[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 thd_ice ! LIM-3: thermodynamics |
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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 wrk_nemo ! work arrays |
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| 25 | USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) |
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[921] | 26 | |
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[825] | 27 | IMPLICIT NONE |
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| 28 | PRIVATE |
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| 29 | |
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[2528] | 30 | PUBLIC lim_thd_dif ! called by lim_thd |
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[825] | 31 | |
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| 32 | !!---------------------------------------------------------------------- |
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[4161] | 33 | !! NEMO/LIM3 4.0 , UCL - NEMO Consortium (2011) |
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[1156] | 34 | !! $Id$ |
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[2591] | 35 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[825] | 36 | !!---------------------------------------------------------------------- |
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| 37 | CONTAINS |
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| 38 | |
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[4688] | 39 | SUBROUTINE lim_thd_dif( kideb , kiut ) |
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[921] | 40 | !!------------------------------------------------------------------ |
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| 41 | !! *** ROUTINE lim_thd_dif *** |
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| 42 | !! ** Purpose : |
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| 43 | !! This routine determines the time evolution of snow and sea-ice |
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| 44 | !! temperature profiles. |
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| 45 | !! ** Method : |
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| 46 | !! This is done by solving the heat equation diffusion with |
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| 47 | !! a Neumann boundary condition at the surface and a Dirichlet one |
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| 48 | !! at the bottom. Solar radiation is partially absorbed into the ice. |
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| 49 | !! The specific heat and thermal conductivities depend on ice salinity |
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| 50 | !! and temperature to take into account brine pocket melting. The |
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| 51 | !! numerical |
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| 52 | !! scheme is an iterative Crank-Nicolson on a non-uniform multilayer grid |
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| 53 | !! in the ice and snow system. |
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| 54 | !! |
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| 55 | !! The successive steps of this routine are |
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| 56 | !! 1. Thermal conductivity at the interfaces of the ice layers |
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| 57 | !! 2. Internal absorbed radiation |
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| 58 | !! 3. Scale factors due to non-uniform grid |
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| 59 | !! 4. Kappa factors |
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| 60 | !! Then iterative procedure begins |
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| 61 | !! 5. specific heat in the ice |
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| 62 | !! 6. eta factors |
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| 63 | !! 7. surface flux computation |
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| 64 | !! 8. tridiagonal system terms |
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| 65 | !! 9. solving the tridiagonal system with Gauss elimination |
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| 66 | !! Iterative procedure ends according to a criterion on evolution |
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| 67 | !! of temperature |
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| 68 | !! |
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| 69 | !! ** Arguments : |
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| 70 | !! kideb , kiut : Starting and ending points on which the |
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| 71 | !! the computation is applied |
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| 72 | !! |
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| 73 | !! ** Inputs / Ouputs : (global commons) |
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[4872] | 74 | !! surface temperature : t_su_1d |
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| 75 | !! ice/snow temperatures : t_i_1d, t_s_1d |
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| 76 | !! ice salinities : s_i_1d |
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[921] | 77 | !! number of layers in the ice/snow: nlay_i, nlay_s |
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| 78 | !! profile of the ice/snow layers : z_i, z_s |
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[4872] | 79 | !! total ice/snow thickness : ht_i_1d, ht_s_1d |
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[921] | 80 | !! |
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| 81 | !! ** External : |
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| 82 | !! |
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| 83 | !! ** References : |
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| 84 | !! |
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| 85 | !! ** History : |
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| 86 | !! (02-2003) Martin Vancoppenolle, Louvain-la-Neuve, Belgium |
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| 87 | !! (06-2005) Martin Vancoppenolle, 3d version |
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| 88 | !! (11-2006) Vectorized by Xavier Fettweis (UCL-ASTR) |
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| 89 | !! (04-2007) Energy conservation tested by M. Vancoppenolle |
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| 90 | !!------------------------------------------------------------------ |
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[4688] | 91 | INTEGER , INTENT(in) :: kideb, kiut ! Start/End point on which the the computation is applied |
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[825] | 92 | |
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[921] | 93 | !! * Local variables |
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[3294] | 94 | INTEGER :: ji ! spatial loop index |
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| 95 | INTEGER :: ii, ij ! temporary dummy loop index |
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| 96 | INTEGER :: numeq ! current reference number of equation |
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[4870] | 97 | INTEGER :: jk ! vertical dummy loop index |
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[3294] | 98 | INTEGER :: nconv ! number of iterations in iterative procedure |
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| 99 | INTEGER :: minnumeqmin, maxnumeqmax |
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[5123] | 100 | |
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[4688] | 101 | INTEGER, POINTER, DIMENSION(:) :: numeqmin ! reference number of top equation |
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| 102 | INTEGER, POINTER, DIMENSION(:) :: numeqmax ! reference number of bottom equation |
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[5123] | 103 | |
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[3294] | 104 | REAL(wp) :: zg1s = 2._wp ! for the tridiagonal system |
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| 105 | REAL(wp) :: zg1 = 2._wp ! |
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| 106 | REAL(wp) :: zgamma = 18009._wp ! for specific heat |
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| 107 | REAL(wp) :: zbeta = 0.117_wp ! for thermal conductivity (could be 0.13) |
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[4990] | 108 | REAL(wp) :: zraext_s = 10._wp ! extinction coefficient of radiation in the snow |
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[3294] | 109 | REAL(wp) :: zkimin = 0.10_wp ! minimum ice thermal conductivity |
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[4688] | 110 | REAL(wp) :: ztsu_err = 1.e-5_wp ! range around which t_su is considered as 0°C |
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[2715] | 111 | REAL(wp) :: ztmelt_i ! ice melting temperature |
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| 112 | REAL(wp) :: zerritmax ! current maximal error on temperature |
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[5123] | 113 | REAL(wp) :: zhsu |
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| 114 | |
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| 115 | REAL(wp), POINTER, DIMENSION(:) :: isnow ! switch for presence (1) or absence (0) of snow |
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| 116 | REAL(wp), POINTER, DIMENSION(:) :: ztsub ! old surface temperature (before the iterative procedure ) |
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| 117 | REAL(wp), POINTER, DIMENSION(:) :: ztsubit ! surface temperature at previous iteration |
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| 118 | REAL(wp), POINTER, DIMENSION(:) :: zh_i ! ice layer thickness |
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| 119 | REAL(wp), POINTER, DIMENSION(:) :: zh_s ! snow layer thickness |
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| 120 | REAL(wp), POINTER, DIMENSION(:) :: zfsw ! solar radiation absorbed at the surface |
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[5146] | 121 | REAL(wp), POINTER, DIMENSION(:) :: zqns_ice_b ! solar radiation absorbed at the surface |
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[5123] | 122 | REAL(wp), POINTER, DIMENSION(:) :: zf ! surface flux function |
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| 123 | REAL(wp), POINTER, DIMENSION(:) :: dzf ! derivative of the surface flux function |
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| 124 | REAL(wp), POINTER, DIMENSION(:) :: zerrit ! current error on temperature |
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| 125 | REAL(wp), POINTER, DIMENSION(:) :: zdifcase ! case of the equation resolution (1->4) |
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| 126 | REAL(wp), POINTER, DIMENSION(:) :: zftrice ! solar radiation transmitted through the ice |
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| 127 | REAL(wp), POINTER, DIMENSION(:) :: zihic |
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| 128 | |
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| 129 | REAL(wp), POINTER, DIMENSION(:,:) :: ztcond_i ! Ice thermal conductivity |
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| 130 | REAL(wp), POINTER, DIMENSION(:,:) :: zradtr_i ! Radiation transmitted through the ice |
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| 131 | REAL(wp), POINTER, DIMENSION(:,:) :: zradab_i ! Radiation absorbed in the ice |
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| 132 | REAL(wp), POINTER, DIMENSION(:,:) :: zkappa_i ! Kappa factor in the ice |
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| 133 | REAL(wp), POINTER, DIMENSION(:,:) :: ztib ! Old temperature in the ice |
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| 134 | REAL(wp), POINTER, DIMENSION(:,:) :: zeta_i ! Eta factor in the ice |
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| 135 | REAL(wp), POINTER, DIMENSION(:,:) :: ztitemp ! Temporary temperature in the ice to check the convergence |
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| 136 | REAL(wp), POINTER, DIMENSION(:,:) :: zspeche_i ! Ice specific heat |
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| 137 | REAL(wp), POINTER, DIMENSION(:,:) :: z_i ! Vertical cotes of the layers in the ice |
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| 138 | REAL(wp), POINTER, DIMENSION(:,:) :: zradtr_s ! Radiation transmited through the snow |
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| 139 | REAL(wp), POINTER, DIMENSION(:,:) :: zradab_s ! Radiation absorbed in the snow |
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| 140 | REAL(wp), POINTER, DIMENSION(:,:) :: zkappa_s ! Kappa factor in the snow |
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| 141 | REAL(wp), POINTER, DIMENSION(:,:) :: zeta_s ! Eta factor in the snow |
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| 142 | REAL(wp), POINTER, DIMENSION(:,:) :: ztstemp ! Temporary temperature in the snow to check the convergence |
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| 143 | REAL(wp), POINTER, DIMENSION(:,:) :: ztsb ! Temporary temperature in the snow |
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| 144 | REAL(wp), POINTER, DIMENSION(:,:) :: z_s ! Vertical cotes of the layers in the snow |
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| 145 | REAL(wp), POINTER, DIMENSION(:,:) :: zindterm ! 'Ind'ependent term |
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| 146 | REAL(wp), POINTER, DIMENSION(:,:) :: zindtbis ! Temporary 'ind'ependent term |
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| 147 | REAL(wp), POINTER, DIMENSION(:,:) :: zdiagbis ! Temporary 'dia'gonal term |
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| 148 | REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrid ! Tridiagonal system terms |
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| 149 | |
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[4688] | 150 | ! diag errors on heat |
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[5123] | 151 | REAL(wp), POINTER, DIMENSION(:) :: zdq, zq_ini, zhfx_err |
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| 152 | |
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| 153 | ! Mono-category |
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| 154 | REAL(wp) :: zepsilon ! determines thres. above which computation of G(h) is done |
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| 155 | REAL(wp) :: zratio_s ! dummy factor |
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| 156 | REAL(wp) :: zratio_i ! dummy factor |
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| 157 | REAL(wp) :: zh_thres ! thickness thres. for G(h) computation |
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| 158 | REAL(wp) :: zhe ! dummy factor |
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| 159 | REAL(wp) :: zkimean ! mean sea ice thermal conductivity |
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| 160 | REAL(wp) :: zfac ! dummy factor |
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| 161 | REAL(wp) :: zihe ! dummy factor |
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| 162 | REAL(wp) :: zheshth ! dummy factor |
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| 163 | |
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| 164 | REAL(wp), POINTER, DIMENSION(:) :: zghe ! G(he), th. conduct enhancement factor, mono-cat |
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| 165 | |
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[3625] | 166 | !!------------------------------------------------------------------ |
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[3610] | 167 | ! |
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[5123] | 168 | CALL wrk_alloc( jpij, numeqmin, numeqmax ) |
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| 169 | CALL wrk_alloc( jpij, isnow, ztsub, ztsubit, zh_i, zh_s, zfsw ) |
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[5146] | 170 | CALL wrk_alloc( jpij, zf, dzf, zqns_ice_b, zerrit, zdifcase, zftrice, zihic, zghe ) |
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[5167] | 171 | CALL wrk_alloc( jpij,nlay_i+1, ztcond_i, zradtr_i, zradab_i, zkappa_i, ztib, zeta_i, ztitemp, z_i, zspeche_i, kjstart=0 ) |
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| 172 | CALL wrk_alloc( jpij,nlay_s+1, zradtr_s, zradab_s, zkappa_s, ztsb, zeta_s, ztstemp, z_s, kjstart=0 ) |
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| 173 | CALL wrk_alloc( jpij,nlay_i+3, zindterm, zindtbis, zdiagbis ) |
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| 174 | CALL wrk_alloc( jpij,nlay_i+3,3, ztrid ) |
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[4688] | 175 | |
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[4990] | 176 | CALL wrk_alloc( jpij, zdq, zq_ini, zhfx_err ) |
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[4688] | 177 | |
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| 178 | ! --- diag error on heat diffusion - PART 1 --- ! |
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| 179 | zdq(:) = 0._wp ; zq_ini(:) = 0._wp |
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| 180 | DO ji = kideb, kiut |
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[5123] | 181 | zq_ini(ji) = ( SUM( q_i_1d(ji,1:nlay_i) ) * ht_i_1d(ji) * r1_nlay_i + & |
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| 182 | & SUM( q_s_1d(ji,1:nlay_s) ) * ht_s_1d(ji) * r1_nlay_s ) |
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[4688] | 183 | END DO |
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| 184 | |
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[921] | 185 | !------------------------------------------------------------------------------! |
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| 186 | ! 1) Initialization ! |
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| 187 | !------------------------------------------------------------------------------! |
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| 188 | DO ji = kideb , kiut |
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[5123] | 189 | isnow(ji)= 1._wp - MAX( 0._wp , SIGN(1._wp, - ht_s_1d(ji) ) ) ! is there snow or not |
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[921] | 190 | ! layer thickness |
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[5123] | 191 | zh_i(ji) = ht_i_1d(ji) * r1_nlay_i |
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| 192 | zh_s(ji) = ht_s_1d(ji) * r1_nlay_s |
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[921] | 193 | END DO |
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[825] | 194 | |
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[921] | 195 | !-------------------- |
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| 196 | ! Ice / snow layers |
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| 197 | !-------------------- |
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[825] | 198 | |
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[2715] | 199 | z_s(:,0) = 0._wp ! vert. coord. of the up. lim. of the 1st snow layer |
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| 200 | z_i(:,0) = 0._wp ! vert. coord. of the up. lim. of the 1st ice layer |
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[825] | 201 | |
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[4870] | 202 | DO jk = 1, nlay_s ! vert. coord of the up. lim. of the layer-th snow layer |
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[921] | 203 | DO ji = kideb , kiut |
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[5123] | 204 | z_s(ji,jk) = z_s(ji,jk-1) + ht_s_1d(ji) * r1_nlay_s |
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[921] | 205 | END DO |
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| 206 | END DO |
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[825] | 207 | |
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[4870] | 208 | DO jk = 1, nlay_i ! vert. coord of the up. lim. of the layer-th ice layer |
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[921] | 209 | DO ji = kideb , kiut |
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[5123] | 210 | z_i(ji,jk) = z_i(ji,jk-1) + ht_i_1d(ji) * r1_nlay_i |
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[921] | 211 | END DO |
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| 212 | END DO |
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| 213 | ! |
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| 214 | !------------------------------------------------------------------------------| |
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[5123] | 215 | ! 2) Radiation | |
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[921] | 216 | !------------------------------------------------------------------------------| |
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| 217 | ! |
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| 218 | !------------------- |
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| 219 | ! Computation of i0 |
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| 220 | !------------------- |
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| 221 | ! i0 describes the fraction of solar radiation which does not contribute |
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| 222 | ! to the surface energy budget but rather penetrates inside the ice. |
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| 223 | ! We assume that no radiation is transmitted through the snow |
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| 224 | ! If there is no no snow |
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| 225 | ! zfsw = (1-i0).qsr_ice is absorbed at the surface |
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| 226 | ! zftrice = io.qsr_ice is below the surface |
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[4688] | 227 | ! ftr_ice = io.qsr_ice.exp(-k(h_i)) transmitted below the ice |
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[5123] | 228 | ! fr1_i0_1d = i0 for a thin ice cover, fr1_i0_2d = i0 for a thick ice cover |
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| 229 | zhsu = 0.1_wp ! threshold for the computation of i0 |
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[921] | 230 | DO ji = kideb , kiut |
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| 231 | ! switches |
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[5123] | 232 | isnow(ji) = 1._wp - MAX( 0._wp , SIGN( 1._wp , - ht_s_1d(ji) ) ) |
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[921] | 233 | ! hs > 0, isnow = 1 |
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[5123] | 234 | zihic(ji) = MAX( 0._wp , 1._wp - ( ht_i_1d(ji) / zhsu ) ) |
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[825] | 235 | |
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[5123] | 236 | i0(ji) = ( 1._wp - isnow(ji) ) * ( fr1_i0_1d(ji) + zihic(ji) * fr2_i0_1d(ji) ) |
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[921] | 237 | END DO |
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[825] | 238 | |
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[921] | 239 | !------------------------------------------------------- |
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| 240 | ! Solar radiation absorbed / transmitted at the surface |
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| 241 | ! Derivative of the non solar flux |
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| 242 | !------------------------------------------------------- |
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| 243 | DO ji = kideb , kiut |
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[5146] | 244 | zfsw (ji) = qsr_ice_1d(ji) * ( 1 - i0(ji) ) ! Shortwave radiation absorbed at surface |
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| 245 | zftrice(ji) = qsr_ice_1d(ji) * i0(ji) ! Solar radiation transmitted below the surface layer |
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| 246 | dzf (ji) = dqns_ice_1d(ji) ! derivative of incoming nonsolar flux |
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| 247 | zqns_ice_b(ji) = qns_ice_1d(ji) ! store previous qns_ice_1d value |
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[921] | 248 | END DO |
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[825] | 249 | |
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[921] | 250 | !--------------------------------------------------------- |
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| 251 | ! Transmission - absorption of solar radiation in the ice |
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| 252 | !--------------------------------------------------------- |
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[825] | 253 | |
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[2715] | 254 | DO ji = kideb, kiut ! snow initialization |
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| 255 | zradtr_s(ji,0) = zftrice(ji) ! radiation penetrating through snow |
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[921] | 256 | END DO |
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[825] | 257 | |
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[4870] | 258 | DO jk = 1, nlay_s ! Radiation through snow |
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[2715] | 259 | DO ji = kideb, kiut |
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| 260 | ! ! radiation transmitted below the layer-th snow layer |
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[4870] | 261 | zradtr_s(ji,jk) = zradtr_s(ji,0) * EXP( - zraext_s * ( MAX ( 0._wp , z_s(ji,jk) ) ) ) |
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[2715] | 262 | ! ! radiation absorbed by the layer-th snow layer |
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[4870] | 263 | zradab_s(ji,jk) = zradtr_s(ji,jk-1) - zradtr_s(ji,jk) |
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[921] | 264 | END DO |
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| 265 | END DO |
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[825] | 266 | |
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[2715] | 267 | DO ji = kideb, kiut ! ice initialization |
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[5123] | 268 | zradtr_i(ji,0) = zradtr_s(ji,nlay_s) * isnow(ji) + zftrice(ji) * ( 1._wp - isnow(ji) ) |
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[921] | 269 | END DO |
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[825] | 270 | |
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[4870] | 271 | DO jk = 1, nlay_i ! Radiation through ice |
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[2715] | 272 | DO ji = kideb, kiut |
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| 273 | ! ! radiation transmitted below the layer-th ice layer |
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[5123] | 274 | zradtr_i(ji,jk) = zradtr_i(ji,0) * EXP( - rn_kappa_i * ( MAX ( 0._wp , z_i(ji,jk) ) ) ) |
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[2715] | 275 | ! ! radiation absorbed by the layer-th ice layer |
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[4870] | 276 | zradab_i(ji,jk) = zradtr_i(ji,jk-1) - zradtr_i(ji,jk) |
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[921] | 277 | END DO |
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| 278 | END DO |
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[825] | 279 | |
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[2715] | 280 | DO ji = kideb, kiut ! Radiation transmitted below the ice |
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[4688] | 281 | ftr_ice_1d(ji) = zradtr_i(ji,nlay_i) |
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[921] | 282 | END DO |
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[834] | 283 | |
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[921] | 284 | !------------------------------------------------------------------------------| |
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| 285 | ! 3) Iterative procedure begins | |
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| 286 | !------------------------------------------------------------------------------| |
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| 287 | ! |
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[2715] | 288 | DO ji = kideb, kiut ! Old surface temperature |
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[4872] | 289 | ztsub (ji) = t_su_1d(ji) ! temperature at the beg of iter pr. |
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| 290 | ztsubit(ji) = t_su_1d(ji) ! temperature at the previous iter |
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[5123] | 291 | t_su_1d(ji) = MIN( t_su_1d(ji), rt0 - ztsu_err ) ! necessary |
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| 292 | zerrit (ji) = 1000._wp ! initial value of error |
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[921] | 293 | END DO |
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[825] | 294 | |
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[4870] | 295 | DO jk = 1, nlay_s ! Old snow temperature |
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[921] | 296 | DO ji = kideb , kiut |
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[4872] | 297 | ztsb(ji,jk) = t_s_1d(ji,jk) |
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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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[4870] | 301 | DO jk = 1, nlay_i ! Old ice temperature |
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[921] | 302 | DO ji = kideb , kiut |
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[4872] | 303 | ztib(ji,jk) = t_i_1d(ji,jk) |
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[921] | 304 | END DO |
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| 305 | END DO |
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[825] | 306 | |
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[2715] | 307 | nconv = 0 ! number of iterations |
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| 308 | zerritmax = 1000._wp ! maximal value of error on all points |
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[825] | 309 | |
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[5123] | 310 | DO WHILE ( zerritmax > rn_terr_dif .AND. nconv < nn_conv_dif ) |
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[921] | 311 | ! |
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[2715] | 312 | nconv = nconv + 1 |
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| 313 | ! |
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[921] | 314 | !------------------------------------------------------------------------------| |
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| 315 | ! 4) Sea ice thermal conductivity | |
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| 316 | !------------------------------------------------------------------------------| |
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| 317 | ! |
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[5123] | 318 | IF( nn_ice_thcon == 0 ) THEN ! Untersteiner (1964) formula |
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[921] | 319 | DO ji = kideb , kiut |
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[5123] | 320 | ztcond_i(ji,0) = rcdic + zbeta * s_i_1d(ji,1) / MIN( -epsi10, t_i_1d(ji,1) - rt0 ) |
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| 321 | ztcond_i(ji,0) = MAX( ztcond_i(ji,0), zkimin ) |
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[921] | 322 | END DO |
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[4870] | 323 | DO jk = 1, nlay_i-1 |
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[921] | 324 | DO ji = kideb , kiut |
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[5123] | 325 | ztcond_i(ji,jk) = rcdic + zbeta * ( s_i_1d(ji,jk) + s_i_1d(ji,jk+1) ) / & |
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| 326 | MIN(-2.0_wp * epsi10, t_i_1d(ji,jk) + t_i_1d(ji,jk+1) - 2.0_wp * rt0) |
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| 327 | ztcond_i(ji,jk) = MAX( ztcond_i(ji,jk), zkimin ) |
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[921] | 328 | END DO |
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| 329 | END DO |
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| 330 | ENDIF |
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[825] | 331 | |
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[5123] | 332 | IF( nn_ice_thcon == 1 ) THEN ! Pringle et al formula included: 2.11 + 0.09 S/T - 0.011.T |
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[921] | 333 | DO ji = kideb , kiut |
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[5123] | 334 | ztcond_i(ji,0) = rcdic + 0.090_wp * s_i_1d(ji,1) / MIN( -epsi10, t_i_1d(ji,1) - rt0 ) & |
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| 335 | & - 0.011_wp * ( t_i_1d(ji,1) - rt0 ) |
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[2715] | 336 | ztcond_i(ji,0) = MAX( ztcond_i(ji,0), zkimin ) |
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[921] | 337 | END DO |
---|
[4870] | 338 | DO jk = 1, nlay_i-1 |
---|
[2715] | 339 | DO ji = kideb , kiut |
---|
[5123] | 340 | ztcond_i(ji,jk) = rcdic + & |
---|
| 341 | & 0.09_wp * ( s_i_1d(ji,jk) + s_i_1d(ji,jk+1) ) & |
---|
| 342 | & / MIN( -2._wp * epsi10, t_i_1d(ji,jk) + t_i_1d(ji,jk+1) - 2.0_wp * rt0 ) & |
---|
| 343 | & - 0.0055_wp * ( t_i_1d(ji,jk) + t_i_1d(ji,jk+1) - 2.0 * rt0 ) |
---|
[4870] | 344 | ztcond_i(ji,jk) = MAX( ztcond_i(ji,jk), zkimin ) |
---|
[2715] | 345 | END DO |
---|
| 346 | END DO |
---|
| 347 | DO ji = kideb , kiut |
---|
[5123] | 348 | ztcond_i(ji,nlay_i) = rcdic + 0.090_wp * s_i_1d(ji,nlay_i) / MIN( -epsi10, t_bo_1d(ji) - rt0 ) & |
---|
| 349 | & - 0.011_wp * ( t_bo_1d(ji) - rt0 ) |
---|
[2715] | 350 | ztcond_i(ji,nlay_i) = MAX( ztcond_i(ji,nlay_i), zkimin ) |
---|
| 351 | END DO |
---|
[921] | 352 | ENDIF |
---|
[5123] | 353 | |
---|
[921] | 354 | ! |
---|
| 355 | !------------------------------------------------------------------------------| |
---|
[5123] | 356 | ! 5) G(he) - enhancement of thermal conductivity in mono-category case | |
---|
[921] | 357 | !------------------------------------------------------------------------------| |
---|
| 358 | ! |
---|
[5123] | 359 | ! Computation of effective thermal conductivity G(h) |
---|
| 360 | ! Used in mono-category case only to simulate an ITD implicitly |
---|
| 361 | ! Fichefet and Morales Maqueda, JGR 1997 |
---|
| 362 | |
---|
| 363 | zghe(:) = 1._wp |
---|
| 364 | |
---|
| 365 | SELECT CASE ( nn_monocat ) |
---|
| 366 | |
---|
| 367 | CASE (1,3) ! LIM3 |
---|
| 368 | |
---|
| 369 | zepsilon = 0.1_wp |
---|
| 370 | zh_thres = EXP( 1._wp ) * zepsilon * 0.5_wp |
---|
| 371 | |
---|
| 372 | DO ji = kideb, kiut |
---|
| 373 | |
---|
| 374 | ! Mean sea ice thermal conductivity |
---|
| 375 | zkimean = SUM( ztcond_i(ji,0:nlay_i) ) / REAL( nlay_i+1, wp ) |
---|
| 376 | |
---|
| 377 | ! Effective thickness he (zhe) |
---|
[7607] | 378 | zfac = 1._wp / ( rn_cdsn + zkimean ) |
---|
| 379 | zratio_s = rn_cdsn * zfac |
---|
[5123] | 380 | zratio_i = zkimean * zfac |
---|
| 381 | zhe = zratio_s * ht_i_1d(ji) + zratio_i * ht_s_1d(ji) |
---|
| 382 | |
---|
| 383 | ! G(he) |
---|
| 384 | rswitch = MAX( 0._wp , SIGN( 1._wp , zhe - zh_thres ) ) ! =0 if zhe < zh_thres, if > |
---|
| 385 | zghe(ji) = ( 1._wp - rswitch ) + rswitch * 0.5_wp * ( 1._wp + LOG( 2._wp * zhe / zepsilon ) ) |
---|
| 386 | |
---|
| 387 | ! Impose G(he) < 2. |
---|
| 388 | zghe(ji) = MIN( zghe(ji), 2._wp ) |
---|
| 389 | |
---|
| 390 | END DO |
---|
| 391 | |
---|
| 392 | END SELECT |
---|
| 393 | |
---|
| 394 | ! |
---|
| 395 | !------------------------------------------------------------------------------| |
---|
| 396 | ! 6) kappa factors | |
---|
| 397 | !------------------------------------------------------------------------------| |
---|
| 398 | ! |
---|
| 399 | !--- Snow |
---|
[921] | 400 | DO ji = kideb, kiut |
---|
[5123] | 401 | zfac = 1. / MAX( epsi10 , zh_s(ji) ) |
---|
[7607] | 402 | zkappa_s(ji,0) = zghe(ji) * rn_cdsn * zfac |
---|
| 403 | zkappa_s(ji,nlay_s) = zghe(ji) * rn_cdsn * zfac |
---|
[921] | 404 | END DO |
---|
[825] | 405 | |
---|
[4870] | 406 | DO jk = 1, nlay_s-1 |
---|
[921] | 407 | DO ji = kideb , kiut |
---|
[7607] | 408 | zkappa_s(ji,jk) = zghe(ji) * 2.0 * rn_cdsn / MAX( epsi10, 2.0 * zh_s(ji) ) |
---|
[921] | 409 | END DO |
---|
| 410 | END DO |
---|
[825] | 411 | |
---|
[5123] | 412 | !--- Ice |
---|
[4870] | 413 | DO jk = 1, nlay_i-1 |
---|
[921] | 414 | DO ji = kideb , kiut |
---|
[5123] | 415 | zkappa_i(ji,jk) = zghe(ji) * 2.0 * ztcond_i(ji,jk) / MAX( epsi10 , 2.0 * zh_i(ji) ) |
---|
[921] | 416 | END DO |
---|
| 417 | END DO |
---|
[825] | 418 | |
---|
[5123] | 419 | !--- Snow-ice interface |
---|
[921] | 420 | DO ji = kideb , kiut |
---|
[5123] | 421 | zfac = 1./ MAX( epsi10 , zh_i(ji) ) |
---|
| 422 | zkappa_i(ji,0) = zghe(ji) * ztcond_i(ji,0) * zfac |
---|
| 423 | zkappa_i(ji,nlay_i) = zghe(ji) * ztcond_i(ji,nlay_i) * zfac |
---|
[7607] | 424 | zkappa_s(ji,nlay_s) = zghe(ji) * zghe(ji) * 2.0 * rn_cdsn * ztcond_i(ji,0) / & |
---|
| 425 | & MAX( epsi10, ( zghe(ji) * ztcond_i(ji,0) * zh_s(ji) + zghe(ji) * rn_cdsn * zh_i(ji) ) ) |
---|
[5123] | 426 | zkappa_i(ji,0) = zkappa_s(ji,nlay_s) * isnow(ji) + zkappa_i(ji,0) * ( 1._wp - isnow(ji) ) |
---|
[921] | 427 | END DO |
---|
[5123] | 428 | |
---|
[921] | 429 | ! |
---|
| 430 | !------------------------------------------------------------------------------| |
---|
[5123] | 431 | ! 7) Sea ice specific heat, eta factors | |
---|
[921] | 432 | !------------------------------------------------------------------------------| |
---|
| 433 | ! |
---|
[4870] | 434 | DO jk = 1, nlay_i |
---|
[921] | 435 | DO ji = kideb , kiut |
---|
[4872] | 436 | ztitemp(ji,jk) = t_i_1d(ji,jk) |
---|
[5123] | 437 | zspeche_i(ji,jk) = cpic + zgamma * s_i_1d(ji,jk) / MAX( ( t_i_1d(ji,jk) - rt0 ) * ( ztib(ji,jk) - rt0 ), epsi10 ) |
---|
| 438 | zeta_i(ji,jk) = rdt_ice / MAX( rhoic * zspeche_i(ji,jk) * zh_i(ji), epsi10 ) |
---|
[921] | 439 | END DO |
---|
| 440 | END DO |
---|
[825] | 441 | |
---|
[4870] | 442 | DO jk = 1, nlay_s |
---|
[921] | 443 | DO ji = kideb , kiut |
---|
[4872] | 444 | ztstemp(ji,jk) = t_s_1d(ji,jk) |
---|
[5123] | 445 | zeta_s(ji,jk) = rdt_ice / MAX( rhosn * cpic * zh_s(ji), epsi10 ) |
---|
[921] | 446 | END DO |
---|
| 447 | END DO |
---|
[5123] | 448 | |
---|
[921] | 449 | ! |
---|
| 450 | !------------------------------------------------------------------------------| |
---|
[5123] | 451 | ! 8) surface flux computation | |
---|
[921] | 452 | !------------------------------------------------------------------------------| |
---|
| 453 | ! |
---|
[5146] | 454 | IF ( ln_it_qnsice ) THEN |
---|
[4990] | 455 | DO ji = kideb , kiut |
---|
| 456 | ! update of the non solar flux according to the update in T_su |
---|
| 457 | qns_ice_1d(ji) = qns_ice_1d(ji) + dqns_ice_1d(ji) * ( t_su_1d(ji) - ztsubit(ji) ) |
---|
| 458 | END DO |
---|
| 459 | ENDIF |
---|
| 460 | |
---|
| 461 | ! Update incoming flux |
---|
[921] | 462 | DO ji = kideb , kiut |
---|
| 463 | ! update incoming flux |
---|
[5123] | 464 | zf(ji) = zfsw(ji) & ! net absorbed solar radiation |
---|
| 465 | & + qns_ice_1d(ji) ! non solar total flux (LWup, LWdw, SH, LH) |
---|
[921] | 466 | END DO |
---|
[825] | 467 | |
---|
[921] | 468 | ! |
---|
| 469 | !------------------------------------------------------------------------------| |
---|
[5123] | 470 | ! 9) tridiagonal system terms | |
---|
[921] | 471 | !------------------------------------------------------------------------------| |
---|
| 472 | ! |
---|
| 473 | !!layer denotes the number of the layer in the snow or in the ice |
---|
| 474 | !!numeq denotes the reference number of the equation in the tridiagonal |
---|
| 475 | !!system, terms of tridiagonal system are indexed as following : |
---|
| 476 | !!1 is subdiagonal term, 2 is diagonal and 3 is superdiagonal one |
---|
[825] | 477 | |
---|
[921] | 478 | !!ice interior terms (top equation has the same form as the others) |
---|
| 479 | |
---|
[4873] | 480 | DO numeq=1,nlay_i+3 |
---|
[921] | 481 | DO ji = kideb , kiut |
---|
| 482 | ztrid(ji,numeq,1) = 0. |
---|
| 483 | ztrid(ji,numeq,2) = 0. |
---|
| 484 | ztrid(ji,numeq,3) = 0. |
---|
[5123] | 485 | zindterm(ji,numeq)= 0. |
---|
| 486 | zindtbis(ji,numeq)= 0. |
---|
[921] | 487 | zdiagbis(ji,numeq)= 0. |
---|
| 488 | ENDDO |
---|
| 489 | ENDDO |
---|
| 490 | |
---|
| 491 | DO numeq = nlay_s + 2, nlay_s + nlay_i |
---|
| 492 | DO ji = kideb , kiut |
---|
[5123] | 493 | jk = numeq - nlay_s - 1 |
---|
| 494 | ztrid(ji,numeq,1) = - zeta_i(ji,jk) * zkappa_i(ji,jk-1) |
---|
| 495 | ztrid(ji,numeq,2) = 1.0 + zeta_i(ji,jk) * ( zkappa_i(ji,jk-1) + zkappa_i(ji,jk) ) |
---|
| 496 | ztrid(ji,numeq,3) = - zeta_i(ji,jk) * zkappa_i(ji,jk) |
---|
| 497 | zindterm(ji,numeq) = ztib(ji,jk) + zeta_i(ji,jk) * zradab_i(ji,jk) |
---|
[921] | 498 | END DO |
---|
| 499 | ENDDO |
---|
| 500 | |
---|
| 501 | numeq = nlay_s + nlay_i + 1 |
---|
| 502 | DO ji = kideb , kiut |
---|
[825] | 503 | !!ice bottom term |
---|
| 504 | ztrid(ji,numeq,1) = - zeta_i(ji,nlay_i)*zkappa_i(ji,nlay_i-1) |
---|
[5123] | 505 | ztrid(ji,numeq,2) = 1.0 + zeta_i(ji,nlay_i) * ( zkappa_i(ji,nlay_i) * zg1 + zkappa_i(ji,nlay_i-1) ) |
---|
[825] | 506 | ztrid(ji,numeq,3) = 0.0 |
---|
[5123] | 507 | zindterm(ji,numeq) = ztib(ji,nlay_i) + zeta_i(ji,nlay_i) * & |
---|
| 508 | & ( zradab_i(ji,nlay_i) + zkappa_i(ji,nlay_i) * zg1 * t_bo_1d(ji) ) |
---|
[921] | 509 | ENDDO |
---|
[825] | 510 | |
---|
| 511 | |
---|
[921] | 512 | DO ji = kideb , kiut |
---|
[5123] | 513 | IF ( ht_s_1d(ji) > 0.0 ) THEN |
---|
[921] | 514 | ! |
---|
| 515 | !------------------------------------------------------------------------------| |
---|
| 516 | ! snow-covered cells | |
---|
| 517 | !------------------------------------------------------------------------------| |
---|
| 518 | ! |
---|
| 519 | !!snow interior terms (bottom equation has the same form as the others) |
---|
| 520 | DO numeq = 3, nlay_s + 1 |
---|
[5123] | 521 | jk = numeq - 1 |
---|
| 522 | ztrid(ji,numeq,1) = - zeta_s(ji,jk) * zkappa_s(ji,jk-1) |
---|
| 523 | ztrid(ji,numeq,2) = 1.0 + zeta_s(ji,jk) * ( zkappa_s(ji,jk-1) + zkappa_s(ji,jk) ) |
---|
[4870] | 524 | ztrid(ji,numeq,3) = - zeta_s(ji,jk)*zkappa_s(ji,jk) |
---|
[5123] | 525 | zindterm(ji,numeq) = ztsb(ji,jk) + zeta_s(ji,jk) * zradab_s(ji,jk) |
---|
[921] | 526 | END DO |
---|
[825] | 527 | |
---|
[921] | 528 | !!case of only one layer in the ice (ice equation is altered) |
---|
| 529 | IF ( nlay_i.eq.1 ) THEN |
---|
| 530 | ztrid(ji,nlay_s+2,3) = 0.0 |
---|
[5123] | 531 | zindterm(ji,nlay_s+2) = zindterm(ji,nlay_s+2) + zkappa_i(ji,1) * t_bo_1d(ji) |
---|
[921] | 532 | ENDIF |
---|
[834] | 533 | |
---|
[5123] | 534 | IF ( t_su_1d(ji) < rt0 ) THEN |
---|
[825] | 535 | |
---|
[921] | 536 | !------------------------------------------------------------------------------| |
---|
| 537 | ! case 1 : no surface melting - snow present | |
---|
| 538 | !------------------------------------------------------------------------------| |
---|
| 539 | zdifcase(ji) = 1.0 |
---|
| 540 | numeqmin(ji) = 1 |
---|
| 541 | numeqmax(ji) = nlay_i + nlay_s + 1 |
---|
[825] | 542 | |
---|
[921] | 543 | !!surface equation |
---|
[5123] | 544 | ztrid(ji,1,1) = 0.0 |
---|
| 545 | ztrid(ji,1,2) = dzf(ji) - zg1s * zkappa_s(ji,0) |
---|
| 546 | ztrid(ji,1,3) = zg1s * zkappa_s(ji,0) |
---|
| 547 | zindterm(ji,1) = dzf(ji) * t_su_1d(ji) - zf(ji) |
---|
[825] | 548 | |
---|
[921] | 549 | !!first layer of snow equation |
---|
[5123] | 550 | ztrid(ji,2,1) = - zkappa_s(ji,0) * zg1s * zeta_s(ji,1) |
---|
| 551 | ztrid(ji,2,2) = 1.0 + zeta_s(ji,1) * ( zkappa_s(ji,1) + zkappa_s(ji,0) * zg1s ) |
---|
[921] | 552 | ztrid(ji,2,3) = - zeta_s(ji,1)* zkappa_s(ji,1) |
---|
[5123] | 553 | zindterm(ji,2) = ztsb(ji,1) + zeta_s(ji,1) * zradab_s(ji,1) |
---|
[825] | 554 | |
---|
[921] | 555 | ELSE |
---|
| 556 | ! |
---|
| 557 | !------------------------------------------------------------------------------| |
---|
| 558 | ! case 2 : surface is melting - snow present | |
---|
| 559 | !------------------------------------------------------------------------------| |
---|
| 560 | ! |
---|
| 561 | zdifcase(ji) = 2.0 |
---|
| 562 | numeqmin(ji) = 2 |
---|
| 563 | numeqmax(ji) = nlay_i + nlay_s + 1 |
---|
[825] | 564 | |
---|
[921] | 565 | !!first layer of snow equation |
---|
| 566 | ztrid(ji,2,1) = 0.0 |
---|
[5123] | 567 | ztrid(ji,2,2) = 1.0 + zeta_s(ji,1) * ( zkappa_s(ji,1) + zkappa_s(ji,0) * zg1s ) |
---|
[921] | 568 | ztrid(ji,2,3) = - zeta_s(ji,1)*zkappa_s(ji,1) |
---|
[5123] | 569 | zindterm(ji,2) = ztsb(ji,1) + zeta_s(ji,1) * & |
---|
| 570 | & ( zradab_s(ji,1) + zkappa_s(ji,0) * zg1s * t_su_1d(ji) ) |
---|
[921] | 571 | ENDIF |
---|
| 572 | ELSE |
---|
| 573 | ! |
---|
| 574 | !------------------------------------------------------------------------------| |
---|
| 575 | ! cells without snow | |
---|
| 576 | !------------------------------------------------------------------------------| |
---|
| 577 | ! |
---|
[5123] | 578 | IF ( t_su_1d(ji) < rt0 ) THEN |
---|
[921] | 579 | ! |
---|
| 580 | !------------------------------------------------------------------------------| |
---|
| 581 | ! case 3 : no surface melting - no snow | |
---|
| 582 | !------------------------------------------------------------------------------| |
---|
| 583 | ! |
---|
| 584 | zdifcase(ji) = 3.0 |
---|
| 585 | numeqmin(ji) = nlay_s + 1 |
---|
| 586 | numeqmax(ji) = nlay_i + nlay_s + 1 |
---|
[825] | 587 | |
---|
[921] | 588 | !!surface equation |
---|
| 589 | ztrid(ji,numeqmin(ji),1) = 0.0 |
---|
| 590 | ztrid(ji,numeqmin(ji),2) = dzf(ji) - zkappa_i(ji,0)*zg1 |
---|
| 591 | ztrid(ji,numeqmin(ji),3) = zkappa_i(ji,0)*zg1 |
---|
[5123] | 592 | zindterm(ji,numeqmin(ji)) = dzf(ji)*t_su_1d(ji) - zf(ji) |
---|
[825] | 593 | |
---|
[921] | 594 | !!first layer of ice equation |
---|
| 595 | ztrid(ji,numeqmin(ji)+1,1) = - zkappa_i(ji,0) * zg1 * zeta_i(ji,1) |
---|
[5123] | 596 | ztrid(ji,numeqmin(ji)+1,2) = 1.0 + zeta_i(ji,1) * ( zkappa_i(ji,1) + zkappa_i(ji,0) * zg1 ) |
---|
| 597 | ztrid(ji,numeqmin(ji)+1,3) = - zeta_i(ji,1) * zkappa_i(ji,1) |
---|
| 598 | zindterm(ji,numeqmin(ji)+1)= ztib(ji,1) + zeta_i(ji,1) * zradab_i(ji,1) |
---|
[825] | 599 | |
---|
[921] | 600 | !!case of only one layer in the ice (surface & ice equations are altered) |
---|
[825] | 601 | |
---|
[5123] | 602 | IF ( nlay_i == 1 ) THEN |
---|
[921] | 603 | ztrid(ji,numeqmin(ji),1) = 0.0 |
---|
[5123] | 604 | ztrid(ji,numeqmin(ji),2) = dzf(ji) - zkappa_i(ji,0) * 2.0 |
---|
| 605 | ztrid(ji,numeqmin(ji),3) = zkappa_i(ji,0) * 2.0 |
---|
| 606 | ztrid(ji,numeqmin(ji)+1,1) = -zkappa_i(ji,0) * 2.0 * zeta_i(ji,1) |
---|
| 607 | ztrid(ji,numeqmin(ji)+1,2) = 1.0 + zeta_i(ji,1) * ( zkappa_i(ji,0) * 2.0 + zkappa_i(ji,1) ) |
---|
[921] | 608 | ztrid(ji,numeqmin(ji)+1,3) = 0.0 |
---|
[825] | 609 | |
---|
[5123] | 610 | zindterm(ji,numeqmin(ji)+1) = ztib(ji,1) + zeta_i(ji,1) * & |
---|
| 611 | & ( zradab_i(ji,1) + zkappa_i(ji,1) * t_bo_1d(ji) ) |
---|
[921] | 612 | ENDIF |
---|
[825] | 613 | |
---|
[921] | 614 | ELSE |
---|
[825] | 615 | |
---|
[921] | 616 | ! |
---|
| 617 | !------------------------------------------------------------------------------| |
---|
| 618 | ! case 4 : surface is melting - no snow | |
---|
| 619 | !------------------------------------------------------------------------------| |
---|
| 620 | ! |
---|
| 621 | zdifcase(ji) = 4.0 |
---|
| 622 | numeqmin(ji) = nlay_s + 2 |
---|
| 623 | numeqmax(ji) = nlay_i + nlay_s + 1 |
---|
[825] | 624 | |
---|
[921] | 625 | !!first layer of ice equation |
---|
| 626 | ztrid(ji,numeqmin(ji),1) = 0.0 |
---|
[5123] | 627 | ztrid(ji,numeqmin(ji),2) = 1.0 + zeta_i(ji,1) * ( zkappa_i(ji,1) + zkappa_i(ji,0) * zg1 ) |
---|
[921] | 628 | ztrid(ji,numeqmin(ji),3) = - zeta_i(ji,1) * zkappa_i(ji,1) |
---|
[5123] | 629 | zindterm(ji,numeqmin(ji)) = ztib(ji,1) + zeta_i(ji,1) * & |
---|
| 630 | & ( zradab_i(ji,1) + zkappa_i(ji,0) * zg1 * t_su_1d(ji) ) |
---|
[825] | 631 | |
---|
[921] | 632 | !!case of only one layer in the ice (surface & ice equations are altered) |
---|
[5123] | 633 | IF ( nlay_i == 1 ) THEN |
---|
[921] | 634 | ztrid(ji,numeqmin(ji),1) = 0.0 |
---|
[5123] | 635 | ztrid(ji,numeqmin(ji),2) = 1.0 + zeta_i(ji,1) * ( zkappa_i(ji,0) * 2.0 + zkappa_i(ji,1) ) |
---|
[921] | 636 | ztrid(ji,numeqmin(ji),3) = 0.0 |
---|
[5123] | 637 | zindterm(ji,numeqmin(ji)) = ztib(ji,1) + zeta_i(ji,1) * ( zradab_i(ji,1) + zkappa_i(ji,1) * t_bo_1d(ji) ) & |
---|
| 638 | & + t_su_1d(ji) * zeta_i(ji,1) * zkappa_i(ji,0) * 2.0 |
---|
[921] | 639 | ENDIF |
---|
[825] | 640 | |
---|
[921] | 641 | ENDIF |
---|
| 642 | ENDIF |
---|
[825] | 643 | |
---|
[921] | 644 | END DO |
---|
[825] | 645 | |
---|
[921] | 646 | ! |
---|
| 647 | !------------------------------------------------------------------------------| |
---|
[5123] | 648 | ! 10) tridiagonal system solving | |
---|
[921] | 649 | !------------------------------------------------------------------------------| |
---|
| 650 | ! |
---|
[825] | 651 | |
---|
[921] | 652 | ! Solve the tridiagonal system with Gauss elimination method. |
---|
| 653 | ! Thomas algorithm, from Computational fluid Dynamics, J.D. ANDERSON, |
---|
| 654 | ! McGraw-Hill 1984. |
---|
[825] | 655 | |
---|
[921] | 656 | maxnumeqmax = 0 |
---|
[4873] | 657 | minnumeqmin = nlay_i+5 |
---|
[825] | 658 | |
---|
[921] | 659 | DO ji = kideb , kiut |
---|
[5123] | 660 | zindtbis(ji,numeqmin(ji)) = zindterm(ji,numeqmin(ji)) |
---|
[921] | 661 | zdiagbis(ji,numeqmin(ji)) = ztrid(ji,numeqmin(ji),2) |
---|
| 662 | minnumeqmin = MIN(numeqmin(ji),minnumeqmin) |
---|
| 663 | maxnumeqmax = MAX(numeqmax(ji),maxnumeqmax) |
---|
| 664 | END DO |
---|
| 665 | |
---|
[4870] | 666 | DO jk = minnumeqmin+1, maxnumeqmax |
---|
[921] | 667 | DO ji = kideb , kiut |
---|
[4870] | 668 | numeq = min(max(numeqmin(ji)+1,jk),numeqmax(ji)) |
---|
[5123] | 669 | zdiagbis(ji,numeq) = ztrid(ji,numeq,2) - ztrid(ji,numeq,1) * ztrid(ji,numeq-1,3) / zdiagbis(ji,numeq-1) |
---|
| 670 | zindtbis(ji,numeq) = zindterm(ji,numeq) - ztrid(ji,numeq,1) * zindtbis(ji,numeq-1) / zdiagbis(ji,numeq-1) |
---|
[921] | 671 | END DO |
---|
| 672 | END DO |
---|
| 673 | |
---|
| 674 | DO ji = kideb , kiut |
---|
| 675 | ! ice temperatures |
---|
[5123] | 676 | t_i_1d(ji,nlay_i) = zindtbis(ji,numeqmax(ji)) / zdiagbis(ji,numeqmax(ji)) |
---|
[921] | 677 | END DO |
---|
| 678 | |
---|
[5180] | 679 | DO numeq = nlay_i + nlay_s, nlay_s + 2, -1 |
---|
[921] | 680 | DO ji = kideb , kiut |
---|
[4870] | 681 | jk = numeq - nlay_s - 1 |
---|
[5123] | 682 | t_i_1d(ji,jk) = ( zindtbis(ji,numeq) - ztrid(ji,numeq,3) * t_i_1d(ji,jk+1) ) / zdiagbis(ji,numeq) |
---|
[921] | 683 | END DO |
---|
| 684 | END DO |
---|
| 685 | |
---|
| 686 | DO ji = kideb , kiut |
---|
[825] | 687 | ! snow temperatures |
---|
[5123] | 688 | IF (ht_s_1d(ji) > 0._wp) & |
---|
| 689 | t_s_1d(ji,nlay_s) = ( zindtbis(ji,nlay_s+1) - ztrid(ji,nlay_s+1,3) * t_i_1d(ji,1) ) & |
---|
| 690 | & / zdiagbis(ji,nlay_s+1) * MAX( 0.0, SIGN( 1.0, ht_s_1d(ji) ) ) |
---|
[825] | 691 | |
---|
| 692 | ! surface temperature |
---|
[5123] | 693 | isnow(ji) = 1._wp - MAX( 0._wp , SIGN( 1._wp , -ht_s_1d(ji) ) ) |
---|
[4872] | 694 | ztsubit(ji) = t_su_1d(ji) |
---|
[5123] | 695 | IF( t_su_1d(ji) < rt0 ) & |
---|
| 696 | t_su_1d(ji) = ( zindtbis(ji,numeqmin(ji)) - ztrid(ji,numeqmin(ji),3) * & |
---|
| 697 | & ( isnow(ji) * t_s_1d(ji,1) + ( 1._wp - isnow(ji) ) * t_i_1d(ji,1) ) ) / zdiagbis(ji,numeqmin(ji)) |
---|
[921] | 698 | END DO |
---|
[7607] | 699 | |
---|
[921] | 700 | ! |
---|
| 701 | !-------------------------------------------------------------------------- |
---|
[5123] | 702 | ! 11) Has the scheme converged ?, end of the iterative procedure | |
---|
[921] | 703 | !-------------------------------------------------------------------------- |
---|
| 704 | ! |
---|
| 705 | ! check that nowhere it has started to melt |
---|
[5123] | 706 | ! zerrit(ji) is a measure of error, it has to be under terr_dif |
---|
[921] | 707 | DO ji = kideb , kiut |
---|
[5123] | 708 | t_su_1d(ji) = MAX( MIN( t_su_1d(ji) , rt0 ) , 190._wp ) |
---|
| 709 | zerrit(ji) = ABS( t_su_1d(ji) - ztsubit(ji) ) |
---|
[921] | 710 | END DO |
---|
[825] | 711 | |
---|
[4870] | 712 | DO jk = 1, nlay_s |
---|
[921] | 713 | DO ji = kideb , kiut |
---|
[5123] | 714 | t_s_1d(ji,jk) = MAX( MIN( t_s_1d(ji,jk), rt0 ), 190._wp ) |
---|
| 715 | zerrit(ji) = MAX( zerrit(ji), ABS( t_s_1d(ji,jk) - ztstemp(ji,jk) ) ) |
---|
[921] | 716 | END DO |
---|
| 717 | END DO |
---|
[825] | 718 | |
---|
[4870] | 719 | DO jk = 1, nlay_i |
---|
[921] | 720 | DO ji = kideb , kiut |
---|
[5123] | 721 | ztmelt_i = -tmut * s_i_1d(ji,jk) + rt0 |
---|
| 722 | t_i_1d(ji,jk) = MAX( MIN( t_i_1d(ji,jk), ztmelt_i ), 190._wp ) |
---|
| 723 | zerrit(ji) = MAX( zerrit(ji), ABS( t_i_1d(ji,jk) - ztitemp(ji,jk) ) ) |
---|
[921] | 724 | END DO |
---|
| 725 | END DO |
---|
[825] | 726 | |
---|
[921] | 727 | ! Compute spatial maximum over all errors |
---|
[2715] | 728 | ! note that this could be optimized substantially by iterating only the non-converging points |
---|
| 729 | zerritmax = 0._wp |
---|
| 730 | DO ji = kideb, kiut |
---|
| 731 | zerritmax = MAX( zerritmax, zerrit(ji) ) |
---|
[921] | 732 | END DO |
---|
[2715] | 733 | IF( lk_mpp ) CALL mpp_max( zerritmax, kcom=ncomm_ice ) |
---|
[825] | 734 | |
---|
| 735 | END DO ! End of the do while iterative procedure |
---|
| 736 | |
---|
[5128] | 737 | IF( ln_icectl .AND. lwp ) THEN |
---|
[1055] | 738 | WRITE(numout,*) ' zerritmax : ', zerritmax |
---|
| 739 | WRITE(numout,*) ' nconv : ', nconv |
---|
| 740 | ENDIF |
---|
[825] | 741 | |
---|
[921] | 742 | ! |
---|
[2715] | 743 | !-------------------------------------------------------------------------! |
---|
[5123] | 744 | ! 12) Fluxes at the interfaces ! |
---|
[2715] | 745 | !-------------------------------------------------------------------------! |
---|
[921] | 746 | DO ji = kideb, kiut |
---|
[2715] | 747 | ! ! surface ice conduction flux |
---|
[5123] | 748 | isnow(ji) = 1._wp - MAX( 0._wp, SIGN( 1._wp, -ht_s_1d(ji) ) ) |
---|
| 749 | fc_su(ji) = - isnow(ji) * zkappa_s(ji,0) * zg1s * (t_s_1d(ji,1) - t_su_1d(ji)) & |
---|
| 750 | & - ( 1._wp - isnow(ji) ) * zkappa_i(ji,0) * zg1 * (t_i_1d(ji,1) - t_su_1d(ji)) |
---|
[2715] | 751 | ! ! bottom ice conduction flux |
---|
[4872] | 752 | fc_bo_i(ji) = - zkappa_i(ji,nlay_i) * ( zg1*(t_bo_1d(ji) - t_i_1d(ji,nlay_i)) ) |
---|
[921] | 753 | END DO |
---|
[825] | 754 | |
---|
[4688] | 755 | ! --- computes sea ice energy of melting compulsory for limthd_dh --- ! |
---|
| 756 | CALL lim_thd_enmelt( kideb, kiut ) |
---|
| 757 | |
---|
[5146] | 758 | ! --- diagnose the change in non-solar flux due to surface temperature change --- ! |
---|
[5474] | 759 | IF ( ln_it_qnsice ) THEN |
---|
| 760 | DO ji = kideb, kiut |
---|
| 761 | hfx_err_dif_1d(ji) = hfx_err_dif_1d(ji) - ( qns_ice_1d(ji) - zqns_ice_b(ji) ) * a_i_1d(ji) |
---|
| 762 | END DO |
---|
| 763 | END IF |
---|
[5123] | 764 | |
---|
[4990] | 765 | ! --- diag conservation imbalance on heat diffusion - PART 2 --- ! |
---|
[4688] | 766 | DO ji = kideb, kiut |
---|
[5123] | 767 | zdq(ji) = - zq_ini(ji) + ( SUM( q_i_1d(ji,1:nlay_i) ) * ht_i_1d(ji) * r1_nlay_i + & |
---|
| 768 | & SUM( q_s_1d(ji,1:nlay_s) ) * ht_s_1d(ji) * r1_nlay_s ) |
---|
| 769 | IF( t_su_1d(ji) < rt0 ) THEN ! case T_su < 0degC |
---|
| 770 | zhfx_err(ji) = qns_ice_1d(ji) + qsr_ice_1d(ji) - zradtr_i(ji,nlay_i) - fc_bo_i(ji) + zdq(ji) * r1_rdtice |
---|
| 771 | ELSE ! case T_su = 0degC |
---|
| 772 | zhfx_err(ji) = fc_su(ji) + i0(ji) * qsr_ice_1d(ji) - zradtr_i(ji,nlay_i) - fc_bo_i(ji) + zdq(ji) * r1_rdtice |
---|
| 773 | ENDIF |
---|
[4990] | 774 | hfx_err_1d(ji) = hfx_err_1d(ji) + zhfx_err(ji) * a_i_1d(ji) |
---|
[5167] | 775 | |
---|
| 776 | ! total heat that is sent to the ocean (i.e. not used in the heat diffusion equation) |
---|
| 777 | hfx_err_dif_1d(ji) = hfx_err_dif_1d(ji) + zhfx_err(ji) * a_i_1d(ji) |
---|
[4990] | 778 | END DO |
---|
| 779 | |
---|
[5123] | 780 | !----------------------------------------- |
---|
| 781 | ! Heat flux used to warm/cool ice in W.m-2 |
---|
| 782 | !----------------------------------------- |
---|
[4990] | 783 | DO ji = kideb, kiut |
---|
[5123] | 784 | IF( t_su_1d(ji) < rt0 ) THEN ! case T_su < 0degC |
---|
| 785 | hfx_dif_1d(ji) = hfx_dif_1d(ji) + & |
---|
| 786 | & ( qns_ice_1d(ji) + qsr_ice_1d(ji) - zradtr_i(ji,nlay_i) - fc_bo_i(ji) ) * a_i_1d(ji) |
---|
| 787 | ELSE ! case T_su = 0degC |
---|
| 788 | hfx_dif_1d(ji) = hfx_dif_1d(ji) + & |
---|
| 789 | & ( fc_su(ji) + i0(ji) * qsr_ice_1d(ji) - zradtr_i(ji,nlay_i) - fc_bo_i(ji) ) * a_i_1d(ji) |
---|
| 790 | ENDIF |
---|
[5167] | 791 | ! correction on the diagnosed heat flux due to non-convergence of the algorithm used to solve heat equation |
---|
| 792 | hfx_dif_1d(ji) = hfx_dif_1d(ji) - zhfx_err(ji) * a_i_1d(ji) |
---|
| 793 | END DO |
---|
[4688] | 794 | ! |
---|
[5123] | 795 | CALL wrk_dealloc( jpij, numeqmin, numeqmax ) |
---|
| 796 | CALL wrk_dealloc( jpij, isnow, ztsub, ztsubit, zh_i, zh_s, zfsw ) |
---|
[5512] | 797 | CALL wrk_dealloc( jpij, zf, dzf, zqns_ice_b, zerrit, zdifcase, zftrice, zihic, zghe ) |
---|
[5167] | 798 | CALL wrk_dealloc( jpij,nlay_i+1, ztcond_i, zradtr_i, zradab_i, zkappa_i, ztib, zeta_i, ztitemp, z_i, zspeche_i, kjstart = 0 ) |
---|
| 799 | CALL wrk_dealloc( jpij,nlay_s+1, zradtr_s, zradab_s, zkappa_s, ztsb, zeta_s, ztstemp, z_s, kjstart = 0 ) |
---|
| 800 | CALL wrk_dealloc( jpij,nlay_i+3, zindterm, zindtbis, zdiagbis ) |
---|
| 801 | CALL wrk_dealloc( jpij,nlay_i+3,3, ztrid ) |
---|
[4990] | 802 | CALL wrk_dealloc( jpij, zdq, zq_ini, zhfx_err ) |
---|
[4688] | 803 | |
---|
| 804 | END SUBROUTINE lim_thd_dif |
---|
| 805 | |
---|
| 806 | SUBROUTINE lim_thd_enmelt( kideb, kiut ) |
---|
| 807 | !!----------------------------------------------------------------------- |
---|
| 808 | !! *** ROUTINE lim_thd_enmelt *** |
---|
| 809 | !! |
---|
| 810 | !! ** Purpose : Computes sea ice energy of melting q_i (J.m-3) from temperature |
---|
| 811 | !! |
---|
| 812 | !! ** Method : Formula (Bitz and Lipscomb, 1999) |
---|
| 813 | !!------------------------------------------------------------------- |
---|
| 814 | INTEGER, INTENT(in) :: kideb, kiut ! bounds for the spatial loop |
---|
| 815 | ! |
---|
| 816 | INTEGER :: ji, jk ! dummy loop indices |
---|
[4990] | 817 | REAL(wp) :: ztmelts ! local scalar |
---|
[4688] | 818 | !!------------------------------------------------------------------- |
---|
| 819 | ! |
---|
| 820 | DO jk = 1, nlay_i ! Sea ice energy of melting |
---|
[921] | 821 | DO ji = kideb, kiut |
---|
[5202] | 822 | ztmelts = - tmut * s_i_1d(ji,jk) + rt0 |
---|
| 823 | t_i_1d(ji,jk) = MIN( t_i_1d(ji,jk), ztmelts ) ! Force t_i_1d to be lower than melting point |
---|
| 824 | ! (sometimes dif scheme produces abnormally high temperatures) |
---|
| 825 | q_i_1d(ji,jk) = rhoic * ( cpic * ( ztmelts - t_i_1d(ji,jk) ) & |
---|
| 826 | & + lfus * ( 1.0 - ( ztmelts-rt0 ) / ( t_i_1d(ji,jk) - rt0 ) ) & |
---|
| 827 | & - rcp * ( ztmelts-rt0 ) ) |
---|
[921] | 828 | END DO |
---|
[4688] | 829 | END DO |
---|
| 830 | DO jk = 1, nlay_s ! Snow energy of melting |
---|
| 831 | DO ji = kideb, kiut |
---|
[5123] | 832 | q_s_1d(ji,jk) = rhosn * ( cpic * ( rt0 - t_s_1d(ji,jk) ) + lfus ) |
---|
[921] | 833 | END DO |
---|
[4688] | 834 | END DO |
---|
[2715] | 835 | ! |
---|
[4688] | 836 | END SUBROUTINE lim_thd_enmelt |
---|
[825] | 837 | |
---|
| 838 | #else |
---|
[2715] | 839 | !!---------------------------------------------------------------------- |
---|
| 840 | !! Dummy Module No LIM-3 sea-ice model |
---|
| 841 | !!---------------------------------------------------------------------- |
---|
[825] | 842 | CONTAINS |
---|
| 843 | SUBROUTINE lim_thd_dif ! Empty routine |
---|
| 844 | END SUBROUTINE lim_thd_dif |
---|
| 845 | #endif |
---|
[2528] | 846 | !!====================================================================== |
---|
[921] | 847 | END MODULE limthd_dif |
---|