| 1 | MODULE icerdgrft |
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| 2 | !!====================================================================== |
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| 3 | !! *** MODULE icerdgrft *** |
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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 , ONLY : sss_m, sst_m ! surface boundary condition: ocean fields |
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| 18 | USE ice1D ! sea-ice: thermodynamics |
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| 19 | USE ice ! sea-ice: variables |
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| 20 | USE icevar ! sea-ice: operations |
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| 21 | USE icectl ! sea-ice: control prints |
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| 22 | ! |
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| 23 | USE lbclnk ! lateral boundary condition - MPP exchanges |
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| 24 | USE lib_mpp ! MPP library |
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| 25 | USE in_out_manager ! I/O manager |
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| 26 | USE iom ! I/O manager |
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| 27 | USE lib_fortran ! glob_sum |
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| 28 | USE timing ! Timing |
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| 29 | |
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| 30 | IMPLICIT NONE |
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| 31 | PRIVATE |
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| 32 | |
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| 33 | PUBLIC ice_rdgrft ! called by ice_stp |
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| 34 | PUBLIC ice_rdgrft_strength ! called by icerhg_evp |
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| 35 | PUBLIC ice_rdgrft_init ! called by ice_stp |
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| 36 | PUBLIC ice_rdgrft_alloc ! called by ice_init |
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| 37 | |
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| 38 | ! Variables shared among ridging subroutines |
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| 39 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: asum ! sum of total ice and open water area |
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| 40 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: aksum ! ratio of area removed to area ridged |
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| 41 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: athorn ! participation function; fraction of ridging/closing associated w/ category n |
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| 42 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: hrmin ! minimum ridge thickness |
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| 43 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: hrmax ! maximum ridge thickness |
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| 44 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: hraft ! thickness of rafted ice |
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| 45 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: krdg ! thickness of ridging ice / mean ridge thickness |
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| 46 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: aridge ! participating ice ridging |
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| 47 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: araft ! participating ice rafting |
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| 48 | ! |
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| 49 | REAL(wp), PARAMETER :: krdgmin = 1.1_wp ! min ridge thickness multiplier |
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| 50 | REAL(wp), PARAMETER :: kraft = 0.5_wp ! rafting multipliyer |
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| 51 | REAL(wp) :: zdrho ! |
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| 52 | ! |
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| 53 | ! ** namelist (namice_rdgrft) ** |
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| 54 | REAL(wp) :: rn_cs ! fraction of shearing energy contributing to ridging |
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| 55 | LOGICAL :: ln_partf_lin ! participation function linear (Thorndike et al. (1975)) |
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| 56 | REAL(wp) :: rn_gstar ! fractional area of young ice contributing to ridging |
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| 57 | LOGICAL :: ln_partf_exp ! participation function exponential (Lipscomb et al. (2007)) |
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| 58 | REAL(wp) :: rn_astar ! equivalent of G* for an exponential participation function |
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| 59 | LOGICAL :: ln_ridging ! ridging of ice or not |
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| 60 | REAL(wp) :: rn_hstar ! thickness that determines the maximal thickness of ridged ice |
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| 61 | REAL(wp) :: rn_porordg ! initial porosity of ridges (0.3 regular value) |
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| 62 | REAL(wp) :: rn_fsnwrdg ! fractional snow loss to the ocean during ridging |
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| 63 | REAL(wp) :: rn_fpndrdg ! fractional pond loss to the ocean during ridging |
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| 64 | LOGICAL :: ln_rafting ! rafting of ice or not |
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| 65 | REAL(wp) :: rn_hraft ! threshold thickness (m) for rafting / ridging |
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| 66 | REAL(wp) :: rn_craft ! coefficient for smoothness of the hyperbolic tangent in rafting |
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| 67 | REAL(wp) :: rn_fsnwrft ! fractional snow loss to the ocean during rafting |
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| 68 | REAL(wp) :: rn_fpndrft ! fractional pond loss to the ocean during rafting |
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| 69 | ! |
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| 70 | !!---------------------------------------------------------------------- |
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| 71 | !! NEMO/ICE 4.0 , NEMO Consortium (2017) |
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| 72 | !! $Id: icerdgrft.F90 8378 2017-07-26 13:55:59Z clem $ |
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| 73 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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| 74 | !!---------------------------------------------------------------------- |
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| 75 | CONTAINS |
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| 76 | |
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| 77 | INTEGER FUNCTION ice_rdgrft_alloc() |
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| 78 | !!---------------------------------------------------------------------! |
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| 79 | !! *** ROUTINE ice_rdgrft_alloc *** |
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| 80 | !!---------------------------------------------------------------------! |
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| 81 | ALLOCATE( asum (jpi,jpj) , athorn(jpi,jpj,0:jpl) , aksum (jpi,jpj) , & |
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| 82 | & hrmin(jpi,jpj,jpl) , hraft (jpi,jpj,jpl) , aridge(jpi,jpj,jpl) , & |
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| 83 | & hrmax(jpi,jpj,jpl) , krdg (jpi,jpj,jpl) , araft (jpi,jpj,jpl) , STAT=ice_rdgrft_alloc ) |
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| 84 | ! |
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| 85 | IF( ice_rdgrft_alloc /= 0 ) CALL ctl_warn( 'ice_rdgrft_alloc: failed to allocate arrays' ) |
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| 86 | ! |
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| 87 | END FUNCTION ice_rdgrft_alloc |
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| 88 | |
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| 89 | |
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| 90 | SUBROUTINE ice_rdgrft( kt ) |
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| 91 | !!---------------------------------------------------------------------! |
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| 92 | !! *** ROUTINE ice_rdgrft *** |
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| 93 | !! |
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| 94 | !! ** Purpose : computes the mechanical redistribution of ice thickness |
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| 95 | !! |
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| 96 | !! ** Method : Steps : |
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| 97 | !! 1) Thickness categories boundaries, ice / o.w. concentrations |
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| 98 | !! Ridge preparation |
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| 99 | !! 2) Dynamical inputs (closing rate, divu_adv, opning) |
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| 100 | !! 3) Ridging iteration |
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| 101 | !! 4) Ridging diagnostics |
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| 102 | !! 5) Heat, salt and freshwater fluxes |
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| 103 | !! 6) Compute increments of tate variables and come back to old values |
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| 104 | !! |
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| 105 | !! References : Flato, G. M., and W. D. Hibler III, 1995, JGR, 100, 18,611-18,626. |
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| 106 | !! Hibler, W. D. III, 1980, MWR, 108, 1943-1973, 1980. |
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| 107 | !! Rothrock, D. A., 1975: JGR, 80, 4514-4519. |
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| 108 | !! Thorndike et al., 1975, JGR, 80, 4501-4513. |
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| 109 | !! Bitz et al., JGR, 2001 |
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| 110 | !! Amundrud and Melling, JGR 2005 |
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| 111 | !! Babko et al., JGR 2002 |
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| 112 | !! |
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| 113 | !! This routine is based on CICE code and authors William H. Lipscomb, |
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| 114 | !! and Elizabeth C. Hunke, LANL are gratefully acknowledged |
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| 115 | !!--------------------------------------------------------------------! |
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| 116 | INTEGER, INTENT(in) :: kt ! number of iteration |
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| 117 | !! |
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| 118 | INTEGER :: ji, jj, jk, jl ! dummy loop index |
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| 119 | INTEGER :: niter ! local integer |
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| 120 | INTEGER :: iterate_ridging ! if =1, repeat the ridging |
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| 121 | REAL(wp) :: za ! local scalar |
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| 122 | REAL(wp), DIMENSION(jpi,jpj) :: closing_net ! net rate at which area is removed (1/s) |
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| 123 | ! ! (ridging ice area - area of new ridges) / dt |
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| 124 | REAL(wp), DIMENSION(jpi,jpj) :: divu_adv ! divu as implied by transport scheme (1/s) |
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| 125 | REAL(wp), DIMENSION(jpi,jpj) :: opning ! rate of opening due to divergence/shear |
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| 126 | REAL(wp), DIMENSION(jpi,jpj) :: closing_gross ! rate at which area removed, not counting area of new ridges |
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| 127 | ! |
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| 128 | INTEGER, PARAMETER :: nitermax = 20 |
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| 129 | ! |
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| 130 | REAL(wp) :: zvi_b, zsmv_b, zei_b, zfs_b, zfw_b, zft_b |
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| 131 | !!----------------------------------------------------------------------------- |
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| 132 | IF( nn_timing == 1 ) CALL timing_start('icerdgrft') |
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| 133 | |
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| 134 | IF( kt == nit000 ) THEN |
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| 135 | IF(lwp) WRITE(numout,*) |
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| 136 | IF(lwp) WRITE(numout,*)'ice_rdgrft: ice ridging and rafting' |
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| 137 | IF(lwp) WRITE(numout,*)'~~~~~~~~~~' |
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| 138 | ! |
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| 139 | zdrho = 0.5 * grav * (rau0-rhoic) * rhoic * r1_rau0 ! proport const for PE |
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| 140 | ! |
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| 141 | ENDIF |
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| 142 | ! ! conservation test |
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| 143 | IF( ln_icediachk ) CALL ice_cons_hsm(0, 'icerdgrft', zvi_b, zsmv_b, zei_b, zfw_b, zfs_b, zft_b) |
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| 144 | |
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| 145 | !-----------------------------------------------------------------------------! |
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| 146 | ! 1) Thickness categories boundaries, ice / o.w. concentrations, init_ons |
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| 147 | !-----------------------------------------------------------------------------! |
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| 148 | ! |
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| 149 | CALL ice_rdgrft_prep ! prepare ridging |
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| 150 | ! |
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| 151 | DO jj = 1, jpj ! Initialize arrays. |
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| 152 | DO ji = 1, jpi |
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| 153 | !-----------------------------------------------------------------------------! |
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| 154 | ! 2) Dynamical inputs (closing rate, divu_adv, opning) |
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| 155 | !-----------------------------------------------------------------------------! |
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| 156 | ! |
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| 157 | ! 2.1 closing_net |
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| 158 | !----------------- |
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| 159 | ! Compute the net rate of closing due to convergence |
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| 160 | ! and shear, based on Flato and Hibler (1995). |
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| 161 | ! |
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| 162 | ! The energy dissipation rate is equal to the net closing rate |
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| 163 | ! times the ice strength. |
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| 164 | ! |
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| 165 | ! NOTE: The NET closing rate is equal to the rate that open water |
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| 166 | ! area is removed, plus the rate at which ice area is removed by |
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| 167 | ! ridging, minus the rate at which area is added in new ridges. |
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| 168 | ! The GROSS closing rate is equal to the first two terms (open |
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| 169 | ! water closing and thin ice ridging) without the third term |
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| 170 | ! (thick, newly ridged ice). |
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| 171 | |
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| 172 | closing_net(ji,jj) = rn_cs * 0.5_wp * ( delta_i(ji,jj) - ABS( divu_i(ji,jj) ) ) - MIN( divu_i(ji,jj), 0._wp ) |
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| 173 | |
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| 174 | ! 2.2 divu_adv |
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| 175 | !-------------- |
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| 176 | ! Compute divu_adv, the divergence rate given by the transport/ |
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| 177 | ! advection scheme, which may not be equal to divu as computed |
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| 178 | ! from the velocity field. |
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| 179 | ! |
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| 180 | ! If divu_adv < 0, make sure the closing rate is large enough |
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| 181 | ! to give asum = 1.0 after ridging. |
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| 182 | |
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| 183 | divu_adv(ji,jj) = ( 1._wp - asum(ji,jj) ) * r1_rdtice ! asum found in ridgeprep |
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| 184 | |
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| 185 | IF( divu_adv(ji,jj) < 0._wp ) closing_net(ji,jj) = MAX( closing_net(ji,jj), -divu_adv(ji,jj) ) |
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| 186 | |
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| 187 | ! 2.3 opning |
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| 188 | !------------ |
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| 189 | ! Compute the (non-negative) opening rate that will give asum = 1.0 after ridging. |
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| 190 | opning(ji,jj) = closing_net(ji,jj) + divu_adv(ji,jj) |
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| 191 | END DO |
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| 192 | END DO |
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| 193 | |
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| 194 | !-----------------------------------------------------------------------------! |
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| 195 | ! 3) Ridging iteration |
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| 196 | !-----------------------------------------------------------------------------! |
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| 197 | niter = 1 ! iteration counter |
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| 198 | iterate_ridging = 1 |
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| 199 | |
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| 200 | DO WHILE ( iterate_ridging > 0 .AND. niter < nitermax ) |
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| 201 | |
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| 202 | ! 3.2 closing_gross |
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| 203 | !-----------------------------------------------------------------------------! |
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| 204 | ! Based on the ITD of ridging and ridged ice, convert the net |
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| 205 | ! closing rate to a gross closing rate. |
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| 206 | ! NOTE: 0 < aksum <= 1 |
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| 207 | closing_gross(:,:) = closing_net(:,:) / aksum(:,:) |
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| 208 | |
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| 209 | ! correction to closing rate and opening if closing rate is excessive |
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| 210 | !--------------------------------------------------------------------- |
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| 211 | ! Reduce the closing rate if more than 100% of the open water |
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| 212 | ! would be removed. Reduce the opening rate proportionately. |
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| 213 | DO jj = 1, jpj |
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| 214 | DO ji = 1, jpi |
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| 215 | za = ( opning(ji,jj) - athorn(ji,jj,0) * closing_gross(ji,jj) ) * rdt_ice |
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| 216 | IF ( za < 0._wp .AND. za > - ato_i(ji,jj) ) THEN ! would lead to negative ato_i |
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| 217 | opning(ji,jj) = athorn(ji,jj,0) * closing_gross(ji,jj) - ato_i(ji,jj) * r1_rdtice |
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| 218 | ELSEIF( za > 0._wp .AND. za > ( asum(ji,jj) - ato_i(ji,jj) ) ) THEN ! would lead to ato_i > asum |
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| 219 | opning(ji,jj) = athorn(ji,jj,0) * closing_gross(ji,jj) + ( asum(ji,jj) - ato_i(ji,jj) ) * r1_rdtice |
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| 220 | ENDIF |
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| 221 | END DO |
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| 222 | END DO |
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| 223 | |
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| 224 | ! correction to closing rate / opening if excessive ice removal |
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| 225 | !--------------------------------------------------------------- |
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| 226 | ! Reduce the closing rate if more than 100% of any ice category |
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| 227 | ! would be removed. Reduce the opening rate proportionately. |
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| 228 | DO jl = 1, jpl |
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| 229 | DO jj = 1, jpj |
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| 230 | DO ji = 1, jpi |
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| 231 | za = athorn(ji,jj,jl) * closing_gross(ji,jj) * rdt_ice |
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| 232 | IF( za > a_i(ji,jj,jl) ) THEN |
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| 233 | closing_gross(ji,jj) = closing_gross(ji,jj) * a_i(ji,jj,jl) / za |
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| 234 | ENDIF |
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| 235 | END DO |
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| 236 | END DO |
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| 237 | END DO |
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| 238 | |
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| 239 | ! 3.3 Redistribute area, volume, and energy. |
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| 240 | !-----------------------------------------------------------------------------! |
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| 241 | CALL ice_rdgrft_ridgeshift( opning, closing_gross ) |
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| 242 | |
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| 243 | ! 3.4 Compute total area of ice plus open water after ridging. |
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| 244 | !-----------------------------------------------------------------------------! |
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| 245 | ! This is in general not equal to one because of divergence during transport |
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| 246 | asum(:,:) = ato_i(:,:) + SUM( a_i, dim=3 ) |
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| 247 | |
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| 248 | ! 3.5 Do we keep on iterating? |
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| 249 | !-----------------------------------------------------------------------------! |
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| 250 | ! Check whether asum = 1. If not (because the closing and opening |
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| 251 | ! rates were reduced above), ridge again with new rates. |
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| 252 | iterate_ridging = 0 |
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| 253 | DO jj = 1, jpj |
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| 254 | DO ji = 1, jpi |
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| 255 | IF( ABS( asum(ji,jj) - 1._wp ) < epsi10 ) THEN |
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| 256 | closing_net(ji,jj) = 0._wp |
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| 257 | opning (ji,jj) = 0._wp |
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| 258 | ato_i (ji,jj) = MAX( 0._wp, 1._wp - SUM( a_i(ji,jj,:) ) ) |
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| 259 | ELSE |
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| 260 | iterate_ridging = 1 |
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| 261 | divu_adv (ji,jj) = ( 1._wp - asum(ji,jj) ) * r1_rdtice |
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| 262 | closing_net(ji,jj) = MAX( 0._wp, -divu_adv(ji,jj) ) |
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| 263 | opning (ji,jj) = MAX( 0._wp, divu_adv(ji,jj) ) |
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| 264 | ENDIF |
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| 265 | END DO |
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| 266 | END DO |
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| 267 | IF( lk_mpp ) CALL mpp_max( iterate_ridging ) |
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| 268 | |
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| 269 | ! Repeat if necessary. |
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| 270 | ! NOTE: If strength smoothing is turned on, the ridging must be |
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| 271 | ! iterated globally because of the boundary update in the smoothing. |
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| 272 | niter = niter + 1 |
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| 273 | ! |
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| 274 | IF( iterate_ridging == 1 ) THEN |
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| 275 | CALL ice_rdgrft_prep |
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| 276 | IF( niter > nitermax ) THEN |
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| 277 | WRITE(numout,*) ' ALERTE : non-converging ridging scheme ' |
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| 278 | WRITE(numout,*) ' niter, iterate_ridging ', niter, iterate_ridging |
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| 279 | ENDIF |
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| 280 | ENDIF |
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| 281 | ! |
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| 282 | END DO !! on the do while over iter |
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| 283 | |
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| 284 | CALL ice_var_agg( 1 ) |
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| 285 | |
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| 286 | !-----------------------------------------------------------------------------! |
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| 287 | ! control prints |
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| 288 | !-----------------------------------------------------------------------------! |
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| 289 | ! ! conservation test |
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| 290 | IF( ln_icediachk ) CALL ice_cons_hsm(1, 'icerdgrft', zvi_b, zsmv_b, zei_b, zfw_b, zfs_b, zft_b) |
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| 291 | |
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| 292 | ! ! control prints |
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| 293 | IF( ln_ctl ) CALL ice_prt3D( 'icerdgrft' ) |
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| 294 | ! |
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| 295 | IF( nn_timing == 1 ) CALL timing_stop('icerdgrft') |
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| 296 | ! |
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| 297 | END SUBROUTINE ice_rdgrft |
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| 298 | |
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| 299 | |
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| 300 | SUBROUTINE ice_rdgrft_prep |
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| 301 | !!---------------------------------------------------------------------! |
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| 302 | !! *** ROUTINE ice_rdgrft_prep *** |
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| 303 | !! |
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| 304 | !! ** Purpose : preparation for ridging and strength calculations |
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| 305 | !! |
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| 306 | !! ** Method : Compute the thickness distribution of the ice and open water |
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| 307 | !! participating in ridging and of the resulting ridges. |
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| 308 | !!---------------------------------------------------------------------! |
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| 309 | INTEGER :: ji, jj, jl ! dummy loop indices |
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| 310 | REAL(wp) :: z1_gstar, z1_astar, zhmean, zdummy ! local scalar |
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| 311 | REAL(wp), DIMENSION(jpi,jpj,-1:jpl) :: zGsum ! zGsum(n) = sum of areas in categories 0 to n |
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| 312 | !------------------------------------------------------------------------------! |
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| 313 | |
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| 314 | z1_gstar = 1._wp / rn_gstar |
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| 315 | z1_astar = 1._wp / rn_astar |
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| 316 | |
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| 317 | CALL ice_var_zapsmall ! Zero out categories with very small areas |
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| 318 | |
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| 319 | ! ! Ice thickness needed for rafting |
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| 320 | WHERE( a_i(:,:,:) >= epsi20 ) ; ht_i(:,:,:) = v_i (:,:,:) / a_i(:,:,:) |
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| 321 | ELSEWHERE ; ht_i(:,:,:) = 0._wp |
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| 322 | END WHERE |
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| 323 | |
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| 324 | !------------------------------------------------------------------------------! |
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| 325 | ! 1) Participation function |
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| 326 | !------------------------------------------------------------------------------! |
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| 327 | ! |
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| 328 | ! Compute total area of ice plus open water. |
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| 329 | ! This is in general not equal to one because of divergence during transport |
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| 330 | asum(:,:) = ato_i(:,:) + SUM( a_i, dim=3 ) |
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| 331 | ! |
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| 332 | ! Compute cumulative thickness distribution function |
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| 333 | ! Compute the cumulative thickness distribution function zGsum, |
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| 334 | ! where zGsum(n) is the fractional area in categories 0 to n. |
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| 335 | ! initial value (in h = 0) equals open water area |
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| 336 | zGsum(:,:,-1) = 0._wp |
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| 337 | zGsum(:,:,0 ) = ato_i(:,:) / asum(:,:) |
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| 338 | DO jl = 1, jpl |
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| 339 | zGsum(:,:,jl) = ( ato_i(:,:) + SUM( a_i(:,:,1:jl), dim=3 ) ) / asum(:,:) ! sum(1:jl) is ok (and not jpl) |
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| 340 | END DO |
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| 341 | |
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| 342 | ! 1.3 Compute participation function a(h) = b(h).g(h) (athorn) |
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| 343 | !-------------------------------------------------------------------------------------------------- |
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| 344 | ! Compute the participation function athorn; this is analogous to |
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| 345 | ! a(h) = b(h)g(h) as defined in Thorndike et al. (1975). |
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| 346 | ! area lost from category n due to ridging/closing |
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| 347 | ! athorn(n) = total area lost due to ridging/closing |
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| 348 | ! assume b(h) = (2/Gstar) * (1 - G(h)/Gstar). |
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| 349 | ! |
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| 350 | ! The expressions for athorn are found by integrating b(h)g(h) between |
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| 351 | ! the category boundaries. |
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| 352 | ! athorn is always >= 0 and SUM(athorn(0:jpl))=1 |
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| 353 | !----------------------------------------------------------------- |
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| 354 | ! |
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| 355 | IF( ln_partf_lin ) THEN !--- Linear formulation (Thorndike et al., 1975) |
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| 356 | DO jl = 0, jpl |
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| 357 | DO jj = 1, jpj |
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| 358 | DO ji = 1, jpi |
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| 359 | IF ( zGsum(ji,jj,jl) < rn_gstar ) THEN |
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| 360 | athorn(ji,jj,jl) = z1_gstar * ( zGsum(ji,jj,jl) - zGsum(ji,jj,jl-1) ) * & |
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| 361 | & ( 2._wp - ( zGsum(ji,jj,jl-1) + zGsum(ji,jj,jl) ) * z1_gstar ) |
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| 362 | ELSEIF( zGsum(ji,jj,jl-1) < rn_gstar ) THEN |
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| 363 | athorn(ji,jj,jl) = z1_gstar * ( rn_gstar - zGsum(ji,jj,jl-1) ) * & |
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| 364 | & ( 2._wp - ( zGsum(ji,jj,jl-1) + rn_gstar ) * z1_gstar ) |
|---|
| 365 | ELSE |
|---|
| 366 | athorn(ji,jj,jl) = 0._wp |
|---|
| 367 | ENDIF |
|---|
| 368 | END DO |
|---|
| 369 | END DO |
|---|
| 370 | END DO |
|---|
| 371 | ! |
|---|
| 372 | ELSEIF( ln_partf_exp ) THEN !--- Exponential, more stable formulation (Lipscomb et al, 2007) |
|---|
| 373 | ! |
|---|
| 374 | zdummy = 1._wp / ( 1._wp - EXP(-z1_astar) ) ! precompute exponential terms using zGsum as a work array |
|---|
| 375 | DO jl = -1, jpl |
|---|
| 376 | zGsum(:,:,jl) = EXP( -zGsum(:,:,jl) * z1_astar ) * zdummy |
|---|
| 377 | END DO |
|---|
| 378 | DO jl = 0, jpl |
|---|
| 379 | athorn(:,:,jl) = zGsum(:,:,jl-1) - zGsum(:,:,jl) |
|---|
| 380 | END DO |
|---|
| 381 | ! |
|---|
| 382 | ENDIF |
|---|
| 383 | |
|---|
| 384 | ! !--- Ridging and rafting participation concentrations |
|---|
| 385 | IF( ln_rafting .AND. ln_ridging ) THEN !- ridging & rafting |
|---|
| 386 | DO jl = 1, jpl |
|---|
| 387 | DO jj = 1, jpj |
|---|
| 388 | DO ji = 1, jpi |
|---|
| 389 | aridge(ji,jj,jl) = ( 1._wp + TANH ( rn_craft * ( ht_i(ji,jj,jl) - rn_hraft ) ) ) * 0.5_wp * athorn(ji,jj,jl) |
|---|
| 390 | araft (ji,jj,jl) = athorn(ji,jj,jl) - aridge(ji,jj,jl) |
|---|
| 391 | END DO |
|---|
| 392 | END DO |
|---|
| 393 | END DO |
|---|
| 394 | ELSEIF( ln_ridging .AND. .NOT. ln_rafting ) THEN !- ridging alone |
|---|
| 395 | aridge(:,:,:) = athorn(:,:,1:jpl) |
|---|
| 396 | araft (:,:,:) = 0._wp |
|---|
| 397 | ELSEIF( ln_rafting .AND. .NOT. ln_ridging ) THEN !- rafting alone |
|---|
| 398 | aridge(:,:,:) = 0._wp |
|---|
| 399 | araft (:,:,:) = athorn(:,:,1:jpl) |
|---|
| 400 | ELSE !- no ridging & no rafting |
|---|
| 401 | aridge(:,:,:) = 0._wp |
|---|
| 402 | araft (:,:,:) = 0._wp |
|---|
| 403 | ENDIF |
|---|
| 404 | |
|---|
| 405 | !----------------------------------------------------------------- |
|---|
| 406 | ! 2) Transfer function |
|---|
| 407 | !----------------------------------------------------------------- |
|---|
| 408 | ! Compute max and min ridged ice thickness for each ridging category. |
|---|
| 409 | ! Assume ridged ice is uniformly distributed between hrmin and hrmax. |
|---|
| 410 | ! |
|---|
| 411 | ! This parameterization is a modified version of Hibler (1980). |
|---|
| 412 | ! The mean ridging thickness, zhmean, is proportional to hi^(0.5) |
|---|
| 413 | ! and for very thick ridging ice must be >= krdgmin*hi |
|---|
| 414 | ! |
|---|
| 415 | ! The minimum ridging thickness, hrmin, is equal to 2*hi |
|---|
| 416 | ! (i.e., rafting) and for very thick ridging ice is |
|---|
| 417 | ! constrained by hrmin <= (zhmean + hi)/2. |
|---|
| 418 | ! |
|---|
| 419 | ! The maximum ridging thickness, hrmax, is determined by |
|---|
| 420 | ! zhmean and hrmin. |
|---|
| 421 | ! |
|---|
| 422 | ! These modifications have the effect of reducing the ice strength |
|---|
| 423 | ! (relative to the Hibler formulation) when very thick ice is |
|---|
| 424 | ! ridging. |
|---|
| 425 | ! |
|---|
| 426 | ! aksum = net area removed/ total area removed |
|---|
| 427 | ! where total area removed = area of ice that ridges |
|---|
| 428 | ! net area removed = total area removed - area of new ridges |
|---|
| 429 | !----------------------------------------------------------------- |
|---|
| 430 | |
|---|
| 431 | aksum(:,:) = athorn(:,:,0) |
|---|
| 432 | ! Transfer function |
|---|
| 433 | DO jl = 1, jpl !all categories have a specific transfer function |
|---|
| 434 | DO jj = 1, jpj |
|---|
| 435 | DO ji = 1, jpi |
|---|
| 436 | IF ( athorn(ji,jj,jl) > 0._wp ) THEN |
|---|
| 437 | zhmean = MAX( SQRT( rn_hstar * ht_i(ji,jj,jl) ), ht_i(ji,jj,jl) * krdgmin ) |
|---|
| 438 | hrmin(ji,jj,jl) = MIN( 2._wp * ht_i(ji,jj,jl), 0.5_wp * ( zhmean + ht_i(ji,jj,jl) ) ) |
|---|
| 439 | hrmax(ji,jj,jl) = 2._wp * zhmean - hrmin(ji,jj,jl) |
|---|
| 440 | hraft(ji,jj,jl) = ht_i(ji,jj,jl) / kraft |
|---|
| 441 | krdg (ji,jj,jl) = ht_i(ji,jj,jl) / MAX( zhmean, epsi20 ) |
|---|
| 442 | ! |
|---|
| 443 | ! Normalization factor : aksum, ensures mass conservation |
|---|
| 444 | aksum(ji,jj) = aksum(ji,jj) + aridge(ji,jj,jl) * ( 1._wp - krdg(ji,jj,jl) ) & |
|---|
| 445 | & + araft (ji,jj,jl) * ( 1._wp - kraft ) |
|---|
| 446 | ELSE |
|---|
| 447 | hrmin(ji,jj,jl) = 0._wp |
|---|
| 448 | hrmax(ji,jj,jl) = 0._wp |
|---|
| 449 | hraft(ji,jj,jl) = 0._wp |
|---|
| 450 | krdg (ji,jj,jl) = 1._wp |
|---|
| 451 | ENDIF |
|---|
| 452 | END DO |
|---|
| 453 | END DO |
|---|
| 454 | END DO |
|---|
| 455 | ! |
|---|
| 456 | END SUBROUTINE ice_rdgrft_prep |
|---|
| 457 | |
|---|
| 458 | |
|---|
| 459 | SUBROUTINE ice_rdgrft_ridgeshift( opning, closing_gross ) |
|---|
| 460 | !!---------------------------------------------------------------------- |
|---|
| 461 | !! *** ROUTINE ice_rdgrft_strength *** |
|---|
| 462 | !! |
|---|
| 463 | !! ** Purpose : shift ridging ice among thickness categories of ice thickness |
|---|
| 464 | !! |
|---|
| 465 | !! ** Method : Remove area, volume, and energy from each ridging category |
|---|
| 466 | !! and add to thicker ice categories. |
|---|
| 467 | !!---------------------------------------------------------------------- |
|---|
| 468 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: opning ! rate of opening due to divergence/shear |
|---|
| 469 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: closing_gross ! rate at which area retreats, excluding area of new ridges |
|---|
| 470 | ! |
|---|
| 471 | INTEGER :: ji, jj, jl, jl1, jl2, jk ! dummy loop indices |
|---|
| 472 | INTEGER :: ij ! horizontal index, combines i and j loops |
|---|
| 473 | INTEGER :: icells ! number of cells with a_i > puny |
|---|
| 474 | REAL(wp) :: hL, hR, farea ! left and right limits of integration and new area going to jl2 |
|---|
| 475 | |
|---|
| 476 | INTEGER , DIMENSION(jpij) :: indxi, indxj ! compressed indices |
|---|
| 477 | REAL(wp), DIMENSION(jpij) :: zswitch, fvol ! new ridge volume going to jl2 |
|---|
| 478 | |
|---|
| 479 | REAL(wp), DIMENSION(jpij) :: afrac ! fraction of category area ridged |
|---|
| 480 | REAL(wp), DIMENSION(jpij) :: ardg1 , ardg2 ! area of ice ridged & new ridges |
|---|
| 481 | REAL(wp), DIMENSION(jpij) :: vsrdg , esrdg ! snow volume & energy of ridging ice |
|---|
| 482 | ! MV MP 2016 |
|---|
| 483 | REAL(wp), DIMENSION(jpij) :: vprdg ! pond volume of ridging ice |
|---|
| 484 | REAL(wp), DIMENSION(jpij) :: aprdg1 ! pond area of ridging ice |
|---|
| 485 | REAL(wp), DIMENSION(jpij) :: aprdg2 ! pond area of ridging ice |
|---|
| 486 | ! END MV MP 2016 |
|---|
| 487 | REAL(wp), DIMENSION(jpij) :: dhr , dhr2 ! hrmax - hrmin & hrmax^2 - hrmin^2 |
|---|
| 488 | |
|---|
| 489 | REAL(wp), DIMENSION(jpij) :: vrdg1 ! volume of ice ridged |
|---|
| 490 | REAL(wp), DIMENSION(jpij) :: vrdg2 ! volume of new ridges |
|---|
| 491 | REAL(wp), DIMENSION(jpij) :: vsw ! volume of seawater trapped into ridges |
|---|
| 492 | REAL(wp), DIMENSION(jpij) :: srdg1 ! sal*volume of ice ridged |
|---|
| 493 | REAL(wp), DIMENSION(jpij) :: srdg2 ! sal*volume of new ridges |
|---|
| 494 | REAL(wp), DIMENSION(jpij) :: smsw ! sal*volume of water trapped into ridges |
|---|
| 495 | REAL(wp), DIMENSION(jpij) :: oirdg1, oirdg2 ! ice age of ice ridged |
|---|
| 496 | |
|---|
| 497 | REAL(wp), DIMENSION(jpij) :: afrft ! fraction of category area rafted |
|---|
| 498 | REAL(wp), DIMENSION(jpij) :: arft1 , arft2 ! area of ice rafted and new rafted zone |
|---|
| 499 | REAL(wp), DIMENSION(jpij) :: virft , vsrft ! ice & snow volume of rafting ice |
|---|
| 500 | ! MV MP 2016 |
|---|
| 501 | REAL(wp), DIMENSION(jpij) :: vprft ! pond volume of rafting ice |
|---|
| 502 | REAL(wp), DIMENSION(jpij) :: aprft1 ! pond area of rafted ice |
|---|
| 503 | REAL(wp), DIMENSION(jpij) :: aprft2 ! pond area of new rafted ice |
|---|
| 504 | ! END MV MP 2016 |
|---|
| 505 | REAL(wp), DIMENSION(jpij) :: esrft , smrft ! snow energy & salinity of rafting ice |
|---|
| 506 | REAL(wp), DIMENSION(jpij) :: oirft1, oirft2 ! ice age of ice rafted |
|---|
| 507 | |
|---|
| 508 | REAL(wp), DIMENSION(jpij,nlay_i) :: eirft ! ice energy of rafting ice |
|---|
| 509 | REAL(wp), DIMENSION(jpij,nlay_i) :: erdg1 ! enth*volume of ice ridged |
|---|
| 510 | REAL(wp), DIMENSION(jpij,nlay_i) :: erdg2 ! enth*volume of new ridges |
|---|
| 511 | REAL(wp), DIMENSION(jpij,nlay_i) :: ersw ! enth of water trapped into ridges |
|---|
| 512 | !!---------------------------------------------------------------------- |
|---|
| 513 | |
|---|
| 514 | !------------------------------------------------------------------------------- |
|---|
| 515 | ! 1) Compute change in open water area due to closing and opening. |
|---|
| 516 | !------------------------------------------------------------------------------- |
|---|
| 517 | DO jj = 1, jpj |
|---|
| 518 | DO ji = 1, jpi |
|---|
| 519 | ato_i(ji,jj) = MAX( 0._wp, ato_i(ji,jj) + & |
|---|
| 520 | & ( opning(ji,jj) - athorn(ji,jj,0) * closing_gross(ji,jj) ) * rdt_ice ) |
|---|
| 521 | END DO |
|---|
| 522 | END DO |
|---|
| 523 | |
|---|
| 524 | !----------------------------------------------------------------- |
|---|
| 525 | ! 3) Pump everything from ice which is being ridged / rafted |
|---|
| 526 | !----------------------------------------------------------------- |
|---|
| 527 | ! Compute the area, volume, and energy of ice ridging in each |
|---|
| 528 | ! category, along with the area of the resulting ridge. |
|---|
| 529 | |
|---|
| 530 | DO jl1 = 1, jpl !jl1 describes the ridging category |
|---|
| 531 | |
|---|
| 532 | !------------------------------------------------ |
|---|
| 533 | ! 3.1) Identify grid cells with nonzero ridging |
|---|
| 534 | !------------------------------------------------ |
|---|
| 535 | icells = 0 |
|---|
| 536 | DO jj = 1, jpj |
|---|
| 537 | DO ji = 1, jpi |
|---|
| 538 | IF( athorn(ji,jj,jl1) > 0._wp .AND. closing_gross(ji,jj) > 0._wp ) THEN |
|---|
| 539 | icells = icells + 1 |
|---|
| 540 | indxi(icells) = ji |
|---|
| 541 | indxj(icells) = jj |
|---|
| 542 | ENDIF |
|---|
| 543 | END DO |
|---|
| 544 | END DO |
|---|
| 545 | |
|---|
| 546 | DO ij = 1, icells |
|---|
| 547 | ji = indxi(ij) ; jj = indxj(ij) |
|---|
| 548 | |
|---|
| 549 | !-------------------------------------------------------------------- |
|---|
| 550 | ! 3.2) Compute area of ridging ice (ardg1) and of new ridge (ardg2) |
|---|
| 551 | !-------------------------------------------------------------------- |
|---|
| 552 | ardg1(ij) = aridge(ji,jj,jl1) * closing_gross(ji,jj) * rdt_ice |
|---|
| 553 | arft1(ij) = araft (ji,jj,jl1) * closing_gross(ji,jj) * rdt_ice |
|---|
| 554 | |
|---|
| 555 | !--------------------------------------------------------------- |
|---|
| 556 | ! 3.3) Compute ridging /rafting fractions, make sure afrac <=1 |
|---|
| 557 | !--------------------------------------------------------------- |
|---|
| 558 | afrac(ij) = ardg1(ij) / a_i(ji,jj,jl1) !ridging |
|---|
| 559 | afrft(ij) = arft1(ij) / a_i(ji,jj,jl1) !rafting |
|---|
| 560 | ardg2(ij) = ardg1(ij) * krdg(ji,jj,jl1) |
|---|
| 561 | arft2(ij) = arft1(ij) * kraft |
|---|
| 562 | |
|---|
| 563 | !-------------------------------------------------------------------------- |
|---|
| 564 | ! 3.4) Substract area, volume, and energy from ridging |
|---|
| 565 | ! / rafting category n1. |
|---|
| 566 | !-------------------------------------------------------------------------- |
|---|
| 567 | vrdg1(ij) = v_i(ji,jj,jl1) * afrac(ij) |
|---|
| 568 | vrdg2(ij) = vrdg1(ij) * ( 1. + rn_porordg ) |
|---|
| 569 | vsw (ij) = vrdg1(ij) * rn_porordg |
|---|
| 570 | |
|---|
| 571 | vsrdg (ij) = v_s (ji,jj, jl1) * afrac(ij) |
|---|
| 572 | esrdg (ij) = e_s (ji,jj,1,jl1) * afrac(ij) |
|---|
| 573 | !MV MP 2016 |
|---|
| 574 | IF ( nn_pnd_scheme > 0 ) THEN |
|---|
| 575 | aprdg1(ij) = a_ip(ji,jj, jl1) * afrac(ij) |
|---|
| 576 | aprdg2(ij) = a_ip(ji,jj, jl1) * afrac(ij) * krdg(ji,jj,jl1) |
|---|
| 577 | vprdg(ij) = v_ip(ji,jj, jl1) * afrac(ij) |
|---|
| 578 | ENDIF |
|---|
| 579 | ! END MV MP 2016 |
|---|
| 580 | srdg1 (ij) = smv_i(ji,jj, jl1) * afrac(ij) |
|---|
| 581 | oirdg1(ij) = oa_i (ji,jj, jl1) * afrac(ij) |
|---|
| 582 | oirdg2(ij) = oa_i (ji,jj, jl1) * afrac(ij) * krdg(ji,jj,jl1) |
|---|
| 583 | |
|---|
| 584 | ! rafting volumes, heat contents ... |
|---|
| 585 | virft (ij) = v_i (ji,jj, jl1) * afrft(ij) |
|---|
| 586 | vsrft (ij) = v_s (ji,jj, jl1) * afrft(ij) |
|---|
| 587 | !MV MP 2016 |
|---|
| 588 | IF ( nn_pnd_scheme > 0 ) THEN |
|---|
| 589 | aprft1(ij) = a_ip (ji,jj, jl1) * afrft(ij) |
|---|
| 590 | aprft2(ij) = a_ip (ji,jj, jl1) * afrft(ij) * kraft |
|---|
| 591 | vprft(ij) = v_ip(ji,jj,jl1) * afrft(ij) |
|---|
| 592 | ENDIF |
|---|
| 593 | ! END MV MP 2016 |
|---|
| 594 | srdg1 (ij) = smv_i(ji,jj, jl1) * afrac(ij) |
|---|
| 595 | esrft (ij) = e_s (ji,jj,1,jl1) * afrft(ij) |
|---|
| 596 | smrft (ij) = smv_i(ji,jj, jl1) * afrft(ij) |
|---|
| 597 | oirft1(ij) = oa_i (ji,jj, jl1) * afrft(ij) |
|---|
| 598 | oirft2(ij) = oa_i (ji,jj, jl1) * afrft(ij) * kraft |
|---|
| 599 | |
|---|
| 600 | !----------------------------------------------------------------- |
|---|
| 601 | ! 3.5) Compute properties of new ridges |
|---|
| 602 | !----------------------------------------------------------------- |
|---|
| 603 | smsw(ij) = vsw(ij) * sss_m(ji,jj) ! salt content of seawater frozen in voids |
|---|
| 604 | srdg2(ij) = srdg1(ij) + smsw(ij) ! salt content of new ridge |
|---|
| 605 | |
|---|
| 606 | sfx_dyn(ji,jj) = sfx_dyn(ji,jj) - smsw(ij) * rhoic * r1_rdtice |
|---|
| 607 | wfx_dyn(ji,jj) = wfx_dyn(ji,jj) - vsw (ij) * rhoic * r1_rdtice ! increase in ice volume due to seawater frozen in voids |
|---|
| 608 | |
|---|
| 609 | ! virtual salt flux to keep salinity constant |
|---|
| 610 | IF( nn_icesal == 1 .OR. nn_icesal == 3 ) THEN |
|---|
| 611 | srdg2(ij) = srdg2(ij) - vsw(ij) * ( sss_m(ji,jj) - sm_i(ji,jj,jl1) ) ! ridge salinity = sm_i |
|---|
| 612 | sfx_bri(ji,jj) = sfx_bri(ji,jj) + sss_m(ji,jj) * vsw(ij) * rhoic * r1_rdtice & ! put back sss_m into the ocean |
|---|
| 613 | & - sm_i(ji,jj,jl1) * vsw(ij) * rhoic * r1_rdtice ! and get sm_i from the ocean |
|---|
| 614 | ENDIF |
|---|
| 615 | |
|---|
| 616 | !------------------------------------------ |
|---|
| 617 | ! 3.7 Put the snow somewhere in the ocean |
|---|
| 618 | !------------------------------------------ |
|---|
| 619 | ! Place part of the snow lost by ridging into the ocean. |
|---|
| 620 | ! Note that esrdg > 0; the ocean must cool to melt snow. |
|---|
| 621 | ! If the ocean temp = Tf already, new ice must grow. |
|---|
| 622 | ! During the next time step, thermo_rates will determine whether |
|---|
| 623 | ! the ocean cools or new ice grows. |
|---|
| 624 | wfx_snw_dyn(ji,jj) = wfx_snw_dyn(ji,jj) + ( rhosn * vsrdg(ij) * ( 1._wp - rn_fsnwrdg ) & |
|---|
| 625 | & + rhosn * vsrft(ij) * ( 1._wp - rn_fsnwrft ) ) * r1_rdtice ! fresh water source for ocean |
|---|
| 626 | |
|---|
| 627 | hfx_dyn(ji,jj) = hfx_dyn(ji,jj) + ( - esrdg(ij) * ( 1._wp - rn_fsnwrdg ) & |
|---|
| 628 | & - esrft(ij) * ( 1._wp - rn_fsnwrft ) ) * r1_rdtice ! heat sink for ocean (<0, W.m-2) |
|---|
| 629 | |
|---|
| 630 | ! MV MP 2016 |
|---|
| 631 | !------------------------------------------ |
|---|
| 632 | ! 3.X Put the melt pond water in the ocean |
|---|
| 633 | !------------------------------------------ |
|---|
| 634 | ! Place part of the melt pond volume into the ocean. |
|---|
| 635 | IF ( ( nn_pnd_scheme > 0 ) .AND. ln_pnd_fw ) THEN |
|---|
| 636 | wfx_pnd(ji,jj) = wfx_pnd(ji,jj) + ( rhofw * vprdg(ij) * ( 1._wp - rn_fpndrdg ) & |
|---|
| 637 | & + rhofw * vprft(ij) * ( 1._wp - rn_fpndrft ) ) * r1_rdtice ! fresh water source for ocean |
|---|
| 638 | ENDIF |
|---|
| 639 | ! END MV MP 2016 |
|---|
| 640 | |
|---|
| 641 | !----------------------------------------------------------------- |
|---|
| 642 | ! 3.8 Compute quantities used to apportion ice among categories |
|---|
| 643 | ! in the n2 loop below |
|---|
| 644 | !----------------------------------------------------------------- |
|---|
| 645 | dhr (ij) = 1._wp / ( hrmax(ji,jj,jl1) - hrmin(ji,jj,jl1) ) |
|---|
| 646 | dhr2(ij) = 1._wp / ( hrmax(ji,jj,jl1) * hrmax(ji,jj,jl1) - hrmin(ji,jj,jl1) * hrmin(ji,jj,jl1) ) |
|---|
| 647 | |
|---|
| 648 | |
|---|
| 649 | ! update jl1 (removing ridged/rafted area) |
|---|
| 650 | a_i (ji,jj, jl1) = a_i (ji,jj, jl1) - ardg1 (ij) - arft1 (ij) |
|---|
| 651 | v_i (ji,jj, jl1) = v_i (ji,jj, jl1) - vrdg1 (ij) - virft (ij) |
|---|
| 652 | v_s (ji,jj, jl1) = v_s (ji,jj, jl1) - vsrdg (ij) - vsrft (ij) |
|---|
| 653 | e_s (ji,jj,1,jl1) = e_s (ji,jj,1,jl1) - esrdg (ij) - esrft (ij) |
|---|
| 654 | smv_i(ji,jj, jl1) = smv_i(ji,jj, jl1) - srdg1 (ij) - smrft (ij) |
|---|
| 655 | oa_i (ji,jj, jl1) = oa_i (ji,jj, jl1) - oirdg1(ij) - oirft1(ij) |
|---|
| 656 | |
|---|
| 657 | ! MV MP 2016 |
|---|
| 658 | IF ( nn_pnd_scheme > 0 ) THEN |
|---|
| 659 | v_ip (ji,jj,jl1) = v_ip (ji,jj,jl1) - vprdg (ij) - vprft (ij) |
|---|
| 660 | a_ip (ji,jj,jl1) = a_ip (ji,jj,jl1) - aprdg1(ij) - aprft1(ij) |
|---|
| 661 | ENDIF |
|---|
| 662 | ! END MV MP 2016 |
|---|
| 663 | |
|---|
| 664 | END DO |
|---|
| 665 | |
|---|
| 666 | !-------------------------------------------------------------------- |
|---|
| 667 | ! 3.9 Compute ridging ice enthalpy, remove it from ridging ice and |
|---|
| 668 | ! compute ridged ice enthalpy |
|---|
| 669 | !-------------------------------------------------------------------- |
|---|
| 670 | DO jk = 1, nlay_i |
|---|
| 671 | DO ij = 1, icells |
|---|
| 672 | ji = indxi(ij) ; jj = indxj(ij) |
|---|
| 673 | ! heat content of ridged ice |
|---|
| 674 | erdg1(ij,jk) = e_i(ji,jj,jk,jl1) * afrac(ij) |
|---|
| 675 | eirft(ij,jk) = e_i(ji,jj,jk,jl1) * afrft(ij) |
|---|
| 676 | |
|---|
| 677 | ! enthalpy of the trapped seawater (J/m2, >0) |
|---|
| 678 | ! clem: if sst>0, then ersw <0 (is that possible?) |
|---|
| 679 | ersw(ij,jk) = - rhoic * vsw(ij) * rcp * sst_m(ji,jj) * r1_nlay_i |
|---|
| 680 | |
|---|
| 681 | ! heat flux to the ocean |
|---|
| 682 | hfx_dyn(ji,jj) = hfx_dyn(ji,jj) + ersw(ij,jk) * r1_rdtice ! > 0 [W.m-2] ocean->ice flux |
|---|
| 683 | |
|---|
| 684 | ! it is added to sea ice because the sign convention is the opposite of the sign convention for the ocean |
|---|
| 685 | erdg2(ij,jk) = erdg1(ij,jk) + ersw(ij,jk) |
|---|
| 686 | |
|---|
| 687 | ! update jl1 |
|---|
| 688 | e_i(ji,jj,jk,jl1) = e_i(ji,jj,jk,jl1) - erdg1(ij,jk) - eirft(ij,jk) |
|---|
| 689 | |
|---|
| 690 | END DO |
|---|
| 691 | END DO |
|---|
| 692 | |
|---|
| 693 | !------------------------------------------------------------------------------- |
|---|
| 694 | ! 4) Add area, volume, and energy of new ridge to each category jl2 |
|---|
| 695 | !------------------------------------------------------------------------------- |
|---|
| 696 | DO jl2 = 1, jpl |
|---|
| 697 | ! over categories to which ridged/rafted ice is transferred |
|---|
| 698 | DO ij = 1, icells |
|---|
| 699 | ji = indxi(ij) ; jj = indxj(ij) |
|---|
| 700 | |
|---|
| 701 | ! Compute the fraction of ridged ice area and volume going to thickness category jl2. |
|---|
| 702 | IF( hrmin(ji,jj,jl1) <= hi_max(jl2) .AND. hrmax(ji,jj,jl1) > hi_max(jl2-1) ) THEN |
|---|
| 703 | hL = MAX( hrmin(ji,jj,jl1), hi_max(jl2-1) ) |
|---|
| 704 | hR = MIN( hrmax(ji,jj,jl1), hi_max(jl2) ) |
|---|
| 705 | farea = ( hR - hL ) * dhr(ij) |
|---|
| 706 | fvol(ij) = ( hR * hR - hL * hL ) * dhr2(ij) |
|---|
| 707 | ELSE |
|---|
| 708 | farea = 0._wp |
|---|
| 709 | fvol(ij) = 0._wp |
|---|
| 710 | ENDIF |
|---|
| 711 | |
|---|
| 712 | ! Compute the fraction of rafted ice area and volume going to thickness category jl2 |
|---|
| 713 | !!gm see above IF( hraft(ji,jj,jl1) <= hi_max(jl2) .AND. hraft(ji,jj,jl1) > hi_max(jl2-1) ) THEN |
|---|
| 714 | IF( hi_max(jl2-1) < hraft(ji,jj,jl1) .AND. hraft(ji,jj,jl1) <= hi_max(jl2) ) THEN ; zswitch(ij) = 1._wp |
|---|
| 715 | ELSE ; zswitch(ij) = 0._wp |
|---|
| 716 | ENDIF |
|---|
| 717 | ! |
|---|
| 718 | a_i (ji,jj ,jl2) = a_i (ji,jj ,jl2) + ( ardg2 (ij) * farea + arft2 (ij) * zswitch(ij) ) |
|---|
| 719 | oa_i (ji,jj ,jl2) = oa_i (ji,jj ,jl2) + ( oirdg2(ij) * farea + oirft2(ij) * zswitch(ij) ) |
|---|
| 720 | v_i (ji,jj ,jl2) = v_i (ji,jj ,jl2) + ( vrdg2 (ij) * fvol(ij) + virft (ij) * zswitch(ij) ) |
|---|
| 721 | smv_i(ji,jj ,jl2) = smv_i(ji,jj ,jl2) + ( srdg2 (ij) * fvol(ij) + smrft (ij) * zswitch(ij) ) |
|---|
| 722 | v_s (ji,jj ,jl2) = v_s (ji,jj ,jl2) + ( vsrdg (ij) * rn_fsnwrdg * fvol(ij) + & |
|---|
| 723 | & vsrft (ij) * rn_fsnwrft * zswitch(ij) ) |
|---|
| 724 | e_s (ji,jj,1,jl2) = e_s (ji,jj,1,jl2) + ( esrdg (ij) * rn_fsnwrdg * fvol(ij) + & |
|---|
| 725 | & esrft (ij) * rn_fsnwrft * zswitch(ij) ) |
|---|
| 726 | ! MV MP 2016 |
|---|
| 727 | IF ( nn_pnd_scheme > 0 ) THEN |
|---|
| 728 | v_ip (ji,jj,jl2) = v_ip(ji,jj,jl2) + ( vprdg (ij) * rn_fpndrdg * fvol (ij) & |
|---|
| 729 | & + vprft (ij) * rn_fpndrft * zswitch(ij) ) |
|---|
| 730 | a_ip (ji,jj,jl2) = a_ip(ji,jj,jl2) + ( aprdg2(ij) * rn_fpndrdg * farea & |
|---|
| 731 | & + aprft2(ij) * rn_fpndrft * zswitch(ji) ) |
|---|
| 732 | ENDIF |
|---|
| 733 | ! END MV MP 2016 |
|---|
| 734 | END DO |
|---|
| 735 | |
|---|
| 736 | ! Transfer ice energy to category jl2 by ridging |
|---|
| 737 | DO jk = 1, nlay_i |
|---|
| 738 | DO ij = 1, icells |
|---|
| 739 | ji = indxi(ij) ; jj = indxj(ij) |
|---|
| 740 | e_i(ji,jj,jk,jl2) = e_i(ji,jj,jk,jl2) + erdg2(ij,jk) * fvol(ij) + eirft(ij,jk) * zswitch(ij) |
|---|
| 741 | END DO |
|---|
| 742 | END DO |
|---|
| 743 | ! |
|---|
| 744 | END DO ! jl2 |
|---|
| 745 | ! |
|---|
| 746 | END DO ! jl1 (deforming categories) |
|---|
| 747 | ! |
|---|
| 748 | END SUBROUTINE ice_rdgrft_ridgeshift |
|---|
| 749 | |
|---|
| 750 | |
|---|
| 751 | SUBROUTINE ice_rdgrft_strength |
|---|
| 752 | !!---------------------------------------------------------------------- |
|---|
| 753 | !! *** ROUTINE ice_rdgrft_strength *** |
|---|
| 754 | !! |
|---|
| 755 | !! ** Purpose : computes ice strength used in dynamics routines of ice thickness |
|---|
| 756 | !! |
|---|
| 757 | !! ** Method : Compute the strength of the ice pack, defined as the energy (J m-2) |
|---|
| 758 | !! dissipated per unit area removed from the ice pack under compression, |
|---|
| 759 | !! and assumed proportional to the change in potential energy caused |
|---|
| 760 | !! by ridging. Note that only Hibler's formulation is stable and that |
|---|
| 761 | !! ice strength has to be smoothed |
|---|
| 762 | !!---------------------------------------------------------------------- |
|---|
| 763 | INTEGER :: ji,jj, jl ! dummy loop indices |
|---|
| 764 | INTEGER :: ismooth ! smoothing the resistance to deformation |
|---|
| 765 | INTEGER :: itframe ! number of time steps for the P smoothing |
|---|
| 766 | REAL(wp) :: zp, z1_3 ! local scalars |
|---|
| 767 | REAL(wp), DIMENSION(jpi,jpj) :: zworka ! temporary array used here |
|---|
| 768 | REAL(wp), DIMENSION(jpi,jpj) :: zstrp1, zstrp2 ! strength at previous time steps |
|---|
| 769 | !!---------------------------------------------------------------------- |
|---|
| 770 | |
|---|
| 771 | ! !--------------------------------------------------! |
|---|
| 772 | CALL ice_rdgrft_prep ! Thickness distribution of ridging and ridged ice ! |
|---|
| 773 | ! !--------------------------------------------------! |
|---|
| 774 | |
|---|
| 775 | ! !--------------------------------------------------! |
|---|
| 776 | IF( ln_str_R75 ) THEN ! Ice strength => Rothrock (1975) method ! |
|---|
| 777 | ! !--------------------------------------------------! |
|---|
| 778 | z1_3 = 1._wp / 3._wp |
|---|
| 779 | DO jl = 1, jpl |
|---|
| 780 | WHERE( athorn(:,:,jl) > 0._wp ) |
|---|
| 781 | strength(:,:) = - athorn(:,:,jl) * ht_i(:,:,jl) * ht_i(:,:,jl) & ! PE loss from deforming ice |
|---|
| 782 | & + 2._wp * araft (:,:,jl) * ht_i(:,:,jl) * ht_i(:,:,jl) & ! PE gain from rafting ice |
|---|
| 783 | & + aridge(:,:,jl) * krdg(:,:,jl) * z1_3 * & ! PE gain from ridging ice |
|---|
| 784 | & ( hrmax(:,:,jl) * hrmax(:,:,jl) + & |
|---|
| 785 | & hrmin(:,:,jl) * hrmin(:,:,jl) + & |
|---|
| 786 | & hrmax(:,:,jl) * hrmin(:,:,jl) ) |
|---|
| 787 | ELSEWHERE |
|---|
| 788 | strength(:,:) = 0._wp |
|---|
| 789 | END WHERE |
|---|
| 790 | END DO |
|---|
| 791 | strength(:,:) = rn_perdg * zdrho * strength(:,:) / aksum(:,:) * tmask(:,:,1) |
|---|
| 792 | ! where zdrho = (g/2)*(rhow-rhoi)*(rhoi/rhow) and rn_perdg accounts for frictional dissipation |
|---|
| 793 | ismooth = 1 |
|---|
| 794 | ! !--------------------------------------------------! |
|---|
| 795 | ELSEIF( ln_str_H79 ) THEN ! Ice strength => Hibler (1979) method ! |
|---|
| 796 | ! !--------------------------------------------------! |
|---|
| 797 | strength(:,:) = rn_pstar * vt_i(:,:) * EXP( - rn_crhg * ( 1._wp - at_i(:,:) ) ) * tmask(:,:,1) |
|---|
| 798 | ! |
|---|
| 799 | ismooth = 1 |
|---|
| 800 | ! |
|---|
| 801 | ENDIF |
|---|
| 802 | ! !--------------------------------------------------! |
|---|
| 803 | SELECT CASE( ismooth ) ! Smoothing ice strength ! |
|---|
| 804 | ! !--------------------------------------------------! |
|---|
| 805 | CASE( 1 ) !--- Spatial smoothing |
|---|
| 806 | DO jj = 2, jpjm1 |
|---|
| 807 | DO ji = 2, jpim1 |
|---|
| 808 | IF ( ( asum(ji,jj) - ato_i(ji,jj) ) > 0._wp ) THEN |
|---|
| 809 | zworka(ji,jj) = ( 4.0 * strength(ji,jj) & |
|---|
| 810 | & + strength(ji-1,jj) * tmask(ji-1,jj,1) + strength(ji+1,jj) * tmask(ji+1,jj,1) & |
|---|
| 811 | & + strength(ji,jj-1) * tmask(ji,jj-1,1) + strength(ji,jj+1) * tmask(ji,jj+1,1) & |
|---|
| 812 | & ) / ( 4.0 + tmask(ji-1,jj,1) + tmask(ji+1,jj,1) + tmask(ji,jj-1,1) + tmask(ji,jj+1,1) ) |
|---|
| 813 | ELSE |
|---|
| 814 | zworka(ji,jj) = 0._wp |
|---|
| 815 | ENDIF |
|---|
| 816 | END DO |
|---|
| 817 | END DO |
|---|
| 818 | |
|---|
| 819 | DO jj = 2, jpjm1 |
|---|
| 820 | DO ji = 2, jpim1 |
|---|
| 821 | strength(ji,jj) = zworka(ji,jj) |
|---|
| 822 | END DO |
|---|
| 823 | END DO |
|---|
| 824 | CALL lbc_lnk( strength, 'T', 1. ) |
|---|
| 825 | ! |
|---|
| 826 | CASE( 2 ) !--- Temporal smoothing |
|---|
| 827 | IF ( kt_ice == nit000 ) THEN |
|---|
| 828 | zstrp1(:,:) = 0._wp |
|---|
| 829 | zstrp2(:,:) = 0._wp |
|---|
| 830 | ENDIF |
|---|
| 831 | ! |
|---|
| 832 | DO jj = 2, jpjm1 |
|---|
| 833 | DO ji = 2, jpim1 |
|---|
| 834 | IF ( ( asum(ji,jj) - ato_i(ji,jj) ) > 0._wp ) THEN |
|---|
| 835 | itframe = 1 ! number of time steps for the running mean |
|---|
| 836 | IF ( zstrp1(ji,jj) > 0._wp ) itframe = itframe + 1 |
|---|
| 837 | IF ( zstrp2(ji,jj) > 0._wp ) itframe = itframe + 1 |
|---|
| 838 | zp = ( strength(ji,jj) + zstrp1(ji,jj) + zstrp2(ji,jj) ) / itframe |
|---|
| 839 | zstrp2 (ji,jj) = zstrp1 (ji,jj) |
|---|
| 840 | zstrp1 (ji,jj) = strength(ji,jj) |
|---|
| 841 | strength(ji,jj) = zp |
|---|
| 842 | ENDIF |
|---|
| 843 | END DO |
|---|
| 844 | END DO |
|---|
| 845 | CALL lbc_lnk( strength, 'T', 1. ) |
|---|
| 846 | ! |
|---|
| 847 | END SELECT |
|---|
| 848 | ! |
|---|
| 849 | END SUBROUTINE ice_rdgrft_strength |
|---|
| 850 | |
|---|
| 851 | |
|---|
| 852 | SUBROUTINE ice_rdgrft_init |
|---|
| 853 | !!------------------------------------------------------------------- |
|---|
| 854 | !! *** ROUTINE ice_rdgrft_init *** |
|---|
| 855 | !! |
|---|
| 856 | !! ** Purpose : Physical constants and parameters linked |
|---|
| 857 | !! to the mechanical ice redistribution |
|---|
| 858 | !! |
|---|
| 859 | !! ** Method : Read the namice_rdgrft namelist |
|---|
| 860 | !! and check the parameters values |
|---|
| 861 | !! called at the first timestep (nit000) |
|---|
| 862 | !! |
|---|
| 863 | !! ** input : Namelist namice_rdgrft |
|---|
| 864 | !!------------------------------------------------------------------- |
|---|
| 865 | INTEGER :: ios ! Local integer output status for namelist read |
|---|
| 866 | !! |
|---|
| 867 | NAMELIST/namice_rdgrft/ ln_str_H79, rn_pstar, rn_crhg, & |
|---|
| 868 | & ln_str_R75, rn_perdg, & |
|---|
| 869 | & rn_cs , & |
|---|
| 870 | & ln_partf_lin, rn_gstar, & |
|---|
| 871 | & ln_partf_exp, rn_astar, & |
|---|
| 872 | & ln_ridging, rn_hstar, rn_porordg, rn_fsnwrdg, rn_fpndrdg, & |
|---|
| 873 | & ln_rafting, rn_hraft, rn_craft , rn_fsnwrft, rn_fpndrft |
|---|
| 874 | !!------------------------------------------------------------------- |
|---|
| 875 | ! |
|---|
| 876 | REWIND( numnam_ice_ref ) ! Namelist namicetdme in reference namelist : Ice mechanical ice redistribution |
|---|
| 877 | READ ( numnam_ice_ref, namice_rdgrft, IOSTAT = ios, ERR = 901) |
|---|
| 878 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namice_rdgrft in reference namelist', lwp ) |
|---|
| 879 | ! |
|---|
| 880 | REWIND( numnam_ice_cfg ) ! Namelist namice_rdgrft in configuration namelist : Ice mechanical ice redistribution |
|---|
| 881 | READ ( numnam_ice_cfg, namice_rdgrft, IOSTAT = ios, ERR = 902 ) |
|---|
| 882 | 902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namice_rdgrft in configuration namelist', lwp ) |
|---|
| 883 | IF(lwm) WRITE ( numoni, namice_rdgrft ) |
|---|
| 884 | ! |
|---|
| 885 | IF (lwp) THEN ! control print |
|---|
| 886 | WRITE(numout,*) |
|---|
| 887 | WRITE(numout,*) 'ice_rdgrft_init: ice parameters for ridging/rafting ' |
|---|
| 888 | WRITE(numout,*) '~~~~~~~~~~~~~~~' |
|---|
| 889 | WRITE(numout,*) ' Namelist namice_rdgrft' |
|---|
| 890 | WRITE(numout,*) ' ice strength parameterization Hibler (1979) ln_str_H79 = ', ln_str_H79 |
|---|
| 891 | WRITE(numout,*) ' 1st bulk-rheology parameter rn_pstar = ', rn_pstar |
|---|
| 892 | WRITE(numout,*) ' 2nd bulk-rhelogy parameter rn_crhg = ', rn_crhg |
|---|
| 893 | WRITE(numout,*) ' ice strength parameterization Rothrock (1975) ln_str_R75 = ', ln_str_R75 |
|---|
| 894 | WRITE(numout,*) ' Ratio of ridging work to PotEner change in ridging rn_perdg = ', rn_perdg |
|---|
| 895 | WRITE(numout,*) ' Fraction of shear energy contributing to ridging rn_cs = ', rn_cs |
|---|
| 896 | WRITE(numout,*) ' linear ridging participation function ln_partf_lin = ', ln_partf_lin |
|---|
| 897 | WRITE(numout,*) ' Fraction of ice coverage contributing to ridging rn_gstar = ', rn_gstar |
|---|
| 898 | WRITE(numout,*) ' Exponential ridging participation function ln_partf_exp = ', ln_partf_exp |
|---|
| 899 | WRITE(numout,*) ' Equivalent to G* for an exponential function rn_astar = ', rn_astar |
|---|
| 900 | WRITE(numout,*) ' Ridging of ice sheets or not ln_ridging = ', ln_ridging |
|---|
| 901 | WRITE(numout,*) ' max ridged ice thickness rn_hstar = ', rn_hstar |
|---|
| 902 | WRITE(numout,*) ' Initial porosity of ridges rn_porordg = ', rn_porordg |
|---|
| 903 | WRITE(numout,*) ' Fraction of snow volume conserved during ridging rn_fsnwrdg = ', rn_fsnwrdg |
|---|
| 904 | WRITE(numout,*) ' Fraction of pond volume conserved during ridging rn_fpndrdg = ', rn_fpndrdg |
|---|
| 905 | WRITE(numout,*) ' Rafting of ice sheets or not ln_rafting = ', ln_rafting |
|---|
| 906 | WRITE(numout,*) ' Parmeter thickness (threshold between ridge-raft) rn_hraft = ', rn_hraft |
|---|
| 907 | WRITE(numout,*) ' Rafting hyperbolic tangent coefficient rn_craft = ', rn_craft |
|---|
| 908 | WRITE(numout,*) ' Fraction of snow volume conserved during rafting rn_fsnwrft = ', rn_fsnwrft |
|---|
| 909 | WRITE(numout,*) ' Fraction of pond volume conserved during rafting rn_fpndrft = ', rn_fpndrft |
|---|
| 910 | ENDIF |
|---|
| 911 | ! |
|---|
| 912 | IF ( ( ln_str_H79 .AND. ln_str_R75 ) .OR. ( .NOT.ln_str_H79 .AND. .NOT.ln_str_R75 ) ) THEN |
|---|
| 913 | CALL ctl_stop( 'ice_rdgrft_init: choose one and only one formulation for ice strength (ln_str_H79 or ln_str_R75)' ) |
|---|
| 914 | ENDIF |
|---|
| 915 | ! |
|---|
| 916 | IF ( ( ln_partf_lin .AND. ln_partf_exp ) .OR. ( .NOT.ln_partf_lin .AND. .NOT.ln_partf_exp ) ) THEN |
|---|
| 917 | CALL ctl_stop( 'ice_rdgrft_init: choose one and only one participation function (ln_partf_lin or ln_partf_exp)' ) |
|---|
| 918 | ENDIF |
|---|
| 919 | ! |
|---|
| 920 | END SUBROUTINE ice_rdgrft_init |
|---|
| 921 | |
|---|
| 922 | #else |
|---|
| 923 | !!---------------------------------------------------------------------- |
|---|
| 924 | !! Default option Empty module NO LIM-3 sea-ice model |
|---|
| 925 | !!---------------------------------------------------------------------- |
|---|
| 926 | #endif |
|---|
| 927 | |
|---|
| 928 | !!====================================================================== |
|---|
| 929 | END MODULE icerdgrft |
|---|
