[8586] | 1 | MODULE icedyn_adv_umx |
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| 2 | !!============================================================================== |
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| 3 | !! *** MODULE icedyn_adv_umx *** |
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| 4 | !! sea-ice : advection using the ULTIMATE-MACHO scheme |
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| 5 | !!============================================================================== |
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| 6 | !! History : 3.6 ! 2014-11 (C. Rousset, G. Madec) Original code |
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[9604] | 7 | !! 4.0 ! 2018 (many people) SI3 [aka Sea Ice cube] |
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[8586] | 8 | !!---------------------------------------------------------------------- |
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[9570] | 9 | #if defined key_si3 |
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[8586] | 10 | !!---------------------------------------------------------------------- |
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[9570] | 11 | !! 'key_si3' SI3 sea-ice model |
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[8586] | 12 | !!---------------------------------------------------------------------- |
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[10911] | 13 | !! ice_dyn_adv_umx : update the tracer fields |
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[8586] | 14 | !! ultimate_x(_y) : compute a tracer value at velocity points using ULTIMATE scheme at various orders |
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[10911] | 15 | !! macho : compute the fluxes |
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| 16 | !! nonosc_ice : limit the fluxes using a non-oscillatory algorithm |
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[8586] | 17 | !!---------------------------------------------------------------------- |
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| 18 | USE phycst ! physical constant |
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| 19 | USE dom_oce ! ocean domain |
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| 20 | USE sbc_oce , ONLY : nn_fsbc ! update frequency of surface boundary condition |
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| 21 | USE ice ! sea-ice variables |
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[10413] | 22 | USE icevar ! sea-ice: operations |
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[8586] | 23 | ! |
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| 24 | USE in_out_manager ! I/O manager |
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[10786] | 25 | USE iom ! I/O manager library |
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[8586] | 26 | USE lib_mpp ! MPP library |
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| 27 | USE lib_fortran ! fortran utilities (glob_sum + no signed zero) |
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| 28 | USE lbclnk ! lateral boundary conditions (or mpp links) |
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| 29 | |
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| 30 | IMPLICIT NONE |
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| 31 | PRIVATE |
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| 32 | |
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| 33 | PUBLIC ice_dyn_adv_umx ! called by icedyn_adv.F90 |
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[10930] | 34 | ! |
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[10945] | 35 | INTEGER, PARAMETER :: np_advS = 1 ! advection for S and T: dVS/dt = -div( uVS ) => np_advS = 1 |
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| 36 | ! or dVS/dt = -div( uA * uHS / u ) => np_advS = 2 |
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| 37 | ! or dVS/dt = -div( uV * uS / u ) => np_advS = 3 |
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| 38 | INTEGER, PARAMETER :: np_limiter = 1 ! limiter: 1 = nonosc |
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| 39 | ! 2 = superbee |
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| 40 | ! 3 = h3 |
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| 41 | LOGICAL :: ll_upsxy = .TRUE. ! alternate directions for upstream |
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| 42 | LOGICAL :: ll_hoxy = .TRUE. ! alternate directions for high order |
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| 43 | LOGICAL :: ll_neg = .TRUE. ! if T interpolated at u/v points is negative or v_i < 1.e-6 |
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| 44 | ! then interpolate T at u/v points using the upstream scheme |
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| 45 | LOGICAL :: ll_prelim = .FALSE. ! prelimiter from: Zalesak(1979) eq. 14 => not well defined in 2D |
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[10930] | 46 | ! |
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[10945] | 47 | REAL(wp) :: z1_6 = 1._wp / 6._wp ! =1/6 |
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| 48 | REAL(wp) :: z1_120 = 1._wp / 120._wp ! =1/120 |
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[10930] | 49 | ! |
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[10945] | 50 | INTEGER, ALLOCATABLE, DIMENSION(:,:,:) :: imsk_small, jmsk_small |
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[10930] | 51 | ! |
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[8586] | 52 | !! * Substitutions |
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| 53 | # include "vectopt_loop_substitute.h90" |
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| 54 | !!---------------------------------------------------------------------- |
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[9598] | 55 | !! NEMO/ICE 4.0 , NEMO Consortium (2018) |
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[10069] | 56 | !! $Id$ |
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[10413] | 57 | !! Software governed by the CeCILL licence (./LICENSE) |
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[8586] | 58 | !!---------------------------------------------------------------------- |
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| 59 | CONTAINS |
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| 60 | |
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[10911] | 61 | SUBROUTINE ice_dyn_adv_umx( kn_umx, kt, pu_ice, pv_ice, ph_i, ph_s, ph_ip, & |
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[10413] | 62 | & 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] | 63 | !!---------------------------------------------------------------------- |
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| 64 | !! *** ROUTINE ice_dyn_adv_umx *** |
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| 65 | !! |
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| 66 | !! ** Purpose : Compute the now trend due to total advection of |
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| 67 | !! tracers and add it to the general trend of tracer equations |
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| 68 | !! using an "Ultimate-Macho" scheme |
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| 69 | !! |
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| 70 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
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| 71 | !!---------------------------------------------------------------------- |
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[10413] | 72 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
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[8586] | 73 | INTEGER , INTENT(in ) :: kt ! time step |
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| 74 | REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pu_ice ! ice i-velocity |
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| 75 | REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pv_ice ! ice j-velocity |
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[10911] | 76 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: ph_i ! ice thickness |
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| 77 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: ph_s ! snw thickness |
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| 78 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: ph_ip ! ice pond thickness |
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[8586] | 79 | REAL(wp), DIMENSION(:,:) , INTENT(inout) :: pato_i ! open water area |
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| 80 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i ! ice volume |
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| 81 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_s ! snw volume |
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| 82 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: psv_i ! salt content |
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| 83 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: poa_i ! age content |
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| 84 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_i ! ice concentration |
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[11627] | 85 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_ip ! melt pond concentration |
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[8586] | 86 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_ip ! melt pond volume |
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| 87 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s ! snw heat content |
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| 88 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_i ! ice heat content |
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| 89 | ! |
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| 90 | INTEGER :: ji, jj, jk, jl, jt ! dummy loop indices |
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[10413] | 91 | INTEGER :: icycle ! number of sub-timestep for the advection |
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| 92 | REAL(wp) :: zamsk ! 1 if advection of concentration, 0 if advection of other tracers |
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[10930] | 93 | REAL(wp) :: zdt, zvi_cen |
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[10911] | 94 | REAL(wp), DIMENSION(1) :: zcflprv, zcflnow ! for global communication |
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[10945] | 95 | REAL(wp), DIMENSION(jpi,jpj) :: zudy, zvdx, zcu_box, zcv_box |
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[10439] | 96 | REAL(wp), DIMENSION(jpi,jpj) :: zati1, zati2 |
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[10945] | 97 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zu_cat, zv_cat |
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[10911] | 98 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zua_ho, zva_ho, zua_ups, zva_ups |
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[10945] | 99 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: z1_ai , z1_aip, zhvar |
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[10911] | 100 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zhi_max, zhs_max, zhip_max |
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[10945] | 101 | ! |
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| 102 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: zuv_ho, zvv_ho, zuv_ups, zvv_ups, z1_vi, z1_vs |
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[8586] | 103 | !!---------------------------------------------------------------------- |
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| 104 | ! |
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| 105 | IF( kt == nit000 .AND. lwp ) WRITE(numout,*) '-- ice_dyn_adv_umx: Ultimate-Macho advection scheme' |
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| 106 | ! |
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[10911] | 107 | ! --- Record max of the surrounding 9-pts ice thick. (for call Hbig) --- ! |
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| 108 | DO jl = 1, jpl |
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| 109 | DO jj = 2, jpjm1 |
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| 110 | DO ji = fs_2, fs_jpim1 |
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| 111 | 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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| 112 | & ph_ip(ji-1,jj ,jl), ph_ip(ji ,jj-1,jl), & |
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| 113 | & ph_ip(ji+1,jj+1,jl), ph_ip(ji-1,jj-1,jl), & |
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| 114 | & ph_ip(ji+1,jj-1,jl), ph_ip(ji-1,jj+1,jl) ) |
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| 115 | 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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| 116 | & ph_i (ji-1,jj ,jl), ph_i (ji ,jj-1,jl), & |
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| 117 | & ph_i (ji+1,jj+1,jl), ph_i (ji-1,jj-1,jl), & |
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| 118 | & ph_i (ji+1,jj-1,jl), ph_i (ji-1,jj+1,jl) ) |
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| 119 | 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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| 120 | & ph_s (ji-1,jj ,jl), ph_s (ji ,jj-1,jl), & |
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| 121 | & ph_s (ji+1,jj+1,jl), ph_s (ji-1,jj-1,jl), & |
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| 122 | & ph_s (ji+1,jj-1,jl), ph_s (ji-1,jj+1,jl) ) |
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| 123 | END DO |
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| 124 | END DO |
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| 125 | END DO |
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[10930] | 126 | CALL lbc_lnk_multi( 'icedyn_adv_umx', zhi_max, 'T', 1., zhs_max, 'T', 1., zhip_max, 'T', 1. ) |
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[10911] | 127 | ! |
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| 128 | ! |
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| 129 | ! --- If ice drift is too fast, use subtime steps for advection (CFL test for stability) --- ! |
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| 130 | ! Note: the advection split is applied at the next time-step in order to avoid blocking global comm. |
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| 131 | ! this should not affect too much the stability |
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[10425] | 132 | zcflnow(1) = MAXVAL( ABS( pu_ice(:,:) ) * rdt_ice * r1_e1u(:,:) ) |
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| 133 | zcflnow(1) = MAX( zcflnow(1), MAXVAL( ABS( pv_ice(:,:) ) * rdt_ice * r1_e2v(:,:) ) ) |
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| 134 | |
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| 135 | ! non-blocking global communication send zcflnow and receive zcflprv |
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| 136 | CALL mpp_delay_max( 'icedyn_adv_umx', 'cflice', zcflnow(:), zcflprv(:), kt == nitend - nn_fsbc + 1 ) |
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[8586] | 137 | |
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[10425] | 138 | IF( zcflprv(1) > .5 ) THEN ; icycle = 2 |
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| 139 | ELSE ; icycle = 1 |
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[8586] | 140 | ENDIF |
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[10413] | 141 | zdt = rdt_ice / REAL(icycle) |
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[8586] | 142 | |
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| 143 | ! --- transport --- ! |
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| 144 | zudy(:,:) = pu_ice(:,:) * e2u(:,:) |
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| 145 | zvdx(:,:) = pv_ice(:,:) * e1v(:,:) |
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[10945] | 146 | ! |
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| 147 | ! setup transport for each ice cat |
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| 148 | DO jl = 1, jpl |
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| 149 | zu_cat(:,:,jl) = zudy(:,:) |
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| 150 | zv_cat(:,:,jl) = zvdx(:,:) |
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| 151 | END DO |
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| 152 | ! |
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[8586] | 153 | ! --- define velocity for advection: u*grad(H) --- ! |
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| 154 | DO jj = 2, jpjm1 |
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| 155 | DO ji = fs_2, fs_jpim1 |
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| 156 | IF ( pu_ice(ji,jj) * pu_ice(ji-1,jj) <= 0._wp ) THEN ; zcu_box(ji,jj) = 0._wp |
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| 157 | ELSEIF( pu_ice(ji,jj) > 0._wp ) THEN ; zcu_box(ji,jj) = pu_ice(ji-1,jj) |
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| 158 | ELSE ; zcu_box(ji,jj) = pu_ice(ji ,jj) |
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| 159 | ENDIF |
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| 160 | |
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| 161 | IF ( pv_ice(ji,jj) * pv_ice(ji,jj-1) <= 0._wp ) THEN ; zcv_box(ji,jj) = 0._wp |
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| 162 | ELSEIF( pv_ice(ji,jj) > 0._wp ) THEN ; zcv_box(ji,jj) = pv_ice(ji,jj-1) |
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| 163 | ELSE ; zcv_box(ji,jj) = pv_ice(ji,jj ) |
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| 164 | ENDIF |
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| 165 | END DO |
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| 166 | END DO |
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| 167 | |
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| 168 | !---------------! |
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| 169 | !== advection ==! |
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| 170 | !---------------! |
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[10413] | 171 | DO jt = 1, icycle |
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| 172 | |
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[10439] | 173 | ! record at_i before advection (for open water) |
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| 174 | zati1(:,:) = SUM( pa_i(:,:,:), dim=3 ) |
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[10413] | 175 | |
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[10439] | 176 | ! inverse of A and Ap |
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[10425] | 177 | WHERE( pa_i(:,:,:) >= epsi20 ) ; z1_ai(:,:,:) = 1._wp / pa_i(:,:,:) |
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| 178 | ELSEWHERE ; z1_ai(:,:,:) = 0. |
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| 179 | END WHERE |
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| 180 | WHERE( pa_ip(:,:,:) >= epsi20 ) ; z1_aip(:,:,:) = 1._wp / pa_ip(:,:,:) |
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| 181 | ELSEWHERE ; z1_aip(:,:,:) = 0. |
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| 182 | END WHERE |
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| 183 | ! |
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[10930] | 184 | ! setup a mask where advection will be upstream |
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| 185 | IF( ll_neg ) THEN |
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[10945] | 186 | IF( .NOT. ALLOCATED(imsk_small) ) ALLOCATE( imsk_small(jpi,jpj,jpl) ) |
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| 187 | IF( .NOT. ALLOCATED(jmsk_small) ) ALLOCATE( jmsk_small(jpi,jpj,jpl) ) |
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[10930] | 188 | DO jl = 1, jpl |
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| 189 | DO jj = 1, jpjm1 |
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| 190 | DO ji = 1, jpim1 |
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| 191 | zvi_cen = 0.5_wp * ( pv_i(ji+1,jj,jl) + pv_i(ji,jj,jl) ) |
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[10945] | 192 | IF( zvi_cen < epsi06) THEN ; imsk_small(ji,jj,jl) = 0 |
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| 193 | ELSE ; imsk_small(ji,jj,jl) = 1 ; ENDIF |
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[10930] | 194 | zvi_cen = 0.5_wp * ( pv_i(ji,jj+1,jl) + pv_i(ji,jj,jl) ) |
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[10945] | 195 | IF( zvi_cen < epsi06) THEN ; jmsk_small(ji,jj,jl) = 0 |
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| 196 | ELSE ; jmsk_small(ji,jj,jl) = 1 ; ENDIF |
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[10930] | 197 | END DO |
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| 198 | END DO |
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| 199 | END DO |
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| 200 | ENDIF |
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| 201 | ! |
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| 202 | ! ----------------------- ! |
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| 203 | ! ==> start advection <== ! |
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| 204 | ! ----------------------- ! |
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| 205 | ! |
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[10911] | 206 | !== Ice area ==! |
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[10425] | 207 | zamsk = 1._wp |
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[10945] | 208 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zu_cat , zv_cat , zcu_box, zcv_box, & |
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[10911] | 209 | & pa_i, pa_i, zua_ups, zva_ups, zua_ho , zva_ho ) |
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[10945] | 210 | ! |
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| 211 | ! ! --------------------------------- ! |
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| 212 | IF( np_advS == 1 ) THEN ! -- advection form: -div( uVS ) -- ! |
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| 213 | ! ! --------------------------------- ! |
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| 214 | zamsk = 0._wp |
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[10911] | 215 | !== Ice volume ==! |
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| 216 | zhvar(:,:,:) = pv_i(:,:,:) * z1_ai(:,:,:) |
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| 217 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
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| 218 | & zhvar, pv_i, zua_ups, zva_ups ) |
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| 219 | !== Snw volume ==! |
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| 220 | zhvar(:,:,:) = pv_s(:,:,:) * z1_ai(:,:,:) |
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| 221 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
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| 222 | & zhvar, pv_s, zua_ups, zva_ups ) |
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| 223 | ! |
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[10945] | 224 | zamsk = 1._wp |
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[10911] | 225 | !== Salt content ==! |
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[10945] | 226 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat, zv_cat, zcu_box, zcv_box, & |
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| 227 | & psv_i, psv_i ) |
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| 228 | !== Ice heat content ==! |
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| 229 | DO jk = 1, nlay_i |
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| 230 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat, zv_cat, zcu_box, zcv_box, & |
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| 231 | & pe_i(:,:,jk,:), pe_i(:,:,jk,:) ) |
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| 232 | END DO |
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| 233 | !== Snw heat content ==! |
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| 234 | DO jk = 1, nlay_s |
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| 235 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat, zv_cat, zcu_box, zcv_box, & |
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| 236 | & pe_s(:,:,jk,:), pe_s(:,:,jk,:) ) |
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| 237 | END DO |
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| 238 | ! |
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| 239 | ! ! ------------------------------------------ ! |
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| 240 | ELSEIF( np_advS == 2 ) THEN ! -- advection form: -div( uA * uHS / u ) -- ! |
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| 241 | ! ! ------------------------------------------ ! |
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| 242 | zamsk = 0._wp |
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| 243 | !== Ice volume ==! |
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| 244 | zhvar(:,:,:) = pv_i(:,:,:) * z1_ai(:,:,:) |
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| 245 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
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| 246 | & zhvar, pv_i, zua_ups, zva_ups ) |
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| 247 | !== Snw volume ==! |
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| 248 | zhvar(:,:,:) = pv_s(:,:,:) * z1_ai(:,:,:) |
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| 249 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
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| 250 | & zhvar, pv_s, zua_ups, zva_ups ) |
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| 251 | !== Salt content ==! |
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[10911] | 252 | zhvar(:,:,:) = psv_i(:,:,:) * z1_ai(:,:,:) |
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| 253 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zua_ho , zva_ho , zcu_box, zcv_box, & |
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| 254 | & zhvar, psv_i, zua_ups, zva_ups ) |
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| 255 | !== Ice heat content ==! |
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| 256 | DO jk = 1, nlay_i |
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| 257 | zhvar(:,:,:) = pe_i(:,:,jk,:) * z1_ai(:,:,:) |
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| 258 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho, zva_ho, zcu_box, zcv_box, & |
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| 259 | & zhvar, pe_i(:,:,jk,:), zua_ups, zva_ups ) |
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| 260 | END DO |
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| 261 | !== Snw heat content ==! |
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| 262 | DO jk = 1, nlay_s |
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| 263 | zhvar(:,:,:) = pe_s(:,:,jk,:) * z1_ai(:,:,:) |
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| 264 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho, zva_ho, zcu_box, zcv_box, & |
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| 265 | & zhvar, pe_s(:,:,jk,:), zua_ups, zva_ups ) |
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| 266 | END DO |
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| 267 | ! |
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[10945] | 268 | ! ! ----------------------------------------- ! |
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| 269 | ELSEIF( np_advS == 3 ) THEN ! -- advection form: -div( uV * uS / u ) -- ! |
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| 270 | ! ! ----------------------------------------- ! |
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| 271 | zamsk = 0._wp |
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| 272 | ! |
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| 273 | ALLOCATE( zuv_ho (jpi,jpj,jpl), zvv_ho (jpi,jpj,jpl), & |
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| 274 | & zuv_ups(jpi,jpj,jpl), zvv_ups(jpi,jpj,jpl), z1_vi(jpi,jpj,jpl), z1_vs(jpi,jpj,jpl) ) |
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| 275 | ! |
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[10911] | 276 | ! inverse of Vi |
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| 277 | WHERE( pv_i(:,:,:) >= epsi20 ) ; z1_vi(:,:,:) = 1._wp / pv_i(:,:,:) |
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| 278 | ELSEWHERE ; z1_vi(:,:,:) = 0. |
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| 279 | END WHERE |
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| 280 | ! inverse of Vs |
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| 281 | WHERE( pv_s(:,:,:) >= epsi20 ) ; z1_vs(:,:,:) = 1._wp / pv_s(:,:,:) |
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| 282 | ELSEWHERE ; z1_vs(:,:,:) = 0. |
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| 283 | END WHERE |
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| 284 | ! |
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| 285 | ! It is important to first calculate the ice fields and then the snow fields (because we use the same arrays) |
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| 286 | ! |
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| 287 | !== Ice volume ==! |
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| 288 | zuv_ups = zua_ups |
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| 289 | zvv_ups = zva_ups |
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| 290 | zhvar(:,:,:) = pv_i(:,:,:) * z1_ai(:,:,:) |
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| 291 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
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| 292 | & zhvar, pv_i, zuv_ups, zvv_ups, zuv_ho , zvv_ho ) |
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| 293 | !== Salt content ==! |
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| 294 | zhvar(:,:,:) = psv_i(:,:,:) * z1_vi(:,:,:) |
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| 295 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zuv_ho , zvv_ho , zcu_box, zcv_box, & |
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| 296 | & zhvar, psv_i, zuv_ups, zvv_ups ) |
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| 297 | !== Ice heat content ==! |
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| 298 | DO jk = 1, nlay_i |
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| 299 | zhvar(:,:,:) = pe_i(:,:,jk,:) * z1_vi(:,:,:) |
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| 300 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zuv_ho, zvv_ho, zcu_box, zcv_box, & |
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| 301 | & zhvar, pe_i(:,:,jk,:), zuv_ups, zvv_ups ) |
---|
| 302 | END DO |
---|
| 303 | !== Snow volume ==! |
---|
| 304 | zuv_ups = zua_ups |
---|
| 305 | zvv_ups = zva_ups |
---|
| 306 | zhvar(:,:,:) = pv_s(:,:,:) * z1_ai(:,:,:) |
---|
| 307 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zua_ho , zva_ho , zcu_box, zcv_box, & |
---|
| 308 | & zhvar, pv_s, zuv_ups, zvv_ups, zuv_ho , zvv_ho ) |
---|
| 309 | !== Snw heat content ==! |
---|
| 310 | DO jk = 1, nlay_s |
---|
| 311 | zhvar(:,:,:) = pe_s(:,:,jk,:) * z1_vs(:,:,:) |
---|
| 312 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx, zuv_ho, zvv_ho, zcu_box, zcv_box, & |
---|
| 313 | & zhvar, pe_s(:,:,jk,:), zuv_ups, zvv_ups ) |
---|
| 314 | END DO |
---|
| 315 | ! |
---|
[10945] | 316 | DEALLOCATE( zuv_ho, zvv_ho, zuv_ups, zvv_ups, z1_vi, z1_vs ) |
---|
| 317 | ! |
---|
[10911] | 318 | ENDIF |
---|
[10425] | 319 | ! |
---|
[10911] | 320 | !== Ice age ==! |
---|
[11612] | 321 | zamsk = 1._wp |
---|
| 322 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat, zv_cat, zcu_box, zcv_box, & |
---|
| 323 | & poa_i, poa_i ) |
---|
[10786] | 324 | ! |
---|
[10911] | 325 | !== melt ponds ==! |
---|
| 326 | IF ( ln_pnd_H12 ) THEN |
---|
[11627] | 327 | ! concentration |
---|
[10425] | 328 | zamsk = 1._wp |
---|
[10945] | 329 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zu_cat , zv_cat , zcu_box, zcv_box, & |
---|
[10911] | 330 | & pa_ip, pa_ip, zua_ups, zva_ups, zua_ho , zva_ho ) |
---|
[10945] | 331 | ! volume |
---|
[10425] | 332 | zamsk = 0._wp |
---|
[10475] | 333 | zhvar(:,:,:) = pv_ip(:,:,:) * z1_aip(:,:,:) |
---|
[10911] | 334 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy , zvdx , zua_ho , zva_ho , zcu_box, zcv_box, & |
---|
| 335 | & zhvar, pv_ip, zua_ups, zva_ups ) |
---|
[10425] | 336 | ENDIF |
---|
[10418] | 337 | ! |
---|
[10911] | 338 | !== Open water area ==! |
---|
[10439] | 339 | zati2(:,:) = SUM( pa_i(:,:,:), dim=3 ) |
---|
| 340 | DO jj = 2, jpjm1 |
---|
| 341 | DO ji = fs_2, fs_jpim1 |
---|
[10911] | 342 | pato_i(ji,jj) = pato_i(ji,jj) - ( zati2(ji,jj) - zati1(ji,jj) ) & |
---|
[10439] | 343 | & - ( zudy(ji,jj) - zudy(ji-1,jj) + zvdx(ji,jj) - zvdx(ji,jj-1) ) * r1_e1e2t(ji,jj) * zdt |
---|
[10413] | 344 | END DO |
---|
[10439] | 345 | END DO |
---|
[10930] | 346 | CALL lbc_lnk( 'icedyn_adv_umx', pato_i, 'T', 1. ) |
---|
[10418] | 347 | ! |
---|
[10911] | 348 | ! |
---|
| 349 | ! --- Ensure non-negative fields and in-bound thicknesses --- ! |
---|
| 350 | ! Remove negative values (conservation is ensured) |
---|
| 351 | ! (because advected fields are not perfectly bounded and tiny negative values can occur, e.g. -1.e-20) |
---|
[10930] | 352 | CALL ice_var_zapneg( zdt, pato_i, pv_i, pv_s, psv_i, poa_i, pa_i, pa_ip, pv_ip, pe_s, pe_i ) |
---|
[10911] | 353 | ! |
---|
[12197] | 354 | ! --- Make sure ice thickness is not too big --- ! |
---|
| 355 | ! (because ice thickness can be too large where ice concentration is very small) |
---|
| 356 | CALL Hbig( zdt, zhi_max, zhs_max, zhip_max, pv_i, pv_s, pa_i, pa_ip, pv_ip, pe_s ) |
---|
| 357 | ! |
---|
| 358 | ! --- Ensure snow load is not too big --- ! |
---|
| 359 | CALL Hsnow( zdt, pv_i, pv_s, pa_i, pa_ip, pe_s ) |
---|
| 360 | ! |
---|
[8586] | 361 | END DO |
---|
| 362 | ! |
---|
| 363 | END SUBROUTINE ice_dyn_adv_umx |
---|
[9929] | 364 | |
---|
[8586] | 365 | |
---|
[10911] | 366 | SUBROUTINE adv_umx( pamsk, kn_umx, jt, kt, pdt, pu, pv, puc, pvc, pubox, pvbox, & |
---|
| 367 | & pt, ptc, pua_ups, pva_ups, pua_ho, pva_ho ) |
---|
[8586] | 368 | !!---------------------------------------------------------------------- |
---|
| 369 | !! *** ROUTINE adv_umx *** |
---|
| 370 | !! |
---|
| 371 | !! ** Purpose : Compute the now trend due to total advection of |
---|
[10446] | 372 | !! tracers and add it to the general trend of tracer equations |
---|
[8586] | 373 | !! |
---|
[10911] | 374 | !! ** Method : - calculate upstream fluxes and upstream solution for tracers V/A(=H) etc |
---|
[10446] | 375 | !! - calculate tracer H at u and v points (Ultimate) |
---|
[10911] | 376 | !! - calculate the high order fluxes using alterning directions (Macho) |
---|
[10519] | 377 | !! - apply a limiter on the fluxes (nonosc_ice) |
---|
[10911] | 378 | !! - convert this tracer flux to a "volume" flux (uH -> uV) |
---|
| 379 | !! - apply a limiter a second time on the volumes fluxes (nonosc_ice) |
---|
| 380 | !! - calculate the high order solution for V |
---|
[8586] | 381 | !! |
---|
[10911] | 382 | !! ** Action : solve 3 equations => a) dA/dt = -div(uA) |
---|
| 383 | !! b) dV/dt = -div(uV) using dH/dt = -u.grad(H) |
---|
| 384 | !! c) dVS/dt = -div(uVS) using either dHS/dt = -u.grad(HS) or dS/dt = -u.grad(S) |
---|
[10446] | 385 | !! |
---|
[10911] | 386 | !! in eq. b), - fluxes uH are evaluated (with UMx) and limited with nonosc_ice. This step is necessary to get a good H. |
---|
| 387 | !! - then we convert this flux to a "volume" flux this way => uH * uA / u |
---|
| 388 | !! where uA is the flux from eq. a) |
---|
| 389 | !! this "volume" flux is also limited with nonosc_ice (otherwise overshoots can occur) |
---|
| 390 | !! - at last we estimate dV/dt = -div(uH * uA / u) |
---|
| 391 | !! |
---|
| 392 | !! in eq. c), one can solve the equation for S (ln_advS=T), then dVS/dt = -div(uV * uS / u) |
---|
| 393 | !! or for HS (ln_advS=F), then dVS/dt = -div(uA * uHS / u) |
---|
| 394 | !! |
---|
| 395 | !! ** Note : - this method can lead to tiny negative V (-1.e-20) => set it to 0 while conserving mass etc. |
---|
| 396 | !! - At the ice edge, Ultimate scheme can lead to: |
---|
| 397 | !! 1) negative interpolated tracers at u-v points |
---|
| 398 | !! 2) non-zero interpolated tracers at u-v points eventhough there is no ice and velocity is outward |
---|
| 399 | !! Solution for 1): apply an upstream scheme when it occurs. A better solution would be to degrade the order of |
---|
| 400 | !! the scheme automatically by applying a mask of the ice cover inside Ultimate (not done). |
---|
| 401 | !! Solution for 2): we set it to 0 in this case |
---|
[10446] | 402 | !! - Eventhough 1D tests give very good results (typically the one from Schar & Smolarkiewiecz), the 2D is less good. |
---|
| 403 | !! Large values of H can appear for very small ice concentration, and when it does it messes the things up since we |
---|
[10911] | 404 | !! work on H (and not V). It is partly related to the multi-category approach |
---|
[10446] | 405 | !! Therefore, after advection we limit the thickness to the largest value of the 9-points around (only if ice |
---|
[10911] | 406 | !! concentration is small). Since we do not limit S and T, large values can occur at the edge but it does not really matter |
---|
| 407 | !! since sv_i and e_i are still good. |
---|
[8586] | 408 | !!---------------------------------------------------------------------- |
---|
[10911] | 409 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 410 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
| 411 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
| 412 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
| 413 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 414 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu , pv ! 2 ice velocity components => u*e2 |
---|
| 415 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: puc , pvc ! 2 ice velocity components => u*e2 or u*a*e2u |
---|
| 416 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pubox, pvbox ! upstream velocity |
---|
| 417 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pt ! tracer field |
---|
| 418 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: ptc ! tracer content field |
---|
| 419 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT(inout), OPTIONAL :: pua_ups, pva_ups ! upstream u*a fluxes |
---|
| 420 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out), OPTIONAL :: pua_ho, pva_ho ! high order u*a fluxes |
---|
[8586] | 421 | ! |
---|
[10425] | 422 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[8586] | 423 | REAL(wp) :: ztra ! local scalar |
---|
[10446] | 424 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zfu_ho , zfv_ho , zpt |
---|
[10439] | 425 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zfu_ups, zfv_ups, zt_ups |
---|
[8586] | 426 | !!---------------------------------------------------------------------- |
---|
| 427 | ! |
---|
[10446] | 428 | ! Upstream (_ups) fluxes |
---|
| 429 | ! ----------------------- |
---|
| 430 | CALL upstream( pamsk, jt, kt, pdt, pt, pu, pv, zt_ups, zfu_ups, zfv_ups ) |
---|
| 431 | |
---|
| 432 | ! High order (_ho) fluxes |
---|
| 433 | ! ----------------------- |
---|
| 434 | SELECT CASE( kn_umx ) |
---|
| 435 | ! |
---|
| 436 | CASE ( 20 ) !== centered second order ==! |
---|
| 437 | ! |
---|
[10475] | 438 | CALL cen2( pamsk, jt, kt, pdt, pt, pu, pv, zt_ups, zfu_ups, zfv_ups, zfu_ho, zfv_ho ) |
---|
[10446] | 439 | ! |
---|
| 440 | CASE ( 1:5 ) !== 1st to 5th order ULTIMATE-MACHO scheme ==! |
---|
| 441 | ! |
---|
[10475] | 442 | CALL macho( pamsk, kn_umx, jt, kt, pdt, pt, pu, pv, pubox, pvbox, zt_ups, zfu_ups, zfv_ups, zfu_ho, zfv_ho ) |
---|
[10446] | 443 | ! |
---|
| 444 | END SELECT |
---|
[10439] | 445 | ! |
---|
[10446] | 446 | ! --ho --ho |
---|
| 447 | ! new fluxes = u*H * u*a / u |
---|
| 448 | ! ---------------------------- |
---|
[10475] | 449 | IF( pamsk == 0._wp ) THEN |
---|
[10446] | 450 | DO jl = 1, jpl |
---|
| 451 | DO jj = 1, jpjm1 |
---|
| 452 | DO ji = 1, fs_jpim1 |
---|
[10911] | 453 | IF( ABS( pu(ji,jj) ) > epsi10 ) THEN |
---|
| 454 | zfu_ho (ji,jj,jl) = zfu_ho (ji,jj,jl) * puc (ji,jj,jl) / pu(ji,jj) |
---|
| 455 | zfu_ups(ji,jj,jl) = zfu_ups(ji,jj,jl) * pua_ups(ji,jj,jl) / pu(ji,jj) |
---|
[10446] | 456 | ELSE |
---|
| 457 | zfu_ho (ji,jj,jl) = 0._wp |
---|
| 458 | zfu_ups(ji,jj,jl) = 0._wp |
---|
| 459 | ENDIF |
---|
| 460 | ! |
---|
[10911] | 461 | IF( ABS( pv(ji,jj) ) > epsi10 ) THEN |
---|
| 462 | zfv_ho (ji,jj,jl) = zfv_ho (ji,jj,jl) * pvc (ji,jj,jl) / pv(ji,jj) |
---|
| 463 | zfv_ups(ji,jj,jl) = zfv_ups(ji,jj,jl) * pva_ups(ji,jj,jl) / pv(ji,jj) |
---|
[10446] | 464 | ELSE |
---|
| 465 | zfv_ho (ji,jj,jl) = 0._wp |
---|
| 466 | zfv_ups(ji,jj,jl) = 0._wp |
---|
| 467 | ENDIF |
---|
| 468 | END DO |
---|
| 469 | END DO |
---|
| 470 | END DO |
---|
[10911] | 471 | |
---|
| 472 | ! the new "volume" fluxes must also be "flux corrected" |
---|
| 473 | ! thus we calculate the upstream solution and apply a limiter again |
---|
| 474 | DO jl = 1, jpl |
---|
| 475 | DO jj = 2, jpjm1 |
---|
| 476 | DO ji = fs_2, fs_jpim1 |
---|
| 477 | ztra = - ( zfu_ups(ji,jj,jl) - zfu_ups(ji-1,jj,jl) + zfv_ups(ji,jj,jl) - zfv_ups(ji,jj-1,jl) ) |
---|
| 478 | ! |
---|
| 479 | zt_ups(ji,jj,jl) = ( ptc(ji,jj,jl) + ztra * r1_e1e2t(ji,jj) * pdt ) * tmask(ji,jj,1) |
---|
| 480 | END DO |
---|
| 481 | END DO |
---|
| 482 | END DO |
---|
| 483 | CALL lbc_lnk( 'icedyn_adv_umx', zt_ups, 'T', 1. ) |
---|
| 484 | ! |
---|
[10945] | 485 | IF ( np_limiter == 1 ) THEN |
---|
[10911] | 486 | CALL nonosc_ice( 1._wp, pdt, pu, pv, ptc, zt_ups, zfu_ups, zfv_ups, zfu_ho, zfv_ho ) |
---|
[10945] | 487 | ELSEIF( np_limiter == 2 .OR. np_limiter == 3 ) THEN |
---|
[10911] | 488 | CALL limiter_x( pdt, pu, ptc, zfu_ups, zfu_ho ) |
---|
| 489 | CALL limiter_y( pdt, pv, ptc, zfv_ups, zfv_ho ) |
---|
| 490 | ENDIF |
---|
| 491 | ! |
---|
[10446] | 492 | ENDIF |
---|
[10911] | 493 | ! --ho --ups |
---|
| 494 | ! in case of advection of A: output u*a and u*a |
---|
| 495 | ! ----------------------------------------------- |
---|
[10446] | 496 | IF( PRESENT( pua_ho ) ) THEN |
---|
| 497 | DO jl = 1, jpl |
---|
| 498 | DO jj = 1, jpjm1 |
---|
| 499 | DO ji = 1, fs_jpim1 |
---|
[10911] | 500 | pua_ho (ji,jj,jl) = zfu_ho (ji,jj,jl) ; pva_ho (ji,jj,jl) = zfv_ho (ji,jj,jl) |
---|
| 501 | pua_ups(ji,jj,jl) = zfu_ups(ji,jj,jl) ; pva_ups(ji,jj,jl) = zfv_ups(ji,jj,jl) |
---|
| 502 | END DO |
---|
[10446] | 503 | END DO |
---|
| 504 | END DO |
---|
| 505 | ENDIF |
---|
| 506 | ! |
---|
| 507 | ! final trend with corrected fluxes |
---|
| 508 | ! --------------------------------- |
---|
| 509 | DO jl = 1, jpl |
---|
| 510 | DO jj = 2, jpjm1 |
---|
| 511 | DO ji = fs_2, fs_jpim1 |
---|
| 512 | ztra = - ( zfu_ho(ji,jj,jl) - zfu_ho(ji-1,jj,jl) + zfv_ho(ji,jj,jl) - zfv_ho(ji,jj-1,jl) ) |
---|
| 513 | ! |
---|
| 514 | ptc(ji,jj,jl) = ( ptc(ji,jj,jl) + ztra * r1_e1e2t(ji,jj) * pdt ) * tmask(ji,jj,1) |
---|
| 515 | END DO |
---|
| 516 | END DO |
---|
| 517 | END DO |
---|
| 518 | CALL lbc_lnk( 'icedyn_adv_umx', ptc, 'T', 1. ) |
---|
| 519 | ! |
---|
| 520 | END SUBROUTINE adv_umx |
---|
| 521 | |
---|
| 522 | |
---|
| 523 | SUBROUTINE upstream( pamsk, jt, kt, pdt, pt, pu, pv, pt_ups, pfu_ups, pfv_ups ) |
---|
| 524 | !!--------------------------------------------------------------------- |
---|
| 525 | !! *** ROUTINE upstream *** |
---|
| 526 | !! |
---|
| 527 | !! ** Purpose : compute the upstream fluxes and upstream guess of tracer |
---|
| 528 | !!---------------------------------------------------------------------- |
---|
| 529 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 530 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
| 531 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
| 532 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 533 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
| 534 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu, pv ! 2 ice velocity components |
---|
| 535 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_ups ! upstream guess of tracer |
---|
| 536 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ups, pfv_ups ! upstream fluxes |
---|
| 537 | ! |
---|
| 538 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
| 539 | REAL(wp) :: ztra ! local scalar |
---|
| 540 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zpt |
---|
| 541 | !!---------------------------------------------------------------------- |
---|
| 542 | |
---|
[10439] | 543 | IF( .NOT. ll_upsxy ) THEN !** no alternate directions **! |
---|
[10446] | 544 | ! |
---|
[10425] | 545 | DO jl = 1, jpl |
---|
| 546 | DO jj = 1, jpjm1 |
---|
| 547 | DO ji = 1, fs_jpim1 |
---|
[10446] | 548 | 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) |
---|
| 549 | 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] | 550 | END DO |
---|
[10413] | 551 | END DO |
---|
| 552 | END DO |
---|
[10446] | 553 | ! |
---|
[10439] | 554 | ELSE !** alternate directions **! |
---|
[10413] | 555 | ! |
---|
| 556 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
---|
[10439] | 557 | ! |
---|
| 558 | DO jl = 1, jpl !-- flux in x-direction |
---|
[10425] | 559 | DO jj = 1, jpjm1 |
---|
| 560 | DO ji = 1, fs_jpim1 |
---|
[10446] | 561 | 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] | 562 | END DO |
---|
[10413] | 563 | END DO |
---|
| 564 | END DO |
---|
[10439] | 565 | ! |
---|
| 566 | DO jl = 1, jpl !-- first guess of tracer from u-flux |
---|
[10425] | 567 | DO jj = 2, jpjm1 |
---|
[10439] | 568 | DO ji = fs_2, fs_jpim1 |
---|
[10446] | 569 | ztra = - ( pfu_ups(ji,jj,jl) - pfu_ups(ji-1,jj,jl) ) & |
---|
| 570 | & + ( pu (ji,jj ) - pu (ji-1,jj ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 571 | ! |
---|
| 572 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
[10425] | 573 | END DO |
---|
[10413] | 574 | END DO |
---|
| 575 | END DO |
---|
[10425] | 576 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
---|
[8586] | 577 | ! |
---|
[10439] | 578 | DO jl = 1, jpl !-- flux in y-direction |
---|
[10425] | 579 | DO jj = 1, jpjm1 |
---|
| 580 | DO ji = 1, fs_jpim1 |
---|
[10446] | 581 | 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] | 582 | END DO |
---|
[10413] | 583 | END DO |
---|
| 584 | END DO |
---|
[10439] | 585 | ! |
---|
[10413] | 586 | ELSE !== even ice time step: adv_y then adv_x ==! |
---|
[10439] | 587 | ! |
---|
| 588 | DO jl = 1, jpl !-- flux in y-direction |
---|
[10425] | 589 | DO jj = 1, jpjm1 |
---|
| 590 | DO ji = 1, fs_jpim1 |
---|
[10446] | 591 | 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] | 592 | END DO |
---|
[10413] | 593 | END DO |
---|
| 594 | END DO |
---|
[10439] | 595 | ! |
---|
| 596 | DO jl = 1, jpl !-- first guess of tracer from v-flux |
---|
[10425] | 597 | DO jj = 2, jpjm1 |
---|
[10439] | 598 | DO ji = fs_2, fs_jpim1 |
---|
[10446] | 599 | ztra = - ( pfv_ups(ji,jj,jl) - pfv_ups(ji,jj-1,jl) ) & |
---|
| 600 | & + ( pv (ji,jj ) - pv (ji,jj-1 ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 601 | ! |
---|
| 602 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
[10425] | 603 | END DO |
---|
| 604 | END DO |
---|
[10413] | 605 | END DO |
---|
[10425] | 606 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
---|
[10413] | 607 | ! |
---|
[10439] | 608 | DO jl = 1, jpl !-- flux in x-direction |
---|
[10425] | 609 | DO jj = 1, jpjm1 |
---|
| 610 | DO ji = 1, fs_jpim1 |
---|
[10446] | 611 | 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] | 612 | END DO |
---|
[10413] | 613 | END DO |
---|
| 614 | END DO |
---|
| 615 | ! |
---|
| 616 | ENDIF |
---|
| 617 | |
---|
| 618 | ENDIF |
---|
[10439] | 619 | ! |
---|
| 620 | DO jl = 1, jpl !-- after tracer with upstream scheme |
---|
[10425] | 621 | DO jj = 2, jpjm1 |
---|
| 622 | DO ji = fs_2, fs_jpim1 |
---|
[10446] | 623 | ztra = - ( pfu_ups(ji,jj,jl) - pfu_ups(ji-1,jj ,jl) & |
---|
| 624 | & + pfv_ups(ji,jj,jl) - pfv_ups(ji ,jj-1,jl) ) & |
---|
| 625 | & + ( pu (ji,jj ) - pu (ji-1,jj ) & |
---|
| 626 | & + pv (ji,jj ) - pv (ji ,jj-1 ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 627 | ! |
---|
[10475] | 628 | pt_ups(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
[10425] | 629 | END DO |
---|
[10413] | 630 | END DO |
---|
[8586] | 631 | END DO |
---|
[10446] | 632 | CALL lbc_lnk( 'icedyn_adv_umx', pt_ups, 'T', 1. ) |
---|
[10413] | 633 | |
---|
[10446] | 634 | END SUBROUTINE upstream |
---|
[8586] | 635 | |
---|
[10446] | 636 | |
---|
[10475] | 637 | SUBROUTINE cen2( pamsk, jt, kt, pdt, pt, pu, pv, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[8586] | 638 | !!--------------------------------------------------------------------- |
---|
[10446] | 639 | !! *** ROUTINE cen2 *** |
---|
[8586] | 640 | !! |
---|
[10446] | 641 | !! ** Purpose : compute the high order fluxes using a centered |
---|
| 642 | !! second order scheme |
---|
[8586] | 643 | !!---------------------------------------------------------------------- |
---|
[10439] | 644 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 645 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
| 646 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
| 647 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 648 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
| 649 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu, pv ! 2 ice velocity components |
---|
[10446] | 650 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt_ups ! upstream guess of tracer |
---|
| 651 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pfu_ups, pfv_ups ! upstream fluxes |
---|
[10425] | 652 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ho, pfv_ho ! high order fluxes |
---|
[8586] | 653 | ! |
---|
[10425] | 654 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[10446] | 655 | REAL(wp) :: ztra ! local scalar |
---|
| 656 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zpt |
---|
[8586] | 657 | !!---------------------------------------------------------------------- |
---|
| 658 | ! |
---|
[10439] | 659 | IF( .NOT.ll_hoxy ) THEN !** no alternate directions **! |
---|
[8586] | 660 | ! |
---|
[10425] | 661 | DO jl = 1, jpl |
---|
| 662 | DO jj = 1, jpjm1 |
---|
| 663 | DO ji = 1, fs_jpim1 |
---|
[10475] | 664 | pfu_ho(ji,jj,jl) = 0.5_wp * pu(ji,jj) * ( pt(ji,jj,jl) + pt(ji+1,jj ,jl) ) |
---|
| 665 | pfv_ho(ji,jj,jl) = 0.5_wp * pv(ji,jj) * ( pt(ji,jj,jl) + pt(ji ,jj+1,jl) ) |
---|
[10425] | 666 | END DO |
---|
[8586] | 667 | END DO |
---|
| 668 | END DO |
---|
[10475] | 669 | ! |
---|
[10945] | 670 | IF ( np_limiter == 1 ) THEN |
---|
[10519] | 671 | CALL nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[10945] | 672 | ELSEIF( np_limiter == 2 .OR. np_limiter == 3 ) THEN |
---|
[10446] | 673 | CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
| 674 | CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 675 | ENDIF |
---|
[8586] | 676 | ! |
---|
[10439] | 677 | ELSE !** alternate directions **! |
---|
[8586] | 678 | ! |
---|
[10413] | 679 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
---|
| 680 | ! |
---|
[10439] | 681 | DO jl = 1, jpl !-- flux in x-direction |
---|
[10425] | 682 | DO jj = 1, jpjm1 |
---|
| 683 | DO ji = 1, fs_jpim1 |
---|
[10475] | 684 | pfu_ho(ji,jj,jl) = 0.5_wp * pu(ji,jj) * ( pt(ji,jj,jl) + pt(ji+1,jj,jl) ) |
---|
[10425] | 685 | END DO |
---|
[10413] | 686 | END DO |
---|
| 687 | END DO |
---|
[10945] | 688 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
[10413] | 689 | |
---|
[10439] | 690 | DO jl = 1, jpl !-- first guess of tracer from u-flux |
---|
[10425] | 691 | DO jj = 2, jpjm1 |
---|
[10439] | 692 | DO ji = fs_2, fs_jpim1 |
---|
[10446] | 693 | ztra = - ( pfu_ho(ji,jj,jl) - pfu_ho(ji-1,jj,jl) ) & |
---|
| 694 | & + ( pu (ji,jj ) - pu (ji-1,jj ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 695 | ! |
---|
| 696 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
[10425] | 697 | END DO |
---|
[10413] | 698 | END DO |
---|
| 699 | END DO |
---|
[10446] | 700 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
---|
[10413] | 701 | |
---|
[10439] | 702 | DO jl = 1, jpl !-- flux in y-direction |
---|
[10425] | 703 | DO jj = 1, jpjm1 |
---|
| 704 | DO ji = 1, fs_jpim1 |
---|
[10475] | 705 | pfv_ho(ji,jj,jl) = 0.5_wp * pv(ji,jj) * ( zpt(ji,jj,jl) + zpt(ji,jj+1,jl) ) |
---|
[10425] | 706 | END DO |
---|
[10413] | 707 | END DO |
---|
| 708 | END DO |
---|
[10945] | 709 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 710 | |
---|
| 711 | ELSE !== even ice time step: adv_y then adv_x ==! |
---|
| 712 | ! |
---|
[10439] | 713 | DO jl = 1, jpl !-- flux in y-direction |
---|
[10425] | 714 | DO jj = 1, jpjm1 |
---|
| 715 | DO ji = 1, fs_jpim1 |
---|
[10475] | 716 | pfv_ho(ji,jj,jl) = 0.5_wp * pv(ji,jj) * ( pt(ji,jj,jl) + pt(ji,jj+1,jl) ) |
---|
[10425] | 717 | END DO |
---|
[10413] | 718 | END DO |
---|
| 719 | END DO |
---|
[10945] | 720 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 721 | ! |
---|
[10439] | 722 | DO jl = 1, jpl !-- first guess of tracer from v-flux |
---|
[10425] | 723 | DO jj = 2, jpjm1 |
---|
[10439] | 724 | DO ji = fs_2, fs_jpim1 |
---|
[10446] | 725 | ztra = - ( pfv_ho(ji,jj,jl) - pfv_ho(ji,jj-1,jl) ) & |
---|
| 726 | & + ( pv (ji,jj ) - pv (ji,jj-1 ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 727 | ! |
---|
| 728 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
[10425] | 729 | END DO |
---|
[10413] | 730 | END DO |
---|
| 731 | END DO |
---|
[10446] | 732 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
---|
[10413] | 733 | ! |
---|
[10439] | 734 | DO jl = 1, jpl !-- flux in x-direction |
---|
[10425] | 735 | DO jj = 1, jpjm1 |
---|
| 736 | DO ji = 1, fs_jpim1 |
---|
[10475] | 737 | pfu_ho(ji,jj,jl) = 0.5_wp * pu(ji,jj) * ( zpt(ji,jj,jl) + zpt(ji+1,jj,jl) ) |
---|
[10425] | 738 | END DO |
---|
[10413] | 739 | END DO |
---|
| 740 | END DO |
---|
[10945] | 741 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
[10413] | 742 | |
---|
| 743 | ENDIF |
---|
[10945] | 744 | IF( np_limiter == 1 ) CALL nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[10413] | 745 | |
---|
| 746 | ENDIF |
---|
| 747 | |
---|
| 748 | END SUBROUTINE cen2 |
---|
| 749 | |
---|
| 750 | |
---|
[10475] | 751 | SUBROUTINE macho( pamsk, kn_umx, jt, kt, pdt, pt, pu, pv, pubox, pvbox, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[10413] | 752 | !!--------------------------------------------------------------------- |
---|
| 753 | !! *** ROUTINE macho *** |
---|
| 754 | !! |
---|
[10446] | 755 | !! ** Purpose : compute the high order fluxes using Ultimate-Macho scheme |
---|
[10413] | 756 | !! |
---|
[10446] | 757 | !! ** Method : ... |
---|
[10413] | 758 | !! |
---|
| 759 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
| 760 | !!---------------------------------------------------------------------- |
---|
[10439] | 761 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 762 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
| 763 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
| 764 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
| 765 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 766 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
| 767 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu, pv ! 2 ice velocity components |
---|
| 768 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pubox, pvbox ! upstream velocity |
---|
[10446] | 769 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt_ups ! upstream guess of tracer |
---|
| 770 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pfu_ups, pfv_ups ! upstream fluxes |
---|
[10425] | 771 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ho, pfv_ho ! high order fluxes |
---|
[10413] | 772 | ! |
---|
[10425] | 773 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[10446] | 774 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zt_u, zt_v, zpt |
---|
[10413] | 775 | !!---------------------------------------------------------------------- |
---|
| 776 | ! |
---|
| 777 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
---|
[8586] | 778 | ! |
---|
[10413] | 779 | ! !-- ultimate interpolation of pt at u-point --! |
---|
[10911] | 780 | CALL ultimate_x( pamsk, kn_umx, pdt, pt, pu, zt_u, pfu_ho ) |
---|
[10413] | 781 | ! !-- limiter in x --! |
---|
[10945] | 782 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
[10446] | 783 | ! !-- advective form update in zpt --! |
---|
[10439] | 784 | DO jl = 1, jpl |
---|
| 785 | DO jj = 2, jpjm1 |
---|
| 786 | DO ji = fs_2, fs_jpim1 |
---|
[10446] | 787 | 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) & |
---|
| 788 | & + pt (ji,jj,jl) * ( pu (ji,jj ) - pu (ji-1,jj ) ) * r1_e1e2t(ji,jj) & |
---|
| 789 | & * pamsk & |
---|
[10911] | 790 | & ) * pdt ) * tmask(ji,jj,1) |
---|
[10413] | 791 | END DO |
---|
[8586] | 792 | END DO |
---|
[10439] | 793 | END DO |
---|
[10446] | 794 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
---|
[8586] | 795 | ! |
---|
[10413] | 796 | ! !-- ultimate interpolation of pt at v-point --! |
---|
| 797 | IF( ll_hoxy ) THEN |
---|
[10911] | 798 | CALL ultimate_y( pamsk, kn_umx, pdt, zpt, pv, zt_v, pfv_ho ) |
---|
[10413] | 799 | ELSE |
---|
[10911] | 800 | CALL ultimate_y( pamsk, kn_umx, pdt, pt , pv, zt_v, pfv_ho ) |
---|
[10413] | 801 | ENDIF |
---|
| 802 | ! !-- limiter in y --! |
---|
[10945] | 803 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 804 | ! |
---|
| 805 | ! |
---|
| 806 | ELSE !== even ice time step: adv_y then adv_x ==! |
---|
| 807 | ! |
---|
| 808 | ! !-- ultimate interpolation of pt at v-point --! |
---|
[10911] | 809 | CALL ultimate_y( pamsk, kn_umx, pdt, pt, pv, zt_v, pfv_ho ) |
---|
[10413] | 810 | ! !-- limiter in y --! |
---|
[10945] | 811 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10446] | 812 | ! !-- advective form update in zpt --! |
---|
[10439] | 813 | DO jl = 1, jpl |
---|
| 814 | DO jj = 2, jpjm1 |
---|
| 815 | DO ji = fs_2, fs_jpim1 |
---|
[10446] | 816 | 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) & |
---|
| 817 | & + pt (ji,jj,jl) * ( pv (ji,jj ) - pv (ji,jj-1 ) ) * r1_e1e2t(ji,jj) & |
---|
| 818 | & * pamsk & |
---|
| 819 | & ) * pdt ) * tmask(ji,jj,1) |
---|
[10425] | 820 | END DO |
---|
[10413] | 821 | END DO |
---|
[10439] | 822 | END DO |
---|
[10446] | 823 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
---|
[10413] | 824 | ! |
---|
| 825 | ! !-- ultimate interpolation of pt at u-point --! |
---|
| 826 | IF( ll_hoxy ) THEN |
---|
[10911] | 827 | CALL ultimate_x( pamsk, kn_umx, pdt, zpt, pu, zt_u, pfu_ho ) |
---|
[10413] | 828 | ELSE |
---|
[10911] | 829 | CALL ultimate_x( pamsk, kn_umx, pdt, pt , pu, zt_u, pfu_ho ) |
---|
[10413] | 830 | ENDIF |
---|
| 831 | ! !-- limiter in x --! |
---|
[10945] | 832 | IF( np_limiter == 2 .OR. np_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
[10413] | 833 | ! |
---|
| 834 | ENDIF |
---|
| 835 | |
---|
[10945] | 836 | IF( np_limiter == 1 ) CALL nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[8586] | 837 | ! |
---|
| 838 | END SUBROUTINE macho |
---|
| 839 | |
---|
| 840 | |
---|
[10911] | 841 | SUBROUTINE ultimate_x( pamsk, kn_umx, pdt, pt, pu, pt_u, pfu_ho ) |
---|
[8586] | 842 | !!--------------------------------------------------------------------- |
---|
| 843 | !! *** ROUTINE ultimate_x *** |
---|
| 844 | !! |
---|
[10446] | 845 | !! ** Purpose : compute tracer at u-points |
---|
[8586] | 846 | !! |
---|
[10446] | 847 | !! ** Method : ... |
---|
[8586] | 848 | !! |
---|
| 849 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
| 850 | !!---------------------------------------------------------------------- |
---|
[10911] | 851 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
[10439] | 852 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
| 853 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 854 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu ! ice i-velocity component |
---|
| 855 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
[10425] | 856 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_u ! tracer at u-point |
---|
| 857 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ho ! high order flux |
---|
[8586] | 858 | ! |
---|
[10425] | 859 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[10930] | 860 | REAL(wp) :: zcu, zdx2, zdx4 ! - - |
---|
[10425] | 861 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: ztu1, ztu2, ztu3, ztu4 |
---|
[8586] | 862 | !!---------------------------------------------------------------------- |
---|
| 863 | ! |
---|
| 864 | ! !-- Laplacian in i-direction --! |
---|
[10425] | 865 | DO jl = 1, jpl |
---|
| 866 | DO jj = 2, jpjm1 ! First derivative (gradient) |
---|
| 867 | DO ji = 1, fs_jpim1 |
---|
| 868 | ztu1(ji,jj,jl) = ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) * r1_e1u(ji,jj) * umask(ji,jj,1) |
---|
| 869 | END DO |
---|
| 870 | ! ! Second derivative (Laplacian) |
---|
| 871 | DO ji = fs_2, fs_jpim1 |
---|
| 872 | ztu2(ji,jj,jl) = ( ztu1(ji,jj,jl) - ztu1(ji-1,jj,jl) ) * r1_e1t(ji,jj) |
---|
| 873 | END DO |
---|
[8586] | 874 | END DO |
---|
| 875 | END DO |
---|
[10425] | 876 | CALL lbc_lnk( 'icedyn_adv_umx', ztu2, 'T', 1. ) |
---|
[8586] | 877 | ! |
---|
| 878 | ! !-- BiLaplacian in i-direction --! |
---|
[10425] | 879 | DO jl = 1, jpl |
---|
| 880 | DO jj = 2, jpjm1 ! Third derivative |
---|
| 881 | DO ji = 1, fs_jpim1 |
---|
| 882 | ztu3(ji,jj,jl) = ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) * r1_e1u(ji,jj) * umask(ji,jj,1) |
---|
| 883 | END DO |
---|
| 884 | ! ! Fourth derivative |
---|
| 885 | DO ji = fs_2, fs_jpim1 |
---|
| 886 | ztu4(ji,jj,jl) = ( ztu3(ji,jj,jl) - ztu3(ji-1,jj,jl) ) * r1_e1t(ji,jj) |
---|
| 887 | END DO |
---|
[8586] | 888 | END DO |
---|
| 889 | END DO |
---|
[10425] | 890 | CALL lbc_lnk( 'icedyn_adv_umx', ztu4, 'T', 1. ) |
---|
[8586] | 891 | ! |
---|
| 892 | ! |
---|
[10413] | 893 | SELECT CASE (kn_umx ) |
---|
[8586] | 894 | ! |
---|
| 895 | CASE( 1 ) !== 1st order central TIM ==! (Eq. 21) |
---|
| 896 | ! |
---|
[10425] | 897 | DO jl = 1, jpl |
---|
| 898 | DO jj = 1, jpjm1 |
---|
| 899 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
[10475] | 900 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj,jl) + pt(ji,jj,jl) & |
---|
| 901 | & - SIGN( 1._wp, pu(ji,jj) ) * ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) ) |
---|
[10425] | 902 | END DO |
---|
[8586] | 903 | END DO |
---|
| 904 | END DO |
---|
| 905 | ! |
---|
| 906 | CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23) |
---|
| 907 | ! |
---|
[10425] | 908 | DO jl = 1, jpl |
---|
| 909 | DO jj = 1, jpjm1 |
---|
| 910 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 911 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
| 912 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj,jl) + pt(ji,jj,jl) & |
---|
[10475] | 913 | & - zcu * ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) ) |
---|
[10425] | 914 | END DO |
---|
[8586] | 915 | END DO |
---|
| 916 | END DO |
---|
| 917 | ! |
---|
| 918 | CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24) |
---|
| 919 | ! |
---|
[10425] | 920 | DO jl = 1, jpl |
---|
| 921 | DO jj = 1, jpjm1 |
---|
| 922 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 923 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
| 924 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
[10439] | 925 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
[10446] | 926 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj,jl) + pt (ji,jj,jl) & |
---|
[10475] | 927 | & - zcu * ( pt (ji+1,jj,jl) - pt (ji,jj,jl) ) ) & |
---|
| 928 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj,jl) + ztu2(ji,jj,jl) & |
---|
[10446] | 929 | & - SIGN( 1._wp, zcu ) * ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) ) ) |
---|
[10425] | 930 | END DO |
---|
[8586] | 931 | END DO |
---|
| 932 | END DO |
---|
| 933 | ! |
---|
| 934 | CASE( 4 ) !== 4th order central TIM ==! (Eq. 27) |
---|
| 935 | ! |
---|
[10425] | 936 | DO jl = 1, jpl |
---|
| 937 | DO jj = 1, jpjm1 |
---|
| 938 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 939 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
| 940 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
[10439] | 941 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
[10475] | 942 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj,jl) + pt (ji,jj,jl) & |
---|
| 943 | & - zcu * ( pt (ji+1,jj,jl) - pt (ji,jj,jl) ) ) & |
---|
| 944 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj,jl) + ztu2(ji,jj,jl) & |
---|
| 945 | & - 0.5_wp * zcu * ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) ) ) |
---|
[10425] | 946 | END DO |
---|
[8586] | 947 | END DO |
---|
| 948 | END DO |
---|
| 949 | ! |
---|
| 950 | CASE( 5 ) !== 5th order central TIM ==! (Eq. 29) |
---|
| 951 | ! |
---|
[10425] | 952 | DO jl = 1, jpl |
---|
| 953 | DO jj = 1, jpjm1 |
---|
| 954 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 955 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
| 956 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
[10439] | 957 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
[10425] | 958 | zdx4 = zdx2 * zdx2 |
---|
[10475] | 959 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj,jl) + pt (ji,jj,jl) & |
---|
| 960 | & - zcu * ( pt (ji+1,jj,jl) - pt (ji,jj,jl) ) ) & |
---|
| 961 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj,jl) + ztu2(ji,jj,jl) & |
---|
| 962 | & - 0.5_wp * zcu * ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) ) & |
---|
[10446] | 963 | & + z1_120 * zdx4 * ( zcu*zcu - 1._wp ) * ( zcu*zcu - 4._wp ) * ( ztu4(ji+1,jj,jl) + ztu4(ji,jj,jl) & |
---|
[10425] | 964 | & - SIGN( 1._wp, zcu ) * ( ztu4(ji+1,jj,jl) - ztu4(ji,jj,jl) ) ) ) |
---|
| 965 | END DO |
---|
[8586] | 966 | END DO |
---|
| 967 | END DO |
---|
| 968 | ! |
---|
| 969 | END SELECT |
---|
[10439] | 970 | ! |
---|
| 971 | ! if pt at u-point is negative then use the upstream value |
---|
| 972 | ! this should not be necessary if a proper sea-ice mask is set in Ultimate |
---|
| 973 | ! to degrade the order of the scheme when necessary (for ex. at the ice edge) |
---|
[10413] | 974 | IF( ll_neg ) THEN |
---|
[10425] | 975 | DO jl = 1, jpl |
---|
| 976 | DO jj = 1, jpjm1 |
---|
| 977 | DO ji = 1, fs_jpim1 |
---|
[10945] | 978 | IF( pt_u(ji,jj,jl) < 0._wp .OR. ( imsk_small(ji,jj,jl) == 0 .AND. pamsk == 0. ) ) THEN |
---|
[10475] | 979 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj,jl) + pt(ji,jj,jl) & |
---|
| 980 | & - SIGN( 1._wp, pu(ji,jj) ) * ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) ) |
---|
[10425] | 981 | ENDIF |
---|
| 982 | END DO |
---|
[10413] | 983 | END DO |
---|
| 984 | END DO |
---|
| 985 | ENDIF |
---|
[10439] | 986 | ! !-- High order flux in i-direction --! |
---|
[10425] | 987 | DO jl = 1, jpl |
---|
| 988 | DO jj = 1, jpjm1 |
---|
| 989 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
[10439] | 990 | pfu_ho(ji,jj,jl) = pu(ji,jj) * pt_u(ji,jj,jl) |
---|
[10425] | 991 | END DO |
---|
[10413] | 992 | END DO |
---|
| 993 | END DO |
---|
[8586] | 994 | ! |
---|
| 995 | END SUBROUTINE ultimate_x |
---|
| 996 | |
---|
| 997 | |
---|
[10911] | 998 | SUBROUTINE ultimate_y( pamsk, kn_umx, pdt, pt, pv, pt_v, pfv_ho ) |
---|
[8586] | 999 | !!--------------------------------------------------------------------- |
---|
| 1000 | !! *** ROUTINE ultimate_y *** |
---|
| 1001 | !! |
---|
[10446] | 1002 | !! ** Purpose : compute tracer at v-points |
---|
[8586] | 1003 | !! |
---|
[10446] | 1004 | !! ** Method : ... |
---|
[8586] | 1005 | !! |
---|
| 1006 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
| 1007 | !!---------------------------------------------------------------------- |
---|
[10911] | 1008 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
[10439] | 1009 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
| 1010 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 1011 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pv ! ice j-velocity component |
---|
| 1012 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
[10425] | 1013 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_v ! tracer at v-point |
---|
| 1014 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfv_ho ! high order flux |
---|
[8586] | 1015 | ! |
---|
[10439] | 1016 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[10930] | 1017 | REAL(wp) :: zcv, zdy2, zdy4 ! - - |
---|
[10425] | 1018 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: ztv1, ztv2, ztv3, ztv4 |
---|
[8586] | 1019 | !!---------------------------------------------------------------------- |
---|
| 1020 | ! |
---|
| 1021 | ! !-- Laplacian in j-direction --! |
---|
[10425] | 1022 | DO jl = 1, jpl |
---|
| 1023 | DO jj = 1, jpjm1 ! First derivative (gradient) |
---|
| 1024 | DO ji = fs_2, fs_jpim1 |
---|
| 1025 | ztv1(ji,jj,jl) = ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) * r1_e2v(ji,jj) * vmask(ji,jj,1) |
---|
| 1026 | END DO |
---|
[8586] | 1027 | END DO |
---|
[10425] | 1028 | DO jj = 2, jpjm1 ! Second derivative (Laplacian) |
---|
| 1029 | DO ji = fs_2, fs_jpim1 |
---|
| 1030 | ztv2(ji,jj,jl) = ( ztv1(ji,jj,jl) - ztv1(ji,jj-1,jl) ) * r1_e2t(ji,jj) |
---|
| 1031 | END DO |
---|
[8586] | 1032 | END DO |
---|
| 1033 | END DO |
---|
[10425] | 1034 | CALL lbc_lnk( 'icedyn_adv_umx', ztv2, 'T', 1. ) |
---|
[8586] | 1035 | ! |
---|
| 1036 | ! !-- BiLaplacian in j-direction --! |
---|
[10425] | 1037 | DO jl = 1, jpl |
---|
| 1038 | DO jj = 1, jpjm1 ! First derivative |
---|
| 1039 | DO ji = fs_2, fs_jpim1 |
---|
| 1040 | ztv3(ji,jj,jl) = ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) * r1_e2v(ji,jj) * vmask(ji,jj,1) |
---|
| 1041 | END DO |
---|
[8586] | 1042 | END DO |
---|
[10425] | 1043 | DO jj = 2, jpjm1 ! Second derivative |
---|
| 1044 | DO ji = fs_2, fs_jpim1 |
---|
| 1045 | ztv4(ji,jj,jl) = ( ztv3(ji,jj,jl) - ztv3(ji,jj-1,jl) ) * r1_e2t(ji,jj) |
---|
| 1046 | END DO |
---|
[8586] | 1047 | END DO |
---|
| 1048 | END DO |
---|
[10425] | 1049 | CALL lbc_lnk( 'icedyn_adv_umx', ztv4, 'T', 1. ) |
---|
[8586] | 1050 | ! |
---|
| 1051 | ! |
---|
[10413] | 1052 | SELECT CASE (kn_umx ) |
---|
[10425] | 1053 | ! |
---|
[8586] | 1054 | CASE( 1 ) !== 1st order central TIM ==! (Eq. 21) |
---|
[10425] | 1055 | DO jl = 1, jpl |
---|
| 1056 | DO jj = 1, jpjm1 |
---|
| 1057 | DO ji = 1, fs_jpim1 |
---|
[10475] | 1058 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( pt(ji,jj+1,jl) + pt(ji,jj,jl) & |
---|
| 1059 | & - SIGN( 1._wp, pv(ji,jj) ) * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) ) |
---|
[10425] | 1060 | END DO |
---|
[8586] | 1061 | END DO |
---|
| 1062 | END DO |
---|
| 1063 | ! |
---|
| 1064 | CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23) |
---|
[10425] | 1065 | DO jl = 1, jpl |
---|
| 1066 | DO jj = 1, jpjm1 |
---|
| 1067 | DO ji = 1, fs_jpim1 |
---|
| 1068 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
[10475] | 1069 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( pt(ji,jj+1,jl) + pt(ji,jj,jl) & |
---|
| 1070 | & - zcv * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) ) |
---|
[10425] | 1071 | END DO |
---|
[8586] | 1072 | END DO |
---|
| 1073 | END DO |
---|
| 1074 | ! |
---|
| 1075 | CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24) |
---|
[10425] | 1076 | DO jl = 1, jpl |
---|
| 1077 | DO jj = 1, jpjm1 |
---|
| 1078 | DO ji = 1, fs_jpim1 |
---|
| 1079 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
| 1080 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
[10439] | 1081 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
[10475] | 1082 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) & |
---|
| 1083 | & - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) & |
---|
[10446] | 1084 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) & |
---|
[10425] | 1085 | & - SIGN( 1._wp, zcv ) * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) ) |
---|
| 1086 | END DO |
---|
[8586] | 1087 | END DO |
---|
| 1088 | END DO |
---|
| 1089 | ! |
---|
| 1090 | CASE( 4 ) !== 4th order central TIM ==! (Eq. 27) |
---|
[10425] | 1091 | DO jl = 1, jpl |
---|
| 1092 | DO jj = 1, jpjm1 |
---|
| 1093 | DO ji = 1, fs_jpim1 |
---|
| 1094 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
| 1095 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
[10439] | 1096 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
[10475] | 1097 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) & |
---|
| 1098 | & - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) & |
---|
| 1099 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) & |
---|
| 1100 | & - 0.5_wp * zcv * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) ) |
---|
[10425] | 1101 | END DO |
---|
[8586] | 1102 | END DO |
---|
| 1103 | END DO |
---|
| 1104 | ! |
---|
| 1105 | CASE( 5 ) !== 5th order central TIM ==! (Eq. 29) |
---|
[10425] | 1106 | DO jl = 1, jpl |
---|
| 1107 | DO jj = 1, jpjm1 |
---|
| 1108 | DO ji = 1, fs_jpim1 |
---|
| 1109 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
| 1110 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
[10439] | 1111 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
[10425] | 1112 | zdy4 = zdy2 * zdy2 |
---|
[10446] | 1113 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) & |
---|
[10475] | 1114 | & - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) & |
---|
| 1115 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) & |
---|
| 1116 | & - 0.5_wp * zcv * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) & |
---|
[10446] | 1117 | & + z1_120 * zdy4 * ( zcv*zcv - 1._wp ) * ( zcv*zcv - 4._wp ) * ( ztv4(ji,jj+1,jl) + ztv4(ji,jj,jl) & |
---|
[10425] | 1118 | & - SIGN( 1._wp, zcv ) * ( ztv4(ji,jj+1,jl) - ztv4(ji,jj,jl) ) ) ) |
---|
| 1119 | END DO |
---|
[8586] | 1120 | END DO |
---|
| 1121 | END DO |
---|
| 1122 | ! |
---|
| 1123 | END SELECT |
---|
[10439] | 1124 | ! |
---|
| 1125 | ! if pt at v-point is negative then use the upstream value |
---|
| 1126 | ! this should not be necessary if a proper sea-ice mask is set in Ultimate |
---|
| 1127 | ! to degrade the order of the scheme when necessary (for ex. at the ice edge) |
---|
[10413] | 1128 | IF( ll_neg ) THEN |
---|
[10425] | 1129 | DO jl = 1, jpl |
---|
| 1130 | DO jj = 1, jpjm1 |
---|
| 1131 | DO ji = 1, fs_jpim1 |
---|
[10945] | 1132 | IF( pt_v(ji,jj,jl) < 0._wp .OR. ( jmsk_small(ji,jj,jl) == 0 .AND. pamsk == 0. ) ) THEN |
---|
[10475] | 1133 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt(ji,jj+1,jl) + pt(ji,jj,jl) ) & |
---|
| 1134 | & - SIGN( 1._wp, pv(ji,jj) ) * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) ) |
---|
[10425] | 1135 | ENDIF |
---|
| 1136 | END DO |
---|
[10413] | 1137 | END DO |
---|
| 1138 | END DO |
---|
| 1139 | ENDIF |
---|
[10439] | 1140 | ! !-- High order flux in j-direction --! |
---|
[10425] | 1141 | DO jl = 1, jpl |
---|
| 1142 | DO jj = 1, jpjm1 |
---|
| 1143 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
[10439] | 1144 | pfv_ho(ji,jj,jl) = pv(ji,jj) * pt_v(ji,jj,jl) |
---|
[10425] | 1145 | END DO |
---|
[10413] | 1146 | END DO |
---|
| 1147 | END DO |
---|
[8586] | 1148 | ! |
---|
| 1149 | END SUBROUTINE ultimate_y |
---|
[10413] | 1150 | |
---|
| 1151 | |
---|
[10519] | 1152 | SUBROUTINE nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[8586] | 1153 | !!--------------------------------------------------------------------- |
---|
[10519] | 1154 | !! *** ROUTINE nonosc_ice *** |
---|
[8586] | 1155 | !! |
---|
[10446] | 1156 | !! ** Purpose : compute monotonic tracer fluxes from the upstream |
---|
[10519] | 1157 | !! scheme and the before field by a non-oscillatory algorithm |
---|
[8586] | 1158 | !! |
---|
[10446] | 1159 | !! ** Method : ... |
---|
[8586] | 1160 | !!---------------------------------------------------------------------- |
---|
[10439] | 1161 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 1162 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
[10425] | 1163 | REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pu ! ice i-velocity => u*e2 |
---|
| 1164 | REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pv ! ice j-velocity => v*e1 |
---|
[10446] | 1165 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pt, pt_ups ! before field & upstream guess of after field |
---|
| 1166 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pfv_ups, pfu_ups ! upstream flux |
---|
[10425] | 1167 | REAL(wp), DIMENSION (:,:,:), INTENT(inout) :: pfv_ho, pfu_ho ! monotonic flux |
---|
[8586] | 1168 | ! |
---|
[10425] | 1169 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[10475] | 1170 | REAL(wp) :: zpos, zneg, zbig, zup, zdo, z1_dt ! local scalars |
---|
| 1171 | REAL(wp) :: zau, zbu, zcu, zav, zbv, zcv, zcoef, zzt ! - - |
---|
[10425] | 1172 | REAL(wp), DIMENSION(jpi,jpj ) :: zbup, zbdo |
---|
[10439] | 1173 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zbetup, zbetdo, zti_ups, ztj_ups |
---|
[8586] | 1174 | !!---------------------------------------------------------------------- |
---|
| 1175 | zbig = 1.e+40_wp |
---|
[10425] | 1176 | |
---|
[10413] | 1177 | ! antidiffusive flux : high order minus low order |
---|
| 1178 | ! -------------------------------------------------- |
---|
[10425] | 1179 | DO jl = 1, jpl |
---|
| 1180 | DO jj = 1, jpjm1 |
---|
| 1181 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
[10439] | 1182 | pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) - pfu_ups(ji,jj,jl) |
---|
| 1183 | pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) - pfv_ups(ji,jj,jl) |
---|
[10425] | 1184 | END DO |
---|
| 1185 | END DO |
---|
[8586] | 1186 | END DO |
---|
| 1187 | |
---|
[10413] | 1188 | ! extreme case where pfu_ho has to be zero |
---|
| 1189 | ! ---------------------------------------- |
---|
| 1190 | ! pfu_ho |
---|
| 1191 | ! * ---> |
---|
| 1192 | ! | | * | | |
---|
| 1193 | ! | | | * | |
---|
| 1194 | ! | | | | * |
---|
[10439] | 1195 | ! t_ups : i-1 i i+1 i+2 |
---|
[10945] | 1196 | IF( ll_prelim ) THEN |
---|
[10413] | 1197 | |
---|
[10425] | 1198 | DO jl = 1, jpl |
---|
| 1199 | DO jj = 2, jpjm1 |
---|
| 1200 | DO ji = fs_2, fs_jpim1 |
---|
[10439] | 1201 | zti_ups(ji,jj,jl)= pt_ups(ji+1,jj ,jl) |
---|
| 1202 | ztj_ups(ji,jj,jl)= pt_ups(ji ,jj+1,jl) |
---|
[10425] | 1203 | END DO |
---|
[10413] | 1204 | END DO |
---|
| 1205 | END DO |
---|
[10439] | 1206 | CALL lbc_lnk_multi( 'icedyn_adv_umx', zti_ups, 'T', 1., ztj_ups, 'T', 1. ) |
---|
[8586] | 1207 | |
---|
[10425] | 1208 | DO jl = 1, jpl |
---|
| 1209 | DO jj = 2, jpjm1 |
---|
| 1210 | DO ji = fs_2, fs_jpim1 |
---|
[10475] | 1211 | IF ( pfu_ho(ji,jj,jl) * ( pt_ups(ji+1,jj ,jl) - pt_ups(ji,jj,jl) ) <= 0._wp .AND. & |
---|
| 1212 | & pfv_ho(ji,jj,jl) * ( pt_ups(ji ,jj+1,jl) - pt_ups(ji,jj,jl) ) <= 0._wp ) THEN |
---|
[10425] | 1213 | ! |
---|
[10475] | 1214 | IF( pfu_ho(ji,jj,jl) * ( zti_ups(ji+1,jj ,jl) - zti_ups(ji,jj,jl) ) <= 0._wp .AND. & |
---|
| 1215 | & pfv_ho(ji,jj,jl) * ( ztj_ups(ji ,jj+1,jl) - ztj_ups(ji,jj,jl) ) <= 0._wp ) THEN |
---|
| 1216 | pfu_ho(ji,jj,jl)=0._wp |
---|
| 1217 | pfv_ho(ji,jj,jl)=0._wp |
---|
[10439] | 1218 | ENDIF |
---|
[10425] | 1219 | ! |
---|
[10475] | 1220 | IF( pfu_ho(ji,jj,jl) * ( pt_ups(ji,jj,jl) - pt_ups(ji-1,jj ,jl) ) <= 0._wp .AND. & |
---|
| 1221 | & pfv_ho(ji,jj,jl) * ( pt_ups(ji,jj,jl) - pt_ups(ji ,jj-1,jl) ) <= 0._wp ) THEN |
---|
| 1222 | pfu_ho(ji,jj,jl)=0._wp |
---|
| 1223 | pfv_ho(ji,jj,jl)=0._wp |
---|
[10439] | 1224 | ENDIF |
---|
[10425] | 1225 | ! |
---|
| 1226 | ENDIF |
---|
| 1227 | END DO |
---|
[10413] | 1228 | END DO |
---|
| 1229 | END DO |
---|
[10425] | 1230 | CALL lbc_lnk_multi( 'icedyn_adv_umx', pfu_ho, 'U', -1., pfv_ho, 'V', -1. ) ! lateral boundary cond. |
---|
[10413] | 1231 | |
---|
| 1232 | ENDIF |
---|
[10425] | 1233 | |
---|
[8586] | 1234 | ! Search local extrema |
---|
| 1235 | ! -------------------- |
---|
[10439] | 1236 | ! max/min of pt & pt_ups with large negative/positive value (-/+zbig) outside ice cover |
---|
[10425] | 1237 | z1_dt = 1._wp / pdt |
---|
| 1238 | DO jl = 1, jpl |
---|
| 1239 | |
---|
| 1240 | DO jj = 1, jpj |
---|
| 1241 | DO ji = 1, jpi |
---|
[10439] | 1242 | IF ( pt(ji,jj,jl) <= 0._wp .AND. pt_ups(ji,jj,jl) <= 0._wp ) THEN |
---|
[10425] | 1243 | zbup(ji,jj) = -zbig |
---|
| 1244 | zbdo(ji,jj) = zbig |
---|
[10439] | 1245 | ELSEIF( pt(ji,jj,jl) <= 0._wp .AND. pt_ups(ji,jj,jl) > 0._wp ) THEN |
---|
| 1246 | zbup(ji,jj) = pt_ups(ji,jj,jl) |
---|
| 1247 | zbdo(ji,jj) = pt_ups(ji,jj,jl) |
---|
| 1248 | ELSEIF( pt(ji,jj,jl) > 0._wp .AND. pt_ups(ji,jj,jl) <= 0._wp ) THEN |
---|
[10425] | 1249 | zbup(ji,jj) = pt(ji,jj,jl) |
---|
| 1250 | zbdo(ji,jj) = pt(ji,jj,jl) |
---|
| 1251 | ELSE |
---|
[10439] | 1252 | zbup(ji,jj) = MAX( pt(ji,jj,jl) , pt_ups(ji,jj,jl) ) |
---|
| 1253 | zbdo(ji,jj) = MIN( pt(ji,jj,jl) , pt_ups(ji,jj,jl) ) |
---|
[10425] | 1254 | ENDIF |
---|
| 1255 | END DO |
---|
[10413] | 1256 | END DO |
---|
[8586] | 1257 | |
---|
[10425] | 1258 | DO jj = 2, jpjm1 |
---|
| 1259 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 1260 | ! |
---|
[10475] | 1261 | 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 |
---|
| 1262 | zdo = MIN( zbdo(ji,jj), zbdo(ji-1,jj), zbdo(ji+1,jj), zbdo(ji,jj-1), zbdo(ji,jj+1) ) |
---|
[10425] | 1263 | ! |
---|
[10475] | 1264 | zpos = MAX( 0._wp, pfu_ho(ji-1,jj ,jl) ) - MIN( 0._wp, pfu_ho(ji ,jj ,jl) ) & ! positive/negative part of the flux |
---|
| 1265 | & + MAX( 0._wp, pfv_ho(ji ,jj-1,jl) ) - MIN( 0._wp, pfv_ho(ji ,jj ,jl) ) |
---|
| 1266 | zneg = MAX( 0._wp, pfu_ho(ji ,jj ,jl) ) - MIN( 0._wp, pfu_ho(ji-1,jj ,jl) ) & |
---|
| 1267 | & + MAX( 0._wp, pfv_ho(ji ,jj ,jl) ) - MIN( 0._wp, pfv_ho(ji ,jj-1,jl) ) |
---|
[10425] | 1268 | ! |
---|
[10475] | 1269 | 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] | 1270 | & ) * ( 1. - pamsk ) |
---|
[10475] | 1271 | 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] | 1272 | & ) * ( 1. - pamsk ) |
---|
[10425] | 1273 | ! |
---|
| 1274 | ! ! up & down beta terms |
---|
[10911] | 1275 | ! 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 !!!) |
---|
| 1276 | IF( zpos > epsi10 ) THEN ; zbetup(ji,jj,jl) = MAX( 0._wp, zup - pt_ups(ji,jj,jl) ) / zpos * e1e2t(ji,jj) * z1_dt |
---|
| 1277 | ELSE ; zbetup(ji,jj,jl) = 0._wp ! zbig |
---|
[10425] | 1278 | ENDIF |
---|
| 1279 | ! |
---|
[10911] | 1280 | IF( zneg > epsi10 ) THEN ; zbetdo(ji,jj,jl) = MAX( 0._wp, pt_ups(ji,jj,jl) - zdo ) / zneg * e1e2t(ji,jj) * z1_dt |
---|
| 1281 | ELSE ; zbetdo(ji,jj,jl) = 0._wp ! zbig |
---|
[10425] | 1282 | ENDIF |
---|
| 1283 | ! |
---|
| 1284 | ! if all the points are outside ice cover |
---|
[10475] | 1285 | IF( zup == -zbig ) zbetup(ji,jj,jl) = 0._wp ! zbig |
---|
| 1286 | IF( zdo == zbig ) zbetdo(ji,jj,jl) = 0._wp ! zbig |
---|
[10425] | 1287 | ! |
---|
| 1288 | END DO |
---|
[8586] | 1289 | END DO |
---|
| 1290 | END DO |
---|
[10425] | 1291 | CALL lbc_lnk_multi( 'icedyn_adv_umx', zbetup, 'T', 1., zbetdo, 'T', 1. ) ! lateral boundary cond. (unchanged sign) |
---|
[8586] | 1292 | |
---|
[10413] | 1293 | |
---|
| 1294 | ! monotonic flux in the y direction |
---|
| 1295 | ! --------------------------------- |
---|
[10425] | 1296 | DO jl = 1, jpl |
---|
| 1297 | DO jj = 1, jpjm1 |
---|
| 1298 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 1299 | zau = MIN( 1._wp , zbetdo(ji,jj,jl) , zbetup(ji+1,jj,jl) ) |
---|
| 1300 | zbu = MIN( 1._wp , zbetup(ji,jj,jl) , zbetdo(ji+1,jj,jl) ) |
---|
[10475] | 1301 | zcu = 0.5_wp + SIGN( 0.5_wp , pfu_ho(ji,jj,jl) ) |
---|
[10425] | 1302 | ! |
---|
| 1303 | zcoef = ( zcu * zau + ( 1._wp - zcu ) * zbu ) |
---|
[10439] | 1304 | ! |
---|
| 1305 | pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) * zcoef + pfu_ups(ji,jj,jl) |
---|
| 1306 | ! |
---|
[10425] | 1307 | END DO |
---|
[8637] | 1308 | END DO |
---|
[10413] | 1309 | |
---|
[10425] | 1310 | DO jj = 1, jpjm1 |
---|
| 1311 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 1312 | zav = MIN( 1._wp , zbetdo(ji,jj,jl) , zbetup(ji,jj+1,jl) ) |
---|
| 1313 | zbv = MIN( 1._wp , zbetup(ji,jj,jl) , zbetdo(ji,jj+1,jl) ) |
---|
[10475] | 1314 | zcv = 0.5_wp + SIGN( 0.5_wp , pfv_ho(ji,jj,jl) ) |
---|
[10425] | 1315 | ! |
---|
| 1316 | zcoef = ( zcv * zav + ( 1._wp - zcv ) * zbv ) |
---|
[10439] | 1317 | ! |
---|
| 1318 | pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) * zcoef + pfv_ups(ji,jj,jl) |
---|
| 1319 | ! |
---|
[10425] | 1320 | END DO |
---|
[8586] | 1321 | END DO |
---|
[10413] | 1322 | |
---|
| 1323 | END DO |
---|
[8586] | 1324 | ! |
---|
[10519] | 1325 | END SUBROUTINE nonosc_ice |
---|
[8586] | 1326 | |
---|
[10446] | 1327 | |
---|
| 1328 | SUBROUTINE limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
[10413] | 1329 | !!--------------------------------------------------------------------- |
---|
| 1330 | !! *** ROUTINE limiter_x *** |
---|
| 1331 | !! |
---|
| 1332 | !! ** Purpose : compute flux limiter |
---|
| 1333 | !!---------------------------------------------------------------------- |
---|
[10446] | 1334 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 1335 | REAL(wp), DIMENSION(:,: ), INTENT(in ) :: pu ! ice i-velocity => u*e2 |
---|
| 1336 | REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pt ! ice tracer |
---|
| 1337 | REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pfu_ups ! upstream flux |
---|
| 1338 | REAL(wp), DIMENSION(:,:,:), INTENT(inout) :: pfu_ho ! high order flux |
---|
[10413] | 1339 | ! |
---|
| 1340 | REAL(wp) :: Cr, Rjm, Rj, Rjp, uCFL, zpsi, zh3, zlimiter, Rr |
---|
[10425] | 1341 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
| 1342 | REAL(wp), DIMENSION (jpi,jpj,jpl) :: zslpx ! tracer slopes |
---|
[10413] | 1343 | !!---------------------------------------------------------------------- |
---|
| 1344 | ! |
---|
[10425] | 1345 | DO jl = 1, jpl |
---|
| 1346 | DO jj = 2, jpjm1 |
---|
| 1347 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 1348 | zslpx(ji,jj,jl) = ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) * umask(ji,jj,1) |
---|
| 1349 | END DO |
---|
[10413] | 1350 | END DO |
---|
| 1351 | END DO |
---|
[10425] | 1352 | CALL lbc_lnk( 'icedyn_adv_umx', zslpx, 'U', -1.) ! lateral boundary cond. |
---|
[10413] | 1353 | |
---|
[10425] | 1354 | DO jl = 1, jpl |
---|
| 1355 | DO jj = 2, jpjm1 |
---|
| 1356 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 1357 | uCFL = pdt * ABS( pu(ji,jj) ) * r1_e1e2t(ji,jj) |
---|
| 1358 | |
---|
| 1359 | Rjm = zslpx(ji-1,jj,jl) |
---|
| 1360 | Rj = zslpx(ji ,jj,jl) |
---|
| 1361 | Rjp = zslpx(ji+1,jj,jl) |
---|
[10413] | 1362 | |
---|
[10945] | 1363 | IF( np_limiter == 3 ) THEN |
---|
[10413] | 1364 | |
---|
[10425] | 1365 | IF( pu(ji,jj) > 0. ) THEN ; Rr = Rjm |
---|
| 1366 | ELSE ; Rr = Rjp |
---|
| 1367 | ENDIF |
---|
[10413] | 1368 | |
---|
[10425] | 1369 | zh3 = pfu_ho(ji,jj,jl) - pfu_ups(ji,jj,jl) |
---|
| 1370 | IF( Rj > 0. ) THEN |
---|
| 1371 | zlimiter = MAX( 0., MIN( zh3, MAX(-Rr * 0.5 * ABS(pu(ji,jj)), & |
---|
| 1372 | & MIN( 2. * Rr * 0.5 * ABS(pu(ji,jj)), zh3, 1.5 * Rj * 0.5 * ABS(pu(ji,jj)) ) ) ) ) |
---|
| 1373 | ELSE |
---|
| 1374 | zlimiter = -MAX( 0., MIN(-zh3, MAX( Rr * 0.5 * ABS(pu(ji,jj)), & |
---|
| 1375 | & MIN(-2. * Rr * 0.5 * ABS(pu(ji,jj)), -zh3, -1.5 * Rj * 0.5 * ABS(pu(ji,jj)) ) ) ) ) |
---|
| 1376 | ENDIF |
---|
| 1377 | pfu_ho(ji,jj,jl) = pfu_ups(ji,jj,jl) + zlimiter |
---|
[10413] | 1378 | |
---|
[10945] | 1379 | ELSEIF( np_limiter == 2 ) THEN |
---|
[10425] | 1380 | IF( Rj /= 0. ) THEN |
---|
| 1381 | IF( pu(ji,jj) > 0. ) THEN ; Cr = Rjm / Rj |
---|
| 1382 | ELSE ; Cr = Rjp / Rj |
---|
| 1383 | ENDIF |
---|
| 1384 | ELSE |
---|
| 1385 | Cr = 0. |
---|
[10413] | 1386 | ENDIF |
---|
[10425] | 1387 | |
---|
| 1388 | ! -- superbee -- |
---|
| 1389 | zpsi = MAX( 0., MAX( MIN(1.,2.*Cr), MIN(2.,Cr) ) ) |
---|
| 1390 | ! -- van albada 2 -- |
---|
| 1391 | !!zpsi = 2.*Cr / (Cr*Cr+1.) |
---|
| 1392 | ! -- sweby (with beta=1) -- |
---|
| 1393 | !!zpsi = MAX( 0., MAX( MIN(1.,1.*Cr), MIN(1.,Cr) ) ) |
---|
| 1394 | ! -- van Leer -- |
---|
| 1395 | !!zpsi = ( Cr + ABS(Cr) ) / ( 1. + ABS(Cr) ) |
---|
| 1396 | ! -- ospre -- |
---|
| 1397 | !!zpsi = 1.5 * ( Cr*Cr + Cr ) / ( Cr*Cr + Cr + 1. ) |
---|
| 1398 | ! -- koren -- |
---|
| 1399 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( (1.+2*Cr)/3., 2. ) ) ) |
---|
| 1400 | ! -- charm -- |
---|
| 1401 | !IF( Cr > 0. ) THEN ; zpsi = Cr * (3.*Cr + 1.) / ( (Cr + 1.) * (Cr + 1.) ) |
---|
| 1402 | !ELSE ; zpsi = 0. |
---|
[10413] | 1403 | !ENDIF |
---|
[10425] | 1404 | ! -- van albada 1 -- |
---|
| 1405 | !!zpsi = (Cr*Cr + Cr) / (Cr*Cr +1) |
---|
| 1406 | ! -- smart -- |
---|
| 1407 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, 4. ) ) ) |
---|
| 1408 | ! -- umist -- |
---|
| 1409 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, MIN(0.75+0.25*Cr, 2. ) ) ) ) |
---|
[10413] | 1410 | |
---|
[10425] | 1411 | ! high order flux corrected by the limiter |
---|
| 1412 | pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) - ABS( pu(ji,jj) ) * ( (1.-zpsi) + uCFL*zpsi ) * Rj * 0.5 |
---|
[10413] | 1413 | |
---|
[10425] | 1414 | ENDIF |
---|
| 1415 | END DO |
---|
[10413] | 1416 | END DO |
---|
| 1417 | END DO |
---|
[10425] | 1418 | CALL lbc_lnk( 'icedyn_adv_umx', pfu_ho, 'U', -1.) ! lateral boundary cond. |
---|
[10413] | 1419 | ! |
---|
| 1420 | END SUBROUTINE limiter_x |
---|
| 1421 | |
---|
[10446] | 1422 | |
---|
| 1423 | SUBROUTINE limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 1424 | !!--------------------------------------------------------------------- |
---|
| 1425 | !! *** ROUTINE limiter_y *** |
---|
| 1426 | !! |
---|
| 1427 | !! ** Purpose : compute flux limiter |
---|
| 1428 | !!---------------------------------------------------------------------- |
---|
[10446] | 1429 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 1430 | REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pv ! ice i-velocity => u*e2 |
---|
| 1431 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pt ! ice tracer |
---|
| 1432 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pfv_ups ! upstream flux |
---|
| 1433 | REAL(wp), DIMENSION (:,:,:), INTENT(inout) :: pfv_ho ! high order flux |
---|
[10413] | 1434 | ! |
---|
| 1435 | REAL(wp) :: Cr, Rjm, Rj, Rjp, vCFL, zpsi, zh3, zlimiter, Rr |
---|
[10425] | 1436 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
| 1437 | REAL(wp), DIMENSION (jpi,jpj,jpl) :: zslpy ! tracer slopes |
---|
[10413] | 1438 | !!---------------------------------------------------------------------- |
---|
| 1439 | ! |
---|
[10425] | 1440 | DO jl = 1, jpl |
---|
| 1441 | DO jj = 2, jpjm1 |
---|
| 1442 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 1443 | zslpy(ji,jj,jl) = ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) * vmask(ji,jj,1) |
---|
| 1444 | END DO |
---|
[10413] | 1445 | END DO |
---|
| 1446 | END DO |
---|
[10425] | 1447 | CALL lbc_lnk( 'icedyn_adv_umx', zslpy, 'V', -1.) ! lateral boundary cond. |
---|
[10413] | 1448 | |
---|
[10425] | 1449 | DO jl = 1, jpl |
---|
| 1450 | DO jj = 2, jpjm1 |
---|
| 1451 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 1452 | vCFL = pdt * ABS( pv(ji,jj) ) * r1_e1e2t(ji,jj) |
---|
[10413] | 1453 | |
---|
[10425] | 1454 | Rjm = zslpy(ji,jj-1,jl) |
---|
| 1455 | Rj = zslpy(ji,jj ,jl) |
---|
| 1456 | Rjp = zslpy(ji,jj+1,jl) |
---|
[10413] | 1457 | |
---|
[10945] | 1458 | IF( np_limiter == 3 ) THEN |
---|
[10413] | 1459 | |
---|
[10425] | 1460 | IF( pv(ji,jj) > 0. ) THEN ; Rr = Rjm |
---|
| 1461 | ELSE ; Rr = Rjp |
---|
| 1462 | ENDIF |
---|
[10413] | 1463 | |
---|
[10425] | 1464 | zh3 = pfv_ho(ji,jj,jl) - pfv_ups(ji,jj,jl) |
---|
| 1465 | IF( Rj > 0. ) THEN |
---|
| 1466 | zlimiter = MAX( 0., MIN( zh3, MAX(-Rr * 0.5 * ABS(pv(ji,jj)), & |
---|
| 1467 | & MIN( 2. * Rr * 0.5 * ABS(pv(ji,jj)), zh3, 1.5 * Rj * 0.5 * ABS(pv(ji,jj)) ) ) ) ) |
---|
| 1468 | ELSE |
---|
| 1469 | zlimiter = -MAX( 0., MIN(-zh3, MAX( Rr * 0.5 * ABS(pv(ji,jj)), & |
---|
| 1470 | & MIN(-2. * Rr * 0.5 * ABS(pv(ji,jj)), -zh3, -1.5 * Rj * 0.5 * ABS(pv(ji,jj)) ) ) ) ) |
---|
| 1471 | ENDIF |
---|
| 1472 | pfv_ho(ji,jj,jl) = pfv_ups(ji,jj,jl) + zlimiter |
---|
[10413] | 1473 | |
---|
[10945] | 1474 | ELSEIF( np_limiter == 2 ) THEN |
---|
[10413] | 1475 | |
---|
[10425] | 1476 | IF( Rj /= 0. ) THEN |
---|
| 1477 | IF( pv(ji,jj) > 0. ) THEN ; Cr = Rjm / Rj |
---|
| 1478 | ELSE ; Cr = Rjp / Rj |
---|
| 1479 | ENDIF |
---|
| 1480 | ELSE |
---|
| 1481 | Cr = 0. |
---|
| 1482 | ENDIF |
---|
[10413] | 1483 | |
---|
[10425] | 1484 | ! -- superbee -- |
---|
| 1485 | zpsi = MAX( 0., MAX( MIN(1.,2.*Cr), MIN(2.,Cr) ) ) |
---|
| 1486 | ! -- van albada 2 -- |
---|
| 1487 | !!zpsi = 2.*Cr / (Cr*Cr+1.) |
---|
| 1488 | ! -- sweby (with beta=1) -- |
---|
| 1489 | !!zpsi = MAX( 0., MAX( MIN(1.,1.*Cr), MIN(1.,Cr) ) ) |
---|
| 1490 | ! -- van Leer -- |
---|
| 1491 | !!zpsi = ( Cr + ABS(Cr) ) / ( 1. + ABS(Cr) ) |
---|
| 1492 | ! -- ospre -- |
---|
| 1493 | !!zpsi = 1.5 * ( Cr*Cr + Cr ) / ( Cr*Cr + Cr + 1. ) |
---|
| 1494 | ! -- koren -- |
---|
| 1495 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( (1.+2*Cr)/3., 2. ) ) ) |
---|
| 1496 | ! -- charm -- |
---|
| 1497 | !IF( Cr > 0. ) THEN ; zpsi = Cr * (3.*Cr + 1.) / ( (Cr + 1.) * (Cr + 1.) ) |
---|
| 1498 | !ELSE ; zpsi = 0. |
---|
| 1499 | !ENDIF |
---|
| 1500 | ! -- van albada 1 -- |
---|
| 1501 | !!zpsi = (Cr*Cr + Cr) / (Cr*Cr +1) |
---|
| 1502 | ! -- smart -- |
---|
| 1503 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, 4. ) ) ) |
---|
| 1504 | ! -- umist -- |
---|
| 1505 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, MIN(0.75+0.25*Cr, 2. ) ) ) ) |
---|
[10413] | 1506 | |
---|
[10425] | 1507 | ! high order flux corrected by the limiter |
---|
| 1508 | pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) - ABS( pv(ji,jj) ) * ( (1.-zpsi) + vCFL*zpsi ) * Rj * 0.5 |
---|
| 1509 | |
---|
| 1510 | ENDIF |
---|
| 1511 | END DO |
---|
[10413] | 1512 | END DO |
---|
| 1513 | END DO |
---|
[10425] | 1514 | CALL lbc_lnk( 'icedyn_adv_umx', pfv_ho, 'V', -1.) ! lateral boundary cond. |
---|
[10413] | 1515 | ! |
---|
| 1516 | END SUBROUTINE limiter_y |
---|
| 1517 | |
---|
[10911] | 1518 | |
---|
[12197] | 1519 | SUBROUTINE Hbig( pdt, phi_max, phs_max, phip_max, pv_i, pv_s, pa_i, pa_ip, pv_ip, pe_s ) |
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[10911] | 1520 | !!------------------------------------------------------------------- |
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| 1521 | !! *** ROUTINE Hbig *** |
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| 1522 | !! |
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| 1523 | !! ** Purpose : Thickness correction in case advection scheme creates |
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| 1524 | !! abnormally tick ice or snow |
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| 1525 | !! |
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| 1526 | !! ** Method : 1- check whether ice thickness is larger than the surrounding 9-points |
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| 1527 | !! (before advection) and reduce it by adapting ice concentration |
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| 1528 | !! 2- check whether snow thickness is larger than the surrounding 9-points |
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| 1529 | !! (before advection) and reduce it by sending the excess in the ocean |
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| 1530 | !! |
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| 1531 | !! ** input : Max thickness of the surrounding 9-points |
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| 1532 | !!------------------------------------------------------------------- |
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[10930] | 1533 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
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[10911] | 1534 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: phi_max, phs_max, phip_max ! max ice thick from surrounding 9-pts |
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[12197] | 1535 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i, pv_s, pa_i, pa_ip, pv_ip |
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[10911] | 1536 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s |
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| 1537 | ! |
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[12197] | 1538 | INTEGER :: ji, jj, jl ! dummy loop indices |
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| 1539 | REAL(wp) :: z1_dt, zhip, zhi, zhs, zfra |
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[10911] | 1540 | !!------------------------------------------------------------------- |
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| 1541 | ! |
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[10930] | 1542 | z1_dt = 1._wp / pdt |
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[10911] | 1543 | ! |
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| 1544 | DO jl = 1, jpl |
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| 1545 | |
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| 1546 | DO jj = 1, jpj |
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| 1547 | DO ji = 1, jpi |
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| 1548 | IF ( pv_i(ji,jj,jl) > 0._wp ) THEN |
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| 1549 | ! |
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| 1550 | ! ! -- check h_ip -- ! |
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| 1551 | ! if h_ip is larger than the surrounding 9 pts => reduce h_ip and increase a_ip |
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| 1552 | IF( ln_pnd_H12 .AND. pv_ip(ji,jj,jl) > 0._wp ) THEN |
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| 1553 | zhip = pv_ip(ji,jj,jl) / MAX( epsi20, pa_ip(ji,jj,jl) ) |
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| 1554 | IF( zhip > phip_max(ji,jj,jl) .AND. pa_ip(ji,jj,jl) < 0.15 ) THEN |
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| 1555 | pa_ip(ji,jj,jl) = pv_ip(ji,jj,jl) / phip_max(ji,jj,jl) |
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| 1556 | ENDIF |
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| 1557 | ENDIF |
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| 1558 | ! |
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| 1559 | ! ! -- check h_i -- ! |
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| 1560 | ! if h_i is larger than the surrounding 9 pts => reduce h_i and increase a_i |
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| 1561 | zhi = pv_i(ji,jj,jl) / pa_i(ji,jj,jl) |
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| 1562 | IF( zhi > phi_max(ji,jj,jl) .AND. pa_i(ji,jj,jl) < 0.15 ) THEN |
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| 1563 | 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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| 1564 | ENDIF |
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| 1565 | ! |
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| 1566 | ! ! -- check h_s -- ! |
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| 1567 | ! if h_s is larger than the surrounding 9 pts => put the snow excess in the ocean |
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| 1568 | zhs = pv_s(ji,jj,jl) / pa_i(ji,jj,jl) |
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| 1569 | IF( pv_s(ji,jj,jl) > 0._wp .AND. zhs > phs_max(ji,jj,jl) .AND. pa_i(ji,jj,jl) < 0.15 ) THEN |
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| 1570 | zfra = phs_max(ji,jj,jl) / MAX( zhs, epsi20 ) |
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| 1571 | ! |
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[10930] | 1572 | wfx_res(ji,jj) = wfx_res(ji,jj) + ( pv_s(ji,jj,jl) - pa_i(ji,jj,jl) * phs_max(ji,jj,jl) ) * rhos * z1_dt |
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| 1573 | hfx_res(ji,jj) = hfx_res(ji,jj) - SUM( pe_s(ji,jj,1:nlay_s,jl) ) * ( 1._wp - zfra ) * z1_dt ! W.m-2 <0 |
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[10911] | 1574 | ! |
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| 1575 | pe_s(ji,jj,1:nlay_s,jl) = pe_s(ji,jj,1:nlay_s,jl) * zfra |
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| 1576 | pv_s(ji,jj,jl) = pa_i(ji,jj,jl) * phs_max(ji,jj,jl) |
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| 1577 | ENDIF |
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[12197] | 1578 | ! |
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| 1579 | ENDIF |
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| 1580 | END DO |
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| 1581 | END DO |
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| 1582 | END DO |
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| 1583 | ! |
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| 1584 | END SUBROUTINE Hbig |
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| 1585 | |
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| 1586 | |
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| 1587 | SUBROUTINE Hsnow( pdt, pv_i, pv_s, pa_i, pa_ip, pe_s ) |
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| 1588 | !!------------------------------------------------------------------- |
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| 1589 | !! *** ROUTINE Hsnow *** |
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| 1590 | !! |
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| 1591 | !! ** Purpose : 1- Check snow load after advection |
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| 1592 | !! 2- Correct pond concentration to avoid a_ip > a_i |
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| 1593 | !! |
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| 1594 | !! ** Method : If snow load makes snow-ice interface to deplet below the ocean surface |
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| 1595 | !! then put the snow excess in the ocean |
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| 1596 | !! |
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| 1597 | !! ** Notes : This correction is crucial because of the call to routine icecor afterwards |
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| 1598 | !! which imposes a mini of ice thick. (rn_himin). This imposed mini can artificially |
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| 1599 | !! make the snow very thick (if concentration decreases drastically) |
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| 1600 | !! This behavior has been seen in Ultimate-Macho and supposedly it can also be true for Prather |
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| 1601 | !!------------------------------------------------------------------- |
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| 1602 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
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| 1603 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i, pv_s, pa_i, pa_ip |
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| 1604 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s |
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| 1605 | ! |
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| 1606 | INTEGER :: ji, jj, jl ! dummy loop indices |
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| 1607 | REAL(wp) :: z1_dt, zvs_excess, zfra |
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| 1608 | !!------------------------------------------------------------------- |
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| 1609 | ! |
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| 1610 | z1_dt = 1._wp / pdt |
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| 1611 | ! |
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| 1612 | ! -- check snow load -- ! |
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| 1613 | DO jl = 1, jpl |
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| 1614 | DO jj = 1, jpj |
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| 1615 | DO ji = 1, jpi |
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| 1616 | IF ( pv_i(ji,jj,jl) > 0._wp ) THEN |
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[10911] | 1617 | ! |
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| 1618 | zvs_excess = MAX( 0._wp, pv_s(ji,jj,jl) - pv_i(ji,jj,jl) * (rau0-rhoi) * r1_rhos ) |
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[12197] | 1619 | ! |
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| 1620 | IF( zvs_excess > 0._wp ) THEN ! snow-ice interface deplets below the ocean surface |
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| 1621 | ! put snow excess in the ocean |
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[10911] | 1622 | zfra = ( pv_s(ji,jj,jl) - zvs_excess ) / MAX( pv_s(ji,jj,jl), epsi20 ) |
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[10930] | 1623 | wfx_res(ji,jj) = wfx_res(ji,jj) + zvs_excess * rhos * z1_dt |
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| 1624 | hfx_res(ji,jj) = hfx_res(ji,jj) - SUM( pe_s(ji,jj,1:nlay_s,jl) ) * ( 1._wp - zfra ) * z1_dt ! W.m-2 <0 |
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[12197] | 1625 | ! correct snow volume and heat content |
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[10911] | 1626 | pe_s(ji,jj,1:nlay_s,jl) = pe_s(ji,jj,1:nlay_s,jl) * zfra |
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| 1627 | pv_s(ji,jj,jl) = pv_s(ji,jj,jl) - zvs_excess |
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| 1628 | ENDIF |
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[12197] | 1629 | ! |
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[10911] | 1630 | ENDIF |
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| 1631 | END DO |
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| 1632 | END DO |
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[12197] | 1633 | END DO |
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| 1634 | ! |
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| 1635 | !-- correct pond concentration to avoid a_ip > a_i -- ! |
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[10911] | 1636 | WHERE( pa_ip(:,:,:) > pa_i(:,:,:) ) pa_ip(:,:,:) = pa_i(:,:,:) |
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| 1637 | ! |
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[12197] | 1638 | END SUBROUTINE Hsnow |
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| 1639 | |
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| 1640 | |
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[8586] | 1641 | #else |
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| 1642 | !!---------------------------------------------------------------------- |
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[9570] | 1643 | !! Default option Dummy module NO SI3 sea-ice model |
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[8586] | 1644 | !!---------------------------------------------------------------------- |
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| 1645 | #endif |
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| 1646 | |
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| 1647 | !!====================================================================== |
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| 1648 | END MODULE icedyn_adv_umx |
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