[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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[10910] | 13 | !! ice_dyn_adv_umx : update the tracer fields |
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[8586] | 14 | !! ultimate_x(_y) : compute a tracer value at velocity points using ULTIMATE scheme at various orders |
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[10910] | 15 | !! macho : compute the fluxes |
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| 16 | !! nonosc_ice : limit the fluxes using a non-oscillatory algorithm |
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[8586] | 17 | !!---------------------------------------------------------------------- |
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| 18 | USE phycst ! physical constant |
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| 19 | USE dom_oce ! ocean domain |
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| 20 | USE sbc_oce , ONLY : nn_fsbc ! update frequency of surface boundary condition |
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| 21 | USE ice ! sea-ice variables |
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[10413] | 22 | USE icevar ! sea-ice: operations |
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[8586] | 23 | ! |
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| 24 | USE in_out_manager ! I/O manager |
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[10785] | 25 | USE iom ! I/O manager library |
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[8586] | 26 | USE lib_mpp ! MPP library |
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| 27 | USE lib_fortran ! fortran utilities (glob_sum + no signed zero) |
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| 28 | USE lbclnk ! lateral boundary conditions (or mpp links) |
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| 29 | |
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| 30 | IMPLICIT NONE |
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| 31 | PRIVATE |
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| 32 | |
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| 33 | PUBLIC ice_dyn_adv_umx ! called by icedyn_adv.F90 |
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| 34 | |
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| 35 | REAL(wp) :: z1_6 = 1._wp / 6._wp ! =1/6 |
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| 36 | REAL(wp) :: z1_120 = 1._wp / 120._wp ! =1/120 |
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[10413] | 37 | |
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[10519] | 38 | ! limiter: 1=nonosc_ice, 2=superbee, 3=h3(rachid) |
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[10446] | 39 | INTEGER :: kn_limiter = 1 |
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| 40 | |
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[10910] | 41 | ! if there is an outward velocity in a grid cell where there is no ice initially (typically at the ice edge), |
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| 42 | ! interpolated T at u/v points can be non-zero while it should |
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| 43 | ! (because of the high order of the advection scheme). Thus set it to 0 in this case |
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| 44 | LOGICAL :: ll_icedge = .TRUE. |
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| 45 | |
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| 46 | ! if T interpolated at u/v points is negative or v_i < 1.e-6 |
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| 47 | ! then interpolate T at u/v points using the upstream scheme |
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[10579] | 48 | LOGICAL :: ll_neg = .TRUE. |
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[10413] | 49 | |
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| 50 | ! alternate directions for upstream |
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[10446] | 51 | LOGICAL :: ll_upsxy = .TRUE. |
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[10413] | 52 | |
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| 53 | ! alternate directions for high order |
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[10446] | 54 | LOGICAL :: ll_hoxy = .TRUE. |
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[10413] | 55 | |
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| 56 | ! prelimiter: use it to avoid overshoot in H |
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[10512] | 57 | LOGICAL :: ll_prelimiter_zalesak = .FALSE. ! from: Zalesak(1979) eq. 14 => better for 1D. Not well defined in 2D |
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[10413] | 58 | |
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[10910] | 59 | ! advection for S and T: dVS/dt = -div( uA * uHS / u ) => ll_advS = F |
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| 60 | ! or dVS/dt = -div( uV * uS / u ) => ll_advS = T |
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| 61 | LOGICAL :: ll_advS = .FALSE. |
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[10413] | 62 | |
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[8586] | 63 | !! * Substitutions |
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| 64 | # include "vectopt_loop_substitute.h90" |
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| 65 | !!---------------------------------------------------------------------- |
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[9598] | 66 | !! NEMO/ICE 4.0 , NEMO Consortium (2018) |
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[10069] | 67 | !! $Id$ |
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[10413] | 68 | !! Software governed by the CeCILL licence (./LICENSE) |
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[8586] | 69 | !!---------------------------------------------------------------------- |
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| 70 | CONTAINS |
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| 71 | |
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[10910] | 72 | SUBROUTINE ice_dyn_adv_umx( kn_umx, kt, pu_ice, pv_ice, ph_i, ph_s, ph_ip, & |
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[10413] | 73 | & 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] | 74 | !!---------------------------------------------------------------------- |
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| 75 | !! *** ROUTINE ice_dyn_adv_umx *** |
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| 76 | !! |
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| 77 | !! ** Purpose : Compute the now trend due to total advection of |
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| 78 | !! tracers and add it to the general trend of tracer equations |
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| 79 | !! using an "Ultimate-Macho" scheme |
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| 80 | !! |
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| 81 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
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| 82 | !!---------------------------------------------------------------------- |
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[10413] | 83 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
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[8586] | 84 | INTEGER , INTENT(in ) :: kt ! time step |
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| 85 | REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pu_ice ! ice i-velocity |
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| 86 | REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pv_ice ! ice j-velocity |
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[10910] | 87 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: ph_i ! ice thickness |
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| 88 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: ph_s ! snw thickness |
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| 89 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: ph_ip ! ice pond thickness |
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[8586] | 90 | REAL(wp), DIMENSION(:,:) , INTENT(inout) :: pato_i ! open water area |
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| 91 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i ! ice volume |
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| 92 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_s ! snw volume |
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| 93 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: psv_i ! salt content |
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| 94 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: poa_i ! age content |
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| 95 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_i ! ice concentration |
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| 96 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_ip ! melt pond fraction |
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| 97 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_ip ! melt pond volume |
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| 98 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s ! snw heat content |
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| 99 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_i ! ice heat content |
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| 100 | ! |
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| 101 | INTEGER :: ji, jj, jk, jl, jt ! dummy loop indices |
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[10413] | 102 | INTEGER :: icycle ! number of sub-timestep for the advection |
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| 103 | REAL(wp) :: zamsk ! 1 if advection of concentration, 0 if advection of other tracers |
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[10425] | 104 | REAL(wp) :: zdt |
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[10910] | 105 | REAL(wp), DIMENSION(1) :: zcflprv, zcflnow ! for global communication |
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[10439] | 106 | REAL(wp), DIMENSION(jpi,jpj) :: zudy, zvdx, zcu_box, zcv_box |
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| 107 | REAL(wp), DIMENSION(jpi,jpj) :: zati1, zati2 |
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[10910] | 108 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zua_ho, zva_ho, zua_ups, zva_ups |
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| 109 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zuv_ho, zvv_ho, zuv_ups, zvv_ups |
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| 110 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: z1_ai, z1_aip, z1_vi, z1_vs |
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[10425] | 111 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zhvar |
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[10910] | 112 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zhi_max, zhs_max, zhip_max |
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[8586] | 113 | !!---------------------------------------------------------------------- |
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| 114 | ! |
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| 115 | IF( kt == nit000 .AND. lwp ) WRITE(numout,*) '-- ice_dyn_adv_umx: Ultimate-Macho advection scheme' |
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| 116 | ! |
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[10910] | 117 | ! --- Record max of the surrounding 9-pts ice thick. (for call Hbig) --- ! |
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| 118 | DO jl = 1, jpl |
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| 119 | DO jj = 2, jpjm1 |
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| 120 | DO ji = fs_2, fs_jpim1 |
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| 121 | zhip_max(ji,jj,jl) = MAX( epsi20, ph_ip(ji,jj,jl), ph_ip(ji+1,jj ,jl), ph_ip(ji ,jj+1,jl), & |
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| 122 | & ph_ip(ji-1,jj ,jl), ph_ip(ji ,jj-1,jl), & |
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| 123 | & ph_ip(ji+1,jj+1,jl), ph_ip(ji-1,jj-1,jl), & |
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| 124 | & ph_ip(ji+1,jj-1,jl), ph_ip(ji-1,jj+1,jl) ) |
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| 125 | zhi_max (ji,jj,jl) = MAX( epsi20, ph_i (ji,jj,jl), ph_i (ji+1,jj ,jl), ph_i (ji ,jj+1,jl), & |
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| 126 | & ph_i (ji-1,jj ,jl), ph_i (ji ,jj-1,jl), & |
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| 127 | & ph_i (ji+1,jj+1,jl), ph_i (ji-1,jj-1,jl), & |
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| 128 | & ph_i (ji+1,jj-1,jl), ph_i (ji-1,jj+1,jl) ) |
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| 129 | zhs_max (ji,jj,jl) = MAX( epsi20, ph_s (ji,jj,jl), ph_s (ji+1,jj ,jl), ph_s (ji ,jj+1,jl), & |
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| 130 | & ph_s (ji-1,jj ,jl), ph_s (ji ,jj-1,jl), & |
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| 131 | & ph_s (ji+1,jj+1,jl), ph_s (ji-1,jj-1,jl), & |
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| 132 | & ph_s (ji+1,jj-1,jl), ph_s (ji-1,jj+1,jl) ) |
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| 133 | END DO |
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| 134 | END DO |
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| 135 | END DO |
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| 136 | CALL lbc_lnk_multi( 'icedyn_adv_umx', zhi_max(:,:,:), 'T', 1., zhs_max(:,:,:), 'T', 1., zhip_max(:,:,:), 'T', 1. ) |
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| 137 | ! |
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| 138 | ! |
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| 139 | ! --- If ice drift is too fast, use subtime steps for advection (CFL test for stability) --- ! |
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| 140 | ! Note: the advection split is applied at the next time-step in order to avoid blocking global comm. |
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| 141 | ! this should not affect too much the stability |
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[10425] | 142 | zcflnow(1) = MAXVAL( ABS( pu_ice(:,:) ) * rdt_ice * r1_e1u(:,:) ) |
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| 143 | zcflnow(1) = MAX( zcflnow(1), MAXVAL( ABS( pv_ice(:,:) ) * rdt_ice * r1_e2v(:,:) ) ) |
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| 144 | |
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| 145 | ! non-blocking global communication send zcflnow and receive zcflprv |
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| 146 | CALL mpp_delay_max( 'icedyn_adv_umx', 'cflice', zcflnow(:), zcflprv(:), kt == nitend - nn_fsbc + 1 ) |
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[8586] | 147 | |
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[10425] | 148 | IF( zcflprv(1) > .5 ) THEN ; icycle = 2 |
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| 149 | ELSE ; icycle = 1 |
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[8586] | 150 | ENDIF |
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[10413] | 151 | zdt = rdt_ice / REAL(icycle) |
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[8586] | 152 | |
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| 153 | ! --- transport --- ! |
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| 154 | zudy(:,:) = pu_ice(:,:) * e2u(:,:) |
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| 155 | zvdx(:,:) = pv_ice(:,:) * e1v(:,:) |
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| 156 | |
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| 157 | ! --- define velocity for advection: u*grad(H) --- ! |
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| 158 | DO jj = 2, jpjm1 |
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| 159 | DO ji = fs_2, fs_jpim1 |
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| 160 | IF ( pu_ice(ji,jj) * pu_ice(ji-1,jj) <= 0._wp ) THEN ; zcu_box(ji,jj) = 0._wp |
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| 161 | ELSEIF( pu_ice(ji,jj) > 0._wp ) THEN ; zcu_box(ji,jj) = pu_ice(ji-1,jj) |
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| 162 | ELSE ; zcu_box(ji,jj) = pu_ice(ji ,jj) |
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| 163 | ENDIF |
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| 164 | |
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| 165 | IF ( pv_ice(ji,jj) * pv_ice(ji,jj-1) <= 0._wp ) THEN ; zcv_box(ji,jj) = 0._wp |
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| 166 | ELSEIF( pv_ice(ji,jj) > 0._wp ) THEN ; zcv_box(ji,jj) = pv_ice(ji,jj-1) |
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| 167 | ELSE ; zcv_box(ji,jj) = pv_ice(ji,jj ) |
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| 168 | ENDIF |
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| 169 | END DO |
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| 170 | END DO |
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| 171 | |
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| 172 | !---------------! |
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| 173 | !== advection ==! |
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| 174 | !---------------! |
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[10413] | 175 | DO jt = 1, icycle |
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| 176 | |
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[10439] | 177 | ! record at_i before advection (for open water) |
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| 178 | zati1(:,:) = SUM( pa_i(:,:,:), dim=3 ) |
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[10413] | 179 | |
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[10439] | 180 | ! inverse of A and Ap |
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[10425] | 181 | WHERE( pa_i(:,:,:) >= epsi20 ) ; z1_ai(:,:,:) = 1._wp / pa_i(:,:,:) |
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| 182 | ELSEWHERE ; z1_ai(:,:,:) = 0. |
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| 183 | END WHERE |
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| 184 | WHERE( pa_ip(:,:,:) >= epsi20 ) ; z1_aip(:,:,:) = 1._wp / pa_ip(:,:,:) |
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| 185 | ELSEWHERE ; z1_aip(:,:,:) = 0. |
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| 186 | END WHERE |
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| 187 | ! |
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[10910] | 188 | ! set u*A=u for advection of A only |
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[10425] | 189 | DO jl = 1, jpl |
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| 190 | zua_ho(:,:,jl) = zudy(:,:) |
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| 191 | zva_ho(:,:,jl) = zvdx(:,:) |
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| 192 | END DO |
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[10910] | 193 | |
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| 194 | !== Ice area ==! |
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[10425] | 195 | zamsk = 1._wp |
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[10910] | 196 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
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| 197 | & pa_i, pa_i, zua_ups, zva_ups, zua_ho , zva_ho ) |
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[10425] | 198 | zamsk = 0._wp |
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[10910] | 199 | |
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| 200 | IF( .NOT. ll_advS ) THEN !-- advection form: uA * uHS / u |
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| 201 | !== Ice volume ==! |
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| 202 | zhvar(:,:,:) = pv_i(:,:,:) * z1_ai(:,:,:) |
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| 203 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
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| 204 | & zhvar, pv_i, zua_ups, zva_ups ) |
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| 205 | ! |
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| 206 | !== Snw volume ==! |
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| 207 | zhvar(:,:,:) = pv_s(:,:,:) * z1_ai(:,:,:) |
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| 208 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
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| 209 | & zhvar, pv_s, zua_ups, zva_ups ) |
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| 210 | ! |
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| 211 | !== Salt content ==! |
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| 212 | zhvar(:,:,:) = psv_i(:,:,:) * z1_ai(:,:,:) |
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| 213 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zua_ho , zva_ho , zcu_box, zcv_box, & |
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| 214 | & zhvar, psv_i, zua_ups, zva_ups ) |
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| 215 | ! |
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| 216 | !== Ice heat content ==! |
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| 217 | DO jk = 1, nlay_i |
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| 218 | zhvar(:,:,:) = pe_i(:,:,jk,:) * z1_ai(:,:,:) |
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| 219 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho, zva_ho, zcu_box, zcv_box, & |
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| 220 | & zhvar, pe_i(:,:,jk,:), zua_ups, zva_ups ) |
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| 221 | END DO |
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| 222 | ! |
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| 223 | !== Snw heat content ==! |
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| 224 | DO jk = 1, nlay_s |
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| 225 | zhvar(:,:,:) = pe_s(:,:,jk,:) * z1_ai(:,:,:) |
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| 226 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho, zva_ho, zcu_box, zcv_box, & |
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| 227 | & zhvar, pe_s(:,:,jk,:), zua_ups, zva_ups ) |
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| 228 | END DO |
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| 229 | ! |
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| 230 | ELSE !-- advection form: uV * uS / u |
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| 231 | ! inverse of Vi |
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| 232 | WHERE( pv_i(:,:,:) >= epsi20 ) ; z1_vi(:,:,:) = 1._wp / pv_i(:,:,:) |
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| 233 | ELSEWHERE ; z1_vi(:,:,:) = 0. |
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| 234 | END WHERE |
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| 235 | ! inverse of Vs |
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| 236 | WHERE( pv_s(:,:,:) >= epsi20 ) ; z1_vs(:,:,:) = 1._wp / pv_s(:,:,:) |
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| 237 | ELSEWHERE ; z1_vs(:,:,:) = 0. |
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| 238 | END WHERE |
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| 239 | ! |
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| 240 | ! It is important to first calculate the ice fields and then the snow fields (because we use the same arrays) |
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| 241 | ! |
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| 242 | !== Ice volume ==! |
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| 243 | zuv_ups = zua_ups |
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| 244 | zvv_ups = zva_ups |
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| 245 | zhvar(:,:,:) = pv_i(:,:,:) * z1_ai(:,:,:) |
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| 246 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
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| 247 | & zhvar, pv_i, zuv_ups, zvv_ups, zuv_ho , zvv_ho ) |
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| 248 | ! |
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| 249 | !== Salt content ==! |
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| 250 | zhvar(:,:,:) = psv_i(:,:,:) * z1_vi(:,:,:) |
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| 251 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zuv_ho , zvv_ho , zcu_box, zcv_box, & |
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| 252 | & zhvar, psv_i, zuv_ups, zvv_ups ) |
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| 253 | ! |
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| 254 | !== Ice heat content ==! |
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| 255 | DO jk = 1, nlay_i |
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| 256 | zhvar(:,:,:) = pe_i(:,:,jk,:) * z1_vi(:,:,:) |
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| 257 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zuv_ho, zvv_ho, zcu_box, zcv_box, & |
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| 258 | & zhvar, pe_i(:,:,jk,:), zuv_ups, zvv_ups ) |
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| 259 | END DO |
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| 260 | ! |
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| 261 | !== Snow volume ==! |
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| 262 | zuv_ups = zua_ups |
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| 263 | zvv_ups = zva_ups |
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| 264 | zhvar(:,:,:) = pv_s(:,:,:) * z1_ai(:,:,:) |
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| 265 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
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| 266 | & zhvar, pv_s, zuv_ups, zvv_ups, zuv_ho , zvv_ho ) |
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| 267 | ! |
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| 268 | !== Snw heat content ==! |
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| 269 | DO jk = 1, nlay_s |
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| 270 | zhvar(:,:,:) = pe_s(:,:,jk,:) * z1_vs(:,:,:) |
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| 271 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zuv_ho, zvv_ho, zcu_box, zcv_box, & |
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| 272 | & zhvar, pe_s(:,:,jk,:), zuv_ups, zvv_ups ) |
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| 273 | END DO |
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| 274 | ! |
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| 275 | ENDIF |
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[10425] | 276 | ! |
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[10910] | 277 | !== Ice age ==! |
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| 278 | IF( iom_use('iceage') .OR. iom_use('iceage_cat') ) THEN |
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[10785] | 279 | ! clem: in theory we should use the formulation below to advect the ice age, but the code is unable to deal with |
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| 280 | ! fields that do not depend on volume (here oa_i depends on concentration). It creates abnormal ages that |
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| 281 | ! spread into the domain. Therefore we cheat and consider that ice age should be advected as ice concentration |
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| 282 | !!zhvar(:,:,:) = poa_i(:,:,:) * z1_ai(:,:,:) |
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| 283 | !!CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zua_ho, zva_ho, zcu_box, zcv_box, zhvar, poa_i ) |
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[10910] | 284 | ! set u*A=u for advection of ice age |
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[10785] | 285 | DO jl = 1, jpl |
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| 286 | zua_ho(:,:,jl) = zudy(:,:) |
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| 287 | zva_ho(:,:,jl) = zvdx(:,:) |
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| 288 | END DO |
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| 289 | zamsk = 1._wp |
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[10910] | 290 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zua_ho, zva_ho, zcu_box, zcv_box, & |
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| 291 | & poa_i, poa_i ) |
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[10785] | 292 | zamsk = 0._wp |
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| 293 | ENDIF |
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| 294 | ! |
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[10910] | 295 | !== melt ponds ==! |
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| 296 | IF ( ln_pnd_H12 ) THEN |
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| 297 | ! set u*A=u for advection of Ap only |
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[10425] | 298 | DO jl = 1, jpl |
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| 299 | zua_ho(:,:,jl) = zudy(:,:) |
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| 300 | zva_ho(:,:,jl) = zvdx(:,:) |
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[8586] | 301 | END DO |
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[10910] | 302 | ! fraction |
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[10425] | 303 | zamsk = 1._wp |
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[10910] | 304 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zua_ho , zva_ho , zcu_box, zcv_box, & |
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| 305 | & pa_ip, pa_ip, zua_ups, zva_ups, zua_ho , zva_ho ) |
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[10425] | 306 | zamsk = 0._wp |
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[10910] | 307 | ! volume |
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[10475] | 308 | zhvar(:,:,:) = pv_ip(:,:,:) * z1_aip(:,:,:) |
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[10910] | 309 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zua_ho , zva_ho , zcu_box, zcv_box, & |
---|
| 310 | & zhvar, pv_ip, zua_ups, zva_ups ) |
---|
[10425] | 311 | ENDIF |
---|
[10418] | 312 | ! |
---|
[10910] | 313 | !== Open water area ==! |
---|
[10439] | 314 | zati2(:,:) = SUM( pa_i(:,:,:), dim=3 ) |
---|
| 315 | DO jj = 2, jpjm1 |
---|
| 316 | DO ji = fs_2, fs_jpim1 |
---|
[10910] | 317 | pato_i(ji,jj) = pato_i(ji,jj) - ( zati2(ji,jj) - zati1(ji,jj) ) & |
---|
[10439] | 318 | & - ( zudy(ji,jj) - zudy(ji-1,jj) + zvdx(ji,jj) - zvdx(ji,jj-1) ) * r1_e1e2t(ji,jj) * zdt |
---|
[10413] | 319 | END DO |
---|
[10439] | 320 | END DO |
---|
| 321 | CALL lbc_lnk( 'icedyn_adv_umx', pato_i(:,:), 'T', 1. ) |
---|
[10418] | 322 | ! |
---|
[10910] | 323 | ! |
---|
| 324 | ! --- Ensure non-negative fields and in-bound thicknesses --- ! |
---|
| 325 | ! |
---|
| 326 | ! Remove negative values (conservation is ensured) |
---|
| 327 | ! (because advected fields are not perfectly bounded and tiny negative values can occur, e.g. -1.e-20) |
---|
| 328 | CALL ice_var_zapneg( pato_i, pv_i, pv_s, psv_i, poa_i, pa_i, pa_ip, pv_ip, pe_s, pe_i ) |
---|
| 329 | ! |
---|
| 330 | ! Make sure ice thickness is not too big |
---|
| 331 | ! (because ice thickness can be too large where ice concentration is very small) |
---|
| 332 | CALL Hbig( zhi_max, zhs_max, zhip_max, pv_i, pv_s, psv_i, poa_i, pa_i, pa_ip, pv_ip, pe_s, pe_i ) |
---|
| 333 | |
---|
[8586] | 334 | END DO |
---|
| 335 | ! |
---|
| 336 | END SUBROUTINE ice_dyn_adv_umx |
---|
[9929] | 337 | |
---|
[8586] | 338 | |
---|
[10910] | 339 | SUBROUTINE adv_umx( pamsk, kn_umx, jt, kt, pdt, pu, pv, puc, pvc, pubox, pvbox, & |
---|
| 340 | & pt, ptc, pua_ups, pva_ups, pua_ho, pva_ho ) |
---|
[8586] | 341 | !!---------------------------------------------------------------------- |
---|
| 342 | !! *** ROUTINE adv_umx *** |
---|
| 343 | !! |
---|
| 344 | !! ** Purpose : Compute the now trend due to total advection of |
---|
[10446] | 345 | !! tracers and add it to the general trend of tracer equations |
---|
[8586] | 346 | !! |
---|
[10910] | 347 | !! ** Method : - calculate upstream fluxes and upstream solution for tracers V/A(=H) etc |
---|
[10446] | 348 | !! - calculate tracer H at u and v points (Ultimate) |
---|
[10910] | 349 | !! - calculate the high order fluxes using alterning directions (Macho) |
---|
[10519] | 350 | !! - apply a limiter on the fluxes (nonosc_ice) |
---|
[10910] | 351 | !! - convert this tracer flux to a "volume" flux (uH -> uV) |
---|
| 352 | !! - apply a limiter a second time on the volumes fluxes (nonosc_ice) |
---|
| 353 | !! - calculate the high order solution for V |
---|
[8586] | 354 | !! |
---|
[10910] | 355 | !! ** Action : solve 3 equations => a) dA/dt = -div(uA) |
---|
| 356 | !! b) dV/dt = -div(uV) using dH/dt = -u.grad(H) |
---|
| 357 | !! c) dVS/dt = -div(uVS) using either dHS/dt = -u.grad(HS) or dS/dt = -u.grad(S) |
---|
[10446] | 358 | !! |
---|
[10910] | 359 | !! in eq. b), - fluxes uH are evaluated (with UMx) and limited with nonosc_ice. This step is necessary to get a good H. |
---|
| 360 | !! - then we convert this flux to a "volume" flux this way => uH * uA / u |
---|
| 361 | !! where uA is the flux from eq. a) |
---|
| 362 | !! this "volume" flux is also limited with nonosc_ice (otherwise overshoots can occur) |
---|
| 363 | !! - at last we estimate dV/dt = -div(uH * uA / u) |
---|
| 364 | !! |
---|
| 365 | !! in eq. c), one can solve the equation for S (ln_advS=T), then dVS/dt = -div(uV * uS / u) |
---|
| 366 | !! or for HS (ln_advS=F), then dVS/dt = -div(uA * uHS / u) |
---|
| 367 | !! |
---|
| 368 | !! ** Note : - this method can lead to tiny negative V (-1.e-20) => set it to 0 while conserving mass etc. |
---|
| 369 | !! - At the ice edge, Ultimate scheme can lead to: |
---|
| 370 | !! 1) negative interpolated tracers at u-v points |
---|
| 371 | !! 2) non-zero interpolated tracers at u-v points eventhough there is no ice and velocity is outward |
---|
| 372 | !! Solution for 1): apply an upstream scheme when it occurs. A better solution would be to degrade the order of |
---|
| 373 | !! the scheme automatically by applying a mask of the ice cover inside Ultimate (not done). |
---|
| 374 | !! Solution for 2): we set it to 0 in this case |
---|
[10446] | 375 | !! - Eventhough 1D tests give very good results (typically the one from Schar & Smolarkiewiecz), the 2D is less good. |
---|
| 376 | !! Large values of H can appear for very small ice concentration, and when it does it messes the things up since we |
---|
[10910] | 377 | !! work on H (and not V). It is partly related to the multi-category approach |
---|
[10446] | 378 | !! Therefore, after advection we limit the thickness to the largest value of the 9-points around (only if ice |
---|
[10910] | 379 | !! concentration is small). Since we do not limit S and T, large values can occur at the edge but it does not really matter |
---|
| 380 | !! since sv_i and e_i are still good. |
---|
[8586] | 381 | !!---------------------------------------------------------------------- |
---|
[10910] | 382 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 383 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
| 384 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
| 385 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
| 386 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 387 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu , pv ! 2 ice velocity components => u*e2 |
---|
| 388 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: puc , pvc ! 2 ice velocity components => u*e2 or u*a*e2u |
---|
| 389 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pubox, pvbox ! upstream velocity |
---|
| 390 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pt ! tracer field |
---|
| 391 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: ptc ! tracer content field |
---|
| 392 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT(inout), OPTIONAL :: pua_ups, pva_ups ! upstream u*a fluxes |
---|
| 393 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out), OPTIONAL :: pua_ho, pva_ho ! high order u*a fluxes |
---|
[8586] | 394 | ! |
---|
[10425] | 395 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[8586] | 396 | REAL(wp) :: ztra ! local scalar |
---|
[10446] | 397 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zfu_ho , zfv_ho , zpt |
---|
[10439] | 398 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zfu_ups, zfv_ups, zt_ups |
---|
[8586] | 399 | !!---------------------------------------------------------------------- |
---|
| 400 | ! |
---|
[10446] | 401 | ! Upstream (_ups) fluxes |
---|
| 402 | ! ----------------------- |
---|
| 403 | CALL upstream( pamsk, jt, kt, pdt, pt, pu, pv, zt_ups, zfu_ups, zfv_ups ) |
---|
| 404 | |
---|
| 405 | ! High order (_ho) fluxes |
---|
| 406 | ! ----------------------- |
---|
| 407 | SELECT CASE( kn_umx ) |
---|
| 408 | ! |
---|
| 409 | CASE ( 20 ) !== centered second order ==! |
---|
| 410 | ! |
---|
[10475] | 411 | CALL cen2( pamsk, jt, kt, pdt, pt, pu, pv, zt_ups, zfu_ups, zfv_ups, zfu_ho, zfv_ho ) |
---|
[10446] | 412 | ! |
---|
| 413 | CASE ( 1:5 ) !== 1st to 5th order ULTIMATE-MACHO scheme ==! |
---|
| 414 | ! |
---|
[10475] | 415 | CALL macho( pamsk, kn_umx, jt, kt, pdt, pt, pu, pv, pubox, pvbox, zt_ups, zfu_ups, zfv_ups, zfu_ho, zfv_ho ) |
---|
[10446] | 416 | ! |
---|
| 417 | END SELECT |
---|
[10439] | 418 | ! |
---|
[10446] | 419 | ! --ho --ho |
---|
| 420 | ! new fluxes = u*H * u*a / u |
---|
| 421 | ! ---------------------------- |
---|
[10475] | 422 | IF( pamsk == 0._wp ) THEN |
---|
[10446] | 423 | DO jl = 1, jpl |
---|
| 424 | DO jj = 1, jpjm1 |
---|
| 425 | DO ji = 1, fs_jpim1 |
---|
[10910] | 426 | IF( ABS( pu(ji,jj) ) > epsi10 ) THEN |
---|
| 427 | zfu_ho (ji,jj,jl) = zfu_ho (ji,jj,jl) * puc (ji,jj,jl) / pu(ji,jj) |
---|
| 428 | zfu_ups(ji,jj,jl) = zfu_ups(ji,jj,jl) * pua_ups(ji,jj,jl) / pu(ji,jj) |
---|
[10446] | 429 | ELSE |
---|
| 430 | zfu_ho (ji,jj,jl) = 0._wp |
---|
| 431 | zfu_ups(ji,jj,jl) = 0._wp |
---|
| 432 | ENDIF |
---|
| 433 | ! |
---|
[10910] | 434 | IF( ABS( pv(ji,jj) ) > epsi10 ) THEN |
---|
| 435 | zfv_ho (ji,jj,jl) = zfv_ho (ji,jj,jl) * pvc (ji,jj,jl) / pv(ji,jj) |
---|
| 436 | zfv_ups(ji,jj,jl) = zfv_ups(ji,jj,jl) * pva_ups(ji,jj,jl) / pv(ji,jj) |
---|
[10446] | 437 | ELSE |
---|
| 438 | zfv_ho (ji,jj,jl) = 0._wp |
---|
| 439 | zfv_ups(ji,jj,jl) = 0._wp |
---|
| 440 | ENDIF |
---|
| 441 | END DO |
---|
| 442 | END DO |
---|
| 443 | END DO |
---|
[10910] | 444 | |
---|
| 445 | ! the new "volume" fluxes must also be "flux corrected" |
---|
| 446 | ! thus we calculate the upstream solution and apply a limiter again |
---|
| 447 | DO jl = 1, jpl |
---|
| 448 | DO jj = 2, jpjm1 |
---|
| 449 | DO ji = fs_2, fs_jpim1 |
---|
| 450 | ztra = - ( zfu_ups(ji,jj,jl) - zfu_ups(ji-1,jj,jl) + zfv_ups(ji,jj,jl) - zfv_ups(ji,jj-1,jl) ) |
---|
| 451 | ! |
---|
| 452 | zt_ups(ji,jj,jl) = ( ptc(ji,jj,jl) + ztra * r1_e1e2t(ji,jj) * pdt ) * tmask(ji,jj,1) |
---|
| 453 | END DO |
---|
| 454 | END DO |
---|
| 455 | END DO |
---|
| 456 | CALL lbc_lnk( 'icedyn_adv_umx', zt_ups, 'T', 1. ) |
---|
| 457 | ! |
---|
| 458 | IF ( kn_limiter == 1 ) THEN |
---|
| 459 | CALL nonosc_ice( 1._wp, pdt, pu, pv, ptc, zt_ups, zfu_ups, zfv_ups, zfu_ho, zfv_ho ) |
---|
| 460 | ELSEIF( kn_limiter == 2 .OR. kn_limiter == 3 ) THEN |
---|
| 461 | CALL limiter_x( pdt, pu, ptc, zfu_ups, zfu_ho ) |
---|
| 462 | CALL limiter_y( pdt, pv, ptc, zfv_ups, zfv_ho ) |
---|
| 463 | ENDIF |
---|
| 464 | ! |
---|
[10446] | 465 | ENDIF |
---|
[10910] | 466 | ! --ho --ups |
---|
| 467 | ! in case of advection of A: output u*a and u*a |
---|
| 468 | ! ----------------------------------------------- |
---|
[10446] | 469 | IF( PRESENT( pua_ho ) ) THEN |
---|
| 470 | DO jl = 1, jpl |
---|
| 471 | DO jj = 1, jpjm1 |
---|
| 472 | DO ji = 1, fs_jpim1 |
---|
[10910] | 473 | pua_ho (ji,jj,jl) = zfu_ho (ji,jj,jl) ; pva_ho (ji,jj,jl) = zfv_ho (ji,jj,jl) |
---|
| 474 | pua_ups(ji,jj,jl) = zfu_ups(ji,jj,jl) ; pva_ups(ji,jj,jl) = zfv_ups(ji,jj,jl) |
---|
| 475 | END DO |
---|
[10446] | 476 | END DO |
---|
| 477 | END DO |
---|
| 478 | ENDIF |
---|
| 479 | ! |
---|
| 480 | ! final trend with corrected fluxes |
---|
| 481 | ! --------------------------------- |
---|
| 482 | DO jl = 1, jpl |
---|
| 483 | DO jj = 2, jpjm1 |
---|
| 484 | DO ji = fs_2, fs_jpim1 |
---|
| 485 | ztra = - ( zfu_ho(ji,jj,jl) - zfu_ho(ji-1,jj,jl) + zfv_ho(ji,jj,jl) - zfv_ho(ji,jj-1,jl) ) |
---|
| 486 | ! |
---|
| 487 | ptc(ji,jj,jl) = ( ptc(ji,jj,jl) + ztra * r1_e1e2t(ji,jj) * pdt ) * tmask(ji,jj,1) |
---|
| 488 | END DO |
---|
| 489 | END DO |
---|
| 490 | END DO |
---|
| 491 | CALL lbc_lnk( 'icedyn_adv_umx', ptc, 'T', 1. ) |
---|
| 492 | ! |
---|
| 493 | END SUBROUTINE adv_umx |
---|
| 494 | |
---|
| 495 | |
---|
| 496 | SUBROUTINE upstream( pamsk, jt, kt, pdt, pt, pu, pv, pt_ups, pfu_ups, pfv_ups ) |
---|
| 497 | !!--------------------------------------------------------------------- |
---|
| 498 | !! *** ROUTINE upstream *** |
---|
| 499 | !! |
---|
| 500 | !! ** Purpose : compute the upstream fluxes and upstream guess of tracer |
---|
| 501 | !!---------------------------------------------------------------------- |
---|
| 502 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 503 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
| 504 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
| 505 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 506 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
| 507 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu, pv ! 2 ice velocity components |
---|
| 508 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_ups ! upstream guess of tracer |
---|
| 509 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ups, pfv_ups ! upstream fluxes |
---|
| 510 | ! |
---|
| 511 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
| 512 | REAL(wp) :: ztra ! local scalar |
---|
| 513 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zpt |
---|
| 514 | !!---------------------------------------------------------------------- |
---|
| 515 | |
---|
[10439] | 516 | IF( .NOT. ll_upsxy ) THEN !** no alternate directions **! |
---|
[10446] | 517 | ! |
---|
[10425] | 518 | DO jl = 1, jpl |
---|
| 519 | DO jj = 1, jpjm1 |
---|
| 520 | DO ji = 1, fs_jpim1 |
---|
[10446] | 521 | pfu_ups(ji,jj,jl) = MAX( pu(ji,jj), 0._wp ) * pt(ji,jj,jl) + MIN( pu(ji,jj), 0._wp ) * pt(ji+1,jj,jl) |
---|
| 522 | pfv_ups(ji,jj,jl) = MAX( pv(ji,jj), 0._wp ) * pt(ji,jj,jl) + MIN( pv(ji,jj), 0._wp ) * pt(ji,jj+1,jl) |
---|
[10425] | 523 | END DO |
---|
[10413] | 524 | END DO |
---|
| 525 | END DO |
---|
[10446] | 526 | ! |
---|
[10439] | 527 | ELSE !** alternate directions **! |
---|
[10413] | 528 | ! |
---|
| 529 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
---|
[10439] | 530 | ! |
---|
| 531 | DO jl = 1, jpl !-- flux in x-direction |
---|
[10425] | 532 | DO jj = 1, jpjm1 |
---|
| 533 | DO ji = 1, fs_jpim1 |
---|
[10446] | 534 | pfu_ups(ji,jj,jl) = MAX( pu(ji,jj), 0._wp ) * pt(ji,jj,jl) + MIN( pu(ji,jj), 0._wp ) * pt(ji+1,jj,jl) |
---|
[10425] | 535 | END DO |
---|
[10413] | 536 | END DO |
---|
| 537 | END DO |
---|
[10439] | 538 | ! |
---|
| 539 | DO jl = 1, jpl !-- first guess of tracer from u-flux |
---|
[10425] | 540 | DO jj = 2, jpjm1 |
---|
[10439] | 541 | DO ji = fs_2, fs_jpim1 |
---|
[10446] | 542 | ztra = - ( pfu_ups(ji,jj,jl) - pfu_ups(ji-1,jj,jl) ) & |
---|
| 543 | & + ( pu (ji,jj ) - pu (ji-1,jj ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 544 | ! |
---|
| 545 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
[10425] | 546 | END DO |
---|
[10413] | 547 | END DO |
---|
| 548 | END DO |
---|
[10425] | 549 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
---|
[8586] | 550 | ! |
---|
[10439] | 551 | DO jl = 1, jpl !-- flux in y-direction |
---|
[10425] | 552 | DO jj = 1, jpjm1 |
---|
| 553 | DO ji = 1, fs_jpim1 |
---|
[10446] | 554 | pfv_ups(ji,jj,jl) = MAX( pv(ji,jj), 0._wp ) * zpt(ji,jj,jl) + MIN( pv(ji,jj), 0._wp ) * zpt(ji,jj+1,jl) |
---|
[10425] | 555 | END DO |
---|
[10413] | 556 | END DO |
---|
| 557 | END DO |
---|
[10439] | 558 | ! |
---|
[10413] | 559 | ELSE !== even ice time step: adv_y then adv_x ==! |
---|
[10439] | 560 | ! |
---|
| 561 | DO jl = 1, jpl !-- flux in y-direction |
---|
[10425] | 562 | DO jj = 1, jpjm1 |
---|
| 563 | DO ji = 1, fs_jpim1 |
---|
[10446] | 564 | pfv_ups(ji,jj,jl) = MAX( pv(ji,jj), 0._wp ) * pt(ji,jj,jl) + MIN( pv(ji,jj), 0._wp ) * pt(ji,jj+1,jl) |
---|
[10425] | 565 | END DO |
---|
[10413] | 566 | END DO |
---|
| 567 | END DO |
---|
[10439] | 568 | ! |
---|
| 569 | DO jl = 1, jpl !-- first guess of tracer from v-flux |
---|
[10425] | 570 | DO jj = 2, jpjm1 |
---|
[10439] | 571 | DO ji = fs_2, fs_jpim1 |
---|
[10446] | 572 | ztra = - ( pfv_ups(ji,jj,jl) - pfv_ups(ji,jj-1,jl) ) & |
---|
| 573 | & + ( pv (ji,jj ) - pv (ji,jj-1 ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 574 | ! |
---|
| 575 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
[10425] | 576 | END DO |
---|
| 577 | END DO |
---|
[10413] | 578 | END DO |
---|
[10425] | 579 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
---|
[10413] | 580 | ! |
---|
[10439] | 581 | DO jl = 1, jpl !-- flux in x-direction |
---|
[10425] | 582 | DO jj = 1, jpjm1 |
---|
| 583 | DO ji = 1, fs_jpim1 |
---|
[10446] | 584 | pfu_ups(ji,jj,jl) = MAX( pu(ji,jj), 0._wp ) * zpt(ji,jj,jl) + MIN( pu(ji,jj), 0._wp ) * zpt(ji+1,jj,jl) |
---|
[10425] | 585 | END DO |
---|
[10413] | 586 | END DO |
---|
| 587 | END DO |
---|
| 588 | ! |
---|
| 589 | ENDIF |
---|
| 590 | |
---|
| 591 | ENDIF |
---|
[10439] | 592 | ! |
---|
| 593 | DO jl = 1, jpl !-- after tracer with upstream scheme |
---|
[10425] | 594 | DO jj = 2, jpjm1 |
---|
| 595 | DO ji = fs_2, fs_jpim1 |
---|
[10446] | 596 | ztra = - ( pfu_ups(ji,jj,jl) - pfu_ups(ji-1,jj ,jl) & |
---|
| 597 | & + pfv_ups(ji,jj,jl) - pfv_ups(ji ,jj-1,jl) ) & |
---|
| 598 | & + ( pu (ji,jj ) - pu (ji-1,jj ) & |
---|
| 599 | & + pv (ji,jj ) - pv (ji ,jj-1 ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 600 | ! |
---|
[10475] | 601 | pt_ups(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
[10425] | 602 | END DO |
---|
[10413] | 603 | END DO |
---|
[8586] | 604 | END DO |
---|
[10446] | 605 | CALL lbc_lnk( 'icedyn_adv_umx', pt_ups, 'T', 1. ) |
---|
[10413] | 606 | |
---|
[10446] | 607 | END SUBROUTINE upstream |
---|
[8586] | 608 | |
---|
[10446] | 609 | |
---|
[10475] | 610 | SUBROUTINE cen2( pamsk, jt, kt, pdt, pt, pu, pv, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[8586] | 611 | !!--------------------------------------------------------------------- |
---|
[10446] | 612 | !! *** ROUTINE cen2 *** |
---|
[8586] | 613 | !! |
---|
[10446] | 614 | !! ** Purpose : compute the high order fluxes using a centered |
---|
| 615 | !! second order scheme |
---|
[8586] | 616 | !!---------------------------------------------------------------------- |
---|
[10439] | 617 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 618 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
| 619 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
| 620 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 621 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
| 622 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu, pv ! 2 ice velocity components |
---|
[10446] | 623 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt_ups ! upstream guess of tracer |
---|
| 624 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pfu_ups, pfv_ups ! upstream fluxes |
---|
[10425] | 625 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ho, pfv_ho ! high order fluxes |
---|
[8586] | 626 | ! |
---|
[10425] | 627 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[10446] | 628 | REAL(wp) :: ztra ! local scalar |
---|
| 629 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zpt |
---|
[8586] | 630 | !!---------------------------------------------------------------------- |
---|
| 631 | ! |
---|
[10439] | 632 | IF( .NOT.ll_hoxy ) THEN !** no alternate directions **! |
---|
[8586] | 633 | ! |
---|
[10425] | 634 | DO jl = 1, jpl |
---|
| 635 | DO jj = 1, jpjm1 |
---|
| 636 | DO ji = 1, fs_jpim1 |
---|
[10475] | 637 | pfu_ho(ji,jj,jl) = 0.5_wp * pu(ji,jj) * ( pt(ji,jj,jl) + pt(ji+1,jj ,jl) ) |
---|
| 638 | pfv_ho(ji,jj,jl) = 0.5_wp * pv(ji,jj) * ( pt(ji,jj,jl) + pt(ji ,jj+1,jl) ) |
---|
[10425] | 639 | END DO |
---|
[8586] | 640 | END DO |
---|
| 641 | END DO |
---|
[10475] | 642 | ! |
---|
[10413] | 643 | IF ( kn_limiter == 1 ) THEN |
---|
[10519] | 644 | CALL nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[10446] | 645 | ELSEIF( kn_limiter == 2 .OR. kn_limiter == 3 ) THEN |
---|
| 646 | CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
| 647 | CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 648 | ENDIF |
---|
[8586] | 649 | ! |
---|
[10439] | 650 | ELSE !** alternate directions **! |
---|
[8586] | 651 | ! |
---|
[10413] | 652 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
---|
| 653 | ! |
---|
[10439] | 654 | DO jl = 1, jpl !-- flux in x-direction |
---|
[10425] | 655 | DO jj = 1, jpjm1 |
---|
| 656 | DO ji = 1, fs_jpim1 |
---|
[10475] | 657 | pfu_ho(ji,jj,jl) = 0.5_wp * pu(ji,jj) * ( pt(ji,jj,jl) + pt(ji+1,jj,jl) ) |
---|
[10425] | 658 | END DO |
---|
[10413] | 659 | END DO |
---|
| 660 | END DO |
---|
[10446] | 661 | IF( kn_limiter == 2 .OR. kn_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
[10413] | 662 | |
---|
[10439] | 663 | DO jl = 1, jpl !-- first guess of tracer from u-flux |
---|
[10425] | 664 | DO jj = 2, jpjm1 |
---|
[10439] | 665 | DO ji = fs_2, fs_jpim1 |
---|
[10446] | 666 | ztra = - ( pfu_ho(ji,jj,jl) - pfu_ho(ji-1,jj,jl) ) & |
---|
| 667 | & + ( pu (ji,jj ) - pu (ji-1,jj ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 668 | ! |
---|
| 669 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
[10425] | 670 | END DO |
---|
[10413] | 671 | END DO |
---|
| 672 | END DO |
---|
[10446] | 673 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
---|
[10413] | 674 | |
---|
[10439] | 675 | DO jl = 1, jpl !-- flux in y-direction |
---|
[10425] | 676 | DO jj = 1, jpjm1 |
---|
| 677 | DO ji = 1, fs_jpim1 |
---|
[10475] | 678 | pfv_ho(ji,jj,jl) = 0.5_wp * pv(ji,jj) * ( zpt(ji,jj,jl) + zpt(ji,jj+1,jl) ) |
---|
[10425] | 679 | END DO |
---|
[10413] | 680 | END DO |
---|
| 681 | END DO |
---|
[10446] | 682 | IF( kn_limiter == 2 .OR. kn_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 683 | |
---|
| 684 | ELSE !== even ice time step: adv_y then adv_x ==! |
---|
| 685 | ! |
---|
[10439] | 686 | DO jl = 1, jpl !-- flux in y-direction |
---|
[10425] | 687 | DO jj = 1, jpjm1 |
---|
| 688 | DO ji = 1, fs_jpim1 |
---|
[10475] | 689 | pfv_ho(ji,jj,jl) = 0.5_wp * pv(ji,jj) * ( pt(ji,jj,jl) + pt(ji,jj+1,jl) ) |
---|
[10425] | 690 | END DO |
---|
[10413] | 691 | END DO |
---|
| 692 | END DO |
---|
[10446] | 693 | IF( kn_limiter == 2 .OR. kn_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 694 | ! |
---|
[10439] | 695 | DO jl = 1, jpl !-- first guess of tracer from v-flux |
---|
[10425] | 696 | DO jj = 2, jpjm1 |
---|
[10439] | 697 | DO ji = fs_2, fs_jpim1 |
---|
[10446] | 698 | ztra = - ( pfv_ho(ji,jj,jl) - pfv_ho(ji,jj-1,jl) ) & |
---|
| 699 | & + ( pv (ji,jj ) - pv (ji,jj-1 ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 700 | ! |
---|
| 701 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
[10425] | 702 | END DO |
---|
[10413] | 703 | END DO |
---|
| 704 | END DO |
---|
[10446] | 705 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
---|
[10413] | 706 | ! |
---|
[10439] | 707 | DO jl = 1, jpl !-- flux in x-direction |
---|
[10425] | 708 | DO jj = 1, jpjm1 |
---|
| 709 | DO ji = 1, fs_jpim1 |
---|
[10475] | 710 | pfu_ho(ji,jj,jl) = 0.5_wp * pu(ji,jj) * ( zpt(ji,jj,jl) + zpt(ji+1,jj,jl) ) |
---|
[10425] | 711 | END DO |
---|
[10413] | 712 | END DO |
---|
| 713 | END DO |
---|
[10446] | 714 | IF( kn_limiter == 2 .OR. kn_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
[10413] | 715 | |
---|
| 716 | ENDIF |
---|
[10519] | 717 | IF( kn_limiter == 1 ) CALL nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[10413] | 718 | |
---|
| 719 | ENDIF |
---|
| 720 | |
---|
| 721 | END SUBROUTINE cen2 |
---|
| 722 | |
---|
| 723 | |
---|
[10475] | 724 | SUBROUTINE macho( pamsk, kn_umx, jt, kt, pdt, pt, pu, pv, pubox, pvbox, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[10413] | 725 | !!--------------------------------------------------------------------- |
---|
| 726 | !! *** ROUTINE macho *** |
---|
| 727 | !! |
---|
[10446] | 728 | !! ** Purpose : compute the high order fluxes using Ultimate-Macho scheme |
---|
[10413] | 729 | !! |
---|
[10446] | 730 | !! ** Method : ... |
---|
[10413] | 731 | !! |
---|
| 732 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
| 733 | !!---------------------------------------------------------------------- |
---|
[10439] | 734 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 735 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
| 736 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
| 737 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
| 738 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 739 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
| 740 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu, pv ! 2 ice velocity components |
---|
| 741 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pubox, pvbox ! upstream velocity |
---|
[10446] | 742 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt_ups ! upstream guess of tracer |
---|
| 743 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pfu_ups, pfv_ups ! upstream fluxes |
---|
[10425] | 744 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ho, pfv_ho ! high order fluxes |
---|
[10413] | 745 | ! |
---|
[10425] | 746 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[10446] | 747 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zt_u, zt_v, zpt |
---|
[10413] | 748 | !!---------------------------------------------------------------------- |
---|
| 749 | ! |
---|
| 750 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
---|
[8586] | 751 | ! |
---|
[10413] | 752 | ! !-- ultimate interpolation of pt at u-point --! |
---|
[10910] | 753 | CALL ultimate_x( pamsk, kn_umx, pdt, pt, pu, zt_u, pfu_ho ) |
---|
[10413] | 754 | ! !-- limiter in x --! |
---|
[10446] | 755 | IF( kn_limiter == 2 .OR. kn_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
| 756 | ! !-- advective form update in zpt --! |
---|
[10439] | 757 | DO jl = 1, jpl |
---|
| 758 | DO jj = 2, jpjm1 |
---|
| 759 | DO ji = fs_2, fs_jpim1 |
---|
[10446] | 760 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) - ( pubox(ji,jj ) * ( zt_u(ji,jj,jl) - zt_u(ji-1,jj,jl) ) * r1_e1t (ji,jj) & |
---|
| 761 | & + pt (ji,jj,jl) * ( pu (ji,jj ) - pu (ji-1,jj ) ) * r1_e1e2t(ji,jj) & |
---|
| 762 | & * pamsk & |
---|
[10910] | 763 | & ) * pdt ) * tmask(ji,jj,1) |
---|
| 764 | !!clem test |
---|
| 765 | !!zpt(ji,jj,jl) = MAX( 0._wp, zpt(ji,jj,jl) ) |
---|
| 766 | !!clem test |
---|
[10413] | 767 | END DO |
---|
[8586] | 768 | END DO |
---|
[10439] | 769 | END DO |
---|
[10446] | 770 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
---|
[8586] | 771 | ! |
---|
[10413] | 772 | ! !-- ultimate interpolation of pt at v-point --! |
---|
| 773 | IF( ll_hoxy ) THEN |
---|
[10910] | 774 | CALL ultimate_y( pamsk, kn_umx, pdt, zpt, pv, zt_v, pfv_ho ) |
---|
[10413] | 775 | ELSE |
---|
[10910] | 776 | CALL ultimate_y( pamsk, kn_umx, pdt, pt , pv, zt_v, pfv_ho ) |
---|
[10413] | 777 | ENDIF |
---|
| 778 | ! !-- limiter in y --! |
---|
[10446] | 779 | IF( kn_limiter == 2 .OR. kn_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 780 | ! |
---|
| 781 | ! |
---|
| 782 | ELSE !== even ice time step: adv_y then adv_x ==! |
---|
| 783 | ! |
---|
| 784 | ! !-- ultimate interpolation of pt at v-point --! |
---|
[10910] | 785 | CALL ultimate_y( pamsk, kn_umx, pdt, pt, pv, zt_v, pfv_ho ) |
---|
[10413] | 786 | ! !-- limiter in y --! |
---|
[10446] | 787 | IF( kn_limiter == 2 .OR. kn_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
| 788 | ! !-- advective form update in zpt --! |
---|
[10439] | 789 | DO jl = 1, jpl |
---|
| 790 | DO jj = 2, jpjm1 |
---|
| 791 | DO ji = fs_2, fs_jpim1 |
---|
[10446] | 792 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) - ( pvbox(ji,jj ) * ( zt_v(ji,jj,jl) - zt_v(ji,jj-1,jl) ) * r1_e2t (ji,jj) & |
---|
| 793 | & + pt (ji,jj,jl) * ( pv (ji,jj ) - pv (ji,jj-1 ) ) * r1_e1e2t(ji,jj) & |
---|
| 794 | & * pamsk & |
---|
| 795 | & ) * pdt ) * tmask(ji,jj,1) |
---|
[10910] | 796 | !!clem test |
---|
| 797 | !!zpt(ji,jj,jl) = MAX( 0._wp, zpt(ji,jj,jl) ) |
---|
| 798 | !!clem test |
---|
[10425] | 799 | END DO |
---|
[10413] | 800 | END DO |
---|
[10439] | 801 | END DO |
---|
[10446] | 802 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
---|
[10413] | 803 | ! |
---|
| 804 | ! !-- ultimate interpolation of pt at u-point --! |
---|
| 805 | IF( ll_hoxy ) THEN |
---|
[10910] | 806 | CALL ultimate_x( pamsk, kn_umx, pdt, zpt, pu, zt_u, pfu_ho ) |
---|
[10413] | 807 | ELSE |
---|
[10910] | 808 | CALL ultimate_x( pamsk, kn_umx, pdt, pt , pu, zt_u, pfu_ho ) |
---|
[10413] | 809 | ENDIF |
---|
| 810 | ! !-- limiter in x --! |
---|
[10446] | 811 | IF( kn_limiter == 2 .OR. kn_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
[10413] | 812 | ! |
---|
| 813 | ENDIF |
---|
| 814 | |
---|
[10519] | 815 | IF( kn_limiter == 1 ) CALL nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[8586] | 816 | ! |
---|
| 817 | END SUBROUTINE macho |
---|
| 818 | |
---|
| 819 | |
---|
[10910] | 820 | SUBROUTINE ultimate_x( pamsk, kn_umx, pdt, pt, pu, pt_u, pfu_ho ) |
---|
[8586] | 821 | !!--------------------------------------------------------------------- |
---|
| 822 | !! *** ROUTINE ultimate_x *** |
---|
| 823 | !! |
---|
[10446] | 824 | !! ** Purpose : compute tracer at u-points |
---|
[8586] | 825 | !! |
---|
[10446] | 826 | !! ** Method : ... |
---|
[8586] | 827 | !! |
---|
| 828 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
| 829 | !!---------------------------------------------------------------------- |
---|
[10910] | 830 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
[10439] | 831 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
| 832 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 833 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu ! ice i-velocity component |
---|
| 834 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
[10425] | 835 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_u ! tracer at u-point |
---|
| 836 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ho ! high order flux |
---|
[8586] | 837 | ! |
---|
[10425] | 838 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[10910] | 839 | REAL(wp) :: zcu, zdx2, zdx4, zvi_cen2 ! - - |
---|
[10425] | 840 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: ztu1, ztu2, ztu3, ztu4 |
---|
[8586] | 841 | !!---------------------------------------------------------------------- |
---|
| 842 | ! |
---|
| 843 | ! !-- Laplacian in i-direction --! |
---|
[10425] | 844 | DO jl = 1, jpl |
---|
| 845 | DO jj = 2, jpjm1 ! First derivative (gradient) |
---|
| 846 | DO ji = 1, fs_jpim1 |
---|
| 847 | ztu1(ji,jj,jl) = ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) * r1_e1u(ji,jj) * umask(ji,jj,1) |
---|
| 848 | END DO |
---|
| 849 | ! ! Second derivative (Laplacian) |
---|
| 850 | DO ji = fs_2, fs_jpim1 |
---|
| 851 | ztu2(ji,jj,jl) = ( ztu1(ji,jj,jl) - ztu1(ji-1,jj,jl) ) * r1_e1t(ji,jj) |
---|
| 852 | END DO |
---|
[8586] | 853 | END DO |
---|
| 854 | END DO |
---|
[10425] | 855 | CALL lbc_lnk( 'icedyn_adv_umx', ztu2, 'T', 1. ) |
---|
[8586] | 856 | ! |
---|
| 857 | ! !-- BiLaplacian in i-direction --! |
---|
[10425] | 858 | DO jl = 1, jpl |
---|
| 859 | DO jj = 2, jpjm1 ! Third derivative |
---|
| 860 | DO ji = 1, fs_jpim1 |
---|
| 861 | ztu3(ji,jj,jl) = ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) * r1_e1u(ji,jj) * umask(ji,jj,1) |
---|
| 862 | END DO |
---|
| 863 | ! ! Fourth derivative |
---|
| 864 | DO ji = fs_2, fs_jpim1 |
---|
| 865 | ztu4(ji,jj,jl) = ( ztu3(ji,jj,jl) - ztu3(ji-1,jj,jl) ) * r1_e1t(ji,jj) |
---|
| 866 | END DO |
---|
[8586] | 867 | END DO |
---|
| 868 | END DO |
---|
[10425] | 869 | CALL lbc_lnk( 'icedyn_adv_umx', ztu4, 'T', 1. ) |
---|
[8586] | 870 | ! |
---|
| 871 | ! |
---|
[10413] | 872 | SELECT CASE (kn_umx ) |
---|
[8586] | 873 | ! |
---|
| 874 | CASE( 1 ) !== 1st order central TIM ==! (Eq. 21) |
---|
| 875 | ! |
---|
[10425] | 876 | DO jl = 1, jpl |
---|
| 877 | DO jj = 1, jpjm1 |
---|
| 878 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
[10475] | 879 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj,jl) + pt(ji,jj,jl) & |
---|
| 880 | & - SIGN( 1._wp, pu(ji,jj) ) * ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) ) |
---|
[10425] | 881 | END DO |
---|
[8586] | 882 | END DO |
---|
| 883 | END DO |
---|
| 884 | ! |
---|
| 885 | CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23) |
---|
| 886 | ! |
---|
[10425] | 887 | DO jl = 1, jpl |
---|
| 888 | DO jj = 1, jpjm1 |
---|
| 889 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 890 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
| 891 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj,jl) + pt(ji,jj,jl) & |
---|
[10475] | 892 | & - zcu * ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) ) |
---|
[10425] | 893 | END DO |
---|
[8586] | 894 | END DO |
---|
| 895 | END DO |
---|
| 896 | ! |
---|
| 897 | CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24) |
---|
| 898 | ! |
---|
[10425] | 899 | DO jl = 1, jpl |
---|
| 900 | DO jj = 1, jpjm1 |
---|
| 901 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 902 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
| 903 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
[10439] | 904 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
[10446] | 905 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj,jl) + pt (ji,jj,jl) & |
---|
[10475] | 906 | & - zcu * ( pt (ji+1,jj,jl) - pt (ji,jj,jl) ) ) & |
---|
| 907 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj,jl) + ztu2(ji,jj,jl) & |
---|
[10446] | 908 | & - SIGN( 1._wp, zcu ) * ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) ) ) |
---|
[10425] | 909 | END DO |
---|
[8586] | 910 | END DO |
---|
| 911 | END DO |
---|
| 912 | ! |
---|
| 913 | CASE( 4 ) !== 4th order central TIM ==! (Eq. 27) |
---|
| 914 | ! |
---|
[10425] | 915 | DO jl = 1, jpl |
---|
| 916 | DO jj = 1, jpjm1 |
---|
| 917 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 918 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
| 919 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
[10439] | 920 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
[10475] | 921 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj,jl) + pt (ji,jj,jl) & |
---|
| 922 | & - zcu * ( pt (ji+1,jj,jl) - pt (ji,jj,jl) ) ) & |
---|
| 923 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj,jl) + ztu2(ji,jj,jl) & |
---|
| 924 | & - 0.5_wp * zcu * ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) ) ) |
---|
[10425] | 925 | END DO |
---|
[8586] | 926 | END DO |
---|
| 927 | END DO |
---|
| 928 | ! |
---|
| 929 | CASE( 5 ) !== 5th order central TIM ==! (Eq. 29) |
---|
| 930 | ! |
---|
[10425] | 931 | DO jl = 1, jpl |
---|
| 932 | DO jj = 1, jpjm1 |
---|
| 933 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 934 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
| 935 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
[10439] | 936 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
[10425] | 937 | zdx4 = zdx2 * zdx2 |
---|
[10475] | 938 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj,jl) + pt (ji,jj,jl) & |
---|
| 939 | & - zcu * ( pt (ji+1,jj,jl) - pt (ji,jj,jl) ) ) & |
---|
| 940 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj,jl) + ztu2(ji,jj,jl) & |
---|
| 941 | & - 0.5_wp * zcu * ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) ) & |
---|
[10446] | 942 | & + z1_120 * zdx4 * ( zcu*zcu - 1._wp ) * ( zcu*zcu - 4._wp ) * ( ztu4(ji+1,jj,jl) + ztu4(ji,jj,jl) & |
---|
[10425] | 943 | & - SIGN( 1._wp, zcu ) * ( ztu4(ji+1,jj,jl) - ztu4(ji,jj,jl) ) ) ) |
---|
| 944 | END DO |
---|
[8586] | 945 | END DO |
---|
| 946 | END DO |
---|
| 947 | ! |
---|
| 948 | END SELECT |
---|
[10439] | 949 | ! |
---|
[10910] | 950 | ! if there is an outward velocity in a grid cell where there is no ice initially (typically at the ice edge), |
---|
| 951 | ! interpolated T at u/v points can be non-zero while it should |
---|
| 952 | ! (because of the high order of the advection scheme). Thus set it to 0 in this case |
---|
| 953 | IF( ll_icedge ) THEN |
---|
| 954 | DO jl = 1, jpl |
---|
| 955 | DO jj = 1, jpjm1 |
---|
| 956 | DO ji = 1, fs_jpim1 |
---|
| 957 | IF( pt(ji,jj,jl) <= 0._wp .AND. pu(ji,jj) >= 0._wp ) THEN |
---|
| 958 | pt_u(ji,jj,jl) = 0._wp |
---|
| 959 | ENDIF |
---|
| 960 | END DO |
---|
| 961 | END DO |
---|
| 962 | END DO |
---|
| 963 | ENDIF |
---|
| 964 | ! |
---|
[10439] | 965 | ! if pt at u-point is negative then use the upstream value |
---|
| 966 | ! this should not be necessary if a proper sea-ice mask is set in Ultimate |
---|
| 967 | ! to degrade the order of the scheme when necessary (for ex. at the ice edge) |
---|
[10413] | 968 | IF( ll_neg ) THEN |
---|
[10425] | 969 | DO jl = 1, jpl |
---|
| 970 | DO jj = 1, jpjm1 |
---|
| 971 | DO ji = 1, fs_jpim1 |
---|
[10910] | 972 | zvi_cen2 = 0.5_wp * ( v_i(ji+1,jj,jl) + v_i(ji,jj,jl) ) |
---|
| 973 | IF( pt_u(ji,jj,jl) < 0._wp .OR. ( zvi_cen2 < epsi06 .AND. pamsk == 0._wp ) ) THEN |
---|
[10475] | 974 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj,jl) + pt(ji,jj,jl) & |
---|
| 975 | & - SIGN( 1._wp, pu(ji,jj) ) * ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) ) |
---|
[10425] | 976 | ENDIF |
---|
| 977 | END DO |
---|
[10413] | 978 | END DO |
---|
| 979 | END DO |
---|
| 980 | ENDIF |
---|
[10439] | 981 | ! !-- High order flux in i-direction --! |
---|
[10425] | 982 | DO jl = 1, jpl |
---|
| 983 | DO jj = 1, jpjm1 |
---|
| 984 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
[10439] | 985 | pfu_ho(ji,jj,jl) = pu(ji,jj) * pt_u(ji,jj,jl) |
---|
[10425] | 986 | END DO |
---|
[10413] | 987 | END DO |
---|
| 988 | END DO |
---|
[8586] | 989 | ! |
---|
| 990 | END SUBROUTINE ultimate_x |
---|
| 991 | |
---|
| 992 | |
---|
[10910] | 993 | SUBROUTINE ultimate_y( pamsk, kn_umx, pdt, pt, pv, pt_v, pfv_ho ) |
---|
[8586] | 994 | !!--------------------------------------------------------------------- |
---|
| 995 | !! *** ROUTINE ultimate_y *** |
---|
| 996 | !! |
---|
[10446] | 997 | !! ** Purpose : compute tracer at v-points |
---|
[8586] | 998 | !! |
---|
[10446] | 999 | !! ** Method : ... |
---|
[8586] | 1000 | !! |
---|
| 1001 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
| 1002 | !!---------------------------------------------------------------------- |
---|
[10910] | 1003 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
[10439] | 1004 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
| 1005 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 1006 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pv ! ice j-velocity component |
---|
| 1007 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
[10425] | 1008 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_v ! tracer at v-point |
---|
| 1009 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfv_ho ! high order flux |
---|
[8586] | 1010 | ! |
---|
[10439] | 1011 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[10910] | 1012 | REAL(wp) :: zcv, zdy2, zdy4, zvi_cen2 ! - - |
---|
[10425] | 1013 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: ztv1, ztv2, ztv3, ztv4 |
---|
[8586] | 1014 | !!---------------------------------------------------------------------- |
---|
| 1015 | ! |
---|
| 1016 | ! !-- Laplacian in j-direction --! |
---|
[10425] | 1017 | DO jl = 1, jpl |
---|
| 1018 | DO jj = 1, jpjm1 ! First derivative (gradient) |
---|
| 1019 | DO ji = fs_2, fs_jpim1 |
---|
| 1020 | ztv1(ji,jj,jl) = ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) * r1_e2v(ji,jj) * vmask(ji,jj,1) |
---|
| 1021 | END DO |
---|
[8586] | 1022 | END DO |
---|
[10425] | 1023 | DO jj = 2, jpjm1 ! Second derivative (Laplacian) |
---|
| 1024 | DO ji = fs_2, fs_jpim1 |
---|
| 1025 | ztv2(ji,jj,jl) = ( ztv1(ji,jj,jl) - ztv1(ji,jj-1,jl) ) * r1_e2t(ji,jj) |
---|
| 1026 | END DO |
---|
[8586] | 1027 | END DO |
---|
| 1028 | END DO |
---|
[10425] | 1029 | CALL lbc_lnk( 'icedyn_adv_umx', ztv2, 'T', 1. ) |
---|
[8586] | 1030 | ! |
---|
| 1031 | ! !-- BiLaplacian in j-direction --! |
---|
[10425] | 1032 | DO jl = 1, jpl |
---|
| 1033 | DO jj = 1, jpjm1 ! First derivative |
---|
| 1034 | DO ji = fs_2, fs_jpim1 |
---|
| 1035 | ztv3(ji,jj,jl) = ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) * r1_e2v(ji,jj) * vmask(ji,jj,1) |
---|
| 1036 | END DO |
---|
[8586] | 1037 | END DO |
---|
[10425] | 1038 | DO jj = 2, jpjm1 ! Second derivative |
---|
| 1039 | DO ji = fs_2, fs_jpim1 |
---|
| 1040 | ztv4(ji,jj,jl) = ( ztv3(ji,jj,jl) - ztv3(ji,jj-1,jl) ) * r1_e2t(ji,jj) |
---|
| 1041 | END DO |
---|
[8586] | 1042 | END DO |
---|
| 1043 | END DO |
---|
[10425] | 1044 | CALL lbc_lnk( 'icedyn_adv_umx', ztv4, 'T', 1. ) |
---|
[8586] | 1045 | ! |
---|
| 1046 | ! |
---|
[10413] | 1047 | SELECT CASE (kn_umx ) |
---|
[10425] | 1048 | ! |
---|
[8586] | 1049 | CASE( 1 ) !== 1st order central TIM ==! (Eq. 21) |
---|
[10425] | 1050 | DO jl = 1, jpl |
---|
| 1051 | DO jj = 1, jpjm1 |
---|
| 1052 | DO ji = 1, fs_jpim1 |
---|
[10475] | 1053 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( pt(ji,jj+1,jl) + pt(ji,jj,jl) & |
---|
| 1054 | & - SIGN( 1._wp, pv(ji,jj) ) * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) ) |
---|
[10425] | 1055 | END DO |
---|
[8586] | 1056 | END DO |
---|
| 1057 | END DO |
---|
| 1058 | ! |
---|
| 1059 | CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23) |
---|
[10425] | 1060 | DO jl = 1, jpl |
---|
| 1061 | DO jj = 1, jpjm1 |
---|
| 1062 | DO ji = 1, fs_jpim1 |
---|
| 1063 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
[10475] | 1064 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( pt(ji,jj+1,jl) + pt(ji,jj,jl) & |
---|
| 1065 | & - zcv * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) ) |
---|
[10425] | 1066 | END DO |
---|
[8586] | 1067 | END DO |
---|
| 1068 | END DO |
---|
| 1069 | ! |
---|
| 1070 | CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24) |
---|
[10425] | 1071 | DO jl = 1, jpl |
---|
| 1072 | DO jj = 1, jpjm1 |
---|
| 1073 | DO ji = 1, fs_jpim1 |
---|
| 1074 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
| 1075 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
[10439] | 1076 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
[10475] | 1077 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) & |
---|
| 1078 | & - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) & |
---|
[10446] | 1079 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) & |
---|
[10425] | 1080 | & - SIGN( 1._wp, zcv ) * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) ) |
---|
| 1081 | END DO |
---|
[8586] | 1082 | END DO |
---|
| 1083 | END DO |
---|
| 1084 | ! |
---|
| 1085 | CASE( 4 ) !== 4th order central TIM ==! (Eq. 27) |
---|
[10425] | 1086 | DO jl = 1, jpl |
---|
| 1087 | DO jj = 1, jpjm1 |
---|
| 1088 | DO ji = 1, fs_jpim1 |
---|
| 1089 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
| 1090 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
[10439] | 1091 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
[10475] | 1092 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) & |
---|
| 1093 | & - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) & |
---|
| 1094 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) & |
---|
| 1095 | & - 0.5_wp * zcv * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) ) |
---|
[10425] | 1096 | END DO |
---|
[8586] | 1097 | END DO |
---|
| 1098 | END DO |
---|
| 1099 | ! |
---|
| 1100 | CASE( 5 ) !== 5th order central TIM ==! (Eq. 29) |
---|
[10425] | 1101 | DO jl = 1, jpl |
---|
| 1102 | DO jj = 1, jpjm1 |
---|
| 1103 | DO ji = 1, fs_jpim1 |
---|
| 1104 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
| 1105 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
[10439] | 1106 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
[10425] | 1107 | zdy4 = zdy2 * zdy2 |
---|
[10446] | 1108 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) & |
---|
[10475] | 1109 | & - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) & |
---|
| 1110 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) & |
---|
| 1111 | & - 0.5_wp * zcv * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) & |
---|
[10446] | 1112 | & + z1_120 * zdy4 * ( zcv*zcv - 1._wp ) * ( zcv*zcv - 4._wp ) * ( ztv4(ji,jj+1,jl) + ztv4(ji,jj,jl) & |
---|
[10425] | 1113 | & - SIGN( 1._wp, zcv ) * ( ztv4(ji,jj+1,jl) - ztv4(ji,jj,jl) ) ) ) |
---|
| 1114 | END DO |
---|
[8586] | 1115 | END DO |
---|
| 1116 | END DO |
---|
| 1117 | ! |
---|
| 1118 | END SELECT |
---|
[10439] | 1119 | ! |
---|
[10910] | 1120 | ! if there is an outward velocity in a grid cell where there is no ice initially (typically at the ice edge), |
---|
| 1121 | ! interpolated T at u/v points can be non-zero while it should |
---|
| 1122 | ! (because of the high order of the advection scheme). Thus set it to 0 in this case |
---|
| 1123 | IF( ll_icedge ) THEN |
---|
| 1124 | DO jl = 1, jpl |
---|
| 1125 | DO jj = 1, jpjm1 |
---|
| 1126 | DO ji = 1, fs_jpim1 |
---|
| 1127 | IF( pt(ji,jj,jl) <= 0._wp .AND. pv(ji,jj) >= 0._wp ) THEN |
---|
| 1128 | pt_v(ji,jj,jl) = 0._wp |
---|
| 1129 | ENDIF |
---|
| 1130 | END DO |
---|
| 1131 | END DO |
---|
| 1132 | END DO |
---|
| 1133 | ENDIF |
---|
| 1134 | ! |
---|
[10439] | 1135 | ! if pt at v-point is negative then use the upstream value |
---|
| 1136 | ! this should not be necessary if a proper sea-ice mask is set in Ultimate |
---|
| 1137 | ! to degrade the order of the scheme when necessary (for ex. at the ice edge) |
---|
[10413] | 1138 | IF( ll_neg ) THEN |
---|
[10425] | 1139 | DO jl = 1, jpl |
---|
| 1140 | DO jj = 1, jpjm1 |
---|
| 1141 | DO ji = 1, fs_jpim1 |
---|
[10910] | 1142 | zvi_cen2 = 0.5_wp * ( v_i(ji,jj+1,jl) + v_i(ji,jj,jl) ) |
---|
| 1143 | IF( pt_v(ji,jj,jl) < 0._wp .OR. ( zvi_cen2 < epsi06 .AND. pamsk == 0._wp ) ) THEN |
---|
[10475] | 1144 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt(ji,jj+1,jl) + pt(ji,jj,jl) ) & |
---|
| 1145 | & - SIGN( 1._wp, pv(ji,jj) ) * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) ) |
---|
[10425] | 1146 | ENDIF |
---|
| 1147 | END DO |
---|
[10413] | 1148 | END DO |
---|
| 1149 | END DO |
---|
| 1150 | ENDIF |
---|
[10439] | 1151 | ! !-- High order flux in j-direction --! |
---|
[10425] | 1152 | DO jl = 1, jpl |
---|
| 1153 | DO jj = 1, jpjm1 |
---|
| 1154 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
[10439] | 1155 | pfv_ho(ji,jj,jl) = pv(ji,jj) * pt_v(ji,jj,jl) |
---|
[10425] | 1156 | END DO |
---|
[10413] | 1157 | END DO |
---|
| 1158 | END DO |
---|
[8586] | 1159 | ! |
---|
| 1160 | END SUBROUTINE ultimate_y |
---|
[10413] | 1161 | |
---|
| 1162 | |
---|
[10519] | 1163 | SUBROUTINE nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[8586] | 1164 | !!--------------------------------------------------------------------- |
---|
[10519] | 1165 | !! *** ROUTINE nonosc_ice *** |
---|
[8586] | 1166 | !! |
---|
[10446] | 1167 | !! ** Purpose : compute monotonic tracer fluxes from the upstream |
---|
[10519] | 1168 | !! scheme and the before field by a non-oscillatory algorithm |
---|
[8586] | 1169 | !! |
---|
[10446] | 1170 | !! ** Method : ... |
---|
[8586] | 1171 | !!---------------------------------------------------------------------- |
---|
[10439] | 1172 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 1173 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
[10425] | 1174 | REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pu ! ice i-velocity => u*e2 |
---|
| 1175 | REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pv ! ice j-velocity => v*e1 |
---|
[10446] | 1176 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pt, pt_ups ! before field & upstream guess of after field |
---|
| 1177 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pfv_ups, pfu_ups ! upstream flux |
---|
[10425] | 1178 | REAL(wp), DIMENSION (:,:,:), INTENT(inout) :: pfv_ho, pfu_ho ! monotonic flux |
---|
[8586] | 1179 | ! |
---|
[10425] | 1180 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[10475] | 1181 | REAL(wp) :: zpos, zneg, zbig, zup, zdo, z1_dt ! local scalars |
---|
| 1182 | REAL(wp) :: zau, zbu, zcu, zav, zbv, zcv, zcoef, zzt ! - - |
---|
[10425] | 1183 | REAL(wp), DIMENSION(jpi,jpj ) :: zbup, zbdo |
---|
[10439] | 1184 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zbetup, zbetdo, zti_ups, ztj_ups |
---|
[8586] | 1185 | !!---------------------------------------------------------------------- |
---|
| 1186 | zbig = 1.e+40_wp |
---|
[10425] | 1187 | |
---|
[10413] | 1188 | ! antidiffusive flux : high order minus low order |
---|
| 1189 | ! -------------------------------------------------- |
---|
[10425] | 1190 | DO jl = 1, jpl |
---|
| 1191 | DO jj = 1, jpjm1 |
---|
| 1192 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
[10439] | 1193 | pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) - pfu_ups(ji,jj,jl) |
---|
| 1194 | pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) - pfv_ups(ji,jj,jl) |
---|
[10425] | 1195 | END DO |
---|
| 1196 | END DO |
---|
[8586] | 1197 | END DO |
---|
| 1198 | |
---|
[10413] | 1199 | ! extreme case where pfu_ho has to be zero |
---|
| 1200 | ! ---------------------------------------- |
---|
| 1201 | ! pfu_ho |
---|
| 1202 | ! * ---> |
---|
| 1203 | ! | | * | | |
---|
| 1204 | ! | | | * | |
---|
| 1205 | ! | | | | * |
---|
[10439] | 1206 | ! t_ups : i-1 i i+1 i+2 |
---|
[10413] | 1207 | IF( ll_prelimiter_zalesak ) THEN |
---|
| 1208 | |
---|
[10425] | 1209 | DO jl = 1, jpl |
---|
| 1210 | DO jj = 2, jpjm1 |
---|
| 1211 | DO ji = fs_2, fs_jpim1 |
---|
[10439] | 1212 | zti_ups(ji,jj,jl)= pt_ups(ji+1,jj ,jl) |
---|
| 1213 | ztj_ups(ji,jj,jl)= pt_ups(ji ,jj+1,jl) |
---|
[10425] | 1214 | END DO |
---|
[10413] | 1215 | END DO |
---|
| 1216 | END DO |
---|
[10439] | 1217 | CALL lbc_lnk_multi( 'icedyn_adv_umx', zti_ups, 'T', 1., ztj_ups, 'T', 1. ) |
---|
[8586] | 1218 | |
---|
[10425] | 1219 | DO jl = 1, jpl |
---|
| 1220 | DO jj = 2, jpjm1 |
---|
| 1221 | DO ji = fs_2, fs_jpim1 |
---|
[10475] | 1222 | IF ( pfu_ho(ji,jj,jl) * ( pt_ups(ji+1,jj ,jl) - pt_ups(ji,jj,jl) ) <= 0._wp .AND. & |
---|
| 1223 | & pfv_ho(ji,jj,jl) * ( pt_ups(ji ,jj+1,jl) - pt_ups(ji,jj,jl) ) <= 0._wp ) THEN |
---|
[10425] | 1224 | ! |
---|
[10475] | 1225 | IF( pfu_ho(ji,jj,jl) * ( zti_ups(ji+1,jj ,jl) - zti_ups(ji,jj,jl) ) <= 0._wp .AND. & |
---|
| 1226 | & pfv_ho(ji,jj,jl) * ( ztj_ups(ji ,jj+1,jl) - ztj_ups(ji,jj,jl) ) <= 0._wp ) THEN |
---|
| 1227 | pfu_ho(ji,jj,jl)=0._wp |
---|
| 1228 | pfv_ho(ji,jj,jl)=0._wp |
---|
[10439] | 1229 | ENDIF |
---|
[10425] | 1230 | ! |
---|
[10475] | 1231 | IF( pfu_ho(ji,jj,jl) * ( pt_ups(ji,jj,jl) - pt_ups(ji-1,jj ,jl) ) <= 0._wp .AND. & |
---|
| 1232 | & pfv_ho(ji,jj,jl) * ( pt_ups(ji,jj,jl) - pt_ups(ji ,jj-1,jl) ) <= 0._wp ) THEN |
---|
| 1233 | pfu_ho(ji,jj,jl)=0._wp |
---|
| 1234 | pfv_ho(ji,jj,jl)=0._wp |
---|
[10439] | 1235 | ENDIF |
---|
[10425] | 1236 | ! |
---|
| 1237 | ENDIF |
---|
| 1238 | END DO |
---|
[10413] | 1239 | END DO |
---|
| 1240 | END DO |
---|
[10425] | 1241 | CALL lbc_lnk_multi( 'icedyn_adv_umx', pfu_ho, 'U', -1., pfv_ho, 'V', -1. ) ! lateral boundary cond. |
---|
[10413] | 1242 | |
---|
| 1243 | ENDIF |
---|
[10425] | 1244 | |
---|
[8586] | 1245 | ! Search local extrema |
---|
| 1246 | ! -------------------- |
---|
[10439] | 1247 | ! max/min of pt & pt_ups with large negative/positive value (-/+zbig) outside ice cover |
---|
[10425] | 1248 | z1_dt = 1._wp / pdt |
---|
| 1249 | DO jl = 1, jpl |
---|
| 1250 | |
---|
| 1251 | DO jj = 1, jpj |
---|
| 1252 | DO ji = 1, jpi |
---|
[10439] | 1253 | IF ( pt(ji,jj,jl) <= 0._wp .AND. pt_ups(ji,jj,jl) <= 0._wp ) THEN |
---|
[10425] | 1254 | zbup(ji,jj) = -zbig |
---|
| 1255 | zbdo(ji,jj) = zbig |
---|
[10439] | 1256 | ELSEIF( pt(ji,jj,jl) <= 0._wp .AND. pt_ups(ji,jj,jl) > 0._wp ) THEN |
---|
| 1257 | zbup(ji,jj) = pt_ups(ji,jj,jl) |
---|
| 1258 | zbdo(ji,jj) = pt_ups(ji,jj,jl) |
---|
| 1259 | ELSEIF( pt(ji,jj,jl) > 0._wp .AND. pt_ups(ji,jj,jl) <= 0._wp ) THEN |
---|
[10425] | 1260 | zbup(ji,jj) = pt(ji,jj,jl) |
---|
| 1261 | zbdo(ji,jj) = pt(ji,jj,jl) |
---|
| 1262 | ELSE |
---|
[10439] | 1263 | zbup(ji,jj) = MAX( pt(ji,jj,jl) , pt_ups(ji,jj,jl) ) |
---|
| 1264 | zbdo(ji,jj) = MIN( pt(ji,jj,jl) , pt_ups(ji,jj,jl) ) |
---|
[10425] | 1265 | ENDIF |
---|
| 1266 | END DO |
---|
[10413] | 1267 | END DO |
---|
[8586] | 1268 | |
---|
[10425] | 1269 | DO jj = 2, jpjm1 |
---|
| 1270 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 1271 | ! |
---|
[10475] | 1272 | 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 |
---|
| 1273 | zdo = MIN( zbdo(ji,jj), zbdo(ji-1,jj), zbdo(ji+1,jj), zbdo(ji,jj-1), zbdo(ji,jj+1) ) |
---|
[10425] | 1274 | ! |
---|
[10475] | 1275 | zpos = MAX( 0._wp, pfu_ho(ji-1,jj ,jl) ) - MIN( 0._wp, pfu_ho(ji ,jj ,jl) ) & ! positive/negative part of the flux |
---|
| 1276 | & + MAX( 0._wp, pfv_ho(ji ,jj-1,jl) ) - MIN( 0._wp, pfv_ho(ji ,jj ,jl) ) |
---|
| 1277 | zneg = MAX( 0._wp, pfu_ho(ji ,jj ,jl) ) - MIN( 0._wp, pfu_ho(ji-1,jj ,jl) ) & |
---|
| 1278 | & + MAX( 0._wp, pfv_ho(ji ,jj ,jl) ) - MIN( 0._wp, pfv_ho(ji ,jj-1,jl) ) |
---|
[10425] | 1279 | ! |
---|
[10475] | 1280 | zpos = zpos - (pt(ji,jj,jl) * MIN( 0., pu(ji,jj) - pu(ji-1,jj) ) + pt(ji,jj,jl) * MIN( 0., pv(ji,jj) - pv(ji,jj-1) ) & |
---|
[10439] | 1281 | & ) * ( 1. - pamsk ) |
---|
[10475] | 1282 | zneg = zneg + (pt(ji,jj,jl) * MAX( 0., pu(ji,jj) - pu(ji-1,jj) ) + pt(ji,jj,jl) * MAX( 0., pv(ji,jj) - pv(ji,jj-1) ) & |
---|
[10439] | 1283 | & ) * ( 1. - pamsk ) |
---|
[10425] | 1284 | ! |
---|
| 1285 | ! ! up & down beta terms |
---|
[10910] | 1286 | ! clem: zbetup and zbetdo must be 0 for zpos>1.e-10 & zneg>1.e-10 (do not put 0 instead of 1.e-10 !!!) |
---|
| 1287 | IF( zpos > epsi10 ) THEN ; zbetup(ji,jj,jl) = MAX( 0._wp, zup - pt_ups(ji,jj,jl) ) / zpos * e1e2t(ji,jj) * z1_dt |
---|
| 1288 | ELSE ; zbetup(ji,jj,jl) = 0._wp ! zbig |
---|
[10425] | 1289 | ENDIF |
---|
| 1290 | ! |
---|
[10910] | 1291 | IF( zneg > epsi10 ) THEN ; zbetdo(ji,jj,jl) = MAX( 0._wp, pt_ups(ji,jj,jl) - zdo ) / zneg * e1e2t(ji,jj) * z1_dt |
---|
| 1292 | ELSE ; zbetdo(ji,jj,jl) = 0._wp ! zbig |
---|
[10425] | 1293 | ENDIF |
---|
| 1294 | ! |
---|
| 1295 | ! if all the points are outside ice cover |
---|
[10475] | 1296 | IF( zup == -zbig ) zbetup(ji,jj,jl) = 0._wp ! zbig |
---|
| 1297 | IF( zdo == zbig ) zbetdo(ji,jj,jl) = 0._wp ! zbig |
---|
[10425] | 1298 | ! |
---|
| 1299 | END DO |
---|
[8586] | 1300 | END DO |
---|
| 1301 | END DO |
---|
[10425] | 1302 | CALL lbc_lnk_multi( 'icedyn_adv_umx', zbetup, 'T', 1., zbetdo, 'T', 1. ) ! lateral boundary cond. (unchanged sign) |
---|
[8586] | 1303 | |
---|
[10413] | 1304 | |
---|
| 1305 | ! monotonic flux in the y direction |
---|
| 1306 | ! --------------------------------- |
---|
[10425] | 1307 | DO jl = 1, jpl |
---|
| 1308 | DO jj = 1, jpjm1 |
---|
| 1309 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 1310 | zau = MIN( 1._wp , zbetdo(ji,jj,jl) , zbetup(ji+1,jj,jl) ) |
---|
| 1311 | zbu = MIN( 1._wp , zbetup(ji,jj,jl) , zbetdo(ji+1,jj,jl) ) |
---|
[10475] | 1312 | zcu = 0.5_wp + SIGN( 0.5_wp , pfu_ho(ji,jj,jl) ) |
---|
[10425] | 1313 | ! |
---|
| 1314 | zcoef = ( zcu * zau + ( 1._wp - zcu ) * zbu ) |
---|
[10439] | 1315 | ! |
---|
| 1316 | pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) * zcoef + pfu_ups(ji,jj,jl) |
---|
| 1317 | ! |
---|
[10425] | 1318 | END DO |
---|
[8637] | 1319 | END DO |
---|
[10413] | 1320 | |
---|
[10425] | 1321 | DO jj = 1, jpjm1 |
---|
| 1322 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 1323 | zav = MIN( 1._wp , zbetdo(ji,jj,jl) , zbetup(ji,jj+1,jl) ) |
---|
| 1324 | zbv = MIN( 1._wp , zbetup(ji,jj,jl) , zbetdo(ji,jj+1,jl) ) |
---|
[10475] | 1325 | zcv = 0.5_wp + SIGN( 0.5_wp , pfv_ho(ji,jj,jl) ) |
---|
[10425] | 1326 | ! |
---|
| 1327 | zcoef = ( zcv * zav + ( 1._wp - zcv ) * zbv ) |
---|
[10439] | 1328 | ! |
---|
| 1329 | pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) * zcoef + pfv_ups(ji,jj,jl) |
---|
| 1330 | ! |
---|
[10425] | 1331 | END DO |
---|
[8586] | 1332 | END DO |
---|
[10413] | 1333 | |
---|
| 1334 | END DO |
---|
[8586] | 1335 | ! |
---|
[10519] | 1336 | END SUBROUTINE nonosc_ice |
---|
[8586] | 1337 | |
---|
[10446] | 1338 | |
---|
| 1339 | SUBROUTINE limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
[10413] | 1340 | !!--------------------------------------------------------------------- |
---|
| 1341 | !! *** ROUTINE limiter_x *** |
---|
| 1342 | !! |
---|
| 1343 | !! ** Purpose : compute flux limiter |
---|
| 1344 | !!---------------------------------------------------------------------- |
---|
[10446] | 1345 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 1346 | REAL(wp), DIMENSION(:,: ), INTENT(in ) :: pu ! ice i-velocity => u*e2 |
---|
| 1347 | REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pt ! ice tracer |
---|
| 1348 | REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pfu_ups ! upstream flux |
---|
| 1349 | REAL(wp), DIMENSION(:,:,:), INTENT(inout) :: pfu_ho ! high order flux |
---|
[10413] | 1350 | ! |
---|
| 1351 | REAL(wp) :: Cr, Rjm, Rj, Rjp, uCFL, zpsi, zh3, zlimiter, Rr |
---|
[10425] | 1352 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
| 1353 | REAL(wp), DIMENSION (jpi,jpj,jpl) :: zslpx ! tracer slopes |
---|
[10413] | 1354 | !!---------------------------------------------------------------------- |
---|
| 1355 | ! |
---|
[10425] | 1356 | DO jl = 1, jpl |
---|
| 1357 | DO jj = 2, jpjm1 |
---|
| 1358 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 1359 | zslpx(ji,jj,jl) = ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) * umask(ji,jj,1) |
---|
| 1360 | END DO |
---|
[10413] | 1361 | END DO |
---|
| 1362 | END DO |
---|
[10425] | 1363 | CALL lbc_lnk( 'icedyn_adv_umx', zslpx, 'U', -1.) ! lateral boundary cond. |
---|
[10413] | 1364 | |
---|
[10425] | 1365 | DO jl = 1, jpl |
---|
| 1366 | DO jj = 2, jpjm1 |
---|
| 1367 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 1368 | uCFL = pdt * ABS( pu(ji,jj) ) * r1_e1e2t(ji,jj) |
---|
| 1369 | |
---|
| 1370 | Rjm = zslpx(ji-1,jj,jl) |
---|
| 1371 | Rj = zslpx(ji ,jj,jl) |
---|
| 1372 | Rjp = zslpx(ji+1,jj,jl) |
---|
[10413] | 1373 | |
---|
[10446] | 1374 | IF( kn_limiter == 3 ) THEN |
---|
[10413] | 1375 | |
---|
[10425] | 1376 | IF( pu(ji,jj) > 0. ) THEN ; Rr = Rjm |
---|
| 1377 | ELSE ; Rr = Rjp |
---|
| 1378 | ENDIF |
---|
[10413] | 1379 | |
---|
[10425] | 1380 | zh3 = pfu_ho(ji,jj,jl) - pfu_ups(ji,jj,jl) |
---|
| 1381 | IF( Rj > 0. ) THEN |
---|
| 1382 | zlimiter = MAX( 0., MIN( zh3, MAX(-Rr * 0.5 * ABS(pu(ji,jj)), & |
---|
| 1383 | & MIN( 2. * Rr * 0.5 * ABS(pu(ji,jj)), zh3, 1.5 * Rj * 0.5 * ABS(pu(ji,jj)) ) ) ) ) |
---|
| 1384 | ELSE |
---|
| 1385 | zlimiter = -MAX( 0., MIN(-zh3, MAX( Rr * 0.5 * ABS(pu(ji,jj)), & |
---|
| 1386 | & MIN(-2. * Rr * 0.5 * ABS(pu(ji,jj)), -zh3, -1.5 * Rj * 0.5 * ABS(pu(ji,jj)) ) ) ) ) |
---|
| 1387 | ENDIF |
---|
| 1388 | pfu_ho(ji,jj,jl) = pfu_ups(ji,jj,jl) + zlimiter |
---|
[10413] | 1389 | |
---|
[10446] | 1390 | ELSEIF( kn_limiter == 2 ) THEN |
---|
[10425] | 1391 | IF( Rj /= 0. ) THEN |
---|
| 1392 | IF( pu(ji,jj) > 0. ) THEN ; Cr = Rjm / Rj |
---|
| 1393 | ELSE ; Cr = Rjp / Rj |
---|
| 1394 | ENDIF |
---|
| 1395 | ELSE |
---|
| 1396 | Cr = 0. |
---|
[10413] | 1397 | ENDIF |
---|
[10425] | 1398 | |
---|
| 1399 | ! -- superbee -- |
---|
| 1400 | zpsi = MAX( 0., MAX( MIN(1.,2.*Cr), MIN(2.,Cr) ) ) |
---|
| 1401 | ! -- van albada 2 -- |
---|
| 1402 | !!zpsi = 2.*Cr / (Cr*Cr+1.) |
---|
| 1403 | ! -- sweby (with beta=1) -- |
---|
| 1404 | !!zpsi = MAX( 0., MAX( MIN(1.,1.*Cr), MIN(1.,Cr) ) ) |
---|
| 1405 | ! -- van Leer -- |
---|
| 1406 | !!zpsi = ( Cr + ABS(Cr) ) / ( 1. + ABS(Cr) ) |
---|
| 1407 | ! -- ospre -- |
---|
| 1408 | !!zpsi = 1.5 * ( Cr*Cr + Cr ) / ( Cr*Cr + Cr + 1. ) |
---|
| 1409 | ! -- koren -- |
---|
| 1410 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( (1.+2*Cr)/3., 2. ) ) ) |
---|
| 1411 | ! -- charm -- |
---|
| 1412 | !IF( Cr > 0. ) THEN ; zpsi = Cr * (3.*Cr + 1.) / ( (Cr + 1.) * (Cr + 1.) ) |
---|
| 1413 | !ELSE ; zpsi = 0. |
---|
[10413] | 1414 | !ENDIF |
---|
[10425] | 1415 | ! -- van albada 1 -- |
---|
| 1416 | !!zpsi = (Cr*Cr + Cr) / (Cr*Cr +1) |
---|
| 1417 | ! -- smart -- |
---|
| 1418 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, 4. ) ) ) |
---|
| 1419 | ! -- umist -- |
---|
| 1420 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, MIN(0.75+0.25*Cr, 2. ) ) ) ) |
---|
[10413] | 1421 | |
---|
[10425] | 1422 | ! high order flux corrected by the limiter |
---|
| 1423 | pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) - ABS( pu(ji,jj) ) * ( (1.-zpsi) + uCFL*zpsi ) * Rj * 0.5 |
---|
[10413] | 1424 | |
---|
[10425] | 1425 | ENDIF |
---|
| 1426 | END DO |
---|
[10413] | 1427 | END DO |
---|
| 1428 | END DO |
---|
[10425] | 1429 | CALL lbc_lnk( 'icedyn_adv_umx', pfu_ho, 'U', -1.) ! lateral boundary cond. |
---|
[10413] | 1430 | ! |
---|
| 1431 | END SUBROUTINE limiter_x |
---|
| 1432 | |
---|
[10446] | 1433 | |
---|
| 1434 | SUBROUTINE limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 1435 | !!--------------------------------------------------------------------- |
---|
| 1436 | !! *** ROUTINE limiter_y *** |
---|
| 1437 | !! |
---|
| 1438 | !! ** Purpose : compute flux limiter |
---|
| 1439 | !!---------------------------------------------------------------------- |
---|
[10446] | 1440 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 1441 | REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pv ! ice i-velocity => u*e2 |
---|
| 1442 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pt ! ice tracer |
---|
| 1443 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pfv_ups ! upstream flux |
---|
| 1444 | REAL(wp), DIMENSION (:,:,:), INTENT(inout) :: pfv_ho ! high order flux |
---|
[10413] | 1445 | ! |
---|
| 1446 | REAL(wp) :: Cr, Rjm, Rj, Rjp, vCFL, zpsi, zh3, zlimiter, Rr |
---|
[10425] | 1447 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
| 1448 | REAL(wp), DIMENSION (jpi,jpj,jpl) :: zslpy ! tracer slopes |
---|
[10413] | 1449 | !!---------------------------------------------------------------------- |
---|
| 1450 | ! |
---|
[10425] | 1451 | DO jl = 1, jpl |
---|
| 1452 | DO jj = 2, jpjm1 |
---|
| 1453 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 1454 | zslpy(ji,jj,jl) = ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) * vmask(ji,jj,1) |
---|
| 1455 | END DO |
---|
[10413] | 1456 | END DO |
---|
| 1457 | END DO |
---|
[10425] | 1458 | CALL lbc_lnk( 'icedyn_adv_umx', zslpy, 'V', -1.) ! lateral boundary cond. |
---|
[10413] | 1459 | |
---|
[10425] | 1460 | DO jl = 1, jpl |
---|
| 1461 | DO jj = 2, jpjm1 |
---|
| 1462 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 1463 | vCFL = pdt * ABS( pv(ji,jj) ) * r1_e1e2t(ji,jj) |
---|
[10413] | 1464 | |
---|
[10425] | 1465 | Rjm = zslpy(ji,jj-1,jl) |
---|
| 1466 | Rj = zslpy(ji,jj ,jl) |
---|
| 1467 | Rjp = zslpy(ji,jj+1,jl) |
---|
[10413] | 1468 | |
---|
[10446] | 1469 | IF( kn_limiter == 3 ) THEN |
---|
[10413] | 1470 | |
---|
[10425] | 1471 | IF( pv(ji,jj) > 0. ) THEN ; Rr = Rjm |
---|
| 1472 | ELSE ; Rr = Rjp |
---|
| 1473 | ENDIF |
---|
[10413] | 1474 | |
---|
[10425] | 1475 | zh3 = pfv_ho(ji,jj,jl) - pfv_ups(ji,jj,jl) |
---|
| 1476 | IF( Rj > 0. ) THEN |
---|
| 1477 | zlimiter = MAX( 0., MIN( zh3, MAX(-Rr * 0.5 * ABS(pv(ji,jj)), & |
---|
| 1478 | & MIN( 2. * Rr * 0.5 * ABS(pv(ji,jj)), zh3, 1.5 * Rj * 0.5 * ABS(pv(ji,jj)) ) ) ) ) |
---|
| 1479 | ELSE |
---|
| 1480 | zlimiter = -MAX( 0., MIN(-zh3, MAX( Rr * 0.5 * ABS(pv(ji,jj)), & |
---|
| 1481 | & MIN(-2. * Rr * 0.5 * ABS(pv(ji,jj)), -zh3, -1.5 * Rj * 0.5 * ABS(pv(ji,jj)) ) ) ) ) |
---|
| 1482 | ENDIF |
---|
| 1483 | pfv_ho(ji,jj,jl) = pfv_ups(ji,jj,jl) + zlimiter |
---|
[10413] | 1484 | |
---|
[10446] | 1485 | ELSEIF( kn_limiter == 2 ) THEN |
---|
[10413] | 1486 | |
---|
[10425] | 1487 | IF( Rj /= 0. ) THEN |
---|
| 1488 | IF( pv(ji,jj) > 0. ) THEN ; Cr = Rjm / Rj |
---|
| 1489 | ELSE ; Cr = Rjp / Rj |
---|
| 1490 | ENDIF |
---|
| 1491 | ELSE |
---|
| 1492 | Cr = 0. |
---|
| 1493 | ENDIF |
---|
[10413] | 1494 | |
---|
[10425] | 1495 | ! -- superbee -- |
---|
| 1496 | zpsi = MAX( 0., MAX( MIN(1.,2.*Cr), MIN(2.,Cr) ) ) |
---|
| 1497 | ! -- van albada 2 -- |
---|
| 1498 | !!zpsi = 2.*Cr / (Cr*Cr+1.) |
---|
| 1499 | ! -- sweby (with beta=1) -- |
---|
| 1500 | !!zpsi = MAX( 0., MAX( MIN(1.,1.*Cr), MIN(1.,Cr) ) ) |
---|
| 1501 | ! -- van Leer -- |
---|
| 1502 | !!zpsi = ( Cr + ABS(Cr) ) / ( 1. + ABS(Cr) ) |
---|
| 1503 | ! -- ospre -- |
---|
| 1504 | !!zpsi = 1.5 * ( Cr*Cr + Cr ) / ( Cr*Cr + Cr + 1. ) |
---|
| 1505 | ! -- koren -- |
---|
| 1506 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( (1.+2*Cr)/3., 2. ) ) ) |
---|
| 1507 | ! -- charm -- |
---|
| 1508 | !IF( Cr > 0. ) THEN ; zpsi = Cr * (3.*Cr + 1.) / ( (Cr + 1.) * (Cr + 1.) ) |
---|
| 1509 | !ELSE ; zpsi = 0. |
---|
| 1510 | !ENDIF |
---|
| 1511 | ! -- van albada 1 -- |
---|
| 1512 | !!zpsi = (Cr*Cr + Cr) / (Cr*Cr +1) |
---|
| 1513 | ! -- smart -- |
---|
| 1514 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, 4. ) ) ) |
---|
| 1515 | ! -- umist -- |
---|
| 1516 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, MIN(0.75+0.25*Cr, 2. ) ) ) ) |
---|
[10413] | 1517 | |
---|
[10425] | 1518 | ! high order flux corrected by the limiter |
---|
| 1519 | pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) - ABS( pv(ji,jj) ) * ( (1.-zpsi) + vCFL*zpsi ) * Rj * 0.5 |
---|
| 1520 | |
---|
| 1521 | ENDIF |
---|
| 1522 | END DO |
---|
[10413] | 1523 | END DO |
---|
| 1524 | END DO |
---|
[10425] | 1525 | CALL lbc_lnk( 'icedyn_adv_umx', pfv_ho, 'V', -1.) ! lateral boundary cond. |
---|
[10413] | 1526 | ! |
---|
| 1527 | END SUBROUTINE limiter_y |
---|
| 1528 | |
---|
[10910] | 1529 | |
---|
| 1530 | SUBROUTINE Hbig( phi_max, phs_max, phip_max, pv_i, pv_s, psv_i, poa_i, pa_i, pa_ip, pv_ip, pe_s, pe_i ) |
---|
| 1531 | !!------------------------------------------------------------------- |
---|
| 1532 | !! *** ROUTINE Hbig *** |
---|
| 1533 | !! |
---|
| 1534 | !! ** Purpose : Thickness correction in case advection scheme creates |
---|
| 1535 | !! abnormally tick ice or snow |
---|
| 1536 | !! |
---|
| 1537 | !! ** Method : 1- check whether ice thickness is larger than the surrounding 9-points |
---|
| 1538 | !! (before advection) and reduce it by adapting ice concentration |
---|
| 1539 | !! 2- check whether snow thickness is larger than the surrounding 9-points |
---|
| 1540 | !! (before advection) and reduce it by sending the excess in the ocean |
---|
| 1541 | !! 3- check whether snow load deplets the snow-ice interface below sea level$ |
---|
| 1542 | !! and reduce it by sending the excess in the ocean |
---|
| 1543 | !! 4- correct pond fraction to avoid a_ip > a_i |
---|
| 1544 | !! |
---|
| 1545 | !! ** input : Max thickness of the surrounding 9-points |
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| 1546 | !!------------------------------------------------------------------- |
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| 1547 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: phi_max, phs_max, phip_max ! max ice thick from surrounding 9-pts |
---|
| 1548 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i, pv_s, psv_i, poa_i, pa_i, pa_ip, pv_ip |
---|
| 1549 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s |
---|
| 1550 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_i |
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| 1551 | ! |
---|
| 1552 | INTEGER :: ji, jj, jk, jl ! dummy loop indices |
---|
| 1553 | REAL(wp) :: zhip, zhi, zhs, zvs_excess, zfra |
---|
| 1554 | REAL(wp), DIMENSION(jpi,jpj) :: zswitch |
---|
| 1555 | !!------------------------------------------------------------------- |
---|
| 1556 | ! |
---|
| 1557 | ! |
---|
| 1558 | DO jl = 1, jpl |
---|
| 1559 | |
---|
| 1560 | DO jj = 1, jpj |
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| 1561 | DO ji = 1, jpi |
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| 1562 | IF ( pv_i(ji,jj,jl) > 0._wp ) THEN |
---|
| 1563 | ! |
---|
| 1564 | ! ! -- check h_ip -- ! |
---|
| 1565 | ! if h_ip is larger than the surrounding 9 pts => reduce h_ip and increase a_ip |
---|
| 1566 | IF( ln_pnd_H12 .AND. pv_ip(ji,jj,jl) > 0._wp ) THEN |
---|
| 1567 | zhip = pv_ip(ji,jj,jl) / MAX( epsi20, pa_ip(ji,jj,jl) ) |
---|
| 1568 | IF( zhip > phip_max(ji,jj,jl) .AND. pa_ip(ji,jj,jl) < 0.15 ) THEN |
---|
| 1569 | pa_ip(ji,jj,jl) = pv_ip(ji,jj,jl) / phip_max(ji,jj,jl) |
---|
| 1570 | ENDIF |
---|
| 1571 | ENDIF |
---|
| 1572 | ! |
---|
| 1573 | ! ! -- check h_i -- ! |
---|
| 1574 | ! if h_i is larger than the surrounding 9 pts => reduce h_i and increase a_i |
---|
| 1575 | zhi = pv_i(ji,jj,jl) / pa_i(ji,jj,jl) |
---|
| 1576 | IF( zhi > phi_max(ji,jj,jl) .AND. pa_i(ji,jj,jl) < 0.15 ) THEN |
---|
| 1577 | pa_i(ji,jj,jl) = pv_i(ji,jj,jl) / MIN( phi_max(ji,jj,jl), hi_max(jpl) ) !-- bound h_i to hi_max (99 m) |
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| 1578 | ENDIF |
---|
| 1579 | ! |
---|
| 1580 | ! ! -- check h_s -- ! |
---|
| 1581 | ! if h_s is larger than the surrounding 9 pts => put the snow excess in the ocean |
---|
| 1582 | zhs = pv_s(ji,jj,jl) / pa_i(ji,jj,jl) |
---|
| 1583 | IF( pv_s(ji,jj,jl) > 0._wp .AND. zhs > phs_max(ji,jj,jl) .AND. pa_i(ji,jj,jl) < 0.15 ) THEN |
---|
| 1584 | zfra = phs_max(ji,jj,jl) / MAX( zhs, epsi20 ) |
---|
| 1585 | ! |
---|
| 1586 | wfx_res(ji,jj) = wfx_res(ji,jj) + ( pv_s(ji,jj,jl) - pa_i(ji,jj,jl) * phs_max(ji,jj,jl) ) * rhos * r1_rdtice |
---|
| 1587 | hfx_res(ji,jj) = hfx_res(ji,jj) - SUM( pe_s(ji,jj,1:nlay_s,jl) ) * ( 1._wp - zfra ) * r1_rdtice ! W.m-2 <0 |
---|
| 1588 | ! |
---|
| 1589 | pe_s(ji,jj,1:nlay_s,jl) = pe_s(ji,jj,1:nlay_s,jl) * zfra |
---|
| 1590 | pv_s(ji,jj,jl) = pa_i(ji,jj,jl) * phs_max(ji,jj,jl) |
---|
| 1591 | ENDIF |
---|
| 1592 | ! |
---|
| 1593 | ! ! -- check snow load -- ! |
---|
| 1594 | ! if snow load makes snow-ice interface to deplet below the ocean surface => put the snow excess in the ocean |
---|
| 1595 | ! this correction is crucial because of the call to routine icecor afterwards which imposes a mini of ice thick. (rn_himin) |
---|
| 1596 | ! this imposed mini can artificially make the snow very thick (if concentration decreases drastically) |
---|
| 1597 | zvs_excess = MAX( 0._wp, pv_s(ji,jj,jl) - pv_i(ji,jj,jl) * (rau0-rhoi) * r1_rhos ) |
---|
| 1598 | IF( zvs_excess > 0._wp ) THEN |
---|
| 1599 | zfra = ( pv_s(ji,jj,jl) - zvs_excess ) / MAX( pv_s(ji,jj,jl), epsi20 ) |
---|
| 1600 | wfx_res(ji,jj) = wfx_res(ji,jj) + zvs_excess * rhos * r1_rdtice |
---|
| 1601 | hfx_res(ji,jj) = hfx_res(ji,jj) - SUM( pe_s(ji,jj,1:nlay_s,jl) ) * ( 1._wp - zfra ) * r1_rdtice ! W.m-2 <0 |
---|
| 1602 | ! |
---|
| 1603 | pe_s(ji,jj,1:nlay_s,jl) = pe_s(ji,jj,1:nlay_s,jl) * zfra |
---|
| 1604 | pv_s(ji,jj,jl) = pv_s(ji,jj,jl) - zvs_excess |
---|
| 1605 | ENDIF |
---|
| 1606 | |
---|
| 1607 | ENDIF |
---|
| 1608 | END DO |
---|
| 1609 | END DO |
---|
| 1610 | END DO |
---|
| 1611 | ! !-- correct pond fraction to avoid a_ip > a_i |
---|
| 1612 | WHERE( pa_ip(:,:,:) > pa_i(:,:,:) ) pa_ip(:,:,:) = pa_i(:,:,:) |
---|
| 1613 | ! |
---|
| 1614 | ! |
---|
| 1615 | END SUBROUTINE Hbig |
---|
| 1616 | |
---|
[8586] | 1617 | #else |
---|
| 1618 | !!---------------------------------------------------------------------- |
---|
[9570] | 1619 | !! Default option Dummy module NO SI3 sea-ice model |
---|
[8586] | 1620 | !!---------------------------------------------------------------------- |
---|
| 1621 | #endif |
---|
| 1622 | |
---|
| 1623 | !!====================================================================== |
---|
| 1624 | END MODULE icedyn_adv_umx |
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