[825] | 1 | MODULE limitd_me |
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| 2 | !!====================================================================== |
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| 3 | !! *** MODULE limitd_me *** |
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[2715] | 4 | !! LIM-3 : Mechanical impact on ice thickness distribution |
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[825] | 5 | !!====================================================================== |
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[1572] | 6 | !! History : LIM ! 2006-02 (M. Vancoppenolle) Original code |
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[4688] | 7 | !! 3.2 ! 2009-07 (M. Vancoppenolle, Y. Aksenov, G. Madec) bug correction in smsw & sfx_dyn |
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[2715] | 8 | !! 4.0 ! 2011-02 (G. Madec) dynamical allocation |
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[825] | 9 | !!---------------------------------------------------------------------- |
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[1572] | 10 | #if defined key_lim3 |
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| 11 | !!---------------------------------------------------------------------- |
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[3625] | 12 | !! 'key_lim3' LIM-3 sea-ice model |
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[1572] | 13 | !!---------------------------------------------------------------------- |
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[4161] | 14 | USE par_oce ! ocean parameters |
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| 15 | USE dom_oce ! ocean domain |
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| 16 | USE phycst ! physical constants (ocean directory) |
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| 17 | USE sbc_oce ! surface boundary condition: ocean fields |
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| 18 | USE thd_ice ! LIM thermodynamics |
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| 19 | USE ice ! LIM variables |
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| 20 | USE limvar ! LIM |
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| 21 | USE lbclnk ! lateral boundary condition - MPP exchanges |
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| 22 | USE lib_mpp ! MPP library |
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| 23 | USE wrk_nemo ! work arrays |
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[5123] | 24 | |
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[5134] | 25 | USE in_out_manager ! I/O manager |
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[4161] | 26 | USE iom ! I/O manager |
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[4688] | 27 | USE lib_fortran ! glob_sum |
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| 28 | USE timing ! Timing |
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| 29 | USE limcons ! conservation tests |
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[7646] | 30 | USE limctl ! control prints |
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[921] | 31 | |
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[825] | 32 | IMPLICIT NONE |
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| 33 | PRIVATE |
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| 34 | |
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[2715] | 35 | PUBLIC lim_itd_me ! called by ice_stp |
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| 36 | PUBLIC lim_itd_me_icestrength |
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| 37 | PUBLIC lim_itd_me_init |
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[5123] | 38 | PUBLIC lim_itd_me_alloc ! called by sbc_lim_init |
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[825] | 39 | |
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[921] | 40 | !----------------------------------------------------------------------- |
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| 41 | ! Variables shared among ridging subroutines |
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| 42 | !----------------------------------------------------------------------- |
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[4333] | 43 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: asum ! sum of total ice and open water area |
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| 44 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: aksum ! ratio of area removed to area ridged |
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[6416] | 45 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: athorn ! participation function; fraction of ridging/closing associated w/ category n |
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[4333] | 46 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: hrmin ! minimum ridge thickness |
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| 47 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: hrmax ! maximum ridge thickness |
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| 48 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: hraft ! thickness of rafted ice |
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[6416] | 49 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: krdg ! thickness of ridging ice / mean ridge thickness |
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[4333] | 50 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: aridge ! participating ice ridging |
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| 51 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: araft ! participating ice rafting |
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[825] | 52 | |
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[2715] | 53 | REAL(wp), PARAMETER :: krdgmin = 1.1_wp ! min ridge thickness multiplier |
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[6416] | 54 | REAL(wp), PARAMETER :: kraft = 0.5_wp ! rafting multipliyer |
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[825] | 55 | |
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[2715] | 56 | REAL(wp) :: Cp ! |
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[921] | 57 | ! |
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[3625] | 58 | ! |
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[825] | 59 | !!---------------------------------------------------------------------- |
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[2528] | 60 | !! NEMO/LIM3 3.3 , UCL - NEMO Consortium (2010) |
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[1156] | 61 | !! $Id$ |
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[2715] | 62 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[825] | 63 | !!---------------------------------------------------------------------- |
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[2715] | 64 | CONTAINS |
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[825] | 65 | |
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[2715] | 66 | INTEGER FUNCTION lim_itd_me_alloc() |
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| 67 | !!---------------------------------------------------------------------! |
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| 68 | !! *** ROUTINE lim_itd_me_alloc *** |
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| 69 | !!---------------------------------------------------------------------! |
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[7646] | 70 | ALLOCATE( & |
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[2715] | 71 | !* Variables shared among ridging subroutines |
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[7646] | 72 | & asum (jpi,jpj) , athorn(jpi,jpj,0:jpl) , aksum (jpi,jpj) , & |
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| 73 | & hrmin(jpi,jpj,jpl) , hraft(jpi,jpj,jpl) , aridge(jpi,jpj,jpl) , & |
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| 74 | & hrmax(jpi,jpj,jpl) , krdg (jpi,jpj,jpl) , araft (jpi,jpj,jpl) , STAT=lim_itd_me_alloc ) |
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[2715] | 75 | ! |
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| 76 | IF( lim_itd_me_alloc /= 0 ) CALL ctl_warn( 'lim_itd_me_alloc: failed to allocate arrays' ) |
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| 77 | ! |
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| 78 | END FUNCTION lim_itd_me_alloc |
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[1156] | 79 | |
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[825] | 80 | |
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[2715] | 81 | SUBROUTINE lim_itd_me |
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[921] | 82 | !!---------------------------------------------------------------------! |
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| 83 | !! *** ROUTINE lim_itd_me *** |
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| 84 | !! |
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[2715] | 85 | !! ** Purpose : computes the mechanical redistribution of ice thickness |
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[921] | 86 | !! |
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[2715] | 87 | !! ** Method : Steps : |
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| 88 | !! 1) Thickness categories boundaries, ice / o.w. concentrations |
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| 89 | !! Ridge preparation |
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| 90 | !! 2) Dynamical inputs (closing rate, divu_adv, opning) |
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| 91 | !! 3) Ridging iteration |
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| 92 | !! 4) Ridging diagnostics |
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| 93 | !! 5) Heat, salt and freshwater fluxes |
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| 94 | !! 6) Compute increments of tate variables and come back to old values |
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[921] | 95 | !! |
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[2715] | 96 | !! References : Flato, G. M., and W. D. Hibler III, 1995, JGR, 100, 18,611-18,626. |
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| 97 | !! Hibler, W. D. III, 1980, MWR, 108, 1943-1973, 1980. |
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| 98 | !! Rothrock, D. A., 1975: JGR, 80, 4514-4519. |
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| 99 | !! Thorndike et al., 1975, JGR, 80, 4501-4513. |
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| 100 | !! Bitz et al., JGR, 2001 |
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| 101 | !! Amundrud and Melling, JGR 2005 |
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| 102 | !! Babko et al., JGR 2002 |
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[921] | 103 | !! |
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[1572] | 104 | !! This routine is based on CICE code and authors William H. Lipscomb, |
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| 105 | !! and Elizabeth C. Hunke, LANL are gratefully acknowledged |
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[921] | 106 | !!--------------------------------------------------------------------! |
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[5123] | 107 | INTEGER :: ji, jj, jk, jl ! dummy loop index |
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| 108 | INTEGER :: niter ! local integer |
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[3625] | 109 | INTEGER :: iterate_ridging ! if true, repeat the ridging |
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[5123] | 110 | REAL(wp) :: za, zfac ! local scalar |
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[2715] | 111 | CHARACTER (len = 15) :: fieldid |
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[5202] | 112 | REAL(wp), POINTER, DIMENSION(:,:) :: closing_net ! net rate at which area is removed (1/s) |
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| 113 | ! (ridging ice area - area of new ridges) / dt |
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| 114 | REAL(wp), POINTER, DIMENSION(:,:) :: divu_adv ! divu as implied by transport scheme (1/s) |
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| 115 | REAL(wp), POINTER, DIMENSION(:,:) :: opning ! rate of opening due to divergence/shear |
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| 116 | REAL(wp), POINTER, DIMENSION(:,:) :: closing_gross ! rate at which area removed, not counting area of new ridges |
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[4688] | 117 | ! |
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[5123] | 118 | INTEGER, PARAMETER :: nitermax = 20 |
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| 119 | ! |
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[4688] | 120 | REAL(wp) :: zvi_b, zsmv_b, zei_b, zfs_b, zfw_b, zft_b |
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[2715] | 121 | !!----------------------------------------------------------------------------- |
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[4161] | 122 | IF( nn_timing == 1 ) CALL timing_start('limitd_me') |
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[825] | 123 | |
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[7753] | 124 | CALL wrk_alloc( jpi,jpj, closing_net, divu_adv, opning, closing_gross ) |
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[825] | 125 | |
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[4688] | 126 | ! conservation test |
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[7646] | 127 | IF( ln_limdiachk ) CALL lim_cons_hsm(0, 'limitd_me', zvi_b, zsmv_b, zei_b, zfw_b, zfs_b, zft_b) |
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[4161] | 128 | |
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[921] | 129 | !-----------------------------------------------------------------------------! |
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| 130 | ! 1) Thickness categories boundaries, ice / o.w. concentrations, init_ons |
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| 131 | !-----------------------------------------------------------------------------! |
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[5134] | 132 | Cp = 0.5 * grav * (rau0-rhoic) * rhoic * r1_rau0 ! proport const for PE |
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[3625] | 133 | ! |
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| 134 | CALL lim_itd_me_ridgeprep ! prepare ridging |
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| 135 | ! |
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[825] | 136 | |
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[2715] | 137 | DO jj = 1, jpj ! Initialize arrays. |
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[825] | 138 | DO ji = 1, jpi |
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| 139 | |
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[921] | 140 | !-----------------------------------------------------------------------------! |
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| 141 | ! 2) Dynamical inputs (closing rate, divu_adv, opning) |
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| 142 | !-----------------------------------------------------------------------------! |
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| 143 | ! |
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| 144 | ! 2.1 closing_net |
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| 145 | !----------------- |
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| 146 | ! Compute the net rate of closing due to convergence |
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| 147 | ! and shear, based on Flato and Hibler (1995). |
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| 148 | ! |
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| 149 | ! The energy dissipation rate is equal to the net closing rate |
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| 150 | ! times the ice strength. |
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| 151 | ! |
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| 152 | ! NOTE: The NET closing rate is equal to the rate that open water |
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| 153 | ! area is removed, plus the rate at which ice area is removed by |
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| 154 | ! ridging, minus the rate at which area is added in new ridges. |
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| 155 | ! The GROSS closing rate is equal to the first two terms (open |
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| 156 | ! water closing and thin ice ridging) without the third term |
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| 157 | ! (thick, newly ridged ice). |
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[825] | 158 | |
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[5123] | 159 | closing_net(ji,jj) = rn_cs * 0.5 * ( delta_i(ji,jj) - ABS( divu_i(ji,jj) ) ) - MIN( divu_i(ji,jj), 0._wp ) |
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[825] | 160 | |
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[921] | 161 | ! 2.2 divu_adv |
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| 162 | !-------------- |
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| 163 | ! Compute divu_adv, the divergence rate given by the transport/ |
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| 164 | ! advection scheme, which may not be equal to divu as computed |
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| 165 | ! from the velocity field. |
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| 166 | ! |
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| 167 | ! If divu_adv < 0, make sure the closing rate is large enough |
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| 168 | ! to give asum = 1.0 after ridging. |
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[6416] | 169 | |
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| 170 | divu_adv(ji,jj) = ( 1._wp - asum(ji,jj) ) * r1_rdtice ! asum found in ridgeprep |
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[825] | 171 | |
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[2715] | 172 | IF( divu_adv(ji,jj) < 0._wp ) closing_net(ji,jj) = MAX( closing_net(ji,jj), -divu_adv(ji,jj) ) |
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[825] | 173 | |
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[921] | 174 | ! 2.3 opning |
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| 175 | !------------ |
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[3625] | 176 | ! Compute the (non-negative) opening rate that will give asum = 1.0 after ridging. |
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[921] | 177 | opning(ji,jj) = closing_net(ji,jj) + divu_adv(ji,jj) |
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[825] | 178 | END DO |
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| 179 | END DO |
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| 180 | |
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[921] | 181 | !-----------------------------------------------------------------------------! |
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| 182 | ! 3) Ridging iteration |
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| 183 | !-----------------------------------------------------------------------------! |
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[2715] | 184 | niter = 1 ! iteration counter |
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[869] | 185 | iterate_ridging = 1 |
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[825] | 186 | |
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[869] | 187 | DO WHILE ( iterate_ridging > 0 .AND. niter < nitermax ) |
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[825] | 188 | |
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[6416] | 189 | ! 3.2 closing_gross |
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| 190 | !-----------------------------------------------------------------------------! |
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| 191 | ! Based on the ITD of ridging and ridged ice, convert the net |
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| 192 | ! closing rate to a gross closing rate. |
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| 193 | ! NOTE: 0 < aksum <= 1 |
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[7753] | 194 | closing_gross(:,:) = closing_net(:,:) / aksum(:,:) |
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[6416] | 195 | |
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| 196 | ! correction to closing rate and opening if closing rate is excessive |
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| 197 | !--------------------------------------------------------------------- |
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| 198 | ! Reduce the closing rate if more than 100% of the open water |
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| 199 | ! would be removed. Reduce the opening rate proportionately. |
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[921] | 200 | DO jj = 1, jpj |
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| 201 | DO ji = 1, jpi |
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[6416] | 202 | za = ( opning(ji,jj) - athorn(ji,jj,0) * closing_gross(ji,jj) ) * rdt_ice |
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[7646] | 203 | IF ( za < 0._wp .AND. za > - ato_i(ji,jj) ) THEN ! would lead to negative ato_i |
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| 204 | zfac = - ato_i(ji,jj) / za |
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[6416] | 205 | opning(ji,jj) = athorn(ji,jj,0) * closing_gross(ji,jj) - ato_i(ji,jj) * r1_rdtice |
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| 206 | ELSEIF( za > 0._wp .AND. za > ( asum(ji,jj) - ato_i(ji,jj) ) ) THEN ! would lead to ato_i > asum |
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[7646] | 207 | zfac = ( asum(ji,jj) - ato_i(ji,jj) ) / za |
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[6416] | 208 | opning(ji,jj) = athorn(ji,jj,0) * closing_gross(ji,jj) + ( asum(ji,jj) - ato_i(ji,jj) ) * r1_rdtice |
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[5123] | 209 | ENDIF |
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| 210 | END DO |
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| 211 | END DO |
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[825] | 212 | |
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[921] | 213 | ! correction to closing rate / opening if excessive ice removal |
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| 214 | !--------------------------------------------------------------- |
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| 215 | ! Reduce the closing rate if more than 100% of any ice category |
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| 216 | ! would be removed. Reduce the opening rate proportionately. |
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| 217 | DO jl = 1, jpl |
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| 218 | DO jj = 1, jpj |
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| 219 | DO ji = 1, jpi |
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[5167] | 220 | za = athorn(ji,jj,jl) * closing_gross(ji,jj) * rdt_ice |
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[6416] | 221 | IF( za > a_i(ji,jj,jl) ) THEN |
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| 222 | zfac = a_i(ji,jj,jl) / za |
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[5167] | 223 | closing_gross(ji,jj) = closing_gross(ji,jj) * zfac |
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[825] | 224 | ENDIF |
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[5123] | 225 | END DO |
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| 226 | END DO |
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| 227 | END DO |
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[825] | 228 | |
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[921] | 229 | ! 3.3 Redistribute area, volume, and energy. |
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| 230 | !-----------------------------------------------------------------------------! |
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[825] | 231 | |
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[6416] | 232 | CALL lim_itd_me_ridgeshift( opning, closing_gross ) |
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[825] | 233 | |
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[6416] | 234 | |
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[921] | 235 | ! 3.4 Compute total area of ice plus open water after ridging. |
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| 236 | !-----------------------------------------------------------------------------! |
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[5134] | 237 | ! This is in general not equal to one because of divergence during transport |
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[7753] | 238 | asum(:,:) = ato_i(:,:) + SUM( a_i, dim=3 ) |
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[825] | 239 | |
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[921] | 240 | ! 3.5 Do we keep on iterating ??? |
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| 241 | !-----------------------------------------------------------------------------! |
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| 242 | ! Check whether asum = 1. If not (because the closing and opening |
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| 243 | ! rates were reduced above), ridge again with new rates. |
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[825] | 244 | |
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[921] | 245 | iterate_ridging = 0 |
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| 246 | DO jj = 1, jpj |
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| 247 | DO ji = 1, jpi |
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[6416] | 248 | IF( ABS( asum(ji,jj) - 1._wp ) < epsi10 ) THEN |
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[2715] | 249 | closing_net(ji,jj) = 0._wp |
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| 250 | opning (ji,jj) = 0._wp |
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[7646] | 251 | ato_i (ji,jj) = MAX( 0._wp, 1._wp - SUM( a_i(ji,jj,:) ) ) |
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[921] | 252 | ELSE |
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| 253 | iterate_ridging = 1 |
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[6416] | 254 | divu_adv (ji,jj) = ( 1._wp - asum(ji,jj) ) * r1_rdtice |
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[2715] | 255 | closing_net(ji,jj) = MAX( 0._wp, -divu_adv(ji,jj) ) |
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| 256 | opning (ji,jj) = MAX( 0._wp, divu_adv(ji,jj) ) |
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[921] | 257 | ENDIF |
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| 258 | END DO |
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[825] | 259 | END DO |
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| 260 | |
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[2715] | 261 | IF( lk_mpp ) CALL mpp_max( iterate_ridging ) |
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[869] | 262 | |
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[921] | 263 | ! Repeat if necessary. |
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| 264 | ! NOTE: If strength smoothing is turned on, the ridging must be |
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| 265 | ! iterated globally because of the boundary update in the |
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| 266 | ! smoothing. |
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[825] | 267 | |
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[921] | 268 | niter = niter + 1 |
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[825] | 269 | |
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[2715] | 270 | IF( iterate_ridging == 1 ) THEN |
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[6416] | 271 | CALL lim_itd_me_ridgeprep |
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[3625] | 272 | IF( niter > nitermax ) THEN |
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[921] | 273 | WRITE(numout,*) ' ALERTE : non-converging ridging scheme ' |
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| 274 | WRITE(numout,*) ' niter, iterate_ridging ', niter, iterate_ridging |
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| 275 | ENDIF |
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[825] | 276 | ENDIF |
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| 277 | |
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| 278 | END DO !! on the do while over iter |
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| 279 | |
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[5123] | 280 | CALL lim_var_agg( 1 ) |
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[825] | 281 | |
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[5134] | 282 | !-----------------------------------------------------------------------------! |
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| 283 | ! control prints |
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| 284 | !-----------------------------------------------------------------------------! |
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[7646] | 285 | ! conservation test |
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| 286 | IF( ln_limdiachk ) CALL lim_cons_hsm(1, 'limitd_me', zvi_b, zsmv_b, zei_b, zfw_b, zfs_b, zft_b) |
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[5167] | 287 | |
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[7646] | 288 | ! control prints |
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| 289 | IF( ln_ctl ) CALL lim_prt3D( 'limitd_me' ) |
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[825] | 290 | |
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[7753] | 291 | CALL wrk_dealloc( jpi, jpj, closing_net, divu_adv, opning, closing_gross ) |
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[2715] | 292 | ! |
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[4161] | 293 | IF( nn_timing == 1 ) CALL timing_stop('limitd_me') |
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[825] | 294 | END SUBROUTINE lim_itd_me |
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| 295 | |
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[2715] | 296 | SUBROUTINE lim_itd_me_ridgeprep |
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[921] | 297 | !!---------------------------------------------------------------------! |
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| 298 | !! *** ROUTINE lim_itd_me_ridgeprep *** |
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| 299 | !! |
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[2715] | 300 | !! ** Purpose : preparation for ridging and strength calculations |
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[921] | 301 | !! |
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[2715] | 302 | !! ** Method : Compute the thickness distribution of the ice and open water |
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| 303 | !! participating in ridging and of the resulting ridges. |
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[921] | 304 | !!---------------------------------------------------------------------! |
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[2715] | 305 | INTEGER :: ji,jj, jl ! dummy loop indices |
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[6416] | 306 | REAL(wp) :: Gstari, astari, hrmean, zdummy ! local scalar |
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[3294] | 307 | REAL(wp), POINTER, DIMENSION(:,:,:) :: Gsum ! Gsum(n) = sum of areas in categories 0 to n |
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| 308 | !------------------------------------------------------------------------------! |
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[825] | 309 | |
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[3294] | 310 | CALL wrk_alloc( jpi,jpj,jpl+2, Gsum, kkstart = -1 ) |
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[825] | 311 | |
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[5123] | 312 | Gstari = 1.0/rn_gstar |
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| 313 | astari = 1.0/rn_astar |
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[7753] | 314 | aksum(:,:) = 0.0 |
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| 315 | athorn(:,:,:) = 0.0 |
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| 316 | aridge(:,:,:) = 0.0 |
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| 317 | araft (:,:,:) = 0.0 |
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[825] | 318 | |
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[6416] | 319 | ! Zero out categories with very small areas |
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[5123] | 320 | CALL lim_var_zapsmall |
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[825] | 321 | |
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[6416] | 322 | ! Ice thickness needed for rafting |
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| 323 | DO jl = 1, jpl |
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| 324 | DO jj = 1, jpj |
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| 325 | DO ji = 1, jpi |
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| 326 | rswitch = MAX( 0._wp , SIGN( 1._wp, a_i(ji,jj,jl) - epsi20 ) ) |
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| 327 | ht_i(ji,jj,jl) = v_i (ji,jj,jl) / MAX( a_i(ji,jj,jl) , epsi20 ) * rswitch |
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[7646] | 328 | END DO |
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[6416] | 329 | END DO |
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| 330 | END DO |
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| 331 | |
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[921] | 332 | !------------------------------------------------------------------------------! |
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| 333 | ! 1) Participation function |
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| 334 | !------------------------------------------------------------------------------! |
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[825] | 335 | |
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| 336 | ! Compute total area of ice plus open water. |
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[5134] | 337 | ! This is in general not equal to one because of divergence during transport |
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[7753] | 338 | asum(:,:) = ato_i(:,:) + SUM( a_i, dim=3 ) |
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[825] | 339 | |
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| 340 | ! Compute cumulative thickness distribution function |
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| 341 | ! Compute the cumulative thickness distribution function Gsum, |
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| 342 | ! where Gsum(n) is the fractional area in categories 0 to n. |
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| 343 | ! initial value (in h = 0) equals open water area |
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[7753] | 344 | Gsum(:,:,-1) = 0._wp |
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| 345 | Gsum(:,:,0 ) = ato_i(:,:) |
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[825] | 346 | ! for each value of h, you have to add ice concentration then |
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| 347 | DO jl = 1, jpl |
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[7753] | 348 | Gsum(:,:,jl) = Gsum(:,:,jl-1) + a_i(:,:,jl) |
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[825] | 349 | END DO |
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| 350 | |
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| 351 | ! Normalize the cumulative distribution to 1 |
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| 352 | DO jl = 0, jpl |
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[7753] | 353 | Gsum(:,:,jl) = Gsum(:,:,jl) / asum(:,:) |
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[825] | 354 | END DO |
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| 355 | |
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[921] | 356 | ! 1.3 Compute participation function a(h) = b(h).g(h) (athorn) |
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| 357 | !-------------------------------------------------------------------------------------------------- |
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| 358 | ! Compute the participation function athorn; this is analogous to |
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| 359 | ! a(h) = b(h)g(h) as defined in Thorndike et al. (1975). |
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| 360 | ! area lost from category n due to ridging/closing |
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| 361 | ! athorn(n) = total area lost due to ridging/closing |
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| 362 | ! assume b(h) = (2/Gstar) * (1 - G(h)/Gstar). |
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| 363 | ! |
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| 364 | ! The expressions for athorn are found by integrating b(h)g(h) between |
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| 365 | ! the category boundaries. |
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[6416] | 366 | ! athorn is always >= 0 and SUM(athorn(0:jpl))=1 |
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[921] | 367 | !----------------------------------------------------------------- |
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[825] | 368 | |
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[5123] | 369 | IF( nn_partfun == 0 ) THEN !--- Linear formulation (Thorndike et al., 1975) |
---|
[4869] | 370 | DO jl = 0, jpl |
---|
[921] | 371 | DO jj = 1, jpj |
---|
| 372 | DO ji = 1, jpi |
---|
[6416] | 373 | IF ( Gsum(ji,jj,jl) < rn_gstar ) THEN |
---|
[5134] | 374 | athorn(ji,jj,jl) = Gstari * ( Gsum(ji,jj,jl) - Gsum(ji,jj,jl-1) ) * & |
---|
[6416] | 375 | & ( 2._wp - ( Gsum(ji,jj,jl-1) + Gsum(ji,jj,jl) ) * Gstari ) |
---|
| 376 | ELSEIF( Gsum(ji,jj,jl-1) < rn_gstar ) THEN |
---|
| 377 | athorn(ji,jj,jl) = Gstari * ( rn_gstar - Gsum(ji,jj,jl-1) ) * & |
---|
| 378 | & ( 2._wp - ( Gsum(ji,jj,jl-1) + rn_gstar ) * Gstari ) |
---|
[921] | 379 | ELSE |
---|
[6416] | 380 | athorn(ji,jj,jl) = 0._wp |
---|
[921] | 381 | ENDIF |
---|
[5123] | 382 | END DO |
---|
| 383 | END DO |
---|
| 384 | END DO |
---|
[825] | 385 | |
---|
[2715] | 386 | ELSE !--- Exponential, more stable formulation (Lipscomb et al, 2007) |
---|
| 387 | ! |
---|
| 388 | zdummy = 1._wp / ( 1._wp - EXP(-astari) ) ! precompute exponential terms using Gsum as a work array |
---|
[921] | 389 | DO jl = -1, jpl |
---|
[7753] | 390 | Gsum(:,:,jl) = EXP( -Gsum(:,:,jl) * astari ) * zdummy |
---|
[5134] | 391 | END DO |
---|
[4869] | 392 | DO jl = 0, jpl |
---|
[7753] | 393 | athorn(:,:,jl) = Gsum(:,:,jl-1) - Gsum(:,:,jl) |
---|
[2715] | 394 | END DO |
---|
| 395 | ! |
---|
[5134] | 396 | ENDIF |
---|
[825] | 397 | |
---|
[7646] | 398 | ! --- Ridging and rafting participation concentrations --- ! |
---|
| 399 | IF( ln_rafting .AND. ln_ridging ) THEN |
---|
[2715] | 400 | ! |
---|
[825] | 401 | DO jl = 1, jpl |
---|
| 402 | DO jj = 1, jpj |
---|
| 403 | DO ji = 1, jpi |
---|
[6416] | 404 | zdummy = TANH ( rn_craft * ( ht_i(ji,jj,jl) - rn_hraft ) ) |
---|
| 405 | aridge(ji,jj,jl) = ( 1._wp + zdummy ) * 0.5_wp * athorn(ji,jj,jl) |
---|
[7646] | 406 | araft (ji,jj,jl) = athorn(ji,jj,jl) - aridge(ji,jj,jl) |
---|
[5123] | 407 | END DO |
---|
| 408 | END DO |
---|
| 409 | END DO |
---|
[2715] | 410 | ! |
---|
[7646] | 411 | ELSEIF( ln_ridging .AND. .NOT. ln_rafting ) THEN |
---|
| 412 | ! |
---|
[825] | 413 | DO jl = 1, jpl |
---|
[7753] | 414 | aridge(:,:,jl) = athorn(:,:,jl) |
---|
[825] | 415 | END DO |
---|
[2715] | 416 | ! |
---|
[7646] | 417 | ELSEIF( ln_rafting .AND. .NOT. ln_ridging ) THEN |
---|
| 418 | ! |
---|
| 419 | DO jl = 1, jpl |
---|
[7753] | 420 | araft(:,:,jl) = athorn(:,:,jl) |
---|
[7646] | 421 | END DO |
---|
| 422 | ! |
---|
[825] | 423 | ENDIF |
---|
| 424 | |
---|
[921] | 425 | !----------------------------------------------------------------- |
---|
| 426 | ! 2) Transfer function |
---|
| 427 | !----------------------------------------------------------------- |
---|
| 428 | ! Compute max and min ridged ice thickness for each ridging category. |
---|
| 429 | ! Assume ridged ice is uniformly distributed between hrmin and hrmax. |
---|
| 430 | ! |
---|
| 431 | ! This parameterization is a modified version of Hibler (1980). |
---|
| 432 | ! The mean ridging thickness, hrmean, is proportional to hi^(0.5) |
---|
| 433 | ! and for very thick ridging ice must be >= krdgmin*hi |
---|
| 434 | ! |
---|
| 435 | ! The minimum ridging thickness, hrmin, is equal to 2*hi |
---|
| 436 | ! (i.e., rafting) and for very thick ridging ice is |
---|
| 437 | ! constrained by hrmin <= (hrmean + hi)/2. |
---|
| 438 | ! |
---|
| 439 | ! The maximum ridging thickness, hrmax, is determined by |
---|
| 440 | ! hrmean and hrmin. |
---|
| 441 | ! |
---|
| 442 | ! These modifications have the effect of reducing the ice strength |
---|
| 443 | ! (relative to the Hibler formulation) when very thick ice is |
---|
| 444 | ! ridging. |
---|
| 445 | ! |
---|
| 446 | ! aksum = net area removed/ total area removed |
---|
| 447 | ! where total area removed = area of ice that ridges |
---|
| 448 | ! net area removed = total area removed - area of new ridges |
---|
| 449 | !----------------------------------------------------------------- |
---|
[825] | 450 | |
---|
[7753] | 451 | aksum(:,:) = athorn(:,:,0) |
---|
[825] | 452 | ! Transfer function |
---|
| 453 | DO jl = 1, jpl !all categories have a specific transfer function |
---|
| 454 | DO jj = 1, jpj |
---|
| 455 | DO ji = 1, jpi |
---|
[6416] | 456 | |
---|
| 457 | IF( athorn(ji,jj,jl) > 0._wp ) THEN |
---|
| 458 | hrmean = MAX( SQRT( rn_hstar * ht_i(ji,jj,jl) ), ht_i(ji,jj,jl) * krdgmin ) |
---|
| 459 | hrmin(ji,jj,jl) = MIN( 2._wp * ht_i(ji,jj,jl), 0.5_wp * ( hrmean + ht_i(ji,jj,jl) ) ) |
---|
| 460 | hrmax(ji,jj,jl) = 2._wp * hrmean - hrmin(ji,jj,jl) |
---|
| 461 | hraft(ji,jj,jl) = ht_i(ji,jj,jl) / kraft |
---|
| 462 | krdg(ji,jj,jl) = ht_i(ji,jj,jl) / MAX( hrmean, epsi20 ) |
---|
[825] | 463 | |
---|
[6416] | 464 | ! Normalization factor : aksum, ensures mass conservation |
---|
| 465 | aksum(ji,jj) = aksum(ji,jj) + aridge(ji,jj,jl) * ( 1._wp - krdg(ji,jj,jl) ) & |
---|
| 466 | & + araft (ji,jj,jl) * ( 1._wp - kraft ) |
---|
| 467 | |
---|
[825] | 468 | ELSE |
---|
[6416] | 469 | hrmin(ji,jj,jl) = 0._wp |
---|
| 470 | hrmax(ji,jj,jl) = 0._wp |
---|
| 471 | hraft(ji,jj,jl) = 0._wp |
---|
| 472 | krdg (ji,jj,jl) = 1._wp |
---|
[825] | 473 | ENDIF |
---|
| 474 | |
---|
[5134] | 475 | END DO |
---|
| 476 | END DO |
---|
| 477 | END DO |
---|
[2715] | 478 | ! |
---|
[3294] | 479 | CALL wrk_dealloc( jpi,jpj,jpl+2, Gsum, kkstart = -1 ) |
---|
| 480 | ! |
---|
[921] | 481 | END SUBROUTINE lim_itd_me_ridgeprep |
---|
[825] | 482 | |
---|
| 483 | |
---|
[6416] | 484 | SUBROUTINE lim_itd_me_ridgeshift( opning, closing_gross ) |
---|
[2715] | 485 | !!---------------------------------------------------------------------- |
---|
[921] | 486 | !! *** ROUTINE lim_itd_me_icestrength *** |
---|
| 487 | !! |
---|
[2715] | 488 | !! ** Purpose : shift ridging ice among thickness categories of ice thickness |
---|
[921] | 489 | !! |
---|
[2715] | 490 | !! ** Method : Remove area, volume, and energy from each ridging category |
---|
| 491 | !! and add to thicker ice categories. |
---|
| 492 | !!---------------------------------------------------------------------- |
---|
| 493 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: opning ! rate of opening due to divergence/shear |
---|
| 494 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: closing_gross ! rate at which area removed, excluding area of new ridges |
---|
| 495 | ! |
---|
| 496 | CHARACTER (len=80) :: fieldid ! field identifier |
---|
| 497 | ! |
---|
| 498 | INTEGER :: ji, jj, jl, jl1, jl2, jk ! dummy loop indices |
---|
| 499 | INTEGER :: ij ! horizontal index, combines i and j loops |
---|
[6416] | 500 | INTEGER :: icells ! number of cells with a_i > puny |
---|
| 501 | REAL(wp) :: hL, hR, farea ! left and right limits of integration |
---|
[825] | 502 | |
---|
[3294] | 503 | INTEGER , POINTER, DIMENSION(:) :: indxi, indxj ! compressed indices |
---|
[6416] | 504 | REAL(wp), POINTER, DIMENSION(:) :: zswitch, fvol ! new ridge volume going to n2 |
---|
[825] | 505 | |
---|
[6416] | 506 | REAL(wp), POINTER, DIMENSION(:) :: afrac ! fraction of category area ridged |
---|
| 507 | REAL(wp), POINTER, DIMENSION(:) :: ardg1 , ardg2 ! area of ice ridged & new ridges |
---|
| 508 | REAL(wp), POINTER, DIMENSION(:) :: vsrdg , esrdg ! snow volume & energy of ridging ice |
---|
| 509 | REAL(wp), POINTER, DIMENSION(:) :: dhr , dhr2 ! hrmax - hrmin & hrmax^2 - hrmin^2 |
---|
[825] | 510 | |
---|
[6416] | 511 | REAL(wp), POINTER, DIMENSION(:) :: vrdg1 ! volume of ice ridged |
---|
| 512 | REAL(wp), POINTER, DIMENSION(:) :: vrdg2 ! volume of new ridges |
---|
| 513 | REAL(wp), POINTER, DIMENSION(:) :: vsw ! volume of seawater trapped into ridges |
---|
| 514 | REAL(wp), POINTER, DIMENSION(:) :: srdg1 ! sal*volume of ice ridged |
---|
| 515 | REAL(wp), POINTER, DIMENSION(:) :: srdg2 ! sal*volume of new ridges |
---|
| 516 | REAL(wp), POINTER, DIMENSION(:) :: smsw ! sal*volume of water trapped into ridges |
---|
| 517 | REAL(wp), POINTER, DIMENSION(:) :: oirdg1, oirdg2 ! ice age of ice ridged |
---|
[825] | 518 | |
---|
[6416] | 519 | REAL(wp), POINTER, DIMENSION(:) :: afrft ! fraction of category area rafted |
---|
| 520 | REAL(wp), POINTER, DIMENSION(:) :: arft1 , arft2 ! area of ice rafted and new rafted zone |
---|
| 521 | REAL(wp), POINTER, DIMENSION(:) :: virft , vsrft ! ice & snow volume of rafting ice |
---|
| 522 | REAL(wp), POINTER, DIMENSION(:) :: esrft , smrft ! snow energy & salinity of rafting ice |
---|
| 523 | REAL(wp), POINTER, DIMENSION(:) :: oirft1, oirft2 ! ice age of ice rafted |
---|
[825] | 524 | |
---|
[6416] | 525 | REAL(wp), POINTER, DIMENSION(:,:) :: eirft ! ice energy of rafting ice |
---|
| 526 | REAL(wp), POINTER, DIMENSION(:,:) :: erdg1 ! enth*volume of ice ridged |
---|
| 527 | REAL(wp), POINTER, DIMENSION(:,:) :: erdg2 ! enth*volume of new ridges |
---|
| 528 | REAL(wp), POINTER, DIMENSION(:,:) :: ersw ! enth of water trapped into ridges |
---|
[3294] | 529 | !!---------------------------------------------------------------------- |
---|
[825] | 530 | |
---|
[6416] | 531 | CALL wrk_alloc( jpij, indxi, indxj ) |
---|
| 532 | CALL wrk_alloc( jpij, zswitch, fvol ) |
---|
| 533 | CALL wrk_alloc( jpij, afrac, ardg1, ardg2, vsrdg, esrdg, dhr, dhr2 ) |
---|
| 534 | CALL wrk_alloc( jpij, vrdg1, vrdg2, vsw , srdg1, srdg2, smsw, oirdg1, oirdg2 ) |
---|
| 535 | CALL wrk_alloc( jpij, afrft, arft1, arft2, virft, vsrft, esrft, smrft, oirft1, oirft2 ) |
---|
| 536 | CALL wrk_alloc( jpij,nlay_i, eirft, erdg1, erdg2, ersw ) |
---|
[3294] | 537 | |
---|
[921] | 538 | !------------------------------------------------------------------------------- |
---|
| 539 | ! 1) Compute change in open water area due to closing and opening. |
---|
| 540 | !------------------------------------------------------------------------------- |
---|
[825] | 541 | DO jj = 1, jpj |
---|
| 542 | DO ji = 1, jpi |
---|
[6416] | 543 | ato_i(ji,jj) = MAX( 0._wp, ato_i(ji,jj) + & |
---|
| 544 | & ( opning(ji,jj) - athorn(ji,jj,0) * closing_gross(ji,jj) ) * rdt_ice ) |
---|
[5134] | 545 | END DO |
---|
| 546 | END DO |
---|
[825] | 547 | |
---|
[921] | 548 | !----------------------------------------------------------------- |
---|
| 549 | ! 3) Pump everything from ice which is being ridged / rafted |
---|
| 550 | !----------------------------------------------------------------- |
---|
| 551 | ! Compute the area, volume, and energy of ice ridging in each |
---|
| 552 | ! category, along with the area of the resulting ridge. |
---|
[825] | 553 | |
---|
| 554 | DO jl1 = 1, jpl !jl1 describes the ridging category |
---|
| 555 | |
---|
[921] | 556 | !------------------------------------------------ |
---|
| 557 | ! 3.1) Identify grid cells with nonzero ridging |
---|
| 558 | !------------------------------------------------ |
---|
[825] | 559 | icells = 0 |
---|
| 560 | DO jj = 1, jpj |
---|
| 561 | DO ji = 1, jpi |
---|
[6416] | 562 | IF( athorn(ji,jj,jl1) > 0._wp .AND. closing_gross(ji,jj) > 0._wp ) THEN |
---|
[825] | 563 | icells = icells + 1 |
---|
| 564 | indxi(icells) = ji |
---|
| 565 | indxj(icells) = jj |
---|
[5134] | 566 | ENDIF |
---|
| 567 | END DO |
---|
| 568 | END DO |
---|
[825] | 569 | |
---|
| 570 | DO ij = 1, icells |
---|
[6416] | 571 | ji = indxi(ij) ; jj = indxj(ij) |
---|
[825] | 572 | |
---|
[921] | 573 | !-------------------------------------------------------------------- |
---|
| 574 | ! 3.2) Compute area of ridging ice (ardg1) and of new ridge (ardg2) |
---|
| 575 | !-------------------------------------------------------------------- |
---|
[6416] | 576 | ardg1(ij) = aridge(ji,jj,jl1) * closing_gross(ji,jj) * rdt_ice |
---|
| 577 | arft1(ij) = araft (ji,jj,jl1) * closing_gross(ji,jj) * rdt_ice |
---|
[825] | 578 | |
---|
[921] | 579 | !--------------------------------------------------------------- |
---|
| 580 | ! 3.3) Compute ridging /rafting fractions, make sure afrac <=1 |
---|
| 581 | !--------------------------------------------------------------- |
---|
[6416] | 582 | afrac(ij) = ardg1(ij) / a_i(ji,jj,jl1) !ridging |
---|
| 583 | afrft(ij) = arft1(ij) / a_i(ji,jj,jl1) !rafting |
---|
| 584 | ardg2(ij) = ardg1(ij) * krdg(ji,jj,jl1) |
---|
| 585 | arft2(ij) = arft1(ij) * kraft |
---|
[825] | 586 | |
---|
[921] | 587 | !-------------------------------------------------------------------------- |
---|
| 588 | ! 3.4) Subtract area, volume, and energy from ridging |
---|
| 589 | ! / rafting category n1. |
---|
| 590 | !-------------------------------------------------------------------------- |
---|
[6416] | 591 | vrdg1(ij) = v_i(ji,jj,jl1) * afrac(ij) |
---|
| 592 | vrdg2(ij) = vrdg1(ij) * ( 1. + rn_por_rdg ) |
---|
| 593 | vsw (ij) = vrdg1(ij) * rn_por_rdg |
---|
[825] | 594 | |
---|
[6416] | 595 | vsrdg (ij) = v_s (ji,jj, jl1) * afrac(ij) |
---|
| 596 | esrdg (ij) = e_s (ji,jj,1,jl1) * afrac(ij) |
---|
| 597 | srdg1 (ij) = smv_i(ji,jj, jl1) * afrac(ij) |
---|
| 598 | oirdg1(ij) = oa_i (ji,jj, jl1) * afrac(ij) |
---|
| 599 | oirdg2(ij) = oa_i (ji,jj, jl1) * afrac(ij) * krdg(ji,jj,jl1) |
---|
[825] | 600 | |
---|
| 601 | ! rafting volumes, heat contents ... |
---|
[6416] | 602 | virft (ij) = v_i (ji,jj, jl1) * afrft(ij) |
---|
| 603 | vsrft (ij) = v_s (ji,jj, jl1) * afrft(ij) |
---|
| 604 | esrft (ij) = e_s (ji,jj,1,jl1) * afrft(ij) |
---|
| 605 | smrft (ij) = smv_i(ji,jj, jl1) * afrft(ij) |
---|
| 606 | oirft1(ij) = oa_i (ji,jj, jl1) * afrft(ij) |
---|
| 607 | oirft2(ij) = oa_i (ji,jj, jl1) * afrft(ij) * kraft |
---|
[825] | 608 | |
---|
[921] | 609 | !----------------------------------------------------------------- |
---|
| 610 | ! 3.5) Compute properties of new ridges |
---|
| 611 | !----------------------------------------------------------------- |
---|
[6416] | 612 | smsw(ij) = vsw(ij) * sss_m(ji,jj) ! salt content of seawater frozen in voids |
---|
| 613 | srdg2(ij) = srdg1(ij) + smsw(ij) ! salt content of new ridge |
---|
[1572] | 614 | |
---|
[6416] | 615 | sfx_dyn(ji,jj) = sfx_dyn(ji,jj) - smsw(ij) * rhoic * r1_rdtice |
---|
| 616 | wfx_dyn(ji,jj) = wfx_dyn(ji,jj) - vsw (ij) * rhoic * r1_rdtice ! increase in ice volume due to seawater frozen in voids |
---|
[6470] | 617 | |
---|
| 618 | ! virtual salt flux to keep salinity constant |
---|
| 619 | IF( nn_icesal == 1 .OR. nn_icesal == 3 ) THEN |
---|
| 620 | srdg2(ij) = srdg2(ij) - vsw(ij) * ( sss_m(ji,jj) - sm_i(ji,jj,jl1) ) ! ridge salinity = sm_i |
---|
| 621 | sfx_bri(ji,jj) = sfx_bri(ji,jj) + sss_m(ji,jj) * vsw(ij) * rhoic * r1_rdtice & ! put back sss_m into the ocean |
---|
| 622 | & - sm_i(ji,jj,jl1) * vsw(ij) * rhoic * r1_rdtice ! and get sm_i from the ocean |
---|
| 623 | ENDIF |
---|
[7646] | 624 | |
---|
[921] | 625 | !------------------------------------------ |
---|
| 626 | ! 3.7 Put the snow somewhere in the ocean |
---|
| 627 | !------------------------------------------ |
---|
| 628 | ! Place part of the snow lost by ridging into the ocean. |
---|
[6416] | 629 | ! Note that esrdg > 0; the ocean must cool to melt snow. |
---|
[921] | 630 | ! If the ocean temp = Tf already, new ice must grow. |
---|
| 631 | ! During the next time step, thermo_rates will determine whether |
---|
| 632 | ! the ocean cools or new ice grows. |
---|
[6416] | 633 | wfx_snw(ji,jj) = wfx_snw(ji,jj) + ( rhosn * vsrdg(ij) * ( 1._wp - rn_fsnowrdg ) & |
---|
| 634 | & + rhosn * vsrft(ij) * ( 1._wp - rn_fsnowrft ) ) * r1_rdtice ! fresh water source for ocean |
---|
[921] | 635 | |
---|
[6416] | 636 | hfx_dyn(ji,jj) = hfx_dyn(ji,jj) + ( - esrdg(ij) * ( 1._wp - rn_fsnowrdg ) & |
---|
| 637 | & - esrft(ij) * ( 1._wp - rn_fsnowrft ) ) * r1_rdtice ! heat sink for ocean (<0, W.m-2) |
---|
[825] | 638 | |
---|
[921] | 639 | !----------------------------------------------------------------- |
---|
| 640 | ! 3.8 Compute quantities used to apportion ice among categories |
---|
| 641 | ! in the n2 loop below |
---|
| 642 | !----------------------------------------------------------------- |
---|
[6416] | 643 | dhr (ij) = 1._wp / ( hrmax(ji,jj,jl1) - hrmin(ji,jj,jl1) ) |
---|
| 644 | dhr2(ij) = 1._wp / ( hrmax(ji,jj,jl1) * hrmax(ji,jj,jl1) - hrmin(ji,jj,jl1) * hrmin(ji,jj,jl1) ) |
---|
[825] | 645 | |
---|
| 646 | |
---|
[6416] | 647 | ! update jl1 (removing ridged/rafted area) |
---|
| 648 | a_i (ji,jj, jl1) = a_i (ji,jj, jl1) - ardg1 (ij) - arft1 (ij) |
---|
| 649 | v_i (ji,jj, jl1) = v_i (ji,jj, jl1) - vrdg1 (ij) - virft (ij) |
---|
| 650 | v_s (ji,jj, jl1) = v_s (ji,jj, jl1) - vsrdg (ij) - vsrft (ij) |
---|
| 651 | e_s (ji,jj,1,jl1) = e_s (ji,jj,1,jl1) - esrdg (ij) - esrft (ij) |
---|
| 652 | smv_i(ji,jj, jl1) = smv_i(ji,jj, jl1) - srdg1 (ij) - smrft (ij) |
---|
| 653 | oa_i (ji,jj, jl1) = oa_i (ji,jj, jl1) - oirdg1(ij) - oirft1(ij) |
---|
[825] | 654 | |
---|
[5134] | 655 | END DO |
---|
[825] | 656 | |
---|
[921] | 657 | !-------------------------------------------------------------------- |
---|
| 658 | ! 3.9 Compute ridging ice enthalpy, remove it from ridging ice and |
---|
| 659 | ! compute ridged ice enthalpy |
---|
| 660 | !-------------------------------------------------------------------- |
---|
[825] | 661 | DO jk = 1, nlay_i |
---|
| 662 | DO ij = 1, icells |
---|
[6416] | 663 | ji = indxi(ij) ; jj = indxj(ij) |
---|
[921] | 664 | ! heat content of ridged ice |
---|
[6416] | 665 | erdg1(ij,jk) = e_i(ji,jj,jk,jl1) * afrac(ij) |
---|
| 666 | eirft(ij,jk) = e_i(ji,jj,jk,jl1) * afrft(ij) |
---|
[4688] | 667 | |
---|
| 668 | ! enthalpy of the trapped seawater (J/m2, >0) |
---|
| 669 | ! clem: if sst>0, then ersw <0 (is that possible?) |
---|
[6416] | 670 | ersw(ij,jk) = - rhoic * vsw(ij) * rcp * sst_m(ji,jj) * r1_nlay_i |
---|
[825] | 671 | |
---|
[4688] | 672 | ! heat flux to the ocean |
---|
[6416] | 673 | hfx_dyn(ji,jj) = hfx_dyn(ji,jj) + ersw(ij,jk) * r1_rdtice ! > 0 [W.m-2] ocean->ice flux |
---|
[825] | 674 | |
---|
[5123] | 675 | ! it is added to sea ice because the sign convention is the opposite of the sign convention for the ocean |
---|
[6416] | 676 | erdg2(ij,jk) = erdg1(ij,jk) + ersw(ij,jk) |
---|
[4688] | 677 | |
---|
[6416] | 678 | ! update jl1 |
---|
| 679 | e_i (ji,jj,jk,jl1) = e_i(ji,jj,jk,jl1) - erdg1(ij,jk) - eirft(ij,jk) |
---|
| 680 | |
---|
[5134] | 681 | END DO |
---|
| 682 | END DO |
---|
[825] | 683 | |
---|
[921] | 684 | !------------------------------------------------------------------------------- |
---|
| 685 | ! 4) Add area, volume, and energy of new ridge to each category jl2 |
---|
| 686 | !------------------------------------------------------------------------------- |
---|
[4869] | 687 | DO jl2 = 1, jpl |
---|
[6416] | 688 | ! over categories to which ridged/rafted ice is transferred |
---|
[825] | 689 | DO ij = 1, icells |
---|
[6416] | 690 | ji = indxi(ij) ; jj = indxj(ij) |
---|
[825] | 691 | |
---|
[6416] | 692 | ! Compute the fraction of ridged ice area and volume going to thickness category jl2. |
---|
| 693 | IF( hrmin(ji,jj,jl1) <= hi_max(jl2) .AND. hrmax(ji,jj,jl1) > hi_max(jl2-1) ) THEN |
---|
[3625] | 694 | hL = MAX( hrmin(ji,jj,jl1), hi_max(jl2-1) ) |
---|
| 695 | hR = MIN( hrmax(ji,jj,jl1), hi_max(jl2) ) |
---|
[6416] | 696 | farea = ( hR - hL ) * dhr(ij) |
---|
| 697 | fvol(ij) = ( hR * hR - hL * hL ) * dhr2(ij) |
---|
| 698 | ELSE |
---|
| 699 | farea = 0._wp |
---|
| 700 | fvol(ij) = 0._wp |
---|
[825] | 701 | ENDIF |
---|
| 702 | |
---|
[6416] | 703 | ! Compute the fraction of rafted ice area and volume going to thickness category jl2 |
---|
| 704 | IF( hraft(ji,jj,jl1) <= hi_max(jl2) .AND. hraft(ji,jj,jl1) > hi_max(jl2-1) ) THEN |
---|
| 705 | zswitch(ij) = 1._wp |
---|
| 706 | ELSE |
---|
| 707 | zswitch(ij) = 0._wp |
---|
| 708 | ENDIF |
---|
[825] | 709 | |
---|
[6416] | 710 | a_i (ji,jj ,jl2) = a_i (ji,jj ,jl2) + ( ardg2 (ij) * farea + arft2 (ij) * zswitch(ij) ) |
---|
| 711 | oa_i (ji,jj ,jl2) = oa_i (ji,jj ,jl2) + ( oirdg2(ij) * farea + oirft2(ij) * zswitch(ij) ) |
---|
| 712 | v_i (ji,jj ,jl2) = v_i (ji,jj ,jl2) + ( vrdg2 (ij) * fvol(ij) + virft (ij) * zswitch(ij) ) |
---|
| 713 | smv_i(ji,jj ,jl2) = smv_i(ji,jj ,jl2) + ( srdg2 (ij) * fvol(ij) + smrft (ij) * zswitch(ij) ) |
---|
| 714 | v_s (ji,jj ,jl2) = v_s (ji,jj ,jl2) + ( vsrdg (ij) * rn_fsnowrdg * fvol(ij) + & |
---|
| 715 | & vsrft (ij) * rn_fsnowrft * zswitch(ij) ) |
---|
| 716 | e_s (ji,jj,1,jl2) = e_s (ji,jj,1,jl2) + ( esrdg (ij) * rn_fsnowrdg * fvol(ij) + & |
---|
| 717 | & esrft (ij) * rn_fsnowrft * zswitch(ij) ) |
---|
[825] | 718 | |
---|
[5202] | 719 | END DO |
---|
[825] | 720 | |
---|
| 721 | ! Transfer ice energy to category jl2 by ridging |
---|
| 722 | DO jk = 1, nlay_i |
---|
| 723 | DO ij = 1, icells |
---|
[6416] | 724 | ji = indxi(ij) ; jj = indxj(ij) |
---|
| 725 | e_i(ji,jj,jk,jl2) = e_i(ji,jj,jk,jl2) + erdg2(ij,jk) * fvol(ij) + eirft(ij,jk) * zswitch(ij) |
---|
[2715] | 726 | END DO |
---|
| 727 | END DO |
---|
| 728 | ! |
---|
[6416] | 729 | END DO ! jl2 |
---|
| 730 | |
---|
| 731 | END DO ! jl1 (deforming categories) |
---|
[7753] | 732 | |
---|
[6416] | 733 | ! |
---|
| 734 | CALL wrk_dealloc( jpij, indxi, indxj ) |
---|
| 735 | CALL wrk_dealloc( jpij, zswitch, fvol ) |
---|
| 736 | CALL wrk_dealloc( jpij, afrac, ardg1, ardg2, vsrdg, esrdg, dhr, dhr2 ) |
---|
| 737 | CALL wrk_dealloc( jpij, vrdg1, vrdg2, vsw , srdg1, srdg2, smsw, oirdg1, oirdg2 ) |
---|
| 738 | CALL wrk_dealloc( jpij, afrft, arft1, arft2, virft, vsrft, esrft, smrft, oirft1, oirft2 ) |
---|
| 739 | CALL wrk_dealloc( jpij,nlay_i, eirft, erdg1, erdg2, ersw ) |
---|
| 740 | ! |
---|
| 741 | END SUBROUTINE lim_itd_me_ridgeshift |
---|
[825] | 742 | |
---|
[6416] | 743 | SUBROUTINE lim_itd_me_icestrength( kstrngth ) |
---|
| 744 | !!---------------------------------------------------------------------- |
---|
| 745 | !! *** ROUTINE lim_itd_me_icestrength *** |
---|
| 746 | !! |
---|
| 747 | !! ** Purpose : computes ice strength used in dynamics routines of ice thickness |
---|
| 748 | !! |
---|
| 749 | !! ** Method : Compute the strength of the ice pack, defined as the energy (J m-2) |
---|
| 750 | !! dissipated per unit area removed from the ice pack under compression, |
---|
| 751 | !! and assumed proportional to the change in potential energy caused |
---|
| 752 | !! by ridging. Note that only Hibler's formulation is stable and that |
---|
| 753 | !! ice strength has to be smoothed |
---|
| 754 | !! |
---|
| 755 | !! ** Inputs / Ouputs : kstrngth (what kind of ice strength we are using) |
---|
| 756 | !!---------------------------------------------------------------------- |
---|
| 757 | INTEGER, INTENT(in) :: kstrngth ! = 1 for Rothrock formulation, 0 for Hibler (1979) |
---|
| 758 | INTEGER :: ji,jj, jl ! dummy loop indices |
---|
| 759 | INTEGER :: ksmooth ! smoothing the resistance to deformation |
---|
| 760 | INTEGER :: numts_rm ! number of time steps for the P smoothing |
---|
| 761 | REAL(wp) :: zp, z1_3 ! local scalars |
---|
[7646] | 762 | REAL(wp), POINTER, DIMENSION(:,:) :: zworka ! temporary array used here |
---|
| 763 | REAL(wp), POINTER, DIMENSION(:,:) :: zstrp1, zstrp2 ! strength at previous time steps |
---|
[6416] | 764 | !!---------------------------------------------------------------------- |
---|
[825] | 765 | |
---|
[7646] | 766 | CALL wrk_alloc( jpi,jpj, zworka, zstrp1, zstrp2 ) |
---|
[6416] | 767 | |
---|
| 768 | !------------------------------------------------------------------------------! |
---|
| 769 | ! 1) Initialize |
---|
| 770 | !------------------------------------------------------------------------------! |
---|
[7753] | 771 | strength(:,:) = 0._wp |
---|
[6416] | 772 | |
---|
| 773 | !------------------------------------------------------------------------------! |
---|
| 774 | ! 2) Compute thickness distribution of ridging and ridged ice |
---|
| 775 | !------------------------------------------------------------------------------! |
---|
| 776 | CALL lim_itd_me_ridgeprep |
---|
| 777 | |
---|
| 778 | !------------------------------------------------------------------------------! |
---|
| 779 | ! 3) Rothrock(1975)'s method |
---|
| 780 | !------------------------------------------------------------------------------! |
---|
| 781 | IF( kstrngth == 1 ) THEN |
---|
| 782 | z1_3 = 1._wp / 3._wp |
---|
| 783 | DO jl = 1, jpl |
---|
| 784 | DO jj= 1, jpj |
---|
| 785 | DO ji = 1, jpi |
---|
| 786 | ! |
---|
| 787 | IF( athorn(ji,jj,jl) > 0._wp ) THEN |
---|
| 788 | !---------------------------- |
---|
| 789 | ! PE loss from deforming ice |
---|
| 790 | !---------------------------- |
---|
| 791 | strength(ji,jj) = strength(ji,jj) - athorn(ji,jj,jl) * ht_i(ji,jj,jl) * ht_i(ji,jj,jl) |
---|
| 792 | |
---|
| 793 | !-------------------------- |
---|
| 794 | ! PE gain from rafting ice |
---|
| 795 | !-------------------------- |
---|
| 796 | strength(ji,jj) = strength(ji,jj) + 2._wp * araft(ji,jj,jl) * ht_i(ji,jj,jl) * ht_i(ji,jj,jl) |
---|
| 797 | |
---|
| 798 | !---------------------------- |
---|
| 799 | ! PE gain from ridging ice |
---|
| 800 | !---------------------------- |
---|
| 801 | strength(ji,jj) = strength(ji,jj) + aridge(ji,jj,jl) * krdg(ji,jj,jl) * z1_3 * & |
---|
| 802 | & ( hrmax(ji,jj,jl) * hrmax(ji,jj,jl) + & |
---|
| 803 | & hrmin(ji,jj,jl) * hrmin(ji,jj,jl) + & |
---|
| 804 | & hrmax(ji,jj,jl) * hrmin(ji,jj,jl) ) |
---|
| 805 | !!(a**3-b**3)/(a-b) = a*a+ab+b*b |
---|
[825] | 806 | ENDIF |
---|
[6416] | 807 | ! |
---|
[5123] | 808 | END DO |
---|
| 809 | END DO |
---|
[6416] | 810 | END DO |
---|
| 811 | |
---|
[7753] | 812 | strength(:,:) = rn_pe_rdg * Cp * strength(:,:) / aksum(:,:) * tmask(:,:,1) |
---|
[6416] | 813 | ! where Cp = (g/2)*(rhow-rhoi)*(rhoi/rhow) and rn_pe_rdg accounts for frictional dissipation |
---|
| 814 | ksmooth = 1 |
---|
[825] | 815 | |
---|
[7646] | 816 | !------------------------------------------------------------------------------! |
---|
| 817 | ! 4) Hibler (1979)' method |
---|
| 818 | !------------------------------------------------------------------------------! |
---|
[6416] | 819 | ELSE ! kstrngth ne 1: Hibler (1979) form |
---|
| 820 | ! |
---|
[7753] | 821 | strength(:,:) = rn_pstar * vt_i(:,:) * EXP( - rn_crhg * ( 1._wp - at_i(:,:) ) ) * tmask(:,:,1) |
---|
| 822 | ! |
---|
[6416] | 823 | ksmooth = 1 |
---|
| 824 | ! |
---|
| 825 | ENDIF ! kstrngth |
---|
| 826 | ! |
---|
| 827 | !------------------------------------------------------------------------------! |
---|
| 828 | ! 5) Impact of brine volume |
---|
| 829 | !------------------------------------------------------------------------------! |
---|
| 830 | ! CAN BE REMOVED |
---|
| 831 | IF( ln_icestr_bvf ) THEN |
---|
| 832 | DO jj = 1, jpj |
---|
| 833 | DO ji = 1, jpi |
---|
[7646] | 834 | strength(ji,jj) = strength(ji,jj) * exp(-5.88*SQRT(MAX(bvm_i(ji,jj),0.0))) |
---|
[6416] | 835 | END DO |
---|
[5123] | 836 | END DO |
---|
[6416] | 837 | ENDIF |
---|
| 838 | ! |
---|
| 839 | !------------------------------------------------------------------------------! |
---|
| 840 | ! 6) Smoothing ice strength |
---|
| 841 | !------------------------------------------------------------------------------! |
---|
| 842 | ! |
---|
| 843 | !------------------- |
---|
| 844 | ! Spatial smoothing |
---|
| 845 | !------------------- |
---|
| 846 | IF ( ksmooth == 1 ) THEN |
---|
[825] | 847 | |
---|
[6416] | 848 | DO jj = 2, jpjm1 |
---|
| 849 | DO ji = 2, jpim1 |
---|
[7646] | 850 | IF ( ( asum(ji,jj) - ato_i(ji,jj) ) > 0._wp ) THEN |
---|
[6416] | 851 | zworka(ji,jj) = ( 4.0 * strength(ji,jj) & |
---|
| 852 | & + strength(ji-1,jj) * tmask(ji-1,jj,1) + strength(ji+1,jj) * tmask(ji+1,jj,1) & |
---|
| 853 | & + strength(ji,jj-1) * tmask(ji,jj-1,1) + strength(ji,jj+1) * tmask(ji,jj+1,1) & |
---|
| 854 | & ) / ( 4.0 + tmask(ji-1,jj,1) + tmask(ji+1,jj,1) + tmask(ji,jj-1,1) + tmask(ji,jj+1,1) ) |
---|
| 855 | ELSE |
---|
| 856 | zworka(ji,jj) = 0._wp |
---|
| 857 | ENDIF |
---|
| 858 | END DO |
---|
| 859 | END DO |
---|
[825] | 860 | |
---|
[6416] | 861 | DO jj = 2, jpjm1 |
---|
| 862 | DO ji = 2, jpim1 |
---|
| 863 | strength(ji,jj) = zworka(ji,jj) |
---|
| 864 | END DO |
---|
| 865 | END DO |
---|
| 866 | CALL lbc_lnk( strength, 'T', 1. ) |
---|
[4333] | 867 | |
---|
[6416] | 868 | ENDIF |
---|
| 869 | |
---|
| 870 | !-------------------- |
---|
| 871 | ! Temporal smoothing |
---|
| 872 | !-------------------- |
---|
| 873 | IF ( ksmooth == 2 ) THEN |
---|
| 874 | |
---|
[7646] | 875 | IF ( numit == nit000 + nn_fsbc - 1 ) THEN |
---|
[7753] | 876 | zstrp1(:,:) = 0._wp |
---|
| 877 | zstrp2(:,:) = 0._wp |
---|
[7646] | 878 | ENDIF |
---|
[6416] | 879 | |
---|
[7646] | 880 | DO jj = 2, jpjm1 |
---|
| 881 | DO ji = 2, jpim1 |
---|
| 882 | IF ( ( asum(ji,jj) - ato_i(ji,jj) ) > 0._wp ) THEN |
---|
[6416] | 883 | numts_rm = 1 ! number of time steps for the running mean |
---|
[7646] | 884 | IF ( zstrp1(ji,jj) > 0._wp ) numts_rm = numts_rm + 1 |
---|
| 885 | IF ( zstrp2(ji,jj) > 0._wp ) numts_rm = numts_rm + 1 |
---|
| 886 | zp = ( strength(ji,jj) + zstrp1(ji,jj) + zstrp2(ji,jj) ) / numts_rm |
---|
| 887 | zstrp2(ji,jj) = zstrp1(ji,jj) |
---|
| 888 | zstrp1(ji,jj) = strength(ji,jj) |
---|
[6416] | 889 | strength(ji,jj) = zp |
---|
| 890 | ENDIF |
---|
[4333] | 891 | END DO |
---|
| 892 | END DO |
---|
[6416] | 893 | |
---|
[7646] | 894 | CALL lbc_lnk( strength, 'T', 1. ) ! Boundary conditions |
---|
| 895 | |
---|
[6416] | 896 | ENDIF ! ksmooth |
---|
| 897 | |
---|
[7646] | 898 | CALL wrk_dealloc( jpi,jpj, zworka, zstrp1, zstrp2 ) |
---|
[2715] | 899 | ! |
---|
[6416] | 900 | END SUBROUTINE lim_itd_me_icestrength |
---|
[825] | 901 | |
---|
[2715] | 902 | SUBROUTINE lim_itd_me_init |
---|
[825] | 903 | !!------------------------------------------------------------------- |
---|
| 904 | !! *** ROUTINE lim_itd_me_init *** |
---|
| 905 | !! |
---|
| 906 | !! ** Purpose : Physical constants and parameters linked |
---|
| 907 | !! to the mechanical ice redistribution |
---|
| 908 | !! |
---|
| 909 | !! ** Method : Read the namiceitdme namelist |
---|
| 910 | !! and check the parameters values |
---|
| 911 | !! called at the first timestep (nit000) |
---|
| 912 | !! |
---|
| 913 | !! ** input : Namelist namiceitdme |
---|
| 914 | !!------------------------------------------------------------------- |
---|
[4298] | 915 | INTEGER :: ios ! Local integer output status for namelist read |
---|
[7646] | 916 | NAMELIST/namiceitdme/ rn_cs, nn_partfun, rn_gstar, rn_astar, & |
---|
| 917 | & ln_ridging, rn_hstar, rn_por_rdg, rn_fsnowrdg, ln_rafting, rn_hraft, rn_craft, rn_fsnowrft |
---|
[825] | 918 | !!------------------------------------------------------------------- |
---|
[2715] | 919 | ! |
---|
[4298] | 920 | REWIND( numnam_ice_ref ) ! Namelist namicetdme in reference namelist : Ice mechanical ice redistribution |
---|
| 921 | READ ( numnam_ice_ref, namiceitdme, IOSTAT = ios, ERR = 901) |
---|
| 922 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namiceitdme in reference namelist', lwp ) |
---|
| 923 | |
---|
| 924 | REWIND( numnam_ice_cfg ) ! Namelist namiceitdme in configuration namelist : Ice mechanical ice redistribution |
---|
| 925 | READ ( numnam_ice_cfg, namiceitdme, IOSTAT = ios, ERR = 902 ) |
---|
| 926 | 902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namiceitdme in configuration namelist', lwp ) |
---|
[4624] | 927 | IF(lwm) WRITE ( numoni, namiceitdme ) |
---|
[2715] | 928 | ! |
---|
| 929 | IF (lwp) THEN ! control print |
---|
[825] | 930 | WRITE(numout,*) |
---|
[7646] | 931 | WRITE(numout,*)'lim_itd_me_init : ice parameters for mechanical ice redistribution ' |
---|
| 932 | WRITE(numout,*)'~~~~~~~~~~~~~~~' |
---|
[5123] | 933 | WRITE(numout,*)' Fraction of shear energy contributing to ridging rn_cs = ', rn_cs |
---|
[7646] | 934 | WRITE(numout,*)' Switch for part. function (0) linear (1) exponential nn_partfun = ', nn_partfun |
---|
[5123] | 935 | WRITE(numout,*)' Fraction of total ice coverage contributing to ridging rn_gstar = ', rn_gstar |
---|
| 936 | WRITE(numout,*)' Equivalent to G* for an exponential part function rn_astar = ', rn_astar |
---|
[7646] | 937 | WRITE(numout,*)' Ridging of ice sheets or not ln_ridging = ', ln_ridging |
---|
[5123] | 938 | WRITE(numout,*)' Quantity playing a role in max ridged ice thickness rn_hstar = ', rn_hstar |
---|
[7646] | 939 | WRITE(numout,*)' Initial porosity of ridges rn_por_rdg = ', rn_por_rdg |
---|
| 940 | WRITE(numout,*)' Fraction of snow volume conserved during ridging rn_fsnowrdg = ', rn_fsnowrdg |
---|
[5123] | 941 | WRITE(numout,*)' Rafting of ice sheets or not ln_rafting = ', ln_rafting |
---|
| 942 | WRITE(numout,*)' Parmeter thickness (threshold between ridge-raft) rn_hraft = ', rn_hraft |
---|
| 943 | WRITE(numout,*)' Rafting hyperbolic tangent coefficient rn_craft = ', rn_craft |
---|
[7646] | 944 | WRITE(numout,*)' Fraction of snow volume conserved during ridging rn_fsnowrft = ', rn_fsnowrft |
---|
[825] | 945 | ENDIF |
---|
[2715] | 946 | ! |
---|
[825] | 947 | END SUBROUTINE lim_itd_me_init |
---|
| 948 | |
---|
| 949 | #else |
---|
[2715] | 950 | !!---------------------------------------------------------------------- |
---|
| 951 | !! Default option Empty module NO LIM-3 sea-ice model |
---|
| 952 | !!---------------------------------------------------------------------- |
---|
[825] | 953 | CONTAINS |
---|
| 954 | SUBROUTINE lim_itd_me ! Empty routines |
---|
| 955 | END SUBROUTINE lim_itd_me |
---|
| 956 | SUBROUTINE lim_itd_me_icestrength |
---|
| 957 | END SUBROUTINE lim_itd_me_icestrength |
---|
| 958 | SUBROUTINE lim_itd_me_init |
---|
| 959 | END SUBROUTINE lim_itd_me_init |
---|
| 960 | #endif |
---|
[2715] | 961 | !!====================================================================== |
---|
[825] | 962 | END MODULE limitd_me |
---|