| 1 | MODULE icethd_zdf_BL99 |
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| 2 | !!====================================================================== |
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| 3 | !! *** MODULE icethd_zdf_BL99 *** |
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| 4 | !! sea-ice: vertical heat diffusion in sea ice (computation of temperatures) |
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| 5 | !!====================================================================== |
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| 6 | !! History : ! 2003-02 (M. Vancoppenolle) original 1D code |
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| 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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| 9 | !!---------------------------------------------------------------------- |
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| 10 | #if defined key_si3 |
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| 11 | !!---------------------------------------------------------------------- |
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| 12 | !! 'key_si3' SI3 sea-ice model |
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| 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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| 17 | USE phycst ! physical constants (ocean directory) |
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| 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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| 32 | !! NEMO/ICE 4.0 , NEMO Consortium (2018) |
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| 33 | !! $Id$ |
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| 34 | !! Software governed by the CeCILL license (see ./LICENSE) |
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| 35 | !!---------------------------------------------------------------------- |
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| 36 | CONTAINS |
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| 37 | |
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| 38 | SUBROUTINE ice_thd_zdf_BL99( k_cnd ) |
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| 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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| 46 | !! condition at the surface and a Dirichlet one at the bottom. |
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| 47 | !! Solar radiation is partially absorbed into the ice. |
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| 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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| 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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| 75 | INTEGER, INTENT(in) :: k_cnd ! conduction flux (off, on, emulated) |
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| 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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| 85 | |
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| 86 | LOGICAL, DIMENSION(jpij) :: l_T_converged ! true when T converges (per grid point) |
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| 87 | ! |
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| 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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| 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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| 96 | REAL(wp) :: zhi_ssl = 0.10_wp ! surface scattering layer in the ice |
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| 97 | REAL(wp) :: ztmelts ! ice melting temperature |
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| 98 | REAL(wp) :: zdti_max ! current maximal error on temperature |
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| 99 | REAL(wp) :: zcpi ! Ice specific heat |
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| 100 | REAL(wp) :: zhfx_err, zdq ! diag errors on heat |
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| 101 | ! |
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| 102 | REAL(wp), DIMENSION(jpij) :: zraext_s ! extinction coefficient of radiation in the snow |
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| 103 | REAL(wp), DIMENSION(jpij) :: ztsub ! surface temperature at previous iteration |
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| 104 | REAL(wp), DIMENSION(jpij) :: zh_i, z1_h_i ! ice layer thickness |
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| 105 | REAL(wp), DIMENSION(jpij) :: zh_s, z1_h_s ! snow layer thickness |
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| 106 | REAL(wp), DIMENSION(jpij) :: zqns_ice_b ! solar radiation absorbed at the surface |
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| 107 | REAL(wp), DIMENSION(jpij) :: zfnet ! surface flux function |
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| 108 | REAL(wp), DIMENSION(jpij) :: zdqns_ice_b ! derivative of the surface flux function |
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| 109 | ! |
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| 110 | REAL(wp), DIMENSION(jpij ) :: ztsuold ! Old surface temperature in the ice |
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| 111 | REAL(wp), DIMENSION(jpij,nlay_i) :: ztiold ! Old temperature in the ice |
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| 112 | REAL(wp), DIMENSION(jpij,nlay_s) :: ztsold ! Old temperature in the snow |
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| 113 | REAL(wp), DIMENSION(jpij,nlay_i) :: ztib ! Temporary temperature in the ice to check the convergence |
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| 114 | REAL(wp), DIMENSION(jpij,nlay_s) :: ztsb ! Temporary temperature in the snow to check the convergence |
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| 115 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: ztcond_i ! Ice thermal conductivity |
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| 116 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: ztcond_i_cp ! copy |
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| 117 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: zradtr_i ! Radiation transmitted through the ice |
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| 118 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: zradab_i ! Radiation absorbed in the ice |
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| 119 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: zkappa_i ! Kappa factor in the ice |
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| 120 | REAL(wp), DIMENSION(jpij,0:nlay_i) :: zeta_i ! Eta factor in the ice |
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| 121 | REAL(wp), DIMENSION(jpij,0:nlay_s) :: zradtr_s ! Radiation transmited through the snow |
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| 122 | REAL(wp), DIMENSION(jpij,0:nlay_s) :: zradab_s ! Radiation absorbed in the snow |
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| 123 | REAL(wp), DIMENSION(jpij,0:nlay_s) :: zkappa_s ! Kappa factor in the snow |
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| 124 | REAL(wp), DIMENSION(jpij,0:nlay_s) :: zeta_s ! Eta factor in the snow |
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| 125 | REAL(wp), DIMENSION(jpij,nlay_i+3) :: zindterm ! 'Ind'ependent term |
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| 126 | REAL(wp), DIMENSION(jpij,nlay_i+3) :: zindtbis ! Temporary 'ind'ependent term |
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| 127 | REAL(wp), DIMENSION(jpij,nlay_i+3) :: zdiagbis ! Temporary 'dia'gonal term |
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| 128 | REAL(wp), DIMENSION(jpij,nlay_i+3,3) :: ztrid ! Tridiagonal system terms |
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| 129 | REAL(wp), DIMENSION(jpij) :: zq_ini ! diag errors on heat |
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| 130 | REAL(wp), DIMENSION(jpij) :: zghe ! G(he), th. conduct enhancement factor, mono-cat |
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| 131 | REAL(wp), DIMENSION(jpij) :: za_s_fra ! ice fraction covered by snow |
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| 132 | ! |
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| 133 | ! Mono-category |
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| 134 | REAL(wp) :: zepsilon ! determines thres. above which computation of G(h) is done |
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| 135 | REAL(wp) :: zhe ! dummy factor |
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| 136 | REAL(wp) :: zcnd_i ! mean sea ice thermal conductivity |
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| 137 | !!------------------------------------------------------------------ |
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| 138 | |
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| 139 | ! --- diag error on heat diffusion - PART 1 --- ! |
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| 140 | DO ji = 1, npti |
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| 141 | zq_ini(ji) = ( SUM( e_i_1d(ji,1:nlay_i) ) * h_i_1d(ji) * r1_nlay_i + & |
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| 142 | & SUM( e_s_1d(ji,1:nlay_s) ) * h_s_1d(ji) * r1_nlay_s ) |
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| 143 | END DO |
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| 144 | |
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| 145 | CALL ice_var_snwfra( h_s_1d(1:npti), za_s_fra(1:npti) ) ! calculate ice fraction covered by snow |
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| 146 | |
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| 147 | !------------------ |
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| 148 | ! 1) Initialization |
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| 149 | !------------------ |
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| 150 | ! |
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| 151 | ! extinction radiation in the snow |
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| 152 | IF ( nn_qtrice == 0 ) THEN ! constant |
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| 153 | zraext_s(1:npti) = rn_kappa_s |
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| 154 | ELSEIF( nn_qtrice == 1 ) THEN ! depends on melting/freezing conditions |
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| 155 | WHERE( t_su_1d(1:npti) < rt0 ) ; zraext_s(1:npti) = rn_kappa_sdry ! no surface melting |
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| 156 | ELSEWHERE ; zraext_s(1:npti) = rn_kappa_smlt ! surface melting |
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| 157 | END WHERE |
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| 158 | ENDIF |
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| 159 | ! |
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| 160 | ! layers thicknesses |
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| 161 | DO ji = 1, npti |
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| 162 | zh_s(ji) = MAX( zhs_ssl , h_s_1d(ji) ) * r1_nlay_s ! set a minimum snw thickness for conduction |
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| 163 | zh_i(ji) = MAX( zhi_ssl , h_i_1d(ji) ) * r1_nlay_i ! set a minimum ice thickness for conduction |
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| 164 | END DO |
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| 165 | ! |
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| 166 | WHERE( h_i_1d(1:npti) >= zhi_ssl ) ; z1_h_i(1:npti) = 1._wp / zh_i(1:npti) |
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| 167 | ELSEWHERE ; z1_h_i(1:npti) = 0._wp ! put 0 if ice thick < scattering layer |
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| 168 | END WHERE |
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| 169 | ! |
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| 170 | WHERE( h_s_1d(1:npti) >= zhs_ssl ) ; z1_h_s(1:npti) = 1._wp / zh_s(1:npti) |
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| 171 | ELSEWHERE ; z1_h_s(1:npti) = 0._wp ! put 0 if snw thick < scattering layer |
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| 172 | END WHERE |
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| 173 | ! |
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| 174 | ! Store initial temperatures and non solar heat fluxes |
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| 175 | IF( k_cnd == np_cnd_OFF .OR. k_cnd == np_cnd_EMU ) THEN |
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| 176 | ! |
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| 177 | ztsub (1:npti) = t_su_1d(1:npti) ! surface temperature at iteration n-1 |
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| 178 | ztsuold (1:npti) = t_su_1d(1:npti) ! surface temperature initial value |
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| 179 | 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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| 180 | zdqns_ice_b(1:npti) = dqns_ice_1d(1:npti) ! derivative of incoming nonsolar flux |
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| 181 | zqns_ice_b (1:npti) = qns_ice_1d(1:npti) ! store previous qns_ice_1d value |
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| 182 | ! |
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| 183 | ENDIF |
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| 184 | ! |
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| 185 | ztsold (1:npti,:) = t_s_1d(1:npti,:) ! Old snow temperature |
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| 186 | ztiold (1:npti,:) = t_i_1d(1:npti,:) ! Old ice temperature |
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| 187 | |
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| 188 | !------------- |
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| 189 | ! 2) Radiation |
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| 190 | !------------- |
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| 191 | ! --- Transmission/absorption of solar radiation in the ice --- ! |
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| 192 | zradtr_s(1:npti,0) = qtr_ice_top_1d(1:npti) |
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| 193 | DO jk = 1, nlay_s |
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| 194 | DO ji = 1, npti |
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| 195 | ! ! radiation transmitted below the layer-th snow layer |
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| 196 | 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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| 197 | ! ! radiation absorbed by the layer-th snow layer |
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| 198 | zradab_s(ji,jk) = zradtr_s(ji,jk-1) - zradtr_s(ji,jk) |
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| 199 | END DO |
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| 200 | END DO |
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| 201 | ! |
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| 202 | 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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| 203 | DO jk = 1, nlay_i |
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| 204 | DO ji = 1, npti |
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| 205 | ! ! radiation transmitted below the layer-th ice layer |
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| 206 | zradtr_i(ji,jk) = za_s_fra(ji) * zradtr_s(ji,nlay_s) & ! part covered by snow |
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| 207 | & * EXP( - rn_kappa_i * zh_i(ji) * REAL(jk) ) & |
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| 208 | & + ( 1._wp - za_s_fra(ji) ) * qtr_ice_top_1d(ji) & ! part snow free |
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| 209 | & * EXP( - rn_kappa_i * MAX( 0._wp, zh_i(ji) * REAL(jk) - zhi_ssl ) ) |
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| 210 | |
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| 211 | zradtr_i(ji,jk) = zradtr_i(ji,0) * EXP( - rn_kappa_i * MAX( 0._wp, zh_i(ji) * REAL(jk) - zhi_ssl ) ) |
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| 212 | ! ! radiation absorbed by the layer-th ice layer |
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| 213 | zradab_i(ji,jk) = zradtr_i(ji,jk-1) - zradtr_i(ji,jk) |
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| 214 | END DO |
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| 215 | END DO |
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| 216 | ! |
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| 217 | qtr_ice_bot_1d(1:npti) = zradtr_i(1:npti,nlay_i) ! record radiation transmitted below the ice |
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| 218 | ! |
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| 219 | iconv = 0 ! number of iterations |
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| 220 | ! |
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| 221 | l_T_converged(:) = .FALSE. |
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| 222 | ! Convergence calculated until all sub-domain grid points have converged |
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| 223 | ! Calculations keep going for all grid points until sub-domain convergence (vectorisation optimisation) |
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| 224 | ! but values are not taken into account (results independant of MPI partitioning) |
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| 225 | ! |
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| 226 | ! !============================! |
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| 227 | DO WHILE ( ( .NOT. ALL (l_T_converged(1:npti)) ) .AND. iconv < iconv_max ) ! Iterative procedure begins ! |
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| 228 | ! !============================! |
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| 229 | iconv = iconv + 1 |
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| 230 | ! |
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| 231 | ztib(1:npti,:) = t_i_1d(1:npti,:) |
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| 232 | ztsb(1:npti,:) = t_s_1d(1:npti,:) |
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| 233 | ! |
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| 234 | !-------------------------------- |
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| 235 | ! 3) Sea ice thermal conductivity |
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| 236 | !-------------------------------- |
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| 237 | IF( ln_cndi_U64 ) THEN !-- Untersteiner (1964) formula: k = k0 + beta.S/T |
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| 238 | ! |
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| 239 | DO ji = 1, npti |
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| 240 | 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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| 241 | 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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| 242 | END DO |
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| 243 | DO jk = 1, nlay_i-1 |
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| 244 | DO ji = 1, npti |
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| 245 | 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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| 246 | & MIN( -epsi10, 0.5_wp * ( t_i_1d(ji,jk) + t_i_1d(ji,jk+1) ) - rt0 ) |
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| 247 | END DO |
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| 248 | END DO |
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| 249 | ! |
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| 250 | ELSEIF( ln_cndi_P07 ) THEN !-- Pringle et al formula: k = k0 + beta1.S/T - beta2.T |
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| 251 | ! |
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| 252 | DO ji = 1, npti |
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| 253 | 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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| 254 | & - 0.011_wp * ( t_i_1d(ji,1) - rt0 ) |
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| 255 | 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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| 256 | & - 0.011_wp * ( t_bo_1d(ji) - rt0 ) |
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| 257 | END DO |
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| 258 | DO jk = 1, nlay_i-1 |
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| 259 | DO ji = 1, npti |
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| 260 | 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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| 261 | & MIN( -epsi10, 0.5_wp * ( t_i_1d(ji,jk) + t_i_1d(ji,jk+1) ) - rt0 ) & |
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| 262 | & - 0.011_wp * ( 0.5_wp * ( t_i_1d(ji,jk) + t_i_1d(ji,jk+1) ) - rt0 ) |
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| 263 | END DO |
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| 264 | END DO |
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| 265 | ! |
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| 266 | ENDIF |
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| 267 | |
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| 268 | ! Variable used after iterations |
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| 269 | ! Value must be frozen after convergence for MPP independance reason |
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| 270 | DO ji = 1, npti |
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| 271 | IF ( .NOT. l_T_converged(ji) ) & |
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| 272 | ztcond_i(ji,:) = MAX( zkimin, ztcond_i_cp(ji,:) ) |
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| 273 | END DO |
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| 274 | ! |
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| 275 | !--- G(he) : enhancement of thermal conductivity in mono-category case |
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| 276 | ! Computation of effective thermal conductivity G(h) |
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| 277 | ! Used in mono-category case only to simulate an ITD implicitly |
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| 278 | ! Fichefet and Morales Maqueda, JGR 1997 |
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| 279 | zghe(1:npti) = 1._wp |
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| 280 | ! |
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| 281 | IF( ln_virtual_itd ) THEN |
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| 282 | ! |
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| 283 | zepsilon = 0.1_wp |
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| 284 | DO ji = 1, npti |
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| 285 | zcnd_i = SUM( ztcond_i(ji,:) ) / REAL( nlay_i+1, wp ) ! Mean sea ice thermal conductivity |
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| 286 | 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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| 287 | IF( zhe >= zepsilon * 0.5_wp * EXP(1._wp) ) & |
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| 288 | & zghe(ji) = MIN( 2._wp, 0.5_wp * ( 1._wp + LOG( 2._wp * zhe / zepsilon ) ) ) ! G(he) |
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| 289 | END DO |
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| 290 | ! |
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| 291 | ENDIF |
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| 292 | ! |
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| 293 | !----------------- |
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| 294 | ! 4) kappa factors |
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| 295 | !----------------- |
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| 296 | !--- Snow |
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| 297 | ! Variable used after iterations |
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| 298 | ! Value must be frozen after convergence for MPP independance reason |
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| 299 | DO jk = 0, nlay_s-1 |
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| 300 | DO ji = 1, npti |
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| 301 | IF ( .NOT. l_T_converged(ji) ) & |
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| 302 | zkappa_s(ji,jk) = zghe(ji) * rn_cnd_s * z1_h_s(ji) |
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| 303 | END DO |
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| 304 | END DO |
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| 305 | DO ji = 1, npti ! Snow-ice interface |
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| 306 | IF ( .NOT. l_T_converged(ji) ) THEN |
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| 307 | IF( h_s_1d(ji) >= zhs_ssl ) THEN |
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| 308 | zkappa_s(ji,nlay_s) = zghe(ji) * rn_cnd_s * ztcond_i(ji,0) / & |
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| 309 | & ( 0.5_wp * ( ztcond_i(ji,0) * zh_s(ji) + rn_cnd_s * zh_i(ji) ) ) |
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| 310 | ELSE |
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| 311 | zkappa_s(ji,nlay_s) = 0._wp |
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| 312 | ENDIF |
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| 313 | ENDIF |
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| 314 | END DO |
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| 315 | |
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| 316 | !--- Ice |
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| 317 | ! Variable used after iterations |
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| 318 | ! Value must be frozen after convergence for MPP independance reason |
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| 319 | DO jk = 0, nlay_i |
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| 320 | DO ji = 1, npti |
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| 321 | IF ( .NOT. l_T_converged(ji) ) & |
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| 322 | zkappa_i(ji,jk) = zghe(ji) * ztcond_i(ji,jk) * z1_h_i(ji) |
|---|
| 323 | END DO |
|---|
| 324 | END DO |
|---|
| 325 | DO ji = 1, npti ! Snow-ice interface |
|---|
| 326 | IF ( .NOT. l_T_converged(ji) ) & |
|---|
| 327 | zkappa_i(ji,0) = zkappa_s(ji,nlay_s) * za_s_fra(ji) + zkappa_i(ji,0) * (1._wp - za_s_fra(ji)) |
|---|
| 328 | END DO |
|---|
| 329 | ! |
|---|
| 330 | !-------------------------------------- |
|---|
| 331 | ! 5) Sea ice specific heat, eta factors |
|---|
| 332 | !-------------------------------------- |
|---|
| 333 | DO jk = 1, nlay_i |
|---|
| 334 | DO ji = 1, npti |
|---|
| 335 | zcpi = rcpi + zgamma * sz_i_1d(ji,jk) / MAX( ( t_i_1d(ji,jk) - rt0 ) * ( ztiold(ji,jk) - rt0 ), epsi10 ) |
|---|
| 336 | zeta_i(ji,jk) = rdt_ice * r1_rhoi * z1_h_i(ji) / MAX( epsi10, zcpi ) |
|---|
| 337 | END DO |
|---|
| 338 | END DO |
|---|
| 339 | |
|---|
| 340 | DO jk = 1, nlay_s |
|---|
| 341 | DO ji = 1, npti |
|---|
| 342 | zeta_s(ji,jk) = rdt_ice * r1_rhos * r1_rcpi * z1_h_s(ji) |
|---|
| 343 | END DO |
|---|
| 344 | END DO |
|---|
| 345 | ! |
|---|
| 346 | !----------------------------------------! |
|---|
| 347 | ! ! |
|---|
| 348 | ! Conduction flux is off or emulated ! |
|---|
| 349 | ! ! |
|---|
| 350 | !----------------------------------------! |
|---|
| 351 | ! |
|---|
| 352 | IF( k_cnd == np_cnd_OFF .OR. k_cnd == np_cnd_EMU ) THEN |
|---|
| 353 | ! |
|---|
| 354 | ! ==> The original BL99 temperature computation is used |
|---|
| 355 | ! (with qsr_ice, qns_ice and dqns_ice as inputs) |
|---|
| 356 | ! |
|---|
| 357 | !---------------------------- |
|---|
| 358 | ! 6) surface flux computation |
|---|
| 359 | !---------------------------- |
|---|
| 360 | ! update of the non solar flux according to the update in T_su |
|---|
| 361 | DO ji = 1, npti |
|---|
| 362 | ! Variable used after iterations |
|---|
| 363 | ! Value must be frozen after convergence for MPP independance reason |
|---|
| 364 | IF ( .NOT. l_T_converged(ji) ) & |
|---|
| 365 | qns_ice_1d(ji) = qns_ice_1d(ji) + dqns_ice_1d(ji) * ( t_su_1d(ji) - ztsub(ji) ) |
|---|
| 366 | END DO |
|---|
| 367 | |
|---|
| 368 | DO ji = 1, npti |
|---|
| 369 | zfnet(ji) = qsr_ice_1d(ji) - qtr_ice_top_1d(ji) + qns_ice_1d(ji) ! net heat flux = net - transmitted solar + non solar |
|---|
| 370 | END DO |
|---|
| 371 | ! |
|---|
| 372 | !---------------------------- |
|---|
| 373 | ! 7) tridiagonal system terms |
|---|
| 374 | !---------------------------- |
|---|
| 375 | ! layer denotes the number of the layer in the snow or in the ice |
|---|
| 376 | ! jm denotes the reference number of the equation in the tridiagonal |
|---|
| 377 | ! system, terms of tridiagonal system are indexed as following : |
|---|
| 378 | ! 1 is subdiagonal term, 2 is diagonal and 3 is superdiagonal one |
|---|
| 379 | |
|---|
| 380 | ! ice interior terms (top equation has the same form as the others) |
|---|
| 381 | ztrid (1:npti,:,:) = 0._wp |
|---|
| 382 | zindterm(1:npti,:) = 0._wp |
|---|
| 383 | zindtbis(1:npti,:) = 0._wp |
|---|
| 384 | zdiagbis(1:npti,:) = 0._wp |
|---|
| 385 | |
|---|
| 386 | DO jm = nlay_s + 2, nlay_s + nlay_i |
|---|
| 387 | DO ji = 1, npti |
|---|
| 388 | jk = jm - nlay_s - 1 |
|---|
| 389 | ztrid (ji,jm,1) = - zeta_i(ji,jk) * zkappa_i(ji,jk-1) |
|---|
| 390 | ztrid (ji,jm,2) = 1._wp + zeta_i(ji,jk) * ( zkappa_i(ji,jk-1) + zkappa_i(ji,jk) ) |
|---|
| 391 | ztrid (ji,jm,3) = - zeta_i(ji,jk) * zkappa_i(ji,jk) |
|---|
| 392 | zindterm(ji,jm) = ztiold(ji,jk) + zeta_i(ji,jk) * zradab_i(ji,jk) |
|---|
| 393 | END DO |
|---|
| 394 | END DO |
|---|
| 395 | |
|---|
| 396 | jm = nlay_s + nlay_i + 1 |
|---|
| 397 | DO ji = 1, npti |
|---|
| 398 | ! ice bottom term |
|---|
| 399 | ztrid (ji,jm,1) = - zeta_i(ji,nlay_i) * zkappa_i(ji,nlay_i-1) |
|---|
| 400 | ztrid (ji,jm,2) = 1._wp + zeta_i(ji,nlay_i) * ( zkappa_i(ji,nlay_i-1) + zkappa_i(ji,nlay_i) * zg1 ) |
|---|
| 401 | ztrid (ji,jm,3) = 0._wp |
|---|
| 402 | zindterm(ji,jm) = ztiold(ji,nlay_i) + zeta_i(ji,nlay_i) * & |
|---|
| 403 | & ( zradab_i(ji,nlay_i) + zkappa_i(ji,nlay_i) * zg1 * t_bo_1d(ji) ) |
|---|
| 404 | END DO |
|---|
| 405 | |
|---|
| 406 | DO ji = 1, npti |
|---|
| 407 | ! !---------------------! |
|---|
| 408 | IF( h_s_1d(ji) > 0._wp ) THEN ! snow-covered cells ! |
|---|
| 409 | ! !---------------------! |
|---|
| 410 | ! snow interior terms (bottom equation has the same form as the others) |
|---|
| 411 | DO jm = 3, nlay_s + 1 |
|---|
| 412 | jk = jm - 1 |
|---|
| 413 | ztrid (ji,jm,1) = - zeta_s(ji,jk) * zkappa_s(ji,jk-1) |
|---|
| 414 | ztrid (ji,jm,2) = 1._wp + zeta_s(ji,jk) * ( zkappa_s(ji,jk-1) + zkappa_s(ji,jk) ) |
|---|
| 415 | ztrid (ji,jm,3) = - zeta_s(ji,jk) * zkappa_s(ji,jk) |
|---|
| 416 | zindterm(ji,jm) = ztsold(ji,jk) + zeta_s(ji,jk) * zradab_s(ji,jk) |
|---|
| 417 | END DO |
|---|
| 418 | |
|---|
| 419 | ! case of only one layer in the ice (ice equation is altered) |
|---|
| 420 | IF( nlay_i == 1 ) THEN |
|---|
| 421 | ztrid (ji,nlay_s+2,3) = 0._wp |
|---|
| 422 | zindterm(ji,nlay_s+2) = zindterm(ji,nlay_s+2) + zeta_i(ji,1) * zkappa_i(ji,1) * t_bo_1d(ji) |
|---|
| 423 | ENDIF |
|---|
| 424 | |
|---|
| 425 | IF( t_su_1d(ji) < rt0 ) THEN !-- case 1 : no surface melting |
|---|
| 426 | |
|---|
| 427 | jm_min(ji) = 1 |
|---|
| 428 | jm_max(ji) = nlay_i + nlay_s + 1 |
|---|
| 429 | |
|---|
| 430 | ! surface equation |
|---|
| 431 | ztrid (ji,1,1) = 0._wp |
|---|
| 432 | ztrid (ji,1,2) = zdqns_ice_b(ji) - zg1s * zkappa_s(ji,0) |
|---|
| 433 | ztrid (ji,1,3) = zg1s * zkappa_s(ji,0) |
|---|
| 434 | zindterm(ji,1) = zdqns_ice_b(ji) * t_su_1d(ji) - zfnet(ji) |
|---|
| 435 | |
|---|
| 436 | ! first layer of snow equation |
|---|
| 437 | ztrid (ji,2,1) = - zeta_s(ji,1) * zkappa_s(ji,0) * zg1s |
|---|
| 438 | ztrid (ji,2,2) = 1._wp + zeta_s(ji,1) * ( zkappa_s(ji,1) + zkappa_s(ji,0) * zg1s ) |
|---|
| 439 | ztrid (ji,2,3) = - zeta_s(ji,1) * zkappa_s(ji,1) |
|---|
| 440 | zindterm(ji,2) = ztsold(ji,1) + zeta_s(ji,1) * zradab_s(ji,1) |
|---|
| 441 | |
|---|
| 442 | ELSE !-- case 2 : surface is melting |
|---|
| 443 | ! |
|---|
| 444 | jm_min(ji) = 2 |
|---|
| 445 | jm_max(ji) = nlay_i + nlay_s + 1 |
|---|
| 446 | |
|---|
| 447 | ! first layer of snow equation |
|---|
| 448 | ztrid (ji,2,1) = 0._wp |
|---|
| 449 | ztrid (ji,2,2) = 1._wp + zeta_s(ji,1) * ( zkappa_s(ji,1) + zkappa_s(ji,0) * zg1s ) |
|---|
| 450 | ztrid (ji,2,3) = - zeta_s(ji,1) * zkappa_s(ji,1) |
|---|
| 451 | zindterm(ji,2) = ztsold(ji,1) + zeta_s(ji,1) * ( zradab_s(ji,1) + zkappa_s(ji,0) * zg1s * t_su_1d(ji) ) |
|---|
| 452 | ENDIF |
|---|
| 453 | ! !---------------------! |
|---|
| 454 | ELSE ! cells without snow ! |
|---|
| 455 | ! !---------------------! |
|---|
| 456 | ! |
|---|
| 457 | IF( t_su_1d(ji) < rt0 ) THEN !-- case 1 : no surface melting |
|---|
| 458 | ! |
|---|
| 459 | jm_min(ji) = nlay_s + 1 |
|---|
| 460 | jm_max(ji) = nlay_i + nlay_s + 1 |
|---|
| 461 | |
|---|
| 462 | ! surface equation |
|---|
| 463 | ztrid (ji,jm_min(ji),1) = 0._wp |
|---|
| 464 | ztrid (ji,jm_min(ji),2) = zdqns_ice_b(ji) - zkappa_i(ji,0) * zg1 |
|---|
| 465 | ztrid (ji,jm_min(ji),3) = zkappa_i(ji,0) * zg1 |
|---|
| 466 | zindterm(ji,jm_min(ji)) = zdqns_ice_b(ji) * t_su_1d(ji) - zfnet(ji) |
|---|
| 467 | |
|---|
| 468 | ! first layer of ice equation |
|---|
| 469 | ztrid (ji,jm_min(ji)+1,1) = - zeta_i(ji,1) * zkappa_i(ji,0) * zg1 |
|---|
| 470 | ztrid (ji,jm_min(ji)+1,2) = 1._wp + zeta_i(ji,1) * ( zkappa_i(ji,1) + zkappa_i(ji,0) * zg1 ) |
|---|
| 471 | ztrid (ji,jm_min(ji)+1,3) = - zeta_i(ji,1) * zkappa_i(ji,1) |
|---|
| 472 | zindterm(ji,jm_min(ji)+1) = ztiold(ji,1) + zeta_i(ji,1) * zradab_i(ji,1) |
|---|
| 473 | |
|---|
| 474 | ! case of only one layer in the ice (surface & ice equations are altered) |
|---|
| 475 | IF( nlay_i == 1 ) THEN |
|---|
| 476 | ztrid (ji,jm_min(ji),1) = 0._wp |
|---|
| 477 | ztrid (ji,jm_min(ji),2) = zdqns_ice_b(ji) - zkappa_i(ji,0) * 2._wp |
|---|
| 478 | ztrid (ji,jm_min(ji),3) = zkappa_i(ji,0) * 2._wp |
|---|
| 479 | ztrid (ji,jm_min(ji)+1,1) = - zeta_i(ji,1) * zkappa_i(ji,0) * 2._wp |
|---|
| 480 | ztrid (ji,jm_min(ji)+1,2) = 1._wp + zeta_i(ji,1) * ( zkappa_i(ji,0) * 2._wp + zkappa_i(ji,1) ) |
|---|
| 481 | ztrid (ji,jm_min(ji)+1,3) = 0._wp |
|---|
| 482 | 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)) |
|---|
| 483 | ENDIF |
|---|
| 484 | |
|---|
| 485 | ELSE !-- case 2 : surface is melting |
|---|
| 486 | |
|---|
| 487 | jm_min(ji) = nlay_s + 2 |
|---|
| 488 | jm_max(ji) = nlay_i + nlay_s + 1 |
|---|
| 489 | |
|---|
| 490 | ! first layer of ice equation |
|---|
| 491 | ztrid (ji,jm_min(ji),1) = 0._wp |
|---|
| 492 | ztrid (ji,jm_min(ji),2) = 1._wp + zeta_i(ji,1) * ( zkappa_i(ji,1) + zkappa_i(ji,0) * zg1 ) |
|---|
| 493 | ztrid (ji,jm_min(ji),3) = - zeta_i(ji,1) * zkappa_i(ji,1) |
|---|
| 494 | 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)) |
|---|
| 495 | |
|---|
| 496 | ! case of only one layer in the ice (surface & ice equations are altered) |
|---|
| 497 | IF( nlay_i == 1 ) THEN |
|---|
| 498 | ztrid (ji,jm_min(ji),1) = 0._wp |
|---|
| 499 | ztrid (ji,jm_min(ji),2) = 1._wp + zeta_i(ji,1) * ( zkappa_i(ji,0) * 2._wp + zkappa_i(ji,1) ) |
|---|
| 500 | ztrid (ji,jm_min(ji),3) = 0._wp |
|---|
| 501 | zindterm(ji,jm_min(ji)) = ztiold(ji,1) + zeta_i(ji,1) * ( zradab_i(ji,1) + zkappa_i(ji,1) * t_bo_1d(ji) ) & |
|---|
| 502 | & + t_su_1d(ji) * zeta_i(ji,1) * zkappa_i(ji,0) * 2._wp |
|---|
| 503 | ENDIF |
|---|
| 504 | |
|---|
| 505 | ENDIF |
|---|
| 506 | ENDIF |
|---|
| 507 | ! |
|---|
| 508 | zindtbis(ji,jm_min(ji)) = zindterm(ji,jm_min(ji)) |
|---|
| 509 | zdiagbis(ji,jm_min(ji)) = ztrid (ji,jm_min(ji),2) |
|---|
| 510 | ! |
|---|
| 511 | END DO |
|---|
| 512 | ! |
|---|
| 513 | !------------------------------ |
|---|
| 514 | ! 8) tridiagonal system solving |
|---|
| 515 | !------------------------------ |
|---|
| 516 | ! Solve the tridiagonal system with Gauss elimination method. |
|---|
| 517 | ! Thomas algorithm, from Computational fluid Dynamics, J.D. ANDERSON, McGraw-Hill 1984 |
|---|
| 518 | jm_maxt = 0 |
|---|
| 519 | jm_mint = nlay_i+5 |
|---|
| 520 | DO ji = 1, npti |
|---|
| 521 | jm_mint = MIN(jm_min(ji),jm_mint) |
|---|
| 522 | jm_maxt = MAX(jm_max(ji),jm_maxt) |
|---|
| 523 | END DO |
|---|
| 524 | |
|---|
| 525 | DO jk = jm_mint+1, jm_maxt |
|---|
| 526 | DO ji = 1, npti |
|---|
| 527 | jm = MIN(MAX(jm_min(ji)+1,jk),jm_max(ji)) |
|---|
| 528 | zdiagbis(ji,jm) = ztrid (ji,jm,2) - ztrid(ji,jm,1) * ztrid (ji,jm-1,3) / zdiagbis(ji,jm-1) |
|---|
| 529 | zindtbis(ji,jm) = zindterm(ji,jm ) - ztrid(ji,jm,1) * zindtbis(ji,jm-1 ) / zdiagbis(ji,jm-1) |
|---|
| 530 | END DO |
|---|
| 531 | END DO |
|---|
| 532 | |
|---|
| 533 | ! ice temperatures |
|---|
| 534 | DO ji = 1, npti |
|---|
| 535 | ! Variable used after iterations |
|---|
| 536 | ! Value must be frozen after convergence for MPP independance reason |
|---|
| 537 | IF ( .NOT. l_T_converged(ji) ) & |
|---|
| 538 | t_i_1d(ji,nlay_i) = zindtbis(ji,jm_max(ji)) / zdiagbis(ji,jm_max(ji)) |
|---|
| 539 | END DO |
|---|
| 540 | |
|---|
| 541 | DO jm = nlay_i + nlay_s, nlay_s + 2, -1 |
|---|
| 542 | DO ji = 1, npti |
|---|
| 543 | jk = jm - nlay_s - 1 |
|---|
| 544 | IF ( .NOT. l_T_converged(ji) ) & |
|---|
| 545 | t_i_1d(ji,jk) = ( zindtbis(ji,jm) - ztrid(ji,jm,3) * t_i_1d(ji,jk+1) ) / zdiagbis(ji,jm) |
|---|
| 546 | END DO |
|---|
| 547 | END DO |
|---|
| 548 | |
|---|
| 549 | DO ji = 1, npti |
|---|
| 550 | ! Variables used after iterations |
|---|
| 551 | ! Value must be frozen after convergence for MPP independance reason |
|---|
| 552 | IF ( .NOT. l_T_converged(ji) ) THEN |
|---|
| 553 | ! snow temperatures |
|---|
| 554 | IF( h_s_1d(ji) > 0._wp ) THEN |
|---|
| 555 | 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) |
|---|
| 556 | ENDIF |
|---|
| 557 | ! surface temperature |
|---|
| 558 | ztsub(ji) = t_su_1d(ji) |
|---|
| 559 | IF( t_su_1d(ji) < rt0 ) THEN |
|---|
| 560 | t_su_1d(ji) = ( zindtbis(ji,jm_min(ji)) - ztrid(ji,jm_min(ji),3) * & |
|---|
| 561 | & ( za_s_fra(ji) * t_s_1d(ji,1) + (1._wp - za_s_fra(ji)) * t_i_1d(ji,1) ) ) / zdiagbis(ji,jm_min(ji)) |
|---|
| 562 | ENDIF |
|---|
| 563 | ENDIF |
|---|
| 564 | END DO |
|---|
| 565 | ! |
|---|
| 566 | !-------------------------------------------------------------- |
|---|
| 567 | ! 9) Has the scheme converged?, end of the iterative procedure |
|---|
| 568 | !-------------------------------------------------------------- |
|---|
| 569 | ! check that nowhere it has started to melt |
|---|
| 570 | ! zdti_max is a measure of error, it has to be under zdti_bnd |
|---|
| 571 | |
|---|
| 572 | DO ji = 1, npti |
|---|
| 573 | |
|---|
| 574 | zdti_max = 0._wp |
|---|
| 575 | |
|---|
| 576 | IF ( .NOT. l_T_converged(ji) ) THEN |
|---|
| 577 | t_su_1d(ji) = MAX( MIN( t_su_1d(ji) , rt0 ) , rt0 - 100._wp ) |
|---|
| 578 | zdti_max = MAX( zdti_max, ABS( t_su_1d(ji) - ztsub(ji) ) ) |
|---|
| 579 | |
|---|
| 580 | t_s_1d(ji,1:nlay_s) = MAX( MIN( t_s_1d(ji,1:nlay_s), rt0 ), rt0 - 100._wp ) |
|---|
| 581 | zdti_max = MAX ( zdti_max , MAXVAL( ABS( t_s_1d(ji,1:nlay_s) - ztsb(ji,1:nlay_s) ) ) ) |
|---|
| 582 | |
|---|
| 583 | DO jk = 1, nlay_i |
|---|
| 584 | ztmelts = -rTmlt * sz_i_1d(ji,jk) + rt0 |
|---|
| 585 | t_i_1d(ji,jk) = MAX( MIN( t_i_1d(ji,jk), ztmelts ), rt0 - 100._wp ) |
|---|
| 586 | zdti_max = MAX( zdti_max, ABS( t_i_1d(ji,jk) - ztib(ji,jk) ) ) |
|---|
| 587 | END DO |
|---|
| 588 | |
|---|
| 589 | IF ( zdti_max < zdti_bnd ) l_T_converged(ji) = .TRUE. |
|---|
| 590 | |
|---|
| 591 | ENDIF |
|---|
| 592 | |
|---|
| 593 | END DO |
|---|
| 594 | |
|---|
| 595 | !----------------------------------------! |
|---|
| 596 | ! ! |
|---|
| 597 | ! Conduction flux is on ! |
|---|
| 598 | ! ! |
|---|
| 599 | !----------------------------------------! |
|---|
| 600 | ! |
|---|
| 601 | ELSEIF( k_cnd == np_cnd_ON ) THEN |
|---|
| 602 | ! |
|---|
| 603 | ! ==> we use a modified BL99 solver with conduction flux (qcn_ice) as forcing term |
|---|
| 604 | ! |
|---|
| 605 | !---------------------------- |
|---|
| 606 | ! 7) tridiagonal system terms |
|---|
| 607 | !---------------------------- |
|---|
| 608 | ! layer denotes the number of the layer in the snow or in the ice |
|---|
| 609 | ! jm denotes the reference number of the equation in the tridiagonal |
|---|
| 610 | ! system, terms of tridiagonal system are indexed as following : |
|---|
| 611 | ! 1 is subdiagonal term, 2 is diagonal and 3 is superdiagonal one |
|---|
| 612 | |
|---|
| 613 | ! ice interior terms (top equation has the same form as the others) |
|---|
| 614 | ztrid (1:npti,:,:) = 0._wp |
|---|
| 615 | zindterm(1:npti,:) = 0._wp |
|---|
| 616 | zindtbis(1:npti,:) = 0._wp |
|---|
| 617 | zdiagbis(1:npti,:) = 0._wp |
|---|
| 618 | |
|---|
| 619 | DO jm = nlay_s + 2, nlay_s + nlay_i |
|---|
| 620 | DO ji = 1, npti |
|---|
| 621 | jk = jm - nlay_s - 1 |
|---|
| 622 | ztrid (ji,jm,1) = - zeta_i(ji,jk) * zkappa_i(ji,jk-1) |
|---|
| 623 | ztrid (ji,jm,2) = 1._wp + zeta_i(ji,jk) * ( zkappa_i(ji,jk-1) + zkappa_i(ji,jk) ) |
|---|
| 624 | ztrid (ji,jm,3) = - zeta_i(ji,jk) * zkappa_i(ji,jk) |
|---|
| 625 | zindterm(ji,jm) = ztiold(ji,jk) + zeta_i(ji,jk) * zradab_i(ji,jk) |
|---|
| 626 | END DO |
|---|
| 627 | ENDDO |
|---|
| 628 | |
|---|
| 629 | jm = nlay_s + nlay_i + 1 |
|---|
| 630 | DO ji = 1, npti |
|---|
| 631 | ! ice bottom term |
|---|
| 632 | ztrid (ji,jm,1) = - zeta_i(ji,nlay_i) * zkappa_i(ji,nlay_i-1) |
|---|
| 633 | ztrid (ji,jm,2) = 1._wp + zeta_i(ji,nlay_i) * ( zkappa_i(ji,nlay_i-1) + zkappa_i(ji,nlay_i) * zg1 ) |
|---|
| 634 | ztrid (ji,jm,3) = 0._wp |
|---|
| 635 | zindterm(ji,jm) = ztiold(ji,nlay_i) + zeta_i(ji,nlay_i) * & |
|---|
| 636 | & ( zradab_i(ji,nlay_i) + zkappa_i(ji,nlay_i) * zg1 * t_bo_1d(ji) ) |
|---|
| 637 | ENDDO |
|---|
| 638 | |
|---|
| 639 | DO ji = 1, npti |
|---|
| 640 | ! !---------------------! |
|---|
| 641 | IF( h_s_1d(ji) > 0._wp ) THEN ! snow-covered cells ! |
|---|
| 642 | ! !---------------------! |
|---|
| 643 | ! snow interior terms (bottom equation has the same form as the others) |
|---|
| 644 | DO jm = 3, nlay_s + 1 |
|---|
| 645 | jk = jm - 1 |
|---|
| 646 | ztrid (ji,jm,1) = - zeta_s(ji,jk) * zkappa_s(ji,jk-1) |
|---|
| 647 | ztrid (ji,jm,2) = 1._wp + zeta_s(ji,jk) * ( zkappa_s(ji,jk-1) + zkappa_s(ji,jk) ) |
|---|
| 648 | ztrid (ji,jm,3) = - zeta_s(ji,jk) * zkappa_s(ji,jk) |
|---|
| 649 | zindterm(ji,jm) = ztsold(ji,jk) + zeta_s(ji,jk) * zradab_s(ji,jk) |
|---|
| 650 | END DO |
|---|
| 651 | |
|---|
| 652 | ! case of only one layer in the ice (ice equation is altered) |
|---|
| 653 | IF ( nlay_i == 1 ) THEN |
|---|
| 654 | ztrid (ji,nlay_s+2,3) = 0._wp |
|---|
| 655 | zindterm(ji,nlay_s+2) = zindterm(ji,nlay_s+2) + zeta_i(ji,1) * zkappa_i(ji,1) * t_bo_1d(ji) |
|---|
| 656 | ENDIF |
|---|
| 657 | |
|---|
| 658 | jm_min(ji) = 2 |
|---|
| 659 | jm_max(ji) = nlay_i + nlay_s + 1 |
|---|
| 660 | |
|---|
| 661 | ! first layer of snow equation |
|---|
| 662 | ztrid (ji,2,1) = 0._wp |
|---|
| 663 | ztrid (ji,2,2) = 1._wp + zeta_s(ji,1) * zkappa_s(ji,1) |
|---|
| 664 | ztrid (ji,2,3) = - zeta_s(ji,1) * zkappa_s(ji,1) |
|---|
| 665 | zindterm(ji,2) = ztsold(ji,1) + zeta_s(ji,1) * ( zradab_s(ji,1) + qcn_ice_1d(ji) ) |
|---|
| 666 | |
|---|
| 667 | ! !---------------------! |
|---|
| 668 | ELSE ! cells without snow ! |
|---|
| 669 | ! !---------------------! |
|---|
| 670 | jm_min(ji) = nlay_s + 2 |
|---|
| 671 | jm_max(ji) = nlay_i + nlay_s + 1 |
|---|
| 672 | |
|---|
| 673 | ! first layer of ice equation |
|---|
| 674 | ztrid (ji,jm_min(ji),1) = 0._wp |
|---|
| 675 | ztrid (ji,jm_min(ji),2) = 1._wp + zeta_i(ji,1) * zkappa_i(ji,1) |
|---|
| 676 | ztrid (ji,jm_min(ji),3) = - zeta_i(ji,1) * zkappa_i(ji,1) |
|---|
| 677 | zindterm(ji,jm_min(ji)) = ztiold(ji,1) + zeta_i(ji,1) * ( zradab_i(ji,1) + qcn_ice_1d(ji) ) |
|---|
| 678 | |
|---|
| 679 | ! case of only one layer in the ice (surface & ice equations are altered) |
|---|
| 680 | IF( nlay_i == 1 ) THEN |
|---|
| 681 | ztrid (ji,jm_min(ji),1) = 0._wp |
|---|
| 682 | ztrid (ji,jm_min(ji),2) = 1._wp + zeta_i(ji,1) * zkappa_i(ji,1) |
|---|
| 683 | ztrid (ji,jm_min(ji),3) = 0._wp |
|---|
| 684 | zindterm(ji,jm_min(ji)) = ztiold(ji,1) + zeta_i(ji,1) * & |
|---|
| 685 | & ( zradab_i(ji,1) + zkappa_i(ji,1) * t_bo_1d(ji) + qcn_ice_1d(ji) ) |
|---|
| 686 | ENDIF |
|---|
| 687 | |
|---|
| 688 | ENDIF |
|---|
| 689 | ! |
|---|
| 690 | zindtbis(ji,jm_min(ji)) = zindterm(ji,jm_min(ji)) |
|---|
| 691 | zdiagbis(ji,jm_min(ji)) = ztrid (ji,jm_min(ji),2) |
|---|
| 692 | ! |
|---|
| 693 | END DO |
|---|
| 694 | ! |
|---|
| 695 | !------------------------------ |
|---|
| 696 | ! 8) tridiagonal system solving |
|---|
| 697 | !------------------------------ |
|---|
| 698 | ! Solve the tridiagonal system with Gauss elimination method. |
|---|
| 699 | ! Thomas algorithm, from Computational fluid Dynamics, J.D. ANDERSON, McGraw-Hill 1984 |
|---|
| 700 | jm_maxt = 0 |
|---|
| 701 | jm_mint = nlay_i+5 |
|---|
| 702 | DO ji = 1, npti |
|---|
| 703 | jm_mint = MIN(jm_min(ji),jm_mint) |
|---|
| 704 | jm_maxt = MAX(jm_max(ji),jm_maxt) |
|---|
| 705 | END DO |
|---|
| 706 | |
|---|
| 707 | DO jk = jm_mint+1, jm_maxt |
|---|
| 708 | DO ji = 1, npti |
|---|
| 709 | jm = MIN(MAX(jm_min(ji)+1,jk),jm_max(ji)) |
|---|
| 710 | zdiagbis(ji,jm) = ztrid (ji,jm,2) - ztrid(ji,jm,1) * ztrid (ji,jm-1,3) / zdiagbis(ji,jm-1) |
|---|
| 711 | zindtbis(ji,jm) = zindterm(ji,jm) - ztrid(ji,jm,1) * zindtbis(ji,jm-1) / zdiagbis(ji,jm-1) |
|---|
| 712 | END DO |
|---|
| 713 | END DO |
|---|
| 714 | |
|---|
| 715 | ! ice temperatures |
|---|
| 716 | DO ji = 1, npti |
|---|
| 717 | ! Variable used after iterations |
|---|
| 718 | ! Value must be frozen after convergence for MPP independance reason |
|---|
| 719 | IF ( .NOT. l_T_converged(ji) ) & |
|---|
| 720 | t_i_1d(ji,nlay_i) = zindtbis(ji,jm_max(ji)) / zdiagbis(ji,jm_max(ji)) |
|---|
| 721 | END DO |
|---|
| 722 | |
|---|
| 723 | DO jm = nlay_i + nlay_s, nlay_s + 2, -1 |
|---|
| 724 | DO ji = 1, npti |
|---|
| 725 | IF ( .NOT. l_T_converged(ji) ) THEN |
|---|
| 726 | jk = jm - nlay_s - 1 |
|---|
| 727 | t_i_1d(ji,jk) = ( zindtbis(ji,jm) - ztrid(ji,jm,3) * t_i_1d(ji,jk+1) ) / zdiagbis(ji,jm) |
|---|
| 728 | ENDIF |
|---|
| 729 | END DO |
|---|
| 730 | END DO |
|---|
| 731 | |
|---|
| 732 | ! snow temperatures |
|---|
| 733 | DO ji = 1, npti |
|---|
| 734 | ! Variable used after iterations |
|---|
| 735 | ! Value must be frozen after convergence for MPP independance reason |
|---|
| 736 | IF ( .NOT. l_T_converged(ji) ) THEN |
|---|
| 737 | IF( h_s_1d(ji) > 0._wp ) THEN |
|---|
| 738 | 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) |
|---|
| 739 | ENDIF |
|---|
| 740 | ENDIF |
|---|
| 741 | END DO |
|---|
| 742 | ! |
|---|
| 743 | !-------------------------------------------------------------- |
|---|
| 744 | ! 9) Has the scheme converged?, end of the iterative procedure |
|---|
| 745 | !-------------------------------------------------------------- |
|---|
| 746 | ! check that nowhere it has started to melt |
|---|
| 747 | ! zdti_max is a measure of error, it has to be under zdti_bnd |
|---|
| 748 | |
|---|
| 749 | DO ji = 1, npti |
|---|
| 750 | |
|---|
| 751 | zdti_max = 0._wp |
|---|
| 752 | |
|---|
| 753 | IF ( .NOT. l_T_converged(ji) ) THEN |
|---|
| 754 | ! t_s |
|---|
| 755 | t_s_1d(ji,1:nlay_s) = MAX( MIN( t_s_1d(ji,1:nlay_s), rt0 ), rt0 - 100._wp ) |
|---|
| 756 | zdti_max = MAX ( zdti_max , MAXVAL( ABS( t_s_1d(ji,1:nlay_s) - ztsb(ji,1:nlay_s) ) ) ) |
|---|
| 757 | ! t_i |
|---|
| 758 | DO jk = 1, nlay_i |
|---|
| 759 | ztmelts = -rTmlt * sz_i_1d(ji,jk) + rt0 |
|---|
| 760 | t_i_1d(ji,jk) = MAX( MIN( t_i_1d(ji,jk), ztmelts ), rt0 - 100._wp ) |
|---|
| 761 | zdti_max = MAX ( zdti_max, ABS( t_i_1d(ji,jk) - ztib(ji,jk) ) ) |
|---|
| 762 | END DO |
|---|
| 763 | |
|---|
| 764 | IF ( zdti_max < zdti_bnd ) l_T_converged(ji) = .TRUE. |
|---|
| 765 | |
|---|
| 766 | ENDIF |
|---|
| 767 | |
|---|
| 768 | END DO |
|---|
| 769 | |
|---|
| 770 | ENDIF ! k_cnd |
|---|
| 771 | |
|---|
| 772 | END DO ! End of the do while iterative procedure |
|---|
| 773 | ! |
|---|
| 774 | ! convergence tests (only for output) |
|---|
| 775 | IF( ln_zdf_chkcvg ) THEN |
|---|
| 776 | tice_cvg_1d(1:npti) = 0._wp |
|---|
| 777 | DO jk = 1, nlay_s ! snow temperature |
|---|
| 778 | DO ji = 1, npti |
|---|
| 779 | tice_cvg_1d(ji) = MAX( tice_cvg_1d(ji), ABS( t_s_1d(ji,jk) - ztsb(ji,jk) ) ) |
|---|
| 780 | ENDDO |
|---|
| 781 | ENDDO |
|---|
| 782 | DO jk = 1, nlay_i ! ice temperature |
|---|
| 783 | DO ji = 1, npti |
|---|
| 784 | tice_cvg_1d(ji) = MAX( tice_cvg_1d(ji), ABS( t_i_1d(ji,jk) - ztib(ji,jk) ) ) |
|---|
| 785 | ENDDO |
|---|
| 786 | ENDDO |
|---|
| 787 | IF( k_cnd == np_cnd_OFF .OR. k_cnd == np_cnd_EMU ) THEN |
|---|
| 788 | DO ji = 1, npti ! surface temperature |
|---|
| 789 | tice_cvg_1d(ji) = MAX( tice_cvg_1d(ji), ABS( t_su_1d(ji) - ztsub(ji) ) ) |
|---|
| 790 | ENDDO |
|---|
| 791 | ENDIF |
|---|
| 792 | ENDIF |
|---|
| 793 | ! |
|---|
| 794 | !----------------------------- |
|---|
| 795 | ! 10) Fluxes at the interfaces |
|---|
| 796 | !----------------------------- |
|---|
| 797 | ! |
|---|
| 798 | ! --- calculate conduction fluxes (positive downward) |
|---|
| 799 | ! bottom ice conduction flux |
|---|
| 800 | DO ji = 1, npti |
|---|
| 801 | qcn_ice_bot_1d(ji) = - zkappa_i(ji,nlay_i) * zg1 * ( t_bo_1d(ji ) - t_i_1d (ji,nlay_i) ) |
|---|
| 802 | END DO |
|---|
| 803 | ! surface ice conduction flux |
|---|
| 804 | IF( k_cnd == np_cnd_OFF .OR. k_cnd == np_cnd_EMU ) THEN |
|---|
| 805 | ! |
|---|
| 806 | DO ji = 1, npti |
|---|
| 807 | qcn_ice_top_1d(ji) = - za_s_fra(ji) * zkappa_s(ji,0) * zg1s * ( t_s_1d(ji,1) - t_su_1d(ji) ) & |
|---|
| 808 | & - ( 1._wp - za_s_fra(ji) ) * zkappa_i(ji,0) * zg1 * ( t_i_1d(ji,1) - t_su_1d(ji) ) |
|---|
| 809 | END DO |
|---|
| 810 | ! |
|---|
| 811 | ELSEIF( k_cnd == np_cnd_ON ) THEN |
|---|
| 812 | ! |
|---|
| 813 | DO ji = 1, npti |
|---|
| 814 | qcn_ice_top_1d(ji) = qcn_ice_1d(ji) |
|---|
| 815 | END DO |
|---|
| 816 | ! |
|---|
| 817 | ENDIF |
|---|
| 818 | ! surface ice temperature |
|---|
| 819 | IF( k_cnd == np_cnd_ON .AND. ln_cndemulate ) THEN |
|---|
| 820 | ! |
|---|
| 821 | DO ji = 1, npti |
|---|
| 822 | t_su_1d(ji) = ( qcn_ice_top_1d(ji) & ! calculate surface temperature |
|---|
| 823 | & + za_s_fra(ji) * zkappa_s(ji,0) * zg1s * t_s_1d(ji,1) & |
|---|
| 824 | & + (1._wp - za_s_fra(ji)) * zkappa_i(ji,0) * zg1 * t_i_1d(ji,1) & |
|---|
| 825 | & ) / MAX( epsi10, za_s_fra(ji) * zkappa_s(ji,0) * zg1s + (1._wp - za_s_fra(ji)) * zkappa_i(ji,0) * zg1 ) |
|---|
| 826 | t_su_1d(ji) = MAX( MIN( t_su_1d(ji), rt0 ), rt0 - 100._wp ) ! cap t_su |
|---|
| 827 | END DO |
|---|
| 828 | ! |
|---|
| 829 | ENDIF |
|---|
| 830 | ! |
|---|
| 831 | ! --- Diagnose the heat loss due to changing non-solar / conduction flux --- ! |
|---|
| 832 | ! |
|---|
| 833 | IF( k_cnd == np_cnd_OFF .OR. k_cnd == np_cnd_EMU ) THEN |
|---|
| 834 | ! |
|---|
| 835 | DO ji = 1, npti |
|---|
| 836 | hfx_err_dif_1d(ji) = hfx_err_dif_1d(ji) - ( qns_ice_1d(ji) - zqns_ice_b(ji) ) * a_i_1d(ji) |
|---|
| 837 | END DO |
|---|
| 838 | ! |
|---|
| 839 | ENDIF |
|---|
| 840 | ! |
|---|
| 841 | ! --- Diagnose the heat loss due to non-fully converged temperature solution (should not be above 10-4 W-m2) --- ! |
|---|
| 842 | ! |
|---|
| 843 | IF( k_cnd == np_cnd_OFF .OR. k_cnd == np_cnd_ON ) THEN |
|---|
| 844 | |
|---|
| 845 | CALL ice_var_enthalpy |
|---|
| 846 | |
|---|
| 847 | ! zhfx_err = correction on the diagnosed heat flux due to non-convergence of the algorithm used to solve heat equation |
|---|
| 848 | DO ji = 1, npti |
|---|
| 849 | zdq = - zq_ini(ji) + ( SUM( e_i_1d(ji,1:nlay_i) ) * h_i_1d(ji) * r1_nlay_i + & |
|---|
| 850 | & SUM( e_s_1d(ji,1:nlay_s) ) * h_s_1d(ji) * r1_nlay_s ) |
|---|
| 851 | |
|---|
| 852 | IF( k_cnd == np_cnd_OFF ) THEN |
|---|
| 853 | |
|---|
| 854 | IF( t_su_1d(ji) < rt0 ) THEN ! case T_su < 0degC |
|---|
| 855 | zhfx_err = ( qns_ice_1d(ji) + qsr_ice_1d(ji) - zradtr_i(ji,nlay_i) - qcn_ice_bot_1d(ji) & |
|---|
| 856 | & + zdq * r1_rdtice ) * a_i_1d(ji) |
|---|
| 857 | ELSE ! case T_su = 0degC |
|---|
| 858 | zhfx_err = ( qcn_ice_top_1d(ji) + qtr_ice_top_1d(ji) - zradtr_i(ji,nlay_i) - qcn_ice_bot_1d(ji) & |
|---|
| 859 | & + zdq * r1_rdtice ) * a_i_1d(ji) |
|---|
| 860 | ENDIF |
|---|
| 861 | |
|---|
| 862 | ELSEIF( k_cnd == np_cnd_ON ) THEN |
|---|
| 863 | |
|---|
| 864 | zhfx_err = ( qcn_ice_top_1d(ji) + qtr_ice_top_1d(ji) - zradtr_i(ji,nlay_i) - qcn_ice_bot_1d(ji) & |
|---|
| 865 | & + zdq * r1_rdtice ) * a_i_1d(ji) |
|---|
| 866 | |
|---|
| 867 | ENDIF |
|---|
| 868 | ! |
|---|
| 869 | ! total heat sink to be sent to the ocean |
|---|
| 870 | hfx_err_dif_1d(ji) = hfx_err_dif_1d(ji) + zhfx_err |
|---|
| 871 | ! |
|---|
| 872 | ! hfx_dif = Heat flux diagnostic of sensible heat used to warm/cool ice in W.m-2 |
|---|
| 873 | hfx_dif_1d(ji) = hfx_dif_1d(ji) - zdq * r1_rdtice * a_i_1d(ji) |
|---|
| 874 | ! |
|---|
| 875 | END DO |
|---|
| 876 | ! |
|---|
| 877 | ENDIF |
|---|
| 878 | ! |
|---|
| 879 | !-------------------------------------------------------------------- |
|---|
| 880 | ! 11) reset inner snow and ice temperatures, update conduction fluxes |
|---|
| 881 | !-------------------------------------------------------------------- |
|---|
| 882 | ! effective conductivity and 1st layer temperature (needed by Met Office) |
|---|
| 883 | ! this is a conductivity at mid-layer, hence the factor 2 |
|---|
| 884 | DO ji = 1, npti |
|---|
| 885 | IF( h_i_1d(ji) >= zhi_ssl ) THEN ! zkappa_i=0 when h_i<zhi_ssl (but ztcond_i/=0) |
|---|
| 886 | cnd_ice_1d(ji) = 2._wp * zkappa_i(ji,0) |
|---|
| 887 | ELSE |
|---|
| 888 | cnd_ice_1d(ji) = 2._wp * ztcond_i(ji,0) / zhi_ssl ! cnd_ice is capped by: cond_i/zhi_ssl |
|---|
| 889 | ENDIF |
|---|
| 890 | t1_ice_1d(ji) = za_s_fra(ji) * t_s_1d(ji,1) + ( 1._wp - za_s_fra(ji) ) * t_i_1d(ji,1) |
|---|
| 891 | END DO |
|---|
| 892 | ! |
|---|
| 893 | IF( k_cnd == np_cnd_EMU ) THEN |
|---|
| 894 | ! Restore temperatures to their initial values |
|---|
| 895 | t_s_1d (1:npti,:) = ztsold (1:npti,:) |
|---|
| 896 | t_i_1d (1:npti,:) = ztiold (1:npti,:) |
|---|
| 897 | qcn_ice_1d(1:npti) = qcn_ice_top_1d(1:npti) |
|---|
| 898 | ENDIF |
|---|
| 899 | ! |
|---|
| 900 | ! --- SIMIP diagnostics |
|---|
| 901 | ! |
|---|
| 902 | DO ji = 1, npti |
|---|
| 903 | !--- Snow-ice interfacial temperature (diagnostic SIMIP) |
|---|
| 904 | IF( h_s_1d(ji) >= zhs_ssl ) THEN |
|---|
| 905 | t_si_1d(ji) = ( rn_cnd_s * zh_i(ji) * t_s_1d(ji,1) + ztcond_i(ji,1) * zh_s(ji) * t_i_1d(ji,1) ) / & |
|---|
| 906 | & ( rn_cnd_s * zh_i(ji) + ztcond_i(ji,1) * zh_s(ji) ) |
|---|
| 907 | ELSE |
|---|
| 908 | t_si_1d(ji) = t_su_1d(ji) |
|---|
| 909 | ENDIF |
|---|
| 910 | END DO |
|---|
| 911 | ! |
|---|
| 912 | END SUBROUTINE ice_thd_zdf_BL99 |
|---|
| 913 | |
|---|
| 914 | #else |
|---|
| 915 | !!---------------------------------------------------------------------- |
|---|
| 916 | !! Default option Dummy Module No SI3 sea-ice model |
|---|
| 917 | !!---------------------------------------------------------------------- |
|---|
| 918 | #endif |
|---|
| 919 | |
|---|
| 920 | !!====================================================================== |
|---|
| 921 | END MODULE icethd_zdf_BL99 |
|---|
