[1000] | 1 | MODULE microphysics_mod |
---|
| 2 | |
---|
[1093] | 3 | !--------------------------------------------------------------------------------! |
---|
| 4 | ! This file is part of PALM. |
---|
| 5 | ! |
---|
| 6 | ! PALM is free software: you can redistribute it and/or modify it under the terms |
---|
| 7 | ! of the GNU General Public License as published by the Free Software Foundation, |
---|
| 8 | ! either version 3 of the License, or (at your option) any later version. |
---|
| 9 | ! |
---|
| 10 | ! PALM is distributed in the hope that it will be useful, but WITHOUT ANY |
---|
| 11 | ! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR |
---|
| 12 | ! A PARTICULAR PURPOSE. See the GNU General Public License for more details. |
---|
| 13 | ! |
---|
| 14 | ! You should have received a copy of the GNU General Public License along with |
---|
| 15 | ! PALM. If not, see <http://www.gnu.org/licenses/>. |
---|
| 16 | ! |
---|
| 17 | ! Copyright 1997-2012 Leibniz University Hannover |
---|
| 18 | !--------------------------------------------------------------------------------! |
---|
| 19 | ! |
---|
[1000] | 20 | ! Current revisions: |
---|
[1092] | 21 | ! ------------------ |
---|
[1106] | 22 | ! small changes in code formatting |
---|
[1000] | 23 | ! |
---|
| 24 | ! Former revisions: |
---|
| 25 | ! ----------------- |
---|
[1052] | 26 | ! $Id: microphysics.f90 1106 2013-03-04 05:31:38Z raasch $ |
---|
[1054] | 27 | ! |
---|
[1093] | 28 | ! 1092 2013-02-02 11:24:22Z raasch |
---|
| 29 | ! unused variables removed |
---|
| 30 | ! file put under GPL |
---|
| 31 | ! |
---|
[1066] | 32 | ! 1065 2012-11-22 17:42:36Z hoffmann |
---|
| 33 | ! Sedimentation process implemented according to Stevens and Seifert (2008). |
---|
| 34 | ! Turbulence effects on autoconversion and accretion added (Seifert, Nuijens |
---|
| 35 | ! and Stevens, 2010). |
---|
| 36 | ! |
---|
[1054] | 37 | ! 1053 2012-11-13 17:11:03Z hoffmann |
---|
| 38 | ! initial revision |
---|
[1000] | 39 | ! |
---|
| 40 | ! Description: |
---|
| 41 | ! ------------ |
---|
| 42 | ! Calculate cloud microphysics according to the two moment bulk |
---|
| 43 | ! scheme by Seifert and Beheng (2006). |
---|
| 44 | !------------------------------------------------------------------------------! |
---|
| 45 | |
---|
| 46 | PRIVATE |
---|
[1022] | 47 | PUBLIC dsd_properties, autoconversion, accretion, selfcollection_breakup, & |
---|
[1012] | 48 | evaporation_rain, sedimentation_cloud, sedimentation_rain |
---|
[1000] | 49 | |
---|
[1022] | 50 | INTERFACE dsd_properties |
---|
| 51 | MODULE PROCEDURE dsd_properties |
---|
| 52 | MODULE PROCEDURE dsd_properties_ij |
---|
| 53 | END INTERFACE dsd_properties |
---|
| 54 | |
---|
[1000] | 55 | INTERFACE autoconversion |
---|
| 56 | MODULE PROCEDURE autoconversion |
---|
| 57 | MODULE PROCEDURE autoconversion_ij |
---|
| 58 | END INTERFACE autoconversion |
---|
| 59 | |
---|
| 60 | INTERFACE accretion |
---|
| 61 | MODULE PROCEDURE accretion |
---|
| 62 | MODULE PROCEDURE accretion_ij |
---|
| 63 | END INTERFACE accretion |
---|
[1005] | 64 | |
---|
| 65 | INTERFACE selfcollection_breakup |
---|
| 66 | MODULE PROCEDURE selfcollection_breakup |
---|
| 67 | MODULE PROCEDURE selfcollection_breakup_ij |
---|
| 68 | END INTERFACE selfcollection_breakup |
---|
[1012] | 69 | |
---|
| 70 | INTERFACE evaporation_rain |
---|
| 71 | MODULE PROCEDURE evaporation_rain |
---|
| 72 | MODULE PROCEDURE evaporation_rain_ij |
---|
| 73 | END INTERFACE evaporation_rain |
---|
| 74 | |
---|
| 75 | INTERFACE sedimentation_cloud |
---|
| 76 | MODULE PROCEDURE sedimentation_cloud |
---|
| 77 | MODULE PROCEDURE sedimentation_cloud_ij |
---|
| 78 | END INTERFACE sedimentation_cloud |
---|
[1000] | 79 | |
---|
[1012] | 80 | INTERFACE sedimentation_rain |
---|
| 81 | MODULE PROCEDURE sedimentation_rain |
---|
| 82 | MODULE PROCEDURE sedimentation_rain_ij |
---|
| 83 | END INTERFACE sedimentation_rain |
---|
| 84 | |
---|
[1000] | 85 | CONTAINS |
---|
| 86 | |
---|
| 87 | |
---|
| 88 | !------------------------------------------------------------------------------! |
---|
| 89 | ! Call for all grid points |
---|
| 90 | !------------------------------------------------------------------------------! |
---|
[1022] | 91 | SUBROUTINE dsd_properties |
---|
| 92 | |
---|
| 93 | USE arrays_3d |
---|
| 94 | USE cloud_parameters |
---|
| 95 | USE constants |
---|
| 96 | USE indices |
---|
| 97 | |
---|
| 98 | IMPLICIT NONE |
---|
| 99 | |
---|
| 100 | INTEGER :: i, j, k |
---|
| 101 | |
---|
| 102 | |
---|
| 103 | DO i = nxl, nxr |
---|
| 104 | DO j = nys, nyn |
---|
| 105 | DO k = nzb_2d(j,i)+1, nzt |
---|
| 106 | |
---|
| 107 | ENDDO |
---|
| 108 | ENDDO |
---|
| 109 | ENDDO |
---|
| 110 | |
---|
| 111 | END SUBROUTINE dsd_properties |
---|
| 112 | |
---|
[1106] | 113 | |
---|
[1000] | 114 | SUBROUTINE autoconversion |
---|
| 115 | |
---|
| 116 | USE arrays_3d |
---|
| 117 | USE cloud_parameters |
---|
| 118 | USE constants |
---|
| 119 | USE indices |
---|
| 120 | |
---|
| 121 | IMPLICIT NONE |
---|
| 122 | |
---|
| 123 | INTEGER :: i, j, k |
---|
| 124 | |
---|
| 125 | |
---|
| 126 | DO i = nxl, nxr |
---|
| 127 | DO j = nys, nyn |
---|
| 128 | DO k = nzb_2d(j,i)+1, nzt |
---|
| 129 | |
---|
| 130 | ENDDO |
---|
| 131 | ENDDO |
---|
| 132 | ENDDO |
---|
| 133 | |
---|
| 134 | END SUBROUTINE autoconversion |
---|
| 135 | |
---|
[1106] | 136 | |
---|
[1005] | 137 | SUBROUTINE accretion |
---|
[1000] | 138 | |
---|
| 139 | USE arrays_3d |
---|
| 140 | USE cloud_parameters |
---|
| 141 | USE constants |
---|
| 142 | USE indices |
---|
[1005] | 143 | |
---|
[1000] | 144 | IMPLICIT NONE |
---|
| 145 | |
---|
| 146 | INTEGER :: i, j, k |
---|
| 147 | |
---|
[1005] | 148 | |
---|
| 149 | DO i = nxl, nxr |
---|
| 150 | DO j = nys, nyn |
---|
| 151 | DO k = nzb_2d(j,i)+1, nzt |
---|
[1000] | 152 | |
---|
[1005] | 153 | ENDDO |
---|
| 154 | ENDDO |
---|
[1000] | 155 | ENDDO |
---|
| 156 | |
---|
[1005] | 157 | END SUBROUTINE accretion |
---|
[1000] | 158 | |
---|
[1106] | 159 | |
---|
[1005] | 160 | SUBROUTINE selfcollection_breakup |
---|
[1000] | 161 | |
---|
| 162 | USE arrays_3d |
---|
| 163 | USE cloud_parameters |
---|
| 164 | USE constants |
---|
| 165 | USE indices |
---|
| 166 | |
---|
| 167 | IMPLICIT NONE |
---|
| 168 | |
---|
| 169 | INTEGER :: i, j, k |
---|
| 170 | |
---|
| 171 | |
---|
| 172 | DO i = nxl, nxr |
---|
| 173 | DO j = nys, nyn |
---|
| 174 | DO k = nzb_2d(j,i)+1, nzt |
---|
| 175 | |
---|
| 176 | ENDDO |
---|
| 177 | ENDDO |
---|
| 178 | ENDDO |
---|
| 179 | |
---|
[1005] | 180 | END SUBROUTINE selfcollection_breakup |
---|
[1000] | 181 | |
---|
[1106] | 182 | |
---|
[1012] | 183 | SUBROUTINE evaporation_rain |
---|
[1000] | 184 | |
---|
[1012] | 185 | USE arrays_3d |
---|
| 186 | USE cloud_parameters |
---|
| 187 | USE constants |
---|
| 188 | USE indices |
---|
| 189 | |
---|
| 190 | IMPLICIT NONE |
---|
| 191 | |
---|
| 192 | INTEGER :: i, j, k |
---|
| 193 | |
---|
| 194 | |
---|
| 195 | DO i = nxl, nxr |
---|
| 196 | DO j = nys, nyn |
---|
| 197 | DO k = nzb_2d(j,i)+1, nzt |
---|
| 198 | |
---|
| 199 | ENDDO |
---|
| 200 | ENDDO |
---|
| 201 | ENDDO |
---|
| 202 | |
---|
| 203 | END SUBROUTINE evaporation_rain |
---|
| 204 | |
---|
[1106] | 205 | |
---|
[1012] | 206 | SUBROUTINE sedimentation_cloud |
---|
| 207 | |
---|
| 208 | USE arrays_3d |
---|
| 209 | USE cloud_parameters |
---|
| 210 | USE constants |
---|
| 211 | USE indices |
---|
| 212 | |
---|
| 213 | IMPLICIT NONE |
---|
| 214 | |
---|
| 215 | INTEGER :: i, j, k |
---|
| 216 | |
---|
| 217 | |
---|
| 218 | DO i = nxl, nxr |
---|
| 219 | DO j = nys, nyn |
---|
| 220 | DO k = nzb_2d(j,i)+1, nzt |
---|
| 221 | |
---|
| 222 | ENDDO |
---|
| 223 | ENDDO |
---|
| 224 | ENDDO |
---|
| 225 | |
---|
| 226 | END SUBROUTINE sedimentation_cloud |
---|
| 227 | |
---|
[1106] | 228 | |
---|
[1012] | 229 | SUBROUTINE sedimentation_rain |
---|
| 230 | |
---|
| 231 | USE arrays_3d |
---|
| 232 | USE cloud_parameters |
---|
| 233 | USE constants |
---|
| 234 | USE indices |
---|
| 235 | |
---|
| 236 | IMPLICIT NONE |
---|
| 237 | |
---|
| 238 | INTEGER :: i, j, k |
---|
| 239 | |
---|
| 240 | |
---|
| 241 | DO i = nxl, nxr |
---|
| 242 | DO j = nys, nyn |
---|
| 243 | DO k = nzb_2d(j,i)+1, nzt |
---|
| 244 | |
---|
| 245 | ENDDO |
---|
| 246 | ENDDO |
---|
| 247 | ENDDO |
---|
| 248 | |
---|
| 249 | END SUBROUTINE sedimentation_rain |
---|
| 250 | |
---|
| 251 | |
---|
[1000] | 252 | !------------------------------------------------------------------------------! |
---|
| 253 | ! Call for grid point i,j |
---|
| 254 | !------------------------------------------------------------------------------! |
---|
[1022] | 255 | SUBROUTINE dsd_properties_ij( i, j ) |
---|
| 256 | |
---|
| 257 | USE arrays_3d |
---|
| 258 | USE cloud_parameters |
---|
| 259 | USE constants |
---|
| 260 | USE indices |
---|
| 261 | USE control_parameters |
---|
[1048] | 262 | USE user |
---|
[1022] | 263 | |
---|
| 264 | IMPLICIT NONE |
---|
| 265 | |
---|
| 266 | INTEGER :: i, j, k |
---|
| 267 | |
---|
| 268 | DO k = nzb_2d(j,i)+1, nzt |
---|
[1065] | 269 | |
---|
| 270 | IF ( qr(k,j,i) <= eps_sb ) THEN |
---|
| 271 | qr(k,j,i) = 0.0 |
---|
| 272 | ELSE |
---|
[1022] | 273 | ! |
---|
[1048] | 274 | !-- Adjust number of raindrops to avoid nonlinear effects in |
---|
| 275 | !-- sedimentation and evaporation of rain drops due to too small or |
---|
[1065] | 276 | !-- too big weights of rain drops (Stevens and Seifert, 2008). |
---|
| 277 | IF ( nr(k,j,i) * xrmin > qr(k,j,i) * hyrho(k) ) THEN |
---|
| 278 | nr(k,j,i) = qr(k,j,i) * hyrho(k) / xrmin |
---|
| 279 | ELSEIF ( nr(k,j,i) * xrmax < qr(k,j,i) * hyrho(k) ) THEN |
---|
| 280 | nr(k,j,i) = qr(k,j,i) * hyrho(k) / xrmax |
---|
[1048] | 281 | ENDIF |
---|
[1065] | 282 | xr(k) = hyrho(k) * qr(k,j,i) / nr(k,j,i) |
---|
[1022] | 283 | ! |
---|
[1065] | 284 | !-- Weight averaged diameter of rain drops: |
---|
| 285 | dr(k) = ( hyrho(k) * qr(k,j,i) / nr(k,j,i) * & |
---|
| 286 | dpirho_l )**( 1.0 / 3.0 ) |
---|
[1048] | 287 | ! |
---|
[1049] | 288 | !-- Shape parameter of gamma distribution (Milbrandt and Yau, 2005; |
---|
| 289 | !-- Stevens and Seifert, 2008): |
---|
[1065] | 290 | mu_r(k) = 10.0 * ( 1.0 + TANH( 1.2E3 * ( dr(k) - 1.4E-3 ) ) ) |
---|
[1049] | 291 | ! |
---|
[1022] | 292 | !-- Slope parameter of gamma distribution (Seifert, 2008): |
---|
[1048] | 293 | lambda_r(k) = ( ( mu_r(k) + 3.0 ) * ( mu_r(k) + 2.0 ) * & |
---|
| 294 | ( mu_r(k) + 1.0 ) )**( 1.0 / 3.0 ) / dr(k) |
---|
[1022] | 295 | ENDIF |
---|
| 296 | ENDDO |
---|
| 297 | |
---|
| 298 | END SUBROUTINE dsd_properties_ij |
---|
| 299 | |
---|
[1106] | 300 | |
---|
[1005] | 301 | SUBROUTINE autoconversion_ij( i, j ) |
---|
[1000] | 302 | |
---|
| 303 | USE arrays_3d |
---|
| 304 | USE cloud_parameters |
---|
| 305 | USE constants |
---|
| 306 | USE indices |
---|
[1005] | 307 | USE control_parameters |
---|
[1048] | 308 | USE statistics |
---|
[1065] | 309 | USE grid_variables |
---|
[1000] | 310 | |
---|
| 311 | IMPLICIT NONE |
---|
| 312 | |
---|
| 313 | INTEGER :: i, j, k |
---|
[1065] | 314 | REAL :: k_au, autocon, phi_au, tau_cloud, xc, nu_c, rc, & |
---|
| 315 | l_mix, re_lambda, alpha_cc, r_cc, sigma_cc, epsilon |
---|
[1000] | 316 | |
---|
[1106] | 317 | |
---|
[1005] | 318 | k_au = k_cc / ( 20.0 * x0 ) |
---|
| 319 | |
---|
[1000] | 320 | DO k = nzb_2d(j,i)+1, nzt |
---|
| 321 | |
---|
[1048] | 322 | IF ( ql(k,j,i) > 0.0 ) THEN |
---|
[1012] | 323 | ! |
---|
[1048] | 324 | !-- Intern time scale of coagulation (Seifert and Beheng, 2006): |
---|
[1012] | 325 | !-- (1.0 - ql(k,j,i) / ( ql(k,j,i) + qr(k,j,i) )) |
---|
[1048] | 326 | tau_cloud = 1.0 - ql(k,j,i) / ( ql(k,j,i) + qr(k,j,i) + 1.0E-20 ) |
---|
[1012] | 327 | ! |
---|
| 328 | !-- Universal function for autoconversion process |
---|
| 329 | !-- (Seifert and Beheng, 2006): |
---|
[1048] | 330 | phi_au = 600.0 * tau_cloud**0.68 * ( 1.0 - tau_cloud**0.68 )**3 |
---|
[1012] | 331 | ! |
---|
| 332 | !-- Shape parameter of gamma distribution (Geoffroy et al., 2010): |
---|
| 333 | !-- (Use constant nu_c = 1.0 instead?) |
---|
[1065] | 334 | nu_c = 1.0 !MAX( 0.0, 1580.0 * hyrho(k) * ql(k,j,i) - 0.28 ) |
---|
[1012] | 335 | ! |
---|
| 336 | !-- Mean weight of cloud droplets: |
---|
[1005] | 337 | xc = hyrho(k) * ql(k,j,i) / nc |
---|
[1012] | 338 | ! |
---|
[1065] | 339 | !-- Parameterized turbulence effects on autoconversion (Seifert, |
---|
| 340 | !-- Nuijens and Stevens, 2010) |
---|
| 341 | IF ( turbulence ) THEN |
---|
| 342 | ! |
---|
| 343 | !-- Weight averaged radius of cloud droplets: |
---|
| 344 | rc = 0.5 * ( xc * dpirho_l )**( 1.0 / 3.0 ) |
---|
| 345 | |
---|
| 346 | alpha_cc = ( a_1 + a_2 * nu_c ) / ( 1.0 + a_3 * nu_c ) |
---|
| 347 | r_cc = ( b_1 + b_2 * nu_c ) / ( 1.0 + b_3 * nu_c ) |
---|
| 348 | sigma_cc = ( c_1 + c_2 * nu_c ) / ( 1.0 + c_3 * nu_c ) |
---|
| 349 | ! |
---|
| 350 | !-- Mixing length (neglecting distance to ground and stratification) |
---|
| 351 | l_mix = ( dx * dy * dzu(k) )**( 1.0 / 3.0 ) |
---|
| 352 | ! |
---|
| 353 | !-- Limit dissipation rate according to Seifert, Nuijens and |
---|
| 354 | !-- Stevens (2010) |
---|
| 355 | epsilon = MIN( 0.06, diss(k,j,i) ) |
---|
| 356 | ! |
---|
| 357 | !-- Compute Taylor-microscale Reynolds number: |
---|
| 358 | re_lambda = 6.0 / 11.0 * ( l_mix / c_const )**( 2.0 / 3.0 ) * & |
---|
| 359 | SQRT( 15.0 / kin_vis_air ) * epsilon**( 1.0 / 6.0 ) |
---|
| 360 | ! |
---|
| 361 | !-- The factor of 1.0E4 is needed to convert the dissipation rate |
---|
| 362 | !-- from m2 s-3 to cm2 s-3. |
---|
| 363 | k_au = k_au * ( 1.0 + & |
---|
| 364 | epsilon * 1.0E4 * ( re_lambda * 1.0E-3 )**0.25 * & |
---|
| 365 | ( alpha_cc * EXP( -1.0 * ( ( rc - r_cc ) / & |
---|
| 366 | sigma_cc )**2 ) + beta_cc ) ) |
---|
| 367 | ENDIF |
---|
| 368 | ! |
---|
[1012] | 369 | !-- Autoconversion rate (Seifert and Beheng, 2006): |
---|
[1065] | 370 | autocon = k_au * ( nu_c + 2.0 ) * ( nu_c + 4.0 ) / & |
---|
| 371 | ( nu_c + 1.0 )**2 * ql(k,j,i)**2 * xc**2 * & |
---|
| 372 | ( 1.0 + phi_au / ( 1.0 - tau_cloud )**2 ) * & |
---|
[1048] | 373 | rho_surface |
---|
[1065] | 374 | autocon = MIN( autocon, ql(k,j,i) / ( dt_3d * & |
---|
[1048] | 375 | weight_substep(intermediate_timestep_count) ) ) |
---|
[1012] | 376 | ! |
---|
[1022] | 377 | !-- Tendencies for q, qr, nr, pt: |
---|
[1005] | 378 | tend_qr(k,j,i) = tend_qr(k,j,i) + autocon |
---|
[1106] | 379 | tend_q(k,j,i) = tend_q(k,j,i) - autocon |
---|
[1005] | 380 | tend_nr(k,j,i) = tend_nr(k,j,i) + autocon / x0 * hyrho(k) |
---|
[1106] | 381 | tend_pt(k,j,i) = tend_pt(k,j,i) + autocon * l_d_cp * pt_d_t(k) |
---|
| 382 | |
---|
[1005] | 383 | ENDIF |
---|
[1000] | 384 | |
---|
| 385 | ENDDO |
---|
| 386 | |
---|
[1005] | 387 | END SUBROUTINE autoconversion_ij |
---|
| 388 | |
---|
[1106] | 389 | |
---|
[1005] | 390 | SUBROUTINE accretion_ij( i, j ) |
---|
| 391 | |
---|
| 392 | USE arrays_3d |
---|
| 393 | USE cloud_parameters |
---|
| 394 | USE constants |
---|
| 395 | USE indices |
---|
| 396 | USE control_parameters |
---|
[1048] | 397 | USE statistics |
---|
[1005] | 398 | |
---|
| 399 | IMPLICIT NONE |
---|
| 400 | |
---|
| 401 | INTEGER :: i, j, k |
---|
[1065] | 402 | REAL :: accr, phi_ac, tau_cloud, k_cr |
---|
[1005] | 403 | |
---|
| 404 | DO k = nzb_2d(j,i)+1, nzt |
---|
[1106] | 405 | |
---|
[1048] | 406 | IF ( ( ql(k,j,i) > 0.0 ) .AND. ( qr(k,j,i) > eps_sb ) ) THEN |
---|
[1012] | 407 | ! |
---|
[1048] | 408 | !-- Intern time scale of coagulation (Seifert and Beheng, 2006): |
---|
| 409 | tau_cloud = 1.0 - ql(k,j,i) / ( ql(k,j,i) + qr(k,j,i) + 1.0E-20) |
---|
[1012] | 410 | ! |
---|
| 411 | !-- Universal function for accretion process |
---|
[1048] | 412 | !-- (Seifert and Beheng, 2001): |
---|
[1065] | 413 | phi_ac = tau_cloud / ( tau_cloud + 5.0E-5 ) |
---|
| 414 | phi_ac = ( phi_ac**2 )**2 |
---|
[1012] | 415 | ! |
---|
[1065] | 416 | !-- Parameterized turbulence effects on autoconversion (Seifert, |
---|
| 417 | !-- Nuijens and Stevens, 2010). The factor of 1.0E4 is needed to |
---|
| 418 | !-- convert the dissipation (diss) from m2 s-3 to cm2 s-3. |
---|
| 419 | IF ( turbulence ) THEN |
---|
| 420 | k_cr = k_cr0 * ( 1.0 + 0.05 * & |
---|
| 421 | MIN( 600.0, diss(k,j,i) * 1.0E4 )**0.25 ) |
---|
| 422 | ELSE |
---|
| 423 | k_cr = k_cr0 |
---|
| 424 | ENDIF |
---|
| 425 | ! |
---|
[1012] | 426 | !-- Accretion rate (Seifert and Beheng, 2006): |
---|
[1065] | 427 | accr = k_cr * ql(k,j,i) * qr(k,j,i) * phi_ac * & |
---|
| 428 | SQRT( rho_surface * hyrho(k) ) |
---|
| 429 | accr = MIN( accr, ql(k,j,i) / ( dt_3d * & |
---|
| 430 | weight_substep(intermediate_timestep_count) ) ) |
---|
[1012] | 431 | ! |
---|
[1022] | 432 | !-- Tendencies for q, qr, pt: |
---|
[1005] | 433 | tend_qr(k,j,i) = tend_qr(k,j,i) + accr |
---|
[1106] | 434 | tend_q(k,j,i) = tend_q(k,j,i) - accr |
---|
[1048] | 435 | tend_pt(k,j,i) = tend_pt(k,j,i) + accr * l_d_cp * pt_d_t(k) |
---|
[1106] | 436 | |
---|
[1005] | 437 | ENDIF |
---|
[1106] | 438 | |
---|
[1005] | 439 | ENDDO |
---|
| 440 | |
---|
[1000] | 441 | END SUBROUTINE accretion_ij |
---|
| 442 | |
---|
[1005] | 443 | |
---|
| 444 | SUBROUTINE selfcollection_breakup_ij( i, j ) |
---|
| 445 | |
---|
| 446 | USE arrays_3d |
---|
| 447 | USE cloud_parameters |
---|
| 448 | USE constants |
---|
| 449 | USE indices |
---|
| 450 | USE control_parameters |
---|
[1048] | 451 | USE statistics |
---|
[1005] | 452 | |
---|
| 453 | IMPLICIT NONE |
---|
| 454 | |
---|
| 455 | INTEGER :: i, j, k |
---|
[1048] | 456 | REAL :: selfcoll, breakup, phi_br, phi_sc |
---|
[1005] | 457 | |
---|
[1106] | 458 | |
---|
[1005] | 459 | DO k = nzb_2d(j,i)+1, nzt |
---|
[1106] | 460 | |
---|
[1065] | 461 | IF ( qr(k,j,i) > eps_sb ) THEN |
---|
[1012] | 462 | ! |
---|
| 463 | !-- Selfcollection rate (Seifert and Beheng, 2006): |
---|
[1048] | 464 | !-- pirho_l**( 1.0 / 3.0 ) is necessary to convert [lambda_r] = m-1 to |
---|
| 465 | !-- kg**( 1.0 / 3.0 ). |
---|
[1065] | 466 | phi_sc = 1.0 !( 1.0 + kappa_rr / lambda_r(k) * & |
---|
| 467 | !pirho_l**( 1.0 / 3.0 ) )**( -9 ) |
---|
[1048] | 468 | |
---|
| 469 | selfcoll = k_rr * nr(k,j,i) * qr(k,j,i) * phi_sc * & |
---|
[1005] | 470 | SQRT( hyrho(k) * rho_surface ) |
---|
[1012] | 471 | ! |
---|
[1048] | 472 | !-- Collisional breakup rate (Seifert, 2008): |
---|
| 473 | IF ( dr(k) >= 0.3E-3 ) THEN |
---|
| 474 | phi_br = k_br * ( dr(k) - 1.1E-3 ) |
---|
[1005] | 475 | breakup = selfcoll * ( phi_br + 1.0 ) |
---|
| 476 | ELSE |
---|
| 477 | breakup = 0.0 |
---|
| 478 | ENDIF |
---|
[1048] | 479 | |
---|
| 480 | selfcoll = MAX( breakup - selfcoll, -nr(k,j,i) / ( dt_3d * & |
---|
| 481 | weight_substep(intermediate_timestep_count) ) ) |
---|
[1012] | 482 | ! |
---|
| 483 | !-- Tendency for nr: |
---|
[1048] | 484 | tend_nr(k,j,i) = tend_nr(k,j,i) + selfcoll |
---|
[1106] | 485 | |
---|
[1005] | 486 | ENDIF |
---|
[1106] | 487 | |
---|
[1005] | 488 | ENDDO |
---|
| 489 | |
---|
| 490 | END SUBROUTINE selfcollection_breakup_ij |
---|
| 491 | |
---|
[1106] | 492 | |
---|
[1012] | 493 | SUBROUTINE evaporation_rain_ij( i, j ) |
---|
[1022] | 494 | ! |
---|
| 495 | !-- Evaporation of precipitable water. Condensation is neglected for |
---|
| 496 | !-- precipitable water. |
---|
[1012] | 497 | |
---|
| 498 | USE arrays_3d |
---|
| 499 | USE cloud_parameters |
---|
| 500 | USE constants |
---|
| 501 | USE indices |
---|
| 502 | USE control_parameters |
---|
[1048] | 503 | USE statistics |
---|
| 504 | |
---|
[1012] | 505 | IMPLICIT NONE |
---|
| 506 | |
---|
| 507 | INTEGER :: i, j, k |
---|
| 508 | REAL :: evap, alpha, e_s, q_s, t_l, sat, temp, g_evap, f_vent, & |
---|
[1049] | 509 | mu_r_2, mu_r_5d2, nr_0 |
---|
[1012] | 510 | |
---|
[1106] | 511 | |
---|
[1012] | 512 | DO k = nzb_2d(j,i)+1, nzt |
---|
[1106] | 513 | |
---|
[1065] | 514 | IF ( qr(k,j,i) > eps_sb ) THEN |
---|
[1012] | 515 | ! |
---|
| 516 | !-- Actual liquid water temperature: |
---|
| 517 | t_l = t_d_pt(k) * pt(k,j,i) |
---|
| 518 | ! |
---|
| 519 | !-- Saturation vapor pressure at t_l: |
---|
| 520 | e_s = 610.78 * EXP( 17.269 * ( t_l - 273.16 ) / ( t_l - 35.86 ) ) |
---|
| 521 | ! |
---|
| 522 | !-- Computation of saturation humidity: |
---|
| 523 | q_s = 0.622 * e_s / ( hyp(k) - 0.378 * e_s ) |
---|
| 524 | alpha = 0.622 * l_d_r * l_d_cp / ( t_l * t_l ) |
---|
| 525 | q_s = q_s * ( 1.0 + alpha * q(k,j,i) ) / ( 1.0 + alpha * q_s ) |
---|
| 526 | ! |
---|
[1106] | 527 | !-- Supersaturation: |
---|
[1012] | 528 | sat = MIN( 0.0, ( q(k,j,i) - ql(k,j,i) ) / q_s - 1.0 ) |
---|
| 529 | ! |
---|
| 530 | !-- Actual temperature: |
---|
[1048] | 531 | temp = t_l + l_d_cp * ql(k,j,i) |
---|
[1012] | 532 | ! |
---|
| 533 | !-- |
---|
| 534 | g_evap = ( l_v / ( r_v * temp ) - 1.0 ) * l_v / & |
---|
[1048] | 535 | ( thermal_conductivity_l * temp ) + rho_l * r_v * temp /& |
---|
[1022] | 536 | ( diff_coeff_l * e_s ) |
---|
[1012] | 537 | g_evap = 1.0 / g_evap |
---|
| 538 | ! |
---|
[1049] | 539 | !-- Compute ventilation factor and intercept parameter |
---|
| 540 | !-- (Seifert and Beheng, 2006; Seifert, 2008): |
---|
[1048] | 541 | IF ( ventilation_effect ) THEN |
---|
| 542 | mu_r_2 = mu_r(k) + 2.0 |
---|
| 543 | mu_r_5d2 = mu_r(k) + 2.5 |
---|
| 544 | f_vent = a_vent * gamm( mu_r_2 ) * & |
---|
| 545 | lambda_r(k)**( -mu_r_2 ) + & |
---|
| 546 | b_vent * schmidt_p_1d3 * & |
---|
| 547 | SQRT( a_term / kin_vis_air ) * gamm( mu_r_5d2 ) * & |
---|
| 548 | lambda_r(k)**( -mu_r_5d2 ) * & |
---|
| 549 | ( 1.0 - 0.5 * ( b_term / a_term ) * & |
---|
| 550 | ( lambda_r(k) / & |
---|
| 551 | ( c_term + lambda_r(k) ) )**mu_r_5d2 - & |
---|
| 552 | 0.125 * ( b_term / a_term )**2 * & |
---|
| 553 | ( lambda_r(k) / & |
---|
| 554 | ( 2.0 * c_term + lambda_r(k) ) )**mu_r_5d2 - & |
---|
| 555 | 0.0625 * ( b_term / a_term )**3 * & |
---|
| 556 | ( lambda_r(k) / & |
---|
| 557 | ( 3.0 * c_term + lambda_r(k) ) )**mu_r_5d2 - & |
---|
| 558 | 0.0390625 * ( b_term / a_term )**4 * & |
---|
| 559 | ( lambda_r(k) / & |
---|
| 560 | ( 4.0 * c_term + lambda_r(k) ) )**mu_r_5d2 ) |
---|
[1049] | 561 | nr_0 = nr(k,j,i) * lambda_r(k)**( mu_r(k) + 1.0 ) / & |
---|
| 562 | gamm( mu_r(k) + 1.0 ) |
---|
[1048] | 563 | ELSE |
---|
| 564 | f_vent = 1.0 |
---|
[1049] | 565 | nr_0 = nr(k,j,i) * dr(k) |
---|
[1048] | 566 | ENDIF |
---|
[1012] | 567 | ! |
---|
[1048] | 568 | !-- Evaporation rate of rain water content (Seifert and Beheng, 2006): |
---|
[1049] | 569 | evap = 2.0 * pi * nr_0 * g_evap * f_vent * sat / & |
---|
[1048] | 570 | hyrho(k) |
---|
[1106] | 571 | evap = MAX( evap, -qr(k,j,i) / ( dt_3d * & |
---|
[1048] | 572 | weight_substep(intermediate_timestep_count) ) ) |
---|
[1012] | 573 | ! |
---|
[1022] | 574 | !-- Tendencies for q, qr, nr, pt: |
---|
[1012] | 575 | tend_qr(k,j,i) = tend_qr(k,j,i) + evap |
---|
[1106] | 576 | tend_q(k,j,i) = tend_q(k,j,i) - evap |
---|
[1049] | 577 | tend_nr(k,j,i) = tend_nr(k,j,i) + c_evap * evap / xr(k) * hyrho(k) |
---|
[1048] | 578 | tend_pt(k,j,i) = tend_pt(k,j,i) + evap * l_d_cp * pt_d_t(k) |
---|
[1106] | 579 | |
---|
[1012] | 580 | ENDIF |
---|
[1106] | 581 | |
---|
[1012] | 582 | ENDDO |
---|
| 583 | |
---|
| 584 | END SUBROUTINE evaporation_rain_ij |
---|
| 585 | |
---|
[1106] | 586 | |
---|
[1012] | 587 | SUBROUTINE sedimentation_cloud_ij( i, j ) |
---|
| 588 | |
---|
| 589 | USE arrays_3d |
---|
| 590 | USE cloud_parameters |
---|
| 591 | USE constants |
---|
| 592 | USE indices |
---|
| 593 | USE control_parameters |
---|
| 594 | |
---|
| 595 | IMPLICIT NONE |
---|
| 596 | |
---|
| 597 | INTEGER :: i, j, k |
---|
[1022] | 598 | REAL :: sed_q_const, sigma_gc = 1.3, k_st = 1.2E8 |
---|
[1106] | 599 | |
---|
[1012] | 600 | ! |
---|
| 601 | !-- Sedimentation of cloud droplets (Heus et al., 2010): |
---|
[1022] | 602 | sed_q_const = k_st * ( 3.0 / ( 4.0 * pi * rho_l ))**( 2.0 / 3.0 ) * & |
---|
[1048] | 603 | EXP( 5.0 * LOG( sigma_gc )**2 ) |
---|
[1012] | 604 | |
---|
[1022] | 605 | sed_q = 0.0 |
---|
[1012] | 606 | |
---|
| 607 | DO k = nzb_2d(j,i)+1, nzt |
---|
[1048] | 608 | IF ( ql(k,j,i) > 0.0 ) THEN |
---|
[1022] | 609 | sed_q(k) = sed_q_const * nc**( -2.0 / 3.0 ) * & |
---|
[1012] | 610 | ( ql(k,j,i) * hyrho(k) )**( 5.0 / 3.0 ) |
---|
| 611 | ENDIF |
---|
| 612 | ENDDO |
---|
| 613 | ! |
---|
[1106] | 614 | !-- Tendency for q, pt: |
---|
[1012] | 615 | DO k = nzb_2d(j,i)+1, nzt |
---|
[1048] | 616 | tend_q(k,j,i) = tend_q(k,j,i) + ( sed_q(k+1) - sed_q(k) ) * & |
---|
| 617 | ddzu(k+1) / hyrho(k) |
---|
[1022] | 618 | tend_pt(k,j,i) = tend_pt(k,j,i) - ( sed_q(k+1) - sed_q(k) ) * & |
---|
[1048] | 619 | ddzu(k+1) / hyrho(k) * l_d_cp * pt_d_t(k) |
---|
[1012] | 620 | ENDDO |
---|
| 621 | |
---|
| 622 | END SUBROUTINE sedimentation_cloud_ij |
---|
| 623 | |
---|
[1106] | 624 | |
---|
[1012] | 625 | SUBROUTINE sedimentation_rain_ij( i, j ) |
---|
| 626 | |
---|
| 627 | USE arrays_3d |
---|
| 628 | USE cloud_parameters |
---|
| 629 | USE constants |
---|
| 630 | USE indices |
---|
| 631 | USE control_parameters |
---|
[1048] | 632 | USE statistics |
---|
[1012] | 633 | |
---|
| 634 | IMPLICIT NONE |
---|
| 635 | |
---|
[1092] | 636 | INTEGER :: i, j, k, k_run |
---|
| 637 | REAL :: c_run, d_max, d_mean, d_min, dt_sedi, flux, z_run |
---|
[1012] | 638 | |
---|
[1092] | 639 | REAL, DIMENSION(nzb:nzt) :: c_nr, c_qr, nr_slope, qr_slope, w_nr, w_qr |
---|
| 640 | |
---|
[1065] | 641 | ! |
---|
| 642 | !-- Computation of sedimentation flux. Implementation according to Stevens |
---|
| 643 | !-- and Seifert (2008). |
---|
[1048] | 644 | IF ( intermediate_timestep_count == 1 ) prr(:,j,i) = 0.0 |
---|
[1012] | 645 | |
---|
[1065] | 646 | dt_sedi = dt_3d * weight_substep(intermediate_timestep_count) |
---|
[1022] | 647 | |
---|
[1065] | 648 | w_nr = 0.0 |
---|
| 649 | w_qr = 0.0 |
---|
[1012] | 650 | ! |
---|
[1065] | 651 | !-- Compute velocities |
---|
| 652 | DO k = nzb_s_inner(j,i)+1, nzt |
---|
| 653 | IF ( qr(k,j,i) > eps_sb ) THEN |
---|
| 654 | w_nr(k) = MAX( 0.1, MIN( 20.0, a_term - b_term * ( 1.0 + & |
---|
| 655 | c_term / lambda_r(k) )**( -1.0 * ( mu_r(k) + 1.0 ) ) ) ) |
---|
| 656 | w_qr(k) = MAX( 0.1, MIN( 20.0, a_term - b_term * ( 1.0 + & |
---|
| 657 | c_term / lambda_r(k) )**( -1.0 * ( mu_r(k) + 4.0 ) ) ) ) |
---|
| 658 | ELSE |
---|
| 659 | w_nr(k) = 0.0 |
---|
| 660 | w_qr(k) = 0.0 |
---|
| 661 | ENDIF |
---|
| 662 | ENDDO |
---|
[1048] | 663 | ! |
---|
[1065] | 664 | !-- Adjust boundary values |
---|
| 665 | w_nr(nzb_2d(j,i)) = w_nr(nzb_2d(j,i)+1) |
---|
| 666 | w_qr(nzb_2d(j,i)) = w_qr(nzb_2d(j,i)+1) |
---|
| 667 | w_nr(nzt) = w_nr(nzt-1) |
---|
| 668 | w_qr(nzt) = w_qr(nzt-1) |
---|
| 669 | ! |
---|
| 670 | !-- Compute Courant number |
---|
| 671 | DO k = nzb_s_inner(j,i)+1, nzt-1 |
---|
| 672 | c_nr(k) = 0.25 * ( w_nr(k-1) + 2.0 * w_nr(k) + w_nr(k+1) ) * & |
---|
| 673 | dt_sedi * ddzu(k) |
---|
| 674 | c_qr(k) = 0.25 * ( w_qr(k-1) + 2.0 * w_qr(k) + w_qr(k+1) ) * & |
---|
| 675 | dt_sedi * ddzu(k) |
---|
| 676 | ENDDO |
---|
| 677 | ! |
---|
| 678 | !-- Limit slopes with monotonized centered (MC) limiter (van Leer, 1977): |
---|
| 679 | IF ( limiter_sedimentation ) THEN |
---|
| 680 | |
---|
| 681 | qr(nzb_s_inner(j,i),j,i) = 0.0 |
---|
| 682 | nr(nzb_s_inner(j,i),j,i) = 0.0 |
---|
| 683 | qr(nzt,j,i) = 0.0 |
---|
| 684 | nr(nzt,j,i) = 0.0 |
---|
| 685 | |
---|
| 686 | DO k = nzb_s_inner(j,i)+1, nzt-1 |
---|
| 687 | d_mean = 0.5 * ( qr(k+1,j,i) + qr(k-1,j,i) ) |
---|
| 688 | d_min = qr(k,j,i) - MIN( qr(k+1,j,i), qr(k,j,i), qr(k-1,j,i) ) |
---|
| 689 | d_max = MAX( qr(k+1,j,i), qr(k,j,i), qr(k-1,j,i) ) - qr(k,j,i) |
---|
| 690 | |
---|
| 691 | qr_slope(k) = SIGN(1.0, d_mean) * MIN ( 2.0 * d_min, 2.0 * d_max, & |
---|
| 692 | ABS( d_mean ) ) |
---|
| 693 | |
---|
| 694 | d_mean = 0.5 * ( nr(k+1,j,i) + nr(k-1,j,i) ) |
---|
| 695 | d_min = nr(k,j,i) - MIN( nr(k+1,j,i), nr(k,j,i), nr(k-1,j,i) ) |
---|
| 696 | d_max = MAX( nr(k+1,j,i), nr(k,j,i), nr(k-1,j,i) ) - nr(k,j,i) |
---|
| 697 | |
---|
| 698 | nr_slope(k) = SIGN(1.0, d_mean) * MIN ( 2.0 * d_min, 2.0 * d_max, & |
---|
| 699 | ABS( d_mean ) ) |
---|
[1022] | 700 | ENDDO |
---|
[1048] | 701 | |
---|
[1065] | 702 | ELSE |
---|
[1106] | 703 | |
---|
[1065] | 704 | nr_slope = 0.0 |
---|
| 705 | qr_slope = 0.0 |
---|
[1106] | 706 | |
---|
[1065] | 707 | ENDIF |
---|
| 708 | ! |
---|
| 709 | !-- Compute sedimentation flux |
---|
| 710 | DO k = nzt-2, nzb_s_inner(j,i)+1, -1 |
---|
| 711 | ! |
---|
| 712 | !-- Sum up all rain drop number densities which contribute to the flux |
---|
| 713 | !-- through k-1/2 |
---|
| 714 | flux = 0.0 |
---|
| 715 | z_run = 0.0 ! height above z(k) |
---|
| 716 | k_run = k |
---|
| 717 | c_run = MIN( 1.0, c_nr(k) ) |
---|
| 718 | DO WHILE ( c_run > 0.0 .AND. k_run <= nzt-1 ) |
---|
| 719 | flux = flux + hyrho(k_run) * & |
---|
| 720 | ( nr(k_run,j,i) + nr_slope(k_run) * ( 1.0 - c_run ) * & |
---|
| 721 | 0.5 ) * c_run * dzu(k_run) |
---|
| 722 | z_run = z_run + dzu(k_run) |
---|
| 723 | k_run = k_run + 1 |
---|
| 724 | c_run = MIN( 1.0, c_nr(k_run) - z_run * ddzu(k_run) ) |
---|
[1022] | 725 | ENDDO |
---|
| 726 | ! |
---|
[1065] | 727 | !-- It is not allowed to sediment more rain drop number density than |
---|
| 728 | !-- available |
---|
| 729 | flux = MIN( flux, & |
---|
| 730 | hyrho(k) * dzu(k) * nr(k,j,i) + sed_nr(k+1) * dt_sedi ) |
---|
| 731 | |
---|
| 732 | sed_nr(k) = flux / dt_sedi |
---|
| 733 | tend_nr(k,j,i) = tend_nr(k,j,i) + ( sed_nr(k+1) - sed_nr(k) ) * & |
---|
| 734 | ddzu(k+1) / hyrho(k) |
---|
| 735 | ! |
---|
| 736 | !-- Sum up all rain water content which contributes to the flux |
---|
| 737 | !-- through k-1/2 |
---|
| 738 | flux = 0.0 |
---|
| 739 | z_run = 0.0 ! height above z(k) |
---|
| 740 | k_run = k |
---|
| 741 | c_run = MIN( 1.0, c_qr(k) ) |
---|
[1106] | 742 | |
---|
[1065] | 743 | DO WHILE ( c_run > 0.0 .AND. k_run <= nzt-1 ) |
---|
[1106] | 744 | |
---|
[1065] | 745 | flux = flux + hyrho(k_run) * & |
---|
| 746 | ( qr(k_run,j,i) + qr_slope(k_run) * ( 1.0 - c_run ) * & |
---|
| 747 | 0.5 ) * c_run * dzu(k_run) |
---|
| 748 | z_run = z_run + dzu(k_run) |
---|
| 749 | k_run = k_run + 1 |
---|
| 750 | c_run = MIN( 1.0, c_qr(k_run) - z_run * ddzu(k_run) ) |
---|
[1106] | 751 | |
---|
[1065] | 752 | ENDDO |
---|
| 753 | ! |
---|
| 754 | !-- It is not allowed to sediment more rain water content than available |
---|
| 755 | flux = MIN( flux, & |
---|
| 756 | hyrho(k) * dzu(k) * qr(k,j,i) + sed_qr(k+1) * dt_sedi ) |
---|
| 757 | |
---|
| 758 | sed_qr(k) = flux / dt_sedi |
---|
| 759 | tend_qr(k,j,i) = tend_qr(k,j,i) + ( sed_qr(k+1) - sed_qr(k) ) * & |
---|
| 760 | ddzu(k+1) / hyrho(k) |
---|
| 761 | ! |
---|
| 762 | !-- Compute the rain rate |
---|
| 763 | prr(k,j,i) = prr(k,j,i) + sed_qr(k) / hyrho(k) * & |
---|
| 764 | weight_substep(intermediate_timestep_count) |
---|
| 765 | ENDDO |
---|
| 766 | ! |
---|
[1048] | 767 | !-- Precipitation amount |
---|
| 768 | IF ( intermediate_timestep_count == intermediate_timestep_count_max & |
---|
| 769 | .AND. ( dt_do2d_xy - time_do2d_xy ) < & |
---|
| 770 | precipitation_amount_interval ) THEN |
---|
[1012] | 771 | |
---|
[1048] | 772 | precipitation_amount(j,i) = precipitation_amount(j,i) + & |
---|
| 773 | prr(nzb_2d(j,i)+1,j,i) * & |
---|
| 774 | hyrho(nzb_2d(j,i)+1) * dt_3d |
---|
| 775 | ENDIF |
---|
| 776 | |
---|
[1012] | 777 | END SUBROUTINE sedimentation_rain_ij |
---|
| 778 | |
---|
[1106] | 779 | |
---|
[1012] | 780 | ! |
---|
| 781 | !-- This function computes the gamma function (Press et al., 1992). |
---|
| 782 | !-- The gamma function is needed for the calculation of the evaporation |
---|
| 783 | !-- of rain drops. |
---|
| 784 | FUNCTION gamm( xx ) |
---|
[1048] | 785 | |
---|
| 786 | USE cloud_parameters |
---|
[1012] | 787 | |
---|
| 788 | IMPLICIT NONE |
---|
| 789 | |
---|
[1065] | 790 | REAL :: gamm, ser, tmp, x_gamm, xx, y_gamm |
---|
[1012] | 791 | INTEGER :: j |
---|
[1106] | 792 | |
---|
[1012] | 793 | |
---|
| 794 | x_gamm = xx |
---|
| 795 | y_gamm = x_gamm |
---|
| 796 | tmp = x_gamm + 5.5 |
---|
| 797 | tmp = ( x_gamm + 0.5 ) * LOG( tmp ) - tmp |
---|
| 798 | ser = 1.000000000190015 |
---|
[1106] | 799 | |
---|
| 800 | DO j = 1, 6 |
---|
[1012] | 801 | y_gamm = y_gamm + 1.0 |
---|
| 802 | ser = ser + cof( j ) / y_gamm |
---|
[1106] | 803 | ENDDO |
---|
| 804 | |
---|
[1012] | 805 | ! |
---|
| 806 | !-- Until this point the algorithm computes the logarithm of the gamma |
---|
| 807 | !-- function. Hence, the exponential function is used. |
---|
| 808 | ! gamm = EXP( tmp + LOG( stp * ser / x_gamm ) ) |
---|
| 809 | gamm = EXP( tmp ) * stp * ser / x_gamm |
---|
[1106] | 810 | |
---|
[1012] | 811 | RETURN |
---|
| 812 | |
---|
| 813 | END FUNCTION gamm |
---|
| 814 | |
---|
| 815 | END MODULE microphysics_mod |
---|