[821] | 1 | MODULE limthd_lac_2 |
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| 2 | #if defined key_lim2 |
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[3] | 3 | !!====================================================================== |
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[821] | 4 | !! *** MODULE limthd_lac_2 *** |
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[3] | 5 | !! lateral thermodynamic growth of the ice |
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| 6 | !!====================================================================== |
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| 7 | |
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| 8 | !!---------------------------------------------------------------------- |
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[3625] | 9 | !! lim_lat_acr_2 : lateral accretion of ice |
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[2715] | 10 | !!---------------------------------------------------------------------- |
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[3625] | 11 | USE par_oce ! ocean parameters |
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[3] | 12 | USE phycst |
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[821] | 13 | USE thd_ice_2 |
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[1228] | 14 | USE ice_2 |
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[821] | 15 | USE limistate_2 |
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[3625] | 16 | USE lib_mpp ! MPP library |
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| 17 | USE wrk_nemo ! work arrays |
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| 18 | USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) |
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[2715] | 19 | |
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[3] | 20 | IMPLICIT NONE |
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| 21 | PRIVATE |
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| 22 | |
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[2715] | 23 | PUBLIC lim_thd_lac_2 ! called by lim_thd_2 |
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[3] | 24 | |
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[106] | 25 | REAL(wp) :: & ! constant values |
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[88] | 26 | epsi20 = 1.e-20 , & |
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| 27 | epsi13 = 1.e-13 , & |
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| 28 | zzero = 0.e0 , & |
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| 29 | zone = 1.e0 |
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[2715] | 30 | |
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[3] | 31 | !!---------------------------------------------------------------------- |
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[2528] | 32 | !! NEMO/LIM2 3.3 , UCL - NEMO Consortium (2010) |
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[1156] | 33 | !! $Id$ |
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[2528] | 34 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[3] | 35 | !!---------------------------------------------------------------------- |
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| 36 | CONTAINS |
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| 37 | |
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[821] | 38 | SUBROUTINE lim_thd_lac_2( kideb, kiut ) |
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[3] | 39 | !!------------------------------------------------------------------- |
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[821] | 40 | !! *** ROUTINE lim_thd_lac_2 *** |
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[3] | 41 | !! |
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| 42 | !! ** Purpose : Computation of the evolution of the ice thickness and |
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| 43 | !! concentration as a function of the heat balance in the leads. |
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| 44 | !! It is only used for lateral accretion |
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| 45 | !! |
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| 46 | !! ** Method : Ice is formed in the open water when ocean lose heat |
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| 47 | !! (heat budget of open water Bl is negative) . |
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| 48 | !! Computation of the increase of 1-A (ice concentration) fol- |
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| 49 | !! lowing the law : |
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| 50 | !! (dA/dt)acc = F[ (1-A)/(1-a) ] * [ Bl / (Li*h0) ] |
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| 51 | !! where - h0 is the thickness of ice created in the lead |
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| 52 | !! - a is a minimum fraction for leads |
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| 53 | !! - F is a monotonic non-increasing function defined as: |
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| 54 | !! F(X)=( 1 - X**exld )**(1.0/exld) |
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| 55 | !! - exld is the exponent closure rate (=2 default val.) |
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| 56 | !! |
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| 57 | !! ** Action : - Adjustment of snow and ice thicknesses and heat |
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| 58 | !! content in brine pockets |
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| 59 | !! - Updating ice internal temperature |
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| 60 | !! - Computation of variation of ice volume and mass |
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| 61 | !! - Computation of frldb after lateral accretion and |
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| 62 | !! update h_snow_1d, h_ice_1d and tbif_1d(:,:) |
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| 63 | !! |
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| 64 | !! ** References : |
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| 65 | !! M. Maqueda, 1995, PhD Thesis, Univesidad Complutense Madrid |
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| 66 | !! Fichefet T. and M. Maqueda 1997, J. Geo. Res., 102(C6), |
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| 67 | !! 12609 -12646 |
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| 68 | !! History : |
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| 69 | !! 1.0 ! 01-04 (LIM) original code |
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| 70 | !! 2.0 ! 02-08 (C. Ethe, G. Madec) F90, mpp |
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| 71 | !!------------------------------------------------------------------- |
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| 72 | INTEGER , INTENT(IN):: & |
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| 73 | kideb , & ! start point on which the the computation is applied |
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| 74 | kiut ! end point on which the the computation is applied |
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| 75 | |
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[2715] | 76 | ! * Local variables |
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[3] | 77 | INTEGER :: & |
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| 78 | ji , & ! dummy loop indices |
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| 79 | iicefr , & ! 1 = existing ice ; 0 = no ice |
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| 80 | iiceform , & ! 1 = ice formed ; 0 = no ice formed |
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| 81 | ihemis ! dummy indice |
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[3294] | 82 | REAL(wp), POINTER, DIMENSION(:) :: zqbgow ! heat budget of the open water (negative) |
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| 83 | REAL(wp), POINTER, DIMENSION(:) :: zfrl_old ! previous sea/ice fraction |
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| 84 | REAL(wp), POINTER, DIMENSION(:) :: zhice_old ! previous ice thickness |
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| 85 | REAL(wp), POINTER, DIMENSION(:) :: zhice0 ! thickness of newly formed ice in leads |
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| 86 | REAL(wp), POINTER, DIMENSION(:) :: zfrlmin ! minimum fraction for leads |
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| 87 | REAL(wp), POINTER, DIMENSION(:) :: zdhicbot ! part of thickness of newly formed ice in leads which |
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[3] | 88 | ! has been already used in transport for example |
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| 89 | REAL(wp) :: & |
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| 90 | zhemis , & ! hemisphere (0 = North, 1 = South) |
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| 91 | zhicenew , & ! new ice thickness |
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| 92 | zholds2 , & ! ratio of previous ice thickness and 2 |
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| 93 | zhnews2 , & ! ratio of new ice thickness and 2 |
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| 94 | zfrlnew , & ! new sea/ice fraction |
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| 95 | zfrld , & ! ratio of sea/ice fraction and minimum fraction for leads |
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| 96 | zfrrate , & ! leads-closure rate |
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| 97 | zdfrl ! sea-ice fraction increment |
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| 98 | REAL(wp) :: & |
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| 99 | zdh1 , zdh2 , zdh3 , zdh4, zdh5 , & ! tempory scalars |
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| 100 | ztint , zta1 , zta2 , zta3 , zta4 , & |
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| 101 | zah, zalpha , zbeta |
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| 102 | !!--------------------------------------------------------------------- |
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[2715] | 103 | |
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[3294] | 104 | CALL wrk_alloc( jpij, zqbgow, zfrl_old, zhice_old, zhice0, zfrlmin, zdhicbot ) |
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[2715] | 105 | |
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[3] | 106 | !-------------------------------------------------------------- |
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| 107 | ! Computation of the heat budget of the open water (negative) |
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| 108 | !-------------------------------------------------------------- |
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| 109 | |
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| 110 | DO ji = kideb , kiut |
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| 111 | zqbgow(ji) = qldif_1d(ji) - qcmif_1d(ji) |
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| 112 | END DO |
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| 113 | |
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| 114 | !----------------------------------------------------------------- |
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| 115 | ! Taking the appropriate values for the corresponding hemisphere |
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| 116 | !----------------------------------------------------------------- |
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| 117 | DO ji = kideb , kiut |
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| 118 | zhemis = MAX( zzero , SIGN( zone , frld_1d(ji) - 2.0 ) ) |
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| 119 | ihemis = INT( 1 + zhemis ) |
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| 120 | zhice0 (ji) = hiccrit( ihemis ) |
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| 121 | zfrlmin (ji) = acrit ( ihemis ) |
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| 122 | frld_1d (ji) = frld_1d(ji) - 2.0 * zhemis |
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| 123 | zfrl_old(ji) = frld_1d(ji) |
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| 124 | END DO |
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| 125 | |
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| 126 | !------------------------------------------------------------------- |
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| 127 | ! Lateral Accretion (modification of the fraction of open water) |
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| 128 | ! The ice formed in the leads has always a thickness zhice0, but |
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| 129 | ! only a fraction zfrrate of the ice formed contributes to the |
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| 130 | ! increase of the ice fraction. The remaining part (1-zfrrate) |
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| 131 | ! is rather assumed to lead to an increase in the thickness of the |
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| 132 | ! pre-existing ice (transport for example). |
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| 133 | ! Morales Maqueda, 1995 - Fichefet and Morales Maqueda, 1997 |
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| 134 | !--------------------------------------------------------------------- |
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| 135 | |
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[1697] | 136 | !CDIR NOVERRCHK |
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[3] | 137 | DO ji = kideb , kiut |
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| 138 | iicefr = 1 - MAX( 0, INT( SIGN( 1.5 * zone , zfrl_old(ji) - 1.0 + epsi13 ) ) ) |
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| 139 | !---computation of the leads-closure rate |
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| 140 | zfrld = MIN( zone , ( 1.0 - frld_1d(ji) ) / ( 1.0 - zfrlmin(ji) ) ) |
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| 141 | zfrrate = ( 1.0 - zfrld**exld )**( 1.0 / exld ) |
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| 142 | !--computation of the sea-ice fraction increment and the new fraction |
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| 143 | zdfrl = ( zfrrate / zhice0(ji) ) * ( zqbgow(ji) / xlic ) |
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| 144 | zfrlnew = zfrl_old(ji) + zdfrl |
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| 145 | !--update the sea-ice fraction |
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| 146 | frld_1d (ji) = MAX( zfrlnew , zfrlmin(ji) ) |
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| 147 | !--computation of the remaining part of ice thickness which has been already used |
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[3625] | 148 | zdhicbot(ji) = ( frld_1d(ji) - zfrlnew ) * zhice0(ji) / ( 1.0 - zfrlmin(ji) ) & |
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| 149 | & - ( ( 1.0 - zfrrate ) / ( 1.0 - frld_1d(ji) ) ) * ( zqbgow(ji) / xlic ) |
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[3] | 150 | END DO |
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| 151 | |
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| 152 | !---------------------------------------------------------------------------------------- |
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| 153 | ! Ajustement of snow and ice thicknesses and updating the total heat stored in brine pockets |
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| 154 | ! The thickness of newly formed ice is averaged with that of the pre-existing |
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| 155 | ! (1-Anew) * hinew = (1-Aold) * hiold + ((1-Anew)-(1-Aold)) * h0 |
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| 156 | ! Snow is distributed over the new ice-covered area |
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| 157 | ! (1-Anew) * hsnew = (1-Aold) * hsold |
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| 158 | !-------------------------------------------------------------------------------------------- |
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| 159 | |
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| 160 | DO ji = kideb , kiut |
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| 161 | iicefr = 1 - MAX( 0, INT( SIGN( 1.5 * zone , zfrl_old(ji) - 1.0 + epsi13 ) ) ) |
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| 162 | zhice_old(ji) = h_ice_1d(ji) |
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| 163 | zhicenew = iicefr * zhice_old(ji) + ( 1 - iicefr ) * zhice0(ji) |
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| 164 | zalpha = ( 1. - zfrl_old(ji) ) / ( 1.- frld_1d(ji) ) |
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| 165 | h_snow_1d(ji) = zalpha * h_snow_1d(ji) |
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| 166 | h_ice_1d (ji) = zalpha * zhicenew + ( 1.0 - zalpha ) * zhice0(ji) |
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| 167 | qstbif_1d(ji) = zalpha * qstbif_1d(ji) |
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| 168 | END DO |
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| 169 | |
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| 170 | !------------------------------------------------------- |
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| 171 | ! Ajustement of ice internal temperatures |
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| 172 | !------------------------------------------------------- |
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| 173 | |
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| 174 | DO ji = kideb , kiut |
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| 175 | iicefr = 1 - MAX( 0, INT( SIGN( 1.5 * zone , zfrl_old(ji) - 1.0 + epsi13 ) ) ) |
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| 176 | iiceform = 1 - MAX( 0 ,INT( SIGN( 1.5 * zone , zhice0(ji) - h_ice_1d(ji) ) ) ) |
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| 177 | zholds2 = zhice_old(ji)/ 2. |
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| 178 | zhnews2 = h_ice_1d(ji) / 2. |
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| 179 | zdh1 = MAX( zzero , zhice_old(ji) - zhnews2 ) |
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| 180 | zdh2 = MAX( zzero , -zhice_old(ji) + zhnews2 ) |
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| 181 | zdh3 = MAX( zzero , h_ice_1d(ji) - zholds2 ) |
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| 182 | zdh4 = MAX( zzero , -h_ice_1d(ji) + zholds2 ) |
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| 183 | zdh5 = MAX( zzero , zhice0(ji) - zholds2 ) |
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| 184 | ztint = iiceform * ( ( zholds2 - zdh3 ) * tbif_1d(ji,3) + zdh4 * tbif_1d(ji,2) ) & |
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| 185 | & / MAX( epsi20 , h_ice_1d(ji) - zhice0(ji) ) & |
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| 186 | & + ( 1 - iiceform ) * tfu_1d(ji) |
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| 187 | zta1 = iicefr * ( 1. - zfrl_old(ji) ) * tbif_1d(ji,2) |
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| 188 | zta2 = iicefr * ( 1. - zfrl_old(ji) ) * tbif_1d(ji,3) |
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| 189 | zta3 = iicefr * ( 1. - zfrl_old(ji) ) * ztint |
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| 190 | zta4 = ( zfrl_old(ji) - frld_1d (ji) ) * tfu_1d(ji) |
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| 191 | zah = ( 1. - frld_1d(ji) ) * zhnews2 |
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| 192 | |
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| 193 | tbif_1d(ji,2) = ( MIN( zhnews2 , zholds2 ) * zta1 & |
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| 194 | & + ( 1 - iiceform ) * ( zholds2 - zdh1 ) * zta2 & |
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| 195 | & + ( iiceform * ( zhnews2 - zhice0(ji) + zdh5 ) + ( 1 - iiceform ) * zdh2 ) * zta3 & |
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| 196 | & + MIN ( zhnews2 , zhice0(ji) ) * zta4 & |
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| 197 | & ) / zah |
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| 198 | |
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[3625] | 199 | tbif_1d(ji,3) = ( iiceform * ( zhnews2 - zdh3 ) * zta1 & |
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[3] | 200 | & + ( iiceform * zdh3 + ( 1 - iiceform ) * zdh1 ) * zta2 & |
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| 201 | & + ( iiceform * ( zhnews2 - zdh5 ) + ( 1 - iiceform ) * ( zhnews2 - zdh1 ) ) * zta3 & |
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| 202 | & + ( iiceform * zdh5 + ( 1 - iiceform ) * zhnews2 ) * zta4 & |
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| 203 | & ) / zah |
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| 204 | !---removing the remaining part of ice formed which has been already used |
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| 205 | zbeta = h_ice_1d(ji) / ( h_ice_1d(ji) + zdhicbot(ji) ) |
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| 206 | h_ice_1d(ji) = h_ice_1d(ji) + zdhicbot(ji) |
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| 207 | tbif_1d (ji,2)= zbeta * tbif_1d(ji,2) + ( 1.0 - zbeta ) * tbif_1d(ji,3) |
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| 208 | tbif_1d (ji,3)= ( 2. * zbeta - 1.0 ) * tbif_1d(ji,3) + ( 2. * zdhicbot(ji) / h_ice_1d(ji) ) * tfu_1d(ji) |
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| 209 | |
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| 210 | END DO |
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| 211 | |
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| 212 | !------------------------------------------------------------- |
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| 213 | ! Computation of variation of ice volume and ice mass |
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| 214 | ! Vold = (1-Aold) * hiold ; Vnew = (1-Anew) * hinew |
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| 215 | ! dV = Vnew - Vold |
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| 216 | !------------------------------------------------------------- |
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| 217 | |
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| 218 | DO ji = kideb , kiut |
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| 219 | dvlbq_1d (ji) = ( 1. - frld_1d(ji) ) * h_ice_1d(ji) - ( 1. - zfrl_old(ji) ) * zhice_old(ji) |
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[3625] | 220 | rdm_ice_1d(ji) = rdm_ice_1d(ji) + rhoic * dvlbq_1d(ji) |
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| 221 | rdq_ice_1d(ji) = rdq_ice_1d(ji) + rcpic * dvlbq_1d(ji) * ( tfu_1d(ji) - rt0 ) ! heat content relative to rt0 |
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[3] | 222 | END DO |
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| 223 | |
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[3294] | 224 | CALL wrk_dealloc( jpij, zqbgow, zfrl_old, zhice_old, zhice0, zfrlmin, zdhicbot ) |
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[2715] | 225 | ! |
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[821] | 226 | END SUBROUTINE lim_thd_lac_2 |
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[3] | 227 | #else |
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[2715] | 228 | !!---------------------------------------------------------------------- |
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[821] | 229 | !! *** MODULE limthd_lac_2 *** |
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[3] | 230 | !! no sea ice model |
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[2715] | 231 | !!---------------------------------------------------------------------- |
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[3] | 232 | CONTAINS |
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[821] | 233 | SUBROUTINE lim_thd_lac_2 ! Empty routine |
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| 234 | END SUBROUTINE lim_thd_lac_2 |
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[3] | 235 | #endif |
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[2715] | 236 | !!====================================================================== |
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[821] | 237 | END MODULE limthd_lac_2 |
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