zfac > epsi10 ) THEN |
|---|
| 359 | zkappa_s(ji,nlay_s) = zghe(ji) * rn_cnd_s * ztcond_i(ji,0) / zfac |
|---|
| 360 | ELSE |
|---|
| 361 | zkappa_s(ji,nlay_s) = 0._wp |
|---|
| 362 | ENDIF |
|---|
| 363 | END DO |
|---|
| 364 | |
|---|
| 365 | !--- Ice |
|---|
| 366 | DO jk = 0, nlay_i |
|---|
| 367 | DO ji = 1, npti |
|---|
| 368 | zkappa_i(ji,jk) = zghe(ji) * ztcond_i(ji,jk) * z1_h_i(ji) |
|---|
| 369 | END DO |
|---|
| 370 | END DO |
|---|
| 371 | DO ji = 1, npti ! Snow-ice interface |
|---|
| 372 | zkappa_i(ji,0) = zkappa_s(ji,nlay_s) * isnow(ji) + zkappa_i(ji,0) * ( 1._wp - isnow(ji) ) |
|---|
| 373 | END DO |
|---|
| 374 | ! |
|---|
| 375 | !-------------------------------------- |
|---|
| 376 | ! 5) Sea ice specific heat, eta factors |
|---|
| 377 | !-------------------------------------- |
|---|
| 378 | DO jk = 1, nlay_i |
|---|
| 379 | DO ji = 1, npti |
|---|
| 380 | zcpi = cpic + zgamma * sz_i_1d(ji,jk) / MAX( ( t_i_1d(ji,jk) - rt0 ) * ( ztiold(ji,jk) - rt0 ), epsi10 ) |
|---|
| 381 | zeta_i(ji,jk) = rdt_ice * r1_rhoic * z1_h_i(ji) / MAX( epsi10, zcpi ) |
|---|
| 382 | END DO |
|---|
| 383 | END DO |
|---|
| 384 | |
|---|
| 385 | DO jk = 1, nlay_s |
|---|
| 386 | DO ji = 1, npti |
|---|
| 387 | zeta_s(ji,jk) = rdt_ice * r1_rhosn * r1_cpic * z1_h_s(ji) |
|---|
| 388 | END DO |
|---|
| 389 | END DO |
|---|
| 390 | |
|---|
| 391 | ! |
|---|
| 392 | !----------------------------------------! |
|---|
| 393 | ! ! |
|---|
| 394 | ! JULES IF (OFF or SND MODE) ! |
|---|
| 395 | ! ! |
|---|
| 396 | !----------------------------------------! |
|---|
| 397 | ! |
|---|
| 398 | |
|---|
| 399 | IF ( k_jules == np_zdf_jules_OFF .OR. k_jules == np_zdf_jules_SND ) THEN ! OFF or SND mode |
|---|
| 400 | |
|---|
| 401 | ! |
|---|
| 402 | ! In OFF mode the original BL99 temperature computation is used |
|---|
| 403 | ! (with qsr_ice, qns_ice and dqns_ice as inputs) |
|---|
| 404 | ! |
|---|
| 405 | ! In SND mode, the computation is required to compute the conduction fluxes |
|---|
| 406 | ! |
|---|
| 407 | |
|---|
| 408 | !---------------------------- |
|---|
| 409 | ! 6) surface flux computation |
|---|
| 410 | !---------------------------- |
|---|
| 411 | |
|---|
| 412 | DO ji = 1, npti |
|---|
| 413 | ! update of the non solar flux according to the update in T_su |
|---|
| 414 | qns_ice_1d(ji) = qns_ice_1d(ji) + dqns_ice_1d(ji) * ( t_su_1d(ji) - ztsub(ji) ) |
|---|
| 415 | END DO |
|---|
| 416 | |
|---|
| 417 | DO ji = 1, npti |
|---|
| 418 | zfnet(ji) = qsr_ice_1d(ji) - qsr_ice_tr_1d(ji) + qns_ice_1d(ji) ! net heat flux = net solar - transmitted solar + non solar |
|---|
| 419 | END DO |
|---|
| 420 | ! |
|---|
| 421 | !---------------------------- |
|---|
| 422 | ! 7) tridiagonal system terms |
|---|
| 423 | !---------------------------- |
|---|
| 424 | !!layer denotes the number of the layer in the snow or in the ice |
|---|
| 425 | !!jm denotes the reference number of the equation in the tridiagonal |
|---|
| 426 | !!system, terms of tridiagonal system are indexed as following : |
|---|
| 427 | !!1 is subdiagonal term, 2 is diagonal and 3 is superdiagonal one |
|---|
| 428 | |
|---|
| 429 | !!ice interior terms (top equation has the same form as the others) |
|---|
| 430 | ztrid (1:npti,:,:) = 0._wp |
|---|
| 431 | zindterm(1:npti,:) = 0._wp |
|---|
| 432 | zindtbis(1:npti,:) = 0._wp |
|---|
| 433 | zdiagbis(1:npti,:) = 0._wp |
|---|
| 434 | |
|---|
| 435 | DO jm = nlay_s + 2, nlay_s + nlay_i |
|---|
| 436 | DO ji = 1, npti |
|---|
| 437 | jk = jm - nlay_s - 1 |
|---|
| 438 | ztrid(ji,jm,1) = - zeta_i(ji,jk) * zkappa_i(ji,jk-1) |
|---|
| 439 | ztrid(ji,jm,2) = 1.0 + zeta_i(ji,jk) * ( zkappa_i(ji,jk-1) + zkappa_i(ji,jk) ) |
|---|
| 440 | ztrid(ji,jm,3) = - zeta_i(ji,jk) * zkappa_i(ji,jk) |
|---|
| 441 | zindterm(ji,jm) = ztiold(ji,jk) + zeta_i(ji,jk) * zradab_i(ji,jk) |
|---|
| 442 | END DO |
|---|
| 443 | ENDDO |
|---|
| 444 | |
|---|
| 445 | jm = nlay_s + nlay_i + 1 |
|---|
| 446 | DO ji = 1, npti |
|---|
| 447 | !!ice bottom term |
|---|
| 448 | ztrid(ji,jm,1) = - zeta_i(ji,nlay_i)*zkappa_i(ji,nlay_i-1) |
|---|
| 449 | ztrid(ji,jm,2) = 1.0 + zeta_i(ji,nlay_i) * ( zkappa_i(ji,nlay_i) * zg1 + zkappa_i(ji,nlay_i-1) ) |
|---|
| 450 | ztrid(ji,jm,3) = 0.0 |
|---|
| 451 | zindterm(ji,jm) = ztiold(ji,nlay_i) + zeta_i(ji,nlay_i) * & |
|---|
| 452 | & ( zradab_i(ji,nlay_i) + zkappa_i(ji,nlay_i) * zg1 * t_bo_1d(ji) ) |
|---|
| 453 | ENDDO |
|---|
| 454 | |
|---|
| 455 | |
|---|
| 456 | DO ji = 1, npti |
|---|
| 457 | ! !---------------------! |
|---|
| 458 | IF ( h_s_1d(ji) > 0.0 ) THEN ! snow-covered cells ! |
|---|
| 459 | ! !---------------------! |
|---|
| 460 | ! snow interior terms (bottom equation has the same form as the others) |
|---|
| 461 | DO jm = 3, nlay_s + 1 |
|---|
| 462 | jk = jm - 1 |
|---|
| 463 | ztrid(ji,jm,1) = - zeta_s(ji,jk) * zkappa_s(ji,jk-1) |
|---|
| 464 | ztrid(ji,jm,2) = 1.0 + zeta_s(ji,jk) * ( zkappa_s(ji,jk-1) + zkappa_s(ji,jk) ) |
|---|
| 465 | ztrid(ji,jm,3) = - zeta_s(ji,jk)*zkappa_s(ji,jk) |
|---|
| 466 | zindterm(ji,jm) = ztsold(ji,jk) + zeta_s(ji,jk) * zradab_s(ji,jk) |
|---|
| 467 | END DO |
|---|
| 468 | |
|---|
| 469 | ! case of only one layer in the ice (ice equation is altered) |
|---|
| 470 | IF ( nlay_i == 1 ) THEN |
|---|
| 471 | ztrid(ji,nlay_s+2,3) = 0.0 |
|---|
| 472 | zindterm(ji,nlay_s+2) = zindterm(ji,nlay_s+2) + zkappa_i(ji,1) * t_bo_1d(ji) |
|---|
| 473 | ENDIF |
|---|
| 474 | |
|---|
| 475 | IF ( t_su_1d(ji) < rt0 ) THEN !-- case 1 : no surface melting |
|---|
| 476 | |
|---|
| 477 | jm_min(ji) = 1 |
|---|
| 478 | jm_max(ji) = nlay_i + nlay_s + 1 |
|---|
| 479 | |
|---|
| 480 | ! surface equation |
|---|
| 481 | ztrid(ji,1,1) = 0.0 |
|---|
| 482 | ztrid(ji,1,2) = zdqns_ice_b(ji) - zg1s * zkappa_s(ji,0) |
|---|
| 483 | ztrid(ji,1,3) = zg1s * zkappa_s(ji,0) |
|---|
| 484 | zindterm(ji,1) = zdqns_ice_b(ji) * t_su_1d(ji) - zfnet(ji) |
|---|
| 485 | |
|---|
| 486 | ! first layer of snow equation |
|---|
| 487 | ztrid(ji,2,1) = - zkappa_s(ji,0) * zg1s * zeta_s(ji,1) |
|---|
| 488 | ztrid(ji,2,2) = 1.0 + zeta_s(ji,1) * ( zkappa_s(ji,1) + zkappa_s(ji,0) * zg1s ) |
|---|
| 489 | ztrid(ji,2,3) = - zeta_s(ji,1)* zkappa_s(ji,1) |
|---|
| 490 | zindterm(ji,2) = ztsold(ji,1) + zeta_s(ji,1) * zradab_s(ji,1) |
|---|
| 491 | |
|---|
| 492 | ELSE !-- case 2 : surface is melting |
|---|
| 493 | ! |
|---|
| 494 | jm_min(ji) = 2 |
|---|
| 495 | jm_max(ji) = nlay_i + nlay_s + 1 |
|---|
| 496 | |
|---|
| 497 | ! first layer of snow equation |
|---|
| 498 | ztrid(ji,2,1) = 0.0 |
|---|
| 499 | ztrid(ji,2,2) = 1.0 + zeta_s(ji,1) * ( zkappa_s(ji,1) + zkappa_s(ji,0) * zg1s ) |
|---|
| 500 | ztrid(ji,2,3) = - zeta_s(ji,1)*zkappa_s(ji,1) |
|---|
| 501 | zindterm(ji,2) = ztsold(ji,1) + zeta_s(ji,1) * & |
|---|
| 502 | & ( zradab_s(ji,1) + zkappa_s(ji,0) * zg1s * t_su_1d(ji) ) |
|---|
| 503 | ENDIF |
|---|
| 504 | ! !---------------------! |
|---|
| 505 | ELSE ! cells without snow ! |
|---|
| 506 | ! !---------------------! |
|---|
| 507 | ! |
|---|
| 508 | IF ( t_su_1d(ji) < rt0 ) THEN !-- case 1 : no surface melting |
|---|
| 509 | ! |
|---|
| 510 | jm_min(ji) = nlay_s + 1 |
|---|
| 511 | jm_max(ji) = nlay_i + nlay_s + 1 |
|---|
| 512 | |
|---|
| 513 | ! surface equation |
|---|
| 514 | ztrid(ji,jm_min(ji),1) = 0.0 |
|---|
| 515 | ztrid(ji,jm_min(ji),2) = zdqns_ice_b(ji) - zkappa_i(ji,0)*zg1 |
|---|
| 516 | ztrid(ji,jm_min(ji),3) = zkappa_i(ji,0)*zg1 |
|---|
| 517 | zindterm(ji,jm_min(ji)) = zdqns_ice_b(ji)*t_su_1d(ji) - zfnet(ji) |
|---|
| 518 | |
|---|
| 519 | ! first layer of ice equation |
|---|
| 520 | ztrid(ji,jm_min(ji)+1,1) = - zkappa_i(ji,0) * zg1 * zeta_i(ji,1) |
|---|
| 521 | ztrid(ji,jm_min(ji)+1,2) = 1.0 + zeta_i(ji,1) * ( zkappa_i(ji,1) + zkappa_i(ji,0) * zg1 ) |
|---|
| 522 | ztrid(ji,jm_min(ji)+1,3) = - zeta_i(ji,1) * zkappa_i(ji,1) |
|---|
| 523 | zindterm(ji,jm_min(ji)+1) = ztiold(ji,1) + zeta_i(ji,1) * zradab_i(ji,1) |
|---|
| 524 | |
|---|
| 525 | ! case of only one layer in the ice (surface & ice equations are altered) |
|---|
| 526 | IF ( nlay_i == 1 ) THEN |
|---|
| 527 | ztrid(ji,jm_min(ji),1) = 0.0 |
|---|
| 528 | ztrid(ji,jm_min(ji),2) = zdqns_ice_b(ji) - zkappa_i(ji,0) * 2.0 |
|---|
| 529 | ztrid(ji,jm_min(ji),3) = zkappa_i(ji,0) * 2.0 |
|---|
| 530 | ztrid(ji,jm_min(ji)+1,1) = -zkappa_i(ji,0) * 2.0 * zeta_i(ji,1) |
|---|
| 531 | ztrid(ji,jm_min(ji)+1,2) = 1.0 + zeta_i(ji,1) * ( zkappa_i(ji,0) * 2.0 + zkappa_i(ji,1) ) |
|---|
| 532 | ztrid(ji,jm_min(ji)+1,3) = 0.0 |
|---|
| 533 | zindterm(ji,jm_min(ji)+1) = ztiold(ji,1) + zeta_i(ji,1) * & |
|---|
| 534 | & ( zradab_i(ji,1) + zkappa_i(ji,1) * t_bo_1d(ji) ) |
|---|
| 535 | ENDIF |
|---|
| 536 | |
|---|
| 537 | ELSE !-- case 2 : surface is melting |
|---|
| 538 | |
|---|
| 539 | jm_min(ji) = nlay_s + 2 |
|---|
| 540 | jm_max(ji) = nlay_i + nlay_s + 1 |
|---|
| 541 | |
|---|
| 542 | ! first layer of ice equation |
|---|
| 543 | ztrid(ji,jm_min(ji),1) = 0.0 |
|---|
| 544 | ztrid(ji,jm_min(ji),2) = 1.0 + zeta_i(ji,1) * ( zkappa_i(ji,1) + zkappa_i(ji,0) * zg1 ) |
|---|
| 545 | ztrid(ji,jm_min(ji),3) = - zeta_i(ji,1) * zkappa_i(ji,1) |
|---|
| 546 | zindterm(ji,jm_min(ji)) = ztiold(ji,1) + zeta_i(ji,1) * & |
|---|
| 547 | & ( zradab_i(ji,1) + zkappa_i(ji,0) * zg1 * t_su_1d(ji) ) |
|---|
| 548 | |
|---|
| 549 | ! case of only one layer in the ice (surface & ice equations are altered) |
|---|
| 550 | IF ( nlay_i == 1 ) THEN |
|---|
| 551 | ztrid(ji,jm_min(ji),1) = 0.0 |
|---|
| 552 | ztrid(ji,jm_min(ji),2) = 1.0 + zeta_i(ji,1) * ( zkappa_i(ji,0) * 2.0 + zkappa_i(ji,1) ) |
|---|
| 553 | ztrid(ji,jm_min(ji),3) = 0.0 |
|---|
| 554 | zindterm(ji,jm_min(ji)) = ztiold(ji,1) + zeta_i(ji,1) * ( zradab_i(ji,1) + zkappa_i(ji,1) * t_bo_1d(ji) ) & |
|---|
| 555 | & + t_su_1d(ji) * zeta_i(ji,1) * zkappa_i(ji,0) * 2.0 |
|---|
| 556 | ENDIF |
|---|
| 557 | |
|---|
| 558 | ENDIF |
|---|
| 559 | ENDIF |
|---|
| 560 | ! |
|---|
| 561 | zindtbis(ji,jm_min(ji)) = zindterm(ji,jm_min(ji)) |
|---|
| 562 | zdiagbis(ji,jm_min(ji)) = ztrid(ji,jm_min(ji),2) |
|---|
| 563 | ! |
|---|
| 564 | END DO |
|---|
| 565 | ! |
|---|
| 566 | !------------------------------ |
|---|
| 567 | ! 8) tridiagonal system solving |
|---|
| 568 | !------------------------------ |
|---|
| 569 | ! Solve the tridiagonal system with Gauss elimination method. |
|---|
| 570 | ! Thomas algorithm, from Computational fluid Dynamics, J.D. ANDERSON, McGraw-Hill 1984 |
|---|
| 571 | jm_maxt = 0 |
|---|
| 572 | jm_mint = nlay_i+5 |
|---|
| 573 | DO ji = 1, npti |
|---|
| 574 | jm_mint = MIN(jm_min(ji),jm_mint) |
|---|
| 575 | jm_maxt = MAX(jm_max(ji),jm_maxt) |
|---|
| 576 | END DO |
|---|
| 577 | |
|---|
| 578 | DO jk = jm_mint+1, jm_maxt |
|---|
| 579 | DO ji = 1, npti |
|---|
| 580 | jm = min(max(jm_min(ji)+1,jk),jm_max(ji)) |
|---|
| 581 | zdiagbis(ji,jm) = ztrid(ji,jm,2) - ztrid(ji,jm,1) * ztrid(ji,jm-1,3) / zdiagbis(ji,jm-1) |
|---|
| 582 | zindtbis(ji,jm) = zindterm(ji,jm) - ztrid(ji,jm,1) * zindtbis(ji,jm-1) / zdiagbis(ji,jm-1) |
|---|
| 583 | END DO |
|---|
| 584 | END DO |
|---|
| 585 | |
|---|
| 586 | DO ji = 1, npti |
|---|
| 587 | ! ice temperatures |
|---|
| 588 | t_i_1d(ji,nlay_i) = zindtbis(ji,jm_max(ji)) / zdiagbis(ji,jm_max(ji)) |
|---|
| 589 | END DO |
|---|
| 590 | |
|---|
| 591 | DO jm = nlay_i + nlay_s, nlay_s + 2, -1 |
|---|
| 592 | DO ji = 1, npti |
|---|
| 593 | jk = jm - nlay_s - 1 |
|---|
| 594 | t_i_1d(ji,jk) = ( zindtbis(ji,jm) - ztrid(ji,jm,3) * t_i_1d(ji,jk+1) ) / zdiagbis(ji,jm) |
|---|
| 595 | END DO |
|---|
| 596 | END DO |
|---|
| 597 | |
|---|
| 598 | DO ji = 1, npti |
|---|
| 599 | ! snow temperatures |
|---|
| 600 | IF( h_s_1d(ji) > 0._wp ) THEN |
|---|
| 601 | t_s_1d(ji,nlay_s) = ( zindtbis(ji,nlay_s+1) - ztrid(ji,nlay_s+1,3) * t_i_1d(ji,1) ) & |
|---|
| 602 | & / zdiagbis(ji,nlay_s+1) |
|---|
| 603 | ENDIF |
|---|
| 604 | ! surface temperature |
|---|
| 605 | ztsub(ji) = t_su_1d(ji) |
|---|
| 606 | IF( t_su_1d(ji) < rt0 ) THEN |
|---|
| 607 | t_su_1d(ji) = ( zindtbis(ji,jm_min(ji)) - ztrid(ji,jm_min(ji),3) * & |
|---|
| 608 | & ( isnow(ji) * t_s_1d(ji,1) + ( 1._wp - isnow(ji) ) * t_i_1d(ji,1) ) ) / zdiagbis(ji,jm_min(ji)) |
|---|
| 609 | ENDIF |
|---|
| 610 | END DO |
|---|
| 611 | ! |
|---|
| 612 | !-------------------------------------------------------------- |
|---|
| 613 | ! 9) Has the scheme converged ?, end of the iterative procedure |
|---|
| 614 | !-------------------------------------------------------------- |
|---|
| 615 | ! check that nowhere it has started to melt |
|---|
| 616 | ! zdti_max is a measure of error, it has to be under zdti_bnd |
|---|
| 617 | zdti_max = 0._wp |
|---|
| 618 | DO ji = 1, npti |
|---|
| 619 | t_su_1d(ji) = MAX( MIN( t_su_1d(ji) , rt0 ) , rt0 - 100._wp ) |
|---|
| 620 | zdti_max = MAX( zdti_max, ABS( t_su_1d(ji) - ztsub(ji) ) ) |
|---|
| 621 | END DO |
|---|
| 622 | |
|---|
| 623 | DO jk = 1, nlay_s |
|---|
| 624 | DO ji = 1, npti |
|---|
| 625 | t_s_1d(ji,jk) = MAX( MIN( t_s_1d(ji,jk), rt0 ), rt0 - 100._wp ) |
|---|
| 626 | zdti_max = MAX( zdti_max, ABS( t_s_1d(ji,jk) - ztsb(ji,jk) ) ) |
|---|
| 627 | END DO |
|---|
| 628 | END DO |
|---|
| 629 | |
|---|
| 630 | DO jk = 1, nlay_i |
|---|
| 631 | DO ji = 1, npti |
|---|
| 632 | ztmelt_i = -tmut * sz_i_1d(ji,jk) + rt0 |
|---|
| 633 | t_i_1d(ji,jk) = MAX( MIN( t_i_1d(ji,jk), ztmelt_i ), rt0 - 100._wp ) |
|---|
| 634 | zdti_max = MAX( zdti_max, ABS( t_i_1d(ji,jk) - ztib(ji,jk) ) ) |
|---|
| 635 | END DO |
|---|
| 636 | END DO |
|---|
| 637 | |
|---|
| 638 | ! Compute spatial maximum over all errors |
|---|
| 639 | ! note that this could be optimized substantially by iterating only the non-converging points |
|---|
| 640 | IF( lk_mpp ) CALL mpp_max( zdti_max, kcom=ncomm_ice ) |
|---|
| 641 | ! |
|---|
| 642 | !----------------------------------------! |
|---|
| 643 | ! ! |
|---|
| 644 | ! JULES IF (RCV MODE) ! |
|---|
| 645 | ! ! |
|---|
| 646 | !----------------------------------------! |
|---|
| 647 | ! |
|---|
| 648 | |
|---|
| 649 | ELSE IF ( k_jules == np_zdf_jules_RCV ) THEN ! RCV mode |
|---|
| 650 | |
|---|
| 651 | ! |
|---|
| 652 | ! In RCV mode, we use a modified BL99 solver |
|---|
| 653 | ! with conduction flux (qcn_ice) as forcing term |
|---|
| 654 | ! |
|---|
| 655 | !---------------------------- |
|---|
| 656 | ! 7) tridiagonal system terms |
|---|
| 657 | !---------------------------- |
|---|
| 658 | !!layer denotes the number of the layer in the snow or in the ice |
|---|
| 659 | !!jm denotes the reference number of the equation in the tridiagonal |
|---|
| 660 | !!system, terms of tridiagonal system are indexed as following : |
|---|
| 661 | !!1 is subdiagonal term, 2 is diagonal and 3 is superdiagonal one |
|---|
| 662 | |
|---|
| 663 | !!ice interior terms (top equation has the same form as the others) |
|---|
| 664 | ztrid (1:npti,:,:) = 0._wp |
|---|
| 665 | zindterm(1:npti,:) = 0._wp |
|---|
| 666 | zindtbis(1:npti,:) = 0._wp |
|---|
| 667 | zdiagbis(1:npti,:) = 0._wp |
|---|
| 668 | |
|---|
| 669 | DO jm = nlay_s + 2, nlay_s + nlay_i |
|---|
| 670 | DO ji = 1, npti |
|---|
| 671 | jk = jm - nlay_s - 1 |
|---|
| 672 | ztrid(ji,jm,1) = - zeta_i(ji,jk) * zkappa_i(ji,jk-1) |
|---|
| 673 | ztrid(ji,jm,2) = 1.0 + zeta_i(ji,jk) * ( zkappa_i(ji,jk-1) + zkappa_i(ji,jk) ) |
|---|
| 674 | ztrid(ji,jm,3) = - zeta_i(ji,jk) * zkappa_i(ji,jk) |
|---|
| 675 | zindterm(ji,jm) = ztiold(ji,jk) + zeta_i(ji,jk) * zradab_i(ji,jk) |
|---|
| 676 | END DO |
|---|
| 677 | ENDDO |
|---|
| 678 | |
|---|
| 679 | jm = nlay_s + nlay_i + 1 |
|---|
| 680 | DO ji = 1, npti |
|---|
| 681 | !!ice bottom term |
|---|
| 682 | ztrid(ji,jm,1) = - zeta_i(ji,nlay_i)*zkappa_i(ji,nlay_i-1) |
|---|
| 683 | ztrid(ji,jm,2) = 1.0 + zeta_i(ji,nlay_i) * ( zkappa_i(ji,nlay_i) * zg1 + zkappa_i(ji,nlay_i-1) ) |
|---|
| 684 | ztrid(ji,jm,3) = 0.0 |
|---|
| 685 | zindterm(ji,jm) = ztiold(ji,nlay_i) + zeta_i(ji,nlay_i) * & |
|---|
| 686 | & ( zradab_i(ji,nlay_i) + zkappa_i(ji,nlay_i) * zg1 * t_bo_1d(ji) ) |
|---|
| 687 | ENDDO |
|---|
| 688 | |
|---|
| 689 | |
|---|
| 690 | DO ji = 1, npti |
|---|
| 691 | ! !---------------------! |
|---|
| 692 | IF ( h_s_1d(ji) > 0.0 ) THEN ! snow-covered cells ! |
|---|
| 693 | ! !---------------------! |
|---|
| 694 | ! snow interior terms (bottom equation has the same form as the others) |
|---|
| 695 | DO jm = 3, nlay_s + 1 |
|---|
| 696 | jk = jm - 1 |
|---|
| 697 | ztrid(ji,jm,1) = - zeta_s(ji,jk) * zkappa_s(ji,jk-1) |
|---|
| 698 | ztrid(ji,jm,2) = 1.0 + zeta_s(ji,jk) * ( zkappa_s(ji,jk-1) + zkappa_s(ji,jk) ) |
|---|
| 699 | ztrid(ji,jm,3) = - zeta_s(ji,jk)*zkappa_s(ji,jk) |
|---|
| 700 | zindterm(ji,jm) = ztsold(ji,jk) + zeta_s(ji,jk) * zradab_s(ji,jk) |
|---|
| 701 | END DO |
|---|
| 702 | |
|---|
| 703 | ! case of only one layer in the ice (ice equation is altered) |
|---|
| 704 | IF ( nlay_i == 1 ) THEN |
|---|
| 705 | ztrid(ji,nlay_s+2,3) = 0.0 |
|---|
| 706 | zindterm(ji,nlay_s+2) = zindterm(ji,nlay_s+2) + zkappa_i(ji,1) * t_bo_1d(ji) |
|---|
| 707 | ENDIF |
|---|
| 708 | |
|---|
| 709 | jm_min(ji) = 2 |
|---|
| 710 | jm_max(ji) = nlay_i + nlay_s + 1 |
|---|
| 711 | |
|---|
| 712 | ! first layer of snow equation |
|---|
| 713 | ztrid(ji,2,1) = 0.0 |
|---|
| 714 | ztrid(ji,2,2) = 1.0 + zeta_s(ji,1) * zkappa_s(ji,1) |
|---|
| 715 | ztrid(ji,2,3) = - zeta_s(ji,1)*zkappa_s(ji,1) |
|---|
| 716 | zindterm(ji,2) = ztsold(ji,1) + zeta_s(ji,1) * & |
|---|
| 717 | & ( zradab_s(ji,1) + qcn_ice_1d(ji) ) |
|---|
| 718 | |
|---|
| 719 | ! !---------------------! |
|---|
| 720 | ELSE ! cells without snow ! |
|---|
| 721 | ! !---------------------! |
|---|
| 722 | |
|---|
| 723 | jm_min(ji) = nlay_s + 2 |
|---|
| 724 | jm_max(ji) = nlay_i + nlay_s + 1 |
|---|
| 725 | |
|---|
| 726 | ! first layer of ice equation |
|---|
| 727 | ztrid(ji,jm_min(ji),1) = 0.0 |
|---|
| 728 | ztrid(ji,jm_min(ji),2) = 1.0 + zeta_i(ji,1) * zkappa_i(ji,1) |
|---|
| 729 | ztrid(ji,jm_min(ji),3) = - zeta_i(ji,1) * zkappa_i(ji,1) |
|---|
| 730 | zindterm(ji,jm_min(ji)) = ztiold(ji,1) + zeta_i(ji,1) * & |
|---|
| 731 | & ( zradab_i(ji,1) + qcn_ice_1d(ji) ) |
|---|
| 732 | |
|---|
| 733 | ! case of only one layer in the ice (surface & ice equations are altered) |
|---|
| 734 | IF ( nlay_i == 1 ) THEN |
|---|
| 735 | ztrid(ji,jm_min(ji),1) = 0.0 |
|---|
| 736 | ztrid(ji,jm_min(ji),2) = 1.0 + zeta_i(ji,1) * zkappa_i(ji,1) |
|---|
| 737 | ztrid(ji,jm_min(ji),3) = 0.0 |
|---|
| 738 | zindterm(ji,jm_min(ji)) = ztiold(ji,1) + zeta_i(ji,1) * ( zradab_i(ji,1) + zkappa_i(ji,1) * t_bo_1d(ji) & |
|---|
| 739 | & + qcn_ice_1d(ji) ) |
|---|
| 740 | |
|---|
| 741 | ENDIF |
|---|
| 742 | |
|---|
| 743 | ENDIF |
|---|
| 744 | ! |
|---|
| 745 | zindtbis(ji,jm_min(ji)) = zindterm(ji,jm_min(ji)) |
|---|
| 746 | zdiagbis(ji,jm_min(ji)) = ztrid(ji,jm_min(ji),2) |
|---|
| 747 | ! |
|---|
| 748 | END DO |
|---|
| 749 | ! |
|---|
| 750 | !------------------------------ |
|---|
| 751 | ! 8) tridiagonal system solving |
|---|
| 752 | !------------------------------ |
|---|
| 753 | ! Solve the tridiagonal system with Gauss elimination method. |
|---|
| 754 | ! Thomas algorithm, from Computational fluid Dynamics, J.D. ANDERSON, McGraw-Hill 1984 |
|---|
| 755 | jm_maxt = 0 |
|---|
| 756 | jm_mint = nlay_i+5 |
|---|
| 757 | DO ji = 1, npti |
|---|
| 758 | jm_mint = MIN(jm_min(ji),jm_mint) |
|---|
| 759 | jm_maxt = MAX(jm_max(ji),jm_maxt) |
|---|
| 760 | END DO |
|---|
| 761 | |
|---|
| 762 | DO jk = jm_mint+1, jm_maxt |
|---|
| 763 | DO ji = 1, npti |
|---|
| 764 | jm = min(max(jm_min(ji)+1,jk),jm_max(ji)) |
|---|
| 765 | zdiagbis(ji,jm) = ztrid(ji,jm,2) - ztrid(ji,jm,1) * ztrid(ji,jm-1,3) / zdiagbis(ji,jm-1) |
|---|
| 766 | zindtbis(ji,jm) = zindterm(ji,jm) - ztrid(ji,jm,1) * zindtbis(ji,jm-1) / zdiagbis(ji,jm-1) |
|---|
| 767 | END DO |
|---|
| 768 | END DO |
|---|
| 769 | |
|---|
| 770 | DO ji = 1, npti |
|---|
| 771 | ! ice temperatures |
|---|
| 772 | t_i_1d(ji,nlay_i) = zindtbis(ji,jm_max(ji)) / zdiagbis(ji,jm_max(ji)) |
|---|
| 773 | END DO |
|---|
| 774 | |
|---|
| 775 | DO jm = nlay_i + nlay_s, nlay_s + 2, -1 |
|---|
| 776 | DO ji = 1, npti |
|---|
| 777 | jk = jm - nlay_s - 1 |
|---|
| 778 | t_i_1d(ji,jk) = ( zindtbis(ji,jm) - ztrid(ji,jm,3) * t_i_1d(ji,jk+1) ) / zdiagbis(ji,jm) |
|---|
| 779 | END DO |
|---|
| 780 | END DO |
|---|
| 781 | |
|---|
| 782 | DO ji = 1, npti |
|---|
| 783 | ! snow temperatures |
|---|
| 784 | IF( h_s_1d(ji) > 0._wp ) THEN |
|---|
| 785 | t_s_1d(ji,nlay_s) = ( zindtbis(ji,nlay_s+1) - ztrid(ji,nlay_s+1,3) * t_i_1d(ji,1) ) & |
|---|
| 786 | & / zdiagbis(ji,nlay_s+1) |
|---|
| 787 | ENDIF |
|---|
| 788 | END DO |
|---|
| 789 | ! |
|---|
| 790 | !-------------------------------------------------------------- |
|---|
| 791 | ! 9) Has the scheme converged ?, end of the iterative procedure |
|---|
| 792 | !-------------------------------------------------------------- |
|---|
| 793 | ! check that nowhere it has started to melt |
|---|
| 794 | ! zdti_max is a measure of error, it has to be under zdti_bnd |
|---|
| 795 | zdti_max = 0._wp |
|---|
| 796 | |
|---|
| 797 | DO jk = 1, nlay_s |
|---|
| 798 | DO ji = 1, npti |
|---|
| 799 | t_s_1d(ji,jk) = MAX( MIN( t_s_1d(ji,jk), rt0 ), rt0 - 100._wp ) |
|---|
| 800 | zdti_max = MAX( zdti_max, ABS( t_s_1d(ji,jk) - ztsb(ji,jk) ) ) |
|---|
| 801 | END DO |
|---|
| 802 | END DO |
|---|
| 803 | |
|---|
| 804 | DO jk = 1, nlay_i |
|---|
| 805 | DO ji = 1, npti |
|---|
| 806 | ztmelt_i = -tmut * sz_i_1d(ji,jk) + rt0 |
|---|
| 807 | t_i_1d(ji,jk) = MAX( MIN( t_i_1d(ji,jk), ztmelt_i ), rt0 - 100._wp ) |
|---|
| 808 | zdti_max = MAX( zdti_max, ABS( t_i_1d(ji,jk) - ztib(ji,jk) ) ) |
|---|
| 809 | END DO |
|---|
| 810 | END DO |
|---|
| 811 | |
|---|
| 812 | ! Compute spatial maximum over all errors |
|---|
| 813 | ! note that this could be optimized substantially by iterating only the non-converging points |
|---|
| 814 | IF( lk_mpp ) CALL mpp_max( zdti_max, kcom=ncomm_ice ) |
|---|
| 815 | |
|---|
| 816 | ENDIF ! k_jules |
|---|
| 817 | |
|---|
| 818 | END DO ! End of the do while iterative procedure |
|---|
| 819 | |
|---|
| 820 | IF( ln_icectl .AND. lwp ) THEN |
|---|
| 821 | WRITE(numout,*) ' zdti_max : ', zdti_max |
|---|
| 822 | WRITE(numout,*) ' iconv : ', iconv |
|---|
| 823 | ENDIF |
|---|
| 824 | |
|---|
| 825 | ! |
|---|
| 826 | !----------------------------- |
|---|
| 827 | ! 10) Fluxes at the interfaces |
|---|
| 828 | !----------------------------- |
|---|
| 829 | ! |
|---|
| 830 | ! --- update conduction fluxes |
|---|
| 831 | ! |
|---|
| 832 | DO ji = 1, npti |
|---|
| 833 | ! ! surface ice conduction flux |
|---|
| 834 | fc_su(ji) = - isnow(ji) * zkappa_s(ji,0) * zg1s * (t_s_1d(ji,1) - t_su_1d(ji)) & |
|---|
| 835 | & - ( 1._wp - isnow(ji) ) * zkappa_i(ji,0) * zg1 * (t_i_1d(ji,1) - t_su_1d(ji)) |
|---|
| 836 | ! ! bottom ice conduction flux |
|---|
| 837 | fc_bo_i(ji) = - zkappa_i(ji,nlay_i) * ( zg1*(t_bo_1d(ji) - t_i_1d(ji,nlay_i)) ) |
|---|
| 838 | END DO |
|---|
| 839 | |
|---|
| 840 | ! |
|---|
| 841 | ! --- Diagnose the heat loss due to changing non-solar / conduction flux --- ! |
|---|
| 842 | ! |
|---|
| 843 | DO ji = 1, npti |
|---|
| 844 | IF ( k_jules == np_zdf_jules_OFF .OR. k_jules == np_zdf_jules_SND ) THEN |
|---|
| 845 | ! OFF or SND mode |
|---|
| 846 | hfx_err_dif_1d(ji) = hfx_err_dif_1d(ji) - ( qns_ice_1d(ji) - zqns_ice_b(ji) ) * a_i_1d(ji) |
|---|
| 847 | ELSE ! RCV mode |
|---|
| 848 | hfx_err_dif_1d(ji) = hfx_err_dif_1d(ji) - ( fc_su(ji) - qcn_ice_1d(ji) ) * a_i_1d(ji) |
|---|
| 849 | ENDIF |
|---|
| 850 | END DO |
|---|
| 851 | |
|---|
| 852 | ! |
|---|
| 853 | ! --- Diagnose the heat loss due to non-fully converged temperature solution (should not be above 10-4 W-m2) --- ! |
|---|
| 854 | ! |
|---|
| 855 | |
|---|
| 856 | IF ( ( k_jules == np_zdf_jules_OFF ) .OR. ( k_jules == np_zdf_jules_RCV ) ) THEN ! OFF |
|---|
| 857 | |
|---|
| 858 | CALL ice_thd_enmelt |
|---|
| 859 | |
|---|
| 860 | ! zhfx_err = correction on the diagnosed heat flux due to non-convergence of the algorithm used to solve heat equation |
|---|
| 861 | DO ji = 1, npti |
|---|
| 862 | zdq = - zq_ini(ji) + ( SUM( e_i_1d(ji,1:nlay_i) ) * h_i_1d(ji) * r1_nlay_i + & |
|---|
| 863 | & SUM( e_s_1d(ji,1:nlay_s) ) * h_s_1d(ji) * r1_nlay_s ) |
|---|
| 864 | |
|---|
| 865 | IF ( ( k_jules == np_zdf_jules_OFF ) ) THEN |
|---|
| 866 | |
|---|
| 867 | IF( t_su_1d(ji) < rt0 ) THEN ! case T_su < 0degC |
|---|
| 868 | zhfx_err = ( qns_ice_1d(ji) + qsr_ice_1d(ji) - zradtr_i(ji,nlay_i) - fc_bo_i(ji) + zdq * r1_rdtice ) * a_i_1d(ji) |
|---|
| 869 | ELSE ! case T_su = 0degC |
|---|
| 870 | zhfx_err = ( fc_su(ji) + qsr_ice_tr_1d(ji) - zradtr_i(ji,nlay_i) - fc_bo_i(ji) + zdq * r1_rdtice ) * a_i_1d(ji) |
|---|
| 871 | ENDIF |
|---|
| 872 | |
|---|
| 873 | ELSE ! RCV CASE |
|---|
| 874 | |
|---|
| 875 | zhfx_err = ( fc_su(ji) + qsr_ice_tr_1d(ji) - zradtr_i(ji,nlay_i) - fc_bo_i(ji) + zdq * r1_rdtice ) * a_i_1d(ji) |
|---|
| 876 | |
|---|
| 877 | ENDIF |
|---|
| 878 | |
|---|
| 879 | ! total heat sink to be sent to the ocean |
|---|
| 880 | hfx_err_dif_1d(ji) = hfx_err_dif_1d(ji) + zhfx_err |
|---|
| 881 | |
|---|
| 882 | ! hfx_dif = Heat flux diagnostic of sensible heat used to warm/cool ice in W.m-2 |
|---|
| 883 | hfx_dif_1d(ji) = hfx_dif_1d(ji) - zdq * r1_rdtice * a_i_1d(ji) |
|---|
| 884 | |
|---|
| 885 | END DO |
|---|
| 886 | |
|---|
| 887 | ! |
|---|
| 888 | ! --- SIMIP diagnostics |
|---|
| 889 | ! |
|---|
| 890 | |
|---|
| 891 | DO ji = 1, npti |
|---|
| 892 | !--- Conduction fluxes (positive downwards) |
|---|
| 893 | diag_fc_bo_1d(ji) = diag_fc_bo_1d(ji) + fc_bo_i(ji) * a_i_1d(ji) / at_i_1d(ji) |
|---|
| 894 | diag_fc_su_1d(ji) = diag_fc_su_1d(ji) + fc_su(ji) * a_i_1d(ji) / at_i_1d(ji) |
|---|
| 895 | |
|---|
| 896 | !--- Snow-ice interfacial temperature (diagnostic SIMIP) |
|---|
| 897 | zfac = rn_cnd_s * zh_i(ji) + ztcond_i(ji,1) * zh_s(ji) |
|---|
| 898 | IF( zh_s(ji) >= 1.e-3 .AND. zfac > epsi10 ) THEN |
|---|
| 899 | t_si_1d(ji) = ( rn_cnd_s * zh_i(ji) * t_s_1d(ji,1) + & |
|---|
| 900 | & ztcond_i(ji,1) * zh_s(ji) * t_i_1d(ji,1) ) / zfac |
|---|
| 901 | ELSE |
|---|
| 902 | t_si_1d(ji) = t_su_1d(ji) |
|---|
| 903 | ENDIF |
|---|
| 904 | END DO |
|---|
| 905 | |
|---|
| 906 | ENDIF |
|---|
| 907 | ! |
|---|
| 908 | !--------------------------------------------------------------------------------------- |
|---|
| 909 | ! 11) Jules coupling: reset inner snow and ice temperatures, update conduction fluxes |
|---|
| 910 | !--------------------------------------------------------------------------------------- |
|---|
| 911 | ! effective conductivity and 1st layer temperature (Jules coupling) |
|---|
| 912 | DO ji = 1, npti |
|---|
| 913 | cnd_ice_1d(ji) = 2._wp * ( isnow(ji) * zkappa_s(ji,0) + ( 1._wp - isnow(ji) ) * zkappa_i(ji,0) ) |
|---|
| 914 | t1_ice_1d (ji) = ( isnow(ji) * t_s_1d (ji,1) + ( 1._wp - isnow(ji) ) * t_i_1d (ji,1) ) |
|---|
| 915 | END DO |
|---|
| 916 | ! |
|---|
| 917 | IF ( k_jules == np_zdf_jules_SND ) THEN ! --- Jules coupling in "SND" mode |
|---|
| 918 | |
|---|
| 919 | ! Restore temperatures to their initial values |
|---|
| 920 | t_s_1d(1:npti,:) = ztsold (1:npti,:) |
|---|
| 921 | t_i_1d(1:npti,:) = ztiold (1:npti,:) |
|---|
| 922 | qcn_ice_1d(1:npti) = fc_su(1:npti) |
|---|
| 923 | |
|---|
| 924 | ENDIF |
|---|
| 925 | |
|---|
| 926 | END SUBROUTINE ice_thd_zdf_BL99 |
|---|
| 927 | |
|---|
| 928 | |
|---|
| 929 | |
|---|
| 930 | SUBROUTINE ice_thd_enmelt |
|---|
| 931 | !!------------------------------------------------------------------- |
|---|
| 932 | !! *** ROUTINE ice_thd_enmelt *** |
|---|
| 933 | !! |
|---|
| 934 | !! ** Purpose : Computes sea ice energy of melting q_i (J.m-3) from temperature |
|---|
| 935 | !! |
|---|
| 936 | !! ** Method : Formula (Bitz and Lipscomb, 1999) |
|---|
| 937 | !!------------------------------------------------------------------- |
|---|
| 938 | INTEGER :: ji, jk ! dummy loop indices |
|---|
| 939 | REAL(wp) :: ztmelts ! local scalar |
|---|
| 940 | !!------------------------------------------------------------------- |
|---|
| 941 | ! |
|---|
| 942 | DO jk = 1, nlay_i ! Sea ice energy of melting |
|---|
| 943 | DO ji = 1, npti |
|---|
| 944 | ztmelts = - tmut * sz_i_1d(ji,jk) |
|---|
| 945 | t_i_1d(ji,jk) = MIN( t_i_1d(ji,jk), ztmelts + rt0 ) ! Force t_i_1d to be lower than melting point |
|---|
| 946 | ! (sometimes dif scheme produces abnormally high temperatures) |
|---|
| 947 | e_i_1d(ji,jk) = rhoic * ( cpic * ( ztmelts - ( t_i_1d(ji,jk) - rt0 ) ) & |
|---|
| 948 | & + lfus * ( 1._wp - ztmelts / ( t_i_1d(ji,jk) - rt0 ) ) & |
|---|
| 949 | & - rcp * ztmelts ) |
|---|
| 950 | END DO |
|---|
| 951 | END DO |
|---|
| 952 | DO jk = 1, nlay_s ! Snow energy of melting |
|---|
| 953 | DO ji = 1, npti |
|---|
| 954 | e_s_1d(ji,jk) = rhosn * ( cpic * ( rt0 - t_s_1d(ji,jk) ) + lfus ) |
|---|
| 955 | END DO |
|---|
| 956 | END DO |
|---|
| 957 | ! |
|---|
| 958 | END SUBROUTINE ice_thd_enmelt |
|---|
| 959 | |
|---|
| 960 | |
|---|
| 961 | |
|---|
| 962 | SUBROUTINE ice_thd_zdf_init |
|---|
| 963 | !!----------------------------------------------------------------------- |
|---|
| 964 | !! *** ROUTINE ice_thd_zdf_init *** |
|---|
| 965 | !! |
|---|
| 966 | !! ** Purpose : Physical constants and parameters associated with |
|---|
| 967 | !! ice thermodynamics |
|---|
| 968 | !! |
|---|
| 969 | !! ** Method : Read the namthd_zdf namelist and check the parameters |
|---|
| 970 | !! called at the first timestep (nit000) |
|---|
| 971 | !! |
|---|
| 972 | !! ** input : Namelist namthd_zdf |
|---|
| 973 | !!------------------------------------------------------------------- |
|---|
| 974 | INTEGER :: ios, ioptio ! Local integer output status for namelist read |
|---|
| 975 | !! |
|---|
| 976 | NAMELIST/namthd_zdf/ ln_zdf_BL99, ln_cndi_U64, ln_cndi_P07, rn_cnd_s, rn_kappa_i |
|---|
| 977 | !!------------------------------------------------------------------- |
|---|
| 978 | ! |
|---|
| 979 | REWIND( numnam_ice_ref ) ! Namelist namthd_zdf in reference namelist : Ice thermodynamics |
|---|
| 980 | READ ( numnam_ice_ref, namthd_zdf, IOSTAT = ios, ERR = 901) |
|---|
| 981 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namthd_zdf in reference namelist', lwp ) |
|---|
| 982 | |
|---|
| 983 | REWIND( numnam_ice_cfg ) ! Namelist namthd_zdf in configuration namelist : Ice thermodynamics |
|---|
| 984 | READ ( numnam_ice_cfg, namthd_zdf, IOSTAT = ios, ERR = 902 ) |
|---|
| 985 | 902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namthd_zdf in configuration namelist', lwp ) |
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| 986 | IF(lwm) WRITE ( numoni, namthd_zdf ) |
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| 987 | ! |
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| 988 | ! |
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| 989 | IF(lwp) THEN ! control print |
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| 990 | WRITE(numout,*) 'ice_thd_zdf_init: Ice vertical heat diffusion' |
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| 991 | WRITE(numout,*) '~~~~~~~~~~~~~~~~' |
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| 992 | WRITE(numout,*) ' Namelist namthd_zdf:' |
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| 993 | WRITE(numout,*) ' Bitz and Lipscomb (1999) formulation ln_zdf_BL99 = ', ln_zdf_BL99 |
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| 994 | WRITE(numout,*) ' thermal conductivity in the ice (Untersteiner 1964) ln_cndi_U64 = ', ln_cndi_U64 |
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| 995 | WRITE(numout,*) ' thermal conductivity in the ice (Pringle et al 2007) ln_cndi_P07 = ', ln_cndi_P07 |
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| 996 | WRITE(numout,*) ' thermal conductivity in the snow rn_cnd_s = ', rn_cnd_s |
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| 997 | WRITE(numout,*) ' extinction radiation parameter in sea ice rn_kappa_i = ', rn_kappa_i |
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| 998 | ENDIF |
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| 999 | |
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| 1000 | ! |
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| 1001 | IF ( ( ln_cndi_U64 .AND. ln_cndi_P07 ) .OR. ( .NOT.ln_cndi_U64 .AND. .NOT.ln_cndi_P07 ) ) THEN |
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| 1002 | CALL ctl_stop( 'ice_thd_zdf_init: choose one and only one formulation for thermal conduction (ln_cndi_U64 or ln_cndi_P07)' ) |
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| 1003 | ENDIF |
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| 1004 | |
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| 1005 | ! !== set the choice of ice vertical thermodynamic formulation ==! |
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| 1006 | ioptio = 0 |
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| 1007 | ! !--- BL99 thermo dynamics (linear liquidus + constant thermal properties) |
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| 1008 | IF( ln_zdf_BL99 ) THEN ; ioptio = ioptio + 1 ; nice_zdf = np_BL99 ; ENDIF |
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| 1009 | IF( ioptio /= 1 ) CALL ctl_stop( 'ice_thd_init: one and only one ice thermo option has to be defined ' ) |
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| 1010 | ! |
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| 1011 | END SUBROUTINE ice_thd_zdf_init |
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| 1012 | |
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| 1013 | #else |
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| 1014 | !!---------------------------------------------------------------------- |
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| 1015 | !! Default option Dummy Module No ESIM sea-ice model |
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| 1016 | !!--------------------------------------------------------------------- |
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| 1017 | #endif |
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| 1018 | |
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| 1019 | !!====================================================================== |
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| 1020 | END MODULE icethd_zdf |
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