[2338] | 1 | !> @file model_1d_mod.f90 |
---|
[2000] | 2 | !------------------------------------------------------------------------------! |
---|
[2696] | 3 | ! This file is part of the PALM model system. |
---|
[1036] | 4 | ! |
---|
[2000] | 5 | ! PALM is free software: you can redistribute it and/or modify it under the |
---|
| 6 | ! terms of the GNU General Public License as published by the Free Software |
---|
| 7 | ! Foundation, either version 3 of the License, or (at your option) any later |
---|
| 8 | ! version. |
---|
[1036] | 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 | ! |
---|
[2718] | 17 | ! Copyright 1997-2018 Leibniz Universitaet Hannover |
---|
[2000] | 18 | !------------------------------------------------------------------------------! |
---|
[1036] | 19 | ! |
---|
[254] | 20 | ! Current revisions: |
---|
[1] | 21 | ! ----------------- |
---|
[1961] | 22 | ! |
---|
[2299] | 23 | ! |
---|
[1961] | 24 | ! Former revisions: |
---|
| 25 | ! ----------------- |
---|
| 26 | ! $Id: model_1d_mod.f90 3045 2018-05-28 07:55:41Z Giersch $ |
---|
[3045] | 27 | ! Error message revised |
---|
| 28 | ! |
---|
| 29 | ! 2965 2018-04-13 07:37:25Z scharf |
---|
[2965] | 30 | ! adjusted format string for 1D run control output |
---|
| 31 | ! |
---|
| 32 | ! 2918 2018-03-21 15:52:14Z gronemeier |
---|
[2918] | 33 | ! - rename l_black into l1d_init |
---|
| 34 | ! - calculate l_grid within init_1d_model and save it as l1d_init |
---|
| 35 | ! |
---|
| 36 | ! 2718 2018-01-02 08:49:38Z maronga |
---|
[2716] | 37 | ! Corrected "Former revisions" section |
---|
| 38 | ! |
---|
| 39 | ! 2696 2017-12-14 17:12:51Z kanani |
---|
| 40 | ! Change in file header (GPL part) |
---|
[2696] | 41 | ! implement TKE-e closure |
---|
| 42 | ! modification of dissipation production according to Detering and Etling |
---|
| 43 | ! reduced factor for timestep criterion to 0.125 and first dt to 1s (TG) |
---|
| 44 | ! |
---|
| 45 | ! 2339 2017-08-07 13:55:26Z gronemeier |
---|
[2339] | 46 | ! corrected timestamp in header |
---|
| 47 | ! |
---|
| 48 | ! 2338 2017-08-07 12:15:38Z gronemeier |
---|
[2338] | 49 | ! renamed init_1d_model to model_1d_mod and and formatted it as a module; |
---|
| 50 | ! reformatted output of profiles |
---|
| 51 | ! |
---|
[2339] | 52 | ! 2337 2017-08-07 08:59:53Z gronemeier |
---|
[2337] | 53 | ! revised calculation of mixing length |
---|
| 54 | ! removed rounding of time step |
---|
| 55 | ! corrected calculation of virtual potential temperature |
---|
| 56 | ! |
---|
| 57 | ! 2334 2017-08-04 11:57:04Z gronemeier |
---|
[2334] | 58 | ! set c_m = 0.4 according to Detering and Etling (1985) |
---|
| 59 | ! |
---|
| 60 | ! 2299 2017-06-29 10:14:38Z maronga |
---|
[2299] | 61 | ! Removed german text |
---|
[1961] | 62 | ! |
---|
[2299] | 63 | ! 2101 2017-01-05 16:42:31Z suehring |
---|
| 64 | ! |
---|
[2060] | 65 | ! 2059 2016-11-10 14:20:40Z maronga |
---|
| 66 | ! Corrected min/max values of Rif. |
---|
| 67 | ! |
---|
[2001] | 68 | ! 2000 2016-08-20 18:09:15Z knoop |
---|
| 69 | ! Forced header and separation lines into 80 columns |
---|
| 70 | ! |
---|
[1961] | 71 | ! 1960 2016-07-12 16:34:24Z suehring |
---|
[1960] | 72 | ! Remove passive_scalar from IF-statements, as 1D-scalar profile is effectively |
---|
| 73 | ! not used. |
---|
| 74 | ! Formatting adjustment |
---|
[1809] | 75 | ! |
---|
| 76 | ! 1808 2016-04-05 19:44:00Z raasch |
---|
| 77 | ! routine local_flush replaced by FORTRAN statement |
---|
| 78 | ! |
---|
[1710] | 79 | ! 1709 2015-11-04 14:47:01Z maronga |
---|
| 80 | ! Set initial time step to 10 s to avoid instability of the 1d model for small |
---|
| 81 | ! grid spacings |
---|
| 82 | ! |
---|
[1698] | 83 | ! 1697 2015-10-28 17:14:10Z raasch |
---|
| 84 | ! small E- and F-FORMAT changes to avoid informative compiler messages about |
---|
| 85 | ! insufficient field width |
---|
| 86 | ! |
---|
[1692] | 87 | ! 1691 2015-10-26 16:17:44Z maronga |
---|
| 88 | ! Renamed prandtl_layer to constant_flux_layer. rif is replaced by ol and zeta. |
---|
| 89 | ! |
---|
[1683] | 90 | ! 1682 2015-10-07 23:56:08Z knoop |
---|
| 91 | ! Code annotations made doxygen readable |
---|
| 92 | ! |
---|
[1354] | 93 | ! 1353 2014-04-08 15:21:23Z heinze |
---|
| 94 | ! REAL constants provided with KIND-attribute |
---|
| 95 | ! |
---|
[1347] | 96 | ! 1346 2014-03-27 13:18:20Z heinze |
---|
| 97 | ! Bugfix: REAL constants provided with KIND-attribute especially in call of |
---|
| 98 | ! intrinsic function like MAX, MIN, SIGN |
---|
| 99 | ! |
---|
[1323] | 100 | ! 1322 2014-03-20 16:38:49Z raasch |
---|
| 101 | ! REAL functions provided with KIND-attribute |
---|
| 102 | ! |
---|
[1321] | 103 | ! 1320 2014-03-20 08:40:49Z raasch |
---|
[1320] | 104 | ! ONLY-attribute added to USE-statements, |
---|
| 105 | ! kind-parameters added to all INTEGER and REAL declaration statements, |
---|
| 106 | ! kinds are defined in new module kinds, |
---|
| 107 | ! revision history before 2012 removed, |
---|
| 108 | ! comment fields (!:) to be used for variable explanations added to |
---|
| 109 | ! all variable declaration statements |
---|
[1321] | 110 | ! |
---|
[1037] | 111 | ! 1036 2012-10-22 13:43:42Z raasch |
---|
| 112 | ! code put under GPL (PALM 3.9) |
---|
| 113 | ! |
---|
[1017] | 114 | ! 1015 2012-09-27 09:23:24Z raasch |
---|
| 115 | ! adjustment of mixing length to the Prandtl mixing length at first grid point |
---|
| 116 | ! above ground removed |
---|
| 117 | ! |
---|
[1002] | 118 | ! 1001 2012-09-13 14:08:46Z raasch |
---|
| 119 | ! all actions concerning leapfrog scheme removed |
---|
| 120 | ! |
---|
[997] | 121 | ! 996 2012-09-07 10:41:47Z raasch |
---|
| 122 | ! little reformatting |
---|
| 123 | ! |
---|
[979] | 124 | ! 978 2012-08-09 08:28:32Z fricke |
---|
| 125 | ! roughness length for scalar quantities z0h1d added |
---|
| 126 | ! |
---|
[1] | 127 | ! Revision 1.1 1998/03/09 16:22:10 raasch |
---|
| 128 | ! Initial revision |
---|
| 129 | ! |
---|
| 130 | ! |
---|
| 131 | ! Description: |
---|
| 132 | ! ------------ |
---|
[1682] | 133 | !> 1D-model to initialize the 3D-arrays. |
---|
| 134 | !> The temperature profile is set as steady and a corresponding steady solution |
---|
| 135 | !> of the wind profile is being computed. |
---|
| 136 | !> All subroutines required can be found within this file. |
---|
[1691] | 137 | !> |
---|
| 138 | !> @todo harmonize code with new surface_layer_fluxes module |
---|
[1709] | 139 | !> @bug 1D model crashes when using small grid spacings in the order of 1 m |
---|
[2965] | 140 | !> @fixme option "as_in_3d_model" seems to be an inappropriate option because |
---|
[2918] | 141 | !> the 1D model uses different turbulence closure approaches at least if |
---|
| 142 | !> the 3D model is set to LES-mode. |
---|
[1] | 143 | !------------------------------------------------------------------------------! |
---|
[2338] | 144 | MODULE model_1d_mod |
---|
[1] | 145 | |
---|
[1320] | 146 | USE arrays_3d, & |
---|
[2918] | 147 | ONLY: dd2zu, ddzu, ddzw, dzu, dzw, pt_init, q_init, ug, u_init, & |
---|
[2338] | 148 | vg, v_init, zu |
---|
[1320] | 149 | |
---|
[2338] | 150 | USE control_parameters, & |
---|
| 151 | ONLY: constant_diffusion, constant_flux_layer, dissipation_1d, f, g, & |
---|
| 152 | humidity, ibc_e_b, intermediate_timestep_count, & |
---|
| 153 | intermediate_timestep_count_max, kappa, km_constant, & |
---|
| 154 | message_string, mixing_length_1d, prandtl_number, & |
---|
[2696] | 155 | roughness_length, run_description_header, simulated_time_chr, & |
---|
| 156 | timestep_scheme, tsc, z0h_factor |
---|
[2338] | 157 | |
---|
[1320] | 158 | USE indices, & |
---|
[2338] | 159 | ONLY: nzb, nzb_diff, nzt |
---|
[1320] | 160 | |
---|
| 161 | USE kinds |
---|
[1] | 162 | |
---|
[2338] | 163 | USE pegrid |
---|
| 164 | |
---|
| 165 | |
---|
[1] | 166 | IMPLICIT NONE |
---|
| 167 | |
---|
[2338] | 168 | INTEGER(iwp) :: current_timestep_number_1d = 0 !< current timestep number (1d-model) |
---|
[2696] | 169 | INTEGER(iwp) :: damp_level_ind_1d !< lower grid index of damping layer (1d-model) |
---|
[2338] | 170 | |
---|
| 171 | LOGICAL :: run_control_header_1d = .FALSE. !< flag for output of run control header (1d-model) |
---|
| 172 | LOGICAL :: stop_dt_1d = .FALSE. !< termination flag, used in case of too small timestep (1d-model) |
---|
| 173 | |
---|
[2696] | 174 | REAL(wp) :: c_1 = 1.44_wp !< model constant |
---|
| 175 | REAL(wp) :: c_2 = 1.92_wp !< model constant |
---|
| 176 | REAL(wp) :: c_3 = 1.44_wp !< model constant |
---|
| 177 | REAL(wp) :: c_h = 0.0015_wp !< model constant according to Detering and Etling (1985) |
---|
[2338] | 178 | REAL(wp) :: c_m = 0.4_wp !< model constant, 0.4 according to Detering and Etling (1985) |
---|
[2696] | 179 | REAL(wp) :: c_mu = 0.09_wp !< model constant |
---|
| 180 | REAL(wp) :: damp_level_1d = -1.0_wp !< namelist parameter |
---|
[2338] | 181 | REAL(wp) :: dt_1d = 60.0_wp !< dynamic timestep (1d-model) |
---|
| 182 | REAL(wp) :: dt_max_1d = 300.0_wp !< timestep limit (1d-model) |
---|
[2696] | 183 | REAL(wp) :: dt_pr_1d = 9999999.9_wp !< namelist parameter |
---|
| 184 | REAL(wp) :: dt_run_control_1d = 60.0_wp !< namelist parameter |
---|
| 185 | REAL(wp) :: end_time_1d = 864000.0_wp !< namelist parameter |
---|
[2338] | 186 | REAL(wp) :: qs1d !< characteristic humidity scale (1d-model) |
---|
| 187 | REAL(wp) :: simulated_time_1d = 0.0_wp !< updated simulated time (1d-model) |
---|
[2696] | 188 | REAL(wp) :: sig_diss = 1.3_wp !< model constant |
---|
[2338] | 189 | REAL(wp) :: time_pr_1d = 0.0_wp !< updated simulated time for profile output (1d-model) |
---|
| 190 | REAL(wp) :: time_run_control_1d = 0.0_wp !< updated simulated time for run-control output (1d-model) |
---|
| 191 | REAL(wp) :: ts1d !< characteristic temperature scale (1d-model) |
---|
[2696] | 192 | REAL(wp) :: us1d !< friction velocity (1d-model) |
---|
| 193 | REAL(wp) :: usws1d !< u-component of the momentum flux (1d-model) |
---|
| 194 | REAL(wp) :: vsws1d !< v-component of the momentum flux (1d-model) |
---|
[2338] | 195 | REAL(wp) :: z01d !< roughness length for momentum (1d-model) |
---|
| 196 | REAL(wp) :: z0h1d !< roughness length for scalars (1d-model) |
---|
| 197 | |
---|
| 198 | |
---|
[2696] | 199 | REAL(wp), DIMENSION(:), ALLOCATABLE :: diss1d !< tke dissipation rate (1d-model) |
---|
| 200 | REAL(wp), DIMENSION(:), ALLOCATABLE :: diss1d_p !< prognostic value of tke dissipation rate (1d-model) |
---|
| 201 | REAL(wp), DIMENSION(:), ALLOCATABLE :: e1d !< tke (1d-model) |
---|
[2338] | 202 | REAL(wp), DIMENSION(:), ALLOCATABLE :: e1d_p !< prognostic value of tke (1d-model) |
---|
[2696] | 203 | REAL(wp), DIMENSION(:), ALLOCATABLE :: kh1d !< turbulent diffusion coefficient for heat (1d-model) |
---|
| 204 | REAL(wp), DIMENSION(:), ALLOCATABLE :: km1d !< turbulent diffusion coefficient for momentum (1d-model) |
---|
| 205 | REAL(wp), DIMENSION(:), ALLOCATABLE :: l1d !< mixing length for turbulent diffusion coefficients (1d-model) |
---|
[2918] | 206 | REAL(wp), DIMENSION(:), ALLOCATABLE :: l1d_init !< initial mixing length (1d-model) |
---|
[2338] | 207 | REAL(wp), DIMENSION(:), ALLOCATABLE :: l1d_diss !< mixing length for dissipation (1d-model) |
---|
[2696] | 208 | REAL(wp), DIMENSION(:), ALLOCATABLE :: rif1d !< Richardson flux number (1d-model) |
---|
| 209 | REAL(wp), DIMENSION(:), ALLOCATABLE :: te_diss !< tendency of diss (1d-model) |
---|
| 210 | REAL(wp), DIMENSION(:), ALLOCATABLE :: te_dissm !< weighted tendency of diss for previous sub-timestep (1d-model) |
---|
[2338] | 211 | REAL(wp), DIMENSION(:), ALLOCATABLE :: te_e !< tendency of e (1d-model) |
---|
| 212 | REAL(wp), DIMENSION(:), ALLOCATABLE :: te_em !< weighted tendency of e for previous sub-timestep (1d-model) |
---|
| 213 | REAL(wp), DIMENSION(:), ALLOCATABLE :: te_u !< tendency of u (1d-model) |
---|
| 214 | REAL(wp), DIMENSION(:), ALLOCATABLE :: te_um !< weighted tendency of u for previous sub-timestep (1d-model) |
---|
| 215 | REAL(wp), DIMENSION(:), ALLOCATABLE :: te_v !< tendency of v (1d-model) |
---|
| 216 | REAL(wp), DIMENSION(:), ALLOCATABLE :: te_vm !< weighted tendency of v for previous sub-timestep (1d-model) |
---|
[2696] | 217 | REAL(wp), DIMENSION(:), ALLOCATABLE :: u1d !< u-velocity component (1d-model) |
---|
[2338] | 218 | REAL(wp), DIMENSION(:), ALLOCATABLE :: u1d_p !< prognostic value of u-velocity component (1d-model) |
---|
[2696] | 219 | REAL(wp), DIMENSION(:), ALLOCATABLE :: v1d !< v-velocity component (1d-model) |
---|
[2338] | 220 | REAL(wp), DIMENSION(:), ALLOCATABLE :: v1d_p !< prognostic value of v-velocity component (1d-model) |
---|
| 221 | |
---|
| 222 | ! |
---|
| 223 | !-- Initialize 1D model |
---|
| 224 | INTERFACE init_1d_model |
---|
| 225 | MODULE PROCEDURE init_1d_model |
---|
| 226 | END INTERFACE init_1d_model |
---|
| 227 | |
---|
| 228 | ! |
---|
| 229 | !-- Print profiles |
---|
| 230 | INTERFACE print_1d_model |
---|
| 231 | MODULE PROCEDURE print_1d_model |
---|
| 232 | END INTERFACE print_1d_model |
---|
| 233 | |
---|
| 234 | ! |
---|
| 235 | !-- Print run control information |
---|
| 236 | INTERFACE run_control_1d |
---|
| 237 | MODULE PROCEDURE run_control_1d |
---|
| 238 | END INTERFACE run_control_1d |
---|
| 239 | |
---|
| 240 | ! |
---|
| 241 | !-- Main procedure |
---|
| 242 | INTERFACE time_integration_1d |
---|
| 243 | MODULE PROCEDURE time_integration_1d |
---|
| 244 | END INTERFACE time_integration_1d |
---|
| 245 | |
---|
| 246 | ! |
---|
| 247 | !-- Calculate time step |
---|
| 248 | INTERFACE timestep_1d |
---|
| 249 | MODULE PROCEDURE timestep_1d |
---|
| 250 | END INTERFACE timestep_1d |
---|
| 251 | |
---|
| 252 | SAVE |
---|
| 253 | |
---|
| 254 | PRIVATE |
---|
| 255 | ! |
---|
| 256 | !-- Public interfaces |
---|
| 257 | PUBLIC init_1d_model |
---|
| 258 | |
---|
| 259 | ! |
---|
| 260 | !-- Public variables |
---|
[2696] | 261 | PUBLIC damp_level_1d, damp_level_ind_1d, diss1d, dt_pr_1d, & |
---|
| 262 | dt_run_control_1d, e1d, end_time_1d, kh1d, km1d, l1d, rif1d, u1d, & |
---|
| 263 | us1d, usws1d, v1d, vsws1d |
---|
[2338] | 264 | |
---|
| 265 | |
---|
| 266 | CONTAINS |
---|
| 267 | |
---|
| 268 | SUBROUTINE init_1d_model |
---|
| 269 | |
---|
[2918] | 270 | USE grid_variables, & |
---|
| 271 | ONLY: dx, dy |
---|
| 272 | |
---|
[2338] | 273 | IMPLICIT NONE |
---|
| 274 | |
---|
[2696] | 275 | CHARACTER (LEN=9) :: time_to_string !< function to transform time from real to character string |
---|
| 276 | |
---|
| 277 | INTEGER(iwp) :: k !< loop index |
---|
[1320] | 278 | |
---|
[2696] | 279 | REAL(wp) :: lambda !< maximum mixing length |
---|
[1] | 280 | |
---|
| 281 | ! |
---|
| 282 | !-- Allocate required 1D-arrays |
---|
[2696] | 283 | ALLOCATE( diss1d(nzb:nzt+1), diss1d_p(nzb:nzt+1), & |
---|
| 284 | e1d(nzb:nzt+1), e1d_p(nzb:nzt+1), kh1d(nzb:nzt+1), & |
---|
[2918] | 285 | km1d(nzb:nzt+1), l1d(nzb:nzt+1), l1d_init(nzb:nzt+1), & |
---|
[2696] | 286 | l1d_diss(nzb:nzt+1), rif1d(nzb:nzt+1), te_diss(nzb:nzt+1), & |
---|
| 287 | te_dissm(nzb:nzt+1), te_e(nzb:nzt+1), & |
---|
[2338] | 288 | te_em(nzb:nzt+1), te_u(nzb:nzt+1), te_um(nzb:nzt+1), & |
---|
| 289 | te_v(nzb:nzt+1), te_vm(nzb:nzt+1), u1d(nzb:nzt+1), & |
---|
| 290 | u1d_p(nzb:nzt+1), v1d(nzb:nzt+1), v1d_p(nzb:nzt+1) ) |
---|
[1] | 291 | |
---|
| 292 | ! |
---|
| 293 | !-- Initialize arrays |
---|
| 294 | IF ( constant_diffusion ) THEN |
---|
[1001] | 295 | km1d = km_constant |
---|
| 296 | kh1d = km_constant / prandtl_number |
---|
[1] | 297 | ELSE |
---|
[2696] | 298 | diss1d = 0.0_wp; diss1d_p = 0.0_wp |
---|
[1353] | 299 | e1d = 0.0_wp; e1d_p = 0.0_wp |
---|
| 300 | kh1d = 0.0_wp; km1d = 0.0_wp |
---|
| 301 | rif1d = 0.0_wp |
---|
[1] | 302 | ! |
---|
| 303 | !-- Compute the mixing length |
---|
[2918] | 304 | l1d_init(nzb) = 0.0_wp |
---|
[1] | 305 | |
---|
| 306 | IF ( TRIM( mixing_length_1d ) == 'blackadar' ) THEN |
---|
| 307 | ! |
---|
| 308 | !-- Blackadar mixing length |
---|
[1353] | 309 | IF ( f /= 0.0_wp ) THEN |
---|
| 310 | lambda = 2.7E-4_wp * SQRT( ug(nzt+1)**2 + vg(nzt+1)**2 ) / & |
---|
| 311 | ABS( f ) + 1E-10_wp |
---|
[1] | 312 | ELSE |
---|
[1353] | 313 | lambda = 30.0_wp |
---|
[1] | 314 | ENDIF |
---|
| 315 | |
---|
| 316 | DO k = nzb+1, nzt+1 |
---|
[2918] | 317 | l1d_init(k) = kappa * zu(k) / ( 1.0_wp + kappa * zu(k) / lambda ) |
---|
[1] | 318 | ENDDO |
---|
| 319 | |
---|
| 320 | ELSEIF ( TRIM( mixing_length_1d ) == 'as_in_3d_model' ) THEN |
---|
| 321 | ! |
---|
[2918] | 322 | !-- Use the same mixing length as in 3D model (LES-mode) |
---|
[2965] | 323 | !@todo: rename (delete?) this option |
---|
| 324 | ! As the mixing length is different between RANS and LES mode, it |
---|
| 325 | ! must be distinguished here between these modes. For RANS mode, |
---|
| 326 | ! the mixing length is calculated accoding to Blackadar, which is |
---|
| 327 | ! the other option at this point. |
---|
| 328 | ! Maybe delete this option entirely (not appropriate in LES case) |
---|
| 329 | ! 2018-03-20, gronemeier |
---|
[2918] | 330 | DO k = nzb+1, nzt |
---|
| 331 | l1d_init(k) = ( dx * dy * dzw(k) )**0.33333333333333_wp |
---|
| 332 | ENDDO |
---|
| 333 | l1d_init(nzt+1) = l1d_init(nzt) |
---|
[1] | 334 | |
---|
| 335 | ENDIF |
---|
| 336 | ENDIF |
---|
[2918] | 337 | l1d = l1d_init |
---|
| 338 | l1d_diss = l1d_init |
---|
[2337] | 339 | u1d = u_init |
---|
| 340 | u1d_p = u_init |
---|
| 341 | v1d = v_init |
---|
| 342 | v1d_p = v_init |
---|
[1] | 343 | |
---|
| 344 | ! |
---|
| 345 | !-- Set initial horizontal velocities at the lowest grid levels to a very small |
---|
| 346 | !-- value in order to avoid too small time steps caused by the diffusion limit |
---|
| 347 | !-- in the initial phase of a run (at k=1, dz/2 occurs in the limiting formula!) |
---|
[1353] | 348 | u1d(0:1) = 0.1_wp |
---|
| 349 | u1d_p(0:1) = 0.1_wp |
---|
| 350 | v1d(0:1) = 0.1_wp |
---|
| 351 | v1d_p(0:1) = 0.1_wp |
---|
[1] | 352 | |
---|
| 353 | ! |
---|
| 354 | !-- For u*, theta* and the momentum fluxes plausible values are set |
---|
[1691] | 355 | IF ( constant_flux_layer ) THEN |
---|
[1353] | 356 | us1d = 0.1_wp ! without initial friction the flow would not change |
---|
[1] | 357 | ELSE |
---|
[2696] | 358 | diss1d(nzb+1) = 1.0_wp |
---|
[1353] | 359 | e1d(nzb+1) = 1.0_wp |
---|
| 360 | km1d(nzb+1) = 1.0_wp |
---|
| 361 | us1d = 0.0_wp |
---|
[1] | 362 | ENDIF |
---|
[1353] | 363 | ts1d = 0.0_wp |
---|
| 364 | usws1d = 0.0_wp |
---|
| 365 | vsws1d = 0.0_wp |
---|
[996] | 366 | z01d = roughness_length |
---|
[978] | 367 | z0h1d = z0h_factor * z01d |
---|
[1960] | 368 | IF ( humidity ) qs1d = 0.0_wp |
---|
[1] | 369 | |
---|
| 370 | ! |
---|
[46] | 371 | !-- Tendencies must be preset in order to avoid runtime errors within the |
---|
| 372 | !-- first Runge-Kutta step |
---|
[2696] | 373 | te_dissm = 0.0_wp |
---|
[1353] | 374 | te_em = 0.0_wp |
---|
| 375 | te_um = 0.0_wp |
---|
| 376 | te_vm = 0.0_wp |
---|
[46] | 377 | |
---|
| 378 | ! |
---|
[2338] | 379 | !-- Set model constant |
---|
| 380 | IF ( dissipation_1d == 'as_in_3d_model' ) c_m = 0.1_wp |
---|
| 381 | |
---|
| 382 | ! |
---|
[1] | 383 | !-- Set start time in hh:mm:ss - format |
---|
| 384 | simulated_time_chr = time_to_string( simulated_time_1d ) |
---|
| 385 | |
---|
| 386 | ! |
---|
[2337] | 387 | !-- Integrate the 1D-model equations using the Runge-Kutta scheme |
---|
[1] | 388 | CALL time_integration_1d |
---|
| 389 | |
---|
| 390 | |
---|
| 391 | END SUBROUTINE init_1d_model |
---|
| 392 | |
---|
| 393 | |
---|
| 394 | |
---|
| 395 | !------------------------------------------------------------------------------! |
---|
| 396 | ! Description: |
---|
| 397 | ! ------------ |
---|
[2338] | 398 | !> Runge-Kutta time differencing scheme for the 1D-model. |
---|
[1] | 399 | !------------------------------------------------------------------------------! |
---|
[1682] | 400 | |
---|
| 401 | SUBROUTINE time_integration_1d |
---|
[1] | 402 | |
---|
| 403 | IMPLICIT NONE |
---|
| 404 | |
---|
[2696] | 405 | CHARACTER (LEN=9) :: time_to_string !< function to transform time from real to character string |
---|
| 406 | |
---|
[2338] | 407 | INTEGER(iwp) :: k !< loop index |
---|
[2696] | 408 | |
---|
[2338] | 409 | REAL(wp) :: a !< auxiliary variable |
---|
| 410 | REAL(wp) :: b !< auxiliary variable |
---|
| 411 | REAL(wp) :: dpt_dz !< vertical temperature gradient |
---|
| 412 | REAL(wp) :: flux !< vertical temperature gradient |
---|
| 413 | REAL(wp) :: kmzm !< Km(z-dz/2) |
---|
| 414 | REAL(wp) :: kmzp !< Km(z+dz/2) |
---|
| 415 | REAL(wp) :: l_stable !< mixing length for stable case |
---|
| 416 | REAL(wp) :: pt_0 !< reference temperature |
---|
| 417 | REAL(wp) :: uv_total !< horizontal wind speed |
---|
[1] | 418 | |
---|
| 419 | ! |
---|
| 420 | !-- Determine the time step at the start of a 1D-simulation and |
---|
| 421 | !-- determine and printout quantities used for run control |
---|
[2696] | 422 | dt_1d = 1.0_wp |
---|
[1] | 423 | CALL run_control_1d |
---|
| 424 | |
---|
| 425 | ! |
---|
| 426 | !-- Start of time loop |
---|
| 427 | DO WHILE ( simulated_time_1d < end_time_1d .AND. .NOT. stop_dt_1d ) |
---|
| 428 | |
---|
| 429 | ! |
---|
| 430 | !-- Depending on the timestep scheme, carry out one or more intermediate |
---|
| 431 | !-- timesteps |
---|
| 432 | |
---|
| 433 | intermediate_timestep_count = 0 |
---|
| 434 | DO WHILE ( intermediate_timestep_count < & |
---|
| 435 | intermediate_timestep_count_max ) |
---|
| 436 | |
---|
| 437 | intermediate_timestep_count = intermediate_timestep_count + 1 |
---|
| 438 | |
---|
| 439 | CALL timestep_scheme_steering |
---|
| 440 | |
---|
| 441 | ! |
---|
[2696] | 442 | !-- Compute all tendency terms. If a constant-flux layer is simulated, |
---|
| 443 | !-- k starts at nzb+2. |
---|
[1] | 444 | DO k = nzb_diff, nzt |
---|
| 445 | |
---|
[1353] | 446 | kmzm = 0.5_wp * ( km1d(k-1) + km1d(k) ) |
---|
| 447 | kmzp = 0.5_wp * ( km1d(k) + km1d(k+1) ) |
---|
[1] | 448 | ! |
---|
| 449 | !-- u-component |
---|
| 450 | te_u(k) = f * ( v1d(k) - vg(k) ) + ( & |
---|
[1001] | 451 | kmzp * ( u1d(k+1) - u1d(k) ) * ddzu(k+1) & |
---|
| 452 | - kmzm * ( u1d(k) - u1d(k-1) ) * ddzu(k) & |
---|
| 453 | ) * ddzw(k) |
---|
[1] | 454 | ! |
---|
| 455 | !-- v-component |
---|
[1001] | 456 | te_v(k) = -f * ( u1d(k) - ug(k) ) + ( & |
---|
| 457 | kmzp * ( v1d(k+1) - v1d(k) ) * ddzu(k+1) & |
---|
| 458 | - kmzm * ( v1d(k) - v1d(k-1) ) * ddzu(k) & |
---|
| 459 | ) * ddzw(k) |
---|
[1] | 460 | ENDDO |
---|
| 461 | IF ( .NOT. constant_diffusion ) THEN |
---|
| 462 | DO k = nzb_diff, nzt |
---|
| 463 | ! |
---|
[2696] | 464 | !-- TKE and dissipation rate |
---|
[1353] | 465 | kmzm = 0.5_wp * ( km1d(k-1) + km1d(k) ) |
---|
| 466 | kmzp = 0.5_wp * ( km1d(k) + km1d(k+1) ) |
---|
[75] | 467 | IF ( .NOT. humidity ) THEN |
---|
[1] | 468 | pt_0 = pt_init(k) |
---|
| 469 | flux = ( pt_init(k+1)-pt_init(k-1) ) * dd2zu(k) |
---|
| 470 | ELSE |
---|
[1353] | 471 | pt_0 = pt_init(k) * ( 1.0_wp + 0.61_wp * q_init(k) ) |
---|
| 472 | flux = ( ( pt_init(k+1) - pt_init(k-1) ) + & |
---|
[2337] | 473 | 0.61_wp * ( pt_init(k+1) * q_init(k+1) - & |
---|
| 474 | pt_init(k-1) * q_init(k-1) ) & |
---|
| 475 | ) * dd2zu(k) |
---|
[1] | 476 | ENDIF |
---|
| 477 | |
---|
[2696] | 478 | ! |
---|
| 479 | !-- Calculate dissipation rate if no prognostic equation is used for |
---|
| 480 | !-- dissipation rate |
---|
[1] | 481 | IF ( dissipation_1d == 'detering' ) THEN |
---|
[2696] | 482 | diss1d(k) = c_m**3 * e1d(k) * SQRT( e1d(k) ) / l1d_diss(k) |
---|
[1] | 483 | ELSEIF ( dissipation_1d == 'as_in_3d_model' ) THEN |
---|
[2918] | 484 | diss1d(k) = ( 0.19_wp + 0.74_wp * l1d_diss(k) / l1d_init(k) & |
---|
[2696] | 485 | ) * e1d(k) * SQRT( e1d(k) ) / l1d_diss(k) |
---|
[1] | 486 | ENDIF |
---|
[2696] | 487 | ! |
---|
| 488 | !-- TKE |
---|
[1] | 489 | te_e(k) = km1d(k) * ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2& |
---|
| 490 | + ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2& |
---|
| 491 | ) & |
---|
| 492 | - g / pt_0 * kh1d(k) * flux & |
---|
| 493 | + ( & |
---|
[1001] | 494 | kmzp * ( e1d(k+1) - e1d(k) ) * ddzu(k+1) & |
---|
| 495 | - kmzm * ( e1d(k) - e1d(k-1) ) * ddzu(k) & |
---|
[1] | 496 | ) * ddzw(k) & |
---|
[2696] | 497 | - diss1d(k) |
---|
| 498 | |
---|
| 499 | IF ( dissipation_1d == 'prognostic' ) THEN |
---|
| 500 | ! |
---|
| 501 | !-- dissipation rate |
---|
| 502 | te_diss(k) = km1d(k) * & |
---|
| 503 | ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 & |
---|
| 504 | + ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 & |
---|
| 505 | ) * c_1 * c_mu**0.75 / c_h * f / us1d & |
---|
| 506 | * SQRT(e1d(k)) & |
---|
| 507 | - g / pt_0 * kh1d(k) * flux * c_3 & |
---|
| 508 | * diss1d(k) / ( e1d(k) + 1.0E-20_wp ) & |
---|
| 509 | + ( kmzp * ( diss1d(k+1) - diss1d(k) ) & |
---|
| 510 | * ddzu(k+1) & |
---|
| 511 | - kmzm * ( diss1d(k) - diss1d(k-1) ) & |
---|
| 512 | * ddzu(k) & |
---|
| 513 | ) * ddzw(k) / sig_diss & |
---|
| 514 | - c_2 * diss1d(k)**2 / ( e1d(k) + 1.0E-20_wp ) |
---|
| 515 | |
---|
| 516 | ENDIF |
---|
| 517 | |
---|
[1] | 518 | ENDDO |
---|
| 519 | ENDIF |
---|
| 520 | |
---|
| 521 | ! |
---|
[2696] | 522 | !-- Tendency terms at the top of the constant-flux layer. |
---|
[1] | 523 | !-- Finite differences of the momentum fluxes are computed using half the |
---|
| 524 | !-- normal grid length (2.0*ddzw(k)) for the sake of enhanced accuracy |
---|
[1691] | 525 | IF ( constant_flux_layer ) THEN |
---|
[1] | 526 | |
---|
| 527 | k = nzb+1 |
---|
[1353] | 528 | kmzm = 0.5_wp * ( km1d(k-1) + km1d(k) ) |
---|
| 529 | kmzp = 0.5_wp * ( km1d(k) + km1d(k+1) ) |
---|
[75] | 530 | IF ( .NOT. humidity ) THEN |
---|
[1] | 531 | pt_0 = pt_init(k) |
---|
| 532 | flux = ( pt_init(k+1)-pt_init(k-1) ) * dd2zu(k) |
---|
| 533 | ELSE |
---|
[1353] | 534 | pt_0 = pt_init(k) * ( 1.0_wp + 0.61_wp * q_init(k) ) |
---|
| 535 | flux = ( ( pt_init(k+1) - pt_init(k-1) ) + & |
---|
[2337] | 536 | 0.61_wp * ( pt_init(k+1) * q_init(k+1) - & |
---|
| 537 | pt_init(k-1) * q_init(k-1) ) & |
---|
[1] | 538 | ) * dd2zu(k) |
---|
| 539 | ENDIF |
---|
| 540 | |
---|
[2696] | 541 | ! |
---|
| 542 | !-- Calculate dissipation rate if no prognostic equation is used for |
---|
| 543 | !-- dissipation rate |
---|
[1] | 544 | IF ( dissipation_1d == 'detering' ) THEN |
---|
[2696] | 545 | diss1d(k) = c_m**3 * e1d(k) * SQRT( e1d(k) ) / l1d_diss(k) |
---|
[1] | 546 | ELSEIF ( dissipation_1d == 'as_in_3d_model' ) THEN |
---|
[2918] | 547 | diss1d(k) = ( 0.19_wp + 0.74_wp * l1d_diss(k) / l1d_init(k) ) & |
---|
[2696] | 548 | * e1d(k) * SQRT( e1d(k) ) / l1d_diss(k) |
---|
[1] | 549 | ENDIF |
---|
| 550 | |
---|
| 551 | ! |
---|
| 552 | !-- u-component |
---|
[1001] | 553 | te_u(k) = f * ( v1d(k) - vg(k) ) + ( & |
---|
| 554 | kmzp * ( u1d(k+1) - u1d(k) ) * ddzu(k+1) + usws1d & |
---|
[1353] | 555 | ) * 2.0_wp * ddzw(k) |
---|
[1] | 556 | ! |
---|
| 557 | !-- v-component |
---|
[1001] | 558 | te_v(k) = -f * ( u1d(k) - ug(k) ) + ( & |
---|
| 559 | kmzp * ( v1d(k+1) - v1d(k) ) * ddzu(k+1) + vsws1d & |
---|
[1353] | 560 | ) * 2.0_wp * ddzw(k) |
---|
[1] | 561 | ! |
---|
| 562 | !-- TKE |
---|
[2696] | 563 | IF ( .NOT. dissipation_1d == 'prognostic' ) THEN |
---|
| 564 | te_e(k) = km1d(k) * ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2& |
---|
| 565 | + ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2& |
---|
| 566 | ) & |
---|
| 567 | - g / pt_0 * kh1d(k) * flux & |
---|
| 568 | + ( & |
---|
| 569 | kmzp * ( e1d(k+1) - e1d(k) ) * ddzu(k+1) & |
---|
| 570 | - kmzm * ( e1d(k) - e1d(k-1) ) * ddzu(k) & |
---|
| 571 | ) * ddzw(k) & |
---|
| 572 | - diss1d(k) |
---|
| 573 | ENDIF |
---|
| 574 | |
---|
[1] | 575 | ENDIF |
---|
| 576 | |
---|
| 577 | ! |
---|
| 578 | !-- Prognostic equations for all 1D variables |
---|
| 579 | DO k = nzb+1, nzt |
---|
| 580 | |
---|
[1001] | 581 | u1d_p(k) = u1d(k) + dt_1d * ( tsc(2) * te_u(k) + & |
---|
| 582 | tsc(3) * te_um(k) ) |
---|
| 583 | v1d_p(k) = v1d(k) + dt_1d * ( tsc(2) * te_v(k) + & |
---|
| 584 | tsc(3) * te_vm(k) ) |
---|
[1] | 585 | |
---|
| 586 | ENDDO |
---|
| 587 | IF ( .NOT. constant_diffusion ) THEN |
---|
[2696] | 588 | |
---|
[1] | 589 | DO k = nzb+1, nzt |
---|
[1001] | 590 | e1d_p(k) = e1d(k) + dt_1d * ( tsc(2) * te_e(k) + & |
---|
| 591 | tsc(3) * te_em(k) ) |
---|
[2696] | 592 | ENDDO |
---|
[1] | 593 | |
---|
[2696] | 594 | IF ( dissipation_1d == 'prognostic' ) THEN |
---|
| 595 | DO k = nzb_diff, nzt |
---|
| 596 | diss1d_p(k) = diss1d(k) + dt_1d * ( tsc(2) * te_diss(k) + & |
---|
| 597 | tsc(3) * te_dissm(k) ) |
---|
| 598 | ENDDO |
---|
| 599 | ENDIF |
---|
[1] | 600 | ! |
---|
| 601 | !-- Eliminate negative TKE values, which can result from the |
---|
| 602 | !-- integration due to numerical inaccuracies. In such cases the TKE |
---|
| 603 | !-- value is reduced to 10 percent of its old value. |
---|
[1353] | 604 | WHERE ( e1d_p < 0.0_wp ) e1d_p = 0.1_wp * e1d |
---|
[1] | 605 | ENDIF |
---|
| 606 | |
---|
| 607 | ! |
---|
| 608 | !-- Calculate tendencies for the next Runge-Kutta step |
---|
| 609 | IF ( timestep_scheme(1:5) == 'runge' ) THEN |
---|
| 610 | IF ( intermediate_timestep_count == 1 ) THEN |
---|
| 611 | |
---|
| 612 | DO k = nzb+1, nzt |
---|
| 613 | te_um(k) = te_u(k) |
---|
| 614 | te_vm(k) = te_v(k) |
---|
| 615 | ENDDO |
---|
| 616 | |
---|
| 617 | IF ( .NOT. constant_diffusion ) THEN |
---|
| 618 | DO k = nzb+1, nzt |
---|
| 619 | te_em(k) = te_e(k) |
---|
| 620 | ENDDO |
---|
[2696] | 621 | IF ( dissipation_1d == 'prognostic' ) THEN |
---|
| 622 | DO k = nzb+1, nzt |
---|
| 623 | te_dissm(k) = te_diss(k) |
---|
| 624 | ENDDO |
---|
| 625 | ENDIF |
---|
[1] | 626 | ENDIF |
---|
| 627 | |
---|
| 628 | ELSEIF ( intermediate_timestep_count < & |
---|
| 629 | intermediate_timestep_count_max ) THEN |
---|
| 630 | |
---|
| 631 | DO k = nzb+1, nzt |
---|
[1353] | 632 | te_um(k) = -9.5625_wp * te_u(k) + 5.3125_wp * te_um(k) |
---|
| 633 | te_vm(k) = -9.5625_wp * te_v(k) + 5.3125_wp * te_vm(k) |
---|
[1] | 634 | ENDDO |
---|
| 635 | |
---|
| 636 | IF ( .NOT. constant_diffusion ) THEN |
---|
| 637 | DO k = nzb+1, nzt |
---|
[1353] | 638 | te_em(k) = -9.5625_wp * te_e(k) + 5.3125_wp * te_em(k) |
---|
[1] | 639 | ENDDO |
---|
[2696] | 640 | IF ( dissipation_1d == 'prognostic' ) THEN |
---|
| 641 | DO k = nzb+1, nzt |
---|
| 642 | te_dissm(k) = -9.5625_wp * te_diss(k) + 5.3125_wp * te_dissm(k) |
---|
| 643 | ENDDO |
---|
| 644 | ENDIF |
---|
[1] | 645 | ENDIF |
---|
| 646 | |
---|
| 647 | ENDIF |
---|
| 648 | ENDIF |
---|
| 649 | |
---|
| 650 | |
---|
| 651 | ! |
---|
| 652 | !-- Boundary conditions for the prognostic variables. |
---|
[2696] | 653 | !-- At the top boundary (nzt+1) u, v, e, and diss keep their initial |
---|
| 654 | !-- values (ug(nzt+1), vg(nzt+1), 0, 0). |
---|
[2334] | 655 | !-- At the bottom boundary, Dirichlet condition is used for u and v (0) |
---|
[2696] | 656 | !-- and Neumann condition for e and diss (e(nzb)=e(nzb+1)). |
---|
[1353] | 657 | u1d_p(nzb) = 0.0_wp |
---|
| 658 | v1d_p(nzb) = 0.0_wp |
---|
[667] | 659 | |
---|
[1] | 660 | ! |
---|
| 661 | !-- Swap the time levels in preparation for the next time step. |
---|
| 662 | u1d = u1d_p |
---|
| 663 | v1d = v1d_p |
---|
| 664 | IF ( .NOT. constant_diffusion ) THEN |
---|
| 665 | e1d = e1d_p |
---|
[2696] | 666 | IF ( dissipation_1d == 'prognostic' ) THEN |
---|
| 667 | diss1d = diss1d_p |
---|
| 668 | ENDIF |
---|
[1] | 669 | ENDIF |
---|
| 670 | |
---|
| 671 | ! |
---|
| 672 | !-- Compute diffusion quantities |
---|
| 673 | IF ( .NOT. constant_diffusion ) THEN |
---|
| 674 | |
---|
| 675 | ! |
---|
[2696] | 676 | !-- First compute the vertical fluxes in the constant-flux layer |
---|
[1691] | 677 | IF ( constant_flux_layer ) THEN |
---|
[1] | 678 | ! |
---|
| 679 | !-- Compute theta* using Rif numbers of the previous time step |
---|
[2334] | 680 | IF ( rif1d(nzb+1) >= 0.0_wp ) THEN |
---|
[1] | 681 | ! |
---|
| 682 | !-- Stable stratification |
---|
[1353] | 683 | ts1d = kappa * ( pt_init(nzb+1) - pt_init(nzb) ) / & |
---|
| 684 | ( LOG( zu(nzb+1) / z0h1d ) + 5.0_wp * rif1d(nzb+1) * & |
---|
| 685 | ( zu(nzb+1) - z0h1d ) / zu(nzb+1) & |
---|
[1] | 686 | ) |
---|
| 687 | ELSE |
---|
| 688 | ! |
---|
| 689 | !-- Unstable stratification |
---|
[1353] | 690 | a = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) ) |
---|
| 691 | b = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) / & |
---|
| 692 | zu(nzb+1) * z0h1d ) |
---|
[2337] | 693 | |
---|
| 694 | ts1d = kappa * ( pt_init(nzb+1) - pt_init(nzb) ) / & |
---|
| 695 | LOG( (a-1.0_wp) / (a+1.0_wp) * & |
---|
| 696 | (b+1.0_wp) / (b-1.0_wp) ) |
---|
[1] | 697 | ENDIF |
---|
| 698 | |
---|
[1691] | 699 | ENDIF ! constant_flux_layer |
---|
[1] | 700 | |
---|
| 701 | ! |
---|
| 702 | !-- Compute the Richardson-flux numbers, |
---|
[2696] | 703 | !-- first at the top of the constant-flux layer using u* of the |
---|
| 704 | !-- previous time step (+1E-30, if u* = 0), then in the remaining area. |
---|
| 705 | !-- There the rif-numbers of the previous time step are used. |
---|
[1] | 706 | |
---|
[1691] | 707 | IF ( constant_flux_layer ) THEN |
---|
[75] | 708 | IF ( .NOT. humidity ) THEN |
---|
[1] | 709 | pt_0 = pt_init(nzb+1) |
---|
| 710 | flux = ts1d |
---|
| 711 | ELSE |
---|
[1353] | 712 | pt_0 = pt_init(nzb+1) * ( 1.0_wp + 0.61_wp * q_init(nzb+1) ) |
---|
| 713 | flux = ts1d + 0.61_wp * pt_init(k) * qs1d |
---|
[1] | 714 | ENDIF |
---|
| 715 | rif1d(nzb+1) = zu(nzb+1) * kappa * g * flux / & |
---|
[1353] | 716 | ( pt_0 * ( us1d**2 + 1E-30_wp ) ) |
---|
[1] | 717 | ENDIF |
---|
| 718 | |
---|
| 719 | DO k = nzb_diff, nzt |
---|
[75] | 720 | IF ( .NOT. humidity ) THEN |
---|
[1] | 721 | pt_0 = pt_init(k) |
---|
| 722 | flux = ( pt_init(k+1) - pt_init(k-1) ) * dd2zu(k) |
---|
| 723 | ELSE |
---|
[1353] | 724 | pt_0 = pt_init(k) * ( 1.0_wp + 0.61_wp * q_init(k) ) |
---|
[1] | 725 | flux = ( ( pt_init(k+1) - pt_init(k-1) ) & |
---|
[2337] | 726 | + 0.61_wp & |
---|
| 727 | * ( pt_init(k+1) * q_init(k+1) & |
---|
| 728 | - pt_init(k-1) * q_init(k-1) ) & |
---|
[1] | 729 | ) * dd2zu(k) |
---|
| 730 | ENDIF |
---|
[1353] | 731 | IF ( rif1d(k) >= 0.0_wp ) THEN |
---|
| 732 | rif1d(k) = g / pt_0 * flux / & |
---|
| 733 | ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 & |
---|
| 734 | + ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 & |
---|
| 735 | + 1E-30_wp & |
---|
[1] | 736 | ) |
---|
| 737 | ELSE |
---|
[1353] | 738 | rif1d(k) = g / pt_0 * flux / & |
---|
| 739 | ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 & |
---|
| 740 | + ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 & |
---|
| 741 | + 1E-30_wp & |
---|
| 742 | ) * ( 1.0_wp - 16.0_wp * rif1d(k) )**0.25_wp |
---|
[1] | 743 | ENDIF |
---|
| 744 | ENDDO |
---|
| 745 | ! |
---|
| 746 | !-- Richardson-numbers must remain restricted to a realistic value |
---|
| 747 | !-- range. It is exceeded excessively for very small velocities |
---|
| 748 | !-- (u,v --> 0). |
---|
[2059] | 749 | WHERE ( rif1d < -5.0_wp ) rif1d = -5.0_wp |
---|
| 750 | WHERE ( rif1d > 1.0_wp ) rif1d = 1.0_wp |
---|
[1] | 751 | |
---|
| 752 | ! |
---|
| 753 | !-- Compute u* from the absolute velocity value |
---|
[1691] | 754 | IF ( constant_flux_layer ) THEN |
---|
[1] | 755 | uv_total = SQRT( u1d(nzb+1)**2 + v1d(nzb+1)**2 ) |
---|
| 756 | |
---|
[1353] | 757 | IF ( rif1d(nzb+1) >= 0.0_wp ) THEN |
---|
[1] | 758 | ! |
---|
| 759 | !-- Stable stratification |
---|
| 760 | us1d = kappa * uv_total / ( & |
---|
[1353] | 761 | LOG( zu(nzb+1) / z01d ) + 5.0_wp * rif1d(nzb+1) * & |
---|
[1] | 762 | ( zu(nzb+1) - z01d ) / zu(nzb+1) & |
---|
| 763 | ) |
---|
| 764 | ELSE |
---|
| 765 | ! |
---|
| 766 | !-- Unstable stratification |
---|
[1353] | 767 | a = 1.0_wp / SQRT( SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) ) ) |
---|
| 768 | b = 1.0_wp / SQRT( SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) / & |
---|
| 769 | zu(nzb+1) * z01d ) ) |
---|
[2337] | 770 | us1d = kappa * uv_total / ( & |
---|
| 771 | LOG( (1.0_wp+b) / (1.0_wp-b) * (1.0_wp-a) / & |
---|
| 772 | (1.0_wp+a) ) + & |
---|
| 773 | 2.0_wp * ( ATAN( b ) - ATAN( a ) ) & |
---|
| 774 | ) |
---|
[1] | 775 | ENDIF |
---|
| 776 | |
---|
| 777 | ! |
---|
| 778 | !-- Compute the momentum fluxes for the diffusion terms |
---|
| 779 | usws1d = - u1d(nzb+1) / uv_total * us1d**2 |
---|
| 780 | vsws1d = - v1d(nzb+1) / uv_total * us1d**2 |
---|
| 781 | |
---|
| 782 | ! |
---|
[2696] | 783 | !-- Boundary condition for the turbulent kinetic energy and |
---|
| 784 | !-- dissipation rate at the top of the constant-flux layer. |
---|
[1] | 785 | !-- Additional Neumann condition de/dz = 0 at nzb is set to ensure |
---|
| 786 | !-- compatibility with the 3D model. |
---|
| 787 | IF ( ibc_e_b == 2 ) THEN |
---|
[2334] | 788 | e1d(nzb+1) = ( us1d / c_m )**2 |
---|
[1] | 789 | ENDIF |
---|
[2696] | 790 | IF ( dissipation_1d == 'prognostic' ) THEN |
---|
| 791 | e1d(nzb+1) = us1d**2 / SQRT( c_mu ) |
---|
| 792 | diss1d(nzb+1) = us1d**3 / ( kappa * zu(nzb+1) ) |
---|
| 793 | diss1d(nzb) = diss1d(nzb+1) |
---|
| 794 | ENDIF |
---|
[1] | 795 | e1d(nzb) = e1d(nzb+1) |
---|
| 796 | |
---|
[1960] | 797 | IF ( humidity ) THEN |
---|
[1] | 798 | ! |
---|
| 799 | !-- Compute q* |
---|
[2334] | 800 | IF ( rif1d(nzb+1) >= 0.0_wp ) THEN |
---|
[1] | 801 | ! |
---|
[1960] | 802 | !-- Stable stratification |
---|
| 803 | qs1d = kappa * ( q_init(nzb+1) - q_init(nzb) ) / & |
---|
[1353] | 804 | ( LOG( zu(nzb+1) / z0h1d ) + 5.0_wp * rif1d(nzb+1) * & |
---|
| 805 | ( zu(nzb+1) - z0h1d ) / zu(nzb+1) & |
---|
[1] | 806 | ) |
---|
[1960] | 807 | ELSE |
---|
[1] | 808 | ! |
---|
[1960] | 809 | !-- Unstable stratification |
---|
| 810 | a = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) ) |
---|
| 811 | b = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) / & |
---|
| 812 | zu(nzb+1) * z0h1d ) |
---|
[2337] | 813 | qs1d = kappa * ( q_init(nzb+1) - q_init(nzb) ) / & |
---|
| 814 | LOG( (a-1.0_wp) / (a+1.0_wp) * & |
---|
| 815 | (b+1.0_wp) / (b-1.0_wp) ) |
---|
| 816 | ENDIF |
---|
[1] | 817 | ELSE |
---|
[1353] | 818 | qs1d = 0.0_wp |
---|
[2337] | 819 | ENDIF |
---|
[1] | 820 | |
---|
[1691] | 821 | ENDIF ! constant_flux_layer |
---|
[1] | 822 | |
---|
| 823 | ! |
---|
[2337] | 824 | !-- Compute the diabatic mixing length. The unstable stratification |
---|
| 825 | !-- must not be considered for l1d (km1d) as it is already considered |
---|
| 826 | !-- in the dissipation of TKE via l1d_diss. Otherwise, km1d would be |
---|
| 827 | !-- too large. |
---|
[1] | 828 | IF ( mixing_length_1d == 'blackadar' ) THEN |
---|
| 829 | DO k = nzb+1, nzt |
---|
[1353] | 830 | IF ( rif1d(k) >= 0.0_wp ) THEN |
---|
[2918] | 831 | l1d(k) = l1d_init(k) / ( 1.0_wp + 5.0_wp * rif1d(k) ) |
---|
[2337] | 832 | l1d_diss(k) = l1d(k) |
---|
[1] | 833 | ELSE |
---|
[2918] | 834 | l1d(k) = l1d_init(k) |
---|
| 835 | l1d_diss(k) = l1d_init(k) * & |
---|
[2337] | 836 | SQRT( 1.0_wp - 16.0_wp * rif1d(k) ) |
---|
[1] | 837 | ENDIF |
---|
| 838 | ENDDO |
---|
| 839 | ELSEIF ( mixing_length_1d == 'as_in_3d_model' ) THEN |
---|
| 840 | DO k = nzb+1, nzt |
---|
| 841 | dpt_dz = ( pt_init(k+1) - pt_init(k-1) ) * dd2zu(k) |
---|
[1353] | 842 | IF ( dpt_dz > 0.0_wp ) THEN |
---|
| 843 | l_stable = 0.76_wp * SQRT( e1d(k) ) / & |
---|
| 844 | SQRT( g / pt_init(k) * dpt_dz ) + 1E-5_wp |
---|
[1] | 845 | ELSE |
---|
[2918] | 846 | l_stable = l1d_init(k) |
---|
[1] | 847 | ENDIF |
---|
[2918] | 848 | l1d(k) = MIN( l1d_init(k), l_stable ) |
---|
[2337] | 849 | l1d_diss(k) = l1d(k) |
---|
[1] | 850 | ENDDO |
---|
| 851 | ENDIF |
---|
| 852 | |
---|
| 853 | ! |
---|
| 854 | !-- Compute the diffusion coefficients for momentum via the |
---|
| 855 | !-- corresponding Prandtl-layer relationship and according to |
---|
[2337] | 856 | !-- Prandtl-Kolmogorov, respectively |
---|
[1691] | 857 | IF ( constant_flux_layer ) THEN |
---|
[1353] | 858 | IF ( rif1d(nzb+1) >= 0.0_wp ) THEN |
---|
| 859 | km1d(nzb+1) = us1d * kappa * zu(nzb+1) / & |
---|
| 860 | ( 1.0_wp + 5.0_wp * rif1d(nzb+1) ) |
---|
[1] | 861 | ELSE |
---|
[1353] | 862 | km1d(nzb+1) = us1d * kappa * zu(nzb+1) * & |
---|
| 863 | ( 1.0_wp - 16.0_wp * rif1d(nzb+1) )**0.25_wp |
---|
[1] | 864 | ENDIF |
---|
| 865 | ENDIF |
---|
[2696] | 866 | IF ( dissipation_1d == 'prognostic' ) THEN |
---|
| 867 | DO k = nzb_diff, nzt |
---|
| 868 | km1d(k) = c_mu * e1d(k)**2 / ( diss1d(k) + 1.0E-30_wp ) |
---|
| 869 | ENDDO |
---|
| 870 | ELSE |
---|
| 871 | DO k = nzb_diff, nzt |
---|
| 872 | km1d(k) = c_m * SQRT( e1d(k) ) * l1d(k) |
---|
| 873 | ENDDO |
---|
| 874 | ENDIF |
---|
[1] | 875 | |
---|
| 876 | ! |
---|
| 877 | !-- Add damping layer |
---|
| 878 | DO k = damp_level_ind_1d+1, nzt+1 |
---|
[1353] | 879 | km1d(k) = 1.1_wp * km1d(k-1) |
---|
[1346] | 880 | km1d(k) = MIN( km1d(k), 10.0_wp ) |
---|
[1] | 881 | ENDDO |
---|
| 882 | |
---|
| 883 | ! |
---|
| 884 | !-- Compute the diffusion coefficient for heat via the relationship |
---|
| 885 | !-- kh = phim / phih * km |
---|
| 886 | DO k = nzb+1, nzt |
---|
[1353] | 887 | IF ( rif1d(k) >= 0.0_wp ) THEN |
---|
[1] | 888 | kh1d(k) = km1d(k) |
---|
| 889 | ELSE |
---|
[1353] | 890 | kh1d(k) = km1d(k) * ( 1.0_wp - 16.0_wp * rif1d(k) )**0.25_wp |
---|
[1] | 891 | ENDIF |
---|
| 892 | ENDDO |
---|
| 893 | |
---|
| 894 | ENDIF ! .NOT. constant_diffusion |
---|
| 895 | |
---|
| 896 | ENDDO ! intermediate step loop |
---|
| 897 | |
---|
| 898 | ! |
---|
| 899 | !-- Increment simulated time and output times |
---|
| 900 | current_timestep_number_1d = current_timestep_number_1d + 1 |
---|
| 901 | simulated_time_1d = simulated_time_1d + dt_1d |
---|
| 902 | simulated_time_chr = time_to_string( simulated_time_1d ) |
---|
| 903 | time_pr_1d = time_pr_1d + dt_1d |
---|
| 904 | time_run_control_1d = time_run_control_1d + dt_1d |
---|
| 905 | |
---|
| 906 | ! |
---|
| 907 | !-- Determine and print out quantities for run control |
---|
| 908 | IF ( time_run_control_1d >= dt_run_control_1d ) THEN |
---|
| 909 | CALL run_control_1d |
---|
| 910 | time_run_control_1d = time_run_control_1d - dt_run_control_1d |
---|
| 911 | ENDIF |
---|
| 912 | |
---|
| 913 | ! |
---|
| 914 | !-- Profile output on file |
---|
| 915 | IF ( time_pr_1d >= dt_pr_1d ) THEN |
---|
| 916 | CALL print_1d_model |
---|
| 917 | time_pr_1d = time_pr_1d - dt_pr_1d |
---|
| 918 | ENDIF |
---|
| 919 | |
---|
| 920 | ! |
---|
| 921 | !-- Determine size of next time step |
---|
| 922 | CALL timestep_1d |
---|
| 923 | |
---|
| 924 | ENDDO ! time loop |
---|
| 925 | |
---|
| 926 | |
---|
| 927 | END SUBROUTINE time_integration_1d |
---|
| 928 | |
---|
| 929 | |
---|
| 930 | !------------------------------------------------------------------------------! |
---|
| 931 | ! Description: |
---|
| 932 | ! ------------ |
---|
[1682] | 933 | !> Compute and print out quantities for run control of the 1D model. |
---|
[1] | 934 | !------------------------------------------------------------------------------! |
---|
[1682] | 935 | |
---|
| 936 | SUBROUTINE run_control_1d |
---|
[1] | 937 | |
---|
[1682] | 938 | |
---|
[1320] | 939 | USE constants, & |
---|
| 940 | ONLY: pi |
---|
[1] | 941 | |
---|
| 942 | IMPLICIT NONE |
---|
| 943 | |
---|
[2338] | 944 | INTEGER(iwp) :: k !< loop index |
---|
[1320] | 945 | |
---|
[2338] | 946 | REAL(wp) :: alpha !< angle of wind vector at top of constant-flux layer |
---|
| 947 | REAL(wp) :: energy !< kinetic energy |
---|
| 948 | REAL(wp) :: umax !< maximum of u |
---|
| 949 | REAL(wp) :: uv_total !< horizontal wind speed |
---|
| 950 | REAL(wp) :: vmax !< maximum of v |
---|
[1] | 951 | |
---|
| 952 | ! |
---|
| 953 | !-- Output |
---|
| 954 | IF ( myid == 0 ) THEN |
---|
| 955 | ! |
---|
| 956 | !-- If necessary, write header |
---|
| 957 | IF ( .NOT. run_control_header_1d ) THEN |
---|
[184] | 958 | CALL check_open( 15 ) |
---|
[1] | 959 | WRITE ( 15, 100 ) |
---|
| 960 | run_control_header_1d = .TRUE. |
---|
| 961 | ENDIF |
---|
| 962 | |
---|
| 963 | ! |
---|
| 964 | !-- Compute control quantities |
---|
| 965 | !-- grid level nzp is excluded due to mirror boundary condition |
---|
[1353] | 966 | umax = 0.0_wp; vmax = 0.0_wp; energy = 0.0_wp |
---|
[1] | 967 | DO k = nzb+1, nzt+1 |
---|
| 968 | umax = MAX( ABS( umax ), ABS( u1d(k) ) ) |
---|
| 969 | vmax = MAX( ABS( vmax ), ABS( v1d(k) ) ) |
---|
[1353] | 970 | energy = energy + 0.5_wp * ( u1d(k)**2 + v1d(k)**2 ) |
---|
[1] | 971 | ENDDO |
---|
[1322] | 972 | energy = energy / REAL( nzt - nzb + 1, KIND=wp ) |
---|
[1] | 973 | |
---|
| 974 | uv_total = SQRT( u1d(nzb+1)**2 + v1d(nzb+1)**2 ) |
---|
[1691] | 975 | IF ( ABS( v1d(nzb+1) ) < 1.0E-5_wp ) THEN |
---|
[1346] | 976 | alpha = ACOS( SIGN( 1.0_wp , u1d(nzb+1) ) ) |
---|
[1] | 977 | ELSE |
---|
| 978 | alpha = ACOS( u1d(nzb+1) / uv_total ) |
---|
[1353] | 979 | IF ( v1d(nzb+1) <= 0.0_wp ) alpha = 2.0_wp * pi - alpha |
---|
[1] | 980 | ENDIF |
---|
[1353] | 981 | alpha = alpha / ( 2.0_wp * pi ) * 360.0_wp |
---|
[1] | 982 | |
---|
| 983 | WRITE ( 15, 101 ) current_timestep_number_1d, simulated_time_chr, & |
---|
| 984 | dt_1d, umax, vmax, us1d, alpha, energy |
---|
| 985 | ! |
---|
| 986 | !-- Write buffer contents to disc immediately |
---|
[1808] | 987 | FLUSH( 15 ) |
---|
[1] | 988 | |
---|
| 989 | ENDIF |
---|
| 990 | |
---|
| 991 | ! |
---|
| 992 | !-- formats |
---|
[2299] | 993 | 100 FORMAT (///'1D run control output:'/ & |
---|
[1] | 994 | &'------------------------------'// & |
---|
[2965] | 995 | &'ITER. HH:MM:SS DT UMAX VMAX U* ALPHA ENERG.'/ & |
---|
[1] | 996 | &'-------------------------------------------------------------') |
---|
[2965] | 997 | 101 FORMAT (I7,1X,A9,1X,F6.2,2X,F6.2,1X,F6.2,1X,F6.3,2X,F5.1,2X,F7.2) |
---|
[1] | 998 | |
---|
| 999 | |
---|
| 1000 | END SUBROUTINE run_control_1d |
---|
| 1001 | |
---|
| 1002 | |
---|
| 1003 | |
---|
| 1004 | !------------------------------------------------------------------------------! |
---|
| 1005 | ! Description: |
---|
| 1006 | ! ------------ |
---|
[1682] | 1007 | !> Compute the time step w.r.t. the diffusion criterion |
---|
[1] | 1008 | !------------------------------------------------------------------------------! |
---|
[1682] | 1009 | |
---|
| 1010 | SUBROUTINE timestep_1d |
---|
[1] | 1011 | |
---|
| 1012 | IMPLICIT NONE |
---|
| 1013 | |
---|
[2338] | 1014 | INTEGER(iwp) :: k !< loop index |
---|
[1] | 1015 | |
---|
[2338] | 1016 | REAL(wp) :: dt_diff !< time step accorind to diffusion criterion |
---|
| 1017 | REAL(wp) :: fac !< factor of criterion |
---|
| 1018 | REAL(wp) :: value !< auxiliary variable |
---|
[1] | 1019 | |
---|
| 1020 | ! |
---|
| 1021 | !-- Compute the currently feasible time step according to the diffusion |
---|
| 1022 | !-- criterion. At nzb+1 the half grid length is used. |
---|
[2696] | 1023 | fac = 0.125 !0.35_wp !### changed from 0.35 |
---|
[1] | 1024 | dt_diff = dt_max_1d |
---|
| 1025 | DO k = nzb+2, nzt |
---|
[1353] | 1026 | value = fac * dzu(k) * dzu(k) / ( km1d(k) + 1E-20_wp ) |
---|
[1] | 1027 | dt_diff = MIN( value, dt_diff ) |
---|
| 1028 | ENDDO |
---|
[1353] | 1029 | value = fac * zu(nzb+1) * zu(nzb+1) / ( km1d(nzb+1) + 1E-20_wp ) |
---|
[1] | 1030 | dt_1d = MIN( value, dt_diff ) |
---|
| 1031 | |
---|
| 1032 | ! |
---|
| 1033 | !-- Set flag when the time step becomes too small |
---|
[1353] | 1034 | IF ( dt_1d < ( 0.00001_wp * dt_max_1d ) ) THEN |
---|
[1] | 1035 | stop_dt_1d = .TRUE. |
---|
[254] | 1036 | |
---|
[3045] | 1037 | WRITE( message_string, * ) 'timestep has exceeded the lower limit ', & |
---|
[254] | 1038 | 'dt_1d = ',dt_1d,' s simulation stopped!' |
---|
| 1039 | CALL message( 'timestep_1d', 'PA0192', 1, 2, 0, 6, 0 ) |
---|
| 1040 | |
---|
[1] | 1041 | ENDIF |
---|
| 1042 | |
---|
| 1043 | END SUBROUTINE timestep_1d |
---|
| 1044 | |
---|
| 1045 | |
---|
| 1046 | |
---|
| 1047 | !------------------------------------------------------------------------------! |
---|
| 1048 | ! Description: |
---|
| 1049 | ! ------------ |
---|
[1682] | 1050 | !> List output of profiles from the 1D-model |
---|
[1] | 1051 | !------------------------------------------------------------------------------! |
---|
[1682] | 1052 | |
---|
| 1053 | SUBROUTINE print_1d_model |
---|
[1] | 1054 | |
---|
| 1055 | IMPLICIT NONE |
---|
| 1056 | |
---|
[2338] | 1057 | INTEGER(iwp) :: k !< loop parameter |
---|
[1] | 1058 | |
---|
[2338] | 1059 | LOGICAL, SAVE :: write_first = .TRUE. !< flag for writing header |
---|
[1] | 1060 | |
---|
| 1061 | |
---|
| 1062 | IF ( myid == 0 ) THEN |
---|
| 1063 | ! |
---|
| 1064 | !-- Open list output file for profiles from the 1D-model |
---|
| 1065 | CALL check_open( 17 ) |
---|
| 1066 | |
---|
| 1067 | ! |
---|
| 1068 | !-- Write Header |
---|
[2338] | 1069 | IF ( write_first ) THEN |
---|
| 1070 | WRITE ( 17, 100 ) TRIM( run_description_header ) |
---|
| 1071 | write_first = .FALSE. |
---|
| 1072 | ENDIF |
---|
[1] | 1073 | |
---|
| 1074 | ! |
---|
| 1075 | !-- Write the values |
---|
[2338] | 1076 | WRITE ( 17, 104 ) TRIM( simulated_time_chr ) |
---|
| 1077 | WRITE ( 17, 101 ) |
---|
[1] | 1078 | WRITE ( 17, 102 ) |
---|
| 1079 | WRITE ( 17, 101 ) |
---|
| 1080 | DO k = nzt+1, nzb, -1 |
---|
| 1081 | WRITE ( 17, 103) k, zu(k), u1d(k), v1d(k), pt_init(k), e1d(k), & |
---|
[2696] | 1082 | rif1d(k), km1d(k), kh1d(k), l1d(k), diss1d(k) |
---|
[1] | 1083 | ENDDO |
---|
| 1084 | WRITE ( 17, 101 ) |
---|
| 1085 | WRITE ( 17, 102 ) |
---|
| 1086 | WRITE ( 17, 101 ) |
---|
| 1087 | |
---|
| 1088 | ! |
---|
| 1089 | !-- Write buffer contents to disc immediately |
---|
[1808] | 1090 | FLUSH( 17 ) |
---|
[1] | 1091 | |
---|
| 1092 | ENDIF |
---|
| 1093 | |
---|
| 1094 | ! |
---|
| 1095 | !-- Formats |
---|
[2338] | 1096 | 100 FORMAT ('# ',A/'#',10('-')/'# 1d-model profiles') |
---|
| 1097 | 104 FORMAT (//'# Time: ',A) |
---|
[2696] | 1098 | 101 FORMAT ('#',111('-')) |
---|
| 1099 | 102 FORMAT ('# k zu u v pt e ', & |
---|
| 1100 | 'rif Km Kh l diss ') |
---|
| 1101 | 103 FORMAT (1X,I4,1X,F7.1,9(1X,E10.3)) |
---|
[1] | 1102 | |
---|
| 1103 | |
---|
| 1104 | END SUBROUTINE print_1d_model |
---|
[2338] | 1105 | |
---|
| 1106 | |
---|
[3045] | 1107 | END MODULE |
---|