[825] | 1 | MODULE limthd_dif |
---|
| 2 | #if defined key_lim3 |
---|
[834] | 3 | !!---------------------------------------------------------------------- |
---|
| 4 | !! 'key_lim3' LIM3 sea-ice model |
---|
| 5 | !!---------------------------------------------------------------------- |
---|
[825] | 6 | !!====================================================================== |
---|
| 7 | !! *** MODULE limthd_dif *** |
---|
| 8 | !! heat diffusion in sea ice |
---|
| 9 | !! computation of surface and inner T |
---|
| 10 | !!====================================================================== |
---|
| 11 | |
---|
| 12 | !!---------------------------------------------------------------------- |
---|
| 13 | !! * Modules used |
---|
| 14 | USE par_oce ! ocean parameters |
---|
| 15 | USE phycst ! physical constants (ocean directory) |
---|
| 16 | USE thd_ice |
---|
| 17 | USE iceini |
---|
| 18 | USE limistate |
---|
| 19 | USE in_out_manager |
---|
| 20 | USE ice |
---|
| 21 | USE par_ice |
---|
[869] | 22 | USE lib_mpp |
---|
[921] | 23 | |
---|
[825] | 24 | IMPLICIT NONE |
---|
| 25 | PRIVATE |
---|
| 26 | |
---|
| 27 | !! * Routine accessibility |
---|
| 28 | PUBLIC lim_thd_dif ! called by lim_thd |
---|
| 29 | |
---|
| 30 | !! * Module variables |
---|
| 31 | REAL(wp) :: & ! constant values |
---|
| 32 | epsi20 = 1e-20 , & |
---|
| 33 | epsi13 = 1e-13 , & |
---|
| 34 | zzero = 0.e0 , & |
---|
| 35 | zone = 1.e0 |
---|
| 36 | |
---|
| 37 | !!---------------------------------------------------------------------- |
---|
[1156] | 38 | !! LIM 3.0, UCL-LOCEAN-IPSL (2005) |
---|
| 39 | !! $Id$ |
---|
[2208] | 40 | !! Software governed by the CeCILL licence (NEMOGCM/License_CeCILL.txt) |
---|
[825] | 41 | !!---------------------------------------------------------------------- |
---|
| 42 | |
---|
| 43 | CONTAINS |
---|
| 44 | |
---|
| 45 | SUBROUTINE lim_thd_dif( kideb , kiut , jl ) |
---|
[921] | 46 | !!------------------------------------------------------------------ |
---|
| 47 | !! *** ROUTINE lim_thd_dif *** |
---|
| 48 | !! ** Purpose : |
---|
| 49 | !! This routine determines the time evolution of snow and sea-ice |
---|
| 50 | !! temperature profiles. |
---|
| 51 | !! ** Method : |
---|
| 52 | !! This is done by solving the heat equation diffusion with |
---|
| 53 | !! a Neumann boundary condition at the surface and a Dirichlet one |
---|
| 54 | !! at the bottom. Solar radiation is partially absorbed into the ice. |
---|
| 55 | !! The specific heat and thermal conductivities depend on ice salinity |
---|
| 56 | !! and temperature to take into account brine pocket melting. The |
---|
| 57 | !! numerical |
---|
| 58 | !! scheme is an iterative Crank-Nicolson on a non-uniform multilayer grid |
---|
| 59 | !! in the ice and snow system. |
---|
| 60 | !! |
---|
| 61 | !! The successive steps of this routine are |
---|
| 62 | !! 1. Thermal conductivity at the interfaces of the ice layers |
---|
| 63 | !! 2. Internal absorbed radiation |
---|
| 64 | !! 3. Scale factors due to non-uniform grid |
---|
| 65 | !! 4. Kappa factors |
---|
| 66 | !! Then iterative procedure begins |
---|
| 67 | !! 5. specific heat in the ice |
---|
| 68 | !! 6. eta factors |
---|
| 69 | !! 7. surface flux computation |
---|
| 70 | !! 8. tridiagonal system terms |
---|
| 71 | !! 9. solving the tridiagonal system with Gauss elimination |
---|
| 72 | !! Iterative procedure ends according to a criterion on evolution |
---|
| 73 | !! of temperature |
---|
| 74 | !! |
---|
| 75 | !! ** Arguments : |
---|
| 76 | !! kideb , kiut : Starting and ending points on which the |
---|
| 77 | !! the computation is applied |
---|
| 78 | !! |
---|
| 79 | !! ** Inputs / Ouputs : (global commons) |
---|
| 80 | !! surface temperature : t_su_b |
---|
| 81 | !! ice/snow temperatures : t_i_b, t_s_b |
---|
| 82 | !! ice salinities : s_i_b |
---|
| 83 | !! number of layers in the ice/snow: nlay_i, nlay_s |
---|
| 84 | !! profile of the ice/snow layers : z_i, z_s |
---|
| 85 | !! total ice/snow thickness : ht_i_b, ht_s_b |
---|
| 86 | !! |
---|
| 87 | !! ** External : |
---|
| 88 | !! |
---|
| 89 | !! ** References : |
---|
| 90 | !! |
---|
| 91 | !! ** History : |
---|
| 92 | !! (02-2003) Martin Vancoppenolle, Louvain-la-Neuve, Belgium |
---|
| 93 | !! (06-2005) Martin Vancoppenolle, 3d version |
---|
| 94 | !! (11-2006) Vectorized by Xavier Fettweis (UCL-ASTR) |
---|
| 95 | !! (04-2007) Energy conservation tested by M. Vancoppenolle |
---|
| 96 | !! |
---|
| 97 | !!------------------------------------------------------------------ |
---|
| 98 | !! * Arguments |
---|
[825] | 99 | |
---|
[921] | 100 | INTEGER , INTENT (in) :: & |
---|
| 101 | kideb , & ! Start point on which the the computation is applied |
---|
| 102 | kiut , & ! End point on which the the computation is applied |
---|
| 103 | jl ! Category number |
---|
[825] | 104 | |
---|
[921] | 105 | !! * Local variables |
---|
| 106 | INTEGER :: ji, & ! spatial loop index |
---|
| 107 | zji, zjj, & ! temporary dummy loop index |
---|
| 108 | numeq, & ! current reference number of equation |
---|
| 109 | layer, & ! vertical dummy loop index |
---|
| 110 | nconv, & ! number of iterations in iterative procedure |
---|
| 111 | minnumeqmin, & ! |
---|
| 112 | maxnumeqmax |
---|
[825] | 113 | |
---|
[1103] | 114 | INTEGER , DIMENSION(kiut) :: & |
---|
[921] | 115 | numeqmin, & ! reference number of top equation |
---|
| 116 | numeqmax, & ! reference number of bottom equation |
---|
| 117 | isnow ! switch for presence (1) or absence (0) of snow |
---|
[825] | 118 | |
---|
[921] | 119 | !! * New local variables |
---|
[1103] | 120 | REAL(wp) , DIMENSION(kiut,0:nlay_i) :: & |
---|
[921] | 121 | ztcond_i, & !Ice thermal conductivity |
---|
| 122 | zradtr_i, & !Radiation transmitted through the ice |
---|
| 123 | zradab_i, & !Radiation absorbed in the ice |
---|
| 124 | zkappa_i !Kappa factor in the ice |
---|
[825] | 125 | |
---|
[1103] | 126 | REAL(wp) , DIMENSION(kiut,0:nlay_s) :: & |
---|
[921] | 127 | zradtr_s, & !Radiation transmited through the snow |
---|
| 128 | zradab_s, & !Radiation absorbed in the snow |
---|
| 129 | zkappa_s !Kappa factor in the snow |
---|
[825] | 130 | |
---|
[1103] | 131 | REAL(wp) , DIMENSION(kiut,0:nlay_i) :: & |
---|
[921] | 132 | ztiold, & !Old temperature in the ice |
---|
| 133 | zeta_i, & !Eta factor in the ice |
---|
| 134 | ztitemp, & !Temporary temperature in the ice to check the convergence |
---|
| 135 | zspeche_i, & !Ice specific heat |
---|
| 136 | z_i !Vertical cotes of the layers in the ice |
---|
[825] | 137 | |
---|
[1103] | 138 | REAL(wp) , DIMENSION(kiut,0:nlay_s) :: & |
---|
[921] | 139 | zeta_s, & !Eta factor in the snow |
---|
| 140 | ztstemp, & !Temporary temperature in the snow to check the convergence |
---|
| 141 | ztsold, & !Temporary temperature in the snow |
---|
| 142 | z_s !Vertical cotes of the layers in the snow |
---|
[825] | 143 | |
---|
[1103] | 144 | REAL(wp) , DIMENSION(kiut,jkmax+2) :: & |
---|
[921] | 145 | zindterm, & ! Independent term |
---|
| 146 | zindtbis, & ! temporary independent term |
---|
| 147 | zdiagbis |
---|
[825] | 148 | |
---|
[1103] | 149 | REAL(wp) , DIMENSION(kiut,jkmax+2,3) :: & |
---|
[921] | 150 | ztrid ! tridiagonal system terms |
---|
[825] | 151 | |
---|
[1103] | 152 | REAL(wp), DIMENSION(kiut) :: & |
---|
[921] | 153 | ztfs , & ! ice melting point |
---|
| 154 | ztsuold , & ! old surface temperature (before the iterative |
---|
| 155 | ! procedure ) |
---|
| 156 | ztsuoldit, & ! surface temperature at previous iteration |
---|
| 157 | zh_i , & !ice layer thickness |
---|
| 158 | zh_s , & !snow layer thickness |
---|
| 159 | zfsw , & !solar radiation absorbed at the surface |
---|
| 160 | zf , & ! surface flux function |
---|
| 161 | dzf ! derivative of the surface flux function |
---|
[825] | 162 | |
---|
[921] | 163 | REAL(wp) :: & ! constant values |
---|
| 164 | zeps = 1.0e-10, & ! |
---|
| 165 | zg1s = 2.0, & !: for the tridiagonal system |
---|
| 166 | zg1 = 2.0, & |
---|
| 167 | zgamma = 18009.0, & !: for specific heat |
---|
| 168 | zbeta = 0.117, & !: for thermal conductivity (could be 0.13) |
---|
| 169 | zraext_s = 1.0e08, & !: extinction coefficient of radiation in the snow |
---|
| 170 | zkimin = 0.10 , & !: minimum ice thermal conductivity |
---|
| 171 | zht_smin = 1.0e-4 !: minimum snow depth |
---|
[825] | 172 | |
---|
[921] | 173 | REAL(wp) :: & ! local variables |
---|
| 174 | ztmelt_i, & ! ice melting temperature |
---|
| 175 | zerritmax ! current maximal error on temperature |
---|
[825] | 176 | |
---|
[1103] | 177 | REAL(wp), DIMENSION(kiut) :: & |
---|
[921] | 178 | zerrit, & ! current error on temperature |
---|
| 179 | zdifcase, & ! case of the equation resolution (1->4) |
---|
| 180 | zftrice, & ! solar radiation transmitted through the ice |
---|
| 181 | zihic, zhsu |
---|
[825] | 182 | |
---|
[921] | 183 | ! |
---|
| 184 | !------------------------------------------------------------------------------! |
---|
| 185 | ! 1) Initialization ! |
---|
| 186 | !------------------------------------------------------------------------------! |
---|
| 187 | ! |
---|
| 188 | DO ji = kideb , kiut |
---|
| 189 | ! is there snow or not |
---|
| 190 | isnow(ji)= INT ( 1.0 - MAX( 0.0 , SIGN (1.0, - ht_s_b(ji) ) ) ) |
---|
| 191 | ! surface temperature of fusion |
---|
| 192 | ztfs(ji) = isnow(ji) * rtt + (1.0-isnow(ji)) * rtt |
---|
| 193 | ! layer thickness |
---|
| 194 | zh_i(ji) = ht_i_b(ji) / nlay_i |
---|
| 195 | zh_s(ji) = ht_s_b(ji) / nlay_s |
---|
| 196 | END DO |
---|
[825] | 197 | |
---|
[921] | 198 | !-------------------- |
---|
| 199 | ! Ice / snow layers |
---|
| 200 | !-------------------- |
---|
[825] | 201 | |
---|
[921] | 202 | z_s(:,0) = 0.0 ! vert. coord. of the up. lim. of the 1st snow layer |
---|
| 203 | z_i(:,0) = 0.0 ! vert. coord. of the up. lim. of the 1st ice layer |
---|
[825] | 204 | |
---|
[921] | 205 | DO layer = 1, nlay_s |
---|
| 206 | DO ji = kideb , kiut |
---|
| 207 | ! vert. coord of the up. lim. of the layer-th snow layer |
---|
| 208 | z_s(ji,layer) = z_s(ji,layer-1) + ht_s_b(ji) / nlay_s |
---|
| 209 | END DO |
---|
| 210 | END DO |
---|
[825] | 211 | |
---|
[921] | 212 | DO layer = 1, nlay_i |
---|
| 213 | DO ji = kideb , kiut |
---|
| 214 | ! vert. coord of the up. lim. of the layer-th ice layer |
---|
| 215 | z_i(ji,layer) = z_i(ji,layer-1) + ht_i_b(ji) / nlay_i |
---|
| 216 | END DO |
---|
| 217 | END DO |
---|
| 218 | ! |
---|
| 219 | !------------------------------------------------------------------------------| |
---|
| 220 | ! 2) Radiations | |
---|
| 221 | !------------------------------------------------------------------------------| |
---|
| 222 | ! |
---|
| 223 | !------------------- |
---|
| 224 | ! Computation of i0 |
---|
| 225 | !------------------- |
---|
| 226 | ! i0 describes the fraction of solar radiation which does not contribute |
---|
| 227 | ! to the surface energy budget but rather penetrates inside the ice. |
---|
| 228 | ! We assume that no radiation is transmitted through the snow |
---|
| 229 | ! If there is no no snow |
---|
| 230 | ! zfsw = (1-i0).qsr_ice is absorbed at the surface |
---|
| 231 | ! zftrice = io.qsr_ice is below the surface |
---|
| 232 | ! fstbif = io.qsr_ice.exp(-k(h_i)) transmitted below the ice |
---|
[825] | 233 | |
---|
[921] | 234 | DO ji = kideb , kiut |
---|
| 235 | ! switches |
---|
| 236 | isnow(ji) = INT ( 1.0 - MAX ( 0.0 , SIGN ( 1.0 , - ht_s_b(ji) ) ) ) |
---|
| 237 | ! hs > 0, isnow = 1 |
---|
| 238 | zhsu(ji) = hnzst !threshold for the computation of i0 |
---|
| 239 | zihic(ji) = MAX( zzero , 1.0 - ( ht_i_b(ji) / zhsu(ji) ) ) |
---|
[825] | 240 | |
---|
[921] | 241 | i0(ji) = ( 1.0 - isnow(ji) ) * & |
---|
| 242 | ( fr1_i0_1d(ji) + zihic(ji) * fr2_i0_1d(ji) ) |
---|
| 243 | !fr1_i0_1d = i0 for a thin ice surface |
---|
| 244 | !fr1_i0_2d = i0 for a thick ice surface |
---|
| 245 | ! a function of the cloud cover |
---|
| 246 | ! |
---|
| 247 | !i0(ji) = (1.0-FLOAT(isnow(ji)))*3.0/(100*ht_s_b(ji)+10.0) |
---|
| 248 | !formula used in Cice |
---|
| 249 | END DO |
---|
[825] | 250 | |
---|
[921] | 251 | !------------------------------------------------------- |
---|
| 252 | ! Solar radiation absorbed / transmitted at the surface |
---|
| 253 | ! Derivative of the non solar flux |
---|
| 254 | !------------------------------------------------------- |
---|
| 255 | DO ji = kideb , kiut |
---|
[825] | 256 | |
---|
[921] | 257 | ! Shortwave radiation absorbed at surface |
---|
| 258 | zfsw(ji) = qsr_ice_1d(ji) * ( 1 - i0(ji) ) |
---|
[825] | 259 | |
---|
[921] | 260 | ! Solar radiation transmitted below the surface layer |
---|
| 261 | zftrice(ji)= qsr_ice_1d(ji) * i0(ji) |
---|
[825] | 262 | |
---|
[921] | 263 | ! derivative of incoming nonsolar flux |
---|
| 264 | dzf(ji) = dqns_ice_1d(ji) |
---|
[825] | 265 | |
---|
[921] | 266 | END DO |
---|
[825] | 267 | |
---|
[921] | 268 | !--------------------------------------------------------- |
---|
| 269 | ! Transmission - absorption of solar radiation in the ice |
---|
| 270 | !--------------------------------------------------------- |
---|
[825] | 271 | |
---|
[921] | 272 | DO ji = kideb , kiut |
---|
| 273 | ! Initialization |
---|
| 274 | zradtr_s(ji,0) = zftrice(ji) ! radiation penetrating through snow |
---|
| 275 | END DO |
---|
[825] | 276 | |
---|
[921] | 277 | ! Radiation through snow |
---|
| 278 | DO layer = 1, nlay_s |
---|
| 279 | DO ji = kideb , kiut |
---|
| 280 | ! radiation transmitted below the layer-th snow layer |
---|
| 281 | zradtr_s(ji,layer) = zradtr_s(ji,0) * EXP ( - zraext_s * ( MAX ( 0.0 , & |
---|
| 282 | z_s(ji,layer) ) ) ) |
---|
| 283 | ! radiation absorbed by the layer-th snow layer |
---|
| 284 | zradab_s(ji,layer) = zradtr_s(ji,layer-1) - zradtr_s(ji,layer) |
---|
| 285 | END DO |
---|
| 286 | END DO |
---|
[825] | 287 | |
---|
[921] | 288 | ! Radiation through ice |
---|
| 289 | DO ji = kideb , kiut |
---|
| 290 | zradtr_i(ji,0) = zradtr_s(ji,nlay_s) * isnow(ji) + & |
---|
| 291 | zftrice(ji) * ( 1 - isnow(ji) ) |
---|
| 292 | END DO |
---|
[825] | 293 | |
---|
[921] | 294 | DO layer = 1, nlay_i |
---|
| 295 | DO ji = kideb , kiut |
---|
| 296 | ! radiation transmitted below the layer-th ice layer |
---|
| 297 | zradtr_i(ji,layer) = zradtr_i(ji,0) * EXP ( - kappa_i * ( MAX ( 0.0 , & |
---|
| 298 | z_i(ji,layer) ) ) ) |
---|
| 299 | ! radiation absorbed by the layer-th ice layer |
---|
| 300 | zradab_i(ji,layer) = zradtr_i(ji,layer-1) - zradtr_i(ji,layer) |
---|
| 301 | END DO |
---|
| 302 | END DO |
---|
[825] | 303 | |
---|
[921] | 304 | ! Radiation transmitted below the ice |
---|
| 305 | DO ji = kideb , kiut |
---|
| 306 | fstbif_1d(ji) = fstbif_1d(ji) + & |
---|
| 307 | zradtr_i(ji,nlay_i) * a_i_b(ji) / at_i_b(ji) |
---|
| 308 | END DO |
---|
[834] | 309 | |
---|
[921] | 310 | ! +++++ |
---|
| 311 | ! just to check energy conservation |
---|
| 312 | DO ji = kideb , kiut |
---|
| 313 | zji = MOD( npb(ji) - 1, jpi ) + 1 |
---|
| 314 | zjj = ( npb(ji) - 1 ) / jpi + 1 |
---|
| 315 | fstroc(zji,zjj,jl) = & |
---|
| 316 | zradtr_i(ji,nlay_i) |
---|
| 317 | END DO |
---|
| 318 | ! +++++ |
---|
[825] | 319 | |
---|
[921] | 320 | DO layer = 1, nlay_i |
---|
| 321 | DO ji = kideb , kiut |
---|
| 322 | radab(ji,layer) = zradab_i(ji,layer) |
---|
| 323 | END DO |
---|
| 324 | END DO |
---|
[825] | 325 | |
---|
| 326 | |
---|
[921] | 327 | ! |
---|
| 328 | !------------------------------------------------------------------------------| |
---|
| 329 | ! 3) Iterative procedure begins | |
---|
| 330 | !------------------------------------------------------------------------------| |
---|
| 331 | ! |
---|
| 332 | ! Old surface temperature |
---|
| 333 | DO ji = kideb, kiut |
---|
| 334 | ztsuold(ji) = t_su_b(ji) ! temperature at the beg of iter pr. |
---|
| 335 | ztsuoldit(ji) = t_su_b(ji) ! temperature at the previous iter |
---|
| 336 | t_su_b(ji) = MIN(t_su_b(ji),ztfs(ji)-0.00001) !necessary |
---|
| 337 | zerrit(ji) = 1000.0 ! initial value of error |
---|
| 338 | END DO |
---|
| 339 | !RB Min global ?? |
---|
[825] | 340 | |
---|
[921] | 341 | ! Old snow temperature |
---|
| 342 | DO layer = 1, nlay_s |
---|
| 343 | DO ji = kideb , kiut |
---|
| 344 | ztsold(ji,layer) = t_s_b(ji,layer) |
---|
| 345 | END DO |
---|
| 346 | END DO |
---|
[825] | 347 | |
---|
[921] | 348 | ! Old ice temperature |
---|
| 349 | DO layer = 1, nlay_i |
---|
| 350 | DO ji = kideb , kiut |
---|
| 351 | ztiold(ji,layer) = t_i_b(ji,layer) |
---|
| 352 | END DO |
---|
| 353 | END DO |
---|
[825] | 354 | |
---|
[921] | 355 | nconv = 0 ! number of iterations |
---|
| 356 | zerritmax = 1000.0 ! maximal value of error on all points |
---|
[825] | 357 | |
---|
[921] | 358 | DO WHILE ((zerritmax > maxer_i_thd).AND.(nconv < nconv_i_thd)) |
---|
[825] | 359 | |
---|
[921] | 360 | nconv = nconv+1 |
---|
[825] | 361 | |
---|
[921] | 362 | ! |
---|
| 363 | !------------------------------------------------------------------------------| |
---|
| 364 | ! 4) Sea ice thermal conductivity | |
---|
| 365 | !------------------------------------------------------------------------------| |
---|
| 366 | ! |
---|
| 367 | IF ( thcon_i_swi .EQ. 0 ) THEN |
---|
| 368 | ! Untersteiner (1964) formula |
---|
| 369 | DO ji = kideb , kiut |
---|
| 370 | ztcond_i(ji,0) = rcdic + zbeta*s_i_b(ji,1) / & |
---|
| 371 | MIN(-zeps,t_i_b(ji,1)-rtt) |
---|
| 372 | ztcond_i(ji,0) = MAX(ztcond_i(ji,0),zkimin) |
---|
| 373 | END DO |
---|
| 374 | ENDIF |
---|
[825] | 375 | |
---|
[921] | 376 | IF ( thcon_i_swi .EQ. 1 ) THEN |
---|
| 377 | ! Pringle et al formula included, |
---|
| 378 | ! 2.11 + 0.09 S/T - 0.011.T |
---|
| 379 | DO ji = kideb , kiut |
---|
| 380 | ztcond_i(ji,0) = rcdic + 0.09*s_i_b(ji,1) / & |
---|
| 381 | MIN(-zeps,t_i_b(ji,1)-rtt) - & |
---|
| 382 | 0.011* ( t_i_b(ji,1) - rtt ) |
---|
| 383 | ztcond_i(ji,0) = MAX(ztcond_i(ji,0),zkimin) |
---|
| 384 | END DO |
---|
| 385 | ENDIF |
---|
[825] | 386 | |
---|
[921] | 387 | IF ( thcon_i_swi .EQ. 0 ) THEN ! Untersteiner |
---|
| 388 | DO layer = 1, nlay_i-1 |
---|
| 389 | DO ji = kideb , kiut |
---|
| 390 | ztcond_i(ji,layer) = rcdic + zbeta*( s_i_b(ji,layer) & |
---|
| 391 | + s_i_b(ji,layer+1) ) / MIN(-zeps, & |
---|
| 392 | t_i_b(ji,layer)+t_i_b(ji,layer+1)-2.0*rtt) |
---|
| 393 | ztcond_i(ji,layer) = MAX(ztcond_i(ji,layer),zkimin) |
---|
| 394 | END DO |
---|
| 395 | END DO |
---|
| 396 | ENDIF |
---|
[825] | 397 | |
---|
[921] | 398 | IF ( thcon_i_swi .EQ. 1 ) THEN ! Pringle |
---|
| 399 | DO layer = 1, nlay_i-1 |
---|
| 400 | DO ji = kideb , kiut |
---|
| 401 | ztcond_i(ji,layer) = rcdic + 0.09*( s_i_b(ji,layer) & |
---|
| 402 | + s_i_b(ji,layer+1) ) / MIN(-zeps, & |
---|
| 403 | t_i_b(ji,layer)+t_i_b(ji,layer+1)-2.0*rtt) - & |
---|
| 404 | 0.011* ( t_i_b(ji,layer) + t_i_b(ji,layer+1) - 2.0*rtt ) |
---|
| 405 | ztcond_i(ji,layer) = MAX(ztcond_i(ji,layer),zkimin) |
---|
| 406 | END DO |
---|
| 407 | END DO |
---|
| 408 | ENDIF |
---|
[825] | 409 | |
---|
[921] | 410 | IF ( thcon_i_swi .EQ. 0 ) THEN ! Untersteiner |
---|
| 411 | DO ji = kideb , kiut |
---|
| 412 | ztcond_i(ji,nlay_i) = rcdic + zbeta*s_i_b(ji,nlay_i) / & |
---|
| 413 | MIN(-zeps,t_bo_b(ji)-rtt) |
---|
| 414 | ztcond_i(ji,nlay_i) = MAX(ztcond_i(ji,nlay_i),zkimin) |
---|
| 415 | END DO |
---|
| 416 | ENDIF |
---|
[825] | 417 | |
---|
[921] | 418 | IF ( thcon_i_swi .EQ. 1 ) THEN ! Pringle |
---|
| 419 | DO ji = kideb , kiut |
---|
| 420 | ztcond_i(ji,nlay_i) = rcdic + 0.09*s_i_b(ji,nlay_i) / & |
---|
| 421 | MIN(-zeps,t_bo_b(ji)-rtt) - & |
---|
| 422 | 0.011* ( t_bo_b(ji) - rtt ) |
---|
| 423 | ztcond_i(ji,nlay_i) = MAX(ztcond_i(ji,nlay_i),zkimin) |
---|
| 424 | END DO |
---|
| 425 | ENDIF |
---|
| 426 | ! |
---|
| 427 | !------------------------------------------------------------------------------| |
---|
| 428 | ! 5) kappa factors | |
---|
| 429 | !------------------------------------------------------------------------------| |
---|
| 430 | ! |
---|
| 431 | DO ji = kideb, kiut |
---|
[825] | 432 | |
---|
[921] | 433 | !-- Snow kappa factors |
---|
| 434 | zkappa_s(ji,0) = rcdsn / MAX(zeps,zh_s(ji)) |
---|
| 435 | zkappa_s(ji,nlay_s) = rcdsn / MAX(zeps,zh_s(ji)) |
---|
| 436 | END DO |
---|
[825] | 437 | |
---|
[921] | 438 | DO layer = 1, nlay_s-1 |
---|
| 439 | DO ji = kideb , kiut |
---|
| 440 | zkappa_s(ji,layer) = 2.0 * rcdsn / & |
---|
| 441 | MAX(zeps,2.0*zh_s(ji)) |
---|
| 442 | END DO |
---|
| 443 | END DO |
---|
[825] | 444 | |
---|
[921] | 445 | DO layer = 1, nlay_i-1 |
---|
| 446 | DO ji = kideb , kiut |
---|
| 447 | !-- Ice kappa factors |
---|
| 448 | zkappa_i(ji,layer) = 2.0*ztcond_i(ji,layer)/ & |
---|
| 449 | MAX(zeps,2.0*zh_i(ji)) |
---|
| 450 | END DO |
---|
| 451 | END DO |
---|
[825] | 452 | |
---|
[921] | 453 | DO ji = kideb , kiut |
---|
| 454 | zkappa_i(ji,0) = ztcond_i(ji,0)/MAX(zeps,zh_i(ji)) |
---|
| 455 | zkappa_i(ji,nlay_i) = ztcond_i(ji,nlay_i) / MAX(zeps,zh_i(ji)) |
---|
| 456 | !-- Interface |
---|
| 457 | zkappa_s(ji,nlay_s) = 2.0*rcdsn*ztcond_i(ji,0)/MAX(zeps, & |
---|
| 458 | (ztcond_i(ji,0)*zh_s(ji) + rcdsn*zh_i(ji))) |
---|
| 459 | zkappa_i(ji,0) = zkappa_s(ji,nlay_s)*isnow(ji) & |
---|
| 460 | + zkappa_i(ji,0)*(1.0-isnow(ji)) |
---|
| 461 | END DO |
---|
| 462 | ! |
---|
| 463 | !------------------------------------------------------------------------------| |
---|
| 464 | ! 6) Sea ice specific heat, eta factors | |
---|
| 465 | !------------------------------------------------------------------------------| |
---|
| 466 | ! |
---|
| 467 | DO layer = 1, nlay_i |
---|
| 468 | DO ji = kideb , kiut |
---|
| 469 | ztitemp(ji,layer) = t_i_b(ji,layer) |
---|
| 470 | zspeche_i(ji,layer) = cpic + zgamma*s_i_b(ji,layer)/ & |
---|
| 471 | MAX((t_i_b(ji,layer)-rtt)*(ztiold(ji,layer)-rtt),zeps) |
---|
| 472 | zeta_i(ji,layer) = rdt_ice / MAX(rhoic*zspeche_i(ji,layer)*zh_i(ji), & |
---|
| 473 | zeps) |
---|
| 474 | END DO |
---|
| 475 | END DO |
---|
[825] | 476 | |
---|
[921] | 477 | DO layer = 1, nlay_s |
---|
| 478 | DO ji = kideb , kiut |
---|
| 479 | ztstemp(ji,layer) = t_s_b(ji,layer) |
---|
| 480 | zeta_s(ji,layer) = rdt_ice / MAX(rhosn*cpic*zh_s(ji),zeps) |
---|
| 481 | END DO |
---|
| 482 | END DO |
---|
| 483 | ! |
---|
| 484 | !------------------------------------------------------------------------------| |
---|
| 485 | ! 7) surface flux computation | |
---|
| 486 | !------------------------------------------------------------------------------| |
---|
| 487 | ! |
---|
| 488 | DO ji = kideb , kiut |
---|
[825] | 489 | |
---|
[921] | 490 | ! update of the non solar flux according to the update in T_su |
---|
| 491 | qnsr_ice_1d(ji) = qnsr_ice_1d(ji) + dqns_ice_1d(ji) * & |
---|
| 492 | ( t_su_b(ji) - ztsuoldit(ji) ) |
---|
[825] | 493 | |
---|
[921] | 494 | ! update incoming flux |
---|
| 495 | zf(ji) = zfsw(ji) & ! net absorbed solar radiation |
---|
| 496 | + qnsr_ice_1d(ji) ! non solar total flux |
---|
| 497 | ! (LWup, LWdw, SH, LH) |
---|
[825] | 498 | |
---|
[921] | 499 | END DO |
---|
[825] | 500 | |
---|
[921] | 501 | ! |
---|
| 502 | !------------------------------------------------------------------------------| |
---|
| 503 | ! 8) tridiagonal system terms | |
---|
| 504 | !------------------------------------------------------------------------------| |
---|
| 505 | ! |
---|
| 506 | !!layer denotes the number of the layer in the snow or in the ice |
---|
| 507 | !!numeq denotes the reference number of the equation in the tridiagonal |
---|
| 508 | !!system, terms of tridiagonal system are indexed as following : |
---|
| 509 | !!1 is subdiagonal term, 2 is diagonal and 3 is superdiagonal one |
---|
[825] | 510 | |
---|
[921] | 511 | !!ice interior terms (top equation has the same form as the others) |
---|
| 512 | |
---|
| 513 | DO numeq=1,jkmax+2 |
---|
| 514 | DO ji = kideb , kiut |
---|
| 515 | ztrid(ji,numeq,1) = 0. |
---|
| 516 | ztrid(ji,numeq,2) = 0. |
---|
| 517 | ztrid(ji,numeq,3) = 0. |
---|
| 518 | zindterm(ji,numeq)= 0. |
---|
| 519 | zindtbis(ji,numeq)= 0. |
---|
| 520 | zdiagbis(ji,numeq)= 0. |
---|
| 521 | ENDDO |
---|
| 522 | ENDDO |
---|
| 523 | |
---|
| 524 | DO numeq = nlay_s + 2, nlay_s + nlay_i |
---|
| 525 | DO ji = kideb , kiut |
---|
| 526 | layer = numeq - nlay_s - 1 |
---|
| 527 | ztrid(ji,numeq,1) = - zeta_i(ji,layer)*zkappa_i(ji,layer-1) |
---|
| 528 | ztrid(ji,numeq,2) = 1.0 + zeta_i(ji,layer)*(zkappa_i(ji,layer-1) + & |
---|
| 529 | zkappa_i(ji,layer)) |
---|
| 530 | ztrid(ji,numeq,3) = - zeta_i(ji,layer)*zkappa_i(ji,layer) |
---|
| 531 | zindterm(ji,numeq) = ztiold(ji,layer) + zeta_i(ji,layer)* & |
---|
| 532 | zradab_i(ji,layer) |
---|
| 533 | END DO |
---|
| 534 | ENDDO |
---|
| 535 | |
---|
| 536 | numeq = nlay_s + nlay_i + 1 |
---|
| 537 | DO ji = kideb , kiut |
---|
[825] | 538 | !!ice bottom term |
---|
| 539 | ztrid(ji,numeq,1) = - zeta_i(ji,nlay_i)*zkappa_i(ji,nlay_i-1) |
---|
| 540 | ztrid(ji,numeq,2) = 1.0 + zeta_i(ji,nlay_i)*( zkappa_i(ji,nlay_i)*zg1 & |
---|
[921] | 541 | + zkappa_i(ji,nlay_i-1) ) |
---|
[825] | 542 | ztrid(ji,numeq,3) = 0.0 |
---|
| 543 | zindterm(ji,numeq) = ztiold(ji,nlay_i) + zeta_i(ji,nlay_i)* & |
---|
[921] | 544 | ( zradab_i(ji,nlay_i) + zkappa_i(ji,nlay_i)*zg1 & |
---|
| 545 | * t_bo_b(ji) ) |
---|
| 546 | ENDDO |
---|
[825] | 547 | |
---|
| 548 | |
---|
[921] | 549 | DO ji = kideb , kiut |
---|
[825] | 550 | IF ( ht_s_b(ji).gt.0.0 ) THEN |
---|
[921] | 551 | ! |
---|
| 552 | !------------------------------------------------------------------------------| |
---|
| 553 | ! snow-covered cells | |
---|
| 554 | !------------------------------------------------------------------------------| |
---|
| 555 | ! |
---|
| 556 | !!snow interior terms (bottom equation has the same form as the others) |
---|
| 557 | DO numeq = 3, nlay_s + 1 |
---|
| 558 | layer = numeq - 1 |
---|
| 559 | ztrid(ji,numeq,1) = - zeta_s(ji,layer)*zkappa_s(ji,layer-1) |
---|
| 560 | ztrid(ji,numeq,2) = 1.0 + zeta_s(ji,layer)*( zkappa_s(ji,layer-1) + & |
---|
| 561 | zkappa_s(ji,layer) ) |
---|
| 562 | ztrid(ji,numeq,3) = - zeta_s(ji,layer)*zkappa_s(ji,layer) |
---|
| 563 | zindterm(ji,numeq) = ztsold(ji,layer) + zeta_s(ji,layer)* & |
---|
| 564 | zradab_s(ji,layer) |
---|
| 565 | END DO |
---|
[825] | 566 | |
---|
[921] | 567 | !!case of only one layer in the ice (ice equation is altered) |
---|
| 568 | IF ( nlay_i.eq.1 ) THEN |
---|
| 569 | ztrid(ji,nlay_s+2,3) = 0.0 |
---|
| 570 | zindterm(ji,nlay_s+2) = zindterm(ji,nlay_s+2) + zkappa_i(ji,1)* & |
---|
| 571 | t_bo_b(ji) |
---|
| 572 | ENDIF |
---|
[834] | 573 | |
---|
[921] | 574 | IF ( t_su_b(ji) .LT. rtt ) THEN |
---|
[825] | 575 | |
---|
[921] | 576 | !------------------------------------------------------------------------------| |
---|
| 577 | ! case 1 : no surface melting - snow present | |
---|
| 578 | !------------------------------------------------------------------------------| |
---|
| 579 | zdifcase(ji) = 1.0 |
---|
| 580 | numeqmin(ji) = 1 |
---|
| 581 | numeqmax(ji) = nlay_i + nlay_s + 1 |
---|
[825] | 582 | |
---|
[921] | 583 | !!surface equation |
---|
| 584 | ztrid(ji,1,1) = 0.0 |
---|
| 585 | ztrid(ji,1,2) = dzf(ji) - zg1s*zkappa_s(ji,0) |
---|
| 586 | ztrid(ji,1,3) = zg1s*zkappa_s(ji,0) |
---|
| 587 | zindterm(ji,1) = dzf(ji)*t_su_b(ji) - zf(ji) |
---|
[825] | 588 | |
---|
[921] | 589 | !!first layer of snow equation |
---|
| 590 | ztrid(ji,2,1) = - zkappa_s(ji,0)*zg1s*zeta_s(ji,1) |
---|
| 591 | ztrid(ji,2,2) = 1.0 + zeta_s(ji,1)*(zkappa_s(ji,1) + zkappa_s(ji,0)*zg1s) |
---|
| 592 | ztrid(ji,2,3) = - zeta_s(ji,1)* zkappa_s(ji,1) |
---|
| 593 | zindterm(ji,2) = ztsold(ji,1) + zeta_s(ji,1)*zradab_s(ji,1) |
---|
[825] | 594 | |
---|
[921] | 595 | ELSE |
---|
| 596 | ! |
---|
| 597 | !------------------------------------------------------------------------------| |
---|
| 598 | ! case 2 : surface is melting - snow present | |
---|
| 599 | !------------------------------------------------------------------------------| |
---|
| 600 | ! |
---|
| 601 | zdifcase(ji) = 2.0 |
---|
| 602 | numeqmin(ji) = 2 |
---|
| 603 | numeqmax(ji) = nlay_i + nlay_s + 1 |
---|
[825] | 604 | |
---|
[921] | 605 | !!first layer of snow equation |
---|
| 606 | ztrid(ji,2,1) = 0.0 |
---|
| 607 | ztrid(ji,2,2) = 1.0 + zeta_s(ji,1) * ( zkappa_s(ji,1) + & |
---|
| 608 | zkappa_s(ji,0) * zg1s ) |
---|
| 609 | ztrid(ji,2,3) = - zeta_s(ji,1)*zkappa_s(ji,1) |
---|
| 610 | zindterm(ji,2) = ztsold(ji,1) + zeta_s(ji,1) * & |
---|
| 611 | ( zradab_s(ji,1) + & |
---|
| 612 | zkappa_s(ji,0) * zg1s * t_su_b(ji) ) |
---|
| 613 | ENDIF |
---|
| 614 | ELSE |
---|
| 615 | ! |
---|
| 616 | !------------------------------------------------------------------------------| |
---|
| 617 | ! cells without snow | |
---|
| 618 | !------------------------------------------------------------------------------| |
---|
| 619 | ! |
---|
| 620 | IF (t_su_b(ji) .LT. rtt) THEN |
---|
| 621 | ! |
---|
| 622 | !------------------------------------------------------------------------------| |
---|
| 623 | ! case 3 : no surface melting - no snow | |
---|
| 624 | !------------------------------------------------------------------------------| |
---|
| 625 | ! |
---|
| 626 | zdifcase(ji) = 3.0 |
---|
| 627 | numeqmin(ji) = nlay_s + 1 |
---|
| 628 | numeqmax(ji) = nlay_i + nlay_s + 1 |
---|
[825] | 629 | |
---|
[921] | 630 | !!surface equation |
---|
| 631 | ztrid(ji,numeqmin(ji),1) = 0.0 |
---|
| 632 | ztrid(ji,numeqmin(ji),2) = dzf(ji) - zkappa_i(ji,0)*zg1 |
---|
| 633 | ztrid(ji,numeqmin(ji),3) = zkappa_i(ji,0)*zg1 |
---|
| 634 | zindterm(ji,numeqmin(ji)) = dzf(ji)*t_su_b(ji) - zf(ji) |
---|
[825] | 635 | |
---|
[921] | 636 | !!first layer of ice equation |
---|
| 637 | ztrid(ji,numeqmin(ji)+1,1) = - zkappa_i(ji,0) * zg1 * zeta_i(ji,1) |
---|
| 638 | ztrid(ji,numeqmin(ji)+1,2) = 1.0 + zeta_i(ji,1) * ( zkappa_i(ji,1) & |
---|
| 639 | + zkappa_i(ji,0) * zg1 ) |
---|
| 640 | ztrid(ji,numeqmin(ji)+1,3) = - zeta_i(ji,1)*zkappa_i(ji,1) |
---|
| 641 | zindterm(ji,numeqmin(ji)+1)= ztiold(ji,1) + zeta_i(ji,1)*zradab_i(ji,1) |
---|
[825] | 642 | |
---|
[921] | 643 | !!case of only one layer in the ice (surface & ice equations are altered) |
---|
[825] | 644 | |
---|
[921] | 645 | IF (nlay_i.eq.1) THEN |
---|
| 646 | ztrid(ji,numeqmin(ji),1) = 0.0 |
---|
| 647 | ztrid(ji,numeqmin(ji),2) = dzf(ji) - zkappa_i(ji,0)*2.0 |
---|
| 648 | ztrid(ji,numeqmin(ji),3) = zkappa_i(ji,0)*2.0 |
---|
| 649 | ztrid(ji,numeqmin(ji)+1,1) = -zkappa_i(ji,0)*2.0*zeta_i(ji,1) |
---|
| 650 | ztrid(ji,numeqmin(ji)+1,2) = 1.0 + zeta_i(ji,1)*(zkappa_i(ji,0)*2.0 + & |
---|
| 651 | zkappa_i(ji,1)) |
---|
| 652 | ztrid(ji,numeqmin(ji)+1,3) = 0.0 |
---|
[825] | 653 | |
---|
[921] | 654 | zindterm(ji,numeqmin(ji)+1) = ztiold(ji,1) + zeta_i(ji,1)* & |
---|
| 655 | ( zradab_i(ji,1) + zkappa_i(ji,1)*t_bo_b(ji) ) |
---|
| 656 | ENDIF |
---|
[825] | 657 | |
---|
[921] | 658 | ELSE |
---|
[825] | 659 | |
---|
[921] | 660 | ! |
---|
| 661 | !------------------------------------------------------------------------------| |
---|
| 662 | ! case 4 : surface is melting - no snow | |
---|
| 663 | !------------------------------------------------------------------------------| |
---|
| 664 | ! |
---|
| 665 | zdifcase(ji) = 4.0 |
---|
| 666 | numeqmin(ji) = nlay_s + 2 |
---|
| 667 | numeqmax(ji) = nlay_i + nlay_s + 1 |
---|
[825] | 668 | |
---|
[921] | 669 | !!first layer of ice equation |
---|
| 670 | ztrid(ji,numeqmin(ji),1) = 0.0 |
---|
| 671 | ztrid(ji,numeqmin(ji),2) = 1.0 + zeta_i(ji,1)*(zkappa_i(ji,1) + zkappa_i(ji,0)* & |
---|
| 672 | zg1) |
---|
| 673 | ztrid(ji,numeqmin(ji),3) = - zeta_i(ji,1) * zkappa_i(ji,1) |
---|
| 674 | zindterm(ji,numeqmin(ji)) = ztiold(ji,1) + zeta_i(ji,1)*( zradab_i(ji,1) + & |
---|
| 675 | zkappa_i(ji,0) * zg1 * t_su_b(ji) ) |
---|
[825] | 676 | |
---|
[921] | 677 | !!case of only one layer in the ice (surface & ice equations are altered) |
---|
| 678 | IF (nlay_i.eq.1) THEN |
---|
| 679 | ztrid(ji,numeqmin(ji),1) = 0.0 |
---|
| 680 | ztrid(ji,numeqmin(ji),2) = 1.0 + zeta_i(ji,1)*(zkappa_i(ji,0)*2.0 + & |
---|
| 681 | zkappa_i(ji,1)) |
---|
| 682 | ztrid(ji,numeqmin(ji),3) = 0.0 |
---|
| 683 | zindterm(ji,numeqmin(ji)) = ztiold(ji,1) + zeta_i(ji,1)* & |
---|
| 684 | (zradab_i(ji,1) + zkappa_i(ji,1)*t_bo_b(ji)) & |
---|
| 685 | + t_su_b(ji)*zeta_i(ji,1)*zkappa_i(ji,0)*2.0 |
---|
| 686 | ENDIF |
---|
[825] | 687 | |
---|
[921] | 688 | ENDIF |
---|
| 689 | ENDIF |
---|
[825] | 690 | |
---|
[921] | 691 | END DO |
---|
[825] | 692 | |
---|
[921] | 693 | ! |
---|
| 694 | !------------------------------------------------------------------------------| |
---|
| 695 | ! 9) tridiagonal system solving | |
---|
| 696 | !------------------------------------------------------------------------------| |
---|
| 697 | ! |
---|
[825] | 698 | |
---|
[921] | 699 | ! Solve the tridiagonal system with Gauss elimination method. |
---|
| 700 | ! Thomas algorithm, from Computational fluid Dynamics, J.D. ANDERSON, |
---|
| 701 | ! McGraw-Hill 1984. |
---|
[825] | 702 | |
---|
[921] | 703 | maxnumeqmax = 0 |
---|
| 704 | minnumeqmin = jkmax+4 |
---|
[825] | 705 | |
---|
[921] | 706 | DO ji = kideb , kiut |
---|
| 707 | zindtbis(ji,numeqmin(ji)) = zindterm(ji,numeqmin(ji)) |
---|
| 708 | zdiagbis(ji,numeqmin(ji)) = ztrid(ji,numeqmin(ji),2) |
---|
| 709 | minnumeqmin = MIN(numeqmin(ji),minnumeqmin) |
---|
| 710 | maxnumeqmax = MAX(numeqmax(ji),maxnumeqmax) |
---|
| 711 | END DO |
---|
| 712 | |
---|
| 713 | DO layer = minnumeqmin+1, maxnumeqmax |
---|
| 714 | DO ji = kideb , kiut |
---|
| 715 | numeq = min(max(numeqmin(ji)+1,layer),numeqmax(ji)) |
---|
| 716 | zdiagbis(ji,numeq) = ztrid(ji,numeq,2) - ztrid(ji,numeq,1)* & |
---|
| 717 | ztrid(ji,numeq-1,3)/zdiagbis(ji,numeq-1) |
---|
| 718 | zindtbis(ji,numeq) = zindterm(ji,numeq) - ztrid(ji,numeq,1)* & |
---|
| 719 | zindtbis(ji,numeq-1)/zdiagbis(ji,numeq-1) |
---|
| 720 | END DO |
---|
| 721 | END DO |
---|
| 722 | |
---|
| 723 | DO ji = kideb , kiut |
---|
| 724 | ! ice temperatures |
---|
| 725 | t_i_b(ji,nlay_i) = zindtbis(ji,numeqmax(ji))/zdiagbis(ji,numeqmax(ji)) |
---|
| 726 | END DO |
---|
| 727 | |
---|
| 728 | DO numeq = nlay_i + nlay_s + 1, nlay_s + 2, -1 |
---|
| 729 | DO ji = kideb , kiut |
---|
| 730 | layer = numeq - nlay_s - 1 |
---|
| 731 | t_i_b(ji,layer) = (zindtbis(ji,numeq) - ztrid(ji,numeq,3)* & |
---|
| 732 | t_i_b(ji,layer+1))/zdiagbis(ji,numeq) |
---|
| 733 | END DO |
---|
| 734 | END DO |
---|
| 735 | |
---|
| 736 | DO ji = kideb , kiut |
---|
[825] | 737 | ! snow temperatures |
---|
| 738 | IF (ht_s_b(ji).GT.0) & |
---|
[921] | 739 | t_s_b(ji,nlay_s) = (zindtbis(ji,nlay_s+1) - ztrid(ji,nlay_s+1,3) & |
---|
| 740 | * t_i_b(ji,1))/zdiagbis(ji,nlay_s+1) & |
---|
| 741 | * MAX(0.0,SIGN(1.0,ht_s_b(ji)-zeps)) |
---|
[825] | 742 | |
---|
| 743 | ! surface temperature |
---|
| 744 | isnow(ji) = INT(1.0-max(0.0,sign(1.0,-ht_s_b(ji)))) |
---|
| 745 | ztsuoldit(ji) = t_su_b(ji) |
---|
| 746 | IF (t_su_b(ji) .LT. ztfs(ji)) & |
---|
[921] | 747 | t_su_b(ji) = ( zindtbis(ji,numeqmin(ji)) - ztrid(ji,numeqmin(ji),3)* & |
---|
| 748 | ( isnow(ji)*t_s_b(ji,1) + & |
---|
| 749 | (1.0-isnow(ji))*t_i_b(ji,1) ) ) / & |
---|
| 750 | zdiagbis(ji,numeqmin(ji)) |
---|
| 751 | END DO |
---|
| 752 | ! |
---|
| 753 | !-------------------------------------------------------------------------- |
---|
| 754 | ! 10) Has the scheme converged ?, end of the iterative procedure | |
---|
| 755 | !-------------------------------------------------------------------------- |
---|
| 756 | ! |
---|
| 757 | ! check that nowhere it has started to melt |
---|
| 758 | ! zerrit(ji) is a measure of error, it has to be under maxer_i_thd |
---|
| 759 | DO ji = kideb , kiut |
---|
| 760 | t_su_b(ji) = MAX(MIN(t_su_b(ji),ztfs(ji)),190.0) |
---|
| 761 | zerrit(ji) = ABS(t_su_b(ji)-ztsuoldit(ji)) |
---|
| 762 | END DO |
---|
[825] | 763 | |
---|
[921] | 764 | DO layer = 1, nlay_s |
---|
| 765 | DO ji = kideb , kiut |
---|
| 766 | zji = MOD( npb(ji) - 1, jpi ) + 1 |
---|
| 767 | zjj = ( npb(ji) - 1 ) / jpi + 1 |
---|
| 768 | t_s_b(ji,layer) = MAX(MIN(t_s_b(ji,layer),rtt),190.0) |
---|
| 769 | zerrit(ji) = MAX(zerrit(ji),ABS(t_s_b(ji,layer) & |
---|
| 770 | - ztstemp(ji,layer))) |
---|
| 771 | END DO |
---|
| 772 | END DO |
---|
[825] | 773 | |
---|
[921] | 774 | DO layer = 1, nlay_i |
---|
| 775 | DO ji = kideb , kiut |
---|
| 776 | ztmelt_i = -tmut*s_i_b(ji,layer) +rtt |
---|
| 777 | t_i_b(ji,layer) = MAX(MIN(t_i_b(ji,layer),ztmelt_i),190.0) |
---|
| 778 | zerrit(ji) = MAX(zerrit(ji),ABS(t_i_b(ji,layer) - ztitemp(ji,layer))) |
---|
| 779 | END DO |
---|
| 780 | END DO |
---|
[825] | 781 | |
---|
[921] | 782 | ! Compute spatial maximum over all errors |
---|
| 783 | ! note that this could be optimized substantially by iterating only |
---|
| 784 | ! the non-converging points |
---|
| 785 | zerritmax = 0.0 |
---|
| 786 | DO ji = kideb , kiut |
---|
| 787 | zerritmax = MAX(zerritmax,zerrit(ji)) |
---|
| 788 | END DO |
---|
| 789 | IF( lk_mpp ) CALL mpp_max(zerritmax, kcom=ncomm_ice) |
---|
[825] | 790 | |
---|
| 791 | END DO ! End of the do while iterative procedure |
---|
| 792 | |
---|
[1055] | 793 | IF( ln_nicep ) THEN |
---|
| 794 | WRITE(numout,*) ' zerritmax : ', zerritmax |
---|
| 795 | WRITE(numout,*) ' nconv : ', nconv |
---|
| 796 | ENDIF |
---|
[825] | 797 | |
---|
[921] | 798 | ! |
---|
| 799 | !-------------------------------------------------------------------------- |
---|
| 800 | ! 11) Fluxes at the interfaces | |
---|
| 801 | !-------------------------------------------------------------------------- |
---|
| 802 | ! |
---|
| 803 | DO ji = kideb, kiut |
---|
| 804 | ! update of latent heat fluxes |
---|
| 805 | qla_ice_1d (ji) = qla_ice_1d (ji) + & |
---|
| 806 | dqla_ice_1d(ji) * ( t_su_b(ji) - ztsuold(ji) ) |
---|
[825] | 807 | |
---|
[921] | 808 | ! surface ice conduction flux |
---|
| 809 | isnow(ji) = int(1.0-max(0.0,sign(1.0,-ht_s_b(ji)))) |
---|
| 810 | fc_su(ji) = - isnow(ji)*zkappa_s(ji,0)*zg1s*(t_s_b(ji,1) - & |
---|
| 811 | t_su_b(ji)) & |
---|
| 812 | - (1.0-isnow(ji))*zkappa_i(ji,0)*zg1* & |
---|
| 813 | (t_i_b(ji,1) - t_su_b(ji)) |
---|
[825] | 814 | |
---|
[921] | 815 | ! bottom ice conduction flux |
---|
| 816 | fc_bo_i(ji) = - zkappa_i(ji,nlay_i)* & |
---|
| 817 | ( zg1*(t_bo_b(ji) - t_i_b(ji,nlay_i)) ) |
---|
[825] | 818 | |
---|
[921] | 819 | END DO |
---|
[825] | 820 | |
---|
[921] | 821 | !-------------------------! |
---|
| 822 | ! Heat conservation ! |
---|
| 823 | !-------------------------! |
---|
| 824 | IF ( con_i ) THEN |
---|
[825] | 825 | |
---|
[921] | 826 | DO ji = kideb, kiut |
---|
| 827 | ! Upper snow value |
---|
| 828 | fc_s(ji,0) = - isnow(ji)* & |
---|
| 829 | zkappa_s(ji,0) * zg1s * ( t_s_b(ji,1) - & |
---|
| 830 | t_su_b(ji) ) |
---|
| 831 | ! Bott. snow value |
---|
| 832 | fc_s(ji,1) = - isnow(ji)* & |
---|
| 833 | zkappa_s(ji,1) * ( t_i_b(ji,1) - & |
---|
| 834 | t_s_b(ji,1) ) |
---|
| 835 | END DO |
---|
[825] | 836 | |
---|
[921] | 837 | ! Upper ice layer |
---|
| 838 | DO ji = kideb, kiut |
---|
| 839 | fc_i(ji,0) = - isnow(ji) * & ! interface flux if there is snow |
---|
| 840 | ( zkappa_i(ji,0) * ( t_i_b(ji,1) - t_s_b(ji,nlay_s ) ) ) & |
---|
| 841 | - ( 1.0 - isnow(ji) ) * ( zkappa_i(ji,0) * & |
---|
| 842 | zg1 * ( t_i_b(ji,1) - t_su_b(ji) ) ) ! upper flux if not |
---|
| 843 | END DO |
---|
[825] | 844 | |
---|
[921] | 845 | ! Internal ice layers |
---|
| 846 | DO layer = 1, nlay_i - 1 |
---|
| 847 | DO ji = kideb, kiut |
---|
| 848 | fc_i(ji,layer) = - zkappa_i(ji,layer) * ( t_i_b(ji,layer+1) - & |
---|
| 849 | t_i_b(ji,layer) ) |
---|
| 850 | zji = MOD( npb(ji) - 1, jpi ) + 1 |
---|
| 851 | zjj = ( npb(ji) - 1 ) / jpi + 1 |
---|
| 852 | END DO |
---|
| 853 | END DO |
---|
[825] | 854 | |
---|
[921] | 855 | ! Bottom ice layers |
---|
| 856 | DO ji = kideb, kiut |
---|
| 857 | fc_i(ji,nlay_i) = - zkappa_i(ji,nlay_i)* & |
---|
| 858 | ( zg1*(t_bo_b(ji) - t_i_b(ji,nlay_i)) ) |
---|
| 859 | END DO |
---|
[825] | 860 | |
---|
[921] | 861 | ENDIF |
---|
[825] | 862 | |
---|
[921] | 863 | END SUBROUTINE lim_thd_dif |
---|
[825] | 864 | |
---|
| 865 | #else |
---|
| 866 | !!====================================================================== |
---|
| 867 | !! *** MODULE limthd_dif *** |
---|
| 868 | !! no sea ice model |
---|
| 869 | !!====================================================================== |
---|
| 870 | CONTAINS |
---|
| 871 | SUBROUTINE lim_thd_dif ! Empty routine |
---|
| 872 | END SUBROUTINE lim_thd_dif |
---|
| 873 | #endif |
---|
[921] | 874 | END MODULE limthd_dif |
---|