[8984] | 1 | MODULE icethd_zdf_BL99 |
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| 2 | !!====================================================================== |
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| 3 | !! *** MODULE icethd_zdf_BL99 *** |
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[14072] | 4 | !! sea-ice: vertical heat diffusion in sea ice (computation of temperatures) |
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[8984] | 5 | !!====================================================================== |
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[9656] | 6 | !! History : ! 2003-02 (M. Vancoppenolle) original 1D code |
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[9604] | 7 | !! ! 2005-06 (M. Vancoppenolle) 3d version |
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| 8 | !! 4.0 ! 2018 (many people) SI3 [aka Sea Ice cube] |
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[8984] | 9 | !!---------------------------------------------------------------------- |
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[9570] | 10 | #if defined key_si3 |
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[8984] | 11 | !!---------------------------------------------------------------------- |
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[9570] | 12 | !! 'key_si3' SI3 sea-ice model |
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[8984] | 13 | !!---------------------------------------------------------------------- |
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| 14 | !! ice_thd_zdf_BL99 : vertical diffusion computation |
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| 15 | !!---------------------------------------------------------------------- |
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| 16 | USE dom_oce ! ocean space and time domain |
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[14072] | 17 | USE phycst ! physical constants (ocean directory) |
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[8984] | 18 | USE ice ! sea-ice: variables |
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| 19 | USE ice1D ! sea-ice: thermodynamics variables |
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| 20 | USE icevar ! sea-ice: operations |
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| 21 | ! |
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| 22 | USE in_out_manager ! I/O manager |
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| 23 | USE lib_mpp ! MPP library |
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| 24 | USE lib_fortran ! fortran utilities (glob_sum + no signed zero) |
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| 25 | |
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| 26 | IMPLICIT NONE |
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| 27 | PRIVATE |
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| 28 | |
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| 29 | PUBLIC ice_thd_zdf_BL99 ! called by icethd_zdf |
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| 30 | |
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| 31 | !!---------------------------------------------------------------------- |
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[9598] | 32 | !! NEMO/ICE 4.0 , NEMO Consortium (2018) |
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[10069] | 33 | !! $Id$ |
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[10068] | 34 | !! Software governed by the CeCILL license (see ./LICENSE) |
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[8984] | 35 | !!---------------------------------------------------------------------- |
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| 36 | CONTAINS |
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| 37 | |
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[10534] | 38 | SUBROUTINE ice_thd_zdf_BL99( k_cnd ) |
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[8984] | 39 | !!------------------------------------------------------------------- |
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| 40 | !! *** ROUTINE ice_thd_zdf_BL99 *** |
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| 41 | !! |
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| 42 | !! ** Purpose : computes the time evolution of snow and sea-ice temperature |
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| 43 | !! profiles, using the original Bitz and Lipscomb (1999) algorithm |
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| 44 | !! |
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| 45 | !! ** Method : solves the heat equation diffusion with a Neumann boundary |
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[14072] | 46 | !! condition at the surface and a Dirichlet one at the bottom. |
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[8984] | 47 | !! Solar radiation is partially absorbed into the ice. |
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[14072] | 48 | !! The specific heat and thermal conductivities depend on ice |
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| 49 | !! salinity and temperature to take into account brine pocket |
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[8984] | 50 | !! melting. The numerical scheme is an iterative Crank-Nicolson |
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| 51 | !! on a non-uniform multilayer grid in the ice and snow system. |
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| 52 | !! |
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| 53 | !! The successive steps of this routine are |
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| 54 | !! 1. initialization of ice-snow layers thicknesses |
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| 55 | !! 2. Internal absorbed and transmitted radiation |
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| 56 | !! Then iterative procedure begins |
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| 57 | !! 3. Thermal conductivity |
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| 58 | !! 4. Kappa factors |
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| 59 | !! 5. specific heat in the ice |
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| 60 | !! 6. eta factors |
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| 61 | !! 7. surface flux computation |
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| 62 | !! 8. tridiagonal system terms |
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| 63 | !! 9. solving the tridiagonal system with Gauss elimination |
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| 64 | !! Iterative procedure ends according to a criterion on evolution |
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| 65 | !! of temperature |
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| 66 | !! 10. Fluxes at the interfaces |
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| 67 | !! |
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| 68 | !! ** Inputs / Ouputs : (global commons) |
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| 69 | !! surface temperature : t_su_1d |
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| 70 | !! ice/snow temperatures : t_i_1d, t_s_1d |
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| 71 | !! ice salinities : sz_i_1d |
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| 72 | !! number of layers in the ice/snow : nlay_i, nlay_s |
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| 73 | !! total ice/snow thickness : h_i_1d, h_s_1d |
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| 74 | !!------------------------------------------------------------------- |
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[10534] | 75 | INTEGER, INTENT(in) :: k_cnd ! conduction flux (off, on, emulated) |
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[8984] | 76 | ! |
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| 77 | INTEGER :: ji, jk ! spatial loop index |
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| 78 | INTEGER :: jm ! current reference number of equation |
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| 79 | INTEGER :: jm_mint, jm_maxt |
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| 80 | INTEGER :: iconv ! number of iterations in iterative procedure |
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| 81 | INTEGER :: iconv_max = 50 ! max number of iterations in iterative procedure |
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| 82 | ! |
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| 83 | INTEGER, DIMENSION(jpij) :: jm_min ! reference number of top equation |
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| 84 | INTEGER, DIMENSION(jpij) :: jm_max ! reference number of bottom equation |
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[10425] | 85 | |
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| 86 | LOGICAL, DIMENSION(jpij) :: l_T_converged ! true when T converges (per grid point) |
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[13472] | 87 | ! |
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[8984] | 88 | REAL(wp) :: zg1s = 2._wp ! for the tridiagonal system |
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| 89 | REAL(wp) :: zg1 = 2._wp ! |
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| 90 | REAL(wp) :: zgamma = 18009._wp ! for specific heat |
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| 91 | REAL(wp) :: zbeta = 0.117_wp ! for thermal conductivity (could be 0.13) |
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| 92 | REAL(wp) :: zkimin = 0.10_wp ! minimum ice thermal conductivity |
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[14072] | 93 | REAL(wp) :: ztsu_err = 1.e-5_wp ! range around which t_su is considered at 0C |
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| 94 | REAL(wp) :: zdti_bnd = 1.e-4_wp ! maximal authorized error on temperature |
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| 95 | REAL(wp) :: zhs_ssl = 0.03_wp ! surface scattering layer in the snow |
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[13472] | 96 | REAL(wp) :: zhi_ssl = 0.10_wp ! surface scattering layer in the ice |
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| 97 | REAL(wp) :: zh_min = 1.e-3_wp ! minimum ice/snow thickness for conduction |
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[9935] | 98 | REAL(wp) :: ztmelts ! ice melting temperature |
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[14072] | 99 | REAL(wp) :: zdti_max ! current maximal error on temperature |
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[8984] | 100 | REAL(wp) :: zcpi ! Ice specific heat |
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| 101 | REAL(wp) :: zhfx_err, zdq ! diag errors on heat |
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| 102 | ! |
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[13472] | 103 | REAL(wp), DIMENSION(jpij) :: zraext_s ! extinction coefficient of radiation in the snow |
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[8984] | 104 | REAL(wp), DIMENSION(jpij) :: ztsub ! surface temperature at previous iteration |
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| 105 | REAL(wp), DIMENSION(jpij) :: zh_i, z1_h_i ! ice layer thickness |
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| 106 | REAL(wp), DIMENSION(jpij) :: zh_s, z1_h_s ! snow layer thickness |
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| 107 | REAL(wp), DIMENSION(jpij) :: zqns_ice_b ! solar radiation absorbed at the surface |
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| 108 | REAL(wp), DIMENSION(jpij) :: zfnet ! surface flux function |
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| 109 | REAL(wp), DIMENSION(jpij) :: zdqns_ice_b ! derivative of the surface flux function |
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| 110 | ! |
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[14005] | 111 | REAL(wp), DIMENSION(jpij ) :: ztsuold ! Old surface temperature in the ice |
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| 112 | REAL(wp), DIMENSION(jpij,nlay_i) :: ztiold ! Old temperature in the ice |
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| 113 | REAL(wp), DIMENSION(jpij,nlay_s) :: ztsold ! Old temperature in the snow |
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| 114 | REAL(wp), DIMENSION(jpij,nlay_i) :: ztib ! Temporary temperature in the ice to check the convergence |
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| 115 | REAL(wp), DIMENSION(jpij,nlay_s) :: ztsb ! Temporary temperature in the snow to check the convergence |
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| 116 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: ztcond_i ! Ice thermal conductivity |
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| 117 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: ztcond_i_cp ! copy |
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| 118 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: zradtr_i ! Radiation transmitted through the ice |
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| 119 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: zradab_i ! Radiation absorbed in the ice |
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| 120 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: zkappa_i ! Kappa factor in the ice |
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| 121 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: zeta_i ! Eta factor in the ice |
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| 122 | REAL(wp), DIMENSION(jpij,0:nlay_s) :: zradtr_s ! Radiation transmited through the snow |
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| 123 | REAL(wp), DIMENSION(jpij,0:nlay_s) :: zradab_s ! Radiation absorbed in the snow |
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| 124 | REAL(wp), DIMENSION(jpij,0:nlay_s) :: zkappa_s ! Kappa factor in the snow |
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| 125 | REAL(wp), DIMENSION(jpij,0:nlay_s) :: zeta_s ! Eta factor in the snow |
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| 126 | REAL(wp), DIMENSION(jpij) :: zkappa_comb ! Combined snow and ice surface conductivity |
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| 127 | REAL(wp), DIMENSION(jpij) :: zq_ini ! diag errors on heat |
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| 128 | REAL(wp), DIMENSION(jpij) :: zghe ! G(he), th. conduct enhancement factor, mono-cat |
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[14072] | 129 | REAL(wp), DIMENSION(jpij) :: za_s_fra ! ice fraction covered by snow |
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| 130 | REAL(wp), DIMENSION(jpij) :: isnow ! snow presence (1) or not (0) |
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| 131 | REAL(wp), DIMENSION(jpij) :: isnow_comb ! snow presence for met-office |
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[14005] | 132 | REAL(wp), DIMENSION(jpij,nlay_i+nlay_s+1) :: zindterm ! 'Ind'ependent term |
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| 133 | REAL(wp), DIMENSION(jpij,nlay_i+nlay_s+1) :: zindtbis ! Temporary 'ind'ependent term |
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| 134 | REAL(wp), DIMENSION(jpij,nlay_i+nlay_s+1) :: zdiagbis ! Temporary 'dia'gonal term |
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| 135 | REAL(wp), DIMENSION(jpij,nlay_i+nlay_s+1,3) :: ztrid ! Tridiagonal system terms |
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[8984] | 136 | ! |
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| 137 | ! Mono-category |
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| 138 | REAL(wp) :: zepsilon ! determines thres. above which computation of G(h) is done |
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| 139 | REAL(wp) :: zhe ! dummy factor |
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| 140 | REAL(wp) :: zcnd_i ! mean sea ice thermal conductivity |
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[14072] | 141 | !!------------------------------------------------------------------ |
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[8984] | 142 | |
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| 143 | ! --- diag error on heat diffusion - PART 1 --- ! |
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| 144 | DO ji = 1, npti |
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| 145 | zq_ini(ji) = ( SUM( e_i_1d(ji,1:nlay_i) ) * h_i_1d(ji) * r1_nlay_i + & |
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[14072] | 146 | & SUM( e_s_1d(ji,1:nlay_s) ) * h_s_1d(ji) * r1_nlay_s ) |
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[8984] | 147 | END DO |
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| 148 | |
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[13472] | 149 | ! calculate ice fraction covered by snow for radiation |
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| 150 | CALL ice_var_snwfra( h_s_1d(1:npti), za_s_fra(1:npti) ) |
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[14072] | 151 | |
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[8984] | 152 | !------------------ |
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| 153 | ! 1) Initialization |
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| 154 | !------------------ |
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[13472] | 155 | ! |
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| 156 | ! extinction radiation in the snow |
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[14072] | 157 | IF ( nn_qtrice == 0 ) THEN ! constant |
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[13472] | 158 | zraext_s(1:npti) = rn_kappa_s |
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| 159 | ELSEIF( nn_qtrice == 1 ) THEN ! depends on melting/freezing conditions |
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| 160 | WHERE( t_su_1d(1:npti) < rt0 ) ; zraext_s(1:npti) = rn_kappa_sdry ! no surface melting |
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| 161 | ELSEWHERE ; zraext_s(1:npti) = rn_kappa_smlt ! surface melting |
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| 162 | END WHERE |
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| 163 | ENDIF |
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| 164 | ! |
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| 165 | ! thicknesses |
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[8984] | 166 | DO ji = 1, npti |
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[13472] | 167 | ! ice thickness |
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[14072] | 168 | IF( h_i_1d(ji) > 0._wp ) THEN |
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[13472] | 169 | zh_i (ji) = MAX( zh_min , h_i_1d(ji) ) * r1_nlay_i ! set a minimum thickness for conduction |
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| 170 | z1_h_i(ji) = 1._wp / zh_i(ji) ! it must be very small |
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| 171 | ELSE |
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| 172 | zh_i (ji) = 0._wp |
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| 173 | z1_h_i(ji) = 0._wp |
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| 174 | ENDIF |
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| 175 | ! snow thickness |
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| 176 | IF( h_s_1d(ji) > 0._wp ) THEN |
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| 177 | zh_s (ji) = MAX( zh_min , h_s_1d(ji) ) * r1_nlay_s ! set a minimum thickness for conduction |
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| 178 | z1_h_s(ji) = 1._wp / zh_s(ji) ! it must be very small |
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| 179 | isnow (ji) = 1._wp |
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| 180 | ELSE |
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| 181 | zh_s (ji) = 0._wp |
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| 182 | z1_h_s(ji) = 0._wp |
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| 183 | isnow (ji) = 0._wp |
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| 184 | ENDIF |
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| 185 | ! for Met-Office |
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| 186 | IF( h_s_1d(ji) < zh_min ) THEN |
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| 187 | isnow_comb(ji) = h_s_1d(ji) / zh_min |
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| 188 | ELSE |
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| 189 | isnow_comb(ji) = 1._wp |
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| 190 | ENDIF |
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[8984] | 191 | END DO |
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[13472] | 192 | ! clem: we should apply correction on snow thickness to take into account snow fraction |
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| 193 | ! it must be a distribution, so it is a bit complicated |
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[8984] | 194 | ! |
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| 195 | ! Store initial temperatures and non solar heat fluxes |
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[10534] | 196 | IF( k_cnd == np_cnd_OFF .OR. k_cnd == np_cnd_EMU ) THEN |
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[8984] | 197 | ztsub (1:npti) = t_su_1d(1:npti) ! surface temperature at iteration n-1 |
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| 198 | ztsuold (1:npti) = t_su_1d(1:npti) ! surface temperature initial value |
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| 199 | t_su_1d (1:npti) = MIN( t_su_1d(1:npti), rt0 - ztsu_err ) ! required to leave the choice between melting or not |
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[14072] | 200 | zdqns_ice_b(1:npti) = dqns_ice_1d(1:npti) ! derivative of incoming nonsolar flux |
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[8984] | 201 | zqns_ice_b (1:npti) = qns_ice_1d(1:npti) ! store previous qns_ice_1d value |
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| 202 | ! |
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| 203 | ENDIF |
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| 204 | ! |
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| 205 | ztsold (1:npti,:) = t_s_1d(1:npti,:) ! Old snow temperature |
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| 206 | ztiold (1:npti,:) = t_i_1d(1:npti,:) ! Old ice temperature |
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| 207 | |
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| 208 | !------------- |
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| 209 | ! 2) Radiation |
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| 210 | !------------- |
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| 211 | ! --- Transmission/absorption of solar radiation in the ice --- ! |
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[9910] | 212 | zradtr_s(1:npti,0) = qtr_ice_top_1d(1:npti) |
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[8984] | 213 | DO jk = 1, nlay_s |
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| 214 | DO ji = 1, npti |
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| 215 | ! ! radiation transmitted below the layer-th snow layer |
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[13472] | 216 | zradtr_s(ji,jk) = zradtr_s(ji,0) * EXP( - zraext_s(ji) * MAX( 0._wp, zh_s(ji) * REAL(jk) - zhs_ssl ) ) |
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[8984] | 217 | ! ! radiation absorbed by the layer-th snow layer |
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| 218 | zradab_s(ji,jk) = zradtr_s(ji,jk-1) - zradtr_s(ji,jk) |
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| 219 | END DO |
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| 220 | END DO |
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| 221 | ! |
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[13472] | 222 | zradtr_i(1:npti,0) = zradtr_s(1:npti,nlay_s) * za_s_fra(1:npti) + qtr_ice_top_1d(1:npti) * ( 1._wp - za_s_fra(1:npti) ) |
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[14072] | 223 | DO jk = 1, nlay_i |
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[8984] | 224 | DO ji = 1, npti |
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| 225 | ! ! radiation transmitted below the layer-th ice layer |
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[13472] | 226 | zradtr_i(ji,jk) = za_s_fra(ji) * zradtr_s(ji,nlay_s) & ! part covered by snow |
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| 227 | & * EXP( - rn_kappa_i * MAX( 0._wp, zh_i(ji) * REAL(jk) - zh_min ) ) & |
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| 228 | & + ( 1._wp - za_s_fra(ji) ) * qtr_ice_top_1d(ji) & ! part snow free |
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[14072] | 229 | & * EXP( - rn_kappa_i * MAX( 0._wp, zh_i(ji) * REAL(jk) - zhi_ssl ) ) |
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[8984] | 230 | ! ! radiation absorbed by the layer-th ice layer |
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| 231 | zradab_i(ji,jk) = zradtr_i(ji,jk-1) - zradtr_i(ji,jk) |
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| 232 | END DO |
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| 233 | END DO |
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| 234 | ! |
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[9910] | 235 | qtr_ice_bot_1d(1:npti) = zradtr_i(1:npti,nlay_i) ! record radiation transmitted below the ice |
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[8984] | 236 | ! |
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[13472] | 237 | iconv = 0 ! number of iterations |
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[8984] | 238 | ! |
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[10425] | 239 | l_T_converged(:) = .FALSE. |
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| 240 | ! Convergence calculated until all sub-domain grid points have converged |
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| 241 | ! Calculations keep going for all grid points until sub-domain convergence (vectorisation optimisation) |
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| 242 | ! but values are not taken into account (results independant of MPI partitioning) |
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| 243 | ! |
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[10926] | 244 | ! !============================! |
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[10425] | 245 | DO WHILE ( ( .NOT. ALL (l_T_converged(1:npti)) ) .AND. iconv < iconv_max ) ! Iterative procedure begins ! |
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[10926] | 246 | ! !============================! |
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[8984] | 247 | iconv = iconv + 1 |
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| 248 | ! |
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| 249 | ztib(1:npti,:) = t_i_1d(1:npti,:) |
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| 250 | ztsb(1:npti,:) = t_s_1d(1:npti,:) |
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| 251 | ! |
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| 252 | !-------------------------------- |
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| 253 | ! 3) Sea ice thermal conductivity |
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| 254 | !-------------------------------- |
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| 255 | IF( ln_cndi_U64 ) THEN !-- Untersteiner (1964) formula: k = k0 + beta.S/T |
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| 256 | ! |
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| 257 | DO ji = 1, npti |
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[10425] | 258 | ztcond_i_cp(ji,0) = rcnd_i + zbeta * sz_i_1d(ji,1) / MIN( -epsi10, t_i_1d(ji,1) - rt0 ) |
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| 259 | ztcond_i_cp(ji,nlay_i) = rcnd_i + zbeta * sz_i_1d(ji,nlay_i) / MIN( -epsi10, t_bo_1d(ji) - rt0 ) |
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[8984] | 260 | END DO |
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| 261 | DO jk = 1, nlay_i-1 |
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| 262 | DO ji = 1, npti |
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[10425] | 263 | ztcond_i_cp(ji,jk) = rcnd_i + zbeta * 0.5_wp * ( sz_i_1d(ji,jk) + sz_i_1d(ji,jk+1) ) / & |
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[13472] | 264 | & MIN( -epsi10, 0.5_wp * ( t_i_1d(ji,jk) + t_i_1d(ji,jk+1) ) - rt0 ) |
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[8984] | 265 | END DO |
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| 266 | END DO |
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| 267 | ! |
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| 268 | ELSEIF( ln_cndi_P07 ) THEN !-- Pringle et al formula: k = k0 + beta1.S/T - beta2.T |
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| 269 | ! |
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| 270 | DO ji = 1, npti |
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[10425] | 271 | ztcond_i_cp(ji,0) = rcnd_i + 0.09_wp * sz_i_1d(ji,1) / MIN( -epsi10, t_i_1d(ji,1) - rt0 ) & |
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[13472] | 272 | & - 0.011_wp * ( t_i_1d(ji,1) - rt0 ) |
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[10425] | 273 | ztcond_i_cp(ji,nlay_i) = rcnd_i + 0.09_wp * sz_i_1d(ji,nlay_i) / MIN( -epsi10, t_bo_1d(ji) - rt0 ) & |
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[13472] | 274 | & - 0.011_wp * ( t_bo_1d(ji) - rt0 ) |
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[8984] | 275 | END DO |
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| 276 | DO jk = 1, nlay_i-1 |
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| 277 | DO ji = 1, npti |
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[13472] | 278 | ztcond_i_cp(ji,jk) = rcnd_i + 0.09_wp * 0.5_wp * ( sz_i_1d(ji,jk) + sz_i_1d(ji,jk+1) ) / & |
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| 279 | & MIN( -epsi10, 0.5_wp * ( t_i_1d(ji,jk) + t_i_1d(ji,jk+1) ) - rt0 ) & |
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| 280 | & - 0.011_wp * ( 0.5_wp * ( t_i_1d(ji,jk) + t_i_1d(ji,jk+1) ) - rt0 ) |
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[8984] | 281 | END DO |
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| 282 | END DO |
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| 283 | ! |
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| 284 | ENDIF |
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[10425] | 285 | |
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| 286 | ! Variable used after iterations |
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| 287 | ! Value must be frozen after convergence for MPP independance reason |
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| 288 | DO ji = 1, npti |
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| 289 | IF ( .NOT. l_T_converged(ji) ) & |
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[14072] | 290 | ztcond_i(ji,:) = MAX( zkimin, ztcond_i_cp(ji,:) ) |
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[10425] | 291 | END DO |
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[8984] | 292 | ! |
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| 293 | !--- G(he) : enhancement of thermal conductivity in mono-category case |
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| 294 | ! Computation of effective thermal conductivity G(h) |
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| 295 | ! Used in mono-category case only to simulate an ITD implicitly |
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| 296 | ! Fichefet and Morales Maqueda, JGR 1997 |
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| 297 | zghe(1:npti) = 1._wp |
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| 298 | ! |
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[10531] | 299 | IF( ln_virtual_itd ) THEN |
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[8984] | 300 | ! |
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| 301 | zepsilon = 0.1_wp |
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| 302 | DO ji = 1, npti |
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| 303 | zcnd_i = SUM( ztcond_i(ji,:) ) / REAL( nlay_i+1, wp ) ! Mean sea ice thermal conductivity |
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| 304 | zhe = ( rn_cnd_s * h_i_1d(ji) + zcnd_i * h_s_1d(ji) ) / ( rn_cnd_s + zcnd_i ) ! Effective thickness he (zhe) |
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| 305 | IF( zhe >= zepsilon * 0.5_wp * EXP(1._wp) ) & |
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| 306 | & zghe(ji) = MIN( 2._wp, 0.5_wp * ( 1._wp + LOG( 2._wp * zhe / zepsilon ) ) ) ! G(he) |
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| 307 | END DO |
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| 308 | ! |
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[10531] | 309 | ENDIF |
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[8984] | 310 | ! |
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| 311 | !----------------- |
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| 312 | ! 4) kappa factors |
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| 313 | !----------------- |
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| 314 | !--- Snow |
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[10425] | 315 | ! Variable used after iterations |
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| 316 | ! Value must be frozen after convergence for MPP independance reason |
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[8984] | 317 | DO jk = 0, nlay_s-1 |
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| 318 | DO ji = 1, npti |
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[10425] | 319 | IF ( .NOT. l_T_converged(ji) ) & |
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| 320 | zkappa_s(ji,jk) = zghe(ji) * rn_cnd_s * z1_h_s(ji) |
---|
[8984] | 321 | END DO |
---|
| 322 | END DO |
---|
| 323 | DO ji = 1, npti ! Snow-ice interface |
---|
[13472] | 324 | IF ( .NOT. l_T_converged(ji) ) & |
---|
| 325 | zkappa_s(ji,nlay_s) = isnow(ji) * zghe(ji) * rn_cnd_s * ztcond_i(ji,0) & |
---|
| 326 | & / ( 0.5_wp * ( ztcond_i(ji,0) * zh_s(ji) + rn_cnd_s * zh_i(ji) ) ) |
---|
[8984] | 327 | END DO |
---|
| 328 | |
---|
| 329 | !--- Ice |
---|
[10425] | 330 | ! Variable used after iterations |
---|
| 331 | ! Value must be frozen after convergence for MPP independance reason |
---|
[8984] | 332 | DO jk = 0, nlay_i |
---|
| 333 | DO ji = 1, npti |
---|
[10425] | 334 | IF ( .NOT. l_T_converged(ji) ) & |
---|
| 335 | zkappa_i(ji,jk) = zghe(ji) * ztcond_i(ji,jk) * z1_h_i(ji) |
---|
[8984] | 336 | END DO |
---|
| 337 | END DO |
---|
| 338 | DO ji = 1, npti ! Snow-ice interface |
---|
[13472] | 339 | IF ( .NOT. l_T_converged(ji) ) THEN |
---|
| 340 | ! Calculate combined surface snow and ice conductivity to pass through the coupler (met-office) |
---|
| 341 | zkappa_comb(ji) = isnow_comb(ji) * zkappa_s(ji,0) + ( 1._wp - isnow_comb(ji) ) * zkappa_i(ji,0) |
---|
| 342 | ! If there is snow then use the same snow-ice interface conductivity for the top layer of ice |
---|
| 343 | IF( h_s_1d(ji) > 0._wp ) zkappa_i(ji,0) = zkappa_s(ji,nlay_s) |
---|
| 344 | ENDIF |
---|
[8984] | 345 | END DO |
---|
| 346 | ! |
---|
| 347 | !-------------------------------------- |
---|
| 348 | ! 5) Sea ice specific heat, eta factors |
---|
| 349 | !-------------------------------------- |
---|
| 350 | DO jk = 1, nlay_i |
---|
| 351 | DO ji = 1, npti |
---|
[9935] | 352 | zcpi = rcpi + zgamma * sz_i_1d(ji,jk) / MAX( ( t_i_1d(ji,jk) - rt0 ) * ( ztiold(ji,jk) - rt0 ), epsi10 ) |
---|
[13472] | 353 | zeta_i(ji,jk) = rDt_ice * r1_rhoi * z1_h_i(ji) / zcpi |
---|
[8984] | 354 | END DO |
---|
| 355 | END DO |
---|
| 356 | |
---|
| 357 | DO jk = 1, nlay_s |
---|
| 358 | DO ji = 1, npti |
---|
[12489] | 359 | zeta_s(ji,jk) = rDt_ice * r1_rhos * r1_rcpi * z1_h_s(ji) |
---|
[8984] | 360 | END DO |
---|
| 361 | END DO |
---|
| 362 | ! |
---|
| 363 | !----------------------------------------! |
---|
| 364 | ! ! |
---|
[10534] | 365 | ! Conduction flux is off or emulated ! |
---|
[8984] | 366 | ! ! |
---|
| 367 | !----------------------------------------! |
---|
| 368 | ! |
---|
[10534] | 369 | IF( k_cnd == np_cnd_OFF .OR. k_cnd == np_cnd_EMU ) THEN |
---|
[8984] | 370 | ! |
---|
| 371 | ! ==> The original BL99 temperature computation is used |
---|
| 372 | ! (with qsr_ice, qns_ice and dqns_ice as inputs) |
---|
| 373 | ! |
---|
| 374 | !---------------------------- |
---|
| 375 | ! 6) surface flux computation |
---|
| 376 | !---------------------------- |
---|
| 377 | ! update of the non solar flux according to the update in T_su |
---|
| 378 | DO ji = 1, npti |
---|
[10425] | 379 | ! Variable used after iterations |
---|
| 380 | ! Value must be frozen after convergence for MPP independance reason |
---|
| 381 | IF ( .NOT. l_T_converged(ji) ) & |
---|
| 382 | qns_ice_1d(ji) = qns_ice_1d(ji) + dqns_ice_1d(ji) * ( t_su_1d(ji) - ztsub(ji) ) |
---|
[8984] | 383 | END DO |
---|
| 384 | |
---|
| 385 | DO ji = 1, npti |
---|
[9910] | 386 | zfnet(ji) = qsr_ice_1d(ji) - qtr_ice_top_1d(ji) + qns_ice_1d(ji) ! net heat flux = net - transmitted solar + non solar |
---|
[8984] | 387 | END DO |
---|
| 388 | ! |
---|
| 389 | !---------------------------- |
---|
| 390 | ! 7) tridiagonal system terms |
---|
| 391 | !---------------------------- |
---|
| 392 | ! layer denotes the number of the layer in the snow or in the ice |
---|
| 393 | ! jm denotes the reference number of the equation in the tridiagonal |
---|
| 394 | ! system, terms of tridiagonal system are indexed as following : |
---|
| 395 | ! 1 is subdiagonal term, 2 is diagonal and 3 is superdiagonal one |
---|
| 396 | |
---|
| 397 | ! ice interior terms (top equation has the same form as the others) |
---|
| 398 | ztrid (1:npti,:,:) = 0._wp |
---|
| 399 | zindterm(1:npti,:) = 0._wp |
---|
| 400 | zindtbis(1:npti,:) = 0._wp |
---|
| 401 | zdiagbis(1:npti,:) = 0._wp |
---|
| 402 | |
---|
[14072] | 403 | DO jm = nlay_s + 2, nlay_s + nlay_i |
---|
[8984] | 404 | DO ji = 1, npti |
---|
| 405 | jk = jm - nlay_s - 1 |
---|
| 406 | ztrid (ji,jm,1) = - zeta_i(ji,jk) * zkappa_i(ji,jk-1) |
---|
| 407 | ztrid (ji,jm,2) = 1._wp + zeta_i(ji,jk) * ( zkappa_i(ji,jk-1) + zkappa_i(ji,jk) ) |
---|
| 408 | ztrid (ji,jm,3) = - zeta_i(ji,jk) * zkappa_i(ji,jk) |
---|
| 409 | zindterm(ji,jm) = ztiold(ji,jk) + zeta_i(ji,jk) * zradab_i(ji,jk) |
---|
| 410 | END DO |
---|
| 411 | END DO |
---|
| 412 | |
---|
| 413 | jm = nlay_s + nlay_i + 1 |
---|
| 414 | DO ji = 1, npti |
---|
| 415 | ! ice bottom term |
---|
[14072] | 416 | ztrid (ji,jm,1) = - zeta_i(ji,nlay_i) * zkappa_i(ji,nlay_i-1) |
---|
[8984] | 417 | ztrid (ji,jm,2) = 1._wp + zeta_i(ji,nlay_i) * ( zkappa_i(ji,nlay_i-1) + zkappa_i(ji,nlay_i) * zg1 ) |
---|
| 418 | ztrid (ji,jm,3) = 0._wp |
---|
| 419 | zindterm(ji,jm) = ztiold(ji,nlay_i) + zeta_i(ji,nlay_i) * & |
---|
[14072] | 420 | & ( zradab_i(ji,nlay_i) + zkappa_i(ji,nlay_i) * zg1 * t_bo_1d(ji) ) |
---|
[8984] | 421 | END DO |
---|
| 422 | |
---|
| 423 | DO ji = 1, npti |
---|
| 424 | ! !---------------------! |
---|
| 425 | IF( h_s_1d(ji) > 0._wp ) THEN ! snow-covered cells ! |
---|
| 426 | ! !---------------------! |
---|
| 427 | ! snow interior terms (bottom equation has the same form as the others) |
---|
| 428 | DO jm = 3, nlay_s + 1 |
---|
| 429 | jk = jm - 1 |
---|
| 430 | ztrid (ji,jm,1) = - zeta_s(ji,jk) * zkappa_s(ji,jk-1) |
---|
| 431 | ztrid (ji,jm,2) = 1._wp + zeta_s(ji,jk) * ( zkappa_s(ji,jk-1) + zkappa_s(ji,jk) ) |
---|
| 432 | ztrid (ji,jm,3) = - zeta_s(ji,jk) * zkappa_s(ji,jk) |
---|
| 433 | zindterm(ji,jm) = ztsold(ji,jk) + zeta_s(ji,jk) * zradab_s(ji,jk) |
---|
| 434 | END DO |
---|
[14072] | 435 | |
---|
[8984] | 436 | ! case of only one layer in the ice (ice equation is altered) |
---|
| 437 | IF( nlay_i == 1 ) THEN |
---|
| 438 | ztrid (ji,nlay_s+2,3) = 0._wp |
---|
[14072] | 439 | zindterm(ji,nlay_s+2) = zindterm(ji,nlay_s+2) + zeta_i(ji,1) * zkappa_i(ji,1) * t_bo_1d(ji) |
---|
[8984] | 440 | ENDIF |
---|
[14072] | 441 | |
---|
[8984] | 442 | IF( t_su_1d(ji) < rt0 ) THEN !-- case 1 : no surface melting |
---|
[14072] | 443 | |
---|
[8984] | 444 | jm_min(ji) = 1 |
---|
| 445 | jm_max(ji) = nlay_i + nlay_s + 1 |
---|
[14072] | 446 | |
---|
[8984] | 447 | ! surface equation |
---|
| 448 | ztrid (ji,1,1) = 0._wp |
---|
| 449 | ztrid (ji,1,2) = zdqns_ice_b(ji) - zg1s * zkappa_s(ji,0) |
---|
| 450 | ztrid (ji,1,3) = zg1s * zkappa_s(ji,0) |
---|
| 451 | zindterm(ji,1) = zdqns_ice_b(ji) * t_su_1d(ji) - zfnet(ji) |
---|
[14072] | 452 | |
---|
[8984] | 453 | ! first layer of snow equation |
---|
| 454 | ztrid (ji,2,1) = - zeta_s(ji,1) * zkappa_s(ji,0) * zg1s |
---|
| 455 | ztrid (ji,2,2) = 1._wp + zeta_s(ji,1) * ( zkappa_s(ji,1) + zkappa_s(ji,0) * zg1s ) |
---|
| 456 | ztrid (ji,2,3) = - zeta_s(ji,1) * zkappa_s(ji,1) |
---|
| 457 | zindterm(ji,2) = ztsold(ji,1) + zeta_s(ji,1) * zradab_s(ji,1) |
---|
[14072] | 458 | |
---|
[8984] | 459 | ELSE !-- case 2 : surface is melting |
---|
| 460 | ! |
---|
| 461 | jm_min(ji) = 2 |
---|
| 462 | jm_max(ji) = nlay_i + nlay_s + 1 |
---|
[14072] | 463 | |
---|
[8984] | 464 | ! first layer of snow equation |
---|
| 465 | ztrid (ji,2,1) = 0._wp |
---|
| 466 | ztrid (ji,2,2) = 1._wp + zeta_s(ji,1) * ( zkappa_s(ji,1) + zkappa_s(ji,0) * zg1s ) |
---|
[14072] | 467 | ztrid (ji,2,3) = - zeta_s(ji,1) * zkappa_s(ji,1) |
---|
| 468 | zindterm(ji,2) = ztsold(ji,1) + zeta_s(ji,1) * ( zradab_s(ji,1) + zkappa_s(ji,0) * zg1s * t_su_1d(ji) ) |
---|
[8984] | 469 | ENDIF |
---|
| 470 | ! !---------------------! |
---|
| 471 | ELSE ! cells without snow ! |
---|
| 472 | ! !---------------------! |
---|
| 473 | ! |
---|
| 474 | IF( t_su_1d(ji) < rt0 ) THEN !-- case 1 : no surface melting |
---|
| 475 | ! |
---|
| 476 | jm_min(ji) = nlay_s + 1 |
---|
| 477 | jm_max(ji) = nlay_i + nlay_s + 1 |
---|
[14072] | 478 | |
---|
| 479 | ! surface equation |
---|
[8984] | 480 | ztrid (ji,jm_min(ji),1) = 0._wp |
---|
[14072] | 481 | ztrid (ji,jm_min(ji),2) = zdqns_ice_b(ji) - zkappa_i(ji,0) * zg1 |
---|
[8984] | 482 | ztrid (ji,jm_min(ji),3) = zkappa_i(ji,0) * zg1 |
---|
| 483 | zindterm(ji,jm_min(ji)) = zdqns_ice_b(ji) * t_su_1d(ji) - zfnet(ji) |
---|
[14072] | 484 | |
---|
[8984] | 485 | ! first layer of ice equation |
---|
| 486 | ztrid (ji,jm_min(ji)+1,1) = - zeta_i(ji,1) * zkappa_i(ji,0) * zg1 |
---|
| 487 | ztrid (ji,jm_min(ji)+1,2) = 1._wp + zeta_i(ji,1) * ( zkappa_i(ji,1) + zkappa_i(ji,0) * zg1 ) |
---|
[14072] | 488 | ztrid (ji,jm_min(ji)+1,3) = - zeta_i(ji,1) * zkappa_i(ji,1) |
---|
| 489 | zindterm(ji,jm_min(ji)+1) = ztiold(ji,1) + zeta_i(ji,1) * zradab_i(ji,1) |
---|
| 490 | |
---|
[8984] | 491 | ! case of only one layer in the ice (surface & ice equations are altered) |
---|
| 492 | IF( nlay_i == 1 ) THEN |
---|
| 493 | ztrid (ji,jm_min(ji),1) = 0._wp |
---|
| 494 | ztrid (ji,jm_min(ji),2) = zdqns_ice_b(ji) - zkappa_i(ji,0) * 2._wp |
---|
| 495 | ztrid (ji,jm_min(ji),3) = zkappa_i(ji,0) * 2._wp |
---|
| 496 | ztrid (ji,jm_min(ji)+1,1) = - zeta_i(ji,1) * zkappa_i(ji,0) * 2._wp |
---|
| 497 | ztrid (ji,jm_min(ji)+1,2) = 1._wp + zeta_i(ji,1) * ( zkappa_i(ji,0) * 2._wp + zkappa_i(ji,1) ) |
---|
| 498 | ztrid (ji,jm_min(ji)+1,3) = 0._wp |
---|
| 499 | zindterm(ji,jm_min(ji)+1) = ztiold(ji,1) + zeta_i(ji,1) * (zradab_i(ji,1) + zkappa_i(ji,1) * t_bo_1d(ji)) |
---|
| 500 | ENDIF |
---|
[14072] | 501 | |
---|
[8984] | 502 | ELSE !-- case 2 : surface is melting |
---|
[14072] | 503 | |
---|
[8984] | 504 | jm_min(ji) = nlay_s + 2 |
---|
| 505 | jm_max(ji) = nlay_i + nlay_s + 1 |
---|
[14072] | 506 | |
---|
[8984] | 507 | ! first layer of ice equation |
---|
| 508 | ztrid (ji,jm_min(ji),1) = 0._wp |
---|
[14072] | 509 | ztrid (ji,jm_min(ji),2) = 1._wp + zeta_i(ji,1) * ( zkappa_i(ji,1) + zkappa_i(ji,0) * zg1 ) |
---|
[8984] | 510 | ztrid (ji,jm_min(ji),3) = - zeta_i(ji,1) * zkappa_i(ji,1) |
---|
[14072] | 511 | zindterm(ji,jm_min(ji)) = ztiold(ji,1) + zeta_i(ji,1) * (zradab_i(ji,1) + zkappa_i(ji,0) * zg1 * t_su_1d(ji)) |
---|
| 512 | |
---|
[8984] | 513 | ! case of only one layer in the ice (surface & ice equations are altered) |
---|
| 514 | IF( nlay_i == 1 ) THEN |
---|
| 515 | ztrid (ji,jm_min(ji),1) = 0._wp |
---|
| 516 | ztrid (ji,jm_min(ji),2) = 1._wp + zeta_i(ji,1) * ( zkappa_i(ji,0) * 2._wp + zkappa_i(ji,1) ) |
---|
| 517 | ztrid (ji,jm_min(ji),3) = 0._wp |
---|
| 518 | zindterm(ji,jm_min(ji)) = ztiold(ji,1) + zeta_i(ji,1) * ( zradab_i(ji,1) + zkappa_i(ji,1) * t_bo_1d(ji) ) & |
---|
| 519 | & + t_su_1d(ji) * zeta_i(ji,1) * zkappa_i(ji,0) * 2._wp |
---|
| 520 | ENDIF |
---|
[14072] | 521 | |
---|
[8984] | 522 | ENDIF |
---|
| 523 | ENDIF |
---|
| 524 | ! |
---|
| 525 | zindtbis(ji,jm_min(ji)) = zindterm(ji,jm_min(ji)) |
---|
| 526 | zdiagbis(ji,jm_min(ji)) = ztrid (ji,jm_min(ji),2) |
---|
| 527 | ! |
---|
| 528 | END DO |
---|
| 529 | ! |
---|
| 530 | !------------------------------ |
---|
| 531 | ! 8) tridiagonal system solving |
---|
| 532 | !------------------------------ |
---|
| 533 | ! Solve the tridiagonal system with Gauss elimination method. |
---|
| 534 | ! Thomas algorithm, from Computational fluid Dynamics, J.D. ANDERSON, McGraw-Hill 1984 |
---|
[14005] | 535 | !!$ jm_maxt = 0 |
---|
| 536 | !!$ jm_mint = nlay_i+5 |
---|
| 537 | !!$ DO ji = 1, npti |
---|
| 538 | !!$ jm_mint = MIN(jm_min(ji),jm_mint) |
---|
| 539 | !!$ jm_maxt = MAX(jm_max(ji),jm_maxt) |
---|
| 540 | !!$ END DO |
---|
| 541 | !!$ !!clem SNWLAY => check why LIM1D does not get this loop. Is nlay_i+5 correct? |
---|
[14072] | 542 | !!$ |
---|
[14005] | 543 | !!$ DO jk = jm_mint+1, jm_maxt |
---|
| 544 | !!$ DO ji = 1, npti |
---|
| 545 | !!$ jm = MIN(MAX(jm_min(ji)+1,jk),jm_max(ji)) |
---|
| 546 | !!$ zdiagbis(ji,jm) = ztrid (ji,jm,2) - ztrid(ji,jm,1) * ztrid (ji,jm-1,3) / zdiagbis(ji,jm-1) |
---|
| 547 | !!$ zindtbis(ji,jm) = zindterm(ji,jm ) - ztrid(ji,jm,1) * zindtbis(ji,jm-1 ) / zdiagbis(ji,jm-1) |
---|
| 548 | !!$ END DO |
---|
| 549 | !!$ END DO |
---|
| 550 | ! clem: maybe one should find a way to reverse this loop for mpi performance |
---|
[8984] | 551 | DO ji = 1, npti |
---|
[14005] | 552 | jm_mint = jm_min(ji) |
---|
| 553 | jm_maxt = jm_max(ji) |
---|
| 554 | DO jm = jm_mint+1, jm_maxt |
---|
[8984] | 555 | zdiagbis(ji,jm) = ztrid (ji,jm,2) - ztrid(ji,jm,1) * ztrid (ji,jm-1,3) / zdiagbis(ji,jm-1) |
---|
| 556 | zindtbis(ji,jm) = zindterm(ji,jm ) - ztrid(ji,jm,1) * zindtbis(ji,jm-1 ) / zdiagbis(ji,jm-1) |
---|
| 557 | END DO |
---|
| 558 | END DO |
---|
| 559 | |
---|
| 560 | ! ice temperatures |
---|
| 561 | DO ji = 1, npti |
---|
[10425] | 562 | ! Variable used after iterations |
---|
| 563 | ! Value must be frozen after convergence for MPP independance reason |
---|
| 564 | IF ( .NOT. l_T_converged(ji) ) & |
---|
| 565 | t_i_1d(ji,nlay_i) = zindtbis(ji,jm_max(ji)) / zdiagbis(ji,jm_max(ji)) |
---|
[8984] | 566 | END DO |
---|
| 567 | |
---|
| 568 | DO jm = nlay_i + nlay_s, nlay_s + 2, -1 |
---|
| 569 | DO ji = 1, npti |
---|
| 570 | jk = jm - nlay_s - 1 |
---|
[10425] | 571 | IF ( .NOT. l_T_converged(ji) ) & |
---|
| 572 | t_i_1d(ji,jk) = ( zindtbis(ji,jm) - ztrid(ji,jm,3) * t_i_1d(ji,jk+1) ) / zdiagbis(ji,jm) |
---|
[8984] | 573 | END DO |
---|
| 574 | END DO |
---|
| 575 | |
---|
[14072] | 576 | ! snow temperatures |
---|
[8984] | 577 | DO ji = 1, npti |
---|
[10425] | 578 | ! Variables used after iterations |
---|
| 579 | ! Value must be frozen after convergence for MPP independance reason |
---|
[14005] | 580 | IF ( .NOT. l_T_converged(ji) .AND. h_s_1d(ji) > 0._wp ) & |
---|
| 581 | & t_s_1d(ji,nlay_s) = ( zindtbis(ji,nlay_s+1) - ztrid(ji,nlay_s+1,3) * t_i_1d(ji,1) ) / zdiagbis(ji,nlay_s+1) |
---|
| 582 | END DO |
---|
| 583 | !!clem SNWLAY |
---|
| 584 | DO jm = nlay_s, 2, -1 |
---|
| 585 | DO ji = 1, npti |
---|
| 586 | jk = jm - 1 |
---|
| 587 | IF ( .NOT. l_T_converged(ji) .AND. h_s_1d(ji) > 0._wp ) & |
---|
| 588 | & t_s_1d(ji,jk) = ( zindtbis(ji,jm) - ztrid(ji,jm,3) * t_s_1d(ji,jk+1) ) / zdiagbis(ji,jm) |
---|
| 589 | END DO |
---|
| 590 | END DO |
---|
[14072] | 591 | |
---|
[14005] | 592 | ! surface temperature |
---|
| 593 | DO ji = 1, npti |
---|
| 594 | IF( .NOT. l_T_converged(ji) ) THEN |
---|
[10425] | 595 | ztsub(ji) = t_su_1d(ji) |
---|
| 596 | IF( t_su_1d(ji) < rt0 ) THEN |
---|
[14005] | 597 | t_su_1d(ji) = ( zindtbis(ji,jm_min(ji)) - ztrid(ji,jm_min(ji),3) * & |
---|
| 598 | & ( isnow(ji) * t_s_1d(ji,1) + ( 1._wp - isnow(ji) ) * t_i_1d(ji,1) ) ) / zdiagbis(ji,jm_min(ji)) |
---|
[10425] | 599 | ENDIF |
---|
[8984] | 600 | ENDIF |
---|
| 601 | END DO |
---|
| 602 | ! |
---|
| 603 | !-------------------------------------------------------------- |
---|
| 604 | ! 9) Has the scheme converged?, end of the iterative procedure |
---|
| 605 | !-------------------------------------------------------------- |
---|
| 606 | ! check that nowhere it has started to melt |
---|
| 607 | ! zdti_max is a measure of error, it has to be under zdti_bnd |
---|
[10425] | 608 | |
---|
[8984] | 609 | DO ji = 1, npti |
---|
| 610 | |
---|
[10425] | 611 | zdti_max = 0._wp |
---|
[8984] | 612 | |
---|
[10425] | 613 | IF ( .NOT. l_T_converged(ji) ) THEN |
---|
[13472] | 614 | |
---|
[10425] | 615 | t_su_1d(ji) = MAX( MIN( t_su_1d(ji) , rt0 ) , rt0 - 100._wp ) |
---|
| 616 | zdti_max = MAX( zdti_max, ABS( t_su_1d(ji) - ztsub(ji) ) ) |
---|
| 617 | |
---|
[13472] | 618 | IF( h_s_1d(ji) > 0._wp ) THEN |
---|
| 619 | DO jk = 1, nlay_s |
---|
| 620 | t_s_1d(ji,jk) = MAX( MIN( t_s_1d(ji,jk), rt0 ), rt0 - 100._wp ) |
---|
| 621 | zdti_max = MAX ( zdti_max , ABS( t_s_1d(ji,jk) - ztsb(ji,jk) ) ) |
---|
| 622 | END DO |
---|
| 623 | ENDIF |
---|
[10425] | 624 | |
---|
| 625 | DO jk = 1, nlay_i |
---|
| 626 | ztmelts = -rTmlt * sz_i_1d(ji,jk) + rt0 |
---|
| 627 | t_i_1d(ji,jk) = MAX( MIN( t_i_1d(ji,jk), ztmelts ), rt0 - 100._wp ) |
---|
| 628 | zdti_max = MAX( zdti_max, ABS( t_i_1d(ji,jk) - ztib(ji,jk) ) ) |
---|
| 629 | END DO |
---|
[14072] | 630 | |
---|
[13472] | 631 | ! convergence test |
---|
| 632 | IF( ln_zdf_chkcvg ) THEN |
---|
| 633 | tice_cvgerr_1d(ji) = zdti_max |
---|
| 634 | tice_cvgstp_1d(ji) = REAL(iconv) |
---|
| 635 | ENDIF |
---|
[10425] | 636 | |
---|
[13472] | 637 | IF( zdti_max < zdti_bnd ) l_T_converged(ji) = .TRUE. |
---|
[10425] | 638 | |
---|
| 639 | ENDIF |
---|
| 640 | |
---|
[8984] | 641 | END DO |
---|
| 642 | |
---|
| 643 | !----------------------------------------! |
---|
| 644 | ! ! |
---|
[10534] | 645 | ! Conduction flux is on ! |
---|
[8984] | 646 | ! ! |
---|
| 647 | !----------------------------------------! |
---|
| 648 | ! |
---|
[10534] | 649 | ELSEIF( k_cnd == np_cnd_ON ) THEN |
---|
[8984] | 650 | ! |
---|
| 651 | ! ==> we use a modified BL99 solver with conduction flux (qcn_ice) as forcing term |
---|
| 652 | ! |
---|
| 653 | !---------------------------- |
---|
| 654 | ! 7) tridiagonal system terms |
---|
| 655 | !---------------------------- |
---|
| 656 | ! layer denotes the number of the layer in the snow or in the ice |
---|
| 657 | ! jm denotes the reference number of the equation in the tridiagonal |
---|
| 658 | ! system, terms of tridiagonal system are indexed as following : |
---|
| 659 | ! 1 is subdiagonal term, 2 is diagonal and 3 is superdiagonal one |
---|
| 660 | |
---|
| 661 | ! ice interior terms (top equation has the same form as the others) |
---|
| 662 | ztrid (1:npti,:,:) = 0._wp |
---|
| 663 | zindterm(1:npti,:) = 0._wp |
---|
| 664 | zindtbis(1:npti,:) = 0._wp |
---|
| 665 | zdiagbis(1:npti,:) = 0._wp |
---|
| 666 | |
---|
[14072] | 667 | DO jm = nlay_s + 2, nlay_s + nlay_i |
---|
[8984] | 668 | DO ji = 1, npti |
---|
| 669 | jk = jm - nlay_s - 1 |
---|
| 670 | ztrid (ji,jm,1) = - zeta_i(ji,jk) * zkappa_i(ji,jk-1) |
---|
| 671 | ztrid (ji,jm,2) = 1._wp + zeta_i(ji,jk) * ( zkappa_i(ji,jk-1) + zkappa_i(ji,jk) ) |
---|
| 672 | ztrid (ji,jm,3) = - zeta_i(ji,jk) * zkappa_i(ji,jk) |
---|
| 673 | zindterm(ji,jm) = ztiold(ji,jk) + zeta_i(ji,jk) * zradab_i(ji,jk) |
---|
| 674 | END DO |
---|
| 675 | ENDDO |
---|
| 676 | |
---|
| 677 | jm = nlay_s + nlay_i + 1 |
---|
| 678 | DO ji = 1, npti |
---|
| 679 | ! ice bottom term |
---|
[14072] | 680 | ztrid (ji,jm,1) = - zeta_i(ji,nlay_i) * zkappa_i(ji,nlay_i-1) |
---|
[8984] | 681 | ztrid (ji,jm,2) = 1._wp + zeta_i(ji,nlay_i) * ( zkappa_i(ji,nlay_i-1) + zkappa_i(ji,nlay_i) * zg1 ) |
---|
| 682 | ztrid (ji,jm,3) = 0._wp |
---|
| 683 | zindterm(ji,jm) = ztiold(ji,nlay_i) + zeta_i(ji,nlay_i) * & |
---|
[14072] | 684 | & ( zradab_i(ji,nlay_i) + zkappa_i(ji,nlay_i) * zg1 * t_bo_1d(ji) ) |
---|
[8984] | 685 | ENDDO |
---|
| 686 | |
---|
| 687 | DO ji = 1, npti |
---|
| 688 | ! !---------------------! |
---|
| 689 | IF( h_s_1d(ji) > 0._wp ) THEN ! snow-covered cells ! |
---|
| 690 | ! !---------------------! |
---|
| 691 | ! snow interior terms (bottom equation has the same form as the others) |
---|
| 692 | DO jm = 3, nlay_s + 1 |
---|
| 693 | jk = jm - 1 |
---|
| 694 | ztrid (ji,jm,1) = - zeta_s(ji,jk) * zkappa_s(ji,jk-1) |
---|
| 695 | ztrid (ji,jm,2) = 1._wp + zeta_s(ji,jk) * ( zkappa_s(ji,jk-1) + zkappa_s(ji,jk) ) |
---|
| 696 | ztrid (ji,jm,3) = - zeta_s(ji,jk) * zkappa_s(ji,jk) |
---|
| 697 | zindterm(ji,jm) = ztsold(ji,jk) + zeta_s(ji,jk) * zradab_s(ji,jk) |
---|
| 698 | END DO |
---|
[14072] | 699 | |
---|
[8984] | 700 | ! case of only one layer in the ice (ice equation is altered) |
---|
| 701 | IF ( nlay_i == 1 ) THEN |
---|
| 702 | ztrid (ji,nlay_s+2,3) = 0._wp |
---|
[14072] | 703 | zindterm(ji,nlay_s+2) = zindterm(ji,nlay_s+2) + zeta_i(ji,1) * zkappa_i(ji,1) * t_bo_1d(ji) |
---|
[8984] | 704 | ENDIF |
---|
[14072] | 705 | |
---|
[8984] | 706 | jm_min(ji) = 2 |
---|
| 707 | jm_max(ji) = nlay_i + nlay_s + 1 |
---|
[14072] | 708 | |
---|
[8984] | 709 | ! first layer of snow equation |
---|
| 710 | ztrid (ji,2,1) = 0._wp |
---|
| 711 | ztrid (ji,2,2) = 1._wp + zeta_s(ji,1) * zkappa_s(ji,1) |
---|
[14072] | 712 | ztrid (ji,2,3) = - zeta_s(ji,1) * zkappa_s(ji,1) |
---|
| 713 | zindterm(ji,2) = ztsold(ji,1) + zeta_s(ji,1) * ( zradab_s(ji,1) + qcn_ice_1d(ji) ) |
---|
| 714 | |
---|
[8984] | 715 | ! !---------------------! |
---|
| 716 | ELSE ! cells without snow ! |
---|
| 717 | ! !---------------------! |
---|
| 718 | jm_min(ji) = nlay_s + 2 |
---|
| 719 | jm_max(ji) = nlay_i + nlay_s + 1 |
---|
[14072] | 720 | |
---|
[8984] | 721 | ! first layer of ice equation |
---|
| 722 | ztrid (ji,jm_min(ji),1) = 0._wp |
---|
[14072] | 723 | ztrid (ji,jm_min(ji),2) = 1._wp + zeta_i(ji,1) * zkappa_i(ji,1) |
---|
[8984] | 724 | ztrid (ji,jm_min(ji),3) = - zeta_i(ji,1) * zkappa_i(ji,1) |
---|
| 725 | zindterm(ji,jm_min(ji)) = ztiold(ji,1) + zeta_i(ji,1) * ( zradab_i(ji,1) + qcn_ice_1d(ji) ) |
---|
[14072] | 726 | |
---|
[8984] | 727 | ! case of only one layer in the ice (surface & ice equations are altered) |
---|
| 728 | IF( nlay_i == 1 ) THEN |
---|
| 729 | ztrid (ji,jm_min(ji),1) = 0._wp |
---|
| 730 | ztrid (ji,jm_min(ji),2) = 1._wp + zeta_i(ji,1) * zkappa_i(ji,1) |
---|
| 731 | ztrid (ji,jm_min(ji),3) = 0._wp |
---|
| 732 | zindterm(ji,jm_min(ji)) = ztiold(ji,1) + zeta_i(ji,1) * & |
---|
| 733 | & ( zradab_i(ji,1) + zkappa_i(ji,1) * t_bo_1d(ji) + qcn_ice_1d(ji) ) |
---|
| 734 | ENDIF |
---|
[14072] | 735 | |
---|
[8984] | 736 | ENDIF |
---|
| 737 | ! |
---|
| 738 | zindtbis(ji,jm_min(ji)) = zindterm(ji,jm_min(ji)) |
---|
| 739 | zdiagbis(ji,jm_min(ji)) = ztrid (ji,jm_min(ji),2) |
---|
| 740 | ! |
---|
| 741 | END DO |
---|
| 742 | ! |
---|
| 743 | !------------------------------ |
---|
| 744 | ! 8) tridiagonal system solving |
---|
| 745 | !------------------------------ |
---|
| 746 | ! Solve the tridiagonal system with Gauss elimination method. |
---|
| 747 | ! Thomas algorithm, from Computational fluid Dynamics, J.D. ANDERSON, McGraw-Hill 1984 |
---|
[14005] | 748 | !!$ jm_maxt = 0 |
---|
| 749 | !!$ jm_mint = nlay_i+5 |
---|
| 750 | !!$ DO ji = 1, npti |
---|
| 751 | !!$ jm_mint = MIN(jm_min(ji),jm_mint) |
---|
| 752 | !!$ jm_maxt = MAX(jm_max(ji),jm_maxt) |
---|
| 753 | !!$ END DO |
---|
[14072] | 754 | !!$ |
---|
[14005] | 755 | !!$ DO jk = jm_mint+1, jm_maxt |
---|
| 756 | !!$ DO ji = 1, npti |
---|
| 757 | !!$ jm = MIN(MAX(jm_min(ji)+1,jk),jm_max(ji)) |
---|
| 758 | !!$ zdiagbis(ji,jm) = ztrid (ji,jm,2) - ztrid(ji,jm,1) * ztrid (ji,jm-1,3) / zdiagbis(ji,jm-1) |
---|
| 759 | !!$ zindtbis(ji,jm) = zindterm(ji,jm) - ztrid(ji,jm,1) * zindtbis(ji,jm-1) / zdiagbis(ji,jm-1) |
---|
| 760 | !!$ END DO |
---|
| 761 | !!$ END DO |
---|
| 762 | ! clem: maybe one should find a way to reverse this loop for mpi performance |
---|
[8984] | 763 | DO ji = 1, npti |
---|
[14005] | 764 | jm_mint = jm_min(ji) |
---|
| 765 | jm_maxt = jm_max(ji) |
---|
| 766 | DO jm = jm_mint+1, jm_maxt |
---|
[8984] | 767 | zdiagbis(ji,jm) = ztrid (ji,jm,2) - ztrid(ji,jm,1) * ztrid (ji,jm-1,3) / zdiagbis(ji,jm-1) |
---|
[14005] | 768 | zindtbis(ji,jm) = zindterm(ji,jm ) - ztrid(ji,jm,1) * zindtbis(ji,jm-1 ) / zdiagbis(ji,jm-1) |
---|
[8984] | 769 | END DO |
---|
| 770 | END DO |
---|
[14005] | 771 | |
---|
[8984] | 772 | ! ice temperatures |
---|
[10425] | 773 | DO ji = 1, npti |
---|
| 774 | ! Variable used after iterations |
---|
| 775 | ! Value must be frozen after convergence for MPP independance reason |
---|
| 776 | IF ( .NOT. l_T_converged(ji) ) & |
---|
| 777 | t_i_1d(ji,nlay_i) = zindtbis(ji,jm_max(ji)) / zdiagbis(ji,jm_max(ji)) |
---|
[8984] | 778 | END DO |
---|
| 779 | |
---|
| 780 | DO jm = nlay_i + nlay_s, nlay_s + 2, -1 |
---|
| 781 | DO ji = 1, npti |
---|
[10425] | 782 | IF ( .NOT. l_T_converged(ji) ) THEN |
---|
| 783 | jk = jm - nlay_s - 1 |
---|
| 784 | t_i_1d(ji,jk) = ( zindtbis(ji,jm) - ztrid(ji,jm,3) * t_i_1d(ji,jk+1) ) / zdiagbis(ji,jm) |
---|
| 785 | ENDIF |
---|
[8984] | 786 | END DO |
---|
| 787 | END DO |
---|
[14072] | 788 | |
---|
| 789 | ! snow temperatures |
---|
[8984] | 790 | DO ji = 1, npti |
---|
[14005] | 791 | ! Variables used after iterations |
---|
[10425] | 792 | ! Value must be frozen after convergence for MPP independance reason |
---|
[14005] | 793 | IF ( .NOT. l_T_converged(ji) .AND. h_s_1d(ji) > 0._wp ) & |
---|
| 794 | & t_s_1d(ji,nlay_s) = ( zindtbis(ji,nlay_s+1) - ztrid(ji,nlay_s+1,3) * t_i_1d(ji,1) ) / zdiagbis(ji,nlay_s+1) |
---|
[8984] | 795 | END DO |
---|
[14005] | 796 | !!clem SNWLAY |
---|
| 797 | DO jm = nlay_s, 2, -1 |
---|
| 798 | DO ji = 1, npti |
---|
| 799 | jk = jm - 1 |
---|
| 800 | IF ( .NOT. l_T_converged(ji) .AND. h_s_1d(ji) > 0._wp ) & |
---|
| 801 | & t_s_1d(ji,jk) = ( zindtbis(ji,jm) - ztrid(ji,jm,3) * t_s_1d(ji,jk+1) ) / zdiagbis(ji,jm) |
---|
| 802 | END DO |
---|
| 803 | END DO |
---|
[8984] | 804 | ! |
---|
| 805 | !-------------------------------------------------------------- |
---|
| 806 | ! 9) Has the scheme converged?, end of the iterative procedure |
---|
| 807 | !-------------------------------------------------------------- |
---|
| 808 | ! check that nowhere it has started to melt |
---|
| 809 | ! zdti_max is a measure of error, it has to be under zdti_bnd |
---|
| 810 | |
---|
[10425] | 811 | DO ji = 1, npti |
---|
| 812 | |
---|
| 813 | zdti_max = 0._wp |
---|
| 814 | |
---|
| 815 | IF ( .NOT. l_T_converged(ji) ) THEN |
---|
[13472] | 816 | |
---|
| 817 | IF( h_s_1d(ji) > 0._wp ) THEN |
---|
| 818 | DO jk = 1, nlay_s |
---|
| 819 | t_s_1d(ji,jk) = MAX( MIN( t_s_1d(ji,jk), rt0 ), rt0 - 100._wp ) |
---|
| 820 | zdti_max = MAX ( zdti_max , ABS( t_s_1d(ji,jk) - ztsb(ji,jk) ) ) |
---|
| 821 | END DO |
---|
| 822 | ENDIF |
---|
| 823 | |
---|
[10924] | 824 | DO jk = 1, nlay_i |
---|
[14072] | 825 | ztmelts = -rTmlt * sz_i_1d(ji,jk) + rt0 |
---|
[10425] | 826 | t_i_1d(ji,jk) = MAX( MIN( t_i_1d(ji,jk), ztmelts ), rt0 - 100._wp ) |
---|
| 827 | zdti_max = MAX ( zdti_max, ABS( t_i_1d(ji,jk) - ztib(ji,jk) ) ) |
---|
| 828 | END DO |
---|
| 829 | |
---|
[13472] | 830 | ! convergence test |
---|
| 831 | IF( ln_zdf_chkcvg ) THEN |
---|
| 832 | tice_cvgerr_1d(ji) = zdti_max |
---|
| 833 | tice_cvgstp_1d(ji) = REAL(iconv) |
---|
| 834 | ENDIF |
---|
[10425] | 835 | |
---|
[13472] | 836 | IF( zdti_max < zdti_bnd ) l_T_converged(ji) = .TRUE. |
---|
| 837 | |
---|
[10425] | 838 | ENDIF |
---|
| 839 | |
---|
[8984] | 840 | END DO |
---|
| 841 | |
---|
[10534] | 842 | ENDIF ! k_cnd |
---|
[13472] | 843 | |
---|
[8984] | 844 | END DO ! End of the do while iterative procedure |
---|
| 845 | ! |
---|
| 846 | !----------------------------- |
---|
| 847 | ! 10) Fluxes at the interfaces |
---|
| 848 | !----------------------------- |
---|
| 849 | ! |
---|
[9916] | 850 | ! --- calculate conduction fluxes (positive downward) |
---|
[12396] | 851 | ! bottom ice conduction flux |
---|
[8984] | 852 | DO ji = 1, npti |
---|
[13472] | 853 | qcn_ice_bot_1d(ji) = - zkappa_i(ji,nlay_i) * zg1 * ( t_bo_1d(ji ) - t_i_1d (ji,nlay_i) ) |
---|
[8984] | 854 | END DO |
---|
[12396] | 855 | ! surface ice conduction flux |
---|
[10534] | 856 | IF( k_cnd == np_cnd_OFF .OR. k_cnd == np_cnd_EMU ) THEN |
---|
[8984] | 857 | ! |
---|
| 858 | DO ji = 1, npti |
---|
[13472] | 859 | qcn_ice_top_1d(ji) = - isnow(ji) * zkappa_s(ji,0) * zg1s * ( t_s_1d(ji,1) - t_su_1d(ji) ) & |
---|
| 860 | & - ( 1._wp - isnow(ji) ) * zkappa_i(ji,0) * zg1 * ( t_i_1d(ji,1) - t_su_1d(ji) ) |
---|
[8984] | 861 | END DO |
---|
| 862 | ! |
---|
[10534] | 863 | ELSEIF( k_cnd == np_cnd_ON ) THEN |
---|
[8984] | 864 | ! |
---|
| 865 | DO ji = 1, npti |
---|
[12396] | 866 | qcn_ice_top_1d(ji) = qcn_ice_1d(ji) |
---|
[8984] | 867 | END DO |
---|
| 868 | ! |
---|
| 869 | ENDIF |
---|
[12396] | 870 | ! surface ice temperature |
---|
| 871 | IF( k_cnd == np_cnd_ON .AND. ln_cndemulate ) THEN |
---|
| 872 | ! |
---|
| 873 | DO ji = 1, npti |
---|
[13472] | 874 | t_su_1d(ji) = ( qcn_ice_top_1d(ji) + isnow(ji) * zkappa_s(ji,0) * zg1s * t_s_1d(ji,1) + & |
---|
| 875 | & ( 1._wp - isnow(ji) ) * zkappa_i(ji,0) * zg1 * t_i_1d(ji,1) ) & |
---|
| 876 | & / MAX( epsi10, isnow(ji) * zkappa_s(ji,0) * zg1s + ( 1._wp - isnow(ji) ) * zkappa_i(ji,0) * zg1 ) |
---|
[12396] | 877 | t_su_1d(ji) = MAX( MIN( t_su_1d(ji), rt0 ), rt0 - 100._wp ) ! cap t_su |
---|
| 878 | END DO |
---|
| 879 | ! |
---|
| 880 | ENDIF |
---|
[8984] | 881 | ! |
---|
[12396] | 882 | ! --- Diagnose the heat loss due to changing non-solar / conduction flux --- ! |
---|
| 883 | ! |
---|
| 884 | IF( k_cnd == np_cnd_OFF .OR. k_cnd == np_cnd_EMU ) THEN |
---|
| 885 | ! |
---|
| 886 | DO ji = 1, npti |
---|
[14072] | 887 | hfx_err_dif_1d(ji) = hfx_err_dif_1d(ji) - ( qns_ice_1d(ji) - zqns_ice_b(ji) ) * a_i_1d(ji) |
---|
[12396] | 888 | END DO |
---|
| 889 | ! |
---|
| 890 | ENDIF |
---|
| 891 | ! |
---|
[8984] | 892 | ! --- Diagnose the heat loss due to non-fully converged temperature solution (should not be above 10-4 W-m2) --- ! |
---|
| 893 | ! |
---|
[10534] | 894 | IF( k_cnd == np_cnd_OFF .OR. k_cnd == np_cnd_ON ) THEN |
---|
[14072] | 895 | |
---|
| 896 | CALL ice_var_enthalpy |
---|
| 897 | |
---|
[8984] | 898 | ! zhfx_err = correction on the diagnosed heat flux due to non-convergence of the algorithm used to solve heat equation |
---|
| 899 | DO ji = 1, npti |
---|
| 900 | zdq = - zq_ini(ji) + ( SUM( e_i_1d(ji,1:nlay_i) ) * h_i_1d(ji) * r1_nlay_i + & |
---|
| 901 | & SUM( e_s_1d(ji,1:nlay_s) ) * h_s_1d(ji) * r1_nlay_s ) |
---|
[14072] | 902 | |
---|
[10534] | 903 | IF( k_cnd == np_cnd_OFF ) THEN |
---|
[14072] | 904 | |
---|
[8984] | 905 | IF( t_su_1d(ji) < rt0 ) THEN ! case T_su < 0degC |
---|
[9916] | 906 | zhfx_err = ( qns_ice_1d(ji) + qsr_ice_1d(ji) - zradtr_i(ji,nlay_i) - qcn_ice_bot_1d(ji) & |
---|
[12489] | 907 | & + zdq * r1_Dt_ice ) * a_i_1d(ji) |
---|
[8984] | 908 | ELSE ! case T_su = 0degC |
---|
[9916] | 909 | zhfx_err = ( qcn_ice_top_1d(ji) + qtr_ice_top_1d(ji) - zradtr_i(ji,nlay_i) - qcn_ice_bot_1d(ji) & |
---|
[12489] | 910 | & + zdq * r1_Dt_ice ) * a_i_1d(ji) |
---|
[8984] | 911 | ENDIF |
---|
[14072] | 912 | |
---|
[10534] | 913 | ELSEIF( k_cnd == np_cnd_ON ) THEN |
---|
[14072] | 914 | |
---|
[9916] | 915 | zhfx_err = ( qcn_ice_top_1d(ji) + qtr_ice_top_1d(ji) - zradtr_i(ji,nlay_i) - qcn_ice_bot_1d(ji) & |
---|
[12489] | 916 | & + zdq * r1_Dt_ice ) * a_i_1d(ji) |
---|
[14072] | 917 | |
---|
[8984] | 918 | ENDIF |
---|
| 919 | ! |
---|
| 920 | ! total heat sink to be sent to the ocean |
---|
| 921 | hfx_err_dif_1d(ji) = hfx_err_dif_1d(ji) + zhfx_err |
---|
| 922 | ! |
---|
[14072] | 923 | ! hfx_dif = Heat flux diagnostic of sensible heat used to warm/cool ice in W.m-2 |
---|
[12489] | 924 | hfx_dif_1d(ji) = hfx_dif_1d(ji) - zdq * r1_Dt_ice * a_i_1d(ji) |
---|
[8984] | 925 | ! |
---|
| 926 | END DO |
---|
| 927 | ! |
---|
| 928 | ENDIF |
---|
| 929 | ! |
---|
[10534] | 930 | !-------------------------------------------------------------------- |
---|
| 931 | ! 11) reset inner snow and ice temperatures, update conduction fluxes |
---|
| 932 | !-------------------------------------------------------------------- |
---|
[8984] | 933 | ! effective conductivity and 1st layer temperature (needed by Met Office) |
---|
[13472] | 934 | ! this is a conductivity at mid-layer, hence the factor 2 |
---|
[8984] | 935 | DO ji = 1, npti |
---|
[13472] | 936 | IF( h_i_1d(ji) >= zhi_ssl ) THEN |
---|
| 937 | cnd_ice_1d(ji) = 2._wp * zkappa_comb(ji) |
---|
| 938 | !!cnd_ice_1d(ji) = 2._wp * zkappa_i(ji,0) |
---|
[8984] | 939 | ELSE |
---|
[13472] | 940 | cnd_ice_1d(ji) = 2._wp * ztcond_i(ji,0) / zhi_ssl ! cnd_ice is capped by: cond_i/zhi_ssl |
---|
[8984] | 941 | ENDIF |
---|
| 942 | t1_ice_1d(ji) = isnow(ji) * t_s_1d(ji,1) + ( 1._wp - isnow(ji) ) * t_i_1d(ji,1) |
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| 943 | END DO |
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| 944 | ! |
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[10534] | 945 | IF( k_cnd == np_cnd_EMU ) THEN |
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[8984] | 946 | ! Restore temperatures to their initial values |
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[9916] | 947 | t_s_1d (1:npti,:) = ztsold (1:npti,:) |
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| 948 | t_i_1d (1:npti,:) = ztiold (1:npti,:) |
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| 949 | qcn_ice_1d(1:npti) = qcn_ice_top_1d(1:npti) |
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[8984] | 950 | ENDIF |
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| 951 | ! |
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[9916] | 952 | ! --- SIMIP diagnostics |
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| 953 | ! |
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[14072] | 954 | DO ji = 1, npti |
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[9916] | 955 | !--- Snow-ice interfacial temperature (diagnostic SIMIP) |
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[13472] | 956 | IF( h_s_1d(ji) >= zhs_ssl ) THEN |
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[14005] | 957 | t_si_1d(ji) = ( rn_cnd_s * h_i_1d(ji) * r1_nlay_i * t_s_1d(ji,nlay_s) & |
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| 958 | & + ztcond_i(ji,1) * h_s_1d(ji) * r1_nlay_s * t_i_1d(ji,1) ) & |
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[13472] | 959 | & / ( rn_cnd_s * h_i_1d(ji) * r1_nlay_i & |
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| 960 | & + ztcond_i(ji,1) * h_s_1d(ji) * r1_nlay_s ) |
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[9916] | 961 | ELSE |
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| 962 | t_si_1d(ji) = t_su_1d(ji) |
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| 963 | ENDIF |
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| 964 | END DO |
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| 965 | ! |
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[8984] | 966 | END SUBROUTINE ice_thd_zdf_BL99 |
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| 967 | |
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| 968 | #else |
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| 969 | !!---------------------------------------------------------------------- |
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[9570] | 970 | !! Default option Dummy Module No SI3 sea-ice model |
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[8984] | 971 | !!---------------------------------------------------------------------- |
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| 972 | #endif |
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| 973 | |
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| 974 | !!====================================================================== |
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| 975 | END MODULE icethd_zdf_BL99 |
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