[8409] | 1 | MODULE icerdgrft |
---|
| 2 | !!====================================================================== |
---|
| 3 | !! *** MODULE icerdgrft *** |
---|
| 4 | !! LIM-3 : Mechanical impact on ice thickness distribution |
---|
| 5 | !!====================================================================== |
---|
| 6 | !! History : LIM ! 2006-02 (M. Vancoppenolle) Original code |
---|
| 7 | !! 3.2 ! 2009-07 (M. Vancoppenolle, Y. Aksenov, G. Madec) bug correction in smsw & sfx_dyn |
---|
| 8 | !! 4.0 ! 2011-02 (G. Madec) dynamical allocation |
---|
| 9 | !!---------------------------------------------------------------------- |
---|
| 10 | #if defined key_lim3 |
---|
| 11 | !!---------------------------------------------------------------------- |
---|
| 12 | !! 'key_lim3' LIM-3 sea-ice model |
---|
| 13 | !!---------------------------------------------------------------------- |
---|
[8486] | 14 | USE par_oce ! ocean parameters |
---|
| 15 | USE dom_oce ! ocean domain |
---|
| 16 | USE phycst ! physical constants (ocean directory) |
---|
| 17 | USE sbc_oce , ONLY : sss_m, sst_m ! surface boundary condition: ocean fields |
---|
| 18 | USE ice1D ! sea-ice: thermodynamics |
---|
| 19 | USE ice ! sea-ice: variables |
---|
| 20 | USE icevar ! sea-ice: operations |
---|
| 21 | USE icectl ! sea-ice: control prints |
---|
[8409] | 22 | ! |
---|
[8486] | 23 | USE lbclnk ! lateral boundary condition - MPP exchanges |
---|
| 24 | USE lib_mpp ! MPP library |
---|
| 25 | USE in_out_manager ! I/O manager |
---|
| 26 | USE iom ! I/O manager |
---|
| 27 | USE lib_fortran ! glob_sum |
---|
| 28 | USE timing ! Timing |
---|
[8409] | 29 | |
---|
| 30 | IMPLICIT NONE |
---|
| 31 | PRIVATE |
---|
| 32 | |
---|
| 33 | PUBLIC ice_rdgrft ! called by ice_stp |
---|
[8486] | 34 | PUBLIC ice_rdgrft_icestrength ! called by icerhg_evp |
---|
| 35 | PUBLIC ice_rdgrft_init ! called by ice_stp |
---|
| 36 | PUBLIC ice_rdgrft_alloc ! called by ice_init |
---|
[8409] | 37 | |
---|
| 38 | !----------------------------------------------------------------------- |
---|
| 39 | ! Variables shared among ridging subroutines |
---|
| 40 | !----------------------------------------------------------------------- |
---|
| 41 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: asum ! sum of total ice and open water area |
---|
| 42 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: aksum ! ratio of area removed to area ridged |
---|
| 43 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: athorn ! participation function; fraction of ridging/closing associated w/ category n |
---|
| 44 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: hrmin ! minimum ridge thickness |
---|
| 45 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: hrmax ! maximum ridge thickness |
---|
| 46 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: hraft ! thickness of rafted ice |
---|
| 47 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: krdg ! thickness of ridging ice / mean ridge thickness |
---|
| 48 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: aridge ! participating ice ridging |
---|
| 49 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: araft ! participating ice rafting |
---|
| 50 | |
---|
| 51 | REAL(wp), PARAMETER :: krdgmin = 1.1_wp ! min ridge thickness multiplier |
---|
| 52 | REAL(wp), PARAMETER :: kraft = 0.5_wp ! rafting multipliyer |
---|
| 53 | |
---|
[8486] | 54 | !!gm Cp is 1) not DOCTOR, |
---|
| 55 | !! 2) misleading name: heat capacity instead of a constant, |
---|
| 56 | !! 3) recomputed at each time-step, whereas it is stored in the module memory... |
---|
| 57 | !! ===>>> compute it one for all inside the IF( kt == nit000 ) (i.e. without the ".AND. lwp") |
---|
| 58 | REAL(wp) :: Cp ! ??? !!gm Not doctor ! |
---|
| 59 | |
---|
[8409] | 60 | ! |
---|
| 61 | ! |
---|
| 62 | !!---------------------------------------------------------------------- |
---|
[8486] | 63 | !! NEMO/ICE 4.0 , NEMO Consortium (2017) |
---|
[8409] | 64 | !! $Id: icerdgrft.F90 8378 2017-07-26 13:55:59Z clem $ |
---|
| 65 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
---|
| 66 | !!---------------------------------------------------------------------- |
---|
| 67 | CONTAINS |
---|
| 68 | |
---|
| 69 | INTEGER FUNCTION ice_rdgrft_alloc() |
---|
| 70 | !!---------------------------------------------------------------------! |
---|
| 71 | !! *** ROUTINE ice_rdgrft_alloc *** |
---|
| 72 | !!---------------------------------------------------------------------! |
---|
[8486] | 73 | ALLOCATE( asum (jpi,jpj) , athorn(jpi,jpj,0:jpl) , aksum (jpi,jpj) , & |
---|
| 74 | & hrmin(jpi,jpj,jpl) , hraft (jpi,jpj,jpl) , aridge(jpi,jpj,jpl) , & |
---|
| 75 | & hrmax(jpi,jpj,jpl) , krdg (jpi,jpj,jpl) , araft (jpi,jpj,jpl) , STAT=ice_rdgrft_alloc ) |
---|
[8409] | 76 | ! |
---|
| 77 | IF( ice_rdgrft_alloc /= 0 ) CALL ctl_warn( 'ice_rdgrft_alloc: failed to allocate arrays' ) |
---|
| 78 | ! |
---|
| 79 | END FUNCTION ice_rdgrft_alloc |
---|
| 80 | |
---|
| 81 | |
---|
[8426] | 82 | SUBROUTINE ice_rdgrft( kt ) |
---|
[8409] | 83 | !!---------------------------------------------------------------------! |
---|
| 84 | !! *** ROUTINE ice_rdgrft *** |
---|
| 85 | !! |
---|
| 86 | !! ** Purpose : computes the mechanical redistribution of ice thickness |
---|
| 87 | !! |
---|
| 88 | !! ** Method : Steps : |
---|
| 89 | !! 1) Thickness categories boundaries, ice / o.w. concentrations |
---|
| 90 | !! Ridge preparation |
---|
| 91 | !! 2) Dynamical inputs (closing rate, divu_adv, opning) |
---|
| 92 | !! 3) Ridging iteration |
---|
| 93 | !! 4) Ridging diagnostics |
---|
| 94 | !! 5) Heat, salt and freshwater fluxes |
---|
| 95 | !! 6) Compute increments of tate variables and come back to old values |
---|
| 96 | !! |
---|
| 97 | !! References : Flato, G. M., and W. D. Hibler III, 1995, JGR, 100, 18,611-18,626. |
---|
| 98 | !! Hibler, W. D. III, 1980, MWR, 108, 1943-1973, 1980. |
---|
| 99 | !! Rothrock, D. A., 1975: JGR, 80, 4514-4519. |
---|
| 100 | !! Thorndike et al., 1975, JGR, 80, 4501-4513. |
---|
| 101 | !! Bitz et al., JGR, 2001 |
---|
| 102 | !! Amundrud and Melling, JGR 2005 |
---|
| 103 | !! Babko et al., JGR 2002 |
---|
| 104 | !! |
---|
| 105 | !! This routine is based on CICE code and authors William H. Lipscomb, |
---|
| 106 | !! and Elizabeth C. Hunke, LANL are gratefully acknowledged |
---|
| 107 | !!--------------------------------------------------------------------! |
---|
[8426] | 108 | INTEGER, INTENT(in) :: kt ! number of iteration |
---|
| 109 | !! |
---|
[8486] | 110 | INTEGER :: ji, jj, jk, jl ! dummy loop index |
---|
| 111 | INTEGER :: niter ! local integer |
---|
| 112 | INTEGER :: iterate_ridging ! if =1, repeat the ridging |
---|
| 113 | REAL(wp) :: za, zfac, zcs_2 ! local scalar |
---|
[8409] | 114 | CHARACTER (len = 15) :: fieldid |
---|
[8486] | 115 | REAL(wp), DIMENSION(jpi,jpj) :: closing_net ! net rate at which area is removed (1/s) |
---|
| 116 | ! ! (ridging ice area - area of new ridges) / dt |
---|
| 117 | REAL(wp), DIMENSION(jpi,jpj) :: divu_adv ! divu as implied by transport scheme (1/s) |
---|
| 118 | REAL(wp), DIMENSION(jpi,jpj) :: opning ! rate of opening due to divergence/shear |
---|
| 119 | REAL(wp), DIMENSION(jpi,jpj) :: closing_gross ! rate at which area removed, not counting area of new ridges |
---|
[8409] | 120 | ! |
---|
| 121 | INTEGER, PARAMETER :: nitermax = 20 |
---|
| 122 | ! |
---|
| 123 | REAL(wp) :: zvi_b, zsmv_b, zei_b, zfs_b, zfw_b, zft_b |
---|
| 124 | !!----------------------------------------------------------------------------- |
---|
| 125 | IF( nn_timing == 1 ) CALL timing_start('icerdgrft') |
---|
| 126 | |
---|
[8426] | 127 | IF( kt == nit000 .AND. lwp ) THEN |
---|
| 128 | WRITE(numout,*) |
---|
[8486] | 129 | WRITE(numout,*)'icerdgrft : ice ridging and rafting' |
---|
| 130 | WRITE(numout,*)'~~~~~~~~~~' |
---|
[8426] | 131 | ENDIF |
---|
[8486] | 132 | !!gm should be: |
---|
| 133 | ! IF( kt == nit000 ) THEN |
---|
| 134 | ! IF(lwp) WRITE(numout,*) |
---|
| 135 | ! IF(lwp) WRITE(numout,*)'icerdgrft : ???' |
---|
| 136 | ! IF(lwp) WRITE(numout,*)'~~~~~~~~~~' |
---|
| 137 | ! ! |
---|
| 138 | ! Cp = 0.5 * grav * (rau0-rhoic) * rhoic * r1_rau0 ! proport const for PE |
---|
| 139 | ! ! |
---|
| 140 | !!gm why not adding here zcs_2 computation |
---|
| 141 | ! ! |
---|
| 142 | ! ENDIF |
---|
| 143 | !!gm end |
---|
| 144 | |
---|
| 145 | ! ! conservation test |
---|
| 146 | IF( ln_limdiachk ) CALL ice_cons_hsm(0, 'icerdgrft', zvi_b, zsmv_b, zei_b, zfw_b, zfs_b, zft_b) |
---|
[8426] | 147 | |
---|
[8409] | 148 | !-----------------------------------------------------------------------------! |
---|
| 149 | ! 1) Thickness categories boundaries, ice / o.w. concentrations, init_ons |
---|
| 150 | !-----------------------------------------------------------------------------! |
---|
[8486] | 151 | Cp = 0.5 * grav * (rau0-rhoic) * rhoic * r1_rau0 ! proport const for PE |
---|
| 152 | zcs_2 = rn_cs * 0.5_wp |
---|
[8409] | 153 | ! |
---|
[8486] | 154 | CALL ice_rdgrft_ridgeprep ! prepare ridging |
---|
[8409] | 155 | ! |
---|
[8486] | 156 | DO jj = 1, jpj ! Initialize arrays. |
---|
[8409] | 157 | DO ji = 1, jpi |
---|
| 158 | !-----------------------------------------------------------------------------! |
---|
| 159 | ! 2) Dynamical inputs (closing rate, divu_adv, opning) |
---|
| 160 | !-----------------------------------------------------------------------------! |
---|
| 161 | ! |
---|
| 162 | ! 2.1 closing_net |
---|
| 163 | !----------------- |
---|
| 164 | ! Compute the net rate of closing due to convergence |
---|
| 165 | ! and shear, based on Flato and Hibler (1995). |
---|
| 166 | ! |
---|
| 167 | ! The energy dissipation rate is equal to the net closing rate |
---|
| 168 | ! times the ice strength. |
---|
| 169 | ! |
---|
| 170 | ! NOTE: The NET closing rate is equal to the rate that open water |
---|
| 171 | ! area is removed, plus the rate at which ice area is removed by |
---|
| 172 | ! ridging, minus the rate at which area is added in new ridges. |
---|
| 173 | ! The GROSS closing rate is equal to the first two terms (open |
---|
| 174 | ! water closing and thin ice ridging) without the third term |
---|
| 175 | ! (thick, newly ridged ice). |
---|
| 176 | |
---|
[8486] | 177 | closing_net(ji,jj) = zcs_2 * ( delta_i(ji,jj) - ABS( divu_i(ji,jj) ) ) - MIN( divu_i(ji,jj), 0._wp ) |
---|
[8409] | 178 | |
---|
| 179 | ! 2.2 divu_adv |
---|
| 180 | !-------------- |
---|
| 181 | ! Compute divu_adv, the divergence rate given by the transport/ |
---|
| 182 | ! advection scheme, which may not be equal to divu as computed |
---|
| 183 | ! from the velocity field. |
---|
| 184 | ! |
---|
| 185 | ! If divu_adv < 0, make sure the closing rate is large enough |
---|
| 186 | ! to give asum = 1.0 after ridging. |
---|
| 187 | |
---|
| 188 | divu_adv(ji,jj) = ( 1._wp - asum(ji,jj) ) * r1_rdtice ! asum found in ridgeprep |
---|
| 189 | |
---|
| 190 | IF( divu_adv(ji,jj) < 0._wp ) closing_net(ji,jj) = MAX( closing_net(ji,jj), -divu_adv(ji,jj) ) |
---|
| 191 | |
---|
| 192 | ! 2.3 opning |
---|
| 193 | !------------ |
---|
| 194 | ! Compute the (non-negative) opening rate that will give asum = 1.0 after ridging. |
---|
| 195 | opning(ji,jj) = closing_net(ji,jj) + divu_adv(ji,jj) |
---|
| 196 | END DO |
---|
| 197 | END DO |
---|
| 198 | |
---|
| 199 | !-----------------------------------------------------------------------------! |
---|
| 200 | ! 3) Ridging iteration |
---|
| 201 | !-----------------------------------------------------------------------------! |
---|
| 202 | niter = 1 ! iteration counter |
---|
| 203 | iterate_ridging = 1 |
---|
| 204 | |
---|
| 205 | DO WHILE ( iterate_ridging > 0 .AND. niter < nitermax ) |
---|
| 206 | |
---|
| 207 | ! 3.2 closing_gross |
---|
| 208 | !-----------------------------------------------------------------------------! |
---|
| 209 | ! Based on the ITD of ridging and ridged ice, convert the net |
---|
| 210 | ! closing rate to a gross closing rate. |
---|
| 211 | ! NOTE: 0 < aksum <= 1 |
---|
| 212 | closing_gross(:,:) = closing_net(:,:) / aksum(:,:) |
---|
| 213 | |
---|
| 214 | ! correction to closing rate and opening if closing rate is excessive |
---|
| 215 | !--------------------------------------------------------------------- |
---|
| 216 | ! Reduce the closing rate if more than 100% of the open water |
---|
| 217 | ! would be removed. Reduce the opening rate proportionately. |
---|
| 218 | DO jj = 1, jpj |
---|
| 219 | DO ji = 1, jpi |
---|
| 220 | za = ( opning(ji,jj) - athorn(ji,jj,0) * closing_gross(ji,jj) ) * rdt_ice |
---|
| 221 | IF ( za < 0._wp .AND. za > - ato_i(ji,jj) ) THEN ! would lead to negative ato_i |
---|
| 222 | zfac = - ato_i(ji,jj) / za |
---|
| 223 | opning(ji,jj) = athorn(ji,jj,0) * closing_gross(ji,jj) - ato_i(ji,jj) * r1_rdtice |
---|
| 224 | ELSEIF( za > 0._wp .AND. za > ( asum(ji,jj) - ato_i(ji,jj) ) ) THEN ! would lead to ato_i > asum |
---|
| 225 | zfac = ( asum(ji,jj) - ato_i(ji,jj) ) / za |
---|
| 226 | opning(ji,jj) = athorn(ji,jj,0) * closing_gross(ji,jj) + ( asum(ji,jj) - ato_i(ji,jj) ) * r1_rdtice |
---|
| 227 | ENDIF |
---|
| 228 | END DO |
---|
| 229 | END DO |
---|
| 230 | |
---|
| 231 | ! correction to closing rate / opening if excessive ice removal |
---|
| 232 | !--------------------------------------------------------------- |
---|
| 233 | ! Reduce the closing rate if more than 100% of any ice category |
---|
| 234 | ! would be removed. Reduce the opening rate proportionately. |
---|
| 235 | DO jl = 1, jpl |
---|
| 236 | DO jj = 1, jpj |
---|
| 237 | DO ji = 1, jpi |
---|
| 238 | za = athorn(ji,jj,jl) * closing_gross(ji,jj) * rdt_ice |
---|
| 239 | IF( za > a_i(ji,jj,jl) ) THEN |
---|
| 240 | zfac = a_i(ji,jj,jl) / za |
---|
| 241 | closing_gross(ji,jj) = closing_gross(ji,jj) * zfac |
---|
| 242 | ENDIF |
---|
| 243 | END DO |
---|
| 244 | END DO |
---|
| 245 | END DO |
---|
| 246 | |
---|
| 247 | ! 3.3 Redistribute area, volume, and energy. |
---|
| 248 | !-----------------------------------------------------------------------------! |
---|
| 249 | CALL ice_rdgrft_ridgeshift( opning, closing_gross ) |
---|
| 250 | |
---|
| 251 | ! 3.4 Compute total area of ice plus open water after ridging. |
---|
| 252 | !-----------------------------------------------------------------------------! |
---|
| 253 | ! This is in general not equal to one because of divergence during transport |
---|
| 254 | asum(:,:) = ato_i(:,:) + SUM( a_i, dim=3 ) |
---|
| 255 | |
---|
| 256 | ! 3.5 Do we keep on iterating ??? |
---|
| 257 | !-----------------------------------------------------------------------------! |
---|
| 258 | ! Check whether asum = 1. If not (because the closing and opening |
---|
| 259 | ! rates were reduced above), ridge again with new rates. |
---|
| 260 | iterate_ridging = 0 |
---|
| 261 | DO jj = 1, jpj |
---|
| 262 | DO ji = 1, jpi |
---|
| 263 | IF( ABS( asum(ji,jj) - 1._wp ) < epsi10 ) THEN |
---|
| 264 | closing_net(ji,jj) = 0._wp |
---|
| 265 | opning (ji,jj) = 0._wp |
---|
| 266 | ato_i (ji,jj) = MAX( 0._wp, 1._wp - SUM( a_i(ji,jj,:) ) ) |
---|
| 267 | ELSE |
---|
| 268 | iterate_ridging = 1 |
---|
| 269 | divu_adv (ji,jj) = ( 1._wp - asum(ji,jj) ) * r1_rdtice |
---|
| 270 | closing_net(ji,jj) = MAX( 0._wp, -divu_adv(ji,jj) ) |
---|
| 271 | opning (ji,jj) = MAX( 0._wp, divu_adv(ji,jj) ) |
---|
| 272 | ENDIF |
---|
| 273 | END DO |
---|
| 274 | END DO |
---|
| 275 | IF( lk_mpp ) CALL mpp_max( iterate_ridging ) |
---|
| 276 | |
---|
| 277 | ! Repeat if necessary. |
---|
| 278 | ! NOTE: If strength smoothing is turned on, the ridging must be |
---|
[8486] | 279 | ! iterated globally because of the boundary update in the smoothing. |
---|
[8409] | 280 | niter = niter + 1 |
---|
[8486] | 281 | ! |
---|
[8409] | 282 | IF( iterate_ridging == 1 ) THEN |
---|
| 283 | CALL ice_rdgrft_ridgeprep |
---|
| 284 | IF( niter > nitermax ) THEN |
---|
| 285 | WRITE(numout,*) ' ALERTE : non-converging ridging scheme ' |
---|
| 286 | WRITE(numout,*) ' niter, iterate_ridging ', niter, iterate_ridging |
---|
| 287 | ENDIF |
---|
| 288 | ENDIF |
---|
[8486] | 289 | ! |
---|
[8409] | 290 | END DO !! on the do while over iter |
---|
| 291 | |
---|
[8424] | 292 | CALL ice_var_agg( 1 ) |
---|
[8409] | 293 | |
---|
| 294 | !-----------------------------------------------------------------------------! |
---|
| 295 | ! control prints |
---|
| 296 | !-----------------------------------------------------------------------------! |
---|
[8486] | 297 | ! ! conservation test |
---|
| 298 | IF( ln_limdiachk ) CALL ice_cons_hsm(1, 'icerdgrft', zvi_b, zsmv_b, zei_b, zfw_b, zfs_b, zft_b) |
---|
[8409] | 299 | |
---|
[8486] | 300 | ! ! control prints |
---|
| 301 | IF( ln_ctl ) CALL ice_prt3D( 'icerdgrft' ) |
---|
[8409] | 302 | ! |
---|
| 303 | IF( nn_timing == 1 ) CALL timing_stop('icerdgrft') |
---|
[8486] | 304 | ! |
---|
[8409] | 305 | END SUBROUTINE ice_rdgrft |
---|
| 306 | |
---|
[8486] | 307 | |
---|
[8409] | 308 | SUBROUTINE ice_rdgrft_ridgeprep |
---|
| 309 | !!---------------------------------------------------------------------! |
---|
| 310 | !! *** ROUTINE ice_rdgrft_ridgeprep *** |
---|
| 311 | !! |
---|
| 312 | !! ** Purpose : preparation for ridging and strength calculations |
---|
| 313 | !! |
---|
| 314 | !! ** Method : Compute the thickness distribution of the ice and open water |
---|
| 315 | !! participating in ridging and of the resulting ridges. |
---|
| 316 | !!---------------------------------------------------------------------! |
---|
[8486] | 317 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
| 318 | REAL(wp) :: Gstari, astari, hrmean, zdummy ! local scalar !!gm DOCTOR norme should start with z !!!!! |
---|
[8409] | 319 | REAL(wp), DIMENSION(jpi,jpj,-1:jpl) :: Gsum ! Gsum(n) = sum of areas in categories 0 to n |
---|
| 320 | !------------------------------------------------------------------------------! |
---|
| 321 | |
---|
[8486] | 322 | Gstari = 1._wp / rn_gstar |
---|
| 323 | astari = 1._wp / rn_astar |
---|
| 324 | aksum(:,:) = 0._wp |
---|
| 325 | athorn(:,:,:) = 0._wp |
---|
| 326 | aridge(:,:,:) = 0._wp |
---|
| 327 | araft (:,:,:) = 0._wp |
---|
[8409] | 328 | |
---|
[8486] | 329 | CALL ice_var_zapsmall ! Zero out categories with very small areas |
---|
[8409] | 330 | |
---|
[8486] | 331 | ! DO jl = 1, jpl ! Ice thickness needed for rafting |
---|
| 332 | ! DO jj = 1, jpj |
---|
| 333 | ! DO ji = 1, jpi |
---|
| 334 | !!gm rswitch = MAX( 0._wp , SIGN( 1._wp, a_i(ji,jj,jl) - epsi20 ) ) |
---|
| 335 | !!gm ht_i(ji,jj,jl) = v_i (ji,jj,jl) / MAX( a_i(ji,jj,jl) , epsi20 ) * rswitch |
---|
| 336 | ! IF( a_i(ji,jj,jl) >= epsi20 ) THEN ; ht_i(ji,jj,jl) = v_i (ji,jj,jl) / a_i(ji,jj,jl) |
---|
| 337 | ! ELSE ; ht_i(ji,jj,jl) = 0._wp |
---|
| 338 | ! ENDIF |
---|
| 339 | ! END DO |
---|
| 340 | ! END DO |
---|
| 341 | ! END DO |
---|
| 342 | !!gm or even better : |
---|
| 343 | ! ! ! Ice thickness needed for rafting |
---|
| 344 | WHERE( a_i(:,:,:) >= epsi20 ) ; ht_i(:,:,:) = v_i (:,:,:) / a_i(:,:,:) |
---|
| 345 | ELSEWHERE ; ht_i(:,:,:) = 0._wp |
---|
| 346 | END WHERE |
---|
| 347 | !!gm end |
---|
[8409] | 348 | |
---|
| 349 | !------------------------------------------------------------------------------! |
---|
| 350 | ! 1) Participation function |
---|
| 351 | !------------------------------------------------------------------------------! |
---|
[8486] | 352 | ! |
---|
[8409] | 353 | ! Compute total area of ice plus open water. |
---|
| 354 | ! This is in general not equal to one because of divergence during transport |
---|
| 355 | asum(:,:) = ato_i(:,:) + SUM( a_i, dim=3 ) |
---|
[8486] | 356 | ! |
---|
[8409] | 357 | ! Compute cumulative thickness distribution function |
---|
| 358 | ! Compute the cumulative thickness distribution function Gsum, |
---|
| 359 | ! where Gsum(n) is the fractional area in categories 0 to n. |
---|
| 360 | ! initial value (in h = 0) equals open water area |
---|
| 361 | Gsum(:,:,-1) = 0._wp |
---|
| 362 | Gsum(:,:,0 ) = ato_i(:,:) |
---|
| 363 | ! for each value of h, you have to add ice concentration then |
---|
| 364 | DO jl = 1, jpl |
---|
| 365 | Gsum(:,:,jl) = Gsum(:,:,jl-1) + a_i(:,:,jl) |
---|
| 366 | END DO |
---|
[8486] | 367 | ! |
---|
[8409] | 368 | ! Normalize the cumulative distribution to 1 |
---|
| 369 | DO jl = 0, jpl |
---|
| 370 | Gsum(:,:,jl) = Gsum(:,:,jl) / asum(:,:) |
---|
| 371 | END DO |
---|
| 372 | |
---|
| 373 | ! 1.3 Compute participation function a(h) = b(h).g(h) (athorn) |
---|
| 374 | !-------------------------------------------------------------------------------------------------- |
---|
| 375 | ! Compute the participation function athorn; this is analogous to |
---|
| 376 | ! a(h) = b(h)g(h) as defined in Thorndike et al. (1975). |
---|
| 377 | ! area lost from category n due to ridging/closing |
---|
| 378 | ! athorn(n) = total area lost due to ridging/closing |
---|
| 379 | ! assume b(h) = (2/Gstar) * (1 - G(h)/Gstar). |
---|
| 380 | ! |
---|
| 381 | ! The expressions for athorn are found by integrating b(h)g(h) between |
---|
| 382 | ! the category boundaries. |
---|
| 383 | ! athorn is always >= 0 and SUM(athorn(0:jpl))=1 |
---|
| 384 | !----------------------------------------------------------------- |
---|
[8486] | 385 | ! |
---|
[8409] | 386 | IF( nn_partfun == 0 ) THEN !--- Linear formulation (Thorndike et al., 1975) |
---|
| 387 | DO jl = 0, jpl |
---|
| 388 | DO jj = 1, jpj |
---|
| 389 | DO ji = 1, jpi |
---|
| 390 | IF ( Gsum(ji,jj,jl) < rn_gstar ) THEN |
---|
| 391 | athorn(ji,jj,jl) = Gstari * ( Gsum(ji,jj,jl) - Gsum(ji,jj,jl-1) ) * & |
---|
| 392 | & ( 2._wp - ( Gsum(ji,jj,jl-1) + Gsum(ji,jj,jl) ) * Gstari ) |
---|
| 393 | ELSEIF( Gsum(ji,jj,jl-1) < rn_gstar ) THEN |
---|
| 394 | athorn(ji,jj,jl) = Gstari * ( rn_gstar - Gsum(ji,jj,jl-1) ) * & |
---|
| 395 | & ( 2._wp - ( Gsum(ji,jj,jl-1) + rn_gstar ) * Gstari ) |
---|
| 396 | ELSE |
---|
| 397 | athorn(ji,jj,jl) = 0._wp |
---|
| 398 | ENDIF |
---|
| 399 | END DO |
---|
| 400 | END DO |
---|
| 401 | END DO |
---|
[8486] | 402 | ! |
---|
[8409] | 403 | ELSE !--- Exponential, more stable formulation (Lipscomb et al, 2007) |
---|
| 404 | ! |
---|
| 405 | zdummy = 1._wp / ( 1._wp - EXP(-astari) ) ! precompute exponential terms using Gsum as a work array |
---|
| 406 | DO jl = -1, jpl |
---|
| 407 | Gsum(:,:,jl) = EXP( -Gsum(:,:,jl) * astari ) * zdummy |
---|
| 408 | END DO |
---|
| 409 | DO jl = 0, jpl |
---|
| 410 | athorn(:,:,jl) = Gsum(:,:,jl-1) - Gsum(:,:,jl) |
---|
| 411 | END DO |
---|
| 412 | ! |
---|
| 413 | ENDIF |
---|
| 414 | |
---|
[8486] | 415 | ! !--- Ridging and rafting participation concentrations |
---|
| 416 | IF( ln_rafting .AND. ln_ridging ) THEN !- ridging & rafting |
---|
[8409] | 417 | DO jl = 1, jpl |
---|
| 418 | DO jj = 1, jpj |
---|
| 419 | DO ji = 1, jpi |
---|
| 420 | zdummy = TANH ( rn_craft * ( ht_i(ji,jj,jl) - rn_hraft ) ) |
---|
| 421 | aridge(ji,jj,jl) = ( 1._wp + zdummy ) * 0.5_wp * athorn(ji,jj,jl) |
---|
| 422 | araft (ji,jj,jl) = athorn(ji,jj,jl) - aridge(ji,jj,jl) |
---|
| 423 | END DO |
---|
| 424 | END DO |
---|
| 425 | END DO |
---|
[8486] | 426 | ELSEIF( ln_ridging .AND. .NOT.ln_rafting ) THEN !- ridging alone |
---|
[8409] | 427 | DO jl = 1, jpl |
---|
| 428 | aridge(:,:,jl) = athorn(:,:,jl) |
---|
| 429 | END DO |
---|
[8486] | 430 | ELSEIF( ln_rafting .AND. .NOT.ln_ridging ) THEN !- rafting alone |
---|
[8409] | 431 | DO jl = 1, jpl |
---|
| 432 | araft(:,:,jl) = athorn(:,:,jl) |
---|
| 433 | END DO |
---|
| 434 | ENDIF |
---|
| 435 | |
---|
| 436 | !----------------------------------------------------------------- |
---|
| 437 | ! 2) Transfer function |
---|
| 438 | !----------------------------------------------------------------- |
---|
| 439 | ! Compute max and min ridged ice thickness for each ridging category. |
---|
| 440 | ! Assume ridged ice is uniformly distributed between hrmin and hrmax. |
---|
| 441 | ! |
---|
| 442 | ! This parameterization is a modified version of Hibler (1980). |
---|
| 443 | ! The mean ridging thickness, hrmean, is proportional to hi^(0.5) |
---|
| 444 | ! and for very thick ridging ice must be >= krdgmin*hi |
---|
| 445 | ! |
---|
| 446 | ! The minimum ridging thickness, hrmin, is equal to 2*hi |
---|
| 447 | ! (i.e., rafting) and for very thick ridging ice is |
---|
| 448 | ! constrained by hrmin <= (hrmean + hi)/2. |
---|
| 449 | ! |
---|
| 450 | ! The maximum ridging thickness, hrmax, is determined by |
---|
| 451 | ! hrmean and hrmin. |
---|
| 452 | ! |
---|
| 453 | ! These modifications have the effect of reducing the ice strength |
---|
| 454 | ! (relative to the Hibler formulation) when very thick ice is |
---|
| 455 | ! ridging. |
---|
| 456 | ! |
---|
| 457 | ! aksum = net area removed/ total area removed |
---|
| 458 | ! where total area removed = area of ice that ridges |
---|
| 459 | ! net area removed = total area removed - area of new ridges |
---|
| 460 | !----------------------------------------------------------------- |
---|
| 461 | |
---|
| 462 | aksum(:,:) = athorn(:,:,0) |
---|
| 463 | ! Transfer function |
---|
| 464 | DO jl = 1, jpl !all categories have a specific transfer function |
---|
| 465 | DO jj = 1, jpj |
---|
| 466 | DO ji = 1, jpi |
---|
[8486] | 467 | IF ( athorn(ji,jj,jl) > 0._wp ) THEN |
---|
[8409] | 468 | hrmean = MAX( SQRT( rn_hstar * ht_i(ji,jj,jl) ), ht_i(ji,jj,jl) * krdgmin ) |
---|
| 469 | hrmin(ji,jj,jl) = MIN( 2._wp * ht_i(ji,jj,jl), 0.5_wp * ( hrmean + ht_i(ji,jj,jl) ) ) |
---|
| 470 | hrmax(ji,jj,jl) = 2._wp * hrmean - hrmin(ji,jj,jl) |
---|
| 471 | hraft(ji,jj,jl) = ht_i(ji,jj,jl) / kraft |
---|
[8486] | 472 | krdg (ji,jj,jl) = ht_i(ji,jj,jl) / MAX( hrmean, epsi20 ) |
---|
| 473 | ! |
---|
[8409] | 474 | ! Normalization factor : aksum, ensures mass conservation |
---|
| 475 | aksum(ji,jj) = aksum(ji,jj) + aridge(ji,jj,jl) * ( 1._wp - krdg(ji,jj,jl) ) & |
---|
| 476 | & + araft (ji,jj,jl) * ( 1._wp - kraft ) |
---|
| 477 | ELSE |
---|
| 478 | hrmin(ji,jj,jl) = 0._wp |
---|
| 479 | hrmax(ji,jj,jl) = 0._wp |
---|
| 480 | hraft(ji,jj,jl) = 0._wp |
---|
| 481 | krdg (ji,jj,jl) = 1._wp |
---|
| 482 | ENDIF |
---|
| 483 | END DO |
---|
| 484 | END DO |
---|
| 485 | END DO |
---|
| 486 | ! |
---|
| 487 | END SUBROUTINE ice_rdgrft_ridgeprep |
---|
| 488 | |
---|
| 489 | |
---|
| 490 | SUBROUTINE ice_rdgrft_ridgeshift( opning, closing_gross ) |
---|
| 491 | !!---------------------------------------------------------------------- |
---|
| 492 | !! *** ROUTINE ice_rdgrft_icestrength *** |
---|
| 493 | !! |
---|
| 494 | !! ** Purpose : shift ridging ice among thickness categories of ice thickness |
---|
| 495 | !! |
---|
| 496 | !! ** Method : Remove area, volume, and energy from each ridging category |
---|
| 497 | !! and add to thicker ice categories. |
---|
| 498 | !!---------------------------------------------------------------------- |
---|
| 499 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: opning ! rate of opening due to divergence/shear |
---|
| 500 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: closing_gross ! rate at which area removed, excluding area of new ridges |
---|
| 501 | ! |
---|
[8486] | 502 | CHARACTER (len=80) :: fieldid ! field identifier !!gm DOCTOR name wrong |
---|
[8409] | 503 | ! |
---|
| 504 | INTEGER :: ji, jj, jl, jl1, jl2, jk ! dummy loop indices |
---|
| 505 | INTEGER :: ij ! horizontal index, combines i and j loops |
---|
| 506 | INTEGER :: icells ! number of cells with a_i > puny |
---|
| 507 | REAL(wp) :: hL, hR, farea ! left and right limits of integration |
---|
| 508 | REAL(wp) :: zwfx_snw ! snow mass flux increment |
---|
| 509 | |
---|
| 510 | INTEGER , DIMENSION(jpij) :: indxi, indxj ! compressed indices |
---|
| 511 | REAL(wp), DIMENSION(jpij) :: zswitch, fvol ! new ridge volume going to n2 |
---|
| 512 | |
---|
| 513 | REAL(wp), DIMENSION(jpij) :: afrac ! fraction of category area ridged |
---|
| 514 | REAL(wp), DIMENSION(jpij) :: ardg1 , ardg2 ! area of ice ridged & new ridges |
---|
| 515 | REAL(wp), DIMENSION(jpij) :: vsrdg , esrdg ! snow volume & energy of ridging ice |
---|
| 516 | ! MV MP 2016 |
---|
| 517 | REAL(wp), DIMENSION(jpij) :: vprdg ! pond volume of ridging ice |
---|
| 518 | REAL(wp), DIMENSION(jpij) :: aprdg1 ! pond area of ridging ice |
---|
| 519 | REAL(wp), DIMENSION(jpij) :: aprdg2 ! pond area of ridging ice |
---|
| 520 | ! END MV MP 2016 |
---|
| 521 | REAL(wp), DIMENSION(jpij) :: dhr , dhr2 ! hrmax - hrmin & hrmax^2 - hrmin^2 |
---|
| 522 | |
---|
| 523 | REAL(wp), DIMENSION(jpij) :: vrdg1 ! volume of ice ridged |
---|
| 524 | REAL(wp), DIMENSION(jpij) :: vrdg2 ! volume of new ridges |
---|
| 525 | REAL(wp), DIMENSION(jpij) :: vsw ! volume of seawater trapped into ridges |
---|
| 526 | REAL(wp), DIMENSION(jpij) :: srdg1 ! sal*volume of ice ridged |
---|
| 527 | REAL(wp), DIMENSION(jpij) :: srdg2 ! sal*volume of new ridges |
---|
| 528 | REAL(wp), DIMENSION(jpij) :: smsw ! sal*volume of water trapped into ridges |
---|
| 529 | REAL(wp), DIMENSION(jpij) :: oirdg1, oirdg2 ! ice age of ice ridged |
---|
| 530 | |
---|
| 531 | REAL(wp), DIMENSION(jpij) :: afrft ! fraction of category area rafted |
---|
| 532 | REAL(wp), DIMENSION(jpij) :: arft1 , arft2 ! area of ice rafted and new rafted zone |
---|
| 533 | REAL(wp), DIMENSION(jpij) :: virft , vsrft ! ice & snow volume of rafting ice |
---|
| 534 | ! MV MP 2016 |
---|
| 535 | REAL(wp), DIMENSION(jpij) :: vprft ! pond volume of rafting ice |
---|
| 536 | REAL(wp), DIMENSION(jpij) :: aprft1 ! pond area of rafted ice |
---|
| 537 | REAL(wp), DIMENSION(jpij) :: aprft2 ! pond area of new rafted ice |
---|
| 538 | ! END MV MP 2016 |
---|
| 539 | REAL(wp), DIMENSION(jpij) :: esrft , smrft ! snow energy & salinity of rafting ice |
---|
| 540 | REAL(wp), DIMENSION(jpij) :: oirft1, oirft2 ! ice age of ice rafted |
---|
| 541 | |
---|
| 542 | REAL(wp), DIMENSION(jpij,nlay_i) :: eirft ! ice energy of rafting ice |
---|
| 543 | REAL(wp), DIMENSION(jpij,nlay_i) :: erdg1 ! enth*volume of ice ridged |
---|
| 544 | REAL(wp), DIMENSION(jpij,nlay_i) :: erdg2 ! enth*volume of new ridges |
---|
| 545 | REAL(wp), DIMENSION(jpij,nlay_i) :: ersw ! enth of water trapped into ridges |
---|
| 546 | !!---------------------------------------------------------------------- |
---|
| 547 | |
---|
| 548 | !------------------------------------------------------------------------------- |
---|
| 549 | ! 1) Compute change in open water area due to closing and opening. |
---|
| 550 | !------------------------------------------------------------------------------- |
---|
| 551 | DO jj = 1, jpj |
---|
| 552 | DO ji = 1, jpi |
---|
| 553 | ato_i(ji,jj) = MAX( 0._wp, ato_i(ji,jj) + & |
---|
| 554 | & ( opning(ji,jj) - athorn(ji,jj,0) * closing_gross(ji,jj) ) * rdt_ice ) |
---|
| 555 | END DO |
---|
| 556 | END DO |
---|
| 557 | |
---|
| 558 | !----------------------------------------------------------------- |
---|
| 559 | ! 3) Pump everything from ice which is being ridged / rafted |
---|
| 560 | !----------------------------------------------------------------- |
---|
| 561 | ! Compute the area, volume, and energy of ice ridging in each |
---|
| 562 | ! category, along with the area of the resulting ridge. |
---|
| 563 | |
---|
| 564 | DO jl1 = 1, jpl !jl1 describes the ridging category |
---|
| 565 | |
---|
| 566 | !------------------------------------------------ |
---|
| 567 | ! 3.1) Identify grid cells with nonzero ridging |
---|
| 568 | !------------------------------------------------ |
---|
| 569 | icells = 0 |
---|
| 570 | DO jj = 1, jpj |
---|
| 571 | DO ji = 1, jpi |
---|
| 572 | IF( athorn(ji,jj,jl1) > 0._wp .AND. closing_gross(ji,jj) > 0._wp ) THEN |
---|
| 573 | icells = icells + 1 |
---|
| 574 | indxi(icells) = ji |
---|
| 575 | indxj(icells) = jj |
---|
| 576 | ENDIF |
---|
| 577 | END DO |
---|
| 578 | END DO |
---|
| 579 | |
---|
| 580 | DO ij = 1, icells |
---|
| 581 | ji = indxi(ij) ; jj = indxj(ij) |
---|
| 582 | |
---|
| 583 | !-------------------------------------------------------------------- |
---|
| 584 | ! 3.2) Compute area of ridging ice (ardg1) and of new ridge (ardg2) |
---|
| 585 | !-------------------------------------------------------------------- |
---|
| 586 | ardg1(ij) = aridge(ji,jj,jl1) * closing_gross(ji,jj) * rdt_ice |
---|
| 587 | arft1(ij) = araft (ji,jj,jl1) * closing_gross(ji,jj) * rdt_ice |
---|
| 588 | |
---|
| 589 | !--------------------------------------------------------------- |
---|
| 590 | ! 3.3) Compute ridging /rafting fractions, make sure afrac <=1 |
---|
| 591 | !--------------------------------------------------------------- |
---|
| 592 | afrac(ij) = ardg1(ij) / a_i(ji,jj,jl1) !ridging |
---|
| 593 | afrft(ij) = arft1(ij) / a_i(ji,jj,jl1) !rafting |
---|
| 594 | ardg2(ij) = ardg1(ij) * krdg(ji,jj,jl1) |
---|
| 595 | arft2(ij) = arft1(ij) * kraft |
---|
| 596 | |
---|
| 597 | !-------------------------------------------------------------------------- |
---|
| 598 | ! 3.4) Substract area, volume, and energy from ridging |
---|
| 599 | ! / rafting category n1. |
---|
| 600 | !-------------------------------------------------------------------------- |
---|
| 601 | vrdg1(ij) = v_i(ji,jj,jl1) * afrac(ij) |
---|
| 602 | vrdg2(ij) = vrdg1(ij) * ( 1. + rn_por_rdg ) |
---|
| 603 | vsw (ij) = vrdg1(ij) * rn_por_rdg |
---|
| 604 | |
---|
| 605 | vsrdg (ij) = v_s (ji,jj, jl1) * afrac(ij) |
---|
| 606 | esrdg (ij) = e_s (ji,jj,1,jl1) * afrac(ij) |
---|
| 607 | !MV MP 2016 |
---|
| 608 | IF ( nn_pnd_scheme > 0 ) THEN |
---|
| 609 | aprdg1(ij) = a_ip(ji,jj, jl1) * afrac(ij) |
---|
| 610 | aprdg2(ij) = a_ip(ji,jj, jl1) * afrac(ij) * krdg(ji,jj,jl1) |
---|
| 611 | vprdg(ij) = v_ip(ji,jj, jl1) * afrac(ij) |
---|
| 612 | ENDIF |
---|
| 613 | ! END MV MP 2016 |
---|
| 614 | srdg1 (ij) = smv_i(ji,jj, jl1) * afrac(ij) |
---|
| 615 | oirdg1(ij) = oa_i (ji,jj, jl1) * afrac(ij) |
---|
| 616 | oirdg2(ij) = oa_i (ji,jj, jl1) * afrac(ij) * krdg(ji,jj,jl1) |
---|
| 617 | |
---|
| 618 | ! rafting volumes, heat contents ... |
---|
| 619 | virft (ij) = v_i (ji,jj, jl1) * afrft(ij) |
---|
| 620 | vsrft (ij) = v_s (ji,jj, jl1) * afrft(ij) |
---|
| 621 | !MV MP 2016 |
---|
| 622 | IF ( nn_pnd_scheme > 0 ) THEN |
---|
| 623 | aprft1(ij) = a_ip (ji,jj, jl1) * afrft(ij) |
---|
| 624 | aprft2(ij) = a_ip (ji,jj, jl1) * afrft(ij) * kraft |
---|
| 625 | vprft(ij) = v_ip(ji,jj,jl1) * afrft(ij) |
---|
| 626 | ENDIF |
---|
| 627 | ! END MV MP 2016 |
---|
| 628 | srdg1 (ij) = smv_i(ji,jj, jl1) * afrac(ij) |
---|
| 629 | esrft (ij) = e_s (ji,jj,1,jl1) * afrft(ij) |
---|
| 630 | smrft (ij) = smv_i(ji,jj, jl1) * afrft(ij) |
---|
| 631 | oirft1(ij) = oa_i (ji,jj, jl1) * afrft(ij) |
---|
| 632 | oirft2(ij) = oa_i (ji,jj, jl1) * afrft(ij) * kraft |
---|
| 633 | |
---|
| 634 | !----------------------------------------------------------------- |
---|
| 635 | ! 3.5) Compute properties of new ridges |
---|
| 636 | !----------------------------------------------------------------- |
---|
| 637 | smsw(ij) = vsw(ij) * sss_m(ji,jj) ! salt content of seawater frozen in voids |
---|
| 638 | srdg2(ij) = srdg1(ij) + smsw(ij) ! salt content of new ridge |
---|
| 639 | |
---|
| 640 | sfx_dyn(ji,jj) = sfx_dyn(ji,jj) - smsw(ij) * rhoic * r1_rdtice |
---|
| 641 | wfx_dyn(ji,jj) = wfx_dyn(ji,jj) - vsw (ij) * rhoic * r1_rdtice ! increase in ice volume due to seawater frozen in voids |
---|
| 642 | |
---|
| 643 | ! virtual salt flux to keep salinity constant |
---|
| 644 | IF( nn_icesal == 1 .OR. nn_icesal == 3 ) THEN |
---|
| 645 | srdg2(ij) = srdg2(ij) - vsw(ij) * ( sss_m(ji,jj) - sm_i(ji,jj,jl1) ) ! ridge salinity = sm_i |
---|
| 646 | sfx_bri(ji,jj) = sfx_bri(ji,jj) + sss_m(ji,jj) * vsw(ij) * rhoic * r1_rdtice & ! put back sss_m into the ocean |
---|
| 647 | & - sm_i(ji,jj,jl1) * vsw(ij) * rhoic * r1_rdtice ! and get sm_i from the ocean |
---|
| 648 | ENDIF |
---|
| 649 | |
---|
| 650 | !------------------------------------------ |
---|
| 651 | ! 3.7 Put the snow somewhere in the ocean |
---|
| 652 | !------------------------------------------ |
---|
| 653 | ! Place part of the snow lost by ridging into the ocean. |
---|
| 654 | ! Note that esrdg > 0; the ocean must cool to melt snow. |
---|
| 655 | ! If the ocean temp = Tf already, new ice must grow. |
---|
| 656 | ! During the next time step, thermo_rates will determine whether |
---|
| 657 | ! the ocean cools or new ice grows. |
---|
| 658 | zwfx_snw = ( rhosn * vsrdg(ij) * ( 1._wp - rn_fsnowrdg ) & |
---|
| 659 | & + rhosn * vsrft(ij) * ( 1._wp - rn_fsnowrft ) ) * r1_rdtice ! fresh water source for ocean |
---|
| 660 | |
---|
| 661 | wfx_snw_dyn(ji,jj) = wfx_snw_dyn(ji,jj) + zwfx_snw |
---|
| 662 | |
---|
| 663 | hfx_dyn(ji,jj) = hfx_dyn(ji,jj) + ( - esrdg(ij) * ( 1._wp - rn_fsnowrdg ) & |
---|
| 664 | & - esrft(ij) * ( 1._wp - rn_fsnowrft ) ) * r1_rdtice ! heat sink for ocean (<0, W.m-2) |
---|
| 665 | |
---|
| 666 | ! MV MP 2016 |
---|
| 667 | !------------------------------------------ |
---|
| 668 | ! 3.X Put the melt pond water in the ocean |
---|
| 669 | !------------------------------------------ |
---|
| 670 | ! Place part of the melt pond volume into the ocean. |
---|
| 671 | IF ( ( nn_pnd_scheme > 0 ) .AND. ln_pnd_fw ) THEN |
---|
| 672 | wfx_pnd(ji,jj) = wfx_pnd(ji,jj) + ( rhofw * vprdg(ij) * ( 1._wp - rn_fpondrdg ) & |
---|
| 673 | & + rhofw * vprft(ij) * ( 1._wp - rn_fpondrft ) ) * r1_rdtice ! fresh water source for ocean |
---|
| 674 | ENDIF |
---|
| 675 | ! END MV MP 2016 |
---|
| 676 | |
---|
| 677 | !----------------------------------------------------------------- |
---|
| 678 | ! 3.8 Compute quantities used to apportion ice among categories |
---|
| 679 | ! in the n2 loop below |
---|
| 680 | !----------------------------------------------------------------- |
---|
| 681 | dhr (ij) = 1._wp / ( hrmax(ji,jj,jl1) - hrmin(ji,jj,jl1) ) |
---|
| 682 | dhr2(ij) = 1._wp / ( hrmax(ji,jj,jl1) * hrmax(ji,jj,jl1) - hrmin(ji,jj,jl1) * hrmin(ji,jj,jl1) ) |
---|
| 683 | |
---|
| 684 | |
---|
| 685 | ! update jl1 (removing ridged/rafted area) |
---|
| 686 | a_i (ji,jj, jl1) = a_i (ji,jj, jl1) - ardg1 (ij) - arft1 (ij) |
---|
| 687 | v_i (ji,jj, jl1) = v_i (ji,jj, jl1) - vrdg1 (ij) - virft (ij) |
---|
| 688 | v_s (ji,jj, jl1) = v_s (ji,jj, jl1) - vsrdg (ij) - vsrft (ij) |
---|
| 689 | e_s (ji,jj,1,jl1) = e_s (ji,jj,1,jl1) - esrdg (ij) - esrft (ij) |
---|
| 690 | smv_i(ji,jj, jl1) = smv_i(ji,jj, jl1) - srdg1 (ij) - smrft (ij) |
---|
| 691 | oa_i (ji,jj, jl1) = oa_i (ji,jj, jl1) - oirdg1(ij) - oirft1(ij) |
---|
| 692 | |
---|
| 693 | ! MV MP 2016 |
---|
| 694 | IF ( nn_pnd_scheme > 0 ) THEN |
---|
| 695 | v_ip (ji,jj,jl1) = v_ip (ji,jj,jl1) - vprdg (ij) - vprft (ij) |
---|
| 696 | a_ip (ji,jj,jl1) = a_ip (ji,jj,jl1) - aprdg1(ij) - aprft1(ij) |
---|
| 697 | ENDIF |
---|
| 698 | ! END MV MP 2016 |
---|
| 699 | |
---|
| 700 | END DO |
---|
| 701 | |
---|
| 702 | !-------------------------------------------------------------------- |
---|
| 703 | ! 3.9 Compute ridging ice enthalpy, remove it from ridging ice and |
---|
| 704 | ! compute ridged ice enthalpy |
---|
| 705 | !-------------------------------------------------------------------- |
---|
| 706 | DO jk = 1, nlay_i |
---|
| 707 | DO ij = 1, icells |
---|
| 708 | ji = indxi(ij) ; jj = indxj(ij) |
---|
| 709 | ! heat content of ridged ice |
---|
| 710 | erdg1(ij,jk) = e_i(ji,jj,jk,jl1) * afrac(ij) |
---|
| 711 | eirft(ij,jk) = e_i(ji,jj,jk,jl1) * afrft(ij) |
---|
| 712 | |
---|
| 713 | ! enthalpy of the trapped seawater (J/m2, >0) |
---|
| 714 | ! clem: if sst>0, then ersw <0 (is that possible?) |
---|
| 715 | ersw(ij,jk) = - rhoic * vsw(ij) * rcp * sst_m(ji,jj) * r1_nlay_i |
---|
| 716 | |
---|
| 717 | ! heat flux to the ocean |
---|
| 718 | hfx_dyn(ji,jj) = hfx_dyn(ji,jj) + ersw(ij,jk) * r1_rdtice ! > 0 [W.m-2] ocean->ice flux |
---|
| 719 | |
---|
| 720 | ! it is added to sea ice because the sign convention is the opposite of the sign convention for the ocean |
---|
| 721 | erdg2(ij,jk) = erdg1(ij,jk) + ersw(ij,jk) |
---|
| 722 | |
---|
| 723 | ! update jl1 |
---|
| 724 | e_i (ji,jj,jk,jl1) = e_i(ji,jj,jk,jl1) - erdg1(ij,jk) - eirft(ij,jk) |
---|
| 725 | |
---|
| 726 | END DO |
---|
| 727 | END DO |
---|
| 728 | |
---|
| 729 | !------------------------------------------------------------------------------- |
---|
| 730 | ! 4) Add area, volume, and energy of new ridge to each category jl2 |
---|
| 731 | !------------------------------------------------------------------------------- |
---|
| 732 | DO jl2 = 1, jpl |
---|
| 733 | ! over categories to which ridged/rafted ice is transferred |
---|
| 734 | DO ij = 1, icells |
---|
| 735 | ji = indxi(ij) ; jj = indxj(ij) |
---|
| 736 | |
---|
| 737 | ! Compute the fraction of ridged ice area and volume going to thickness category jl2. |
---|
| 738 | IF( hrmin(ji,jj,jl1) <= hi_max(jl2) .AND. hrmax(ji,jj,jl1) > hi_max(jl2-1) ) THEN |
---|
| 739 | hL = MAX( hrmin(ji,jj,jl1), hi_max(jl2-1) ) |
---|
| 740 | hR = MIN( hrmax(ji,jj,jl1), hi_max(jl2) ) |
---|
| 741 | farea = ( hR - hL ) * dhr(ij) |
---|
| 742 | fvol(ij) = ( hR * hR - hL * hL ) * dhr2(ij) |
---|
| 743 | ELSE |
---|
| 744 | farea = 0._wp |
---|
| 745 | fvol(ij) = 0._wp |
---|
| 746 | ENDIF |
---|
| 747 | |
---|
| 748 | ! Compute the fraction of rafted ice area and volume going to thickness category jl2 |
---|
[8486] | 749 | !!gm see above IF( hraft(ji,jj,jl1) <= hi_max(jl2) .AND. hraft(ji,jj,jl1) > hi_max(jl2-1) ) THEN |
---|
| 750 | IF( hi_max(jl2-1) < hraft(ji,jj,jl1) .AND. hraft(ji,jj,jl1) <= hi_max(jl2) ) THEN ; zswitch(ij) = 1._wp |
---|
| 751 | ELSE ; zswitch(ij) = 0._wp |
---|
[8409] | 752 | ENDIF |
---|
[8486] | 753 | ! |
---|
[8409] | 754 | a_i (ji,jj ,jl2) = a_i (ji,jj ,jl2) + ( ardg2 (ij) * farea + arft2 (ij) * zswitch(ij) ) |
---|
| 755 | oa_i (ji,jj ,jl2) = oa_i (ji,jj ,jl2) + ( oirdg2(ij) * farea + oirft2(ij) * zswitch(ij) ) |
---|
| 756 | v_i (ji,jj ,jl2) = v_i (ji,jj ,jl2) + ( vrdg2 (ij) * fvol(ij) + virft (ij) * zswitch(ij) ) |
---|
| 757 | smv_i(ji,jj ,jl2) = smv_i(ji,jj ,jl2) + ( srdg2 (ij) * fvol(ij) + smrft (ij) * zswitch(ij) ) |
---|
| 758 | v_s (ji,jj ,jl2) = v_s (ji,jj ,jl2) + ( vsrdg (ij) * rn_fsnowrdg * fvol(ij) + & |
---|
| 759 | & vsrft (ij) * rn_fsnowrft * zswitch(ij) ) |
---|
| 760 | e_s (ji,jj,1,jl2) = e_s (ji,jj,1,jl2) + ( esrdg (ij) * rn_fsnowrdg * fvol(ij) + & |
---|
| 761 | & esrft (ij) * rn_fsnowrft * zswitch(ij) ) |
---|
| 762 | ! MV MP 2016 |
---|
| 763 | IF ( nn_pnd_scheme > 0 ) THEN |
---|
[8486] | 764 | v_ip (ji,jj,jl2) = v_ip(ji,jj,jl2) + ( vprdg (ij) * rn_fpondrdg * fvol (ij) & |
---|
| 765 | & + vprft (ij) * rn_fpondrft * zswitch(ij) ) |
---|
| 766 | a_ip (ji,jj,jl2) = a_ip(ji,jj,jl2) + ( aprdg2(ij) * rn_fpondrdg * farea & |
---|
| 767 | & + aprft2(ij) * rn_fpondrft * zswitch(ji) ) |
---|
[8409] | 768 | ENDIF |
---|
| 769 | ! END MV MP 2016 |
---|
| 770 | END DO |
---|
| 771 | |
---|
| 772 | ! Transfer ice energy to category jl2 by ridging |
---|
| 773 | DO jk = 1, nlay_i |
---|
| 774 | DO ij = 1, icells |
---|
| 775 | ji = indxi(ij) ; jj = indxj(ij) |
---|
| 776 | e_i(ji,jj,jk,jl2) = e_i(ji,jj,jk,jl2) + erdg2(ij,jk) * fvol(ij) + eirft(ij,jk) * zswitch(ij) |
---|
| 777 | END DO |
---|
| 778 | END DO |
---|
| 779 | ! |
---|
| 780 | END DO ! jl2 |
---|
[8486] | 781 | ! |
---|
[8409] | 782 | END DO ! jl1 (deforming categories) |
---|
| 783 | |
---|
| 784 | ! SIMIP diagnostics |
---|
| 785 | diag_dmi_dyn(:,:) = - wfx_dyn(:,:) + rhoic * diag_trp_vi(:,:) |
---|
| 786 | diag_dms_dyn(:,:) = - wfx_snw_dyn(:,:) + rhosn * diag_trp_vs(:,:) |
---|
| 787 | ! |
---|
| 788 | END SUBROUTINE ice_rdgrft_ridgeshift |
---|
| 789 | |
---|
[8486] | 790 | |
---|
[8409] | 791 | SUBROUTINE ice_rdgrft_icestrength( kstrngth ) |
---|
| 792 | !!---------------------------------------------------------------------- |
---|
| 793 | !! *** ROUTINE ice_rdgrft_icestrength *** |
---|
| 794 | !! |
---|
| 795 | !! ** Purpose : computes ice strength used in dynamics routines of ice thickness |
---|
| 796 | !! |
---|
| 797 | !! ** Method : Compute the strength of the ice pack, defined as the energy (J m-2) |
---|
| 798 | !! dissipated per unit area removed from the ice pack under compression, |
---|
| 799 | !! and assumed proportional to the change in potential energy caused |
---|
| 800 | !! by ridging. Note that only Hibler's formulation is stable and that |
---|
| 801 | !! ice strength has to be smoothed |
---|
| 802 | !! |
---|
| 803 | !! ** Inputs / Ouputs : kstrngth (what kind of ice strength we are using) |
---|
| 804 | !!---------------------------------------------------------------------- |
---|
| 805 | INTEGER, INTENT(in) :: kstrngth ! = 1 for Rothrock formulation, 0 for Hibler (1979) |
---|
[8486] | 806 | ! |
---|
[8409] | 807 | INTEGER :: ji,jj, jl ! dummy loop indices |
---|
[8486] | 808 | INTEGER :: ksmooth ! smoothing the resistance to deformation !!gm not DOCTOR : start with i !!! |
---|
| 809 | INTEGER :: numts_rm ! number of time steps for the P smoothing !!gm not DOCTOR : start with i !!! |
---|
[8409] | 810 | REAL(wp) :: zp, z1_3 ! local scalars |
---|
| 811 | REAL(wp), DIMENSION(jpi,jpj) :: zworka ! temporary array used here |
---|
| 812 | REAL(wp), DIMENSION(jpi,jpj) :: zstrp1, zstrp2 ! strength at previous time steps |
---|
| 813 | !!---------------------------------------------------------------------- |
---|
| 814 | |
---|
| 815 | !------------------------------------------------------------------------------! |
---|
| 816 | ! 1) Initialize |
---|
| 817 | !------------------------------------------------------------------------------! |
---|
| 818 | strength(:,:) = 0._wp |
---|
| 819 | |
---|
| 820 | !------------------------------------------------------------------------------! |
---|
| 821 | ! 2) Compute thickness distribution of ridging and ridged ice |
---|
| 822 | !------------------------------------------------------------------------------! |
---|
| 823 | CALL ice_rdgrft_ridgeprep |
---|
| 824 | |
---|
| 825 | !------------------------------------------------------------------------------! |
---|
| 826 | ! 3) Rothrock(1975)'s method |
---|
| 827 | !------------------------------------------------------------------------------! |
---|
| 828 | IF( kstrngth == 1 ) THEN |
---|
| 829 | z1_3 = 1._wp / 3._wp |
---|
| 830 | DO jl = 1, jpl |
---|
| 831 | DO jj= 1, jpj |
---|
| 832 | DO ji = 1, jpi |
---|
| 833 | ! |
---|
| 834 | IF( athorn(ji,jj,jl) > 0._wp ) THEN |
---|
| 835 | !---------------------------- |
---|
| 836 | ! PE loss from deforming ice |
---|
| 837 | !---------------------------- |
---|
| 838 | strength(ji,jj) = strength(ji,jj) - athorn(ji,jj,jl) * ht_i(ji,jj,jl) * ht_i(ji,jj,jl) |
---|
| 839 | |
---|
| 840 | !-------------------------- |
---|
| 841 | ! PE gain from rafting ice |
---|
| 842 | !-------------------------- |
---|
| 843 | strength(ji,jj) = strength(ji,jj) + 2._wp * araft(ji,jj,jl) * ht_i(ji,jj,jl) * ht_i(ji,jj,jl) |
---|
| 844 | |
---|
| 845 | !---------------------------- |
---|
| 846 | ! PE gain from ridging ice |
---|
| 847 | !---------------------------- |
---|
| 848 | strength(ji,jj) = strength(ji,jj) + aridge(ji,jj,jl) * krdg(ji,jj,jl) * z1_3 * & |
---|
| 849 | & ( hrmax(ji,jj,jl) * hrmax(ji,jj,jl) + & |
---|
| 850 | & hrmin(ji,jj,jl) * hrmin(ji,jj,jl) + & |
---|
| 851 | & hrmax(ji,jj,jl) * hrmin(ji,jj,jl) ) |
---|
| 852 | !!(a**3-b**3)/(a-b) = a*a+ab+b*b |
---|
| 853 | ENDIF |
---|
| 854 | ! |
---|
| 855 | END DO |
---|
| 856 | END DO |
---|
| 857 | END DO |
---|
| 858 | |
---|
| 859 | strength(:,:) = rn_pe_rdg * Cp * strength(:,:) / aksum(:,:) * tmask(:,:,1) |
---|
| 860 | ! where Cp = (g/2)*(rhow-rhoi)*(rhoi/rhow) and rn_pe_rdg accounts for frictional dissipation |
---|
| 861 | ksmooth = 1 |
---|
| 862 | |
---|
| 863 | !------------------------------------------------------------------------------! |
---|
| 864 | ! 4) Hibler (1979)' method |
---|
| 865 | !------------------------------------------------------------------------------! |
---|
| 866 | ELSE ! kstrngth ne 1: Hibler (1979) form |
---|
| 867 | ! |
---|
| 868 | strength(:,:) = rn_pstar * vt_i(:,:) * EXP( - rn_crhg * ( 1._wp - at_i(:,:) ) ) * tmask(:,:,1) |
---|
| 869 | ! |
---|
| 870 | ksmooth = 1 |
---|
| 871 | ! |
---|
| 872 | ENDIF ! kstrngth |
---|
| 873 | ! |
---|
| 874 | !------------------------------------------------------------------------------! |
---|
| 875 | ! 5) Impact of brine volume |
---|
| 876 | !------------------------------------------------------------------------------! |
---|
| 877 | ! CAN BE REMOVED |
---|
| 878 | IF( ln_icestr_bvf ) THEN |
---|
| 879 | DO jj = 1, jpj |
---|
| 880 | DO ji = 1, jpi |
---|
| 881 | strength(ji,jj) = strength(ji,jj) * exp(-5.88*SQRT(MAX(bvm_i(ji,jj),0.0))) |
---|
| 882 | END DO |
---|
| 883 | END DO |
---|
| 884 | ENDIF |
---|
| 885 | ! |
---|
| 886 | !------------------------------------------------------------------------------! |
---|
| 887 | ! 6) Smoothing ice strength |
---|
| 888 | !------------------------------------------------------------------------------! |
---|
[8486] | 889 | SELECT CASE( ksmooth ) |
---|
| 890 | ! !------------------- |
---|
| 891 | CASE( 1 ) ! Spatial smoothing |
---|
| 892 | ! !------------------- |
---|
[8409] | 893 | DO jj = 2, jpjm1 |
---|
| 894 | DO ji = 2, jpim1 |
---|
| 895 | IF ( ( asum(ji,jj) - ato_i(ji,jj) ) > 0._wp ) THEN |
---|
| 896 | zworka(ji,jj) = ( 4.0 * strength(ji,jj) & |
---|
| 897 | & + strength(ji-1,jj) * tmask(ji-1,jj,1) + strength(ji+1,jj) * tmask(ji+1,jj,1) & |
---|
| 898 | & + strength(ji,jj-1) * tmask(ji,jj-1,1) + strength(ji,jj+1) * tmask(ji,jj+1,1) & |
---|
| 899 | & ) / ( 4.0 + tmask(ji-1,jj,1) + tmask(ji+1,jj,1) + tmask(ji,jj-1,1) + tmask(ji,jj+1,1) ) |
---|
| 900 | ELSE |
---|
| 901 | zworka(ji,jj) = 0._wp |
---|
| 902 | ENDIF |
---|
| 903 | END DO |
---|
| 904 | END DO |
---|
| 905 | |
---|
| 906 | DO jj = 2, jpjm1 |
---|
| 907 | DO ji = 2, jpim1 |
---|
| 908 | strength(ji,jj) = zworka(ji,jj) |
---|
| 909 | END DO |
---|
| 910 | END DO |
---|
| 911 | CALL lbc_lnk( strength, 'T', 1. ) |
---|
[8486] | 912 | ! |
---|
| 913 | ! !-------------------- |
---|
| 914 | CASE( 2 ) ! Temporal smoothing |
---|
| 915 | ! !-------------------- |
---|
[8409] | 916 | IF ( kt_ice == nit000 ) THEN |
---|
| 917 | zstrp1(:,:) = 0._wp |
---|
| 918 | zstrp2(:,:) = 0._wp |
---|
| 919 | ENDIF |
---|
[8486] | 920 | ! |
---|
[8409] | 921 | DO jj = 2, jpjm1 |
---|
| 922 | DO ji = 2, jpim1 |
---|
| 923 | IF ( ( asum(ji,jj) - ato_i(ji,jj) ) > 0._wp ) THEN |
---|
| 924 | numts_rm = 1 ! number of time steps for the running mean |
---|
| 925 | IF ( zstrp1(ji,jj) > 0._wp ) numts_rm = numts_rm + 1 |
---|
| 926 | IF ( zstrp2(ji,jj) > 0._wp ) numts_rm = numts_rm + 1 |
---|
| 927 | zp = ( strength(ji,jj) + zstrp1(ji,jj) + zstrp2(ji,jj) ) / numts_rm |
---|
[8486] | 928 | zstrp2 (ji,jj) = zstrp1 (ji,jj) |
---|
| 929 | zstrp1 (ji,jj) = strength(ji,jj) |
---|
[8409] | 930 | strength(ji,jj) = zp |
---|
| 931 | ENDIF |
---|
| 932 | END DO |
---|
| 933 | END DO |
---|
| 934 | CALL lbc_lnk( strength, 'T', 1. ) ! Boundary conditions |
---|
[8486] | 935 | ! |
---|
| 936 | END SELECT |
---|
[8409] | 937 | ! |
---|
| 938 | END SUBROUTINE ice_rdgrft_icestrength |
---|
| 939 | |
---|
[8486] | 940 | |
---|
[8409] | 941 | SUBROUTINE ice_rdgrft_init |
---|
| 942 | !!------------------------------------------------------------------- |
---|
[8486] | 943 | !! *** ROUTINE ice_rdgrft_init *** |
---|
[8409] | 944 | !! |
---|
| 945 | !! ** Purpose : Physical constants and parameters linked |
---|
| 946 | !! to the mechanical ice redistribution |
---|
| 947 | !! |
---|
| 948 | !! ** Method : Read the namiceitdme namelist |
---|
| 949 | !! and check the parameters values |
---|
| 950 | !! called at the first timestep (nit000) |
---|
| 951 | !! |
---|
| 952 | !! ** input : Namelist namiceitdme |
---|
| 953 | !!------------------------------------------------------------------- |
---|
| 954 | INTEGER :: ios ! Local integer output status for namelist read |
---|
[8486] | 955 | !! |
---|
| 956 | NAMELIST/namiceitdme/ rn_cs , nn_partfun, rn_gstar , rn_astar , & |
---|
| 957 | & ln_ridging, rn_hstar , rn_por_rdg, rn_fsnowrdg, rn_fpondrdg, & |
---|
| 958 | & ln_rafting, rn_hraft , rn_craft , rn_fsnowrft, rn_fpondrft |
---|
[8409] | 959 | !!------------------------------------------------------------------- |
---|
| 960 | ! |
---|
| 961 | REWIND( numnam_ice_ref ) ! Namelist namicetdme in reference namelist : Ice mechanical ice redistribution |
---|
| 962 | READ ( numnam_ice_ref, namiceitdme, IOSTAT = ios, ERR = 901) |
---|
| 963 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namiceitdme in reference namelist', lwp ) |
---|
[8486] | 964 | ! |
---|
[8409] | 965 | REWIND( numnam_ice_cfg ) ! Namelist namiceitdme in configuration namelist : Ice mechanical ice redistribution |
---|
| 966 | READ ( numnam_ice_cfg, namiceitdme, IOSTAT = ios, ERR = 902 ) |
---|
| 967 | 902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namiceitdme in configuration namelist', lwp ) |
---|
| 968 | IF(lwm) WRITE ( numoni, namiceitdme ) |
---|
| 969 | ! |
---|
| 970 | IF (lwp) THEN ! control print |
---|
| 971 | WRITE(numout,*) |
---|
| 972 | WRITE(numout,*)'ice_rdgrft_init : ice parameters for mechanical ice redistribution ' |
---|
| 973 | WRITE(numout,*)'~~~~~~~~~~~~~~~' |
---|
| 974 | WRITE(numout,*)' Fraction of shear energy contributing to ridging rn_cs = ', rn_cs |
---|
| 975 | WRITE(numout,*)' Switch for part. function (0) linear (1) exponential nn_partfun = ', nn_partfun |
---|
| 976 | WRITE(numout,*)' Fraction of total ice coverage contributing to ridging rn_gstar = ', rn_gstar |
---|
| 977 | WRITE(numout,*)' Equivalent to G* for an exponential part function rn_astar = ', rn_astar |
---|
| 978 | WRITE(numout,*)' Ridging of ice sheets or not ln_ridging = ', ln_ridging |
---|
| 979 | WRITE(numout,*)' Quantity playing a role in max ridged ice thickness rn_hstar = ', rn_hstar |
---|
| 980 | WRITE(numout,*)' Initial porosity of ridges rn_por_rdg = ', rn_por_rdg |
---|
| 981 | WRITE(numout,*)' Fraction of snow volume conserved during ridging rn_fsnowrdg = ', rn_fsnowrdg |
---|
| 982 | WRITE(numout,*)' Fraction of pond volume conserved during ridging rn_fpondrdg = ', rn_fpondrdg |
---|
| 983 | WRITE(numout,*)' Rafting of ice sheets or not ln_rafting = ', ln_rafting |
---|
| 984 | WRITE(numout,*)' Parmeter thickness (threshold between ridge-raft) rn_hraft = ', rn_hraft |
---|
| 985 | WRITE(numout,*)' Rafting hyperbolic tangent coefficient rn_craft = ', rn_craft |
---|
| 986 | WRITE(numout,*)' Fraction of snow volume conserved during ridging rn_fsnowrft = ', rn_fsnowrft |
---|
| 987 | WRITE(numout,*)' Fraction of pond volume conserved during rafting rn_fpondrft = ', rn_fpondrft |
---|
| 988 | ENDIF |
---|
| 989 | ! |
---|
| 990 | END SUBROUTINE ice_rdgrft_init |
---|
| 991 | |
---|
| 992 | #else |
---|
| 993 | !!---------------------------------------------------------------------- |
---|
| 994 | !! Default option Empty module NO LIM-3 sea-ice model |
---|
| 995 | !!---------------------------------------------------------------------- |
---|
| 996 | #endif |
---|
[8486] | 997 | |
---|
[8409] | 998 | !!====================================================================== |
---|
| 999 | END MODULE icerdgrft |
---|