[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 dom_ice ! LIM domain |
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| 21 | USE limvar ! LIM |
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| 22 | USE lbclnk ! lateral boundary condition - MPP exchanges |
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| 23 | USE lib_mpp ! MPP library |
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| 24 | USE wrk_nemo ! work arrays |
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| 25 | USE prtctl ! Print control |
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[5123] | 26 | |
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[5134] | 27 | USE in_out_manager ! I/O manager |
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[4161] | 28 | USE iom ! I/O manager |
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[4688] | 29 | USE lib_fortran ! glob_sum |
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[4161] | 30 | USE limdiahsb |
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[4688] | 31 | USE timing ! Timing |
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| 32 | USE limcons ! conservation tests |
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[921] | 33 | |
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[825] | 34 | IMPLICIT NONE |
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| 35 | PRIVATE |
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| 36 | |
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[2715] | 37 | PUBLIC lim_itd_me ! called by ice_stp |
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| 38 | PUBLIC lim_itd_me_icestrength |
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| 39 | PUBLIC lim_itd_me_init |
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[5123] | 40 | PUBLIC lim_itd_me_alloc ! called by sbc_lim_init |
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[825] | 41 | |
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[921] | 42 | !----------------------------------------------------------------------- |
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| 43 | ! Variables shared among ridging subroutines |
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| 44 | !----------------------------------------------------------------------- |
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[4333] | 45 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: asum ! sum of total ice and open water area |
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| 46 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: aksum ! ratio of area removed to area ridged |
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| 47 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: athorn ! participation function; fraction of ridging/ |
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| 48 | ! ! closing associated w/ category n |
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| 49 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: hrmin ! minimum ridge thickness |
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| 50 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: hrmax ! maximum ridge thickness |
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| 51 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: hraft ! thickness of rafted ice |
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| 52 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: krdg ! mean ridge thickness/thickness of ridging ice |
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| 53 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: aridge ! participating ice ridging |
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| 54 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: araft ! participating ice rafting |
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[825] | 55 | |
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[2715] | 56 | REAL(wp), PARAMETER :: krdgmin = 1.1_wp ! min ridge thickness multiplier |
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| 57 | REAL(wp), PARAMETER :: kraft = 2.0_wp ! rafting multipliyer |
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[4333] | 58 | REAL(wp), PARAMETER :: kamax = 1.0_wp ! max of ice area authorized (clem: scheme is not stable if kamax <= 0.99) |
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[825] | 59 | |
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[2715] | 60 | REAL(wp) :: Cp ! |
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[921] | 61 | ! |
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| 62 | !----------------------------------------------------------------------- |
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| 63 | ! Ridging diagnostic arrays for history files |
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| 64 | !----------------------------------------------------------------------- |
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[2715] | 65 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: dardg1dt ! rate of fractional area loss by ridging ice (1/s) |
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| 66 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: dardg2dt ! rate of fractional area gain by new ridges (1/s) |
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| 67 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: dvirdgdt ! rate of ice volume ridged (m/s) |
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| 68 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: opening ! rate of opening due to divergence/shear (1/s) |
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[3625] | 69 | ! |
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[825] | 70 | !!---------------------------------------------------------------------- |
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[2528] | 71 | !! NEMO/LIM3 3.3 , UCL - NEMO Consortium (2010) |
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[1156] | 72 | !! $Id$ |
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[2715] | 73 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[825] | 74 | !!---------------------------------------------------------------------- |
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[2715] | 75 | CONTAINS |
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[825] | 76 | |
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[2715] | 77 | INTEGER FUNCTION lim_itd_me_alloc() |
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| 78 | !!---------------------------------------------------------------------! |
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| 79 | !! *** ROUTINE lim_itd_me_alloc *** |
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| 80 | !!---------------------------------------------------------------------! |
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| 81 | ALLOCATE( & |
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| 82 | !* Variables shared among ridging subroutines |
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| 83 | & asum (jpi,jpj) , athorn(jpi,jpj,0:jpl) , & |
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| 84 | & aksum(jpi,jpj) , & |
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| 85 | ! |
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| 86 | & hrmin(jpi,jpj,jpl) , hraft(jpi,jpj,jpl) , aridge(jpi,jpj,jpl) , & |
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| 87 | & hrmax(jpi,jpj,jpl) , krdg (jpi,jpj,jpl) , araft (jpi,jpj,jpl) , & |
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| 88 | ! |
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| 89 | !* Ridging diagnostic arrays for history files |
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| 90 | & dardg1dt(jpi,jpj) , dardg2dt(jpi,jpj) , & |
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| 91 | & dvirdgdt(jpi,jpj) , opening(jpi,jpj) , STAT=lim_itd_me_alloc ) |
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| 92 | ! |
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| 93 | IF( lim_itd_me_alloc /= 0 ) CALL ctl_warn( 'lim_itd_me_alloc: failed to allocate arrays' ) |
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| 94 | ! |
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| 95 | END FUNCTION lim_itd_me_alloc |
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[1156] | 96 | |
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[825] | 97 | |
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[2715] | 98 | SUBROUTINE lim_itd_me |
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[921] | 99 | !!---------------------------------------------------------------------! |
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| 100 | !! *** ROUTINE lim_itd_me *** |
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| 101 | !! |
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[2715] | 102 | !! ** Purpose : computes the mechanical redistribution of ice thickness |
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[921] | 103 | !! |
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[2715] | 104 | !! ** Method : Steps : |
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| 105 | !! 1) Thickness categories boundaries, ice / o.w. concentrations |
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| 106 | !! Ridge preparation |
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| 107 | !! 2) Dynamical inputs (closing rate, divu_adv, opning) |
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| 108 | !! 3) Ridging iteration |
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| 109 | !! 4) Ridging diagnostics |
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| 110 | !! 5) Heat, salt and freshwater fluxes |
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| 111 | !! 6) Compute increments of tate variables and come back to old values |
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[921] | 112 | !! |
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[2715] | 113 | !! References : Flato, G. M., and W. D. Hibler III, 1995, JGR, 100, 18,611-18,626. |
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| 114 | !! Hibler, W. D. III, 1980, MWR, 108, 1943-1973, 1980. |
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| 115 | !! Rothrock, D. A., 1975: JGR, 80, 4514-4519. |
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| 116 | !! Thorndike et al., 1975, JGR, 80, 4501-4513. |
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| 117 | !! Bitz et al., JGR, 2001 |
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| 118 | !! Amundrud and Melling, JGR 2005 |
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| 119 | !! Babko et al., JGR 2002 |
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[921] | 120 | !! |
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[1572] | 121 | !! This routine is based on CICE code and authors William H. Lipscomb, |
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| 122 | !! and Elizabeth C. Hunke, LANL are gratefully acknowledged |
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[921] | 123 | !!--------------------------------------------------------------------! |
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[5123] | 124 | INTEGER :: ji, jj, jk, jl ! dummy loop index |
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| 125 | INTEGER :: niter ! local integer |
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[3625] | 126 | INTEGER :: iterate_ridging ! if true, repeat the ridging |
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[5123] | 127 | REAL(wp) :: za, zfac ! local scalar |
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[2715] | 128 | CHARACTER (len = 15) :: fieldid |
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[5202] | 129 | REAL(wp), POINTER, DIMENSION(:,:) :: closing_net ! net rate at which area is removed (1/s) |
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| 130 | ! (ridging ice area - area of new ridges) / dt |
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| 131 | REAL(wp), POINTER, DIMENSION(:,:) :: divu_adv ! divu as implied by transport scheme (1/s) |
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| 132 | REAL(wp), POINTER, DIMENSION(:,:) :: opning ! rate of opening due to divergence/shear |
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| 133 | REAL(wp), POINTER, DIMENSION(:,:) :: closing_gross ! rate at which area removed, not counting area of new ridges |
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| 134 | REAL(wp), POINTER, DIMENSION(:,:) :: msnow_mlt ! mass of snow added to ocean (kg m-2) |
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| 135 | REAL(wp), POINTER, DIMENSION(:,:) :: esnow_mlt ! energy needed to melt snow in ocean (J m-2) |
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| 136 | REAL(wp), POINTER, DIMENSION(:,:) :: vt_i_init, vt_i_final ! ice volume summed over categories |
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[4688] | 137 | ! |
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[5123] | 138 | INTEGER, PARAMETER :: nitermax = 20 |
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| 139 | ! |
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[4688] | 140 | REAL(wp) :: zvi_b, zsmv_b, zei_b, zfs_b, zfw_b, zft_b |
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[2715] | 141 | !!----------------------------------------------------------------------------- |
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[4161] | 142 | IF( nn_timing == 1 ) CALL timing_start('limitd_me') |
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[825] | 143 | |
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[5202] | 144 | CALL wrk_alloc( jpi,jpj, closing_net, divu_adv, opning, closing_gross, msnow_mlt, esnow_mlt, vt_i_init, vt_i_final ) |
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[825] | 145 | |
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| 146 | IF(ln_ctl) THEN |
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| 147 | CALL prt_ctl(tab2d_1=ato_i , clinfo1=' lim_itd_me: ato_i : ', tab2d_2=at_i , clinfo2=' at_i : ') |
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| 148 | CALL prt_ctl(tab2d_1=divu_i, clinfo1=' lim_itd_me: divu_i : ', tab2d_2=delta_i, clinfo2=' delta_i : ') |
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| 149 | ENDIF |
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| 150 | |
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[4161] | 151 | IF( ln_limdyn ) THEN ! Start ridging and rafting ! |
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| 152 | |
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[4688] | 153 | ! conservation test |
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| 154 | IF( ln_limdiahsb ) CALL lim_cons_hsm(0, 'limitd_me', zvi_b, zsmv_b, zei_b, zfw_b, zfs_b, zft_b) |
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[4161] | 155 | |
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[5202] | 156 | CALL lim_var_zapsmall |
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[5167] | 157 | CALL lim_var_glo2eqv ! equivalent variables, requested for rafting |
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[5202] | 158 | |
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[921] | 159 | !-----------------------------------------------------------------------------! |
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| 160 | ! 1) Thickness categories boundaries, ice / o.w. concentrations, init_ons |
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| 161 | !-----------------------------------------------------------------------------! |
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[5134] | 162 | Cp = 0.5 * grav * (rau0-rhoic) * rhoic * r1_rau0 ! proport const for PE |
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[3625] | 163 | ! |
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| 164 | CALL lim_itd_me_ridgeprep ! prepare ridging |
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| 165 | ! |
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[2715] | 166 | IF( con_i) CALL lim_column_sum( jpl, v_i, vt_i_init ) ! conservation check |
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[825] | 167 | |
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[2715] | 168 | DO jj = 1, jpj ! Initialize arrays. |
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[825] | 169 | DO ji = 1, jpi |
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[2715] | 170 | msnow_mlt(ji,jj) = 0._wp |
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| 171 | esnow_mlt(ji,jj) = 0._wp |
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[3625] | 172 | dardg1dt (ji,jj) = 0._wp |
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| 173 | dardg2dt (ji,jj) = 0._wp |
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| 174 | dvirdgdt (ji,jj) = 0._wp |
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| 175 | opening (ji,jj) = 0._wp |
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[825] | 176 | |
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[921] | 177 | !-----------------------------------------------------------------------------! |
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| 178 | ! 2) Dynamical inputs (closing rate, divu_adv, opning) |
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| 179 | !-----------------------------------------------------------------------------! |
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| 180 | ! |
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| 181 | ! 2.1 closing_net |
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| 182 | !----------------- |
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| 183 | ! Compute the net rate of closing due to convergence |
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| 184 | ! and shear, based on Flato and Hibler (1995). |
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| 185 | ! |
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| 186 | ! The energy dissipation rate is equal to the net closing rate |
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| 187 | ! times the ice strength. |
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| 188 | ! |
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| 189 | ! NOTE: The NET closing rate is equal to the rate that open water |
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| 190 | ! area is removed, plus the rate at which ice area is removed by |
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| 191 | ! ridging, minus the rate at which area is added in new ridges. |
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| 192 | ! The GROSS closing rate is equal to the first two terms (open |
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| 193 | ! water closing and thin ice ridging) without the third term |
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| 194 | ! (thick, newly ridged ice). |
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[825] | 195 | |
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[5123] | 196 | 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] | 197 | |
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[921] | 198 | ! 2.2 divu_adv |
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| 199 | !-------------- |
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| 200 | ! Compute divu_adv, the divergence rate given by the transport/ |
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| 201 | ! advection scheme, which may not be equal to divu as computed |
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| 202 | ! from the velocity field. |
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| 203 | ! |
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| 204 | ! If divu_adv < 0, make sure the closing rate is large enough |
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| 205 | ! to give asum = 1.0 after ridging. |
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[825] | 206 | |
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[4161] | 207 | divu_adv(ji,jj) = ( kamax - asum(ji,jj) ) * r1_rdtice ! asum found in ridgeprep |
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[825] | 208 | |
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[2715] | 209 | 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] | 210 | |
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[921] | 211 | ! 2.3 opning |
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| 212 | !------------ |
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[3625] | 213 | ! Compute the (non-negative) opening rate that will give asum = 1.0 after ridging. |
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[921] | 214 | opning(ji,jj) = closing_net(ji,jj) + divu_adv(ji,jj) |
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[825] | 215 | END DO |
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| 216 | END DO |
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| 217 | |
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[921] | 218 | !-----------------------------------------------------------------------------! |
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| 219 | ! 3) Ridging iteration |
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| 220 | !-----------------------------------------------------------------------------! |
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[2715] | 221 | niter = 1 ! iteration counter |
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[869] | 222 | iterate_ridging = 1 |
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[825] | 223 | |
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[869] | 224 | DO WHILE ( iterate_ridging > 0 .AND. niter < nitermax ) |
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[825] | 225 | |
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[921] | 226 | DO jj = 1, jpj |
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| 227 | DO ji = 1, jpi |
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[825] | 228 | |
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[921] | 229 | ! 3.2 closing_gross |
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| 230 | !-----------------------------------------------------------------------------! |
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| 231 | ! Based on the ITD of ridging and ridged ice, convert the net |
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| 232 | ! closing rate to a gross closing rate. |
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| 233 | ! NOTE: 0 < aksum <= 1 |
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| 234 | closing_gross(ji,jj) = closing_net(ji,jj) / aksum(ji,jj) |
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[825] | 235 | |
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[921] | 236 | ! correction to closing rate and opening if closing rate is excessive |
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| 237 | !--------------------------------------------------------------------- |
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| 238 | ! Reduce the closing rate if more than 100% of the open water |
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| 239 | ! would be removed. Reduce the opening rate proportionately. |
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[5167] | 240 | za = athorn(ji,jj,0) * closing_gross(ji,jj) * rdt_ice |
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| 241 | IF( za > epsi20 ) THEN |
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| 242 | zfac = MIN( 1._wp, ato_i(ji,jj) / za ) |
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| 243 | closing_gross(ji,jj) = closing_gross(ji,jj) * zfac |
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| 244 | opning (ji,jj) = opning (ji,jj) * zfac |
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[5123] | 245 | ENDIF |
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[825] | 246 | |
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[5123] | 247 | END DO |
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| 248 | END DO |
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[825] | 249 | |
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[921] | 250 | ! correction to closing rate / opening if excessive ice removal |
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| 251 | !--------------------------------------------------------------- |
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| 252 | ! Reduce the closing rate if more than 100% of any ice category |
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| 253 | ! would be removed. Reduce the opening rate proportionately. |
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| 254 | DO jl = 1, jpl |
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| 255 | DO jj = 1, jpj |
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| 256 | DO ji = 1, jpi |
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[5167] | 257 | za = athorn(ji,jj,jl) * closing_gross(ji,jj) * rdt_ice |
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| 258 | IF( za > epsi20 ) THEN |
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| 259 | zfac = MIN( 1._wp, a_i(ji,jj,jl) / za ) |
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| 260 | closing_gross(ji,jj) = closing_gross(ji,jj) * zfac |
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| 261 | opning (ji,jj) = opning (ji,jj) * zfac |
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[825] | 262 | ENDIF |
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[5123] | 263 | END DO |
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| 264 | END DO |
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| 265 | END DO |
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[825] | 266 | |
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[921] | 267 | ! 3.3 Redistribute area, volume, and energy. |
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| 268 | !-----------------------------------------------------------------------------! |
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[825] | 269 | |
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[2715] | 270 | CALL lim_itd_me_ridgeshift( opning, closing_gross, msnow_mlt, esnow_mlt ) |
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[825] | 271 | |
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[921] | 272 | ! 3.4 Compute total area of ice plus open water after ridging. |
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| 273 | !-----------------------------------------------------------------------------! |
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[5134] | 274 | ! This is in general not equal to one because of divergence during transport |
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| 275 | asum(:,:) = ato_i(:,:) |
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| 276 | DO jl = 1, jpl |
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| 277 | asum(:,:) = asum(:,:) + a_i(:,:,jl) |
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| 278 | END DO |
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[825] | 279 | |
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[921] | 280 | ! 3.5 Do we keep on iterating ??? |
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| 281 | !-----------------------------------------------------------------------------! |
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| 282 | ! Check whether asum = 1. If not (because the closing and opening |
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| 283 | ! rates were reduced above), ridge again with new rates. |
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[825] | 284 | |
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[921] | 285 | iterate_ridging = 0 |
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[825] | 286 | |
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[921] | 287 | DO jj = 1, jpj |
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| 288 | DO ji = 1, jpi |
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[5123] | 289 | IF (ABS(asum(ji,jj) - kamax ) < epsi10) THEN |
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[2715] | 290 | closing_net(ji,jj) = 0._wp |
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| 291 | opning (ji,jj) = 0._wp |
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[921] | 292 | ELSE |
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| 293 | iterate_ridging = 1 |
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[4161] | 294 | divu_adv (ji,jj) = ( kamax - asum(ji,jj) ) * r1_rdtice |
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[2715] | 295 | closing_net(ji,jj) = MAX( 0._wp, -divu_adv(ji,jj) ) |
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| 296 | opning (ji,jj) = MAX( 0._wp, divu_adv(ji,jj) ) |
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[921] | 297 | ENDIF |
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| 298 | END DO |
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[825] | 299 | END DO |
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| 300 | |
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[2715] | 301 | IF( lk_mpp ) CALL mpp_max( iterate_ridging ) |
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[869] | 302 | |
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[921] | 303 | ! Repeat if necessary. |
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| 304 | ! NOTE: If strength smoothing is turned on, the ridging must be |
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| 305 | ! iterated globally because of the boundary update in the |
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| 306 | ! smoothing. |
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[825] | 307 | |
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[921] | 308 | niter = niter + 1 |
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[825] | 309 | |
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[2715] | 310 | IF( iterate_ridging == 1 ) THEN |
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[3625] | 311 | IF( niter > nitermax ) THEN |
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[921] | 312 | WRITE(numout,*) ' ALERTE : non-converging ridging scheme ' |
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| 313 | WRITE(numout,*) ' niter, iterate_ridging ', niter, iterate_ridging |
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| 314 | ENDIF |
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| 315 | CALL lim_itd_me_ridgeprep |
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[825] | 316 | ENDIF |
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| 317 | |
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| 318 | END DO !! on the do while over iter |
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| 319 | |
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[921] | 320 | !-----------------------------------------------------------------------------! |
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| 321 | ! 4) Ridging diagnostics |
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| 322 | !-----------------------------------------------------------------------------! |
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| 323 | ! Convert ridging rate diagnostics to correct units. |
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| 324 | ! Update fresh water and heat fluxes due to snow melt. |
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[825] | 325 | DO jj = 1, jpj |
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| 326 | DO ji = 1, jpi |
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| 327 | |
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[3625] | 328 | dardg1dt(ji,jj) = dardg1dt(ji,jj) * r1_rdtice |
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| 329 | dardg2dt(ji,jj) = dardg2dt(ji,jj) * r1_rdtice |
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| 330 | dvirdgdt(ji,jj) = dvirdgdt(ji,jj) * r1_rdtice |
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| 331 | opening (ji,jj) = opening (ji,jj) * r1_rdtice |
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[825] | 332 | |
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[921] | 333 | !-----------------------------------------------------------------------------! |
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| 334 | ! 5) Heat, salt and freshwater fluxes |
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| 335 | !-----------------------------------------------------------------------------! |
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[4688] | 336 | wfx_snw(ji,jj) = wfx_snw(ji,jj) + msnow_mlt(ji,jj) * r1_rdtice ! fresh water source for ocean |
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[5123] | 337 | hfx_dyn(ji,jj) = hfx_dyn(ji,jj) + esnow_mlt(ji,jj) * r1_rdtice ! heat sink for ocean (<0, W.m-2) |
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[825] | 338 | |
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| 339 | END DO |
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| 340 | END DO |
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| 341 | |
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| 342 | ! Check if there is a ridging error |
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[5134] | 343 | IF( lwp ) THEN |
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| 344 | DO jj = 1, jpj |
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| 345 | DO ji = 1, jpi |
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| 346 | IF( ABS( asum(ji,jj) - kamax) > epsi10 ) THEN ! there is a bug |
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| 347 | WRITE(numout,*) ' ' |
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| 348 | WRITE(numout,*) ' ALERTE : Ridging error: total area = ', asum(ji,jj) |
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| 349 | WRITE(numout,*) ' limitd_me ' |
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| 350 | WRITE(numout,*) ' POINT : ', ji, jj |
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| 351 | WRITE(numout,*) ' jpl, a_i, athorn ' |
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| 352 | WRITE(numout,*) 0, ato_i(ji,jj), athorn(ji,jj,0) |
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| 353 | DO jl = 1, jpl |
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| 354 | WRITE(numout,*) jl, a_i(ji,jj,jl), athorn(ji,jj,jl) |
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| 355 | END DO |
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| 356 | ENDIF |
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| 357 | END DO |
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[5123] | 358 | END DO |
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[5134] | 359 | END IF |
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[825] | 360 | |
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| 361 | ! Conservation check |
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[834] | 362 | IF ( con_i ) THEN |
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| 363 | CALL lim_column_sum (jpl, v_i, vt_i_final) |
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| 364 | fieldid = ' v_i : limitd_me ' |
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| 365 | CALL lim_cons_check (vt_i_init, vt_i_final, 1.0e-6, fieldid) |
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| 366 | ENDIF |
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[825] | 367 | |
---|
[5123] | 368 | CALL lim_var_agg( 1 ) |
---|
[825] | 369 | |
---|
[5134] | 370 | !-----------------------------------------------------------------------------! |
---|
| 371 | ! control prints |
---|
| 372 | !-----------------------------------------------------------------------------! |
---|
| 373 | IF(ln_ctl) THEN |
---|
[5167] | 374 | CALL lim_var_glo2eqv |
---|
| 375 | |
---|
[867] | 376 | CALL prt_ctl_info(' ') |
---|
| 377 | CALL prt_ctl_info(' - Cell values : ') |
---|
| 378 | CALL prt_ctl_info(' ~~~~~~~~~~~~~ ') |
---|
[5123] | 379 | CALL prt_ctl(tab2d_1=e12t , clinfo1=' lim_itd_me : cell area :') |
---|
[863] | 380 | CALL prt_ctl(tab2d_1=at_i , clinfo1=' lim_itd_me : at_i :') |
---|
| 381 | CALL prt_ctl(tab2d_1=vt_i , clinfo1=' lim_itd_me : vt_i :') |
---|
| 382 | CALL prt_ctl(tab2d_1=vt_s , clinfo1=' lim_itd_me : vt_s :') |
---|
| 383 | DO jl = 1, jpl |
---|
[867] | 384 | CALL prt_ctl_info(' ') |
---|
[863] | 385 | CALL prt_ctl_info(' - Category : ', ivar1=jl) |
---|
| 386 | CALL prt_ctl_info(' ~~~~~~~~~~') |
---|
| 387 | CALL prt_ctl(tab2d_1=a_i (:,:,jl) , clinfo1= ' lim_itd_me : a_i : ') |
---|
| 388 | CALL prt_ctl(tab2d_1=ht_i (:,:,jl) , clinfo1= ' lim_itd_me : ht_i : ') |
---|
| 389 | CALL prt_ctl(tab2d_1=ht_s (:,:,jl) , clinfo1= ' lim_itd_me : ht_s : ') |
---|
| 390 | CALL prt_ctl(tab2d_1=v_i (:,:,jl) , clinfo1= ' lim_itd_me : v_i : ') |
---|
| 391 | CALL prt_ctl(tab2d_1=v_s (:,:,jl) , clinfo1= ' lim_itd_me : v_s : ') |
---|
| 392 | CALL prt_ctl(tab2d_1=e_s (:,:,1,jl) , clinfo1= ' lim_itd_me : e_s : ') |
---|
| 393 | CALL prt_ctl(tab2d_1=t_su (:,:,jl) , clinfo1= ' lim_itd_me : t_su : ') |
---|
| 394 | CALL prt_ctl(tab2d_1=t_s (:,:,1,jl) , clinfo1= ' lim_itd_me : t_snow : ') |
---|
| 395 | CALL prt_ctl(tab2d_1=sm_i (:,:,jl) , clinfo1= ' lim_itd_me : sm_i : ') |
---|
| 396 | CALL prt_ctl(tab2d_1=smv_i (:,:,jl) , clinfo1= ' lim_itd_me : smv_i : ') |
---|
| 397 | DO jk = 1, nlay_i |
---|
[867] | 398 | CALL prt_ctl_info(' ') |
---|
[863] | 399 | CALL prt_ctl_info(' - Layer : ', ivar1=jk) |
---|
| 400 | CALL prt_ctl_info(' ~~~~~~~') |
---|
| 401 | CALL prt_ctl(tab2d_1=t_i(:,:,jk,jl) , clinfo1= ' lim_itd_me : t_i : ') |
---|
| 402 | CALL prt_ctl(tab2d_1=e_i(:,:,jk,jl) , clinfo1= ' lim_itd_me : e_i : ') |
---|
| 403 | END DO |
---|
| 404 | END DO |
---|
| 405 | ENDIF |
---|
[825] | 406 | |
---|
[4688] | 407 | ! conservation test |
---|
| 408 | IF( ln_limdiahsb ) CALL lim_cons_hsm(1, 'limitd_me', zvi_b, zsmv_b, zei_b, zfw_b, zfs_b, zft_b) |
---|
[4161] | 409 | |
---|
| 410 | ENDIF ! ln_limdyn=.true. |
---|
[3625] | 411 | ! |
---|
[3294] | 412 | CALL wrk_dealloc( jpi, jpj, closing_net, divu_adv, opning, closing_gross, msnow_mlt, esnow_mlt, vt_i_init, vt_i_final ) |
---|
[2715] | 413 | ! |
---|
[4161] | 414 | IF( nn_timing == 1 ) CALL timing_stop('limitd_me') |
---|
[825] | 415 | END SUBROUTINE lim_itd_me |
---|
| 416 | |
---|
| 417 | |
---|
[2715] | 418 | SUBROUTINE lim_itd_me_icestrength( kstrngth ) |
---|
[921] | 419 | !!---------------------------------------------------------------------- |
---|
| 420 | !! *** ROUTINE lim_itd_me_icestrength *** |
---|
| 421 | !! |
---|
[2715] | 422 | !! ** Purpose : computes ice strength used in dynamics routines of ice thickness |
---|
[921] | 423 | !! |
---|
[2715] | 424 | !! ** Method : Compute the strength of the ice pack, defined as the energy (J m-2) |
---|
| 425 | !! dissipated per unit area removed from the ice pack under compression, |
---|
| 426 | !! and assumed proportional to the change in potential energy caused |
---|
| 427 | !! by ridging. Note that only Hibler's formulation is stable and that |
---|
| 428 | !! ice strength has to be smoothed |
---|
| 429 | !! |
---|
[921] | 430 | !! ** Inputs / Ouputs : kstrngth (what kind of ice strength we are using) |
---|
| 431 | !!---------------------------------------------------------------------- |
---|
[2715] | 432 | INTEGER, INTENT(in) :: kstrngth ! = 1 for Rothrock formulation, 0 for Hibler (1979) |
---|
[5123] | 433 | INTEGER :: ji,jj, jl ! dummy loop indices |
---|
| 434 | INTEGER :: ksmooth ! smoothing the resistance to deformation |
---|
| 435 | INTEGER :: numts_rm ! number of time steps for the P smoothing |
---|
| 436 | REAL(wp) :: zhi, zp, z1_3 ! local scalars |
---|
[3294] | 437 | REAL(wp), POINTER, DIMENSION(:,:) :: zworka ! temporary array used here |
---|
[2715] | 438 | !!---------------------------------------------------------------------- |
---|
[825] | 439 | |
---|
[3294] | 440 | CALL wrk_alloc( jpi, jpj, zworka ) |
---|
[825] | 441 | |
---|
[921] | 442 | !------------------------------------------------------------------------------! |
---|
| 443 | ! 1) Initialize |
---|
| 444 | !------------------------------------------------------------------------------! |
---|
[2715] | 445 | strength(:,:) = 0._wp |
---|
[825] | 446 | |
---|
[921] | 447 | !------------------------------------------------------------------------------! |
---|
| 448 | ! 2) Compute thickness distribution of ridging and ridged ice |
---|
| 449 | !------------------------------------------------------------------------------! |
---|
[825] | 450 | CALL lim_itd_me_ridgeprep |
---|
| 451 | |
---|
[921] | 452 | !------------------------------------------------------------------------------! |
---|
| 453 | ! 3) Rothrock(1975)'s method |
---|
| 454 | !------------------------------------------------------------------------------! |
---|
[2715] | 455 | IF( kstrngth == 1 ) THEN |
---|
| 456 | z1_3 = 1._wp / 3._wp |
---|
[825] | 457 | DO jl = 1, jpl |
---|
| 458 | DO jj= 1, jpj |
---|
| 459 | DO ji = 1, jpi |
---|
[2715] | 460 | ! |
---|
[4333] | 461 | IF( a_i(ji,jj,jl) > epsi10 .AND. athorn(ji,jj,jl) > 0._wp ) THEN |
---|
[5123] | 462 | zhi = v_i(ji,jj,jl) / a_i(ji,jj,jl) |
---|
[825] | 463 | !---------------------------- |
---|
| 464 | ! PE loss from deforming ice |
---|
| 465 | !---------------------------- |
---|
[5123] | 466 | strength(ji,jj) = strength(ji,jj) - athorn(ji,jj,jl) * zhi * zhi |
---|
[825] | 467 | |
---|
| 468 | !-------------------------- |
---|
| 469 | ! PE gain from rafting ice |
---|
| 470 | !-------------------------- |
---|
[5123] | 471 | strength(ji,jj) = strength(ji,jj) + 2._wp * araft(ji,jj,jl) * zhi * zhi |
---|
[825] | 472 | |
---|
| 473 | !---------------------------- |
---|
| 474 | ! PE gain from ridging ice |
---|
| 475 | !---------------------------- |
---|
[5134] | 476 | strength(ji,jj) = strength(ji,jj) + aridge(ji,jj,jl) / krdg(ji,jj,jl) & |
---|
[5123] | 477 | * z1_3 * ( hrmax(ji,jj,jl)**2 + hrmin(ji,jj,jl)**2 + hrmax(ji,jj,jl) * hrmin(ji,jj,jl) ) |
---|
| 478 | !!(a**3-b**3)/(a-b) = a*a+ab+b*b |
---|
| 479 | ENDIF |
---|
[2715] | 480 | ! |
---|
[5123] | 481 | END DO |
---|
| 482 | END DO |
---|
| 483 | END DO |
---|
| 484 | |
---|
| 485 | strength(:,:) = rn_pe_rdg * Cp * strength(:,:) / aksum(:,:) |
---|
| 486 | ! where Cp = (g/2)*(rhow-rhoi)*(rhoi/rhow) and rn_pe_rdg accounts for frictional dissipation |
---|
[825] | 487 | ksmooth = 1 |
---|
| 488 | |
---|
[921] | 489 | !------------------------------------------------------------------------------! |
---|
| 490 | ! 4) Hibler (1979)' method |
---|
| 491 | !------------------------------------------------------------------------------! |
---|
[825] | 492 | ELSE ! kstrngth ne 1: Hibler (1979) form |
---|
[2715] | 493 | ! |
---|
[5123] | 494 | strength(:,:) = rn_pstar * vt_i(:,:) * EXP( - rn_crhg * ( 1._wp - at_i(:,:) ) ) |
---|
[2715] | 495 | ! |
---|
[825] | 496 | ksmooth = 1 |
---|
[2715] | 497 | ! |
---|
[825] | 498 | ENDIF ! kstrngth |
---|
| 499 | |
---|
[921] | 500 | ! |
---|
| 501 | !------------------------------------------------------------------------------! |
---|
| 502 | ! 5) Impact of brine volume |
---|
| 503 | !------------------------------------------------------------------------------! |
---|
| 504 | ! CAN BE REMOVED |
---|
| 505 | ! |
---|
[5123] | 506 | IF( ln_icestr_bvf ) THEN |
---|
[825] | 507 | |
---|
| 508 | DO jj = 1, jpj |
---|
| 509 | DO ji = 1, jpi |
---|
| 510 | strength(ji,jj) = strength(ji,jj) * exp(-5.88*SQRT(MAX(bv_i(ji,jj),0.0))) |
---|
[5123] | 511 | END DO |
---|
| 512 | END DO |
---|
[825] | 513 | |
---|
| 514 | ENDIF |
---|
| 515 | |
---|
[921] | 516 | ! |
---|
| 517 | !------------------------------------------------------------------------------! |
---|
| 518 | ! 6) Smoothing ice strength |
---|
| 519 | !------------------------------------------------------------------------------! |
---|
| 520 | ! |
---|
[825] | 521 | !------------------- |
---|
| 522 | ! Spatial smoothing |
---|
| 523 | !------------------- |
---|
[2715] | 524 | IF ( ksmooth == 1 ) THEN |
---|
[825] | 525 | |
---|
| 526 | CALL lbc_lnk( strength, 'T', 1. ) |
---|
| 527 | |
---|
[5123] | 528 | DO jj = 2, jpjm1 |
---|
| 529 | DO ji = 2, jpim1 |
---|
[5167] | 530 | IF ( ( asum(ji,jj) - ato_i(ji,jj) ) > 0._wp) THEN |
---|
[5134] | 531 | zworka(ji,jj) = ( 4.0 * strength(ji,jj) & |
---|
| 532 | & + strength(ji-1,jj) * tmask(ji-1,jj,1) + strength(ji+1,jj) * tmask(ji+1,jj,1) & |
---|
| 533 | & + strength(ji,jj-1) * tmask(ji,jj-1,1) + strength(ji,jj+1) * tmask(ji,jj+1,1) & |
---|
| 534 | & ) / ( 4.0 + tmask(ji-1,jj,1) + tmask(ji+1,jj,1) + tmask(ji,jj-1,1) + tmask(ji,jj+1,1) ) |
---|
[825] | 535 | ELSE |
---|
[3625] | 536 | zworka(ji,jj) = 0._wp |
---|
[825] | 537 | ENDIF |
---|
| 538 | END DO |
---|
| 539 | END DO |
---|
| 540 | |
---|
[5123] | 541 | DO jj = 2, jpjm1 |
---|
| 542 | DO ji = 2, jpim1 |
---|
[825] | 543 | strength(ji,jj) = zworka(ji,jj) |
---|
| 544 | END DO |
---|
| 545 | END DO |
---|
[869] | 546 | CALL lbc_lnk( strength, 'T', 1. ) |
---|
[825] | 547 | |
---|
[5123] | 548 | ENDIF |
---|
[825] | 549 | |
---|
| 550 | !-------------------- |
---|
| 551 | ! Temporal smoothing |
---|
| 552 | !-------------------- |
---|
[2715] | 553 | IF ( numit == nit000 + nn_fsbc - 1 ) THEN |
---|
[825] | 554 | strp1(:,:) = 0.0 |
---|
| 555 | strp2(:,:) = 0.0 |
---|
| 556 | ENDIF |
---|
| 557 | |
---|
[2715] | 558 | IF ( ksmooth == 2 ) THEN |
---|
[921] | 559 | |
---|
| 560 | |
---|
[825] | 561 | CALL lbc_lnk( strength, 'T', 1. ) |
---|
[921] | 562 | |
---|
[825] | 563 | DO jj = 1, jpj - 1 |
---|
| 564 | DO ji = 1, jpi - 1 |
---|
[5167] | 565 | IF ( ( asum(ji,jj) - ato_i(ji,jj) ) > 0._wp) THEN |
---|
[825] | 566 | numts_rm = 1 ! number of time steps for the running mean |
---|
[5123] | 567 | IF ( strp1(ji,jj) > 0.0 ) numts_rm = numts_rm + 1 |
---|
| 568 | IF ( strp2(ji,jj) > 0.0 ) numts_rm = numts_rm + 1 |
---|
[2715] | 569 | zp = ( strength(ji,jj) + strp1(ji,jj) + strp2(ji,jj) ) / numts_rm |
---|
[825] | 570 | strp2(ji,jj) = strp1(ji,jj) |
---|
| 571 | strp1(ji,jj) = strength(ji,jj) |
---|
| 572 | strength(ji,jj) = zp |
---|
| 573 | |
---|
| 574 | ENDIF |
---|
| 575 | END DO |
---|
| 576 | END DO |
---|
| 577 | |
---|
| 578 | ENDIF ! ksmooth |
---|
[921] | 579 | |
---|
[2715] | 580 | CALL lbc_lnk( strength, 'T', 1. ) ! Boundary conditions |
---|
[825] | 581 | |
---|
[3294] | 582 | CALL wrk_dealloc( jpi, jpj, zworka ) |
---|
[2715] | 583 | ! |
---|
[921] | 584 | END SUBROUTINE lim_itd_me_icestrength |
---|
[825] | 585 | |
---|
| 586 | |
---|
[2715] | 587 | SUBROUTINE lim_itd_me_ridgeprep |
---|
[921] | 588 | !!---------------------------------------------------------------------! |
---|
| 589 | !! *** ROUTINE lim_itd_me_ridgeprep *** |
---|
| 590 | !! |
---|
[2715] | 591 | !! ** Purpose : preparation for ridging and strength calculations |
---|
[921] | 592 | !! |
---|
[2715] | 593 | !! ** Method : Compute the thickness distribution of the ice and open water |
---|
| 594 | !! participating in ridging and of the resulting ridges. |
---|
[921] | 595 | !!---------------------------------------------------------------------! |
---|
[2715] | 596 | INTEGER :: ji,jj, jl ! dummy loop indices |
---|
[5123] | 597 | REAL(wp) :: Gstari, astari, zhi, hrmean, zdummy ! local scalar |
---|
[3294] | 598 | REAL(wp), POINTER, DIMENSION(:,:) :: zworka ! temporary array used here |
---|
| 599 | REAL(wp), POINTER, DIMENSION(:,:,:) :: Gsum ! Gsum(n) = sum of areas in categories 0 to n |
---|
| 600 | !------------------------------------------------------------------------------! |
---|
[825] | 601 | |
---|
[3294] | 602 | CALL wrk_alloc( jpi,jpj, zworka ) |
---|
| 603 | CALL wrk_alloc( jpi,jpj,jpl+2, Gsum, kkstart = -1 ) |
---|
[825] | 604 | |
---|
[5123] | 605 | Gstari = 1.0/rn_gstar |
---|
| 606 | astari = 1.0/rn_astar |
---|
[825] | 607 | aksum(:,:) = 0.0 |
---|
| 608 | athorn(:,:,:) = 0.0 |
---|
| 609 | aridge(:,:,:) = 0.0 |
---|
| 610 | araft (:,:,:) = 0.0 |
---|
| 611 | hrmin(:,:,:) = 0.0 |
---|
| 612 | hrmax(:,:,:) = 0.0 |
---|
| 613 | hraft(:,:,:) = 0.0 |
---|
| 614 | krdg (:,:,:) = 1.0 |
---|
| 615 | |
---|
[921] | 616 | ! ! Zero out categories with very small areas |
---|
[5123] | 617 | CALL lim_var_zapsmall |
---|
[825] | 618 | |
---|
[921] | 619 | !------------------------------------------------------------------------------! |
---|
| 620 | ! 1) Participation function |
---|
| 621 | !------------------------------------------------------------------------------! |
---|
[825] | 622 | |
---|
| 623 | ! Compute total area of ice plus open water. |
---|
[5134] | 624 | ! This is in general not equal to one because of divergence during transport |
---|
| 625 | asum(:,:) = ato_i(:,:) |
---|
| 626 | DO jl = 1, jpl |
---|
| 627 | asum(:,:) = asum(:,:) + a_i(:,:,jl) |
---|
| 628 | END DO |
---|
[825] | 629 | |
---|
| 630 | ! Compute cumulative thickness distribution function |
---|
| 631 | ! Compute the cumulative thickness distribution function Gsum, |
---|
| 632 | ! where Gsum(n) is the fractional area in categories 0 to n. |
---|
| 633 | ! initial value (in h = 0) equals open water area |
---|
| 634 | |
---|
[2715] | 635 | Gsum(:,:,-1) = 0._wp |
---|
[5167] | 636 | Gsum(:,:,0 ) = ato_i(:,:) |
---|
[825] | 637 | |
---|
| 638 | ! for each value of h, you have to add ice concentration then |
---|
| 639 | DO jl = 1, jpl |
---|
[5167] | 640 | Gsum(:,:,jl) = Gsum(:,:,jl-1) + a_i(:,:,jl) |
---|
[825] | 641 | END DO |
---|
| 642 | |
---|
| 643 | ! Normalize the cumulative distribution to 1 |
---|
[2715] | 644 | zworka(:,:) = 1._wp / Gsum(:,:,jpl) |
---|
[825] | 645 | DO jl = 0, jpl |
---|
[2715] | 646 | Gsum(:,:,jl) = Gsum(:,:,jl) * zworka(:,:) |
---|
[825] | 647 | END DO |
---|
| 648 | |
---|
[921] | 649 | ! 1.3 Compute participation function a(h) = b(h).g(h) (athorn) |
---|
| 650 | !-------------------------------------------------------------------------------------------------- |
---|
| 651 | ! Compute the participation function athorn; this is analogous to |
---|
| 652 | ! a(h) = b(h)g(h) as defined in Thorndike et al. (1975). |
---|
| 653 | ! area lost from category n due to ridging/closing |
---|
| 654 | ! athorn(n) = total area lost due to ridging/closing |
---|
| 655 | ! assume b(h) = (2/Gstar) * (1 - G(h)/Gstar). |
---|
| 656 | ! |
---|
| 657 | ! The expressions for athorn are found by integrating b(h)g(h) between |
---|
| 658 | ! the category boundaries. |
---|
| 659 | !----------------------------------------------------------------- |
---|
[825] | 660 | |
---|
[5123] | 661 | IF( nn_partfun == 0 ) THEN !--- Linear formulation (Thorndike et al., 1975) |
---|
[4869] | 662 | DO jl = 0, jpl |
---|
[921] | 663 | DO jj = 1, jpj |
---|
| 664 | DO ji = 1, jpi |
---|
[5123] | 665 | IF( Gsum(ji,jj,jl) < rn_gstar) THEN |
---|
[5134] | 666 | athorn(ji,jj,jl) = Gstari * ( Gsum(ji,jj,jl) - Gsum(ji,jj,jl-1) ) * & |
---|
| 667 | & ( 2.0 - (Gsum(ji,jj,jl-1) + Gsum(ji,jj,jl) ) * Gstari ) |
---|
[5123] | 668 | ELSEIF (Gsum(ji,jj,jl-1) < rn_gstar) THEN |
---|
[5134] | 669 | athorn(ji,jj,jl) = Gstari * ( rn_gstar - Gsum(ji,jj,jl-1) ) * & |
---|
| 670 | & ( 2.0 - ( Gsum(ji,jj,jl-1) + rn_gstar ) * Gstari ) |
---|
[921] | 671 | ELSE |
---|
| 672 | athorn(ji,jj,jl) = 0.0 |
---|
| 673 | ENDIF |
---|
[5123] | 674 | END DO |
---|
| 675 | END DO |
---|
| 676 | END DO |
---|
[825] | 677 | |
---|
[2715] | 678 | ELSE !--- Exponential, more stable formulation (Lipscomb et al, 2007) |
---|
| 679 | ! |
---|
| 680 | zdummy = 1._wp / ( 1._wp - EXP(-astari) ) ! precompute exponential terms using Gsum as a work array |
---|
[921] | 681 | DO jl = -1, jpl |
---|
[2715] | 682 | Gsum(:,:,jl) = EXP( -Gsum(:,:,jl) * astari ) * zdummy |
---|
[5134] | 683 | END DO |
---|
[4869] | 684 | DO jl = 0, jpl |
---|
[2715] | 685 | athorn(:,:,jl) = Gsum(:,:,jl-1) - Gsum(:,:,jl) |
---|
| 686 | END DO |
---|
| 687 | ! |
---|
[5134] | 688 | ENDIF |
---|
[825] | 689 | |
---|
[5123] | 690 | IF( ln_rafting ) THEN ! Ridging and rafting ice participation functions |
---|
[2715] | 691 | ! |
---|
[825] | 692 | DO jl = 1, jpl |
---|
| 693 | DO jj = 1, jpj |
---|
| 694 | DO ji = 1, jpi |
---|
[5123] | 695 | IF ( athorn(ji,jj,jl) > 0._wp ) THEN |
---|
[2715] | 696 | !!gm TANH( -X ) = - TANH( X ) so can be computed only 1 time.... |
---|
[5123] | 697 | aridge(ji,jj,jl) = ( TANH ( rn_craft * ( ht_i(ji,jj,jl) - rn_hraft ) ) + 1.0 ) * 0.5 * athorn(ji,jj,jl) |
---|
| 698 | araft (ji,jj,jl) = ( TANH ( -rn_craft * ( ht_i(ji,jj,jl) - rn_hraft ) ) + 1.0 ) * 0.5 * athorn(ji,jj,jl) |
---|
[2715] | 699 | IF ( araft(ji,jj,jl) < epsi06 ) araft(ji,jj,jl) = 0._wp |
---|
| 700 | aridge(ji,jj,jl) = MAX( athorn(ji,jj,jl) - araft(ji,jj,jl), 0.0 ) |
---|
[5123] | 701 | ENDIF |
---|
| 702 | END DO |
---|
| 703 | END DO |
---|
| 704 | END DO |
---|
[825] | 705 | |
---|
[5123] | 706 | ELSE |
---|
[2715] | 707 | ! |
---|
[825] | 708 | DO jl = 1, jpl |
---|
[2715] | 709 | aridge(:,:,jl) = athorn(:,:,jl) |
---|
[825] | 710 | END DO |
---|
[2715] | 711 | ! |
---|
[825] | 712 | ENDIF |
---|
| 713 | |
---|
[5123] | 714 | IF( ln_rafting ) THEN |
---|
[825] | 715 | |
---|
[5134] | 716 | IF( MAXVAL(aridge + araft - athorn(:,:,1:jpl)) > epsi10 .AND. lwp ) THEN |
---|
[921] | 717 | DO jl = 1, jpl |
---|
| 718 | DO jj = 1, jpj |
---|
| 719 | DO ji = 1, jpi |
---|
[5123] | 720 | IF ( aridge(ji,jj,jl) + araft(ji,jj,jl) - athorn(ji,jj,jl) > epsi10 ) THEN |
---|
[921] | 721 | WRITE(numout,*) ' ALERTE 96 : wrong participation function ... ' |
---|
| 722 | WRITE(numout,*) ' ji, jj, jl : ', ji, jj, jl |
---|
| 723 | WRITE(numout,*) ' lat, lon : ', gphit(ji,jj), glamt(ji,jj) |
---|
| 724 | WRITE(numout,*) ' aridge : ', aridge(ji,jj,1:jpl) |
---|
| 725 | WRITE(numout,*) ' araft : ', araft(ji,jj,1:jpl) |
---|
| 726 | WRITE(numout,*) ' athorn : ', athorn(ji,jj,1:jpl) |
---|
| 727 | ENDIF |
---|
| 728 | END DO |
---|
[868] | 729 | END DO |
---|
[825] | 730 | END DO |
---|
[921] | 731 | ENDIF |
---|
[825] | 732 | |
---|
| 733 | ENDIF |
---|
| 734 | |
---|
[921] | 735 | !----------------------------------------------------------------- |
---|
| 736 | ! 2) Transfer function |
---|
| 737 | !----------------------------------------------------------------- |
---|
| 738 | ! Compute max and min ridged ice thickness for each ridging category. |
---|
| 739 | ! Assume ridged ice is uniformly distributed between hrmin and hrmax. |
---|
| 740 | ! |
---|
| 741 | ! This parameterization is a modified version of Hibler (1980). |
---|
| 742 | ! The mean ridging thickness, hrmean, is proportional to hi^(0.5) |
---|
| 743 | ! and for very thick ridging ice must be >= krdgmin*hi |
---|
| 744 | ! |
---|
| 745 | ! The minimum ridging thickness, hrmin, is equal to 2*hi |
---|
| 746 | ! (i.e., rafting) and for very thick ridging ice is |
---|
| 747 | ! constrained by hrmin <= (hrmean + hi)/2. |
---|
| 748 | ! |
---|
| 749 | ! The maximum ridging thickness, hrmax, is determined by |
---|
| 750 | ! hrmean and hrmin. |
---|
| 751 | ! |
---|
| 752 | ! These modifications have the effect of reducing the ice strength |
---|
| 753 | ! (relative to the Hibler formulation) when very thick ice is |
---|
| 754 | ! ridging. |
---|
| 755 | ! |
---|
| 756 | ! aksum = net area removed/ total area removed |
---|
| 757 | ! where total area removed = area of ice that ridges |
---|
| 758 | ! net area removed = total area removed - area of new ridges |
---|
| 759 | !----------------------------------------------------------------- |
---|
[825] | 760 | |
---|
| 761 | ! Transfer function |
---|
| 762 | DO jl = 1, jpl !all categories have a specific transfer function |
---|
| 763 | DO jj = 1, jpj |
---|
| 764 | DO ji = 1, jpi |
---|
| 765 | |
---|
[5123] | 766 | IF (a_i(ji,jj,jl) > epsi10 .AND. athorn(ji,jj,jl) > 0.0 ) THEN |
---|
| 767 | zhi = v_i(ji,jj,jl) / a_i(ji,jj,jl) |
---|
| 768 | hrmean = MAX(SQRT(rn_hstar*zhi), zhi*krdgmin) |
---|
| 769 | hrmin(ji,jj,jl) = MIN(2.0*zhi, 0.5*(hrmean + zhi)) |
---|
[825] | 770 | hrmax(ji,jj,jl) = 2.0*hrmean - hrmin(ji,jj,jl) |
---|
[5123] | 771 | hraft(ji,jj,jl) = kraft*zhi |
---|
| 772 | krdg(ji,jj,jl) = hrmean / zhi |
---|
[825] | 773 | ELSE |
---|
| 774 | hraft(ji,jj,jl) = 0.0 |
---|
| 775 | hrmin(ji,jj,jl) = 0.0 |
---|
| 776 | hrmax(ji,jj,jl) = 0.0 |
---|
| 777 | krdg (ji,jj,jl) = 1.0 |
---|
| 778 | ENDIF |
---|
| 779 | |
---|
[5134] | 780 | END DO |
---|
| 781 | END DO |
---|
| 782 | END DO |
---|
[825] | 783 | |
---|
| 784 | ! Normalization factor : aksum, ensures mass conservation |
---|
[2777] | 785 | aksum(:,:) = athorn(:,:,0) |
---|
[825] | 786 | DO jl = 1, jpl |
---|
[2715] | 787 | aksum(:,:) = aksum(:,:) + aridge(:,:,jl) * ( 1._wp - 1._wp / krdg(:,:,jl) ) & |
---|
| 788 | & + araft (:,:,jl) * ( 1._wp - 1._wp / kraft ) |
---|
[825] | 789 | END DO |
---|
[2715] | 790 | ! |
---|
[3294] | 791 | CALL wrk_dealloc( jpi,jpj, zworka ) |
---|
| 792 | CALL wrk_dealloc( jpi,jpj,jpl+2, Gsum, kkstart = -1 ) |
---|
| 793 | ! |
---|
[921] | 794 | END SUBROUTINE lim_itd_me_ridgeprep |
---|
[825] | 795 | |
---|
| 796 | |
---|
[2715] | 797 | SUBROUTINE lim_itd_me_ridgeshift( opning, closing_gross, msnow_mlt, esnow_mlt ) |
---|
| 798 | !!---------------------------------------------------------------------- |
---|
[921] | 799 | !! *** ROUTINE lim_itd_me_icestrength *** |
---|
| 800 | !! |
---|
[2715] | 801 | !! ** Purpose : shift ridging ice among thickness categories of ice thickness |
---|
[921] | 802 | !! |
---|
[2715] | 803 | !! ** Method : Remove area, volume, and energy from each ridging category |
---|
| 804 | !! and add to thicker ice categories. |
---|
| 805 | !!---------------------------------------------------------------------- |
---|
| 806 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: opning ! rate of opening due to divergence/shear |
---|
| 807 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: closing_gross ! rate at which area removed, excluding area of new ridges |
---|
| 808 | REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: msnow_mlt ! mass of snow added to ocean (kg m-2) |
---|
| 809 | REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: esnow_mlt ! energy needed to melt snow in ocean (J m-2) |
---|
| 810 | ! |
---|
| 811 | CHARACTER (len=80) :: fieldid ! field identifier |
---|
| 812 | LOGICAL, PARAMETER :: l_conservation_check = .true. ! if true, check conservation (useful for debugging) |
---|
| 813 | ! |
---|
| 814 | INTEGER :: ji, jj, jl, jl1, jl2, jk ! dummy loop indices |
---|
| 815 | INTEGER :: ij ! horizontal index, combines i and j loops |
---|
| 816 | INTEGER :: icells ! number of cells with aicen > puny |
---|
[5123] | 817 | REAL(wp) :: hL, hR, farea, ztmelts ! left and right limits of integration |
---|
[825] | 818 | |
---|
[3294] | 819 | INTEGER , POINTER, DIMENSION(:) :: indxi, indxj ! compressed indices |
---|
[825] | 820 | |
---|
[3294] | 821 | REAL(wp), POINTER, DIMENSION(:,:) :: vice_init, vice_final ! ice volume summed over categories |
---|
| 822 | REAL(wp), POINTER, DIMENSION(:,:) :: eice_init, eice_final ! ice energy summed over layers |
---|
[825] | 823 | |
---|
[3294] | 824 | REAL(wp), POINTER, DIMENSION(:,:,:) :: aicen_init, vicen_init ! ice area & volume before ridging |
---|
[4688] | 825 | REAL(wp), POINTER, DIMENSION(:,:,:) :: vsnwn_init, esnwn_init ! snow volume & energy before ridging |
---|
[3294] | 826 | REAL(wp), POINTER, DIMENSION(:,:,:) :: smv_i_init, oa_i_init ! ice salinity & age before ridging |
---|
[825] | 827 | |
---|
[3294] | 828 | REAL(wp), POINTER, DIMENSION(:,:,:,:) :: eicen_init ! ice energy before ridging |
---|
[825] | 829 | |
---|
[3294] | 830 | REAL(wp), POINTER, DIMENSION(:,:) :: afrac , fvol ! fraction of category area ridged & new ridge volume going to n2 |
---|
| 831 | REAL(wp), POINTER, DIMENSION(:,:) :: ardg1 , ardg2 ! area of ice ridged & new ridges |
---|
| 832 | REAL(wp), POINTER, DIMENSION(:,:) :: vsrdg , esrdg ! snow volume & energy of ridging ice |
---|
| 833 | REAL(wp), POINTER, DIMENSION(:,:) :: dhr , dhr2 ! hrmax - hrmin & hrmax^2 - hrmin^2 |
---|
[825] | 834 | |
---|
[3294] | 835 | REAL(wp), POINTER, DIMENSION(:,:) :: vrdg1 ! volume of ice ridged |
---|
| 836 | REAL(wp), POINTER, DIMENSION(:,:) :: vrdg2 ! volume of new ridges |
---|
| 837 | REAL(wp), POINTER, DIMENSION(:,:) :: vsw ! volume of seawater trapped into ridges |
---|
| 838 | REAL(wp), POINTER, DIMENSION(:,:) :: srdg1 ! sal*volume of ice ridged |
---|
| 839 | REAL(wp), POINTER, DIMENSION(:,:) :: srdg2 ! sal*volume of new ridges |
---|
| 840 | REAL(wp), POINTER, DIMENSION(:,:) :: smsw ! sal*volume of water trapped into ridges |
---|
[5202] | 841 | REAL(wp), POINTER, DIMENSION(:,:) :: oirdg1, oirdg2 ! ice age of ice ridged |
---|
[825] | 842 | |
---|
[3294] | 843 | REAL(wp), POINTER, DIMENSION(:,:) :: afrft ! fraction of category area rafted |
---|
| 844 | REAL(wp), POINTER, DIMENSION(:,:) :: arft1 , arft2 ! area of ice rafted and new rafted zone |
---|
| 845 | REAL(wp), POINTER, DIMENSION(:,:) :: virft , vsrft ! ice & snow volume of rafting ice |
---|
| 846 | REAL(wp), POINTER, DIMENSION(:,:) :: esrft , smrft ! snow energy & salinity of rafting ice |
---|
[5202] | 847 | REAL(wp), POINTER, DIMENSION(:,:) :: oirft1, oirft2 ! ice age of ice rafted |
---|
[825] | 848 | |
---|
[3294] | 849 | REAL(wp), POINTER, DIMENSION(:,:,:) :: eirft ! ice energy of rafting ice |
---|
| 850 | REAL(wp), POINTER, DIMENSION(:,:,:) :: erdg1 ! enth*volume of ice ridged |
---|
| 851 | REAL(wp), POINTER, DIMENSION(:,:,:) :: erdg2 ! enth*volume of new ridges |
---|
| 852 | REAL(wp), POINTER, DIMENSION(:,:,:) :: ersw ! enth of water trapped into ridges |
---|
| 853 | !!---------------------------------------------------------------------- |
---|
[825] | 854 | |
---|
[5181] | 855 | CALL wrk_alloc( (jpi+1)*(jpj+1), indxi, indxj ) |
---|
| 856 | CALL wrk_alloc( jpi, jpj, vice_init, vice_final, eice_init, eice_final ) |
---|
[5202] | 857 | CALL wrk_alloc( jpi, jpj, afrac, fvol , ardg1, ardg2, vsrdg, esrdg, dhr, dhr2 ) |
---|
| 858 | CALL wrk_alloc( jpi, jpj, vrdg1, vrdg2, vsw , srdg1, srdg2, smsw, oirdg1, oirdg2 ) |
---|
[5181] | 859 | CALL wrk_alloc( jpi, jpj, afrft, arft1, arft2, virft, vsrft, esrft, smrft, oirft1, oirft2 ) |
---|
| 860 | CALL wrk_alloc( jpi, jpj, jpl, aicen_init, vicen_init, vsnwn_init, esnwn_init, smv_i_init, oa_i_init ) |
---|
| 861 | CALL wrk_alloc( jpi, jpj, nlay_i, eirft, erdg1, erdg2, ersw ) |
---|
| 862 | CALL wrk_alloc( jpi, jpj, nlay_i, jpl, eicen_init ) |
---|
[3294] | 863 | |
---|
[825] | 864 | ! Conservation check |
---|
[2715] | 865 | eice_init(:,:) = 0._wp |
---|
[825] | 866 | |
---|
[2715] | 867 | IF( con_i ) THEN |
---|
[4333] | 868 | CALL lim_column_sum (jpl, v_i, vice_init ) |
---|
[825] | 869 | CALL lim_column_sum_energy (jpl, nlay_i, e_i, eice_init ) |
---|
[5128] | 870 | DO ji = mi0(iiceprt), mi1(iiceprt) |
---|
| 871 | DO jj = mj0(jiceprt), mj1(jiceprt) |
---|
[4333] | 872 | WRITE(numout,*) ' vice_init : ', vice_init(ji,jj) |
---|
| 873 | WRITE(numout,*) ' eice_init : ', eice_init(ji,jj) |
---|
| 874 | END DO |
---|
| 875 | END DO |
---|
[825] | 876 | ENDIF |
---|
| 877 | |
---|
[921] | 878 | !------------------------------------------------------------------------------- |
---|
| 879 | ! 1) Compute change in open water area due to closing and opening. |
---|
| 880 | !------------------------------------------------------------------------------- |
---|
[825] | 881 | DO jj = 1, jpj |
---|
| 882 | DO ji = 1, jpi |
---|
[2715] | 883 | ato_i(ji,jj) = ato_i(ji,jj) - athorn(ji,jj,0) * closing_gross(ji,jj) * rdt_ice & |
---|
| 884 | & + opning(ji,jj) * rdt_ice |
---|
[5167] | 885 | IF ( ato_i(ji,jj) < -epsi10 ) THEN ! there is a bug |
---|
| 886 | IF(lwp) WRITE(numout,*) 'Ridging error: ato_i < 0 -- ato_i : ',ato_i(ji,jj) |
---|
| 887 | ELSEIF( ato_i(ji,jj) < 0._wp ) THEN ! roundoff error |
---|
[2715] | 888 | ato_i(ji,jj) = 0._wp |
---|
[825] | 889 | ENDIF |
---|
[5134] | 890 | END DO |
---|
| 891 | END DO |
---|
[825] | 892 | |
---|
[921] | 893 | !----------------------------------------------------------------- |
---|
| 894 | ! 2) Save initial state variables |
---|
| 895 | !----------------------------------------------------------------- |
---|
[5167] | 896 | aicen_init(:,:,:) = a_i (:,:,:) |
---|
| 897 | vicen_init(:,:,:) = v_i (:,:,:) |
---|
| 898 | vsnwn_init(:,:,:) = v_s (:,:,:) |
---|
| 899 | smv_i_init(:,:,:) = smv_i(:,:,:) |
---|
| 900 | esnwn_init(:,:,:) = e_s (:,:,1,:) |
---|
| 901 | eicen_init(:,:,:,:) = e_i (:,:,:,:) |
---|
[5202] | 902 | oa_i_init (:,:,:) = oa_i (:,:,:) |
---|
[825] | 903 | |
---|
[921] | 904 | ! |
---|
| 905 | !----------------------------------------------------------------- |
---|
| 906 | ! 3) Pump everything from ice which is being ridged / rafted |
---|
| 907 | !----------------------------------------------------------------- |
---|
| 908 | ! Compute the area, volume, and energy of ice ridging in each |
---|
| 909 | ! category, along with the area of the resulting ridge. |
---|
[825] | 910 | |
---|
| 911 | DO jl1 = 1, jpl !jl1 describes the ridging category |
---|
| 912 | |
---|
[921] | 913 | !------------------------------------------------ |
---|
| 914 | ! 3.1) Identify grid cells with nonzero ridging |
---|
| 915 | !------------------------------------------------ |
---|
[825] | 916 | |
---|
| 917 | icells = 0 |
---|
| 918 | DO jj = 1, jpj |
---|
| 919 | DO ji = 1, jpi |
---|
[4333] | 920 | IF( aicen_init(ji,jj,jl1) > epsi10 .AND. athorn(ji,jj,jl1) > 0._wp & |
---|
| 921 | & .AND. closing_gross(ji,jj) > 0._wp ) THEN |
---|
[825] | 922 | icells = icells + 1 |
---|
| 923 | indxi(icells) = ji |
---|
| 924 | indxj(icells) = jj |
---|
[5134] | 925 | ENDIF |
---|
| 926 | END DO |
---|
| 927 | END DO |
---|
[825] | 928 | |
---|
| 929 | DO ij = 1, icells |
---|
| 930 | ji = indxi(ij) |
---|
| 931 | jj = indxj(ij) |
---|
| 932 | |
---|
[921] | 933 | !-------------------------------------------------------------------- |
---|
| 934 | ! 3.2) Compute area of ridging ice (ardg1) and of new ridge (ardg2) |
---|
| 935 | !-------------------------------------------------------------------- |
---|
[825] | 936 | |
---|
| 937 | ardg1(ji,jj) = aridge(ji,jj,jl1)*closing_gross(ji,jj)*rdt_ice |
---|
| 938 | arft1(ji,jj) = araft (ji,jj,jl1)*closing_gross(ji,jj)*rdt_ice |
---|
| 939 | ardg2(ji,jj) = ardg1(ji,jj) / krdg(ji,jj,jl1) |
---|
| 940 | arft2(ji,jj) = arft1(ji,jj) / kraft |
---|
| 941 | |
---|
[921] | 942 | !--------------------------------------------------------------- |
---|
| 943 | ! 3.3) Compute ridging /rafting fractions, make sure afrac <=1 |
---|
| 944 | !--------------------------------------------------------------- |
---|
[825] | 945 | |
---|
| 946 | afrac(ji,jj) = ardg1(ji,jj) / aicen_init(ji,jj,jl1) !ridging |
---|
| 947 | afrft(ji,jj) = arft1(ji,jj) / aicen_init(ji,jj,jl1) !rafting |
---|
| 948 | |
---|
[5167] | 949 | IF( afrac(ji,jj) > kamax + epsi10 ) THEN ! there is a bug |
---|
| 950 | IF(lwp) WRITE(numout,*) ' ardg > a_i -- ardg, aicen_init : ', ardg1(ji,jj), aicen_init(ji,jj,jl1) |
---|
| 951 | ELSEIF( afrac(ji,jj) > kamax ) THEN ! roundoff error |
---|
[4161] | 952 | afrac(ji,jj) = kamax |
---|
[825] | 953 | ENDIF |
---|
[5167] | 954 | |
---|
| 955 | IF( afrft(ji,jj) > kamax + epsi10 ) THEN ! there is a bug |
---|
| 956 | IF(lwp) WRITE(numout,*) ' arft > a_i -- arft, aicen_init : ', arft1(ji,jj), aicen_init(ji,jj,jl1) |
---|
| 957 | ELSEIF( afrft(ji,jj) > kamax) THEN ! roundoff error |
---|
[4161] | 958 | afrft(ji,jj) = kamax |
---|
[825] | 959 | ENDIF |
---|
| 960 | |
---|
[921] | 961 | !-------------------------------------------------------------------------- |
---|
| 962 | ! 3.4) Subtract area, volume, and energy from ridging |
---|
| 963 | ! / rafting category n1. |
---|
| 964 | !-------------------------------------------------------------------------- |
---|
[4788] | 965 | vrdg1(ji,jj) = vicen_init(ji,jj,jl1) * afrac(ji,jj) |
---|
[5123] | 966 | vrdg2(ji,jj) = vrdg1(ji,jj) * ( 1. + rn_por_rdg ) |
---|
| 967 | vsw (ji,jj) = vrdg1(ji,jj) * rn_por_rdg |
---|
[825] | 968 | |
---|
[5202] | 969 | vsrdg (ji,jj) = vsnwn_init(ji,jj,jl1) * afrac(ji,jj) |
---|
| 970 | esrdg (ji,jj) = esnwn_init(ji,jj,jl1) * afrac(ji,jj) |
---|
| 971 | srdg1 (ji,jj) = smv_i_init(ji,jj,jl1) * afrac(ji,jj) |
---|
| 972 | oirdg1(ji,jj) = oa_i_init (ji,jj,jl1) * afrac(ji,jj) |
---|
| 973 | oirdg2(ji,jj) = oa_i_init (ji,jj,jl1) * afrac(ji,jj) / krdg(ji,jj,jl1) |
---|
[825] | 974 | |
---|
| 975 | ! rafting volumes, heat contents ... |
---|
[5202] | 976 | virft (ji,jj) = vicen_init(ji,jj,jl1) * afrft(ji,jj) |
---|
| 977 | vsrft (ji,jj) = vsnwn_init(ji,jj,jl1) * afrft(ji,jj) |
---|
| 978 | esrft (ji,jj) = esnwn_init(ji,jj,jl1) * afrft(ji,jj) |
---|
| 979 | smrft (ji,jj) = smv_i_init(ji,jj,jl1) * afrft(ji,jj) |
---|
| 980 | oirft1(ji,jj) = oa_i_init (ji,jj,jl1) * afrft(ji,jj) |
---|
| 981 | oirft2(ji,jj) = oa_i_init (ji,jj,jl1) * afrft(ji,jj) / kraft |
---|
[825] | 982 | |
---|
| 983 | ! substract everything |
---|
[5202] | 984 | a_i(ji,jj,jl1) = a_i(ji,jj,jl1) - ardg1 (ji,jj) - arft1 (ji,jj) |
---|
| 985 | v_i(ji,jj,jl1) = v_i(ji,jj,jl1) - vrdg1 (ji,jj) - virft (ji,jj) |
---|
| 986 | v_s(ji,jj,jl1) = v_s(ji,jj,jl1) - vsrdg (ji,jj) - vsrft (ji,jj) |
---|
| 987 | e_s(ji,jj,1,jl1) = e_s(ji,jj,1,jl1) - esrdg (ji,jj) - esrft (ji,jj) |
---|
| 988 | smv_i(ji,jj,jl1) = smv_i(ji,jj,jl1) - srdg1 (ji,jj) - smrft (ji,jj) |
---|
[825] | 989 | oa_i(ji,jj,jl1) = oa_i(ji,jj,jl1) - oirdg1(ji,jj) - oirft1(ji,jj) |
---|
| 990 | |
---|
[921] | 991 | !----------------------------------------------------------------- |
---|
| 992 | ! 3.5) Compute properties of new ridges |
---|
| 993 | !----------------------------------------------------------------- |
---|
[5202] | 994 | !--------- |
---|
[825] | 995 | ! Salinity |
---|
[5202] | 996 | !--------- |
---|
[4688] | 997 | smsw(ji,jj) = vsw(ji,jj) * sss_m(ji,jj) ! salt content of seawater frozen in voids !! MV HC2014 |
---|
| 998 | srdg2(ji,jj) = srdg1(ji,jj) + smsw(ji,jj) ! salt content of new ridge |
---|
[1572] | 999 | |
---|
[5123] | 1000 | !srdg2(ji,jj) = MIN( rn_simax * vrdg2(ji,jj) , zsrdg2 ) ! impose a maximum salinity |
---|
[1572] | 1001 | |
---|
[4688] | 1002 | sfx_dyn(ji,jj) = sfx_dyn(ji,jj) - smsw(ji,jj) * rhoic * r1_rdtice |
---|
[5167] | 1003 | wfx_dyn(ji,jj) = wfx_dyn(ji,jj) - vsw (ji,jj) * rhoic * r1_rdtice ! increase in ice volume du to seawater frozen in voids |
---|
[1572] | 1004 | |
---|
[921] | 1005 | !------------------------------------ |
---|
| 1006 | ! 3.6 Increment ridging diagnostics |
---|
| 1007 | !------------------------------------ |
---|
[825] | 1008 | |
---|
[921] | 1009 | ! jl1 looping 1-jpl |
---|
| 1010 | ! ij looping 1-icells |
---|
[825] | 1011 | |
---|
[2715] | 1012 | dardg1dt (ji,jj) = dardg1dt(ji,jj) + ardg1(ji,jj) + arft1(ji,jj) |
---|
| 1013 | dardg2dt (ji,jj) = dardg2dt(ji,jj) + ardg2(ji,jj) + arft2(ji,jj) |
---|
[3625] | 1014 | opening (ji,jj) = opening (ji,jj) + opning(ji,jj) * rdt_ice |
---|
[825] | 1015 | |
---|
[2715] | 1016 | IF( con_i ) vice_init(ji,jj) = vice_init(ji,jj) + vrdg2(ji,jj) - vrdg1(ji,jj) |
---|
[825] | 1017 | |
---|
[921] | 1018 | !------------------------------------------ |
---|
| 1019 | ! 3.7 Put the snow somewhere in the ocean |
---|
| 1020 | !------------------------------------------ |
---|
| 1021 | ! Place part of the snow lost by ridging into the ocean. |
---|
| 1022 | ! Note that esnow_mlt < 0; the ocean must cool to melt snow. |
---|
| 1023 | ! If the ocean temp = Tf already, new ice must grow. |
---|
| 1024 | ! During the next time step, thermo_rates will determine whether |
---|
| 1025 | ! the ocean cools or new ice grows. |
---|
| 1026 | ! jl1 looping 1-jpl |
---|
| 1027 | ! ij looping 1-icells |
---|
| 1028 | |
---|
[5123] | 1029 | msnow_mlt(ji,jj) = msnow_mlt(ji,jj) + rhosn*vsrdg(ji,jj)*(1.0-rn_fsnowrdg) & ! rafting included |
---|
| 1030 | & + rhosn*vsrft(ji,jj)*(1.0-rn_fsnowrft) |
---|
[825] | 1031 | |
---|
[5123] | 1032 | ! in J/m2 (same as e_s) |
---|
| 1033 | esnow_mlt(ji,jj) = esnow_mlt(ji,jj) - esrdg(ji,jj)*(1.0-rn_fsnowrdg) & !rafting included |
---|
| 1034 | & - esrft(ji,jj)*(1.0-rn_fsnowrft) |
---|
[825] | 1035 | |
---|
[921] | 1036 | !----------------------------------------------------------------- |
---|
| 1037 | ! 3.8 Compute quantities used to apportion ice among categories |
---|
| 1038 | ! in the n2 loop below |
---|
| 1039 | !----------------------------------------------------------------- |
---|
[825] | 1040 | |
---|
[921] | 1041 | ! jl1 looping 1-jpl |
---|
| 1042 | ! ij looping 1-icells |
---|
[825] | 1043 | |
---|
[3625] | 1044 | dhr (ji,jj) = hrmax(ji,jj,jl1) - hrmin(ji,jj,jl1) |
---|
[2715] | 1045 | dhr2(ji,jj) = hrmax(ji,jj,jl1) * hrmax(ji,jj,jl1) - hrmin(ji,jj,jl1) * hrmin(ji,jj,jl1) |
---|
[825] | 1046 | |
---|
[5134] | 1047 | END DO |
---|
[825] | 1048 | |
---|
[921] | 1049 | !-------------------------------------------------------------------- |
---|
| 1050 | ! 3.9 Compute ridging ice enthalpy, remove it from ridging ice and |
---|
| 1051 | ! compute ridged ice enthalpy |
---|
| 1052 | !-------------------------------------------------------------------- |
---|
[825] | 1053 | DO jk = 1, nlay_i |
---|
| 1054 | DO ij = 1, icells |
---|
[921] | 1055 | ji = indxi(ij) |
---|
| 1056 | jj = indxj(ij) |
---|
| 1057 | ! heat content of ridged ice |
---|
[4788] | 1058 | erdg1(ji,jj,jk) = eicen_init(ji,jj,jk,jl1) * afrac(ji,jj) |
---|
[921] | 1059 | eirft(ji,jj,jk) = eicen_init(ji,jj,jk,jl1) * afrft(ji,jj) |
---|
[2715] | 1060 | e_i (ji,jj,jk,jl1) = e_i(ji,jj,jk,jl1) - erdg1(ji,jj,jk) - eirft(ji,jj,jk) |
---|
[4688] | 1061 | |
---|
| 1062 | |
---|
| 1063 | ! enthalpy of the trapped seawater (J/m2, >0) |
---|
| 1064 | ! clem: if sst>0, then ersw <0 (is that possible?) |
---|
[5134] | 1065 | ersw(ji,jj,jk) = - rhoic * vsw(ji,jj) * rcp * sst_m(ji,jj) * r1_nlay_i |
---|
[825] | 1066 | |
---|
[4688] | 1067 | ! heat flux to the ocean |
---|
| 1068 | hfx_dyn(ji,jj) = hfx_dyn(ji,jj) + ersw(ji,jj,jk) * r1_rdtice ! > 0 [W.m-2] ocean->ice flux |
---|
[825] | 1069 | |
---|
[5123] | 1070 | ! it is added to sea ice because the sign convention is the opposite of the sign convention for the ocean |
---|
[921] | 1071 | erdg2(ji,jj,jk) = erdg1(ji,jj,jk) + ersw(ji,jj,jk) |
---|
[4688] | 1072 | |
---|
[5134] | 1073 | END DO |
---|
| 1074 | END DO |
---|
[825] | 1075 | |
---|
| 1076 | |
---|
[2715] | 1077 | IF( con_i ) THEN |
---|
[825] | 1078 | DO jk = 1, nlay_i |
---|
| 1079 | DO ij = 1, icells |
---|
| 1080 | ji = indxi(ij) |
---|
| 1081 | jj = indxj(ij) |
---|
[2715] | 1082 | eice_init(ji,jj) = eice_init(ji,jj) + erdg2(ji,jj,jk) - erdg1(ji,jj,jk) |
---|
[5134] | 1083 | END DO |
---|
| 1084 | END DO |
---|
[825] | 1085 | ENDIF |
---|
| 1086 | |
---|
[921] | 1087 | !------------------------------------------------------------------------------- |
---|
| 1088 | ! 4) Add area, volume, and energy of new ridge to each category jl2 |
---|
| 1089 | !------------------------------------------------------------------------------- |
---|
| 1090 | ! jl1 looping 1-jpl |
---|
[4869] | 1091 | DO jl2 = 1, jpl |
---|
[921] | 1092 | ! over categories to which ridged ice is transferred |
---|
[825] | 1093 | DO ij = 1, icells |
---|
| 1094 | ji = indxi(ij) |
---|
| 1095 | jj = indxj(ij) |
---|
| 1096 | |
---|
| 1097 | ! Compute the fraction of ridged ice area and volume going to |
---|
| 1098 | ! thickness category jl2. |
---|
| 1099 | ! Transfer area, volume, and energy accordingly. |
---|
| 1100 | |
---|
[5134] | 1101 | IF( hrmin(ji,jj,jl1) >= hi_max(jl2) .OR. hrmax(ji,jj,jl1) <= hi_max(jl2-1) ) THEN |
---|
[3625] | 1102 | hL = 0._wp |
---|
| 1103 | hR = 0._wp |
---|
[825] | 1104 | ELSE |
---|
[3625] | 1105 | hL = MAX( hrmin(ji,jj,jl1), hi_max(jl2-1) ) |
---|
| 1106 | hR = MIN( hrmax(ji,jj,jl1), hi_max(jl2) ) |
---|
[825] | 1107 | ENDIF |
---|
| 1108 | |
---|
| 1109 | ! fraction of ridged ice area and volume going to n2 |
---|
[3625] | 1110 | farea = ( hR - hL ) / dhr(ji,jj) |
---|
| 1111 | fvol(ji,jj) = ( hR*hR - hL*hL ) / dhr2(ji,jj) |
---|
[825] | 1112 | |
---|
[3625] | 1113 | a_i (ji,jj ,jl2) = a_i (ji,jj ,jl2) + ardg2 (ji,jj) * farea |
---|
| 1114 | v_i (ji,jj ,jl2) = v_i (ji,jj ,jl2) + vrdg2 (ji,jj) * fvol(ji,jj) |
---|
[5123] | 1115 | v_s (ji,jj ,jl2) = v_s (ji,jj ,jl2) + vsrdg (ji,jj) * fvol(ji,jj) * rn_fsnowrdg |
---|
| 1116 | e_s (ji,jj,1,jl2) = e_s (ji,jj,1,jl2) + esrdg (ji,jj) * fvol(ji,jj) * rn_fsnowrdg |
---|
[3625] | 1117 | smv_i(ji,jj ,jl2) = smv_i(ji,jj ,jl2) + srdg2 (ji,jj) * fvol(ji,jj) |
---|
| 1118 | oa_i (ji,jj ,jl2) = oa_i (ji,jj ,jl2) + oirdg2(ji,jj) * farea |
---|
[825] | 1119 | |
---|
[5202] | 1120 | END DO |
---|
[825] | 1121 | |
---|
| 1122 | ! Transfer ice energy to category jl2 by ridging |
---|
| 1123 | DO jk = 1, nlay_i |
---|
| 1124 | DO ij = 1, icells |
---|
| 1125 | ji = indxi(ij) |
---|
| 1126 | jj = indxj(ij) |
---|
[5134] | 1127 | e_i(ji,jj,jk,jl2) = e_i(ji,jj,jk,jl2) + fvol(ji,jj) * erdg2(ji,jj,jk) |
---|
[2715] | 1128 | END DO |
---|
| 1129 | END DO |
---|
| 1130 | ! |
---|
[825] | 1131 | END DO ! jl2 (new ridges) |
---|
| 1132 | |
---|
[4869] | 1133 | DO jl2 = 1, jpl |
---|
[825] | 1134 | |
---|
| 1135 | DO ij = 1, icells |
---|
| 1136 | ji = indxi(ij) |
---|
| 1137 | jj = indxj(ij) |
---|
| 1138 | ! Compute the fraction of rafted ice area and volume going to |
---|
| 1139 | ! thickness category jl2, transfer area, volume, and energy accordingly. |
---|
[3625] | 1140 | ! |
---|
[5134] | 1141 | IF( hraft(ji,jj,jl1) <= hi_max(jl2) .AND. hraft(ji,jj,jl1) > hi_max(jl2-1) ) THEN |
---|
[3625] | 1142 | a_i (ji,jj ,jl2) = a_i (ji,jj ,jl2) + arft2 (ji,jj) |
---|
| 1143 | v_i (ji,jj ,jl2) = v_i (ji,jj ,jl2) + virft (ji,jj) |
---|
[5123] | 1144 | v_s (ji,jj ,jl2) = v_s (ji,jj ,jl2) + vsrft (ji,jj) * rn_fsnowrft |
---|
| 1145 | e_s (ji,jj,1,jl2) = e_s (ji,jj,1,jl2) + esrft (ji,jj) * rn_fsnowrft |
---|
[3625] | 1146 | smv_i(ji,jj ,jl2) = smv_i(ji,jj ,jl2) + smrft (ji,jj) |
---|
[5202] | 1147 | oa_i (ji,jj ,jl2) = oa_i (ji,jj ,jl2) + oirft2(ji,jj) |
---|
[5123] | 1148 | ENDIF |
---|
[3625] | 1149 | ! |
---|
[5123] | 1150 | END DO |
---|
[825] | 1151 | |
---|
| 1152 | ! Transfer rafted ice energy to category jl2 |
---|
| 1153 | DO jk = 1, nlay_i |
---|
| 1154 | DO ij = 1, icells |
---|
| 1155 | ji = indxi(ij) |
---|
| 1156 | jj = indxj(ij) |
---|
[5134] | 1157 | IF( hraft(ji,jj,jl1) <= hi_max(jl2) .AND. hraft(ji,jj,jl1) > hi_max(jl2-1) ) THEN |
---|
[2715] | 1158 | e_i(ji,jj,jk,jl2) = e_i(ji,jj,jk,jl2) + eirft(ji,jj,jk) |
---|
[825] | 1159 | ENDIF |
---|
[5123] | 1160 | END DO |
---|
| 1161 | END DO |
---|
[825] | 1162 | |
---|
[5123] | 1163 | END DO |
---|
[825] | 1164 | |
---|
| 1165 | END DO ! jl1 (deforming categories) |
---|
| 1166 | |
---|
| 1167 | ! Conservation check |
---|
| 1168 | IF ( con_i ) THEN |
---|
| 1169 | CALL lim_column_sum (jpl, v_i, vice_final) |
---|
| 1170 | fieldid = ' v_i : limitd_me ' |
---|
| 1171 | CALL lim_cons_check (vice_init, vice_final, 1.0e-6, fieldid) |
---|
| 1172 | |
---|
| 1173 | CALL lim_column_sum_energy (jpl, nlay_i, e_i, eice_final ) |
---|
| 1174 | fieldid = ' e_i : limitd_me ' |
---|
| 1175 | CALL lim_cons_check (eice_init, eice_final, 1.0e-2, fieldid) |
---|
[4333] | 1176 | |
---|
[5128] | 1177 | DO ji = mi0(iiceprt), mi1(iiceprt) |
---|
| 1178 | DO jj = mj0(jiceprt), mj1(jiceprt) |
---|
[4333] | 1179 | WRITE(numout,*) ' vice_init : ', vice_init (ji,jj) |
---|
| 1180 | WRITE(numout,*) ' vice_final : ', vice_final(ji,jj) |
---|
| 1181 | WRITE(numout,*) ' eice_init : ', eice_init (ji,jj) |
---|
| 1182 | WRITE(numout,*) ' eice_final : ', eice_final(ji,jj) |
---|
| 1183 | END DO |
---|
| 1184 | END DO |
---|
[825] | 1185 | ENDIF |
---|
[2715] | 1186 | ! |
---|
[5181] | 1187 | CALL wrk_dealloc( (jpi+1)*(jpj+1), indxi, indxj ) |
---|
| 1188 | CALL wrk_dealloc( jpi, jpj, vice_init, vice_final, eice_init, eice_final ) |
---|
[5202] | 1189 | CALL wrk_dealloc( jpi, jpj, afrac, fvol , ardg1, ardg2, vsrdg, esrdg, dhr, dhr2 ) |
---|
| 1190 | CALL wrk_dealloc( jpi, jpj, vrdg1, vrdg2, vsw , srdg1, srdg2, smsw, oirdg1, oirdg2 ) |
---|
[5181] | 1191 | CALL wrk_dealloc( jpi, jpj, afrft, arft1, arft2, virft, vsrft, esrft, smrft, oirft1, oirft2 ) |
---|
| 1192 | CALL wrk_dealloc( jpi, jpj, jpl, aicen_init, vicen_init, vsnwn_init, esnwn_init, smv_i_init, oa_i_init ) |
---|
| 1193 | CALL wrk_dealloc( jpi, jpj, nlay_i, eirft, erdg1, erdg2, ersw ) |
---|
| 1194 | CALL wrk_dealloc( jpi, jpj, nlay_i, jpl, eicen_init ) |
---|
[3294] | 1195 | ! |
---|
[825] | 1196 | END SUBROUTINE lim_itd_me_ridgeshift |
---|
| 1197 | |
---|
[2715] | 1198 | SUBROUTINE lim_itd_me_init |
---|
[825] | 1199 | !!------------------------------------------------------------------- |
---|
| 1200 | !! *** ROUTINE lim_itd_me_init *** |
---|
| 1201 | !! |
---|
| 1202 | !! ** Purpose : Physical constants and parameters linked |
---|
| 1203 | !! to the mechanical ice redistribution |
---|
| 1204 | !! |
---|
| 1205 | !! ** Method : Read the namiceitdme namelist |
---|
| 1206 | !! and check the parameters values |
---|
| 1207 | !! called at the first timestep (nit000) |
---|
| 1208 | !! |
---|
| 1209 | !! ** input : Namelist namiceitdme |
---|
| 1210 | !!------------------------------------------------------------------- |
---|
[4298] | 1211 | INTEGER :: ios ! Local integer output status for namelist read |
---|
[5123] | 1212 | NAMELIST/namiceitdme/ rn_cs, rn_fsnowrdg, rn_fsnowrft, & |
---|
| 1213 | & rn_gstar, rn_astar, rn_hstar, ln_rafting, rn_hraft, rn_craft, rn_por_rdg, & |
---|
| 1214 | & nn_partfun |
---|
[825] | 1215 | !!------------------------------------------------------------------- |
---|
[2715] | 1216 | ! |
---|
[4298] | 1217 | REWIND( numnam_ice_ref ) ! Namelist namicetdme in reference namelist : Ice mechanical ice redistribution |
---|
| 1218 | READ ( numnam_ice_ref, namiceitdme, IOSTAT = ios, ERR = 901) |
---|
| 1219 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namiceitdme in reference namelist', lwp ) |
---|
| 1220 | |
---|
| 1221 | REWIND( numnam_ice_cfg ) ! Namelist namiceitdme in configuration namelist : Ice mechanical ice redistribution |
---|
| 1222 | READ ( numnam_ice_cfg, namiceitdme, IOSTAT = ios, ERR = 902 ) |
---|
| 1223 | 902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namiceitdme in configuration namelist', lwp ) |
---|
[4624] | 1224 | IF(lwm) WRITE ( numoni, namiceitdme ) |
---|
[2715] | 1225 | ! |
---|
| 1226 | IF (lwp) THEN ! control print |
---|
[825] | 1227 | WRITE(numout,*) |
---|
| 1228 | WRITE(numout,*)' lim_itd_me_init : ice parameters for mechanical ice redistribution ' |
---|
| 1229 | WRITE(numout,*)' ~~~~~~~~~~~~~~~' |
---|
[5123] | 1230 | WRITE(numout,*)' Fraction of shear energy contributing to ridging rn_cs = ', rn_cs |
---|
| 1231 | WRITE(numout,*)' Fraction of snow volume conserved during ridging rn_fsnowrdg = ', rn_fsnowrdg |
---|
| 1232 | WRITE(numout,*)' Fraction of snow volume conserved during ridging rn_fsnowrft = ', rn_fsnowrft |
---|
| 1233 | WRITE(numout,*)' Fraction of total ice coverage contributing to ridging rn_gstar = ', rn_gstar |
---|
| 1234 | WRITE(numout,*)' Equivalent to G* for an exponential part function rn_astar = ', rn_astar |
---|
| 1235 | WRITE(numout,*)' Quantity playing a role in max ridged ice thickness rn_hstar = ', rn_hstar |
---|
| 1236 | WRITE(numout,*)' Rafting of ice sheets or not ln_rafting = ', ln_rafting |
---|
| 1237 | WRITE(numout,*)' Parmeter thickness (threshold between ridge-raft) rn_hraft = ', rn_hraft |
---|
| 1238 | WRITE(numout,*)' Rafting hyperbolic tangent coefficient rn_craft = ', rn_craft |
---|
| 1239 | WRITE(numout,*)' Initial porosity of ridges rn_por_rdg = ', rn_por_rdg |
---|
| 1240 | WRITE(numout,*)' Switch for part. function (0) linear (1) exponential nn_partfun = ', nn_partfun |
---|
[825] | 1241 | ENDIF |
---|
[2715] | 1242 | ! |
---|
[825] | 1243 | END SUBROUTINE lim_itd_me_init |
---|
| 1244 | |
---|
| 1245 | #else |
---|
[2715] | 1246 | !!---------------------------------------------------------------------- |
---|
| 1247 | !! Default option Empty module NO LIM-3 sea-ice model |
---|
| 1248 | !!---------------------------------------------------------------------- |
---|
[825] | 1249 | CONTAINS |
---|
| 1250 | SUBROUTINE lim_itd_me ! Empty routines |
---|
| 1251 | END SUBROUTINE lim_itd_me |
---|
| 1252 | SUBROUTINE lim_itd_me_icestrength |
---|
| 1253 | END SUBROUTINE lim_itd_me_icestrength |
---|
| 1254 | SUBROUTINE lim_itd_me_init |
---|
| 1255 | END SUBROUTINE lim_itd_me_init |
---|
| 1256 | #endif |
---|
[2715] | 1257 | !!====================================================================== |
---|
[825] | 1258 | END MODULE limitd_me |
---|