| 1 | MODULE limthd_lac_2 |
|---|
| 2 | #if defined key_lim2 |
|---|
| 3 | !!====================================================================== |
|---|
| 4 | !! *** MODULE limthd_lac_2 *** |
|---|
| 5 | !! lateral thermodynamic growth of the ice |
|---|
| 6 | !!====================================================================== |
|---|
| 7 | |
|---|
| 8 | !!---------------------------------------------------------------------- |
|---|
| 9 | !! lim_lat_acr_2 : lateral accretion of ice |
|---|
| 10 | !!---------------------------------------------------------------------- |
|---|
| 11 | USE par_oce ! ocean parameters |
|---|
| 12 | USE phycst |
|---|
| 13 | USE thd_ice_2 |
|---|
| 14 | USE ice_2 |
|---|
| 15 | USE limistate_2 |
|---|
| 16 | USE lib_mpp ! MPP library |
|---|
| 17 | |
|---|
| 18 | IMPLICIT NONE |
|---|
| 19 | PRIVATE |
|---|
| 20 | |
|---|
| 21 | PUBLIC lim_thd_lac_2 ! called by lim_thd_2 |
|---|
| 22 | |
|---|
| 23 | REAL(wp) :: & ! constant values |
|---|
| 24 | epsi20 = 1.e-20 , & |
|---|
| 25 | epsi13 = 1.e-13 , & |
|---|
| 26 | zzero = 0.e0 , & |
|---|
| 27 | zone = 1.e0 |
|---|
| 28 | |
|---|
| 29 | !!---------------------------------------------------------------------- |
|---|
| 30 | !! NEMO/LIM2 3.3 , UCL - NEMO Consortium (2010) |
|---|
| 31 | !! $Id$ |
|---|
| 32 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
|---|
| 33 | !!---------------------------------------------------------------------- |
|---|
| 34 | CONTAINS |
|---|
| 35 | |
|---|
| 36 | SUBROUTINE lim_thd_lac_2( kideb, kiut ) |
|---|
| 37 | !!------------------------------------------------------------------- |
|---|
| 38 | !! *** ROUTINE lim_thd_lac_2 *** |
|---|
| 39 | !! |
|---|
| 40 | !! ** Purpose : Computation of the evolution of the ice thickness and |
|---|
| 41 | !! concentration as a function of the heat balance in the leads. |
|---|
| 42 | !! It is only used for lateral accretion |
|---|
| 43 | !! |
|---|
| 44 | !! ** Method : Ice is formed in the open water when ocean lose heat |
|---|
| 45 | !! (heat budget of open water Bl is negative) . |
|---|
| 46 | !! Computation of the increase of 1-A (ice concentration) fol- |
|---|
| 47 | !! lowing the law : |
|---|
| 48 | !! (dA/dt)acc = F[ (1-A)/(1-a) ] * [ Bl / (Li*h0) ] |
|---|
| 49 | !! where - h0 is the thickness of ice created in the lead |
|---|
| 50 | !! - a is a minimum fraction for leads |
|---|
| 51 | !! - F is a monotonic non-increasing function defined as: |
|---|
| 52 | !! F(X)=( 1 - X**exld )**(1.0/exld) |
|---|
| 53 | !! - exld is the exponent closure rate (=2 default val.) |
|---|
| 54 | !! |
|---|
| 55 | !! ** Action : - Adjustment of snow and ice thicknesses and heat |
|---|
| 56 | !! content in brine pockets |
|---|
| 57 | !! - Updating ice internal temperature |
|---|
| 58 | !! - Computation of variation of ice volume and mass |
|---|
| 59 | !! - Computation of frldb after lateral accretion and |
|---|
| 60 | !! update h_snow_1d, h_ice_1d and tbif_1d(:,:) |
|---|
| 61 | !! |
|---|
| 62 | !! ** References : |
|---|
| 63 | !! M. Maqueda, 1995, PhD Thesis, Univesidad Complutense Madrid |
|---|
| 64 | !! Fichefet T. and M. Maqueda 1997, J. Geo. Res., 102(C6), |
|---|
| 65 | !! 12609 -12646 |
|---|
| 66 | !! History : |
|---|
| 67 | !! 1.0 ! 01-04 (LIM) original code |
|---|
| 68 | !! 2.0 ! 02-08 (C. Ethe, G. Madec) F90, mpp |
|---|
| 69 | !!------------------------------------------------------------------- |
|---|
| 70 | USE wrk_nemo, ONLY: wrk_in_use, wrk_not_released |
|---|
| 71 | USE wrk_nemo, ONLY: wrk_1d_1, wrk_1d_2, wrk_1d_3, wrk_1d_4, wrk_1d_5, wrk_1d_6 |
|---|
| 72 | ! |
|---|
| 73 | INTEGER , INTENT(IN):: & |
|---|
| 74 | kideb , & ! start point on which the the computation is applied |
|---|
| 75 | kiut ! end point on which the the computation is applied |
|---|
| 76 | |
|---|
| 77 | ! * Local variables |
|---|
| 78 | INTEGER :: & |
|---|
| 79 | ji , & ! dummy loop indices |
|---|
| 80 | iicefr , & ! 1 = existing ice ; 0 = no ice |
|---|
| 81 | iiceform , & ! 1 = ice formed ; 0 = no ice formed |
|---|
| 82 | ihemis ! dummy indice |
|---|
| 83 | REAL(wp), POINTER, DIMENSION(:) :: & |
|---|
| 84 | zqbgow , & ! heat budget of the open water (negative) |
|---|
| 85 | zfrl_old , & ! previous sea/ice fraction |
|---|
| 86 | zhice_old , & ! previous ice thickness |
|---|
| 87 | zhice0 , & ! thickness of newly formed ice in leads |
|---|
| 88 | zfrlmin , & ! minimum fraction for leads |
|---|
| 89 | zdhicbot ! part of thickness of newly formed ice in leads which |
|---|
| 90 | ! has been already used in transport for example |
|---|
| 91 | REAL(wp) :: & |
|---|
| 92 | zhemis , & ! hemisphere (0 = North, 1 = South) |
|---|
| 93 | zhicenew , & ! new ice thickness |
|---|
| 94 | zholds2 , & ! ratio of previous ice thickness and 2 |
|---|
| 95 | zhnews2 , & ! ratio of new ice thickness and 2 |
|---|
| 96 | zfrlnew , & ! new sea/ice fraction |
|---|
| 97 | zfrld , & ! ratio of sea/ice fraction and minimum fraction for leads |
|---|
| 98 | zfrrate , & ! leads-closure rate |
|---|
| 99 | zdfrl ! sea-ice fraction increment |
|---|
| 100 | REAL(wp) :: & |
|---|
| 101 | zdh1 , zdh2 , zdh3 , zdh4, zdh5 , & ! tempory scalars |
|---|
| 102 | ztint , zta1 , zta2 , zta3 , zta4 , & |
|---|
| 103 | zah, zalpha , zbeta |
|---|
| 104 | !!--------------------------------------------------------------------- |
|---|
| 105 | |
|---|
| 106 | IF( wrk_in_use(1, 1,2,3,4,5,6) ) THEN |
|---|
| 107 | CALL ctl_stop('lim_thd_lac_2 : requestead workspace arrays unavailable') ; RETURN |
|---|
| 108 | ENDIF |
|---|
| 109 | ! Set-up pointers to sub-arrays of workspace arrays |
|---|
| 110 | zqbgow => wrk_1d_1(1:jpij) |
|---|
| 111 | zfrl_old => wrk_1d_2(1:jpij) |
|---|
| 112 | zhice_old => wrk_1d_3(1:jpij) |
|---|
| 113 | zhice0 => wrk_1d_4(1:jpij) |
|---|
| 114 | zfrlmin => wrk_1d_5(1:jpij) |
|---|
| 115 | zdhicbot => wrk_1d_6(1:jpij) |
|---|
| 116 | |
|---|
| 117 | !-------------------------------------------------------------- |
|---|
| 118 | ! Computation of the heat budget of the open water (negative) |
|---|
| 119 | !-------------------------------------------------------------- |
|---|
| 120 | |
|---|
| 121 | DO ji = kideb , kiut |
|---|
| 122 | zqbgow(ji) = qldif_1d(ji) - qcmif_1d(ji) |
|---|
| 123 | END DO |
|---|
| 124 | |
|---|
| 125 | !----------------------------------------------------------------- |
|---|
| 126 | ! Taking the appropriate values for the corresponding hemisphere |
|---|
| 127 | !----------------------------------------------------------------- |
|---|
| 128 | DO ji = kideb , kiut |
|---|
| 129 | zhemis = MAX( zzero , SIGN( zone , frld_1d(ji) - 2.0 ) ) |
|---|
| 130 | ihemis = INT( 1 + zhemis ) |
|---|
| 131 | zhice0 (ji) = hiccrit( ihemis ) |
|---|
| 132 | zfrlmin (ji) = acrit ( ihemis ) |
|---|
| 133 | frld_1d (ji) = frld_1d(ji) - 2.0 * zhemis |
|---|
| 134 | zfrl_old(ji) = frld_1d(ji) |
|---|
| 135 | END DO |
|---|
| 136 | |
|---|
| 137 | !------------------------------------------------------------------- |
|---|
| 138 | ! Lateral Accretion (modification of the fraction of open water) |
|---|
| 139 | ! The ice formed in the leads has always a thickness zhice0, but |
|---|
| 140 | ! only a fraction zfrrate of the ice formed contributes to the |
|---|
| 141 | ! increase of the ice fraction. The remaining part (1-zfrrate) |
|---|
| 142 | ! is rather assumed to lead to an increase in the thickness of the |
|---|
| 143 | ! pre-existing ice (transport for example). |
|---|
| 144 | ! Morales Maqueda, 1995 - Fichefet and Morales Maqueda, 1997 |
|---|
| 145 | !--------------------------------------------------------------------- |
|---|
| 146 | |
|---|
| 147 | !CDIR NOVERRCHK |
|---|
| 148 | DO ji = kideb , kiut |
|---|
| 149 | iicefr = 1 - MAX( 0, INT( SIGN( 1.5 * zone , zfrl_old(ji) - 1.0 + epsi13 ) ) ) |
|---|
| 150 | !---computation of the leads-closure rate |
|---|
| 151 | zfrld = MIN( zone , ( 1.0 - frld_1d(ji) ) / ( 1.0 - zfrlmin(ji) ) ) |
|---|
| 152 | zfrrate = ( 1.0 - zfrld**exld )**( 1.0 / exld ) |
|---|
| 153 | !--computation of the sea-ice fraction increment and the new fraction |
|---|
| 154 | zdfrl = ( zfrrate / zhice0(ji) ) * ( zqbgow(ji) / xlic ) |
|---|
| 155 | zfrlnew = zfrl_old(ji) + zdfrl |
|---|
| 156 | !--update the sea-ice fraction |
|---|
| 157 | frld_1d (ji) = MAX( zfrlnew , zfrlmin(ji) ) |
|---|
| 158 | !--computation of the remaining part of ice thickness which has been already used |
|---|
| 159 | zdhicbot(ji) = ( frld_1d(ji) - zfrlnew ) * zhice0(ji) / ( 1.0 - zfrlmin(ji) ) & |
|---|
| 160 | - ( ( 1.0 - zfrrate ) / ( 1.0 - frld_1d(ji) ) ) * ( zqbgow(ji) / xlic ) |
|---|
| 161 | END DO |
|---|
| 162 | |
|---|
| 163 | !---------------------------------------------------------------------------------------- |
|---|
| 164 | ! Ajustement of snow and ice thicknesses and updating the total heat stored in brine pockets |
|---|
| 165 | ! The thickness of newly formed ice is averaged with that of the pre-existing |
|---|
| 166 | ! (1-Anew) * hinew = (1-Aold) * hiold + ((1-Anew)-(1-Aold)) * h0 |
|---|
| 167 | ! Snow is distributed over the new ice-covered area |
|---|
| 168 | ! (1-Anew) * hsnew = (1-Aold) * hsold |
|---|
| 169 | !-------------------------------------------------------------------------------------------- |
|---|
| 170 | |
|---|
| 171 | DO ji = kideb , kiut |
|---|
| 172 | iicefr = 1 - MAX( 0, INT( SIGN( 1.5 * zone , zfrl_old(ji) - 1.0 + epsi13 ) ) ) |
|---|
| 173 | zhice_old(ji) = h_ice_1d(ji) |
|---|
| 174 | zhicenew = iicefr * zhice_old(ji) + ( 1 - iicefr ) * zhice0(ji) |
|---|
| 175 | zalpha = ( 1. - zfrl_old(ji) ) / ( 1.- frld_1d(ji) ) |
|---|
| 176 | h_snow_1d(ji) = zalpha * h_snow_1d(ji) |
|---|
| 177 | h_ice_1d (ji) = zalpha * zhicenew + ( 1.0 - zalpha ) * zhice0(ji) |
|---|
| 178 | qstbif_1d(ji) = zalpha * qstbif_1d(ji) |
|---|
| 179 | END DO |
|---|
| 180 | |
|---|
| 181 | !------------------------------------------------------- |
|---|
| 182 | ! Ajustement of ice internal temperatures |
|---|
| 183 | !------------------------------------------------------- |
|---|
| 184 | |
|---|
| 185 | DO ji = kideb , kiut |
|---|
| 186 | iicefr = 1 - MAX( 0, INT( SIGN( 1.5 * zone , zfrl_old(ji) - 1.0 + epsi13 ) ) ) |
|---|
| 187 | iiceform = 1 - MAX( 0 ,INT( SIGN( 1.5 * zone , zhice0(ji) - h_ice_1d(ji) ) ) ) |
|---|
| 188 | zholds2 = zhice_old(ji)/ 2. |
|---|
| 189 | zhnews2 = h_ice_1d(ji) / 2. |
|---|
| 190 | zdh1 = MAX( zzero , zhice_old(ji) - zhnews2 ) |
|---|
| 191 | zdh2 = MAX( zzero , -zhice_old(ji) + zhnews2 ) |
|---|
| 192 | zdh3 = MAX( zzero , h_ice_1d(ji) - zholds2 ) |
|---|
| 193 | zdh4 = MAX( zzero , -h_ice_1d(ji) + zholds2 ) |
|---|
| 194 | zdh5 = MAX( zzero , zhice0(ji) - zholds2 ) |
|---|
| 195 | ztint = iiceform * ( ( zholds2 - zdh3 ) * tbif_1d(ji,3) + zdh4 * tbif_1d(ji,2) ) & |
|---|
| 196 | & / MAX( epsi20 , h_ice_1d(ji) - zhice0(ji) ) & |
|---|
| 197 | & + ( 1 - iiceform ) * tfu_1d(ji) |
|---|
| 198 | zta1 = iicefr * ( 1. - zfrl_old(ji) ) * tbif_1d(ji,2) |
|---|
| 199 | zta2 = iicefr * ( 1. - zfrl_old(ji) ) * tbif_1d(ji,3) |
|---|
| 200 | zta3 = iicefr * ( 1. - zfrl_old(ji) ) * ztint |
|---|
| 201 | zta4 = ( zfrl_old(ji) - frld_1d (ji) ) * tfu_1d(ji) |
|---|
| 202 | zah = ( 1. - frld_1d(ji) ) * zhnews2 |
|---|
| 203 | |
|---|
| 204 | tbif_1d(ji,2) = ( MIN( zhnews2 , zholds2 ) * zta1 & |
|---|
| 205 | & + ( 1 - iiceform ) * ( zholds2 - zdh1 ) * zta2 & |
|---|
| 206 | & + ( iiceform * ( zhnews2 - zhice0(ji) + zdh5 ) + ( 1 - iiceform ) * zdh2 ) * zta3 & |
|---|
| 207 | & + MIN ( zhnews2 , zhice0(ji) ) * zta4 & |
|---|
| 208 | & ) / zah |
|---|
| 209 | |
|---|
| 210 | tbif_1d(ji,3) = ( iiceform * ( zhnews2 - zdh3 ) * zta1 & |
|---|
| 211 | & + ( iiceform * zdh3 + ( 1 - iiceform ) * zdh1 ) * zta2 & |
|---|
| 212 | & + ( iiceform * ( zhnews2 - zdh5 ) + ( 1 - iiceform ) * ( zhnews2 - zdh1 ) ) * zta3 & |
|---|
| 213 | & + ( iiceform * zdh5 + ( 1 - iiceform ) * zhnews2 ) * zta4 & |
|---|
| 214 | & ) / zah |
|---|
| 215 | !---removing the remaining part of ice formed which has been already used |
|---|
| 216 | zbeta = h_ice_1d(ji) / ( h_ice_1d(ji) + zdhicbot(ji) ) |
|---|
| 217 | h_ice_1d(ji) = h_ice_1d(ji) + zdhicbot(ji) |
|---|
| 218 | tbif_1d (ji,2)= zbeta * tbif_1d(ji,2) + ( 1.0 - zbeta ) * tbif_1d(ji,3) |
|---|
| 219 | tbif_1d (ji,3)= ( 2. * zbeta - 1.0 ) * tbif_1d(ji,3) + ( 2. * zdhicbot(ji) / h_ice_1d(ji) ) * tfu_1d(ji) |
|---|
| 220 | |
|---|
| 221 | END DO |
|---|
| 222 | |
|---|
| 223 | !------------------------------------------------------------- |
|---|
| 224 | ! Computation of variation of ice volume and ice mass |
|---|
| 225 | ! Vold = (1-Aold) * hiold ; Vnew = (1-Anew) * hinew |
|---|
| 226 | ! dV = Vnew - Vold |
|---|
| 227 | !------------------------------------------------------------- |
|---|
| 228 | |
|---|
| 229 | DO ji = kideb , kiut |
|---|
| 230 | dvlbq_1d (ji) = ( 1. - frld_1d(ji) ) * h_ice_1d(ji) - ( 1. - zfrl_old(ji) ) * zhice_old(ji) |
|---|
| 231 | rdmicif_1d(ji) = rdmicif_1d(ji) + rhoic * dvlbq_1d(ji) |
|---|
| 232 | END DO |
|---|
| 233 | |
|---|
| 234 | IF( wrk_not_released(1, 1,2,3,4,5,6) ) CALL ctl_stop('lim_thd_lac_2 : failed to release workspace arrays.') |
|---|
| 235 | ! |
|---|
| 236 | END SUBROUTINE lim_thd_lac_2 |
|---|
| 237 | #else |
|---|
| 238 | !!---------------------------------------------------------------------- |
|---|
| 239 | !! *** MODULE limthd_lac_2 *** |
|---|
| 240 | !! no sea ice model |
|---|
| 241 | !!---------------------------------------------------------------------- |
|---|
| 242 | CONTAINS |
|---|
| 243 | SUBROUTINE lim_thd_lac_2 ! Empty routine |
|---|
| 244 | END SUBROUTINE lim_thd_lac_2 |
|---|
| 245 | #endif |
|---|
| 246 | !!====================================================================== |
|---|
| 247 | END MODULE limthd_lac_2 |
|---|
