[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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| 13 | !! ice_dyn_adv_umx : update the tracer trend with the 3D advection trends using a TVD scheme |
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| 14 | !! ultimate_x(_y) : compute a tracer value at velocity points using ULTIMATE scheme at various orders |
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| 15 | !! macho : ??? |
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[10267] | 16 | !! nonosc : compute monotonic tracer fluxes by 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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[10267] | 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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| 25 | USE lib_mpp ! MPP library |
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| 26 | USE lib_fortran ! fortran utilities (glob_sum + no signed zero) |
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| 27 | USE lbclnk ! lateral boundary conditions (or mpp links) |
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| 28 | |
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| 29 | IMPLICIT NONE |
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| 30 | PRIVATE |
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| 31 | |
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| 32 | PUBLIC ice_dyn_adv_umx ! called by icedyn_adv.F90 |
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| 33 | |
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| 34 | REAL(wp) :: z1_6 = 1._wp / 6._wp ! =1/6 |
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| 35 | REAL(wp) :: z1_120 = 1._wp / 120._wp ! =1/120 |
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| 36 | |
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| 37 | !! * Substitutions |
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| 38 | # include "vectopt_loop_substitute.h90" |
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| 39 | !!---------------------------------------------------------------------- |
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[9598] | 40 | !! NEMO/ICE 4.0 , NEMO Consortium (2018) |
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[8586] | 41 | !! $Id: icedyn_adv_umx.F90 4499 2014-02-18 15:14:31Z timgraham $ |
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[9598] | 42 | !! Software governed by the CeCILL licence (./LICENSE) |
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[8586] | 43 | !!---------------------------------------------------------------------- |
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| 44 | CONTAINS |
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| 45 | |
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[10267] | 46 | SUBROUTINE ice_dyn_adv_umx( kn_umx, kt, pu_ice, pv_ice, & |
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| 47 | & pato_i, pv_i, pv_s, psv_i, poa_i, pa_i, pa_ip, pv_ip, pe_s, pe_i ) |
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[8586] | 48 | !!---------------------------------------------------------------------- |
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| 49 | !! *** ROUTINE ice_dyn_adv_umx *** |
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| 50 | !! |
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| 51 | !! ** Purpose : Compute the now trend due to total advection of |
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| 52 | !! tracers and add it to the general trend of tracer equations |
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| 53 | !! using an "Ultimate-Macho" scheme |
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| 54 | !! |
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| 55 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
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| 56 | !!---------------------------------------------------------------------- |
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[10267] | 57 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
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[8586] | 58 | INTEGER , INTENT(in ) :: kt ! time step |
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| 59 | REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pu_ice ! ice i-velocity |
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| 60 | REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pv_ice ! ice j-velocity |
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| 61 | REAL(wp), DIMENSION(:,:) , INTENT(inout) :: pato_i ! open water area |
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| 62 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i ! ice volume |
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| 63 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_s ! snw volume |
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| 64 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: psv_i ! salt content |
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| 65 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: poa_i ! age content |
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| 66 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_i ! ice concentration |
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| 67 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_ip ! melt pond fraction |
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| 68 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_ip ! melt pond volume |
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| 69 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s ! snw heat content |
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| 70 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_i ! ice heat content |
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| 71 | ! |
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| 72 | INTEGER :: ji, jj, jk, jl, jt ! dummy loop indices |
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[10267] | 73 | INTEGER :: icycle ! number of sub-timestep for the advection |
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| 74 | REAL(wp) :: zamsk ! 1 if advection of concentration, 0 if advection of other tracers |
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| 75 | REAL(wp) :: zcfl , zdt |
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| 76 | REAL(wp) :: zeps = 0.1_wp ! shift in concentration to avoid division by 0 |
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| 77 | ! ! must be >= 0.01 and the best seems to be 0.1 |
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| 78 | REAL(wp), DIMENSION(jpi,jpj) :: zudy, zvdx, zcu_box, zcv_box, zfu, zfv |
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| 79 | REAL(wp), DIMENSION(jpi,jpj) :: z1_a, zh_i, zh_s, zs_i, zo_i, ze_i, ze_s, z1_ap, zh_ip |
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[8586] | 80 | !!---------------------------------------------------------------------- |
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| 81 | ! |
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| 82 | IF( kt == nit000 .AND. lwp ) WRITE(numout,*) '-- ice_dyn_adv_umx: Ultimate-Macho advection scheme' |
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| 83 | ! |
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| 84 | ! --- If ice drift field is too fast, use an appropriate time step for advection (CFL test for stability) --- ! |
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| 85 | zcfl = MAXVAL( ABS( pu_ice(:,:) ) * rdt_ice * r1_e1u(:,:) ) |
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| 86 | zcfl = MAX( zcfl, MAXVAL( ABS( pv_ice(:,:) ) * rdt_ice * r1_e2v(:,:) ) ) |
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| 87 | IF( lk_mpp ) CALL mpp_max( zcfl ) |
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| 88 | |
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[10267] | 89 | IF( zcfl > 0.5 ) THEN ; icycle = 2 |
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| 90 | ELSE ; icycle = 1 |
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[8586] | 91 | ENDIF |
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| 92 | |
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[10267] | 93 | zdt = rdt_ice / REAL(icycle) |
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[8586] | 94 | |
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| 95 | ! --- transport --- ! |
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| 96 | zudy(:,:) = pu_ice(:,:) * e2u(:,:) |
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| 97 | zvdx(:,:) = pv_ice(:,:) * e1v(:,:) |
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| 98 | |
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| 99 | ! --- define velocity for advection: u*grad(H) --- ! |
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| 100 | DO jj = 2, jpjm1 |
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| 101 | DO ji = fs_2, fs_jpim1 |
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| 102 | IF ( pu_ice(ji,jj) * pu_ice(ji-1,jj) <= 0._wp ) THEN ; zcu_box(ji,jj) = 0._wp |
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| 103 | ELSEIF( pu_ice(ji,jj) > 0._wp ) THEN ; zcu_box(ji,jj) = pu_ice(ji-1,jj) |
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| 104 | ELSE ; zcu_box(ji,jj) = pu_ice(ji ,jj) |
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| 105 | ENDIF |
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| 106 | |
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| 107 | IF ( pv_ice(ji,jj) * pv_ice(ji,jj-1) <= 0._wp ) THEN ; zcv_box(ji,jj) = 0._wp |
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| 108 | ELSEIF( pv_ice(ji,jj) > 0._wp ) THEN ; zcv_box(ji,jj) = pv_ice(ji,jj-1) |
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| 109 | ELSE ; zcv_box(ji,jj) = pv_ice(ji,jj ) |
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| 110 | ENDIF |
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| 111 | END DO |
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| 112 | END DO |
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| 113 | |
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| 114 | !---------------! |
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| 115 | !== advection ==! |
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| 116 | !---------------! |
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[10267] | 117 | DO jt = 1, icycle |
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| 118 | |
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| 119 | zamsk = 1._wp |
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| 120 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zudy, zvdx, zcu_box, zcv_box, pato_i(:,:), pato_i(:,:) ) ! Open water area |
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| 121 | |
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[8586] | 122 | DO jl = 1, jpl |
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[10267] | 123 | ! to avoid a problem with the limiter nonosc when A gets close to 0 |
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| 124 | pa_i(:,:,jl) = pa_i(:,:,jl) + zeps * tmask(:,:,1) |
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| 125 | ! |
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| 126 | WHERE( pa_i(:,:,jl) > epsi20 ) ; z1_a(:,:) = 1._wp / pa_i(:,:,jl) |
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| 127 | ELSEWHERE ; z1_a(:,:) = 0. !!; pa_i(:,:,jl) = 0. ; pv_i(:,:,jl) = 0. |
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| 128 | END WHERE |
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| 129 | ! |
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| 130 | zamsk = 1._wp |
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| 131 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zudy, zvdx, zcu_box, zcv_box, pa_i(:,:,jl), pa_i(:,:,jl), zfu, zfv ) ! Ice area |
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| 132 | !!zfu = zudy ; zfv = zvdx |
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| 133 | !!CALL adv_umx( kn_umx, kt, zdt, zudy, zvdx, zfu , zfv , zcu_box, zcv_box, pv_i(:,:,jl), pv_i(:,:,jl) ) |
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| 134 | zamsk = 0._wp ; zh_i(:,:) = pv_i (:,:,jl) * z1_a(:,:) |
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| 135 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zfu , zfv , zcu_box, zcv_box, zh_i(:,:), pv_i (:,:,jl) ) ! Ice volume |
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| 136 | zamsk = 0._wp ; zh_s(:,:) = pv_s (:,:,jl) * z1_a(:,:) |
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| 137 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zfu , zfv , zcu_box, zcv_box, zh_s(:,:), pv_s (:,:,jl) ) ! Snw volume |
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| 138 | zamsk = 0._wp ; zs_i(:,:) = psv_i(:,:,jl) * z1_a(:,:) |
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| 139 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zfu , zfv , zcu_box, zcv_box, zs_i(:,:), psv_i(:,:,jl) ) ! Salt content |
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| 140 | zamsk = 0._wp ; zo_i(:,:) = poa_i(:,:,jl) * z1_a(:,:) |
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| 141 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zfu , zfv , zcu_box, zcv_box, zo_i(:,:), poa_i(:,:,jl) ) ! Age content |
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[8586] | 142 | DO jk = 1, nlay_i |
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[10267] | 143 | zamsk = 0._wp ; ze_i(:,:) = pe_i(:,:,jk,jl) * z1_a(:,:) |
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| 144 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zfu, zfv, zcu_box, zcv_box, ze_i(:,:), pe_i(:,:,jk,jl) ) ! Ice heat content |
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[8586] | 145 | END DO |
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[9271] | 146 | DO jk = 1, nlay_s |
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[10267] | 147 | zamsk = 0._wp ; ze_s(:,:) = pe_s(:,:,jk,jl) * z1_a(:,:) |
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| 148 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zfu, zfv, zcu_box, zcv_box, ze_s(:,:), pe_s(:,:,jk,jl) ) ! Snw heat content |
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[9271] | 149 | END DO |
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[10267] | 150 | ! |
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| 151 | IF ( ln_pnd_H12 ) THEN ! melt ponds |
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| 152 | ! to avoid a problem with the limiter nonosc when A gets close to 0 |
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| 153 | pa_ip(:,:,jl) = pa_ip(:,:,jl) + zeps * tmask(:,:,1) |
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| 154 | ! |
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| 155 | WHERE( pa_ip(:,:,jl) > epsi20 ) ; z1_ap(:,:) = 1._wp / pa_ip(:,:,jl) |
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| 156 | ELSEWHERE ; z1_ap(:,:) = 0. |
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| 157 | END WHERE |
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| 158 | ! |
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| 159 | zamsk = 1._wp |
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| 160 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zudy, zvdx, zcu_box, zcv_box, pa_ip(:,:,jl), pa_ip(:,:,jl), zfu, zfv ) ! mp fraction |
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| 161 | zamsk = 0._wp ; zh_ip(:,:) = pv_ip(:,:,jl) * z1_a(:,:) |
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| 162 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zfu , zfv , zcu_box, zcv_box, zh_ip(:,:), pv_ip(:,:,jl) ) ! mp volume |
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[8586] | 163 | ENDIF |
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[10267] | 164 | ! |
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| 165 | ! to avoid a problem with the limiter nonosc when A gets close to 0 |
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| 166 | DO jj = 2, jpjm1 |
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| 167 | DO ji = fs_2, fs_jpim1 |
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| 168 | !pa_i(ji,jj,jl) = ( pa_i(ji,jj,jl) - zeps ) * tmask(ji,jj,1) |
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| 169 | pa_i(ji,jj,jl) = ( pa_i(ji,jj,jl) - zeps & |
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| 170 | & + zeps * ( zudy(ji,jj) - zudy(ji-1,jj) + zvdx(ji,jj) - zvdx(ji,jj-1) )*r1_e1e2t(ji,jj)*zdt & |
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| 171 | & ) * tmask(ji,jj,1) |
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| 172 | IF ( ln_pnd_H12 ) THEN ! melt ponds |
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| 173 | pa_ip(ji,jj,jl) = ( pa_ip(ji,jj,jl) - zeps & |
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| 174 | & + zeps * ( zudy(ji,jj) - zudy(ji-1,jj) + zvdx(ji,jj) - zvdx(ji,jj-1) )*r1_e1e2t(ji,jj)*zdt & |
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| 175 | & ) * tmask(ji,jj,1) |
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| 176 | ENDIF |
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| 177 | END DO |
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| 178 | END DO |
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| 179 | CALL lbc_lnk( pa_i(:,:,jl), 'T', 1. ) |
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| 180 | ! |
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[8586] | 181 | END DO |
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[10267] | 182 | |
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[8586] | 183 | END DO |
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| 184 | ! |
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| 185 | END SUBROUTINE ice_dyn_adv_umx |
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[9929] | 186 | |
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[8586] | 187 | |
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[10267] | 188 | SUBROUTINE adv_umx( pamsk, kn_umx, jt, kt, pdt, pu, pv, puc, pvc, pubox, pvbox, pt, ptc, pfu, pfv ) |
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[8586] | 189 | !!---------------------------------------------------------------------- |
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| 190 | !! *** ROUTINE adv_umx *** |
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| 191 | !! |
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| 192 | !! ** Purpose : Compute the now trend due to total advection of |
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| 193 | !! tracers and add it to the general trend of tracer equations |
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| 194 | !! |
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| 195 | !! ** Method : TVD scheme, i.e. 2nd order centered scheme with |
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| 196 | !! corrected flux (monotonic correction) |
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| 197 | !! note: - this advection scheme needs a leap-frog time scheme |
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| 198 | !! |
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| 199 | !! ** Action : - pt the after advective tracer |
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| 200 | !!---------------------------------------------------------------------- |
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[10267] | 201 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
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| 202 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
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| 203 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
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| 204 | INTEGER , INTENT(in ) :: kt ! number of iteration |
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| 205 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
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| 206 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pu , pv ! 2 ice velocity components => u*e2 |
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| 207 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: puc , pvc ! 2 ice velocity components => u*e2 or u*a*e2u |
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| 208 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pubox, pvbox ! upstream velocity |
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| 209 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pt ! tracer field |
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| 210 | REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: ptc ! tracer content field |
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| 211 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out), OPTIONAL :: pfu, pfv ! high order fluxes |
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[8586] | 212 | ! |
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| 213 | INTEGER :: ji, jj ! dummy loop indices |
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| 214 | REAL(wp) :: ztra ! local scalar |
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[10267] | 215 | !!clem REAL(wp) :: zeps = 1.e-02 ! local scalar |
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| 216 | INTEGER :: kn_limiter = 1 ! 1=nonosc ; 2=superbee ; 3=h3(rachid) |
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| 217 | REAL(wp), DIMENSION(jpi,jpj) :: zfu_ho , zfv_ho , zt_u, zt_v, zpt |
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| 218 | REAL(wp), DIMENSION(jpi,jpj) :: zfu_ups, zfv_ups, zt_ups ! only for nonosc |
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[8586] | 219 | !!---------------------------------------------------------------------- |
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| 220 | ! |
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[10267] | 221 | ! add a constant value to avoid problems with zeros |
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| 222 | DO jj = 1, jpj |
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| 223 | DO ji = 1, jpi |
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| 224 | zpt(ji,jj) = pt(ji,jj) !!clem + zeps * tmask(ji,jj,1) |
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[8586] | 225 | END DO |
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| 226 | END DO |
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[10267] | 227 | |
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| 228 | ! upstream (_ups) advection with initial mass fluxes |
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| 229 | ! --------------------------------------------------- |
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| 230 | ! fluxes |
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| 231 | DO jj = 1, jpjm1 |
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| 232 | DO ji = 1, fs_jpim1 |
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| 233 | zfu_ups(ji,jj) = MAX( puc(ji,jj), 0._wp ) * zpt(ji,jj) + MIN( puc(ji,jj), 0._wp ) * zpt(ji+1,jj) |
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| 234 | zfv_ups(ji,jj) = MAX( pvc(ji,jj), 0._wp ) * zpt(ji,jj) + MIN( pvc(ji,jj), 0._wp ) * zpt(ji,jj+1) |
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[8586] | 235 | END DO |
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| 236 | END DO |
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[10267] | 237 | ! guess after content field with upstream scheme |
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| 238 | DO jj = 2, jpjm1 |
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| 239 | DO ji = fs_2, fs_jpim1 |
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| 240 | ztra = - ( zfu_ups(ji,jj) - zfu_ups(ji-1,jj ) & |
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| 241 | & + zfv_ups(ji,jj) - zfv_ups(ji ,jj-1) ) * r1_e1e2t(ji,jj) |
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| 242 | zt_ups(ji,jj) = ( ptc(ji,jj) + pdt * ztra ) * tmask(ji,jj,1) |
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| 243 | END DO |
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| 244 | END DO |
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| 245 | CALL lbc_lnk( zt_ups, 'T', 1. ) |
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[8586] | 246 | |
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| 247 | ! High order (_ho) fluxes |
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| 248 | ! ----------------------- |
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[10267] | 249 | SELECT CASE( kn_umx ) |
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[8586] | 250 | ! |
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[10267] | 251 | CASE ( 20 ) !== centered second order ==! |
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[8586] | 252 | ! |
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[10267] | 253 | CALL cen2( kn_limiter, jt, kt, pdt, zpt, pu, pv, puc, pvc, ptc, zfu_ho, zfv_ho, & |
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| 254 | & zt_ups, zfu_ups, zfv_ups ) |
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[8586] | 255 | ! |
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[10267] | 256 | CASE ( 1:5 ) !== 1st to 5th order ULTIMATE-MACHO scheme ==! |
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| 257 | ! |
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| 258 | CALL macho( pamsk, kn_limiter, kn_umx, jt, kt, pdt, zpt, pu, pv, puc, pvc, pubox, pvbox, ptc, zt_u, zt_v, zfu_ho, zfv_ho, & |
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| 259 | & zt_ups, zfu_ups, zfv_ups ) |
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| 260 | ! |
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[8586] | 261 | END SELECT |
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| 262 | |
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[10267] | 263 | ! output high order fluxes |
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| 264 | ! ------------------------ |
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| 265 | IF( PRESENT(pfu) ) THEN |
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| 266 | DO jj = 1, jpjm1 |
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| 267 | DO ji = 1, fs_jpim1 |
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| 268 | pfu(ji,jj) = zfu_ho(ji,jj) !!clem - zeps * puc(ji,jj) |
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| 269 | pfv(ji,jj) = zfv_ho(ji,jj) !!clem - zeps * pvc(ji,jj) |
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| 270 | END DO |
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[8586] | 271 | END DO |
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[10267] | 272 | !!CALL lbc_lnk( pfu, 'U', -1. ) ! clem: not needed I think |
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| 273 | !!CALL lbc_lnk( pfv, 'V', -1. ) |
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| 274 | ENDIF |
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[8586] | 275 | |
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| 276 | ! final trend with corrected fluxes |
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| 277 | ! ------------------------------------ |
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| 278 | DO jj = 2, jpjm1 |
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[10267] | 279 | DO ji = fs_2, fs_jpim1 |
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| 280 | ztra = ( - ( zfu_ho(ji,jj) - zfu_ho(ji-1,jj) + zfv_ho(ji,jj) - zfv_ho(ji,jj-1) ) & ! Div(uaH) or Div(ua) |
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| 281 | !!clem & + ( puc (ji,jj) - puc (ji-1,jj) + pvc (ji,jj) - pvc (ji,jj-1) ) * zeps & ! epsi * Div(ua) or epsi * Div(u) |
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| 282 | & ) * r1_e1e2t(ji,jj) |
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[9866] | 283 | ptc(ji,jj) = ( ptc(ji,jj) + pdt * ztra ) * tmask(ji,jj,1) |
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[8586] | 284 | END DO |
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| 285 | END DO |
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[9421] | 286 | CALL lbc_lnk( ptc, 'T', 1. ) |
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[8586] | 287 | ! |
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| 288 | END SUBROUTINE adv_umx |
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| 289 | |
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[10267] | 290 | SUBROUTINE cen2( kn_limiter, jt, kt, pdt, pt, pu, pv, puc, pvc, ptc, pfu_ho, pfv_ho, & |
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| 291 | & pt_ups, pfu_ups, pfv_ups ) |
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| 292 | !!--------------------------------------------------------------------- |
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| 293 | !! *** ROUTINE macho *** |
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| 294 | !! |
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| 295 | !! ** Purpose : compute |
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| 296 | !! |
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| 297 | !! ** Method : ... ??? |
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| 298 | !! TIM = transient interpolation Modeling |
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| 299 | !! |
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| 300 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
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| 301 | !!---------------------------------------------------------------------- |
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| 302 | INTEGER , INTENT(in ) :: kn_limiter ! limiter |
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| 303 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
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| 304 | INTEGER , INTENT(in ) :: kt ! number of iteration |
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| 305 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
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| 306 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pt ! tracer fields |
---|
| 307 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pu, pv ! 2 ice velocity components |
---|
| 308 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: puc, pvc ! 2 ice velocity * A components |
---|
| 309 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: ptc ! tracer content at before time step |
---|
| 310 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pfu_ho, pfv_ho ! high order fluxes |
---|
| 311 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pt_ups ! upstream guess of tracer content |
---|
| 312 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pfu_ups, pfv_ups ! upstream fluxes |
---|
| 313 | ! |
---|
| 314 | INTEGER :: ji, jj ! dummy loop indices |
---|
| 315 | LOGICAL :: ll_xy = .TRUE. |
---|
| 316 | REAL(wp), DIMENSION(jpi,jpj) :: zzt |
---|
| 317 | !!---------------------------------------------------------------------- |
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| 318 | ! |
---|
| 319 | IF( .NOT.ll_xy ) THEN !-- no alternate directions --! |
---|
| 320 | ! |
---|
| 321 | DO jj = 1, jpjm1 |
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| 322 | DO ji = 1, fs_jpim1 |
---|
| 323 | pfu_ho(ji,jj) = 0.5 * puc(ji,jj) * ( pt(ji,jj) + pt(ji+1,jj) ) |
---|
| 324 | pfv_ho(ji,jj) = 0.5 * pvc(ji,jj) * ( pt(ji,jj) + pt(ji,jj+1) ) |
---|
| 325 | END DO |
---|
| 326 | END DO |
---|
| 327 | IF ( kn_limiter == 1 ) THEN |
---|
| 328 | CALL nonosc_2d( pdt, ptc, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
| 329 | ELSEIF( kn_limiter == 2 ) THEN |
---|
| 330 | CALL limiter_x( pdt, pu, puc, pt, pfu_ho ) |
---|
| 331 | CALL limiter_y( pdt, pv, pvc, pt, pfv_ho ) |
---|
| 332 | ELSEIF( kn_limiter == 3 ) THEN |
---|
| 333 | CALL limiter_x( pdt, pu, puc, pt, pfu_ho, pfu_ups ) |
---|
| 334 | CALL limiter_y( pdt, pv, pvc, pt, pfv_ho, pfv_ups ) |
---|
| 335 | ENDIF |
---|
| 336 | ! |
---|
| 337 | ELSE !-- alternate directions --! |
---|
| 338 | ! |
---|
| 339 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
---|
| 340 | ! |
---|
| 341 | ! flux in x-direction |
---|
| 342 | DO jj = 1, jpjm1 |
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| 343 | DO ji = 1, fs_jpim1 |
---|
| 344 | pfu_ho(ji,jj) = 0.5 * puc(ji,jj) * ( pt(ji,jj) + pt(ji+1,jj) ) |
---|
| 345 | END DO |
---|
| 346 | END DO |
---|
| 347 | IF( kn_limiter == 2 ) CALL limiter_x( pdt, pu, puc, pt, pfu_ho ) |
---|
| 348 | IF( kn_limiter == 3 ) CALL limiter_x( pdt, pu, puc, pt, pfu_ho, pfu_ups ) |
---|
[8586] | 349 | |
---|
[10267] | 350 | ! first guess of tracer content from u-flux |
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| 351 | DO jj = 2, jpjm1 |
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| 352 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 353 | zzt(ji,jj) = ( ptc(ji,jj) - ( pfu_ho(ji,jj) - pfu_ho(ji-1,jj) ) * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
| 354 | END DO |
---|
| 355 | END DO |
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| 356 | CALL lbc_lnk( zzt, 'T', 1. ) |
---|
| 357 | |
---|
| 358 | ! flux in y-direction |
---|
| 359 | DO jj = 1, jpjm1 |
---|
| 360 | DO ji = 1, fs_jpim1 |
---|
| 361 | pfv_ho(ji,jj) = 0.5 * pv(ji,jj) * ( zzt(ji,jj) + zzt(ji,jj+1) ) |
---|
| 362 | END DO |
---|
| 363 | END DO |
---|
| 364 | IF( kn_limiter == 2 ) CALL limiter_y( pdt, pv, pvc, pt, pfv_ho ) |
---|
| 365 | IF( kn_limiter == 3 ) CALL limiter_y( pdt, pv, pvc, pt, pfv_ho, pfv_ups ) |
---|
| 366 | |
---|
| 367 | ELSE !== even ice time step: adv_y then adv_x ==! |
---|
| 368 | ! |
---|
| 369 | ! flux in y-direction |
---|
| 370 | DO jj = 1, jpjm1 |
---|
| 371 | DO ji = 1, fs_jpim1 |
---|
| 372 | pfv_ho(ji,jj) = 0.5 * pvc(ji,jj) * ( pt(ji,jj) + pt(ji,jj+1) ) |
---|
| 373 | END DO |
---|
| 374 | END DO |
---|
| 375 | IF( kn_limiter == 2 ) CALL limiter_y( pdt, pv, pvc, pt, pfv_ho ) |
---|
| 376 | IF( kn_limiter == 3 ) CALL limiter_y( pdt, pv, pvc, pt, pfv_ho, pfv_ups ) |
---|
| 377 | ! |
---|
| 378 | ! first guess of tracer content from v-flux |
---|
| 379 | DO jj = 2, jpjm1 |
---|
| 380 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 381 | zzt(ji,jj) = ( ptc(ji,jj) - ( pfv_ho(ji,jj) - pfv_ho(ji,jj-1) ) * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
| 382 | END DO |
---|
| 383 | END DO |
---|
| 384 | CALL lbc_lnk( zzt, 'T', 1. ) |
---|
| 385 | ! |
---|
| 386 | ! flux in x-direction |
---|
| 387 | DO jj = 1, jpjm1 |
---|
| 388 | DO ji = 1, fs_jpim1 |
---|
| 389 | pfu_ho(ji,jj) = 0.5 * pu(ji,jj) * ( zzt(ji,jj) + zzt(ji+1,jj) ) |
---|
| 390 | END DO |
---|
| 391 | END DO |
---|
| 392 | IF( kn_limiter == 2 ) CALL limiter_x( pdt, pu, puc, pt, pfu_ho ) |
---|
| 393 | IF( kn_limiter == 3 ) CALL limiter_x( pdt, pu, puc, pt, pfu_ho, pfu_ups ) |
---|
| 394 | |
---|
| 395 | ENDIF |
---|
| 396 | IF( kn_limiter == 1 ) CALL nonosc_2d( pdt, ptc, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
| 397 | |
---|
| 398 | ENDIF |
---|
| 399 | |
---|
| 400 | END SUBROUTINE cen2 |
---|
| 401 | |
---|
| 402 | |
---|
| 403 | SUBROUTINE macho( pamsk, kn_limiter, kn_umx, jt, kt, pdt, pt, pu, pv, puc, pvc, pubox, pvbox, ptc, pt_u, pt_v, pfu_ho, pfv_ho, & |
---|
| 404 | & pt_ups, pfu_ups, pfv_ups ) |
---|
[8586] | 405 | !!--------------------------------------------------------------------- |
---|
[10267] | 406 | !! *** ROUTINE macho *** |
---|
[8586] | 407 | !! |
---|
| 408 | !! ** Purpose : compute |
---|
| 409 | !! |
---|
| 410 | !! ** Method : ... ??? |
---|
| 411 | !! TIM = transient interpolation Modeling |
---|
| 412 | !! |
---|
| 413 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
| 414 | !!---------------------------------------------------------------------- |
---|
[10267] | 415 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 416 | INTEGER , INTENT(in ) :: kn_limiter ! limiter |
---|
| 417 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
| 418 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
| 419 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
| 420 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 421 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pt ! tracer fields |
---|
| 422 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pu, pv ! 2 ice velocity components |
---|
| 423 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: puc, pvc ! 2 ice velocity * A components |
---|
| 424 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pubox, pvbox ! upstream velocity |
---|
| 425 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: ptc ! tracer content at before time step |
---|
| 426 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pt_u, pt_v ! tracer at u- and v-points |
---|
| 427 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pfu_ho, pfv_ho ! high order fluxes |
---|
| 428 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pt_ups ! upstream guess of tracer content |
---|
| 429 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pfu_ups, pfv_ups ! upstream fluxes |
---|
[8586] | 430 | ! |
---|
| 431 | INTEGER :: ji, jj ! dummy loop indices |
---|
[10267] | 432 | REAL(wp), DIMENSION(jpi,jpj) :: zzt |
---|
[8586] | 433 | !!---------------------------------------------------------------------- |
---|
| 434 | ! |
---|
[10267] | 435 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
---|
[8586] | 436 | ! |
---|
[10267] | 437 | ! !-- ultimate interpolation of pt at u-point --! |
---|
| 438 | CALL ultimate_x( kn_umx, pdt, pt, pu, puc, pt_u, pfu_ho ) |
---|
| 439 | ! !-- limiter in x --! |
---|
| 440 | IF( kn_limiter == 2 ) CALL limiter_x( pdt, pu, puc, pt, pfu_ho ) |
---|
| 441 | IF( kn_limiter == 3 ) CALL limiter_x( pdt, pu, puc, pt, pfu_ho, pfu_ups ) |
---|
| 442 | ! !-- advective form update in zzt --! |
---|
[8586] | 443 | DO jj = 2, jpjm1 |
---|
| 444 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[10267] | 445 | zzt(ji,jj) = pt(ji,jj) - pubox(ji,jj) * pdt * ( pt_u(ji,jj) - pt_u(ji-1,jj) ) * r1_e1t(ji,jj) & |
---|
| 446 | & - pt (ji,jj) * pdt * ( pu (ji,jj) - pu (ji-1,jj) ) * r1_e1e2t(ji,jj) * pamsk |
---|
[8586] | 447 | zzt(ji,jj) = zzt(ji,jj) * tmask(ji,jj,1) |
---|
| 448 | END DO |
---|
| 449 | END DO |
---|
| 450 | CALL lbc_lnk( zzt, 'T', 1. ) |
---|
[10267] | 451 | ! !-- ultimate interpolation of pt at v-point --! |
---|
| 452 | CALL ultimate_y( kn_umx, pdt, zzt, pv, pvc, pt_v, pfv_ho ) |
---|
| 453 | ! !-- limiter in y --! |
---|
| 454 | IF( kn_limiter == 2 ) CALL limiter_y( pdt, pv, pvc, pt, pfv_ho ) |
---|
| 455 | IF( kn_limiter == 3 ) CALL limiter_y( pdt, pv, pvc, pt, pfv_ho, pfv_ups ) |
---|
[8586] | 456 | ! |
---|
[10267] | 457 | ELSE !== even ice time step: adv_y then adv_x ==! |
---|
[8586] | 458 | ! |
---|
[10267] | 459 | ! !-- ultimate interpolation of pt at v-point --! |
---|
| 460 | CALL ultimate_y( kn_umx, pdt, pt, pv, pvc, pt_v, pfv_ho ) |
---|
| 461 | ! !-- limiter in y --! |
---|
| 462 | IF( kn_limiter == 2 ) CALL limiter_y( pdt, pv, pvc, pt, pfv_ho ) |
---|
| 463 | IF( kn_limiter == 3 ) CALL limiter_y( pdt, pv, pvc, pt, pfv_ho, pfv_ups ) |
---|
| 464 | ! !-- advective form update in zzt --! |
---|
[8586] | 465 | DO jj = 2, jpjm1 |
---|
| 466 | DO ji = fs_2, fs_jpim1 |
---|
[10267] | 467 | zzt(ji,jj) = pt(ji,jj) - pvbox(ji,jj) * pdt * ( pt_v(ji,jj) - pt_v(ji,jj-1) ) * r1_e2t(ji,jj) & |
---|
| 468 | & - pt (ji,jj) * pdt * ( pv (ji,jj) - pv (ji,jj-1) ) * r1_e1e2t(ji,jj) * pamsk |
---|
[8586] | 469 | zzt(ji,jj) = zzt(ji,jj) * tmask(ji,jj,1) |
---|
| 470 | END DO |
---|
| 471 | END DO |
---|
| 472 | CALL lbc_lnk( zzt, 'T', 1. ) |
---|
[10267] | 473 | ! !-- ultimate interpolation of pt at u-point --! |
---|
| 474 | CALL ultimate_x( kn_umx, pdt, zzt, pu, puc, pt_u, pfu_ho ) |
---|
| 475 | ! !-- limiter in x --! |
---|
| 476 | IF( kn_limiter == 2 ) CALL limiter_x( pdt, pu, puc, pt, pfu_ho ) |
---|
| 477 | IF( kn_limiter == 3 ) CALL limiter_x( pdt, pu, puc, pt, pfu_ho, pfu_ups ) |
---|
[8586] | 478 | ! |
---|
[10267] | 479 | ENDIF |
---|
| 480 | IF( kn_limiter == 1 ) CALL nonosc_2d ( pdt, ptc, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[8586] | 481 | ! |
---|
| 482 | END SUBROUTINE macho |
---|
| 483 | |
---|
| 484 | |
---|
[10267] | 485 | SUBROUTINE ultimate_x( kn_umx, pdt, pt, pu, puc, pt_u, pfu_ho ) |
---|
[8586] | 486 | !!--------------------------------------------------------------------- |
---|
| 487 | !! *** ROUTINE ultimate_x *** |
---|
| 488 | !! |
---|
| 489 | !! ** Purpose : compute |
---|
| 490 | !! |
---|
| 491 | !! ** Method : ... ??? |
---|
| 492 | !! TIM = transient interpolation Modeling |
---|
| 493 | !! |
---|
| 494 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
| 495 | !!---------------------------------------------------------------------- |
---|
[10267] | 496 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
[8586] | 497 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
[10267] | 498 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pu ! ice i-velocity component |
---|
| 499 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: puc ! ice i-velocity * A component |
---|
[8586] | 500 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pt ! tracer fields |
---|
| 501 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pt_u ! tracer at u-point |
---|
[10267] | 502 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pfu_ho ! high order flux |
---|
[8586] | 503 | ! |
---|
[10267] | 504 | INTEGER :: ji, jj ! dummy loop indices |
---|
[8586] | 505 | REAL(wp) :: zcu, zdx2, zdx4 ! - - |
---|
[10267] | 506 | REAL(wp), DIMENSION(jpi,jpj) :: ztu1, ztu2, ztu3, ztu4 |
---|
[8586] | 507 | !!---------------------------------------------------------------------- |
---|
| 508 | ! |
---|
| 509 | ! !-- Laplacian in i-direction --! |
---|
| 510 | DO jj = 2, jpjm1 ! First derivative (gradient) |
---|
| 511 | DO ji = 1, fs_jpim1 |
---|
| 512 | ztu1(ji,jj) = ( pt(ji+1,jj) - pt(ji,jj) ) * r1_e1u(ji,jj) * umask(ji,jj,1) |
---|
| 513 | END DO |
---|
| 514 | ! ! Second derivative (Laplacian) |
---|
| 515 | DO ji = fs_2, fs_jpim1 |
---|
| 516 | ztu2(ji,jj) = ( ztu1(ji,jj) - ztu1(ji-1,jj) ) * r1_e1t(ji,jj) |
---|
| 517 | END DO |
---|
| 518 | END DO |
---|
| 519 | CALL lbc_lnk( ztu2, 'T', 1. ) |
---|
| 520 | ! |
---|
| 521 | ! !-- BiLaplacian in i-direction --! |
---|
| 522 | DO jj = 2, jpjm1 ! Third derivative |
---|
| 523 | DO ji = 1, fs_jpim1 |
---|
| 524 | ztu3(ji,jj) = ( ztu2(ji+1,jj) - ztu2(ji,jj) ) * r1_e1u(ji,jj) * umask(ji,jj,1) |
---|
| 525 | END DO |
---|
| 526 | ! ! Fourth derivative |
---|
| 527 | DO ji = fs_2, fs_jpim1 |
---|
| 528 | ztu4(ji,jj) = ( ztu3(ji,jj) - ztu3(ji-1,jj) ) * r1_e1t(ji,jj) |
---|
| 529 | END DO |
---|
| 530 | END DO |
---|
| 531 | CALL lbc_lnk( ztu4, 'T', 1. ) |
---|
| 532 | ! |
---|
| 533 | ! |
---|
[10267] | 534 | SELECT CASE (kn_umx ) |
---|
[8586] | 535 | ! |
---|
| 536 | CASE( 1 ) !== 1st order central TIM ==! (Eq. 21) |
---|
| 537 | ! |
---|
[8637] | 538 | DO jj = 2, jpjm1 |
---|
[8586] | 539 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
[10267] | 540 | pt_u(ji,jj) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj) + pt(ji,jj) & |
---|
| 541 | & - SIGN( 1._wp, pu(ji,jj) ) * ( pt(ji+1,jj) - pt(ji,jj) ) ) |
---|
[8586] | 542 | END DO |
---|
| 543 | END DO |
---|
| 544 | ! |
---|
| 545 | CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23) |
---|
| 546 | ! |
---|
[8637] | 547 | DO jj = 2, jpjm1 |
---|
[8586] | 548 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
[10267] | 549 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
[8586] | 550 | pt_u(ji,jj) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj) + pt(ji,jj) & |
---|
| 551 | & - zcu * ( pt(ji+1,jj) - pt(ji,jj) ) ) |
---|
| 552 | END DO |
---|
| 553 | END DO |
---|
| 554 | ! |
---|
| 555 | CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24) |
---|
| 556 | ! |
---|
[8637] | 557 | DO jj = 2, jpjm1 |
---|
[8586] | 558 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
[10267] | 559 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
[8586] | 560 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
| 561 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
| 562 | pt_u(ji,jj) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj) + pt (ji,jj) & |
---|
| 563 | & - zcu * ( pt (ji+1,jj) - pt (ji,jj) ) ) & |
---|
| 564 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj) + ztu2(ji,jj) & |
---|
| 565 | & - SIGN( 1._wp, zcu ) * ( ztu2(ji+1,jj) - ztu2(ji,jj) ) ) ) |
---|
| 566 | END DO |
---|
| 567 | END DO |
---|
| 568 | ! |
---|
| 569 | CASE( 4 ) !== 4th order central TIM ==! (Eq. 27) |
---|
| 570 | ! |
---|
[8637] | 571 | DO jj = 2, jpjm1 |
---|
[8586] | 572 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
[10267] | 573 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
[8586] | 574 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
| 575 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
| 576 | pt_u(ji,jj) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj) + pt (ji,jj) & |
---|
| 577 | & - zcu * ( pt (ji+1,jj) - pt (ji,jj) ) ) & |
---|
| 578 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj) + ztu2(ji,jj) & |
---|
| 579 | & - 0.5_wp * zcu * ( ztu2(ji+1,jj) - ztu2(ji,jj) ) ) ) |
---|
| 580 | END DO |
---|
| 581 | END DO |
---|
| 582 | ! |
---|
| 583 | CASE( 5 ) !== 5th order central TIM ==! (Eq. 29) |
---|
| 584 | ! |
---|
[8637] | 585 | DO jj = 2, jpjm1 |
---|
[8586] | 586 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
[10267] | 587 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
[8586] | 588 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
| 589 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
| 590 | zdx4 = zdx2 * zdx2 |
---|
| 591 | pt_u(ji,jj) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj) + pt (ji,jj) & |
---|
| 592 | & - zcu * ( pt (ji+1,jj) - pt (ji,jj) ) ) & |
---|
| 593 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj) + ztu2(ji,jj) & |
---|
| 594 | & - 0.5_wp * zcu * ( ztu2(ji+1,jj) - ztu2(ji,jj) ) ) & |
---|
| 595 | & + z1_120 * zdx4 * ( zcu*zcu - 1._wp ) * ( zcu*zcu - 4._wp ) * ( ztu4(ji+1,jj) + ztu4(ji,jj) & |
---|
| 596 | & - SIGN( 1._wp, zcu ) * ( ztu4(ji+1,jj) - ztu4(ji,jj) ) ) ) |
---|
| 597 | END DO |
---|
| 598 | END DO |
---|
| 599 | ! |
---|
| 600 | END SELECT |
---|
[10267] | 601 | ! !-- High order flux in i-direction --! |
---|
| 602 | DO jj = 1, jpjm1 |
---|
| 603 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 604 | pfu_ho(ji,jj) = puc(ji,jj) * pt_u(ji,jj) |
---|
| 605 | END DO |
---|
| 606 | END DO |
---|
[8586] | 607 | ! |
---|
| 608 | END SUBROUTINE ultimate_x |
---|
| 609 | |
---|
| 610 | |
---|
[10267] | 611 | SUBROUTINE ultimate_y( kn_umx, pdt, pt, pv, pvc, pt_v, pfv_ho ) |
---|
[8586] | 612 | !!--------------------------------------------------------------------- |
---|
| 613 | !! *** ROUTINE ultimate_y *** |
---|
| 614 | !! |
---|
| 615 | !! ** Purpose : compute |
---|
| 616 | !! |
---|
| 617 | !! ** Method : ... ??? |
---|
| 618 | !! TIM = transient interpolation Modeling |
---|
| 619 | !! |
---|
| 620 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
| 621 | !!---------------------------------------------------------------------- |
---|
[10267] | 622 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
[8586] | 623 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
[10267] | 624 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pv ! ice j-velocity component |
---|
| 625 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pvc ! ice j-velocity*A component |
---|
[8586] | 626 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pt ! tracer fields |
---|
| 627 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pt_v ! tracer at v-point |
---|
[10267] | 628 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pfv_ho ! high order flux |
---|
[8586] | 629 | ! |
---|
| 630 | INTEGER :: ji, jj ! dummy loop indices |
---|
| 631 | REAL(wp) :: zcv, zdy2, zdy4 ! - - |
---|
[10267] | 632 | REAL(wp), DIMENSION(jpi,jpj) :: ztv1, ztv2, ztv3, ztv4 |
---|
[8586] | 633 | !!---------------------------------------------------------------------- |
---|
| 634 | ! |
---|
| 635 | ! !-- Laplacian in j-direction --! |
---|
| 636 | DO jj = 1, jpjm1 ! First derivative (gradient) |
---|
| 637 | DO ji = fs_2, fs_jpim1 |
---|
| 638 | ztv1(ji,jj) = ( pt(ji,jj+1) - pt(ji,jj) ) * r1_e2v(ji,jj) * vmask(ji,jj,1) |
---|
| 639 | END DO |
---|
| 640 | END DO |
---|
| 641 | DO jj = 2, jpjm1 ! Second derivative (Laplacian) |
---|
| 642 | DO ji = fs_2, fs_jpim1 |
---|
| 643 | ztv2(ji,jj) = ( ztv1(ji,jj) - ztv1(ji,jj-1) ) * r1_e2t(ji,jj) |
---|
| 644 | END DO |
---|
| 645 | END DO |
---|
| 646 | CALL lbc_lnk( ztv2, 'T', 1. ) |
---|
| 647 | ! |
---|
| 648 | ! !-- BiLaplacian in j-direction --! |
---|
| 649 | DO jj = 1, jpjm1 ! First derivative |
---|
| 650 | DO ji = fs_2, fs_jpim1 |
---|
| 651 | ztv3(ji,jj) = ( ztv2(ji,jj+1) - ztv2(ji,jj) ) * r1_e2v(ji,jj) * vmask(ji,jj,1) |
---|
| 652 | END DO |
---|
| 653 | END DO |
---|
| 654 | DO jj = 2, jpjm1 ! Second derivative |
---|
| 655 | DO ji = fs_2, fs_jpim1 |
---|
| 656 | ztv4(ji,jj) = ( ztv3(ji,jj) - ztv3(ji,jj-1) ) * r1_e2t(ji,jj) |
---|
| 657 | END DO |
---|
| 658 | END DO |
---|
| 659 | CALL lbc_lnk( ztv4, 'T', 1. ) |
---|
| 660 | ! |
---|
| 661 | ! |
---|
[10267] | 662 | SELECT CASE (kn_umx ) |
---|
[8586] | 663 | ! |
---|
| 664 | CASE( 1 ) !== 1st order central TIM ==! (Eq. 21) |
---|
| 665 | DO jj = 1, jpjm1 |
---|
[8637] | 666 | DO ji = fs_2, fs_jpim1 |
---|
[10267] | 667 | pt_v(ji,jj) = 0.5_wp * vmask(ji,jj,1) * ( ( pt(ji,jj+1) + pt(ji,jj) ) & |
---|
| 668 | & - SIGN( 1._wp, pv(ji,jj) ) * ( pt(ji,jj+1) - pt(ji,jj) ) ) |
---|
[8586] | 669 | END DO |
---|
| 670 | END DO |
---|
| 671 | ! |
---|
| 672 | CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23) |
---|
| 673 | DO jj = 1, jpjm1 |
---|
[8637] | 674 | DO ji = fs_2, fs_jpim1 |
---|
[10267] | 675 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
[8586] | 676 | pt_v(ji,jj) = 0.5_wp * vmask(ji,jj,1) * ( ( pt(ji,jj+1) + pt(ji,jj) ) & |
---|
| 677 | & - zcv * ( pt(ji,jj+1) - pt(ji,jj) ) ) |
---|
| 678 | END DO |
---|
| 679 | END DO |
---|
[9421] | 680 | CALL lbc_lnk( pt_v, 'V', 1. ) |
---|
[8586] | 681 | ! |
---|
| 682 | CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24) |
---|
| 683 | DO jj = 1, jpjm1 |
---|
[8637] | 684 | DO ji = fs_2, fs_jpim1 |
---|
[10267] | 685 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
[8586] | 686 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
| 687 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
| 688 | pt_v(ji,jj) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1) + pt (ji,jj) & |
---|
| 689 | & - zcv * ( pt (ji,jj+1) - pt (ji,jj) ) ) & |
---|
| 690 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1) + ztv2(ji,jj) & |
---|
| 691 | & - SIGN( 1._wp, zcv ) * ( ztv2(ji,jj+1) - ztv2(ji,jj) ) ) ) |
---|
| 692 | END DO |
---|
| 693 | END DO |
---|
| 694 | ! |
---|
| 695 | CASE( 4 ) !== 4th order central TIM ==! (Eq. 27) |
---|
| 696 | DO jj = 1, jpjm1 |
---|
[8637] | 697 | DO ji = fs_2, fs_jpim1 |
---|
[10267] | 698 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
[8586] | 699 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
| 700 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
| 701 | pt_v(ji,jj) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1) + pt (ji,jj) & |
---|
| 702 | & - zcv * ( pt (ji,jj+1) - pt (ji,jj) ) ) & |
---|
| 703 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1) + ztv2(ji,jj) & |
---|
| 704 | & - 0.5_wp * zcv * ( ztv2(ji,jj+1) - ztv2(ji,jj) ) ) ) |
---|
| 705 | END DO |
---|
| 706 | END DO |
---|
| 707 | ! |
---|
| 708 | CASE( 5 ) !== 5th order central TIM ==! (Eq. 29) |
---|
| 709 | DO jj = 1, jpjm1 |
---|
[8637] | 710 | DO ji = fs_2, fs_jpim1 |
---|
[10267] | 711 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
[8586] | 712 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
| 713 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
| 714 | zdy4 = zdy2 * zdy2 |
---|
| 715 | pt_v(ji,jj) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1) + pt (ji,jj) & |
---|
| 716 | & - zcv * ( pt (ji,jj+1) - pt (ji,jj) ) ) & |
---|
| 717 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1) + ztv2(ji,jj) & |
---|
| 718 | & - 0.5_wp * zcv * ( ztv2(ji,jj+1) - ztv2(ji,jj) ) ) & |
---|
| 719 | & + z1_120 * zdy4 * ( zcv*zcv - 1._wp ) * ( zcv*zcv - 4._wp ) * ( ztv4(ji,jj+1) + ztv4(ji,jj) & |
---|
| 720 | & - SIGN( 1._wp, zcv ) * ( ztv4(ji,jj+1) - ztv4(ji,jj) ) ) ) |
---|
| 721 | END DO |
---|
| 722 | END DO |
---|
| 723 | ! |
---|
| 724 | END SELECT |
---|
[10267] | 725 | ! !-- High order flux in j-direction --! |
---|
| 726 | DO jj = 1, jpjm1 |
---|
| 727 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 728 | pfv_ho(ji,jj) = pvc(ji,jj) * pt_v(ji,jj) |
---|
| 729 | END DO |
---|
| 730 | END DO |
---|
[8586] | 731 | ! |
---|
| 732 | END SUBROUTINE ultimate_y |
---|
[10267] | 733 | |
---|
| 734 | |
---|
| 735 | SUBROUTINE nonosc_2d( pdt, ptc, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[8586] | 736 | !!--------------------------------------------------------------------- |
---|
| 737 | !! *** ROUTINE nonosc *** |
---|
| 738 | !! |
---|
| 739 | !! ** Purpose : compute monotonic tracer fluxes from the upstream |
---|
| 740 | !! scheme and the before field by a nonoscillatory algorithm |
---|
| 741 | !! |
---|
| 742 | !! ** Method : ... ??? |
---|
[10267] | 743 | !! warning : ptc and pt_ups must be masked, but the boundaries |
---|
[8586] | 744 | !! conditions on the fluxes are not necessary zalezak (1979) |
---|
| 745 | !! drange (1995) multi-dimensional forward-in-time and upstream- |
---|
| 746 | !! in-space based differencing for fluid |
---|
| 747 | !!---------------------------------------------------------------------- |
---|
[10267] | 748 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 749 | REAL(wp), DIMENSION (jpi,jpj), INTENT(in ) :: ptc, pt_ups ! before field & upstream guess of after field |
---|
| 750 | REAL(wp), DIMENSION (jpi,jpj), INTENT(in ) :: pfv_ups, pfu_ups ! upstream flux |
---|
| 751 | REAL(wp), DIMENSION (jpi,jpj), INTENT(inout) :: pfv_ho, pfu_ho ! monotonic flux |
---|
[8586] | 752 | ! |
---|
| 753 | INTEGER :: ji, jj ! dummy loop indices |
---|
[10267] | 754 | REAL(wp) :: zpos, zneg, zbig, zsml, z1_dt ! local scalars |
---|
| 755 | REAL(wp) :: zau, zbu, zcu, zav, zbv, zcv, zup, zdo ! - - |
---|
| 756 | REAL(wp), DIMENSION(jpi,jpj) :: zbetup, zbetdo, zbup, zbdo, zdiv |
---|
[8586] | 757 | !!---------------------------------------------------------------------- |
---|
| 758 | zbig = 1.e+40_wp |
---|
| 759 | zsml = 1.e-15_wp |
---|
| 760 | |
---|
[8885] | 761 | ! test on divergence |
---|
[8586] | 762 | DO jj = 2, jpjm1 |
---|
| 763 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[10267] | 764 | zdiv(ji,jj) = - ( pfv_ho(ji,jj) - pfv_ho(ji,jj-1) + pfu_ho(ji,jj) - pfu_ho(ji-1,jj) ) |
---|
[8586] | 765 | END DO |
---|
| 766 | END DO |
---|
| 767 | CALL lbc_lnk( zdiv, 'T', 1. ) ! Lateral boundary conditions (unchanged sign) |
---|
| 768 | |
---|
[10267] | 769 | ! antidiffusive flux : high order minus low order |
---|
| 770 | ! -------------------------------------------------- |
---|
| 771 | DO jj = 1, jpjm1 |
---|
| 772 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 773 | pfu_ho(ji,jj) = pfu_ho(ji,jj) - pfu_ups(ji,jj) |
---|
| 774 | pfv_ho(ji,jj) = pfv_ho(ji,jj) - pfv_ups(ji,jj) |
---|
| 775 | END DO |
---|
| 776 | END DO |
---|
[8586] | 777 | |
---|
| 778 | ! Search local extrema |
---|
| 779 | ! -------------------- |
---|
[10267] | 780 | ! max/min of ptc & pt_ups with large negative/positive value (-/+zbig) outside ice cover |
---|
| 781 | DO jj = 1, jpj |
---|
| 782 | DO ji = fs_2, fs_jpim1 |
---|
| 783 | IF( ptc(ji,jj) == 0._wp .AND. pt_ups(ji,jj) == 0._wp .AND. zdiv(ji,jj) == 0._wp ) THEN |
---|
| 784 | zbup(ji,jj) = -zbig |
---|
| 785 | zbdo(ji,jj) = zbig |
---|
| 786 | ELSE |
---|
| 787 | zbup(ji,jj) = MAX( ptc(ji,jj) , pt_ups(ji,jj) ) |
---|
| 788 | zbdo(ji,jj) = MIN( ptc(ji,jj) , pt_ups(ji,jj) ) |
---|
| 789 | ENDIF |
---|
| 790 | END DO |
---|
| 791 | END DO |
---|
[8586] | 792 | |
---|
| 793 | z1_dt = 1._wp / pdt |
---|
| 794 | DO jj = 2, jpjm1 |
---|
| 795 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 796 | ! |
---|
[10267] | 797 | 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 |
---|
| 798 | zdo = MIN( zbdo(ji,jj), zbdo(ji-1,jj), zbdo(ji+1,jj), zbdo(ji,jj-1), zbdo(ji,jj+1) ) |
---|
| 799 | ! |
---|
| 800 | zpos = MAX( 0., pfu_ho(ji-1,jj) ) - MIN( 0., pfu_ho(ji ,jj) ) & |
---|
| 801 | & + MAX( 0., pfv_ho(ji,jj-1) ) - MIN( 0., pfv_ho(ji,jj ) ) ! positive/negative part of the flux |
---|
| 802 | zneg = MAX( 0., pfu_ho(ji ,jj) ) - MIN( 0., pfu_ho(ji-1,jj) ) & |
---|
| 803 | & + MAX( 0., pfv_ho(ji,jj ) ) - MIN( 0., pfv_ho(ji,jj-1) ) |
---|
| 804 | ! |
---|
| 805 | ! ! up & down beta terms |
---|
| 806 | !!clem zbetup(ji,jj) = ( zup - pt_ups(ji,jj) ) / ( zpos + zsml ) * e1e2t(ji,jj) * z1_dt |
---|
| 807 | !!clem zbetdo(ji,jj) = ( pt_ups(ji,jj) - zdo ) / ( zneg + zsml ) * e1e2t(ji,jj) * z1_dt |
---|
| 808 | IF( zpos >= epsi20 ) THEN |
---|
| 809 | zbetup(ji,jj) = ( zup - pt_ups(ji,jj) ) / zpos * e1e2t(ji,jj) * z1_dt |
---|
| 810 | ELSE |
---|
| 811 | zbetup(ji,jj) = zbig |
---|
| 812 | ENDIF |
---|
| 813 | ! |
---|
| 814 | IF( zneg >= epsi20 ) THEN |
---|
| 815 | zbetdo(ji,jj) = ( pt_ups(ji,jj) - zdo ) / zneg * e1e2t(ji,jj) * z1_dt |
---|
| 816 | ELSE |
---|
| 817 | zbetdo(ji,jj) = zbig |
---|
| 818 | ENDIF |
---|
| 819 | ! |
---|
[8586] | 820 | END DO |
---|
| 821 | END DO |
---|
| 822 | CALL lbc_lnk_multi( zbetup, 'T', 1., zbetdo, 'T', 1. ) ! lateral boundary cond. (unchanged sign) |
---|
| 823 | |
---|
[10267] | 824 | ! monotonic flux in the y direction |
---|
| 825 | ! --------------------------------- |
---|
| 826 | DO jj = 1, jpjm1 |
---|
[8637] | 827 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
[8586] | 828 | zau = MIN( 1._wp , zbetdo(ji,jj) , zbetup(ji+1,jj) ) |
---|
| 829 | zbu = MIN( 1._wp , zbetup(ji,jj) , zbetdo(ji+1,jj) ) |
---|
[10267] | 830 | zcu = 0.5 + SIGN( 0.5 , pfu_ho(ji,jj) ) |
---|
[8586] | 831 | ! |
---|
[10267] | 832 | pfu_ho(ji,jj) = pfu_ho(ji,jj) * ( zcu * zau + ( 1._wp - zcu ) * zbu ) + pfu_ups(ji,jj) |
---|
[8637] | 833 | END DO |
---|
| 834 | END DO |
---|
[10267] | 835 | |
---|
[8637] | 836 | DO jj = 1, jpjm1 |
---|
[10267] | 837 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
[8586] | 838 | zav = MIN( 1._wp , zbetdo(ji,jj) , zbetup(ji,jj+1) ) |
---|
| 839 | zbv = MIN( 1._wp , zbetup(ji,jj) , zbetdo(ji,jj+1) ) |
---|
[10267] | 840 | zcv = 0.5 + SIGN( 0.5 , pfv_ho(ji,jj) ) |
---|
[8586] | 841 | ! |
---|
[10267] | 842 | pfv_ho(ji,jj) = pfv_ho(ji,jj) * ( zcv * zav + ( 1._wp - zcv ) * zbv ) + pfv_ups(ji,jj) |
---|
[8586] | 843 | END DO |
---|
| 844 | END DO |
---|
| 845 | ! |
---|
| 846 | END SUBROUTINE nonosc_2d |
---|
| 847 | |
---|
[10267] | 848 | SUBROUTINE limiter_x( pdt, pu, puc, pt, pfu_ho, pfu_ups ) |
---|
| 849 | !!--------------------------------------------------------------------- |
---|
| 850 | !! *** ROUTINE limiter_x *** |
---|
| 851 | !! |
---|
| 852 | !! ** Purpose : compute flux limiter |
---|
| 853 | !!---------------------------------------------------------------------- |
---|
| 854 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 855 | REAL(wp), DIMENSION (jpi,jpj), INTENT(in ) :: pu ! ice i-velocity => u*e2 |
---|
| 856 | REAL(wp), DIMENSION (jpi,jpj), INTENT(in ) :: puc ! ice i-velocity *A => u*e2*a |
---|
| 857 | REAL(wp), DIMENSION (jpi,jpj), INTENT(in ) :: pt ! ice tracer |
---|
| 858 | REAL(wp), DIMENSION (jpi,jpj), INTENT(inout) :: pfu_ho ! high order flux |
---|
| 859 | REAL(wp), DIMENSION (jpi,jpj), INTENT(in ), OPTIONAL :: pfu_ups ! upstream flux |
---|
| 860 | ! |
---|
| 861 | REAL(wp) :: Cr, Rjm, Rj, Rjp, uCFL, zpsi, zh3, zlimiter, Rr |
---|
| 862 | INTEGER :: ji, jj ! dummy loop indices |
---|
| 863 | REAL(wp), DIMENSION (jpi,jpj) :: zslpx ! tracer slopes |
---|
| 864 | !!---------------------------------------------------------------------- |
---|
| 865 | ! |
---|
| 866 | DO jj = 2, jpjm1 |
---|
| 867 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 868 | zslpx(ji,jj) = ( pt(ji+1,jj) - pt(ji,jj) ) * umask(ji,jj,1) |
---|
| 869 | END DO |
---|
| 870 | END DO |
---|
| 871 | CALL lbc_lnk( zslpx, 'U', -1.) ! lateral boundary cond. |
---|
| 872 | |
---|
| 873 | DO jj = 2, jpjm1 |
---|
| 874 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 875 | uCFL = pdt * ABS( pu(ji,jj) ) * r1_e1e2t(ji,jj) |
---|
| 876 | |
---|
| 877 | Rjm = zslpx(ji-1,jj) |
---|
| 878 | Rj = zslpx(ji ,jj) |
---|
| 879 | Rjp = zslpx(ji+1,jj) |
---|
| 880 | |
---|
| 881 | IF( PRESENT(pfu_ups) ) THEN |
---|
| 882 | |
---|
| 883 | IF( pu(ji,jj) > 0. ) THEN ; Rr = Rjm |
---|
| 884 | ELSE ; Rr = Rjp |
---|
| 885 | ENDIF |
---|
| 886 | |
---|
| 887 | zh3 = pfu_ho(ji,jj) - pfu_ups(ji,jj) |
---|
| 888 | IF( Rj > 0. ) THEN |
---|
| 889 | zlimiter = MAX( 0., MIN( zh3, MAX(-Rr * 0.5 * ABS(puc(ji,jj)), & |
---|
| 890 | & MIN( 2. * Rr * 0.5 * ABS(puc(ji,jj)), zh3, 1.5 * Rj * 0.5 * ABS(puc(ji,jj)) ) ) ) ) |
---|
| 891 | ELSE |
---|
| 892 | zlimiter = -MAX( 0., MIN(-zh3, MAX( Rr * 0.5 * ABS(puc(ji,jj)), & |
---|
| 893 | & MIN(-2. * Rr * 0.5 * ABS(puc(ji,jj)), -zh3, -1.5 * Rj * 0.5 * ABS(puc(ji,jj)) ) ) ) ) |
---|
| 894 | ENDIF |
---|
| 895 | pfu_ho(ji,jj) = pfu_ups(ji,jj) + zlimiter |
---|
| 896 | |
---|
| 897 | ELSE |
---|
| 898 | IF( Rj /= 0. ) THEN |
---|
| 899 | IF( pu(ji,jj) > 0. ) THEN ; Cr = Rjm / Rj |
---|
| 900 | ELSE ; Cr = Rjp / Rj |
---|
| 901 | ENDIF |
---|
| 902 | ELSE |
---|
| 903 | Cr = 0. |
---|
| 904 | !IF( pu(ji,jj) > 0. ) THEN ; Cr = Rjm * 1.e20 |
---|
| 905 | !ELSE ; Cr = Rjp * 1.e20 |
---|
| 906 | !ENDIF |
---|
| 907 | ENDIF |
---|
| 908 | |
---|
| 909 | ! -- superbee -- |
---|
| 910 | zpsi = MAX( 0., MAX( MIN(1.,2.*Cr), MIN(2.,Cr) ) ) |
---|
| 911 | ! -- van albada 2 -- |
---|
| 912 | !!zpsi = 2.*Cr / (Cr*Cr+1.) |
---|
| 913 | |
---|
| 914 | ! -- sweby (with beta=1) -- |
---|
| 915 | !!zpsi = MAX( 0., MAX( MIN(1.,1.*Cr), MIN(1.,Cr) ) ) |
---|
| 916 | ! -- van Leer -- |
---|
| 917 | !!zpsi = ( Cr + ABS(Cr) ) / ( 1. + ABS(Cr) ) |
---|
| 918 | ! -- ospre -- |
---|
| 919 | !!zpsi = 1.5 * ( Cr*Cr + Cr ) / ( Cr*Cr + Cr + 1. ) |
---|
| 920 | ! -- koren -- |
---|
| 921 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( (1.+2*Cr)/3., 2. ) ) ) |
---|
| 922 | ! -- charm -- |
---|
| 923 | !IF( Cr > 0. ) THEN ; zpsi = Cr * (3.*Cr + 1.) / ( (Cr + 1.) * (Cr + 1.) ) |
---|
| 924 | !ELSE ; zpsi = 0. |
---|
| 925 | !ENDIF |
---|
| 926 | ! -- van albada 1 -- |
---|
| 927 | !!zpsi = (Cr*Cr + Cr) / (Cr*Cr +1) |
---|
| 928 | ! -- smart -- |
---|
| 929 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, 4. ) ) ) |
---|
| 930 | ! -- umist -- |
---|
| 931 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, MIN(0.75+0.25*Cr, 2. ) ) ) ) |
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| 932 | |
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| 933 | ! high order flux corrected by the limiter |
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| 934 | pfu_ho(ji,jj) = pfu_ho(ji,jj) - ABS( puc(ji,jj) ) * ( (1.-zpsi) + uCFL*zpsi ) * Rj * 0.5 |
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| 935 | |
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| 936 | ENDIF |
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| 937 | END DO |
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| 938 | END DO |
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| 939 | CALL lbc_lnk( pfu_ho, 'U', -1.) ! lateral boundary cond. |
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| 940 | ! |
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| 941 | END SUBROUTINE limiter_x |
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| 942 | |
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| 943 | SUBROUTINE limiter_y( pdt, pv, pvc, pt, pfv_ho, pfv_ups ) |
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| 944 | !!--------------------------------------------------------------------- |
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| 945 | !! *** ROUTINE limiter_y *** |
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| 946 | !! |
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| 947 | !! ** Purpose : compute flux limiter |
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| 948 | !!---------------------------------------------------------------------- |
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| 949 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
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| 950 | REAL(wp), DIMENSION (jpi,jpj), INTENT(in ) :: pv ! ice i-velocity => u*e2 |
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| 951 | REAL(wp), DIMENSION (jpi,jpj), INTENT(in ) :: pvc ! ice i-velocity *A => u*e2*a |
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| 952 | REAL(wp), DIMENSION (jpi,jpj), INTENT(in ) :: pt ! ice tracer |
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| 953 | REAL(wp), DIMENSION (jpi,jpj), INTENT(inout) :: pfv_ho ! high order flux |
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| 954 | REAL(wp), DIMENSION (jpi,jpj), INTENT(in ), OPTIONAL :: pfv_ups ! upstream flux |
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| 955 | ! |
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| 956 | REAL(wp) :: Cr, Rjm, Rj, Rjp, vCFL, zpsi, zh3, zlimiter, Rr |
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| 957 | INTEGER :: ji, jj ! dummy loop indices |
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| 958 | REAL(wp), DIMENSION (jpi,jpj) :: zslpy ! tracer slopes |
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| 959 | !!---------------------------------------------------------------------- |
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| 960 | ! |
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| 961 | DO jj = 2, jpjm1 |
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| 962 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 963 | zslpy(ji,jj) = ( pt(ji,jj+1) - pt(ji,jj) ) * vmask(ji,jj,1) |
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| 964 | END DO |
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| 965 | END DO |
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| 966 | CALL lbc_lnk( zslpy, 'V', -1.) ! lateral boundary cond. |
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| 967 | |
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| 968 | DO jj = 2, jpjm1 |
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| 969 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 970 | vCFL = pdt * ABS( pv(ji,jj) ) * r1_e1e2t(ji,jj) |
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| 971 | |
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| 972 | Rjm = zslpy(ji,jj-1) |
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| 973 | Rj = zslpy(ji,jj ) |
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| 974 | Rjp = zslpy(ji,jj+1) |
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| 975 | |
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| 976 | IF( PRESENT(pfv_ups) ) THEN |
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| 977 | |
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| 978 | IF( pv(ji,jj) > 0. ) THEN ; Rr = Rjm |
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| 979 | ELSE ; Rr = Rjp |
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| 980 | ENDIF |
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| 981 | |
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| 982 | zh3 = pfv_ho(ji,jj) - pfv_ups(ji,jj) |
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| 983 | IF( Rj > 0. ) THEN |
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| 984 | zlimiter = MAX( 0., MIN( zh3, MAX(-Rr * 0.5 * ABS(pvc(ji,jj)), & |
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| 985 | & MIN( 2. * Rr * 0.5 * ABS(pvc(ji,jj)), zh3, 1.5 * Rj * 0.5 * ABS(pvc(ji,jj)) ) ) ) ) |
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| 986 | ELSE |
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| 987 | zlimiter = -MAX( 0., MIN(-zh3, MAX( Rr * 0.5 * ABS(pvc(ji,jj)), & |
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| 988 | & MIN(-2. * Rr * 0.5 * ABS(pvc(ji,jj)), -zh3, -1.5 * Rj * 0.5 * ABS(pvc(ji,jj)) ) ) ) ) |
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| 989 | ENDIF |
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| 990 | pfv_ho(ji,jj) = pfv_ups(ji,jj) + zlimiter |
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| 991 | |
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| 992 | ELSE |
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| 993 | |
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| 994 | IF( Rj /= 0. ) THEN |
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| 995 | IF( pv(ji,jj) > 0. ) THEN ; Cr = Rjm / Rj |
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| 996 | ELSE ; Cr = Rjp / Rj |
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| 997 | ENDIF |
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| 998 | ELSE |
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| 999 | Cr = 0. |
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| 1000 | !IF( pv(ji,jj) > 0. ) THEN ; Cr = Rjm * 1.e20 |
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| 1001 | !ELSE ; Cr = Rjp * 1.e20 |
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| 1002 | !ENDIF |
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| 1003 | ENDIF |
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| 1004 | |
---|
| 1005 | ! -- superbee -- |
---|
| 1006 | zpsi = MAX( 0., MAX( MIN(1.,2.*Cr), MIN(2.,Cr) ) ) |
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| 1007 | ! -- van albada 2 -- |
---|
| 1008 | !!zpsi = 2.*Cr / (Cr*Cr+1.) |
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| 1009 | |
---|
| 1010 | ! -- sweby (with beta=1) -- |
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| 1011 | !!zpsi = MAX( 0., MAX( MIN(1.,1.*Cr), MIN(1.,Cr) ) ) |
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| 1012 | ! -- van Leer -- |
---|
| 1013 | !!zpsi = ( Cr + ABS(Cr) ) / ( 1. + ABS(Cr) ) |
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| 1014 | ! -- ospre -- |
---|
| 1015 | !!zpsi = 1.5 * ( Cr*Cr + Cr ) / ( Cr*Cr + Cr + 1. ) |
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| 1016 | ! -- koren -- |
---|
| 1017 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( (1.+2*Cr)/3., 2. ) ) ) |
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| 1018 | ! -- charm -- |
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| 1019 | !IF( Cr > 0. ) THEN ; zpsi = Cr * (3.*Cr + 1.) / ( (Cr + 1.) * (Cr + 1.) ) |
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| 1020 | !ELSE ; zpsi = 0. |
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| 1021 | !ENDIF |
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| 1022 | ! -- van albada 1 -- |
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| 1023 | !!zpsi = (Cr*Cr + Cr) / (Cr*Cr +1) |
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| 1024 | ! -- smart -- |
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| 1025 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, 4. ) ) ) |
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| 1026 | ! -- umist -- |
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| 1027 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, MIN(0.75+0.25*Cr, 2. ) ) ) ) |
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| 1028 | |
---|
| 1029 | ! high order flux corrected by the limiter |
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| 1030 | pfv_ho(ji,jj) = pfv_ho(ji,jj) - ABS( pvc(ji,jj) ) * ( (1.-zpsi) + vCFL*zpsi ) * Rj * 0.5 |
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| 1031 | |
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| 1032 | ENDIF |
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| 1033 | END DO |
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| 1034 | END DO |
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| 1035 | CALL lbc_lnk( pfv_ho, 'V', -1.) ! lateral boundary cond. |
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| 1036 | ! |
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| 1037 | END SUBROUTINE limiter_y |
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| 1038 | |
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[8586] | 1039 | #else |
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| 1040 | !!---------------------------------------------------------------------- |
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[9570] | 1041 | !! Default option Dummy module NO SI3 sea-ice model |
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[8586] | 1042 | !!---------------------------------------------------------------------- |
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| 1043 | #endif |
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| 1044 | |
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| 1045 | !!====================================================================== |
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| 1046 | END MODULE icedyn_adv_umx |
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