[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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| 7 | !!---------------------------------------------------------------------- |
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[2475] | 8 | #if defined key_lim3 |
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| 9 | !!---------------------------------------------------------------------- |
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| 10 | !! 'key_lim3' LIM3 sea-ice model |
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| 11 | !!---------------------------------------------------------------------- |
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[825] | 12 | USE par_oce ! ocean parameters |
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| 13 | USE phycst ! physical constants (ocean directory) |
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| 14 | USE thd_ice |
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| 15 | USE in_out_manager |
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| 16 | USE ice |
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| 17 | USE par_ice |
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[869] | 18 | USE lib_mpp |
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[921] | 19 | |
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[825] | 20 | IMPLICIT NONE |
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| 21 | PRIVATE |
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| 22 | |
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[2475] | 23 | PUBLIC lim_thd_dif ! called by lim_thd |
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[825] | 24 | |
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| 25 | REAL(wp) :: & ! constant values |
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| 26 | epsi20 = 1e-20 , & |
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| 27 | epsi13 = 1e-13 , & |
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| 28 | zzero = 0.e0 , & |
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| 29 | zone = 1.e0 |
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| 30 | |
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| 31 | !!---------------------------------------------------------------------- |
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[2287] | 32 | !! NEMO/LIM3 3.3 , UCL - NEMO Consortium (2010) |
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[1156] | 33 | !! $Id$ |
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[2287] | 34 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[825] | 35 | !!---------------------------------------------------------------------- |
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| 36 | CONTAINS |
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| 37 | |
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| 38 | SUBROUTINE lim_thd_dif( kideb , kiut , jl ) |
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[921] | 39 | !!------------------------------------------------------------------ |
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| 40 | !! *** ROUTINE lim_thd_dif *** |
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| 41 | !! ** Purpose : |
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| 42 | !! This routine determines the time evolution of snow and sea-ice |
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| 43 | !! temperature profiles. |
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| 44 | !! ** Method : |
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| 45 | !! This is done by solving the heat equation diffusion with |
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| 46 | !! a Neumann boundary condition at the surface and a Dirichlet one |
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| 47 | !! at the bottom. Solar radiation is partially absorbed into the ice. |
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| 48 | !! The specific heat and thermal conductivities depend on ice salinity |
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| 49 | !! and temperature to take into account brine pocket melting. The |
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| 50 | !! numerical |
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| 51 | !! scheme is an iterative Crank-Nicolson on a non-uniform multilayer grid |
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| 52 | !! in the ice and snow system. |
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| 53 | !! |
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| 54 | !! The successive steps of this routine are |
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| 55 | !! 1. Thermal conductivity at the interfaces of the ice layers |
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| 56 | !! 2. Internal absorbed radiation |
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| 57 | !! 3. Scale factors due to non-uniform grid |
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| 58 | !! 4. Kappa factors |
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| 59 | !! Then iterative procedure begins |
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| 60 | !! 5. specific heat in the ice |
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| 61 | !! 6. eta factors |
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| 62 | !! 7. surface flux computation |
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| 63 | !! 8. tridiagonal system terms |
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| 64 | !! 9. solving the tridiagonal system with Gauss elimination |
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| 65 | !! Iterative procedure ends according to a criterion on evolution |
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| 66 | !! of temperature |
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| 67 | !! |
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| 68 | !! ** Arguments : |
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| 69 | !! kideb , kiut : Starting and ending points on which the |
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| 70 | !! the computation is applied |
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| 71 | !! |
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| 72 | !! ** Inputs / Ouputs : (global commons) |
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| 73 | !! surface temperature : t_su_b |
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| 74 | !! ice/snow temperatures : t_i_b, t_s_b |
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| 75 | !! ice salinities : s_i_b |
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| 76 | !! number of layers in the ice/snow: nlay_i, nlay_s |
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| 77 | !! profile of the ice/snow layers : z_i, z_s |
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| 78 | !! total ice/snow thickness : ht_i_b, ht_s_b |
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| 79 | !! |
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| 80 | !! ** External : |
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| 81 | !! |
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| 82 | !! ** References : |
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| 83 | !! |
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| 84 | !! ** History : |
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| 85 | !! (02-2003) Martin Vancoppenolle, Louvain-la-Neuve, Belgium |
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| 86 | !! (06-2005) Martin Vancoppenolle, 3d version |
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| 87 | !! (11-2006) Vectorized by Xavier Fettweis (UCL-ASTR) |
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| 88 | !! (04-2007) Energy conservation tested by M. Vancoppenolle |
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| 89 | !! |
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| 90 | !!------------------------------------------------------------------ |
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| 91 | !! * Arguments |
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[825] | 92 | |
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[921] | 93 | INTEGER , INTENT (in) :: & |
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| 94 | kideb , & ! Start point on which the the computation is applied |
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| 95 | kiut , & ! End point on which the the computation is applied |
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| 96 | jl ! Category number |
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[825] | 97 | |
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[921] | 98 | !! * Local variables |
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| 99 | INTEGER :: ji, & ! spatial loop index |
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| 100 | zji, zjj, & ! temporary dummy loop index |
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| 101 | numeq, & ! current reference number of equation |
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| 102 | layer, & ! vertical dummy loop index |
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| 103 | nconv, & ! number of iterations in iterative procedure |
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| 104 | minnumeqmin, & ! |
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| 105 | maxnumeqmax |
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[825] | 106 | |
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[1103] | 107 | INTEGER , DIMENSION(kiut) :: & |
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[921] | 108 | numeqmin, & ! reference number of top equation |
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| 109 | numeqmax, & ! reference number of bottom equation |
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| 110 | isnow ! switch for presence (1) or absence (0) of snow |
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[825] | 111 | |
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[921] | 112 | !! * New local variables |
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[1103] | 113 | REAL(wp) , DIMENSION(kiut,0:nlay_i) :: & |
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[921] | 114 | ztcond_i, & !Ice thermal conductivity |
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| 115 | zradtr_i, & !Radiation transmitted through the ice |
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| 116 | zradab_i, & !Radiation absorbed in the ice |
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| 117 | zkappa_i !Kappa factor 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 | zradtr_s, & !Radiation transmited through the snow |
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| 121 | zradab_s, & !Radiation absorbed in the snow |
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| 122 | zkappa_s !Kappa factor in the snow |
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[825] | 123 | |
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[1103] | 124 | REAL(wp) , DIMENSION(kiut,0:nlay_i) :: & |
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[921] | 125 | ztiold, & !Old temperature in the ice |
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| 126 | zeta_i, & !Eta factor in the ice |
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| 127 | ztitemp, & !Temporary temperature in the ice to check the convergence |
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| 128 | zspeche_i, & !Ice specific heat |
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| 129 | z_i !Vertical cotes of the layers in the ice |
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[825] | 130 | |
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[1103] | 131 | REAL(wp) , DIMENSION(kiut,0:nlay_s) :: & |
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[921] | 132 | zeta_s, & !Eta factor in the snow |
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| 133 | ztstemp, & !Temporary temperature in the snow to check the convergence |
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| 134 | ztsold, & !Temporary temperature in the snow |
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| 135 | z_s !Vertical cotes of the layers in the snow |
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[825] | 136 | |
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[1103] | 137 | REAL(wp) , DIMENSION(kiut,jkmax+2) :: & |
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[921] | 138 | zindterm, & ! Independent term |
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| 139 | zindtbis, & ! temporary independent term |
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| 140 | zdiagbis |
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[825] | 141 | |
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[1103] | 142 | REAL(wp) , DIMENSION(kiut,jkmax+2,3) :: & |
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[921] | 143 | ztrid ! tridiagonal system terms |
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[825] | 144 | |
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[1103] | 145 | REAL(wp), DIMENSION(kiut) :: & |
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[921] | 146 | ztfs , & ! ice melting point |
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| 147 | ztsuold , & ! old surface temperature (before the iterative |
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| 148 | ! procedure ) |
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| 149 | ztsuoldit, & ! surface temperature at previous iteration |
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| 150 | zh_i , & !ice layer thickness |
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| 151 | zh_s , & !snow layer thickness |
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| 152 | zfsw , & !solar radiation absorbed at the surface |
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| 153 | zf , & ! surface flux function |
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| 154 | dzf ! derivative of the surface flux function |
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[825] | 155 | |
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[921] | 156 | REAL(wp) :: & ! constant values |
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| 157 | zeps = 1.0e-10, & ! |
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| 158 | zg1s = 2.0, & !: for the tridiagonal system |
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| 159 | zg1 = 2.0, & |
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| 160 | zgamma = 18009.0, & !: for specific heat |
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| 161 | zbeta = 0.117, & !: for thermal conductivity (could be 0.13) |
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| 162 | zraext_s = 1.0e08, & !: extinction coefficient of radiation in the snow |
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| 163 | zkimin = 0.10 , & !: minimum ice thermal conductivity |
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| 164 | zht_smin = 1.0e-4 !: minimum snow depth |
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[825] | 165 | |
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[921] | 166 | REAL(wp) :: & ! local variables |
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| 167 | ztmelt_i, & ! ice melting temperature |
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| 168 | zerritmax ! current maximal error on temperature |
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[825] | 169 | |
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[1103] | 170 | REAL(wp), DIMENSION(kiut) :: & |
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[921] | 171 | zerrit, & ! current error on temperature |
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| 172 | zdifcase, & ! case of the equation resolution (1->4) |
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| 173 | zftrice, & ! solar radiation transmitted through the ice |
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| 174 | zihic, zhsu |
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[825] | 175 | |
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[921] | 176 | ! |
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| 177 | !------------------------------------------------------------------------------! |
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| 178 | ! 1) Initialization ! |
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| 179 | !------------------------------------------------------------------------------! |
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| 180 | ! |
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| 181 | DO ji = kideb , kiut |
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| 182 | ! is there snow or not |
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| 183 | isnow(ji)= INT ( 1.0 - MAX( 0.0 , SIGN (1.0, - ht_s_b(ji) ) ) ) |
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| 184 | ! surface temperature of fusion |
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| 185 | ztfs(ji) = isnow(ji) * rtt + (1.0-isnow(ji)) * rtt |
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| 186 | ! layer thickness |
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| 187 | zh_i(ji) = ht_i_b(ji) / nlay_i |
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| 188 | zh_s(ji) = ht_s_b(ji) / nlay_s |
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| 189 | END DO |
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[825] | 190 | |
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[921] | 191 | !-------------------- |
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| 192 | ! Ice / snow layers |
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| 193 | !-------------------- |
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[825] | 194 | |
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[921] | 195 | z_s(:,0) = 0.0 ! vert. coord. of the up. lim. of the 1st snow layer |
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| 196 | z_i(:,0) = 0.0 ! vert. coord. of the up. lim. of the 1st ice layer |
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[825] | 197 | |
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[921] | 198 | DO layer = 1, nlay_s |
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| 199 | DO ji = kideb , kiut |
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| 200 | ! vert. coord of the up. lim. of the layer-th snow layer |
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| 201 | z_s(ji,layer) = z_s(ji,layer-1) + ht_s_b(ji) / nlay_s |
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| 202 | END DO |
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| 203 | END DO |
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[825] | 204 | |
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[921] | 205 | DO layer = 1, nlay_i |
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| 206 | DO ji = kideb , kiut |
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| 207 | ! vert. coord of the up. lim. of the layer-th ice layer |
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| 208 | z_i(ji,layer) = z_i(ji,layer-1) + ht_i_b(ji) / nlay_i |
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| 209 | END DO |
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| 210 | END DO |
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| 211 | ! |
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| 212 | !------------------------------------------------------------------------------| |
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| 213 | ! 2) Radiations | |
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| 214 | !------------------------------------------------------------------------------| |
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| 215 | ! |
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| 216 | !------------------- |
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| 217 | ! Computation of i0 |
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| 218 | !------------------- |
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| 219 | ! i0 describes the fraction of solar radiation which does not contribute |
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| 220 | ! to the surface energy budget but rather penetrates inside the ice. |
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| 221 | ! We assume that no radiation is transmitted through the snow |
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| 222 | ! If there is no no snow |
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| 223 | ! zfsw = (1-i0).qsr_ice is absorbed at the surface |
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| 224 | ! zftrice = io.qsr_ice is below the surface |
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| 225 | ! fstbif = io.qsr_ice.exp(-k(h_i)) transmitted below the ice |
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[825] | 226 | |
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[921] | 227 | DO ji = kideb , kiut |
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| 228 | ! switches |
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| 229 | isnow(ji) = INT ( 1.0 - MAX ( 0.0 , SIGN ( 1.0 , - ht_s_b(ji) ) ) ) |
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| 230 | ! hs > 0, isnow = 1 |
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| 231 | zhsu(ji) = hnzst !threshold for the computation of i0 |
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| 232 | zihic(ji) = MAX( zzero , 1.0 - ( ht_i_b(ji) / zhsu(ji) ) ) |
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[825] | 233 | |
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[921] | 234 | i0(ji) = ( 1.0 - isnow(ji) ) * & |
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| 235 | ( fr1_i0_1d(ji) + zihic(ji) * fr2_i0_1d(ji) ) |
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| 236 | !fr1_i0_1d = i0 for a thin ice surface |
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| 237 | !fr1_i0_2d = i0 for a thick ice surface |
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| 238 | ! a function of the cloud cover |
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| 239 | ! |
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| 240 | !i0(ji) = (1.0-FLOAT(isnow(ji)))*3.0/(100*ht_s_b(ji)+10.0) |
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| 241 | !formula used in Cice |
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| 242 | END DO |
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[825] | 243 | |
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[921] | 244 | !------------------------------------------------------- |
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| 245 | ! Solar radiation absorbed / transmitted at the surface |
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| 246 | ! Derivative of the non solar flux |
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| 247 | !------------------------------------------------------- |
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| 248 | DO ji = kideb , kiut |
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[825] | 249 | |
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[921] | 250 | ! Shortwave radiation absorbed at surface |
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| 251 | zfsw(ji) = qsr_ice_1d(ji) * ( 1 - i0(ji) ) |
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[825] | 252 | |
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[921] | 253 | ! Solar radiation transmitted below the surface layer |
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| 254 | zftrice(ji)= qsr_ice_1d(ji) * i0(ji) |
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[825] | 255 | |
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[921] | 256 | ! derivative of incoming nonsolar flux |
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| 257 | dzf(ji) = dqns_ice_1d(ji) |
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[825] | 258 | |
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[921] | 259 | END DO |
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[825] | 260 | |
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[921] | 261 | !--------------------------------------------------------- |
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| 262 | ! Transmission - absorption of solar radiation in the ice |
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| 263 | !--------------------------------------------------------- |
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[825] | 264 | |
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[921] | 265 | DO ji = kideb , kiut |
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| 266 | ! Initialization |
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| 267 | zradtr_s(ji,0) = zftrice(ji) ! radiation penetrating through snow |
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| 268 | END DO |
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[825] | 269 | |
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[921] | 270 | ! Radiation through snow |
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| 271 | DO layer = 1, nlay_s |
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| 272 | DO ji = kideb , kiut |
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| 273 | ! radiation transmitted below the layer-th snow layer |
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| 274 | zradtr_s(ji,layer) = zradtr_s(ji,0) * EXP ( - zraext_s * ( MAX ( 0.0 , & |
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| 275 | z_s(ji,layer) ) ) ) |
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| 276 | ! radiation absorbed by the layer-th snow layer |
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| 277 | zradab_s(ji,layer) = zradtr_s(ji,layer-1) - zradtr_s(ji,layer) |
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| 278 | END DO |
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| 279 | END DO |
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[825] | 280 | |
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[921] | 281 | ! Radiation through ice |
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| 282 | DO ji = kideb , kiut |
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| 283 | zradtr_i(ji,0) = zradtr_s(ji,nlay_s) * isnow(ji) + & |
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| 284 | zftrice(ji) * ( 1 - isnow(ji) ) |
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| 285 | END DO |
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[825] | 286 | |
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[921] | 287 | DO layer = 1, nlay_i |
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| 288 | DO ji = kideb , kiut |
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| 289 | ! radiation transmitted below the layer-th ice layer |
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| 290 | zradtr_i(ji,layer) = zradtr_i(ji,0) * EXP ( - kappa_i * ( MAX ( 0.0 , & |
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| 291 | z_i(ji,layer) ) ) ) |
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| 292 | ! radiation absorbed by the layer-th ice layer |
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| 293 | zradab_i(ji,layer) = zradtr_i(ji,layer-1) - zradtr_i(ji,layer) |
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| 294 | END DO |
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| 295 | END DO |
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[825] | 296 | |
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[921] | 297 | ! Radiation transmitted below the ice |
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| 298 | DO ji = kideb , kiut |
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| 299 | fstbif_1d(ji) = fstbif_1d(ji) + & |
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| 300 | zradtr_i(ji,nlay_i) * a_i_b(ji) / at_i_b(ji) |
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| 301 | END DO |
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[834] | 302 | |
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[921] | 303 | ! +++++ |
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| 304 | ! just to check energy conservation |
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| 305 | DO ji = kideb , kiut |
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| 306 | zji = MOD( npb(ji) - 1, jpi ) + 1 |
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| 307 | zjj = ( npb(ji) - 1 ) / jpi + 1 |
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| 308 | fstroc(zji,zjj,jl) = & |
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| 309 | zradtr_i(ji,nlay_i) |
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| 310 | END DO |
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| 311 | ! +++++ |
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[825] | 312 | |
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[921] | 313 | DO layer = 1, nlay_i |
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| 314 | DO ji = kideb , kiut |
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| 315 | radab(ji,layer) = zradab_i(ji,layer) |
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| 316 | END DO |
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| 317 | END DO |
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[825] | 318 | |
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| 319 | |
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[921] | 320 | ! |
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| 321 | !------------------------------------------------------------------------------| |
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| 322 | ! 3) Iterative procedure begins | |
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| 323 | !------------------------------------------------------------------------------| |
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| 324 | ! |
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| 325 | ! Old surface temperature |
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| 326 | DO ji = kideb, kiut |
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| 327 | ztsuold(ji) = t_su_b(ji) ! temperature at the beg of iter pr. |
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| 328 | ztsuoldit(ji) = t_su_b(ji) ! temperature at the previous iter |
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| 329 | t_su_b(ji) = MIN(t_su_b(ji),ztfs(ji)-0.00001) !necessary |
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| 330 | zerrit(ji) = 1000.0 ! initial value of error |
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| 331 | END DO |
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| 332 | !RB Min global ?? |
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[825] | 333 | |
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[921] | 334 | ! Old snow temperature |
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| 335 | DO layer = 1, nlay_s |
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| 336 | DO ji = kideb , kiut |
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| 337 | ztsold(ji,layer) = t_s_b(ji,layer) |
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| 338 | END DO |
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| 339 | END DO |
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[825] | 340 | |
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[921] | 341 | ! Old ice temperature |
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| 342 | DO layer = 1, nlay_i |
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| 343 | DO ji = kideb , kiut |
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| 344 | ztiold(ji,layer) = t_i_b(ji,layer) |
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| 345 | END DO |
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| 346 | END DO |
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[825] | 347 | |
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[921] | 348 | nconv = 0 ! number of iterations |
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| 349 | zerritmax = 1000.0 ! maximal value of error on all points |
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[825] | 350 | |
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[921] | 351 | DO WHILE ((zerritmax > maxer_i_thd).AND.(nconv < nconv_i_thd)) |
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[825] | 352 | |
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[921] | 353 | nconv = nconv+1 |
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[825] | 354 | |
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[921] | 355 | ! |
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| 356 | !------------------------------------------------------------------------------| |
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| 357 | ! 4) Sea ice thermal conductivity | |
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| 358 | !------------------------------------------------------------------------------| |
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| 359 | ! |
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| 360 | IF ( thcon_i_swi .EQ. 0 ) THEN |
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| 361 | ! Untersteiner (1964) formula |
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| 362 | DO ji = kideb , kiut |
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| 363 | ztcond_i(ji,0) = rcdic + zbeta*s_i_b(ji,1) / & |
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| 364 | MIN(-zeps,t_i_b(ji,1)-rtt) |
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| 365 | ztcond_i(ji,0) = MAX(ztcond_i(ji,0),zkimin) |
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| 366 | END DO |
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| 367 | ENDIF |
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[825] | 368 | |
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[921] | 369 | IF ( thcon_i_swi .EQ. 1 ) THEN |
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| 370 | ! Pringle et al formula included, |
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| 371 | ! 2.11 + 0.09 S/T - 0.011.T |
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| 372 | DO ji = kideb , kiut |
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| 373 | ztcond_i(ji,0) = rcdic + 0.09*s_i_b(ji,1) / & |
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| 374 | MIN(-zeps,t_i_b(ji,1)-rtt) - & |
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| 375 | 0.011* ( t_i_b(ji,1) - rtt ) |
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| 376 | ztcond_i(ji,0) = MAX(ztcond_i(ji,0),zkimin) |
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| 377 | END DO |
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| 378 | ENDIF |
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[825] | 379 | |
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[921] | 380 | IF ( thcon_i_swi .EQ. 0 ) THEN ! Untersteiner |
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| 381 | DO layer = 1, nlay_i-1 |
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| 382 | DO ji = kideb , kiut |
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| 383 | ztcond_i(ji,layer) = rcdic + zbeta*( s_i_b(ji,layer) & |
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| 384 | + s_i_b(ji,layer+1) ) / MIN(-zeps, & |
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| 385 | t_i_b(ji,layer)+t_i_b(ji,layer+1)-2.0*rtt) |
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| 386 | ztcond_i(ji,layer) = MAX(ztcond_i(ji,layer),zkimin) |
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| 387 | END DO |
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| 388 | END DO |
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| 389 | ENDIF |
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[825] | 390 | |
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[921] | 391 | IF ( thcon_i_swi .EQ. 1 ) THEN ! Pringle |
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| 392 | DO layer = 1, nlay_i-1 |
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| 393 | DO ji = kideb , kiut |
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| 394 | ztcond_i(ji,layer) = rcdic + 0.09*( s_i_b(ji,layer) & |
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| 395 | + s_i_b(ji,layer+1) ) / MIN(-zeps, & |
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| 396 | t_i_b(ji,layer)+t_i_b(ji,layer+1)-2.0*rtt) - & |
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| 397 | 0.011* ( t_i_b(ji,layer) + t_i_b(ji,layer+1) - 2.0*rtt ) |
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| 398 | ztcond_i(ji,layer) = MAX(ztcond_i(ji,layer),zkimin) |
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| 399 | END DO |
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| 400 | END DO |
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| 401 | ENDIF |
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[825] | 402 | |
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[921] | 403 | IF ( thcon_i_swi .EQ. 0 ) THEN ! Untersteiner |
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| 404 | DO ji = kideb , kiut |
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| 405 | ztcond_i(ji,nlay_i) = rcdic + zbeta*s_i_b(ji,nlay_i) / & |
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| 406 | MIN(-zeps,t_bo_b(ji)-rtt) |
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| 407 | ztcond_i(ji,nlay_i) = MAX(ztcond_i(ji,nlay_i),zkimin) |
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| 408 | END DO |
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| 409 | ENDIF |
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[825] | 410 | |
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[921] | 411 | IF ( thcon_i_swi .EQ. 1 ) THEN ! Pringle |
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| 412 | DO ji = kideb , kiut |
---|
| 413 | ztcond_i(ji,nlay_i) = rcdic + 0.09*s_i_b(ji,nlay_i) / & |
---|
| 414 | MIN(-zeps,t_bo_b(ji)-rtt) - & |
---|
| 415 | 0.011* ( t_bo_b(ji) - rtt ) |
---|
| 416 | ztcond_i(ji,nlay_i) = MAX(ztcond_i(ji,nlay_i),zkimin) |
---|
| 417 | END DO |
---|
| 418 | ENDIF |
---|
| 419 | ! |
---|
| 420 | !------------------------------------------------------------------------------| |
---|
| 421 | ! 5) kappa factors | |
---|
| 422 | !------------------------------------------------------------------------------| |
---|
| 423 | ! |
---|
| 424 | DO ji = kideb, kiut |
---|
[825] | 425 | |
---|
[921] | 426 | !-- Snow kappa factors |
---|
| 427 | zkappa_s(ji,0) = rcdsn / MAX(zeps,zh_s(ji)) |
---|
| 428 | zkappa_s(ji,nlay_s) = rcdsn / MAX(zeps,zh_s(ji)) |
---|
| 429 | END DO |
---|
[825] | 430 | |
---|
[921] | 431 | DO layer = 1, nlay_s-1 |
---|
| 432 | DO ji = kideb , kiut |
---|
| 433 | zkappa_s(ji,layer) = 2.0 * rcdsn / & |
---|
| 434 | MAX(zeps,2.0*zh_s(ji)) |
---|
| 435 | END DO |
---|
| 436 | END DO |
---|
[825] | 437 | |
---|
[921] | 438 | DO layer = 1, nlay_i-1 |
---|
| 439 | DO ji = kideb , kiut |
---|
| 440 | !-- Ice kappa factors |
---|
| 441 | zkappa_i(ji,layer) = 2.0*ztcond_i(ji,layer)/ & |
---|
| 442 | MAX(zeps,2.0*zh_i(ji)) |
---|
| 443 | END DO |
---|
| 444 | END DO |
---|
[825] | 445 | |
---|
[921] | 446 | DO ji = kideb , kiut |
---|
| 447 | zkappa_i(ji,0) = ztcond_i(ji,0)/MAX(zeps,zh_i(ji)) |
---|
| 448 | zkappa_i(ji,nlay_i) = ztcond_i(ji,nlay_i) / MAX(zeps,zh_i(ji)) |
---|
| 449 | !-- Interface |
---|
| 450 | zkappa_s(ji,nlay_s) = 2.0*rcdsn*ztcond_i(ji,0)/MAX(zeps, & |
---|
| 451 | (ztcond_i(ji,0)*zh_s(ji) + rcdsn*zh_i(ji))) |
---|
| 452 | zkappa_i(ji,0) = zkappa_s(ji,nlay_s)*isnow(ji) & |
---|
| 453 | + zkappa_i(ji,0)*(1.0-isnow(ji)) |
---|
| 454 | END DO |
---|
| 455 | ! |
---|
| 456 | !------------------------------------------------------------------------------| |
---|
| 457 | ! 6) Sea ice specific heat, eta factors | |
---|
| 458 | !------------------------------------------------------------------------------| |
---|
| 459 | ! |
---|
| 460 | DO layer = 1, nlay_i |
---|
| 461 | DO ji = kideb , kiut |
---|
| 462 | ztitemp(ji,layer) = t_i_b(ji,layer) |
---|
| 463 | zspeche_i(ji,layer) = cpic + zgamma*s_i_b(ji,layer)/ & |
---|
| 464 | MAX((t_i_b(ji,layer)-rtt)*(ztiold(ji,layer)-rtt),zeps) |
---|
| 465 | zeta_i(ji,layer) = rdt_ice / MAX(rhoic*zspeche_i(ji,layer)*zh_i(ji), & |
---|
| 466 | zeps) |
---|
| 467 | END DO |
---|
| 468 | END DO |
---|
[825] | 469 | |
---|
[921] | 470 | DO layer = 1, nlay_s |
---|
| 471 | DO ji = kideb , kiut |
---|
| 472 | ztstemp(ji,layer) = t_s_b(ji,layer) |
---|
| 473 | zeta_s(ji,layer) = rdt_ice / MAX(rhosn*cpic*zh_s(ji),zeps) |
---|
| 474 | END DO |
---|
| 475 | END DO |
---|
| 476 | ! |
---|
| 477 | !------------------------------------------------------------------------------| |
---|
| 478 | ! 7) surface flux computation | |
---|
| 479 | !------------------------------------------------------------------------------| |
---|
| 480 | ! |
---|
| 481 | DO ji = kideb , kiut |
---|
[825] | 482 | |
---|
[921] | 483 | ! update of the non solar flux according to the update in T_su |
---|
| 484 | qnsr_ice_1d(ji) = qnsr_ice_1d(ji) + dqns_ice_1d(ji) * & |
---|
| 485 | ( t_su_b(ji) - ztsuoldit(ji) ) |
---|
[825] | 486 | |
---|
[921] | 487 | ! update incoming flux |
---|
| 488 | zf(ji) = zfsw(ji) & ! net absorbed solar radiation |
---|
| 489 | + qnsr_ice_1d(ji) ! non solar total flux |
---|
| 490 | ! (LWup, LWdw, SH, LH) |
---|
[825] | 491 | |
---|
[921] | 492 | END DO |
---|
[825] | 493 | |
---|
[921] | 494 | ! |
---|
| 495 | !------------------------------------------------------------------------------| |
---|
| 496 | ! 8) tridiagonal system terms | |
---|
| 497 | !------------------------------------------------------------------------------| |
---|
| 498 | ! |
---|
| 499 | !!layer denotes the number of the layer in the snow or in the ice |
---|
| 500 | !!numeq denotes the reference number of the equation in the tridiagonal |
---|
| 501 | !!system, terms of tridiagonal system are indexed as following : |
---|
| 502 | !!1 is subdiagonal term, 2 is diagonal and 3 is superdiagonal one |
---|
[825] | 503 | |
---|
[921] | 504 | !!ice interior terms (top equation has the same form as the others) |
---|
| 505 | |
---|
| 506 | DO numeq=1,jkmax+2 |
---|
| 507 | DO ji = kideb , kiut |
---|
| 508 | ztrid(ji,numeq,1) = 0. |
---|
| 509 | ztrid(ji,numeq,2) = 0. |
---|
| 510 | ztrid(ji,numeq,3) = 0. |
---|
| 511 | zindterm(ji,numeq)= 0. |
---|
| 512 | zindtbis(ji,numeq)= 0. |
---|
| 513 | zdiagbis(ji,numeq)= 0. |
---|
| 514 | ENDDO |
---|
| 515 | ENDDO |
---|
| 516 | |
---|
| 517 | DO numeq = nlay_s + 2, nlay_s + nlay_i |
---|
| 518 | DO ji = kideb , kiut |
---|
| 519 | layer = numeq - nlay_s - 1 |
---|
| 520 | ztrid(ji,numeq,1) = - zeta_i(ji,layer)*zkappa_i(ji,layer-1) |
---|
| 521 | ztrid(ji,numeq,2) = 1.0 + zeta_i(ji,layer)*(zkappa_i(ji,layer-1) + & |
---|
| 522 | zkappa_i(ji,layer)) |
---|
| 523 | ztrid(ji,numeq,3) = - zeta_i(ji,layer)*zkappa_i(ji,layer) |
---|
| 524 | zindterm(ji,numeq) = ztiold(ji,layer) + zeta_i(ji,layer)* & |
---|
| 525 | zradab_i(ji,layer) |
---|
| 526 | END DO |
---|
| 527 | ENDDO |
---|
| 528 | |
---|
| 529 | numeq = nlay_s + nlay_i + 1 |
---|
| 530 | DO ji = kideb , kiut |
---|
[825] | 531 | !!ice bottom term |
---|
| 532 | ztrid(ji,numeq,1) = - zeta_i(ji,nlay_i)*zkappa_i(ji,nlay_i-1) |
---|
| 533 | ztrid(ji,numeq,2) = 1.0 + zeta_i(ji,nlay_i)*( zkappa_i(ji,nlay_i)*zg1 & |
---|
[921] | 534 | + zkappa_i(ji,nlay_i-1) ) |
---|
[825] | 535 | ztrid(ji,numeq,3) = 0.0 |
---|
| 536 | zindterm(ji,numeq) = ztiold(ji,nlay_i) + zeta_i(ji,nlay_i)* & |
---|
[921] | 537 | ( zradab_i(ji,nlay_i) + zkappa_i(ji,nlay_i)*zg1 & |
---|
| 538 | * t_bo_b(ji) ) |
---|
| 539 | ENDDO |
---|
[825] | 540 | |
---|
| 541 | |
---|
[921] | 542 | DO ji = kideb , kiut |
---|
[825] | 543 | IF ( ht_s_b(ji).gt.0.0 ) THEN |
---|
[921] | 544 | ! |
---|
| 545 | !------------------------------------------------------------------------------| |
---|
| 546 | ! snow-covered cells | |
---|
| 547 | !------------------------------------------------------------------------------| |
---|
| 548 | ! |
---|
| 549 | !!snow interior terms (bottom equation has the same form as the others) |
---|
| 550 | DO numeq = 3, nlay_s + 1 |
---|
| 551 | layer = numeq - 1 |
---|
| 552 | ztrid(ji,numeq,1) = - zeta_s(ji,layer)*zkappa_s(ji,layer-1) |
---|
| 553 | ztrid(ji,numeq,2) = 1.0 + zeta_s(ji,layer)*( zkappa_s(ji,layer-1) + & |
---|
| 554 | zkappa_s(ji,layer) ) |
---|
| 555 | ztrid(ji,numeq,3) = - zeta_s(ji,layer)*zkappa_s(ji,layer) |
---|
| 556 | zindterm(ji,numeq) = ztsold(ji,layer) + zeta_s(ji,layer)* & |
---|
| 557 | zradab_s(ji,layer) |
---|
| 558 | END DO |
---|
[825] | 559 | |
---|
[921] | 560 | !!case of only one layer in the ice (ice equation is altered) |
---|
| 561 | IF ( nlay_i.eq.1 ) THEN |
---|
| 562 | ztrid(ji,nlay_s+2,3) = 0.0 |
---|
| 563 | zindterm(ji,nlay_s+2) = zindterm(ji,nlay_s+2) + zkappa_i(ji,1)* & |
---|
| 564 | t_bo_b(ji) |
---|
| 565 | ENDIF |
---|
[834] | 566 | |
---|
[921] | 567 | IF ( t_su_b(ji) .LT. rtt ) THEN |
---|
[825] | 568 | |
---|
[921] | 569 | !------------------------------------------------------------------------------| |
---|
| 570 | ! case 1 : no surface melting - snow present | |
---|
| 571 | !------------------------------------------------------------------------------| |
---|
| 572 | zdifcase(ji) = 1.0 |
---|
| 573 | numeqmin(ji) = 1 |
---|
| 574 | numeqmax(ji) = nlay_i + nlay_s + 1 |
---|
[825] | 575 | |
---|
[921] | 576 | !!surface equation |
---|
| 577 | ztrid(ji,1,1) = 0.0 |
---|
| 578 | ztrid(ji,1,2) = dzf(ji) - zg1s*zkappa_s(ji,0) |
---|
| 579 | ztrid(ji,1,3) = zg1s*zkappa_s(ji,0) |
---|
| 580 | zindterm(ji,1) = dzf(ji)*t_su_b(ji) - zf(ji) |
---|
[825] | 581 | |
---|
[921] | 582 | !!first layer of snow equation |
---|
| 583 | ztrid(ji,2,1) = - zkappa_s(ji,0)*zg1s*zeta_s(ji,1) |
---|
| 584 | ztrid(ji,2,2) = 1.0 + zeta_s(ji,1)*(zkappa_s(ji,1) + zkappa_s(ji,0)*zg1s) |
---|
| 585 | ztrid(ji,2,3) = - zeta_s(ji,1)* zkappa_s(ji,1) |
---|
| 586 | zindterm(ji,2) = ztsold(ji,1) + zeta_s(ji,1)*zradab_s(ji,1) |
---|
[825] | 587 | |
---|
[921] | 588 | ELSE |
---|
| 589 | ! |
---|
| 590 | !------------------------------------------------------------------------------| |
---|
| 591 | ! case 2 : surface is melting - snow present | |
---|
| 592 | !------------------------------------------------------------------------------| |
---|
| 593 | ! |
---|
| 594 | zdifcase(ji) = 2.0 |
---|
| 595 | numeqmin(ji) = 2 |
---|
| 596 | numeqmax(ji) = nlay_i + nlay_s + 1 |
---|
[825] | 597 | |
---|
[921] | 598 | !!first layer of snow equation |
---|
| 599 | ztrid(ji,2,1) = 0.0 |
---|
| 600 | ztrid(ji,2,2) = 1.0 + zeta_s(ji,1) * ( zkappa_s(ji,1) + & |
---|
| 601 | zkappa_s(ji,0) * zg1s ) |
---|
| 602 | ztrid(ji,2,3) = - zeta_s(ji,1)*zkappa_s(ji,1) |
---|
| 603 | zindterm(ji,2) = ztsold(ji,1) + zeta_s(ji,1) * & |
---|
| 604 | ( zradab_s(ji,1) + & |
---|
| 605 | zkappa_s(ji,0) * zg1s * t_su_b(ji) ) |
---|
| 606 | ENDIF |
---|
| 607 | ELSE |
---|
| 608 | ! |
---|
| 609 | !------------------------------------------------------------------------------| |
---|
| 610 | ! cells without snow | |
---|
| 611 | !------------------------------------------------------------------------------| |
---|
| 612 | ! |
---|
| 613 | IF (t_su_b(ji) .LT. rtt) THEN |
---|
| 614 | ! |
---|
| 615 | !------------------------------------------------------------------------------| |
---|
| 616 | ! case 3 : no surface melting - no snow | |
---|
| 617 | !------------------------------------------------------------------------------| |
---|
| 618 | ! |
---|
| 619 | zdifcase(ji) = 3.0 |
---|
| 620 | numeqmin(ji) = nlay_s + 1 |
---|
| 621 | numeqmax(ji) = nlay_i + nlay_s + 1 |
---|
[825] | 622 | |
---|
[921] | 623 | !!surface equation |
---|
| 624 | ztrid(ji,numeqmin(ji),1) = 0.0 |
---|
| 625 | ztrid(ji,numeqmin(ji),2) = dzf(ji) - zkappa_i(ji,0)*zg1 |
---|
| 626 | ztrid(ji,numeqmin(ji),3) = zkappa_i(ji,0)*zg1 |
---|
| 627 | zindterm(ji,numeqmin(ji)) = dzf(ji)*t_su_b(ji) - zf(ji) |
---|
[825] | 628 | |
---|
[921] | 629 | !!first layer of ice equation |
---|
| 630 | ztrid(ji,numeqmin(ji)+1,1) = - zkappa_i(ji,0) * zg1 * zeta_i(ji,1) |
---|
| 631 | ztrid(ji,numeqmin(ji)+1,2) = 1.0 + zeta_i(ji,1) * ( zkappa_i(ji,1) & |
---|
| 632 | + zkappa_i(ji,0) * zg1 ) |
---|
| 633 | ztrid(ji,numeqmin(ji)+1,3) = - zeta_i(ji,1)*zkappa_i(ji,1) |
---|
| 634 | zindterm(ji,numeqmin(ji)+1)= ztiold(ji,1) + zeta_i(ji,1)*zradab_i(ji,1) |
---|
[825] | 635 | |
---|
[921] | 636 | !!case of only one layer in the ice (surface & ice equations are altered) |
---|
[825] | 637 | |
---|
[921] | 638 | IF (nlay_i.eq.1) THEN |
---|
| 639 | ztrid(ji,numeqmin(ji),1) = 0.0 |
---|
| 640 | ztrid(ji,numeqmin(ji),2) = dzf(ji) - zkappa_i(ji,0)*2.0 |
---|
| 641 | ztrid(ji,numeqmin(ji),3) = zkappa_i(ji,0)*2.0 |
---|
| 642 | ztrid(ji,numeqmin(ji)+1,1) = -zkappa_i(ji,0)*2.0*zeta_i(ji,1) |
---|
| 643 | ztrid(ji,numeqmin(ji)+1,2) = 1.0 + zeta_i(ji,1)*(zkappa_i(ji,0)*2.0 + & |
---|
| 644 | zkappa_i(ji,1)) |
---|
| 645 | ztrid(ji,numeqmin(ji)+1,3) = 0.0 |
---|
[825] | 646 | |
---|
[921] | 647 | zindterm(ji,numeqmin(ji)+1) = ztiold(ji,1) + zeta_i(ji,1)* & |
---|
| 648 | ( zradab_i(ji,1) + zkappa_i(ji,1)*t_bo_b(ji) ) |
---|
| 649 | ENDIF |
---|
[825] | 650 | |
---|
[921] | 651 | ELSE |
---|
[825] | 652 | |
---|
[921] | 653 | ! |
---|
| 654 | !------------------------------------------------------------------------------| |
---|
| 655 | ! case 4 : surface is melting - no snow | |
---|
| 656 | !------------------------------------------------------------------------------| |
---|
| 657 | ! |
---|
| 658 | zdifcase(ji) = 4.0 |
---|
| 659 | numeqmin(ji) = nlay_s + 2 |
---|
| 660 | numeqmax(ji) = nlay_i + nlay_s + 1 |
---|
[825] | 661 | |
---|
[921] | 662 | !!first layer of ice equation |
---|
| 663 | ztrid(ji,numeqmin(ji),1) = 0.0 |
---|
| 664 | ztrid(ji,numeqmin(ji),2) = 1.0 + zeta_i(ji,1)*(zkappa_i(ji,1) + zkappa_i(ji,0)* & |
---|
| 665 | zg1) |
---|
| 666 | ztrid(ji,numeqmin(ji),3) = - zeta_i(ji,1) * zkappa_i(ji,1) |
---|
| 667 | zindterm(ji,numeqmin(ji)) = ztiold(ji,1) + zeta_i(ji,1)*( zradab_i(ji,1) + & |
---|
| 668 | zkappa_i(ji,0) * zg1 * t_su_b(ji) ) |
---|
[825] | 669 | |
---|
[921] | 670 | !!case of only one layer in the ice (surface & ice equations are altered) |
---|
| 671 | IF (nlay_i.eq.1) THEN |
---|
| 672 | ztrid(ji,numeqmin(ji),1) = 0.0 |
---|
| 673 | ztrid(ji,numeqmin(ji),2) = 1.0 + zeta_i(ji,1)*(zkappa_i(ji,0)*2.0 + & |
---|
| 674 | zkappa_i(ji,1)) |
---|
| 675 | ztrid(ji,numeqmin(ji),3) = 0.0 |
---|
| 676 | zindterm(ji,numeqmin(ji)) = ztiold(ji,1) + zeta_i(ji,1)* & |
---|
| 677 | (zradab_i(ji,1) + zkappa_i(ji,1)*t_bo_b(ji)) & |
---|
| 678 | + t_su_b(ji)*zeta_i(ji,1)*zkappa_i(ji,0)*2.0 |
---|
| 679 | ENDIF |
---|
[825] | 680 | |
---|
[921] | 681 | ENDIF |
---|
| 682 | ENDIF |
---|
[825] | 683 | |
---|
[921] | 684 | END DO |
---|
[825] | 685 | |
---|
[921] | 686 | ! |
---|
| 687 | !------------------------------------------------------------------------------| |
---|
| 688 | ! 9) tridiagonal system solving | |
---|
| 689 | !------------------------------------------------------------------------------| |
---|
| 690 | ! |
---|
[825] | 691 | |
---|
[921] | 692 | ! Solve the tridiagonal system with Gauss elimination method. |
---|
| 693 | ! Thomas algorithm, from Computational fluid Dynamics, J.D. ANDERSON, |
---|
| 694 | ! McGraw-Hill 1984. |
---|
[825] | 695 | |
---|
[921] | 696 | maxnumeqmax = 0 |
---|
| 697 | minnumeqmin = jkmax+4 |
---|
[825] | 698 | |
---|
[921] | 699 | DO ji = kideb , kiut |
---|
| 700 | zindtbis(ji,numeqmin(ji)) = zindterm(ji,numeqmin(ji)) |
---|
| 701 | zdiagbis(ji,numeqmin(ji)) = ztrid(ji,numeqmin(ji),2) |
---|
| 702 | minnumeqmin = MIN(numeqmin(ji),minnumeqmin) |
---|
| 703 | maxnumeqmax = MAX(numeqmax(ji),maxnumeqmax) |
---|
| 704 | END DO |
---|
| 705 | |
---|
| 706 | DO layer = minnumeqmin+1, maxnumeqmax |
---|
| 707 | DO ji = kideb , kiut |
---|
| 708 | numeq = min(max(numeqmin(ji)+1,layer),numeqmax(ji)) |
---|
| 709 | zdiagbis(ji,numeq) = ztrid(ji,numeq,2) - ztrid(ji,numeq,1)* & |
---|
| 710 | ztrid(ji,numeq-1,3)/zdiagbis(ji,numeq-1) |
---|
| 711 | zindtbis(ji,numeq) = zindterm(ji,numeq) - ztrid(ji,numeq,1)* & |
---|
| 712 | zindtbis(ji,numeq-1)/zdiagbis(ji,numeq-1) |
---|
| 713 | END DO |
---|
| 714 | END DO |
---|
| 715 | |
---|
| 716 | DO ji = kideb , kiut |
---|
| 717 | ! ice temperatures |
---|
| 718 | t_i_b(ji,nlay_i) = zindtbis(ji,numeqmax(ji))/zdiagbis(ji,numeqmax(ji)) |
---|
| 719 | END DO |
---|
| 720 | |
---|
| 721 | DO numeq = nlay_i + nlay_s + 1, nlay_s + 2, -1 |
---|
| 722 | DO ji = kideb , kiut |
---|
| 723 | layer = numeq - nlay_s - 1 |
---|
| 724 | t_i_b(ji,layer) = (zindtbis(ji,numeq) - ztrid(ji,numeq,3)* & |
---|
| 725 | t_i_b(ji,layer+1))/zdiagbis(ji,numeq) |
---|
| 726 | END DO |
---|
| 727 | END DO |
---|
| 728 | |
---|
| 729 | DO ji = kideb , kiut |
---|
[825] | 730 | ! snow temperatures |
---|
| 731 | IF (ht_s_b(ji).GT.0) & |
---|
[921] | 732 | t_s_b(ji,nlay_s) = (zindtbis(ji,nlay_s+1) - ztrid(ji,nlay_s+1,3) & |
---|
| 733 | * t_i_b(ji,1))/zdiagbis(ji,nlay_s+1) & |
---|
| 734 | * MAX(0.0,SIGN(1.0,ht_s_b(ji)-zeps)) |
---|
[825] | 735 | |
---|
| 736 | ! surface temperature |
---|
| 737 | isnow(ji) = INT(1.0-max(0.0,sign(1.0,-ht_s_b(ji)))) |
---|
| 738 | ztsuoldit(ji) = t_su_b(ji) |
---|
| 739 | IF (t_su_b(ji) .LT. ztfs(ji)) & |
---|
[921] | 740 | t_su_b(ji) = ( zindtbis(ji,numeqmin(ji)) - ztrid(ji,numeqmin(ji),3)* & |
---|
| 741 | ( isnow(ji)*t_s_b(ji,1) + & |
---|
| 742 | (1.0-isnow(ji))*t_i_b(ji,1) ) ) / & |
---|
| 743 | zdiagbis(ji,numeqmin(ji)) |
---|
| 744 | END DO |
---|
| 745 | ! |
---|
| 746 | !-------------------------------------------------------------------------- |
---|
| 747 | ! 10) Has the scheme converged ?, end of the iterative procedure | |
---|
| 748 | !-------------------------------------------------------------------------- |
---|
| 749 | ! |
---|
| 750 | ! check that nowhere it has started to melt |
---|
| 751 | ! zerrit(ji) is a measure of error, it has to be under maxer_i_thd |
---|
| 752 | DO ji = kideb , kiut |
---|
| 753 | t_su_b(ji) = MAX(MIN(t_su_b(ji),ztfs(ji)),190.0) |
---|
| 754 | zerrit(ji) = ABS(t_su_b(ji)-ztsuoldit(ji)) |
---|
| 755 | END DO |
---|
[825] | 756 | |
---|
[921] | 757 | DO layer = 1, nlay_s |
---|
| 758 | DO ji = kideb , kiut |
---|
| 759 | zji = MOD( npb(ji) - 1, jpi ) + 1 |
---|
| 760 | zjj = ( npb(ji) - 1 ) / jpi + 1 |
---|
| 761 | t_s_b(ji,layer) = MAX(MIN(t_s_b(ji,layer),rtt),190.0) |
---|
| 762 | zerrit(ji) = MAX(zerrit(ji),ABS(t_s_b(ji,layer) & |
---|
| 763 | - ztstemp(ji,layer))) |
---|
| 764 | END DO |
---|
| 765 | END DO |
---|
[825] | 766 | |
---|
[921] | 767 | DO layer = 1, nlay_i |
---|
| 768 | DO ji = kideb , kiut |
---|
| 769 | ztmelt_i = -tmut*s_i_b(ji,layer) +rtt |
---|
| 770 | t_i_b(ji,layer) = MAX(MIN(t_i_b(ji,layer),ztmelt_i),190.0) |
---|
| 771 | zerrit(ji) = MAX(zerrit(ji),ABS(t_i_b(ji,layer) - ztitemp(ji,layer))) |
---|
| 772 | END DO |
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| 773 | END DO |
---|
[825] | 774 | |
---|
[921] | 775 | ! Compute spatial maximum over all errors |
---|
| 776 | ! note that this could be optimized substantially by iterating only |
---|
| 777 | ! the non-converging points |
---|
| 778 | zerritmax = 0.0 |
---|
| 779 | DO ji = kideb , kiut |
---|
| 780 | zerritmax = MAX(zerritmax,zerrit(ji)) |
---|
| 781 | END DO |
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| 782 | IF( lk_mpp ) CALL mpp_max(zerritmax, kcom=ncomm_ice) |
---|
[825] | 783 | |
---|
| 784 | END DO ! End of the do while iterative procedure |
---|
| 785 | |
---|
[1055] | 786 | IF( ln_nicep ) THEN |
---|
| 787 | WRITE(numout,*) ' zerritmax : ', zerritmax |
---|
| 788 | WRITE(numout,*) ' nconv : ', nconv |
---|
| 789 | ENDIF |
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[825] | 790 | |
---|
[921] | 791 | ! |
---|
| 792 | !-------------------------------------------------------------------------- |
---|
| 793 | ! 11) Fluxes at the interfaces | |
---|
| 794 | !-------------------------------------------------------------------------- |
---|
| 795 | ! |
---|
| 796 | DO ji = kideb, kiut |
---|
| 797 | ! update of latent heat fluxes |
---|
| 798 | qla_ice_1d (ji) = qla_ice_1d (ji) + & |
---|
| 799 | dqla_ice_1d(ji) * ( t_su_b(ji) - ztsuold(ji) ) |
---|
[825] | 800 | |
---|
[921] | 801 | ! surface ice conduction flux |
---|
| 802 | isnow(ji) = int(1.0-max(0.0,sign(1.0,-ht_s_b(ji)))) |
---|
| 803 | fc_su(ji) = - isnow(ji)*zkappa_s(ji,0)*zg1s*(t_s_b(ji,1) - & |
---|
| 804 | t_su_b(ji)) & |
---|
| 805 | - (1.0-isnow(ji))*zkappa_i(ji,0)*zg1* & |
---|
| 806 | (t_i_b(ji,1) - t_su_b(ji)) |
---|
[825] | 807 | |
---|
[921] | 808 | ! bottom ice conduction flux |
---|
| 809 | fc_bo_i(ji) = - zkappa_i(ji,nlay_i)* & |
---|
| 810 | ( zg1*(t_bo_b(ji) - t_i_b(ji,nlay_i)) ) |
---|
[825] | 811 | |
---|
[921] | 812 | END DO |
---|
[825] | 813 | |
---|
[921] | 814 | !-------------------------! |
---|
| 815 | ! Heat conservation ! |
---|
| 816 | !-------------------------! |
---|
| 817 | IF ( con_i ) THEN |
---|
[825] | 818 | |
---|
[921] | 819 | DO ji = kideb, kiut |
---|
| 820 | ! Upper snow value |
---|
| 821 | fc_s(ji,0) = - isnow(ji)* & |
---|
| 822 | zkappa_s(ji,0) * zg1s * ( t_s_b(ji,1) - & |
---|
| 823 | t_su_b(ji) ) |
---|
| 824 | ! Bott. snow value |
---|
| 825 | fc_s(ji,1) = - isnow(ji)* & |
---|
| 826 | zkappa_s(ji,1) * ( t_i_b(ji,1) - & |
---|
| 827 | t_s_b(ji,1) ) |
---|
| 828 | END DO |
---|
[825] | 829 | |
---|
[921] | 830 | ! Upper ice layer |
---|
| 831 | DO ji = kideb, kiut |
---|
| 832 | fc_i(ji,0) = - isnow(ji) * & ! interface flux if there is snow |
---|
| 833 | ( zkappa_i(ji,0) * ( t_i_b(ji,1) - t_s_b(ji,nlay_s ) ) ) & |
---|
| 834 | - ( 1.0 - isnow(ji) ) * ( zkappa_i(ji,0) * & |
---|
| 835 | zg1 * ( t_i_b(ji,1) - t_su_b(ji) ) ) ! upper flux if not |
---|
| 836 | END DO |
---|
[825] | 837 | |
---|
[921] | 838 | ! Internal ice layers |
---|
| 839 | DO layer = 1, nlay_i - 1 |
---|
| 840 | DO ji = kideb, kiut |
---|
| 841 | fc_i(ji,layer) = - zkappa_i(ji,layer) * ( t_i_b(ji,layer+1) - & |
---|
| 842 | t_i_b(ji,layer) ) |
---|
| 843 | zji = MOD( npb(ji) - 1, jpi ) + 1 |
---|
| 844 | zjj = ( npb(ji) - 1 ) / jpi + 1 |
---|
| 845 | END DO |
---|
| 846 | END DO |
---|
[825] | 847 | |
---|
[921] | 848 | ! Bottom ice layers |
---|
| 849 | DO ji = kideb, kiut |
---|
| 850 | fc_i(ji,nlay_i) = - zkappa_i(ji,nlay_i)* & |
---|
| 851 | ( zg1*(t_bo_b(ji) - t_i_b(ji,nlay_i)) ) |
---|
| 852 | END DO |
---|
[825] | 853 | |
---|
[921] | 854 | ENDIF |
---|
[825] | 855 | |
---|
[921] | 856 | END SUBROUTINE lim_thd_dif |
---|
[825] | 857 | |
---|
| 858 | #else |
---|
| 859 | !!====================================================================== |
---|
| 860 | !! *** MODULE limthd_dif *** |
---|
| 861 | !! no sea ice model |
---|
| 862 | !!====================================================================== |
---|
| 863 | CONTAINS |
---|
| 864 | SUBROUTINE lim_thd_dif ! Empty routine |
---|
| 865 | END SUBROUTINE lim_thd_dif |
---|
| 866 | #endif |
---|
[2475] | 867 | !!====================================================================== |
---|
[921] | 868 | END MODULE limthd_dif |
---|