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source: palm/trunk/SOURCE/lpm_init.f90 @ 2265

Last change on this file since 2265 was 2265, checked in by schwenkel, 7 years ago
unused variables removed
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1	!> @file lpm_init.f90
2	!------------------------------------------------------------------------------!
3	! This file is part of PALM.
4	!
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.
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 1997-2017 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: lpm_init.f90 2265 2017-06-08 16:58:28Z schwenkel $
27	! Unused variables removed.
28	!
29	! 2263 2017-06-08 14:59:01Z schwenkel
30	! Implemented splitting and merging algorithm
31	!
32	! 2233 2017-05-30 18:08:54Z suehring
33	!
34	! 2232 2017-05-30 17:47:52Z suehring
35	! Adjustments according to new topography realization
36	!
37	!
38	! 2223 2017-05-15 16:38:09Z suehring
39	! Add check for particle release at model top
40	!
41	! 2182 2017-03-17 14:27:40Z schwenkel
42	! Added parameters for simplified particle initialization.
43	!
44	! 2122 2017-01-18 12:22:54Z hoffmann
45	! Improved initialization of equilibrium aerosol radii
46	! Calculation of particle ID
47	!
48	! 2000 2016-08-20 18:09:15Z knoop
49	! Forced header and separation lines into 80 columns
50	!
51	! 2016-06-09 16:25:25Z suehring
52	! Bugfix in determining initial particle height and grid index in case of
53	! seed_follows_topography.
54	! Bugfix concerning random positions, ensure that particles do not move more
55	! than one grid length.
56	! Bugfix logarithmic interpolation.
57	! Initial setting of sgs_wf_part.
58	!
59	! 1890 2016-04-22 08:52:11Z hoffmann
60	! Initialization of aerosol equilibrium radius not possible in supersaturated
61	! environments. Therefore, a maximum supersaturation of -1 % is assumed during
62	! initialization.
63	!
64	! 1873 2016-04-18 14:50:06Z maronga
65	! Module renamed (removed _mod
66	!
67	! 1871 2016-04-15 11:46:09Z hoffmann
68	! Initialization of aerosols added.
69	!
70	! 1850 2016-04-08 13:29:27Z maronga
71	! Module renamed
72	!
73	! 1831 2016-04-07 13:15:51Z hoffmann
74	! curvature_solution_effects moved to particle_attributes
75	!
76	! 1822 2016-04-07 07:49:42Z hoffmann
77	! Unused variables removed.
78	!
79	! 1783 2016-03-06 18:36:17Z raasch
80	! netcdf module added
81	!
82	! 1725 2015-11-17 13:01:51Z hoffmann
83	! Bugfix: Processor-dependent seed for random function is generated before it is
84	! used.
85	!
86	! 1691 2015-10-26 16:17:44Z maronga
87	! Renamed prandtl_layer to constant_flux_layer.
88	!
89	! 1685 2015-10-08 07:32:13Z raasch
90	! bugfix concerning vertical index offset in case of ocean
91	!
92	! 1682 2015-10-07 23:56:08Z knoop
93	! Code annotations made doxygen readable
94	!
95	! 1575 2015-03-27 09:56:27Z raasch
96	! initial vertical particle position is allowed to follow the topography
97	!
98	! 1359 2014-04-11 17:15:14Z hoffmann
99	! New particle structure integrated.
100	! Kind definition added to all floating point numbers.
101	! lpm_init changed form a subroutine to a module.
102	!
103	! 1327 2014-03-21 11:00:16Z raasch
104	! -netcdf_output
105	!
106	! 1322 2014-03-20 16:38:49Z raasch
107	! REAL functions provided with KIND-attribute
108	!
109	! 1320 2014-03-20 08:40:49Z raasch
110	! ONLY-attribute added to USE-statements,
111	! kind-parameters added to all INTEGER and REAL declaration statements,
112	! kinds are defined in new module kinds,
113	! revision history before 2012 removed,
114	! comment fields (!:) to be used for variable explanations added to
115	! all variable declaration statements
116	! bugfix: #if defined( __parallel ) added
117	!
118	! 1314 2014-03-14 18:25:17Z suehring
119	! Vertical logarithmic interpolation of horizontal particle speed for particles
120	! between roughness height and first vertical grid level.
121	!
122	! 1092 2013-02-02 11:24:22Z raasch
123	! unused variables removed
124	!
125	! 1036 2012-10-22 13:43:42Z raasch
126	! code put under GPL (PALM 3.9)
127	!
128	! 849 2012-03-15 10:35:09Z raasch
129	! routine renamed: init_particles -> lpm_init
130	! de_dx, de_dy, de_dz are allocated here (instead of automatic arrays in
131	! advec_particles),
132	! sort_particles renamed lpm_sort_arrays, user_init_particles renamed lpm_init
133	!
134	! 828 2012-02-21 12:00:36Z raasch
135	! call of init_kernels, particle feature color renamed class
136	!
137	! 824 2012-02-17 09:09:57Z raasch
138	! particle attributes speed_x\|y\|z_sgs renamed rvar1\|2\|3,
139	! array particles implemented as pointer
140	!
141	! 667 2010-12-23 12:06:00Z suehring/gryschka
142	! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng for allocation
143	! of arrays.
144	!
145	! Revision 1.1 1999/11/25 16:22:38 raasch
146	! Initial revision
147	!
148	!
149	! Description:
150	! ------------
151	!> This routine initializes a set of particles and their attributes (position,
152	!> radius, ..) which are used by the Lagrangian particle model (see lpm).
153	!------------------------------------------------------------------------------!
154	MODULE lpm_init_mod
155
156
157	USE arrays_3d, &
158	ONLY: de_dx, de_dy, de_dz, zu, zw
159
160	USE control_parameters, &
161	ONLY: cloud_droplets, constant_flux_layer, current_timestep_number, &
162	dz, initializing_actions, message_string, ocean, simulated_time
163
164	USE grid_variables, &
165	ONLY: ddx, dx, ddy, dy
166
167	USE indices, &
168	ONLY: nx, nxl, nxlg, nxrg, nxr, ny, nyn, nys, nyng, nysg, nz, nzb, &
169	nzb_max, nzt, wall_flags_0
170
171	USE kinds
172
173	USE lpm_collision_kernels_mod, &
174	ONLY: init_kernels
175
176	USE netcdf_interface, &
177	ONLY: netcdf_data_format
178
179	USE particle_attributes, &
180	ONLY: alloc_factor, bc_par_b, bc_par_lr, bc_par_ns, bc_par_t, &
181	block_offset, block_offset_def, collision_kernel, &
182	curvature_solution_effects, density_ratio, grid_particles, &
183	isf,i_splitting_mode, initial_weighting_factor, ibc_par_b, &
184	ibc_par_lr, ibc_par_ns, ibc_par_t, iran_part, log_z_z0, &
185	max_number_of_particle_groups, min_nr_particle, &
186	mpi_particle_type, number_concentration, &
187	number_particles_per_gridbox, number_of_particles, &
188	number_of_particle_groups, number_of_sublayers, &
189	offset_ocean_nzt, offset_ocean_nzt_m1, &
190	particles, particle_advection_start, particle_groups, &
191	particle_groups_type, particles_per_point, &
192	particle_type, pdx, pdy, pdz, prt_count, psb, psl, psn, psr, &
193	pss, pst, radius, random_start_position, &
194	read_particles_from_restartfile, seed_follows_topography, &
195	sgs_wf_part, sort_count, splitting_function, splitting_mode, &
196	total_number_of_particles, use_sgs_for_particles, &
197	write_particle_statistics, zero_particle, z0_av_global
198
199	USE pegrid
200
201	USE random_function_mod, &
202	ONLY: random_function
203
204	USE surface_mod, &
205	ONLY: surf_def_h, surf_lsm_h, surf_usm_h
206
207	IMPLICIT NONE
208
209	PRIVATE
210
211	INTEGER(iwp), PARAMETER :: PHASE_INIT = 1 !<
212	INTEGER(iwp), PARAMETER, PUBLIC :: PHASE_RELEASE = 2 !<
213
214	INTERFACE lpm_init
215	MODULE PROCEDURE lpm_init
216	END INTERFACE lpm_init
217
218	INTERFACE lpm_create_particle
219	MODULE PROCEDURE lpm_create_particle
220	END INTERFACE lpm_create_particle
221
222	PUBLIC lpm_init, lpm_create_particle
223
224	CONTAINS
225
226	!------------------------------------------------------------------------------!
227	! Description:
228	! ------------
229	!> @todo Missing subroutine description.
230	!------------------------------------------------------------------------------!
231	SUBROUTINE lpm_init
232
233	USE lpm_collision_kernels_mod, &
234	ONLY: init_kernels
235
236	IMPLICIT NONE
237
238	INTEGER(iwp) :: i !<
239	INTEGER(iwp) :: j !<
240	INTEGER(iwp) :: k !<
241
242	#if defined( __parallel )
243	INTEGER(iwp), DIMENSION(3) :: blocklengths !<
244	INTEGER(iwp), DIMENSION(3) :: displacements !<
245	INTEGER(iwp), DIMENSION(3) :: types !<
246	#endif
247
248	REAL(wp) :: div !<
249	REAL(wp) :: height_int !<
250	REAL(wp) :: height_p !<
251	REAL(wp) :: z_p !<
252	REAL(wp) :: z0_av_local !<
253
254	#if defined( __parallel )
255	!
256	!-- Define MPI derived datatype for FORTRAN datatype particle_type (see module
257	!-- particle_attributes). Integer length is 4 byte, Real is 8 byte
258	blocklengths(1) = 19; blocklengths(2) = 6; blocklengths(3) = 1
259	displacements(1) = 0; displacements(2) = 152; displacements(3) = 176
260
261	types(1) = MPI_REAL
262	types(2) = MPI_INTEGER
263	types(3) = MPI_UB
264	CALL MPI_TYPE_STRUCT( 3, blocklengths, displacements, types, &
265	mpi_particle_type, ierr )
266	CALL MPI_TYPE_COMMIT( mpi_particle_type, ierr )
267	#endif
268
269	!
270	!-- In case of oceans runs, the vertical index calculations need an offset,
271	!-- because otherwise the k indices will become negative
272	IF ( ocean ) THEN
273	offset_ocean_nzt = nzt
274	offset_ocean_nzt_m1 = nzt - 1
275	ENDIF
276
277	!
278	!-- Define block offsets for dividing a gridcell in 8 sub cells
279
280	block_offset(0) = block_offset_def (-1,-1,-1)
281	block_offset(1) = block_offset_def (-1,-1, 0)
282	block_offset(2) = block_offset_def (-1, 0,-1)
283	block_offset(3) = block_offset_def (-1, 0, 0)
284	block_offset(4) = block_offset_def ( 0,-1,-1)
285	block_offset(5) = block_offset_def ( 0,-1, 0)
286	block_offset(6) = block_offset_def ( 0, 0,-1)
287	block_offset(7) = block_offset_def ( 0, 0, 0)
288	!
289	!-- Check the number of particle groups.
290	IF ( number_of_particle_groups > max_number_of_particle_groups ) THEN
291	WRITE( message_string, * ) 'max_number_of_particle_groups =', &
292	max_number_of_particle_groups , &
293	'&number_of_particle_groups reset to ', &
294	max_number_of_particle_groups
295	CALL message( 'lpm_init', 'PA0213', 0, 1, 0, 6, 0 )
296	number_of_particle_groups = max_number_of_particle_groups
297	ENDIF
298	!
299	!-- Check if downward-facing walls exist. This case, reflection boundary
300	!-- conditions (as well as subgrid-scale velocities) may do not work
301	!-- propably (not realized so far).
302	IF ( surf_def_h(1)%ns >= 1 ) THEN
303	WRITE( message_string, * ) 'Overhanging topograpyh do not work '// &
304	'with particles'
305	CALL message( 'lpm_init', 'PA0212', 0, 1, 0, 6, 0 )
306
307	ENDIF
308
309	!
310	!-- Set default start positions, if necessary
311	IF ( psl(1) == 9999999.9_wp ) psl(1) = -0.5_wp * dx
312	IF ( psr(1) == 9999999.9_wp ) psr(1) = ( nx + 0.5_wp ) * dx
313	IF ( pss(1) == 9999999.9_wp ) pss(1) = -0.5_wp * dy
314	IF ( psn(1) == 9999999.9_wp ) psn(1) = ( ny + 0.5_wp ) * dy
315	IF ( psb(1) == 9999999.9_wp ) psb(1) = zu(nz/2)
316	IF ( pst(1) == 9999999.9_wp ) pst(1) = psb(1)
317
318	IF ( pdx(1) == 9999999.9_wp .OR. pdx(1) == 0.0_wp ) pdx(1) = dx
319	IF ( pdy(1) == 9999999.9_wp .OR. pdy(1) == 0.0_wp ) pdy(1) = dy
320	IF ( pdz(1) == 9999999.9_wp .OR. pdz(1) == 0.0_wp ) pdz(1) = zu(2) - zu(1)
321
322	!
323	!-- If number_particles_per_gridbox is set, the parametres pdx, pdy and pdz are
324	!-- calculated diagnostically. Therfore an isotropic distribution is prescribed.
325	IF ( number_particles_per_gridbox /= -1 .AND. &
326	number_particles_per_gridbox >= 1 ) THEN
327	pdx(1) = (( dx * dy * ( zu(2) - zu(1) ) ) / &
328	REAL(number_particles_per_gridbox))**0.3333333_wp
329	!
330	!-- Ensure a smooth value (two significant digits) of distance between
331	!-- particles (pdx, pdy, pdz).
332	div = 1000.0_wp
333	DO WHILE ( pdx(1) < div )
334	div = div / 10.0_wp
335	ENDDO
336	pdx(1) = NINT( pdx(1) * 100.0_wp / div ) * div / 100.0_wp
337	pdy(1) = pdx(1)
338	pdz(1) = pdx(1)
339
340	ENDIF
341
342	DO j = 2, number_of_particle_groups
343	IF ( psl(j) == 9999999.9_wp ) psl(j) = psl(j-1)
344	IF ( psr(j) == 9999999.9_wp ) psr(j) = psr(j-1)
345	IF ( pss(j) == 9999999.9_wp ) pss(j) = pss(j-1)
346	IF ( psn(j) == 9999999.9_wp ) psn(j) = psn(j-1)
347	IF ( psb(j) == 9999999.9_wp ) psb(j) = psb(j-1)
348	IF ( pst(j) == 9999999.9_wp ) pst(j) = pst(j-1)
349	IF ( pdx(j) == 9999999.9_wp .OR. pdx(j) == 0.0_wp ) pdx(j) = pdx(j-1)
350	IF ( pdy(j) == 9999999.9_wp .OR. pdy(j) == 0.0_wp ) pdy(j) = pdy(j-1)
351	IF ( pdz(j) == 9999999.9_wp .OR. pdz(j) == 0.0_wp ) pdz(j) = pdz(j-1)
352	ENDDO
353
354	!
355	!-- Allocate arrays required for calculating particle SGS velocities.
356	!-- Initialize prefactor required for stoachastic Weil equation.
357	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
358	ALLOCATE( de_dx(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
359	de_dy(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
360	de_dz(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
361
362	sgs_wf_part = 1.0_wp / 3.0_wp
363	ENDIF
364
365	!
366	!-- Allocate array required for logarithmic vertical interpolation of
367	!-- horizontal particle velocities between the surface and the first vertical
368	!-- grid level. In order to avoid repeated CPU cost-intensive CALLS of
369	!-- intrinsic FORTRAN procedure LOG(z/z0), LOG(z/z0) is precalculated for
370	!-- several heights. Splitting into 20 sublayers turned out to be sufficient.
371	!-- To obtain exact height levels of particles, linear interpolation is applied
372	!-- (see lpm_advec.f90).
373	IF ( constant_flux_layer ) THEN
374
375	ALLOCATE ( log_z_z0(0:number_of_sublayers) )
376	z_p = zu(nzb+1) - zw(nzb)
377
378	!
379	!-- Calculate horizontal mean value of z0 used for logartihmic
380	!-- interpolation. Note: this is not exact for heterogeneous z0.
381	!-- However, sensitivity studies showed that the effect is
382	!-- negligible.
383	z0_av_local = SUM( surf_def_h(0)%z0 ) + SUM( surf_lsm_h%z0 ) + &
384	SUM( surf_usm_h%z0 )
385	z0_av_global = 0.0_wp
386
387	#if defined( __parallel )
388	CALL MPI_ALLREDUCE(z0_av_local, z0_av_global, 1, MPI_REAL, MPI_SUM, &
389	comm2d, ierr )
390	#else
391	z0_av_global = z0_av_local
392	#endif
393
394	z0_av_global = z0_av_global / ( ( ny + 1 ) * ( nx + 1 ) )
395	!
396	!-- Horizontal wind speed is zero below and at z0
397	log_z_z0(0) = 0.0_wp
398	!
399	!-- Calculate vertical depth of the sublayers
400	height_int = ( z_p - z0_av_global ) / REAL( number_of_sublayers, KIND=wp )
401	!
402	!-- Precalculate LOG(z/z0)
403	height_p = z0_av_global
404	DO k = 1, number_of_sublayers
405
406	height_p = height_p + height_int
407	log_z_z0(k) = LOG( height_p / z0_av_global )
408
409	ENDDO
410
411	ENDIF
412
413	!
414	!-- Check boundary condition and set internal variables
415	SELECT CASE ( bc_par_b )
416
417	CASE ( 'absorb' )
418	ibc_par_b = 1
419
420	CASE ( 'reflect' )
421	ibc_par_b = 2
422
423	CASE DEFAULT
424	WRITE( message_string, * ) 'unknown boundary condition ', &
425	'bc_par_b = "', TRIM( bc_par_b ), '"'
426	CALL message( 'lpm_init', 'PA0217', 1, 2, 0, 6, 0 )
427
428	END SELECT
429	SELECT CASE ( bc_par_t )
430
431	CASE ( 'absorb' )
432	ibc_par_t = 1
433
434	CASE ( 'reflect' )
435	ibc_par_t = 2
436
437	CASE DEFAULT
438	WRITE( message_string, * ) 'unknown boundary condition ', &
439	'bc_par_t = "', TRIM( bc_par_t ), '"'
440	CALL message( 'lpm_init', 'PA0218', 1, 2, 0, 6, 0 )
441
442	END SELECT
443	SELECT CASE ( bc_par_lr )
444
445	CASE ( 'cyclic' )
446	ibc_par_lr = 0
447
448	CASE ( 'absorb' )
449	ibc_par_lr = 1
450
451	CASE ( 'reflect' )
452	ibc_par_lr = 2
453
454	CASE DEFAULT
455	WRITE( message_string, * ) 'unknown boundary condition ', &
456	'bc_par_lr = "', TRIM( bc_par_lr ), '"'
457	CALL message( 'lpm_init', 'PA0219', 1, 2, 0, 6, 0 )
458
459	END SELECT
460	SELECT CASE ( bc_par_ns )
461
462	CASE ( 'cyclic' )
463	ibc_par_ns = 0
464
465	CASE ( 'absorb' )
466	ibc_par_ns = 1
467
468	CASE ( 'reflect' )
469	ibc_par_ns = 2
470
471	CASE DEFAULT
472	WRITE( message_string, * ) 'unknown boundary condition ', &
473	'bc_par_ns = "', TRIM( bc_par_ns ), '"'
474	CALL message( 'lpm_init', 'PA0220', 1, 2, 0, 6, 0 )
475
476	END SELECT
477	SELECT CASE ( splitting_mode )
478
479	CASE ( 'const' )
480	i_splitting_mode = 1
481
482	CASE ( 'cl_av' )
483	i_splitting_mode = 2
484
485	CASE ( 'gb_av' )
486	i_splitting_mode = 3
487
488	CASE DEFAULT
489	WRITE( message_string, * ) 'unknown splitting condition ', &
490	'splitting_mode = "', TRIM( splitting_mode ), '"'
491	CALL message( 'lpm_init', 'PA0146', 1, 2, 0, 6, 0 )
492
493	END SELECT
494	SELECT CASE ( splitting_function )
495
496	CASE ( 'gamma' )
497	isf = 1
498
499	CASE ( 'log' )
500	isf = 2
501
502	CASE ( 'exp' )
503	isf = 3
504
505	CASE DEFAULT
506	WRITE( message_string, * ) 'unknown splitting function ', &
507	'splitting_function = "', TRIM( splitting_function ), '"'
508	CALL message( 'lpm_init', 'PA0147', 1, 2, 0, 6, 0 )
509
510	END SELECT
511
512
513	!
514	!-- Initialize collision kernels
515	IF ( collision_kernel /= 'none' ) CALL init_kernels
516
517	!
518	!-- For the first model run of a possible job chain initialize the
519	!-- particles, otherwise read the particle data from restart file.
520	IF ( TRIM( initializing_actions ) == 'read_restart_data' &
521	.AND. read_particles_from_restartfile ) THEN
522
523	CALL lpm_read_restart_file
524
525	ELSE
526
527	!
528	!-- Allocate particle arrays and set attributes of the initial set of
529	!-- particles, which can be also periodically released at later times.
530	ALLOCATE( prt_count(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
531	grid_particles(nzb+1:nzt,nys:nyn,nxl:nxr) )
532
533	number_of_particles = 0
534
535	sort_count = 0
536	prt_count = 0
537
538	!
539	!-- initialize counter for particle IDs
540	grid_particles%id_counter = 0
541
542	!
543	!-- Initialize all particles with dummy values (otherwise errors may
544	!-- occur within restart runs). The reason for this is still not clear
545	!-- and may be presumably caused by errors in the respective user-interface.
546	zero_particle = particle_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
547	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
548	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
549	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
550	0, 0, 0, 0, .FALSE., -1 )
551
552	particle_groups = particle_groups_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp )
553
554	!
555	!-- Set values for the density ratio and radius for all particle
556	!-- groups, if necessary
557	IF ( density_ratio(1) == 9999999.9_wp ) density_ratio(1) = 0.0_wp
558	IF ( radius(1) == 9999999.9_wp ) radius(1) = 0.0_wp
559	DO i = 2, number_of_particle_groups
560	IF ( density_ratio(i) == 9999999.9_wp ) THEN
561	density_ratio(i) = density_ratio(i-1)
562	ENDIF
563	IF ( radius(i) == 9999999.9_wp ) radius(i) = radius(i-1)
564	ENDDO
565
566	DO i = 1, number_of_particle_groups
567	IF ( density_ratio(i) /= 0.0_wp .AND. radius(i) == 0 ) THEN
568	WRITE( message_string, * ) 'particle group #', i, 'has a', &
569	'density ratio /= 0 but radius = 0'
570	CALL message( 'lpm_init', 'PA0215', 1, 2, 0, 6, 0 )
571	ENDIF
572	particle_groups(i)%density_ratio = density_ratio(i)
573	particle_groups(i)%radius = radius(i)
574	ENDDO
575
576	!
577	!-- Set a seed value for the random number generator to be exclusively
578	!-- used for the particle code. The generated random numbers should be
579	!-- different on the different PEs.
580	iran_part = iran_part + myid
581
582	CALL lpm_create_particle (PHASE_INIT)
583	!
584	!-- User modification of initial particles
585	CALL user_lpm_init
586
587	!
588	!-- Open file for statistical informations about particle conditions
589	IF ( write_particle_statistics ) THEN
590	CALL check_open( 80 )
591	WRITE ( 80, 8000 ) current_timestep_number, simulated_time, &
592	number_of_particles
593	CALL close_file( 80 )
594	ENDIF
595
596	ENDIF
597
598	!
599	!-- To avoid programm abort, assign particles array to the local version of
600	!-- first grid cell
601	number_of_particles = prt_count(nzb+1,nys,nxl)
602	particles => grid_particles(nzb+1,nys,nxl)%particles(1:number_of_particles)
603	!
604	!-- Formats
605	8000 FORMAT (I6,1X,F7.2,4X,I10,71X,I10)
606
607	END SUBROUTINE lpm_init
608
609	!------------------------------------------------------------------------------!
610	! Description:
611	! ------------
612	!> @todo Missing subroutine description.
613	!------------------------------------------------------------------------------!
614	SUBROUTINE lpm_create_particle (phase)
615
616	USE lpm_exchange_horiz_mod, &
617	ONLY: lpm_exchange_horiz, lpm_move_particle, realloc_particles_array
618
619	USE lpm_pack_arrays_mod, &
620	ONLY: lpm_pack_all_arrays
621
622	USE particle_attributes, &
623	ONLY: deleted_particles, monodisperse_aerosols
624
625	IMPLICIT NONE
626
627	INTEGER(iwp) :: alloc_size !< relative increase of allocated memory for particles
628	INTEGER(iwp) :: i !< loop variable ( particle groups )
629	INTEGER(iwp) :: ip !< index variable along x
630	INTEGER(iwp) :: j !< loop variable ( particles per point )
631	INTEGER(iwp) :: jp !< index variable along y
632	INTEGER(iwp) :: k !< index variable along z
633	INTEGER(iwp) :: k_surf !< index of surface grid point
634	INTEGER(iwp) :: kp !< index variable along z
635	INTEGER(iwp) :: loop_stride !< loop variable for initialization
636	INTEGER(iwp) :: n !< loop variable ( number of particles )
637	INTEGER(iwp) :: new_size !< new size of allocated memory for particles
638
639	INTEGER(iwp), INTENT(IN) :: phase !< mode of inititialization
640
641	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: local_count !< start address of new particle
642	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: local_start !< start address of new particle
643
644	LOGICAL :: first_stride !< flag for initialization
645
646	REAL(wp) :: pos_x !< increment for particle position in x
647	REAL(wp) :: pos_y !< increment for particle position in y
648	REAL(wp) :: pos_z !< increment for particle position in z
649	REAL(wp) :: rand_contr !< dummy argument for random position
650
651	TYPE(particle_type),TARGET :: tmp_particle !< temporary particle used for initialization
652
653	!
654	!-- Calculate particle positions and store particle attributes, if
655	!-- particle is situated on this PE
656	DO loop_stride = 1, 2
657	first_stride = (loop_stride == 1)
658	IF ( first_stride ) THEN
659	local_count = 0 ! count number of particles
660	ELSE
661	local_count = prt_count ! Start address of new particles
662	ENDIF
663
664	!
665	!-- Calculate initial_weighting_factor diagnostically
666	IF ( number_concentration /= -1.0_wp .AND. number_concentration > 0.0_wp ) THEN
667	initial_weighting_factor = number_concentration * 1.0E6_wp * &
668	pdx(1) * pdy(1) * pdz(1)
669	END IF
670
671	n = 0
672	DO i = 1, number_of_particle_groups
673
674	pos_z = psb(i)
675
676	DO WHILE ( pos_z <= pst(i) )
677
678	IF ( pos_z >= 0.0_wp .AND. pos_z < zw(nzt) ) THEN
679
680
681	pos_y = pss(i)
682
683	DO WHILE ( pos_y <= psn(i) )
684
685	IF ( pos_y >= ( nys - 0.5_wp ) * dy .AND. &
686	pos_y < ( nyn + 0.5_wp ) * dy ) THEN
687
688	pos_x = psl(i)
689
690	xloop: DO WHILE ( pos_x <= psr(i) )
691
692	IF ( pos_x >= ( nxl - 0.5_wp ) * dx .AND. &
693	pos_x < ( nxr + 0.5_wp ) * dx ) THEN
694
695	DO j = 1, particles_per_point
696
697	n = n + 1
698	tmp_particle%x = pos_x
699	tmp_particle%y = pos_y
700	tmp_particle%z = pos_z
701	tmp_particle%age = 0.0_wp
702	tmp_particle%age_m = 0.0_wp
703	tmp_particle%dt_sum = 0.0_wp
704	tmp_particle%user = 0.0_wp !unused, free for the user
705	tmp_particle%e_m = 0.0_wp
706	IF ( curvature_solution_effects ) THEN
707	!
708	!-- Initial values (internal timesteps, derivative)
709	!-- for Rosenbrock method
710	tmp_particle%rvar1 = 1.0E-6_wp !last Rosenbrock timestep
711	tmp_particle%rvar2 = 0.1E-6_wp !dry aerosol radius
712	tmp_particle%rvar3 = -9999999.9_wp !unused in this configuration
713	ELSE
714	!
715	!-- Initial values for SGS velocities
716	tmp_particle%rvar1 = 0.0_wp
717	tmp_particle%rvar2 = 0.0_wp
718	tmp_particle%rvar3 = 0.0_wp
719	ENDIF
720	tmp_particle%speed_x = 0.0_wp
721	tmp_particle%speed_y = 0.0_wp
722	tmp_particle%speed_z = 0.0_wp
723	tmp_particle%origin_x = pos_x
724	tmp_particle%origin_y = pos_y
725	tmp_particle%origin_z = pos_z
726	tmp_particle%radius = particle_groups(i)%radius
727	tmp_particle%weight_factor = initial_weighting_factor
728	tmp_particle%class = 1
729	tmp_particle%group = i
730	tmp_particle%id1 = 0
731	tmp_particle%id2 = 0
732	tmp_particle%particle_mask = .TRUE.
733	tmp_particle%block_nr = -1
734	!
735	!-- Determine the grid indices of the particle position
736	ip = ( tmp_particle%x + 0.5_wp * dx ) * ddx
737	jp = ( tmp_particle%y + 0.5_wp * dy ) * ddy
738	kp = tmp_particle%z / dz + 1 + offset_ocean_nzt
739	!
740	!-- Determine surface level. Therefore, check for
741	!-- upward-facing wall on w-grid. MAXLOC will return
742	!-- the index of the lowest upward-facing wall.
743	k_surf = MAXLOC( &
744	MERGE( 1, 0, &
745	BTEST( wall_flags_0(nzb:nzb_max,jp,ip), 18 )&
746	), DIM = 1 &
747	) - 1
748
749	IF ( seed_follows_topography ) THEN
750	!
751	!-- Particle height is given relative to topography
752	kp = kp + k_surf
753	tmp_particle%z = tmp_particle%z + zw(k_surf)
754	!-- Skip particle release if particle position is
755	!-- above model top, or within topography in case
756	!-- of overhanging structures.
757	IF ( kp > nzt .OR. &
758	.NOT. BTEST( wall_flags_0(kp,jp,ip), 0 ) ) THEN
759	pos_x = pos_x + pdx(i)
760	CYCLE xloop
761	ENDIF
762	!
763	!-- Skip particle release if particle position is
764	!-- below surface, or within topography in case
765	!-- of overhanging structures.
766	ELSEIF ( .NOT. seed_follows_topography .AND. &
767	tmp_particle%z <= zw(k_surf) .OR. &
768	.NOT. BTEST( wall_flags_0(kp,jp,ip), 0 ) )&
769	THEN
770	pos_x = pos_x + pdx(i)
771	CYCLE xloop
772	ENDIF
773
774	local_count(kp,jp,ip) = local_count(kp,jp,ip) + 1
775
776	IF ( .NOT. first_stride ) THEN
777	IF ( ip < nxl .OR. jp < nys .OR. kp < nzb+1 ) THEN
778	write(6,*) 'xl ',ip,jp,kp,nxl,nys,nzb+1
779	ENDIF
780	IF ( ip > nxr .OR. jp > nyn .OR. kp > nzt ) THEN
781	write(6,*) 'xu ',ip,jp,kp,nxr,nyn,nzt
782	ENDIF
783	grid_particles(kp,jp,ip)%particles(local_count(kp,jp,ip)) = tmp_particle
784
785	ENDIF
786	ENDDO
787
788	ENDIF
789
790	pos_x = pos_x + pdx(i)
791
792	ENDDO xloop
793
794	ENDIF
795
796	pos_y = pos_y + pdy(i)
797
798	ENDDO
799
800	ENDIF
801
802	pos_z = pos_z + pdz(i)
803
804	ENDDO
805
806	ENDDO
807
808	IF ( first_stride ) THEN
809	DO ip = nxl, nxr
810	DO jp = nys, nyn
811	DO kp = nzb+1, nzt
812	IF ( phase == PHASE_INIT ) THEN
813	IF ( local_count(kp,jp,ip) > 0 ) THEN
814	alloc_size = MAX( INT( local_count(kp,jp,ip) * &
815	( 1.0_wp + alloc_factor / 100.0_wp ) ), &
816	min_nr_particle )
817	ELSE
818	alloc_size = min_nr_particle
819	ENDIF
820	ALLOCATE(grid_particles(kp,jp,ip)%particles(1:alloc_size))
821	DO n = 1, alloc_size
822	grid_particles(kp,jp,ip)%particles(n) = zero_particle
823	ENDDO
824	ELSEIF ( phase == PHASE_RELEASE ) THEN
825	IF ( local_count(kp,jp,ip) > 0 ) THEN
826	new_size = local_count(kp,jp,ip) + prt_count(kp,jp,ip)
827	alloc_size = MAX( INT( new_size * ( 1.0_wp + &
828	alloc_factor / 100.0_wp ) ), min_nr_particle )
829	IF( alloc_size > SIZE( grid_particles(kp,jp,ip)%particles) ) THEN
830	CALL realloc_particles_array(ip,jp,kp,alloc_size)
831	ENDIF
832	ENDIF
833	ENDIF
834	ENDDO
835	ENDDO
836	ENDDO
837	ENDIF
838
839	ENDDO
840
841
842
843	local_start = prt_count+1
844	prt_count = local_count
845
846	!
847	!-- Calculate particle IDs
848	DO ip = nxl, nxr
849	DO jp = nys, nyn
850	DO kp = nzb+1, nzt
851	number_of_particles = prt_count(kp,jp,ip)
852	IF ( number_of_particles <= 0 ) CYCLE
853	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
854
855	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
856
857	particles(n)%id1 = 10000_iwp * grid_particles(kp,jp,ip)%id_counter + kp
858	particles(n)%id2 = 10000_iwp * jp + ip
859
860	grid_particles(kp,jp,ip)%id_counter = &
861	grid_particles(kp,jp,ip)%id_counter + 1
862
863	ENDDO
864
865	ENDDO
866	ENDDO
867	ENDDO
868
869	!
870	!-- Initialize aerosol background spectrum
871	IF ( curvature_solution_effects .AND. .NOT. monodisperse_aerosols ) THEN
872	CALL lpm_init_aerosols(local_start)
873	ENDIF
874
875	!
876	!-- Add random fluctuation to particle positions.
877	IF ( random_start_position ) THEN
878	DO ip = nxl, nxr
879	DO jp = nys, nyn
880	DO kp = nzb+1, nzt
881	number_of_particles = prt_count(kp,jp,ip)
882	IF ( number_of_particles <= 0 ) CYCLE
883	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
884	!
885	!-- Move only new particles. Moreover, limit random fluctuation
886	!-- in order to prevent that particles move more than one grid box,
887	!-- which would lead to problems concerning particle exchange
888	!-- between processors in case pdx/pdy are larger than dx/dy,
889	!-- respectively.
890	DO n = local_start(kp,jp,ip), number_of_particles
891	IF ( psl(particles(n)%group) /= psr(particles(n)%group) ) THEN
892	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
893	pdx(particles(n)%group)
894	particles(n)%x = particles(n)%x + &
895	MERGE( rand_contr, SIGN( dx, rand_contr ), &
896	ABS( rand_contr ) < dx &
897	)
898	ENDIF
899	IF ( pss(particles(n)%group) /= psn(particles(n)%group) ) THEN
900	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
901	pdy(particles(n)%group)
902	particles(n)%y = particles(n)%y + &
903	MERGE( rand_contr, SIGN( dy, rand_contr ), &
904	ABS( rand_contr ) < dy &
905	)
906	ENDIF
907	IF ( psb(particles(n)%group) /= pst(particles(n)%group) ) THEN
908	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
909	pdz(particles(n)%group)
910	particles(n)%z = particles(n)%z + &
911	MERGE( rand_contr, SIGN( dz, rand_contr ), &
912	ABS( rand_contr ) < dz &
913	)
914	ENDIF
915	ENDDO
916	!
917	!-- Identify particles located outside the model domain and reflect
918	!-- or absorb them if necessary.
919	CALL lpm_boundary_conds( 'bottom/top' )
920	!
921	!-- Furthermore, remove particles located in topography. Note, as
922	!-- the particle speed is still zero at this point, wall
923	!-- reflection boundary conditions will not work in this case.
924	particles => &
925	grid_particles(kp,jp,ip)%particles(1:number_of_particles)
926	DO n = local_start(kp,jp,ip), number_of_particles
927	i = ( particles(n)%x + 0.5_wp * dx ) * ddx
928	j = ( particles(n)%y + 0.5_wp * dy ) * ddy
929	k = particles(n)%z / dz + 1 + offset_ocean_nzt
930	!
931	!-- Check if particle is within topography
932	IF ( .NOT. BTEST( wall_flags_0(k,j,i), 0 ) ) THEN
933	particles(n)%particle_mask = .FALSE.
934	deleted_particles = deleted_particles + 1
935	ENDIF
936
937	ENDDO
938	ENDDO
939	ENDDO
940	ENDDO
941	!
942	!-- Exchange particles between grid cells and processors
943	CALL lpm_move_particle
944	CALL lpm_exchange_horiz
945
946	ENDIF
947	!
948	!-- In case of random_start_position, delete particles identified by
949	!-- lpm_exchange_horiz and lpm_boundary_conds. Then sort particles into blocks,
950	!-- which is needed for a fast interpolation of the LES fields on the particle
951	!-- position.
952	CALL lpm_pack_all_arrays
953
954	!
955	!-- Determine the current number of particles
956	DO ip = nxl, nxr
957	DO jp = nys, nyn
958	DO kp = nzb+1, nzt
959	number_of_particles = number_of_particles &
960	+ prt_count(kp,jp,ip)
961	ENDDO
962	ENDDO
963	ENDDO
964	!
965	!-- Calculate the number of particles of the total domain
966	#if defined( __parallel )
967	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
968	CALL MPI_ALLREDUCE( number_of_particles, total_number_of_particles, 1, &
969	MPI_INTEGER, MPI_SUM, comm2d, ierr )
970	#else
971	total_number_of_particles = number_of_particles
972	#endif
973
974	RETURN
975
976	END SUBROUTINE lpm_create_particle
977
978	SUBROUTINE lpm_init_aerosols(local_start)
979
980	USE arrays_3d, &
981	ONLY: hyp, pt, q
982
983	USE cloud_parameters, &
984	ONLY: l_d_rv, rho_l, r_v
985
986	USE constants, &
987	ONLY: pi
988
989	USE kinds
990
991	USE particle_attributes, &
992	ONLY: init_aerosol_probabilistic, molecular_weight_of_solute, &
993	molecular_weight_of_water, n1, n2, n3, rho_s, rm1, rm2, rm3, &
994	s1, s2, s3, vanthoff
995
996	IMPLICIT NONE
997
998	REAL(wp), DIMENSION(:), ALLOCATABLE :: cdf !< CDF of aerosol spectrum
999	REAL(wp), DIMENSION(:), ALLOCATABLE :: r_temp !< dry aerosol radius spectrum
1000
1001	REAL(wp) :: afactor !< curvature effects
1002	REAL(wp) :: bfactor !< solute effects
1003	REAL(wp) :: dr !< width of radius bin
1004	REAL(wp) :: e_a !< vapor pressure
1005	REAL(wp) :: e_s !< saturation vapor pressure
1006	REAL(wp) :: n_init !< sum of all aerosol concentrations
1007	REAL(wp) :: pdf !< PDF of aerosol spectrum
1008	REAL(wp) :: rmin = 1.0e-8_wp !< minimum aerosol radius
1009	REAL(wp) :: rmax = 1.0e-6_wp !< maximum aerosol radius
1010	REAL(wp) :: rs_rand !< random number
1011	REAL(wp) :: r_mid !< mean radius
1012	REAL(wp) :: sigma !< surface tension
1013	REAL(wp) :: t_int !< temperature
1014	REAL(wp) :: weight_sum !< sum of all weighting factors
1015
1016	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg), INTENT(IN) :: local_start !<
1017
1018	INTEGER(iwp) :: n !<
1019	INTEGER(iwp) :: nn !<
1020	INTEGER(iwp) :: no_bins = 999 !< number of bins
1021	INTEGER(iwp) :: ip !<
1022	INTEGER(iwp) :: jp !<
1023	INTEGER(iwp) :: kp !<
1024
1025	LOGICAL :: new_pdf = .FALSE. !< check if aerosol PDF has to be recalculated
1026
1027	!
1028	!-- Compute aerosol background distribution
1029	IF ( init_aerosol_probabilistic ) THEN
1030	ALLOCATE( cdf(0:no_bins), r_temp(0:no_bins) )
1031	DO n = 0, no_bins
1032	r_temp(n) = EXP( LOG(rmin) + ( LOG(rmax) - LOG(rmin ) ) / &
1033	REAL(no_bins, KIND=wp) * REAL(n, KIND=wp) )
1034
1035	cdf(n) = 0.0_wp
1036	n_init = n1 + n2 + n3
1037	IF ( n1 > 0.0_wp ) THEN
1038	cdf(n) = cdf(n) + n1 / n_init * ( 0.5_wp + 0.5_wp * &
1039	ERF( LOG( r_temp(n) / rm1 ) / &
1040	( SQRT(2.0_wp) * LOG(s1) ) &
1041	) )
1042	ENDIF
1043	IF ( n2 > 0.0_wp ) THEN
1044	cdf(n) = cdf(n) + n2 / n_init * ( 0.5_wp + 0.5_wp * &
1045	ERF( LOG( r_temp(n) / rm2 ) / &
1046	( SQRT(2.0_wp) * LOG(s2) ) &
1047	) )
1048	ENDIF
1049	IF ( n3 > 0.0_wp ) THEN
1050	cdf(n) = cdf(n) + n3 / n_init * ( 0.5_wp + 0.5_wp * &
1051	ERF( LOG( r_temp(n) / rm3 ) / &
1052	( SQRT(2.0_wp) * LOG(s3) ) &
1053	) )
1054	ENDIF
1055
1056	ENDDO
1057	ENDIF
1058
1059	DO ip = nxl, nxr
1060	DO jp = nys, nyn
1061	DO kp = nzb+1, nzt
1062
1063	number_of_particles = prt_count(kp,jp,ip)
1064	IF ( number_of_particles <= 0 ) CYCLE
1065	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
1066	!
1067	!-- Initialize the aerosols with a predefined spectral distribution
1068	!-- of the dry radius (logarithmically increasing bins) and a varying
1069	!-- weighting factor
1070	IF ( .NOT. init_aerosol_probabilistic ) THEN
1071
1072	new_pdf = .FALSE.
1073	IF ( .NOT. ALLOCATED( r_temp ) ) THEN
1074	new_pdf = .TRUE.
1075	ELSE
1076	IF ( SIZE( r_temp ) .NE. &
1077	number_of_particles - local_start(kp,jp,ip) + 2 ) THEN
1078	new_pdf = .TRUE.
1079	DEALLOCATE( r_temp )
1080	ENDIF
1081	ENDIF
1082
1083	IF ( new_pdf ) THEN
1084
1085	no_bins = number_of_particles + 1 - local_start(kp,jp,ip)
1086	ALLOCATE( r_temp(0:no_bins) )
1087
1088	DO n = 0, no_bins
1089	r_temp(n) = EXP( LOG(rmin) + ( LOG(rmax) - LOG(rmin ) ) / &
1090	REAL(no_bins, KIND=wp) * &
1091	REAL(n, KIND=wp) )
1092	ENDDO
1093
1094	ENDIF
1095
1096	!
1097	!-- Calculate radius and concentration of each aerosol
1098	DO n = local_start(kp,jp,ip), number_of_particles
1099
1100	nn = n - local_start(kp,jp,ip)
1101
1102	r_mid = SQRT( r_temp(nn) * r_temp(nn+1) )
1103	dr = r_temp(nn+1) - r_temp(nn)
1104
1105	pdf = 0.0_wp
1106	n_init = n1 + n2 + n3
1107	IF ( n1 > 0.0_wp ) THEN
1108	pdf = pdf + n1 / n_init * ( 1.0_wp / ( r_mid * LOG(s1) * &
1109	SQRT( 2.0_wp * pi ) &
1110	) * &
1111	EXP( -( LOG( r_mid / rm1 ) )**2 / &
1112	( 2.0_wp * LOG(s1)**2 ) &
1113	) &
1114	)
1115	ENDIF
1116	IF ( n2 > 0.0_wp ) THEN
1117	pdf = pdf + n2 / n_init * ( 1.0_wp / ( r_mid * LOG(s2) * &
1118	SQRT( 2.0_wp * pi ) &
1119	) * &
1120	EXP( -( LOG( r_mid / rm2 ) )**2 / &
1121	( 2.0_wp * LOG(s2)**2 ) &
1122	) &
1123	)
1124	ENDIF
1125	IF ( n3 > 0.0_wp ) THEN
1126	pdf = pdf + n3 / n_init * ( 1.0_wp / ( r_mid * LOG(s3) * &
1127	SQRT( 2.0_wp * pi ) &
1128	) * &
1129	EXP( -( LOG( r_mid / rm3 ) )**2 / &
1130	( 2.0_wp * LOG(s3)**2 ) &
1131	) &
1132	)
1133	ENDIF
1134
1135	particles(n)%rvar2 = r_mid
1136	particles(n)%weight_factor = pdf * dr
1137
1138	END DO
1139	!
1140	!-- Adjust weighting factors to initialize the same number of aerosols
1141	!-- in every grid box
1142	weight_sum = SUM(particles(local_start(kp,jp,ip):number_of_particles)%weight_factor)
1143
1144	particles(local_start(kp,jp,ip):number_of_particles)%weight_factor = &
1145	particles(local_start(kp,jp,ip):number_of_particles)%weight_factor / &
1146	weight_sum * initial_weighting_factor * ( no_bins + 1 )
1147
1148	ENDIF
1149	!
1150	!-- Initialize the aerosols with a predefined weighting factor but
1151	!-- a randomly choosen dry radius
1152	IF ( init_aerosol_probabilistic ) THEN
1153
1154	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
1155
1156	rs_rand = -1.0_wp
1157	DO WHILE ( rs_rand .LT. cdf(0) .OR. rs_rand .GE. cdf(no_bins) )
1158	rs_rand = random_function( iran_part )
1159	ENDDO
1160	!
1161	!-- Determine aerosol dry radius by a random number generator
1162	DO nn = 0, no_bins-1
1163	IF ( cdf(nn) .LE. rs_rand .AND. cdf(nn+1) .GT. rs_rand ) THEN
1164	particles(n)%rvar2 = r_temp(nn) + ( r_temp(nn+1) - r_temp(nn) ) / &
1165	( cdf(nn+1) - cdf(nn) ) * ( rs_rand - cdf(nn) )
1166	EXIT
1167	ENDIF
1168	ENDDO
1169
1170	ENDDO
1171
1172	ENDIF
1173
1174	!
1175	!-- Set particle radius to equilibrium radius based on the environmental
1176	!-- supersaturation (Khvorostyanov and Curry, 2007, JGR). This avoids
1177	!-- the sometimes lengthy growth toward their equilibrium radius within
1178	!-- the simulation.
1179	t_int = pt(kp,jp,ip) * ( hyp(kp) / 100000.0_wp )**0.286_wp
1180
1181	e_s = 611.0_wp * EXP( l_d_rv * ( 3.6609E-3_wp - 1.0_wp / t_int ) )
1182	e_a = q(kp,jp,ip) * hyp(kp) / ( 0.378_wp * q(kp,jp,ip) + 0.622_wp )
1183
1184	sigma = 0.0761_wp - 0.000155_wp * ( t_int - 273.15_wp )
1185	afactor = 2.0_wp * sigma / ( rho_l * r_v * t_int )
1186
1187	bfactor = vanthoff * molecular_weight_of_water * &
1188	rho_s / ( molecular_weight_of_solute * rho_l )
1189	!
1190	!-- The formula is only valid for subsaturated environments. For
1191	!-- supersaturations higher than -5 %, the supersaturation is set to -5%.
1192	IF ( e_a / e_s >= 0.95_wp ) e_a = 0.95_wp * e_s
1193
1194	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
1195	!
1196	!-- For details on this equation, see Eq. (14) of Khvorostyanov and
1197	!-- Curry (2007, JGR)
1198	particles(n)%radius = bfactor*0.3333333_wp &
1199	particles(n)%rvar2 / ( 1.0_wp - e_a / e_s )**0.3333333_wp / &
1200	( 1.0_wp + ( afactor / ( 3.0_wp * bfactor*0.3333333_wp &
1201	particles(n)%rvar2 ) ) / &
1202	( 1.0_wp - e_a / e_s )**0.6666666_wp &
1203	)
1204
1205	ENDDO
1206
1207	ENDDO
1208	ENDDO
1209	ENDDO
1210	!
1211	!-- Deallocate used arrays
1212	IF ( ALLOCATED(r_temp) ) DEALLOCATE( r_temp )
1213	IF ( ALLOCATED(cdf) ) DEALLOCATE( cdf )
1214
1215	END SUBROUTINE lpm_init_aerosols
1216
1217	END MODULE lpm_init_mod

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