[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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[2612] | 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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[825] | 12 | !!---------------------------------------------------------------------- |
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[2528] | 13 | #if defined key_lim3 |
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| 14 | !!---------------------------------------------------------------------- |
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| 15 | !! 'key_lim3' LIM3 sea-ice model |
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| 16 | !!---------------------------------------------------------------------- |
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[825] | 17 | USE par_oce ! ocean parameters |
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| 18 | USE phycst ! physical constants (ocean directory) |
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[2612] | 19 | USE ice ! LIM-3 variables |
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| 20 | USE par_ice ! LIM-3 parameters |
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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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[921] | 24 | |
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[825] | 25 | IMPLICIT NONE |
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| 26 | PRIVATE |
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| 27 | |
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[2528] | 28 | PUBLIC lim_thd_dif ! called by lim_thd |
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[825] | 29 | |
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[2612] | 30 | REAL(wp) :: epsi20 = 1e-20 ! constant values |
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| 31 | REAL(wp) :: epsi13 = 1e-13 ! constant values |
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[825] | 32 | |
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| 33 | !!---------------------------------------------------------------------- |
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[2612] | 34 | !! NEMO/LIM3 4.0 , UCL - NEMO Consortium (2011) |
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[1156] | 35 | !! $Id$ |
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[2612] | 36 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[825] | 37 | !!---------------------------------------------------------------------- |
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| 38 | CONTAINS |
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| 39 | |
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| 40 | SUBROUTINE lim_thd_dif( kideb , kiut , jl ) |
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[921] | 41 | !!------------------------------------------------------------------ |
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| 42 | !! *** ROUTINE lim_thd_dif *** |
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| 43 | !! ** Purpose : |
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| 44 | !! This routine determines the time evolution of snow and sea-ice |
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| 45 | !! temperature profiles. |
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| 46 | !! ** Method : |
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| 47 | !! This is done by solving the heat equation diffusion with |
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| 48 | !! a Neumann boundary condition at the surface and a Dirichlet one |
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| 49 | !! at the bottom. Solar radiation is partially absorbed into the ice. |
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| 50 | !! The specific heat and thermal conductivities depend on ice salinity |
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| 51 | !! and temperature to take into account brine pocket melting. The |
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| 52 | !! numerical |
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| 53 | !! scheme is an iterative Crank-Nicolson on a non-uniform multilayer grid |
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| 54 | !! in the ice and snow system. |
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| 55 | !! |
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| 56 | !! The successive steps of this routine are |
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| 57 | !! 1. Thermal conductivity at the interfaces of the ice layers |
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| 58 | !! 2. Internal absorbed radiation |
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| 59 | !! 3. Scale factors due to non-uniform grid |
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| 60 | !! 4. Kappa factors |
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| 61 | !! Then iterative procedure begins |
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| 62 | !! 5. specific heat in the ice |
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| 63 | !! 6. eta factors |
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| 64 | !! 7. surface flux computation |
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| 65 | !! 8. tridiagonal system terms |
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| 66 | !! 9. solving the tridiagonal system with Gauss elimination |
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| 67 | !! Iterative procedure ends according to a criterion on evolution |
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| 68 | !! of temperature |
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| 69 | !! |
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| 70 | !! ** Arguments : |
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| 71 | !! kideb , kiut : Starting and ending points on which the |
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| 72 | !! the computation is applied |
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| 73 | !! |
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| 74 | !! ** Inputs / Ouputs : (global commons) |
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| 75 | !! surface temperature : t_su_b |
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| 76 | !! ice/snow temperatures : t_i_b, t_s_b |
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| 77 | !! ice salinities : s_i_b |
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| 78 | !! number of layers in the ice/snow: nlay_i, nlay_s |
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| 79 | !! profile of the ice/snow layers : z_i, z_s |
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| 80 | !! total ice/snow thickness : ht_i_b, ht_s_b |
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| 81 | !!------------------------------------------------------------------ |
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| 82 | INTEGER , INTENT (in) :: & |
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| 83 | kideb , & ! Start point on which the the computation is applied |
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| 84 | kiut , & ! End point on which the the computation is applied |
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| 85 | jl ! Category number |
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[825] | 86 | |
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[921] | 87 | !! * Local variables |
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| 88 | INTEGER :: ji, & ! spatial loop index |
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[2612] | 89 | ii, ij, & ! temporary dummy loop index |
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[921] | 90 | numeq, & ! current reference number of equation |
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| 91 | layer, & ! vertical dummy loop index |
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| 92 | nconv, & ! number of iterations in iterative procedure |
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[2612] | 93 | minnumeqmin, maxnumeqmax |
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[825] | 94 | |
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[1103] | 95 | INTEGER , DIMENSION(kiut) :: & |
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[921] | 96 | numeqmin, & ! reference number of top equation |
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| 97 | numeqmax, & ! reference number of bottom equation |
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| 98 | isnow ! switch for presence (1) or absence (0) of snow |
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[825] | 99 | |
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[921] | 100 | !! * New local variables |
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[1103] | 101 | REAL(wp) , DIMENSION(kiut,0:nlay_i) :: & |
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[921] | 102 | ztcond_i, & !Ice thermal conductivity |
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| 103 | zradtr_i, & !Radiation transmitted through the ice |
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| 104 | zradab_i, & !Radiation absorbed in the ice |
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| 105 | zkappa_i !Kappa factor in the ice |
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[825] | 106 | |
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[1103] | 107 | REAL(wp) , DIMENSION(kiut,0:nlay_s) :: & |
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[921] | 108 | zradtr_s, & !Radiation transmited through the snow |
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| 109 | zradab_s, & !Radiation absorbed in the snow |
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| 110 | zkappa_s !Kappa factor in the snow |
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[825] | 111 | |
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[1103] | 112 | REAL(wp) , DIMENSION(kiut,0:nlay_i) :: & |
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[921] | 113 | ztiold, & !Old temperature in the ice |
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| 114 | zeta_i, & !Eta factor in the ice |
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| 115 | ztitemp, & !Temporary temperature in the ice to check the convergence |
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| 116 | zspeche_i, & !Ice specific heat |
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| 117 | z_i !Vertical cotes of the layers in the ice |
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[825] | 118 | |
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[1103] | 119 | REAL(wp) , DIMENSION(kiut,0:nlay_s) :: & |
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[921] | 120 | zeta_s, & !Eta factor in the snow |
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| 121 | ztstemp, & !Temporary temperature in the snow to check the convergence |
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| 122 | ztsold, & !Temporary temperature in the snow |
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| 123 | z_s !Vertical cotes of the layers in the snow |
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[825] | 124 | |
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[1103] | 125 | REAL(wp) , DIMENSION(kiut,jkmax+2) :: & |
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[921] | 126 | zindterm, & ! Independent term |
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| 127 | zindtbis, & ! temporary independent term |
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| 128 | zdiagbis |
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[825] | 129 | |
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[2612] | 130 | REAL(wp) , DIMENSION(kiut,jkmax+2,3) :: ztrid ! tridiagonal system terms |
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[825] | 131 | |
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[1103] | 132 | REAL(wp), DIMENSION(kiut) :: & |
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[921] | 133 | ztfs , & ! ice melting point |
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[2612] | 134 | ztsuold , & ! old surface temperature (before the iterative procedure ) |
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[921] | 135 | ztsuoldit, & ! surface temperature at previous iteration |
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| 136 | zh_i , & !ice layer thickness |
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| 137 | zh_s , & !snow layer thickness |
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| 138 | zfsw , & !solar radiation absorbed at the surface |
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| 139 | zf , & ! surface flux function |
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| 140 | dzf ! derivative of the surface flux function |
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[825] | 141 | |
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[921] | 142 | REAL(wp) :: & ! constant values |
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[2612] | 143 | zeps = 1.e-10_wp, & ! |
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| 144 | zg1s = 2._wp, & !: for the tridiagonal system |
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| 145 | zg1 = 2._wp, & |
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| 146 | zgamma = 18009._wp, & !: for specific heat |
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| 147 | zbeta = 0.117_wp, & !: for thermal conductivity (could be 0.13) |
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| 148 | zraext_s = 1.e+8_wp, & !: extinction coefficient of radiation in the snow |
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| 149 | zkimin = 0.10_wp , & !: minimum ice thermal conductivity |
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| 150 | zht_smin = 1.e-4_wp !: minimum snow depth |
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[825] | 151 | |
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[2612] | 152 | REAL(wp) :: ztmelt_i ! ice melting temperature |
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| 153 | REAL(wp) :: zerritmax ! current maximal error on temperature |
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[825] | 154 | |
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[2612] | 155 | REAL(wp), DIMENSION(kiut) :: zerrit ! current error on temperature |
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| 156 | REAL(wp), DIMENSION(kiut) :: zdifcase ! case of the equation resolution (1->4) |
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| 157 | REAL(wp), DIMENSION(kiut) :: zftrice ! solar radiation transmitted through the ice |
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| 158 | REAL(wp), DIMENSION(kiut) :: zihic, zhsu |
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| 159 | !!------------------------------------------------------------------ |
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[921] | 160 | ! |
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| 161 | !------------------------------------------------------------------------------! |
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| 162 | ! 1) Initialization ! |
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| 163 | !------------------------------------------------------------------------------! |
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| 164 | ! |
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| 165 | DO ji = kideb , kiut |
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| 166 | ! is there snow or not |
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[2612] | 167 | isnow(ji)= INT( 1._wp - MAX( 0._wp , SIGN(1._wp, - ht_s_b(ji) ) ) ) |
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[921] | 168 | ! surface temperature of fusion |
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[2612] | 169 | !!gm ??? ztfs(ji) = rtt !!!???? |
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[921] | 170 | ztfs(ji) = isnow(ji) * rtt + (1.0-isnow(ji)) * rtt |
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| 171 | ! layer thickness |
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[2612] | 172 | zh_i(ji) = ht_i_b(ji) / nlay_i |
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| 173 | zh_s(ji) = ht_s_b(ji) / nlay_s |
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[921] | 174 | END DO |
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[825] | 175 | |
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[921] | 176 | !-------------------- |
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| 177 | ! Ice / snow layers |
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| 178 | !-------------------- |
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[825] | 179 | |
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[2612] | 180 | z_s(:,0) = 0._wp ! vert. coord. of the up. lim. of the 1st snow layer |
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| 181 | z_i(:,0) = 0._wp ! vert. coord. of the up. lim. of the 1st ice layer |
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[825] | 182 | |
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[2612] | 183 | DO layer = 1, nlay_s ! vert. coord of the up. lim. of the layer-th snow layer |
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[921] | 184 | DO ji = kideb , kiut |
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[2612] | 185 | z_s(ji,layer) = z_s(ji,layer-1) + ht_s_b(ji) / nlay_s |
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[921] | 186 | END DO |
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| 187 | END DO |
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[825] | 188 | |
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[2612] | 189 | DO layer = 1, nlay_i ! vert. coord of the up. lim. of the layer-th ice layer |
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[921] | 190 | DO ji = kideb , kiut |
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[2612] | 191 | z_i(ji,layer) = z_i(ji,layer-1) + ht_i_b(ji) / nlay_i |
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[921] | 192 | END DO |
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| 193 | END DO |
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| 194 | ! |
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| 195 | !------------------------------------------------------------------------------| |
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| 196 | ! 2) Radiations | |
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| 197 | !------------------------------------------------------------------------------| |
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| 198 | ! |
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| 199 | !------------------- |
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| 200 | ! Computation of i0 |
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| 201 | !------------------- |
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| 202 | ! i0 describes the fraction of solar radiation which does not contribute |
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| 203 | ! to the surface energy budget but rather penetrates inside the ice. |
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| 204 | ! We assume that no radiation is transmitted through the snow |
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| 205 | ! If there is no no snow |
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| 206 | ! zfsw = (1-i0).qsr_ice is absorbed at the surface |
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| 207 | ! zftrice = io.qsr_ice is below the surface |
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| 208 | ! fstbif = io.qsr_ice.exp(-k(h_i)) transmitted below the ice |
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[825] | 209 | |
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[921] | 210 | DO ji = kideb , kiut |
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| 211 | ! switches |
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[2612] | 212 | isnow(ji) = INT( 1._wp - MAX( 0._wp , SIGN( 1._wp , - ht_s_b(ji) ) ) ) |
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[921] | 213 | ! hs > 0, isnow = 1 |
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[2612] | 214 | zhsu (ji) = hnzst ! threshold for the computation of i0 |
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| 215 | zihic(ji) = MAX( 0._wp , 1._wp - ( ht_i_b(ji) / zhsu(ji) ) ) |
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[825] | 216 | |
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[2612] | 217 | i0(ji) = ( 1._wp - isnow(ji) ) * ( fr1_i0_1d(ji) + zihic(ji) * fr2_i0_1d(ji) ) |
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[921] | 218 | !fr1_i0_1d = i0 for a thin ice surface |
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| 219 | !fr1_i0_2d = i0 for a thick ice surface |
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| 220 | ! a function of the cloud cover |
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| 221 | ! |
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| 222 | !i0(ji) = (1.0-FLOAT(isnow(ji)))*3.0/(100*ht_s_b(ji)+10.0) |
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| 223 | !formula used in Cice |
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| 224 | END DO |
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[825] | 225 | |
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[921] | 226 | !------------------------------------------------------- |
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| 227 | ! Solar radiation absorbed / transmitted at the surface |
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| 228 | ! Derivative of the non solar flux |
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| 229 | !------------------------------------------------------- |
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| 230 | DO ji = kideb , kiut |
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[2612] | 231 | zfsw (ji) = qsr_ice_1d(ji) * ( 1 - i0(ji) ) ! Shortwave radiation absorbed at surface |
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| 232 | zftrice(ji) = qsr_ice_1d(ji) * i0(ji) ! Solar radiation transmitted below the surface layer |
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| 233 | dzf (ji) = dqns_ice_1d(ji) ! derivative of incoming nonsolar flux |
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[921] | 234 | END DO |
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[825] | 235 | |
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[921] | 236 | !--------------------------------------------------------- |
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| 237 | ! Transmission - absorption of solar radiation in the ice |
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| 238 | !--------------------------------------------------------- |
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[825] | 239 | |
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[2612] | 240 | DO ji = kideb, kiut ! snow initialization |
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| 241 | zradtr_s(ji,0) = zftrice(ji) ! radiation penetrating through snow |
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[921] | 242 | END DO |
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[825] | 243 | |
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[2612] | 244 | DO layer = 1, nlay_s ! Radiation through snow |
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| 245 | DO ji = kideb, kiut |
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| 246 | ! ! radiation transmitted below the layer-th snow layer |
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| 247 | zradtr_s(ji,layer) = zradtr_s(ji,0) * EXP( - zraext_s * ( MAX ( 0._wp , z_s(ji,layer) ) ) ) |
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| 248 | ! ! radiation absorbed by the layer-th snow layer |
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[921] | 249 | zradab_s(ji,layer) = zradtr_s(ji,layer-1) - zradtr_s(ji,layer) |
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| 250 | END DO |
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| 251 | END DO |
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[825] | 252 | |
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[2612] | 253 | DO ji = kideb, kiut ! ice initialization |
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| 254 | zradtr_i(ji,0) = zradtr_s(ji,nlay_s) * isnow(ji) + zftrice(ji) * ( 1._wp - isnow(ji) ) |
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[921] | 255 | END DO |
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[825] | 256 | |
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[2612] | 257 | DO layer = 1, nlay_i ! Radiation through ice |
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| 258 | DO ji = kideb, kiut |
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| 259 | ! ! radiation transmitted below the layer-th ice layer |
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| 260 | zradtr_i(ji,layer) = zradtr_i(ji,0) * EXP( - kappa_i * ( MAX ( 0._wp , z_i(ji,layer) ) ) ) |
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| 261 | ! ! radiation absorbed by the layer-th ice layer |
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[921] | 262 | zradab_i(ji,layer) = zradtr_i(ji,layer-1) - zradtr_i(ji,layer) |
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| 263 | END DO |
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| 264 | END DO |
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[825] | 265 | |
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[2612] | 266 | DO ji = kideb, kiut ! Radiation transmitted below the ice |
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| 267 | fstbif_1d(ji) = fstbif_1d(ji) + zradtr_i(ji,nlay_i) * a_i_b(ji) / at_i_b(ji) |
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[921] | 268 | END DO |
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[834] | 269 | |
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[921] | 270 | ! +++++ |
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| 271 | ! just to check energy conservation |
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[2612] | 272 | DO ji = kideb, kiut |
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| 273 | ii = MOD( npb(ji) - 1, jpi ) + 1 |
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| 274 | ij = ( npb(ji) - 1 ) / jpi + 1 |
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| 275 | fstroc(ii,ij,jl) = zradtr_i(ji,nlay_i) |
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[921] | 276 | END DO |
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| 277 | ! +++++ |
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[825] | 278 | |
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[921] | 279 | DO layer = 1, nlay_i |
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[2612] | 280 | DO ji = kideb, kiut |
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[921] | 281 | radab(ji,layer) = zradab_i(ji,layer) |
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| 282 | END DO |
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| 283 | END DO |
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[825] | 284 | |
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| 285 | |
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[921] | 286 | ! |
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| 287 | !------------------------------------------------------------------------------| |
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| 288 | ! 3) Iterative procedure begins | |
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| 289 | !------------------------------------------------------------------------------| |
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| 290 | ! |
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[2612] | 291 | DO ji = kideb, kiut ! Old surface temperature |
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| 292 | ztsuold (ji) = t_su_b(ji) ! temperature at the beg of iter pr. |
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| 293 | ztsuoldit(ji) = t_su_b(ji) ! temperature at the previous iter |
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| 294 | t_su_b (ji) = MIN( t_su_b(ji), ztfs(ji)-0.00001 ) ! necessary |
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| 295 | zerrit (ji) = 1000._wp ! initial value of error |
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[921] | 296 | END DO |
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[825] | 297 | |
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[2612] | 298 | DO layer = 1, nlay_s ! Old snow temperature |
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[921] | 299 | DO ji = kideb , kiut |
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[2612] | 300 | ztsold(ji,layer) = t_s_b(ji,layer) |
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[921] | 301 | END DO |
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| 302 | END DO |
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[825] | 303 | |
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[2612] | 304 | DO layer = 1, nlay_i ! Old ice temperature |
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[921] | 305 | DO ji = kideb , kiut |
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[2612] | 306 | ztiold(ji,layer) = t_i_b(ji,layer) |
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[921] | 307 | END DO |
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| 308 | END DO |
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[825] | 309 | |
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[2612] | 310 | nconv = 0 ! number of iterations |
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| 311 | zerritmax = 1000._wp ! maximal value of error on all points |
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[825] | 312 | |
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[2612] | 313 | DO WHILE ( zerritmax > maxer_i_thd .AND. nconv < nconv_i_thd ) |
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[921] | 314 | ! |
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[2612] | 315 | nconv = nconv + 1 |
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| 316 | ! |
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[921] | 317 | !------------------------------------------------------------------------------| |
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| 318 | ! 4) Sea ice thermal conductivity | |
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| 319 | !------------------------------------------------------------------------------| |
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| 320 | ! |
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[2612] | 321 | IF( thcon_i_swi == 0 ) THEN ! Untersteiner (1964) formula |
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[921] | 322 | DO ji = kideb , kiut |
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| 323 | ztcond_i(ji,0) = rcdic + zbeta*s_i_b(ji,1) / & |
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| 324 | MIN(-zeps,t_i_b(ji,1)-rtt) |
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| 325 | ztcond_i(ji,0) = MAX(ztcond_i(ji,0),zkimin) |
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| 326 | END DO |
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| 327 | DO layer = 1, nlay_i-1 |
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| 328 | DO ji = kideb , kiut |
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| 329 | ztcond_i(ji,layer) = rcdic + zbeta*( s_i_b(ji,layer) & |
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[2612] | 330 | + s_i_b(ji,layer+1) ) / MIN(-2.0*zeps, & |
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[921] | 331 | t_i_b(ji,layer)+t_i_b(ji,layer+1)-2.0*rtt) |
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| 332 | ztcond_i(ji,layer) = MAX(ztcond_i(ji,layer),zkimin) |
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| 333 | END DO |
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| 334 | END DO |
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| 335 | DO ji = kideb , kiut |
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| 336 | ztcond_i(ji,nlay_i) = rcdic + zbeta*s_i_b(ji,nlay_i) / & |
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| 337 | MIN(-zeps,t_bo_b(ji)-rtt) |
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| 338 | ztcond_i(ji,nlay_i) = MAX(ztcond_i(ji,nlay_i),zkimin) |
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| 339 | END DO |
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| 340 | ENDIF |
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[825] | 341 | |
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[2612] | 342 | 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] | 343 | DO ji = kideb , kiut |
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[2612] | 344 | 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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| 345 | & - 0.011_wp * ( t_i_b(ji,1) - rtt ) |
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| 346 | ztcond_i(ji,0) = MAX( ztcond_i(ji,0), zkimin ) |
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[921] | 347 | END DO |
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[2612] | 348 | DO layer = 1, nlay_i-1 |
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| 349 | DO ji = kideb , kiut |
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| 350 | ztcond_i(ji,layer) = rcdic + 0.090_wp * ( s_i_b(ji,layer) + s_i_b(ji,layer+1) ) & |
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| 351 | & / MIN(-2.0*zeps, t_i_b(ji,layer)+t_i_b(ji,layer+1)-2.0*rtt) & |
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| 352 | & - 0.0055_wp* ( t_i_b(ji,layer) + t_i_b(ji,layer+1) - 2.0*rtt ) |
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| 353 | ztcond_i(ji,layer) = MAX( ztcond_i(ji,layer), zkimin ) |
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| 354 | END DO |
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| 355 | END DO |
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| 356 | DO ji = kideb , kiut |
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| 357 | 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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| 358 | & - 0.011_wp * ( t_bo_b(ji) - rtt ) |
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| 359 | ztcond_i(ji,nlay_i) = MAX( ztcond_i(ji,nlay_i), zkimin ) |
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| 360 | END DO |
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[921] | 361 | ENDIF |
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| 362 | ! |
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| 363 | !------------------------------------------------------------------------------| |
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| 364 | ! 5) kappa factors | |
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| 365 | !------------------------------------------------------------------------------| |
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| 366 | ! |
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| 367 | DO ji = kideb, kiut |
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[825] | 368 | |
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[921] | 369 | !-- Snow kappa factors |
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| 370 | zkappa_s(ji,0) = rcdsn / MAX(zeps,zh_s(ji)) |
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| 371 | zkappa_s(ji,nlay_s) = rcdsn / MAX(zeps,zh_s(ji)) |
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| 372 | END DO |
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[825] | 373 | |
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[921] | 374 | DO layer = 1, nlay_s-1 |
---|
| 375 | DO ji = kideb , kiut |
---|
| 376 | zkappa_s(ji,layer) = 2.0 * rcdsn / & |
---|
| 377 | MAX(zeps,2.0*zh_s(ji)) |
---|
| 378 | END DO |
---|
| 379 | END DO |
---|
[825] | 380 | |
---|
[921] | 381 | DO layer = 1, nlay_i-1 |
---|
| 382 | DO ji = kideb , kiut |
---|
| 383 | !-- Ice kappa factors |
---|
| 384 | zkappa_i(ji,layer) = 2.0*ztcond_i(ji,layer)/ & |
---|
| 385 | MAX(zeps,2.0*zh_i(ji)) |
---|
| 386 | END DO |
---|
| 387 | END DO |
---|
[825] | 388 | |
---|
[921] | 389 | DO ji = kideb , kiut |
---|
| 390 | zkappa_i(ji,0) = ztcond_i(ji,0)/MAX(zeps,zh_i(ji)) |
---|
| 391 | zkappa_i(ji,nlay_i) = ztcond_i(ji,nlay_i) / MAX(zeps,zh_i(ji)) |
---|
| 392 | !-- Interface |
---|
| 393 | zkappa_s(ji,nlay_s) = 2.0*rcdsn*ztcond_i(ji,0)/MAX(zeps, & |
---|
| 394 | (ztcond_i(ji,0)*zh_s(ji) + rcdsn*zh_i(ji))) |
---|
| 395 | zkappa_i(ji,0) = zkappa_s(ji,nlay_s)*isnow(ji) & |
---|
| 396 | + zkappa_i(ji,0)*(1.0-isnow(ji)) |
---|
| 397 | END DO |
---|
| 398 | ! |
---|
| 399 | !------------------------------------------------------------------------------| |
---|
| 400 | ! 6) Sea ice specific heat, eta factors | |
---|
| 401 | !------------------------------------------------------------------------------| |
---|
| 402 | ! |
---|
| 403 | DO layer = 1, nlay_i |
---|
| 404 | DO ji = kideb , kiut |
---|
| 405 | ztitemp(ji,layer) = t_i_b(ji,layer) |
---|
| 406 | zspeche_i(ji,layer) = cpic + zgamma*s_i_b(ji,layer)/ & |
---|
| 407 | MAX((t_i_b(ji,layer)-rtt)*(ztiold(ji,layer)-rtt),zeps) |
---|
| 408 | zeta_i(ji,layer) = rdt_ice / MAX(rhoic*zspeche_i(ji,layer)*zh_i(ji), & |
---|
| 409 | zeps) |
---|
| 410 | END DO |
---|
| 411 | END DO |
---|
[825] | 412 | |
---|
[921] | 413 | DO layer = 1, nlay_s |
---|
| 414 | DO ji = kideb , kiut |
---|
| 415 | ztstemp(ji,layer) = t_s_b(ji,layer) |
---|
| 416 | zeta_s(ji,layer) = rdt_ice / MAX(rhosn*cpic*zh_s(ji),zeps) |
---|
| 417 | END DO |
---|
| 418 | END DO |
---|
| 419 | ! |
---|
| 420 | !------------------------------------------------------------------------------| |
---|
| 421 | ! 7) surface flux computation | |
---|
| 422 | !------------------------------------------------------------------------------| |
---|
| 423 | ! |
---|
| 424 | DO ji = kideb , kiut |
---|
[825] | 425 | |
---|
[921] | 426 | ! update of the non solar flux according to the update in T_su |
---|
| 427 | qnsr_ice_1d(ji) = qnsr_ice_1d(ji) + dqns_ice_1d(ji) * & |
---|
| 428 | ( t_su_b(ji) - ztsuoldit(ji) ) |
---|
[825] | 429 | |
---|
[921] | 430 | ! update incoming flux |
---|
| 431 | zf(ji) = zfsw(ji) & ! net absorbed solar radiation |
---|
| 432 | + qnsr_ice_1d(ji) ! non solar total flux |
---|
| 433 | ! (LWup, LWdw, SH, LH) |
---|
[825] | 434 | |
---|
[921] | 435 | END DO |
---|
[825] | 436 | |
---|
[921] | 437 | ! |
---|
| 438 | !------------------------------------------------------------------------------| |
---|
| 439 | ! 8) tridiagonal system terms | |
---|
| 440 | !------------------------------------------------------------------------------| |
---|
| 441 | ! |
---|
| 442 | !!layer denotes the number of the layer in the snow or in the ice |
---|
| 443 | !!numeq denotes the reference number of the equation in the tridiagonal |
---|
| 444 | !!system, terms of tridiagonal system are indexed as following : |
---|
| 445 | !!1 is subdiagonal term, 2 is diagonal and 3 is superdiagonal one |
---|
[825] | 446 | |
---|
[921] | 447 | !!ice interior terms (top equation has the same form as the others) |
---|
| 448 | |
---|
| 449 | DO numeq=1,jkmax+2 |
---|
| 450 | DO ji = kideb , kiut |
---|
| 451 | ztrid(ji,numeq,1) = 0. |
---|
| 452 | ztrid(ji,numeq,2) = 0. |
---|
| 453 | ztrid(ji,numeq,3) = 0. |
---|
| 454 | zindterm(ji,numeq)= 0. |
---|
| 455 | zindtbis(ji,numeq)= 0. |
---|
| 456 | zdiagbis(ji,numeq)= 0. |
---|
| 457 | ENDDO |
---|
| 458 | ENDDO |
---|
| 459 | |
---|
| 460 | DO numeq = nlay_s + 2, nlay_s + nlay_i |
---|
| 461 | DO ji = kideb , kiut |
---|
| 462 | layer = numeq - nlay_s - 1 |
---|
| 463 | ztrid(ji,numeq,1) = - zeta_i(ji,layer)*zkappa_i(ji,layer-1) |
---|
| 464 | ztrid(ji,numeq,2) = 1.0 + zeta_i(ji,layer)*(zkappa_i(ji,layer-1) + & |
---|
| 465 | zkappa_i(ji,layer)) |
---|
| 466 | ztrid(ji,numeq,3) = - zeta_i(ji,layer)*zkappa_i(ji,layer) |
---|
| 467 | zindterm(ji,numeq) = ztiold(ji,layer) + zeta_i(ji,layer)* & |
---|
| 468 | zradab_i(ji,layer) |
---|
| 469 | END DO |
---|
| 470 | ENDDO |
---|
| 471 | |
---|
| 472 | numeq = nlay_s + nlay_i + 1 |
---|
| 473 | DO ji = kideb , kiut |
---|
[825] | 474 | !!ice bottom term |
---|
| 475 | ztrid(ji,numeq,1) = - zeta_i(ji,nlay_i)*zkappa_i(ji,nlay_i-1) |
---|
| 476 | ztrid(ji,numeq,2) = 1.0 + zeta_i(ji,nlay_i)*( zkappa_i(ji,nlay_i)*zg1 & |
---|
[921] | 477 | + zkappa_i(ji,nlay_i-1) ) |
---|
[825] | 478 | ztrid(ji,numeq,3) = 0.0 |
---|
| 479 | zindterm(ji,numeq) = ztiold(ji,nlay_i) + zeta_i(ji,nlay_i)* & |
---|
[921] | 480 | ( zradab_i(ji,nlay_i) + zkappa_i(ji,nlay_i)*zg1 & |
---|
| 481 | * t_bo_b(ji) ) |
---|
| 482 | ENDDO |
---|
[825] | 483 | |
---|
| 484 | |
---|
[921] | 485 | DO ji = kideb , kiut |
---|
[825] | 486 | IF ( ht_s_b(ji).gt.0.0 ) THEN |
---|
[921] | 487 | ! |
---|
| 488 | !------------------------------------------------------------------------------| |
---|
| 489 | ! snow-covered cells | |
---|
| 490 | !------------------------------------------------------------------------------| |
---|
| 491 | ! |
---|
| 492 | !!snow interior terms (bottom equation has the same form as the others) |
---|
| 493 | DO numeq = 3, nlay_s + 1 |
---|
| 494 | layer = numeq - 1 |
---|
| 495 | ztrid(ji,numeq,1) = - zeta_s(ji,layer)*zkappa_s(ji,layer-1) |
---|
| 496 | ztrid(ji,numeq,2) = 1.0 + zeta_s(ji,layer)*( zkappa_s(ji,layer-1) + & |
---|
| 497 | zkappa_s(ji,layer) ) |
---|
| 498 | ztrid(ji,numeq,3) = - zeta_s(ji,layer)*zkappa_s(ji,layer) |
---|
| 499 | zindterm(ji,numeq) = ztsold(ji,layer) + zeta_s(ji,layer)* & |
---|
| 500 | zradab_s(ji,layer) |
---|
| 501 | END DO |
---|
[825] | 502 | |
---|
[921] | 503 | !!case of only one layer in the ice (ice equation is altered) |
---|
| 504 | IF ( nlay_i.eq.1 ) THEN |
---|
| 505 | ztrid(ji,nlay_s+2,3) = 0.0 |
---|
| 506 | zindterm(ji,nlay_s+2) = zindterm(ji,nlay_s+2) + zkappa_i(ji,1)* & |
---|
| 507 | t_bo_b(ji) |
---|
| 508 | ENDIF |
---|
[834] | 509 | |
---|
[921] | 510 | IF ( t_su_b(ji) .LT. rtt ) THEN |
---|
[825] | 511 | |
---|
[921] | 512 | !------------------------------------------------------------------------------| |
---|
| 513 | ! case 1 : no surface melting - snow present | |
---|
| 514 | !------------------------------------------------------------------------------| |
---|
| 515 | zdifcase(ji) = 1.0 |
---|
| 516 | numeqmin(ji) = 1 |
---|
| 517 | numeqmax(ji) = nlay_i + nlay_s + 1 |
---|
[825] | 518 | |
---|
[921] | 519 | !!surface equation |
---|
| 520 | ztrid(ji,1,1) = 0.0 |
---|
| 521 | ztrid(ji,1,2) = dzf(ji) - zg1s*zkappa_s(ji,0) |
---|
| 522 | ztrid(ji,1,3) = zg1s*zkappa_s(ji,0) |
---|
| 523 | zindterm(ji,1) = dzf(ji)*t_su_b(ji) - zf(ji) |
---|
[825] | 524 | |
---|
[921] | 525 | !!first layer of snow equation |
---|
| 526 | ztrid(ji,2,1) = - zkappa_s(ji,0)*zg1s*zeta_s(ji,1) |
---|
| 527 | ztrid(ji,2,2) = 1.0 + zeta_s(ji,1)*(zkappa_s(ji,1) + zkappa_s(ji,0)*zg1s) |
---|
| 528 | ztrid(ji,2,3) = - zeta_s(ji,1)* zkappa_s(ji,1) |
---|
| 529 | zindterm(ji,2) = ztsold(ji,1) + zeta_s(ji,1)*zradab_s(ji,1) |
---|
[825] | 530 | |
---|
[921] | 531 | ELSE |
---|
| 532 | ! |
---|
| 533 | !------------------------------------------------------------------------------| |
---|
| 534 | ! case 2 : surface is melting - snow present | |
---|
| 535 | !------------------------------------------------------------------------------| |
---|
| 536 | ! |
---|
| 537 | zdifcase(ji) = 2.0 |
---|
| 538 | numeqmin(ji) = 2 |
---|
| 539 | numeqmax(ji) = nlay_i + nlay_s + 1 |
---|
[825] | 540 | |
---|
[921] | 541 | !!first layer of snow equation |
---|
| 542 | ztrid(ji,2,1) = 0.0 |
---|
| 543 | ztrid(ji,2,2) = 1.0 + zeta_s(ji,1) * ( zkappa_s(ji,1) + & |
---|
| 544 | zkappa_s(ji,0) * zg1s ) |
---|
| 545 | ztrid(ji,2,3) = - zeta_s(ji,1)*zkappa_s(ji,1) |
---|
| 546 | zindterm(ji,2) = ztsold(ji,1) + zeta_s(ji,1) * & |
---|
| 547 | ( zradab_s(ji,1) + & |
---|
| 548 | zkappa_s(ji,0) * zg1s * t_su_b(ji) ) |
---|
| 549 | ENDIF |
---|
| 550 | ELSE |
---|
| 551 | ! |
---|
| 552 | !------------------------------------------------------------------------------| |
---|
| 553 | ! cells without snow | |
---|
| 554 | !------------------------------------------------------------------------------| |
---|
| 555 | ! |
---|
| 556 | IF (t_su_b(ji) .LT. rtt) THEN |
---|
| 557 | ! |
---|
| 558 | !------------------------------------------------------------------------------| |
---|
| 559 | ! case 3 : no surface melting - no snow | |
---|
| 560 | !------------------------------------------------------------------------------| |
---|
| 561 | ! |
---|
| 562 | zdifcase(ji) = 3.0 |
---|
| 563 | numeqmin(ji) = nlay_s + 1 |
---|
| 564 | numeqmax(ji) = nlay_i + nlay_s + 1 |
---|
[825] | 565 | |
---|
[921] | 566 | !!surface equation |
---|
| 567 | ztrid(ji,numeqmin(ji),1) = 0.0 |
---|
| 568 | ztrid(ji,numeqmin(ji),2) = dzf(ji) - zkappa_i(ji,0)*zg1 |
---|
| 569 | ztrid(ji,numeqmin(ji),3) = zkappa_i(ji,0)*zg1 |
---|
| 570 | zindterm(ji,numeqmin(ji)) = dzf(ji)*t_su_b(ji) - zf(ji) |
---|
[825] | 571 | |
---|
[921] | 572 | !!first layer of ice equation |
---|
| 573 | ztrid(ji,numeqmin(ji)+1,1) = - zkappa_i(ji,0) * zg1 * zeta_i(ji,1) |
---|
| 574 | ztrid(ji,numeqmin(ji)+1,2) = 1.0 + zeta_i(ji,1) * ( zkappa_i(ji,1) & |
---|
| 575 | + zkappa_i(ji,0) * zg1 ) |
---|
| 576 | ztrid(ji,numeqmin(ji)+1,3) = - zeta_i(ji,1)*zkappa_i(ji,1) |
---|
| 577 | zindterm(ji,numeqmin(ji)+1)= ztiold(ji,1) + zeta_i(ji,1)*zradab_i(ji,1) |
---|
[825] | 578 | |
---|
[921] | 579 | !!case of only one layer in the ice (surface & ice equations are altered) |
---|
[825] | 580 | |
---|
[921] | 581 | IF (nlay_i.eq.1) THEN |
---|
| 582 | ztrid(ji,numeqmin(ji),1) = 0.0 |
---|
| 583 | ztrid(ji,numeqmin(ji),2) = dzf(ji) - zkappa_i(ji,0)*2.0 |
---|
| 584 | ztrid(ji,numeqmin(ji),3) = zkappa_i(ji,0)*2.0 |
---|
| 585 | ztrid(ji,numeqmin(ji)+1,1) = -zkappa_i(ji,0)*2.0*zeta_i(ji,1) |
---|
| 586 | ztrid(ji,numeqmin(ji)+1,2) = 1.0 + zeta_i(ji,1)*(zkappa_i(ji,0)*2.0 + & |
---|
| 587 | zkappa_i(ji,1)) |
---|
| 588 | ztrid(ji,numeqmin(ji)+1,3) = 0.0 |
---|
[825] | 589 | |
---|
[921] | 590 | zindterm(ji,numeqmin(ji)+1) = ztiold(ji,1) + zeta_i(ji,1)* & |
---|
| 591 | ( zradab_i(ji,1) + zkappa_i(ji,1)*t_bo_b(ji) ) |
---|
| 592 | ENDIF |
---|
[825] | 593 | |
---|
[921] | 594 | ELSE |
---|
[825] | 595 | |
---|
[921] | 596 | ! |
---|
| 597 | !------------------------------------------------------------------------------| |
---|
| 598 | ! case 4 : surface is melting - no snow | |
---|
| 599 | !------------------------------------------------------------------------------| |
---|
| 600 | ! |
---|
| 601 | zdifcase(ji) = 4.0 |
---|
| 602 | numeqmin(ji) = nlay_s + 2 |
---|
| 603 | numeqmax(ji) = nlay_i + nlay_s + 1 |
---|
[825] | 604 | |
---|
[921] | 605 | !!first layer of ice equation |
---|
| 606 | ztrid(ji,numeqmin(ji),1) = 0.0 |
---|
| 607 | ztrid(ji,numeqmin(ji),2) = 1.0 + zeta_i(ji,1)*(zkappa_i(ji,1) + zkappa_i(ji,0)* & |
---|
| 608 | zg1) |
---|
| 609 | ztrid(ji,numeqmin(ji),3) = - zeta_i(ji,1) * zkappa_i(ji,1) |
---|
| 610 | zindterm(ji,numeqmin(ji)) = ztiold(ji,1) + zeta_i(ji,1)*( zradab_i(ji,1) + & |
---|
| 611 | zkappa_i(ji,0) * zg1 * t_su_b(ji) ) |
---|
[825] | 612 | |
---|
[921] | 613 | !!case of only one layer in the ice (surface & ice equations are altered) |
---|
| 614 | IF (nlay_i.eq.1) THEN |
---|
| 615 | ztrid(ji,numeqmin(ji),1) = 0.0 |
---|
| 616 | ztrid(ji,numeqmin(ji),2) = 1.0 + zeta_i(ji,1)*(zkappa_i(ji,0)*2.0 + & |
---|
| 617 | zkappa_i(ji,1)) |
---|
| 618 | ztrid(ji,numeqmin(ji),3) = 0.0 |
---|
| 619 | zindterm(ji,numeqmin(ji)) = ztiold(ji,1) + zeta_i(ji,1)* & |
---|
| 620 | (zradab_i(ji,1) + zkappa_i(ji,1)*t_bo_b(ji)) & |
---|
| 621 | + t_su_b(ji)*zeta_i(ji,1)*zkappa_i(ji,0)*2.0 |
---|
| 622 | ENDIF |
---|
[825] | 623 | |
---|
[921] | 624 | ENDIF |
---|
| 625 | ENDIF |
---|
[825] | 626 | |
---|
[921] | 627 | END DO |
---|
[825] | 628 | |
---|
[921] | 629 | ! |
---|
| 630 | !------------------------------------------------------------------------------| |
---|
| 631 | ! 9) tridiagonal system solving | |
---|
| 632 | !------------------------------------------------------------------------------| |
---|
| 633 | ! |
---|
[825] | 634 | |
---|
[921] | 635 | ! Solve the tridiagonal system with Gauss elimination method. |
---|
| 636 | ! Thomas algorithm, from Computational fluid Dynamics, J.D. ANDERSON, |
---|
| 637 | ! McGraw-Hill 1984. |
---|
[825] | 638 | |
---|
[921] | 639 | maxnumeqmax = 0 |
---|
| 640 | minnumeqmin = jkmax+4 |
---|
[825] | 641 | |
---|
[921] | 642 | DO ji = kideb , kiut |
---|
| 643 | zindtbis(ji,numeqmin(ji)) = zindterm(ji,numeqmin(ji)) |
---|
| 644 | zdiagbis(ji,numeqmin(ji)) = ztrid(ji,numeqmin(ji),2) |
---|
| 645 | minnumeqmin = MIN(numeqmin(ji),minnumeqmin) |
---|
| 646 | maxnumeqmax = MAX(numeqmax(ji),maxnumeqmax) |
---|
| 647 | END DO |
---|
| 648 | |
---|
| 649 | DO layer = minnumeqmin+1, maxnumeqmax |
---|
| 650 | DO ji = kideb , kiut |
---|
| 651 | numeq = min(max(numeqmin(ji)+1,layer),numeqmax(ji)) |
---|
| 652 | zdiagbis(ji,numeq) = ztrid(ji,numeq,2) - ztrid(ji,numeq,1)* & |
---|
| 653 | ztrid(ji,numeq-1,3)/zdiagbis(ji,numeq-1) |
---|
| 654 | zindtbis(ji,numeq) = zindterm(ji,numeq) - ztrid(ji,numeq,1)* & |
---|
| 655 | zindtbis(ji,numeq-1)/zdiagbis(ji,numeq-1) |
---|
| 656 | END DO |
---|
| 657 | END DO |
---|
| 658 | |
---|
| 659 | DO ji = kideb , kiut |
---|
| 660 | ! ice temperatures |
---|
| 661 | t_i_b(ji,nlay_i) = zindtbis(ji,numeqmax(ji))/zdiagbis(ji,numeqmax(ji)) |
---|
| 662 | END DO |
---|
| 663 | |
---|
| 664 | DO numeq = nlay_i + nlay_s + 1, nlay_s + 2, -1 |
---|
| 665 | DO ji = kideb , kiut |
---|
| 666 | layer = numeq - nlay_s - 1 |
---|
| 667 | t_i_b(ji,layer) = (zindtbis(ji,numeq) - ztrid(ji,numeq,3)* & |
---|
| 668 | t_i_b(ji,layer+1))/zdiagbis(ji,numeq) |
---|
| 669 | END DO |
---|
| 670 | END DO |
---|
| 671 | |
---|
| 672 | DO ji = kideb , kiut |
---|
[825] | 673 | ! snow temperatures |
---|
| 674 | IF (ht_s_b(ji).GT.0) & |
---|
[921] | 675 | t_s_b(ji,nlay_s) = (zindtbis(ji,nlay_s+1) - ztrid(ji,nlay_s+1,3) & |
---|
| 676 | * t_i_b(ji,1))/zdiagbis(ji,nlay_s+1) & |
---|
| 677 | * MAX(0.0,SIGN(1.0,ht_s_b(ji)-zeps)) |
---|
[825] | 678 | |
---|
| 679 | ! surface temperature |
---|
[2612] | 680 | isnow(ji) = INT(1.0-max(0.0,sign(1.0,-ht_s_b(ji)))) |
---|
| 681 | ztsuoldit(ji) = t_su_b(ji) |
---|
[825] | 682 | IF (t_su_b(ji) .LT. ztfs(ji)) & |
---|
[2612] | 683 | t_su_b(ji) = ( zindtbis(ji,numeqmin(ji)) - ztrid(ji,numeqmin(ji),3)* ( isnow(ji)*t_s_b(ji,1) & |
---|
| 684 | & + (1.0-isnow(ji))*t_i_b(ji,1) ) ) / zdiagbis(ji,numeqmin(ji)) |
---|
[921] | 685 | END DO |
---|
| 686 | ! |
---|
| 687 | !-------------------------------------------------------------------------- |
---|
| 688 | ! 10) Has the scheme converged ?, end of the iterative procedure | |
---|
| 689 | !-------------------------------------------------------------------------- |
---|
| 690 | ! |
---|
| 691 | ! check that nowhere it has started to melt |
---|
| 692 | ! zerrit(ji) is a measure of error, it has to be under maxer_i_thd |
---|
| 693 | DO ji = kideb , kiut |
---|
[2612] | 694 | t_su_b(ji) = MAX( MIN( t_su_b(ji) , ztfs(ji) ) , 190._wp ) |
---|
| 695 | zerrit(ji) = ABS( t_su_b(ji) - ztsuoldit(ji) ) |
---|
[921] | 696 | END DO |
---|
[825] | 697 | |
---|
[921] | 698 | DO layer = 1, nlay_s |
---|
| 699 | DO ji = kideb , kiut |
---|
[2612] | 700 | ii = MOD( npb(ji) - 1, jpi ) + 1 |
---|
| 701 | ij = ( npb(ji) - 1 ) / jpi + 1 |
---|
| 702 | t_s_b(ji,layer) = MAX( MIN( t_s_b(ji,layer), rtt ), 190._wp ) |
---|
| 703 | zerrit(ji) = MAX(zerrit(ji),ABS(t_s_b(ji,layer) - ztstemp(ji,layer))) |
---|
[921] | 704 | END DO |
---|
| 705 | END DO |
---|
[825] | 706 | |
---|
[921] | 707 | DO layer = 1, nlay_i |
---|
| 708 | DO ji = kideb , kiut |
---|
[2612] | 709 | ztmelt_i = -tmut * s_i_b(ji,layer) + rtt |
---|
| 710 | t_i_b(ji,layer) = MAX(MIN(t_i_b(ji,layer),ztmelt_i),190.0) |
---|
| 711 | zerrit(ji) = MAX(zerrit(ji),ABS(t_i_b(ji,layer) - ztitemp(ji,layer))) |
---|
[921] | 712 | END DO |
---|
| 713 | END DO |
---|
[825] | 714 | |
---|
[921] | 715 | ! Compute spatial maximum over all errors |
---|
[2612] | 716 | ! note that this could be optimized substantially by iterating only the non-converging points |
---|
| 717 | zerritmax = 0._wp |
---|
| 718 | DO ji = kideb, kiut |
---|
| 719 | zerritmax = MAX( zerritmax, zerrit(ji) ) |
---|
[921] | 720 | END DO |
---|
[2612] | 721 | IF( lk_mpp ) CALL mpp_max( zerritmax, kcom=ncomm_ice ) |
---|
[825] | 722 | |
---|
| 723 | END DO ! End of the do while iterative procedure |
---|
| 724 | |
---|
[1055] | 725 | IF( ln_nicep ) THEN |
---|
| 726 | WRITE(numout,*) ' zerritmax : ', zerritmax |
---|
| 727 | WRITE(numout,*) ' nconv : ', nconv |
---|
| 728 | ENDIF |
---|
[825] | 729 | |
---|
[921] | 730 | ! |
---|
[2612] | 731 | !-------------------------------------------------------------------------! |
---|
| 732 | ! 11) Fluxes at the interfaces ! |
---|
| 733 | !-------------------------------------------------------------------------! |
---|
[921] | 734 | DO ji = kideb, kiut |
---|
[2612] | 735 | ! ! update of latent heat fluxes |
---|
| 736 | qla_ice_1d (ji) = qla_ice_1d (ji) + dqla_ice_1d(ji) * ( t_su_b(ji) - ztsuold(ji) ) |
---|
| 737 | ! ! surface ice conduction flux |
---|
| 738 | isnow(ji) = INT( 1._wp - MAX( 0._wp, SIGN( 1._wp, -ht_s_b(ji) ) ) ) |
---|
| 739 | fc_su(ji) = - isnow(ji) * zkappa_s(ji,0) * zg1s * (t_s_b(ji,1) - t_su_b(ji)) & |
---|
| 740 | & - ( 1._wp - isnow(ji) ) * zkappa_i(ji,0) * zg1 * (t_i_b(ji,1) - t_su_b(ji)) |
---|
| 741 | ! ! bottom ice conduction flux |
---|
| 742 | fc_bo_i(ji) = - zkappa_i(ji,nlay_i) * ( zg1*(t_bo_b(ji) - t_i_b(ji,nlay_i)) ) |
---|
[921] | 743 | END DO |
---|
[825] | 744 | |
---|
[921] | 745 | !-------------------------! |
---|
| 746 | ! Heat conservation ! |
---|
| 747 | !-------------------------! |
---|
[2612] | 748 | IF( con_i ) THEN |
---|
[921] | 749 | DO ji = kideb, kiut |
---|
| 750 | ! Upper snow value |
---|
[2612] | 751 | fc_s(ji,0) = - isnow(ji) * zkappa_s(ji,0) * zg1s * ( t_s_b(ji,1) - t_su_b(ji) ) |
---|
[921] | 752 | ! Bott. snow value |
---|
[2612] | 753 | fc_s(ji,1) = - isnow(ji)* zkappa_s(ji,1) * ( t_i_b(ji,1) - t_s_b(ji,1) ) |
---|
[921] | 754 | END DO |
---|
[2612] | 755 | DO ji = kideb, kiut ! Upper ice layer |
---|
[921] | 756 | fc_i(ji,0) = - isnow(ji) * & ! interface flux if there is snow |
---|
| 757 | ( zkappa_i(ji,0) * ( t_i_b(ji,1) - t_s_b(ji,nlay_s ) ) ) & |
---|
| 758 | - ( 1.0 - isnow(ji) ) * ( zkappa_i(ji,0) * & |
---|
| 759 | zg1 * ( t_i_b(ji,1) - t_su_b(ji) ) ) ! upper flux if not |
---|
| 760 | END DO |
---|
[2612] | 761 | DO layer = 1, nlay_i - 1 ! Internal ice layers |
---|
[921] | 762 | DO ji = kideb, kiut |
---|
[2612] | 763 | fc_i(ji,layer) = - zkappa_i(ji,layer) * ( t_i_b(ji,layer+1) - t_i_b(ji,layer) ) |
---|
| 764 | ii = MOD( npb(ji) - 1, jpi ) + 1 |
---|
| 765 | ij = ( npb(ji) - 1 ) / jpi + 1 |
---|
[921] | 766 | END DO |
---|
| 767 | END DO |
---|
[2612] | 768 | DO ji = kideb, kiut ! Bottom ice layers |
---|
| 769 | fc_i(ji,nlay_i) = - zkappa_i(ji,nlay_i) * ( zg1*(t_bo_b(ji) - t_i_b(ji,nlay_i)) ) |
---|
[921] | 770 | END DO |
---|
| 771 | ENDIF |
---|
[2612] | 772 | ! |
---|
[921] | 773 | END SUBROUTINE lim_thd_dif |
---|
[825] | 774 | |
---|
| 775 | #else |
---|
[2612] | 776 | !!---------------------------------------------------------------------- |
---|
| 777 | !! Dummy Module No LIM-3 sea-ice model |
---|
| 778 | !!---------------------------------------------------------------------- |
---|
[825] | 779 | CONTAINS |
---|
| 780 | SUBROUTINE lim_thd_dif ! Empty routine |
---|
| 781 | END SUBROUTINE lim_thd_dif |
---|
| 782 | #endif |
---|
[2528] | 783 | !!====================================================================== |
---|
[921] | 784 | END MODULE limthd_dif |
---|