[825] | 1 | MODULE limitd_me |
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| 2 | |
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| 3 | #if defined key_lim3 |
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[834] | 4 | !!---------------------------------------------------------------------- |
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| 5 | !! 'key_lim3' : LIM3 sea-ice model |
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| 6 | !!---------------------------------------------------------------------- |
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| 7 | !! |
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[825] | 8 | !!====================================================================== |
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| 9 | !! *** MODULE limitd_me *** |
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| 10 | !! Mechanical impact on ice thickness distribution |
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| 11 | !! computation of changes in g(h) |
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| 12 | !!====================================================================== |
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[834] | 13 | !! |
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[825] | 14 | !!---------------------------------------------------------------------- |
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| 15 | !! * Modules used |
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| 16 | USE dom_ice |
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| 17 | USE par_oce ! ocean parameters |
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| 18 | USE dom_oce |
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| 19 | USE lbclnk |
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| 20 | USE phycst ! physical constants (ocean directory) |
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| 21 | USE ice_oce ! ice variables |
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| 22 | USE thd_ice |
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| 23 | USE limistate |
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| 24 | USE in_out_manager |
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| 25 | USE ice |
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| 26 | USE par_ice |
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| 27 | USE limthd_lac |
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| 28 | USE limvar |
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| 29 | USE iceini |
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| 30 | USE limcons |
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| 31 | USE prtctl ! Print control |
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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 | !! * Routine accessibility |
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| 37 | PUBLIC lim_itd_me ! called by ice_stp |
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| 38 | PUBLIC lim_itd_me_icestrength |
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| 39 | PUBLIC lim_itd_me_ridgeprep |
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| 40 | PUBLIC lim_itd_me_ridgeshift |
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| 41 | PUBLIC lim_itd_me_asumr |
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| 42 | PUBLIC lim_itd_me_init |
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| 43 | PUBLIC lim_itd_me_zapsmall |
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| 44 | |
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| 45 | !! * Module variables |
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| 46 | REAL(wp) :: & ! constant values |
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| 47 | epsi20 = 1e-20 , & |
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| 48 | epsi13 = 1e-13 , & |
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| 49 | epsi11 = 1e-11 , & |
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| 50 | zzero = 0.e0 , & |
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| 51 | zone = 1.e0 |
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| 52 | |
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| 53 | !----------------------------------------------------------------------- |
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| 54 | ! Variables shared among ridging subroutines |
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| 55 | !----------------------------------------------------------------------- |
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| 56 | REAL(wp), DIMENSION (jpi,jpj) :: & |
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| 57 | asum , & ! sum of total ice and open water area |
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| 58 | aksum ! ratio of area removed to area ridged |
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| 59 | |
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| 60 | REAL(wp), DIMENSION(jpi,jpj,0:jpl) :: & |
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| 61 | athorn ! participation function; fraction of ridging/ |
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| 62 | ! closing associated w/ category n |
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| 63 | |
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| 64 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: & |
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| 65 | hrmin , & ! minimum ridge thickness |
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| 66 | hrmax , & ! maximum ridge thickness |
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| 67 | hraft , & ! thickness of rafted ice |
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| 68 | krdg , & ! mean ridge thickness/thickness of ridging ice |
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| 69 | aridge , & ! participating ice ridging |
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| 70 | araft ! participating ice rafting |
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| 71 | |
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| 72 | REAL(wp), PARAMETER :: & |
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| 73 | krdgmin = 1.1, & ! min ridge thickness multiplier |
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| 74 | kraft = 2.0 ! rafting multipliyer |
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| 75 | |
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| 76 | REAL(wp) :: & |
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| 77 | Cp |
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| 78 | ! |
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| 79 | !----------------------------------------------------------------------- |
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[834] | 80 | ! Ridging diagnostic arrays for history files |
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[825] | 81 | !----------------------------------------------------------------------- |
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| 82 | ! |
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| 83 | REAL (wp), DIMENSION(jpi,jpj) :: & |
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| 84 | dardg1dt , & ! rate of fractional area loss by ridging ice (1/s) |
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| 85 | dardg2dt , & ! rate of fractional area gain by new ridges (1/s) |
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| 86 | dvirdgdt , & ! rate of ice volume ridged (m/s) |
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| 87 | opening ! rate of opening due to divergence/shear (1/s) |
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| 88 | |
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| 89 | |
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| 90 | !!---------------------------------------------------------------------- |
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[834] | 91 | !! LIM-@ 3.0, UCL-ASTR (2008) |
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[825] | 92 | !! (c) UCL-ASTR and Martin Vancoppenolle |
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| 93 | !!---------------------------------------------------------------------- |
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| 94 | |
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| 95 | CONTAINS |
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| 96 | |
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| 97 | !!-----------------------------------------------------------------------------! |
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| 98 | !!-----------------------------------------------------------------------------! |
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| 99 | |
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| 100 | SUBROUTINE lim_itd_me ! (subroutine 1/6) |
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| 101 | !!---------------------------------------------------------------------! |
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| 102 | !! *** ROUTINE lim_itd_me *** |
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| 103 | !! ** Purpose : |
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| 104 | !! This routine computes the mechanical redistribution |
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| 105 | !! of ice thickness |
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| 106 | !! |
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| 107 | !! ** Method : a very simple method :-) |
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| 108 | !! |
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| 109 | !! ** Arguments : |
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| 110 | !! kideb , kiut : Starting and ending points on which the |
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| 111 | !! the computation is applied |
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| 112 | !! |
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| 113 | !! ** Inputs / Ouputs : (global commons) |
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| 114 | !! |
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| 115 | !! ** External : |
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| 116 | !! |
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[834] | 117 | !! ** Steps : |
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| 118 | !! 1) Thickness categories boundaries, ice / o.w. concentrations |
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| 119 | !! Ridge preparation |
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| 120 | !! 2) Dynamical inputs (closing rate, divu_adv, opning) |
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| 121 | !! 3) Ridging iteration |
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| 122 | !! 4) Ridging diagnostics |
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| 123 | !! 5) Heat, salt and freshwater fluxes |
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| 124 | !! 6) Compute increments of tate variables and come back to old values |
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| 125 | !! |
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[825] | 126 | !! ** References : There are a lot of references and can be difficult / |
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| 127 | !! boring to read |
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| 128 | !! |
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| 129 | !! Flato, G. M., and W. D. Hibler III, 1995: Ridging and strength |
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| 130 | !! in modeling the thickness distribution of Arctic sea ice, |
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| 131 | !! J. Geophys. Res., 100, 18,611-18,626. |
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| 132 | !! |
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| 133 | !! Hibler, W. D. III, 1980: Modeling a variable thickness sea ice |
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| 134 | !! cover, Mon. Wea. Rev., 108, 1943-1973, 1980. |
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| 135 | !! |
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| 136 | !! Rothrock, D. A., 1975: The energetics of the plastic deformation of |
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| 137 | !! pack ice by ridging, J. Geophys. Res., 80, 4514-4519. |
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| 138 | !! |
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| 139 | !! Thorndike, A. S., D. A. Rothrock, G. A. Maykut, and R. Colony, |
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| 140 | !! 1975: The thickness distribution of sea ice, J. Geophys. Res., |
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| 141 | !! 80, 4501-4513. |
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| 142 | !! |
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| 143 | !! Bitz et al., JGR 2001 |
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| 144 | !! |
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| 145 | !! Amundrud and Melling, JGR 2005 |
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| 146 | !! |
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| 147 | !! Babko et al., JGR 2002 |
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| 148 | !! |
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| 149 | !! ** History : |
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[834] | 150 | !! This routine is based on CICE code |
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| 151 | !! and authors William H. Lipscomb, |
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| 152 | !! and Elizabeth C. Hunke, LANL |
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| 153 | !! are gratefully acknowledged |
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[825] | 154 | !! |
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| 155 | !! (02-2006) Martin Vancoppenolle, UCL-ASTR |
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| 156 | !! |
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| 157 | !!--------------------------------------------------------------------! |
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| 158 | !! * Arguments |
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| 159 | |
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[834] | 160 | !! * Local variables |
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| 161 | INTEGER :: ji, & ! spatial dummy loop index |
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| 162 | jj, & ! spatial dummy loop index |
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| 163 | jk, & ! vertical layering dummy loop index |
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| 164 | jl, & ! ice category dummy loop index |
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| 165 | niter, & ! iteration counter |
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| 166 | nitermax = 20 ! max number of ridging iterations |
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[825] | 167 | |
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[834] | 168 | REAL(wp) :: & ! constant values |
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| 169 | zeps = 1.0e-10, & |
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| 170 | epsi10 = 1.0e-10, & |
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| 171 | epsi06 = 1.0e-6 |
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[825] | 172 | |
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[834] | 173 | REAL(wp), DIMENSION(jpi,jpj) :: & |
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| 174 | closing_net, & ! net rate at which area is removed (1/s) |
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| 175 | ! (ridging ice area - area of new ridges) / dt |
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| 176 | divu_adv , & ! divu as implied by transport scheme (1/s) |
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| 177 | opning , & ! rate of opening due to divergence/shear |
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| 178 | closing_gross, & ! rate at which area removed, not counting |
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| 179 | ! area of new ridges |
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| 180 | msnow_mlt , & ! mass of snow added to ocean (kg m-2) |
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| 181 | esnow_mlt ! energy needed to melt snow in ocean (J m-2) |
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[825] | 182 | |
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[834] | 183 | REAL(wp) :: & |
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| 184 | w1, & ! temporary variable |
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| 185 | tmpfac, & ! factor by which opening/closing rates are cut |
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| 186 | dti ! 1 / dt |
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[825] | 187 | |
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[834] | 188 | LOGICAL :: & |
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| 189 | iterate_ridging, & ! if true, repeat the ridging |
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| 190 | asum_error ! flag for asum .ne. 1 |
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[825] | 191 | |
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[834] | 192 | REAL(wp) :: & |
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| 193 | big = 1.0e8 |
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[825] | 194 | |
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[834] | 195 | REAL (wp), DIMENSION(jpi,jpj) :: & ! |
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| 196 | vt_i_init, vt_i_final ! ice volume summed over categories |
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[825] | 197 | |
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[834] | 198 | CHARACTER (len = 15) :: fieldid |
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[825] | 199 | |
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| 200 | !!-- End of declarations |
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| 201 | !-----------------------------------------------------------------------------! |
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| 202 | |
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| 203 | IF( numit == nstart ) CALL lim_itd_me_init ! Initialization (first time-step only) |
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| 204 | |
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| 205 | IF(ln_ctl) THEN |
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| 206 | CALL prt_ctl(tab2d_1=ato_i , clinfo1=' lim_itd_me: ato_i : ', tab2d_2=at_i , clinfo2=' at_i : ') |
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| 207 | CALL prt_ctl(tab2d_1=divu_i, clinfo1=' lim_itd_me: divu_i : ', tab2d_2=delta_i, clinfo2=' delta_i : ') |
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| 208 | ENDIF |
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| 209 | |
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| 210 | !-----------------------------------------------------------------------------! |
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| 211 | ! 1) Thickness categories boundaries, ice / o.w. concentrations, init_ons |
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| 212 | !-----------------------------------------------------------------------------! |
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| 213 | ! Set hi_max(ncat) to a big value to ensure that all ridged ice |
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| 214 | ! is thinner than hi_max(ncat). |
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[834] | 215 | |
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[862] | 216 | hi_max(jpl) = 999.99 |
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| 217 | |
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[825] | 218 | Cp = 0.5* grav * (rau0-rhoic)*rhoic/rau0 ! proport const for PE |
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[834] | 219 | CALL lim_itd_me_ridgeprep ! prepare ridging |
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[825] | 220 | |
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[834] | 221 | ! conservation check |
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| 222 | IF ( con_i) CALL lim_column_sum (jpl, v_i, vt_i_init) |
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[825] | 223 | |
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| 224 | ! Initialize arrays. |
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| 225 | DO jj = 1, jpj |
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| 226 | DO ji = 1, jpi |
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| 227 | |
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| 228 | msnow_mlt(ji,jj) = 0.0 |
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| 229 | esnow_mlt(ji,jj) = 0.0 |
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| 230 | dardg1dt(ji,jj) = 0.0 |
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| 231 | dardg2dt(ji,jj) = 0.0 |
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| 232 | dvirdgdt(ji,jj) = 0.0 |
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| 233 | opening (ji,jj) = 0.0 |
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| 234 | |
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| 235 | !-----------------------------------------------------------------------------! |
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| 236 | ! 2) Dynamical inputs (closing rate, divu_adv, opning) |
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| 237 | !-----------------------------------------------------------------------------! |
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| 238 | ! |
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| 239 | ! 2.1 closing_net |
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| 240 | !----------------- |
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| 241 | ! Compute the net rate of closing due to convergence |
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| 242 | ! and shear, based on Flato and Hibler (1995). |
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| 243 | ! |
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| 244 | ! The energy dissipation rate is equal to the net closing rate |
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| 245 | ! times the ice strength. |
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| 246 | ! |
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| 247 | ! NOTE: The NET closing rate is equal to the rate that open water |
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| 248 | ! area is removed, plus the rate at which ice area is removed by |
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| 249 | ! ridging, minus the rate at which area is added in new ridges. |
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| 250 | ! The GROSS closing rate is equal to the first two terms (open |
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| 251 | ! water closing and thin ice ridging) without the third term |
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| 252 | ! (thick, newly ridged ice). |
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| 253 | |
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| 254 | closing_net(ji,jj) = & |
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| 255 | Cs*0.5*(Delta_i(ji,jj)-ABS(divu_i(ji,jj))) - MIN(divu_i(ji,jj),0.0) |
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| 256 | |
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| 257 | ! 2.2 divu_adv |
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| 258 | !-------------- |
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| 259 | ! Compute divu_adv, the divergence rate given by the transport/ |
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| 260 | ! advection scheme, which may not be equal to divu as computed |
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| 261 | ! from the velocity field. |
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| 262 | ! |
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| 263 | ! If divu_adv < 0, make sure the closing rate is large enough |
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| 264 | ! to give asum = 1.0 after ridging. |
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| 265 | |
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| 266 | divu_adv(ji,jj) = (1.0-asum(ji,jj)) / rdt_ice ! asum found in ridgeprep |
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| 267 | |
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| 268 | IF (divu_adv(ji,jj) .LT. 0.0) & |
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| 269 | closing_net(ji,jj) = max(closing_net(ji,jj), -divu_adv(ji,jj)) |
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| 270 | |
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| 271 | ! 2.3 opning |
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| 272 | !------------ |
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| 273 | ! Compute the (non-negative) opening rate that will give |
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| 274 | ! asum = 1.0 after ridging. |
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| 275 | opning(ji,jj) = closing_net(ji,jj) + divu_adv(ji,jj) |
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| 276 | |
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| 277 | END DO |
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| 278 | END DO |
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| 279 | |
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| 280 | !-----------------------------------------------------------------------------! |
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| 281 | ! 3) Ridging iteration |
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| 282 | !-----------------------------------------------------------------------------! |
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| 283 | niter = 1 ! iteration counter |
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| 284 | iterate_ridging = .true. |
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| 285 | |
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| 286 | |
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| 287 | DO WHILE ( iterate_ridging .AND. niter < nitermax ) |
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| 288 | |
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| 289 | DO jj = 1, jpj |
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| 290 | DO ji = 1, jpi |
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| 291 | |
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| 292 | ! 3.2 closing_gross |
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| 293 | !-----------------------------------------------------------------------------! |
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| 294 | ! Based on the ITD of ridging and ridged ice, convert the net |
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| 295 | ! closing rate to a gross closing rate. |
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| 296 | ! NOTE: 0 < aksum <= 1 |
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| 297 | closing_gross(ji,jj) = closing_net(ji,jj) / aksum(ji,jj) |
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| 298 | |
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| 299 | ! correction to closing rate and opening if closing rate is excessive |
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| 300 | !--------------------------------------------------------------------- |
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| 301 | ! Reduce the closing rate if more than 100% of the open water |
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| 302 | ! would be removed. Reduce the opening rate proportionately. |
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| 303 | IF ( ato_i(ji,jj) .GT. epsi11 .AND. athorn(ji,jj,0) .GT. 0.0 ) THEN |
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| 304 | w1 = athorn(ji,jj,0) * closing_gross(ji,jj) * rdt_ice |
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| 305 | IF ( w1 .GT. ato_i(ji,jj)) THEN |
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| 306 | tmpfac = ato_i(ji,jj) / w1 |
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| 307 | closing_gross(ji,jj) = closing_gross(ji,jj) * tmpfac |
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| 308 | opning(ji,jj) = opning(ji,jj) * tmpfac |
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| 309 | ENDIF !w1 |
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| 310 | ENDIF !at0i and athorn |
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| 311 | |
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| 312 | END DO ! ji |
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| 313 | END DO ! jj |
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| 314 | |
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| 315 | ! correction to closing rate / opening if excessive ice removal |
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| 316 | !--------------------------------------------------------------- |
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| 317 | ! Reduce the closing rate if more than 100% of any ice category |
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| 318 | ! would be removed. Reduce the opening rate proportionately. |
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| 319 | |
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| 320 | DO jl = 1, jpl |
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| 321 | DO jj = 1, jpj |
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| 322 | DO ji = 1, jpi |
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| 323 | IF ( a_i(ji,jj,jl) .GT. epsi11 .AND. athorn(ji,jj,jl) .GT. 0.0 ) THEN |
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| 324 | w1 = athorn(ji,jj,jl) * closing_gross(ji,jj) * rdt_ice |
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| 325 | IF ( w1 .GT. a_i(ji,jj,jl) ) THEN |
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| 326 | tmpfac = a_i(ji,jj,jl) / w1 |
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| 327 | closing_gross(ji,jj) = closing_gross(ji,jj) * tmpfac |
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| 328 | opning(ji,jj) = opning(ji,jj) * tmpfac |
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| 329 | ENDIF |
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| 330 | ENDIF |
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| 331 | END DO !ji |
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| 332 | END DO ! jj |
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| 333 | END DO !jl |
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| 334 | |
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| 335 | ! 3.3 Redistribute area, volume, and energy. |
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| 336 | !-----------------------------------------------------------------------------! |
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| 337 | |
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| 338 | CALL lim_itd_me_ridgeshift (opning, closing_gross, & |
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| 339 | msnow_mlt, esnow_mlt) |
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| 340 | |
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| 341 | ! 3.4 Compute total area of ice plus open water after ridging. |
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| 342 | !-----------------------------------------------------------------------------! |
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| 343 | |
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| 344 | CALL lim_itd_me_asumr |
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| 345 | |
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| 346 | ! 3.5 Do we keep on iterating ??? |
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| 347 | !-----------------------------------------------------------------------------! |
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| 348 | ! Check whether asum = 1. If not (because the closing and opening |
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| 349 | ! rates were reduced above), ridge again with new rates. |
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| 350 | |
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| 351 | iterate_ridging = .false. |
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| 352 | |
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| 353 | DO jj = 1, jpj |
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| 354 | DO ji = 1, jpi |
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| 355 | IF (ABS(asum(ji,jj) - 1.0) .LT. epsi11) THEN |
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| 356 | closing_net(ji,jj) = 0.0 |
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| 357 | opning(ji,jj) = 0.0 |
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| 358 | ELSE |
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| 359 | iterate_ridging = .true. |
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| 360 | divu_adv(ji,jj) = (1.0 - asum(ji,jj)) / rdt_ice |
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| 361 | closing_net(ji,jj) = MAX(0.0, -divu_adv(ji,jj)) |
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| 362 | opning(ji,jj) = MAX(0.0, divu_adv(ji,jj)) |
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| 363 | ENDIF |
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| 364 | END DO |
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| 365 | END DO |
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| 366 | |
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| 367 | ! Repeat if necessary. |
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| 368 | ! NOTE: If strength smoothing is turned on, the ridging must be |
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| 369 | ! iterated globally because of the boundary update in the |
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| 370 | ! smoothing. |
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| 371 | |
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| 372 | niter = niter + 1 |
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| 373 | |
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| 374 | IF (iterate_ridging) THEN |
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| 375 | IF (niter .GT. nitermax) THEN |
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| 376 | WRITE(numout,*) ' ALERTE : non-converging ridging scheme ' |
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| 377 | WRITE(numout,*) ' niter, iterate_ridging ', niter, iterate_ridging |
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| 378 | ENDIF |
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| 379 | CALL lim_itd_me_ridgeprep |
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| 380 | ENDIF |
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| 381 | |
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| 382 | END DO !! on the do while over iter |
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| 383 | |
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| 384 | !-----------------------------------------------------------------------------! |
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| 385 | ! 4) Ridging diagnostics |
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| 386 | !-----------------------------------------------------------------------------! |
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| 387 | ! Convert ridging rate diagnostics to correct units. |
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| 388 | ! Update fresh water and heat fluxes due to snow melt. |
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| 389 | |
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| 390 | dti = 1.0/rdt_ice |
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| 391 | |
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| 392 | asum_error = .false. |
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| 393 | |
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| 394 | DO jj = 1, jpj |
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| 395 | DO ji = 1, jpi |
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| 396 | |
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| 397 | IF (ABS(asum(ji,jj) - 1.0) .GT. epsi11) asum_error = .true. |
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| 398 | |
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| 399 | dardg1dt(ji,jj) = dardg1dt(ji,jj) * dti |
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| 400 | dardg2dt(ji,jj) = dardg2dt(ji,jj) * dti |
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| 401 | dvirdgdt(ji,jj) = dvirdgdt(ji,jj) * dti |
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| 402 | opening (ji,jj) = opening (ji,jj) * dti |
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| 403 | |
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| 404 | !-----------------------------------------------------------------------------! |
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| 405 | ! 5) Heat, salt and freshwater fluxes |
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| 406 | !-----------------------------------------------------------------------------! |
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| 407 | ! fresh water source for ocean |
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[834] | 408 | fmmec(ji,jj) = fmmec(ji,jj) + msnow_mlt(ji,jj)*dti |
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[825] | 409 | |
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| 410 | ! heat sink for ocean |
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| 411 | fhmec(ji,jj) = fhmec(ji,jj) + esnow_mlt(ji,jj)*dti |
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| 412 | |
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| 413 | END DO |
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| 414 | END DO |
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| 415 | |
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| 416 | ! Check if there is a ridging error |
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| 417 | DO jj = 1, jpj |
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| 418 | DO ji = 1, jpi |
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| 419 | IF (ABS(asum(ji,jj) - 1.0) .GT. epsi11) THEN ! there is a bug |
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| 420 | WRITE(numout,*) ' ' |
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| 421 | WRITE(numout,*) ' ALERTE : Ridging error: total area = ', asum(ji,jj) |
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| 422 | WRITE(numout,*) ' limitd_me ' |
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| 423 | WRITE(numout,*) ' POINT : ', ji, jj |
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| 424 | WRITE(numout,*) ' jpl, a_i, athorn ' |
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| 425 | WRITE(numout,*) 0, ato_i(ji,jj), athorn(ji,jj,0) |
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| 426 | DO jl = 1, jpl |
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| 427 | WRITE(numout,*) jl, a_i(ji,jj,jl), athorn(ji,jj,jl) |
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| 428 | END DO |
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| 429 | ENDIF ! asum |
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| 430 | |
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| 431 | END DO !ji |
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| 432 | END DO !jj |
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| 433 | |
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| 434 | ! Conservation check |
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[834] | 435 | IF ( con_i ) THEN |
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| 436 | CALL lim_column_sum (jpl, v_i, vt_i_final) |
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| 437 | fieldid = ' v_i : limitd_me ' |
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| 438 | CALL lim_cons_check (vt_i_init, vt_i_final, 1.0e-6, fieldid) |
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| 439 | ENDIF |
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[825] | 440 | |
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| 441 | !-----------------------------------------------------------------------------! |
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| 442 | ! 6) Updating state variables and trend terms |
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| 443 | !-----------------------------------------------------------------------------! |
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| 444 | |
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[834] | 445 | CALL lim_var_glo2eqv |
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[825] | 446 | CALL lim_itd_me_zapsmall |
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| 447 | |
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| 448 | !----------------- |
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| 449 | ! Trend terms |
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| 450 | !----------------- |
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| 451 | |
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| 452 | d_u_ice_dyn(:,:) = u_ice(:,:) - old_u_ice(:,:) |
---|
| 453 | d_v_ice_dyn(:,:) = v_ice(:,:) - old_v_ice(:,:) |
---|
| 454 | d_a_i_trp(:,:,:) = a_i(:,:,:) - old_a_i(:,:,:) |
---|
| 455 | d_v_s_trp(:,:,:) = v_s(:,:,:) - old_v_s(:,:,:) |
---|
| 456 | d_v_i_trp(:,:,:) = v_i(:,:,:) - old_v_i(:,:,:) |
---|
| 457 | d_e_s_trp(:,:,:,:) = e_s(:,:,:,:) - old_e_s(:,:,:,:) |
---|
| 458 | d_e_i_trp(:,:,:,:) = e_i(:,:,:,:) - old_e_i(:,:,:,:) |
---|
| 459 | d_oa_i_trp(:,:,:) = oa_i(:,:,:) - old_oa_i(:,:,:) |
---|
| 460 | d_smv_i_trp(:,:,:) = 0.0 |
---|
| 461 | IF ( ( num_sal .EQ. 2 ) .OR. ( num_sal .EQ. 4 ) ) & |
---|
| 462 | d_smv_i_trp(:,:,:) = smv_i(:,:,:) - old_smv_i(:,:,:) |
---|
| 463 | |
---|
| 464 | !-------------------------! |
---|
| 465 | ! Back to initial values |
---|
| 466 | !-------------------------! |
---|
| 467 | |
---|
| 468 | ! update of fields will be made later in lim update |
---|
| 469 | u_ice(:,:) = old_u_ice(:,:) |
---|
| 470 | v_ice(:,:) = old_v_ice(:,:) |
---|
| 471 | a_i(:,:,:) = old_a_i(:,:,:) |
---|
| 472 | v_s(:,:,:) = old_v_s(:,:,:) |
---|
| 473 | v_i(:,:,:) = old_v_i(:,:,:) |
---|
| 474 | e_s(:,:,:,:) = old_e_s(:,:,:,:) |
---|
| 475 | e_i(:,:,:,:) = old_e_i(:,:,:,:) |
---|
| 476 | oa_i(:,:,:) = old_oa_i(:,:,:) |
---|
| 477 | IF ( ( num_sal .EQ. 2 ) .OR. ( num_sal .EQ. 4 ) ) & |
---|
| 478 | smv_i(:,:,:) = old_smv_i(:,:,:) |
---|
| 479 | |
---|
[863] | 480 | IF(ln_ctl) THEN ! Control print |
---|
| 481 | CALL prt_ctl(tab2d_1=area , clinfo1=' lim_itd_me : cell area :') |
---|
| 482 | CALL prt_ctl(tab2d_1=at_i , clinfo1=' lim_itd_me : at_i :') |
---|
| 483 | CALL prt_ctl(tab2d_1=vt_i , clinfo1=' lim_itd_me : vt_i :') |
---|
| 484 | CALL prt_ctl(tab2d_1=vt_s , clinfo1=' lim_itd_me : vt_s :') |
---|
| 485 | DO jl = 1, jpl |
---|
| 486 | CALL prt_ctl_info(' - Category : ', ivar1=jl) |
---|
| 487 | CALL prt_ctl_info(' ~~~~~~~~~~') |
---|
| 488 | CALL prt_ctl(tab2d_1=a_i (:,:,jl) , clinfo1= ' lim_itd_me : a_i : ') |
---|
| 489 | CALL prt_ctl(tab2d_1=ht_i (:,:,jl) , clinfo1= ' lim_itd_me : ht_i : ') |
---|
| 490 | CALL prt_ctl(tab2d_1=ht_s (:,:,jl) , clinfo1= ' lim_itd_me : ht_s : ') |
---|
| 491 | CALL prt_ctl(tab2d_1=v_i (:,:,jl) , clinfo1= ' lim_itd_me : v_i : ') |
---|
| 492 | CALL prt_ctl(tab2d_1=v_s (:,:,jl) , clinfo1= ' lim_itd_me : v_s : ') |
---|
| 493 | CALL prt_ctl(tab2d_1=e_s (:,:,1,jl) , clinfo1= ' lim_itd_me : e_s : ') |
---|
| 494 | CALL prt_ctl(tab2d_1=t_su (:,:,jl) , clinfo1= ' lim_itd_me : t_su : ') |
---|
| 495 | CALL prt_ctl(tab2d_1=t_s (:,:,1,jl) , clinfo1= ' lim_itd_me : t_snow : ') |
---|
| 496 | CALL prt_ctl(tab2d_1=sm_i (:,:,jl) , clinfo1= ' lim_itd_me : sm_i : ') |
---|
| 497 | CALL prt_ctl(tab2d_1=smv_i (:,:,jl) , clinfo1= ' lim_itd_me : smv_i : ') |
---|
| 498 | DO jk = 1, nlay_i |
---|
| 499 | CALL prt_ctl_info(' - Layer : ', ivar1=jk) |
---|
| 500 | CALL prt_ctl_info(' ~~~~~~~') |
---|
| 501 | CALL prt_ctl(tab2d_1=t_i(:,:,jk,jl) , clinfo1= ' lim_itd_me : t_i : ') |
---|
| 502 | CALL prt_ctl(tab2d_1=e_i(:,:,jk,jl) , clinfo1= ' lim_itd_me : e_i : ') |
---|
| 503 | END DO |
---|
| 504 | END DO |
---|
| 505 | ENDIF |
---|
[825] | 506 | |
---|
[863] | 507 | |
---|
[825] | 508 | !----------------------------------------------------! |
---|
| 509 | ! Advection of ice in a free cell, newly ridged ice |
---|
| 510 | !----------------------------------------------------! |
---|
| 511 | |
---|
| 512 | ! to allow for thermodynamics to melt new ice |
---|
| 513 | ! we immediately advect ice in free cells |
---|
| 514 | |
---|
| 515 | ! heat content has to be corrected before ice volume |
---|
| 516 | DO jl = 1, jpl |
---|
| 517 | DO jk = 1, nlay_i |
---|
| 518 | DO jj = 1, jpj |
---|
| 519 | DO ji = 1, jpi |
---|
| 520 | IF ( ( old_v_i(ji,jj,jl) .LT. epsi06 ) .AND. & |
---|
| 521 | ( d_v_i_trp(ji,jj,jl) .GT. epsi06 ) ) THEN |
---|
| 522 | old_e_i(ji,jj,jk,jl) = d_e_i_trp(ji,jj,jk,jl) |
---|
| 523 | d_e_i_trp(ji,jj,jk,jl) = 0.0 |
---|
| 524 | ENDIF |
---|
| 525 | END DO |
---|
| 526 | END DO |
---|
| 527 | END DO |
---|
| 528 | END DO |
---|
| 529 | |
---|
| 530 | DO jl = 1, jpl |
---|
| 531 | DO jj = 1, jpj |
---|
| 532 | DO ji = 1, jpi |
---|
| 533 | IF ( ( old_v_i(ji,jj,jl) .LT. epsi06 ) .AND. & |
---|
| 534 | ( d_v_i_trp(ji,jj,jl) .GT. epsi06 ) ) THEN |
---|
| 535 | old_v_i(ji,jj,jl) = d_v_i_trp(ji,jj,jl) |
---|
| 536 | d_v_i_trp(ji,jj,jl) = 0.0 |
---|
| 537 | old_a_i(ji,jj,jl) = d_a_i_trp(ji,jj,jl) |
---|
| 538 | d_a_i_trp(ji,jj,jl) = 0.0 |
---|
| 539 | old_v_s(ji,jj,jl) = d_v_s_trp(ji,jj,jl) |
---|
| 540 | d_v_s_trp(ji,jj,jl) = 0.0 |
---|
| 541 | old_e_s(ji,jj,1,jl) = d_e_s_trp(ji,jj,1,jl) |
---|
| 542 | d_e_s_trp(ji,jj,1,jl) = 0.0 |
---|
| 543 | old_oa_i(ji,jj,jl) = d_oa_i_trp(ji,jj,jl) |
---|
| 544 | d_oa_i_trp(ji,jj,jl) = 0.0 |
---|
| 545 | IF ( ( num_sal .EQ. 2 ) .OR. ( num_sal .EQ. 4 ) ) & |
---|
| 546 | old_smv_i(ji,jj,jl) = d_smv_i_trp(ji,jj,jl) |
---|
| 547 | d_smv_i_trp(ji,jj,jl) = 0.0 |
---|
| 548 | ENDIF |
---|
| 549 | END DO |
---|
| 550 | END DO |
---|
| 551 | END DO |
---|
| 552 | |
---|
| 553 | END SUBROUTINE lim_itd_me |
---|
| 554 | |
---|
| 555 | !=============================================================================== |
---|
| 556 | |
---|
| 557 | SUBROUTINE lim_itd_me_icestrength (kstrngth) ! (subroutine 2/6) |
---|
| 558 | |
---|
[834] | 559 | !!---------------------------------------------------------------------- |
---|
[825] | 560 | !! *** ROUTINE lim_itd_me_icestrength *** |
---|
| 561 | !! ** Purpose : |
---|
| 562 | !! This routine computes ice strength used in dynamics routines |
---|
| 563 | !! of ice thickness |
---|
| 564 | !! |
---|
| 565 | !! ** Method : |
---|
| 566 | !! Compute the strength of the ice pack, defined as the energy (J m-2) |
---|
| 567 | !! dissipated per unit area removed from the ice pack under compression, |
---|
| 568 | !! and assumed proportional to the change in potential energy caused |
---|
[834] | 569 | !! by ridging. Note that only Hibler's formulation is stable and that |
---|
| 570 | !! ice strength has to be smoothed |
---|
[825] | 571 | !! |
---|
| 572 | !! ** Inputs / Ouputs : kstrngth (what kind of ice strength we are using) |
---|
| 573 | !! |
---|
| 574 | !! ** External : |
---|
| 575 | !! |
---|
[834] | 576 | !! ** References : |
---|
| 577 | !! |
---|
| 578 | !!---------------------------------------------------------------------- |
---|
[825] | 579 | !! * Arguments |
---|
| 580 | |
---|
| 581 | INTEGER, INTENT(in) :: & |
---|
| 582 | kstrngth ! = 1 for Rothrock formulation, 0 for Hibler (1979) |
---|
| 583 | |
---|
| 584 | INTEGER :: & |
---|
| 585 | ji,jj, & !: horizontal indices |
---|
| 586 | jl, & !: thickness category index |
---|
| 587 | ksmooth, & !: smoothing the resistance to deformation |
---|
| 588 | numts_rm !: number of time steps for the P smoothing |
---|
| 589 | |
---|
| 590 | REAL(wp) :: & |
---|
| 591 | hi, & !: ice thickness (m) |
---|
| 592 | zw1, & !: temporary variable |
---|
| 593 | zp, & !: temporary ice strength |
---|
| 594 | zdummy |
---|
| 595 | |
---|
| 596 | REAL(wp), DIMENSION(jpi,jpj) :: & |
---|
| 597 | zworka !: temporary array used here |
---|
| 598 | |
---|
| 599 | !------------------------------------------------------------------------------! |
---|
| 600 | ! 1) Initialize |
---|
| 601 | !------------------------------------------------------------------------------! |
---|
| 602 | strength(:,:) = 0.0 |
---|
| 603 | |
---|
| 604 | !------------------------------------------------------------------------------! |
---|
| 605 | ! 2) Compute thickness distribution of ridging and ridged ice |
---|
| 606 | !------------------------------------------------------------------------------! |
---|
| 607 | CALL lim_itd_me_ridgeprep |
---|
| 608 | |
---|
| 609 | !------------------------------------------------------------------------------! |
---|
| 610 | ! 3) Rothrock(1975)'s method |
---|
| 611 | !------------------------------------------------------------------------------! |
---|
| 612 | IF (kstrngth == 1) then |
---|
| 613 | |
---|
| 614 | DO jl = 1, jpl |
---|
| 615 | DO jj= 1, jpj |
---|
| 616 | DO ji = 1, jpi |
---|
| 617 | |
---|
| 618 | IF & |
---|
| 619 | ( ( a_i(ji,jj,jl) .GT. epsi11 ) & |
---|
| 620 | .AND. ( athorn(ji,jj,jl) .GT. 0.0 ) ) THEN |
---|
| 621 | hi = v_i(ji,jj,jl) / a_i(ji,jj,jl) |
---|
| 622 | !---------------------------- |
---|
| 623 | ! PE loss from deforming ice |
---|
| 624 | !---------------------------- |
---|
| 625 | strength(ji,jj) = strength(ji,jj) - athorn(ji,jj,jl) * & |
---|
| 626 | hi * hi |
---|
| 627 | |
---|
| 628 | !-------------------------- |
---|
| 629 | ! PE gain from rafting ice |
---|
| 630 | !-------------------------- |
---|
| 631 | strength(ji,jj) = strength(ji,jj) + 2.0 * araft(ji,jj,jl) & |
---|
| 632 | * hi * hi |
---|
| 633 | |
---|
| 634 | !---------------------------- |
---|
| 635 | ! PE gain from ridging ice |
---|
| 636 | !---------------------------- |
---|
| 637 | strength(ji,jj) = strength(ji,jj) & |
---|
| 638 | + aridge(ji,jj,jl)/krdg(ji,jj,jl) & |
---|
| 639 | * 1.0/3.0 * (hrmax(ji,jj,jl)**3 - hrmin(ji,jj,jl)**3) & |
---|
| 640 | / (hrmax(ji,jj,jl)-hrmin(ji,jj,jl)) |
---|
| 641 | ENDIF ! aicen > epsi11 |
---|
| 642 | |
---|
| 643 | END DO ! ji |
---|
| 644 | END DO !jj |
---|
| 645 | END DO !jl |
---|
| 646 | |
---|
| 647 | DO jj = 1, jpj |
---|
| 648 | DO ji = 1, jpi |
---|
| 649 | strength(ji,jj) = Cf * Cp * strength(ji,jj) / aksum(ji,jj) |
---|
| 650 | ! Cp = (g/2)*(rhow-rhoi)*(rhoi/rhow) |
---|
| 651 | ! Cf accounts for frictional dissipation |
---|
| 652 | |
---|
| 653 | END DO ! j |
---|
| 654 | END DO ! i |
---|
| 655 | |
---|
| 656 | ksmooth = 1 |
---|
| 657 | |
---|
| 658 | !------------------------------------------------------------------------------! |
---|
| 659 | ! 4) Hibler (1979)' method |
---|
| 660 | !------------------------------------------------------------------------------! |
---|
| 661 | ELSE ! kstrngth ne 1: Hibler (1979) form |
---|
| 662 | |
---|
| 663 | DO jj = 1, jpj |
---|
| 664 | DO ji = 1, jpi |
---|
| 665 | strength(ji,jj) = Pstar*vt_i(ji,jj)*exp(-C_rhg*(1.0-at_i(ji,jj))) |
---|
| 666 | END DO ! j |
---|
| 667 | END DO ! i |
---|
| 668 | |
---|
| 669 | ksmooth = 1 |
---|
| 670 | |
---|
| 671 | ENDIF ! kstrngth |
---|
| 672 | |
---|
| 673 | ! |
---|
| 674 | !------------------------------------------------------------------------------! |
---|
| 675 | ! 5) Impact of brine volume |
---|
| 676 | !------------------------------------------------------------------------------! |
---|
[834] | 677 | ! CAN BE REMOVED |
---|
[825] | 678 | ! |
---|
| 679 | IF ( brinstren_swi .EQ. 1 ) THEN |
---|
| 680 | |
---|
| 681 | DO jj = 1, jpj |
---|
| 682 | DO ji = 1, jpi |
---|
| 683 | IF ( bv_i(ji,jj) .GT. 0.0 ) THEN |
---|
| 684 | zdummy = MIN ( bv_i(ji,jj), 0.10 ) * MIN( bv_i(ji,jj), 0.10 ) |
---|
| 685 | ELSE |
---|
| 686 | zdummy = 0.0 |
---|
| 687 | ENDIF |
---|
| 688 | strength(ji,jj) = strength(ji,jj) * exp(-5.88*SQRT(MAX(bv_i(ji,jj),0.0))) |
---|
| 689 | END DO ! j |
---|
| 690 | END DO ! i |
---|
| 691 | |
---|
| 692 | ENDIF |
---|
| 693 | |
---|
| 694 | ! |
---|
| 695 | !------------------------------------------------------------------------------! |
---|
| 696 | ! 6) Smoothing ice strength |
---|
| 697 | !------------------------------------------------------------------------------! |
---|
| 698 | ! |
---|
| 699 | !------------------- |
---|
| 700 | ! Spatial smoothing |
---|
| 701 | !------------------- |
---|
| 702 | IF ( ksmooth .EQ. 1 ) THEN |
---|
| 703 | |
---|
| 704 | CALL lbc_lnk( strength, 'T', 1. ) |
---|
| 705 | |
---|
| 706 | DO jj = 1, jpj - 1 |
---|
| 707 | DO ji = 1, jpi - 1 |
---|
| 708 | IF ( ( asum(ji,jj) - ato_i(ji,jj) ) .GT. epsi11) THEN ! ice is |
---|
| 709 | ! present |
---|
| 710 | zworka(ji,jj) = 4.0 * strength(ji,jj) & |
---|
| 711 | + strength(ji-1,jj) * tms(ji-1,jj) & |
---|
| 712 | + strength(ji+1,jj) * tms(ji+1,jj) & |
---|
| 713 | + strength(ji,jj-1) * tms(ji,jj-1) & |
---|
| 714 | + strength(ji,jj+1) * tms(ji,jj+1) |
---|
| 715 | |
---|
| 716 | zw1 = 4.0 + tms(ji-1,jj) + tms(ji+1,jj) & |
---|
| 717 | + tms(ji,jj-1) + tms(ji,jj+1) |
---|
| 718 | zworka(ji,jj) = zworka(ji,jj) / zw1 |
---|
| 719 | ELSE |
---|
| 720 | zworka(ji,jj) = 0.0 |
---|
| 721 | ENDIF |
---|
| 722 | END DO |
---|
| 723 | END DO |
---|
| 724 | |
---|
| 725 | DO jj = 1, jpj - 1 |
---|
| 726 | DO ji = 1, jpi - 1 |
---|
| 727 | strength(ji,jj) = zworka(ji,jj) |
---|
| 728 | END DO |
---|
| 729 | END DO |
---|
| 730 | |
---|
| 731 | ENDIF ! ksmooth |
---|
| 732 | |
---|
| 733 | !-------------------- |
---|
| 734 | ! Temporal smoothing |
---|
| 735 | !-------------------- |
---|
| 736 | IF ( numit .EQ. nit000 + nfice - 1 ) THEN |
---|
| 737 | strp1(:,:) = 0.0 |
---|
| 738 | strp2(:,:) = 0.0 |
---|
| 739 | ENDIF |
---|
| 740 | |
---|
| 741 | IF ( ksmooth .EQ. 2 ) THEN |
---|
| 742 | |
---|
| 743 | |
---|
| 744 | CALL lbc_lnk( strength, 'T', 1. ) |
---|
| 745 | |
---|
| 746 | DO jj = 1, jpj - 1 |
---|
| 747 | DO ji = 1, jpi - 1 |
---|
| 748 | IF ( ( asum(ji,jj) - ato_i(ji,jj) ) .GT. epsi11) THEN ! ice is |
---|
| 749 | ! present |
---|
| 750 | numts_rm = 1 ! number of time steps for the running mean |
---|
| 751 | IF ( strp1(ji,jj) .GT. 0.0 ) numts_rm = numts_rm + 1 |
---|
| 752 | IF ( strp2(ji,jj) .GT. 0.0 ) numts_rm = numts_rm + 1 |
---|
| 753 | zp = ( strength(ji,jj) + strp1(ji,jj) + strp2(ji,jj) ) / & |
---|
| 754 | numts_rm |
---|
| 755 | strp2(ji,jj) = strp1(ji,jj) |
---|
| 756 | strp1(ji,jj) = strength(ji,jj) |
---|
| 757 | strength(ji,jj) = zp |
---|
| 758 | |
---|
| 759 | ENDIF |
---|
| 760 | END DO |
---|
| 761 | END DO |
---|
| 762 | |
---|
| 763 | ENDIF ! ksmooth |
---|
| 764 | |
---|
| 765 | ! Boundary conditions |
---|
| 766 | CALL lbc_lnk( strength, 'T', 1. ) |
---|
| 767 | |
---|
| 768 | END SUBROUTINE lim_itd_me_icestrength |
---|
| 769 | |
---|
| 770 | !=============================================================================== |
---|
| 771 | |
---|
| 772 | SUBROUTINE lim_itd_me_ridgeprep !(subroutine 3/6) |
---|
| 773 | |
---|
| 774 | !!---------------------------------------------------------------------! |
---|
| 775 | !! *** ROUTINE lim_itd_me_ridgeprep *** |
---|
| 776 | !! ** Purpose : |
---|
| 777 | !! preparation for ridging and strength calculations |
---|
| 778 | !! |
---|
| 779 | !! ** Method : |
---|
| 780 | !! Compute the thickness distribution of the ice and open water |
---|
| 781 | !! participating in ridging and of the resulting ridges. |
---|
| 782 | !! |
---|
| 783 | !! ** Arguments : |
---|
| 784 | !! |
---|
| 785 | !! ** External : |
---|
| 786 | !! |
---|
| 787 | !!---------------------------------------------------------------------! |
---|
| 788 | !! * Arguments |
---|
| 789 | |
---|
| 790 | INTEGER :: & |
---|
| 791 | ji,jj, & ! horizontal indices |
---|
[834] | 792 | jl, & ! thickness category index |
---|
[825] | 793 | krdg_index ! which participation function using |
---|
| 794 | |
---|
| 795 | REAL(wp) :: & |
---|
| 796 | Gstari, & ! = 1.0/Gstar |
---|
| 797 | astari ! = 1.0/astar |
---|
| 798 | |
---|
| 799 | REAL(wp), DIMENSION(jpi,jpj,-1:jpl) :: & |
---|
| 800 | Gsum ! Gsum(n) = sum of areas in categories 0 to n |
---|
| 801 | |
---|
| 802 | REAL(wp) :: & |
---|
| 803 | hi, & ! ice thickness for each cat (m) |
---|
| 804 | hrmean ! mean ridge thickness (m) |
---|
| 805 | |
---|
| 806 | REAL(wp), DIMENSION(jpi,jpj) :: & |
---|
| 807 | zworka ! temporary array used here |
---|
| 808 | |
---|
| 809 | REAL(wp) :: & |
---|
[834] | 810 | zdummy, & |
---|
[825] | 811 | epsi06 = 1.0e-6 |
---|
| 812 | |
---|
| 813 | !------------------------------------------------------------------------------! |
---|
| 814 | |
---|
| 815 | Gstari = 1.0/Gstar |
---|
| 816 | astari = 1.0/astar |
---|
| 817 | aksum(:,:) = 0.0 |
---|
| 818 | athorn(:,:,:) = 0.0 |
---|
| 819 | aridge(:,:,:) = 0.0 |
---|
| 820 | araft (:,:,:) = 0.0 |
---|
| 821 | hrmin(:,:,:) = 0.0 |
---|
| 822 | hrmax(:,:,:) = 0.0 |
---|
| 823 | hraft(:,:,:) = 0.0 |
---|
| 824 | krdg (:,:,:) = 1.0 |
---|
| 825 | |
---|
| 826 | ! ! Zero out categories with very small areas |
---|
| 827 | CALL lim_itd_me_zapsmall |
---|
| 828 | |
---|
| 829 | !------------------------------------------------------------------------------! |
---|
| 830 | ! 1) Participation function |
---|
| 831 | !------------------------------------------------------------------------------! |
---|
| 832 | |
---|
| 833 | ! Compute total area of ice plus open water. |
---|
| 834 | CALL lim_itd_me_asumr |
---|
| 835 | ! This is in general not equal to one |
---|
| 836 | ! because of divergence during transport |
---|
| 837 | |
---|
| 838 | ! Compute cumulative thickness distribution function |
---|
| 839 | ! Compute the cumulative thickness distribution function Gsum, |
---|
| 840 | ! where Gsum(n) is the fractional area in categories 0 to n. |
---|
| 841 | ! initial value (in h = 0) equals open water area |
---|
| 842 | |
---|
| 843 | Gsum(:,:,-1) = 0.0 |
---|
| 844 | |
---|
| 845 | DO jj = 1, jpj |
---|
| 846 | DO ji = 1, jpi |
---|
| 847 | IF (ato_i(ji,jj) .GT. epsi11) THEN |
---|
| 848 | Gsum(ji,jj,0) = ato_i(ji,jj) |
---|
| 849 | ELSE |
---|
| 850 | Gsum(ji,jj,0) = 0.0 |
---|
| 851 | ENDIF |
---|
| 852 | END DO |
---|
| 853 | END DO |
---|
| 854 | |
---|
| 855 | ! for each value of h, you have to add ice concentration then |
---|
| 856 | DO jl = 1, jpl |
---|
| 857 | DO jj = 1, jpj |
---|
| 858 | DO ji = 1, jpi |
---|
| 859 | IF ( a_i(ji,jj,jl) .GT. epsi11 ) THEN |
---|
| 860 | Gsum(ji,jj,jl) = Gsum(ji,jj,jl-1) + a_i(ji,jj,jl) |
---|
| 861 | ELSE |
---|
| 862 | Gsum(ji,jj,jl) = Gsum(ji,jj,jl-1) |
---|
| 863 | ENDIF |
---|
| 864 | END DO |
---|
| 865 | END DO |
---|
| 866 | END DO |
---|
| 867 | |
---|
| 868 | ! Normalize the cumulative distribution to 1 |
---|
| 869 | DO jj = 1, jpj |
---|
| 870 | DO ji = 1, jpi |
---|
| 871 | zworka(ji,jj) = 1.0 / Gsum(ji,jj,jpl) |
---|
| 872 | END DO |
---|
| 873 | END DO |
---|
| 874 | |
---|
| 875 | DO jl = 0, jpl |
---|
| 876 | DO jj = 1, jpj |
---|
| 877 | DO ji = 1, jpi |
---|
| 878 | Gsum(ji,jj,jl) = Gsum(ji,jj,jl) * zworka(ji,jj) |
---|
| 879 | END DO |
---|
| 880 | END DO |
---|
| 881 | END DO |
---|
| 882 | |
---|
| 883 | ! 1.3 Compute participation function a(h) = b(h).g(h) (athorn) |
---|
| 884 | !-------------------------------------------------------------------------------------------------- |
---|
| 885 | ! Compute the participation function athorn; this is analogous to |
---|
| 886 | ! a(h) = b(h)g(h) as defined in Thorndike et al. (1975). |
---|
| 887 | ! area lost from category n due to ridging/closing |
---|
| 888 | ! athorn(n) = total area lost due to ridging/closing |
---|
| 889 | ! assume b(h) = (2/Gstar) * (1 - G(h)/Gstar). |
---|
| 890 | ! |
---|
| 891 | ! The expressions for athorn are found by integrating b(h)g(h) between |
---|
| 892 | ! the category boundaries. |
---|
| 893 | !----------------------------------------------------------------- |
---|
| 894 | |
---|
| 895 | krdg_index = 1 |
---|
| 896 | |
---|
| 897 | IF ( krdg_index .EQ. 0 ) THEN |
---|
| 898 | |
---|
| 899 | !--- Linear formulation (Thorndike et al., 1975) |
---|
| 900 | DO jl = 0, ice_cat_bounds(1,2) ! only undeformed ice participates |
---|
| 901 | DO jj = 1, jpj |
---|
| 902 | DO ji = 1, jpi |
---|
| 903 | IF (Gsum(ji,jj,jl) < Gstar) THEN |
---|
| 904 | athorn(ji,jj,jl) = Gstari * (Gsum(ji,jj,jl)-Gsum(ji,jj,jl-1)) * & |
---|
| 905 | (2.0 - (Gsum(ji,jj,jl-1)+Gsum(ji,jj,jl))*Gstari) |
---|
| 906 | ELSEIF (Gsum(ji,jj,jl-1) < Gstar) THEN |
---|
| 907 | athorn(ji,jj,jl) = Gstari * (Gstar-Gsum(ji,jj,jl-1)) * & |
---|
| 908 | (2.0 - (Gsum(ji,jj,jl-1)+Gstar)*Gstari) |
---|
| 909 | ELSE |
---|
| 910 | athorn(ji,jj,jl) = 0.0 |
---|
| 911 | ENDIF |
---|
| 912 | END DO ! ji |
---|
| 913 | END DO ! jj |
---|
| 914 | END DO ! jl |
---|
| 915 | |
---|
| 916 | ELSE ! krdg_index = 1 |
---|
| 917 | |
---|
| 918 | !--- Exponential, more stable formulation (Lipscomb et al, 2007) |
---|
| 919 | ! precompute exponential terms using Gsum as a work array |
---|
| 920 | zdummy = 1.0 / (1.0-EXP(-astari)) |
---|
| 921 | |
---|
| 922 | DO jl = -1, jpl |
---|
| 923 | DO jj = 1, jpj |
---|
| 924 | DO ji = 1, jpi |
---|
| 925 | Gsum(ji,jj,jl) = EXP(-Gsum(ji,jj,jl)*astari)*zdummy |
---|
| 926 | END DO !ji |
---|
| 927 | END DO !jj |
---|
| 928 | END DO !jl |
---|
| 929 | |
---|
| 930 | ! compute athorn |
---|
| 931 | DO jl = 0, ice_cat_bounds(1,2) |
---|
| 932 | DO jj = 1, jpj |
---|
| 933 | DO ji = 1, jpi |
---|
| 934 | athorn(ji,jj,jl) = Gsum(ji,jj,jl-1) - Gsum(ji,jj,jl) |
---|
| 935 | END DO !ji |
---|
| 936 | END DO ! jj |
---|
| 937 | END DO !jl |
---|
| 938 | |
---|
| 939 | ENDIF ! krdg_index |
---|
| 940 | |
---|
| 941 | ! Ridging and rafting ice participation functions |
---|
| 942 | IF ( raftswi .EQ. 1 ) THEN |
---|
| 943 | |
---|
| 944 | DO jl = 1, jpl |
---|
| 945 | DO jj = 1, jpj |
---|
| 946 | DO ji = 1, jpi |
---|
| 947 | IF ( athorn(ji,jj,jl) .GT. 0.0 ) THEN |
---|
| 948 | aridge(ji,jj,jl) = ( TANH ( Craft * ( ht_i(ji,jj,jl) - & |
---|
| 949 | hparmeter ) ) + 1.0 ) / 2.0 * & |
---|
| 950 | athorn(ji,jj,jl) |
---|
| 951 | araft (ji,jj,jl) = ( TANH ( - Craft * ( ht_i(ji,jj,jl) - & |
---|
| 952 | hparmeter ) ) + 1.0 ) / 2.0 * & |
---|
| 953 | athorn(ji,jj,jl) |
---|
| 954 | IF ( araft(ji,jj,jl) .LT. epsi06 ) araft(ji,jj,jl) = 0.0 |
---|
| 955 | aridge(ji,jj,jl) = MAX( athorn(ji,jj,jl) - araft(ji,jj,jl), 0.0) |
---|
| 956 | ENDIF ! athorn |
---|
| 957 | END DO ! ji |
---|
| 958 | END DO ! jj |
---|
| 959 | END DO ! jl |
---|
| 960 | |
---|
| 961 | ELSE ! raftswi = 0 |
---|
| 962 | |
---|
| 963 | DO jl = 1, jpl |
---|
| 964 | DO jj = 1, jpj |
---|
| 965 | DO ji = 1, jpi |
---|
| 966 | aridge(ji,jj,jl) = 1.0*athorn(ji,jj,jl) |
---|
| 967 | END DO |
---|
| 968 | END DO |
---|
| 969 | END DO |
---|
| 970 | |
---|
| 971 | ENDIF |
---|
| 972 | |
---|
| 973 | IF ( raftswi .EQ. 1 ) THEN |
---|
| 974 | |
---|
| 975 | DO jl = 1, jpl |
---|
| 976 | DO jj = 1, jpj |
---|
| 977 | DO ji = 1, jpi |
---|
| 978 | IF ( aridge(ji,jj,jl) + araft(ji,jj,jl) - athorn(ji,jj,jl) .GT. & |
---|
| 979 | epsi11 ) THEN |
---|
| 980 | WRITE(numout,*) ' ALERTE 96 : wrong participation function ... ' |
---|
| 981 | WRITE(numout,*) ' ji, jj, jl : ', ji, jj, jl |
---|
| 982 | WRITE(numout,*) ' lat, lon : ', gphit(ji,jj), glamt(ji,jj) |
---|
| 983 | WRITE(numout,*) ' aridge : ', aridge(ji,jj,1:jpl) |
---|
| 984 | WRITE(numout,*) ' araft : ', araft(ji,jj,1:jpl) |
---|
| 985 | WRITE(numout,*) ' athorn : ', athorn(ji,jj,1:jpl) |
---|
| 986 | ENDIF |
---|
| 987 | END DO |
---|
| 988 | END DO |
---|
| 989 | END DO |
---|
| 990 | |
---|
| 991 | ENDIF |
---|
| 992 | |
---|
| 993 | !----------------------------------------------------------------- |
---|
| 994 | ! 2) Transfer function |
---|
| 995 | !----------------------------------------------------------------- |
---|
| 996 | ! Compute max and min ridged ice thickness for each ridging category. |
---|
| 997 | ! Assume ridged ice is uniformly distributed between hrmin and hrmax. |
---|
| 998 | ! |
---|
| 999 | ! This parameterization is a modified version of Hibler (1980). |
---|
| 1000 | ! The mean ridging thickness, hrmean, is proportional to hi^(0.5) |
---|
| 1001 | ! and for very thick ridging ice must be >= krdgmin*hi |
---|
| 1002 | ! |
---|
| 1003 | ! The minimum ridging thickness, hrmin, is equal to 2*hi |
---|
| 1004 | ! (i.e., rafting) and for very thick ridging ice is |
---|
| 1005 | ! constrained by hrmin <= (hrmean + hi)/2. |
---|
| 1006 | ! |
---|
| 1007 | ! The maximum ridging thickness, hrmax, is determined by |
---|
| 1008 | ! hrmean and hrmin. |
---|
| 1009 | ! |
---|
| 1010 | ! These modifications have the effect of reducing the ice strength |
---|
| 1011 | ! (relative to the Hibler formulation) when very thick ice is |
---|
| 1012 | ! ridging. |
---|
| 1013 | ! |
---|
| 1014 | ! aksum = net area removed/ total area removed |
---|
| 1015 | ! where total area removed = area of ice that ridges |
---|
| 1016 | ! net area removed = total area removed - area of new ridges |
---|
| 1017 | !----------------------------------------------------------------- |
---|
| 1018 | |
---|
| 1019 | ! Transfer function |
---|
| 1020 | DO jl = 1, jpl !all categories have a specific transfer function |
---|
| 1021 | DO jj = 1, jpj |
---|
| 1022 | DO ji = 1, jpi |
---|
| 1023 | |
---|
| 1024 | IF (a_i(ji,jj,jl) .GT. epsi11 .AND. athorn(ji,jj,jl) .GT. 0.0 ) THEN |
---|
| 1025 | hi = v_i(ji,jj,jl) / a_i(ji,jj,jl) |
---|
| 1026 | hrmean = MAX(SQRT(Hstar*hi), hi*krdgmin) |
---|
| 1027 | hrmin(ji,jj,jl) = MIN(2.0*hi, 0.5*(hrmean + hi)) |
---|
| 1028 | hrmax(ji,jj,jl) = 2.0*hrmean - hrmin(ji,jj,jl) |
---|
| 1029 | hraft(ji,jj,jl) = kraft*hi |
---|
| 1030 | krdg(ji,jj,jl) = hrmean / hi |
---|
| 1031 | ELSE |
---|
| 1032 | hraft(ji,jj,jl) = 0.0 |
---|
| 1033 | hrmin(ji,jj,jl) = 0.0 |
---|
| 1034 | hrmax(ji,jj,jl) = 0.0 |
---|
| 1035 | krdg (ji,jj,jl) = 1.0 |
---|
| 1036 | ENDIF |
---|
| 1037 | |
---|
| 1038 | END DO ! ji |
---|
| 1039 | END DO ! jj |
---|
| 1040 | END DO ! jl |
---|
| 1041 | |
---|
| 1042 | ! Normalization factor : aksum, ensures mass conservation |
---|
| 1043 | DO jj = 1, jpj |
---|
| 1044 | DO ji = 1, jpi |
---|
| 1045 | aksum(ji,jj) = athorn(ji,jj,0) |
---|
| 1046 | END DO |
---|
| 1047 | END DO |
---|
| 1048 | |
---|
| 1049 | DO jl = 1, jpl |
---|
| 1050 | DO jj = 1, jpj |
---|
| 1051 | DO ji = 1, jpi |
---|
| 1052 | aksum(ji,jj) = aksum(ji,jj) & |
---|
| 1053 | + aridge(ji,jj,jl) * (1.0 - 1.0/krdg(ji,jj,jl)) & |
---|
| 1054 | + araft (ji,jj,jl) * (1.0 - 1.0/kraft) |
---|
| 1055 | END DO |
---|
| 1056 | END DO |
---|
| 1057 | END DO |
---|
| 1058 | |
---|
| 1059 | END SUBROUTINE lim_itd_me_ridgeprep |
---|
| 1060 | |
---|
| 1061 | !=============================================================================== |
---|
| 1062 | |
---|
| 1063 | SUBROUTINE lim_itd_me_ridgeshift(opning, closing_gross, & |
---|
| 1064 | msnow_mlt, esnow_mlt) ! (subroutine 4/6) |
---|
| 1065 | |
---|
| 1066 | !!----------------------------------------------------------------------------- |
---|
| 1067 | !! *** ROUTINE lim_itd_me_icestrength *** |
---|
| 1068 | !! ** Purpose : |
---|
| 1069 | !! This routine shift ridging ice among thickness categories |
---|
| 1070 | !! of ice thickness |
---|
| 1071 | !! |
---|
| 1072 | !! ** Method : |
---|
| 1073 | !! Remove area, volume, and energy from each ridging category |
---|
| 1074 | !! and add to thicker ice categories. |
---|
| 1075 | !! |
---|
| 1076 | !! ** Arguments : |
---|
| 1077 | !! |
---|
| 1078 | !! ** Inputs / Ouputs : |
---|
| 1079 | !! |
---|
| 1080 | !! ** External : |
---|
| 1081 | !! |
---|
| 1082 | |
---|
| 1083 | REAL (wp), DIMENSION(jpi,jpj), INTENT(IN) :: & |
---|
| 1084 | opning, & ! rate of opening due to divergence/shear |
---|
| 1085 | closing_gross ! rate at which area removed, not counting |
---|
| 1086 | ! area of new ridges |
---|
| 1087 | |
---|
| 1088 | REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: & |
---|
| 1089 | msnow_mlt, & ! mass of snow added to ocean (kg m-2) |
---|
| 1090 | esnow_mlt ! energy needed to melt snow in ocean (J m-2) |
---|
| 1091 | |
---|
| 1092 | INTEGER :: & |
---|
| 1093 | ji, jj, & ! horizontal indices |
---|
| 1094 | jl, jl1, jl2, & ! thickness category indices |
---|
| 1095 | jk, & ! ice layer index |
---|
| 1096 | ij, & ! horizontal index, combines i and j loops |
---|
[834] | 1097 | icells ! number of cells with aicen > puny |
---|
[825] | 1098 | |
---|
| 1099 | INTEGER, DIMENSION(1:(jpi+1)*(jpj+1)) :: & |
---|
| 1100 | indxi, indxj ! compressed indices |
---|
| 1101 | |
---|
| 1102 | REAL(wp), DIMENSION(jpi,jpj) :: & |
---|
| 1103 | vice_init, vice_final, & ! ice volume summed over categories |
---|
| 1104 | eice_init, eice_final ! ice energy summed over layers |
---|
| 1105 | |
---|
| 1106 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: & |
---|
| 1107 | aicen_init, & ! ice area before ridging |
---|
| 1108 | vicen_init, & ! ice volume before ridging |
---|
| 1109 | vsnon_init, & ! snow volume before ridging |
---|
| 1110 | esnon_init, & ! snow energy before ridging |
---|
[834] | 1111 | smv_i_init, & ! ice salinity before ridging |
---|
| 1112 | oa_i_init ! ice age before ridging |
---|
[825] | 1113 | |
---|
| 1114 | REAL(wp), DIMENSION(jpi,jpj,jkmax,jpl) :: & |
---|
| 1115 | eicen_init ! ice energy before ridging |
---|
| 1116 | |
---|
| 1117 | REAL(wp), DIMENSION(jpi,jpj) :: & |
---|
| 1118 | afrac , & ! fraction of category area ridged |
---|
| 1119 | ardg1 , & ! area of ice ridged |
---|
| 1120 | ardg2 , & ! area of new ridges |
---|
| 1121 | vsrdg , & ! snow volume of ridging ice |
---|
| 1122 | esrdg , & ! snow energy of ridging ice |
---|
| 1123 | oirdg1 , & ! areal age content of ridged ice |
---|
| 1124 | oirdg2 , & ! areal age content of ridging ice |
---|
| 1125 | dhr , & ! hrmax - hrmin |
---|
| 1126 | dhr2 , & ! hrmax^2 - hrmin^2 |
---|
| 1127 | fvol ! fraction of new ridge volume going to n2 |
---|
| 1128 | |
---|
| 1129 | REAL(wp), DIMENSION(jpi,jpj) :: & |
---|
| 1130 | vrdg1 , & ! volume of ice ridged |
---|
| 1131 | vrdg2 , & ! volume of new ridges |
---|
| 1132 | vsw , & ! volume of seawater trapped into ridges |
---|
| 1133 | srdg1 , & ! sal*volume of ice ridged |
---|
| 1134 | srdg2 , & ! sal*volume of new ridges |
---|
[834] | 1135 | smsw ! sal*volume of water trapped into ridges |
---|
[825] | 1136 | |
---|
| 1137 | REAL(wp), DIMENSION(jpi,jpj) :: & |
---|
| 1138 | afrft , & ! fraction of category area rafted |
---|
| 1139 | arft1 , & ! area of ice rafted |
---|
| 1140 | arft2 , & ! area of new rafted zone |
---|
| 1141 | virft , & ! ice volume of rafting ice |
---|
| 1142 | vsrft , & ! snow volume of rafting ice |
---|
| 1143 | esrft , & ! snow energy of rafting ice |
---|
| 1144 | smrft , & ! salinity of rafting ice |
---|
| 1145 | oirft1 , & ! areal age content of rafted ice |
---|
| 1146 | oirft2 ! areal age content of rafting ice |
---|
| 1147 | |
---|
| 1148 | REAL(wp), DIMENSION(jpi,jpj,jkmax) :: & |
---|
| 1149 | eirft , & ! ice energy of rafting ice |
---|
| 1150 | erdg1 , & ! enth*volume of ice ridged |
---|
| 1151 | erdg2 , & ! enth*volume of new ridges |
---|
| 1152 | ersw ! enth of water trapped into ridges |
---|
| 1153 | |
---|
| 1154 | REAL(wp) :: & |
---|
| 1155 | hL, hR , & ! left and right limits of integration |
---|
| 1156 | farea , & ! fraction of new ridge area going to n2 |
---|
| 1157 | zdummy , & ! dummy argument |
---|
| 1158 | zdummy0 , & ! dummy argument |
---|
| 1159 | ztmelts , & ! ice melting point |
---|
| 1160 | sm_newridge ! new ridged ice salinity |
---|
| 1161 | |
---|
| 1162 | CHARACTER (len=80) :: & |
---|
| 1163 | fieldid ! field identifier |
---|
| 1164 | |
---|
| 1165 | LOGICAL, PARAMETER :: & |
---|
| 1166 | l_conservation_check = .true. ! if true, check conservation |
---|
| 1167 | ! (useful for debugging) |
---|
| 1168 | LOGICAL :: & |
---|
| 1169 | neg_ato_i , & ! flag for ato_i(i,j) < -puny |
---|
| 1170 | large_afrac , & ! flag for afrac > 1 |
---|
| 1171 | large_afrft ! flag for afrac > 1 |
---|
| 1172 | |
---|
| 1173 | REAL(wp) :: & |
---|
| 1174 | zeps , & |
---|
| 1175 | epsi10 , & |
---|
| 1176 | zindb ! switch for the presence of ridge poros or not |
---|
| 1177 | |
---|
| 1178 | !---------------------------------------------------------------------------- |
---|
| 1179 | |
---|
| 1180 | ! Conservation check |
---|
| 1181 | eice_init(:,:) = 0.0 |
---|
| 1182 | |
---|
| 1183 | IF ( con_i ) THEN |
---|
| 1184 | CALL lim_column_sum (jpl, v_i, vice_init ) |
---|
| 1185 | WRITE(numout,*) ' vice_init : ', vice_init(jiindex,jjindex) |
---|
| 1186 | CALL lim_column_sum_energy (jpl, nlay_i, e_i, eice_init ) |
---|
| 1187 | WRITE(numout,*) ' eice_init : ', eice_init(jiindex,jjindex) |
---|
| 1188 | ENDIF |
---|
| 1189 | |
---|
| 1190 | zeps = 1.0d-20 |
---|
| 1191 | epsi10 = 1.0d-10 |
---|
| 1192 | |
---|
| 1193 | !------------------------------------------------------------------------------- |
---|
| 1194 | ! 1) Compute change in open water area due to closing and opening. |
---|
| 1195 | !------------------------------------------------------------------------------- |
---|
| 1196 | |
---|
| 1197 | neg_ato_i = .false. |
---|
| 1198 | |
---|
| 1199 | DO jj = 1, jpj |
---|
| 1200 | DO ji = 1, jpi |
---|
| 1201 | ato_i(ji,jj) = ato_i(ji,jj) & |
---|
| 1202 | - athorn(ji,jj,0)*closing_gross(ji,jj)*rdt_ice & |
---|
| 1203 | + opning(ji,jj)*rdt_ice |
---|
| 1204 | IF (ato_i(ji,jj) .LT. -epsi11) THEN |
---|
| 1205 | neg_ato_i = .true. |
---|
| 1206 | ELSEIF (ato_i(ji,jj) .LT. 0.0) THEN ! roundoff error |
---|
| 1207 | ato_i(ji,jj) = 0.0 |
---|
| 1208 | ENDIF |
---|
| 1209 | END DO !jj |
---|
| 1210 | END DO !ji |
---|
| 1211 | |
---|
| 1212 | ! if negative open water area alert it |
---|
| 1213 | IF (neg_ato_i) THEN ! there is a bug |
---|
| 1214 | DO jj = 1, jpj |
---|
| 1215 | DO ji = 1, jpi |
---|
| 1216 | IF (ato_i(ji,jj) .LT. -epsi11) THEN |
---|
| 1217 | WRITE(numout,*) '' |
---|
| 1218 | WRITE(numout,*) 'Ridging error: ato_i < 0' |
---|
| 1219 | WRITE(numout,*) 'ato_i : ', ato_i(ji,jj) |
---|
| 1220 | ENDIF ! ato_i < -epsi11 |
---|
| 1221 | END DO ! ji |
---|
| 1222 | END DO ! jj |
---|
| 1223 | ENDIF ! neg_ato_i |
---|
| 1224 | |
---|
| 1225 | !----------------------------------------------------------------- |
---|
| 1226 | ! 2) Save initial state variables |
---|
| 1227 | !----------------------------------------------------------------- |
---|
| 1228 | |
---|
| 1229 | DO jl = 1, jpl |
---|
| 1230 | DO jj = 1, jpj |
---|
| 1231 | DO ji = 1, jpi |
---|
| 1232 | aicen_init(ji,jj,jl) = a_i(ji,jj,jl) |
---|
| 1233 | vicen_init(ji,jj,jl) = v_i(ji,jj,jl) |
---|
| 1234 | vsnon_init(ji,jj,jl) = v_s(ji,jj,jl) |
---|
| 1235 | |
---|
| 1236 | esnon_init(ji,jj,jl) = e_s(ji,jj,1,jl) |
---|
| 1237 | smv_i_init(ji,jj,jl) = smv_i(ji,jj,jl) |
---|
| 1238 | oa_i_init (ji,jj,jl) = oa_i(ji,jj,jl) |
---|
| 1239 | END DO !ji |
---|
| 1240 | END DO ! jj |
---|
| 1241 | END DO !jl |
---|
| 1242 | |
---|
| 1243 | DO jl = 1, jpl |
---|
| 1244 | DO jk = 1, nlay_i |
---|
| 1245 | DO jj = 1, jpj |
---|
| 1246 | DO ji = 1, jpi |
---|
| 1247 | eicen_init(ji,jj,jk,jl) = e_i(ji,jj,jk,jl) |
---|
| 1248 | END DO !ji |
---|
| 1249 | END DO !jj |
---|
| 1250 | END DO !jk |
---|
| 1251 | END DO !jl |
---|
| 1252 | |
---|
[834] | 1253 | ! |
---|
[825] | 1254 | !----------------------------------------------------------------- |
---|
| 1255 | ! 3) Pump everything from ice which is being ridged / rafted |
---|
| 1256 | !----------------------------------------------------------------- |
---|
| 1257 | ! Compute the area, volume, and energy of ice ridging in each |
---|
| 1258 | ! category, along with the area of the resulting ridge. |
---|
| 1259 | |
---|
| 1260 | DO jl1 = 1, jpl !jl1 describes the ridging category |
---|
| 1261 | |
---|
| 1262 | !------------------------------------------------ |
---|
| 1263 | ! 3.1) Identify grid cells with nonzero ridging |
---|
| 1264 | !------------------------------------------------ |
---|
| 1265 | |
---|
| 1266 | icells = 0 |
---|
| 1267 | DO jj = 1, jpj |
---|
| 1268 | DO ji = 1, jpi |
---|
| 1269 | IF (aicen_init(ji,jj,jl1) .GT. epsi11 .AND. athorn(ji,jj,jl1) .GT. 0.0 & |
---|
| 1270 | .AND. closing_gross(ji,jj) > 0.0) THEN |
---|
| 1271 | icells = icells + 1 |
---|
| 1272 | indxi(icells) = ji |
---|
| 1273 | indxj(icells) = jj |
---|
| 1274 | ENDIF ! test on a_icen_init |
---|
| 1275 | END DO ! ji |
---|
| 1276 | END DO ! jj |
---|
| 1277 | |
---|
| 1278 | large_afrac = .false. |
---|
| 1279 | large_afrft = .false. |
---|
| 1280 | |
---|
| 1281 | DO ij = 1, icells |
---|
| 1282 | ji = indxi(ij) |
---|
| 1283 | jj = indxj(ij) |
---|
| 1284 | |
---|
| 1285 | !-------------------------------------------------------------------- |
---|
| 1286 | ! 3.2) Compute area of ridging ice (ardg1) and of new ridge (ardg2) |
---|
| 1287 | !-------------------------------------------------------------------- |
---|
| 1288 | |
---|
| 1289 | ardg1(ji,jj) = aridge(ji,jj,jl1)*closing_gross(ji,jj)*rdt_ice |
---|
| 1290 | arft1(ji,jj) = araft (ji,jj,jl1)*closing_gross(ji,jj)*rdt_ice |
---|
| 1291 | ardg2(ji,jj) = ardg1(ji,jj) / krdg(ji,jj,jl1) |
---|
| 1292 | arft2(ji,jj) = arft1(ji,jj) / kraft |
---|
| 1293 | |
---|
| 1294 | oirdg1(ji,jj)= aridge(ji,jj,jl1)*closing_gross(ji,jj)*rdt_ice |
---|
| 1295 | oirft1(ji,jj)= araft (ji,jj,jl1)*closing_gross(ji,jj)*rdt_ice |
---|
| 1296 | oirdg2(ji,jj)= oirdg1(ji,jj) / krdg(ji,jj,jl1) |
---|
| 1297 | oirft2(ji,jj)= oirft1(ji,jj) / kraft |
---|
| 1298 | |
---|
| 1299 | !--------------------------------------------------------------- |
---|
| 1300 | ! 3.3) Compute ridging /rafting fractions, make sure afrac <=1 |
---|
| 1301 | !--------------------------------------------------------------- |
---|
| 1302 | |
---|
| 1303 | afrac(ji,jj) = ardg1(ji,jj) / aicen_init(ji,jj,jl1) !ridging |
---|
| 1304 | afrft(ji,jj) = arft1(ji,jj) / aicen_init(ji,jj,jl1) !rafting |
---|
| 1305 | |
---|
| 1306 | IF (afrac(ji,jj) > 1.0 + epsi11) THEN !riging |
---|
| 1307 | large_afrac = .true. |
---|
| 1308 | ELSEIF (afrac(ji,jj) > 1.0) THEN ! roundoff error |
---|
| 1309 | afrac(ji,jj) = 1.0 |
---|
| 1310 | ENDIF |
---|
| 1311 | IF (afrft(ji,jj) > 1.0 + epsi11) THEN !rafting |
---|
| 1312 | large_afrft = .true. |
---|
| 1313 | ELSEIF (afrft(ji,jj) > 1.0) THEN ! roundoff error |
---|
| 1314 | afrft(ji,jj) = 1.0 |
---|
| 1315 | ENDIF |
---|
| 1316 | |
---|
| 1317 | !-------------------------------------------------------------------------- |
---|
| 1318 | ! 3.4) Subtract area, volume, and energy from ridging |
---|
| 1319 | ! / rafting category n1. |
---|
| 1320 | !-------------------------------------------------------------------------- |
---|
| 1321 | vrdg1(ji,jj) = vicen_init(ji,jj,jl1) * afrac(ji,jj) / & |
---|
| 1322 | ( 1.0 + ridge_por ) |
---|
| 1323 | vrdg2(ji,jj) = vrdg1(ji,jj) * ( 1. + ridge_por ) |
---|
| 1324 | vsw (ji,jj) = vrdg1(ji,jj) * ridge_por |
---|
| 1325 | |
---|
| 1326 | vsrdg(ji,jj) = vsnon_init(ji,jj,jl1) * afrac(ji,jj) |
---|
| 1327 | esrdg(ji,jj) = esnon_init(ji,jj,jl1) * afrac(ji,jj) |
---|
| 1328 | srdg1(ji,jj) = smv_i_init(ji,jj,jl1) * afrac(ji,jj) / & |
---|
| 1329 | ( 1. + ridge_por ) |
---|
| 1330 | srdg2(ji,jj) = smv_i_init(ji,jj,jl1) * afrac(ji,jj) |
---|
| 1331 | |
---|
| 1332 | ! rafting volumes, heat contents ... |
---|
| 1333 | virft(ji,jj) = vicen_init(ji,jj,jl1) * afrft(ji,jj) |
---|
| 1334 | vsrft(ji,jj) = vsnon_init(ji,jj,jl1) * afrft(ji,jj) |
---|
| 1335 | esrft(ji,jj) = esnon_init(ji,jj,jl1) * afrft(ji,jj) |
---|
| 1336 | smrft(ji,jj) = smv_i_init(ji,jj,jl1) * afrft(ji,jj) |
---|
| 1337 | |
---|
| 1338 | ! substract everything |
---|
| 1339 | a_i(ji,jj,jl1) = a_i(ji,jj,jl1) - ardg1(ji,jj) - arft1(ji,jj) |
---|
| 1340 | v_i(ji,jj,jl1) = v_i(ji,jj,jl1) - vrdg1(ji,jj) - virft(ji,jj) |
---|
| 1341 | v_s(ji,jj,jl1) = v_s(ji,jj,jl1) - vsrdg(ji,jj) - vsrft(ji,jj) |
---|
| 1342 | e_s(ji,jj,1,jl1) = e_s(ji,jj,1,jl1) - esrdg(ji,jj) - esrft(ji,jj) |
---|
| 1343 | oa_i(ji,jj,jl1) = oa_i(ji,jj,jl1) - oirdg1(ji,jj) - oirft1(ji,jj) |
---|
| 1344 | smv_i(ji,jj,jl1) = smv_i(ji,jj,jl1) - srdg1(ji,jj) - smrft(ji,jj) |
---|
| 1345 | |
---|
| 1346 | !----------------------------------------------------------------- |
---|
| 1347 | ! 3.5) Compute properties of new ridges |
---|
| 1348 | !----------------------------------------------------------------- |
---|
| 1349 | !------------- |
---|
| 1350 | ! Salinity |
---|
| 1351 | !------------- |
---|
| 1352 | smsw(ji,jj) = sss_io(ji,jj) * vsw(ji,jj) * ridge_por |
---|
| 1353 | |
---|
| 1354 | ! salinity of new ridge |
---|
| 1355 | sm_newridge = ( srdg1(ji,jj) + smsw(ji,jj) ) / vrdg2(ji,jj) |
---|
| 1356 | zdummy = sm_newridge * vrdg2(ji,jj) |
---|
| 1357 | ! has to be smaller than s_i_max |
---|
| 1358 | sm_newridge = MIN( s_i_max, sm_newridge ) |
---|
| 1359 | |
---|
| 1360 | ! salt flux due to ridge creation |
---|
| 1361 | fsalt_rpo(ji,jj) = fsalt_rpo(ji,jj) + & |
---|
| 1362 | MAX ( zdummy - srdg2(ji,jj) , 0.0 ) & |
---|
| 1363 | * rhoic / rdt_ice |
---|
| 1364 | |
---|
| 1365 | ! sal times volume for new ridges |
---|
| 1366 | srdg2(ji,jj) = sm_newridge * vrdg2(ji,jj) |
---|
| 1367 | |
---|
| 1368 | !------------------------------------ |
---|
[834] | 1369 | ! 3.6 Increment ridging diagnostics |
---|
[825] | 1370 | !------------------------------------ |
---|
| 1371 | |
---|
| 1372 | ! jl1 looping 1-jpl |
---|
| 1373 | ! ij looping 1-icells |
---|
| 1374 | |
---|
| 1375 | dardg1dt(ji,jj) = dardg1dt(ji,jj) + ardg1(ji,jj) + arft1(ji,jj) |
---|
| 1376 | dardg2dt(ji,jj) = dardg2dt(ji,jj) + ardg2(ji,jj) + arft2(ji,jj) |
---|
| 1377 | diag_dyn_gr(ji,jj) = diag_dyn_gr(ji,jj) + ( vrdg2(ji,jj) + virft(ji,jj) ) / rdt_ice |
---|
| 1378 | opening(ji,jj) = opening (ji,jj) + opning(ji,jj)*rdt_ice |
---|
| 1379 | |
---|
| 1380 | IF (con_i) vice_init(ji,jj) = vice_init(ji,jj) + vrdg2(ji,jj) - vrdg1(ji,jj) |
---|
| 1381 | |
---|
| 1382 | !------------------------------------------ |
---|
[834] | 1383 | ! 3.7 Put the snow somewhere in the ocean |
---|
[825] | 1384 | !------------------------------------------ |
---|
| 1385 | |
---|
| 1386 | ! Place part of the snow lost by ridging into the ocean. |
---|
| 1387 | ! Note that esnow_mlt < 0; the ocean must cool to melt snow. |
---|
| 1388 | ! If the ocean temp = Tf already, new ice must grow. |
---|
| 1389 | ! During the next time step, thermo_rates will determine whether |
---|
| 1390 | ! the ocean cools or new ice grows. |
---|
| 1391 | ! jl1 looping 1-jpl |
---|
| 1392 | ! ij looping 1-icells |
---|
| 1393 | |
---|
| 1394 | msnow_mlt(ji,jj) = msnow_mlt(ji,jj) & |
---|
| 1395 | + rhosn*vsrdg(ji,jj)*(1.0-fsnowrdg) & |
---|
| 1396 | !rafting included |
---|
| 1397 | + rhosn*vsrft(ji,jj)*(1.0-fsnowrft) |
---|
| 1398 | |
---|
| 1399 | esnow_mlt(ji,jj) = esnow_mlt(ji,jj) & |
---|
| 1400 | + esrdg(ji,jj)*(1.0-fsnowrdg) & |
---|
| 1401 | !rafting included |
---|
| 1402 | + esrft(ji,jj)*(1.0-fsnowrft) |
---|
| 1403 | |
---|
| 1404 | !----------------------------------------------------------------- |
---|
[834] | 1405 | ! 3.8 Compute quantities used to apportion ice among categories |
---|
[825] | 1406 | ! in the n2 loop below |
---|
| 1407 | !----------------------------------------------------------------- |
---|
| 1408 | |
---|
| 1409 | ! jl1 looping 1-jpl |
---|
| 1410 | ! ij looping 1-icells |
---|
| 1411 | |
---|
| 1412 | dhr(ji,jj) = hrmax(ji,jj,jl1) - hrmin(ji,jj,jl1) |
---|
| 1413 | dhr2(ji,jj) = hrmax(ji,jj,jl1) * hrmax(ji,jj,jl1) & |
---|
| 1414 | - hrmin(ji,jj,jl1) * hrmin(ji,jj,jl1) |
---|
| 1415 | |
---|
| 1416 | |
---|
| 1417 | END DO ! ij |
---|
| 1418 | |
---|
| 1419 | !-------------------------------------------------------------------- |
---|
[834] | 1420 | ! 3.9 Compute ridging ice enthalpy, remove it from ridging ice and |
---|
[825] | 1421 | ! compute ridged ice enthalpy |
---|
| 1422 | !-------------------------------------------------------------------- |
---|
| 1423 | DO jk = 1, nlay_i |
---|
| 1424 | DO ij = 1, icells |
---|
| 1425 | ji = indxi(ij) |
---|
| 1426 | jj = indxj(ij) |
---|
| 1427 | ! heat content of ridged ice |
---|
| 1428 | erdg1(ji,jj,jk) = eicen_init(ji,jj,jk,jl1) * afrac(ji,jj) / & |
---|
| 1429 | ( 1.0 + ridge_por ) |
---|
| 1430 | eirft(ji,jj,jk) = eicen_init(ji,jj,jk,jl1) * afrft(ji,jj) |
---|
| 1431 | e_i(ji,jj,jk,jl1) = e_i(ji,jj,jk,jl1) & |
---|
| 1432 | - erdg1(ji,jj,jk) & |
---|
| 1433 | - eirft(ji,jj,jk) |
---|
| 1434 | ! sea water heat content |
---|
| 1435 | ztmelts = - tmut * sss_io(ji,jj) + rtt |
---|
| 1436 | ! heat content per unit volume |
---|
| 1437 | zdummy0 = - rcp * ( sst_io(ji,jj) - rtt ) * vsw(ji,jj) |
---|
| 1438 | |
---|
| 1439 | ! corrected sea water salinity |
---|
| 1440 | zindb = MAX( 0.0, SIGN( 1.0, vsw(ji,jj) - zeps ) ) |
---|
| 1441 | zdummy = zindb * ( srdg1(ji,jj) - srdg2(ji,jj) ) / & |
---|
| 1442 | MAX( ridge_por * vsw(ji,jj), zeps ) |
---|
| 1443 | |
---|
| 1444 | ztmelts = - tmut * zdummy + rtt |
---|
| 1445 | ersw(ji,jj,jk) = - rcp * ( ztmelts - rtt ) * vsw(ji,jj) |
---|
| 1446 | |
---|
| 1447 | ! heat flux |
---|
| 1448 | fheat_rpo(ji,jj) = fheat_rpo(ji,jj) + ( ersw(ji,jj,jk) - zdummy0 ) / & |
---|
| 1449 | rdt_ice |
---|
| 1450 | |
---|
| 1451 | ! Correct dimensions to avoid big values |
---|
| 1452 | ersw(ji,jj,jk) = ersw(ji,jj,jk) / 1.0d+09 |
---|
| 1453 | |
---|
| 1454 | ! Mutliply by ice volume, and divide by number of layers to get heat content in 10^9 J |
---|
| 1455 | ersw(ji,jj,jk) = ersw(ji,jj,jk) * & |
---|
| 1456 | area(ji,jj) * vsw(ji,jj) / & |
---|
| 1457 | nlay_i |
---|
| 1458 | |
---|
| 1459 | erdg2(ji,jj,jk) = erdg1(ji,jj,jk) + ersw(ji,jj,jk) |
---|
| 1460 | END DO ! ij |
---|
| 1461 | END DO !jk |
---|
| 1462 | |
---|
| 1463 | |
---|
| 1464 | IF ( con_i ) THEN |
---|
| 1465 | DO jk = 1, nlay_i |
---|
| 1466 | DO ij = 1, icells |
---|
| 1467 | ji = indxi(ij) |
---|
| 1468 | jj = indxj(ij) |
---|
| 1469 | eice_init(ji,jj) = eice_init(ji,jj) + erdg2(ji,jj,jk) - & |
---|
| 1470 | erdg1(ji,jj,jk) |
---|
| 1471 | END DO ! ij |
---|
| 1472 | END DO !jk |
---|
| 1473 | ENDIF |
---|
| 1474 | |
---|
| 1475 | IF (large_afrac) THEN ! there is a bug |
---|
| 1476 | DO ij = 1, icells |
---|
| 1477 | ji = indxi(ij) |
---|
| 1478 | jj = indxj(ij) |
---|
| 1479 | IF ( afrac(ji,jj) > 1.0 + epsi11 ) THEN |
---|
| 1480 | WRITE(numout,*) '' |
---|
| 1481 | WRITE(numout,*) ' ardg > a_i' |
---|
| 1482 | WRITE(numout,*) ' ardg, aicen_init : ', & |
---|
| 1483 | ardg1(ji,jj), aicen_init(ji,jj,jl1) |
---|
| 1484 | ENDIF ! afrac > 1 + puny |
---|
| 1485 | ENDDO ! if |
---|
| 1486 | ENDIF ! large_afrac |
---|
| 1487 | IF (large_afrft) THEN ! there is a bug |
---|
| 1488 | DO ij = 1, icells |
---|
| 1489 | ji = indxi(ij) |
---|
| 1490 | jj = indxj(ij) |
---|
| 1491 | IF ( afrft(ji,jj) > 1.0 + epsi11 ) THEN |
---|
| 1492 | WRITE(numout,*) '' |
---|
| 1493 | WRITE(numout,*) ' arft > a_i' |
---|
| 1494 | WRITE(numout,*) ' arft, aicen_init : ', & |
---|
| 1495 | arft1(ji,jj), aicen_init(ji,jj,jl1) |
---|
| 1496 | ENDIF ! afrft > 1 + puny |
---|
| 1497 | ENDDO ! if |
---|
| 1498 | ENDIF ! large_afrft |
---|
| 1499 | |
---|
| 1500 | !------------------------------------------------------------------------------- |
---|
| 1501 | ! 4) Add area, volume, and energy of new ridge to each category jl2 |
---|
| 1502 | !------------------------------------------------------------------------------- |
---|
| 1503 | ! jl1 looping 1-jpl |
---|
| 1504 | DO jl2 = ice_cat_bounds(1,1), ice_cat_bounds(1,2) |
---|
| 1505 | ! over categories to which ridged ice is transferred |
---|
| 1506 | DO ij = 1, icells |
---|
| 1507 | ji = indxi(ij) |
---|
| 1508 | jj = indxj(ij) |
---|
| 1509 | |
---|
| 1510 | ! Compute the fraction of ridged ice area and volume going to |
---|
| 1511 | ! thickness category jl2. |
---|
| 1512 | ! Transfer area, volume, and energy accordingly. |
---|
| 1513 | |
---|
| 1514 | IF (hrmin(ji,jj,jl1) .GE. hi_max(jl2) .OR. & |
---|
| 1515 | hrmax(ji,jj,jl1) .LE. hi_max(jl2-1)) THEN |
---|
| 1516 | hL = 0.0 |
---|
| 1517 | hR = 0.0 |
---|
| 1518 | ELSE |
---|
| 1519 | hL = MAX (hrmin(ji,jj,jl1), hi_max(jl2-1)) |
---|
| 1520 | hR = MIN (hrmax(ji,jj,jl1), hi_max(jl2)) |
---|
| 1521 | ENDIF |
---|
| 1522 | |
---|
| 1523 | ! fraction of ridged ice area and volume going to n2 |
---|
| 1524 | farea = (hR-hL) / dhr(ji,jj) |
---|
| 1525 | fvol(ji,jj) = (hR*hR - hL*hL) / dhr2(ji,jj) |
---|
| 1526 | |
---|
| 1527 | a_i(ji,jj,jl2) = a_i(ji,jj,jl2) + farea * ardg2(ji,jj) |
---|
| 1528 | v_i(ji,jj,jl2) = v_i(ji,jj,jl2) + fvol(ji,jj) * vrdg2(ji,jj) |
---|
| 1529 | v_s(ji,jj,jl2) = v_s(ji,jj,jl2) & |
---|
| 1530 | + fvol(ji,jj) * vsrdg(ji,jj) * fsnowrdg |
---|
| 1531 | e_s(ji,jj,1,jl2) = e_s(ji,jj,1,jl2) & |
---|
| 1532 | + fvol(ji,jj) * esrdg(ji,jj) * fsnowrdg |
---|
| 1533 | smv_i(ji,jj,jl2) = smv_i(ji,jj,jl2) + fvol(ji,jj) * srdg2(ji,jj) |
---|
| 1534 | oa_i(ji,jj,jl2) = oa_i(ji,jj,jl2) + farea * oirdg2(ji,jj) |
---|
| 1535 | |
---|
| 1536 | END DO ! ij |
---|
| 1537 | |
---|
| 1538 | ! Transfer ice energy to category jl2 by ridging |
---|
| 1539 | DO jk = 1, nlay_i |
---|
| 1540 | DO ij = 1, icells |
---|
| 1541 | ji = indxi(ij) |
---|
| 1542 | jj = indxj(ij) |
---|
| 1543 | e_i(ji,jj,jk,jl2) = e_i(ji,jj,jk,jl2) & |
---|
| 1544 | + fvol(ji,jj)*erdg2(ji,jj,jk) |
---|
| 1545 | END DO ! ij |
---|
| 1546 | END DO !jk |
---|
| 1547 | |
---|
| 1548 | |
---|
| 1549 | END DO ! jl2 (new ridges) |
---|
| 1550 | |
---|
| 1551 | DO jl2 = ice_cat_bounds(1,1), ice_cat_bounds(1,2) |
---|
| 1552 | |
---|
| 1553 | DO ij = 1, icells |
---|
| 1554 | ji = indxi(ij) |
---|
| 1555 | jj = indxj(ij) |
---|
| 1556 | ! Compute the fraction of rafted ice area and volume going to |
---|
| 1557 | ! thickness category jl2, transfer area, volume, and energy accordingly. |
---|
| 1558 | |
---|
| 1559 | IF (hraft(ji,jj,jl1) .LE. hi_max(jl2) .AND. & |
---|
| 1560 | hraft(ji,jj,jl1) .GT. hi_max(jl2-1)) THEN |
---|
| 1561 | a_i(ji,jj,jl2) = a_i(ji,jj,jl2) + arft2(ji,jj) |
---|
| 1562 | v_i(ji,jj,jl2) = v_i(ji,jj,jl2) + virft(ji,jj) |
---|
| 1563 | v_s(ji,jj,jl2) = v_s(ji,jj,jl2) & |
---|
| 1564 | + vsrft(ji,jj)*fsnowrft |
---|
| 1565 | e_s(ji,jj,1,jl2) = e_s(ji,jj,1,jl2) & |
---|
| 1566 | + esrft(ji,jj)*fsnowrft |
---|
| 1567 | smv_i(ji,jj,jl2) = smv_i(ji,jj,jl2) & |
---|
| 1568 | + smrft(ji,jj) |
---|
| 1569 | oa_i(ji,jj,jl2) = oa_i(ji,jj,jl2) & |
---|
| 1570 | + oirft2(ji,jj) |
---|
| 1571 | ENDIF ! hraft |
---|
| 1572 | |
---|
| 1573 | END DO ! ij |
---|
| 1574 | |
---|
| 1575 | ! Transfer rafted ice energy to category jl2 |
---|
| 1576 | DO jk = 1, nlay_i |
---|
| 1577 | DO ij = 1, icells |
---|
| 1578 | ji = indxi(ij) |
---|
| 1579 | jj = indxj(ij) |
---|
| 1580 | IF (hraft(ji,jj,jl1) .LE. hi_max(jl2) .AND. & |
---|
| 1581 | hraft(ji,jj,jl1) .GT. hi_max(jl2-1)) THEN |
---|
| 1582 | e_i(ji,jj,jk,jl2) = e_i(ji,jj,jk,jl2) & |
---|
| 1583 | + eirft(ji,jj,jk) |
---|
| 1584 | ENDIF |
---|
| 1585 | END DO ! ij |
---|
| 1586 | END DO !jk |
---|
| 1587 | |
---|
| 1588 | END DO ! jl2 |
---|
| 1589 | |
---|
| 1590 | END DO ! jl1 (deforming categories) |
---|
| 1591 | |
---|
| 1592 | ! Conservation check |
---|
| 1593 | IF ( con_i ) THEN |
---|
| 1594 | CALL lim_column_sum (jpl, v_i, vice_final) |
---|
| 1595 | fieldid = ' v_i : limitd_me ' |
---|
| 1596 | CALL lim_cons_check (vice_init, vice_final, 1.0e-6, fieldid) |
---|
| 1597 | WRITE(numout,*) ' vice_init : ', vice_init(jiindex,jjindex) |
---|
| 1598 | WRITE(numout,*) ' vice_final : ', vice_final(jiindex,jjindex) |
---|
| 1599 | |
---|
| 1600 | CALL lim_column_sum_energy (jpl, nlay_i, e_i, eice_final ) |
---|
| 1601 | fieldid = ' e_i : limitd_me ' |
---|
| 1602 | CALL lim_cons_check (eice_init, eice_final, 1.0e-2, fieldid) |
---|
| 1603 | WRITE(numout,*) ' eice_init : ', eice_init(jiindex,jjindex) |
---|
| 1604 | WRITE(numout,*) ' eice_final : ', eice_final(jiindex,jjindex) |
---|
| 1605 | ENDIF |
---|
| 1606 | |
---|
| 1607 | END SUBROUTINE lim_itd_me_ridgeshift |
---|
| 1608 | |
---|
| 1609 | !============================================================================== |
---|
| 1610 | |
---|
| 1611 | SUBROUTINE lim_itd_me_asumr !(subroutine 5/6) |
---|
| 1612 | |
---|
| 1613 | !!----------------------------------------------------------------------------- |
---|
| 1614 | !! *** ROUTINE lim_itd_me_asumr *** |
---|
| 1615 | !! ** Purpose : |
---|
| 1616 | !! This routine finds total fractional area |
---|
| 1617 | !! |
---|
| 1618 | !! ** Method : |
---|
| 1619 | !! Find the total area of ice plus open water in each grid cell. |
---|
| 1620 | !! |
---|
| 1621 | !! This is similar to the aggregate_area subroutine except that the |
---|
| 1622 | !! total area can be greater than 1, so the open water area is |
---|
| 1623 | !! included in the sum instead of being computed as a residual. |
---|
| 1624 | !! |
---|
| 1625 | !! ** Arguments : |
---|
| 1626 | |
---|
| 1627 | INTEGER :: ji, jj, jl |
---|
| 1628 | |
---|
| 1629 | !----------------------------------------------------------------- |
---|
| 1630 | ! open water |
---|
| 1631 | !----------------------------------------------------------------- |
---|
| 1632 | |
---|
| 1633 | DO jj = 1, jpj |
---|
| 1634 | DO ji = 1, jpi |
---|
| 1635 | asum(ji,jj) = ato_i(ji,jj) |
---|
| 1636 | END DO |
---|
| 1637 | END DO |
---|
| 1638 | |
---|
| 1639 | !----------------------------------------------------------------- |
---|
| 1640 | ! ice categories |
---|
| 1641 | !----------------------------------------------------------------- |
---|
| 1642 | |
---|
| 1643 | DO jl = 1, jpl |
---|
| 1644 | DO jj= 1, jpj |
---|
| 1645 | DO ji = 1, jpi |
---|
| 1646 | asum(ji,jj) = asum(ji,jj) + a_i(ji,jj,jl) |
---|
| 1647 | END DO !ji |
---|
| 1648 | END DO !jj |
---|
| 1649 | END DO ! jl |
---|
| 1650 | |
---|
| 1651 | END SUBROUTINE lim_itd_me_asumr |
---|
| 1652 | |
---|
| 1653 | !============================================================================== |
---|
| 1654 | |
---|
| 1655 | SUBROUTINE lim_itd_me_init ! (subroutine 6/6) |
---|
| 1656 | !!------------------------------------------------------------------- |
---|
| 1657 | !! *** ROUTINE lim_itd_me_init *** |
---|
| 1658 | !! |
---|
| 1659 | !! ** Purpose : Physical constants and parameters linked |
---|
| 1660 | !! to the mechanical ice redistribution |
---|
| 1661 | !! |
---|
| 1662 | !! ** Method : Read the namiceitdme namelist |
---|
| 1663 | !! and check the parameters values |
---|
| 1664 | !! called at the first timestep (nit000) |
---|
| 1665 | !! |
---|
| 1666 | !! ** input : Namelist namiceitdme |
---|
| 1667 | !! |
---|
| 1668 | !! history : |
---|
| 1669 | !! 9.0, LIM3.0 - 02-2006 (M. Vancoppenolle) original code |
---|
| 1670 | !!------------------------------------------------------------------- |
---|
| 1671 | NAMELIST/namiceitdme/ ridge_scheme_swi, Cs, Cf, fsnowrdg, fsnowrft,& |
---|
| 1672 | Gstar, astar, & |
---|
| 1673 | Hstar, raftswi, hparmeter, Craft, ridge_por, & |
---|
| 1674 | sal_max_ridge, partfun_swi, transfun_swi, & |
---|
| 1675 | brinstren_swi |
---|
| 1676 | !!------------------------------------------------------------------- |
---|
| 1677 | |
---|
| 1678 | ! Define the initial parameters |
---|
| 1679 | ! ------------------------- |
---|
| 1680 | REWIND( numnam_ice ) |
---|
| 1681 | READ ( numnam_ice , namiceitdme) |
---|
| 1682 | IF (lwp) THEN |
---|
| 1683 | WRITE(numout,*) |
---|
| 1684 | WRITE(numout,*)' lim_itd_me_init : ice parameters for mechanical ice redistribution ' |
---|
| 1685 | WRITE(numout,*)' ~~~~~~~~~~~~~~~' |
---|
| 1686 | WRITE(numout,*)' Switch choosing the ice redistribution scheme ridge_scheme_swi', ridge_scheme_swi |
---|
| 1687 | WRITE(numout,*)' Fraction of shear energy contributing to ridging Cs ', Cs |
---|
| 1688 | WRITE(numout,*)' Ratio of ridging work to PotEner change in ridging Cf ', Cf |
---|
| 1689 | WRITE(numout,*)' Fraction of snow volume conserved during ridging fsnowrdg ', fsnowrdg |
---|
| 1690 | WRITE(numout,*)' Fraction of snow volume conserved during ridging fsnowrft ', fsnowrft |
---|
| 1691 | WRITE(numout,*)' Fraction of total ice coverage contributing to ridging Gstar ', Gstar |
---|
| 1692 | WRITE(numout,*)' Equivalent to G* for an exponential part function astar ', astar |
---|
| 1693 | WRITE(numout,*)' Quantity playing a role in max ridged ice thickness Hstar ', Hstar |
---|
| 1694 | WRITE(numout,*)' Rafting of ice sheets or not raftswi ', raftswi |
---|
| 1695 | WRITE(numout,*)' Parmeter thickness (threshold between ridge-raft) hparmeter ', hparmeter |
---|
| 1696 | WRITE(numout,*)' Rafting hyperbolic tangent coefficient Craft ', Craft |
---|
| 1697 | WRITE(numout,*)' Initial porosity of ridges ridge_por ', ridge_por |
---|
| 1698 | WRITE(numout,*)' Maximum salinity of ridging ice sal_max_ridge ', sal_max_ridge |
---|
| 1699 | WRITE(numout,*)' Switch for part. function (0) linear (1) exponential partfun_swi ', partfun_swi |
---|
| 1700 | WRITE(numout,*)' Switch for tran. function (0) linear (1) exponential transfun_swi ', transfun_swi |
---|
| 1701 | WRITE(numout,*)' Switch for including brine volume in ice strength comp. brinstren_swi ', brinstren_swi |
---|
| 1702 | ENDIF |
---|
| 1703 | |
---|
| 1704 | END SUBROUTINE lim_itd_me_init |
---|
| 1705 | |
---|
| 1706 | !============================================================================== |
---|
| 1707 | |
---|
| 1708 | SUBROUTINE lim_itd_me_zapsmall |
---|
| 1709 | !!------------------------------------------------------------------- |
---|
| 1710 | !! *** ROUTINE lim_itd_me_zapsmall *** |
---|
| 1711 | !! |
---|
| 1712 | !! ** Purpose : Remove too small sea ice areas and correct salt fluxes |
---|
| 1713 | !! |
---|
| 1714 | !! |
---|
| 1715 | !! history : |
---|
| 1716 | !! author: William H. Lipscomb, LANL |
---|
| 1717 | !! Nov 2003: Modified by Julie Schramm to conserve volume and energy |
---|
| 1718 | !! Sept 2004: Modified by William Lipscomb; replaced normalize_state with |
---|
| 1719 | !! additions to local freshwater, salt, and heat fluxes |
---|
| 1720 | !! 9.0, LIM3.0 - 02-2006 (M. Vancoppenolle) original code |
---|
| 1721 | !!------------------------------------------------------------------- |
---|
| 1722 | |
---|
| 1723 | INTEGER :: & |
---|
| 1724 | ji,jj, & ! horizontal indices |
---|
| 1725 | jl, & ! ice category index |
---|
| 1726 | jk, & ! ice layer index |
---|
| 1727 | icells, & ! number of cells with ice to zap |
---|
| 1728 | ij ! combined i/j horizontal index |
---|
| 1729 | |
---|
| 1730 | INTEGER, DIMENSION(1:(jpi+1)*(jpj+1)) :: & |
---|
| 1731 | indxi, & ! compressed indices for i/j directions |
---|
| 1732 | indxj |
---|
| 1733 | |
---|
| 1734 | REAL(wp) :: & |
---|
| 1735 | xtmp ! temporary variable |
---|
| 1736 | |
---|
| 1737 | DO jl = 1, jpl |
---|
| 1738 | |
---|
| 1739 | !----------------------------------------------------------------- |
---|
| 1740 | ! Count categories to be zapped. |
---|
| 1741 | ! Abort model in case of negative area. |
---|
| 1742 | !----------------------------------------------------------------- |
---|
| 1743 | |
---|
| 1744 | icells = 0 |
---|
| 1745 | DO jj = 1, jpj |
---|
| 1746 | DO ji = 1, jpi |
---|
| 1747 | IF ( a_i(ji,jj,jl) .LT. -1.0e-11 ) THEN |
---|
| 1748 | WRITE (numout,*) ' ALERTE 98 ' |
---|
| 1749 | WRITE (numout,*) ' Negative ice area: ji, jj, jl: ', ji, jj,jl |
---|
| 1750 | WRITE (numout,*) ' a_i ', a_i(ji,jj,jl) |
---|
| 1751 | ELSEIF ( ( a_i(ji,jj,jl) .GE. -epsi11 .AND. a_i(ji,jj,jl) .LT. 0.0) & |
---|
| 1752 | .OR. & |
---|
| 1753 | ( a_i(ji,jj,jl) .GT. 0.0 .AND. a_i(ji,jj,jl) .LE. 1.0e-11 ) & |
---|
| 1754 | .OR. & |
---|
| 1755 | !new line |
---|
| 1756 | ( v_i(ji,jj,jl) .EQ. 0.0 .AND. a_i(ji,jj,jl) .GT. 0.0 ) & |
---|
| 1757 | .OR. & |
---|
| 1758 | ( v_i(ji,jj,jl) .GT. 0.0 .AND. v_i(ji,jj,jl) .LT. 1.e-12 ) ) THEN |
---|
| 1759 | icells = icells + 1 |
---|
| 1760 | indxi(icells) = ji |
---|
| 1761 | indxj(icells) = jj |
---|
| 1762 | ENDIF |
---|
| 1763 | END DO |
---|
| 1764 | END DO |
---|
| 1765 | WRITE(numout,*) icells, ' cells of ice zapped in the ocean ' |
---|
| 1766 | |
---|
| 1767 | !----------------------------------------------------------------- |
---|
| 1768 | ! Zap ice energy and use ocean heat to melt ice |
---|
| 1769 | !----------------------------------------------------------------- |
---|
| 1770 | |
---|
| 1771 | DO jk = 1, nlay_i |
---|
| 1772 | DO ij = 1, icells |
---|
| 1773 | ji = indxi(ij) |
---|
| 1774 | jj = indxj(ij) |
---|
| 1775 | |
---|
| 1776 | xtmp = e_i(ji,jj,jk,jl) / area(ji,jj) / rdt_ice |
---|
| 1777 | xtmp = xtmp * unit_fac |
---|
| 1778 | ! fheat_res(ji,jj) = fheat_res(ji,jj) - xtmp |
---|
| 1779 | e_i(ji,jj,jk,jl) = 0.0 |
---|
| 1780 | |
---|
| 1781 | END DO ! ij |
---|
| 1782 | END DO ! jk |
---|
| 1783 | |
---|
| 1784 | DO ij = 1, icells |
---|
| 1785 | ji = indxi(ij) |
---|
| 1786 | jj = indxj(ij) |
---|
| 1787 | |
---|
| 1788 | !----------------------------------------------------------------- |
---|
| 1789 | ! Zap snow energy and use ocean heat to melt snow |
---|
| 1790 | !----------------------------------------------------------------- |
---|
| 1791 | |
---|
| 1792 | ! xtmp = esnon(i,j,n) / dt ! < 0 |
---|
| 1793 | ! fhnet(i,j) = fhnet(i,j) + xtmp |
---|
| 1794 | ! fhnet_hist(i,j) = fhnet_hist(i,j) + xtmp |
---|
| 1795 | ! xtmp is greater than 0 |
---|
| 1796 | ! fluxes are positive to the ocean |
---|
| 1797 | ! here the flux has to be negative for the ocean |
---|
| 1798 | xtmp = ( rhosn*cpic*( rtt-t_s(ji,jj,1,jl) ) + rhosn*lfus ) / rdt_ice |
---|
| 1799 | ! fheat_res(ji,jj) = fheat_res(ji,jj) - xtmp |
---|
| 1800 | |
---|
| 1801 | t_s(ji,jj,1,jl) = rtt |
---|
| 1802 | |
---|
| 1803 | !----------------------------------------------------------------- |
---|
| 1804 | ! zap ice and snow volume, add water and salt to ocean |
---|
| 1805 | !----------------------------------------------------------------- |
---|
| 1806 | |
---|
| 1807 | ! xtmp = (rhoi*vicen(i,j,n) + rhos*vsnon(i,j,n)) / dt |
---|
| 1808 | ! fresh(i,j) = fresh(i,j) + xtmp |
---|
| 1809 | ! fresh_hist(i,j) = fresh_hist(i,j) + xtmp |
---|
| 1810 | |
---|
| 1811 | ! fsalt_res(ji,jj) = fsalt_res(ji,jj) + ( sss_io(ji,jj) ) * & |
---|
| 1812 | ! rhosn * v_s(ji,jj,jl) / rdt_ice |
---|
| 1813 | |
---|
| 1814 | ! fsalt_res(ji,jj) = fsalt_res(ji,jj) + ( sss_io(ji,jj) - sm_i(ji,jj,jl) ) * & |
---|
| 1815 | ! rhoic * v_i(ji,jj,jl) / rdt_ice |
---|
| 1816 | |
---|
| 1817 | ! fsalt(i,j) = fsalt(i,j) + xtmp |
---|
| 1818 | ! fsalt_hist(i,j) = fsalt_hist(i,j) + xtmp |
---|
| 1819 | |
---|
| 1820 | ato_i(ji,jj) = ato_i(ji,jj) + a_i(ji,jj,jl) |
---|
| 1821 | a_i(ji,jj,jl) = 0.0 |
---|
| 1822 | v_i(ji,jj,jl) = 0.0 |
---|
| 1823 | v_s(ji,jj,jl) = 0.0 |
---|
| 1824 | t_su(ji,jj,jl) = t_bo(ji,jj) |
---|
| 1825 | oa_i(ji,jj,jl) = 0.0 |
---|
| 1826 | smv_i(ji,jj,jl) = 0.0 |
---|
| 1827 | |
---|
| 1828 | END DO ! ij |
---|
| 1829 | |
---|
| 1830 | END DO ! jl |
---|
| 1831 | |
---|
| 1832 | END SUBROUTINE lim_itd_me_zapsmall |
---|
| 1833 | |
---|
| 1834 | #else |
---|
| 1835 | !!====================================================================== |
---|
| 1836 | !! *** MODULE limitd_me *** |
---|
| 1837 | !! no sea ice model |
---|
| 1838 | !!====================================================================== |
---|
| 1839 | |
---|
| 1840 | CONTAINS |
---|
| 1841 | |
---|
| 1842 | SUBROUTINE lim_itd_me ! Empty routines |
---|
| 1843 | END SUBROUTINE lim_itd_me |
---|
| 1844 | SUBROUTINE lim_itd_me_icestrength |
---|
| 1845 | END SUBROUTINE lim_itd_me_icestrength |
---|
| 1846 | SUBROUTINE lim_itd_me_ridgeprep |
---|
| 1847 | END SUBROUTINE lim_itd_me_ridgeprep |
---|
| 1848 | SUBROUTINE lim_itd_th_me_ridgeshift |
---|
| 1849 | END SUBROUTINE lim_itd_me_ridgeshift |
---|
| 1850 | SUBROUTINE lim_itd_me_asumr |
---|
| 1851 | END SUBROUTINE lim_itd_me_asumr |
---|
| 1852 | SUBROUTINE lim_itd_me_sort |
---|
| 1853 | END SUBROUTINE lim_itd_me_sort |
---|
| 1854 | SUBROUTINE lim_itd_me_init |
---|
| 1855 | END SUBROUTINE lim_itd_me_init |
---|
| 1856 | SUBROUTINE lim_itd_me_zapsmall |
---|
| 1857 | END SUBROUTINE lim_itd_me_zapsmall |
---|
| 1858 | #endif |
---|
| 1859 | END MODULE limitd_me |
---|