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