[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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| 16 | !! nonosc_2d : compute monotonic tracer fluxes by a non-oscillatory algorithm |
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| 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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| 22 | ! |
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| 23 | USE in_out_manager ! I/O manager |
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| 24 | USE lib_mpp ! MPP library |
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| 25 | USE lib_fortran ! fortran utilities (glob_sum + no signed zero) |
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| 26 | USE lbclnk ! lateral boundary conditions (or mpp links) |
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| 27 | |
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| 28 | IMPLICIT NONE |
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| 29 | PRIVATE |
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| 30 | |
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| 31 | PUBLIC ice_dyn_adv_umx ! called by icedyn_adv.F90 |
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| 32 | |
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| 33 | REAL(wp) :: z1_6 = 1._wp / 6._wp ! =1/6 |
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| 34 | REAL(wp) :: z1_120 = 1._wp / 120._wp ! =1/120 |
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| 35 | |
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| 36 | !! * Substitutions |
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| 37 | # include "vectopt_loop_substitute.h90" |
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| 38 | !!---------------------------------------------------------------------- |
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[9598] | 39 | !! NEMO/ICE 4.0 , NEMO Consortium (2018) |
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[10069] | 40 | !! $Id$ |
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[10068] | 41 | !! Software governed by the CeCILL license (see ./LICENSE) |
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[8586] | 42 | !!---------------------------------------------------------------------- |
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| 43 | CONTAINS |
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| 44 | |
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| 45 | SUBROUTINE ice_dyn_adv_umx( k_order, kt, pu_ice, pv_ice, & |
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| 46 | & pato_i, pv_i, pv_s, psv_i, poa_i, pa_i, pa_ip, pv_ip, pe_s, pe_i ) |
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| 47 | !!---------------------------------------------------------------------- |
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| 48 | !! *** ROUTINE ice_dyn_adv_umx *** |
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| 49 | !! |
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| 50 | !! ** Purpose : Compute the now trend due to total advection of |
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| 51 | !! tracers and add it to the general trend of tracer equations |
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| 52 | !! using an "Ultimate-Macho" scheme |
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| 53 | !! |
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| 54 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
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| 55 | !!---------------------------------------------------------------------- |
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| 56 | INTEGER , INTENT(in ) :: k_order ! order of the scheme (1-5 or 20) |
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| 57 | INTEGER , INTENT(in ) :: kt ! time step |
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| 58 | REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pu_ice ! ice i-velocity |
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| 59 | REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pv_ice ! ice j-velocity |
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| 60 | REAL(wp), DIMENSION(:,:) , INTENT(inout) :: pato_i ! open water area |
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| 61 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i ! ice volume |
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| 62 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_s ! snw volume |
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| 63 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: psv_i ! salt content |
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| 64 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: poa_i ! age content |
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| 65 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_i ! ice concentration |
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| 66 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_ip ! melt pond fraction |
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| 67 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_ip ! melt pond volume |
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| 68 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s ! snw heat content |
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| 69 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_i ! ice heat content |
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| 70 | ! |
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| 71 | INTEGER :: ji, jj, jk, jl, jt ! dummy loop indices |
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| 72 | INTEGER :: initad ! number of sub-timestep for the advection |
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| 73 | REAL(wp) :: zcfl , zusnit, zdt ! - - |
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| 74 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: zudy, zvdx, zcu_box, zcv_box |
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| 75 | !!---------------------------------------------------------------------- |
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| 76 | ! |
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| 77 | IF( kt == nit000 .AND. lwp ) WRITE(numout,*) '-- ice_dyn_adv_umx: Ultimate-Macho advection scheme' |
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| 78 | ! |
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| 79 | ALLOCATE( zudy(jpi,jpj) , zvdx(jpi,jpj) , zcu_box(jpi,jpj) , zcv_box(jpi,jpj) ) |
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| 80 | ! |
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| 81 | ! --- If ice drift field is too fast, use an appropriate time step for advection (CFL test for stability) --- ! |
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| 82 | zcfl = MAXVAL( ABS( pu_ice(:,:) ) * rdt_ice * r1_e1u(:,:) ) |
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| 83 | zcfl = MAX( zcfl, MAXVAL( ABS( pv_ice(:,:) ) * rdt_ice * r1_e2v(:,:) ) ) |
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| 84 | IF( lk_mpp ) CALL mpp_max( zcfl ) |
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| 85 | |
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| 86 | IF( zcfl > 0.5 ) THEN ; initad = 2 ; zusnit = 0.5_wp |
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| 87 | ELSE ; initad = 1 ; zusnit = 1.0_wp |
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| 88 | ENDIF |
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| 89 | |
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| 90 | zdt = rdt_ice / REAL(initad) |
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| 91 | |
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| 92 | ! --- transport --- ! |
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| 93 | zudy(:,:) = pu_ice(:,:) * e2u(:,:) |
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| 94 | zvdx(:,:) = pv_ice(:,:) * e1v(:,:) |
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| 95 | |
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| 96 | ! --- define velocity for advection: u*grad(H) --- ! |
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| 97 | DO jj = 2, jpjm1 |
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| 98 | DO ji = fs_2, fs_jpim1 |
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| 99 | IF ( pu_ice(ji,jj) * pu_ice(ji-1,jj) <= 0._wp ) THEN ; zcu_box(ji,jj) = 0._wp |
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| 100 | ELSEIF( pu_ice(ji,jj) > 0._wp ) THEN ; zcu_box(ji,jj) = pu_ice(ji-1,jj) |
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| 101 | ELSE ; zcu_box(ji,jj) = pu_ice(ji ,jj) |
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| 102 | ENDIF |
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| 103 | |
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| 104 | IF ( pv_ice(ji,jj) * pv_ice(ji,jj-1) <= 0._wp ) THEN ; zcv_box(ji,jj) = 0._wp |
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| 105 | ELSEIF( pv_ice(ji,jj) > 0._wp ) THEN ; zcv_box(ji,jj) = pv_ice(ji,jj-1) |
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| 106 | ELSE ; zcv_box(ji,jj) = pv_ice(ji,jj ) |
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| 107 | ENDIF |
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| 108 | END DO |
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| 109 | END DO |
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| 110 | |
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| 111 | !---------------! |
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| 112 | !== advection ==! |
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| 113 | !---------------! |
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| 114 | DO jt = 1, initad |
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| 115 | CALL adv_umx( k_order, kt, zdt, zudy, zvdx, zcu_box, zcv_box, pato_i(:,:) ) ! Open water area |
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| 116 | DO jl = 1, jpl |
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| 117 | CALL adv_umx( k_order, kt, zdt, zudy, zvdx, zcu_box, zcv_box, pa_i(:,:,jl) ) ! Ice area |
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| 118 | CALL adv_umx( k_order, kt, zdt, zudy, zvdx, zcu_box, zcv_box, pv_i(:,:,jl) ) ! Ice volume |
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| 119 | CALL adv_umx( k_order, kt, zdt, zudy, zvdx, zcu_box, zcv_box, psv_i(:,:,jl) ) ! Salt content |
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| 120 | CALL adv_umx( k_order, kt, zdt, zudy, zvdx, zcu_box, zcv_box, poa_i(:,:,jl) ) ! Age content |
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| 121 | DO jk = 1, nlay_i |
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| 122 | CALL adv_umx( k_order, kt, zdt, zudy, zvdx, zcu_box, zcv_box, pe_i(:,:,jk,jl) ) ! Ice heat content |
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| 123 | END DO |
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| 124 | CALL adv_umx( k_order, kt, zdt, zudy, zvdx, zcu_box, zcv_box, pv_s(:,:,jl) ) ! Snow volume |
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[9271] | 125 | DO jk = 1, nlay_s |
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| 126 | CALL adv_umx( k_order, kt, zdt, zudy, zvdx, zcu_box, zcv_box, pe_s(:,:,jk,jl) ) ! Snow heat content |
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| 127 | END DO |
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[8637] | 128 | IF ( ln_pnd_H12 ) THEN |
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[8586] | 129 | CALL adv_umx( k_order, kt, zdt, zudy, zvdx, zcu_box, zcv_box, pa_ip(:,:,jl) ) ! Melt pond fraction |
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| 130 | CALL adv_umx( k_order, kt, zdt, zudy, zvdx, zcu_box, zcv_box, pv_ip(:,:,jl) ) ! Melt pond volume |
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| 131 | ENDIF |
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| 132 | END DO |
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| 133 | END DO |
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| 134 | ! |
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| 135 | DEALLOCATE( zudy, zvdx, zcu_box, zcv_box ) |
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| 136 | ! |
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| 137 | END SUBROUTINE ice_dyn_adv_umx |
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[9929] | 138 | |
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[8586] | 139 | |
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| 140 | SUBROUTINE adv_umx( k_order, kt, pdt, puc, pvc, pubox, pvbox, ptc ) |
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| 141 | !!---------------------------------------------------------------------- |
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| 142 | !! *** ROUTINE adv_umx *** |
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| 143 | !! |
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| 144 | !! ** Purpose : Compute the now trend due to total advection of |
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| 145 | !! tracers and add it to the general trend of tracer equations |
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| 146 | !! |
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| 147 | !! ** Method : TVD scheme, i.e. 2nd order centered scheme with |
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| 148 | !! corrected flux (monotonic correction) |
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| 149 | !! note: - this advection scheme needs a leap-frog time scheme |
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| 150 | !! |
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| 151 | !! ** Action : - pt the after advective tracer |
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| 152 | !!---------------------------------------------------------------------- |
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| 153 | INTEGER , INTENT(in ) :: k_order ! order of the ULTIMATE scheme |
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| 154 | INTEGER , INTENT(in ) :: kt ! number of iteration |
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| 155 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
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| 156 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: puc , pvc ! 2 ice velocity components => u*e2 |
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| 157 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pubox, pvbox ! upstream velocity |
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| 158 | REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: ptc ! tracer content field |
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| 159 | ! |
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| 160 | INTEGER :: ji, jj ! dummy loop indices |
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| 161 | REAL(wp) :: ztra ! local scalar |
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| 162 | REAL(wp), DIMENSION(jpi,jpj) :: zfu_ups, zfu_ho, zt_u, zt_ups |
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| 163 | REAL(wp), DIMENSION(jpi,jpj) :: zfv_ups, zfv_ho, zt_v, ztrd |
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| 164 | !!---------------------------------------------------------------------- |
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| 165 | ! |
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| 166 | ! upstream advection with initial mass fluxes & intermediate update |
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| 167 | ! -------------------------------------------------------------------- |
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| 168 | DO jj = 1, jpjm1 ! upstream tracer flux in the i and j direction |
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| 169 | DO ji = 1, fs_jpim1 ! vector opt. |
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[9929] | 170 | zfu_ups(ji,jj) = MAX( puc(ji,jj), 0._wp ) * ptc(ji,jj) + MIN( puc(ji,jj), 0._wp ) * ptc(ji+1,jj) |
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| 171 | zfv_ups(ji,jj) = MAX( pvc(ji,jj), 0._wp ) * ptc(ji,jj) + MIN( pvc(ji,jj), 0._wp ) * ptc(ji,jj+1) |
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[8586] | 172 | END DO |
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| 173 | END DO |
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| 174 | |
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| 175 | DO jj = 2, jpjm1 ! total intermediate advective trends |
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| 176 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 177 | ztra = - ( zfu_ups(ji,jj) - zfu_ups(ji-1,jj ) & |
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| 178 | & + zfv_ups(ji,jj) - zfv_ups(ji ,jj-1) ) * r1_e1e2t(ji,jj) |
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| 179 | ! |
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| 180 | ztrd(ji,jj) = ztra ! upstream trend [ -div(uh) or -div(uhT) ] |
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| 181 | zt_ups (ji,jj) = ( ptc(ji,jj) + pdt * ztra ) * tmask(ji,jj,1) ! guess after content field with monotonic scheme |
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| 182 | END DO |
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| 183 | END DO |
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| 184 | CALL lbc_lnk( zt_ups, 'T', 1. ) ! Lateral boundary conditions (unchanged sign) |
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| 185 | |
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| 186 | ! High order (_ho) fluxes |
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| 187 | ! ----------------------- |
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| 188 | SELECT CASE( k_order ) |
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| 189 | CASE ( 20 ) ! centered second order |
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[8637] | 190 | DO jj = 1, jpjm1 |
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| 191 | DO ji = 1, fs_jpim1 ! vector opt. |
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[8586] | 192 | zfu_ho(ji,jj) = 0.5 * puc(ji,jj) * ( ptc(ji,jj) + ptc(ji+1,jj) ) |
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| 193 | zfv_ho(ji,jj) = 0.5 * pvc(ji,jj) * ( ptc(ji,jj) + ptc(ji,jj+1) ) |
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| 194 | END DO |
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| 195 | END DO |
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| 196 | ! |
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| 197 | CASE ( 1:5 ) ! 1st to 5th order ULTIMATE-MACHO scheme |
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| 198 | CALL macho( k_order, kt, pdt, ptc, puc, pvc, pubox, pvbox, zt_u, zt_v ) |
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| 199 | ! |
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[8637] | 200 | DO jj = 1, jpjm1 |
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| 201 | DO ji = 1, fs_jpim1 ! vector opt. |
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[8586] | 202 | zfu_ho(ji,jj) = puc(ji,jj) * zt_u(ji,jj) |
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| 203 | zfv_ho(ji,jj) = pvc(ji,jj) * zt_v(ji,jj) |
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| 204 | END DO |
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| 205 | END DO |
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| 206 | ! |
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| 207 | END SELECT |
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| 208 | |
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| 209 | ! antidiffusive flux : high order minus low order |
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| 210 | ! -------------------------------------------------- |
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[8637] | 211 | DO jj = 1, jpjm1 |
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| 212 | DO ji = 1, fs_jpim1 ! vector opt. |
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[8586] | 213 | zfu_ho(ji,jj) = zfu_ho(ji,jj) - zfu_ups(ji,jj) |
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| 214 | zfv_ho(ji,jj) = zfv_ho(ji,jj) - zfv_ups(ji,jj) |
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| 215 | END DO |
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| 216 | END DO |
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| 217 | |
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| 218 | ! monotonicity algorithm |
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| 219 | ! ------------------------- |
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| 220 | CALL nonosc_2d( ptc, zfu_ho, zfv_ho, zt_ups, pdt ) |
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| 221 | |
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| 222 | ! final trend with corrected fluxes |
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| 223 | ! ------------------------------------ |
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| 224 | DO jj = 2, jpjm1 |
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| 225 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 226 | ztra = ztrd(ji,jj) - ( zfu_ho(ji,jj) - zfu_ho(ji-1,jj ) & |
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| 227 | & + zfv_ho(ji,jj) - zfv_ho(ji ,jj-1) ) * r1_e1e2t(ji,jj) |
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[9866] | 228 | ptc(ji,jj) = ( ptc(ji,jj) + pdt * ztra ) * tmask(ji,jj,1) |
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[8586] | 229 | END DO |
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| 230 | END DO |
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[9421] | 231 | CALL lbc_lnk( ptc, 'T', 1. ) |
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[8586] | 232 | ! |
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| 233 | END SUBROUTINE adv_umx |
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| 234 | |
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| 235 | |
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| 236 | SUBROUTINE macho( k_order, kt, pdt, ptc, puc, pvc, pubox, pvbox, pt_u, pt_v ) |
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| 237 | !!--------------------------------------------------------------------- |
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| 238 | !! *** ROUTINE ultimate_x *** |
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| 239 | !! |
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| 240 | !! ** Purpose : compute |
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| 241 | !! |
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| 242 | !! ** Method : ... ??? |
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| 243 | !! TIM = transient interpolation Modeling |
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| 244 | !! |
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| 245 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
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| 246 | !!---------------------------------------------------------------------- |
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| 247 | INTEGER , INTENT(in ) :: k_order ! order of the ULTIMATE scheme |
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| 248 | INTEGER , INTENT(in ) :: kt ! number of iteration |
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| 249 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
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| 250 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: ptc ! tracer fields |
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| 251 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: puc, pvc ! 2 ice velocity components |
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| 252 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pubox, pvbox ! upstream velocity |
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| 253 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pt_u, pt_v ! tracer at u- and v-points |
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| 254 | ! |
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| 255 | INTEGER :: ji, jj ! dummy loop indices |
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| 256 | REAL(wp) :: zc_box ! - - |
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| 257 | REAL(wp), DIMENSION(jpi,jpj) :: zzt |
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| 258 | !!---------------------------------------------------------------------- |
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| 259 | ! |
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| 260 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == 0 ) THEN !== odd ice time step: adv_x then adv_y ==! |
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| 261 | ! |
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| 262 | ! !-- ultimate interpolation of pt at u-point --! |
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| 263 | CALL ultimate_x( k_order, pdt, ptc, puc, pt_u ) |
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| 264 | ! |
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| 265 | ! !-- advective form update in zzt --! |
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| 266 | DO jj = 2, jpjm1 |
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| 267 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 268 | zzt(ji,jj) = ptc(ji,jj) - pubox(ji,jj) * pdt * ( pt_u(ji,jj) - pt_u(ji-1,jj) ) * r1_e1t(ji,jj) & |
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| 269 | & - ptc (ji,jj) * pdt * ( puc (ji,jj) - puc (ji-1,jj) ) * r1_e1e2t(ji,jj) |
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| 270 | zzt(ji,jj) = zzt(ji,jj) * tmask(ji,jj,1) |
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| 271 | END DO |
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| 272 | END DO |
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| 273 | CALL lbc_lnk( zzt, 'T', 1. ) |
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| 274 | ! |
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| 275 | ! !-- ultimate interpolation of pt at v-point --! |
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| 276 | CALL ultimate_y( k_order, pdt, zzt, pvc, pt_v ) |
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| 277 | ! |
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| 278 | ELSE !== even ice time step: adv_y then adv_x ==! |
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| 279 | ! |
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| 280 | ! !-- ultimate interpolation of pt at v-point --! |
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| 281 | CALL ultimate_y( k_order, pdt, ptc, pvc, pt_v ) |
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| 282 | ! |
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| 283 | ! !-- advective form update in zzt --! |
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| 284 | DO jj = 2, jpjm1 |
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| 285 | DO ji = fs_2, fs_jpim1 |
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| 286 | zzt(ji,jj) = ptc(ji,jj) - pvbox(ji,jj) * pdt * ( pt_v(ji,jj) - pt_v(ji,jj-1) ) * r1_e2t(ji,jj) & |
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| 287 | & - ptc (ji,jj) * pdt * ( pvc (ji,jj) - pvc (ji,jj-1) ) * r1_e1e2t(ji,jj) |
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| 288 | zzt(ji,jj) = zzt(ji,jj) * tmask(ji,jj,1) |
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| 289 | END DO |
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| 290 | END DO |
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| 291 | CALL lbc_lnk( zzt, 'T', 1. ) |
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| 292 | ! |
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| 293 | ! !-- ultimate interpolation of pt at u-point --! |
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| 294 | CALL ultimate_x( k_order, pdt, zzt, puc, pt_u ) |
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| 295 | ! |
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| 296 | ENDIF |
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| 297 | ! |
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| 298 | END SUBROUTINE macho |
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| 299 | |
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| 300 | |
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| 301 | SUBROUTINE ultimate_x( k_order, pdt, pt, puc, pt_u ) |
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| 302 | !!--------------------------------------------------------------------- |
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| 303 | !! *** ROUTINE ultimate_x *** |
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| 304 | !! |
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| 305 | !! ** Purpose : compute |
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| 306 | !! |
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| 307 | !! ** Method : ... ??? |
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| 308 | !! TIM = transient interpolation Modeling |
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| 309 | !! |
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| 310 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
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| 311 | !!---------------------------------------------------------------------- |
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| 312 | INTEGER , INTENT(in ) :: k_order ! ocean time-step index |
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| 313 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
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| 314 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: puc ! ice i-velocity component |
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| 315 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pt ! tracer fields |
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| 316 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pt_u ! tracer at u-point |
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| 317 | ! |
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| 318 | INTEGER :: ji, jj ! dummy loop indices |
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| 319 | REAL(wp) :: zcu, zdx2, zdx4 ! - - |
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| 320 | REAL(wp), DIMENSION(jpi,jpj) :: ztu1, ztu2, ztu3, ztu4 |
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| 321 | !!---------------------------------------------------------------------- |
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| 322 | ! |
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| 323 | ! !-- Laplacian in i-direction --! |
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| 324 | DO jj = 2, jpjm1 ! First derivative (gradient) |
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| 325 | DO ji = 1, fs_jpim1 |
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| 326 | ztu1(ji,jj) = ( pt(ji+1,jj) - pt(ji,jj) ) * r1_e1u(ji,jj) * umask(ji,jj,1) |
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| 327 | END DO |
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| 328 | ! ! Second derivative (Laplacian) |
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| 329 | DO ji = fs_2, fs_jpim1 |
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| 330 | ztu2(ji,jj) = ( ztu1(ji,jj) - ztu1(ji-1,jj) ) * r1_e1t(ji,jj) |
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| 331 | END DO |
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| 332 | END DO |
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| 333 | CALL lbc_lnk( ztu2, 'T', 1. ) |
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| 334 | ! |
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| 335 | ! !-- BiLaplacian in i-direction --! |
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| 336 | DO jj = 2, jpjm1 ! Third derivative |
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| 337 | DO ji = 1, fs_jpim1 |
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| 338 | ztu3(ji,jj) = ( ztu2(ji+1,jj) - ztu2(ji,jj) ) * r1_e1u(ji,jj) * umask(ji,jj,1) |
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| 339 | END DO |
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| 340 | ! ! Fourth derivative |
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| 341 | DO ji = fs_2, fs_jpim1 |
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| 342 | ztu4(ji,jj) = ( ztu3(ji,jj) - ztu3(ji-1,jj) ) * r1_e1t(ji,jj) |
---|
| 343 | END DO |
---|
| 344 | END DO |
---|
| 345 | CALL lbc_lnk( ztu4, 'T', 1. ) |
---|
| 346 | ! |
---|
| 347 | ! |
---|
| 348 | SELECT CASE (k_order ) |
---|
| 349 | ! |
---|
| 350 | CASE( 1 ) !== 1st order central TIM ==! (Eq. 21) |
---|
| 351 | ! |
---|
[8637] | 352 | DO jj = 2, jpjm1 |
---|
[8586] | 353 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 354 | pt_u(ji,jj) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj) + pt(ji,jj) & |
---|
| 355 | & - SIGN( 1._wp, puc(ji,jj) ) * ( pt(ji+1,jj) - pt(ji,jj) ) ) |
---|
| 356 | END DO |
---|
| 357 | END DO |
---|
| 358 | ! |
---|
| 359 | CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23) |
---|
| 360 | ! |
---|
[8637] | 361 | DO jj = 2, jpjm1 |
---|
[8586] | 362 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 363 | zcu = puc(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
| 364 | pt_u(ji,jj) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj) + pt(ji,jj) & |
---|
| 365 | & - zcu * ( pt(ji+1,jj) - pt(ji,jj) ) ) |
---|
| 366 | END DO |
---|
| 367 | END DO |
---|
| 368 | ! |
---|
| 369 | CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24) |
---|
| 370 | ! |
---|
[8637] | 371 | DO jj = 2, jpjm1 |
---|
[8586] | 372 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 373 | zcu = puc(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
| 374 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
| 375 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
| 376 | pt_u(ji,jj) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj) + pt (ji,jj) & |
---|
| 377 | & - zcu * ( pt (ji+1,jj) - pt (ji,jj) ) ) & |
---|
| 378 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj) + ztu2(ji,jj) & |
---|
| 379 | & - SIGN( 1._wp, zcu ) * ( ztu2(ji+1,jj) - ztu2(ji,jj) ) ) ) |
---|
| 380 | END DO |
---|
| 381 | END DO |
---|
| 382 | ! |
---|
| 383 | CASE( 4 ) !== 4th order central TIM ==! (Eq. 27) |
---|
| 384 | ! |
---|
[8637] | 385 | DO jj = 2, jpjm1 |
---|
[8586] | 386 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 387 | zcu = puc(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
| 388 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
| 389 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
| 390 | pt_u(ji,jj) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj) + pt (ji,jj) & |
---|
| 391 | & - zcu * ( pt (ji+1,jj) - pt (ji,jj) ) ) & |
---|
| 392 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj) + ztu2(ji,jj) & |
---|
| 393 | & - 0.5_wp * zcu * ( ztu2(ji+1,jj) - ztu2(ji,jj) ) ) ) |
---|
| 394 | END DO |
---|
| 395 | END DO |
---|
| 396 | ! |
---|
| 397 | CASE( 5 ) !== 5th order central TIM ==! (Eq. 29) |
---|
| 398 | ! |
---|
[8637] | 399 | DO jj = 2, jpjm1 |
---|
[8586] | 400 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 401 | zcu = puc(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
| 402 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
| 403 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
| 404 | zdx4 = zdx2 * zdx2 |
---|
| 405 | pt_u(ji,jj) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj) + pt (ji,jj) & |
---|
| 406 | & - zcu * ( pt (ji+1,jj) - pt (ji,jj) ) ) & |
---|
| 407 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj) + ztu2(ji,jj) & |
---|
| 408 | & - 0.5_wp * zcu * ( ztu2(ji+1,jj) - ztu2(ji,jj) ) ) & |
---|
| 409 | & + z1_120 * zdx4 * ( zcu*zcu - 1._wp ) * ( zcu*zcu - 4._wp ) * ( ztu4(ji+1,jj) + ztu4(ji,jj) & |
---|
| 410 | & - SIGN( 1._wp, zcu ) * ( ztu4(ji+1,jj) - ztu4(ji,jj) ) ) ) |
---|
| 411 | END DO |
---|
| 412 | END DO |
---|
| 413 | ! |
---|
| 414 | END SELECT |
---|
| 415 | ! |
---|
| 416 | END SUBROUTINE ultimate_x |
---|
| 417 | |
---|
| 418 | |
---|
| 419 | SUBROUTINE ultimate_y( k_order, pdt, pt, pvc, pt_v ) |
---|
| 420 | !!--------------------------------------------------------------------- |
---|
| 421 | !! *** ROUTINE ultimate_y *** |
---|
| 422 | !! |
---|
| 423 | !! ** Purpose : compute |
---|
| 424 | !! |
---|
| 425 | !! ** Method : ... ??? |
---|
| 426 | !! TIM = transient interpolation Modeling |
---|
| 427 | !! |
---|
| 428 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
| 429 | !!---------------------------------------------------------------------- |
---|
| 430 | INTEGER , INTENT(in ) :: k_order ! ocean time-step index |
---|
| 431 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 432 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pvc ! ice j-velocity component |
---|
| 433 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pt ! tracer fields |
---|
| 434 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pt_v ! tracer at v-point |
---|
| 435 | ! |
---|
| 436 | INTEGER :: ji, jj ! dummy loop indices |
---|
| 437 | REAL(wp) :: zcv, zdy2, zdy4 ! - - |
---|
| 438 | REAL(wp), DIMENSION(jpi,jpj) :: ztv1, ztv2, ztv3, ztv4 |
---|
| 439 | !!---------------------------------------------------------------------- |
---|
| 440 | ! |
---|
| 441 | ! !-- Laplacian in j-direction --! |
---|
| 442 | DO jj = 1, jpjm1 ! First derivative (gradient) |
---|
| 443 | DO ji = fs_2, fs_jpim1 |
---|
| 444 | ztv1(ji,jj) = ( pt(ji,jj+1) - pt(ji,jj) ) * r1_e2v(ji,jj) * vmask(ji,jj,1) |
---|
| 445 | END DO |
---|
| 446 | END DO |
---|
| 447 | DO jj = 2, jpjm1 ! Second derivative (Laplacian) |
---|
| 448 | DO ji = fs_2, fs_jpim1 |
---|
| 449 | ztv2(ji,jj) = ( ztv1(ji,jj) - ztv1(ji,jj-1) ) * r1_e2t(ji,jj) |
---|
| 450 | END DO |
---|
| 451 | END DO |
---|
| 452 | CALL lbc_lnk( ztv2, 'T', 1. ) |
---|
| 453 | ! |
---|
| 454 | ! !-- BiLaplacian in j-direction --! |
---|
| 455 | DO jj = 1, jpjm1 ! First derivative |
---|
| 456 | DO ji = fs_2, fs_jpim1 |
---|
| 457 | ztv3(ji,jj) = ( ztv2(ji,jj+1) - ztv2(ji,jj) ) * r1_e2v(ji,jj) * vmask(ji,jj,1) |
---|
| 458 | END DO |
---|
| 459 | END DO |
---|
| 460 | DO jj = 2, jpjm1 ! Second derivative |
---|
| 461 | DO ji = fs_2, fs_jpim1 |
---|
| 462 | ztv4(ji,jj) = ( ztv3(ji,jj) - ztv3(ji,jj-1) ) * r1_e2t(ji,jj) |
---|
| 463 | END DO |
---|
| 464 | END DO |
---|
| 465 | CALL lbc_lnk( ztv4, 'T', 1. ) |
---|
| 466 | ! |
---|
| 467 | ! |
---|
| 468 | SELECT CASE (k_order ) |
---|
| 469 | ! |
---|
| 470 | CASE( 1 ) !== 1st order central TIM ==! (Eq. 21) |
---|
| 471 | DO jj = 1, jpjm1 |
---|
[8637] | 472 | DO ji = fs_2, fs_jpim1 |
---|
[8586] | 473 | pt_v(ji,jj) = 0.5_wp * vmask(ji,jj,1) * ( ( pt(ji,jj+1) + pt(ji,jj) ) & |
---|
| 474 | & - SIGN( 1._wp, pvc(ji,jj) ) * ( pt(ji,jj+1) - pt(ji,jj) ) ) |
---|
| 475 | END DO |
---|
| 476 | END DO |
---|
| 477 | ! |
---|
| 478 | CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23) |
---|
| 479 | DO jj = 1, jpjm1 |
---|
[8637] | 480 | DO ji = fs_2, fs_jpim1 |
---|
[8586] | 481 | zcv = pvc(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
| 482 | pt_v(ji,jj) = 0.5_wp * vmask(ji,jj,1) * ( ( pt(ji,jj+1) + pt(ji,jj) ) & |
---|
| 483 | & - zcv * ( pt(ji,jj+1) - pt(ji,jj) ) ) |
---|
| 484 | END DO |
---|
| 485 | END DO |
---|
[9421] | 486 | CALL lbc_lnk( pt_v, 'V', 1. ) |
---|
[8586] | 487 | ! |
---|
| 488 | CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24) |
---|
| 489 | DO jj = 1, jpjm1 |
---|
[8637] | 490 | DO ji = fs_2, fs_jpim1 |
---|
[8586] | 491 | zcv = pvc(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
| 492 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
| 493 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
| 494 | pt_v(ji,jj) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1) + pt (ji,jj) & |
---|
| 495 | & - zcv * ( pt (ji,jj+1) - pt (ji,jj) ) ) & |
---|
| 496 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1) + ztv2(ji,jj) & |
---|
| 497 | & - SIGN( 1._wp, zcv ) * ( ztv2(ji,jj+1) - ztv2(ji,jj) ) ) ) |
---|
| 498 | END DO |
---|
| 499 | END DO |
---|
| 500 | ! |
---|
| 501 | CASE( 4 ) !== 4th order central TIM ==! (Eq. 27) |
---|
| 502 | DO jj = 1, jpjm1 |
---|
[8637] | 503 | DO ji = fs_2, fs_jpim1 |
---|
[8586] | 504 | zcv = pvc(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
| 505 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
| 506 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
| 507 | pt_v(ji,jj) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1) + pt (ji,jj) & |
---|
| 508 | & - zcv * ( pt (ji,jj+1) - pt (ji,jj) ) ) & |
---|
| 509 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1) + ztv2(ji,jj) & |
---|
| 510 | & - 0.5_wp * zcv * ( ztv2(ji,jj+1) - ztv2(ji,jj) ) ) ) |
---|
| 511 | END DO |
---|
| 512 | END DO |
---|
| 513 | ! |
---|
| 514 | CASE( 5 ) !== 5th order central TIM ==! (Eq. 29) |
---|
| 515 | DO jj = 1, jpjm1 |
---|
[8637] | 516 | DO ji = fs_2, fs_jpim1 |
---|
[8586] | 517 | zcv = pvc(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
| 518 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
| 519 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
| 520 | zdy4 = zdy2 * zdy2 |
---|
| 521 | pt_v(ji,jj) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1) + pt (ji,jj) & |
---|
| 522 | & - zcv * ( pt (ji,jj+1) - pt (ji,jj) ) ) & |
---|
| 523 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1) + ztv2(ji,jj) & |
---|
| 524 | & - 0.5_wp * zcv * ( ztv2(ji,jj+1) - ztv2(ji,jj) ) ) & |
---|
| 525 | & + z1_120 * zdy4 * ( zcv*zcv - 1._wp ) * ( zcv*zcv - 4._wp ) * ( ztv4(ji,jj+1) + ztv4(ji,jj) & |
---|
| 526 | & - SIGN( 1._wp, zcv ) * ( ztv4(ji,jj+1) - ztv4(ji,jj) ) ) ) |
---|
| 527 | END DO |
---|
| 528 | END DO |
---|
| 529 | ! |
---|
| 530 | END SELECT |
---|
| 531 | ! |
---|
| 532 | END SUBROUTINE ultimate_y |
---|
| 533 | |
---|
| 534 | |
---|
| 535 | SUBROUTINE nonosc_2d( pbef, paa, pbb, paft, pdt ) |
---|
| 536 | !!--------------------------------------------------------------------- |
---|
| 537 | !! *** ROUTINE nonosc *** |
---|
| 538 | !! |
---|
| 539 | !! ** Purpose : compute monotonic tracer fluxes from the upstream |
---|
| 540 | !! scheme and the before field by a nonoscillatory algorithm |
---|
| 541 | !! |
---|
| 542 | !! ** Method : ... ??? |
---|
| 543 | !! warning : pbef and paft must be masked, but the boundaries |
---|
| 544 | !! conditions on the fluxes are not necessary zalezak (1979) |
---|
| 545 | !! drange (1995) multi-dimensional forward-in-time and upstream- |
---|
| 546 | !! in-space based differencing for fluid |
---|
| 547 | !!---------------------------------------------------------------------- |
---|
| 548 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 549 | REAL(wp), DIMENSION (jpi,jpj), INTENT(in ) :: pbef, paft ! before & after field |
---|
| 550 | REAL(wp), DIMENSION (jpi,jpj), INTENT(inout) :: paa, pbb ! monotonic fluxes in the 2 directions |
---|
| 551 | ! |
---|
| 552 | INTEGER :: ji, jj ! dummy loop indices |
---|
| 553 | INTEGER :: ikm1 ! local integer |
---|
| 554 | REAL(wp) :: zpos, zneg, zbt, za, zb, zc, zbig, zsml, z1_dt ! local scalars |
---|
| 555 | REAL(wp) :: zau, zbu, zcu, zav, zbv, zcv, zup, zdo ! - - |
---|
| 556 | REAL(wp), DIMENSION(jpi,jpj) :: zbetup, zbetdo, zbup, zbdo, zmsk, zdiv |
---|
| 557 | !!---------------------------------------------------------------------- |
---|
| 558 | ! |
---|
| 559 | zbig = 1.e+40_wp |
---|
| 560 | zsml = 1.e-15_wp |
---|
| 561 | |
---|
[8885] | 562 | ! test on divergence |
---|
[8586] | 563 | DO jj = 2, jpjm1 |
---|
| 564 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 565 | zdiv(ji,jj) = - ( paa(ji,jj) - paa(ji-1,jj ) & |
---|
| 566 | & + pbb(ji,jj) - pbb(ji ,jj-1) ) |
---|
| 567 | END DO |
---|
| 568 | END DO |
---|
| 569 | CALL lbc_lnk( zdiv, 'T', 1. ) ! Lateral boundary conditions (unchanged sign) |
---|
| 570 | |
---|
| 571 | ! Determine ice masks for before and after tracers |
---|
| 572 | WHERE( pbef(:,:) == 0._wp .AND. paft(:,:) == 0._wp .AND. zdiv(:,:) == 0._wp ) ; zmsk(:,:) = 0._wp |
---|
| 573 | ELSEWHERE ; zmsk(:,:) = 1._wp * tmask(:,:,1) |
---|
| 574 | END WHERE |
---|
| 575 | |
---|
| 576 | ! Search local extrema |
---|
| 577 | ! -------------------- |
---|
| 578 | ! max/min of pbef & paft with large negative/positive value (-/+zbig) inside land |
---|
| 579 | ! zbup(:,:) = MAX( pbef(:,:) * tmask(:,:,1) - zbig * ( 1.e0 - tmask(:,:,1) ), & |
---|
| 580 | ! & paft(:,:) * tmask(:,:,1) - zbig * ( 1.e0 - tmask(:,:,1) ) ) |
---|
| 581 | ! zbdo(:,:) = MIN( pbef(:,:) * tmask(:,:,1) + zbig * ( 1.e0 - tmask(:,:,1) ), & |
---|
| 582 | ! & paft(:,:) * tmask(:,:,1) + zbig * ( 1.e0 - tmask(:,:,1) ) ) |
---|
| 583 | zbup(:,:) = MAX( pbef(:,:) * zmsk(:,:) - zbig * ( 1.e0 - zmsk(:,:) ), & |
---|
| 584 | & paft(:,:) * zmsk(:,:) - zbig * ( 1.e0 - zmsk(:,:) ) ) |
---|
| 585 | zbdo(:,:) = MIN( pbef(:,:) * zmsk(:,:) + zbig * ( 1.e0 - zmsk(:,:) ), & |
---|
| 586 | & paft(:,:) * zmsk(:,:) + zbig * ( 1.e0 - zmsk(:,:) ) ) |
---|
| 587 | |
---|
| 588 | z1_dt = 1._wp / pdt |
---|
| 589 | DO jj = 2, jpjm1 |
---|
| 590 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 591 | ! |
---|
| 592 | zup = MAX( zbup(ji,jj), zbup(ji-1,jj ), zbup(ji+1,jj ), & ! search max/min in neighbourhood |
---|
| 593 | & zbup(ji ,jj-1), zbup(ji ,jj+1) ) |
---|
| 594 | zdo = MIN( zbdo(ji,jj), zbdo(ji-1,jj ), zbdo(ji+1,jj ), & |
---|
| 595 | & zbdo(ji ,jj-1), zbdo(ji ,jj+1) ) |
---|
| 596 | ! |
---|
| 597 | zpos = MAX( 0., paa(ji-1,jj ) ) - MIN( 0., paa(ji ,jj ) ) & ! positive/negative part of the flux |
---|
| 598 | & + MAX( 0., pbb(ji ,jj-1) ) - MIN( 0., pbb(ji ,jj ) ) |
---|
| 599 | zneg = MAX( 0., paa(ji ,jj ) ) - MIN( 0., paa(ji-1,jj ) ) & |
---|
| 600 | & + MAX( 0., pbb(ji ,jj ) ) - MIN( 0., pbb(ji ,jj-1) ) |
---|
| 601 | ! |
---|
| 602 | zbt = e1e2t(ji,jj) * z1_dt ! up & down beta terms |
---|
| 603 | zbetup(ji,jj) = ( zup - paft(ji,jj) ) / ( zpos + zsml ) * zbt |
---|
| 604 | zbetdo(ji,jj) = ( paft(ji,jj) - zdo ) / ( zneg + zsml ) * zbt |
---|
| 605 | END DO |
---|
| 606 | END DO |
---|
| 607 | CALL lbc_lnk_multi( zbetup, 'T', 1., zbetdo, 'T', 1. ) ! lateral boundary cond. (unchanged sign) |
---|
| 608 | |
---|
| 609 | ! monotonic flux in the i & j direction (paa & pbb) |
---|
| 610 | ! ------------------------------------- |
---|
| 611 | DO jj = 2, jpjm1 |
---|
[8637] | 612 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
[8586] | 613 | zau = MIN( 1._wp , zbetdo(ji,jj) , zbetup(ji+1,jj) ) |
---|
| 614 | zbu = MIN( 1._wp , zbetup(ji,jj) , zbetdo(ji+1,jj) ) |
---|
| 615 | zcu = 0.5 + SIGN( 0.5 , paa(ji,jj) ) |
---|
| 616 | ! |
---|
[8637] | 617 | paa(ji,jj) = paa(ji,jj) * ( zcu * zau + ( 1._wp - zcu) * zbu ) |
---|
| 618 | END DO |
---|
| 619 | END DO |
---|
| 620 | ! |
---|
| 621 | DO jj = 1, jpjm1 |
---|
| 622 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[8586] | 623 | zav = MIN( 1._wp , zbetdo(ji,jj) , zbetup(ji,jj+1) ) |
---|
| 624 | zbv = MIN( 1._wp , zbetup(ji,jj) , zbetdo(ji,jj+1) ) |
---|
| 625 | zcv = 0.5 + SIGN( 0.5 , pbb(ji,jj) ) |
---|
| 626 | ! |
---|
| 627 | pbb(ji,jj) = pbb(ji,jj) * ( zcv * zav + ( 1._wp - zcv) * zbv ) |
---|
| 628 | END DO |
---|
| 629 | END DO |
---|
| 630 | ! |
---|
| 631 | END SUBROUTINE nonosc_2d |
---|
| 632 | |
---|
| 633 | #else |
---|
| 634 | !!---------------------------------------------------------------------- |
---|
[9570] | 635 | !! Default option Dummy module NO SI3 sea-ice model |
---|
[8586] | 636 | !!---------------------------------------------------------------------- |
---|
| 637 | #endif |
---|
| 638 | |
---|
| 639 | !!====================================================================== |
---|
| 640 | END MODULE icedyn_adv_umx |
---|