| 1 | MODULE icedyn_rdgrft |
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| 2 | !!====================================================================== |
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| 3 | !! *** MODULE icedyn_rdgrft *** |
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| 4 | !! sea-ice : Mechanical impact on ice thickness distribution |
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| 5 | !!====================================================================== |
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| 6 | !! History : ! 2006-02 (M. Vancoppenolle) Original code |
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| 7 | !! 4.0 ! 2018 (many people) SI3 [aka Sea Ice cube] |
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| 8 | !!---------------------------------------------------------------------- |
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| 9 | #if defined key_si3 |
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| 10 | !!---------------------------------------------------------------------- |
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| 11 | !! 'key_si3' SI3 sea-ice model |
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| 12 | !!---------------------------------------------------------------------- |
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| 13 | !! ice_dyn_rdgrft : ridging/rafting of sea ice |
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| 14 | !! ice_dyn_rdgrft_init : initialization of ridging/rafting of sea ice |
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| 15 | !! ice_strength : ice strength calculation |
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| 16 | !!---------------------------------------------------------------------- |
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| 17 | USE dom_oce ! ocean domain |
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| 18 | USE phycst ! physical constants (ocean directory) |
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| 19 | USE sbc_oce , ONLY : sss_m, sst_m ! surface boundary condition: ocean fields |
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| 20 | USE ice1D ! sea-ice: thermodynamics |
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| 21 | USE ice ! sea-ice: variables |
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| 22 | USE icetab ! sea-ice: 1D <==> 2D transformation |
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| 23 | USE icevar ! sea-ice: operations |
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| 24 | USE icectl ! sea-ice: control prints |
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| 25 | ! |
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| 26 | USE in_out_manager ! I/O manager |
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| 27 | USE iom ! I/O manager library |
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| 28 | USE lib_mpp ! MPP library |
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| 29 | USE lib_fortran ! fortran utilities (glob_sum + no signed zero) |
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| 30 | USE lbclnk ! lateral boundary conditions (or mpp links) |
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| 31 | USE timing ! Timing |
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| 32 | |
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| 33 | IMPLICIT NONE |
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| 34 | PRIVATE |
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| 35 | |
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| 36 | PUBLIC ice_dyn_rdgrft ! called by icestp |
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| 37 | PUBLIC ice_dyn_rdgrft_init ! called by icedyn |
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| 38 | PUBLIC ice_strength ! called by icedyn_rhg_evp |
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| 39 | |
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| 40 | ! Variables shared among ridging subroutines |
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| 41 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:) :: closing_net ! net rate at which area is removed (1/s) |
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| 42 | ! ! (ridging ice area - area of new ridges) / dt |
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| 43 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:) :: opning ! rate of opening due to divergence/shear |
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| 44 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:) :: closing_gross ! rate at which area removed, not counting area of new ridges |
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| 45 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: apartf ! participation function; fraction of ridging/closing associated w/ category n |
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| 46 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: hrmin ! minimum ridge thickness |
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| 47 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: hrmax ! maximum ridge thickness |
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| 48 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: hraft ! thickness of rafted ice |
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| 49 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: hi_hrdg ! thickness of ridging ice / mean ridge thickness |
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| 50 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: aridge ! participating ice ridging |
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| 51 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: araft ! participating ice rafting |
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| 52 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: ze_i_2d |
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| 53 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: ze_s_2d |
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| 54 | ! |
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| 55 | REAL(wp), PARAMETER :: hrdg_hi_min = 1.1_wp ! min ridge thickness multiplier: min(hrdg/hi) |
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| 56 | REAL(wp), PARAMETER :: hi_hrft = 0.5_wp ! rafting multipliyer: (hi/hraft) |
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| 57 | ! |
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| 58 | ! ** namelist (namdyn_rdgrft) ** |
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| 59 | LOGICAL :: ln_str_H79 ! ice strength parameterization (Hibler79) |
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| 60 | REAL(wp) :: rn_pstar ! determines ice strength, Hibler JPO79 |
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| 61 | REAL(wp) :: rn_csrdg ! fraction of shearing energy contributing to ridging |
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| 62 | LOGICAL :: ln_partf_lin ! participation function linear (Thorndike et al. (1975)) |
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| 63 | REAL(wp) :: rn_gstar ! fractional area of young ice contributing to ridging |
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| 64 | LOGICAL :: ln_partf_exp ! participation function exponential (Lipscomb et al. (2007)) |
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| 65 | REAL(wp) :: rn_astar ! equivalent of G* for an exponential participation function |
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| 66 | LOGICAL :: ln_ridging ! ridging of ice or not |
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| 67 | REAL(wp) :: rn_hstar ! thickness that determines the maximal thickness of ridged ice |
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| 68 | REAL(wp) :: rn_porordg ! initial porosity of ridges (0.3 regular value) |
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| 69 | REAL(wp) :: rn_fsnwrdg ! fractional snow loss to the ocean during ridging |
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| 70 | REAL(wp) :: rn_fpndrdg ! fractional pond loss to the ocean during ridging |
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| 71 | LOGICAL :: ln_rafting ! rafting of ice or not |
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| 72 | REAL(wp) :: rn_hraft ! threshold thickness (m) for rafting / ridging |
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| 73 | REAL(wp) :: rn_craft ! coefficient for smoothness of the hyperbolic tangent in rafting |
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| 74 | REAL(wp) :: rn_fsnwrft ! fractional snow loss to the ocean during rafting |
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| 75 | REAL(wp) :: rn_fpndrft ! fractional pond loss to the ocean during rafting |
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| 76 | ! |
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| 77 | !!---------------------------------------------------------------------- |
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| 78 | !! NEMO/ICE 4.0 , NEMO Consortium (2018) |
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| 79 | !! $Id: icedyn_rdgrft.F90 8378 2017-07-26 13:55:59Z clem $ |
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| 80 | !! Software governed by the CeCILL licence (./LICENSE) |
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| 81 | !!---------------------------------------------------------------------- |
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| 82 | CONTAINS |
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| 83 | |
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| 84 | INTEGER FUNCTION ice_dyn_rdgrft_alloc() |
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| 85 | !!------------------------------------------------------------------- |
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| 86 | !! *** ROUTINE ice_dyn_rdgrft_alloc *** |
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| 87 | !!------------------------------------------------------------------- |
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| 88 | ALLOCATE( closing_net(jpij), opning(jpij) , closing_gross(jpij), & |
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| 89 | & apartf(jpij,0:jpl), hrmin(jpij,jpl), hraft(jpij,jpl) , aridge(jpij,jpl), & |
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| 90 | & hrmax(jpij,jpl), hi_hrdg(jpij,jpl) , araft (jpij,jpl), & |
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| 91 | & ze_i_2d(jpij,nlay_i,jpl), ze_s_2d(jpij,nlay_s,jpl), STAT=ice_dyn_rdgrft_alloc ) |
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| 92 | |
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| 93 | IF( lk_mpp ) CALL mpp_sum ( ice_dyn_rdgrft_alloc ) |
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| 94 | IF( ice_dyn_rdgrft_alloc /= 0 ) CALL ctl_warn( 'ice_dyn_rdgrft_alloc: failed to allocate arrays' ) |
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| 95 | ! |
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| 96 | END FUNCTION ice_dyn_rdgrft_alloc |
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| 97 | |
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| 98 | |
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| 99 | SUBROUTINE ice_dyn_rdgrft( kt ) |
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| 100 | !!------------------------------------------------------------------- |
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| 101 | !! *** ROUTINE ice_dyn_rdgrft *** |
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| 102 | !! |
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| 103 | !! ** Purpose : computes the mechanical redistribution of ice thickness |
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| 104 | !! |
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| 105 | !! ** Method : Steps : |
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| 106 | !! 0) Identify grid cells with ice |
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| 107 | !! 1) Calculate closing rate, divergence and opening |
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| 108 | !! 2) Identify grid cells with ridging |
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| 109 | !! 3) Start ridging iterations |
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| 110 | !! - prep = ridged and rafted ice + closing_gross |
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| 111 | !! - shift = move ice from one category to another |
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| 112 | !! |
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| 113 | !! ** Details |
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| 114 | !! step1: The net rate of closing is due to convergence and shear, based on Flato and Hibler (1995). |
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| 115 | !! The energy dissipation rate is equal to the net closing rate times the ice strength. |
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| 116 | !! |
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| 117 | !! step3: The gross closing rate is equal to the first two terms (open |
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| 118 | !! water closing and thin ice ridging) without the third term |
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| 119 | !! (thick, newly ridged ice). |
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| 120 | !! |
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| 121 | !! References : Flato, G. M., and W. D. Hibler III, 1995, JGR, 100, 18,611-18,626. |
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| 122 | !! Hibler, W. D. III, 1980, MWR, 108, 1943-1973, 1980. |
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| 123 | !! Rothrock, D. A., 1975: JGR, 80, 4514-4519. |
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| 124 | !! Thorndike et al., 1975, JGR, 80, 4501-4513. |
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| 125 | !! Bitz et al., JGR, 2001 |
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| 126 | !! Amundrud and Melling, JGR 2005 |
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| 127 | !! Babko et al., JGR 2002 |
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| 128 | !! |
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| 129 | !! This routine is based on CICE code and authors William H. Lipscomb, |
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| 130 | !! and Elizabeth C. Hunke, LANL are gratefully acknowledged |
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| 131 | !!------------------------------------------------------------------- |
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| 132 | INTEGER, INTENT(in) :: kt ! number of iteration |
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| 133 | !! |
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| 134 | INTEGER :: ji, jj, jk, jl ! dummy loop index |
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| 135 | INTEGER :: iter, iterate_ridging ! local integer |
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| 136 | INTEGER :: ipti ! local integer |
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| 137 | REAL(wp) :: zfac ! local scalar |
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| 138 | INTEGER , DIMENSION(jpij) :: iptidx ! compute ridge/raft or not |
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| 139 | REAL(wp), DIMENSION(jpij) :: zdivu_adv ! divu as implied by transport scheme (1/s) |
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| 140 | REAL(wp), DIMENSION(jpij) :: zdivu, zdelt ! 1D divu_i & delta_i |
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| 141 | ! |
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| 142 | INTEGER, PARAMETER :: jp_itermax = 20 |
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| 143 | !!------------------------------------------------------------------- |
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| 144 | ! clem: The redistribution of ice between categories can lead to small negative values (as for the remapping in ice_itd_rem) |
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| 145 | ! likely due to truncation error ( i.e. 1. - 1. /= 0 ) |
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| 146 | ! I do not think it should be a concern since small areas and volumes are erased (in ice_var_zapsmall.F90) |
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| 147 | |
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| 148 | ! controls |
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| 149 | IF( ln_timing ) CALL timing_start('icedyn_rdgrft') ! timing |
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| 150 | IF( ln_icediachk ) CALL ice_cons_hsm(0, 'icedyn_rdgrft', rdiag_v, rdiag_s, rdiag_t, rdiag_fv, rdiag_fs, rdiag_ft) ! conservation |
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| 151 | |
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| 152 | IF( kt == nit000 ) THEN |
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| 153 | IF(lwp) WRITE(numout,*) |
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| 154 | IF(lwp) WRITE(numout,*)'ice_dyn_rdgrft: ice ridging and rafting' |
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| 155 | IF(lwp) WRITE(numout,*)'~~~~~~~~~~~~~~' |
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| 156 | ENDIF |
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| 157 | |
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| 158 | CALL ice_var_zapsmall ! Zero out categories with very small areas |
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| 159 | |
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| 160 | !-------------------------------- |
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| 161 | ! 0) Identify grid cells with ice |
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| 162 | !-------------------------------- |
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| 163 | npti = 0 ; nptidx(:) = 0 |
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| 164 | ipti = 0 ; iptidx(:) = 0 |
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| 165 | DO jj = 1, jpj |
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| 166 | DO ji = 1, jpi |
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| 167 | IF ( at_i(ji,jj) > 0._wp ) THEN |
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| 168 | npti = npti + 1 |
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| 169 | nptidx( npti ) = (jj - 1) * jpi + ji |
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| 170 | ENDIF |
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| 171 | END DO |
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| 172 | END DO |
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| 173 | |
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| 174 | !-------------------------------------------------------- |
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| 175 | ! 1) Dynamical inputs (closing rate, divergence, opening) |
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| 176 | !-------------------------------------------------------- |
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| 177 | IF( npti > 0 ) THEN |
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| 178 | |
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| 179 | ! just needed here |
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| 180 | CALL tab_2d_1d( npti, nptidx(1:npti), zdivu(1:npti), divu_i(:,:) ) |
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| 181 | CALL tab_2d_1d( npti, nptidx(1:npti), zdelt(1:npti), delta_i(:,:) ) |
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| 182 | ! needed here and in the iteration loop |
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| 183 | CALL tab_3d_2d( npti, nptidx(1:npti), a_i_2d (1:npti,1:jpl), a_i(:,:,:) ) |
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| 184 | CALL tab_3d_2d( npti, nptidx(1:npti), v_i_2d (1:npti,1:jpl), v_i(:,:,:) ) |
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| 185 | CALL tab_2d_1d( npti, nptidx(1:npti), ato_i_1d(1:npti) , ato_i(:,:) ) |
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| 186 | |
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| 187 | DO ji = 1, npti |
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| 188 | ! closing_net = rate at which open water area is removed + ice area removed by ridging |
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| 189 | ! - ice area added in new ridges |
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| 190 | closing_net(ji) = rn_csrdg * 0.5_wp * ( zdelt(ji) - ABS( zdivu(ji) ) ) - MIN( zdivu(ji), 0._wp ) |
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| 191 | ! |
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| 192 | ! divergence given by the advection scheme |
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| 193 | ! (which may not be equal to divu as computed from the velocity field) |
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| 194 | zdivu_adv(ji) = ( 1._wp - ato_i_1d(ji) - SUM( a_i_2d(ji,:) ) ) * r1_rdtice |
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| 195 | ! |
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| 196 | IF( zdivu_adv(ji) < 0._wp ) closing_net(ji) = MAX( closing_net(ji), -zdivu_adv(ji) ) ! make sure the closing rate is large enough |
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| 197 | ! ! to give asum = 1.0 after ridging |
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| 198 | ! Opening rate (non-negative) that will give asum = 1.0 after ridging. |
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| 199 | opning(ji) = closing_net(ji) + zdivu_adv(ji) |
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| 200 | END DO |
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| 201 | ! |
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| 202 | !------------------------------------ |
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| 203 | ! 2) Identify grid cells with ridging |
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| 204 | !------------------------------------ |
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| 205 | CALL rdgrft_prep( a_i_2d, v_i_2d, ato_i_1d, closing_net ) |
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| 206 | |
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| 207 | DO ji = 1, npti |
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| 208 | IF( SUM( apartf(ji,1:jpl) ) > 0._wp .AND. closing_gross(ji) > 0._wp ) THEN |
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| 209 | ipti = ipti + 1 |
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| 210 | iptidx (ipti) = nptidx (ji) |
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| 211 | ! adjust to new indices |
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| 212 | a_i_2d (ipti,:) = a_i_2d (ji,:) |
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| 213 | v_i_2d (ipti,:) = v_i_2d (ji,:) |
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| 214 | ato_i_1d (ipti) = ato_i_1d (ji) |
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| 215 | closing_net(ipti) = closing_net(ji) |
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| 216 | zdivu_adv (ipti) = zdivu_adv (ji) |
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| 217 | opning (ipti) = opning (ji) |
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| 218 | ENDIF |
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| 219 | END DO |
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| 220 | |
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| 221 | ENDIF |
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| 222 | |
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| 223 | ! grid cells with ridging |
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| 224 | nptidx(:) = iptidx(:) |
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| 225 | npti = ipti |
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| 226 | |
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| 227 | !----------------- |
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| 228 | ! 3) Start ridging |
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| 229 | !----------------- |
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| 230 | IF( npti > 0 ) THEN |
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| 231 | |
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| 232 | CALL ice_dyn_1d2d( 1 ) ! --- Move to 1D arrays --- ! |
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| 233 | |
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| 234 | iter = 1 |
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| 235 | iterate_ridging = 1 |
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| 236 | ! !----------------------! |
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| 237 | DO WHILE( iterate_ridging > 0 .AND. iter < jp_itermax ) ! ridging iterations ! |
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| 238 | ! !----------------------! |
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| 239 | ! Calculate participation function (apartf) |
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| 240 | ! and transfer function |
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| 241 | ! and closing_gross (+correction on opening) |
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| 242 | CALL rdgrft_prep( a_i_2d, v_i_2d, ato_i_1d, closing_net ) |
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| 243 | |
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| 244 | ! Redistribute area, volume, and energy between categories |
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| 245 | CALL rdgrft_shift |
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| 246 | |
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| 247 | ! Do we keep on iterating? |
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| 248 | !------------------------- |
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| 249 | ! Check whether a_i + ato_i = 0 |
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| 250 | ! If not, because the closing and opening rates were reduced above, ridge again with new rates |
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| 251 | iterate_ridging = 0 |
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| 252 | DO ji = 1, npti |
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| 253 | zfac = 1._wp - ( ato_i_1d(ji) + SUM( a_i_2d(ji,:) ) ) |
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| 254 | IF( ABS( zfac ) < epsi10 ) THEN |
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| 255 | closing_net(ji) = 0._wp |
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| 256 | opning (ji) = 0._wp |
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| 257 | ato_i_1d (ji) = MAX( 0._wp, 1._wp - SUM( a_i_2d(ji,:) ) ) |
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| 258 | ELSE |
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| 259 | iterate_ridging = 1 |
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| 260 | zdivu_adv (ji) = zfac * r1_rdtice |
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| 261 | closing_net(ji) = MAX( 0._wp, -zdivu_adv(ji) ) |
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| 262 | opning (ji) = MAX( 0._wp, zdivu_adv(ji) ) |
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| 263 | ENDIF |
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| 264 | END DO |
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| 265 | ! |
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| 266 | iter = iter + 1 |
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| 267 | IF( iter > jp_itermax ) CALL ctl_warn( 'icedyn_rdgrft: non-converging ridging scheme' ) |
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| 268 | ! |
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| 269 | END DO |
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| 270 | |
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| 271 | CALL ice_dyn_1d2d( 2 ) ! --- Move to 2D arrays --- ! |
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| 272 | |
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| 273 | ENDIF |
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| 274 | |
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| 275 | CALL ice_var_agg( 1 ) |
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| 276 | |
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| 277 | ! controls |
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| 278 | IF( ln_icediachk ) CALL ice_cons_hsm(1, 'icedyn_rdgrft', rdiag_v, rdiag_s, rdiag_t, rdiag_fv, rdiag_fs, rdiag_ft) ! conservation |
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| 279 | IF( ln_ctl ) CALL ice_prt3D ('icedyn_rdgrft') ! prints |
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| 280 | IF( ln_timing ) CALL timing_stop ('icedyn_rdgrft') ! timing |
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| 281 | ! |
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| 282 | END SUBROUTINE ice_dyn_rdgrft |
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| 283 | |
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| 284 | |
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| 285 | SUBROUTINE rdgrft_prep( pa_i, pv_i, pato_i, pclosing_net ) |
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| 286 | !!------------------------------------------------------------------- |
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| 287 | !! *** ROUTINE rdgrft_prep *** |
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| 288 | !! |
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| 289 | !! ** Purpose : preparation for ridging calculations |
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| 290 | !! |
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| 291 | !! ** Method : Compute the thickness distribution of the ice and open water |
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| 292 | !! participating in ridging and of the resulting ridges. |
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| 293 | !!------------------------------------------------------------------- |
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| 294 | REAL(wp), DIMENSION(:) , INTENT(in) :: pato_i, pclosing_net |
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| 295 | REAL(wp), DIMENSION(:,:), INTENT(in) :: pa_i, pv_i |
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| 296 | !! |
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| 297 | INTEGER :: ji, jl ! dummy loop indices |
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| 298 | REAL(wp) :: z1_gstar, z1_astar, zhmean, zfac ! local scalar |
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| 299 | REAL(wp), DIMENSION(jpij) :: zasum, z1_asum, zaksum ! sum of a_i+ato_i and reverse |
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| 300 | REAL(wp), DIMENSION(jpij,jpl) :: zhi ! ice thickness |
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| 301 | REAL(wp), DIMENSION(jpij,-1:jpl) :: zGsum ! zGsum(n) = sum of areas in categories 0 to n |
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| 302 | !-------------------------------------------------------------------- |
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| 303 | |
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| 304 | z1_gstar = 1._wp / rn_gstar |
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| 305 | z1_astar = 1._wp / rn_astar |
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| 306 | |
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| 307 | ! ! Ice thickness needed for rafting |
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| 308 | WHERE( pa_i(1:npti,:) > 0._wp ) ; zhi(1:npti,:) = pv_i(1:npti,:) / pa_i(1:npti,:) |
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| 309 | ELSEWHERE ; zhi(1:npti,:) = 0._wp |
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| 310 | END WHERE |
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| 311 | |
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| 312 | ! 1) Participation function (apartf): a(h) = b(h).g(h) |
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| 313 | !----------------------------------------------------------------- |
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| 314 | ! Compute the participation function = total area lost due to ridging/closing |
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| 315 | ! This is analogous to |
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| 316 | ! a(h) = b(h)g(h) as defined in Thorndike et al. (1975). |
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| 317 | ! assuming b(h) = (2/Gstar) * (1 - G(h)/Gstar). |
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| 318 | ! |
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| 319 | ! apartf = integrating b(h)g(h) between the category boundaries |
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| 320 | ! apartf is always >= 0 and SUM(apartf(0:jpl))=1 |
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| 321 | !----------------------------------------------------------------- |
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| 322 | ! |
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| 323 | ! Compute total area of ice plus open water. |
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| 324 | ! This is in general not equal to one because of divergence during transport |
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| 325 | zasum(1:npti) = pato_i(1:npti) + SUM( pa_i(1:npti,:), dim=2 ) |
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| 326 | ! |
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| 327 | WHERE( zasum(1:npti) > 0._wp ) ; z1_asum(1:npti) = 1._wp / zasum(1:npti) |
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| 328 | ELSEWHERE ; z1_asum(1:npti) = 0._wp |
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| 329 | END WHERE |
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| 330 | ! |
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| 331 | ! Compute cumulative thickness distribution function |
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| 332 | ! Compute the cumulative thickness distribution function zGsum, |
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| 333 | ! where zGsum(n) is the fractional area in categories 0 to n. |
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| 334 | ! initial value (in h = 0) = open water area |
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| 335 | zGsum(1:npti,-1) = 0._wp |
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| 336 | zGsum(1:npti,0 ) = pato_i(1:npti) * z1_asum(1:npti) |
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| 337 | DO jl = 1, jpl |
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| 338 | zGsum(1:npti,jl) = ( pato_i(1:npti) + SUM( pa_i(1:npti,1:jl), dim=2 ) ) * z1_asum(1:npti) ! sum(1:jl) is ok (and not jpl) |
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| 339 | END DO |
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| 340 | ! |
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| 341 | IF( ln_partf_lin ) THEN !--- Linear formulation (Thorndike et al., 1975) |
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| 342 | DO jl = 0, jpl |
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| 343 | DO ji = 1, npti |
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| 344 | IF ( zGsum(ji,jl) < rn_gstar ) THEN |
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| 345 | apartf(ji,jl) = z1_gstar * ( zGsum(ji,jl) - zGsum(ji,jl-1) ) * & |
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| 346 | & ( 2._wp - ( zGsum(ji,jl-1) + zGsum(ji,jl) ) * z1_gstar ) |
|---|
| 347 | ELSEIF( zGsum(ji,jl-1) < rn_gstar ) THEN |
|---|
| 348 | apartf(ji,jl) = z1_gstar * ( rn_gstar - zGsum(ji,jl-1) ) * & |
|---|
| 349 | & ( 2._wp - ( zGsum(ji,jl-1) + rn_gstar ) * z1_gstar ) |
|---|
| 350 | ELSE |
|---|
| 351 | apartf(ji,jl) = 0._wp |
|---|
| 352 | ENDIF |
|---|
| 353 | END DO |
|---|
| 354 | END DO |
|---|
| 355 | ! |
|---|
| 356 | ELSEIF( ln_partf_exp ) THEN !--- Exponential, more stable formulation (Lipscomb et al, 2007) |
|---|
| 357 | ! |
|---|
| 358 | zfac = 1._wp / ( 1._wp - EXP(-z1_astar) ) |
|---|
| 359 | DO jl = -1, jpl |
|---|
| 360 | DO ji = 1, npti |
|---|
| 361 | zGsum(ji,jl) = EXP( -zGsum(ji,jl) * z1_astar ) * zfac |
|---|
| 362 | END DO |
|---|
| 363 | END DO |
|---|
| 364 | DO jl = 0, jpl |
|---|
| 365 | DO ji = 1, npti |
|---|
| 366 | apartf(ji,jl) = zGsum(ji,jl-1) - zGsum(ji,jl) |
|---|
| 367 | END DO |
|---|
| 368 | END DO |
|---|
| 369 | ! |
|---|
| 370 | ENDIF |
|---|
| 371 | |
|---|
| 372 | ! !--- Ridging and rafting participation concentrations |
|---|
| 373 | IF( ln_rafting .AND. ln_ridging ) THEN !- ridging & rafting |
|---|
| 374 | DO jl = 1, jpl |
|---|
| 375 | DO ji = 1, npti |
|---|
| 376 | aridge(ji,jl) = ( 1._wp + TANH ( rn_craft * ( zhi(ji,jl) - rn_hraft ) ) ) * 0.5_wp * apartf(ji,jl) |
|---|
| 377 | araft (ji,jl) = apartf(ji,jl) - aridge(ji,jl) |
|---|
| 378 | END DO |
|---|
| 379 | END DO |
|---|
| 380 | ELSEIF( ln_ridging .AND. .NOT. ln_rafting ) THEN !- ridging alone |
|---|
| 381 | DO jl = 1, jpl |
|---|
| 382 | DO ji = 1, npti |
|---|
| 383 | aridge(ji,jl) = apartf(ji,jl) |
|---|
| 384 | araft (ji,jl) = 0._wp |
|---|
| 385 | END DO |
|---|
| 386 | END DO |
|---|
| 387 | ELSEIF( ln_rafting .AND. .NOT. ln_ridging ) THEN !- rafting alone |
|---|
| 388 | DO jl = 1, jpl |
|---|
| 389 | DO ji = 1, npti |
|---|
| 390 | aridge(ji,jl) = 0._wp |
|---|
| 391 | araft (ji,jl) = apartf(ji,jl) |
|---|
| 392 | END DO |
|---|
| 393 | END DO |
|---|
| 394 | ELSE !- no ridging & no rafting |
|---|
| 395 | DO jl = 1, jpl |
|---|
| 396 | DO ji = 1, npti |
|---|
| 397 | aridge(ji,jl) = 0._wp |
|---|
| 398 | araft (ji,jl) = 0._wp |
|---|
| 399 | END DO |
|---|
| 400 | END DO |
|---|
| 401 | ENDIF |
|---|
| 402 | |
|---|
| 403 | ! 2) Transfer function |
|---|
| 404 | !----------------------------------------------------------------- |
|---|
| 405 | ! Compute max and min ridged ice thickness for each ridging category. |
|---|
| 406 | ! Assume ridged ice is uniformly distributed between hrmin and hrmax. |
|---|
| 407 | ! |
|---|
| 408 | ! This parameterization is a modified version of Hibler (1980). |
|---|
| 409 | ! The mean ridging thickness, zhmean, is proportional to hi^(0.5) |
|---|
| 410 | ! and for very thick ridging ice must be >= hrdg_hi_min*hi |
|---|
| 411 | ! |
|---|
| 412 | ! The minimum ridging thickness, hrmin, is equal to 2*hi |
|---|
| 413 | ! (i.e., rafting) and for very thick ridging ice is |
|---|
| 414 | ! constrained by hrmin <= (zhmean + hi)/2. |
|---|
| 415 | ! |
|---|
| 416 | ! The maximum ridging thickness, hrmax, is determined by zhmean and hrmin. |
|---|
| 417 | ! |
|---|
| 418 | ! These modifications have the effect of reducing the ice strength |
|---|
| 419 | ! (relative to the Hibler formulation) when very thick ice is ridging. |
|---|
| 420 | ! |
|---|
| 421 | ! zaksum = net area removed/ total area removed |
|---|
| 422 | ! where total area removed = area of ice that ridges |
|---|
| 423 | ! net area removed = total area removed - area of new ridges |
|---|
| 424 | !----------------------------------------------------------------- |
|---|
| 425 | zfac = 1._wp / hi_hrft |
|---|
| 426 | zaksum(1:npti) = apartf(1:npti,0) |
|---|
| 427 | ! |
|---|
| 428 | DO jl = 1, jpl |
|---|
| 429 | DO ji = 1, npti |
|---|
| 430 | IF ( apartf(ji,jl) > 0._wp ) THEN |
|---|
| 431 | zhmean = MAX( SQRT( rn_hstar * zhi(ji,jl) ), zhi(ji,jl) * hrdg_hi_min ) |
|---|
| 432 | hrmin (ji,jl) = MIN( 2._wp * zhi(ji,jl), 0.5_wp * ( zhmean + zhi(ji,jl) ) ) |
|---|
| 433 | hrmax (ji,jl) = 2._wp * zhmean - hrmin(ji,jl) |
|---|
| 434 | hraft (ji,jl) = zhi(ji,jl) * zfac |
|---|
| 435 | hi_hrdg(ji,jl) = zhi(ji,jl) / MAX( zhmean, epsi20 ) |
|---|
| 436 | ! |
|---|
| 437 | ! Normalization factor : zaksum, ensures mass conservation |
|---|
| 438 | zaksum(ji) = zaksum(ji) + aridge(ji,jl) * ( 1._wp - hi_hrdg(ji,jl) ) & |
|---|
| 439 | & + araft (ji,jl) * ( 1._wp - hi_hrft ) |
|---|
| 440 | ELSE |
|---|
| 441 | hrmin (ji,jl) = 0._wp |
|---|
| 442 | hrmax (ji,jl) = 0._wp |
|---|
| 443 | hraft (ji,jl) = 0._wp |
|---|
| 444 | hi_hrdg(ji,jl) = 1._wp |
|---|
| 445 | ENDIF |
|---|
| 446 | END DO |
|---|
| 447 | END DO |
|---|
| 448 | ! |
|---|
| 449 | ! 3) closing_gross |
|---|
| 450 | !----------------- |
|---|
| 451 | ! Based on the ITD of ridging and ridged ice, convert the net closing rate to a gross closing rate. |
|---|
| 452 | ! NOTE: 0 < aksum <= 1 |
|---|
| 453 | WHERE( zaksum(1:npti) > 0._wp ) ; closing_gross(1:npti) = pclosing_net(1:npti) / zaksum(1:npti) |
|---|
| 454 | ELSEWHERE ; closing_gross(1:npti) = 0._wp |
|---|
| 455 | END WHERE |
|---|
| 456 | |
|---|
| 457 | ! correction to closing rate if excessive ice removal |
|---|
| 458 | !---------------------------------------------------- |
|---|
| 459 | ! Reduce the closing rate if more than 100% of any ice category would be removed |
|---|
| 460 | ! Reduce the opening rate in proportion |
|---|
| 461 | DO jl = 1, jpl |
|---|
| 462 | DO ji = 1, npti |
|---|
| 463 | zfac = apartf(ji,jl) * closing_gross(ji) * rdt_ice |
|---|
| 464 | IF( zfac > pa_i(ji,jl) ) THEN |
|---|
| 465 | closing_gross(ji) = pa_i(ji,jl) / apartf(ji,jl) * r1_rdtice |
|---|
| 466 | ENDIF |
|---|
| 467 | END DO |
|---|
| 468 | END DO |
|---|
| 469 | |
|---|
| 470 | ! 4) correction to opening if excessive open water removal |
|---|
| 471 | !--------------------------------------------------------- |
|---|
| 472 | ! Reduce the closing rate if more than 100% of the open water would be removed |
|---|
| 473 | ! Reduce the opening rate in proportion |
|---|
| 474 | DO ji = 1, npti |
|---|
| 475 | zfac = pato_i(ji) + ( opning(ji) - apartf(ji,0) * closing_gross(ji) ) * rdt_ice |
|---|
| 476 | IF( zfac < 0._wp ) THEN ! would lead to negative ato_i |
|---|
| 477 | opning(ji) = apartf(ji,0) * closing_gross(ji) - pato_i(ji) * r1_rdtice |
|---|
| 478 | ELSEIF( zfac > zasum(ji) ) THEN ! would lead to ato_i > asum |
|---|
| 479 | opning(ji) = apartf(ji,0) * closing_gross(ji) + ( zasum(ji) - pato_i(ji) ) * r1_rdtice |
|---|
| 480 | ENDIF |
|---|
| 481 | END DO |
|---|
| 482 | ! |
|---|
| 483 | END SUBROUTINE rdgrft_prep |
|---|
| 484 | |
|---|
| 485 | |
|---|
| 486 | SUBROUTINE rdgrft_shift |
|---|
| 487 | !!------------------------------------------------------------------- |
|---|
| 488 | !! *** ROUTINE rdgrft_shift *** |
|---|
| 489 | !! |
|---|
| 490 | !! ** Purpose : shift ridging ice among thickness categories of ice thickness |
|---|
| 491 | !! |
|---|
| 492 | !! ** Method : Remove area, volume, and energy from each ridging category |
|---|
| 493 | !! and add to thicker ice categories. |
|---|
| 494 | !!------------------------------------------------------------------- |
|---|
| 495 | ! |
|---|
| 496 | INTEGER :: ji, jj, jl, jl1, jl2, jk ! dummy loop indices |
|---|
| 497 | REAL(wp) :: hL, hR, farea ! left and right limits of integration and new area going to jl2 |
|---|
| 498 | REAL(wp) :: vsw ! vol of water trapped into ridges |
|---|
| 499 | REAL(wp) :: afrdg, afrft ! fraction of category area ridged/rafted |
|---|
| 500 | REAL(wp) :: airdg1, oirdg1, aprdg1, virdg1, sirdg1 |
|---|
| 501 | REAL(wp) :: airft1, oirft1, aprft1 |
|---|
| 502 | REAL(wp), DIMENSION(jpij) :: airdg2, oirdg2, aprdg2, virdg2, sirdg2, vsrdg, vprdg ! area etc of new ridges |
|---|
| 503 | REAL(wp), DIMENSION(jpij) :: airft2, oirft2, aprft2, virft , sirft , vsrft, vprft ! area etc of rafted ice |
|---|
| 504 | ! |
|---|
| 505 | REAL(wp), DIMENSION(jpij) :: ersw ! enth of water trapped into ridges |
|---|
| 506 | REAL(wp), DIMENSION(jpij) :: zswitch, fvol ! new ridge volume going to jl2 |
|---|
| 507 | REAL(wp), DIMENSION(jpij) :: z1_ai ! 1 / a |
|---|
| 508 | ! |
|---|
| 509 | REAL(wp), DIMENSION(jpij,nlay_s) :: esrft ! snow energy of rafting ice |
|---|
| 510 | REAL(wp), DIMENSION(jpij,nlay_i) :: eirft ! ice energy of rafting ice |
|---|
| 511 | REAL(wp), DIMENSION(jpij,nlay_s) :: esrdg ! enth*volume of new ridges |
|---|
| 512 | REAL(wp), DIMENSION(jpij,nlay_i) :: eirdg ! enth*volume of new ridges |
|---|
| 513 | ! |
|---|
| 514 | INTEGER , DIMENSION(jpij) :: itest_rdg, itest_rft ! test for conservation |
|---|
| 515 | !!------------------------------------------------------------------- |
|---|
| 516 | |
|---|
| 517 | ! 1) Change in open water area due to closing and opening |
|---|
| 518 | !-------------------------------------------------------- |
|---|
| 519 | DO ji = 1, npti |
|---|
| 520 | ato_i_1d(ji) = MAX( 0._wp, ato_i_1d(ji) + ( opning(ji) - apartf(ji,0) * closing_gross(ji) ) * rdt_ice ) |
|---|
| 521 | END DO |
|---|
| 522 | |
|---|
| 523 | ! 2) compute categories in which ice is removed (jl1) |
|---|
| 524 | !---------------------------------------------------- |
|---|
| 525 | DO jl1 = 1, jpl |
|---|
| 526 | |
|---|
| 527 | CALL tab_2d_1d( npti, nptidx(1:npti), s_i_1d(1:npti), s_i(:,:,jl1) ) |
|---|
| 528 | |
|---|
| 529 | DO ji = 1, npti |
|---|
| 530 | |
|---|
| 531 | IF( apartf(ji,jl1) > 0._wp .AND. closing_gross(ji) > 0._wp ) THEN ! only if ice is ridging |
|---|
| 532 | |
|---|
| 533 | z1_ai(ji) = 1._wp / a_i_2d(ji,jl1) |
|---|
| 534 | |
|---|
| 535 | ! area of ridging / rafting ice (airdg1) and of new ridge (airdg2) |
|---|
| 536 | airdg1 = aridge(ji,jl1) * closing_gross(ji) * rdt_ice |
|---|
| 537 | airft1 = araft (ji,jl1) * closing_gross(ji) * rdt_ice |
|---|
| 538 | |
|---|
| 539 | airdg2(ji) = airdg1 * hi_hrdg(ji,jl1) |
|---|
| 540 | airft2(ji) = airft1 * hi_hrft |
|---|
| 541 | |
|---|
| 542 | ! ridging /rafting fractions |
|---|
| 543 | afrdg = airdg1 * z1_ai(ji) |
|---|
| 544 | afrft = airft1 * z1_ai(ji) |
|---|
| 545 | |
|---|
| 546 | ! volume and enthalpy (J/m2, >0) of seawater trapped into ridges |
|---|
| 547 | vsw = v_i_2d(ji,jl1) * afrdg * rn_porordg |
|---|
| 548 | ersw(ji) = -rhoi * vsw * rcp * sst_1d(ji) ! clem: if sst>0, then ersw <0 (is that possible?) |
|---|
| 549 | |
|---|
| 550 | ! volume etc of ridging / rafting ice and new ridges (vi, vs, sm, oi, es, ei) |
|---|
| 551 | virdg1 = v_i_2d (ji,jl1) * afrdg |
|---|
| 552 | virdg2(ji) = v_i_2d (ji,jl1) * afrdg * ( 1. + rn_porordg ) |
|---|
| 553 | vsrdg(ji) = v_s_2d (ji,jl1) * afrdg |
|---|
| 554 | sirdg1 = sv_i_2d(ji,jl1) * afrdg |
|---|
| 555 | sirdg2(ji) = sv_i_2d(ji,jl1) * afrdg + vsw * sss_1d(ji) |
|---|
| 556 | oirdg1 = oa_i_2d(ji,jl1) * afrdg |
|---|
| 557 | oirdg2(ji) = oa_i_2d(ji,jl1) * afrdg * hi_hrdg(ji,jl1) |
|---|
| 558 | |
|---|
| 559 | virft(ji) = v_i_2d (ji,jl1) * afrft |
|---|
| 560 | vsrft(ji) = v_s_2d (ji,jl1) * afrft |
|---|
| 561 | sirft(ji) = sv_i_2d(ji,jl1) * afrft |
|---|
| 562 | oirft1 = oa_i_2d(ji,jl1) * afrft |
|---|
| 563 | oirft2(ji) = oa_i_2d(ji,jl1) * afrft * hi_hrft |
|---|
| 564 | |
|---|
| 565 | IF ( ln_pnd_H12 ) THEN |
|---|
| 566 | aprdg1 = a_ip_2d(ji,jl1) * afrdg |
|---|
| 567 | aprdg2(ji) = a_ip_2d(ji,jl1) * afrdg * hi_hrdg(ji,jl1) |
|---|
| 568 | vprdg (ji) = v_ip_2d(ji,jl1) * afrdg |
|---|
| 569 | aprft1 = a_ip_2d(ji,jl1) * afrft |
|---|
| 570 | aprft2(ji) = a_ip_2d(ji,jl1) * afrft * hi_hrft |
|---|
| 571 | vprft (ji) = v_ip_2d(ji,jl1) * afrft |
|---|
| 572 | ENDIF |
|---|
| 573 | |
|---|
| 574 | ! Ice-ocean exchanges associated with ice porosity |
|---|
| 575 | wfx_dyn_1d(ji) = wfx_dyn_1d(ji) - vsw * rhoi * r1_rdtice ! increase in ice volume due to seawater frozen in voids |
|---|
| 576 | sfx_dyn_1d(ji) = sfx_dyn_1d(ji) - vsw * sss_1d(ji) * rhoi * r1_rdtice |
|---|
| 577 | hfx_dyn_1d(ji) = hfx_dyn_1d(ji) + ersw(ji) * r1_rdtice ! > 0 [W.m-2] |
|---|
| 578 | |
|---|
| 579 | ! Put the snow lost by ridging into the ocean |
|---|
| 580 | ! Note that esrdg > 0; the ocean must cool to melt snow. If the ocean temp = Tf already, new ice must grow. |
|---|
| 581 | wfx_snw_dyn_1d(ji) = wfx_snw_dyn_1d(ji) + ( rhos * vsrdg(ji) * ( 1._wp - rn_fsnwrdg ) & ! fresh water source for ocean |
|---|
| 582 | & + rhos * vsrft(ji) * ( 1._wp - rn_fsnwrft ) ) * r1_rdtice |
|---|
| 583 | |
|---|
| 584 | ! Put the melt pond water into the ocean |
|---|
| 585 | ! clem: I think the following lines must be commented since there |
|---|
| 586 | ! is no net mass flux between melt ponds and the ocean (see icethd_pnd.F90 for ex.) |
|---|
| 587 | !IF ( ln_pnd_fwb ) THEN |
|---|
| 588 | ! wfx_pnd_1d(ji) = wfx_pnd_1d(ji) + ( rhow * vprdg(ji) * ( 1._wp - rn_fpndrdg ) & ! fresh water source for ocean |
|---|
| 589 | ! & + rhow * vprft(ji) * ( 1._wp - rn_fpndrft ) ) * r1_rdtice |
|---|
| 590 | !ENDIF |
|---|
| 591 | |
|---|
| 592 | ! virtual salt flux to keep salinity constant |
|---|
| 593 | IF( nn_icesal /= 2 ) THEN |
|---|
| 594 | sirdg2(ji) = sirdg2(ji) - vsw * ( sss_1d(ji) - s_i_1d(ji) ) ! ridge salinity = s_i |
|---|
| 595 | sfx_bri_1d(ji) = sfx_bri_1d(ji) + sss_1d(ji) * vsw * rhoi * r1_rdtice & ! put back sss_m into the ocean |
|---|
| 596 | & - s_i_1d(ji) * vsw * rhoi * r1_rdtice ! and get s_i from the ocean |
|---|
| 597 | ENDIF |
|---|
| 598 | |
|---|
| 599 | ! Remove area, volume of new ridge to each category jl1 |
|---|
| 600 | !------------------------------------------------------ |
|---|
| 601 | a_i_2d (ji,jl1) = a_i_2d (ji,jl1) - airdg1 - airft1 |
|---|
| 602 | v_i_2d (ji,jl1) = v_i_2d (ji,jl1) - virdg1 - virft(ji) |
|---|
| 603 | v_s_2d (ji,jl1) = v_s_2d (ji,jl1) - vsrdg(ji) - vsrft(ji) |
|---|
| 604 | sv_i_2d(ji,jl1) = sv_i_2d(ji,jl1) - sirdg1 - sirft(ji) |
|---|
| 605 | oa_i_2d(ji,jl1) = oa_i_2d(ji,jl1) - oirdg1 - oirft1 |
|---|
| 606 | IF ( ln_pnd_H12 ) THEN |
|---|
| 607 | a_ip_2d(ji,jl1) = a_ip_2d(ji,jl1) - aprdg1 - aprft1 |
|---|
| 608 | v_ip_2d(ji,jl1) = v_ip_2d(ji,jl1) - vprdg(ji) - vprft(ji) |
|---|
| 609 | ENDIF |
|---|
| 610 | ENDIF |
|---|
| 611 | |
|---|
| 612 | END DO ! ji |
|---|
| 613 | |
|---|
| 614 | ! special loop for e_s because of layers jk |
|---|
| 615 | DO jk = 1, nlay_s |
|---|
| 616 | DO ji = 1, npti |
|---|
| 617 | IF( apartf(ji,jl1) > 0._wp .AND. closing_gross(ji) > 0._wp ) THEN |
|---|
| 618 | ! Compute ridging /rafting fractions |
|---|
| 619 | afrdg = aridge(ji,jl1) * closing_gross(ji) * rdt_ice * z1_ai(ji) |
|---|
| 620 | afrft = araft (ji,jl1) * closing_gross(ji) * rdt_ice * z1_ai(ji) |
|---|
| 621 | ! Compute ridging /rafting ice and new ridges for es |
|---|
| 622 | esrdg(ji,jk) = ze_s_2d (ji,jk,jl1) * afrdg |
|---|
| 623 | esrft(ji,jk) = ze_s_2d (ji,jk,jl1) * afrft |
|---|
| 624 | ! Put the snow lost by ridging into the ocean |
|---|
| 625 | hfx_dyn_1d(ji) = hfx_dyn_1d(ji) + ( - esrdg(ji,jk) * ( 1._wp - rn_fsnwrdg ) & ! heat sink for ocean (<0, W.m-2) |
|---|
| 626 | & - esrft(ji,jk) * ( 1._wp - rn_fsnwrft ) ) * r1_rdtice |
|---|
| 627 | ! |
|---|
| 628 | ! Remove energy of new ridge to each category jl1 |
|---|
| 629 | !------------------------------------------------- |
|---|
| 630 | ze_s_2d(ji,jk,jl1) = ze_s_2d(ji,jk,jl1) * ( 1._wp - afrdg - afrft ) |
|---|
| 631 | ENDIF |
|---|
| 632 | END DO |
|---|
| 633 | END DO |
|---|
| 634 | |
|---|
| 635 | ! special loop for e_i because of layers jk |
|---|
| 636 | DO jk = 1, nlay_i |
|---|
| 637 | DO ji = 1, npti |
|---|
| 638 | IF( apartf(ji,jl1) > 0._wp .AND. closing_gross(ji) > 0._wp ) THEN |
|---|
| 639 | ! Compute ridging /rafting fractions |
|---|
| 640 | afrdg = aridge(ji,jl1) * closing_gross(ji) * rdt_ice * z1_ai(ji) |
|---|
| 641 | afrft = araft (ji,jl1) * closing_gross(ji) * rdt_ice * z1_ai(ji) |
|---|
| 642 | ! Compute ridging ice and new ridges for ei |
|---|
| 643 | eirdg(ji,jk) = ze_i_2d (ji,jk,jl1) * afrdg + ersw(ji) * r1_nlay_i |
|---|
| 644 | eirft(ji,jk) = ze_i_2d (ji,jk,jl1) * afrft |
|---|
| 645 | ! |
|---|
| 646 | ! Remove energy of new ridge to each category jl1 |
|---|
| 647 | !------------------------------------------------- |
|---|
| 648 | ze_i_2d(ji,jk,jl1) = ze_i_2d(ji,jk,jl1) * ( 1._wp - afrdg - afrft ) |
|---|
| 649 | ENDIF |
|---|
| 650 | END DO |
|---|
| 651 | END DO |
|---|
| 652 | |
|---|
| 653 | ! 3) compute categories in which ice is added (jl2) |
|---|
| 654 | !-------------------------------------------------- |
|---|
| 655 | itest_rdg(1:npti) = 0 |
|---|
| 656 | itest_rft(1:npti) = 0 |
|---|
| 657 | DO jl2 = 1, jpl |
|---|
| 658 | ! |
|---|
| 659 | DO ji = 1, npti |
|---|
| 660 | |
|---|
| 661 | IF( apartf(ji,jl1) > 0._wp .AND. closing_gross(ji) > 0._wp ) THEN |
|---|
| 662 | |
|---|
| 663 | ! Compute the fraction of ridged ice area and volume going to thickness category jl2 |
|---|
| 664 | IF( hrmin(ji,jl1) <= hi_max(jl2) .AND. hrmax(ji,jl1) > hi_max(jl2-1) ) THEN |
|---|
| 665 | hL = MAX( hrmin(ji,jl1), hi_max(jl2-1) ) |
|---|
| 666 | hR = MIN( hrmax(ji,jl1), hi_max(jl2) ) |
|---|
| 667 | farea = ( hR - hL ) / ( hrmax(ji,jl1) - hrmin(ji,jl1) ) |
|---|
| 668 | fvol(ji) = ( hR * hR - hL * hL ) / ( hrmax(ji,jl1) * hrmax(ji,jl1) - hrmin(ji,jl1) * hrmin(ji,jl1) ) |
|---|
| 669 | ! |
|---|
| 670 | itest_rdg(ji) = 1 ! test for conservation |
|---|
| 671 | ELSE |
|---|
| 672 | farea = 0._wp |
|---|
| 673 | fvol(ji) = 0._wp |
|---|
| 674 | ENDIF |
|---|
| 675 | |
|---|
| 676 | ! Compute the fraction of rafted ice area and volume going to thickness category jl2 |
|---|
| 677 | IF( hraft(ji,jl1) <= hi_max(jl2) .AND. hraft(ji,jl1) > hi_max(jl2-1) ) THEN |
|---|
| 678 | zswitch(ji) = 1._wp |
|---|
| 679 | ! |
|---|
| 680 | itest_rft(ji) = 1 ! test for conservation |
|---|
| 681 | ELSE |
|---|
| 682 | zswitch(ji) = 0._wp |
|---|
| 683 | ENDIF |
|---|
| 684 | ! |
|---|
| 685 | ! Patch to ensure perfect conservation if ice thickness goes mad |
|---|
| 686 | ! Sometimes thickness is larger than hi_max(jpl) because of advection scheme (for very small areas) |
|---|
| 687 | ! Then ice volume is removed from one category but the ridging/rafting scheme |
|---|
| 688 | ! does not know where to move it, leading to a conservation issue. |
|---|
| 689 | IF( itest_rdg(ji) == 0 .AND. jl2 == jpl ) THEN ; farea = 1._wp ; fvol(ji) = 1._wp ; ENDIF |
|---|
| 690 | IF( itest_rft(ji) == 0 .AND. jl2 == jpl ) zswitch(ji) = 1._wp |
|---|
| 691 | ! |
|---|
| 692 | ! Add area, volume of new ridge to category jl2 |
|---|
| 693 | !---------------------------------------------- |
|---|
| 694 | a_i_2d (ji,jl2) = a_i_2d (ji,jl2) + ( airdg2(ji) * farea + airft2(ji) * zswitch(ji) ) |
|---|
| 695 | oa_i_2d(ji,jl2) = oa_i_2d(ji,jl2) + ( oirdg2(ji) * farea + oirft2(ji) * zswitch(ji) ) |
|---|
| 696 | v_i_2d (ji,jl2) = v_i_2d (ji,jl2) + ( virdg2(ji) * fvol(ji) + virft (ji) * zswitch(ji) ) |
|---|
| 697 | sv_i_2d(ji,jl2) = sv_i_2d(ji,jl2) + ( sirdg2(ji) * fvol(ji) + sirft (ji) * zswitch(ji) ) |
|---|
| 698 | v_s_2d (ji,jl2) = v_s_2d (ji,jl2) + ( vsrdg (ji) * rn_fsnwrdg * fvol(ji) + & |
|---|
| 699 | & vsrft (ji) * rn_fsnwrft * zswitch(ji) ) |
|---|
| 700 | IF ( ln_pnd_H12 ) THEN |
|---|
| 701 | v_ip_2d (ji,jl2) = v_ip_2d(ji,jl2) + ( vprdg (ji) * rn_fpndrdg * fvol (ji) & |
|---|
| 702 | & + vprft (ji) * rn_fpndrft * zswitch(ji) ) |
|---|
| 703 | a_ip_2d (ji,jl2) = a_ip_2d(ji,jl2) + ( aprdg2(ji) * rn_fpndrdg * farea & |
|---|
| 704 | & + aprft2(ji) * rn_fpndrft * zswitch(ji) ) |
|---|
| 705 | ENDIF |
|---|
| 706 | |
|---|
| 707 | ENDIF |
|---|
| 708 | |
|---|
| 709 | END DO |
|---|
| 710 | ! Add snow energy of new ridge to category jl2 |
|---|
| 711 | !--------------------------------------------- |
|---|
| 712 | DO jk = 1, nlay_s |
|---|
| 713 | DO ji = 1, npti |
|---|
| 714 | IF( apartf(ji,jl1) > 0._wp .AND. closing_gross(ji) > 0._wp ) & |
|---|
| 715 | & ze_s_2d(ji,jk,jl2) = ze_s_2d(ji,jk,jl2) + ( esrdg(ji,jk) * rn_fsnwrdg * fvol(ji) + & |
|---|
| 716 | & esrft(ji,jk) * rn_fsnwrft * zswitch(ji) ) |
|---|
| 717 | END DO |
|---|
| 718 | END DO |
|---|
| 719 | ! Add ice energy of new ridge to category jl2 |
|---|
| 720 | !-------------------------------------------- |
|---|
| 721 | DO jk = 1, nlay_i |
|---|
| 722 | DO ji = 1, npti |
|---|
| 723 | IF( apartf(ji,jl1) > 0._wp .AND. closing_gross(ji) > 0._wp ) & |
|---|
| 724 | & ze_i_2d(ji,jk,jl2) = ze_i_2d(ji,jk,jl2) + eirdg(ji,jk) * fvol(ji) + eirft(ji,jk) * zswitch(ji) |
|---|
| 725 | END DO |
|---|
| 726 | END DO |
|---|
| 727 | ! |
|---|
| 728 | END DO ! jl2 |
|---|
| 729 | ! |
|---|
| 730 | END DO ! jl1 |
|---|
| 731 | ! |
|---|
| 732 | ! In case ridging/rafting lead to very small negative values (sometimes it happens) |
|---|
| 733 | WHERE( a_i_2d(1:npti,:) < 0._wp ) a_i_2d(1:npti,:) = 0._wp |
|---|
| 734 | WHERE( v_i_2d(1:npti,:) < 0._wp ) v_i_2d(1:npti,:) = 0._wp |
|---|
| 735 | ! |
|---|
| 736 | END SUBROUTINE rdgrft_shift |
|---|
| 737 | |
|---|
| 738 | |
|---|
| 739 | SUBROUTINE ice_strength |
|---|
| 740 | !!---------------------------------------------------------------------- |
|---|
| 741 | !! *** ROUTINE ice_strength *** |
|---|
| 742 | !! |
|---|
| 743 | !! ** Purpose : computes ice strength used in dynamics routines of ice thickness |
|---|
| 744 | !! |
|---|
| 745 | !! ** Method : Compute the strength of the ice pack, defined as the energy (J m-2) |
|---|
| 746 | !! dissipated per unit area removed from the ice pack under compression, |
|---|
| 747 | !! and assumed proportional to the change in potential energy caused |
|---|
| 748 | !! by ridging. Note that only Hibler's formulation is stable and that |
|---|
| 749 | !! ice strength has to be smoothed |
|---|
| 750 | !!---------------------------------------------------------------------- |
|---|
| 751 | INTEGER :: ji, jj, jl ! dummy loop indices |
|---|
| 752 | INTEGER :: ismooth ! smoothing the resistance to deformation |
|---|
| 753 | INTEGER :: itframe ! number of time steps for the P smoothing |
|---|
| 754 | REAL(wp) :: zp, z1_3 ! local scalars |
|---|
| 755 | REAL(wp), DIMENSION(jpi,jpj) :: zworka ! temporary array used here |
|---|
| 756 | REAL(wp), DIMENSION(jpi,jpj) :: zstrp1, zstrp2 ! strength at previous time steps |
|---|
| 757 | !!---------------------------------------------------------------------- |
|---|
| 758 | ! !--------------------------------------------------! |
|---|
| 759 | IF( ln_str_H79 ) THEN ! Ice strength => Hibler (1979) method ! |
|---|
| 760 | ! !--------------------------------------------------! |
|---|
| 761 | strength(:,:) = rn_pstar * SUM( v_i(:,:,:), dim=3 ) * EXP( -rn_crhg * ( 1._wp - SUM( a_i(:,:,:), dim=3 ) ) ) |
|---|
| 762 | ismooth = 1 |
|---|
| 763 | ! !--------------------------------------------------! |
|---|
| 764 | ELSE ! Zero strength ! |
|---|
| 765 | ! !--------------------------------------------------! |
|---|
| 766 | strength(:,:) = 0._wp |
|---|
| 767 | ismooth = 0 |
|---|
| 768 | ENDIF |
|---|
| 769 | ! !--------------------------------------------------! |
|---|
| 770 | SELECT CASE( ismooth ) ! Smoothing ice strength ! |
|---|
| 771 | ! !--------------------------------------------------! |
|---|
| 772 | CASE( 1 ) !--- Spatial smoothing |
|---|
| 773 | DO jj = 2, jpjm1 |
|---|
| 774 | DO ji = 2, jpim1 |
|---|
| 775 | IF ( SUM( a_i(ji,jj,:) ) > 0._wp ) THEN |
|---|
| 776 | zworka(ji,jj) = ( 4.0 * strength(ji,jj) & |
|---|
| 777 | & + strength(ji-1,jj) * tmask(ji-1,jj,1) + strength(ji+1,jj) * tmask(ji+1,jj,1) & |
|---|
| 778 | & + strength(ji,jj-1) * tmask(ji,jj-1,1) + strength(ji,jj+1) * tmask(ji,jj+1,1) & |
|---|
| 779 | & ) / ( 4.0 + tmask(ji-1,jj,1) + tmask(ji+1,jj,1) + tmask(ji,jj-1,1) + tmask(ji,jj+1,1) ) |
|---|
| 780 | ELSE |
|---|
| 781 | zworka(ji,jj) = 0._wp |
|---|
| 782 | ENDIF |
|---|
| 783 | END DO |
|---|
| 784 | END DO |
|---|
| 785 | |
|---|
| 786 | DO jj = 2, jpjm1 |
|---|
| 787 | DO ji = 2, jpim1 |
|---|
| 788 | strength(ji,jj) = zworka(ji,jj) |
|---|
| 789 | END DO |
|---|
| 790 | END DO |
|---|
| 791 | CALL lbc_lnk( strength, 'T', 1. ) |
|---|
| 792 | ! |
|---|
| 793 | CASE( 2 ) !--- Temporal smoothing |
|---|
| 794 | IF ( kt_ice == nit000 ) THEN |
|---|
| 795 | zstrp1(:,:) = 0._wp |
|---|
| 796 | zstrp2(:,:) = 0._wp |
|---|
| 797 | ENDIF |
|---|
| 798 | ! |
|---|
| 799 | DO jj = 2, jpjm1 |
|---|
| 800 | DO ji = 2, jpim1 |
|---|
| 801 | IF ( SUM( a_i(ji,jj,:) ) > 0._wp ) THEN |
|---|
| 802 | itframe = 1 ! number of time steps for the running mean |
|---|
| 803 | IF ( zstrp1(ji,jj) > 0._wp ) itframe = itframe + 1 |
|---|
| 804 | IF ( zstrp2(ji,jj) > 0._wp ) itframe = itframe + 1 |
|---|
| 805 | zp = ( strength(ji,jj) + zstrp1(ji,jj) + zstrp2(ji,jj) ) / itframe |
|---|
| 806 | zstrp2 (ji,jj) = zstrp1 (ji,jj) |
|---|
| 807 | zstrp1 (ji,jj) = strength(ji,jj) |
|---|
| 808 | strength(ji,jj) = zp |
|---|
| 809 | ENDIF |
|---|
| 810 | END DO |
|---|
| 811 | END DO |
|---|
| 812 | CALL lbc_lnk( strength, 'T', 1. ) |
|---|
| 813 | ! |
|---|
| 814 | END SELECT |
|---|
| 815 | ! |
|---|
| 816 | END SUBROUTINE ice_strength |
|---|
| 817 | |
|---|
| 818 | |
|---|
| 819 | SUBROUTINE ice_dyn_1d2d( kn ) |
|---|
| 820 | !!----------------------------------------------------------------------- |
|---|
| 821 | !! *** ROUTINE ice_dyn_1d2d *** |
|---|
| 822 | !! |
|---|
| 823 | !! ** Purpose : move arrays from 1d to 2d and the reverse |
|---|
| 824 | !!----------------------------------------------------------------------- |
|---|
| 825 | INTEGER, INTENT(in) :: kn ! 1= from 2D to 1D ; 2= from 1D to 2D |
|---|
| 826 | ! |
|---|
| 827 | INTEGER :: jl, jk ! dummy loop indices |
|---|
| 828 | !!----------------------------------------------------------------------- |
|---|
| 829 | ! |
|---|
| 830 | SELECT CASE( kn ) |
|---|
| 831 | ! !---------------------! |
|---|
| 832 | CASE( 1 ) !== from 2D to 1D ==! |
|---|
| 833 | ! !---------------------! |
|---|
| 834 | ! fields used but not modified |
|---|
| 835 | CALL tab_2d_1d( npti, nptidx(1:npti), sss_1d(1:npti), sss_m(:,:) ) |
|---|
| 836 | CALL tab_2d_1d( npti, nptidx(1:npti), sst_1d(1:npti), sst_m(:,:) ) |
|---|
| 837 | ! the following fields are modified in this routine |
|---|
| 838 | !!CALL tab_2d_1d( npti, nptidx(1:npti), ato_i_1d(1:npti), ato_i(:,:) ) |
|---|
| 839 | !!CALL tab_3d_2d( npti, nptidx(1:npti), a_i_2d(1:npti,1:jpl), a_i(:,:,:) ) |
|---|
| 840 | !!CALL tab_3d_2d( npti, nptidx(1:npti), v_i_2d (1:npti,1:jpl), v_i (:,:,:) ) |
|---|
| 841 | CALL tab_3d_2d( npti, nptidx(1:npti), v_s_2d (1:npti,1:jpl), v_s (:,:,:) ) |
|---|
| 842 | CALL tab_3d_2d( npti, nptidx(1:npti), sv_i_2d(1:npti,1:jpl), sv_i(:,:,:) ) |
|---|
| 843 | CALL tab_3d_2d( npti, nptidx(1:npti), oa_i_2d(1:npti,1:jpl), oa_i(:,:,:) ) |
|---|
| 844 | CALL tab_3d_2d( npti, nptidx(1:npti), a_ip_2d(1:npti,1:jpl), a_ip(:,:,:) ) |
|---|
| 845 | CALL tab_3d_2d( npti, nptidx(1:npti), v_ip_2d(1:npti,1:jpl), v_ip(:,:,:) ) |
|---|
| 846 | DO jl = 1, jpl |
|---|
| 847 | DO jk = 1, nlay_s |
|---|
| 848 | CALL tab_2d_1d( npti, nptidx(1:npti), ze_s_2d(1:npti,jk,jl), e_s(:,:,jk,jl) ) |
|---|
| 849 | END DO |
|---|
| 850 | DO jk = 1, nlay_i |
|---|
| 851 | CALL tab_2d_1d( npti, nptidx(1:npti), ze_i_2d(1:npti,jk,jl), e_i(:,:,jk,jl) ) |
|---|
| 852 | END DO |
|---|
| 853 | END DO |
|---|
| 854 | CALL tab_2d_1d( npti, nptidx(1:npti), sfx_dyn_1d (1:npti), sfx_dyn (:,:) ) |
|---|
| 855 | CALL tab_2d_1d( npti, nptidx(1:npti), sfx_bri_1d (1:npti), sfx_bri (:,:) ) |
|---|
| 856 | CALL tab_2d_1d( npti, nptidx(1:npti), wfx_dyn_1d (1:npti), wfx_dyn (:,:) ) |
|---|
| 857 | CALL tab_2d_1d( npti, nptidx(1:npti), hfx_dyn_1d (1:npti), hfx_dyn (:,:) ) |
|---|
| 858 | CALL tab_2d_1d( npti, nptidx(1:npti), wfx_snw_dyn_1d(1:npti), wfx_snw_dyn(:,:) ) |
|---|
| 859 | CALL tab_2d_1d( npti, nptidx(1:npti), wfx_pnd_1d(1:npti), wfx_pnd(:,:) ) |
|---|
| 860 | |
|---|
| 861 | ! !---------------------! |
|---|
| 862 | CASE( 2 ) !== from 1D to 2D ==! |
|---|
| 863 | ! !---------------------! |
|---|
| 864 | CALL tab_1d_2d( npti, nptidx(1:npti), ato_i_1d(1:npti), ato_i(:,:) ) |
|---|
| 865 | CALL tab_2d_3d( npti, nptidx(1:npti), a_i_2d (1:npti,1:jpl), a_i (:,:,:) ) |
|---|
| 866 | CALL tab_2d_3d( npti, nptidx(1:npti), v_i_2d (1:npti,1:jpl), v_i (:,:,:) ) |
|---|
| 867 | CALL tab_2d_3d( npti, nptidx(1:npti), v_s_2d (1:npti,1:jpl), v_s (:,:,:) ) |
|---|
| 868 | CALL tab_2d_3d( npti, nptidx(1:npti), sv_i_2d(1:npti,1:jpl), sv_i(:,:,:) ) |
|---|
| 869 | CALL tab_2d_3d( npti, nptidx(1:npti), oa_i_2d(1:npti,1:jpl), oa_i(:,:,:) ) |
|---|
| 870 | CALL tab_2d_3d( npti, nptidx(1:npti), a_ip_2d(1:npti,1:jpl), a_ip(:,:,:) ) |
|---|
| 871 | CALL tab_2d_3d( npti, nptidx(1:npti), v_ip_2d(1:npti,1:jpl), v_ip(:,:,:) ) |
|---|
| 872 | DO jl = 1, jpl |
|---|
| 873 | DO jk = 1, nlay_s |
|---|
| 874 | CALL tab_1d_2d( npti, nptidx(1:npti), ze_s_2d(1:npti,jk,jl), e_s(:,:,jk,jl) ) |
|---|
| 875 | END DO |
|---|
| 876 | DO jk = 1, nlay_i |
|---|
| 877 | CALL tab_1d_2d( npti, nptidx(1:npti), ze_i_2d(1:npti,jk,jl), e_i(:,:,jk,jl) ) |
|---|
| 878 | END DO |
|---|
| 879 | END DO |
|---|
| 880 | CALL tab_1d_2d( npti, nptidx(1:npti), sfx_dyn_1d (1:npti), sfx_dyn (:,:) ) |
|---|
| 881 | CALL tab_1d_2d( npti, nptidx(1:npti), sfx_bri_1d (1:npti), sfx_bri (:,:) ) |
|---|
| 882 | CALL tab_1d_2d( npti, nptidx(1:npti), wfx_dyn_1d (1:npti), wfx_dyn (:,:) ) |
|---|
| 883 | CALL tab_1d_2d( npti, nptidx(1:npti), hfx_dyn_1d (1:npti), hfx_dyn (:,:) ) |
|---|
| 884 | CALL tab_1d_2d( npti, nptidx(1:npti), wfx_snw_dyn_1d(1:npti), wfx_snw_dyn(:,:) ) |
|---|
| 885 | CALL tab_1d_2d( npti, nptidx(1:npti), wfx_pnd_1d(1:npti), wfx_pnd(:,:) ) |
|---|
| 886 | ! |
|---|
| 887 | END SELECT |
|---|
| 888 | ! |
|---|
| 889 | END SUBROUTINE ice_dyn_1d2d |
|---|
| 890 | |
|---|
| 891 | |
|---|
| 892 | SUBROUTINE ice_dyn_rdgrft_init |
|---|
| 893 | !!------------------------------------------------------------------- |
|---|
| 894 | !! *** ROUTINE ice_dyn_rdgrft_init *** |
|---|
| 895 | !! |
|---|
| 896 | !! ** Purpose : Physical constants and parameters linked |
|---|
| 897 | !! to the mechanical ice redistribution |
|---|
| 898 | !! |
|---|
| 899 | !! ** Method : Read the namdyn_rdgrft namelist |
|---|
| 900 | !! and check the parameters values |
|---|
| 901 | !! called at the first timestep (nit000) |
|---|
| 902 | !! |
|---|
| 903 | !! ** input : Namelist namdyn_rdgrft |
|---|
| 904 | !!------------------------------------------------------------------- |
|---|
| 905 | INTEGER :: ios ! Local integer output status for namelist read |
|---|
| 906 | !! |
|---|
| 907 | NAMELIST/namdyn_rdgrft/ ln_str_H79, rn_pstar, rn_crhg, & |
|---|
| 908 | & rn_csrdg , & |
|---|
| 909 | & ln_partf_lin, rn_gstar, & |
|---|
| 910 | & ln_partf_exp, rn_astar, & |
|---|
| 911 | & ln_ridging, rn_hstar, rn_porordg, rn_fsnwrdg, rn_fpndrdg, & |
|---|
| 912 | & ln_rafting, rn_hraft, rn_craft , rn_fsnwrft, rn_fpndrft |
|---|
| 913 | !!------------------------------------------------------------------- |
|---|
| 914 | ! |
|---|
| 915 | REWIND( numnam_ice_ref ) ! Namelist namicetdme in reference namelist : Ice mechanical ice redistribution |
|---|
| 916 | READ ( numnam_ice_ref, namdyn_rdgrft, IOSTAT = ios, ERR = 901) |
|---|
| 917 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_rdgrft in reference namelist', lwp ) |
|---|
| 918 | REWIND( numnam_ice_cfg ) ! Namelist namdyn_rdgrft in configuration namelist : Ice mechanical ice redistribution |
|---|
| 919 | READ ( numnam_ice_cfg, namdyn_rdgrft, IOSTAT = ios, ERR = 902 ) |
|---|
| 920 | 902 IF( ios > 0 ) CALL ctl_nam ( ios , 'namdyn_rdgrft in configuration namelist', lwp ) |
|---|
| 921 | IF(lwm) WRITE ( numoni, namdyn_rdgrft ) |
|---|
| 922 | ! |
|---|
| 923 | IF (lwp) THEN ! control print |
|---|
| 924 | WRITE(numout,*) |
|---|
| 925 | WRITE(numout,*) 'ice_dyn_rdgrft_init: ice parameters for ridging/rafting ' |
|---|
| 926 | WRITE(numout,*) '~~~~~~~~~~~~~~~~~~' |
|---|
| 927 | WRITE(numout,*) ' Namelist namdyn_rdgrft:' |
|---|
| 928 | WRITE(numout,*) ' ice strength parameterization Hibler (1979) ln_str_H79 = ', ln_str_H79 |
|---|
| 929 | WRITE(numout,*) ' 1st bulk-rheology parameter rn_pstar = ', rn_pstar |
|---|
| 930 | WRITE(numout,*) ' 2nd bulk-rhelogy parameter rn_crhg = ', rn_crhg |
|---|
| 931 | WRITE(numout,*) ' Fraction of shear energy contributing to ridging rn_csrdg = ', rn_csrdg |
|---|
| 932 | WRITE(numout,*) ' linear ridging participation function ln_partf_lin = ', ln_partf_lin |
|---|
| 933 | WRITE(numout,*) ' Fraction of ice coverage contributing to ridging rn_gstar = ', rn_gstar |
|---|
| 934 | WRITE(numout,*) ' Exponential ridging participation function ln_partf_exp = ', ln_partf_exp |
|---|
| 935 | WRITE(numout,*) ' Equivalent to G* for an exponential function rn_astar = ', rn_astar |
|---|
| 936 | WRITE(numout,*) ' Ridging of ice sheets or not ln_ridging = ', ln_ridging |
|---|
| 937 | WRITE(numout,*) ' max ridged ice thickness rn_hstar = ', rn_hstar |
|---|
| 938 | WRITE(numout,*) ' Initial porosity of ridges rn_porordg = ', rn_porordg |
|---|
| 939 | WRITE(numout,*) ' Fraction of snow volume conserved during ridging rn_fsnwrdg = ', rn_fsnwrdg |
|---|
| 940 | WRITE(numout,*) ' Fraction of pond volume conserved during ridging rn_fpndrdg = ', rn_fpndrdg |
|---|
| 941 | WRITE(numout,*) ' Rafting of ice sheets or not ln_rafting = ', ln_rafting |
|---|
| 942 | WRITE(numout,*) ' Parmeter thickness (threshold between ridge-raft) rn_hraft = ', rn_hraft |
|---|
| 943 | WRITE(numout,*) ' Rafting hyperbolic tangent coefficient rn_craft = ', rn_craft |
|---|
| 944 | WRITE(numout,*) ' Fraction of snow volume conserved during rafting rn_fsnwrft = ', rn_fsnwrft |
|---|
| 945 | WRITE(numout,*) ' Fraction of pond volume conserved during rafting rn_fpndrft = ', rn_fpndrft |
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| 946 | ENDIF |
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| 947 | ! |
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| 948 | IF ( ( ln_partf_lin .AND. ln_partf_exp ) .OR. ( .NOT.ln_partf_lin .AND. .NOT.ln_partf_exp ) ) THEN |
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| 949 | CALL ctl_stop( 'ice_dyn_rdgrft_init: choose one and only one participation function (ln_partf_lin or ln_partf_exp)' ) |
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| 950 | ENDIF |
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| 951 | ! ! allocate tke arrays |
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| 952 | IF( ice_dyn_rdgrft_alloc() /= 0 ) CALL ctl_stop( 'STOP', 'ice_dyn_rdgrft_init: unable to allocate arrays' ) |
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| 953 | ! |
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| 954 | END SUBROUTINE ice_dyn_rdgrft_init |
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| 955 | |
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| 956 | #else |
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| 957 | !!---------------------------------------------------------------------- |
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| 958 | !! Default option Empty module NO SI3 sea-ice model |
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| 959 | !!---------------------------------------------------------------------- |
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| 960 | #endif |
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| 961 | |
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| 962 | !!====================================================================== |
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| 963 | END MODULE icedyn_rdgrft |
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