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source: palm/trunk/SOURCE/lpm_init.f90 @ 2230

Last change on this file since 2230 was 2224, checked in by suehring, 8 years ago
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[1873]	1	!> @file lpm_init.f90
[2000]	2	!------------------------------------------------------------------------------!
[1036]	3	! This file is part of PALM.
	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	!
[2101]	17	! Copyright 1997-2017 Leibniz Universitaet Hannover
[2000]	18	!------------------------------------------------------------------------------!
[1036]	19	!
[254]	20	! Current revisions:
[1]	21	! -----------------
[1930]	22	!
[2224]	23	!
[1930]	24	! Former revisions:
	25	! -----------------
	26	! $Id: lpm_init.f90 2224 2017-05-15 16:38:37Z hellstea $
	27	!
[2224]	28	! 2223 2017-05-15 16:38:09Z suehring
	29	! Add check for particle release at model top
	30	!
[2183]	31	! 2182 2017-03-17 14:27:40Z schwenkel
	32	! Added parameters for simplified particle initialization.
	33	!
[2123]	34	! 2122 2017-01-18 12:22:54Z hoffmann
	35	! Improved initialization of equilibrium aerosol radii
	36	! Calculation of particle ID
	37	!
[2001]	38	! 2000 2016-08-20 18:09:15Z knoop
	39	! Forced header and separation lines into 80 columns
	40	!
[1930]	41	! 2016-06-09 16:25:25Z suehring
[1929]	42	! Bugfix in determining initial particle height and grid index in case of
	43	! seed_follows_topography.
	44	! Bugfix concerning random positions, ensure that particles do not move more
	45	! than one grid length.
	46	! Bugfix logarithmic interpolation.
	47	! Initial setting of sgs_wf_part.
[1321]	48	!
[1891]	49	! 1890 2016-04-22 08:52:11Z hoffmann
	50	! Initialization of aerosol equilibrium radius not possible in supersaturated
	51	! environments. Therefore, a maximum supersaturation of -1 % is assumed during
	52	! initialization.
	53	!
[1874]	54	! 1873 2016-04-18 14:50:06Z maronga
[1929]	55	! Module renamed (removed _mod
[1874]	56	!
[1872]	57	! 1871 2016-04-15 11:46:09Z hoffmann
	58	! Initialization of aerosols added.
	59	!
[1851]	60	! 1850 2016-04-08 13:29:27Z maronga
	61	! Module renamed
	62	!
[1832]	63	! 1831 2016-04-07 13:15:51Z hoffmann
	64	! curvature_solution_effects moved to particle_attributes
	65	!
[1823]	66	! 1822 2016-04-07 07:49:42Z hoffmann
	67	! Unused variables removed.
	68	!
[1784]	69	! 1783 2016-03-06 18:36:17Z raasch
	70	! netcdf module added
	71	!
[1726]	72	! 1725 2015-11-17 13:01:51Z hoffmann
	73	! Bugfix: Processor-dependent seed for random function is generated before it is
	74	! used.
	75	!
[1692]	76	! 1691 2015-10-26 16:17:44Z maronga
	77	! Renamed prandtl_layer to constant_flux_layer.
	78	!
[1686]	79	! 1685 2015-10-08 07:32:13Z raasch
	80	! bugfix concerning vertical index offset in case of ocean
	81	!
[1683]	82	! 1682 2015-10-07 23:56:08Z knoop
	83	! Code annotations made doxygen readable
	84	!
[1576]	85	! 1575 2015-03-27 09:56:27Z raasch
	86	! initial vertical particle position is allowed to follow the topography
	87	!
[1360]	88	! 1359 2014-04-11 17:15:14Z hoffmann
	89	! New particle structure integrated.
	90	! Kind definition added to all floating point numbers.
	91	! lpm_init changed form a subroutine to a module.
	92	!
[1329]	93	! 1327 2014-03-21 11:00:16Z raasch
	94	! -netcdf_output
	95	!
[1323]	96	! 1322 2014-03-20 16:38:49Z raasch
	97	! REAL functions provided with KIND-attribute
	98	!
[1321]	99	! 1320 2014-03-20 08:40:49Z raasch
[1320]	100	! ONLY-attribute added to USE-statements,
	101	! kind-parameters added to all INTEGER and REAL declaration statements,
	102	! kinds are defined in new module kinds,
	103	! revision history before 2012 removed,
	104	! comment fields (!:) to be used for variable explanations added to
	105	! all variable declaration statements
	106	! bugfix: #if defined( __parallel ) added
[850]	107	!
[1315]	108	! 1314 2014-03-14 18:25:17Z suehring
	109	! Vertical logarithmic interpolation of horizontal particle speed for particles
	110	! between roughness height and first vertical grid level.
	111	!
[1093]	112	! 1092 2013-02-02 11:24:22Z raasch
	113	! unused variables removed
	114	!
[1037]	115	! 1036 2012-10-22 13:43:42Z raasch
	116	! code put under GPL (PALM 3.9)
	117	!
[850]	118	! 849 2012-03-15 10:35:09Z raasch
[849]	119	! routine renamed: init_particles -> lpm_init
	120	! de_dx, de_dy, de_dz are allocated here (instead of automatic arrays in
	121	! advec_particles),
	122	! sort_particles renamed lpm_sort_arrays, user_init_particles renamed lpm_init
[392]	123	!
[829]	124	! 828 2012-02-21 12:00:36Z raasch
	125	! call of init_kernels, particle feature color renamed class
	126	!
[826]	127	! 824 2012-02-17 09:09:57Z raasch
	128	! particle attributes speed_x\|y\|z_sgs renamed rvar1\|2\|3,
	129	! array particles implemented as pointer
	130	!
[668]	131	! 667 2010-12-23 12:06:00Z suehring/gryschka
	132	! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng for allocation
	133	! of arrays.
	134	!
[1]	135	! Revision 1.1 1999/11/25 16:22:38 raasch
	136	! Initial revision
	137	!
	138	!
	139	! Description:
	140	! ------------
[1682]	141	!> This routine initializes a set of particles and their attributes (position,
	142	!> radius, ..) which are used by the Lagrangian particle model (see lpm).
[1]	143	!------------------------------------------------------------------------------!
[1682]	144	MODULE lpm_init_mod
	145
[1]	146
[1320]	147	USE arrays_3d, &
	148	ONLY: de_dx, de_dy, de_dz, zu, zw, z0
	149
	150	USE control_parameters, &
[1691]	151	ONLY: cloud_droplets, constant_flux_layer, current_timestep_number, &
[1783]	152	dz, initializing_actions, message_string, ocean, simulated_time
[1320]	153
	154	USE grid_variables, &
[1359]	155	ONLY: ddx, dx, ddy, dy
[1320]	156
	157	USE indices, &
[1575]	158	ONLY: nx, nxl, nxlg, nxrg, nxr, ny, nyn, nys, nyng, nysg, nz, nzb, &
	159	nzb_w_inner, nzt
[1320]	160
	161	USE kinds
	162
	163	USE lpm_collision_kernels_mod, &
	164	ONLY: init_kernels
	165
[1783]	166	USE netcdf_interface, &
	167	ONLY: netcdf_data_format
	168
[1320]	169	USE particle_attributes, &
[1359]	170	ONLY: alloc_factor, bc_par_b, bc_par_lr, bc_par_ns, bc_par_t, &
	171	block_offset, block_offset_def, collision_kernel, &
[1831]	172	curvature_solution_effects, &
[1822]	173	density_ratio, grid_particles, &
[1359]	174	initial_weighting_factor, ibc_par_b, ibc_par_lr, ibc_par_ns, &
	175	ibc_par_t, iran_part, log_z_z0, &
	176	max_number_of_particle_groups, maximum_number_of_particles, &
[1822]	177	min_nr_particle, mpi_particle_type, &
[2182]	178	number_concentration, number_particles_per_gridbox, &
[1822]	179	number_of_particles, &
[1320]	180	number_of_particle_groups, number_of_sublayers, &
[1822]	181	offset_ocean_nzt, offset_ocean_nzt_m1, &
[1359]	182	particles, particle_advection_start, particle_groups, &
	183	particle_groups_type, particles_per_point, &
[1822]	184	particle_type, pdx, pdy, pdz, &
[1359]	185	prt_count, psb, psl, psn, psr, pss, pst, &
[1320]	186	radius, random_start_position, read_particles_from_restartfile,&
[1929]	187	seed_follows_topography, sgs_wf_part, sort_count, &
[1822]	188	total_number_of_particles, &
	189	use_sgs_for_particles, &
[1359]	190	write_particle_statistics, uniform_particles, zero_particle, &
	191	z0_av_global
[1320]	192
[1]	193	USE pegrid
	194
[1320]	195	USE random_function_mod, &
	196	ONLY: random_function
[1]	197
[1359]	198	IMPLICIT NONE
[1320]	199
[1359]	200	PRIVATE
	201
[1682]	202	INTEGER(iwp), PARAMETER :: PHASE_INIT = 1 !<
	203	INTEGER(iwp), PARAMETER, PUBLIC :: PHASE_RELEASE = 2 !<
[1359]	204
	205	INTERFACE lpm_init
	206	MODULE PROCEDURE lpm_init
	207	END INTERFACE lpm_init
	208
	209	INTERFACE lpm_create_particle
	210	MODULE PROCEDURE lpm_create_particle
	211	END INTERFACE lpm_create_particle
	212
	213	PUBLIC lpm_init, lpm_create_particle
	214
[1929]	215	CONTAINS
[1359]	216
[1682]	217	!------------------------------------------------------------------------------!
	218	! Description:
	219	! ------------
	220	!> @todo Missing subroutine description.
	221	!------------------------------------------------------------------------------!
[1359]	222	SUBROUTINE lpm_init
	223
	224	USE lpm_collision_kernels_mod, &
	225	ONLY: init_kernels
	226
[1]	227	IMPLICIT NONE
	228
[1682]	229	INTEGER(iwp) :: i !<
	230	INTEGER(iwp) :: j !<
	231	INTEGER(iwp) :: k !<
[1320]	232
[1]	233	#if defined( __parallel )
[1682]	234	INTEGER(iwp), DIMENSION(3) :: blocklengths !<
	235	INTEGER(iwp), DIMENSION(3) :: displacements !<
	236	INTEGER(iwp), DIMENSION(3) :: types !<
[1]	237	#endif
	238
[2182]	239	REAL(wp) :: div !<
[1682]	240	REAL(wp) :: height_int !<
	241	REAL(wp) :: height_p !<
	242	REAL(wp) :: z_p !<
	243	REAL(wp) :: z0_av_local !<
[1]	244
	245	#if defined( __parallel )
	246	!
	247	!-- Define MPI derived datatype for FORTRAN datatype particle_type (see module
[82]	248	!-- particle_attributes). Integer length is 4 byte, Real is 8 byte
[1359]	249	blocklengths(1) = 19; blocklengths(2) = 6; blocklengths(3) = 1
	250	displacements(1) = 0; displacements(2) = 152; displacements(3) = 176
	251
[1]	252	types(1) = MPI_REAL
	253	types(2) = MPI_INTEGER
	254	types(3) = MPI_UB
	255	CALL MPI_TYPE_STRUCT( 3, blocklengths, displacements, types, &
	256	mpi_particle_type, ierr )
	257	CALL MPI_TYPE_COMMIT( mpi_particle_type, ierr )
	258	#endif
	259
	260	!
[150]	261	!-- In case of oceans runs, the vertical index calculations need an offset,
	262	!-- because otherwise the k indices will become negative
	263	IF ( ocean ) THEN
	264	offset_ocean_nzt = nzt
	265	offset_ocean_nzt_m1 = nzt - 1
	266	ENDIF
	267
[1359]	268	!
	269	!-- Define block offsets for dividing a gridcell in 8 sub cells
[150]	270
[1359]	271	block_offset(0) = block_offset_def (-1,-1,-1)
	272	block_offset(1) = block_offset_def (-1,-1, 0)
	273	block_offset(2) = block_offset_def (-1, 0,-1)
	274	block_offset(3) = block_offset_def (-1, 0, 0)
	275	block_offset(4) = block_offset_def ( 0,-1,-1)
	276	block_offset(5) = block_offset_def ( 0,-1, 0)
	277	block_offset(6) = block_offset_def ( 0, 0,-1)
	278	block_offset(7) = block_offset_def ( 0, 0, 0)
[150]	279	!
[1]	280	!-- Check the number of particle groups.
	281	IF ( number_of_particle_groups > max_number_of_particle_groups ) THEN
[274]	282	WRITE( message_string, * ) 'max_number_of_particle_groups =', &
	283	max_number_of_particle_groups , &
[254]	284	'&number_of_particle_groups reset to ', &
	285	max_number_of_particle_groups
[849]	286	CALL message( 'lpm_init', 'PA0213', 0, 1, 0, 6, 0 )
[1]	287	number_of_particle_groups = max_number_of_particle_groups
	288	ENDIF
	289
	290	!
	291	!-- Set default start positions, if necessary
[1359]	292	IF ( psl(1) == 9999999.9_wp ) psl(1) = -0.5_wp * dx
	293	IF ( psr(1) == 9999999.9_wp ) psr(1) = ( nx + 0.5_wp ) * dx
	294	IF ( pss(1) == 9999999.9_wp ) pss(1) = -0.5_wp * dy
	295	IF ( psn(1) == 9999999.9_wp ) psn(1) = ( ny + 0.5_wp ) * dy
	296	IF ( psb(1) == 9999999.9_wp ) psb(1) = zu(nz/2)
	297	IF ( pst(1) == 9999999.9_wp ) pst(1) = psb(1)
[1]	298
[1359]	299	IF ( pdx(1) == 9999999.9_wp .OR. pdx(1) == 0.0_wp ) pdx(1) = dx
	300	IF ( pdy(1) == 9999999.9_wp .OR. pdy(1) == 0.0_wp ) pdy(1) = dy
	301	IF ( pdz(1) == 9999999.9_wp .OR. pdz(1) == 0.0_wp ) pdz(1) = zu(2) - zu(1)
[1]	302
[2182]	303	!
	304	!-- If number_particles_per_gridbox is set, the parametres pdx, pdy and pdz are
	305	!-- calculated diagnostically. Therfore an isotropic distribution is prescribed.
	306	IF ( number_particles_per_gridbox /= -1 .AND. &
	307	number_particles_per_gridbox >= 1 ) THEN
	308	pdx(1) = (( dx * dy * ( zu(2) - zu(1) ) ) / &
	309	REAL(number_particles_per_gridbox))**0.3333333_wp
	310	!
	311	!-- Ensure a smooth value (two significant digits) of distance between
	312	!-- particles (pdx, pdy, pdz).
	313	div = 1000.0_wp
	314	DO WHILE ( pdx(1) < div )
	315	div = div / 10.0_wp
	316	ENDDO
	317	pdx(1) = NINT( pdx(1) * 100.0_wp / div ) * div / 100.0_wp
	318	pdy(1) = pdx(1)
	319	pdz(1) = pdx(1)
	320
	321	ENDIF
	322
[1]	323	DO j = 2, number_of_particle_groups
[1359]	324	IF ( psl(j) == 9999999.9_wp ) psl(j) = psl(j-1)
	325	IF ( psr(j) == 9999999.9_wp ) psr(j) = psr(j-1)
	326	IF ( pss(j) == 9999999.9_wp ) pss(j) = pss(j-1)
	327	IF ( psn(j) == 9999999.9_wp ) psn(j) = psn(j-1)
	328	IF ( psb(j) == 9999999.9_wp ) psb(j) = psb(j-1)
	329	IF ( pst(j) == 9999999.9_wp ) pst(j) = pst(j-1)
	330	IF ( pdx(j) == 9999999.9_wp .OR. pdx(j) == 0.0_wp ) pdx(j) = pdx(j-1)
	331	IF ( pdy(j) == 9999999.9_wp .OR. pdy(j) == 0.0_wp ) pdy(j) = pdy(j-1)
	332	IF ( pdz(j) == 9999999.9_wp .OR. pdz(j) == 0.0_wp ) pdz(j) = pdz(j-1)
[1]	333	ENDDO
	334
	335	!
[1929]	336	!-- Allocate arrays required for calculating particle SGS velocities.
	337	!-- Initialize prefactor required for stoachastic Weil equation.
[1822]	338	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
[849]	339	ALLOCATE( de_dx(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
	340	de_dy(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
	341	de_dz(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
[1929]	342
	343	sgs_wf_part = 1.0_wp / 3.0_wp
[849]	344	ENDIF
	345
	346	!
[1314]	347	!-- Allocate array required for logarithmic vertical interpolation of
	348	!-- horizontal particle velocities between the surface and the first vertical
	349	!-- grid level. In order to avoid repeated CPU cost-intensive CALLS of
	350	!-- intrinsic FORTRAN procedure LOG(z/z0), LOG(z/z0) is precalculated for
	351	!-- several heights. Splitting into 20 sublayers turned out to be sufficient.
	352	!-- To obtain exact height levels of particles, linear interpolation is applied
	353	!-- (see lpm_advec.f90).
[1691]	354	IF ( constant_flux_layer ) THEN
[1314]	355
	356	ALLOCATE ( log_z_z0(0:number_of_sublayers) )
	357	z_p = zu(nzb+1) - zw(nzb)
	358
	359	!
	360	!-- Calculate horizontal mean value of z0 used for logartihmic
	361	!-- interpolation. Note: this is not exact for heterogeneous z0.
	362	!-- However, sensitivity studies showed that the effect is
	363	!-- negligible.
	364	z0_av_local = SUM( z0(nys:nyn,nxl:nxr) )
[1359]	365	z0_av_global = 0.0_wp
[1314]	366
[1320]	367	#if defined( __parallel )
[1314]	368	CALL MPI_ALLREDUCE(z0_av_local, z0_av_global, 1, MPI_REAL, MPI_SUM, &
	369	comm2d, ierr )
[1320]	370	#else
	371	z0_av_global = z0_av_local
	372	#endif
[1314]	373
	374	z0_av_global = z0_av_global / ( ( ny + 1 ) * ( nx + 1 ) )
	375	!
	376	!-- Horizontal wind speed is zero below and at z0
[1359]	377	log_z_z0(0) = 0.0_wp
[1314]	378	!
	379	!-- Calculate vertical depth of the sublayers
[1322]	380	height_int = ( z_p - z0_av_global ) / REAL( number_of_sublayers, KIND=wp )
[1314]	381	!
	382	!-- Precalculate LOG(z/z0)
[1929]	383	height_p = z0_av_global
[1314]	384	DO k = 1, number_of_sublayers
	385
	386	height_p = height_p + height_int
	387	log_z_z0(k) = LOG( height_p / z0_av_global )
	388
	389	ENDDO
	390
	391	ENDIF
	392
	393	!
[1359]	394	!-- Check boundary condition and set internal variables
	395	SELECT CASE ( bc_par_b )
	396
	397	CASE ( 'absorb' )
	398	ibc_par_b = 1
	399
	400	CASE ( 'reflect' )
	401	ibc_par_b = 2
	402
	403	CASE DEFAULT
	404	WRITE( message_string, * ) 'unknown boundary condition ', &
	405	'bc_par_b = "', TRIM( bc_par_b ), '"'
	406	CALL message( 'lpm_init', 'PA0217', 1, 2, 0, 6, 0 )
	407
	408	END SELECT
	409	SELECT CASE ( bc_par_t )
	410
	411	CASE ( 'absorb' )
	412	ibc_par_t = 1
	413
	414	CASE ( 'reflect' )
	415	ibc_par_t = 2
	416
	417	CASE DEFAULT
	418	WRITE( message_string, * ) 'unknown boundary condition ', &
	419	'bc_par_t = "', TRIM( bc_par_t ), '"'
	420	CALL message( 'lpm_init', 'PA0218', 1, 2, 0, 6, 0 )
	421
	422	END SELECT
	423	SELECT CASE ( bc_par_lr )
	424
	425	CASE ( 'cyclic' )
	426	ibc_par_lr = 0
	427
	428	CASE ( 'absorb' )
	429	ibc_par_lr = 1
	430
	431	CASE ( 'reflect' )
	432	ibc_par_lr = 2
	433
	434	CASE DEFAULT
	435	WRITE( message_string, * ) 'unknown boundary condition ', &
	436	'bc_par_lr = "', TRIM( bc_par_lr ), '"'
	437	CALL message( 'lpm_init', 'PA0219', 1, 2, 0, 6, 0 )
	438
	439	END SELECT
	440	SELECT CASE ( bc_par_ns )
	441
	442	CASE ( 'cyclic' )
	443	ibc_par_ns = 0
	444
	445	CASE ( 'absorb' )
	446	ibc_par_ns = 1
	447
	448	CASE ( 'reflect' )
	449	ibc_par_ns = 2
	450
	451	CASE DEFAULT
	452	WRITE( message_string, * ) 'unknown boundary condition ', &
	453	'bc_par_ns = "', TRIM( bc_par_ns ), '"'
	454	CALL message( 'lpm_init', 'PA0220', 1, 2, 0, 6, 0 )
	455
	456	END SELECT
	457
	458	!
[828]	459	!-- Initialize collision kernels
	460	IF ( collision_kernel /= 'none' ) CALL init_kernels
	461
	462	!
[1]	463	!-- For the first model run of a possible job chain initialize the
[849]	464	!-- particles, otherwise read the particle data from restart file.
[1]	465	IF ( TRIM( initializing_actions ) == 'read_restart_data' &
	466	.AND. read_particles_from_restartfile ) THEN
	467
[849]	468	CALL lpm_read_restart_file
[1]	469
	470	ELSE
	471
	472	!
	473	!-- Allocate particle arrays and set attributes of the initial set of
	474	!-- particles, which can be also periodically released at later times.
[1359]	475	ALLOCATE( prt_count(nzb:nzt+1,nysg:nyng,nxlg:nxrg), &
	476	grid_particles(nzb+1:nzt,nys:nyn,nxl:nxr) )
[1]	477
[1359]	478	maximum_number_of_particles = 0
	479	number_of_particles = 0
[792]	480
	481	sort_count = 0
[1359]	482	prt_count = 0
[792]	483
[1]	484	!
[2122]	485	!-- initialize counter for particle IDs
	486	grid_particles%id_counter = 0
	487
	488	!
[1]	489	!-- Initialize all particles with dummy values (otherwise errors may
	490	!-- occur within restart runs). The reason for this is still not clear
	491	!-- and may be presumably caused by errors in the respective user-interface.
[1359]	492	zero_particle = particle_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
	493	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
	494	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
[2122]	495	0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, &
	496	0, 0, 0, 0, .FALSE., -1 )
[1822]	497
[1359]	498	particle_groups = particle_groups_type( 0.0_wp, 0.0_wp, 0.0_wp, 0.0_wp )
[1]	499
	500	!
	501	!-- Set values for the density ratio and radius for all particle
	502	!-- groups, if necessary
[1359]	503	IF ( density_ratio(1) == 9999999.9_wp ) density_ratio(1) = 0.0_wp
	504	IF ( radius(1) == 9999999.9_wp ) radius(1) = 0.0_wp
[1]	505	DO i = 2, number_of_particle_groups
[1359]	506	IF ( density_ratio(i) == 9999999.9_wp ) THEN
[1]	507	density_ratio(i) = density_ratio(i-1)
	508	ENDIF
[1359]	509	IF ( radius(i) == 9999999.9_wp ) radius(i) = radius(i-1)
[1]	510	ENDDO
	511
	512	DO i = 1, number_of_particle_groups
[1359]	513	IF ( density_ratio(i) /= 0.0_wp .AND. radius(i) == 0 ) THEN
[254]	514	WRITE( message_string, * ) 'particle group #', i, 'has a', &
	515	'density ratio /= 0 but radius = 0'
[849]	516	CALL message( 'lpm_init', 'PA0215', 1, 2, 0, 6, 0 )
[1]	517	ENDIF
	518	particle_groups(i)%density_ratio = density_ratio(i)
	519	particle_groups(i)%radius = radius(i)
	520	ENDDO
	521
	522	!
[1359]	523	!-- Set a seed value for the random number generator to be exclusively
	524	!-- used for the particle code. The generated random numbers should be
	525	!-- different on the different PEs.
	526	iran_part = iran_part + myid
	527
[1725]	528	CALL lpm_create_particle (PHASE_INIT)
[1359]	529	!
	530	!-- User modification of initial particles
	531	CALL user_lpm_init
	532
	533	!
	534	!-- Open file for statistical informations about particle conditions
	535	IF ( write_particle_statistics ) THEN
	536	CALL check_open( 80 )
	537	WRITE ( 80, 8000 ) current_timestep_number, simulated_time, &
	538	number_of_particles, &
	539	maximum_number_of_particles
	540	CALL close_file( 80 )
	541	ENDIF
	542
	543	ENDIF
	544
	545	!
	546	!-- To avoid programm abort, assign particles array to the local version of
	547	!-- first grid cell
	548	number_of_particles = prt_count(nzb+1,nys,nxl)
	549	particles => grid_particles(nzb+1,nys,nxl)%particles(1:number_of_particles)
	550	!
	551	!-- Formats
	552	8000 FORMAT (I6,1X,F7.2,4X,I10,71X,I10)
	553
	554	END SUBROUTINE lpm_init
	555
[1682]	556	!------------------------------------------------------------------------------!
	557	! Description:
	558	! ------------
	559	!> @todo Missing subroutine description.
	560	!------------------------------------------------------------------------------!
[1359]	561	SUBROUTINE lpm_create_particle (phase)
	562
	563	USE lpm_exchange_horiz_mod, &
	564	ONLY: lpm_exchange_horiz, lpm_move_particle, realloc_particles_array
	565
	566	USE lpm_pack_arrays_mod, &
	567	ONLY: lpm_pack_all_arrays
	568
[1871]	569	USE particle_attributes, &
[1929]	570	ONLY: deleted_particles, monodisperse_aerosols
[1871]	571
[1359]	572	IMPLICIT NONE
	573
[1929]	574	INTEGER(iwp) :: alloc_size !< relative increase of allocated memory for particles
	575	INTEGER(iwp) :: i !< loop variable ( particle groups )
	576	INTEGER(iwp) :: ip !< index variable along x
	577	INTEGER(iwp) :: j !< loop variable ( particles per point )
	578	INTEGER(iwp) :: jp !< index variable along y
	579	INTEGER(iwp) :: kp !< index variable along z
	580	INTEGER(iwp) :: loop_stride !< loop variable for initialization
	581	INTEGER(iwp) :: n !< loop variable ( number of particles )
	582	INTEGER(iwp) :: new_size !< new size of allocated memory for particles
[1359]	583
[1929]	584	INTEGER(iwp), INTENT(IN) :: phase !< mode of inititialization
[1359]	585
[1929]	586	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: local_count !< start address of new particle
	587	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: local_start !< start address of new particle
[1359]	588
[1929]	589	LOGICAL :: first_stride !< flag for initialization
[1359]	590
[1929]	591	REAL(wp) :: pos_x !< increment for particle position in x
	592	REAL(wp) :: pos_y !< increment for particle position in y
	593	REAL(wp) :: pos_z !< increment for particle position in z
	594	REAL(wp) :: rand_contr !< dummy argument for random position
[1359]	595
[1929]	596	TYPE(particle_type),TARGET :: tmp_particle !< temporary particle used for initialization
[1359]	597
	598	!
	599	!-- Calculate particle positions and store particle attributes, if
	600	!-- particle is situated on this PE
	601	DO loop_stride = 1, 2
	602	first_stride = (loop_stride == 1)
	603	IF ( first_stride ) THEN
	604	local_count = 0 ! count number of particles
	605	ELSE
	606	local_count = prt_count ! Start address of new particles
	607	ENDIF
	608
[2182]	609	!
	610	!-- Calculate initial_weighting_factor diagnostically
	611	IF ( number_concentration /= -1.0_wp .AND. number_concentration > 0.0_wp ) THEN
	612	initial_weighting_factor = number_concentration * 1.0E6_wp * &
	613	pdx(1) * pdy(1) * pdz(1)
	614	END IF
	615
[1]	616	n = 0
	617	DO i = 1, number_of_particle_groups
	618
	619	pos_z = psb(i)
	620
	621	DO WHILE ( pos_z <= pst(i) )
	622
[2223]	623	IF ( pos_z >= 0.0_wp .AND. pos_z < zw(nzt) ) THEN
[1]	624
	625
[2223]	626	pos_y = pss(i)
[1]	627
[2223]	628	DO WHILE ( pos_y <= psn(i) )
[1]	629
[2223]	630	IF ( pos_y >= ( nys - 0.5_wp ) * dy .AND. &
	631	pos_y < ( nyn + 0.5_wp ) * dy ) THEN
[1]	632
[2223]	633	pos_x = psl(i)
[1]	634
[2223]	635	xloop: DO WHILE ( pos_x <= psr(i) )
[1]	636
[2223]	637	IF ( pos_x >= ( nxl - 0.5_wp ) * dx .AND. &
	638	pos_x < ( nxr + 0.5_wp ) * dx ) THEN
	639
	640	DO j = 1, particles_per_point
	641
	642	n = n + 1
	643	tmp_particle%x = pos_x
	644	tmp_particle%y = pos_y
	645	tmp_particle%z = pos_z
	646	tmp_particle%age = 0.0_wp
	647	tmp_particle%age_m = 0.0_wp
	648	tmp_particle%dt_sum = 0.0_wp
	649	tmp_particle%user = 0.0_wp !unused, free for the user
	650	tmp_particle%e_m = 0.0_wp
	651	IF ( curvature_solution_effects ) THEN
[824]	652	!
[2223]	653	!-- Initial values (internal timesteps, derivative)
	654	!-- for Rosenbrock method
	655	tmp_particle%rvar1 = 1.0E-6_wp !last Rosenbrock timestep
	656	tmp_particle%rvar2 = 0.1E-6_wp !dry aerosol radius
	657	tmp_particle%rvar3 = -9999999.9_wp !unused in this configuration
	658	ELSE
[824]	659	!
[2223]	660	!-- Initial values for SGS velocities
	661	tmp_particle%rvar1 = 0.0_wp
	662	tmp_particle%rvar2 = 0.0_wp
	663	tmp_particle%rvar3 = 0.0_wp
	664	ENDIF
	665	tmp_particle%speed_x = 0.0_wp
	666	tmp_particle%speed_y = 0.0_wp
	667	tmp_particle%speed_z = 0.0_wp
	668	tmp_particle%origin_x = pos_x
	669	tmp_particle%origin_y = pos_y
	670	tmp_particle%origin_z = pos_z
	671	tmp_particle%radius = particle_groups(i)%radius
	672	tmp_particle%weight_factor = initial_weighting_factor
	673	tmp_particle%class = 1
	674	tmp_particle%group = i
	675	tmp_particle%id1 = 0
	676	tmp_particle%id2 = 0
	677	tmp_particle%particle_mask = .TRUE.
	678	tmp_particle%block_nr = -1
[1]	679	!
[2223]	680	!-- Determine the grid indices of the particle position
	681	ip = ( tmp_particle%x + 0.5_wp * dx ) * ddx
	682	jp = ( tmp_particle%y + 0.5_wp * dy ) * ddy
	683	kp = tmp_particle%z / dz + 1 + offset_ocean_nzt
[1]	684
[2223]	685	IF ( seed_follows_topography ) THEN
[1575]	686	!
[2223]	687	!-- Particle height is given relative to topography
	688	kp = kp + nzb_w_inner(jp,ip)
	689	tmp_particle%z = tmp_particle%z + &
[1929]	690	zw(nzb_w_inner(jp,ip))
[2223]	691	IF ( kp > nzt ) THEN
	692	pos_x = pos_x + pdx(i)
	693	CYCLE xloop
	694	ENDIF
	695	ELSEIF ( .NOT. seed_follows_topography .AND. &
	696	tmp_particle%z <= zw(nzb_w_inner(jp,ip)) ) THEN
[1575]	697	pos_x = pos_x + pdx(i)
[2223]	698	CYCLE xloop
[1575]	699	ENDIF
	700
[2223]	701	local_count(kp,jp,ip) = local_count(kp,jp,ip) + 1
[2182]	702
[2223]	703	IF ( .NOT. first_stride ) THEN
	704	IF ( ip < nxl .OR. jp < nys .OR. kp < nzb+1 ) THEN
	705	write(6,*) 'xl ',ip,jp,kp,nxl,nys,nzb+1
	706	ENDIF
	707	IF ( ip > nxr .OR. jp > nyn .OR. kp > nzt ) THEN
	708	write(6,*) 'xu ',ip,jp,kp,nxr,nyn,nzt
	709	ENDIF
	710	grid_particles(kp,jp,ip)%particles(local_count(kp,jp,ip)) = tmp_particle
	711
[1359]	712	ENDIF
[2223]	713	ENDDO
[1929]	714
[2223]	715	ENDIF
[1]	716
[2223]	717	pos_x = pos_x + pdx(i)
[1]	718
[2223]	719	ENDDO xloop
[1]	720
[2223]	721	ENDIF
[1]	722
[2223]	723	pos_y = pos_y + pdy(i)
[1]	724
[2223]	725	ENDDO
[1]	726
[2223]	727	ENDIF
[1]	728
	729	pos_z = pos_z + pdz(i)
	730
	731	ENDDO
	732
	733	ENDDO
	734
[1359]	735	IF ( first_stride ) THEN
	736	DO ip = nxl, nxr
	737	DO jp = nys, nyn
	738	DO kp = nzb+1, nzt
	739	IF ( phase == PHASE_INIT ) THEN
	740	IF ( local_count(kp,jp,ip) > 0 ) THEN
	741	alloc_size = MAX( INT( local_count(kp,jp,ip) * &
	742	( 1.0_wp + alloc_factor / 100.0_wp ) ), &
	743	min_nr_particle )
	744	ELSE
	745	alloc_size = min_nr_particle
	746	ENDIF
	747	ALLOCATE(grid_particles(kp,jp,ip)%particles(1:alloc_size))
	748	DO n = 1, alloc_size
	749	grid_particles(kp,jp,ip)%particles(n) = zero_particle
	750	ENDDO
	751	ELSEIF ( phase == PHASE_RELEASE ) THEN
	752	IF ( local_count(kp,jp,ip) > 0 ) THEN
	753	new_size = local_count(kp,jp,ip) + prt_count(kp,jp,ip)
	754	alloc_size = MAX( INT( new_size * ( 1.0_wp + &
	755	alloc_factor / 100.0_wp ) ), min_nr_particle )
	756	IF( alloc_size > SIZE( grid_particles(kp,jp,ip)%particles) ) THEN
[2182]	757	CALL realloc_particles_array(ip,jp,kp,alloc_size)
[1359]	758	ENDIF
	759	ENDIF
	760	ENDIF
	761	ENDDO
	762	ENDDO
	763	ENDDO
	764	ENDIF
[1929]	765
[1359]	766	ENDDO
[1]	767
[2182]	768
	769
[1359]	770	local_start = prt_count+1
	771	prt_count = local_count
[1871]	772
[1]	773	!
[2122]	774	!-- Calculate particle IDs
	775	DO ip = nxl, nxr
	776	DO jp = nys, nyn
	777	DO kp = nzb+1, nzt
	778	number_of_particles = prt_count(kp,jp,ip)
	779	IF ( number_of_particles <= 0 ) CYCLE
	780	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
	781
	782	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
	783
[2182]	784	particles(n)%id1 = 10000_iwp * grid_particles(kp,jp,ip)%id_counter + kp
	785	particles(n)%id2 = 10000_iwp * jp + ip
[2122]	786
	787	grid_particles(kp,jp,ip)%id_counter = &
	788	grid_particles(kp,jp,ip)%id_counter + 1
	789
	790	ENDDO
	791
	792	ENDDO
	793	ENDDO
	794	ENDDO
	795
	796	!
[1871]	797	!-- Initialize aerosol background spectrum
	798	IF ( curvature_solution_effects .AND. .NOT. monodisperse_aerosols ) THEN
	799	CALL lpm_init_aerosols(local_start)
	800	ENDIF
	801
	802	!
[1929]	803	!-- Add random fluctuation to particle positions.
[1359]	804	IF ( random_start_position ) THEN
	805	DO ip = nxl, nxr
	806	DO jp = nys, nyn
	807	DO kp = nzb+1, nzt
	808	number_of_particles = prt_count(kp,jp,ip)
	809	IF ( number_of_particles <= 0 ) CYCLE
	810	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
[1929]	811	!
	812	!-- Move only new particles. Moreover, limit random fluctuation
	813	!-- in order to prevent that particles move more than one grid box,
	814	!-- which would lead to problems concerning particle exchange
	815	!-- between processors in case pdx/pdy are larger than dx/dy,
	816	!-- respectively.
	817	DO n = local_start(kp,jp,ip), number_of_particles
[1359]	818	IF ( psl(particles(n)%group) /= psr(particles(n)%group) ) THEN
[1929]	819	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
	820	pdx(particles(n)%group)
[1359]	821	particles(n)%x = particles(n)%x + &
[1929]	822	MERGE( rand_contr, SIGN( dx, rand_contr ), &
	823	ABS( rand_contr ) < dx &
	824	)
[1359]	825	ENDIF
	826	IF ( pss(particles(n)%group) /= psn(particles(n)%group) ) THEN
[1929]	827	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
	828	pdy(particles(n)%group)
[1359]	829	particles(n)%y = particles(n)%y + &
[1929]	830	MERGE( rand_contr, SIGN( dy, rand_contr ), &
	831	ABS( rand_contr ) < dy &
	832	)
[1359]	833	ENDIF
	834	IF ( psb(particles(n)%group) /= pst(particles(n)%group) ) THEN
[1929]	835	rand_contr = ( random_function( iran_part ) - 0.5_wp ) * &
	836	pdz(particles(n)%group)
[1359]	837	particles(n)%z = particles(n)%z + &
[1929]	838	MERGE( rand_contr, SIGN( dz, rand_contr ), &
	839	ABS( rand_contr ) < dz &
	840	)
[1359]	841	ENDIF
	842	ENDDO
[1]	843	!
[1929]	844	!-- Identify particles located outside the model domain and reflect
	845	!-- or absorb them if necessary.
[1359]	846	CALL lpm_boundary_conds( 'bottom/top' )
[1929]	847	!
	848	!-- Furthermore, remove particles located in topography. Note, as
	849	!-- the particle speed is still zero at this point, wall
	850	!-- reflection boundary conditions will not work in this case.
	851	particles => &
	852	grid_particles(kp,jp,ip)%particles(1:number_of_particles)
	853	DO n = local_start(kp,jp,ip), number_of_particles
	854	i = ( particles(n)%x + 0.5_wp * dx ) * ddx
	855	j = ( particles(n)%y + 0.5_wp * dy ) * ddy
	856	IF ( particles(n)%z <= zw(nzb_w_inner(j,i)) ) THEN
	857	particles(n)%particle_mask = .FALSE.
	858	deleted_particles = deleted_particles + 1
	859	ENDIF
	860	ENDDO
[1359]	861	ENDDO
	862	ENDDO
	863	ENDDO
[1]	864	!
[1359]	865	!-- Exchange particles between grid cells and processors
	866	CALL lpm_move_particle
	867	CALL lpm_exchange_horiz
[1]	868
[1359]	869	ENDIF
[1]	870	!
[1359]	871	!-- In case of random_start_position, delete particles identified by
	872	!-- lpm_exchange_horiz and lpm_boundary_conds. Then sort particles into blocks,
	873	!-- which is needed for a fast interpolation of the LES fields on the particle
	874	!-- position.
	875	CALL lpm_pack_all_arrays
[1]	876
	877	!
[1359]	878	!-- Determine maximum number of particles (i.e., all possible particles that
	879	!-- have been allocated) and the current number of particles
	880	DO ip = nxl, nxr
	881	DO jp = nys, nyn
	882	DO kp = nzb+1, nzt
	883	maximum_number_of_particles = maximum_number_of_particles &
	884	+ SIZE(grid_particles(kp,jp,ip)%particles)
	885	number_of_particles = number_of_particles &
	886	+ prt_count(kp,jp,ip)
[1]	887	ENDDO
[1359]	888	ENDDO
	889	ENDDO
[1]	890	!
[1822]	891	!-- Calculate the number of particles of the total domain
[1]	892	#if defined( __parallel )
[1359]	893	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
	894	CALL MPI_ALLREDUCE( number_of_particles, total_number_of_particles, 1, &
	895	MPI_INTEGER, MPI_SUM, comm2d, ierr )
[1]	896	#else
[1359]	897	total_number_of_particles = number_of_particles
[1]	898	#endif
	899
[1359]	900	RETURN
[1]	901
[1359]	902	END SUBROUTINE lpm_create_particle
[336]	903
[1871]	904	SUBROUTINE lpm_init_aerosols(local_start)
	905
	906	USE arrays_3d, &
	907	ONLY: hyp, pt, q
	908
	909	USE cloud_parameters, &
[2122]	910	ONLY: l_d_rv, rho_l, r_v
[1871]	911
	912	USE constants, &
	913	ONLY: pi
	914
	915	USE kinds
	916
	917	USE particle_attributes, &
	918	ONLY: init_aerosol_probabilistic, molecular_weight_of_solute, &
	919	molecular_weight_of_water, n1, n2, n3, rho_s, rm1, rm2, rm3, &
	920	s1, s2, s3, vanthoff
	921
	922	IMPLICIT NONE
	923
	924	REAL(wp), DIMENSION(:), ALLOCATABLE :: cdf !< CDF of aerosol spectrum
	925	REAL(wp), DIMENSION(:), ALLOCATABLE :: r_temp !< dry aerosol radius spectrum
	926
[2122]	927	REAL(wp) :: afactor !< curvature effects
[1871]	928	REAL(wp) :: bfactor !< solute effects
	929	REAL(wp) :: dr !< width of radius bin
	930	REAL(wp) :: e_a !< vapor pressure
	931	REAL(wp) :: e_s !< saturation vapor pressure
	932	REAL(wp) :: n_init !< sum of all aerosol concentrations
	933	REAL(wp) :: pdf !< PDF of aerosol spectrum
	934	REAL(wp) :: rmin = 1.0e-8_wp !< minimum aerosol radius
	935	REAL(wp) :: rmax = 1.0e-6_wp !< maximum aerosol radius
	936	REAL(wp) :: rs_rand !< random number
	937	REAL(wp) :: r_mid !< mean radius
[2122]	938	REAL(wp) :: sigma !< surface tension
[1871]	939	REAL(wp) :: t_int !< temperature
	940	REAL(wp) :: weight_sum !< sum of all weighting factors
	941
[1890]	942	INTEGER(iwp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg), INTENT(IN) :: local_start !<
[1871]	943
	944	INTEGER(iwp) :: n !<
	945	INTEGER(iwp) :: nn !<
	946	INTEGER(iwp) :: no_bins = 999 !< number of bins
	947	INTEGER(iwp) :: ip !<
	948	INTEGER(iwp) :: jp !<
	949	INTEGER(iwp) :: kp !<
	950
	951	LOGICAL :: new_pdf = .FALSE. !< check if aerosol PDF has to be recalculated
	952
	953	!
	954	!-- Compute aerosol background distribution
	955	IF ( init_aerosol_probabilistic ) THEN
	956	ALLOCATE( cdf(0:no_bins), r_temp(0:no_bins) )
	957	DO n = 0, no_bins
	958	r_temp(n) = EXP( LOG(rmin) + ( LOG(rmax) - LOG(rmin ) ) / &
	959	REAL(no_bins, KIND=wp) * REAL(n, KIND=wp) )
	960
	961	cdf(n) = 0.0_wp
	962	n_init = n1 + n2 + n3
	963	IF ( n1 > 0.0_wp ) THEN
	964	cdf(n) = cdf(n) + n1 / n_init * ( 0.5_wp + 0.5_wp * &
	965	ERF( LOG( r_temp(n) / rm1 ) / &
	966	( SQRT(2.0_wp) * LOG(s1) ) &
	967	) )
	968	ENDIF
	969	IF ( n2 > 0.0_wp ) THEN
	970	cdf(n) = cdf(n) + n2 / n_init * ( 0.5_wp + 0.5_wp * &
	971	ERF( LOG( r_temp(n) / rm2 ) / &
	972	( SQRT(2.0_wp) * LOG(s2) ) &
	973	) )
	974	ENDIF
	975	IF ( n3 > 0.0_wp ) THEN
	976	cdf(n) = cdf(n) + n3 / n_init * ( 0.5_wp + 0.5_wp * &
	977	ERF( LOG( r_temp(n) / rm3 ) / &
	978	( SQRT(2.0_wp) * LOG(s3) ) &
	979	) )
	980	ENDIF
	981
	982	ENDDO
	983	ENDIF
	984
	985	DO ip = nxl, nxr
	986	DO jp = nys, nyn
	987	DO kp = nzb+1, nzt
	988
	989	number_of_particles = prt_count(kp,jp,ip)
	990	IF ( number_of_particles <= 0 ) CYCLE
	991	particles => grid_particles(kp,jp,ip)%particles(1:number_of_particles)
	992	!
	993	!-- Initialize the aerosols with a predefined spectral distribution
	994	!-- of the dry radius (logarithmically increasing bins) and a varying
	995	!-- weighting factor
	996	IF ( .NOT. init_aerosol_probabilistic ) THEN
	997
	998	new_pdf = .FALSE.
	999	IF ( .NOT. ALLOCATED( r_temp ) ) THEN
	1000	new_pdf = .TRUE.
	1001	ELSE
	1002	IF ( SIZE( r_temp ) .NE. &
	1003	number_of_particles - local_start(kp,jp,ip) + 2 ) THEN
	1004	new_pdf = .TRUE.
	1005	DEALLOCATE( r_temp )
	1006	ENDIF
	1007	ENDIF
	1008
	1009	IF ( new_pdf ) THEN
	1010
	1011	no_bins = number_of_particles + 1 - local_start(kp,jp,ip)
	1012	ALLOCATE( r_temp(0:no_bins) )
	1013
	1014	DO n = 0, no_bins
	1015	r_temp(n) = EXP( LOG(rmin) + ( LOG(rmax) - LOG(rmin ) ) / &
	1016	REAL(no_bins, KIND=wp) * &
	1017	REAL(n, KIND=wp) )
	1018	ENDDO
	1019
	1020	ENDIF
	1021
	1022	!
	1023	!-- Calculate radius and concentration of each aerosol
	1024	DO n = local_start(kp,jp,ip), number_of_particles
	1025
	1026	nn = n - local_start(kp,jp,ip)
	1027
	1028	r_mid = SQRT( r_temp(nn) * r_temp(nn+1) )
	1029	dr = r_temp(nn+1) - r_temp(nn)
	1030
	1031	pdf = 0.0_wp
	1032	n_init = n1 + n2 + n3
	1033	IF ( n1 > 0.0_wp ) THEN
	1034	pdf = pdf + n1 / n_init * ( 1.0_wp / ( r_mid * LOG(s1) * &
	1035	SQRT( 2.0_wp * pi ) &
	1036	) * &
	1037	EXP( -( LOG( r_mid / rm1 ) )**2 / &
	1038	( 2.0_wp * LOG(s1)**2 ) &
	1039	) &
	1040	)
	1041	ENDIF
	1042	IF ( n2 > 0.0_wp ) THEN
	1043	pdf = pdf + n2 / n_init * ( 1.0_wp / ( r_mid * LOG(s2) * &
	1044	SQRT( 2.0_wp * pi ) &
	1045	) * &
	1046	EXP( -( LOG( r_mid / rm2 ) )**2 / &
	1047	( 2.0_wp * LOG(s2)**2 ) &
	1048	) &
	1049	)
	1050	ENDIF
	1051	IF ( n3 > 0.0_wp ) THEN
	1052	pdf = pdf + n3 / n_init * ( 1.0_wp / ( r_mid * LOG(s3) * &
	1053	SQRT( 2.0_wp * pi ) &
	1054	) * &
	1055	EXP( -( LOG( r_mid / rm3 ) )**2 / &
	1056	( 2.0_wp * LOG(s3)**2 ) &
	1057	) &
	1058	)
	1059	ENDIF
	1060
	1061	particles(n)%rvar2 = r_mid
	1062	particles(n)%weight_factor = pdf * dr
	1063
	1064	END DO
	1065	!
	1066	!-- Adjust weighting factors to initialize the same number of aerosols
	1067	!-- in every grid box
	1068	weight_sum = SUM(particles(local_start(kp,jp,ip):number_of_particles)%weight_factor)
	1069
	1070	particles(local_start(kp,jp,ip):number_of_particles)%weight_factor = &
	1071	particles(local_start(kp,jp,ip):number_of_particles)%weight_factor / &
	1072	weight_sum * initial_weighting_factor * ( no_bins + 1 )
	1073
	1074	ENDIF
	1075	!
	1076	!-- Initialize the aerosols with a predefined weighting factor but
	1077	!-- a randomly choosen dry radius
	1078	IF ( init_aerosol_probabilistic ) THEN
	1079
	1080	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
	1081
	1082	rs_rand = -1.0_wp
	1083	DO WHILE ( rs_rand .LT. cdf(0) .OR. rs_rand .GE. cdf(no_bins) )
	1084	rs_rand = random_function( iran_part )
	1085	ENDDO
	1086	!
	1087	!-- Determine aerosol dry radius by a random number generator
	1088	DO nn = 0, no_bins-1
	1089	IF ( cdf(nn) .LE. rs_rand .AND. cdf(nn+1) .GT. rs_rand ) THEN
	1090	particles(n)%rvar2 = r_temp(nn) + ( r_temp(nn+1) - r_temp(nn) ) / &
	1091	( cdf(nn+1) - cdf(nn) ) * ( rs_rand - cdf(nn) )
	1092	EXIT
	1093	ENDIF
	1094	ENDDO
	1095
	1096	ENDDO
	1097
	1098	ENDIF
	1099
	1100	!
	1101	!-- Set particle radius to equilibrium radius based on the environmental
	1102	!-- supersaturation (Khvorostyanov and Curry, 2007, JGR). This avoids
	1103	!-- the sometimes lengthy growth toward their equilibrium radius within
	1104	!-- the simulation.
	1105	t_int = pt(kp,jp,ip) * ( hyp(kp) / 100000.0_wp )**0.286_wp
	1106
	1107	e_s = 611.0_wp * EXP( l_d_rv * ( 3.6609E-3_wp - 1.0_wp / t_int ) )
	1108	e_a = q(kp,jp,ip) * hyp(kp) / ( 0.378_wp * q(kp,jp,ip) + 0.622_wp )
	1109
[2122]	1110	sigma = 0.0761_wp - 0.000155_wp * ( t_int - 273.15_wp )
	1111	afactor = 2.0_wp * sigma / ( rho_l * r_v * t_int )
	1112
	1113	bfactor = vanthoff * molecular_weight_of_water * &
	1114	rho_s / ( molecular_weight_of_solute * rho_l )
[1871]	1115	!
[1890]	1116	!-- The formula is only valid for subsaturated environments. For
[2122]	1117	!-- supersaturations higher than -5 %, the supersaturation is set to -5%.
	1118	IF ( e_a / e_s >= 0.95_wp ) e_a = 0.95_wp * e_s
[1871]	1119
[2122]	1120	DO n = local_start(kp,jp,ip), number_of_particles !only new particles
	1121	!
	1122	!-- For details on this equation, see Eq. (14) of Khvorostyanov and
	1123	!-- Curry (2007, JGR)
	1124	particles(n)%radius = bfactor*0.3333333_wp &
	1125	particles(n)%rvar2 / ( 1.0_wp - e_a / e_s )**0.3333333_wp / &
	1126	( 1.0_wp + ( afactor / ( 3.0_wp * bfactor*0.3333333_wp &
	1127	particles(n)%rvar2 ) ) / &
	1128	( 1.0_wp - e_a / e_s )**0.6666666_wp &
	1129	)
[1871]	1130
[2122]	1131	ENDDO
[1871]	1132
	1133	ENDDO
	1134	ENDDO
	1135	ENDDO
	1136	!
	1137	!-- Deallocate used arrays
	1138	IF ( ALLOCATED(r_temp) ) DEALLOCATE( r_temp )
	1139	IF ( ALLOCATED(cdf) ) DEALLOCATE( cdf )
	1140
	1141	END SUBROUTINE lpm_init_aerosols
	1142
[1359]	1143	END MODULE lpm_init_mod

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