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source: palm/trunk/SOURCE/lpm_collision_kernels.f90 @ 2837

Last change on this file since 2837 was 2718, checked in by maronga, 7 years ago
deleting of deprecated files; headers updated where needed
Property svn:keywords set to `Id`
File size: 39.1 KB

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[1873]	1	!> @file lpm_collision_kernels.f90
[2000]	2	!------------------------------------------------------------------------------!
[2696]	3	! This file is part of the PALM model system.
[1036]	4	!
[2000]	5	! PALM is free software: you can redistribute it and/or modify it under the
	6	! terms of the GNU General Public License as published by the Free Software
	7	! Foundation, either version 3 of the License, or (at your option) any later
	8	! version.
[1036]	9	!
	10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
	11	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	12	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
	13	!
	14	! You should have received a copy of the GNU General Public License along with
	15	! PALM. If not, see <http://www.gnu.org/licenses/>.
	16	!
[2718]	17	! Copyright 1997-2018 Leibniz Universitaet Hannover
[2000]	18	!------------------------------------------------------------------------------!
[1036]	19	!
[790]	20	! Current revisions:
	21	! -----------------
[1347]	22	!
[2001]	23	!
[1321]	24	! Former revisions:
	25	! -----------------
	26	! $Id: lpm_collision_kernels.f90 2718 2018-01-02 08:49:38Z gronemeier $
[2716]	27	! Corrected "Former revisions" section
	28	!
	29	! 2696 2017-12-14 17:12:51Z kanani
	30	! Change in file header (GPL part)
[1321]	31	!
[2716]	32	! 2101 2017-01-05 16:42:31Z suehring
	33	!
[2001]	34	! 2000 2016-08-20 18:09:15Z knoop
	35	! Forced header and separation lines into 80 columns
	36	!
[1881]	37	! 1880 2016-04-20 09:36:50Z hoffmann
	38	! Bugfix: The index of the larger particle has to be chosen for interpolation.
	39	!
[1874]	40	! 1873 2016-04-18 14:50:06Z maronga
	41	! Module renamed (removed _mod)
	42	!
[1859]	43	! 1858 2016-04-13 13:12:11Z hoffmann
	44	! Interpolation of collision kernels adjusted to more reasonable values.
	45	! Reformatting of the code.
	46	!
[1851]	47	! 1850 2016-04-08 13:29:27Z maronga
	48	! Module renamed
	49	!
[1823]	50	! 1822 2016-04-07 07:49:42Z hoffmann
	51	! PALM kernel has been deleted.
	52	! Bugfix in the calculation of the turbulent enhancement factor of the
	53	! collection efficiency.
	54	!
	55	! Unused variables removed.
	56	!
[1777]	57	! 1776 2016-03-02 17:54:58Z hoffmann
	58	! Bugfix: Collection efficiencies must be calculated for the larger droplet.
	59	!
[1683]	60	! 1682 2015-10-07 23:56:08Z knoop
	61	! Code annotations made doxygen readable
	62	!
[1520]	63	! 1519 2015-01-08 10:20:42Z hoffmann
	64	! Bugfix: Using the new particle structure, particles are not sorted by size.
	65	! Hence, computation of collision efficiencies must ensure that the ratio of
	66	! two colliding droplets is < 1.
	67	!
[1360]	68	! 1359 2014-04-11 17:15:14Z hoffmann
	69	! New particle structure integrated.
	70	! Kind definition added to all floating point numbers.
	71	!
[1347]	72	! 1346 2014-03-27 13:18:20Z heinze
	73	! Bugfix: REAL constants provided with KIND-attribute especially in call of
	74	! intrinsic function like MAX, MIN, SIGN
	75	!
[1323]	76	! 1322 2014-03-20 16:38:49Z raasch
	77	! REAL constants defined as wp_kind
	78	!
[1321]	79	! 1320 2014-03-20 08:40:49Z
[1320]	80	! ONLY-attribute added to USE-statements,
	81	! kind-parameters added to all INTEGER and REAL declaration statements,
	82	! kinds are defined in new module kinds,
	83	! revision history before 2012 removed,
	84	! comment fields (!:) to be used for variable explanations added to
	85	! all variable declaration statements
[1008]	86	!
[1093]	87	! 1092 2013-02-02 11:24:22Z raasch
	88	! unused variables removed
	89	!
[1072]	90	! 1071 2012-11-29 16:54:55Z franke
	91	! Bugfix: collision efficiencies for Hall kernel should not be < 1.0E-20
	92	!
[1037]	93	! 1036 2012-10-22 13:43:42Z raasch
	94	! code put under GPL (PALM 3.9)
	95	!
[1008]	96	! 1007 2012-09-19 14:30:36Z franke
[1007]	97	! converted all units to SI units and replaced some parameters by corresponding
	98	! PALM parameters
	99	! Bugfix: factor in calculation of enhancement factor for collision efficencies
	100	! changed from 10. to 1.0
[829]	101	!
[850]	102	! 849 2012-03-15 10:35:09Z raasch
	103	! routine collision_efficiency_rogers added (moved from former advec_particles
	104	! to here)
	105	!
[836]	106	! 835 2012-02-22 11:21:19Z raasch $
	107	! Bugfix: array diss can be used only in case of Wang kernel
	108	!
[829]	109	! 828 2012-02-21 12:00:36Z raasch
[828]	110	! code has been completely reformatted, routine colker renamed
	111	! recalculate_kernel,
	112	! routine init_kernels added, radius is now communicated to the collision
	113	! routines by array radclass
[790]	114	!
[828]	115	! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4
	116	!
[826]	117	! 825 2012-02-19 03:03:44Z raasch
	118	! routine renamed from wang_kernel to lpm_collision_kernels,
	119	! turbulence_effects on collision replaced by wang_kernel
	120	!
[791]	121	! 790 2011-11-29 03:11:20Z raasch
	122	! initial revision
[790]	123	!
	124	! Description:
	125	! ------------
[1682]	126	!> This module calculates collision efficiencies either due to pure gravitational
	127	!> effects (Hall kernel, see Hall, 1980: J. Atmos. Sci., 2486-2507) or
[1822]	128	!> including the effects of turbulence (Wang kernel, see Wang and
	129	!> Grabowski, 2009: Atmos. Sci. Lett., 10, 1-8, and Ayala et al., 2008:
	130	!> New J. Phys., 10, 075016). The original code has been
[1682]	131	!> provided by L.-P. Wang but is substantially reformatted and speed optimized
	132	!> here.
[790]	133	!------------------------------------------------------------------------------!
[1682]	134	MODULE lpm_collision_kernels_mod
	135
[790]	136
[1320]	137	USE constants, &
	138	ONLY: pi
	139
	140	USE kinds
	141
	142	USE particle_attributes, &
[1822]	143	ONLY: collision_kernel, dissipation_classes, particles, &
	144	radius_classes
[1320]	145
[828]	146	USE pegrid
[790]	147
[828]	148
[790]	149	IMPLICIT NONE
	150
	151	PRIVATE
	152
[1822]	153	PUBLIC ckernel, init_kernels, rclass_lbound, rclass_ubound, &
	154	recalculate_kernel
[790]	155
[1682]	156	REAL(wp) :: epsilon !<
	157	REAL(wp) :: rclass_lbound !<
	158	REAL(wp) :: rclass_ubound !<
	159	REAL(wp) :: urms !<
[790]	160
[1822]	161	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !< dissipation rate class
	162	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !< radius class
	163	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !<
[1320]	164
[1822]	165	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !<
	166	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !<
	167	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !<
	168	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !<
	169	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !<
[1320]	170
[1822]	171	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !<
[792]	172
[828]	173	SAVE
[792]	174
[790]	175	!
	176	!-- Public interfaces
[828]	177	INTERFACE init_kernels
	178	MODULE PROCEDURE init_kernels
	179	END INTERFACE init_kernels
[790]	180
[828]	181	INTERFACE recalculate_kernel
	182	MODULE PROCEDURE recalculate_kernel
	183	END INTERFACE recalculate_kernel
[790]	184
	185
[828]	186	CONTAINS
[790]	187
[792]	188
[828]	189	!------------------------------------------------------------------------------!
[1682]	190	! Description:
	191	! ------------
	192	!> Initialization of the collision efficiency matrix with fixed radius and
	193	!> dissipation classes, calculated at simulation start only.
[828]	194	!------------------------------------------------------------------------------!
[1682]	195
	196	SUBROUTINE init_kernels
[792]	197
[828]	198	IMPLICIT NONE
[792]	199
[1682]	200	INTEGER(iwp) :: i !<
	201	INTEGER(iwp) :: j !<
	202	INTEGER(iwp) :: k !<
[790]	203
[828]	204
	205	!
	206	!-- Calculate collision efficiencies for fixed radius- and dissipation
	207	!-- classes
	208	IF ( collision_kernel(6:9) == 'fast' ) THEN
	209
[1822]	210	ALLOCATE( ckernel(1:radius_classes,1:radius_classes, &
	211	0:dissipation_classes), epsclass(1:dissipation_classes), &
[828]	212	radclass(1:radius_classes) )
	213
	214	!
	215	!-- Calculate the radius class bounds with logarithmic distances
[1858]	216	!-- in the interval [1.0E-6, 1000.0E-6] m
[1322]	217	rclass_lbound = LOG( 1.0E-6_wp )
[1858]	218	rclass_ubound = LOG( 1000.0E-6_wp )
[1822]	219	radclass(1) = EXP( rclass_lbound )
[828]	220	DO i = 2, radius_classes
	221	radclass(i) = EXP( rclass_lbound + &
[1359]	222	( rclass_ubound - rclass_lbound ) * &
	223	( i - 1.0_wp ) / ( radius_classes - 1.0_wp ) )
[828]	224	ENDDO
	225
	226	!
[1858]	227	!-- Set the class bounds for dissipation in interval [0.0, 600.0] cm2/s3
[828]	228	DO i = 1, dissipation_classes
[1858]	229	epsclass(i) = 0.06_wp * REAL( i, KIND=wp ) / dissipation_classes
[828]	230	ENDDO
	231	!
	232	!-- Calculate collision efficiencies of the Wang/ayala kernel
	233	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
	234	ecf(1:radius_classes,1:radius_classes), &
	235	gck(1:radius_classes,1:radius_classes), &
	236	winf(1:radius_classes) )
	237
	238	DO k = 1, dissipation_classes
	239
	240	epsilon = epsclass(k)
[1359]	241	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 1.0_wp / 3.0_wp )
[828]	242
	243	CALL turbsd
	244	CALL turb_enhance_eff
	245	CALL effic
	246
	247	DO j = 1, radius_classes
	248	DO i = 1, radius_classes
	249	ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j)
	250	ENDDO
	251	ENDDO
	252
	253	ENDDO
	254
	255	!
	256	!-- Calculate collision efficiencies of the Hall kernel
	257	ALLOCATE( hkernel(1:radius_classes,1:radius_classes), &
	258	hwratio(1:radius_classes,1:radius_classes) )
	259
	260	CALL fallg
	261	CALL effic
	262
	263	DO j = 1, radius_classes
	264	DO i = 1, radius_classes
	265	hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 &
	266	* ec(i,j) * ABS( winf(j) - winf(i) )
	267	ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0
	268	ENDDO
	269	ENDDO
	270
	271	!
	272	!-- Test output of efficiencies
	273	IF ( j == -1 ) THEN
	274
	275	PRINT, '** Hall kernel'
[1359]	276	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6_wp, &
[1007]	277	i = 1,radius_classes )
[828]	278	DO j = 1, radius_classes
[1007]	279	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
	280	( hkernel(i,j), i = 1,radius_classes )
[828]	281	ENDDO
	282
	283	DO k = 1, dissipation_classes
	284	DO i = 1, radius_classes
	285	DO j = 1, radius_classes
[1359]	286	IF ( hkernel(i,j) == 0.0_wp ) THEN
	287	hwratio(i,j) = 9999999.9_wp
[828]	288	ELSE
	289	hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j)
	290	ENDIF
	291	ENDDO
	292	ENDDO
	293
	294	PRINT, '** epsilon = ', epsclass(k)
[1359]	295	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i) 1.0E6_wp, &
[1007]	296	i = 1,radius_classes )
[828]	297	DO j = 1, radius_classes
[1359]	298	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j) 1.0E6_wp, &
[1007]	299	( hwratio(i,j), i = 1,radius_classes )
[828]	300	ENDDO
	301	ENDDO
	302
	303	ENDIF
	304
	305	DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf )
	306
	307	ENDIF
	308
	309	END SUBROUTINE init_kernels
	310
	311
[790]	312	!------------------------------------------------------------------------------!
[1682]	313	! Description:
	314	! ------------
	315	!> Calculation of collision kernels during each timestep and for each grid box
[790]	316	!------------------------------------------------------------------------------!
[828]	317	SUBROUTINE recalculate_kernel( i1, j1, k1 )
[790]	318
[1320]	319	USE arrays_3d, &
	320	ONLY: diss
[790]	321
[1320]	322	USE particle_attributes, &
[1858]	323	ONLY: number_of_particles, prt_count, radius_classes, wang_kernel
[1320]	324
[790]	325	IMPLICIT NONE
	326
[1682]	327	INTEGER(iwp) :: i !<
	328	INTEGER(iwp) :: i1 !<
	329	INTEGER(iwp) :: j !<
	330	INTEGER(iwp) :: j1 !<
	331	INTEGER(iwp) :: k1 !<
[790]	332
	333
[1858]	334	number_of_particles = prt_count(k1,j1,i1)
	335	radius_classes = number_of_particles ! necessary to use the same
	336	! subroutines as for
	337	! precalculated kernels
[792]	338
[1858]	339	ALLOCATE( ec(1:number_of_particles,1:number_of_particles), &
	340	radclass(1:number_of_particles), winf(1:number_of_particles) )
[790]	341
[828]	342	!
[1007]	343	!-- Store particle radii on the radclass array
[1858]	344	radclass(1:number_of_particles) = particles(1:number_of_particles)%radius
[790]	345
[835]	346	IF ( wang_kernel ) THEN
[1007]	347	epsilon = diss(k1,j1,i1) ! dissipation rate in m2/s3
[835]	348	ELSE
[1359]	349	epsilon = 0.0_wp
[835]	350	ENDIF
[1359]	351	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 0.33333333333_wp )
[790]	352
[1359]	353	IF ( wang_kernel .AND. epsilon > 1.0E-7_wp ) THEN
[828]	354	!
	355	!-- Call routines to calculate efficiencies for the Wang kernel
[1858]	356	ALLOCATE( gck(1:number_of_particles,1:number_of_particles), &
	357	ecf(1:number_of_particles,1:number_of_particles) )
[790]	358
[828]	359	CALL turbsd
	360	CALL turb_enhance_eff
	361	CALL effic
[790]	362
[1858]	363	DO j = 1, number_of_particles
	364	DO i = 1, number_of_particles
	365	ckernel(1+i-1,1+j-1,1) = ec(i,j) * gck(i,j) * ecf(i,j)
[790]	366	ENDDO
[828]	367	ENDDO
[790]	368
[828]	369	DEALLOCATE( gck, ecf )
[790]	370
	371	ELSE
[828]	372	!
	373	!-- Call routines to calculate efficiencies for the Hall kernel
[790]	374	CALL fallg
	375	CALL effic
	376
[1858]	377	DO j = 1, number_of_particles
	378	DO i = 1, number_of_particles
	379	ckernel(i,j,1) = pi * ( radclass(j) + radclass(i) )**2 &
	380	* ec(i,j) * ABS( winf(j) - winf(i) )
[790]	381	ENDDO
	382	ENDDO
	383
	384	ENDIF
	385
[828]	386	DEALLOCATE( ec, radclass, winf )
[790]	387
[828]	388	END SUBROUTINE recalculate_kernel
[790]	389
[828]	390
[790]	391	!------------------------------------------------------------------------------!
[1682]	392	! Description:
	393	! ------------
[1822]	394	!> Calculation of effects of turbulence on the geometric collision kernel
	395	!> (by including the droplets' average radial relative velocities and their
	396	!> radial distribution function) following the analytic model by Aayala et al.
	397	!> (2008, New J. Phys.). For details check the second part 2 of the publication,
	398	!> page 37ff.
	399	!>
	400	!> Input parameters, which need to be replaced by PALM parameters:
	401	!> water density, air density
[790]	402	!------------------------------------------------------------------------------!
[792]	403	SUBROUTINE turbsd
[799]	404
[1320]	405	USE control_parameters, &
	406	ONLY: g, molecular_viscosity
	407
	408	USE particle_attributes, &
	409	ONLY: radius_classes
[790]	410
	411	IMPLICIT NONE
	412
[1682]	413	INTEGER(iwp) :: i !<
	414	INTEGER(iwp) :: j !<
[790]	415
[1682]	416	REAL(wp) :: ao !<
	417	REAL(wp) :: ao_gr !<
	418	REAL(wp) :: bbb !<
	419	REAL(wp) :: be !<
	420	REAL(wp) :: b1 !<
	421	REAL(wp) :: b2 !<
	422	REAL(wp) :: ccc !<
	423	REAL(wp) :: c1 !<
	424	REAL(wp) :: c1_gr !<
	425	REAL(wp) :: c2 !<
	426	REAL(wp) :: d1 !<
	427	REAL(wp) :: d2 !<
	428	REAL(wp) :: eta !<
	429	REAL(wp) :: e1 !<
	430	REAL(wp) :: e2 !<
	431	REAL(wp) :: fao_gr !<
	432	REAL(wp) :: fr !<
	433	REAL(wp) :: grfin !<
	434	REAL(wp) :: lambda !<
	435	REAL(wp) :: lambda_re !<
	436	REAL(wp) :: lf !<
	437	REAL(wp) :: rc !<
	438	REAL(wp) :: rrp !<
	439	REAL(wp) :: sst !<
	440	REAL(wp) :: tauk !<
	441	REAL(wp) :: tl !<
	442	REAL(wp) :: t2 !<
	443	REAL(wp) :: tt !<
	444	REAL(wp) :: t1 !<
	445	REAL(wp) :: vk !<
	446	REAL(wp) :: vrms1xy !<
	447	REAL(wp) :: vrms2xy !<
	448	REAL(wp) :: v1 !<
	449	REAL(wp) :: v1v2xy !<
	450	REAL(wp) :: v1xysq !<
	451	REAL(wp) :: v2 !<
	452	REAL(wp) :: v2xysq !<
	453	REAL(wp) :: wrfin !<
	454	REAL(wp) :: wrgrav2 !<
	455	REAL(wp) :: wrtur2xy !<
	456	REAL(wp) :: xx !<
	457	REAL(wp) :: yy !<
	458	REAL(wp) :: z !<
[790]	459
[1822]	460	REAL(wp), DIMENSION(1:radius_classes) :: st !< Stokes number
	461	REAL(wp), DIMENSION(1:radius_classes) :: tau !< inertial time scale
[790]	462
[1822]	463	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon )
[1322]	464	lambda_re = urms*2 SQRT( 15.0_wp / epsilon / molecular_viscosity )
[1822]	465	tl = urms**2 / epsilon
	466	lf = 0.5_wp * urms**3 / epsilon
	467	tauk = SQRT( molecular_viscosity / epsilon )
	468	eta = ( molecular_viscosity3 / epsilon )0.25_wp
[1007]	469	vk = eta / tauk
[790]	470
[1359]	471	ao = ( 11.0_wp + 7.0_wp * lambda_re ) / ( 205.0_wp + lambda_re )
[1822]	472	tt = SQRT( 2.0_wp * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk
[799]	473
[1822]	474	!
	475	!-- Get terminal velocity of droplets
	476	CALL fallg
[790]	477
[828]	478	DO i = 1, radius_classes
[1822]	479	tau(i) = winf(i) / g ! inertial time scale
	480	st(i) = tau(i) / tauk ! Stokes number
[790]	481	ENDDO
	482
[828]	483	!
[1822]	484	!-- Calculate average radial relative velocity at contact (wrfin)
[828]	485	z = tt / tl
[1322]	486	be = SQRT( 2.0_wp ) * lambda / lf
[1359]	487	bbb = SQRT( 1.0_wp - 2.0_wp * be**2 )
	488	d1 = ( 1.0_wp + bbb ) / ( 2.0_wp * bbb )
[1822]	489	e1 = lf * ( 1.0_wp + bbb ) * 0.5_wp
[1359]	490	d2 = ( 1.0_wp - bbb ) * 0.5_wp / bbb
[1822]	491	e2 = lf * ( 1.0_wp - bbb ) * 0.5_wp
[1359]	492	ccc = SQRT( 1.0_wp - 2.0_wp * z**2 )
	493	b1 = ( 1.0_wp + ccc ) * 0.5_wp / ccc
[1822]	494	c1 = tl * ( 1.0_wp + ccc ) * 0.5_wp
[1359]	495	b2 = ( 1.0_wp - ccc ) * 0.5_wp / ccc
[1822]	496	c2 = tl * ( 1.0_wp - ccc ) * 0.5_wp
[790]	497
[828]	498	DO i = 1, radius_classes
[790]	499
[1822]	500	v1 = winf(i)
	501	t1 = tau(i)
[790]	502
[828]	503	DO j = 1, i
[1007]	504	rrp = radclass(i) + radclass(j)
[1822]	505	v2 = winf(j)
	506	t2 = tau(j)
[790]	507
[1007]	508	v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) &
	509	- b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1)
[1822]	510	v1xysq = v1xysq * urms**2 / t1
	511	vrms1xy = SQRT( v1xysq )
[790]	512
[1007]	513	v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) &
	514	- b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2)
[1822]	515	v2xysq = v2xysq * urms**2 / t2
	516	vrms2xy = SQRT( v2xysq )
[790]	517
[828]	518	IF ( winf(i) >= winf(j) ) THEN
[799]	519	v1 = winf(i)
[790]	520	t1 = tau(i)
[799]	521	v2 = winf(j)
[790]	522	t2 = tau(j)
	523	ELSE
[799]	524	v1 = winf(j)
[790]	525	t1 = tau(j)
[799]	526	v2 = winf(i)
[790]	527	t2 = tau(i)
	528	ENDIF
	529
[828]	530	v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - &
	531	b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - &
	532	b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + &
	533	b2 * d2* zhi(c2,e2,v1,t1,v2,t2)
	534	fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 )
[1822]	535	v1v2xy = v1v2xy * fr * urms**2 / tau(i) / tau(j)
	536	wrtur2xy = vrms1xy2 + vrms2xy2 - 2.0_wp * v1v2xy
[1359]	537	IF ( wrtur2xy < 0.0_wp ) wrtur2xy = 0.0_wp
[1322]	538	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
[1822]	539	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) )
[790]	540
[828]	541	!
[1822]	542	!-- Calculate radial distribution function (grfin)
[828]	543	IF ( st(j) > st(i) ) THEN
	544	sst = st(j)
[790]	545	ELSE
[828]	546	sst = st(i)
[790]	547	ENDIF
	548
[1359]	549	xx = -0.1988_wp * sst*4 + 1.5275_wp sst*3 - 4.2942_wp &
	550	sst*2 + 5.3406_wp sst
	551	IF ( xx < 0.0_wp ) xx = 0.0_wp
	552	yy = 0.1886_wp * EXP( 20.306_wp / lambda_re )
[790]	553
[1007]	554	c1_gr = xx / ( g / vk * tauk )**yy
[790]	555
[1322]	556	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
[1359]	557	fao_gr = 20.115_wp * SQRT( ao_gr / lambda_re )
[1822]	558	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta
[790]	559
[1359]	560	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5_wp )
	561	IF ( grfin < 1.0_wp ) grfin = 1.0_wp
[790]	562
[1822]	563	!
	564	!-- Calculate general collection kernel (without the consideration of
	565	!-- collection efficiencies)
	566	gck(i,j) = 2.0_wp * pi * rrp*2 wrfin * grfin
[790]	567	gck(j,i) = gck(i,j)
	568
	569	ENDDO
	570	ENDDO
	571
[828]	572	END SUBROUTINE turbsd
[790]	573
[1320]	574	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
[1822]	575	!
	576	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
	577	!-- effects on the collision kernel
[790]	578	IMPLICIT NONE
	579
[1682]	580	REAL(wp) :: a !<
	581	REAL(wp) :: aa1 !<
	582	REAL(wp) :: b !<
	583	REAL(wp) :: tau0 !<
	584	REAL(wp) :: vsett !<
[790]	585
[1359]	586	aa1 = 1.0_wp / tau0 + 1.0_wp / a + vsett / b
[1822]	587	phi_w = 1.0_wp / aa1 - 0.5_wp * vsett / b / aa1**2
[790]	588
[1007]	589	END FUNCTION phi_w
[792]	590
[1320]	591	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
[1822]	592	!
	593	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
	594	!-- effects on the collision kernel
[790]	595	IMPLICIT NONE
	596
[1682]	597	REAL(wp) :: a !<
	598	REAL(wp) :: aa1 !<
	599	REAL(wp) :: aa2 !<
	600	REAL(wp) :: aa3 !<
	601	REAL(wp) :: aa4 !<
	602	REAL(wp) :: aa5 !<
	603	REAL(wp) :: aa6 !<
	604	REAL(wp) :: b !<
	605	REAL(wp) :: tau1 !<
	606	REAL(wp) :: tau2 !<
	607	REAL(wp) :: vsett1 !<
	608	REAL(wp) :: vsett2 !<
[790]	609
[1359]	610	aa1 = vsett2 / b - 1.0_wp / tau2 - 1.0_wp / a
	611	aa2 = vsett1 / b + 1.0_wp / tau1 + 1.0_wp / a
	612	aa3 = ( vsett1 - vsett2 ) / b + 1.0_wp / tau1 + 1.0_wp / tau2
	613	aa4 = ( vsett2 / b )2 - ( 1.0_wp / tau2 + 1.0_wp / a )2
	614	aa5 = vsett2 / b + 1.0_wp / tau2 + 1.0_wp / a
	615	aa6 = 1.0_wp / tau1 - 1.0_wp / a + ( 1.0_wp / tau2 + 1.0_wp / a) * &
	616	vsett1 / vsett2
	617	zhi = (1.0_wp / aa1 - 1.0_wp / aa2 ) * ( vsett1 - vsett2 ) * 0.5_wp / &
	618	b / aa32 + ( 4.0_wp / aa4 - 1.0_wp / aa52 - 1.0_wp / aa1**2 ) &
	619	* vsett2 * 0.5_wp / b /aa6 + ( 2.0_wp * ( b / aa2 - b / aa1 ) - &
[1822]	620	vsett1 / aa22 + vsett2 / aa12 ) * 0.5_wp / b / aa3
[799]	621
[828]	622	END FUNCTION zhi
[790]	623
[828]	624
[790]	625	!------------------------------------------------------------------------------!
[1682]	626	! Description:
	627	! ------------
[1822]	628	!> Parameterization of terminal velocity following Rogers et al. (1993, J. Appl.
	629	!> Meteorol.)
[790]	630	!------------------------------------------------------------------------------!
[828]	631	SUBROUTINE fallg
[790]	632
[1320]	633	USE particle_attributes, &
	634	ONLY: radius_classes
[790]	635
[828]	636	IMPLICIT NONE
[790]	637
[1822]	638	INTEGER(iwp) :: j !<
[790]	639
[1822]	640	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter
	641	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter
	642	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter
	643	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter
	644	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter
	645	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< seperation diameter
[790]	646
[1822]	647	REAL(wp) :: diameter !< droplet diameter in mm
[790]	648
[799]	649
[828]	650	DO j = 1, radius_classes
[790]	651
[1822]	652	diameter = radclass(j) * 2000.0_wp
[799]	653
[1822]	654	IF ( diameter <= d0_rog ) THEN
	655	winf(j) = k_cap_rog * diameter * ( 1.0_wp - &
	656	EXP( -k_low_rog * diameter ) )
	657	ELSE
	658	winf(j) = a_rog - b_rog * EXP( -c_rog * diameter )
[828]	659	ENDIF
[790]	660
[828]	661	ENDDO
[790]	662
[828]	663	END SUBROUTINE fallg
[790]	664
[828]	665
[790]	666	!------------------------------------------------------------------------------!
[1682]	667	! Description:
	668	! ------------
[1822]	669	!> Interpolation of collision efficiencies (Hall, 1980, J. Atmos. Sci.)
[790]	670	!------------------------------------------------------------------------------!
[828]	671	SUBROUTINE effic
[1320]	672
	673	USE particle_attributes, &
	674	ONLY: radius_classes
[790]	675
[828]	676	IMPLICIT NONE
[790]	677
[1682]	678	INTEGER(iwp) :: i !<
	679	INTEGER(iwp) :: iq !<
	680	INTEGER(iwp) :: ir !<
	681	INTEGER(iwp) :: j !<
	682	INTEGER(iwp) :: k !<
[790]	683
[1682]	684	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
[790]	685
[1682]	686	LOGICAL, SAVE :: first = .TRUE. !<
[790]	687
[1682]	688	REAL(wp) :: ek !<
	689	REAL(wp) :: particle_radius !<
	690	REAL(wp) :: pp !<
	691	REAL(wp) :: qq !<
	692	REAL(wp) :: rq !<
[790]	693
[1682]	694	REAL(wp), DIMENSION(1:21), SAVE :: rat !<
[1320]	695
[1682]	696	REAL(wp), DIMENSION(1:15), SAVE :: r0 !<
[1320]	697
[1682]	698	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !<
[790]	699
[792]	700	!
[828]	701	!-- Initial assignment of constants
	702	IF ( first ) THEN
[790]	703
[792]	704	first = .FALSE.
[1822]	705	r0 = (/ 6.0_wp, 8.0_wp, 10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp, &
	706	30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, 70.0_wp, 100.0_wp, &
[1359]	707	150.0_wp, 200.0_wp, 300.0_wp /)
[790]	708
[1822]	709	rat = (/ 0.00_wp, 0.05_wp, 0.10_wp, 0.15_wp, 0.20_wp, 0.25_wp, &
	710	0.30_wp, 0.35_wp, 0.40_wp, 0.45_wp, 0.50_wp, 0.55_wp, &
	711	0.60_wp, 0.65_wp, 0.70_wp, 0.75_wp, 0.80_wp, 0.85_wp, &
[1359]	712	0.90_wp, 0.95_wp, 1.00_wp /)
	713
[1822]	714	ecoll(:,1) = (/ 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
	715	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
[1359]	716	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp /)
[1822]	717	ecoll(:,2) = (/ 0.003_wp, 0.003_wp, 0.003_wp, 0.004_wp, 0.005_wp, &
	718	0.005_wp, 0.005_wp, 0.010_wp, 0.100_wp, 0.050_wp, &
[1359]	719	0.200_wp, 0.500_wp, 0.770_wp, 0.870_wp, 0.970_wp /)
[1822]	720	ecoll(:,3) = (/ 0.007_wp, 0.007_wp, 0.007_wp, 0.008_wp, 0.009_wp, &
	721	0.010_wp, 0.010_wp, 0.070_wp, 0.400_wp, 0.430_wp, &
[1359]	722	0.580_wp, 0.790_wp, 0.930_wp, 0.960_wp, 1.000_wp /)
[1822]	723	ecoll(:,4) = (/ 0.009_wp, 0.009_wp, 0.009_wp, 0.012_wp, 0.015_wp, &
	724	0.010_wp, 0.020_wp, 0.280_wp, 0.600_wp, 0.640_wp, &
[1359]	725	0.750_wp, 0.910_wp, 0.970_wp, 0.980_wp, 1.000_wp /)
[1822]	726	ecoll(:,5) = (/ 0.014_wp, 0.014_wp, 0.014_wp, 0.015_wp, 0.016_wp, &
	727	0.030_wp, 0.060_wp, 0.500_wp, 0.700_wp, 0.770_wp, &
[1359]	728	0.840_wp, 0.950_wp, 0.970_wp, 1.000_wp, 1.000_wp /)
[1822]	729	ecoll(:,6) = (/ 0.017_wp, 0.017_wp, 0.017_wp, 0.020_wp, 0.022_wp, &
	730	0.060_wp, 0.100_wp, 0.620_wp, 0.780_wp, 0.840_wp, &
[1359]	731	0.880_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	732	ecoll(:,7) = (/ 0.030_wp, 0.030_wp, 0.024_wp, 0.022_wp, 0.032_wp, &
	733	0.062_wp, 0.200_wp, 0.680_wp, 0.830_wp, 0.870_wp, &
[1359]	734	0.900_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	735	ecoll(:,8) = (/ 0.025_wp, 0.025_wp, 0.025_wp, 0.036_wp, 0.043_wp, &
	736	0.130_wp, 0.270_wp, 0.740_wp, 0.860_wp, 0.890_wp, &
[1359]	737	0.920_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	738	ecoll(:,9) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.040_wp, 0.052_wp, &
	739	0.200_wp, 0.400_wp, 0.780_wp, 0.880_wp, 0.900_wp, &
[1359]	740	0.940_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	741	ecoll(:,10) = (/ 0.030_wp, 0.030_wp, 0.030_wp, 0.047_wp, 0.064_wp, &
	742	0.250_wp, 0.500_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
[1359]	743	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	744	ecoll(:,11) = (/ 0.040_wp, 0.040_wp, 0.033_wp, 0.037_wp, 0.068_wp, &
	745	0.240_wp, 0.550_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
[1359]	746	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	747	ecoll(:,12) = (/ 0.035_wp, 0.035_wp, 0.035_wp, 0.055_wp, 0.079_wp, &
	748	0.290_wp, 0.580_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
[1359]	749	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	750	ecoll(:,13) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.062_wp, 0.082_wp, &
	751	0.290_wp, 0.590_wp, 0.780_wp, 0.900_wp, 0.910_wp, &
[1359]	752	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	753	ecoll(:,14) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.060_wp, 0.080_wp, &
	754	0.290_wp, 0.580_wp, 0.770_wp, 0.890_wp, 0.910_wp, &
[1359]	755	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	756	ecoll(:,15) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.041_wp, 0.075_wp, &
	757	0.250_wp, 0.540_wp, 0.760_wp, 0.880_wp, 0.920_wp, &
[1359]	758	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	759	ecoll(:,16) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.052_wp, 0.067_wp, &
	760	0.250_wp, 0.510_wp, 0.770_wp, 0.880_wp, 0.930_wp, &
[1359]	761	0.970_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	762	ecoll(:,17) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.047_wp, 0.057_wp, &
	763	0.250_wp, 0.490_wp, 0.770_wp, 0.890_wp, 0.950_wp, &
[1359]	764	1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	765	ecoll(:,18) = (/ 0.036_wp, 0.036_wp, 0.036_wp, 0.042_wp, 0.048_wp, &
	766	0.230_wp, 0.470_wp, 0.780_wp, 0.920_wp, 1.000_wp, &
[1359]	767	1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp /)
[1822]	768	ecoll(:,19) = (/ 0.040_wp, 0.040_wp, 0.035_wp, 0.033_wp, 0.040_wp, &
	769	0.112_wp, 0.450_wp, 0.790_wp, 1.010_wp, 1.030_wp, &
[1359]	770	1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp /)
[1822]	771	ecoll(:,20) = (/ 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, &
	772	0.119_wp, 0.470_wp, 0.950_wp, 1.300_wp, 1.700_wp, &
[1359]	773	2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp /)
[1822]	774	ecoll(:,21) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, &
	775	0.125_wp, 0.520_wp, 1.400_wp, 2.300_wp, 3.000_wp, &
[1359]	776	4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp /)
[828]	777	ENDIF
[790]	778
[792]	779	!
[828]	780	!-- Calculate the radius class index of particles with respect to array r
[1822]	781	!-- Radius has to be in microns
[828]	782	ALLOCATE( ira(1:radius_classes) )
	783	DO j = 1, radius_classes
[1322]	784	particle_radius = radclass(j) * 1.0E6_wp
[828]	785	DO k = 1, 15
	786	IF ( particle_radius < r0(k) ) THEN
	787	ira(j) = k
	788	EXIT
	789	ENDIF
	790	ENDDO
	791	IF ( particle_radius >= r0(15) ) ira(j) = 16
	792	ENDDO
[790]	793
[792]	794	!
[828]	795	!-- Two-dimensional linear interpolation of the collision efficiency.
[1822]	796	!-- Radius has to be in microns
[828]	797	DO j = 1, radius_classes
	798	DO i = 1, j
[792]	799
[1880]	800	ir = MAX( ira(i), ira(j) )
[1519]	801	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
[828]	802	iq = INT( rq * 20 ) + 1
	803	iq = MAX( iq , 2)
[792]	804
[828]	805	IF ( ir < 16 ) THEN
	806	IF ( ir >= 2 ) THEN
[1822]	807	pp = ( ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp ) - &
	808	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
[1359]	809	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	810	ec(j,i) = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) &
	811	* ecoll(ir-1,iq-1) &
	812	+ pp * ( 1.0_wp - qq ) * ecoll(ir,iq-1) &
	813	+ qq * ( 1.0_wp - pp ) * ecoll(ir-1,iq) &
[828]	814	+ pp * qq * ecoll(ir,iq)
	815	ELSE
	816	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	817	ec(j,i) = ( 1.0_wp - qq ) * ecoll(1,iq-1) + qq * ecoll(1,iq)
[828]	818	ENDIF
	819	ELSE
	820	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	821	ek = ( 1.0_wp - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
[1346]	822	ec(j,i) = MIN( ek, 1.0_wp )
[1071]	823	ENDIF
[792]	824
[1359]	825	IF ( ec(j,i) < 1.0E-20_wp ) ec(j,i) = 0.0_wp
[1071]	826
[828]	827	ec(i,j) = ec(j,i)
[792]	828
[828]	829	ENDDO
	830	ENDDO
[792]	831
[828]	832	DEALLOCATE( ira )
[792]	833
[828]	834	END SUBROUTINE effic
[792]	835
	836
[790]	837	!------------------------------------------------------------------------------!
[1682]	838	! Description:
	839	! ------------
[1822]	840	!> Interpolation of turbulent enhancement factor for collision efficencies
	841	!> following Wang and Grabowski (2009, Atmos. Sci. Let.)
[790]	842	!------------------------------------------------------------------------------!
[828]	843	SUBROUTINE turb_enhance_eff
[790]	844
[1320]	845	USE particle_attributes, &
	846	ONLY: radius_classes
[790]	847
[828]	848	IMPLICIT NONE
[790]	849
[1682]	850	INTEGER(iwp) :: i !<
	851	INTEGER(iwp) :: iq !<
	852	INTEGER(iwp) :: ir !<
	853	INTEGER(iwp) :: j !<
	854	INTEGER(iwp) :: k !<
	855	INTEGER(iwp) :: kk !<
[790]	856
[1682]	857	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
[1320]	858
[1682]	859	LOGICAL, SAVE :: first = .TRUE. !<
[790]	860
[1682]	861	REAL(wp) :: particle_radius !<
	862	REAL(wp) :: pp !<
	863	REAL(wp) :: qq !<
	864	REAL(wp) :: rq !<
	865	REAL(wp) :: y1 !<
	866	REAL(wp) :: y2 !<
	867	REAL(wp) :: y3 !<
[790]	868
[1682]	869	REAL(wp), DIMENSION(1:11), SAVE :: rat !<
	870	REAL(wp), DIMENSION(1:7), SAVE :: r0 !<
[1320]	871
[1682]	872	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !<
	873	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !<
[799]	874
	875	!
[828]	876	!-- Initial assignment of constants
	877	IF ( first ) THEN
[799]	878
[828]	879	first = .FALSE.
[799]	880
[1359]	881	r0 = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, &
	882	100.0_wp /)
	883
	884	rat = (/ 0.0_wp, 0.1_wp, 0.2_wp, 0.3_wp, 0.4_wp, 0.5_wp, 0.6_wp, &
	885	0.7_wp, 0.8_wp, 0.9_wp, 1.0_wp /)
[828]	886	!
[1822]	887	!-- Tabulated turbulent enhancement factor at 100 cm2/s3
[1359]	888	ecoll_100(:,1) = (/ 1.74_wp, 1.74_wp, 1.773_wp, 1.49_wp, &
	889	1.207_wp, 1.207_wp, 1.0_wp /)
	890	ecoll_100(:,2) = (/ 1.46_wp, 1.46_wp, 1.421_wp, 1.245_wp, &
	891	1.069_wp, 1.069_wp, 1.0_wp /)
	892	ecoll_100(:,3) = (/ 1.32_wp, 1.32_wp, 1.245_wp, 1.123_wp, &
	893	1.000_wp, 1.000_wp, 1.0_wp /)
	894	ecoll_100(:,4) = (/ 1.250_wp, 1.250_wp, 1.148_wp, 1.087_wp, &
	895	1.025_wp, 1.025_wp, 1.0_wp /)
	896	ecoll_100(:,5) = (/ 1.186_wp, 1.186_wp, 1.066_wp, 1.060_wp, &
	897	1.056_wp, 1.056_wp, 1.0_wp /)
	898	ecoll_100(:,6) = (/ 1.045_wp, 1.045_wp, 1.000_wp, 1.014_wp, &
	899	1.028_wp, 1.028_wp, 1.0_wp /)
	900	ecoll_100(:,7) = (/ 1.070_wp, 1.070_wp, 1.030_wp, 1.038_wp, &
	901	1.046_wp, 1.046_wp, 1.0_wp /)
	902	ecoll_100(:,8) = (/ 1.000_wp, 1.000_wp, 1.054_wp, 1.042_wp, &
	903	1.029_wp, 1.029_wp, 1.0_wp /)
	904	ecoll_100(:,9) = (/ 1.223_wp, 1.223_wp, 1.117_wp, 1.069_wp, &
	905	1.021_wp, 1.021_wp, 1.0_wp /)
	906	ecoll_100(:,10) = (/ 1.570_wp, 1.570_wp, 1.244_wp, 1.166_wp, &
	907	1.088_wp, 1.088_wp, 1.0_wp /)
[1822]	908	ecoll_100(:,11) = (/ 20.3_wp, 20.3_wp, 14.6_wp, 8.61_wp, &
[1359]	909	2.60_wp, 2.60_wp, 1.0_wp /)
[828]	910	!
[1822]	911	!-- Tabulated turbulent enhancement factor at 400 cm2/s3
[1359]	912	ecoll_400(:,1) = (/ 4.976_wp, 4.976_wp, 3.593_wp, 2.519_wp, &
	913	1.445_wp, 1.445_wp, 1.0_wp /)
	914	ecoll_400(:,2) = (/ 2.984_wp, 2.984_wp, 2.181_wp, 1.691_wp, &
	915	1.201_wp, 1.201_wp, 1.0_wp /)
	916	ecoll_400(:,3) = (/ 1.988_wp, 1.988_wp, 1.475_wp, 1.313_wp, &
	917	1.150_wp, 1.150_wp, 1.0_wp /)
	918	ecoll_400(:,4) = (/ 1.490_wp, 1.490_wp, 1.187_wp, 1.156_wp, &
	919	1.126_wp, 1.126_wp, 1.0_wp /)
	920	ecoll_400(:,5) = (/ 1.249_wp, 1.249_wp, 1.088_wp, 1.090_wp, &
	921	1.092_wp, 1.092_wp, 1.0_wp /)
	922	ecoll_400(:,6) = (/ 1.139_wp, 1.139_wp, 1.130_wp, 1.091_wp, &
	923	1.051_wp, 1.051_wp, 1.0_wp /)
	924	ecoll_400(:,7) = (/ 1.220_wp, 1.220_wp, 1.190_wp, 1.138_wp, &
	925	1.086_wp, 1.086_wp, 1.0_wp /)
	926	ecoll_400(:,8) = (/ 1.325_wp, 1.325_wp, 1.267_wp, 1.165_wp, &
	927	1.063_wp, 1.063_wp, 1.0_wp /)
	928	ecoll_400(:,9) = (/ 1.716_wp, 1.716_wp, 1.345_wp, 1.223_wp, &
	929	1.100_wp, 1.100_wp, 1.0_wp /)
	930	ecoll_400(:,10) = (/ 3.788_wp, 3.788_wp, 1.501_wp, 1.311_wp, &
	931	1.120_wp, 1.120_wp, 1.0_wp /)
	932	ecoll_400(:,11) = (/ 36.52_wp, 36.52_wp, 19.16_wp, 22.80_wp, &
	933	26.0_wp, 26.0_wp, 1.0_wp /)
[799]	934
[828]	935	ENDIF
[790]	936
[828]	937	!
	938	!-- Calculate the radius class index of particles with respect to array r0
[1822]	939	!-- The droplet radius has to be given in microns.
[828]	940	ALLOCATE( ira(1:radius_classes) )
[790]	941
[828]	942	DO j = 1, radius_classes
[1322]	943	particle_radius = radclass(j) * 1.0E6_wp
[828]	944	DO k = 1, 7
	945	IF ( particle_radius < r0(k) ) THEN
	946	ira(j) = k
	947	EXIT
	948	ENDIF
	949	ENDDO
	950	IF ( particle_radius >= r0(7) ) ira(j) = 8
	951	ENDDO
[799]	952
	953	!
[1822]	954	!-- Two-dimensional linear interpolation of the turbulent enhancement factor.
	955	!-- The droplet radius has to be given in microns.
[828]	956	DO j = 1, radius_classes
	957	DO i = 1, j
[799]	958
[1880]	959	ir = MAX( ira(i), ira(j) )
[1519]	960	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
[799]	961
[828]	962	DO kk = 2, 11
	963	IF ( rq <= rat(kk) ) THEN
	964	iq = kk
	965	EXIT
	966	ENDIF
	967	ENDDO
[790]	968
[1822]	969	y1 = 1.0_wp ! turbulent enhancement factor at 0 m2/s3
[1007]	970
[828]	971	IF ( ir < 8 ) THEN
	972	IF ( ir >= 2 ) THEN
[1822]	973	pp = ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp - &
	974	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
[828]	975	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	976	y2 = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) * ecoll_100(ir-1,iq-1) + &
	977	pp * ( 1.0_wp - qq ) * ecoll_100(ir,iq-1) + &
	978	qq * ( 1.0_wp - pp ) * ecoll_100(ir-1,iq) + &
	979	pp * qq * ecoll_100(ir,iq)
	980	y3 = ( 1.0-pp ) * ( 1.0_wp - qq ) * ecoll_400(ir-1,iq-1) + &
	981	pp * ( 1.0_wp - qq ) * ecoll_400(ir,iq-1) + &
	982	qq * ( 1.0_wp - pp ) * ecoll_400(ir-1,iq) + &
	983	pp * qq * ecoll_400(ir,iq)
[828]	984	ELSE
	985	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	986	y2 = ( 1.0_wp - qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq)
	987	y3 = ( 1.0_wp - qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq)
[828]	988	ENDIF
	989	ELSE
	990	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	991	y2 = ( 1.0_wp - qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq)
	992	y3 = ( 1.0_wp - qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq)
[828]	993	ENDIF
	994	!
[1822]	995	!-- Linear interpolation of turbulent enhancement factor
[1359]	996	IF ( epsilon <= 0.01_wp ) THEN
	997	ecf(j,i) = ( epsilon - 0.01_wp ) / ( 0.0_wp - 0.01_wp ) * y1 &
	998	+ ( epsilon - 0.0_wp ) / ( 0.01_wp - 0.0_wp ) * y2
	999	ELSEIF ( epsilon <= 0.06_wp ) THEN
	1000	ecf(j,i) = ( epsilon - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	1001	+ ( epsilon - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	1002	ELSE
[1359]	1003	ecf(j,i) = ( 0.06_wp - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	1004	+ ( 0.06_wp - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	1005	ENDIF
[790]	1006
[1359]	1007	IF ( ecf(j,i) < 1.0_wp ) ecf(j,i) = 1.0_wp
[790]	1008
[828]	1009	ecf(i,j) = ecf(j,i)
[790]	1010
[828]	1011	ENDDO
	1012	ENDDO
[790]	1013
[828]	1014	END SUBROUTINE turb_enhance_eff
[790]	1015
[825]	1016	END MODULE lpm_collision_kernels_mod

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