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source: palm/trunk/SOURCE/lpm_collision_kernels.f90 @ 1873

Last change on this file since 1873 was 1873, checked in by maronga, 9 years ago
revised renaming of modules
Property svn:keywords set to `Id`
File size: 38.7 KB

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[1873]	1	!> @file lpm_collision_kernels.f90
[1036]	2	!--------------------------------------------------------------------------------!
	3	! This file is part of PALM.
	4	!
	5	! PALM is free software: you can redistribute it and/or modify it under the terms
	6	! of the GNU General Public License as published by the Free Software Foundation,
	7	! either version 3 of the License, or (at your option) any later version.
	8	!
	9	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
	10	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	11	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
	12	!
	13	! You should have received a copy of the GNU General Public License along with
	14	! PALM. If not, see <http://www.gnu.org/licenses/>.
	15	!
[1818]	16	! Copyright 1997-2016 Leibniz Universitaet Hannover
[1036]	17	!--------------------------------------------------------------------------------!
	18	!
[790]	19	! Current revisions:
	20	! -----------------
[1873]	21	! Module renamed (removed _mod)
[1859]	22	!
[1347]	23	!
[1321]	24	! Former revisions:
	25	! -----------------
	26	! $Id: lpm_collision_kernels.f90 1873 2016-04-18 14:50:06Z maronga $
	27	!
[1859]	28	! 1858 2016-04-13 13:12:11Z hoffmann
	29	! Interpolation of collision kernels adjusted to more reasonable values.
	30	! Reformatting of the code.
	31	!
[1851]	32	! 1850 2016-04-08 13:29:27Z maronga
	33	! Module renamed
	34	!
[1823]	35	! 1822 2016-04-07 07:49:42Z hoffmann
	36	! PALM kernel has been deleted.
	37	! Bugfix in the calculation of the turbulent enhancement factor of the
	38	! collection efficiency.
	39	!
	40	! Unused variables removed.
	41	!
[1777]	42	! 1776 2016-03-02 17:54:58Z hoffmann
	43	! Bugfix: Collection efficiencies must be calculated for the larger droplet.
	44	!
[1683]	45	! 1682 2015-10-07 23:56:08Z knoop
	46	! Code annotations made doxygen readable
	47	!
[1520]	48	! 1519 2015-01-08 10:20:42Z hoffmann
	49	! Bugfix: Using the new particle structure, particles are not sorted by size.
	50	! Hence, computation of collision efficiencies must ensure that the ratio of
	51	! two colliding droplets is < 1.
	52	!
[1360]	53	! 1359 2014-04-11 17:15:14Z hoffmann
	54	! New particle structure integrated.
	55	! Kind definition added to all floating point numbers.
	56	!
[1347]	57	! 1346 2014-03-27 13:18:20Z heinze
	58	! Bugfix: REAL constants provided with KIND-attribute especially in call of
	59	! intrinsic function like MAX, MIN, SIGN
	60	!
[1323]	61	! 1322 2014-03-20 16:38:49Z raasch
	62	! REAL constants defined as wp_kind
	63	!
[1321]	64	! 1320 2014-03-20 08:40:49Z
[1320]	65	! ONLY-attribute added to USE-statements,
	66	! kind-parameters added to all INTEGER and REAL declaration statements,
	67	! kinds are defined in new module kinds,
	68	! revision history before 2012 removed,
	69	! comment fields (!:) to be used for variable explanations added to
	70	! all variable declaration statements
[1008]	71	!
[1093]	72	! 1092 2013-02-02 11:24:22Z raasch
	73	! unused variables removed
	74	!
[1072]	75	! 1071 2012-11-29 16:54:55Z franke
	76	! Bugfix: collision efficiencies for Hall kernel should not be < 1.0E-20
	77	!
[1037]	78	! 1036 2012-10-22 13:43:42Z raasch
	79	! code put under GPL (PALM 3.9)
	80	!
[1008]	81	! 1007 2012-09-19 14:30:36Z franke
[1007]	82	! converted all units to SI units and replaced some parameters by corresponding
	83	! PALM parameters
	84	! Bugfix: factor in calculation of enhancement factor for collision efficencies
	85	! changed from 10. to 1.0
[829]	86	!
[850]	87	! 849 2012-03-15 10:35:09Z raasch
	88	! routine collision_efficiency_rogers added (moved from former advec_particles
	89	! to here)
	90	!
[836]	91	! 835 2012-02-22 11:21:19Z raasch $
	92	! Bugfix: array diss can be used only in case of Wang kernel
	93	!
[829]	94	! 828 2012-02-21 12:00:36Z raasch
[828]	95	! code has been completely reformatted, routine colker renamed
	96	! recalculate_kernel,
	97	! routine init_kernels added, radius is now communicated to the collision
	98	! routines by array radclass
[790]	99	!
[828]	100	! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4
	101	!
[826]	102	! 825 2012-02-19 03:03:44Z raasch
	103	! routine renamed from wang_kernel to lpm_collision_kernels,
	104	! turbulence_effects on collision replaced by wang_kernel
	105	!
[791]	106	! 790 2011-11-29 03:11:20Z raasch
	107	! initial revision
[790]	108	!
	109	! Description:
	110	! ------------
[1682]	111	!> This module calculates collision efficiencies either due to pure gravitational
	112	!> effects (Hall kernel, see Hall, 1980: J. Atmos. Sci., 2486-2507) or
[1822]	113	!> including the effects of turbulence (Wang kernel, see Wang and
	114	!> Grabowski, 2009: Atmos. Sci. Lett., 10, 1-8, and Ayala et al., 2008:
	115	!> New J. Phys., 10, 075016). The original code has been
[1682]	116	!> provided by L.-P. Wang but is substantially reformatted and speed optimized
	117	!> here.
[790]	118	!------------------------------------------------------------------------------!
[1682]	119	MODULE lpm_collision_kernels_mod
	120
[790]	121
[1320]	122	USE constants, &
	123	ONLY: pi
	124
	125	USE kinds
	126
	127	USE particle_attributes, &
[1822]	128	ONLY: collision_kernel, dissipation_classes, particles, &
	129	radius_classes
[1320]	130
[828]	131	USE pegrid
[790]	132
[828]	133
[790]	134	IMPLICIT NONE
	135
	136	PRIVATE
	137
[1822]	138	PUBLIC ckernel, init_kernels, rclass_lbound, rclass_ubound, &
	139	recalculate_kernel
[790]	140
[1682]	141	REAL(wp) :: epsilon !<
	142	REAL(wp) :: rclass_lbound !<
	143	REAL(wp) :: rclass_ubound !<
	144	REAL(wp) :: urms !<
[790]	145
[1822]	146	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !< dissipation rate class
	147	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !< radius class
	148	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !<
[1320]	149
[1822]	150	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !<
	151	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !<
	152	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !<
	153	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !<
	154	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !<
[1320]	155
[1822]	156	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !<
[792]	157
[828]	158	SAVE
[792]	159
[790]	160	!
	161	!-- Public interfaces
[828]	162	INTERFACE init_kernels
	163	MODULE PROCEDURE init_kernels
	164	END INTERFACE init_kernels
[790]	165
[828]	166	INTERFACE recalculate_kernel
	167	MODULE PROCEDURE recalculate_kernel
	168	END INTERFACE recalculate_kernel
[790]	169
	170
[828]	171	CONTAINS
[790]	172
[792]	173
[828]	174	!------------------------------------------------------------------------------!
[1682]	175	! Description:
	176	! ------------
	177	!> Initialization of the collision efficiency matrix with fixed radius and
	178	!> dissipation classes, calculated at simulation start only.
[828]	179	!------------------------------------------------------------------------------!
[1682]	180
	181	SUBROUTINE init_kernels
[792]	182
[828]	183	IMPLICIT NONE
[792]	184
[1682]	185	INTEGER(iwp) :: i !<
	186	INTEGER(iwp) :: j !<
	187	INTEGER(iwp) :: k !<
[790]	188
[828]	189
	190	!
	191	!-- Calculate collision efficiencies for fixed radius- and dissipation
	192	!-- classes
	193	IF ( collision_kernel(6:9) == 'fast' ) THEN
	194
[1822]	195	ALLOCATE( ckernel(1:radius_classes,1:radius_classes, &
	196	0:dissipation_classes), epsclass(1:dissipation_classes), &
[828]	197	radclass(1:radius_classes) )
	198
	199	!
	200	!-- Calculate the radius class bounds with logarithmic distances
[1858]	201	!-- in the interval [1.0E-6, 1000.0E-6] m
[1322]	202	rclass_lbound = LOG( 1.0E-6_wp )
[1858]	203	rclass_ubound = LOG( 1000.0E-6_wp )
[1822]	204	radclass(1) = EXP( rclass_lbound )
[828]	205	DO i = 2, radius_classes
	206	radclass(i) = EXP( rclass_lbound + &
[1359]	207	( rclass_ubound - rclass_lbound ) * &
	208	( i - 1.0_wp ) / ( radius_classes - 1.0_wp ) )
[828]	209	ENDDO
	210
	211	!
[1858]	212	!-- Set the class bounds for dissipation in interval [0.0, 600.0] cm2/s3
[828]	213	DO i = 1, dissipation_classes
[1858]	214	epsclass(i) = 0.06_wp * REAL( i, KIND=wp ) / dissipation_classes
[828]	215	ENDDO
	216	!
	217	!-- Calculate collision efficiencies of the Wang/ayala kernel
	218	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
	219	ecf(1:radius_classes,1:radius_classes), &
	220	gck(1:radius_classes,1:radius_classes), &
	221	winf(1:radius_classes) )
	222
	223	DO k = 1, dissipation_classes
	224
	225	epsilon = epsclass(k)
[1359]	226	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 1.0_wp / 3.0_wp )
[828]	227
	228	CALL turbsd
	229	CALL turb_enhance_eff
	230	CALL effic
	231
	232	DO j = 1, radius_classes
	233	DO i = 1, radius_classes
	234	ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j)
	235	ENDDO
	236	ENDDO
	237
	238	ENDDO
	239
	240	!
	241	!-- Calculate collision efficiencies of the Hall kernel
	242	ALLOCATE( hkernel(1:radius_classes,1:radius_classes), &
	243	hwratio(1:radius_classes,1:radius_classes) )
	244
	245	CALL fallg
	246	CALL effic
	247
	248	DO j = 1, radius_classes
	249	DO i = 1, radius_classes
	250	hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 &
	251	* ec(i,j) * ABS( winf(j) - winf(i) )
	252	ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0
	253	ENDDO
	254	ENDDO
	255
	256	!
	257	!-- Test output of efficiencies
	258	IF ( j == -1 ) THEN
	259
	260	PRINT, '** Hall kernel'
[1359]	261	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6_wp, &
[1007]	262	i = 1,radius_classes )
[828]	263	DO j = 1, radius_classes
[1007]	264	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
	265	( hkernel(i,j), i = 1,radius_classes )
[828]	266	ENDDO
	267
	268	DO k = 1, dissipation_classes
	269	DO i = 1, radius_classes
	270	DO j = 1, radius_classes
[1359]	271	IF ( hkernel(i,j) == 0.0_wp ) THEN
	272	hwratio(i,j) = 9999999.9_wp
[828]	273	ELSE
	274	hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j)
	275	ENDIF
	276	ENDDO
	277	ENDDO
	278
	279	PRINT, '** epsilon = ', epsclass(k)
[1359]	280	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i) 1.0E6_wp, &
[1007]	281	i = 1,radius_classes )
[828]	282	DO j = 1, radius_classes
[1359]	283	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j) 1.0E6_wp, &
[1007]	284	( hwratio(i,j), i = 1,radius_classes )
[828]	285	ENDDO
	286	ENDDO
	287
	288	ENDIF
	289
	290	DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf )
	291
	292	ENDIF
	293
	294	END SUBROUTINE init_kernels
	295
	296
[790]	297	!------------------------------------------------------------------------------!
[1682]	298	! Description:
	299	! ------------
	300	!> Calculation of collision kernels during each timestep and for each grid box
[790]	301	!------------------------------------------------------------------------------!
[828]	302	SUBROUTINE recalculate_kernel( i1, j1, k1 )
[790]	303
[1320]	304	USE arrays_3d, &
	305	ONLY: diss
[790]	306
[1320]	307	USE particle_attributes, &
[1858]	308	ONLY: number_of_particles, prt_count, radius_classes, wang_kernel
[1320]	309
[790]	310	IMPLICIT NONE
	311
[1682]	312	INTEGER(iwp) :: i !<
	313	INTEGER(iwp) :: i1 !<
	314	INTEGER(iwp) :: j !<
	315	INTEGER(iwp) :: j1 !<
	316	INTEGER(iwp) :: k1 !<
[790]	317
	318
[1858]	319	number_of_particles = prt_count(k1,j1,i1)
	320	radius_classes = number_of_particles ! necessary to use the same
	321	! subroutines as for
	322	! precalculated kernels
[792]	323
[1858]	324	ALLOCATE( ec(1:number_of_particles,1:number_of_particles), &
	325	radclass(1:number_of_particles), winf(1:number_of_particles) )
[790]	326
[828]	327	!
[1007]	328	!-- Store particle radii on the radclass array
[1858]	329	radclass(1:number_of_particles) = particles(1:number_of_particles)%radius
[790]	330
[835]	331	IF ( wang_kernel ) THEN
[1007]	332	epsilon = diss(k1,j1,i1) ! dissipation rate in m2/s3
[835]	333	ELSE
[1359]	334	epsilon = 0.0_wp
[835]	335	ENDIF
[1359]	336	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 0.33333333333_wp )
[790]	337
[1359]	338	IF ( wang_kernel .AND. epsilon > 1.0E-7_wp ) THEN
[828]	339	!
	340	!-- Call routines to calculate efficiencies for the Wang kernel
[1858]	341	ALLOCATE( gck(1:number_of_particles,1:number_of_particles), &
	342	ecf(1:number_of_particles,1:number_of_particles) )
[790]	343
[828]	344	CALL turbsd
	345	CALL turb_enhance_eff
	346	CALL effic
[790]	347
[1858]	348	DO j = 1, number_of_particles
	349	DO i = 1, number_of_particles
	350	ckernel(1+i-1,1+j-1,1) = ec(i,j) * gck(i,j) * ecf(i,j)
[790]	351	ENDDO
[828]	352	ENDDO
[790]	353
[828]	354	DEALLOCATE( gck, ecf )
[790]	355
	356	ELSE
[828]	357	!
	358	!-- Call routines to calculate efficiencies for the Hall kernel
[790]	359	CALL fallg
	360	CALL effic
	361
[1858]	362	DO j = 1, number_of_particles
	363	DO i = 1, number_of_particles
	364	ckernel(i,j,1) = pi * ( radclass(j) + radclass(i) )**2 &
	365	* ec(i,j) * ABS( winf(j) - winf(i) )
[790]	366	ENDDO
	367	ENDDO
	368
	369	ENDIF
	370
[828]	371	DEALLOCATE( ec, radclass, winf )
[790]	372
[828]	373	END SUBROUTINE recalculate_kernel
[790]	374
[828]	375
[790]	376	!------------------------------------------------------------------------------!
[1682]	377	! Description:
	378	! ------------
[1822]	379	!> Calculation of effects of turbulence on the geometric collision kernel
	380	!> (by including the droplets' average radial relative velocities and their
	381	!> radial distribution function) following the analytic model by Aayala et al.
	382	!> (2008, New J. Phys.). For details check the second part 2 of the publication,
	383	!> page 37ff.
	384	!>
	385	!> Input parameters, which need to be replaced by PALM parameters:
	386	!> water density, air density
[790]	387	!------------------------------------------------------------------------------!
[792]	388	SUBROUTINE turbsd
[799]	389
[1320]	390	USE control_parameters, &
	391	ONLY: g, molecular_viscosity
	392
	393	USE particle_attributes, &
	394	ONLY: radius_classes
[790]	395
	396	IMPLICIT NONE
	397
[1682]	398	INTEGER(iwp) :: i !<
	399	INTEGER(iwp) :: j !<
[790]	400
[1682]	401	REAL(wp) :: ao !<
	402	REAL(wp) :: ao_gr !<
	403	REAL(wp) :: bbb !<
	404	REAL(wp) :: be !<
	405	REAL(wp) :: b1 !<
	406	REAL(wp) :: b2 !<
	407	REAL(wp) :: ccc !<
	408	REAL(wp) :: c1 !<
	409	REAL(wp) :: c1_gr !<
	410	REAL(wp) :: c2 !<
	411	REAL(wp) :: d1 !<
	412	REAL(wp) :: d2 !<
	413	REAL(wp) :: eta !<
	414	REAL(wp) :: e1 !<
	415	REAL(wp) :: e2 !<
	416	REAL(wp) :: fao_gr !<
	417	REAL(wp) :: fr !<
	418	REAL(wp) :: grfin !<
	419	REAL(wp) :: lambda !<
	420	REAL(wp) :: lambda_re !<
	421	REAL(wp) :: lf !<
	422	REAL(wp) :: rc !<
	423	REAL(wp) :: rrp !<
	424	REAL(wp) :: sst !<
	425	REAL(wp) :: tauk !<
	426	REAL(wp) :: tl !<
	427	REAL(wp) :: t2 !<
	428	REAL(wp) :: tt !<
	429	REAL(wp) :: t1 !<
	430	REAL(wp) :: vk !<
	431	REAL(wp) :: vrms1xy !<
	432	REAL(wp) :: vrms2xy !<
	433	REAL(wp) :: v1 !<
	434	REAL(wp) :: v1v2xy !<
	435	REAL(wp) :: v1xysq !<
	436	REAL(wp) :: v2 !<
	437	REAL(wp) :: v2xysq !<
	438	REAL(wp) :: wrfin !<
	439	REAL(wp) :: wrgrav2 !<
	440	REAL(wp) :: wrtur2xy !<
	441	REAL(wp) :: xx !<
	442	REAL(wp) :: yy !<
	443	REAL(wp) :: z !<
[790]	444
[1822]	445	REAL(wp), DIMENSION(1:radius_classes) :: st !< Stokes number
	446	REAL(wp), DIMENSION(1:radius_classes) :: tau !< inertial time scale
[790]	447
[1822]	448	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon )
[1322]	449	lambda_re = urms*2 SQRT( 15.0_wp / epsilon / molecular_viscosity )
[1822]	450	tl = urms**2 / epsilon
	451	lf = 0.5_wp * urms**3 / epsilon
	452	tauk = SQRT( molecular_viscosity / epsilon )
	453	eta = ( molecular_viscosity3 / epsilon )0.25_wp
[1007]	454	vk = eta / tauk
[790]	455
[1359]	456	ao = ( 11.0_wp + 7.0_wp * lambda_re ) / ( 205.0_wp + lambda_re )
[1822]	457	tt = SQRT( 2.0_wp * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk
[799]	458
[1822]	459	!
	460	!-- Get terminal velocity of droplets
	461	CALL fallg
[790]	462
[828]	463	DO i = 1, radius_classes
[1822]	464	tau(i) = winf(i) / g ! inertial time scale
	465	st(i) = tau(i) / tauk ! Stokes number
[790]	466	ENDDO
	467
[828]	468	!
[1822]	469	!-- Calculate average radial relative velocity at contact (wrfin)
[828]	470	z = tt / tl
[1322]	471	be = SQRT( 2.0_wp ) * lambda / lf
[1359]	472	bbb = SQRT( 1.0_wp - 2.0_wp * be**2 )
	473	d1 = ( 1.0_wp + bbb ) / ( 2.0_wp * bbb )
[1822]	474	e1 = lf * ( 1.0_wp + bbb ) * 0.5_wp
[1359]	475	d2 = ( 1.0_wp - bbb ) * 0.5_wp / bbb
[1822]	476	e2 = lf * ( 1.0_wp - bbb ) * 0.5_wp
[1359]	477	ccc = SQRT( 1.0_wp - 2.0_wp * z**2 )
	478	b1 = ( 1.0_wp + ccc ) * 0.5_wp / ccc
[1822]	479	c1 = tl * ( 1.0_wp + ccc ) * 0.5_wp
[1359]	480	b2 = ( 1.0_wp - ccc ) * 0.5_wp / ccc
[1822]	481	c2 = tl * ( 1.0_wp - ccc ) * 0.5_wp
[790]	482
[828]	483	DO i = 1, radius_classes
[790]	484
[1822]	485	v1 = winf(i)
	486	t1 = tau(i)
[790]	487
[828]	488	DO j = 1, i
[1007]	489	rrp = radclass(i) + radclass(j)
[1822]	490	v2 = winf(j)
	491	t2 = tau(j)
[790]	492
[1007]	493	v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) &
	494	- b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1)
[1822]	495	v1xysq = v1xysq * urms**2 / t1
	496	vrms1xy = SQRT( v1xysq )
[790]	497
[1007]	498	v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) &
	499	- b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2)
[1822]	500	v2xysq = v2xysq * urms**2 / t2
	501	vrms2xy = SQRT( v2xysq )
[790]	502
[828]	503	IF ( winf(i) >= winf(j) ) THEN
[799]	504	v1 = winf(i)
[790]	505	t1 = tau(i)
[799]	506	v2 = winf(j)
[790]	507	t2 = tau(j)
	508	ELSE
[799]	509	v1 = winf(j)
[790]	510	t1 = tau(j)
[799]	511	v2 = winf(i)
[790]	512	t2 = tau(i)
	513	ENDIF
	514
[828]	515	v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - &
	516	b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - &
	517	b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + &
	518	b2 * d2* zhi(c2,e2,v1,t1,v2,t2)
	519	fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 )
[1822]	520	v1v2xy = v1v2xy * fr * urms**2 / tau(i) / tau(j)
	521	wrtur2xy = vrms1xy2 + vrms2xy2 - 2.0_wp * v1v2xy
[1359]	522	IF ( wrtur2xy < 0.0_wp ) wrtur2xy = 0.0_wp
[1322]	523	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
[1822]	524	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) )
[790]	525
[828]	526	!
[1822]	527	!-- Calculate radial distribution function (grfin)
[828]	528	IF ( st(j) > st(i) ) THEN
	529	sst = st(j)
[790]	530	ELSE
[828]	531	sst = st(i)
[790]	532	ENDIF
	533
[1359]	534	xx = -0.1988_wp * sst*4 + 1.5275_wp sst*3 - 4.2942_wp &
	535	sst*2 + 5.3406_wp sst
	536	IF ( xx < 0.0_wp ) xx = 0.0_wp
	537	yy = 0.1886_wp * EXP( 20.306_wp / lambda_re )
[790]	538
[1007]	539	c1_gr = xx / ( g / vk * tauk )**yy
[790]	540
[1322]	541	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
[1359]	542	fao_gr = 20.115_wp * SQRT( ao_gr / lambda_re )
[1822]	543	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta
[790]	544
[1359]	545	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5_wp )
	546	IF ( grfin < 1.0_wp ) grfin = 1.0_wp
[790]	547
[1822]	548	!
	549	!-- Calculate general collection kernel (without the consideration of
	550	!-- collection efficiencies)
	551	gck(i,j) = 2.0_wp * pi * rrp*2 wrfin * grfin
[790]	552	gck(j,i) = gck(i,j)
	553
	554	ENDDO
	555	ENDDO
	556
[828]	557	END SUBROUTINE turbsd
[790]	558
[1320]	559	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
[1822]	560	!
	561	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
	562	!-- effects on the collision kernel
[790]	563	IMPLICIT NONE
	564
[1682]	565	REAL(wp) :: a !<
	566	REAL(wp) :: aa1 !<
	567	REAL(wp) :: b !<
	568	REAL(wp) :: tau0 !<
	569	REAL(wp) :: vsett !<
[790]	570
[1359]	571	aa1 = 1.0_wp / tau0 + 1.0_wp / a + vsett / b
[1822]	572	phi_w = 1.0_wp / aa1 - 0.5_wp * vsett / b / aa1**2
[790]	573
[1007]	574	END FUNCTION phi_w
[792]	575
[1320]	576	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
[1822]	577	!
	578	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
	579	!-- effects on the collision kernel
[790]	580	IMPLICIT NONE
	581
[1682]	582	REAL(wp) :: a !<
	583	REAL(wp) :: aa1 !<
	584	REAL(wp) :: aa2 !<
	585	REAL(wp) :: aa3 !<
	586	REAL(wp) :: aa4 !<
	587	REAL(wp) :: aa5 !<
	588	REAL(wp) :: aa6 !<
	589	REAL(wp) :: b !<
	590	REAL(wp) :: tau1 !<
	591	REAL(wp) :: tau2 !<
	592	REAL(wp) :: vsett1 !<
	593	REAL(wp) :: vsett2 !<
[790]	594
[1359]	595	aa1 = vsett2 / b - 1.0_wp / tau2 - 1.0_wp / a
	596	aa2 = vsett1 / b + 1.0_wp / tau1 + 1.0_wp / a
	597	aa3 = ( vsett1 - vsett2 ) / b + 1.0_wp / tau1 + 1.0_wp / tau2
	598	aa4 = ( vsett2 / b )2 - ( 1.0_wp / tau2 + 1.0_wp / a )2
	599	aa5 = vsett2 / b + 1.0_wp / tau2 + 1.0_wp / a
	600	aa6 = 1.0_wp / tau1 - 1.0_wp / a + ( 1.0_wp / tau2 + 1.0_wp / a) * &
	601	vsett1 / vsett2
	602	zhi = (1.0_wp / aa1 - 1.0_wp / aa2 ) * ( vsett1 - vsett2 ) * 0.5_wp / &
	603	b / aa32 + ( 4.0_wp / aa4 - 1.0_wp / aa52 - 1.0_wp / aa1**2 ) &
	604	* vsett2 * 0.5_wp / b /aa6 + ( 2.0_wp * ( b / aa2 - b / aa1 ) - &
[1822]	605	vsett1 / aa22 + vsett2 / aa12 ) * 0.5_wp / b / aa3
[799]	606
[828]	607	END FUNCTION zhi
[790]	608
[828]	609
[790]	610	!------------------------------------------------------------------------------!
[1682]	611	! Description:
	612	! ------------
[1822]	613	!> Parameterization of terminal velocity following Rogers et al. (1993, J. Appl.
	614	!> Meteorol.)
[790]	615	!------------------------------------------------------------------------------!
[828]	616	SUBROUTINE fallg
[790]	617
[1320]	618	USE particle_attributes, &
	619	ONLY: radius_classes
[790]	620
[828]	621	IMPLICIT NONE
[790]	622
[1822]	623	INTEGER(iwp) :: j !<
[790]	624
[1822]	625	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter
	626	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter
	627	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter
	628	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter
	629	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter
	630	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< seperation diameter
[790]	631
[1822]	632	REAL(wp) :: diameter !< droplet diameter in mm
[790]	633
[799]	634
[828]	635	DO j = 1, radius_classes
[790]	636
[1822]	637	diameter = radclass(j) * 2000.0_wp
[799]	638
[1822]	639	IF ( diameter <= d0_rog ) THEN
	640	winf(j) = k_cap_rog * diameter * ( 1.0_wp - &
	641	EXP( -k_low_rog * diameter ) )
	642	ELSE
	643	winf(j) = a_rog - b_rog * EXP( -c_rog * diameter )
[828]	644	ENDIF
[790]	645
[828]	646	ENDDO
[790]	647
[828]	648	END SUBROUTINE fallg
[790]	649
[828]	650
[790]	651	!------------------------------------------------------------------------------!
[1682]	652	! Description:
	653	! ------------
[1822]	654	!> Interpolation of collision efficiencies (Hall, 1980, J. Atmos. Sci.)
[790]	655	!------------------------------------------------------------------------------!
[828]	656	SUBROUTINE effic
[1320]	657
	658	USE particle_attributes, &
	659	ONLY: radius_classes
[790]	660
[828]	661	IMPLICIT NONE
[790]	662
[1682]	663	INTEGER(iwp) :: i !<
	664	INTEGER(iwp) :: iq !<
	665	INTEGER(iwp) :: ir !<
	666	INTEGER(iwp) :: j !<
	667	INTEGER(iwp) :: k !<
[790]	668
[1682]	669	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
[790]	670
[1682]	671	LOGICAL, SAVE :: first = .TRUE. !<
[790]	672
[1682]	673	REAL(wp) :: ek !<
	674	REAL(wp) :: particle_radius !<
	675	REAL(wp) :: pp !<
	676	REAL(wp) :: qq !<
	677	REAL(wp) :: rq !<
[790]	678
[1682]	679	REAL(wp), DIMENSION(1:21), SAVE :: rat !<
[1320]	680
[1682]	681	REAL(wp), DIMENSION(1:15), SAVE :: r0 !<
[1320]	682
[1682]	683	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !<
[790]	684
[792]	685	!
[828]	686	!-- Initial assignment of constants
	687	IF ( first ) THEN
[790]	688
[792]	689	first = .FALSE.
[1822]	690	r0 = (/ 6.0_wp, 8.0_wp, 10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp, &
	691	30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, 70.0_wp, 100.0_wp, &
[1359]	692	150.0_wp, 200.0_wp, 300.0_wp /)
[790]	693
[1822]	694	rat = (/ 0.00_wp, 0.05_wp, 0.10_wp, 0.15_wp, 0.20_wp, 0.25_wp, &
	695	0.30_wp, 0.35_wp, 0.40_wp, 0.45_wp, 0.50_wp, 0.55_wp, &
	696	0.60_wp, 0.65_wp, 0.70_wp, 0.75_wp, 0.80_wp, 0.85_wp, &
[1359]	697	0.90_wp, 0.95_wp, 1.00_wp /)
	698
[1822]	699	ecoll(:,1) = (/ 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
	700	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
[1359]	701	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp /)
[1822]	702	ecoll(:,2) = (/ 0.003_wp, 0.003_wp, 0.003_wp, 0.004_wp, 0.005_wp, &
	703	0.005_wp, 0.005_wp, 0.010_wp, 0.100_wp, 0.050_wp, &
[1359]	704	0.200_wp, 0.500_wp, 0.770_wp, 0.870_wp, 0.970_wp /)
[1822]	705	ecoll(:,3) = (/ 0.007_wp, 0.007_wp, 0.007_wp, 0.008_wp, 0.009_wp, &
	706	0.010_wp, 0.010_wp, 0.070_wp, 0.400_wp, 0.430_wp, &
[1359]	707	0.580_wp, 0.790_wp, 0.930_wp, 0.960_wp, 1.000_wp /)
[1822]	708	ecoll(:,4) = (/ 0.009_wp, 0.009_wp, 0.009_wp, 0.012_wp, 0.015_wp, &
	709	0.010_wp, 0.020_wp, 0.280_wp, 0.600_wp, 0.640_wp, &
[1359]	710	0.750_wp, 0.910_wp, 0.970_wp, 0.980_wp, 1.000_wp /)
[1822]	711	ecoll(:,5) = (/ 0.014_wp, 0.014_wp, 0.014_wp, 0.015_wp, 0.016_wp, &
	712	0.030_wp, 0.060_wp, 0.500_wp, 0.700_wp, 0.770_wp, &
[1359]	713	0.840_wp, 0.950_wp, 0.970_wp, 1.000_wp, 1.000_wp /)
[1822]	714	ecoll(:,6) = (/ 0.017_wp, 0.017_wp, 0.017_wp, 0.020_wp, 0.022_wp, &
	715	0.060_wp, 0.100_wp, 0.620_wp, 0.780_wp, 0.840_wp, &
[1359]	716	0.880_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	717	ecoll(:,7) = (/ 0.030_wp, 0.030_wp, 0.024_wp, 0.022_wp, 0.032_wp, &
	718	0.062_wp, 0.200_wp, 0.680_wp, 0.830_wp, 0.870_wp, &
[1359]	719	0.900_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	720	ecoll(:,8) = (/ 0.025_wp, 0.025_wp, 0.025_wp, 0.036_wp, 0.043_wp, &
	721	0.130_wp, 0.270_wp, 0.740_wp, 0.860_wp, 0.890_wp, &
[1359]	722	0.920_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	723	ecoll(:,9) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.040_wp, 0.052_wp, &
	724	0.200_wp, 0.400_wp, 0.780_wp, 0.880_wp, 0.900_wp, &
[1359]	725	0.940_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	726	ecoll(:,10) = (/ 0.030_wp, 0.030_wp, 0.030_wp, 0.047_wp, 0.064_wp, &
	727	0.250_wp, 0.500_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
[1359]	728	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	729	ecoll(:,11) = (/ 0.040_wp, 0.040_wp, 0.033_wp, 0.037_wp, 0.068_wp, &
	730	0.240_wp, 0.550_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
[1359]	731	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	732	ecoll(:,12) = (/ 0.035_wp, 0.035_wp, 0.035_wp, 0.055_wp, 0.079_wp, &
	733	0.290_wp, 0.580_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
[1359]	734	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	735	ecoll(:,13) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.062_wp, 0.082_wp, &
	736	0.290_wp, 0.590_wp, 0.780_wp, 0.900_wp, 0.910_wp, &
[1359]	737	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	738	ecoll(:,14) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.060_wp, 0.080_wp, &
	739	0.290_wp, 0.580_wp, 0.770_wp, 0.890_wp, 0.910_wp, &
[1359]	740	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	741	ecoll(:,15) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.041_wp, 0.075_wp, &
	742	0.250_wp, 0.540_wp, 0.760_wp, 0.880_wp, 0.920_wp, &
[1359]	743	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	744	ecoll(:,16) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.052_wp, 0.067_wp, &
	745	0.250_wp, 0.510_wp, 0.770_wp, 0.880_wp, 0.930_wp, &
[1359]	746	0.970_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	747	ecoll(:,17) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.047_wp, 0.057_wp, &
	748	0.250_wp, 0.490_wp, 0.770_wp, 0.890_wp, 0.950_wp, &
[1359]	749	1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	750	ecoll(:,18) = (/ 0.036_wp, 0.036_wp, 0.036_wp, 0.042_wp, 0.048_wp, &
	751	0.230_wp, 0.470_wp, 0.780_wp, 0.920_wp, 1.000_wp, &
[1359]	752	1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp /)
[1822]	753	ecoll(:,19) = (/ 0.040_wp, 0.040_wp, 0.035_wp, 0.033_wp, 0.040_wp, &
	754	0.112_wp, 0.450_wp, 0.790_wp, 1.010_wp, 1.030_wp, &
[1359]	755	1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp /)
[1822]	756	ecoll(:,20) = (/ 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, &
	757	0.119_wp, 0.470_wp, 0.950_wp, 1.300_wp, 1.700_wp, &
[1359]	758	2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp /)
[1822]	759	ecoll(:,21) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, &
	760	0.125_wp, 0.520_wp, 1.400_wp, 2.300_wp, 3.000_wp, &
[1359]	761	4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp /)
[828]	762	ENDIF
[790]	763
[792]	764	!
[828]	765	!-- Calculate the radius class index of particles with respect to array r
[1822]	766	!-- Radius has to be in microns
[828]	767	ALLOCATE( ira(1:radius_classes) )
	768	DO j = 1, radius_classes
[1322]	769	particle_radius = radclass(j) * 1.0E6_wp
[828]	770	DO k = 1, 15
	771	IF ( particle_radius < r0(k) ) THEN
	772	ira(j) = k
	773	EXIT
	774	ENDIF
	775	ENDDO
	776	IF ( particle_radius >= r0(15) ) ira(j) = 16
	777	ENDDO
[790]	778
[792]	779	!
[828]	780	!-- Two-dimensional linear interpolation of the collision efficiency.
[1822]	781	!-- Radius has to be in microns
[828]	782	DO j = 1, radius_classes
	783	DO i = 1, j
[792]	784
[828]	785	ir = ira(j)
[1519]	786	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
[828]	787	iq = INT( rq * 20 ) + 1
	788	iq = MAX( iq , 2)
[792]	789
[828]	790	IF ( ir < 16 ) THEN
	791	IF ( ir >= 2 ) THEN
[1822]	792	pp = ( ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp ) - &
	793	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
[1359]	794	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	795	ec(j,i) = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) &
	796	* ecoll(ir-1,iq-1) &
	797	+ pp * ( 1.0_wp - qq ) * ecoll(ir,iq-1) &
	798	+ qq * ( 1.0_wp - pp ) * ecoll(ir-1,iq) &
[828]	799	+ pp * qq * ecoll(ir,iq)
	800	ELSE
	801	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	802	ec(j,i) = ( 1.0_wp - qq ) * ecoll(1,iq-1) + qq * ecoll(1,iq)
[828]	803	ENDIF
	804	ELSE
	805	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	806	ek = ( 1.0_wp - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
[1346]	807	ec(j,i) = MIN( ek, 1.0_wp )
[1071]	808	ENDIF
[792]	809
[1359]	810	IF ( ec(j,i) < 1.0E-20_wp ) ec(j,i) = 0.0_wp
[1071]	811
[828]	812	ec(i,j) = ec(j,i)
[792]	813
[828]	814	ENDDO
	815	ENDDO
[792]	816
[828]	817	DEALLOCATE( ira )
[792]	818
[828]	819	END SUBROUTINE effic
[792]	820
	821
[790]	822	!------------------------------------------------------------------------------!
[1682]	823	! Description:
	824	! ------------
[1822]	825	!> Interpolation of turbulent enhancement factor for collision efficencies
	826	!> following Wang and Grabowski (2009, Atmos. Sci. Let.)
[790]	827	!------------------------------------------------------------------------------!
[828]	828	SUBROUTINE turb_enhance_eff
[790]	829
[1320]	830	USE particle_attributes, &
	831	ONLY: radius_classes
[790]	832
[828]	833	IMPLICIT NONE
[790]	834
[1682]	835	INTEGER(iwp) :: i !<
	836	INTEGER(iwp) :: iq !<
	837	INTEGER(iwp) :: ir !<
	838	INTEGER(iwp) :: j !<
	839	INTEGER(iwp) :: k !<
	840	INTEGER(iwp) :: kk !<
[790]	841
[1682]	842	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
[1320]	843
[1682]	844	LOGICAL, SAVE :: first = .TRUE. !<
[790]	845
[1682]	846	REAL(wp) :: particle_radius !<
	847	REAL(wp) :: pp !<
	848	REAL(wp) :: qq !<
	849	REAL(wp) :: rq !<
	850	REAL(wp) :: y1 !<
	851	REAL(wp) :: y2 !<
	852	REAL(wp) :: y3 !<
[790]	853
[1682]	854	REAL(wp), DIMENSION(1:11), SAVE :: rat !<
	855	REAL(wp), DIMENSION(1:7), SAVE :: r0 !<
[1320]	856
[1682]	857	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !<
	858	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !<
[799]	859
	860	!
[828]	861	!-- Initial assignment of constants
	862	IF ( first ) THEN
[799]	863
[828]	864	first = .FALSE.
[799]	865
[1359]	866	r0 = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, &
	867	100.0_wp /)
	868
	869	rat = (/ 0.0_wp, 0.1_wp, 0.2_wp, 0.3_wp, 0.4_wp, 0.5_wp, 0.6_wp, &
	870	0.7_wp, 0.8_wp, 0.9_wp, 1.0_wp /)
[828]	871	!
[1822]	872	!-- Tabulated turbulent enhancement factor at 100 cm2/s3
[1359]	873	ecoll_100(:,1) = (/ 1.74_wp, 1.74_wp, 1.773_wp, 1.49_wp, &
	874	1.207_wp, 1.207_wp, 1.0_wp /)
	875	ecoll_100(:,2) = (/ 1.46_wp, 1.46_wp, 1.421_wp, 1.245_wp, &
	876	1.069_wp, 1.069_wp, 1.0_wp /)
	877	ecoll_100(:,3) = (/ 1.32_wp, 1.32_wp, 1.245_wp, 1.123_wp, &
	878	1.000_wp, 1.000_wp, 1.0_wp /)
	879	ecoll_100(:,4) = (/ 1.250_wp, 1.250_wp, 1.148_wp, 1.087_wp, &
	880	1.025_wp, 1.025_wp, 1.0_wp /)
	881	ecoll_100(:,5) = (/ 1.186_wp, 1.186_wp, 1.066_wp, 1.060_wp, &
	882	1.056_wp, 1.056_wp, 1.0_wp /)
	883	ecoll_100(:,6) = (/ 1.045_wp, 1.045_wp, 1.000_wp, 1.014_wp, &
	884	1.028_wp, 1.028_wp, 1.0_wp /)
	885	ecoll_100(:,7) = (/ 1.070_wp, 1.070_wp, 1.030_wp, 1.038_wp, &
	886	1.046_wp, 1.046_wp, 1.0_wp /)
	887	ecoll_100(:,8) = (/ 1.000_wp, 1.000_wp, 1.054_wp, 1.042_wp, &
	888	1.029_wp, 1.029_wp, 1.0_wp /)
	889	ecoll_100(:,9) = (/ 1.223_wp, 1.223_wp, 1.117_wp, 1.069_wp, &
	890	1.021_wp, 1.021_wp, 1.0_wp /)
	891	ecoll_100(:,10) = (/ 1.570_wp, 1.570_wp, 1.244_wp, 1.166_wp, &
	892	1.088_wp, 1.088_wp, 1.0_wp /)
[1822]	893	ecoll_100(:,11) = (/ 20.3_wp, 20.3_wp, 14.6_wp, 8.61_wp, &
[1359]	894	2.60_wp, 2.60_wp, 1.0_wp /)
[828]	895	!
[1822]	896	!-- Tabulated turbulent enhancement factor at 400 cm2/s3
[1359]	897	ecoll_400(:,1) = (/ 4.976_wp, 4.976_wp, 3.593_wp, 2.519_wp, &
	898	1.445_wp, 1.445_wp, 1.0_wp /)
	899	ecoll_400(:,2) = (/ 2.984_wp, 2.984_wp, 2.181_wp, 1.691_wp, &
	900	1.201_wp, 1.201_wp, 1.0_wp /)
	901	ecoll_400(:,3) = (/ 1.988_wp, 1.988_wp, 1.475_wp, 1.313_wp, &
	902	1.150_wp, 1.150_wp, 1.0_wp /)
	903	ecoll_400(:,4) = (/ 1.490_wp, 1.490_wp, 1.187_wp, 1.156_wp, &
	904	1.126_wp, 1.126_wp, 1.0_wp /)
	905	ecoll_400(:,5) = (/ 1.249_wp, 1.249_wp, 1.088_wp, 1.090_wp, &
	906	1.092_wp, 1.092_wp, 1.0_wp /)
	907	ecoll_400(:,6) = (/ 1.139_wp, 1.139_wp, 1.130_wp, 1.091_wp, &
	908	1.051_wp, 1.051_wp, 1.0_wp /)
	909	ecoll_400(:,7) = (/ 1.220_wp, 1.220_wp, 1.190_wp, 1.138_wp, &
	910	1.086_wp, 1.086_wp, 1.0_wp /)
	911	ecoll_400(:,8) = (/ 1.325_wp, 1.325_wp, 1.267_wp, 1.165_wp, &
	912	1.063_wp, 1.063_wp, 1.0_wp /)
	913	ecoll_400(:,9) = (/ 1.716_wp, 1.716_wp, 1.345_wp, 1.223_wp, &
	914	1.100_wp, 1.100_wp, 1.0_wp /)
	915	ecoll_400(:,10) = (/ 3.788_wp, 3.788_wp, 1.501_wp, 1.311_wp, &
	916	1.120_wp, 1.120_wp, 1.0_wp /)
	917	ecoll_400(:,11) = (/ 36.52_wp, 36.52_wp, 19.16_wp, 22.80_wp, &
	918	26.0_wp, 26.0_wp, 1.0_wp /)
[799]	919
[828]	920	ENDIF
[790]	921
[828]	922	!
	923	!-- Calculate the radius class index of particles with respect to array r0
[1822]	924	!-- The droplet radius has to be given in microns.
[828]	925	ALLOCATE( ira(1:radius_classes) )
[790]	926
[828]	927	DO j = 1, radius_classes
[1322]	928	particle_radius = radclass(j) * 1.0E6_wp
[828]	929	DO k = 1, 7
	930	IF ( particle_radius < r0(k) ) THEN
	931	ira(j) = k
	932	EXIT
	933	ENDIF
	934	ENDDO
	935	IF ( particle_radius >= r0(7) ) ira(j) = 8
	936	ENDDO
[799]	937
	938	!
[1822]	939	!-- Two-dimensional linear interpolation of the turbulent enhancement factor.
	940	!-- The droplet radius has to be given in microns.
[828]	941	DO j = 1, radius_classes
	942	DO i = 1, j
[799]	943
[828]	944	ir = ira(j)
[1519]	945	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
[799]	946
[828]	947	DO kk = 2, 11
	948	IF ( rq <= rat(kk) ) THEN
	949	iq = kk
	950	EXIT
	951	ENDIF
	952	ENDDO
[790]	953
[1822]	954	y1 = 1.0_wp ! turbulent enhancement factor at 0 m2/s3
[1007]	955
[828]	956	IF ( ir < 8 ) THEN
	957	IF ( ir >= 2 ) THEN
[1822]	958	pp = ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp - &
	959	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
[828]	960	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	961	y2 = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) * ecoll_100(ir-1,iq-1) + &
	962	pp * ( 1.0_wp - qq ) * ecoll_100(ir,iq-1) + &
	963	qq * ( 1.0_wp - pp ) * ecoll_100(ir-1,iq) + &
	964	pp * qq * ecoll_100(ir,iq)
	965	y3 = ( 1.0-pp ) * ( 1.0_wp - qq ) * ecoll_400(ir-1,iq-1) + &
	966	pp * ( 1.0_wp - qq ) * ecoll_400(ir,iq-1) + &
	967	qq * ( 1.0_wp - pp ) * ecoll_400(ir-1,iq) + &
	968	pp * qq * ecoll_400(ir,iq)
[828]	969	ELSE
	970	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	971	y2 = ( 1.0_wp - qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq)
	972	y3 = ( 1.0_wp - qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq)
[828]	973	ENDIF
	974	ELSE
	975	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	976	y2 = ( 1.0_wp - qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq)
	977	y3 = ( 1.0_wp - qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq)
[828]	978	ENDIF
	979	!
[1822]	980	!-- Linear interpolation of turbulent enhancement factor
[1359]	981	IF ( epsilon <= 0.01_wp ) THEN
	982	ecf(j,i) = ( epsilon - 0.01_wp ) / ( 0.0_wp - 0.01_wp ) * y1 &
	983	+ ( epsilon - 0.0_wp ) / ( 0.01_wp - 0.0_wp ) * y2
	984	ELSEIF ( epsilon <= 0.06_wp ) THEN
	985	ecf(j,i) = ( epsilon - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	986	+ ( epsilon - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	987	ELSE
[1359]	988	ecf(j,i) = ( 0.06_wp - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	989	+ ( 0.06_wp - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	990	ENDIF
[790]	991
[1359]	992	IF ( ecf(j,i) < 1.0_wp ) ecf(j,i) = 1.0_wp
[790]	993
[828]	994	ecf(i,j) = ecf(j,i)
[790]	995
[828]	996	ENDDO
	997	ENDDO
[790]	998
[828]	999	END SUBROUTINE turb_enhance_eff
[790]	1000
[825]	1001	END MODULE lpm_collision_kernels_mod

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