[8586] | 1 | MODULE icedyn_adv_umx |
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| 2 | !!============================================================================== |
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| 3 | !! *** MODULE icedyn_adv_umx *** |
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| 4 | !! sea-ice : advection using the ULTIMATE-MACHO scheme |
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| 5 | !!============================================================================== |
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| 6 | !! History : 3.6 ! 2014-11 (C. Rousset, G. Madec) Original code |
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[9604] | 7 | !! 4.0 ! 2018 (many people) SI3 [aka Sea Ice cube] |
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[8586] | 8 | !!---------------------------------------------------------------------- |
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[9570] | 9 | #if defined key_si3 |
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[8586] | 10 | !!---------------------------------------------------------------------- |
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[9570] | 11 | !! 'key_si3' SI3 sea-ice model |
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[8586] | 12 | !!---------------------------------------------------------------------- |
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[10911] | 13 | !! ice_dyn_adv_umx : update the tracer fields |
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[8586] | 14 | !! ultimate_x(_y) : compute a tracer value at velocity points using ULTIMATE scheme at various orders |
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[10911] | 15 | !! macho : compute the fluxes |
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| 16 | !! nonosc_ice : limit the fluxes using a non-oscillatory algorithm |
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[8586] | 17 | !!---------------------------------------------------------------------- |
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| 18 | USE phycst ! physical constant |
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| 19 | USE dom_oce ! ocean domain |
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| 20 | USE sbc_oce , ONLY : nn_fsbc ! update frequency of surface boundary condition |
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| 21 | USE ice ! sea-ice variables |
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[10413] | 22 | USE icevar ! sea-ice: operations |
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[8586] | 23 | ! |
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| 24 | USE in_out_manager ! I/O manager |
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[10786] | 25 | USE iom ! I/O manager library |
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[8586] | 26 | USE lib_mpp ! MPP library |
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| 27 | USE lib_fortran ! fortran utilities (glob_sum + no signed zero) |
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| 28 | USE lbclnk ! lateral boundary conditions (or mpp links) |
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| 29 | |
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| 30 | IMPLICIT NONE |
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| 31 | PRIVATE |
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| 32 | |
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| 33 | PUBLIC ice_dyn_adv_umx ! called by icedyn_adv.F90 |
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[10930] | 34 | ! |
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[10945] | 35 | INTEGER, PARAMETER :: np_advS = 1 ! advection for S and T: dVS/dt = -div( uVS ) => np_advS = 1 |
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| 36 | ! or dVS/dt = -div( uA * uHS / u ) => np_advS = 2 |
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| 37 | ! or dVS/dt = -div( uV * uS / u ) => np_advS = 3 |
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| 38 | INTEGER, PARAMETER :: np_limiter = 1 ! limiter: 1 = nonosc |
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| 39 | ! 2 = superbee |
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| 40 | ! 3 = h3 |
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| 41 | LOGICAL :: ll_upsxy = .TRUE. ! alternate directions for upstream |
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| 42 | LOGICAL :: ll_hoxy = .TRUE. ! alternate directions for high order |
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| 43 | LOGICAL :: ll_neg = .TRUE. ! if T interpolated at u/v points is negative or v_i < 1.e-6 |
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| 44 | ! then interpolate T at u/v points using the upstream scheme |
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| 45 | LOGICAL :: ll_prelim = .FALSE. ! prelimiter from: Zalesak(1979) eq. 14 => not well defined in 2D |
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[10930] | 46 | ! |
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[10945] | 47 | REAL(wp) :: z1_6 = 1._wp / 6._wp ! =1/6 |
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| 48 | REAL(wp) :: z1_120 = 1._wp / 120._wp ! =1/120 |
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[10930] | 49 | ! |
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[10945] | 50 | INTEGER, ALLOCATABLE, DIMENSION(:,:,:) :: imsk_small, jmsk_small |
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[10930] | 51 | ! |
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[8586] | 52 | !! * Substitutions |
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[12377] | 53 | # include "do_loop_substitute.h90" |
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[8586] | 54 | !!---------------------------------------------------------------------- |
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[9598] | 55 | !! NEMO/ICE 4.0 , NEMO Consortium (2018) |
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[10069] | 56 | !! $Id$ |
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[10413] | 57 | !! Software governed by the CeCILL licence (./LICENSE) |
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[8586] | 58 | !!---------------------------------------------------------------------- |
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| 59 | CONTAINS |
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| 60 | |
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[10911] | 61 | SUBROUTINE ice_dyn_adv_umx( kn_umx, kt, pu_ice, pv_ice, ph_i, ph_s, ph_ip, & |
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[13472] | 62 | & pato_i, pv_i, pv_s, psv_i, poa_i, pa_i, pa_ip, pv_ip, pv_il, pe_s, pe_i ) |
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[8586] | 63 | !!---------------------------------------------------------------------- |
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| 64 | !! *** ROUTINE ice_dyn_adv_umx *** |
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| 65 | !! |
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| 66 | !! ** Purpose : Compute the now trend due to total advection of |
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| 67 | !! tracers and add it to the general trend of tracer equations |
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| 68 | !! using an "Ultimate-Macho" scheme |
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| 69 | !! |
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| 70 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
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| 71 | !!---------------------------------------------------------------------- |
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[10413] | 72 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
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[8586] | 73 | INTEGER , INTENT(in ) :: kt ! time step |
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| 74 | REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pu_ice ! ice i-velocity |
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| 75 | REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pv_ice ! ice j-velocity |
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[10911] | 76 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: ph_i ! ice thickness |
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| 77 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: ph_s ! snw thickness |
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| 78 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: ph_ip ! ice pond thickness |
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[8586] | 79 | REAL(wp), DIMENSION(:,:) , INTENT(inout) :: pato_i ! open water area |
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| 80 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i ! ice volume |
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| 81 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_s ! snw volume |
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| 82 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: psv_i ! salt content |
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| 83 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: poa_i ! age content |
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| 84 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_i ! ice concentration |
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[11627] | 85 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_ip ! melt pond concentration |
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[8586] | 86 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_ip ! melt pond volume |
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[13472] | 87 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_il ! melt pond lid volume |
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[8586] | 88 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s ! snw heat content |
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| 89 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_i ! ice heat content |
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| 90 | ! |
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| 91 | INTEGER :: ji, jj, jk, jl, jt ! dummy loop indices |
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[10413] | 92 | INTEGER :: icycle ! number of sub-timestep for the advection |
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| 93 | REAL(wp) :: zamsk ! 1 if advection of concentration, 0 if advection of other tracers |
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[13886] | 94 | REAL(wp) :: zdt, z1_dt, zvi_cen |
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[13472] | 95 | REAL(wp), DIMENSION(1) :: zcflprv, zcflnow ! for global communication |
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| 96 | REAL(wp), DIMENSION(jpi,jpj) :: zudy, zvdx, zcu_box, zcv_box |
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| 97 | REAL(wp), DIMENSION(jpi,jpj) :: zati1, zati2 |
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| 98 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zu_cat, zv_cat |
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| 99 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zua_ho, zva_ho, zua_ups, zva_ups |
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| 100 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: z1_ai , z1_aip, zhvar |
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| 101 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zhi_max, zhs_max, zhip_max, zs_i, zsi_max |
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| 102 | REAL(wp), DIMENSION(jpi,jpj,nlay_i,jpl) :: ze_i, zei_max |
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| 103 | REAL(wp), DIMENSION(jpi,jpj,nlay_s,jpl) :: ze_s, zes_max |
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[10945] | 104 | ! |
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| 105 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: zuv_ho, zvv_ho, zuv_ups, zvv_ups, z1_vi, z1_vs |
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[13886] | 106 | !! diagnostics |
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| 107 | REAL(wp), DIMENSION(jpi,jpj) :: zdiag_adv_mass, zdiag_adv_salt, zdiag_adv_heat |
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[8586] | 108 | !!---------------------------------------------------------------------- |
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| 109 | ! |
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| 110 | IF( kt == nit000 .AND. lwp ) WRITE(numout,*) '-- ice_dyn_adv_umx: Ultimate-Macho advection scheme' |
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| 111 | ! |
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[13472] | 112 | ! --- Record max of the surrounding 9-pts (for call Hbig) --- ! |
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| 113 | ! thickness and salinity |
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| 114 | WHERE( pv_i(:,:,:) >= epsi10 ) ; zs_i(:,:,:) = psv_i(:,:,:) / pv_i(:,:,:) |
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| 115 | ELSEWHERE ; zs_i(:,:,:) = 0._wp |
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| 116 | END WHERE |
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[13886] | 117 | CALL icemax3D( ph_i , zhi_max ) |
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| 118 | CALL icemax3D( ph_s , zhs_max ) |
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| 119 | CALL icemax3D( ph_ip, zhip_max) |
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| 120 | CALL icemax3D( zs_i , zsi_max ) |
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[13472] | 121 | CALL lbc_lnk_multi( 'icedyn_adv_umx', zhi_max, 'T', 1._wp, zhs_max, 'T', 1._wp, zhip_max, 'T', 1._wp, zsi_max, 'T', 1._wp ) |
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[10911] | 122 | ! |
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[13472] | 123 | ! enthalpies |
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| 124 | DO jk = 1, nlay_i |
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| 125 | WHERE( pv_i(:,:,:) >= epsi10 ) ; ze_i(:,:,jk,:) = pe_i(:,:,jk,:) / pv_i(:,:,:) |
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| 126 | ELSEWHERE ; ze_i(:,:,jk,:) = 0._wp |
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| 127 | END WHERE |
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| 128 | END DO |
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| 129 | DO jk = 1, nlay_s |
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| 130 | WHERE( pv_s(:,:,:) >= epsi10 ) ; ze_s(:,:,jk,:) = pe_s(:,:,jk,:) / pv_s(:,:,:) |
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| 131 | ELSEWHERE ; ze_s(:,:,jk,:) = 0._wp |
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| 132 | END WHERE |
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[13886] | 133 | END DO |
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| 134 | CALL icemax4D( ze_i , zei_max ) |
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| 135 | CALL icemax4D( ze_s , zes_max ) |
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| 136 | CALL lbc_lnk( 'icedyn_adv_umx', zei_max, 'T', 1._wp ) |
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| 137 | CALL lbc_lnk( 'icedyn_adv_umx', zes_max, 'T', 1._wp ) |
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[10911] | 138 | ! |
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[13472] | 139 | ! |
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[10911] | 140 | ! --- If ice drift is too fast, use subtime steps for advection (CFL test for stability) --- ! |
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| 141 | ! Note: the advection split is applied at the next time-step in order to avoid blocking global comm. |
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| 142 | ! this should not affect too much the stability |
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[12489] | 143 | zcflnow(1) = MAXVAL( ABS( pu_ice(:,:) ) * rDt_ice * r1_e1u(:,:) ) |
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| 144 | zcflnow(1) = MAX( zcflnow(1), MAXVAL( ABS( pv_ice(:,:) ) * rDt_ice * r1_e2v(:,:) ) ) |
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[10425] | 145 | |
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| 146 | ! non-blocking global communication send zcflnow and receive zcflprv |
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| 147 | CALL mpp_delay_max( 'icedyn_adv_umx', 'cflice', zcflnow(:), zcflprv(:), kt == nitend - nn_fsbc + 1 ) |
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[8586] | 148 | |
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[10425] | 149 | IF( zcflprv(1) > .5 ) THEN ; icycle = 2 |
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| 150 | ELSE ; icycle = 1 |
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[8586] | 151 | ENDIF |
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[12489] | 152 | zdt = rDt_ice / REAL(icycle) |
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[13886] | 153 | z1_dt = 1._wp / zdt |
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[8586] | 154 | |
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| 155 | ! --- transport --- ! |
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| 156 | zudy(:,:) = pu_ice(:,:) * e2u(:,:) |
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| 157 | zvdx(:,:) = pv_ice(:,:) * e1v(:,:) |
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[10945] | 158 | ! |
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| 159 | ! setup transport for each ice cat |
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| 160 | DO jl = 1, jpl |
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| 161 | zu_cat(:,:,jl) = zudy(:,:) |
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| 162 | zv_cat(:,:,jl) = zvdx(:,:) |
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| 163 | END DO |
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| 164 | ! |
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[8586] | 165 | ! --- define velocity for advection: u*grad(H) --- ! |
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[13295] | 166 | DO_2D( 0, 0, 0, 0 ) |
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[12377] | 167 | IF ( pu_ice(ji,jj) * pu_ice(ji-1,jj) <= 0._wp ) THEN ; zcu_box(ji,jj) = 0._wp |
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| 168 | ELSEIF( pu_ice(ji,jj) > 0._wp ) THEN ; zcu_box(ji,jj) = pu_ice(ji-1,jj) |
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| 169 | ELSE ; zcu_box(ji,jj) = pu_ice(ji ,jj) |
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| 170 | ENDIF |
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[8586] | 171 | |
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[12377] | 172 | IF ( pv_ice(ji,jj) * pv_ice(ji,jj-1) <= 0._wp ) THEN ; zcv_box(ji,jj) = 0._wp |
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| 173 | ELSEIF( pv_ice(ji,jj) > 0._wp ) THEN ; zcv_box(ji,jj) = pv_ice(ji,jj-1) |
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| 174 | ELSE ; zcv_box(ji,jj) = pv_ice(ji,jj ) |
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| 175 | ENDIF |
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| 176 | END_2D |
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[8586] | 177 | |
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| 178 | !---------------! |
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| 179 | !== advection ==! |
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| 180 | !---------------! |
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[10413] | 181 | DO jt = 1, icycle |
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| 182 | |
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[13886] | 183 | ! diagnostics |
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| 184 | zdiag_adv_mass(:,:) = SUM( pv_i(:,:,:) , dim=3 ) * rhoi + SUM( pv_s(:,:,:) , dim=3 ) * rhos |
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| 185 | zdiag_adv_salt(:,:) = SUM( psv_i(:,:,:) , dim=3 ) * rhoi |
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| 186 | zdiag_adv_heat(:,:) = - SUM(SUM( pe_i(:,:,1:nlay_i,:) , dim=4 ), dim=3 ) & |
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| 187 | & - SUM(SUM( pe_s(:,:,1:nlay_s,:) , dim=4 ), dim=3 ) |
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| 188 | |
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[10439] | 189 | ! record at_i before advection (for open water) |
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| 190 | zati1(:,:) = SUM( pa_i(:,:,:), dim=3 ) |
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[10413] | 191 | |
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[10439] | 192 | ! inverse of A and Ap |
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[10425] | 193 | WHERE( pa_i(:,:,:) >= epsi20 ) ; z1_ai(:,:,:) = 1._wp / pa_i(:,:,:) |
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| 194 | ELSEWHERE ; z1_ai(:,:,:) = 0. |
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| 195 | END WHERE |
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| 196 | WHERE( pa_ip(:,:,:) >= epsi20 ) ; z1_aip(:,:,:) = 1._wp / pa_ip(:,:,:) |
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| 197 | ELSEWHERE ; z1_aip(:,:,:) = 0. |
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| 198 | END WHERE |
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| 199 | ! |
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[10930] | 200 | ! setup a mask where advection will be upstream |
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| 201 | IF( ll_neg ) THEN |
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[10945] | 202 | IF( .NOT. ALLOCATED(imsk_small) ) ALLOCATE( imsk_small(jpi,jpj,jpl) ) |
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| 203 | IF( .NOT. ALLOCATED(jmsk_small) ) ALLOCATE( jmsk_small(jpi,jpj,jpl) ) |
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[10930] | 204 | DO jl = 1, jpl |
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[13295] | 205 | DO_2D( 1, 0, 1, 0 ) |
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[12377] | 206 | zvi_cen = 0.5_wp * ( pv_i(ji+1,jj,jl) + pv_i(ji,jj,jl) ) |
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| 207 | IF( zvi_cen < epsi06) THEN ; imsk_small(ji,jj,jl) = 0 |
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| 208 | ELSE ; imsk_small(ji,jj,jl) = 1 ; ENDIF |
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| 209 | zvi_cen = 0.5_wp * ( pv_i(ji,jj+1,jl) + pv_i(ji,jj,jl) ) |
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| 210 | IF( zvi_cen < epsi06) THEN ; jmsk_small(ji,jj,jl) = 0 |
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| 211 | ELSE ; jmsk_small(ji,jj,jl) = 1 ; ENDIF |
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| 212 | END_2D |
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[10930] | 213 | END DO |
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| 214 | ENDIF |
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| 215 | ! |
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| 216 | ! ----------------------- ! |
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| 217 | ! ==> start advection <== ! |
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| 218 | ! ----------------------- ! |
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| 219 | ! |
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[10911] | 220 | !== Ice area ==! |
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[10425] | 221 | zamsk = 1._wp |
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[10945] | 222 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zu_cat , zv_cat , zcu_box, zcv_box, & |
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[10911] | 223 | & pa_i, pa_i, zua_ups, zva_ups, zua_ho , zva_ho ) |
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[10945] | 224 | ! |
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| 225 | ! ! --------------------------------- ! |
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| 226 | IF( np_advS == 1 ) THEN ! -- advection form: -div( uVS ) -- ! |
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| 227 | ! ! --------------------------------- ! |
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| 228 | zamsk = 0._wp |
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[10911] | 229 | !== Ice volume ==! |
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| 230 | zhvar(:,:,:) = pv_i(:,:,:) * z1_ai(:,:,:) |
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| 231 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
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| 232 | & zhvar, pv_i, zua_ups, zva_ups ) |
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| 233 | !== Snw volume ==! |
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| 234 | zhvar(:,:,:) = pv_s(:,:,:) * z1_ai(:,:,:) |
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| 235 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
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| 236 | & zhvar, pv_s, zua_ups, zva_ups ) |
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| 237 | ! |
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[10945] | 238 | zamsk = 1._wp |
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[10911] | 239 | !== Salt content ==! |
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[10945] | 240 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat, zv_cat, zcu_box, zcv_box, & |
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| 241 | & psv_i, psv_i ) |
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| 242 | !== Ice heat content ==! |
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| 243 | DO jk = 1, nlay_i |
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| 244 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat, zv_cat, zcu_box, zcv_box, & |
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| 245 | & pe_i(:,:,jk,:), pe_i(:,:,jk,:) ) |
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| 246 | END DO |
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| 247 | !== Snw heat content ==! |
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| 248 | DO jk = 1, nlay_s |
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| 249 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat, zv_cat, zcu_box, zcv_box, & |
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| 250 | & pe_s(:,:,jk,:), pe_s(:,:,jk,:) ) |
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| 251 | END DO |
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| 252 | ! |
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| 253 | ! ! ------------------------------------------ ! |
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| 254 | ELSEIF( np_advS == 2 ) THEN ! -- advection form: -div( uA * uHS / u ) -- ! |
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| 255 | ! ! ------------------------------------------ ! |
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| 256 | zamsk = 0._wp |
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| 257 | !== Ice volume ==! |
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| 258 | zhvar(:,:,:) = pv_i(:,:,:) * z1_ai(:,:,:) |
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| 259 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
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| 260 | & zhvar, pv_i, zua_ups, zva_ups ) |
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| 261 | !== Snw volume ==! |
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| 262 | zhvar(:,:,:) = pv_s(:,:,:) * z1_ai(:,:,:) |
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| 263 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
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| 264 | & zhvar, pv_s, zua_ups, zva_ups ) |
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| 265 | !== Salt content ==! |
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[10911] | 266 | zhvar(:,:,:) = psv_i(:,:,:) * z1_ai(:,:,:) |
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| 267 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zua_ho , zva_ho , zcu_box, zcv_box, & |
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| 268 | & zhvar, psv_i, zua_ups, zva_ups ) |
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| 269 | !== Ice heat content ==! |
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| 270 | DO jk = 1, nlay_i |
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| 271 | zhvar(:,:,:) = pe_i(:,:,jk,:) * z1_ai(:,:,:) |
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| 272 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho, zva_ho, zcu_box, zcv_box, & |
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| 273 | & zhvar, pe_i(:,:,jk,:), zua_ups, zva_ups ) |
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| 274 | END DO |
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| 275 | !== Snw heat content ==! |
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| 276 | DO jk = 1, nlay_s |
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| 277 | zhvar(:,:,:) = pe_s(:,:,jk,:) * z1_ai(:,:,:) |
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| 278 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho, zva_ho, zcu_box, zcv_box, & |
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| 279 | & zhvar, pe_s(:,:,jk,:), zua_ups, zva_ups ) |
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| 280 | END DO |
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| 281 | ! |
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[10945] | 282 | ! ! ----------------------------------------- ! |
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| 283 | ELSEIF( np_advS == 3 ) THEN ! -- advection form: -div( uV * uS / u ) -- ! |
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| 284 | ! ! ----------------------------------------- ! |
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| 285 | zamsk = 0._wp |
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| 286 | ! |
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| 287 | ALLOCATE( zuv_ho (jpi,jpj,jpl), zvv_ho (jpi,jpj,jpl), & |
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| 288 | & zuv_ups(jpi,jpj,jpl), zvv_ups(jpi,jpj,jpl), z1_vi(jpi,jpj,jpl), z1_vs(jpi,jpj,jpl) ) |
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| 289 | ! |
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[10911] | 290 | ! inverse of Vi |
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| 291 | WHERE( pv_i(:,:,:) >= epsi20 ) ; z1_vi(:,:,:) = 1._wp / pv_i(:,:,:) |
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| 292 | ELSEWHERE ; z1_vi(:,:,:) = 0. |
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| 293 | END WHERE |
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| 294 | ! inverse of Vs |
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| 295 | WHERE( pv_s(:,:,:) >= epsi20 ) ; z1_vs(:,:,:) = 1._wp / pv_s(:,:,:) |
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| 296 | ELSEWHERE ; z1_vs(:,:,:) = 0. |
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| 297 | END WHERE |
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| 298 | ! |
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| 299 | ! It is important to first calculate the ice fields and then the snow fields (because we use the same arrays) |
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| 300 | ! |
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| 301 | !== Ice volume ==! |
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| 302 | zuv_ups = zua_ups |
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| 303 | zvv_ups = zva_ups |
---|
| 304 | zhvar(:,:,:) = pv_i(:,:,:) * z1_ai(:,:,:) |
---|
| 305 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
---|
| 306 | & zhvar, pv_i, zuv_ups, zvv_ups, zuv_ho , zvv_ho ) |
---|
| 307 | !== Salt content ==! |
---|
| 308 | zhvar(:,:,:) = psv_i(:,:,:) * z1_vi(:,:,:) |
---|
| 309 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zuv_ho , zvv_ho , zcu_box, zcv_box, & |
---|
| 310 | & zhvar, psv_i, zuv_ups, zvv_ups ) |
---|
| 311 | !== Ice heat content ==! |
---|
| 312 | DO jk = 1, nlay_i |
---|
| 313 | zhvar(:,:,:) = pe_i(:,:,jk,:) * z1_vi(:,:,:) |
---|
| 314 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zuv_ho, zvv_ho, zcu_box, zcv_box, & |
---|
| 315 | & zhvar, pe_i(:,:,jk,:), zuv_ups, zvv_ups ) |
---|
| 316 | END DO |
---|
| 317 | !== Snow volume ==! |
---|
| 318 | zuv_ups = zua_ups |
---|
| 319 | zvv_ups = zva_ups |
---|
| 320 | zhvar(:,:,:) = pv_s(:,:,:) * z1_ai(:,:,:) |
---|
| 321 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
---|
| 322 | & zhvar, pv_s, zuv_ups, zvv_ups, zuv_ho , zvv_ho ) |
---|
| 323 | !== Snw heat content ==! |
---|
| 324 | DO jk = 1, nlay_s |
---|
| 325 | zhvar(:,:,:) = pe_s(:,:,jk,:) * z1_vs(:,:,:) |
---|
| 326 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zuv_ho, zvv_ho, zcu_box, zcv_box, & |
---|
| 327 | & zhvar, pe_s(:,:,jk,:), zuv_ups, zvv_ups ) |
---|
| 328 | END DO |
---|
| 329 | ! |
---|
[10945] | 330 | DEALLOCATE( zuv_ho, zvv_ho, zuv_ups, zvv_ups, z1_vi, z1_vs ) |
---|
| 331 | ! |
---|
[10911] | 332 | ENDIF |
---|
[10425] | 333 | ! |
---|
[10911] | 334 | !== Ice age ==! |
---|
[11612] | 335 | zamsk = 1._wp |
---|
| 336 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat, zv_cat, zcu_box, zcv_box, & |
---|
| 337 | & poa_i, poa_i ) |
---|
[10786] | 338 | ! |
---|
[10911] | 339 | !== melt ponds ==! |
---|
[13472] | 340 | IF ( ln_pnd_LEV ) THEN |
---|
[11627] | 341 | ! concentration |
---|
[10425] | 342 | zamsk = 1._wp |
---|
[10945] | 343 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat , zv_cat , zcu_box, zcv_box, & |
---|
[10911] | 344 | & pa_ip, pa_ip, zua_ups, zva_ups, zua_ho , zva_ho ) |
---|
[10945] | 345 | ! volume |
---|
[10425] | 346 | zamsk = 0._wp |
---|
[10475] | 347 | zhvar(:,:,:) = pv_ip(:,:,:) * z1_aip(:,:,:) |
---|
[10911] | 348 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zua_ho , zva_ho , zcu_box, zcv_box, & |
---|
| 349 | & zhvar, pv_ip, zua_ups, zva_ups ) |
---|
[13472] | 350 | ! lid |
---|
| 351 | IF ( ln_pnd_lids ) THEN |
---|
| 352 | zamsk = 0._wp |
---|
| 353 | zhvar(:,:,:) = pv_il(:,:,:) * z1_aip(:,:,:) |
---|
| 354 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zua_ho , zva_ho , zcu_box, zcv_box, & |
---|
| 355 | & zhvar, pv_il, zua_ups, zva_ups ) |
---|
| 356 | ENDIF |
---|
[10425] | 357 | ENDIF |
---|
[13886] | 358 | |
---|
| 359 | ! --- Lateral boundary conditions --- ! |
---|
| 360 | IF ( ln_pnd_LEV .AND. ln_pnd_lids ) THEN |
---|
| 361 | CALL lbc_lnk_multi( 'icedyn_adv_umx', pa_i,'T',1._wp, pv_i,'T',1._wp, pv_s,'T',1._wp, psv_i,'T',1._wp, poa_i,'T',1._wp & |
---|
| 362 | & , pa_ip,'T',1._wp, pv_ip,'T',1._wp, pv_il,'T',1._wp ) |
---|
| 363 | ELSEIF( ln_pnd_LEV .AND. .NOT.ln_pnd_lids ) THEN |
---|
| 364 | CALL lbc_lnk_multi( 'icedyn_adv_umx', pa_i,'T',1._wp, pv_i,'T',1._wp, pv_s,'T',1._wp, psv_i,'T',1._wp, poa_i,'T',1._wp & |
---|
| 365 | & , pa_ip,'T',1._wp, pv_ip,'T',1._wp ) |
---|
| 366 | ELSE |
---|
| 367 | CALL lbc_lnk_multi( 'icedyn_adv_umx', pa_i,'T',1._wp, pv_i,'T',1._wp, pv_s,'T',1._wp, psv_i,'T',1._wp, poa_i,'T',1._wp ) |
---|
| 368 | ENDIF |
---|
| 369 | CALL lbc_lnk( 'icedyn_adv_umx', pe_i, 'T', 1._wp ) |
---|
| 370 | CALL lbc_lnk( 'icedyn_adv_umx', pe_s, 'T', 1._wp ) |
---|
[10418] | 371 | ! |
---|
[10911] | 372 | !== Open water area ==! |
---|
[10439] | 373 | zati2(:,:) = SUM( pa_i(:,:,:), dim=3 ) |
---|
[13295] | 374 | DO_2D( 0, 0, 0, 0 ) |
---|
[12377] | 375 | pato_i(ji,jj) = pato_i(ji,jj) - ( zati2(ji,jj) - zati1(ji,jj) ) & |
---|
| 376 | & - ( zudy(ji,jj) - zudy(ji-1,jj) + zvdx(ji,jj) - zvdx(ji,jj-1) ) * r1_e1e2t(ji,jj) * zdt |
---|
| 377 | END_2D |
---|
[13886] | 378 | CALL lbc_lnk( 'icedyn_adv_umx', pato_i, 'T', 1._wp ) |
---|
[10418] | 379 | ! |
---|
[13886] | 380 | ! --- diagnostics --- ! |
---|
| 381 | diag_adv_mass(:,:) = diag_adv_mass(:,:) + ( SUM( pv_i(:,:,:) , dim=3 ) * rhoi + SUM( pv_s(:,:,:) , dim=3 ) * rhos & |
---|
| 382 | & - zdiag_adv_mass(:,:) ) * z1_dt |
---|
| 383 | diag_adv_salt(:,:) = diag_adv_salt(:,:) + ( SUM( psv_i(:,:,:) , dim=3 ) * rhoi & |
---|
| 384 | & - zdiag_adv_salt(:,:) ) * z1_dt |
---|
| 385 | diag_adv_heat(:,:) = diag_adv_heat(:,:) + ( - SUM(SUM( pe_i(:,:,1:nlay_i,:) , dim=4 ), dim=3 ) & |
---|
| 386 | & - SUM(SUM( pe_s(:,:,1:nlay_s,:) , dim=4 ), dim=3 ) & |
---|
| 387 | & - zdiag_adv_heat(:,:) ) * z1_dt |
---|
[10911] | 388 | ! |
---|
| 389 | ! --- Ensure non-negative fields and in-bound thicknesses --- ! |
---|
| 390 | ! Remove negative values (conservation is ensured) |
---|
| 391 | ! (because advected fields are not perfectly bounded and tiny negative values can occur, e.g. -1.e-20) |
---|
[13472] | 392 | CALL ice_var_zapneg( zdt, pato_i, pv_i, pv_s, psv_i, poa_i, pa_i, pa_ip, pv_ip, pv_il, pe_s, pe_i ) |
---|
[10911] | 393 | ! |
---|
[12197] | 394 | ! --- Make sure ice thickness is not too big --- ! |
---|
| 395 | ! (because ice thickness can be too large where ice concentration is very small) |
---|
[13472] | 396 | CALL Hbig( zdt, zhi_max, zhs_max, zhip_max, zsi_max, zes_max, zei_max, & |
---|
| 397 | & pv_i, pv_s, pa_i, pa_ip, pv_ip, psv_i, pe_s, pe_i ) |
---|
[12197] | 398 | ! |
---|
| 399 | ! --- Ensure snow load is not too big --- ! |
---|
| 400 | CALL Hsnow( zdt, pv_i, pv_s, pa_i, pa_ip, pe_s ) |
---|
| 401 | ! |
---|
[8586] | 402 | END DO |
---|
| 403 | ! |
---|
| 404 | END SUBROUTINE ice_dyn_adv_umx |
---|
[9929] | 405 | |
---|
[8586] | 406 | |
---|
[10911] | 407 | SUBROUTINE adv_umx( pamsk, kn_umx, jt, kt, pdt, pu, pv, puc, pvc, pubox, pvbox, & |
---|
| 408 | & pt, ptc, pua_ups, pva_ups, pua_ho, pva_ho ) |
---|
[8586] | 409 | !!---------------------------------------------------------------------- |
---|
| 410 | !! *** ROUTINE adv_umx *** |
---|
| 411 | !! |
---|
| 412 | !! ** Purpose : Compute the now trend due to total advection of |
---|
[10446] | 413 | !! tracers and add it to the general trend of tracer equations |
---|
[8586] | 414 | !! |
---|
[10911] | 415 | !! ** Method : - calculate upstream fluxes and upstream solution for tracers V/A(=H) etc |
---|
[10446] | 416 | !! - calculate tracer H at u and v points (Ultimate) |
---|
[10911] | 417 | !! - calculate the high order fluxes using alterning directions (Macho) |
---|
[10519] | 418 | !! - apply a limiter on the fluxes (nonosc_ice) |
---|
[10911] | 419 | !! - convert this tracer flux to a "volume" flux (uH -> uV) |
---|
| 420 | !! - apply a limiter a second time on the volumes fluxes (nonosc_ice) |
---|
| 421 | !! - calculate the high order solution for V |
---|
[8586] | 422 | !! |
---|
[10911] | 423 | !! ** Action : solve 3 equations => a) dA/dt = -div(uA) |
---|
| 424 | !! b) dV/dt = -div(uV) using dH/dt = -u.grad(H) |
---|
| 425 | !! c) dVS/dt = -div(uVS) using either dHS/dt = -u.grad(HS) or dS/dt = -u.grad(S) |
---|
[10446] | 426 | !! |
---|
[10911] | 427 | !! in eq. b), - fluxes uH are evaluated (with UMx) and limited with nonosc_ice. This step is necessary to get a good H. |
---|
| 428 | !! - then we convert this flux to a "volume" flux this way => uH * uA / u |
---|
| 429 | !! where uA is the flux from eq. a) |
---|
| 430 | !! this "volume" flux is also limited with nonosc_ice (otherwise overshoots can occur) |
---|
| 431 | !! - at last we estimate dV/dt = -div(uH * uA / u) |
---|
| 432 | !! |
---|
| 433 | !! in eq. c), one can solve the equation for S (ln_advS=T), then dVS/dt = -div(uV * uS / u) |
---|
| 434 | !! or for HS (ln_advS=F), then dVS/dt = -div(uA * uHS / u) |
---|
| 435 | !! |
---|
| 436 | !! ** Note : - this method can lead to tiny negative V (-1.e-20) => set it to 0 while conserving mass etc. |
---|
| 437 | !! - At the ice edge, Ultimate scheme can lead to: |
---|
| 438 | !! 1) negative interpolated tracers at u-v points |
---|
| 439 | !! 2) non-zero interpolated tracers at u-v points eventhough there is no ice and velocity is outward |
---|
| 440 | !! Solution for 1): apply an upstream scheme when it occurs. A better solution would be to degrade the order of |
---|
| 441 | !! the scheme automatically by applying a mask of the ice cover inside Ultimate (not done). |
---|
| 442 | !! Solution for 2): we set it to 0 in this case |
---|
[10446] | 443 | !! - Eventhough 1D tests give very good results (typically the one from Schar & Smolarkiewiecz), the 2D is less good. |
---|
| 444 | !! Large values of H can appear for very small ice concentration, and when it does it messes the things up since we |
---|
[10911] | 445 | !! work on H (and not V). It is partly related to the multi-category approach |
---|
[10446] | 446 | !! Therefore, after advection we limit the thickness to the largest value of the 9-points around (only if ice |
---|
[13886] | 447 | !! concentration is small). We also limit S and T. |
---|
[8586] | 448 | !!---------------------------------------------------------------------- |
---|
[10911] | 449 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 450 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
| 451 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
| 452 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
| 453 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 454 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu , pv ! 2 ice velocity components => u*e2 |
---|
| 455 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: puc , pvc ! 2 ice velocity components => u*e2 or u*a*e2u |
---|
| 456 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pubox, pvbox ! upstream velocity |
---|
| 457 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pt ! tracer field |
---|
| 458 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: ptc ! tracer content field |
---|
| 459 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT(inout), OPTIONAL :: pua_ups, pva_ups ! upstream u*a fluxes |
---|
| 460 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out), OPTIONAL :: pua_ho, pva_ho ! high order u*a fluxes |
---|
[8586] | 461 | ! |
---|
[10425] | 462 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[8586] | 463 | REAL(wp) :: ztra ! local scalar |
---|
[10446] | 464 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zfu_ho , zfv_ho , zpt |
---|
[10439] | 465 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zfu_ups, zfv_ups, zt_ups |
---|
[8586] | 466 | !!---------------------------------------------------------------------- |
---|
| 467 | ! |
---|
[10446] | 468 | ! Upstream (_ups) fluxes |
---|
| 469 | ! ----------------------- |
---|
| 470 | CALL upstream( pamsk, jt, kt, pdt, pt, pu, pv, zt_ups, zfu_ups, zfv_ups ) |
---|
| 471 | |
---|
| 472 | ! High order (_ho) fluxes |
---|
| 473 | ! ----------------------- |
---|
| 474 | SELECT CASE( kn_umx ) |
---|
| 475 | ! |
---|
| 476 | CASE ( 20 ) !== centered second order ==! |
---|
| 477 | ! |
---|
[10475] | 478 | CALL cen2( pamsk, jt, kt, pdt, pt, pu, pv, zt_ups, zfu_ups, zfv_ups, zfu_ho, zfv_ho ) |
---|
[10446] | 479 | ! |
---|
| 480 | CASE ( 1:5 ) !== 1st to 5th order ULTIMATE-MACHO scheme ==! |
---|
| 481 | ! |
---|
[10475] | 482 | CALL macho( pamsk, kn_umx, jt, kt, pdt, pt, pu, pv, pubox, pvbox, zt_ups, zfu_ups, zfv_ups, zfu_ho, zfv_ho ) |
---|
[10446] | 483 | ! |
---|
| 484 | END SELECT |
---|
[10439] | 485 | ! |
---|
[10446] | 486 | ! --ho --ho |
---|
| 487 | ! new fluxes = u*H * u*a / u |
---|
| 488 | ! ---------------------------- |
---|
[10475] | 489 | IF( pamsk == 0._wp ) THEN |
---|
[10446] | 490 | DO jl = 1, jpl |
---|
[13886] | 491 | DO_2D( 0, 0, 1, 0 ) |
---|
[12377] | 492 | IF( ABS( pu(ji,jj) ) > epsi10 ) THEN |
---|
| 493 | zfu_ho (ji,jj,jl) = zfu_ho (ji,jj,jl) * puc (ji,jj,jl) / pu(ji,jj) |
---|
| 494 | zfu_ups(ji,jj,jl) = zfu_ups(ji,jj,jl) * pua_ups(ji,jj,jl) / pu(ji,jj) |
---|
| 495 | ELSE |
---|
| 496 | zfu_ho (ji,jj,jl) = 0._wp |
---|
| 497 | zfu_ups(ji,jj,jl) = 0._wp |
---|
| 498 | ENDIF |
---|
| 499 | ! |
---|
[13886] | 500 | END_2D |
---|
| 501 | DO_2D( 1, 0, 0, 0 ) |
---|
[12377] | 502 | IF( ABS( pv(ji,jj) ) > epsi10 ) THEN |
---|
| 503 | zfv_ho (ji,jj,jl) = zfv_ho (ji,jj,jl) * pvc (ji,jj,jl) / pv(ji,jj) |
---|
| 504 | zfv_ups(ji,jj,jl) = zfv_ups(ji,jj,jl) * pva_ups(ji,jj,jl) / pv(ji,jj) |
---|
| 505 | ELSE |
---|
| 506 | zfv_ho (ji,jj,jl) = 0._wp |
---|
| 507 | zfv_ups(ji,jj,jl) = 0._wp |
---|
| 508 | ENDIF |
---|
| 509 | END_2D |
---|
[10446] | 510 | END DO |
---|
[10911] | 511 | |
---|
| 512 | ! the new "volume" fluxes must also be "flux corrected" |
---|
| 513 | ! thus we calculate the upstream solution and apply a limiter again |
---|
| 514 | DO jl = 1, jpl |
---|
[13295] | 515 | DO_2D( 0, 0, 0, 0 ) |
---|
[12377] | 516 | ztra = - ( zfu_ups(ji,jj,jl) - zfu_ups(ji-1,jj,jl) + zfv_ups(ji,jj,jl) - zfv_ups(ji,jj-1,jl) ) |
---|
| 517 | ! |
---|
| 518 | zt_ups(ji,jj,jl) = ( ptc(ji,jj,jl) + ztra * r1_e1e2t(ji,jj) * pdt ) * tmask(ji,jj,1) |
---|
| 519 | END_2D |
---|
[10911] | 520 | END DO |
---|
[13226] | 521 | CALL lbc_lnk( 'icedyn_adv_umx', zt_ups, 'T', 1.0_wp ) |
---|
[10911] | 522 | ! |
---|
[10945] | 523 | IF ( np_limiter == 1 ) THEN |
---|
[10911] | 524 | CALL nonosc_ice( 1._wp, pdt, pu, pv, ptc, zt_ups, zfu_ups, zfv_ups, zfu_ho, zfv_ho ) |
---|
[10945] | 525 | ELSEIF( np_limiter == 2 .OR. np_limiter == 3 ) THEN |
---|
[10911] | 526 | CALL limiter_x( pdt, pu, ptc, zfu_ups, zfu_ho ) |
---|
| 527 | CALL limiter_y( pdt, pv, ptc, zfv_ups, zfv_ho ) |
---|
| 528 | ENDIF |
---|
| 529 | ! |
---|
[10446] | 530 | ENDIF |
---|
[10911] | 531 | ! --ho --ups |
---|
| 532 | ! in case of advection of A: output u*a and u*a |
---|
| 533 | ! ----------------------------------------------- |
---|
[10446] | 534 | IF( PRESENT( pua_ho ) ) THEN |
---|
| 535 | DO jl = 1, jpl |
---|
[13886] | 536 | DO_2D( 0, 0, 1, 0 ) |
---|
| 537 | pua_ho (ji,jj,jl) = zfu_ho (ji,jj,jl) |
---|
| 538 | pua_ups(ji,jj,jl) = zfu_ups(ji,jj,jl) |
---|
[12377] | 539 | END_2D |
---|
[13886] | 540 | DO_2D( 1, 0, 0, 0 ) |
---|
| 541 | pva_ho (ji,jj,jl) = zfv_ho (ji,jj,jl) |
---|
| 542 | pva_ups(ji,jj,jl) = zfv_ups(ji,jj,jl) |
---|
| 543 | END_2D |
---|
[10446] | 544 | END DO |
---|
| 545 | ENDIF |
---|
| 546 | ! |
---|
| 547 | ! final trend with corrected fluxes |
---|
| 548 | ! --------------------------------- |
---|
| 549 | DO jl = 1, jpl |
---|
[13295] | 550 | DO_2D( 0, 0, 0, 0 ) |
---|
[12377] | 551 | ztra = - ( zfu_ho(ji,jj,jl) - zfu_ho(ji-1,jj,jl) + zfv_ho(ji,jj,jl) - zfv_ho(ji,jj-1,jl) ) |
---|
| 552 | ! |
---|
| 553 | ptc(ji,jj,jl) = ( ptc(ji,jj,jl) + ztra * r1_e1e2t(ji,jj) * pdt ) * tmask(ji,jj,1) |
---|
| 554 | END_2D |
---|
[10446] | 555 | END DO |
---|
| 556 | ! |
---|
| 557 | END SUBROUTINE adv_umx |
---|
| 558 | |
---|
| 559 | |
---|
| 560 | SUBROUTINE upstream( pamsk, jt, kt, pdt, pt, pu, pv, pt_ups, pfu_ups, pfv_ups ) |
---|
| 561 | !!--------------------------------------------------------------------- |
---|
| 562 | !! *** ROUTINE upstream *** |
---|
| 563 | !! |
---|
| 564 | !! ** Purpose : compute the upstream fluxes and upstream guess of tracer |
---|
| 565 | !!---------------------------------------------------------------------- |
---|
| 566 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 567 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
| 568 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
| 569 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 570 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
| 571 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu, pv ! 2 ice velocity components |
---|
| 572 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_ups ! upstream guess of tracer |
---|
| 573 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ups, pfv_ups ! upstream fluxes |
---|
| 574 | ! |
---|
| 575 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
| 576 | REAL(wp) :: ztra ! local scalar |
---|
| 577 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zpt |
---|
| 578 | !!---------------------------------------------------------------------- |
---|
| 579 | |
---|
[10439] | 580 | IF( .NOT. ll_upsxy ) THEN !** no alternate directions **! |
---|
[10446] | 581 | ! |
---|
[10425] | 582 | DO jl = 1, jpl |
---|
[13295] | 583 | DO_2D( 1, 0, 1, 0 ) |
---|
[12377] | 584 | pfu_ups(ji,jj,jl) = MAX( pu(ji,jj), 0._wp ) * pt(ji,jj,jl) + MIN( pu(ji,jj), 0._wp ) * pt(ji+1,jj,jl) |
---|
| 585 | pfv_ups(ji,jj,jl) = MAX( pv(ji,jj), 0._wp ) * pt(ji,jj,jl) + MIN( pv(ji,jj), 0._wp ) * pt(ji,jj+1,jl) |
---|
| 586 | END_2D |
---|
[10413] | 587 | END DO |
---|
[10446] | 588 | ! |
---|
[10439] | 589 | ELSE !** alternate directions **! |
---|
[10413] | 590 | ! |
---|
| 591 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
---|
[10439] | 592 | ! |
---|
| 593 | DO jl = 1, jpl !-- flux in x-direction |
---|
[13886] | 594 | DO_2D( 1, 1, 1, 0 ) |
---|
[12377] | 595 | pfu_ups(ji,jj,jl) = MAX( pu(ji,jj), 0._wp ) * pt(ji,jj,jl) + MIN( pu(ji,jj), 0._wp ) * pt(ji+1,jj,jl) |
---|
| 596 | END_2D |
---|
[10413] | 597 | END DO |
---|
[10439] | 598 | ! |
---|
| 599 | DO jl = 1, jpl !-- first guess of tracer from u-flux |
---|
[13886] | 600 | DO_2D( 1, 1, 0, 0 ) |
---|
[12377] | 601 | ztra = - ( pfu_ups(ji,jj,jl) - pfu_ups(ji-1,jj,jl) ) & |
---|
| 602 | & + ( pu (ji,jj ) - pu (ji-1,jj ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 603 | ! |
---|
| 604 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
| 605 | END_2D |
---|
[10413] | 606 | END DO |
---|
[8586] | 607 | ! |
---|
[10439] | 608 | DO jl = 1, jpl !-- flux in y-direction |
---|
[13886] | 609 | DO_2D( 1, 0, 0, 0 ) |
---|
[12377] | 610 | pfv_ups(ji,jj,jl) = MAX( pv(ji,jj), 0._wp ) * zpt(ji,jj,jl) + MIN( pv(ji,jj), 0._wp ) * zpt(ji,jj+1,jl) |
---|
| 611 | END_2D |
---|
[10413] | 612 | END DO |
---|
[10439] | 613 | ! |
---|
[10413] | 614 | ELSE !== even ice time step: adv_y then adv_x ==! |
---|
[10439] | 615 | ! |
---|
| 616 | DO jl = 1, jpl !-- flux in y-direction |
---|
[13886] | 617 | DO_2D( 1, 0, 1, 1 ) |
---|
[12377] | 618 | pfv_ups(ji,jj,jl) = MAX( pv(ji,jj), 0._wp ) * pt(ji,jj,jl) + MIN( pv(ji,jj), 0._wp ) * pt(ji,jj+1,jl) |
---|
| 619 | END_2D |
---|
[10413] | 620 | END DO |
---|
[10439] | 621 | ! |
---|
| 622 | DO jl = 1, jpl !-- first guess of tracer from v-flux |
---|
[13886] | 623 | DO_2D( 0, 0, 1, 1 ) |
---|
[12377] | 624 | ztra = - ( pfv_ups(ji,jj,jl) - pfv_ups(ji,jj-1,jl) ) & |
---|
| 625 | & + ( pv (ji,jj ) - pv (ji,jj-1 ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 626 | ! |
---|
| 627 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
| 628 | END_2D |
---|
[10413] | 629 | END DO |
---|
| 630 | ! |
---|
[10439] | 631 | DO jl = 1, jpl !-- flux in x-direction |
---|
[13886] | 632 | DO_2D( 0, 0, 1, 0 ) |
---|
[12377] | 633 | pfu_ups(ji,jj,jl) = MAX( pu(ji,jj), 0._wp ) * zpt(ji,jj,jl) + MIN( pu(ji,jj), 0._wp ) * zpt(ji+1,jj,jl) |
---|
| 634 | END_2D |
---|
[10413] | 635 | END DO |
---|
| 636 | ! |
---|
| 637 | ENDIF |
---|
| 638 | |
---|
| 639 | ENDIF |
---|
[10439] | 640 | ! |
---|
| 641 | DO jl = 1, jpl !-- after tracer with upstream scheme |
---|
[13295] | 642 | DO_2D( 0, 0, 0, 0 ) |
---|
[12377] | 643 | ztra = - ( pfu_ups(ji,jj,jl) - pfu_ups(ji-1,jj ,jl) & |
---|
| 644 | & + pfv_ups(ji,jj,jl) - pfv_ups(ji ,jj-1,jl) ) & |
---|
| 645 | & + ( pu (ji,jj ) - pu (ji-1,jj ) & |
---|
| 646 | & + pv (ji,jj ) - pv (ji ,jj-1 ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 647 | ! |
---|
| 648 | pt_ups(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
| 649 | END_2D |
---|
[8586] | 650 | END DO |
---|
[13226] | 651 | CALL lbc_lnk( 'icedyn_adv_umx', pt_ups, 'T', 1.0_wp ) |
---|
[10413] | 652 | |
---|
[10446] | 653 | END SUBROUTINE upstream |
---|
[8586] | 654 | |
---|
[10446] | 655 | |
---|
[10475] | 656 | SUBROUTINE cen2( pamsk, jt, kt, pdt, pt, pu, pv, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[8586] | 657 | !!--------------------------------------------------------------------- |
---|
[10446] | 658 | !! *** ROUTINE cen2 *** |
---|
[8586] | 659 | !! |
---|
[10446] | 660 | !! ** Purpose : compute the high order fluxes using a centered |
---|
| 661 | !! second order scheme |
---|
[8586] | 662 | !!---------------------------------------------------------------------- |
---|
[10439] | 663 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 664 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
| 665 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
| 666 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 667 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
| 668 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu, pv ! 2 ice velocity components |
---|
[10446] | 669 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt_ups ! upstream guess of tracer |
---|
| 670 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pfu_ups, pfv_ups ! upstream fluxes |
---|
[10425] | 671 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ho, pfv_ho ! high order fluxes |
---|
[8586] | 672 | ! |
---|
[10425] | 673 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[10446] | 674 | REAL(wp) :: ztra ! local scalar |
---|
| 675 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zpt |
---|
[8586] | 676 | !!---------------------------------------------------------------------- |
---|
| 677 | ! |
---|
[10439] | 678 | IF( .NOT.ll_hoxy ) THEN !** no alternate directions **! |
---|
[8586] | 679 | ! |
---|
[10425] | 680 | DO jl = 1, jpl |
---|
[13886] | 681 | DO_2D( 1, 1, 1, 0 ) |
---|
[12377] | 682 | pfu_ho(ji,jj,jl) = 0.5_wp * pu(ji,jj) * ( pt(ji,jj,jl) + pt(ji+1,jj ,jl) ) |
---|
[13886] | 683 | END_2D |
---|
| 684 | DO_2D( 1, 0, 1, 1 ) |
---|
[12377] | 685 | pfv_ho(ji,jj,jl) = 0.5_wp * pv(ji,jj) * ( pt(ji,jj,jl) + pt(ji ,jj+1,jl) ) |
---|
| 686 | END_2D |
---|
[8586] | 687 | END DO |
---|
[10475] | 688 | ! |
---|
[10945] | 689 | IF ( np_limiter == 1 ) THEN |
---|
[10519] | 690 | CALL nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[10945] | 691 | ELSEIF( np_limiter == 2 .OR. np_limiter == 3 ) THEN |
---|
[10446] | 692 | CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
| 693 | CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 694 | ENDIF |
---|
[8586] | 695 | ! |
---|
[10439] | 696 | ELSE !** alternate directions **! |
---|
[8586] | 697 | ! |
---|
[10413] | 698 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
---|
| 699 | ! |
---|
[10439] | 700 | DO jl = 1, jpl !-- flux in x-direction |
---|
[13886] | 701 | DO_2D( 1, 1, 1, 0 ) |
---|
[12377] | 702 | pfu_ho(ji,jj,jl) = 0.5_wp * pu(ji,jj) * ( pt(ji,jj,jl) + pt(ji+1,jj,jl) ) |
---|
| 703 | END_2D |
---|
[10413] | 704 | END DO |
---|
[10945] | 705 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
[10413] | 706 | |
---|
[10439] | 707 | DO jl = 1, jpl !-- first guess of tracer from u-flux |
---|
[13886] | 708 | DO_2D( 1, 1, 0, 0 ) |
---|
[12377] | 709 | ztra = - ( pfu_ho(ji,jj,jl) - pfu_ho(ji-1,jj,jl) ) & |
---|
| 710 | & + ( pu (ji,jj ) - pu (ji-1,jj ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 711 | ! |
---|
| 712 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
| 713 | END_2D |
---|
[10413] | 714 | END DO |
---|
| 715 | |
---|
[10439] | 716 | DO jl = 1, jpl !-- flux in y-direction |
---|
[13886] | 717 | DO_2D( 1, 0, 0, 0 ) |
---|
[12377] | 718 | pfv_ho(ji,jj,jl) = 0.5_wp * pv(ji,jj) * ( zpt(ji,jj,jl) + zpt(ji,jj+1,jl) ) |
---|
| 719 | END_2D |
---|
[10413] | 720 | END DO |
---|
[10945] | 721 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 722 | |
---|
| 723 | ELSE !== even ice time step: adv_y then adv_x ==! |
---|
| 724 | ! |
---|
[10439] | 725 | DO jl = 1, jpl !-- flux in y-direction |
---|
[13886] | 726 | DO_2D( 1, 0, 1, 1 ) |
---|
[12377] | 727 | pfv_ho(ji,jj,jl) = 0.5_wp * pv(ji,jj) * ( pt(ji,jj,jl) + pt(ji,jj+1,jl) ) |
---|
| 728 | END_2D |
---|
[10413] | 729 | END DO |
---|
[10945] | 730 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 731 | ! |
---|
[10439] | 732 | DO jl = 1, jpl !-- first guess of tracer from v-flux |
---|
[13886] | 733 | DO_2D( 0, 0, 1, 1 ) |
---|
[12377] | 734 | ztra = - ( pfv_ho(ji,jj,jl) - pfv_ho(ji,jj-1,jl) ) & |
---|
| 735 | & + ( pv (ji,jj ) - pv (ji,jj-1 ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 736 | ! |
---|
| 737 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
| 738 | END_2D |
---|
[10413] | 739 | END DO |
---|
| 740 | ! |
---|
[10439] | 741 | DO jl = 1, jpl !-- flux in x-direction |
---|
[13886] | 742 | DO_2D( 0, 0, 1, 0 ) |
---|
[12377] | 743 | pfu_ho(ji,jj,jl) = 0.5_wp * pu(ji,jj) * ( zpt(ji,jj,jl) + zpt(ji+1,jj,jl) ) |
---|
| 744 | END_2D |
---|
[10413] | 745 | END DO |
---|
[10945] | 746 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
[10413] | 747 | |
---|
| 748 | ENDIF |
---|
[10945] | 749 | IF( np_limiter == 1 ) CALL nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[10413] | 750 | |
---|
| 751 | ENDIF |
---|
| 752 | |
---|
| 753 | END SUBROUTINE cen2 |
---|
| 754 | |
---|
| 755 | |
---|
[10475] | 756 | SUBROUTINE macho( pamsk, kn_umx, jt, kt, pdt, pt, pu, pv, pubox, pvbox, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[10413] | 757 | !!--------------------------------------------------------------------- |
---|
| 758 | !! *** ROUTINE macho *** |
---|
| 759 | !! |
---|
[10446] | 760 | !! ** Purpose : compute the high order fluxes using Ultimate-Macho scheme |
---|
[10413] | 761 | !! |
---|
[10446] | 762 | !! ** Method : ... |
---|
[10413] | 763 | !! |
---|
| 764 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
| 765 | !!---------------------------------------------------------------------- |
---|
[10439] | 766 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 767 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
| 768 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
| 769 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
| 770 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 771 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
| 772 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu, pv ! 2 ice velocity components |
---|
| 773 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pubox, pvbox ! upstream velocity |
---|
[10446] | 774 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt_ups ! upstream guess of tracer |
---|
| 775 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pfu_ups, pfv_ups ! upstream fluxes |
---|
[10425] | 776 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ho, pfv_ho ! high order fluxes |
---|
[10413] | 777 | ! |
---|
[10425] | 778 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[10446] | 779 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zt_u, zt_v, zpt |
---|
[10413] | 780 | !!---------------------------------------------------------------------- |
---|
| 781 | ! |
---|
| 782 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
---|
[8586] | 783 | ! |
---|
[10413] | 784 | ! !-- ultimate interpolation of pt at u-point --! |
---|
[10911] | 785 | CALL ultimate_x( pamsk, kn_umx, pdt, pt, pu, zt_u, pfu_ho ) |
---|
[10413] | 786 | ! !-- limiter in x --! |
---|
[10945] | 787 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
[10446] | 788 | ! !-- advective form update in zpt --! |
---|
[10439] | 789 | DO jl = 1, jpl |
---|
[13295] | 790 | DO_2D( 0, 0, 0, 0 ) |
---|
[12377] | 791 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) - ( pubox(ji,jj ) * ( zt_u(ji,jj,jl) - zt_u(ji-1,jj,jl) ) * r1_e1t (ji,jj) & |
---|
| 792 | & + pt (ji,jj,jl) * ( pu (ji,jj ) - pu (ji-1,jj ) ) * r1_e1e2t(ji,jj) & |
---|
| 793 | & * pamsk & |
---|
| 794 | & ) * pdt ) * tmask(ji,jj,1) |
---|
| 795 | END_2D |
---|
[10439] | 796 | END DO |
---|
[13226] | 797 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1.0_wp ) |
---|
[8586] | 798 | ! |
---|
[10413] | 799 | ! !-- ultimate interpolation of pt at v-point --! |
---|
| 800 | IF( ll_hoxy ) THEN |
---|
[10911] | 801 | CALL ultimate_y( pamsk, kn_umx, pdt, zpt, pv, zt_v, pfv_ho ) |
---|
[10413] | 802 | ELSE |
---|
[10911] | 803 | CALL ultimate_y( pamsk, kn_umx, pdt, pt , pv, zt_v, pfv_ho ) |
---|
[10413] | 804 | ENDIF |
---|
| 805 | ! !-- limiter in y --! |
---|
[10945] | 806 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 807 | ! |
---|
| 808 | ! |
---|
| 809 | ELSE !== even ice time step: adv_y then adv_x ==! |
---|
| 810 | ! |
---|
| 811 | ! !-- ultimate interpolation of pt at v-point --! |
---|
[10911] | 812 | CALL ultimate_y( pamsk, kn_umx, pdt, pt, pv, zt_v, pfv_ho ) |
---|
[10413] | 813 | ! !-- limiter in y --! |
---|
[10945] | 814 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10446] | 815 | ! !-- advective form update in zpt --! |
---|
[10439] | 816 | DO jl = 1, jpl |
---|
[13295] | 817 | DO_2D( 0, 0, 0, 0 ) |
---|
[12377] | 818 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) - ( pvbox(ji,jj ) * ( zt_v(ji,jj,jl) - zt_v(ji,jj-1,jl) ) * r1_e2t (ji,jj) & |
---|
| 819 | & + pt (ji,jj,jl) * ( pv (ji,jj ) - pv (ji,jj-1 ) ) * r1_e1e2t(ji,jj) & |
---|
| 820 | & * pamsk & |
---|
| 821 | & ) * pdt ) * tmask(ji,jj,1) |
---|
| 822 | END_2D |
---|
[10439] | 823 | END DO |
---|
[13226] | 824 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1.0_wp ) |
---|
[10413] | 825 | ! |
---|
| 826 | ! !-- ultimate interpolation of pt at u-point --! |
---|
| 827 | IF( ll_hoxy ) THEN |
---|
[10911] | 828 | CALL ultimate_x( pamsk, kn_umx, pdt, zpt, pu, zt_u, pfu_ho ) |
---|
[10413] | 829 | ELSE |
---|
[10911] | 830 | CALL ultimate_x( pamsk, kn_umx, pdt, pt , pu, zt_u, pfu_ho ) |
---|
[10413] | 831 | ENDIF |
---|
| 832 | ! !-- limiter in x --! |
---|
[10945] | 833 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
[10413] | 834 | ! |
---|
| 835 | ENDIF |
---|
| 836 | |
---|
[10945] | 837 | IF( np_limiter == 1 ) CALL nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[8586] | 838 | ! |
---|
| 839 | END SUBROUTINE macho |
---|
| 840 | |
---|
| 841 | |
---|
[10911] | 842 | SUBROUTINE ultimate_x( pamsk, kn_umx, pdt, pt, pu, pt_u, pfu_ho ) |
---|
[8586] | 843 | !!--------------------------------------------------------------------- |
---|
| 844 | !! *** ROUTINE ultimate_x *** |
---|
| 845 | !! |
---|
[10446] | 846 | !! ** Purpose : compute tracer at u-points |
---|
[8586] | 847 | !! |
---|
[10446] | 848 | !! ** Method : ... |
---|
[8586] | 849 | !! |
---|
| 850 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
| 851 | !!---------------------------------------------------------------------- |
---|
[10911] | 852 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
[10439] | 853 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
| 854 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 855 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu ! ice i-velocity component |
---|
| 856 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
[10425] | 857 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_u ! tracer at u-point |
---|
| 858 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ho ! high order flux |
---|
[8586] | 859 | ! |
---|
[10425] | 860 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[10930] | 861 | REAL(wp) :: zcu, zdx2, zdx4 ! - - |
---|
[10425] | 862 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: ztu1, ztu2, ztu3, ztu4 |
---|
[8586] | 863 | !!---------------------------------------------------------------------- |
---|
| 864 | ! |
---|
| 865 | ! !-- Laplacian in i-direction --! |
---|
[10425] | 866 | DO jl = 1, jpl |
---|
| 867 | DO jj = 2, jpjm1 ! First derivative (gradient) |
---|
[12377] | 868 | DO ji = 1, jpim1 |
---|
[10425] | 869 | ztu1(ji,jj,jl) = ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) * r1_e1u(ji,jj) * umask(ji,jj,1) |
---|
| 870 | END DO |
---|
| 871 | ! ! Second derivative (Laplacian) |
---|
[12377] | 872 | DO ji = 2, jpim1 |
---|
[10425] | 873 | ztu2(ji,jj,jl) = ( ztu1(ji,jj,jl) - ztu1(ji-1,jj,jl) ) * r1_e1t(ji,jj) |
---|
| 874 | END DO |
---|
[8586] | 875 | END DO |
---|
| 876 | END DO |
---|
[13226] | 877 | CALL lbc_lnk( 'icedyn_adv_umx', ztu2, 'T', 1.0_wp ) |
---|
[8586] | 878 | ! |
---|
| 879 | ! !-- BiLaplacian in i-direction --! |
---|
[10425] | 880 | DO jl = 1, jpl |
---|
| 881 | DO jj = 2, jpjm1 ! Third derivative |
---|
[12377] | 882 | DO ji = 1, jpim1 |
---|
[10425] | 883 | ztu3(ji,jj,jl) = ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) * r1_e1u(ji,jj) * umask(ji,jj,1) |
---|
| 884 | END DO |
---|
| 885 | ! ! Fourth derivative |
---|
[12377] | 886 | DO ji = 2, jpim1 |
---|
[10425] | 887 | ztu4(ji,jj,jl) = ( ztu3(ji,jj,jl) - ztu3(ji-1,jj,jl) ) * r1_e1t(ji,jj) |
---|
| 888 | END DO |
---|
[8586] | 889 | END DO |
---|
| 890 | END DO |
---|
[13226] | 891 | CALL lbc_lnk( 'icedyn_adv_umx', ztu4, 'T', 1.0_wp ) |
---|
[8586] | 892 | ! |
---|
| 893 | ! |
---|
[10413] | 894 | SELECT CASE (kn_umx ) |
---|
[8586] | 895 | ! |
---|
| 896 | CASE( 1 ) !== 1st order central TIM ==! (Eq. 21) |
---|
| 897 | ! |
---|
[10425] | 898 | DO jl = 1, jpl |
---|
[13886] | 899 | DO_2D( 0, 0, 1, 0 ) |
---|
[12377] | 900 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj,jl) + pt(ji,jj,jl) & |
---|
| 901 | & - SIGN( 1._wp, pu(ji,jj) ) * ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) ) |
---|
| 902 | END_2D |
---|
[8586] | 903 | END DO |
---|
| 904 | ! |
---|
| 905 | CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23) |
---|
| 906 | ! |
---|
[10425] | 907 | DO jl = 1, jpl |
---|
[13886] | 908 | DO_2D( 0, 0, 1, 0 ) |
---|
[12377] | 909 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
| 910 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj,jl) + pt(ji,jj,jl) & |
---|
| 911 | & - zcu * ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) ) |
---|
| 912 | END_2D |
---|
[8586] | 913 | END DO |
---|
| 914 | ! |
---|
| 915 | CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24) |
---|
| 916 | ! |
---|
[10425] | 917 | DO jl = 1, jpl |
---|
[13886] | 918 | DO_2D( 0, 0, 1, 0 ) |
---|
[12377] | 919 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
| 920 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
[10439] | 921 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
[12377] | 922 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj,jl) + pt (ji,jj,jl) & |
---|
| 923 | & - zcu * ( pt (ji+1,jj,jl) - pt (ji,jj,jl) ) ) & |
---|
| 924 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj,jl) + ztu2(ji,jj,jl) & |
---|
| 925 | & - SIGN( 1._wp, zcu ) * ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) ) ) |
---|
| 926 | END_2D |
---|
[8586] | 927 | END DO |
---|
| 928 | ! |
---|
| 929 | CASE( 4 ) !== 4th order central TIM ==! (Eq. 27) |
---|
| 930 | ! |
---|
[10425] | 931 | DO jl = 1, jpl |
---|
[13886] | 932 | DO_2D( 0, 0, 1, 0 ) |
---|
[12377] | 933 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
| 934 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
[10439] | 935 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
[12377] | 936 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj,jl) + pt (ji,jj,jl) & |
---|
| 937 | & - zcu * ( pt (ji+1,jj,jl) - pt (ji,jj,jl) ) ) & |
---|
| 938 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj,jl) + ztu2(ji,jj,jl) & |
---|
| 939 | & - 0.5_wp * zcu * ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) ) ) |
---|
| 940 | END_2D |
---|
[8586] | 941 | END DO |
---|
| 942 | ! |
---|
| 943 | CASE( 5 ) !== 5th order central TIM ==! (Eq. 29) |
---|
| 944 | ! |
---|
[10425] | 945 | DO jl = 1, jpl |
---|
[13886] | 946 | DO_2D( 0, 0, 1, 0 ) |
---|
[12377] | 947 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
| 948 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
[10439] | 949 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
[12377] | 950 | zdx4 = zdx2 * zdx2 |
---|
| 951 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj,jl) + pt (ji,jj,jl) & |
---|
| 952 | & - zcu * ( pt (ji+1,jj,jl) - pt (ji,jj,jl) ) ) & |
---|
| 953 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj,jl) + ztu2(ji,jj,jl) & |
---|
| 954 | & - 0.5_wp * zcu * ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) ) & |
---|
| 955 | & + z1_120 * zdx4 * ( zcu*zcu - 1._wp ) * ( zcu*zcu - 4._wp ) * ( ztu4(ji+1,jj,jl) + ztu4(ji,jj,jl) & |
---|
| 956 | & - SIGN( 1._wp, zcu ) * ( ztu4(ji+1,jj,jl) - ztu4(ji,jj,jl) ) ) ) |
---|
| 957 | END_2D |
---|
[8586] | 958 | END DO |
---|
| 959 | ! |
---|
| 960 | END SELECT |
---|
[10439] | 961 | ! |
---|
| 962 | ! if pt at u-point is negative then use the upstream value |
---|
| 963 | ! this should not be necessary if a proper sea-ice mask is set in Ultimate |
---|
| 964 | ! to degrade the order of the scheme when necessary (for ex. at the ice edge) |
---|
[10413] | 965 | IF( ll_neg ) THEN |
---|
[10425] | 966 | DO jl = 1, jpl |
---|
[13886] | 967 | DO_2D( 0, 0, 1, 0 ) |
---|
[12377] | 968 | IF( pt_u(ji,jj,jl) < 0._wp .OR. ( imsk_small(ji,jj,jl) == 0 .AND. pamsk == 0. ) ) THEN |
---|
| 969 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj,jl) + pt(ji,jj,jl) & |
---|
| 970 | & - SIGN( 1._wp, pu(ji,jj) ) * ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) ) |
---|
| 971 | ENDIF |
---|
| 972 | END_2D |
---|
[10413] | 973 | END DO |
---|
| 974 | ENDIF |
---|
[10439] | 975 | ! !-- High order flux in i-direction --! |
---|
[10425] | 976 | DO jl = 1, jpl |
---|
[13886] | 977 | DO_2D( 0, 0, 1, 0 ) |
---|
[12377] | 978 | pfu_ho(ji,jj,jl) = pu(ji,jj) * pt_u(ji,jj,jl) |
---|
| 979 | END_2D |
---|
[10413] | 980 | END DO |
---|
[8586] | 981 | ! |
---|
| 982 | END SUBROUTINE ultimate_x |
---|
| 983 | |
---|
| 984 | |
---|
[10911] | 985 | SUBROUTINE ultimate_y( pamsk, kn_umx, pdt, pt, pv, pt_v, pfv_ho ) |
---|
[8586] | 986 | !!--------------------------------------------------------------------- |
---|
| 987 | !! *** ROUTINE ultimate_y *** |
---|
| 988 | !! |
---|
[10446] | 989 | !! ** Purpose : compute tracer at v-points |
---|
[8586] | 990 | !! |
---|
[10446] | 991 | !! ** Method : ... |
---|
[8586] | 992 | !! |
---|
| 993 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
| 994 | !!---------------------------------------------------------------------- |
---|
[10911] | 995 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
[10439] | 996 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
| 997 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 998 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pv ! ice j-velocity component |
---|
| 999 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
[10425] | 1000 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_v ! tracer at v-point |
---|
| 1001 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfv_ho ! high order flux |
---|
[8586] | 1002 | ! |
---|
[10439] | 1003 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[10930] | 1004 | REAL(wp) :: zcv, zdy2, zdy4 ! - - |
---|
[10425] | 1005 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: ztv1, ztv2, ztv3, ztv4 |
---|
[8586] | 1006 | !!---------------------------------------------------------------------- |
---|
| 1007 | ! |
---|
| 1008 | ! !-- Laplacian in j-direction --! |
---|
[10425] | 1009 | DO jl = 1, jpl |
---|
[13497] | 1010 | DO_2D( 1, 0, 0, 0 ) ! First derivative (gradient) |
---|
[12377] | 1011 | ztv1(ji,jj,jl) = ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) * r1_e2v(ji,jj) * vmask(ji,jj,1) |
---|
| 1012 | END_2D |
---|
[13497] | 1013 | DO_2D( 0, 0, 0, 0 ) ! Second derivative (Laplacian) |
---|
[12377] | 1014 | ztv2(ji,jj,jl) = ( ztv1(ji,jj,jl) - ztv1(ji,jj-1,jl) ) * r1_e2t(ji,jj) |
---|
| 1015 | END_2D |
---|
[8586] | 1016 | END DO |
---|
[13226] | 1017 | CALL lbc_lnk( 'icedyn_adv_umx', ztv2, 'T', 1.0_wp ) |
---|
[8586] | 1018 | ! |
---|
| 1019 | ! !-- BiLaplacian in j-direction --! |
---|
[10425] | 1020 | DO jl = 1, jpl |
---|
[13497] | 1021 | DO_2D( 1, 0, 0, 0 ) ! First derivative |
---|
[12377] | 1022 | ztv3(ji,jj,jl) = ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) * r1_e2v(ji,jj) * vmask(ji,jj,1) |
---|
| 1023 | END_2D |
---|
[13497] | 1024 | DO_2D( 0, 0, 0, 0 ) ! Second derivative |
---|
[12377] | 1025 | ztv4(ji,jj,jl) = ( ztv3(ji,jj,jl) - ztv3(ji,jj-1,jl) ) * r1_e2t(ji,jj) |
---|
| 1026 | END_2D |
---|
[8586] | 1027 | END DO |
---|
[13226] | 1028 | CALL lbc_lnk( 'icedyn_adv_umx', ztv4, 'T', 1.0_wp ) |
---|
[8586] | 1029 | ! |
---|
| 1030 | ! |
---|
[10413] | 1031 | SELECT CASE (kn_umx ) |
---|
[10425] | 1032 | ! |
---|
[8586] | 1033 | CASE( 1 ) !== 1st order central TIM ==! (Eq. 21) |
---|
[10425] | 1034 | DO jl = 1, jpl |
---|
[13886] | 1035 | DO_2D( 1, 0, 0, 0 ) |
---|
[12377] | 1036 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( pt(ji,jj+1,jl) + pt(ji,jj,jl) & |
---|
| 1037 | & - SIGN( 1._wp, pv(ji,jj) ) * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) ) |
---|
| 1038 | END_2D |
---|
[8586] | 1039 | END DO |
---|
| 1040 | ! |
---|
| 1041 | CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23) |
---|
[10425] | 1042 | DO jl = 1, jpl |
---|
[13886] | 1043 | DO_2D( 1, 0, 0, 0 ) |
---|
[12377] | 1044 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
| 1045 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( pt(ji,jj+1,jl) + pt(ji,jj,jl) & |
---|
| 1046 | & - zcv * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) ) |
---|
| 1047 | END_2D |
---|
[8586] | 1048 | END DO |
---|
| 1049 | ! |
---|
| 1050 | CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24) |
---|
[10425] | 1051 | DO jl = 1, jpl |
---|
[13886] | 1052 | DO_2D( 1, 0, 0, 0 ) |
---|
[12377] | 1053 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
| 1054 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
[10439] | 1055 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
[12377] | 1056 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) & |
---|
| 1057 | & - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) & |
---|
| 1058 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) & |
---|
| 1059 | & - SIGN( 1._wp, zcv ) * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) ) |
---|
| 1060 | END_2D |
---|
[8586] | 1061 | END DO |
---|
| 1062 | ! |
---|
| 1063 | CASE( 4 ) !== 4th order central TIM ==! (Eq. 27) |
---|
[10425] | 1064 | DO jl = 1, jpl |
---|
[13886] | 1065 | DO_2D( 1, 0, 0, 0 ) |
---|
[12377] | 1066 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
| 1067 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
[10439] | 1068 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
[12377] | 1069 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) & |
---|
| 1070 | & - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) & |
---|
| 1071 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) & |
---|
| 1072 | & - 0.5_wp * zcv * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) ) |
---|
| 1073 | END_2D |
---|
[8586] | 1074 | END DO |
---|
| 1075 | ! |
---|
| 1076 | CASE( 5 ) !== 5th order central TIM ==! (Eq. 29) |
---|
[10425] | 1077 | DO jl = 1, jpl |
---|
[13886] | 1078 | DO_2D( 1, 0, 0, 0 ) |
---|
[12377] | 1079 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
| 1080 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
[10439] | 1081 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
[12377] | 1082 | zdy4 = zdy2 * zdy2 |
---|
| 1083 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) & |
---|
| 1084 | & - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) & |
---|
| 1085 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) & |
---|
| 1086 | & - 0.5_wp * zcv * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) & |
---|
| 1087 | & + z1_120 * zdy4 * ( zcv*zcv - 1._wp ) * ( zcv*zcv - 4._wp ) * ( ztv4(ji,jj+1,jl) + ztv4(ji,jj,jl) & |
---|
| 1088 | & - SIGN( 1._wp, zcv ) * ( ztv4(ji,jj+1,jl) - ztv4(ji,jj,jl) ) ) ) |
---|
| 1089 | END_2D |
---|
[8586] | 1090 | END DO |
---|
| 1091 | ! |
---|
| 1092 | END SELECT |
---|
[10439] | 1093 | ! |
---|
| 1094 | ! if pt at v-point is negative then use the upstream value |
---|
| 1095 | ! this should not be necessary if a proper sea-ice mask is set in Ultimate |
---|
| 1096 | ! to degrade the order of the scheme when necessary (for ex. at the ice edge) |
---|
[10413] | 1097 | IF( ll_neg ) THEN |
---|
[10425] | 1098 | DO jl = 1, jpl |
---|
[13886] | 1099 | DO_2D( 1, 0, 0, 0 ) |
---|
[12377] | 1100 | IF( pt_v(ji,jj,jl) < 0._wp .OR. ( jmsk_small(ji,jj,jl) == 0 .AND. pamsk == 0. ) ) THEN |
---|
| 1101 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt(ji,jj+1,jl) + pt(ji,jj,jl) ) & |
---|
| 1102 | & - SIGN( 1._wp, pv(ji,jj) ) * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) ) |
---|
| 1103 | ENDIF |
---|
| 1104 | END_2D |
---|
[10413] | 1105 | END DO |
---|
| 1106 | ENDIF |
---|
[10439] | 1107 | ! !-- High order flux in j-direction --! |
---|
[10425] | 1108 | DO jl = 1, jpl |
---|
[13886] | 1109 | DO_2D( 1, 0, 0, 0 ) |
---|
[12377] | 1110 | pfv_ho(ji,jj,jl) = pv(ji,jj) * pt_v(ji,jj,jl) |
---|
| 1111 | END_2D |
---|
[10413] | 1112 | END DO |
---|
[8586] | 1113 | ! |
---|
| 1114 | END SUBROUTINE ultimate_y |
---|
[10413] | 1115 | |
---|
| 1116 | |
---|
[10519] | 1117 | SUBROUTINE nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[8586] | 1118 | !!--------------------------------------------------------------------- |
---|
[10519] | 1119 | !! *** ROUTINE nonosc_ice *** |
---|
[8586] | 1120 | !! |
---|
[10446] | 1121 | !! ** Purpose : compute monotonic tracer fluxes from the upstream |
---|
[10519] | 1122 | !! scheme and the before field by a non-oscillatory algorithm |
---|
[8586] | 1123 | !! |
---|
[10446] | 1124 | !! ** Method : ... |
---|
[8586] | 1125 | !!---------------------------------------------------------------------- |
---|
[10439] | 1126 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 1127 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
[10425] | 1128 | REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pu ! ice i-velocity => u*e2 |
---|
| 1129 | REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pv ! ice j-velocity => v*e1 |
---|
[10446] | 1130 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pt, pt_ups ! before field & upstream guess of after field |
---|
| 1131 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pfv_ups, pfu_ups ! upstream flux |
---|
[10425] | 1132 | REAL(wp), DIMENSION (:,:,:), INTENT(inout) :: pfv_ho, pfu_ho ! monotonic flux |
---|
[8586] | 1133 | ! |
---|
[10425] | 1134 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[10475] | 1135 | REAL(wp) :: zpos, zneg, zbig, zup, zdo, z1_dt ! local scalars |
---|
| 1136 | REAL(wp) :: zau, zbu, zcu, zav, zbv, zcv, zcoef, zzt ! - - |
---|
[10425] | 1137 | REAL(wp), DIMENSION(jpi,jpj ) :: zbup, zbdo |
---|
[10439] | 1138 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zbetup, zbetdo, zti_ups, ztj_ups |
---|
[8586] | 1139 | !!---------------------------------------------------------------------- |
---|
| 1140 | zbig = 1.e+40_wp |
---|
[10425] | 1141 | |
---|
[10413] | 1142 | ! antidiffusive flux : high order minus low order |
---|
| 1143 | ! -------------------------------------------------- |
---|
[10425] | 1144 | DO jl = 1, jpl |
---|
[13886] | 1145 | DO_2D( 0, 0, 1, 0 ) |
---|
[12377] | 1146 | pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) - pfu_ups(ji,jj,jl) |
---|
[13886] | 1147 | END_2D |
---|
| 1148 | DO_2D( 1, 0, 0, 0 ) |
---|
[12377] | 1149 | pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) - pfv_ups(ji,jj,jl) |
---|
| 1150 | END_2D |
---|
[8586] | 1151 | END DO |
---|
| 1152 | |
---|
[10413] | 1153 | ! extreme case where pfu_ho has to be zero |
---|
| 1154 | ! ---------------------------------------- |
---|
| 1155 | ! pfu_ho |
---|
| 1156 | ! * ---> |
---|
| 1157 | ! | | * | | |
---|
| 1158 | ! | | | * | |
---|
| 1159 | ! | | | | * |
---|
[10439] | 1160 | ! t_ups : i-1 i i+1 i+2 |
---|
[10945] | 1161 | IF( ll_prelim ) THEN |
---|
[10413] | 1162 | |
---|
[10425] | 1163 | DO jl = 1, jpl |
---|
[13295] | 1164 | DO_2D( 0, 0, 0, 0 ) |
---|
[12377] | 1165 | zti_ups(ji,jj,jl)= pt_ups(ji+1,jj ,jl) |
---|
| 1166 | ztj_ups(ji,jj,jl)= pt_ups(ji ,jj+1,jl) |
---|
| 1167 | END_2D |
---|
[10413] | 1168 | END DO |
---|
[13226] | 1169 | CALL lbc_lnk_multi( 'icedyn_adv_umx', zti_ups, 'T', 1.0_wp, ztj_ups, 'T', 1.0_wp ) |
---|
[8586] | 1170 | |
---|
[10425] | 1171 | DO jl = 1, jpl |
---|
[13295] | 1172 | DO_2D( 0, 0, 0, 0 ) |
---|
[12377] | 1173 | IF ( pfu_ho(ji,jj,jl) * ( pt_ups(ji+1,jj ,jl) - pt_ups(ji,jj,jl) ) <= 0._wp .AND. & |
---|
| 1174 | & pfv_ho(ji,jj,jl) * ( pt_ups(ji ,jj+1,jl) - pt_ups(ji,jj,jl) ) <= 0._wp ) THEN |
---|
| 1175 | ! |
---|
| 1176 | IF( pfu_ho(ji,jj,jl) * ( zti_ups(ji+1,jj ,jl) - zti_ups(ji,jj,jl) ) <= 0._wp .AND. & |
---|
| 1177 | & pfv_ho(ji,jj,jl) * ( ztj_ups(ji ,jj+1,jl) - ztj_ups(ji,jj,jl) ) <= 0._wp ) THEN |
---|
| 1178 | pfu_ho(ji,jj,jl)=0._wp |
---|
| 1179 | pfv_ho(ji,jj,jl)=0._wp |
---|
[10425] | 1180 | ENDIF |
---|
[12377] | 1181 | ! |
---|
| 1182 | IF( pfu_ho(ji,jj,jl) * ( pt_ups(ji,jj,jl) - pt_ups(ji-1,jj ,jl) ) <= 0._wp .AND. & |
---|
| 1183 | & pfv_ho(ji,jj,jl) * ( pt_ups(ji,jj,jl) - pt_ups(ji ,jj-1,jl) ) <= 0._wp ) THEN |
---|
| 1184 | pfu_ho(ji,jj,jl)=0._wp |
---|
| 1185 | pfv_ho(ji,jj,jl)=0._wp |
---|
| 1186 | ENDIF |
---|
| 1187 | ! |
---|
| 1188 | ENDIF |
---|
| 1189 | END_2D |
---|
[10413] | 1190 | END DO |
---|
[13226] | 1191 | CALL lbc_lnk_multi( 'icedyn_adv_umx', pfu_ho, 'U', -1.0_wp, pfv_ho, 'V', -1.0_wp ) ! lateral boundary cond. |
---|
[10413] | 1192 | |
---|
| 1193 | ENDIF |
---|
[10425] | 1194 | |
---|
[8586] | 1195 | ! Search local extrema |
---|
| 1196 | ! -------------------- |
---|
[10439] | 1197 | ! max/min of pt & pt_ups with large negative/positive value (-/+zbig) outside ice cover |
---|
[10425] | 1198 | z1_dt = 1._wp / pdt |
---|
| 1199 | DO jl = 1, jpl |
---|
| 1200 | |
---|
[13295] | 1201 | DO_2D( 1, 1, 1, 1 ) |
---|
[12377] | 1202 | IF ( pt(ji,jj,jl) <= 0._wp .AND. pt_ups(ji,jj,jl) <= 0._wp ) THEN |
---|
| 1203 | zbup(ji,jj) = -zbig |
---|
| 1204 | zbdo(ji,jj) = zbig |
---|
| 1205 | ELSEIF( pt(ji,jj,jl) <= 0._wp .AND. pt_ups(ji,jj,jl) > 0._wp ) THEN |
---|
| 1206 | zbup(ji,jj) = pt_ups(ji,jj,jl) |
---|
| 1207 | zbdo(ji,jj) = pt_ups(ji,jj,jl) |
---|
| 1208 | ELSEIF( pt(ji,jj,jl) > 0._wp .AND. pt_ups(ji,jj,jl) <= 0._wp ) THEN |
---|
| 1209 | zbup(ji,jj) = pt(ji,jj,jl) |
---|
| 1210 | zbdo(ji,jj) = pt(ji,jj,jl) |
---|
| 1211 | ELSE |
---|
| 1212 | zbup(ji,jj) = MAX( pt(ji,jj,jl) , pt_ups(ji,jj,jl) ) |
---|
| 1213 | zbdo(ji,jj) = MIN( pt(ji,jj,jl) , pt_ups(ji,jj,jl) ) |
---|
| 1214 | ENDIF |
---|
| 1215 | END_2D |
---|
[8586] | 1216 | |
---|
[13295] | 1217 | DO_2D( 0, 0, 0, 0 ) |
---|
[12377] | 1218 | ! |
---|
| 1219 | zup = MAX( zbup(ji,jj), zbup(ji-1,jj), zbup(ji+1,jj), zbup(ji,jj-1), zbup(ji,jj+1) ) ! search max/min in neighbourhood |
---|
| 1220 | zdo = MIN( zbdo(ji,jj), zbdo(ji-1,jj), zbdo(ji+1,jj), zbdo(ji,jj-1), zbdo(ji,jj+1) ) |
---|
| 1221 | ! |
---|
| 1222 | zpos = MAX( 0._wp, pfu_ho(ji-1,jj ,jl) ) - MIN( 0._wp, pfu_ho(ji ,jj ,jl) ) & ! positive/negative part of the flux |
---|
| 1223 | & + MAX( 0._wp, pfv_ho(ji ,jj-1,jl) ) - MIN( 0._wp, pfv_ho(ji ,jj ,jl) ) |
---|
| 1224 | zneg = MAX( 0._wp, pfu_ho(ji ,jj ,jl) ) - MIN( 0._wp, pfu_ho(ji-1,jj ,jl) ) & |
---|
| 1225 | & + MAX( 0._wp, pfv_ho(ji ,jj ,jl) ) - MIN( 0._wp, pfv_ho(ji ,jj-1,jl) ) |
---|
| 1226 | ! |
---|
| 1227 | zpos = zpos - (pt(ji,jj,jl) * MIN( 0., pu(ji,jj) - pu(ji-1,jj) ) + pt(ji,jj,jl) * MIN( 0., pv(ji,jj) - pv(ji,jj-1) ) & |
---|
| 1228 | & ) * ( 1. - pamsk ) |
---|
| 1229 | zneg = zneg + (pt(ji,jj,jl) * MAX( 0., pu(ji,jj) - pu(ji-1,jj) ) + pt(ji,jj,jl) * MAX( 0., pv(ji,jj) - pv(ji,jj-1) ) & |
---|
| 1230 | & ) * ( 1. - pamsk ) |
---|
| 1231 | ! |
---|
| 1232 | ! ! up & down beta terms |
---|
| 1233 | ! clem: zbetup and zbetdo must be 0 for zpos>1.e-10 & zneg>1.e-10 (do not put 0 instead of 1.e-10 !!!) |
---|
| 1234 | IF( zpos > epsi10 ) THEN ; zbetup(ji,jj,jl) = MAX( 0._wp, zup - pt_ups(ji,jj,jl) ) / zpos * e1e2t(ji,jj) * z1_dt |
---|
| 1235 | ELSE ; zbetup(ji,jj,jl) = 0._wp ! zbig |
---|
| 1236 | ENDIF |
---|
| 1237 | ! |
---|
| 1238 | IF( zneg > epsi10 ) THEN ; zbetdo(ji,jj,jl) = MAX( 0._wp, pt_ups(ji,jj,jl) - zdo ) / zneg * e1e2t(ji,jj) * z1_dt |
---|
| 1239 | ELSE ; zbetdo(ji,jj,jl) = 0._wp ! zbig |
---|
| 1240 | ENDIF |
---|
| 1241 | ! |
---|
| 1242 | ! if all the points are outside ice cover |
---|
| 1243 | IF( zup == -zbig ) zbetup(ji,jj,jl) = 0._wp ! zbig |
---|
| 1244 | IF( zdo == zbig ) zbetdo(ji,jj,jl) = 0._wp ! zbig |
---|
| 1245 | ! |
---|
| 1246 | END_2D |
---|
[8586] | 1247 | END DO |
---|
[13226] | 1248 | CALL lbc_lnk_multi( 'icedyn_adv_umx', zbetup, 'T', 1.0_wp, zbetdo, 'T', 1.0_wp ) ! lateral boundary cond. (unchanged sign) |
---|
[8586] | 1249 | |
---|
[10413] | 1250 | |
---|
| 1251 | ! monotonic flux in the y direction |
---|
| 1252 | ! --------------------------------- |
---|
[10425] | 1253 | DO jl = 1, jpl |
---|
[13886] | 1254 | DO_2D( 0, 0, 1, 0 ) |
---|
[12377] | 1255 | zau = MIN( 1._wp , zbetdo(ji,jj,jl) , zbetup(ji+1,jj,jl) ) |
---|
| 1256 | zbu = MIN( 1._wp , zbetup(ji,jj,jl) , zbetdo(ji+1,jj,jl) ) |
---|
| 1257 | zcu = 0.5_wp + SIGN( 0.5_wp , pfu_ho(ji,jj,jl) ) |
---|
| 1258 | ! |
---|
| 1259 | zcoef = ( zcu * zau + ( 1._wp - zcu ) * zbu ) |
---|
| 1260 | ! |
---|
| 1261 | pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) * zcoef + pfu_ups(ji,jj,jl) |
---|
| 1262 | ! |
---|
| 1263 | END_2D |
---|
[10413] | 1264 | |
---|
[13886] | 1265 | DO_2D( 1, 0, 0, 0 ) |
---|
[12377] | 1266 | zav = MIN( 1._wp , zbetdo(ji,jj,jl) , zbetup(ji,jj+1,jl) ) |
---|
| 1267 | zbv = MIN( 1._wp , zbetup(ji,jj,jl) , zbetdo(ji,jj+1,jl) ) |
---|
| 1268 | zcv = 0.5_wp + SIGN( 0.5_wp , pfv_ho(ji,jj,jl) ) |
---|
| 1269 | ! |
---|
| 1270 | zcoef = ( zcv * zav + ( 1._wp - zcv ) * zbv ) |
---|
| 1271 | ! |
---|
| 1272 | pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) * zcoef + pfv_ups(ji,jj,jl) |
---|
| 1273 | ! |
---|
| 1274 | END_2D |
---|
[10413] | 1275 | |
---|
| 1276 | END DO |
---|
[8586] | 1277 | ! |
---|
[10519] | 1278 | END SUBROUTINE nonosc_ice |
---|
[8586] | 1279 | |
---|
[10446] | 1280 | |
---|
| 1281 | SUBROUTINE limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
[10413] | 1282 | !!--------------------------------------------------------------------- |
---|
| 1283 | !! *** ROUTINE limiter_x *** |
---|
| 1284 | !! |
---|
| 1285 | !! ** Purpose : compute flux limiter |
---|
| 1286 | !!---------------------------------------------------------------------- |
---|
[10446] | 1287 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 1288 | REAL(wp), DIMENSION(:,: ), INTENT(in ) :: pu ! ice i-velocity => u*e2 |
---|
| 1289 | REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pt ! ice tracer |
---|
| 1290 | REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pfu_ups ! upstream flux |
---|
| 1291 | REAL(wp), DIMENSION(:,:,:), INTENT(inout) :: pfu_ho ! high order flux |
---|
[10413] | 1292 | ! |
---|
| 1293 | REAL(wp) :: Cr, Rjm, Rj, Rjp, uCFL, zpsi, zh3, zlimiter, Rr |
---|
[10425] | 1294 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
| 1295 | REAL(wp), DIMENSION (jpi,jpj,jpl) :: zslpx ! tracer slopes |
---|
[10413] | 1296 | !!---------------------------------------------------------------------- |
---|
| 1297 | ! |
---|
[10425] | 1298 | DO jl = 1, jpl |
---|
[13295] | 1299 | DO_2D( 0, 0, 0, 0 ) |
---|
[12377] | 1300 | zslpx(ji,jj,jl) = ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) * umask(ji,jj,1) |
---|
| 1301 | END_2D |
---|
[10413] | 1302 | END DO |
---|
[13226] | 1303 | CALL lbc_lnk( 'icedyn_adv_umx', zslpx, 'U', -1.0_wp) ! lateral boundary cond. |
---|
[10413] | 1304 | |
---|
[10425] | 1305 | DO jl = 1, jpl |
---|
[13295] | 1306 | DO_2D( 0, 0, 0, 0 ) |
---|
[12377] | 1307 | uCFL = pdt * ABS( pu(ji,jj) ) * r1_e1e2t(ji,jj) |
---|
| 1308 | |
---|
| 1309 | Rjm = zslpx(ji-1,jj,jl) |
---|
| 1310 | Rj = zslpx(ji ,jj,jl) |
---|
| 1311 | Rjp = zslpx(ji+1,jj,jl) |
---|
[10413] | 1312 | |
---|
[12377] | 1313 | IF( np_limiter == 3 ) THEN |
---|
[10413] | 1314 | |
---|
[12377] | 1315 | IF( pu(ji,jj) > 0. ) THEN ; Rr = Rjm |
---|
| 1316 | ELSE ; Rr = Rjp |
---|
| 1317 | ENDIF |
---|
[10413] | 1318 | |
---|
[12377] | 1319 | zh3 = pfu_ho(ji,jj,jl) - pfu_ups(ji,jj,jl) |
---|
| 1320 | IF( Rj > 0. ) THEN |
---|
| 1321 | zlimiter = MAX( 0., MIN( zh3, MAX(-Rr * 0.5 * ABS(pu(ji,jj)), & |
---|
| 1322 | & MIN( 2. * Rr * 0.5 * ABS(pu(ji,jj)), zh3, 1.5 * Rj * 0.5 * ABS(pu(ji,jj)) ) ) ) ) |
---|
| 1323 | ELSE |
---|
| 1324 | zlimiter = -MAX( 0., MIN(-zh3, MAX( Rr * 0.5 * ABS(pu(ji,jj)), & |
---|
| 1325 | & MIN(-2. * Rr * 0.5 * ABS(pu(ji,jj)), -zh3, -1.5 * Rj * 0.5 * ABS(pu(ji,jj)) ) ) ) ) |
---|
| 1326 | ENDIF |
---|
| 1327 | pfu_ho(ji,jj,jl) = pfu_ups(ji,jj,jl) + zlimiter |
---|
[10413] | 1328 | |
---|
[12377] | 1329 | ELSEIF( np_limiter == 2 ) THEN |
---|
| 1330 | IF( Rj /= 0. ) THEN |
---|
| 1331 | IF( pu(ji,jj) > 0. ) THEN ; Cr = Rjm / Rj |
---|
| 1332 | ELSE ; Cr = Rjp / Rj |
---|
[10413] | 1333 | ENDIF |
---|
[12377] | 1334 | ELSE |
---|
| 1335 | Cr = 0. |
---|
| 1336 | ENDIF |
---|
[10425] | 1337 | |
---|
[12377] | 1338 | ! -- superbee -- |
---|
| 1339 | zpsi = MAX( 0., MAX( MIN(1.,2.*Cr), MIN(2.,Cr) ) ) |
---|
| 1340 | ! -- van albada 2 -- |
---|
| 1341 | !!zpsi = 2.*Cr / (Cr*Cr+1.) |
---|
| 1342 | ! -- sweby (with beta=1) -- |
---|
| 1343 | !!zpsi = MAX( 0., MAX( MIN(1.,1.*Cr), MIN(1.,Cr) ) ) |
---|
| 1344 | ! -- van Leer -- |
---|
| 1345 | !!zpsi = ( Cr + ABS(Cr) ) / ( 1. + ABS(Cr) ) |
---|
| 1346 | ! -- ospre -- |
---|
| 1347 | !!zpsi = 1.5 * ( Cr*Cr + Cr ) / ( Cr*Cr + Cr + 1. ) |
---|
| 1348 | ! -- koren -- |
---|
| 1349 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( (1.+2*Cr)/3., 2. ) ) ) |
---|
| 1350 | ! -- charm -- |
---|
| 1351 | !IF( Cr > 0. ) THEN ; zpsi = Cr * (3.*Cr + 1.) / ( (Cr + 1.) * (Cr + 1.) ) |
---|
| 1352 | !ELSE ; zpsi = 0. |
---|
| 1353 | !ENDIF |
---|
| 1354 | ! -- van albada 1 -- |
---|
| 1355 | !!zpsi = (Cr*Cr + Cr) / (Cr*Cr +1) |
---|
| 1356 | ! -- smart -- |
---|
| 1357 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, 4. ) ) ) |
---|
| 1358 | ! -- umist -- |
---|
| 1359 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, MIN(0.75+0.25*Cr, 2. ) ) ) ) |
---|
[10413] | 1360 | |
---|
[12377] | 1361 | ! high order flux corrected by the limiter |
---|
| 1362 | pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) - ABS( pu(ji,jj) ) * ( (1.-zpsi) + uCFL*zpsi ) * Rj * 0.5 |
---|
[10413] | 1363 | |
---|
[12377] | 1364 | ENDIF |
---|
| 1365 | END_2D |
---|
[10413] | 1366 | END DO |
---|
[13226] | 1367 | CALL lbc_lnk( 'icedyn_adv_umx', pfu_ho, 'U', -1.0_wp) ! lateral boundary cond. |
---|
[10413] | 1368 | ! |
---|
| 1369 | END SUBROUTINE limiter_x |
---|
| 1370 | |
---|
[10446] | 1371 | |
---|
| 1372 | SUBROUTINE limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 1373 | !!--------------------------------------------------------------------- |
---|
| 1374 | !! *** ROUTINE limiter_y *** |
---|
| 1375 | !! |
---|
| 1376 | !! ** Purpose : compute flux limiter |
---|
| 1377 | !!---------------------------------------------------------------------- |
---|
[10446] | 1378 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 1379 | REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pv ! ice i-velocity => u*e2 |
---|
| 1380 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pt ! ice tracer |
---|
| 1381 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pfv_ups ! upstream flux |
---|
| 1382 | REAL(wp), DIMENSION (:,:,:), INTENT(inout) :: pfv_ho ! high order flux |
---|
[10413] | 1383 | ! |
---|
| 1384 | REAL(wp) :: Cr, Rjm, Rj, Rjp, vCFL, zpsi, zh3, zlimiter, Rr |
---|
[10425] | 1385 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
| 1386 | REAL(wp), DIMENSION (jpi,jpj,jpl) :: zslpy ! tracer slopes |
---|
[10413] | 1387 | !!---------------------------------------------------------------------- |
---|
| 1388 | ! |
---|
[10425] | 1389 | DO jl = 1, jpl |
---|
[13295] | 1390 | DO_2D( 0, 0, 0, 0 ) |
---|
[12377] | 1391 | zslpy(ji,jj,jl) = ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) * vmask(ji,jj,1) |
---|
| 1392 | END_2D |
---|
[10413] | 1393 | END DO |
---|
[13226] | 1394 | CALL lbc_lnk( 'icedyn_adv_umx', zslpy, 'V', -1.0_wp) ! lateral boundary cond. |
---|
[10413] | 1395 | |
---|
[10425] | 1396 | DO jl = 1, jpl |
---|
[13295] | 1397 | DO_2D( 0, 0, 0, 0 ) |
---|
[12377] | 1398 | vCFL = pdt * ABS( pv(ji,jj) ) * r1_e1e2t(ji,jj) |
---|
[10413] | 1399 | |
---|
[12377] | 1400 | Rjm = zslpy(ji,jj-1,jl) |
---|
| 1401 | Rj = zslpy(ji,jj ,jl) |
---|
| 1402 | Rjp = zslpy(ji,jj+1,jl) |
---|
[10413] | 1403 | |
---|
[12377] | 1404 | IF( np_limiter == 3 ) THEN |
---|
[10413] | 1405 | |
---|
[12377] | 1406 | IF( pv(ji,jj) > 0. ) THEN ; Rr = Rjm |
---|
| 1407 | ELSE ; Rr = Rjp |
---|
| 1408 | ENDIF |
---|
[10413] | 1409 | |
---|
[12377] | 1410 | zh3 = pfv_ho(ji,jj,jl) - pfv_ups(ji,jj,jl) |
---|
| 1411 | IF( Rj > 0. ) THEN |
---|
| 1412 | zlimiter = MAX( 0., MIN( zh3, MAX(-Rr * 0.5 * ABS(pv(ji,jj)), & |
---|
| 1413 | & MIN( 2. * Rr * 0.5 * ABS(pv(ji,jj)), zh3, 1.5 * Rj * 0.5 * ABS(pv(ji,jj)) ) ) ) ) |
---|
| 1414 | ELSE |
---|
| 1415 | zlimiter = -MAX( 0., MIN(-zh3, MAX( Rr * 0.5 * ABS(pv(ji,jj)), & |
---|
| 1416 | & MIN(-2. * Rr * 0.5 * ABS(pv(ji,jj)), -zh3, -1.5 * Rj * 0.5 * ABS(pv(ji,jj)) ) ) ) ) |
---|
| 1417 | ENDIF |
---|
| 1418 | pfv_ho(ji,jj,jl) = pfv_ups(ji,jj,jl) + zlimiter |
---|
[10413] | 1419 | |
---|
[12377] | 1420 | ELSEIF( np_limiter == 2 ) THEN |
---|
[10413] | 1421 | |
---|
[12377] | 1422 | IF( Rj /= 0. ) THEN |
---|
| 1423 | IF( pv(ji,jj) > 0. ) THEN ; Cr = Rjm / Rj |
---|
| 1424 | ELSE ; Cr = Rjp / Rj |
---|
[10425] | 1425 | ENDIF |
---|
[12377] | 1426 | ELSE |
---|
| 1427 | Cr = 0. |
---|
| 1428 | ENDIF |
---|
[10413] | 1429 | |
---|
[12377] | 1430 | ! -- superbee -- |
---|
| 1431 | zpsi = MAX( 0., MAX( MIN(1.,2.*Cr), MIN(2.,Cr) ) ) |
---|
| 1432 | ! -- van albada 2 -- |
---|
| 1433 | !!zpsi = 2.*Cr / (Cr*Cr+1.) |
---|
| 1434 | ! -- sweby (with beta=1) -- |
---|
| 1435 | !!zpsi = MAX( 0., MAX( MIN(1.,1.*Cr), MIN(1.,Cr) ) ) |
---|
| 1436 | ! -- van Leer -- |
---|
| 1437 | !!zpsi = ( Cr + ABS(Cr) ) / ( 1. + ABS(Cr) ) |
---|
| 1438 | ! -- ospre -- |
---|
| 1439 | !!zpsi = 1.5 * ( Cr*Cr + Cr ) / ( Cr*Cr + Cr + 1. ) |
---|
| 1440 | ! -- koren -- |
---|
| 1441 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( (1.+2*Cr)/3., 2. ) ) ) |
---|
| 1442 | ! -- charm -- |
---|
| 1443 | !IF( Cr > 0. ) THEN ; zpsi = Cr * (3.*Cr + 1.) / ( (Cr + 1.) * (Cr + 1.) ) |
---|
| 1444 | !ELSE ; zpsi = 0. |
---|
| 1445 | !ENDIF |
---|
| 1446 | ! -- van albada 1 -- |
---|
| 1447 | !!zpsi = (Cr*Cr + Cr) / (Cr*Cr +1) |
---|
| 1448 | ! -- smart -- |
---|
| 1449 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, 4. ) ) ) |
---|
| 1450 | ! -- umist -- |
---|
| 1451 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, MIN(0.75+0.25*Cr, 2. ) ) ) ) |
---|
[10413] | 1452 | |
---|
[12377] | 1453 | ! high order flux corrected by the limiter |
---|
| 1454 | pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) - ABS( pv(ji,jj) ) * ( (1.-zpsi) + vCFL*zpsi ) * Rj * 0.5 |
---|
[10425] | 1455 | |
---|
[12377] | 1456 | ENDIF |
---|
| 1457 | END_2D |
---|
[10413] | 1458 | END DO |
---|
[13226] | 1459 | CALL lbc_lnk( 'icedyn_adv_umx', pfv_ho, 'V', -1.0_wp) ! lateral boundary cond. |
---|
[10413] | 1460 | ! |
---|
| 1461 | END SUBROUTINE limiter_y |
---|
| 1462 | |
---|
[10911] | 1463 | |
---|
[13472] | 1464 | SUBROUTINE Hbig( pdt, phi_max, phs_max, phip_max, psi_max, pes_max, pei_max, & |
---|
| 1465 | & pv_i, pv_s, pa_i, pa_ip, pv_ip, psv_i, pe_s, pe_i ) |
---|
[10911] | 1466 | !!------------------------------------------------------------------- |
---|
| 1467 | !! *** ROUTINE Hbig *** |
---|
| 1468 | !! |
---|
| 1469 | !! ** Purpose : Thickness correction in case advection scheme creates |
---|
| 1470 | !! abnormally tick ice or snow |
---|
| 1471 | !! |
---|
| 1472 | !! ** Method : 1- check whether ice thickness is larger than the surrounding 9-points |
---|
| 1473 | !! (before advection) and reduce it by adapting ice concentration |
---|
| 1474 | !! 2- check whether snow thickness is larger than the surrounding 9-points |
---|
| 1475 | !! (before advection) and reduce it by sending the excess in the ocean |
---|
| 1476 | !! |
---|
| 1477 | !! ** input : Max thickness of the surrounding 9-points |
---|
| 1478 | !!------------------------------------------------------------------- |
---|
[13472] | 1479 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 1480 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: phi_max, phs_max, phip_max, psi_max ! max ice thick from surrounding 9-pts |
---|
| 1481 | REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pes_max |
---|
| 1482 | REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pei_max |
---|
| 1483 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i, pv_s, pa_i, pa_ip, pv_ip, psv_i |
---|
[10911] | 1484 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s |
---|
[13472] | 1485 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_i |
---|
[10911] | 1486 | ! |
---|
[13472] | 1487 | INTEGER :: ji, jj, jk, jl ! dummy loop indices |
---|
| 1488 | REAL(wp) :: z1_dt, zhip, zhi, zhs, zsi, zes, zei, zfra |
---|
[10911] | 1489 | !!------------------------------------------------------------------- |
---|
| 1490 | ! |
---|
[10930] | 1491 | z1_dt = 1._wp / pdt |
---|
[10911] | 1492 | ! |
---|
| 1493 | DO jl = 1, jpl |
---|
[13295] | 1494 | DO_2D( 1, 1, 1, 1 ) |
---|
[12377] | 1495 | IF ( pv_i(ji,jj,jl) > 0._wp ) THEN |
---|
| 1496 | ! |
---|
| 1497 | ! ! -- check h_ip -- ! |
---|
| 1498 | ! if h_ip is larger than the surrounding 9 pts => reduce h_ip and increase a_ip |
---|
[13472] | 1499 | IF( ln_pnd_LEV .AND. pv_ip(ji,jj,jl) > 0._wp ) THEN |
---|
[12377] | 1500 | zhip = pv_ip(ji,jj,jl) / MAX( epsi20, pa_ip(ji,jj,jl) ) |
---|
| 1501 | IF( zhip > phip_max(ji,jj,jl) .AND. pa_ip(ji,jj,jl) < 0.15 ) THEN |
---|
| 1502 | pa_ip(ji,jj,jl) = pv_ip(ji,jj,jl) / phip_max(ji,jj,jl) |
---|
[10911] | 1503 | ENDIF |
---|
[12377] | 1504 | ENDIF |
---|
| 1505 | ! |
---|
| 1506 | ! ! -- check h_i -- ! |
---|
| 1507 | ! if h_i is larger than the surrounding 9 pts => reduce h_i and increase a_i |
---|
| 1508 | zhi = pv_i(ji,jj,jl) / pa_i(ji,jj,jl) |
---|
| 1509 | IF( zhi > phi_max(ji,jj,jl) .AND. pa_i(ji,jj,jl) < 0.15 ) THEN |
---|
| 1510 | pa_i(ji,jj,jl) = pv_i(ji,jj,jl) / MIN( phi_max(ji,jj,jl), hi_max(jpl) ) !-- bound h_i to hi_max (99 m) |
---|
| 1511 | ENDIF |
---|
| 1512 | ! |
---|
| 1513 | ! ! -- check h_s -- ! |
---|
| 1514 | ! if h_s is larger than the surrounding 9 pts => put the snow excess in the ocean |
---|
| 1515 | zhs = pv_s(ji,jj,jl) / pa_i(ji,jj,jl) |
---|
| 1516 | IF( pv_s(ji,jj,jl) > 0._wp .AND. zhs > phs_max(ji,jj,jl) .AND. pa_i(ji,jj,jl) < 0.15 ) THEN |
---|
| 1517 | zfra = phs_max(ji,jj,jl) / MAX( zhs, epsi20 ) |
---|
[10911] | 1518 | ! |
---|
[12377] | 1519 | wfx_res(ji,jj) = wfx_res(ji,jj) + ( pv_s(ji,jj,jl) - pa_i(ji,jj,jl) * phs_max(ji,jj,jl) ) * rhos * z1_dt |
---|
| 1520 | hfx_res(ji,jj) = hfx_res(ji,jj) - SUM( pe_s(ji,jj,1:nlay_s,jl) ) * ( 1._wp - zfra ) * z1_dt ! W.m-2 <0 |
---|
[10911] | 1521 | ! |
---|
[12377] | 1522 | pe_s(ji,jj,1:nlay_s,jl) = pe_s(ji,jj,1:nlay_s,jl) * zfra |
---|
| 1523 | pv_s(ji,jj,jl) = pa_i(ji,jj,jl) * phs_max(ji,jj,jl) |
---|
| 1524 | ENDIF |
---|
| 1525 | ! |
---|
[13472] | 1526 | ! ! -- check s_i -- ! |
---|
| 1527 | ! if s_i is larger than the surrounding 9 pts => put salt excess in the ocean |
---|
| 1528 | zsi = psv_i(ji,jj,jl) / pv_i(ji,jj,jl) |
---|
| 1529 | IF( zsi > psi_max(ji,jj,jl) .AND. pa_i(ji,jj,jl) < 0.15 ) THEN |
---|
| 1530 | zfra = psi_max(ji,jj,jl) / zsi |
---|
| 1531 | sfx_res(ji,jj) = sfx_res(ji,jj) + psv_i(ji,jj,jl) * ( 1._wp - zfra ) * rhoi * z1_dt |
---|
| 1532 | psv_i(ji,jj,jl) = psv_i(ji,jj,jl) * zfra |
---|
| 1533 | ENDIF |
---|
| 1534 | ! |
---|
[12377] | 1535 | ENDIF |
---|
| 1536 | END_2D |
---|
[12197] | 1537 | END DO |
---|
| 1538 | ! |
---|
[13472] | 1539 | ! ! -- check e_i/v_i -- ! |
---|
| 1540 | DO jl = 1, jpl |
---|
| 1541 | DO_3D( 1, 1, 1, 1, 1, nlay_i ) |
---|
| 1542 | IF ( pv_i(ji,jj,jl) > 0._wp ) THEN |
---|
| 1543 | ! if e_i/v_i is larger than the surrounding 9 pts => put the heat excess in the ocean |
---|
| 1544 | zei = pe_i(ji,jj,jk,jl) / pv_i(ji,jj,jl) |
---|
| 1545 | IF( zei > pei_max(ji,jj,jk,jl) .AND. pa_i(ji,jj,jl) < 0.15 ) THEN |
---|
| 1546 | zfra = pei_max(ji,jj,jk,jl) / zei |
---|
| 1547 | hfx_res(ji,jj) = hfx_res(ji,jj) - pe_i(ji,jj,jk,jl) * ( 1._wp - zfra ) * z1_dt ! W.m-2 <0 |
---|
| 1548 | pe_i(ji,jj,jk,jl) = pe_i(ji,jj,jk,jl) * zfra |
---|
| 1549 | ENDIF |
---|
| 1550 | ENDIF |
---|
| 1551 | END_3D |
---|
| 1552 | END DO |
---|
| 1553 | ! ! -- check e_s/v_s -- ! |
---|
| 1554 | DO jl = 1, jpl |
---|
| 1555 | DO_3D( 1, 1, 1, 1, 1, nlay_s ) |
---|
| 1556 | IF ( pv_s(ji,jj,jl) > 0._wp ) THEN |
---|
| 1557 | ! if e_s/v_s is larger than the surrounding 9 pts => put the heat excess in the ocean |
---|
| 1558 | zes = pe_s(ji,jj,jk,jl) / pv_s(ji,jj,jl) |
---|
| 1559 | IF( zes > pes_max(ji,jj,jk,jl) .AND. pa_i(ji,jj,jl) < 0.15 ) THEN |
---|
| 1560 | zfra = pes_max(ji,jj,jk,jl) / zes |
---|
| 1561 | hfx_res(ji,jj) = hfx_res(ji,jj) - pe_s(ji,jj,jk,jl) * ( 1._wp - zfra ) * z1_dt ! W.m-2 <0 |
---|
| 1562 | pe_s(ji,jj,jk,jl) = pe_s(ji,jj,jk,jl) * zfra |
---|
| 1563 | ENDIF |
---|
| 1564 | ENDIF |
---|
| 1565 | END_3D |
---|
| 1566 | END DO |
---|
| 1567 | ! |
---|
[12197] | 1568 | END SUBROUTINE Hbig |
---|
| 1569 | |
---|
| 1570 | |
---|
| 1571 | SUBROUTINE Hsnow( pdt, pv_i, pv_s, pa_i, pa_ip, pe_s ) |
---|
| 1572 | !!------------------------------------------------------------------- |
---|
| 1573 | !! *** ROUTINE Hsnow *** |
---|
| 1574 | !! |
---|
| 1575 | !! ** Purpose : 1- Check snow load after advection |
---|
| 1576 | !! 2- Correct pond concentration to avoid a_ip > a_i |
---|
| 1577 | !! |
---|
| 1578 | !! ** Method : If snow load makes snow-ice interface to deplet below the ocean surface |
---|
| 1579 | !! then put the snow excess in the ocean |
---|
| 1580 | !! |
---|
| 1581 | !! ** Notes : This correction is crucial because of the call to routine icecor afterwards |
---|
| 1582 | !! which imposes a mini of ice thick. (rn_himin). This imposed mini can artificially |
---|
| 1583 | !! make the snow very thick (if concentration decreases drastically) |
---|
| 1584 | !! This behavior has been seen in Ultimate-Macho and supposedly it can also be true for Prather |
---|
| 1585 | !!------------------------------------------------------------------- |
---|
| 1586 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 1587 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i, pv_s, pa_i, pa_ip |
---|
| 1588 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s |
---|
| 1589 | ! |
---|
| 1590 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
| 1591 | REAL(wp) :: z1_dt, zvs_excess, zfra |
---|
| 1592 | !!------------------------------------------------------------------- |
---|
| 1593 | ! |
---|
| 1594 | z1_dt = 1._wp / pdt |
---|
| 1595 | ! |
---|
| 1596 | ! -- check snow load -- ! |
---|
| 1597 | DO jl = 1, jpl |
---|
[13295] | 1598 | DO_2D( 1, 1, 1, 1 ) |
---|
[12377] | 1599 | IF ( pv_i(ji,jj,jl) > 0._wp ) THEN |
---|
| 1600 | ! |
---|
[12489] | 1601 | zvs_excess = MAX( 0._wp, pv_s(ji,jj,jl) - pv_i(ji,jj,jl) * (rho0-rhoi) * r1_rhos ) |
---|
[12377] | 1602 | ! |
---|
| 1603 | IF( zvs_excess > 0._wp ) THEN ! snow-ice interface deplets below the ocean surface |
---|
| 1604 | ! put snow excess in the ocean |
---|
| 1605 | zfra = ( pv_s(ji,jj,jl) - zvs_excess ) / MAX( pv_s(ji,jj,jl), epsi20 ) |
---|
| 1606 | wfx_res(ji,jj) = wfx_res(ji,jj) + zvs_excess * rhos * z1_dt |
---|
| 1607 | hfx_res(ji,jj) = hfx_res(ji,jj) - SUM( pe_s(ji,jj,1:nlay_s,jl) ) * ( 1._wp - zfra ) * z1_dt ! W.m-2 <0 |
---|
| 1608 | ! correct snow volume and heat content |
---|
| 1609 | pe_s(ji,jj,1:nlay_s,jl) = pe_s(ji,jj,1:nlay_s,jl) * zfra |
---|
| 1610 | pv_s(ji,jj,jl) = pv_s(ji,jj,jl) - zvs_excess |
---|
[10911] | 1611 | ENDIF |
---|
[12377] | 1612 | ! |
---|
| 1613 | ENDIF |
---|
| 1614 | END_2D |
---|
[12197] | 1615 | END DO |
---|
| 1616 | ! |
---|
| 1617 | !-- correct pond concentration to avoid a_ip > a_i -- ! |
---|
[10911] | 1618 | WHERE( pa_ip(:,:,:) > pa_i(:,:,:) ) pa_ip(:,:,:) = pa_i(:,:,:) |
---|
| 1619 | ! |
---|
[12197] | 1620 | END SUBROUTINE Hsnow |
---|
| 1621 | |
---|
[13886] | 1622 | SUBROUTINE icemax3D( pice , pmax ) |
---|
| 1623 | !!--------------------------------------------------------------------- |
---|
| 1624 | !! *** ROUTINE icemax3D *** |
---|
| 1625 | !! ** Purpose : compute the max of the 9 points around |
---|
| 1626 | !!---------------------------------------------------------------------- |
---|
| 1627 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pice ! input |
---|
| 1628 | REAL(wp), DIMENSION(:,:,:) , INTENT(out) :: pmax ! output |
---|
| 1629 | REAL(wp), DIMENSION(2:jpim1,jpj) :: zmax ! temporary array |
---|
| 1630 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
| 1631 | !!---------------------------------------------------------------------- |
---|
| 1632 | DO jl = 1, jpl |
---|
| 1633 | DO jj = Njs0-1, Nje0+1 |
---|
| 1634 | DO ji = Nis0, Nie0 |
---|
| 1635 | zmax(ji,jj) = MAX( epsi20, pice(ji,jj,jl), pice(ji-1,jj,jl), pice(ji+1,jj,jl) ) |
---|
| 1636 | END DO |
---|
| 1637 | END DO |
---|
| 1638 | DO jj = Njs0, Nje0 |
---|
| 1639 | DO ji = Nis0, Nie0 |
---|
| 1640 | pmax(ji,jj,jl) = MAX( epsi20, zmax(ji,jj), zmax(ji,jj-1), zmax(ji,jj+1) ) |
---|
| 1641 | END DO |
---|
| 1642 | END DO |
---|
| 1643 | END DO |
---|
| 1644 | END SUBROUTINE icemax3D |
---|
[12197] | 1645 | |
---|
[13886] | 1646 | SUBROUTINE icemax4D( pice , pmax ) |
---|
| 1647 | !!--------------------------------------------------------------------- |
---|
| 1648 | !! *** ROUTINE icemax4D *** |
---|
| 1649 | !! ** Purpose : compute the max of the 9 points around |
---|
| 1650 | !!---------------------------------------------------------------------- |
---|
| 1651 | REAL(wp), DIMENSION(:,:,:,:) , INTENT(in ) :: pice ! input |
---|
| 1652 | REAL(wp), DIMENSION(:,:,:,:) , INTENT(out) :: pmax ! output |
---|
| 1653 | REAL(wp), DIMENSION(2:jpim1,jpj) :: zmax ! temporary array |
---|
| 1654 | INTEGER :: jlay, ji, jj, jk, jl ! dummy loop indices |
---|
| 1655 | !!---------------------------------------------------------------------- |
---|
| 1656 | jlay = SIZE( pice , 3 ) ! size of input arrays |
---|
| 1657 | DO jl = 1, jpl |
---|
| 1658 | DO jk = 1, jlay |
---|
| 1659 | DO jj = Njs0-1, Nje0+1 |
---|
| 1660 | DO ji = Nis0, Nie0 |
---|
| 1661 | zmax(ji,jj) = MAX( epsi20, pice(ji,jj,jk,jl), pice(ji-1,jj,jk,jl), pice(ji+1,jj,jk,jl) ) |
---|
| 1662 | END DO |
---|
| 1663 | END DO |
---|
| 1664 | DO jj = Njs0, Nje0 |
---|
| 1665 | DO ji = Nis0, Nie0 |
---|
| 1666 | pmax(ji,jj,jk,jl) = MAX( epsi20, zmax(ji,jj), zmax(ji,jj-1), zmax(ji,jj+1) ) |
---|
| 1667 | END DO |
---|
| 1668 | END DO |
---|
| 1669 | END DO |
---|
| 1670 | END DO |
---|
| 1671 | END SUBROUTINE icemax4D |
---|
| 1672 | |
---|
[8586] | 1673 | #else |
---|
| 1674 | !!---------------------------------------------------------------------- |
---|
[9570] | 1675 | !! Default option Dummy module NO SI3 sea-ice model |
---|
[8586] | 1676 | !!---------------------------------------------------------------------- |
---|
| 1677 | #endif |
---|
| 1678 | |
---|
| 1679 | !!====================================================================== |
---|
| 1680 | END MODULE icedyn_adv_umx |
---|