[825] | 1 | MODULE limthd_dif |
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| 2 | !!====================================================================== |
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| 3 | !! *** MODULE limthd_dif *** |
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| 4 | !! heat diffusion in sea ice |
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| 5 | !! computation of surface and inner T |
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| 6 | !!====================================================================== |
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[2715] | 7 | !! History : LIM ! 02-2003 (M. Vancoppenolle) original 1D code |
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| 8 | !! ! 06-2005 (M. Vancoppenolle) 3d version |
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| 9 | !! ! 11-2006 (X Fettweis) Vectorization by Xavier |
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| 10 | !! ! 04-2007 (M. Vancoppenolle) Energy conservation |
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| 11 | !! 4.0 ! 2011-02 (G. Madec) dynamical allocation |
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[4161] | 12 | !! - ! 2012-05 (C. Rousset) add penetration solar flux |
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[825] | 13 | !!---------------------------------------------------------------------- |
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[2528] | 14 | #if defined key_lim3 |
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| 15 | !!---------------------------------------------------------------------- |
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| 16 | !! 'key_lim3' LIM3 sea-ice model |
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| 17 | !!---------------------------------------------------------------------- |
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[3625] | 18 | USE par_oce ! ocean parameters |
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| 19 | USE phycst ! physical constants (ocean directory) |
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| 20 | USE ice ! LIM-3 variables |
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| 21 | USE par_ice ! LIM-3 parameters |
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| 22 | USE thd_ice ! LIM-3: thermodynamics |
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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 wrk_nemo ! work arrays |
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| 26 | USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) |
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[921] | 27 | |
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[825] | 28 | IMPLICIT NONE |
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| 29 | PRIVATE |
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| 30 | |
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[2528] | 31 | PUBLIC lim_thd_dif ! called by lim_thd |
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[825] | 32 | |
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[2715] | 33 | REAL(wp) :: epsi20 = 1e-20 ! constant values |
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| 34 | REAL(wp) :: epsi13 = 1e-13 ! constant values |
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[825] | 35 | |
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| 36 | !!---------------------------------------------------------------------- |
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[4161] | 37 | !! NEMO/LIM3 4.0 , UCL - NEMO Consortium (2011) |
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[1156] | 38 | !! $Id$ |
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[2591] | 39 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[825] | 40 | !!---------------------------------------------------------------------- |
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| 41 | CONTAINS |
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| 42 | |
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| 43 | SUBROUTINE lim_thd_dif( kideb , kiut , jl ) |
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[921] | 44 | !!------------------------------------------------------------------ |
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| 45 | !! *** ROUTINE lim_thd_dif *** |
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| 46 | !! ** Purpose : |
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| 47 | !! This routine determines the time evolution of snow and sea-ice |
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| 48 | !! temperature profiles. |
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| 49 | !! ** Method : |
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| 50 | !! This is done by solving the heat equation diffusion with |
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| 51 | !! a Neumann boundary condition at the surface and a Dirichlet one |
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| 52 | !! at the bottom. Solar radiation is partially absorbed into the ice. |
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| 53 | !! The specific heat and thermal conductivities depend on ice salinity |
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| 54 | !! and temperature to take into account brine pocket melting. The |
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| 55 | !! numerical |
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| 56 | !! scheme is an iterative Crank-Nicolson on a non-uniform multilayer grid |
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| 57 | !! in the ice and snow system. |
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| 58 | !! |
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| 59 | !! The successive steps of this routine are |
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| 60 | !! 1. Thermal conductivity at the interfaces of the ice layers |
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| 61 | !! 2. Internal absorbed radiation |
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| 62 | !! 3. Scale factors due to non-uniform grid |
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| 63 | !! 4. Kappa factors |
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| 64 | !! Then iterative procedure begins |
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| 65 | !! 5. specific heat in the ice |
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| 66 | !! 6. eta factors |
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| 67 | !! 7. surface flux computation |
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| 68 | !! 8. tridiagonal system terms |
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| 69 | !! 9. solving the tridiagonal system with Gauss elimination |
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| 70 | !! Iterative procedure ends according to a criterion on evolution |
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| 71 | !! of temperature |
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| 72 | !! |
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| 73 | !! ** Arguments : |
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| 74 | !! kideb , kiut : Starting and ending points on which the |
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| 75 | !! the computation is applied |
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| 76 | !! |
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| 77 | !! ** Inputs / Ouputs : (global commons) |
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| 78 | !! surface temperature : t_su_b |
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| 79 | !! ice/snow temperatures : t_i_b, t_s_b |
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| 80 | !! ice salinities : s_i_b |
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| 81 | !! number of layers in the ice/snow: nlay_i, nlay_s |
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| 82 | !! profile of the ice/snow layers : z_i, z_s |
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| 83 | !! total ice/snow thickness : ht_i_b, ht_s_b |
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| 84 | !! |
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| 85 | !! ** External : |
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| 86 | !! |
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| 87 | !! ** References : |
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| 88 | !! |
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| 89 | !! ** History : |
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| 90 | !! (02-2003) Martin Vancoppenolle, Louvain-la-Neuve, Belgium |
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| 91 | !! (06-2005) Martin Vancoppenolle, 3d version |
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| 92 | !! (11-2006) Vectorized by Xavier Fettweis (UCL-ASTR) |
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| 93 | !! (04-2007) Energy conservation tested by M. Vancoppenolle |
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| 94 | !!------------------------------------------------------------------ |
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[3294] | 95 | INTEGER , INTENT (in) :: kideb ! Start point on which the the computation is applied |
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| 96 | INTEGER , INTENT (in) :: kiut ! End point on which the the computation is applied |
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| 97 | INTEGER , INTENT (in) :: jl ! Category number |
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[825] | 98 | |
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[921] | 99 | !! * Local variables |
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[3294] | 100 | INTEGER :: ji ! spatial loop index |
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| 101 | INTEGER :: ii, ij ! temporary dummy loop index |
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| 102 | INTEGER :: numeq ! current reference number of equation |
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| 103 | INTEGER :: layer ! vertical dummy loop index |
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| 104 | INTEGER :: nconv ! number of iterations in iterative procedure |
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| 105 | INTEGER :: minnumeqmin, maxnumeqmax |
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[3610] | 106 | INTEGER, DIMENSION(kiut) :: numeqmin ! reference number of top equation |
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| 107 | INTEGER, DIMENSION(kiut) :: numeqmax ! reference number of bottom equation |
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| 108 | INTEGER, DIMENSION(kiut) :: isnow ! switch for presence (1) or absence (0) of snow |
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[3294] | 109 | REAL(wp) :: zeps = 1.e-10_wp ! |
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| 110 | REAL(wp) :: zg1s = 2._wp ! for the tridiagonal system |
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| 111 | REAL(wp) :: zg1 = 2._wp ! |
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| 112 | REAL(wp) :: zgamma = 18009._wp ! for specific heat |
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| 113 | REAL(wp) :: zbeta = 0.117_wp ! for thermal conductivity (could be 0.13) |
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| 114 | REAL(wp) :: zraext_s = 1.e+8_wp ! extinction coefficient of radiation in the snow |
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| 115 | REAL(wp) :: zkimin = 0.10_wp ! minimum ice thermal conductivity |
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| 116 | REAL(wp) :: zht_smin = 1.e-4_wp ! minimum snow depth |
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[2715] | 117 | REAL(wp) :: ztmelt_i ! ice melting temperature |
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| 118 | REAL(wp) :: zerritmax ! current maximal error on temperature |
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[3610] | 119 | REAL(wp), DIMENSION(kiut) :: ztfs ! ice melting point |
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| 120 | REAL(wp), DIMENSION(kiut) :: ztsuold ! old surface temperature (before the iterative procedure ) |
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| 121 | REAL(wp), DIMENSION(kiut) :: ztsuoldit ! surface temperature at previous iteration |
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| 122 | REAL(wp), DIMENSION(kiut) :: zh_i ! ice layer thickness |
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| 123 | REAL(wp), DIMENSION(kiut) :: zh_s ! snow layer thickness |
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| 124 | REAL(wp), DIMENSION(kiut) :: zfsw ! solar radiation absorbed at the surface |
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| 125 | REAL(wp), DIMENSION(kiut) :: zf ! surface flux function |
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| 126 | REAL(wp), DIMENSION(kiut) :: dzf ! derivative of the surface flux function |
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| 127 | REAL(wp), DIMENSION(kiut) :: zerrit ! current error on temperature |
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| 128 | REAL(wp), DIMENSION(kiut) :: zdifcase ! case of the equation resolution (1->4) |
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| 129 | REAL(wp), DIMENSION(kiut) :: zftrice ! solar radiation transmitted through the ice |
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| 130 | REAL(wp), DIMENSION(kiut) :: zihic, zhsu |
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| 131 | REAL(wp), DIMENSION(kiut,0:nlay_i) :: ztcond_i ! Ice thermal conductivity |
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| 132 | REAL(wp), DIMENSION(kiut,0:nlay_i) :: zradtr_i ! Radiation transmitted through the ice |
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| 133 | REAL(wp), DIMENSION(kiut,0:nlay_i) :: zradab_i ! Radiation absorbed in the ice |
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| 134 | REAL(wp), DIMENSION(kiut,0:nlay_i) :: zkappa_i ! Kappa factor in the ice |
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| 135 | REAL(wp), DIMENSION(kiut,0:nlay_i) :: ztiold ! Old temperature in the ice |
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| 136 | REAL(wp), DIMENSION(kiut,0:nlay_i) :: zeta_i ! Eta factor in the ice |
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| 137 | REAL(wp), DIMENSION(kiut,0:nlay_i) :: ztitemp ! Temporary temperature in the ice to check the convergence |
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| 138 | REAL(wp), DIMENSION(kiut,0:nlay_i) :: zspeche_i ! Ice specific heat |
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| 139 | REAL(wp), DIMENSION(kiut,0:nlay_i) :: z_i ! Vertical cotes of the layers in the ice |
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| 140 | REAL(wp), DIMENSION(kiut,0:nlay_s) :: zradtr_s ! Radiation transmited through the snow |
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| 141 | REAL(wp), DIMENSION(kiut,0:nlay_s) :: zradab_s ! Radiation absorbed in the snow |
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| 142 | REAL(wp), DIMENSION(kiut,0:nlay_s) :: zkappa_s ! Kappa factor in the snow |
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| 143 | REAL(wp), DIMENSION(kiut,0:nlay_s) :: zeta_s ! Eta factor in the snow |
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| 144 | REAL(wp), DIMENSION(kiut,0:nlay_s) :: ztstemp ! Temporary temperature in the snow to check the convergence |
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| 145 | REAL(wp), DIMENSION(kiut,0:nlay_s) :: ztsold ! Temporary temperature in the snow |
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| 146 | REAL(wp), DIMENSION(kiut,0:nlay_s) :: z_s ! Vertical cotes of the layers in the snow |
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| 147 | REAL(wp), DIMENSION(kiut,jkmax+2) :: zindterm ! Independent term |
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| 148 | REAL(wp), DIMENSION(kiut,jkmax+2) :: zindtbis ! temporary independent term |
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| 149 | REAL(wp), DIMENSION(kiut,jkmax+2) :: zdiagbis |
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| 150 | REAL(wp), DIMENSION(kiut,jkmax+2,3) :: ztrid ! tridiagonal system terms |
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[3625] | 151 | !!------------------------------------------------------------------ |
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[3610] | 152 | ! |
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[921] | 153 | !------------------------------------------------------------------------------! |
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| 154 | ! 1) Initialization ! |
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| 155 | !------------------------------------------------------------------------------! |
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| 156 | ! |
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| 157 | DO ji = kideb , kiut |
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| 158 | ! is there snow or not |
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[4161] | 159 | isnow(ji)= NINT( 1._wp - MAX( 0._wp , SIGN(1._wp, - ht_s_b(ji) ) ) ) |
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[921] | 160 | ! surface temperature of fusion |
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[2715] | 161 | !!gm ??? ztfs(ji) = rtt !!!???? |
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[4161] | 162 | ztfs(ji) = REAL( isnow(ji) ) * rtt + REAL( 1 - isnow(ji) ) * rtt |
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[921] | 163 | ! layer thickness |
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[4161] | 164 | zh_i(ji) = ht_i_b(ji) / REAL( nlay_i ) |
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| 165 | zh_s(ji) = ht_s_b(ji) / REAL( nlay_s ) |
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[921] | 166 | END DO |
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[825] | 167 | |
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[921] | 168 | !-------------------- |
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| 169 | ! Ice / snow layers |
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| 170 | !-------------------- |
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[825] | 171 | |
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[2715] | 172 | z_s(:,0) = 0._wp ! vert. coord. of the up. lim. of the 1st snow layer |
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| 173 | z_i(:,0) = 0._wp ! vert. coord. of the up. lim. of the 1st ice layer |
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[825] | 174 | |
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[2715] | 175 | DO layer = 1, nlay_s ! vert. coord of the up. lim. of the layer-th snow layer |
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[921] | 176 | DO ji = kideb , kiut |
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[4161] | 177 | z_s(ji,layer) = z_s(ji,layer-1) + ht_s_b(ji) / REAL( nlay_s ) |
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[921] | 178 | END DO |
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| 179 | END DO |
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[825] | 180 | |
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[2715] | 181 | DO layer = 1, nlay_i ! vert. coord of the up. lim. of the layer-th ice layer |
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[921] | 182 | DO ji = kideb , kiut |
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[4161] | 183 | z_i(ji,layer) = z_i(ji,layer-1) + ht_i_b(ji) / REAL( nlay_i ) |
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[921] | 184 | END DO |
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| 185 | END DO |
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| 186 | ! |
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| 187 | !------------------------------------------------------------------------------| |
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| 188 | ! 2) Radiations | |
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| 189 | !------------------------------------------------------------------------------| |
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| 190 | ! |
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| 191 | !------------------- |
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| 192 | ! Computation of i0 |
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| 193 | !------------------- |
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| 194 | ! i0 describes the fraction of solar radiation which does not contribute |
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| 195 | ! to the surface energy budget but rather penetrates inside the ice. |
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| 196 | ! We assume that no radiation is transmitted through the snow |
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| 197 | ! If there is no no snow |
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| 198 | ! zfsw = (1-i0).qsr_ice is absorbed at the surface |
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| 199 | ! zftrice = io.qsr_ice is below the surface |
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| 200 | ! fstbif = io.qsr_ice.exp(-k(h_i)) transmitted below the ice |
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[825] | 201 | |
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[921] | 202 | DO ji = kideb , kiut |
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| 203 | ! switches |
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[4161] | 204 | isnow(ji) = NINT( 1._wp - MAX( 0._wp , SIGN( 1._wp , - ht_s_b(ji) ) ) ) |
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[921] | 205 | ! hs > 0, isnow = 1 |
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[2715] | 206 | zhsu (ji) = hnzst ! threshold for the computation of i0 |
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| 207 | zihic(ji) = MAX( 0._wp , 1._wp - ( ht_i_b(ji) / zhsu(ji) ) ) |
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[825] | 208 | |
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[4161] | 209 | i0(ji) = REAL( 1 - isnow(ji) ) * ( fr1_i0_1d(ji) + zihic(ji) * fr2_i0_1d(ji) ) |
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[921] | 210 | !fr1_i0_1d = i0 for a thin ice surface |
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| 211 | !fr1_i0_2d = i0 for a thick ice surface |
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| 212 | ! a function of the cloud cover |
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| 213 | ! |
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| 214 | !i0(ji) = (1.0-FLOAT(isnow(ji)))*3.0/(100*ht_s_b(ji)+10.0) |
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| 215 | !formula used in Cice |
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| 216 | END DO |
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[825] | 217 | |
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[921] | 218 | !------------------------------------------------------- |
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| 219 | ! Solar radiation absorbed / transmitted at the surface |
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| 220 | ! Derivative of the non solar flux |
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| 221 | !------------------------------------------------------- |
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| 222 | DO ji = kideb , kiut |
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[2715] | 223 | zfsw (ji) = qsr_ice_1d(ji) * ( 1 - i0(ji) ) ! Shortwave radiation absorbed at surface |
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| 224 | zftrice(ji) = qsr_ice_1d(ji) * i0(ji) ! Solar radiation transmitted below the surface layer |
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| 225 | dzf (ji) = dqns_ice_1d(ji) ! derivative of incoming nonsolar flux |
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[921] | 226 | END DO |
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[825] | 227 | |
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[921] | 228 | !--------------------------------------------------------- |
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| 229 | ! Transmission - absorption of solar radiation in the ice |
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| 230 | !--------------------------------------------------------- |
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[825] | 231 | |
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[2715] | 232 | DO ji = kideb, kiut ! snow initialization |
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| 233 | zradtr_s(ji,0) = zftrice(ji) ! radiation penetrating through snow |
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[921] | 234 | END DO |
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[825] | 235 | |
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[2715] | 236 | DO layer = 1, nlay_s ! Radiation through snow |
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| 237 | DO ji = kideb, kiut |
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| 238 | ! ! radiation transmitted below the layer-th snow layer |
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| 239 | zradtr_s(ji,layer) = zradtr_s(ji,0) * EXP( - zraext_s * ( MAX ( 0._wp , z_s(ji,layer) ) ) ) |
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| 240 | ! ! radiation absorbed by the layer-th snow layer |
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[921] | 241 | zradab_s(ji,layer) = zradtr_s(ji,layer-1) - zradtr_s(ji,layer) |
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| 242 | END DO |
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| 243 | END DO |
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[825] | 244 | |
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[2715] | 245 | DO ji = kideb, kiut ! ice initialization |
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[4161] | 246 | zradtr_i(ji,0) = zradtr_s(ji,nlay_s) * REAL( isnow(ji) ) + zftrice(ji) * REAL( 1 - isnow(ji) ) |
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[921] | 247 | END DO |
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[825] | 248 | |
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[2715] | 249 | DO layer = 1, nlay_i ! Radiation through ice |
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| 250 | DO ji = kideb, kiut |
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| 251 | ! ! radiation transmitted below the layer-th ice layer |
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| 252 | zradtr_i(ji,layer) = zradtr_i(ji,0) * EXP( - kappa_i * ( MAX ( 0._wp , z_i(ji,layer) ) ) ) |
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| 253 | ! ! radiation absorbed by the layer-th ice layer |
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[921] | 254 | zradab_i(ji,layer) = zradtr_i(ji,layer-1) - zradtr_i(ji,layer) |
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| 255 | END DO |
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| 256 | END DO |
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[825] | 257 | |
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[2715] | 258 | DO ji = kideb, kiut ! Radiation transmitted below the ice |
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[4161] | 259 | fstbif_1d(ji) = fstbif_1d(ji) + iatte_1d(ji) * zradtr_i(ji,nlay_i) * a_i_b(ji) / at_i_b(ji) ! clem modif |
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[921] | 260 | END DO |
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[834] | 261 | |
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[921] | 262 | ! +++++ |
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| 263 | ! just to check energy conservation |
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[2715] | 264 | DO ji = kideb, kiut |
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[3625] | 265 | ii = MOD( npb(ji) - 1 , jpi ) + 1 |
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| 266 | ij = ( npb(ji) - 1 ) / jpi + 1 |
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[4161] | 267 | fstroc(ii,ij,jl) = iatte_1d(ji) * zradtr_i(ji,nlay_i) ! clem modif |
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[921] | 268 | END DO |
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| 269 | ! +++++ |
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[825] | 270 | |
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[921] | 271 | DO layer = 1, nlay_i |
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[2715] | 272 | DO ji = kideb, kiut |
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[921] | 273 | radab(ji,layer) = zradab_i(ji,layer) |
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| 274 | END DO |
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| 275 | END DO |
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[825] | 276 | |
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[921] | 277 | ! |
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| 278 | !------------------------------------------------------------------------------| |
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| 279 | ! 3) Iterative procedure begins | |
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| 280 | !------------------------------------------------------------------------------| |
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| 281 | ! |
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[2715] | 282 | DO ji = kideb, kiut ! Old surface temperature |
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| 283 | ztsuold (ji) = t_su_b(ji) ! temperature at the beg of iter pr. |
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| 284 | ztsuoldit(ji) = t_su_b(ji) ! temperature at the previous iter |
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| 285 | t_su_b (ji) = MIN( t_su_b(ji), ztfs(ji)-0.00001 ) ! necessary |
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| 286 | zerrit (ji) = 1000._wp ! initial value of error |
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[921] | 287 | END DO |
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[825] | 288 | |
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[2715] | 289 | DO layer = 1, nlay_s ! Old snow temperature |
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[921] | 290 | DO ji = kideb , kiut |
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[2715] | 291 | ztsold(ji,layer) = t_s_b(ji,layer) |
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[921] | 292 | END DO |
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| 293 | END DO |
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[825] | 294 | |
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[2715] | 295 | DO layer = 1, nlay_i ! Old ice temperature |
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[921] | 296 | DO ji = kideb , kiut |
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[2715] | 297 | ztiold(ji,layer) = t_i_b(ji,layer) |
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[921] | 298 | END DO |
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| 299 | END DO |
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[825] | 300 | |
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[2715] | 301 | nconv = 0 ! number of iterations |
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| 302 | zerritmax = 1000._wp ! maximal value of error on all points |
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[825] | 303 | |
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[2715] | 304 | DO WHILE ( zerritmax > maxer_i_thd .AND. nconv < nconv_i_thd ) |
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[921] | 305 | ! |
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[2715] | 306 | nconv = nconv + 1 |
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| 307 | ! |
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[921] | 308 | !------------------------------------------------------------------------------| |
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| 309 | ! 4) Sea ice thermal conductivity | |
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| 310 | !------------------------------------------------------------------------------| |
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| 311 | ! |
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[2715] | 312 | IF( thcon_i_swi == 0 ) THEN ! Untersteiner (1964) formula |
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[921] | 313 | DO ji = kideb , kiut |
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[2777] | 314 | ztcond_i(ji,0) = rcdic + zbeta*s_i_b(ji,1) / MIN(-zeps,t_i_b(ji,1)-rtt) |
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[921] | 315 | ztcond_i(ji,0) = MAX(ztcond_i(ji,0),zkimin) |
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| 316 | END DO |
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| 317 | DO layer = 1, nlay_i-1 |
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| 318 | DO ji = kideb , kiut |
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[2777] | 319 | ztcond_i(ji,layer) = rcdic + zbeta*( s_i_b(ji,layer) + s_i_b(ji,layer+1) ) / & |
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| 320 | MIN(-2.0_wp * zeps, t_i_b(ji,layer)+t_i_b(ji,layer+1) - 2.0_wp * rtt) |
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[921] | 321 | ztcond_i(ji,layer) = MAX(ztcond_i(ji,layer),zkimin) |
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| 322 | END DO |
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| 323 | END DO |
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| 324 | ENDIF |
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[825] | 325 | |
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[2715] | 326 | IF( thcon_i_swi == 1 ) THEN ! Pringle et al formula included: 2.11 + 0.09 S/T - 0.011.T |
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[921] | 327 | DO ji = kideb , kiut |
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[2715] | 328 | ztcond_i(ji,0) = rcdic + 0.090_wp * s_i_b(ji,1) / MIN( -zeps, t_i_b(ji,1)-rtt ) & |
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| 329 | & - 0.011_wp * ( t_i_b(ji,1) - rtt ) |
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| 330 | ztcond_i(ji,0) = MAX( ztcond_i(ji,0), zkimin ) |
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[921] | 331 | END DO |
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[2715] | 332 | DO layer = 1, nlay_i-1 |
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| 333 | DO ji = kideb , kiut |
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| 334 | ztcond_i(ji,layer) = rcdic + 0.090_wp * ( s_i_b(ji,layer) + s_i_b(ji,layer+1) ) & |
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[2777] | 335 | & / MIN(-2.0_wp * zeps, t_i_b(ji,layer)+t_i_b(ji,layer+1) - 2.0_wp * rtt) & |
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[2715] | 336 | & - 0.0055_wp* ( t_i_b(ji,layer) + t_i_b(ji,layer+1) - 2.0*rtt ) |
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| 337 | ztcond_i(ji,layer) = MAX( ztcond_i(ji,layer), zkimin ) |
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| 338 | END DO |
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| 339 | END DO |
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| 340 | DO ji = kideb , kiut |
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| 341 | ztcond_i(ji,nlay_i) = rcdic + 0.090_wp * s_i_b(ji,nlay_i) / MIN(-zeps,t_bo_b(ji)-rtt) & |
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| 342 | & - 0.011_wp * ( t_bo_b(ji) - rtt ) |
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| 343 | ztcond_i(ji,nlay_i) = MAX( ztcond_i(ji,nlay_i), zkimin ) |
---|
| 344 | END DO |
---|
[921] | 345 | ENDIF |
---|
| 346 | ! |
---|
| 347 | !------------------------------------------------------------------------------| |
---|
| 348 | ! 5) kappa factors | |
---|
| 349 | !------------------------------------------------------------------------------| |
---|
| 350 | ! |
---|
| 351 | DO ji = kideb, kiut |
---|
[825] | 352 | |
---|
[921] | 353 | !-- Snow kappa factors |
---|
| 354 | zkappa_s(ji,0) = rcdsn / MAX(zeps,zh_s(ji)) |
---|
| 355 | zkappa_s(ji,nlay_s) = rcdsn / MAX(zeps,zh_s(ji)) |
---|
| 356 | END DO |
---|
[825] | 357 | |
---|
[921] | 358 | DO layer = 1, nlay_s-1 |
---|
| 359 | DO ji = kideb , kiut |
---|
| 360 | zkappa_s(ji,layer) = 2.0 * rcdsn / & |
---|
| 361 | MAX(zeps,2.0*zh_s(ji)) |
---|
| 362 | END DO |
---|
| 363 | END DO |
---|
[825] | 364 | |
---|
[921] | 365 | DO layer = 1, nlay_i-1 |
---|
| 366 | DO ji = kideb , kiut |
---|
| 367 | !-- Ice kappa factors |
---|
| 368 | zkappa_i(ji,layer) = 2.0*ztcond_i(ji,layer)/ & |
---|
| 369 | MAX(zeps,2.0*zh_i(ji)) |
---|
| 370 | END DO |
---|
| 371 | END DO |
---|
[825] | 372 | |
---|
[921] | 373 | DO ji = kideb , kiut |
---|
| 374 | zkappa_i(ji,0) = ztcond_i(ji,0)/MAX(zeps,zh_i(ji)) |
---|
| 375 | zkappa_i(ji,nlay_i) = ztcond_i(ji,nlay_i) / MAX(zeps,zh_i(ji)) |
---|
| 376 | !-- Interface |
---|
| 377 | zkappa_s(ji,nlay_s) = 2.0*rcdsn*ztcond_i(ji,0)/MAX(zeps, & |
---|
| 378 | (ztcond_i(ji,0)*zh_s(ji) + rcdsn*zh_i(ji))) |
---|
[4161] | 379 | zkappa_i(ji,0) = zkappa_s(ji,nlay_s)*REAL( isnow(ji) ) & |
---|
| 380 | + zkappa_i(ji,0)*REAL( 1 - isnow(ji) ) |
---|
[921] | 381 | END DO |
---|
| 382 | ! |
---|
| 383 | !------------------------------------------------------------------------------| |
---|
| 384 | ! 6) Sea ice specific heat, eta factors | |
---|
| 385 | !------------------------------------------------------------------------------| |
---|
| 386 | ! |
---|
| 387 | DO layer = 1, nlay_i |
---|
| 388 | DO ji = kideb , kiut |
---|
| 389 | ztitemp(ji,layer) = t_i_b(ji,layer) |
---|
| 390 | zspeche_i(ji,layer) = cpic + zgamma*s_i_b(ji,layer)/ & |
---|
| 391 | MAX((t_i_b(ji,layer)-rtt)*(ztiold(ji,layer)-rtt),zeps) |
---|
| 392 | zeta_i(ji,layer) = rdt_ice / MAX(rhoic*zspeche_i(ji,layer)*zh_i(ji), & |
---|
| 393 | zeps) |
---|
| 394 | END DO |
---|
| 395 | END DO |
---|
[825] | 396 | |
---|
[921] | 397 | DO layer = 1, nlay_s |
---|
| 398 | DO ji = kideb , kiut |
---|
| 399 | ztstemp(ji,layer) = t_s_b(ji,layer) |
---|
| 400 | zeta_s(ji,layer) = rdt_ice / MAX(rhosn*cpic*zh_s(ji),zeps) |
---|
| 401 | END DO |
---|
| 402 | END DO |
---|
| 403 | ! |
---|
| 404 | !------------------------------------------------------------------------------| |
---|
| 405 | ! 7) surface flux computation | |
---|
| 406 | !------------------------------------------------------------------------------| |
---|
| 407 | ! |
---|
| 408 | DO ji = kideb , kiut |
---|
[825] | 409 | |
---|
[921] | 410 | ! update of the non solar flux according to the update in T_su |
---|
| 411 | qnsr_ice_1d(ji) = qnsr_ice_1d(ji) + dqns_ice_1d(ji) * & |
---|
| 412 | ( t_su_b(ji) - ztsuoldit(ji) ) |
---|
[825] | 413 | |
---|
[921] | 414 | ! update incoming flux |
---|
| 415 | zf(ji) = zfsw(ji) & ! net absorbed solar radiation |
---|
| 416 | + qnsr_ice_1d(ji) ! non solar total flux |
---|
| 417 | ! (LWup, LWdw, SH, LH) |
---|
[825] | 418 | |
---|
[921] | 419 | END DO |
---|
[825] | 420 | |
---|
[921] | 421 | ! |
---|
| 422 | !------------------------------------------------------------------------------| |
---|
| 423 | ! 8) tridiagonal system terms | |
---|
| 424 | !------------------------------------------------------------------------------| |
---|
| 425 | ! |
---|
| 426 | !!layer denotes the number of the layer in the snow or in the ice |
---|
| 427 | !!numeq denotes the reference number of the equation in the tridiagonal |
---|
| 428 | !!system, terms of tridiagonal system are indexed as following : |
---|
| 429 | !!1 is subdiagonal term, 2 is diagonal and 3 is superdiagonal one |
---|
[825] | 430 | |
---|
[921] | 431 | !!ice interior terms (top equation has the same form as the others) |
---|
| 432 | |
---|
| 433 | DO numeq=1,jkmax+2 |
---|
| 434 | DO ji = kideb , kiut |
---|
| 435 | ztrid(ji,numeq,1) = 0. |
---|
| 436 | ztrid(ji,numeq,2) = 0. |
---|
| 437 | ztrid(ji,numeq,3) = 0. |
---|
| 438 | zindterm(ji,numeq)= 0. |
---|
| 439 | zindtbis(ji,numeq)= 0. |
---|
| 440 | zdiagbis(ji,numeq)= 0. |
---|
| 441 | ENDDO |
---|
| 442 | ENDDO |
---|
| 443 | |
---|
| 444 | DO numeq = nlay_s + 2, nlay_s + nlay_i |
---|
| 445 | DO ji = kideb , kiut |
---|
| 446 | layer = numeq - nlay_s - 1 |
---|
| 447 | ztrid(ji,numeq,1) = - zeta_i(ji,layer)*zkappa_i(ji,layer-1) |
---|
| 448 | ztrid(ji,numeq,2) = 1.0 + zeta_i(ji,layer)*(zkappa_i(ji,layer-1) + & |
---|
| 449 | zkappa_i(ji,layer)) |
---|
| 450 | ztrid(ji,numeq,3) = - zeta_i(ji,layer)*zkappa_i(ji,layer) |
---|
| 451 | zindterm(ji,numeq) = ztiold(ji,layer) + zeta_i(ji,layer)* & |
---|
| 452 | zradab_i(ji,layer) |
---|
| 453 | END DO |
---|
| 454 | ENDDO |
---|
| 455 | |
---|
| 456 | numeq = nlay_s + nlay_i + 1 |
---|
| 457 | DO ji = kideb , kiut |
---|
[825] | 458 | !!ice bottom term |
---|
| 459 | ztrid(ji,numeq,1) = - zeta_i(ji,nlay_i)*zkappa_i(ji,nlay_i-1) |
---|
| 460 | ztrid(ji,numeq,2) = 1.0 + zeta_i(ji,nlay_i)*( zkappa_i(ji,nlay_i)*zg1 & |
---|
[921] | 461 | + zkappa_i(ji,nlay_i-1) ) |
---|
[825] | 462 | ztrid(ji,numeq,3) = 0.0 |
---|
| 463 | zindterm(ji,numeq) = ztiold(ji,nlay_i) + zeta_i(ji,nlay_i)* & |
---|
[921] | 464 | ( zradab_i(ji,nlay_i) + zkappa_i(ji,nlay_i)*zg1 & |
---|
| 465 | * t_bo_b(ji) ) |
---|
| 466 | ENDDO |
---|
[825] | 467 | |
---|
| 468 | |
---|
[921] | 469 | DO ji = kideb , kiut |
---|
[825] | 470 | IF ( ht_s_b(ji).gt.0.0 ) THEN |
---|
[921] | 471 | ! |
---|
| 472 | !------------------------------------------------------------------------------| |
---|
| 473 | ! snow-covered cells | |
---|
| 474 | !------------------------------------------------------------------------------| |
---|
| 475 | ! |
---|
| 476 | !!snow interior terms (bottom equation has the same form as the others) |
---|
| 477 | DO numeq = 3, nlay_s + 1 |
---|
| 478 | layer = numeq - 1 |
---|
| 479 | ztrid(ji,numeq,1) = - zeta_s(ji,layer)*zkappa_s(ji,layer-1) |
---|
| 480 | ztrid(ji,numeq,2) = 1.0 + zeta_s(ji,layer)*( zkappa_s(ji,layer-1) + & |
---|
| 481 | zkappa_s(ji,layer) ) |
---|
| 482 | ztrid(ji,numeq,3) = - zeta_s(ji,layer)*zkappa_s(ji,layer) |
---|
| 483 | zindterm(ji,numeq) = ztsold(ji,layer) + zeta_s(ji,layer)* & |
---|
| 484 | zradab_s(ji,layer) |
---|
| 485 | END DO |
---|
[825] | 486 | |
---|
[921] | 487 | !!case of only one layer in the ice (ice equation is altered) |
---|
| 488 | IF ( nlay_i.eq.1 ) THEN |
---|
| 489 | ztrid(ji,nlay_s+2,3) = 0.0 |
---|
| 490 | zindterm(ji,nlay_s+2) = zindterm(ji,nlay_s+2) + zkappa_i(ji,1)* & |
---|
| 491 | t_bo_b(ji) |
---|
| 492 | ENDIF |
---|
[834] | 493 | |
---|
[921] | 494 | IF ( t_su_b(ji) .LT. rtt ) THEN |
---|
[825] | 495 | |
---|
[921] | 496 | !------------------------------------------------------------------------------| |
---|
| 497 | ! case 1 : no surface melting - snow present | |
---|
| 498 | !------------------------------------------------------------------------------| |
---|
| 499 | zdifcase(ji) = 1.0 |
---|
| 500 | numeqmin(ji) = 1 |
---|
| 501 | numeqmax(ji) = nlay_i + nlay_s + 1 |
---|
[825] | 502 | |
---|
[921] | 503 | !!surface equation |
---|
| 504 | ztrid(ji,1,1) = 0.0 |
---|
| 505 | ztrid(ji,1,2) = dzf(ji) - zg1s*zkappa_s(ji,0) |
---|
| 506 | ztrid(ji,1,3) = zg1s*zkappa_s(ji,0) |
---|
| 507 | zindterm(ji,1) = dzf(ji)*t_su_b(ji) - zf(ji) |
---|
[825] | 508 | |
---|
[921] | 509 | !!first layer of snow equation |
---|
| 510 | ztrid(ji,2,1) = - zkappa_s(ji,0)*zg1s*zeta_s(ji,1) |
---|
| 511 | ztrid(ji,2,2) = 1.0 + zeta_s(ji,1)*(zkappa_s(ji,1) + zkappa_s(ji,0)*zg1s) |
---|
| 512 | ztrid(ji,2,3) = - zeta_s(ji,1)* zkappa_s(ji,1) |
---|
| 513 | zindterm(ji,2) = ztsold(ji,1) + zeta_s(ji,1)*zradab_s(ji,1) |
---|
[825] | 514 | |
---|
[921] | 515 | ELSE |
---|
| 516 | ! |
---|
| 517 | !------------------------------------------------------------------------------| |
---|
| 518 | ! case 2 : surface is melting - snow present | |
---|
| 519 | !------------------------------------------------------------------------------| |
---|
| 520 | ! |
---|
| 521 | zdifcase(ji) = 2.0 |
---|
| 522 | numeqmin(ji) = 2 |
---|
| 523 | numeqmax(ji) = nlay_i + nlay_s + 1 |
---|
[825] | 524 | |
---|
[921] | 525 | !!first layer of snow equation |
---|
| 526 | ztrid(ji,2,1) = 0.0 |
---|
| 527 | ztrid(ji,2,2) = 1.0 + zeta_s(ji,1) * ( zkappa_s(ji,1) + & |
---|
| 528 | zkappa_s(ji,0) * zg1s ) |
---|
| 529 | ztrid(ji,2,3) = - zeta_s(ji,1)*zkappa_s(ji,1) |
---|
| 530 | zindterm(ji,2) = ztsold(ji,1) + zeta_s(ji,1) * & |
---|
| 531 | ( zradab_s(ji,1) + & |
---|
| 532 | zkappa_s(ji,0) * zg1s * t_su_b(ji) ) |
---|
| 533 | ENDIF |
---|
| 534 | ELSE |
---|
| 535 | ! |
---|
| 536 | !------------------------------------------------------------------------------| |
---|
| 537 | ! cells without snow | |
---|
| 538 | !------------------------------------------------------------------------------| |
---|
| 539 | ! |
---|
| 540 | IF (t_su_b(ji) .LT. rtt) THEN |
---|
| 541 | ! |
---|
| 542 | !------------------------------------------------------------------------------| |
---|
| 543 | ! case 3 : no surface melting - no snow | |
---|
| 544 | !------------------------------------------------------------------------------| |
---|
| 545 | ! |
---|
| 546 | zdifcase(ji) = 3.0 |
---|
| 547 | numeqmin(ji) = nlay_s + 1 |
---|
| 548 | numeqmax(ji) = nlay_i + nlay_s + 1 |
---|
[825] | 549 | |
---|
[921] | 550 | !!surface equation |
---|
| 551 | ztrid(ji,numeqmin(ji),1) = 0.0 |
---|
| 552 | ztrid(ji,numeqmin(ji),2) = dzf(ji) - zkappa_i(ji,0)*zg1 |
---|
| 553 | ztrid(ji,numeqmin(ji),3) = zkappa_i(ji,0)*zg1 |
---|
| 554 | zindterm(ji,numeqmin(ji)) = dzf(ji)*t_su_b(ji) - zf(ji) |
---|
[825] | 555 | |
---|
[921] | 556 | !!first layer of ice equation |
---|
| 557 | ztrid(ji,numeqmin(ji)+1,1) = - zkappa_i(ji,0) * zg1 * zeta_i(ji,1) |
---|
| 558 | ztrid(ji,numeqmin(ji)+1,2) = 1.0 + zeta_i(ji,1) * ( zkappa_i(ji,1) & |
---|
| 559 | + zkappa_i(ji,0) * zg1 ) |
---|
| 560 | ztrid(ji,numeqmin(ji)+1,3) = - zeta_i(ji,1)*zkappa_i(ji,1) |
---|
| 561 | zindterm(ji,numeqmin(ji)+1)= ztiold(ji,1) + zeta_i(ji,1)*zradab_i(ji,1) |
---|
[825] | 562 | |
---|
[921] | 563 | !!case of only one layer in the ice (surface & ice equations are altered) |
---|
[825] | 564 | |
---|
[921] | 565 | IF (nlay_i.eq.1) THEN |
---|
| 566 | ztrid(ji,numeqmin(ji),1) = 0.0 |
---|
| 567 | ztrid(ji,numeqmin(ji),2) = dzf(ji) - zkappa_i(ji,0)*2.0 |
---|
| 568 | ztrid(ji,numeqmin(ji),3) = zkappa_i(ji,0)*2.0 |
---|
| 569 | ztrid(ji,numeqmin(ji)+1,1) = -zkappa_i(ji,0)*2.0*zeta_i(ji,1) |
---|
| 570 | ztrid(ji,numeqmin(ji)+1,2) = 1.0 + zeta_i(ji,1)*(zkappa_i(ji,0)*2.0 + & |
---|
| 571 | zkappa_i(ji,1)) |
---|
| 572 | ztrid(ji,numeqmin(ji)+1,3) = 0.0 |
---|
[825] | 573 | |
---|
[921] | 574 | zindterm(ji,numeqmin(ji)+1) = ztiold(ji,1) + zeta_i(ji,1)* & |
---|
| 575 | ( zradab_i(ji,1) + zkappa_i(ji,1)*t_bo_b(ji) ) |
---|
| 576 | ENDIF |
---|
[825] | 577 | |
---|
[921] | 578 | ELSE |
---|
[825] | 579 | |
---|
[921] | 580 | ! |
---|
| 581 | !------------------------------------------------------------------------------| |
---|
| 582 | ! case 4 : surface is melting - no snow | |
---|
| 583 | !------------------------------------------------------------------------------| |
---|
| 584 | ! |
---|
| 585 | zdifcase(ji) = 4.0 |
---|
| 586 | numeqmin(ji) = nlay_s + 2 |
---|
| 587 | numeqmax(ji) = nlay_i + nlay_s + 1 |
---|
[825] | 588 | |
---|
[921] | 589 | !!first layer of ice equation |
---|
| 590 | ztrid(ji,numeqmin(ji),1) = 0.0 |
---|
| 591 | ztrid(ji,numeqmin(ji),2) = 1.0 + zeta_i(ji,1)*(zkappa_i(ji,1) + zkappa_i(ji,0)* & |
---|
| 592 | zg1) |
---|
| 593 | ztrid(ji,numeqmin(ji),3) = - zeta_i(ji,1) * zkappa_i(ji,1) |
---|
| 594 | zindterm(ji,numeqmin(ji)) = ztiold(ji,1) + zeta_i(ji,1)*( zradab_i(ji,1) + & |
---|
| 595 | zkappa_i(ji,0) * zg1 * t_su_b(ji) ) |
---|
[825] | 596 | |
---|
[921] | 597 | !!case of only one layer in the ice (surface & ice equations are altered) |
---|
| 598 | IF (nlay_i.eq.1) THEN |
---|
| 599 | ztrid(ji,numeqmin(ji),1) = 0.0 |
---|
| 600 | ztrid(ji,numeqmin(ji),2) = 1.0 + zeta_i(ji,1)*(zkappa_i(ji,0)*2.0 + & |
---|
| 601 | zkappa_i(ji,1)) |
---|
| 602 | ztrid(ji,numeqmin(ji),3) = 0.0 |
---|
| 603 | zindterm(ji,numeqmin(ji)) = ztiold(ji,1) + zeta_i(ji,1)* & |
---|
| 604 | (zradab_i(ji,1) + zkappa_i(ji,1)*t_bo_b(ji)) & |
---|
| 605 | + t_su_b(ji)*zeta_i(ji,1)*zkappa_i(ji,0)*2.0 |
---|
| 606 | ENDIF |
---|
[825] | 607 | |
---|
[921] | 608 | ENDIF |
---|
| 609 | ENDIF |
---|
[825] | 610 | |
---|
[921] | 611 | END DO |
---|
[825] | 612 | |
---|
[921] | 613 | ! |
---|
| 614 | !------------------------------------------------------------------------------| |
---|
| 615 | ! 9) tridiagonal system solving | |
---|
| 616 | !------------------------------------------------------------------------------| |
---|
| 617 | ! |
---|
[825] | 618 | |
---|
[921] | 619 | ! Solve the tridiagonal system with Gauss elimination method. |
---|
| 620 | ! Thomas algorithm, from Computational fluid Dynamics, J.D. ANDERSON, |
---|
| 621 | ! McGraw-Hill 1984. |
---|
[825] | 622 | |
---|
[921] | 623 | maxnumeqmax = 0 |
---|
| 624 | minnumeqmin = jkmax+4 |
---|
[825] | 625 | |
---|
[921] | 626 | DO ji = kideb , kiut |
---|
| 627 | zindtbis(ji,numeqmin(ji)) = zindterm(ji,numeqmin(ji)) |
---|
| 628 | zdiagbis(ji,numeqmin(ji)) = ztrid(ji,numeqmin(ji),2) |
---|
| 629 | minnumeqmin = MIN(numeqmin(ji),minnumeqmin) |
---|
| 630 | maxnumeqmax = MAX(numeqmax(ji),maxnumeqmax) |
---|
| 631 | END DO |
---|
| 632 | |
---|
| 633 | DO layer = minnumeqmin+1, maxnumeqmax |
---|
| 634 | DO ji = kideb , kiut |
---|
| 635 | numeq = min(max(numeqmin(ji)+1,layer),numeqmax(ji)) |
---|
| 636 | zdiagbis(ji,numeq) = ztrid(ji,numeq,2) - ztrid(ji,numeq,1)* & |
---|
| 637 | ztrid(ji,numeq-1,3)/zdiagbis(ji,numeq-1) |
---|
| 638 | zindtbis(ji,numeq) = zindterm(ji,numeq) - ztrid(ji,numeq,1)* & |
---|
| 639 | zindtbis(ji,numeq-1)/zdiagbis(ji,numeq-1) |
---|
| 640 | END DO |
---|
| 641 | END DO |
---|
| 642 | |
---|
| 643 | DO ji = kideb , kiut |
---|
| 644 | ! ice temperatures |
---|
| 645 | t_i_b(ji,nlay_i) = zindtbis(ji,numeqmax(ji))/zdiagbis(ji,numeqmax(ji)) |
---|
| 646 | END DO |
---|
| 647 | |
---|
| 648 | DO numeq = nlay_i + nlay_s + 1, nlay_s + 2, -1 |
---|
| 649 | DO ji = kideb , kiut |
---|
| 650 | layer = numeq - nlay_s - 1 |
---|
| 651 | t_i_b(ji,layer) = (zindtbis(ji,numeq) - ztrid(ji,numeq,3)* & |
---|
| 652 | t_i_b(ji,layer+1))/zdiagbis(ji,numeq) |
---|
| 653 | END DO |
---|
| 654 | END DO |
---|
| 655 | |
---|
| 656 | DO ji = kideb , kiut |
---|
[825] | 657 | ! snow temperatures |
---|
[4205] | 658 | IF (ht_s_b(ji).GT.0._wp) & |
---|
[921] | 659 | t_s_b(ji,nlay_s) = (zindtbis(ji,nlay_s+1) - ztrid(ji,nlay_s+1,3) & |
---|
| 660 | * t_i_b(ji,1))/zdiagbis(ji,nlay_s+1) & |
---|
[4161] | 661 | * MAX(0.0,SIGN(1.0,ht_s_b(ji))) |
---|
[825] | 662 | |
---|
| 663 | ! surface temperature |
---|
[4161] | 664 | isnow(ji) = NINT( 1.0 - MAX( 0.0 , SIGN( 1.0 , -ht_s_b(ji) ) ) ) |
---|
[2715] | 665 | ztsuoldit(ji) = t_su_b(ji) |
---|
[4161] | 666 | IF( t_su_b(ji) < ztfs(ji) ) & |
---|
| 667 | t_su_b(ji) = ( zindtbis(ji,numeqmin(ji)) - ztrid(ji,numeqmin(ji),3)* ( REAL( isnow(ji) )*t_s_b(ji,1) & |
---|
| 668 | & + REAL( 1 - isnow(ji) )*t_i_b(ji,1) ) ) / zdiagbis(ji,numeqmin(ji)) |
---|
[921] | 669 | END DO |
---|
| 670 | ! |
---|
| 671 | !-------------------------------------------------------------------------- |
---|
| 672 | ! 10) Has the scheme converged ?, end of the iterative procedure | |
---|
| 673 | !-------------------------------------------------------------------------- |
---|
| 674 | ! |
---|
| 675 | ! check that nowhere it has started to melt |
---|
| 676 | ! zerrit(ji) is a measure of error, it has to be under maxer_i_thd |
---|
| 677 | DO ji = kideb , kiut |
---|
[2715] | 678 | t_su_b(ji) = MAX( MIN( t_su_b(ji) , ztfs(ji) ) , 190._wp ) |
---|
| 679 | zerrit(ji) = ABS( t_su_b(ji) - ztsuoldit(ji) ) |
---|
[921] | 680 | END DO |
---|
[825] | 681 | |
---|
[921] | 682 | DO layer = 1, nlay_s |
---|
| 683 | DO ji = kideb , kiut |
---|
[2715] | 684 | ii = MOD( npb(ji) - 1, jpi ) + 1 |
---|
| 685 | ij = ( npb(ji) - 1 ) / jpi + 1 |
---|
| 686 | t_s_b(ji,layer) = MAX( MIN( t_s_b(ji,layer), rtt ), 190._wp ) |
---|
| 687 | zerrit(ji) = MAX(zerrit(ji),ABS(t_s_b(ji,layer) - ztstemp(ji,layer))) |
---|
[921] | 688 | END DO |
---|
| 689 | END DO |
---|
[825] | 690 | |
---|
[921] | 691 | DO layer = 1, nlay_i |
---|
| 692 | DO ji = kideb , kiut |
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[2715] | 693 | ztmelt_i = -tmut * s_i_b(ji,layer) + rtt |
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[4205] | 694 | t_i_b(ji,layer) = MAX(MIN(t_i_b(ji,layer),ztmelt_i), 190._wp) |
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[2715] | 695 | zerrit(ji) = MAX(zerrit(ji),ABS(t_i_b(ji,layer) - ztitemp(ji,layer))) |
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[921] | 696 | END DO |
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| 697 | END DO |
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[825] | 698 | |
---|
[921] | 699 | ! Compute spatial maximum over all errors |
---|
[2715] | 700 | ! note that this could be optimized substantially by iterating only the non-converging points |
---|
| 701 | zerritmax = 0._wp |
---|
| 702 | DO ji = kideb, kiut |
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| 703 | zerritmax = MAX( zerritmax, zerrit(ji) ) |
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[921] | 704 | END DO |
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[2715] | 705 | IF( lk_mpp ) CALL mpp_max( zerritmax, kcom=ncomm_ice ) |
---|
[825] | 706 | |
---|
| 707 | END DO ! End of the do while iterative procedure |
---|
| 708 | |
---|
[1055] | 709 | IF( ln_nicep ) THEN |
---|
| 710 | WRITE(numout,*) ' zerritmax : ', zerritmax |
---|
| 711 | WRITE(numout,*) ' nconv : ', nconv |
---|
| 712 | ENDIF |
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[825] | 713 | |
---|
[921] | 714 | ! |
---|
[2715] | 715 | !-------------------------------------------------------------------------! |
---|
| 716 | ! 11) Fluxes at the interfaces ! |
---|
| 717 | !-------------------------------------------------------------------------! |
---|
[921] | 718 | DO ji = kideb, kiut |
---|
[3808] | 719 | #if ! defined key_coupled |
---|
| 720 | ! forced mode only : update of latent heat fluxes (sublimation) (always >=0, upward flux) |
---|
| 721 | qla_ice_1d (ji) = MAX( 0._wp, qla_ice_1d (ji) + dqla_ice_1d(ji) * ( t_su_b(ji) - ztsuold(ji) ) ) |
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| 722 | #endif |
---|
[2715] | 723 | ! ! surface ice conduction flux |
---|
[4161] | 724 | isnow(ji) = NINT( 1._wp - MAX( 0._wp, SIGN( 1._wp, -ht_s_b(ji) ) ) ) |
---|
| 725 | fc_su(ji) = - REAL( isnow(ji) ) * zkappa_s(ji,0) * zg1s * (t_s_b(ji,1) - t_su_b(ji)) & |
---|
| 726 | & - REAL( 1 - isnow(ji) ) * zkappa_i(ji,0) * zg1 * (t_i_b(ji,1) - t_su_b(ji)) |
---|
[2715] | 727 | ! ! bottom ice conduction flux |
---|
| 728 | fc_bo_i(ji) = - zkappa_i(ji,nlay_i) * ( zg1*(t_bo_b(ji) - t_i_b(ji,nlay_i)) ) |
---|
[921] | 729 | END DO |
---|
[825] | 730 | |
---|
[921] | 731 | !-------------------------! |
---|
| 732 | ! Heat conservation ! |
---|
| 733 | !-------------------------! |
---|
[2715] | 734 | IF( con_i ) THEN |
---|
[921] | 735 | DO ji = kideb, kiut |
---|
| 736 | ! Upper snow value |
---|
[4161] | 737 | fc_s(ji,0) = - REAL( isnow(ji) ) * zkappa_s(ji,0) * zg1s * ( t_s_b(ji,1) - t_su_b(ji) ) |
---|
[921] | 738 | ! Bott. snow value |
---|
[4161] | 739 | fc_s(ji,1) = - REAL( isnow(ji) ) * zkappa_s(ji,1) * ( t_i_b(ji,1) - t_s_b(ji,1) ) |
---|
[921] | 740 | END DO |
---|
[2715] | 741 | DO ji = kideb, kiut ! Upper ice layer |
---|
[4161] | 742 | fc_i(ji,0) = - REAL( isnow(ji) ) * & ! interface flux if there is snow |
---|
[921] | 743 | ( zkappa_i(ji,0) * ( t_i_b(ji,1) - t_s_b(ji,nlay_s ) ) ) & |
---|
[4161] | 744 | - REAL( 1 - isnow(ji) ) * ( zkappa_i(ji,0) * & |
---|
[921] | 745 | zg1 * ( t_i_b(ji,1) - t_su_b(ji) ) ) ! upper flux if not |
---|
| 746 | END DO |
---|
[2715] | 747 | DO layer = 1, nlay_i - 1 ! Internal ice layers |
---|
[921] | 748 | DO ji = kideb, kiut |
---|
[2715] | 749 | fc_i(ji,layer) = - zkappa_i(ji,layer) * ( t_i_b(ji,layer+1) - t_i_b(ji,layer) ) |
---|
| 750 | ii = MOD( npb(ji) - 1, jpi ) + 1 |
---|
| 751 | ij = ( npb(ji) - 1 ) / jpi + 1 |
---|
[921] | 752 | END DO |
---|
| 753 | END DO |
---|
[2715] | 754 | DO ji = kideb, kiut ! Bottom ice layers |
---|
| 755 | fc_i(ji,nlay_i) = - zkappa_i(ji,nlay_i) * ( zg1*(t_bo_b(ji) - t_i_b(ji,nlay_i)) ) |
---|
[921] | 756 | END DO |
---|
| 757 | ENDIF |
---|
[2715] | 758 | ! |
---|
[921] | 759 | END SUBROUTINE lim_thd_dif |
---|
[825] | 760 | |
---|
| 761 | #else |
---|
[2715] | 762 | !!---------------------------------------------------------------------- |
---|
| 763 | !! Dummy Module No LIM-3 sea-ice model |
---|
| 764 | !!---------------------------------------------------------------------- |
---|
[825] | 765 | CONTAINS |
---|
| 766 | SUBROUTINE lim_thd_dif ! Empty routine |
---|
| 767 | END SUBROUTINE lim_thd_dif |
---|
| 768 | #endif |
---|
[2528] | 769 | !!====================================================================== |
---|
[921] | 770 | END MODULE limthd_dif |
---|