| 1 | MODULE limthd_lac_2 |
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| 2 | #if defined key_lim2 |
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| 3 | !!====================================================================== |
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| 4 | !! *** MODULE limthd_lac_2 *** |
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| 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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| 9 | !! lim_lat_acr_2 : lateral accretion of ice |
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| 10 | !! * Modules used |
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| 11 | USE par_oce ! ocean parameters |
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| 12 | USE phycst |
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| 13 | USE thd_ice_2 |
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| 14 | USE ice_2 |
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| 15 | USE limistate_2 |
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| 16 | |
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| 17 | IMPLICIT NONE |
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| 18 | PRIVATE |
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| 19 | |
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| 20 | !! * Routine accessibility |
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| 21 | PUBLIC lim_thd_lac_2 ! called by lim_thd_2 |
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| 22 | |
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| 23 | !! * Module variables |
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| 24 | REAL(wp) :: & ! constant values |
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| 25 | epsi20 = 1.e-20 , & |
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| 26 | epsi13 = 1.e-13 , & |
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| 27 | zzero = 0.e0 , & |
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| 28 | zone = 1.e0 |
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| 29 | !!---------------------------------------------------------------------- |
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| 30 | !! NEMO/LIM2 3.3 , UCL - NEMO Consortium (2010) |
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| 31 | !! $Id$ |
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| 32 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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| 33 | !!---------------------------------------------------------------------- |
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| 34 | CONTAINS |
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| 35 | |
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| 36 | SUBROUTINE lim_thd_lac_2( kideb, kiut ) |
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| 37 | !!------------------------------------------------------------------- |
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| 38 | !! *** ROUTINE lim_thd_lac_2 *** |
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| 39 | !! |
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| 40 | !! ** Purpose : Computation of the evolution of the ice thickness and |
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| 41 | !! concentration as a function of the heat balance in the leads. |
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| 42 | !! It is only used for lateral accretion |
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| 43 | !! |
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| 44 | !! ** Method : Ice is formed in the open water when ocean lose heat |
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| 45 | !! (heat budget of open water Bl is negative) . |
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| 46 | !! Computation of the increase of 1-A (ice concentration) fol- |
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| 47 | !! lowing the law : |
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| 48 | !! (dA/dt)acc = F[ (1-A)/(1-a) ] * [ Bl / (Li*h0) ] |
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| 49 | !! where - h0 is the thickness of ice created in the lead |
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| 50 | !! - a is a minimum fraction for leads |
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| 51 | !! - F is a monotonic non-increasing function defined as: |
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| 52 | !! F(X)=( 1 - X**exld )**(1.0/exld) |
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| 53 | !! - exld is the exponent closure rate (=2 default val.) |
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| 54 | !! |
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| 55 | !! ** Action : - Adjustment of snow and ice thicknesses and heat |
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| 56 | !! content in brine pockets |
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| 57 | !! - Updating ice internal temperature |
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| 58 | !! - Computation of variation of ice volume and mass |
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| 59 | !! - Computation of frldb after lateral accretion and |
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| 60 | !! update h_snow_1d, h_ice_1d and tbif_1d(:,:) |
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| 61 | !! |
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| 62 | !! ** References : |
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| 63 | !! M. Maqueda, 1995, PhD Thesis, Univesidad Complutense Madrid |
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| 64 | !! Fichefet T. and M. Maqueda 1997, J. Geo. Res., 102(C6), |
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| 65 | !! 12609 -12646 |
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| 66 | !! History : |
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| 67 | !! 1.0 ! 01-04 (LIM) original code |
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| 68 | !! 2.0 ! 02-08 (C. Ethe, G. Madec) F90, mpp |
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| 69 | !!------------------------------------------------------------------- |
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| 70 | USE wrk_nemo, ONLY: wrk_in_use, wrk_not_released |
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| 71 | USE wrk_nemo, ONLY: wrk_1d_1, wrk_1d_2, wrk_1d_3, wrk_1d_4, wrk_1d_5, wrk_1d_6 |
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| 72 | USE in_out_manager, ONLY: ctl_stop |
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| 73 | !! |
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| 74 | !! * Arguments |
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| 75 | INTEGER , INTENT(IN):: & |
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| 76 | kideb , & ! start point on which the the computation is applied |
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| 77 | kiut ! end point on which the the computation is applied |
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| 78 | |
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| 79 | !! * Local variables |
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| 80 | INTEGER :: & |
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| 81 | ji , & ! dummy loop indices |
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| 82 | iicefr , & ! 1 = existing ice ; 0 = no ice |
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| 83 | iiceform , & ! 1 = ice formed ; 0 = no ice formed |
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| 84 | ihemis ! dummy indice |
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| 85 | REAL(wp), POINTER, DIMENSION(:) :: & |
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| 86 | zqbgow , & ! heat budget of the open water (negative) |
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| 87 | zfrl_old , & ! previous sea/ice fraction |
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| 88 | zhice_old , & ! previous ice thickness |
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| 89 | zhice0 , & ! thickness of newly formed ice in leads |
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| 90 | zfrlmin , & ! minimum fraction for leads |
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| 91 | zdhicbot ! part of thickness of newly formed ice in leads which |
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| 92 | ! has been already used in transport for example |
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| 93 | REAL(wp) :: & |
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| 94 | zhemis , & ! hemisphere (0 = North, 1 = South) |
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| 95 | zhicenew , & ! new ice thickness |
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| 96 | zholds2 , & ! ratio of previous ice thickness and 2 |
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| 97 | zhnews2 , & ! ratio of new ice thickness and 2 |
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| 98 | zfrlnew , & ! new sea/ice fraction |
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| 99 | zfrld , & ! ratio of sea/ice fraction and minimum fraction for leads |
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| 100 | zfrrate , & ! leads-closure rate |
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| 101 | zdfrl ! sea-ice fraction increment |
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| 102 | REAL(wp) :: & |
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| 103 | zdh1 , zdh2 , zdh3 , zdh4, zdh5 , & ! tempory scalars |
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| 104 | ztint , zta1 , zta2 , zta3 , zta4 , & |
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| 105 | zah, zalpha , zbeta |
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| 106 | !!--------------------------------------------------------------------- |
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| 107 | |
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| 108 | IF(wrk_in_use(1, 1,2,3,4,5,6))THEN |
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| 109 | CALL ctl_stop('lim_thd_lac_2 : requestead workspace arrays unavailable.') |
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| 110 | RETURN |
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| 111 | END IF |
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| 112 | ! Set-up pointers to sub-arrays of workspace arrays |
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| 113 | zqbgow => wrk_1d_1(1:jpij) |
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| 114 | zfrl_old => wrk_1d_2(1:jpij) |
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| 115 | zhice_old => wrk_1d_3(1:jpij) |
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| 116 | zhice0 => wrk_1d_4(1:jpij) |
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| 117 | zfrlmin => wrk_1d_5(1:jpij) |
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| 118 | zdhicbot => wrk_1d_6(1:jpij) |
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| 119 | |
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| 120 | !-------------------------------------------------------------- |
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| 121 | ! Computation of the heat budget of the open water (negative) |
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| 122 | !-------------------------------------------------------------- |
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| 123 | |
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| 124 | DO ji = kideb , kiut |
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| 125 | zqbgow(ji) = qldif_1d(ji) - qcmif_1d(ji) |
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| 126 | END DO |
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| 127 | |
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| 128 | !----------------------------------------------------------------- |
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| 129 | ! Taking the appropriate values for the corresponding hemisphere |
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| 130 | !----------------------------------------------------------------- |
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| 131 | DO ji = kideb , kiut |
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| 132 | zhemis = MAX( zzero , SIGN( zone , frld_1d(ji) - 2.0 ) ) |
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| 133 | ihemis = INT( 1 + zhemis ) |
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| 134 | zhice0 (ji) = hiccrit( ihemis ) |
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| 135 | zfrlmin (ji) = acrit ( ihemis ) |
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| 136 | frld_1d (ji) = frld_1d(ji) - 2.0 * zhemis |
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| 137 | zfrl_old(ji) = frld_1d(ji) |
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| 138 | END DO |
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| 139 | |
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| 140 | !------------------------------------------------------------------- |
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| 141 | ! Lateral Accretion (modification of the fraction of open water) |
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| 142 | ! The ice formed in the leads has always a thickness zhice0, but |
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| 143 | ! only a fraction zfrrate of the ice formed contributes to the |
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| 144 | ! increase of the ice fraction. The remaining part (1-zfrrate) |
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| 145 | ! is rather assumed to lead to an increase in the thickness of the |
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| 146 | ! pre-existing ice (transport for example). |
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| 147 | ! Morales Maqueda, 1995 - Fichefet and Morales Maqueda, 1997 |
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| 148 | !--------------------------------------------------------------------- |
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| 149 | |
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| 150 | !CDIR NOVERRCHK |
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| 151 | DO ji = kideb , kiut |
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| 152 | iicefr = 1 - MAX( 0, INT( SIGN( 1.5 * zone , zfrl_old(ji) - 1.0 + epsi13 ) ) ) |
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| 153 | !---computation of the leads-closure rate |
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| 154 | zfrld = MIN( zone , ( 1.0 - frld_1d(ji) ) / ( 1.0 - zfrlmin(ji) ) ) |
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| 155 | zfrrate = ( 1.0 - zfrld**exld )**( 1.0 / exld ) |
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| 156 | !--computation of the sea-ice fraction increment and the new fraction |
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| 157 | zdfrl = ( zfrrate / zhice0(ji) ) * ( zqbgow(ji) / xlic ) |
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| 158 | zfrlnew = zfrl_old(ji) + zdfrl |
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| 159 | !--update the sea-ice fraction |
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| 160 | frld_1d (ji) = MAX( zfrlnew , zfrlmin(ji) ) |
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| 161 | !--computation of the remaining part of ice thickness which has been already used |
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| 162 | zdhicbot(ji) = ( frld_1d(ji) - zfrlnew ) * zhice0(ji) / ( 1.0 - zfrlmin(ji) ) & |
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| 163 | - ( ( 1.0 - zfrrate ) / ( 1.0 - frld_1d(ji) ) ) * ( zqbgow(ji) / xlic ) |
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| 164 | END DO |
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| 165 | |
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| 166 | !---------------------------------------------------------------------------------------- |
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| 167 | ! Ajustement of snow and ice thicknesses and updating the total heat stored in brine pockets |
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| 168 | ! The thickness of newly formed ice is averaged with that of the pre-existing |
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| 169 | ! (1-Anew) * hinew = (1-Aold) * hiold + ((1-Anew)-(1-Aold)) * h0 |
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| 170 | ! Snow is distributed over the new ice-covered area |
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| 171 | ! (1-Anew) * hsnew = (1-Aold) * hsold |
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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 | zhice_old(ji) = h_ice_1d(ji) |
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| 177 | zhicenew = iicefr * zhice_old(ji) + ( 1 - iicefr ) * zhice0(ji) |
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| 178 | zalpha = ( 1. - zfrl_old(ji) ) / ( 1.- frld_1d(ji) ) |
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| 179 | h_snow_1d(ji) = zalpha * h_snow_1d(ji) |
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| 180 | h_ice_1d (ji) = zalpha * zhicenew + ( 1.0 - zalpha ) * zhice0(ji) |
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| 181 | qstbif_1d(ji) = zalpha * qstbif_1d(ji) |
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| 182 | END DO |
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| 183 | |
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| 184 | !------------------------------------------------------- |
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| 185 | ! Ajustement of ice internal temperatures |
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| 186 | !------------------------------------------------------- |
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| 187 | |
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| 188 | DO ji = kideb , kiut |
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| 189 | iicefr = 1 - MAX( 0, INT( SIGN( 1.5 * zone , zfrl_old(ji) - 1.0 + epsi13 ) ) ) |
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| 190 | iiceform = 1 - MAX( 0 ,INT( SIGN( 1.5 * zone , zhice0(ji) - h_ice_1d(ji) ) ) ) |
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| 191 | zholds2 = zhice_old(ji)/ 2. |
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| 192 | zhnews2 = h_ice_1d(ji) / 2. |
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| 193 | zdh1 = MAX( zzero , zhice_old(ji) - zhnews2 ) |
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| 194 | zdh2 = MAX( zzero , -zhice_old(ji) + zhnews2 ) |
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| 195 | zdh3 = MAX( zzero , h_ice_1d(ji) - zholds2 ) |
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| 196 | zdh4 = MAX( zzero , -h_ice_1d(ji) + zholds2 ) |
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| 197 | zdh5 = MAX( zzero , zhice0(ji) - zholds2 ) |
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| 198 | ztint = iiceform * ( ( zholds2 - zdh3 ) * tbif_1d(ji,3) + zdh4 * tbif_1d(ji,2) ) & |
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| 199 | & / MAX( epsi20 , h_ice_1d(ji) - zhice0(ji) ) & |
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| 200 | & + ( 1 - iiceform ) * tfu_1d(ji) |
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| 201 | zta1 = iicefr * ( 1. - zfrl_old(ji) ) * tbif_1d(ji,2) |
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| 202 | zta2 = iicefr * ( 1. - zfrl_old(ji) ) * tbif_1d(ji,3) |
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| 203 | zta3 = iicefr * ( 1. - zfrl_old(ji) ) * ztint |
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| 204 | zta4 = ( zfrl_old(ji) - frld_1d (ji) ) * tfu_1d(ji) |
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| 205 | zah = ( 1. - frld_1d(ji) ) * zhnews2 |
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| 206 | |
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| 207 | tbif_1d(ji,2) = ( MIN( zhnews2 , zholds2 ) * zta1 & |
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| 208 | & + ( 1 - iiceform ) * ( zholds2 - zdh1 ) * zta2 & |
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| 209 | & + ( iiceform * ( zhnews2 - zhice0(ji) + zdh5 ) + ( 1 - iiceform ) * zdh2 ) * zta3 & |
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| 210 | & + MIN ( zhnews2 , zhice0(ji) ) * zta4 & |
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| 211 | & ) / zah |
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| 212 | |
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| 213 | tbif_1d(ji,3) = ( iiceform * ( zhnews2 - zdh3 ) * zta1 & |
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| 214 | & + ( iiceform * zdh3 + ( 1 - iiceform ) * zdh1 ) * zta2 & |
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| 215 | & + ( iiceform * ( zhnews2 - zdh5 ) + ( 1 - iiceform ) * ( zhnews2 - zdh1 ) ) * zta3 & |
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| 216 | & + ( iiceform * zdh5 + ( 1 - iiceform ) * zhnews2 ) * zta4 & |
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| 217 | & ) / zah |
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| 218 | !---removing the remaining part of ice formed which has been already used |
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| 219 | zbeta = h_ice_1d(ji) / ( h_ice_1d(ji) + zdhicbot(ji) ) |
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| 220 | h_ice_1d(ji) = h_ice_1d(ji) + zdhicbot(ji) |
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| 221 | tbif_1d (ji,2)= zbeta * tbif_1d(ji,2) + ( 1.0 - zbeta ) * tbif_1d(ji,3) |
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| 222 | 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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| 223 | |
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| 224 | END DO |
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| 225 | |
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| 226 | !------------------------------------------------------------- |
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| 227 | ! Computation of variation of ice volume and ice mass |
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| 228 | ! Vold = (1-Aold) * hiold ; Vnew = (1-Anew) * hinew |
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| 229 | ! dV = Vnew - Vold |
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| 230 | !------------------------------------------------------------- |
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| 231 | |
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| 232 | DO ji = kideb , kiut |
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| 233 | dvlbq_1d (ji) = ( 1. - frld_1d(ji) ) * h_ice_1d(ji) - ( 1. - zfrl_old(ji) ) * zhice_old(ji) |
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| 234 | rdmicif_1d(ji) = rdmicif_1d(ji) + rhoic * dvlbq_1d(ji) |
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| 235 | END DO |
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| 236 | |
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| 237 | IF(wrk_not_released(1, 1,2,3,4,5,6))THEN |
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| 238 | CALL ctl_stop('lim_thd_lac_2 : failed to release workspace arrays.') |
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| 239 | END IF |
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| 240 | |
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| 241 | END SUBROUTINE lim_thd_lac_2 |
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| 242 | #else |
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| 243 | !!====================================================================== |
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| 244 | !! *** MODULE limthd_lac_2 *** |
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| 245 | !! no sea ice model |
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| 246 | !!====================================================================== |
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| 247 | CONTAINS |
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| 248 | SUBROUTINE lim_thd_lac_2 ! Empty routine |
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| 249 | END SUBROUTINE lim_thd_lac_2 |
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| 250 | #endif |
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| 251 | END MODULE limthd_lac_2 |
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