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source: palm/trunk/SOURCE/lpm_collision_kernels.f90 @ 1776

Last change on this file since 1776 was 1776, checked in by hoffmann, 8 years ago
Bugfix in computation of collection efficiencies
Property svn:keywords set to `Id`
File size: 46.9 KB

Rev	Line
[1682]	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	!
[1310]	16	! Copyright 1997-2014 Leibniz Universitaet Hannover
[1036]	17	!--------------------------------------------------------------------------------!
	18	!
[790]	19	! Current revisions:
	20	! -----------------
[1776]	21	! Bugfix: Collection efficiencies must be calculated for the larger droplet.
[1347]	22	!
[1321]	23	! Former revisions:
	24	! -----------------
	25	! $Id: lpm_collision_kernels.f90 1776 2016-03-02 17:54:58Z hoffmann $
	26	!
[1683]	27	! 1682 2015-10-07 23:56:08Z knoop
	28	! Code annotations made doxygen readable
	29	!
[1520]	30	! 1519 2015-01-08 10:20:42Z hoffmann
	31	! Bugfix: Using the new particle structure, particles are not sorted by size.
	32	! Hence, computation of collision efficiencies must ensure that the ratio of
	33	! two colliding droplets is < 1.
	34	!
[1360]	35	! 1359 2014-04-11 17:15:14Z hoffmann
	36	! New particle structure integrated.
	37	! Kind definition added to all floating point numbers.
	38	!
[1347]	39	! 1346 2014-03-27 13:18:20Z heinze
	40	! Bugfix: REAL constants provided with KIND-attribute especially in call of
	41	! intrinsic function like MAX, MIN, SIGN
	42	!
[1323]	43	! 1322 2014-03-20 16:38:49Z raasch
	44	! REAL constants defined as wp_kind
	45	!
[1321]	46	! 1320 2014-03-20 08:40:49Z
[1320]	47	! ONLY-attribute added to USE-statements,
	48	! kind-parameters added to all INTEGER and REAL declaration statements,
	49	! kinds are defined in new module kinds,
	50	! revision history before 2012 removed,
	51	! comment fields (!:) to be used for variable explanations added to
	52	! all variable declaration statements
[1008]	53	!
[1093]	54	! 1092 2013-02-02 11:24:22Z raasch
	55	! unused variables removed
	56	!
[1072]	57	! 1071 2012-11-29 16:54:55Z franke
	58	! Bugfix: collision efficiencies for Hall kernel should not be < 1.0E-20
	59	!
[1037]	60	! 1036 2012-10-22 13:43:42Z raasch
	61	! code put under GPL (PALM 3.9)
	62	!
[1008]	63	! 1007 2012-09-19 14:30:36Z franke
[1007]	64	! converted all units to SI units and replaced some parameters by corresponding
	65	! PALM parameters
	66	! Bugfix: factor in calculation of enhancement factor for collision efficencies
	67	! changed from 10. to 1.0
[829]	68	!
[850]	69	! 849 2012-03-15 10:35:09Z raasch
	70	! routine collision_efficiency_rogers added (moved from former advec_particles
	71	! to here)
	72	!
[836]	73	! 835 2012-02-22 11:21:19Z raasch $
	74	! Bugfix: array diss can be used only in case of Wang kernel
	75	!
[829]	76	! 828 2012-02-21 12:00:36Z raasch
[828]	77	! code has been completely reformatted, routine colker renamed
	78	! recalculate_kernel,
	79	! routine init_kernels added, radius is now communicated to the collision
	80	! routines by array radclass
[790]	81	!
[828]	82	! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4
	83	!
[826]	84	! 825 2012-02-19 03:03:44Z raasch
	85	! routine renamed from wang_kernel to lpm_collision_kernels,
	86	! turbulence_effects on collision replaced by wang_kernel
	87	!
[791]	88	! 790 2011-11-29 03:11:20Z raasch
	89	! initial revision
[790]	90	!
	91	! Description:
	92	! ------------
[1682]	93	!> This module calculates collision efficiencies either due to pure gravitational
	94	!> effects (Hall kernel, see Hall, 1980: J. Atmos. Sci., 2486-2507) or
	95	!> including the effects of (SGS) turbulence (Wang kernel, see Wang and
	96	!> Grabowski, 2009: Atmos. Sci. Lett., 10, 1-8). The original code has been
	97	!> provided by L.-P. Wang but is substantially reformatted and speed optimized
	98	!> here.
	99	!>
	100	!> @attention Physical quantities (like g, densities, etc.) used in this module
	101	!> still have to be adjusted to those values used in the main PALM code.
	102	!> Also, quantities in CGS-units should be converted to SI-units eventually.
[790]	103	!------------------------------------------------------------------------------!
[1682]	104	MODULE lpm_collision_kernels_mod
	105
[790]	106
[1320]	107	USE constants, &
	108	ONLY: pi
	109
	110	USE kinds
	111
	112	USE particle_attributes, &
	113	ONLY: collision_kernel, dissipation_classes, particles, radius_classes
	114
[828]	115	USE pegrid
[790]	116
[828]	117
[790]	118	IMPLICIT NONE
	119
	120	PRIVATE
	121
[849]	122	PUBLIC ckernel, collision_efficiency_rogers, init_kernels, &
[1007]	123	rclass_lbound, rclass_ubound, recalculate_kernel
[790]	124
[1682]	125	REAL(wp) :: epsilon !<
	126	REAL(wp) :: eps2 !<
	127	REAL(wp) :: rclass_lbound !<
	128	REAL(wp) :: rclass_ubound !<
	129	REAL(wp) :: urms !<
	130	REAL(wp) :: urms2 !<
[790]	131
[1682]	132	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !<
	133	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !<
	134	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !<
[1320]	135
[1682]	136	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !<
	137	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !<
	138	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !<
	139	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !<
	140	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !<
[1320]	141
[1682]	142	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !<
[792]	143
[828]	144	SAVE
[792]	145
[790]	146	!
	147	!-- Public interfaces
[849]	148	INTERFACE collision_efficiency_rogers
	149	MODULE PROCEDURE collision_efficiency_rogers
	150	END INTERFACE collision_efficiency_rogers
	151
[828]	152	INTERFACE init_kernels
	153	MODULE PROCEDURE init_kernels
	154	END INTERFACE init_kernels
[790]	155
[828]	156	INTERFACE recalculate_kernel
	157	MODULE PROCEDURE recalculate_kernel
	158	END INTERFACE recalculate_kernel
[790]	159
	160
[828]	161	CONTAINS
[790]	162
[792]	163
[828]	164	!------------------------------------------------------------------------------!
[1682]	165	! Description:
	166	! ------------
	167	!> Initialization of the collision efficiency matrix with fixed radius and
	168	!> dissipation classes, calculated at simulation start only.
[828]	169	!------------------------------------------------------------------------------!
[1682]	170
	171	SUBROUTINE init_kernels
[792]	172
[828]	173	IMPLICIT NONE
[792]	174
[1682]	175	INTEGER(iwp) :: i !<
	176	INTEGER(iwp) :: j !<
	177	INTEGER(iwp) :: k !<
[790]	178
[828]	179
	180	!
	181	!-- Calculate collision efficiencies for fixed radius- and dissipation
	182	!-- classes
	183	IF ( collision_kernel(6:9) == 'fast' ) THEN
	184
	185	ALLOCATE( ckernel(1:radius_classes,1:radius_classes, &
	186	0:dissipation_classes), epsclass(1:dissipation_classes), &
	187	radclass(1:radius_classes) )
	188
	189	!
	190	!-- Calculate the radius class bounds with logarithmic distances
	191	!-- in the interval [1.0E-6, 2.0E-4] m
[1322]	192	rclass_lbound = LOG( 1.0E-6_wp )
	193	rclass_ubound = LOG( 2.0E-4_wp )
[1359]	194	radclass(1) = 1.0E-6_wp
[828]	195	DO i = 2, radius_classes
	196	radclass(i) = EXP( rclass_lbound + &
[1359]	197	( rclass_ubound - rclass_lbound ) * &
	198	( i - 1.0_wp ) / ( radius_classes - 1.0_wp ) )
[828]	199	ENDDO
	200
	201	!
[1007]	202	!-- Set the class bounds for dissipation in interval [0.0, 0.1] m2/s3
[828]	203	DO i = 1, dissipation_classes
[1359]	204	epsclass(i) = 0.1_wp * REAL( i, KIND=wp ) / dissipation_classes
[828]	205	ENDDO
	206	!
	207	!-- Calculate collision efficiencies of the Wang/ayala kernel
	208	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
	209	ecf(1:radius_classes,1:radius_classes), &
	210	gck(1:radius_classes,1:radius_classes), &
	211	winf(1:radius_classes) )
	212
	213	DO k = 1, dissipation_classes
	214
	215	epsilon = epsclass(k)
[1359]	216	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 1.0_wp / 3.0_wp )
[828]	217
	218	CALL turbsd
	219	CALL turb_enhance_eff
	220	CALL effic
	221
	222	DO j = 1, radius_classes
	223	DO i = 1, radius_classes
	224	ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j)
	225	ENDDO
	226	ENDDO
	227
	228	ENDDO
	229
	230	!
	231	!-- Calculate collision efficiencies of the Hall kernel
	232	ALLOCATE( hkernel(1:radius_classes,1:radius_classes), &
	233	hwratio(1:radius_classes,1:radius_classes) )
	234
	235	CALL fallg
	236	CALL effic
	237
	238	DO j = 1, radius_classes
	239	DO i = 1, radius_classes
	240	hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 &
	241	* ec(i,j) * ABS( winf(j) - winf(i) )
	242	ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0
	243	ENDDO
	244	ENDDO
	245
	246	!
	247	!-- Test output of efficiencies
	248	IF ( j == -1 ) THEN
	249
	250	PRINT, '** Hall kernel'
[1359]	251	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6_wp, &
[1007]	252	i = 1,radius_classes )
[828]	253	DO j = 1, radius_classes
[1007]	254	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
	255	( hkernel(i,j), i = 1,radius_classes )
[828]	256	ENDDO
	257
	258	DO k = 1, dissipation_classes
	259	DO i = 1, radius_classes
	260	DO j = 1, radius_classes
[1359]	261	IF ( hkernel(i,j) == 0.0_wp ) THEN
	262	hwratio(i,j) = 9999999.9_wp
[828]	263	ELSE
	264	hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j)
	265	ENDIF
	266	ENDDO
	267	ENDDO
	268
	269	PRINT, '** epsilon = ', epsclass(k)
[1359]	270	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i) 1.0E6_wp, &
[1007]	271	i = 1,radius_classes )
[828]	272	DO j = 1, radius_classes
[1359]	273	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j) 1.0E6_wp, &
[1007]	274	( hwratio(i,j), i = 1,radius_classes )
[828]	275	ENDDO
	276	ENDDO
	277
	278	ENDIF
	279
	280	DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf )
	281
	282	ELSEIF( collision_kernel == 'hall' .OR. collision_kernel == 'wang' ) &
	283	THEN
	284	!
	285	!-- Initial settings for Hall- and Wang-Kernel
	286	!-- To be done: move here parts from turbsd, fallg, ecoll, etc.
	287	ENDIF
	288
	289	END SUBROUTINE init_kernels
	290
	291
[790]	292	!------------------------------------------------------------------------------!
[1682]	293	! Description:
	294	! ------------
	295	!> Calculation of collision kernels during each timestep and for each grid box
[790]	296	!------------------------------------------------------------------------------!
[828]	297	SUBROUTINE recalculate_kernel( i1, j1, k1 )
[790]	298
[1320]	299	USE arrays_3d, &
	300	ONLY: diss
[790]	301
[1320]	302	USE particle_attributes, &
[1359]	303	ONLY: prt_count, radius_classes, wang_kernel
[1320]	304
[790]	305	IMPLICIT NONE
	306
[1682]	307	INTEGER(iwp) :: i !<
	308	INTEGER(iwp) :: i1 !<
	309	INTEGER(iwp) :: j !<
	310	INTEGER(iwp) :: j1 !<
	311	INTEGER(iwp) :: k1 !<
	312	INTEGER(iwp) :: pend !<
	313	INTEGER(iwp) :: pstart !<
[790]	314
	315
[1359]	316	pstart = 1
	317	pend = prt_count(k1,j1,i1)
[828]	318	radius_classes = prt_count(k1,j1,i1)
[792]	319
[828]	320	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
	321	radclass(1:radius_classes), winf(1:radius_classes) )
[790]	322
[828]	323	!
[1007]	324	!-- Store particle radii on the radclass array
	325	radclass(1:radius_classes) = particles(pstart:pend)%radius
[790]	326
[835]	327	IF ( wang_kernel ) THEN
[1007]	328	epsilon = diss(k1,j1,i1) ! dissipation rate in m2/s3
[835]	329	ELSE
[1359]	330	epsilon = 0.0_wp
[835]	331	ENDIF
[1359]	332	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 0.33333333333_wp )
[790]	333
[1359]	334	IF ( wang_kernel .AND. epsilon > 1.0E-7_wp ) THEN
[828]	335	!
	336	!-- Call routines to calculate efficiencies for the Wang kernel
	337	ALLOCATE( gck(1:radius_classes,1:radius_classes), &
	338	ecf(1:radius_classes,1:radius_classes) )
[790]	339
[828]	340	CALL turbsd
	341	CALL turb_enhance_eff
	342	CALL effic
[790]	343
[828]	344	DO j = 1, radius_classes
	345	DO i = 1, radius_classes
	346	ckernel(pstart+i-1,pstart+j-1,1) = ec(i,j) * gck(i,j) * ecf(i,j)
[790]	347	ENDDO
[828]	348	ENDDO
[790]	349
[828]	350	DEALLOCATE( gck, ecf )
[790]	351
	352	ELSE
[828]	353	!
	354	!-- Call routines to calculate efficiencies for the Hall kernel
[790]	355	CALL fallg
	356	CALL effic
	357
[828]	358	DO j = 1, radius_classes
	359	DO i = 1, radius_classes
	360	ckernel(pstart+i-1,pstart+j-1,1) = pi * &
	361	( radclass(j) + radclass(i) )**2 &
	362	* ec(i,j) * ABS( winf(j) - winf(i) )
[790]	363	ENDDO
	364	ENDDO
	365
	366	ENDIF
	367
[828]	368	DEALLOCATE( ec, radclass, winf )
[790]	369
[828]	370	END SUBROUTINE recalculate_kernel
[790]	371
[828]	372
[790]	373	!------------------------------------------------------------------------------!
[1682]	374	! Description:
	375	! ------------
	376	!> Calculation of gck
	377	!> This is from Aayala 2008b, page 37ff.
	378	!> Necessary input parameters: water density, radii of droplets, air density,
	379	!> air viscosity, turbulent dissipation rate, taylor microscale reynolds number,
	380	!> gravitational acceleration --> to be replaced by PALM parameters
[790]	381	!------------------------------------------------------------------------------!
[792]	382	SUBROUTINE turbsd
[799]	383
[1320]	384	USE control_parameters, &
	385	ONLY: g, molecular_viscosity
	386
	387	USE particle_attributes, &
	388	ONLY: radius_classes
[790]	389
	390	IMPLICIT NONE
[1320]	391
[1682]	392	LOGICAL, SAVE :: first = .TRUE. !<
[790]	393
[1682]	394	INTEGER(iwp) :: i !<
	395	INTEGER(iwp) :: j !<
[790]	396
[1682]	397	REAL(wp) :: ao !<
	398	REAL(wp) :: ao_gr !<
	399	REAL(wp) :: bbb !<
	400	REAL(wp) :: be !<
	401	REAL(wp) :: b1 !<
	402	REAL(wp) :: b2 !<
	403	REAL(wp) :: ccc !<
	404	REAL(wp) :: c1 !<
	405	REAL(wp) :: c1_gr !<
	406	REAL(wp) :: c2 !<
	407	REAL(wp) :: d1 !<
	408	REAL(wp) :: d2 !<
	409	REAL(wp) :: eta !<
	410	REAL(wp) :: e1 !<
	411	REAL(wp) :: e2 !<
	412	REAL(wp) :: fao_gr !<
	413	REAL(wp) :: fr !<
	414	REAL(wp) :: grfin !<
	415	REAL(wp) :: lambda !<
	416	REAL(wp) :: lambda_re !<
	417	REAL(wp) :: lf !<
	418	REAL(wp) :: rc !<
	419	REAL(wp) :: rrp !<
	420	REAL(wp) :: sst !<
	421	REAL(wp) :: tauk !<
	422	REAL(wp) :: tl !<
	423	REAL(wp) :: t2 !<
	424	REAL(wp) :: tt !<
	425	REAL(wp) :: t1 !<
	426	REAL(wp) :: vk !<
	427	REAL(wp) :: vrms1xy !<
	428	REAL(wp) :: vrms2xy !<
	429	REAL(wp) :: v1 !<
	430	REAL(wp) :: v1v2xy !<
	431	REAL(wp) :: v1xysq !<
	432	REAL(wp) :: v2 !<
	433	REAL(wp) :: v2xysq !<
	434	REAL(wp) :: wrfin !<
	435	REAL(wp) :: wrgrav2 !<
	436	REAL(wp) :: wrtur2xy !<
	437	REAL(wp) :: xx !<
	438	REAL(wp) :: yy !<
	439	REAL(wp) :: z !<
[790]	440
[1682]	441	REAL(wp), DIMENSION(1:radius_classes) :: st !<
	442	REAL(wp), DIMENSION(1:radius_classes) :: tau !<
[1320]	443
[799]	444	!
[828]	445	!-- Initial assignment of constants
[799]	446	IF ( first ) THEN
[790]	447
[799]	448	first = .FALSE.
[790]	449
[1007]	450	ENDIF
[790]	451
[1322]	452	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon ) ! in m
	453	lambda_re = urms*2 SQRT( 15.0_wp / epsilon / molecular_viscosity )
[828]	454	tl = urms**2 / epsilon ! in s
[1359]	455	lf = 0.5_wp * urms**3 / epsilon ! in m
[1007]	456	tauk = SQRT( molecular_viscosity / epsilon ) ! in s
[1322]	457	eta = ( molecular_viscosity3 / epsilon )0.25_wp ! in m
[1007]	458	vk = eta / tauk
[790]	459
[1359]	460	ao = ( 11.0_wp + 7.0_wp * lambda_re ) / ( 205.0_wp + lambda_re )
	461	tt = SQRT( 2.0_wp * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk ! in s
[799]	462
[1007]	463	CALL fallg ! gives winf in m/s
[790]	464
[828]	465	DO i = 1, radius_classes
[1007]	466	tau(i) = winf(i) / g ! in s
[828]	467	st(i) = tau(i) / tauk
[790]	468	ENDDO
	469
[828]	470	!
	471	!-- Calculate wr (from Aayala 2008b, page 38f)
	472	z = tt / tl
[1322]	473	be = SQRT( 2.0_wp ) * lambda / lf
[1359]	474	bbb = SQRT( 1.0_wp - 2.0_wp * be**2 )
	475	d1 = ( 1.0_wp + bbb ) / ( 2.0_wp * bbb )
	476	e1 = lf * ( 1.0_wp + bbb ) * 0.5_wp ! in m
	477	d2 = ( 1.0_wp - bbb ) * 0.5_wp / bbb
	478	e2 = lf * ( 1.0_wp - bbb ) * 0.5_wp ! in m
	479	ccc = SQRT( 1.0_wp - 2.0_wp * z**2 )
	480	b1 = ( 1.0_wp + ccc ) * 0.5_wp / ccc
	481	c1 = tl * ( 1.0_wp + ccc ) * 0.5_wp ! in s
	482	b2 = ( 1.0_wp - ccc ) * 0.5_wp / ccc
	483	c2 = tl * ( 1.0_wp - ccc ) * 0.5_wp ! in s
[790]	484
[828]	485	DO i = 1, radius_classes
[790]	486
[1007]	487	v1 = winf(i) ! in m/s
[828]	488	t1 = tau(i) ! in s
[790]	489
[828]	490	DO j = 1, i
[1007]	491	rrp = radclass(i) + radclass(j)
	492	v2 = winf(j) ! in m/s
[828]	493	t2 = tau(j) ! in s
[790]	494
[1007]	495	v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) &
	496	- b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1)
	497	v1xysq = v1xysq * urms2 / t1 ! in m2/s**2
	498	vrms1xy = SQRT( v1xysq ) ! in m/s
[790]	499
[1007]	500	v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) &
	501	- b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2)
	502	v2xysq = v2xysq * urms2 / t2 ! in m2/s**2
	503	vrms2xy = SQRT( v2xysq ) ! in m/s
[790]	504
[828]	505	IF ( winf(i) >= winf(j) ) THEN
[799]	506	v1 = winf(i)
[790]	507	t1 = tau(i)
[799]	508	v2 = winf(j)
[790]	509	t2 = tau(j)
	510	ELSE
[799]	511	v1 = winf(j)
[790]	512	t1 = tau(j)
[799]	513	v2 = winf(i)
[790]	514	t2 = tau(i)
	515	ENDIF
	516
[828]	517	v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - &
	518	b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - &
	519	b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + &
	520	b2 * d2* zhi(c2,e2,v1,t1,v2,t2)
	521	fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 )
[1359]	522	v1v2xy = v1v2xy * fr * urms2 / tau(i) / tau(j) ! in m2/s**2
	523	wrtur2xy = vrms1xy2 + vrms2xy2 - 2.0_wp * v1v2xy ! in m2/s2
	524	IF ( wrtur2xy < 0.0_wp ) wrtur2xy = 0.0_wp
[1322]	525	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
	526	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) ) ! in m/s
[790]	527
[828]	528	!
	529	!-- Calculate gr
	530	IF ( st(j) > st(i) ) THEN
	531	sst = st(j)
[790]	532	ELSE
[828]	533	sst = st(i)
[790]	534	ENDIF
	535
[1359]	536	xx = -0.1988_wp * sst*4 + 1.5275_wp sst*3 - 4.2942_wp &
	537	sst*2 + 5.3406_wp sst
	538	IF ( xx < 0.0_wp ) xx = 0.0_wp
	539	yy = 0.1886_wp * EXP( 20.306_wp / lambda_re )
[790]	540
[1007]	541	c1_gr = xx / ( g / vk * tauk )**yy
[790]	542
[1322]	543	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
[1359]	544	fao_gr = 20.115_wp * SQRT( ao_gr / lambda_re )
[828]	545	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta ! in cm
[790]	546
[1359]	547	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5_wp )
	548	IF ( grfin < 1.0_wp ) grfin = 1.0_wp
[790]	549
[1359]	550	gck(i,j) = 2.0_wp * pi * rrp*2 wrfin * grfin ! in cm**3/s
[790]	551	gck(j,i) = gck(i,j)
	552
	553	ENDDO
	554	ENDDO
	555
[828]	556	END SUBROUTINE turbsd
[790]	557
[828]	558
[790]	559	!------------------------------------------------------------------------------!
[1682]	560	! Description:
	561	! ------------
	562	!> phi_w as a function
[790]	563	!------------------------------------------------------------------------------!
[1320]	564	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
[790]	565
	566	IMPLICIT NONE
	567
[1682]	568	REAL(wp) :: a !<
	569	REAL(wp) :: aa1 !<
	570	REAL(wp) :: b !<
	571	REAL(wp) :: tau0 !<
	572	REAL(wp) :: vsett !<
[790]	573
[1359]	574	aa1 = 1.0_wp / tau0 + 1.0_wp / a + vsett / b
	575	phi_w = 1.0_wp / aa1 - 0.5_wp * vsett / b / aa1**2 ! in s
[790]	576
[1007]	577	END FUNCTION phi_w
[792]	578
[790]	579
	580	!------------------------------------------------------------------------------!
[1682]	581	! Description:
	582	! ------------
	583	!> zhi as a function
[790]	584	!------------------------------------------------------------------------------!
[1320]	585	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
[790]	586
	587	IMPLICIT NONE
	588
[1682]	589	REAL(wp) :: a !<
	590	REAL(wp) :: aa1 !<
	591	REAL(wp) :: aa2 !<
	592	REAL(wp) :: aa3 !<
	593	REAL(wp) :: aa4 !<
	594	REAL(wp) :: aa5 !<
	595	REAL(wp) :: aa6 !<
	596	REAL(wp) :: b !<
	597	REAL(wp) :: tau1 !<
	598	REAL(wp) :: tau2 !<
	599	REAL(wp) :: vsett1 !<
	600	REAL(wp) :: vsett2 !<
[790]	601
[1359]	602	aa1 = vsett2 / b - 1.0_wp / tau2 - 1.0_wp / a
	603	aa2 = vsett1 / b + 1.0_wp / tau1 + 1.0_wp / a
	604	aa3 = ( vsett1 - vsett2 ) / b + 1.0_wp / tau1 + 1.0_wp / tau2
	605	aa4 = ( vsett2 / b )2 - ( 1.0_wp / tau2 + 1.0_wp / a )2
	606	aa5 = vsett2 / b + 1.0_wp / tau2 + 1.0_wp / a
	607	aa6 = 1.0_wp / tau1 - 1.0_wp / a + ( 1.0_wp / tau2 + 1.0_wp / a) * &
	608	vsett1 / vsett2
	609	zhi = (1.0_wp / aa1 - 1.0_wp / aa2 ) * ( vsett1 - vsett2 ) * 0.5_wp / &
	610	b / aa32 + ( 4.0_wp / aa4 - 1.0_wp / aa52 - 1.0_wp / aa1**2 ) &
	611	* vsett2 * 0.5_wp / b /aa6 + ( 2.0_wp * ( b / aa2 - b / aa1 ) - &
	612	vsett1 / aa22 + vsett2 / aa12 ) * 0.5_wp / b / aa3 ! in s**2
[799]	613
[828]	614	END FUNCTION zhi
[790]	615
[828]	616
[790]	617	!------------------------------------------------------------------------------!
[1682]	618	! Description:
	619	! ------------
	620	!> Calculation of terminal velocity winf following Equations 10-138 to 10-145
	621	!> from (Pruppacher and Klett, 1997)
[790]	622	!------------------------------------------------------------------------------!
[828]	623	SUBROUTINE fallg
[1320]	624
	625	USE cloud_parameters, &
	626	ONLY: rho_l
	627
	628	USE control_parameters, &
	629	ONLY: g
[790]	630
[1320]	631	USE particle_attributes, &
	632	ONLY: radius_classes
[790]	633
[1320]	634
[828]	635	IMPLICIT NONE
[790]	636
[1682]	637	INTEGER(iwp) :: i !<
	638	INTEGER(iwp) :: j !<
[790]	639
[1682]	640	LOGICAL, SAVE :: first = .TRUE. !<
[790]	641
[1682]	642	REAL(wp), SAVE :: cunh !<
	643	REAL(wp), SAVE :: eta !<
	644	REAL(wp), SAVE :: phy !<
	645	REAL(wp), SAVE :: py !<
	646	REAL(wp), SAVE :: rho_a !<
	647	REAL(wp), SAVE :: sigma !<
	648	REAL(wp), SAVE :: stb !<
	649	REAL(wp), SAVE :: stok !<
	650	REAL(wp), SAVE :: xlamb !<
[790]	651
[1682]	652	REAL(wp) :: bond !<
	653	REAL(wp) :: x !<
	654	REAL(wp) :: xrey !<
	655	REAL(wp) :: y !<
[799]	656
[1682]	657	REAL(wp), DIMENSION(1:7), SAVE :: b !<
	658	REAL(wp), DIMENSION(1:6), SAVE :: c !<
[799]	659
	660	!
[828]	661	!-- Initial assignment of constants
	662	IF ( first ) THEN
[799]	663
[828]	664	first = .FALSE.
[1359]	665	b = (/ -0.318657E1_wp, 0.992696E0_wp, -0.153193E-2_wp, &
	666	-0.987059E-3_wp, -0.578878E-3_wp, 0.855176E-4_wp, &
	667	-0.327815E-5_wp /)
	668	c = (/ -0.500015E1_wp, 0.523778E1_wp, -0.204914E1_wp, &
	669	0.475294E0_wp, -0.542819E-1_wp, 0.238449E-2_wp /)
[790]	670
[1007]	671	!
	672	!-- Parameter values for p = 1013,25 hPa and T = 293,15 K
[1359]	673	eta = 1.818E-5_wp ! in kg/(m s)
	674	xlamb = 6.6E-8_wp ! in m
	675	rho_a = 1.204_wp ! in kg/m**3
	676	cunh = 1.26_wp * xlamb ! in m
	677	sigma = 0.07363_wp ! in kg/s**2
	678	stok = 2.0_wp * g * ( rho_l - rho_a ) / ( 9.0_wp * eta ) ! in 1/(m s)
	679	stb = 32.0_wp * rho_a * ( rho_l - rho_a) * g / (3.0_wp * eta * eta)
[1007]	680	phy = sigma*3 rho_a2 / ( eta4 * g * ( rho_l - rho_a ) )
[1322]	681	py = phy**( 1.0_wp / 6.0_wp )
[790]	682
[828]	683	ENDIF
[790]	684
[828]	685	DO j = 1, radius_classes
[790]	686
[1359]	687	IF ( radclass(j) <= 1.0E-5_wp ) THEN
[799]	688
[1007]	689	winf(j) = stok * ( radclass(j)*2 + cunh radclass(j) )
[790]	690
[1359]	691	ELSEIF ( radclass(j) > 1.0E-5_wp .AND. radclass(j) <= 5.35E-4_wp ) THEN
[790]	692
[828]	693	x = LOG( stb * radclass(j)**3 )
[1359]	694	y = 0.0_wp
[790]	695
[828]	696	DO i = 1, 7
	697	y = y + b(i) * x**(i-1)
	698	ENDDO
[1007]	699	!
	700	!-- Note: this Eq. is wrong in (Pruppacher and Klett, 1997, p. 418)
	701	!-- for correct version see (Beard, 1976)
[1359]	702	xrey = ( 1.0_wp + cunh / radclass(j) ) * EXP( y )
[790]	703
[1359]	704	winf(j) = xrey * eta / ( 2.0_wp * rho_a * radclass(j) )
[790]	705
[1359]	706	ELSEIF ( radclass(j) > 5.35E-4_wp ) THEN
[790]	707
[1359]	708	IF ( radclass(j) > 0.0035_wp ) THEN
	709	bond = g * ( rho_l - rho_a ) * 0.0035_wp**2 / sigma
[828]	710	ELSE
[1007]	711	bond = g * ( rho_l - rho_a ) * radclass(j)**2 / sigma
[828]	712	ENDIF
[790]	713
[1359]	714	x = LOG( 16.0_wp * bond * py / 3.0_wp )
	715	y = 0.0_wp
[790]	716
[828]	717	DO i = 1, 6
	718	y = y + c(i) * x**(i-1)
	719	ENDDO
[790]	720
[828]	721	xrey = py * EXP( y )
[790]	722
[1359]	723	IF ( radclass(j) > 0.0035_wp ) THEN
	724	winf(j) = xrey * eta / ( 2.0_wp * rho_a * 0.0035_wp )
[828]	725	ELSE
[1359]	726	winf(j) = xrey * eta / ( 2.0_wp * rho_a * radclass(j) )
[828]	727	ENDIF
[790]	728
[828]	729	ENDIF
[790]	730
[828]	731	ENDDO
[790]	732
[828]	733	END SUBROUTINE fallg
[790]	734
[828]	735
[790]	736	!------------------------------------------------------------------------------!
[1682]	737	! Description:
	738	! ------------
	739	!> Calculation of collision efficiencies for the Hall kernel
[790]	740	!------------------------------------------------------------------------------!
[828]	741	SUBROUTINE effic
[1320]	742
	743	USE particle_attributes, &
	744	ONLY: radius_classes
[790]	745
[828]	746	IMPLICIT NONE
[790]	747
[1682]	748	INTEGER(iwp) :: i !<
	749	INTEGER(iwp) :: iq !<
	750	INTEGER(iwp) :: ir !<
	751	INTEGER(iwp) :: j !<
	752	INTEGER(iwp) :: k !<
[790]	753
[1682]	754	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
[790]	755
[1682]	756	LOGICAL, SAVE :: first = .TRUE. !<
[790]	757
[1682]	758	REAL(wp) :: ek !<
	759	REAL(wp) :: particle_radius !<
	760	REAL(wp) :: pp !<
	761	REAL(wp) :: qq !<
	762	REAL(wp) :: rq !<
[790]	763
[1682]	764	REAL(wp), DIMENSION(1:21), SAVE :: rat !<
[1320]	765
[1682]	766	REAL(wp), DIMENSION(1:15), SAVE :: r0 !<
[1320]	767
[1682]	768	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !<
[790]	769
[792]	770	!
[828]	771	!-- Initial assignment of constants
	772	IF ( first ) THEN
[790]	773
[792]	774	first = .FALSE.
[1359]	775	r0 = (/ 6.0_wp, 8.0_wp, 10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp, &
	776	30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, 70.0_wp, 100.0_wp, &
	777	150.0_wp, 200.0_wp, 300.0_wp /)
[790]	778
[1359]	779	rat = (/ 0.00_wp, 0.05_wp, 0.10_wp, 0.15_wp, 0.20_wp, 0.25_wp, &
	780	0.30_wp, 0.35_wp, 0.40_wp, 0.45_wp, 0.50_wp, 0.55_wp, &
	781	0.60_wp, 0.65_wp, 0.70_wp, 0.75_wp, 0.80_wp, 0.85_wp, &
	782	0.90_wp, 0.95_wp, 1.00_wp /)
	783
	784	ecoll(:,1) = (/ 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
	785	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
	786	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp /)
	787	ecoll(:,2) = (/ 0.003_wp, 0.003_wp, 0.003_wp, 0.004_wp, 0.005_wp, &
	788	0.005_wp, 0.005_wp, 0.010_wp, 0.100_wp, 0.050_wp, &
	789	0.200_wp, 0.500_wp, 0.770_wp, 0.870_wp, 0.970_wp /)
	790	ecoll(:,3) = (/ 0.007_wp, 0.007_wp, 0.007_wp, 0.008_wp, 0.009_wp, &
	791	0.010_wp, 0.010_wp, 0.070_wp, 0.400_wp, 0.430_wp, &
	792	0.580_wp, 0.790_wp, 0.930_wp, 0.960_wp, 1.000_wp /)
	793	ecoll(:,4) = (/ 0.009_wp, 0.009_wp, 0.009_wp, 0.012_wp, 0.015_wp, &
	794	0.010_wp, 0.020_wp, 0.280_wp, 0.600_wp, 0.640_wp, &
	795	0.750_wp, 0.910_wp, 0.970_wp, 0.980_wp, 1.000_wp /)
	796	ecoll(:,5) = (/ 0.014_wp, 0.014_wp, 0.014_wp, 0.015_wp, 0.016_wp, &
	797	0.030_wp, 0.060_wp, 0.500_wp, 0.700_wp, 0.770_wp, &
	798	0.840_wp, 0.950_wp, 0.970_wp, 1.000_wp, 1.000_wp /)
	799	ecoll(:,6) = (/ 0.017_wp, 0.017_wp, 0.017_wp, 0.020_wp, 0.022_wp, &
	800	0.060_wp, 0.100_wp, 0.620_wp, 0.780_wp, 0.840_wp, &
	801	0.880_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	802	ecoll(:,7) = (/ 0.030_wp, 0.030_wp, 0.024_wp, 0.022_wp, 0.032_wp, &
	803	0.062_wp, 0.200_wp, 0.680_wp, 0.830_wp, 0.870_wp, &
	804	0.900_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	805	ecoll(:,8) = (/ 0.025_wp, 0.025_wp, 0.025_wp, 0.036_wp, 0.043_wp, &
	806	0.130_wp, 0.270_wp, 0.740_wp, 0.860_wp, 0.890_wp, &
	807	0.920_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	808	ecoll(:,9) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.040_wp, 0.052_wp, &
	809	0.200_wp, 0.400_wp, 0.780_wp, 0.880_wp, 0.900_wp, &
	810	0.940_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	811	ecoll(:,10) = (/ 0.030_wp, 0.030_wp, 0.030_wp, 0.047_wp, 0.064_wp, &
	812	0.250_wp, 0.500_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
	813	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	814	ecoll(:,11) = (/ 0.040_wp, 0.040_wp, 0.033_wp, 0.037_wp, 0.068_wp, &
	815	0.240_wp, 0.550_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
	816	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	817	ecoll(:,12) = (/ 0.035_wp, 0.035_wp, 0.035_wp, 0.055_wp, 0.079_wp, &
	818	0.290_wp, 0.580_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
	819	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	820	ecoll(:,13) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.062_wp, 0.082_wp, &
	821	0.290_wp, 0.590_wp, 0.780_wp, 0.900_wp, 0.910_wp, &
	822	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	823	ecoll(:,14) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.060_wp, 0.080_wp, &
	824	0.290_wp, 0.580_wp, 0.770_wp, 0.890_wp, 0.910_wp, &
	825	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	826	ecoll(:,15) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.041_wp, 0.075_wp, &
	827	0.250_wp, 0.540_wp, 0.760_wp, 0.880_wp, 0.920_wp, &
	828	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	829	ecoll(:,16) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.052_wp, 0.067_wp, &
	830	0.250_wp, 0.510_wp, 0.770_wp, 0.880_wp, 0.930_wp, &
	831	0.970_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	832	ecoll(:,17) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.047_wp, 0.057_wp, &
	833	0.250_wp, 0.490_wp, 0.770_wp, 0.890_wp, 0.950_wp, &
	834	1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	835	ecoll(:,18) = (/ 0.036_wp, 0.036_wp, 0.036_wp, 0.042_wp, 0.048_wp, &
	836	0.230_wp, 0.470_wp, 0.780_wp, 0.920_wp, 1.000_wp, &
	837	1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp /)
	838	ecoll(:,19) = (/ 0.040_wp, 0.040_wp, 0.035_wp, 0.033_wp, 0.040_wp, &
	839	0.112_wp, 0.450_wp, 0.790_wp, 1.010_wp, 1.030_wp, &
	840	1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp /)
	841	ecoll(:,20) = (/ 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, &
	842	0.119_wp, 0.470_wp, 0.950_wp, 1.300_wp, 1.700_wp, &
	843	2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp /)
	844	ecoll(:,21) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, &
	845	0.125_wp, 0.520_wp, 1.400_wp, 2.300_wp, 3.000_wp, &
	846	4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp /)
[828]	847	ENDIF
[790]	848
[792]	849	!
[828]	850	!-- Calculate the radius class index of particles with respect to array r
[1007]	851	!-- Radius has to be in Âµm
[828]	852	ALLOCATE( ira(1:radius_classes) )
	853	DO j = 1, radius_classes
[1322]	854	particle_radius = radclass(j) * 1.0E6_wp
[828]	855	DO k = 1, 15
	856	IF ( particle_radius < r0(k) ) THEN
	857	ira(j) = k
	858	EXIT
	859	ENDIF
	860	ENDDO
	861	IF ( particle_radius >= r0(15) ) ira(j) = 16
	862	ENDDO
[790]	863
[792]	864	!
[828]	865	!-- Two-dimensional linear interpolation of the collision efficiency.
	866	!-- Radius has to be in Âµm
	867	DO j = 1, radius_classes
	868	DO i = 1, j
[792]	869
[828]	870	ir = ira(j)
[1519]	871	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
[828]	872	iq = INT( rq * 20 ) + 1
	873	iq = MAX( iq , 2)
[792]	874
[828]	875	IF ( ir < 16 ) THEN
	876	IF ( ir >= 2 ) THEN
[1776]	877	pp = ( ( MAX(radclass(j),radclass(i)) * 1.0E06_wp ) - r0(ir-1) ) / &
[828]	878	( r0(ir) - r0(ir-1) )
[1359]	879	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	880	ec(j,i) = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) &
	881	* ecoll(ir-1,iq-1) &
	882	+ pp * ( 1.0_wp - qq ) * ecoll(ir,iq-1) &
	883	+ qq * ( 1.0_wp - pp ) * ecoll(ir-1,iq) &
[828]	884	+ pp * qq * ecoll(ir,iq)
	885	ELSE
	886	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	887	ec(j,i) = ( 1.0_wp - qq ) * ecoll(1,iq-1) + qq * ecoll(1,iq)
[828]	888	ENDIF
	889	ELSE
	890	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	891	ek = ( 1.0_wp - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
[1346]	892	ec(j,i) = MIN( ek, 1.0_wp )
[1071]	893	ENDIF
[792]	894
[1359]	895	IF ( ec(j,i) < 1.0E-20_wp ) ec(j,i) = 0.0_wp
[1071]	896
[828]	897	ec(i,j) = ec(j,i)
[792]	898
[828]	899	ENDDO
	900	ENDDO
[792]	901
[828]	902	DEALLOCATE( ira )
[792]	903
[828]	904	END SUBROUTINE effic
[792]	905
	906
[790]	907	!------------------------------------------------------------------------------!
[1682]	908	! Description:
	909	! ------------
	910	!> Calculation of enhancement factor for collision efficencies due to turbulence
[790]	911	!------------------------------------------------------------------------------!
[828]	912	SUBROUTINE turb_enhance_eff
[790]	913
[1320]	914	USE particle_attributes, &
	915	ONLY: radius_classes
[790]	916
[828]	917	IMPLICIT NONE
[790]	918
[1682]	919	INTEGER(iwp) :: i !<
	920	INTEGER(iwp) :: iq !<
	921	INTEGER(iwp) :: ir !<
	922	INTEGER(iwp) :: j !<
	923	INTEGER(iwp) :: k !<
	924	INTEGER(iwp) :: kk !<
[790]	925
[1682]	926	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
[1320]	927
[1682]	928	LOGICAL, SAVE :: first = .TRUE. !<
[790]	929
[1682]	930	REAL(wp) :: particle_radius !<
	931	REAL(wp) :: pp !<
	932	REAL(wp) :: qq !<
	933	REAL(wp) :: rq !<
	934	REAL(wp) :: y1 !<
	935	REAL(wp) :: y2 !<
	936	REAL(wp) :: y3 !<
[790]	937
[1682]	938	REAL(wp), DIMENSION(1:11), SAVE :: rat !<
[1320]	939
[1682]	940	REAL(wp), DIMENSION(1:7), SAVE :: r0 !<
[1320]	941
[1682]	942	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !<
	943	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !<
[799]	944
	945	!
[828]	946	!-- Initial assignment of constants
	947	IF ( first ) THEN
[799]	948
[828]	949	first = .FALSE.
[799]	950
[1359]	951	r0 = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, &
	952	100.0_wp /)
	953
	954	rat = (/ 0.0_wp, 0.1_wp, 0.2_wp, 0.3_wp, 0.4_wp, 0.5_wp, 0.6_wp, &
	955	0.7_wp, 0.8_wp, 0.9_wp, 1.0_wp /)
[828]	956	!
[1007]	957	!-- for 100 cm2/s3
[1359]	958	ecoll_100(:,1) = (/ 1.74_wp, 1.74_wp, 1.773_wp, 1.49_wp, &
	959	1.207_wp, 1.207_wp, 1.0_wp /)
	960	ecoll_100(:,2) = (/ 1.46_wp, 1.46_wp, 1.421_wp, 1.245_wp, &
	961	1.069_wp, 1.069_wp, 1.0_wp /)
	962	ecoll_100(:,3) = (/ 1.32_wp, 1.32_wp, 1.245_wp, 1.123_wp, &
	963	1.000_wp, 1.000_wp, 1.0_wp /)
	964	ecoll_100(:,4) = (/ 1.250_wp, 1.250_wp, 1.148_wp, 1.087_wp, &
	965	1.025_wp, 1.025_wp, 1.0_wp /)
	966	ecoll_100(:,5) = (/ 1.186_wp, 1.186_wp, 1.066_wp, 1.060_wp, &
	967	1.056_wp, 1.056_wp, 1.0_wp /)
	968	ecoll_100(:,6) = (/ 1.045_wp, 1.045_wp, 1.000_wp, 1.014_wp, &
	969	1.028_wp, 1.028_wp, 1.0_wp /)
	970	ecoll_100(:,7) = (/ 1.070_wp, 1.070_wp, 1.030_wp, 1.038_wp, &
	971	1.046_wp, 1.046_wp, 1.0_wp /)
	972	ecoll_100(:,8) = (/ 1.000_wp, 1.000_wp, 1.054_wp, 1.042_wp, &
	973	1.029_wp, 1.029_wp, 1.0_wp /)
	974	ecoll_100(:,9) = (/ 1.223_wp, 1.223_wp, 1.117_wp, 1.069_wp, &
	975	1.021_wp, 1.021_wp, 1.0_wp /)
	976	ecoll_100(:,10) = (/ 1.570_wp, 1.570_wp, 1.244_wp, 1.166_wp, &
	977	1.088_wp, 1.088_wp, 1.0_wp /)
	978	ecoll_100(:,11) = (/ 20.3_wp, 20.3_wp, 14.6_wp, 8.61_wp, &
	979	2.60_wp, 2.60_wp, 1.0_wp /)
[828]	980	!
[1007]	981	!-- for 400 cm2/s3
[1359]	982	ecoll_400(:,1) = (/ 4.976_wp, 4.976_wp, 3.593_wp, 2.519_wp, &
	983	1.445_wp, 1.445_wp, 1.0_wp /)
	984	ecoll_400(:,2) = (/ 2.984_wp, 2.984_wp, 2.181_wp, 1.691_wp, &
	985	1.201_wp, 1.201_wp, 1.0_wp /)
	986	ecoll_400(:,3) = (/ 1.988_wp, 1.988_wp, 1.475_wp, 1.313_wp, &
	987	1.150_wp, 1.150_wp, 1.0_wp /)
	988	ecoll_400(:,4) = (/ 1.490_wp, 1.490_wp, 1.187_wp, 1.156_wp, &
	989	1.126_wp, 1.126_wp, 1.0_wp /)
	990	ecoll_400(:,5) = (/ 1.249_wp, 1.249_wp, 1.088_wp, 1.090_wp, &
	991	1.092_wp, 1.092_wp, 1.0_wp /)
	992	ecoll_400(:,6) = (/ 1.139_wp, 1.139_wp, 1.130_wp, 1.091_wp, &
	993	1.051_wp, 1.051_wp, 1.0_wp /)
	994	ecoll_400(:,7) = (/ 1.220_wp, 1.220_wp, 1.190_wp, 1.138_wp, &
	995	1.086_wp, 1.086_wp, 1.0_wp /)
	996	ecoll_400(:,8) = (/ 1.325_wp, 1.325_wp, 1.267_wp, 1.165_wp, &
	997	1.063_wp, 1.063_wp, 1.0_wp /)
	998	ecoll_400(:,9) = (/ 1.716_wp, 1.716_wp, 1.345_wp, 1.223_wp, &
	999	1.100_wp, 1.100_wp, 1.0_wp /)
	1000	ecoll_400(:,10) = (/ 3.788_wp, 3.788_wp, 1.501_wp, 1.311_wp, &
	1001	1.120_wp, 1.120_wp, 1.0_wp /)
	1002	ecoll_400(:,11) = (/ 36.52_wp, 36.52_wp, 19.16_wp, 22.80_wp, &
	1003	26.0_wp, 26.0_wp, 1.0_wp /)
[799]	1004
[828]	1005	ENDIF
[790]	1006
[828]	1007	!
	1008	!-- Calculate the radius class index of particles with respect to array r0
[1007]	1009	!-- Radius has to be in Âµm
[828]	1010	ALLOCATE( ira(1:radius_classes) )
[790]	1011
[828]	1012	DO j = 1, radius_classes
[1322]	1013	particle_radius = radclass(j) * 1.0E6_wp
[828]	1014	DO k = 1, 7
	1015	IF ( particle_radius < r0(k) ) THEN
	1016	ira(j) = k
	1017	EXIT
	1018	ENDIF
	1019	ENDDO
	1020	IF ( particle_radius >= r0(7) ) ira(j) = 8
	1021	ENDDO
[799]	1022
	1023	!
[828]	1024	!-- Two-dimensional linear interpolation of the collision efficiencies
[1007]	1025	!-- Radius has to be in Âµm
[828]	1026	DO j = 1, radius_classes
	1027	DO i = 1, j
[799]	1028
[828]	1029	ir = ira(j)
[1519]	1030	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
[799]	1031
[828]	1032	DO kk = 2, 11
	1033	IF ( rq <= rat(kk) ) THEN
	1034	iq = kk
	1035	EXIT
	1036	ENDIF
	1037	ENDDO
[790]	1038
[1359]	1039	y1 = 0.0001_wp ! for 0 m2/s3
[1007]	1040
[828]	1041	IF ( ir < 8 ) THEN
	1042	IF ( ir >= 2 ) THEN
[1776]	1043	pp = ( MAX(radclass(j),radclass(i))*1.0E6_wp - r0(ir-1) ) / &
	1044	( r0(ir) - r0(ir-1) )
[828]	1045	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	1046	y2 = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) * ecoll_100(ir-1,iq-1) + &
	1047	pp * ( 1.0_wp - qq ) * ecoll_100(ir,iq-1) + &
	1048	qq * ( 1.0_wp - pp ) * ecoll_100(ir-1,iq) + &
	1049	pp * qq * ecoll_100(ir,iq)
	1050	y3 = ( 1.0-pp ) * ( 1.0_wp - qq ) * ecoll_400(ir-1,iq-1) + &
	1051	pp * ( 1.0_wp - qq ) * ecoll_400(ir,iq-1) + &
	1052	qq * ( 1.0_wp - pp ) * ecoll_400(ir-1,iq) + &
	1053	pp * qq * ecoll_400(ir,iq)
[828]	1054	ELSE
	1055	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	1056	y2 = ( 1.0_wp - qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq)
	1057	y3 = ( 1.0_wp - qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq)
[828]	1058	ENDIF
	1059	ELSE
	1060	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	1061	y2 = ( 1.0_wp - qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq)
	1062	y3 = ( 1.0_wp - qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq)
[828]	1063	ENDIF
	1064	!
[1007]	1065	!-- Linear interpolation of dissipation rate in m2/s3
[1359]	1066	IF ( epsilon <= 0.01_wp ) THEN
	1067	ecf(j,i) = ( epsilon - 0.01_wp ) / ( 0.0_wp - 0.01_wp ) * y1 &
	1068	+ ( epsilon - 0.0_wp ) / ( 0.01_wp - 0.0_wp ) * y2
	1069	ELSEIF ( epsilon <= 0.06_wp ) THEN
	1070	ecf(j,i) = ( epsilon - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	1071	+ ( epsilon - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	1072	ELSE
[1359]	1073	ecf(j,i) = ( 0.06_wp - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	1074	+ ( 0.06_wp - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	1075	ENDIF
[790]	1076
[1359]	1077	IF ( ecf(j,i) < 1.0_wp ) ecf(j,i) = 1.0_wp
[790]	1078
[828]	1079	ecf(i,j) = ecf(j,i)
[790]	1080
[828]	1081	ENDDO
	1082	ENDDO
[790]	1083
[828]	1084	END SUBROUTINE turb_enhance_eff
[790]	1085
[849]	1086
	1087
	1088	!------------------------------------------------------------------------------!
[1682]	1089	! Description:
	1090	! ------------
	1091	!> Collision efficiencies from table 8.2 in Rogers and Yau (1989, 3rd edition).
	1092	!> Values are calculated from table by bilinear interpolation.
[849]	1093	!------------------------------------------------------------------------------!
[1682]	1094
	1095	SUBROUTINE collision_efficiency_rogers( mean_r, r, e)
[849]	1096
	1097	IMPLICIT NONE
	1098
[1682]	1099	INTEGER(iwp) :: i !<
	1100	INTEGER(iwp) :: j !<
	1101	INTEGER(iwp) :: k !<
[849]	1102
[1682]	1103	LOGICAL, SAVE :: first = .TRUE. !<
[849]	1104
[1682]	1105	REAL(wp) :: aa !<
	1106	REAL(wp) :: bb !<
	1107	REAL(wp) :: cc !<
	1108	REAL(wp) :: dd !<
	1109	REAL(wp) :: dx !<
	1110	REAL(wp) :: dy !<
	1111	REAL(wp) :: e !<
	1112	REAL(wp) :: gg !<
	1113	REAL(wp) :: mean_r !<
	1114	REAL(wp) :: mean_rm !<
	1115	REAL(wp) :: r !<
	1116	REAL(wp) :: rm !<
	1117	REAL(wp) :: x !<
	1118	REAL(wp) :: y !<
[1320]	1119
[1682]	1120	REAL(wp), DIMENSION(1:9), SAVE :: collected_r = 0.0_wp !<
[1320]	1121
[1682]	1122	REAL(wp), DIMENSION(1:19), SAVE :: collector_r = 0.0_wp !<
[1320]	1123
[1682]	1124	REAL(wp), DIMENSION(1:9,1:19), SAVE :: ef = 0.0_wp !<
[849]	1125
[1322]	1126	mean_rm = mean_r * 1.0E06_wp
	1127	rm = r * 1.0E06_wp
[849]	1128
	1129	IF ( first ) THEN
	1130
[1359]	1131	collected_r = (/ 2.0_wp, 3.0_wp, 4.0_wp, 6.0_wp, 8.0_wp, &
	1132	10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp /)
	1133	collector_r = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, &
	1134	60.0_wp, 80.0_wp, 100.0_wp, 150.0_wp, 200.0_wp, &
	1135	300.0_wp, 400.0_wp, 500.0_wp, 600.0_wp, 1000.0_wp, &
	1136	1400.0_wp, 1800.0_wp, 2400.0_wp, 3000.0_wp /)
[849]	1137
[1359]	1138	ef(:,1) = (/ 0.017_wp, 0.027_wp, 0.037_wp, 0.052_wp, 0.052_wp, &
	1139	0.052_wp, 0.052_wp, 0.0_wp, 0.0_wp /)
	1140	ef(:,2) = (/ 0.001_wp, 0.016_wp, 0.027_wp, 0.060_wp, 0.12_wp, &
	1141	0.17_wp, 0.17_wp, 0.17_wp, 0.0_wp /)
	1142	ef(:,3) = (/ 0.001_wp, 0.001_wp, 0.02_wp, 0.13_wp, 0.28_wp, &
	1143	0.37_wp, 0.54_wp, 0.55_wp, 0.47_wp/)
	1144	ef(:,4) = (/ 0.001_wp, 0.001_wp, 0.02_wp, 0.23_wp, 0.4_wp, &
	1145	0.55_wp, 0.7_wp, 0.75_wp, 0.75_wp/)
	1146	ef(:,5) = (/ 0.01_wp, 0.01_wp, 0.03_wp, 0.3_wp, 0.4_wp, &
	1147	0.58_wp, 0.73_wp, 0.75_wp, 0.79_wp/)
	1148	ef(:,6) = (/ 0.01_wp, 0.01_wp, 0.13_wp, 0.38_wp, 0.57_wp, &
	1149	0.68_wp, 0.80_wp, 0.86_wp, 0.91_wp/)
	1150	ef(:,7) = (/ 0.01_wp, 0.085_wp, 0.23_wp, 0.52_wp, 0.68_wp, &
	1151	0.76_wp, 0.86_wp, 0.92_wp, 0.95_wp/)
	1152	ef(:,8) = (/ 0.01_wp, 0.14_wp, 0.32_wp, 0.60_wp, 0.73_wp, &
	1153	0.81_wp, 0.90_wp, 0.94_wp, 0.96_wp/)
	1154	ef(:,9) = (/ 0.025_wp, 0.25_wp, 0.43_wp, 0.66_wp, 0.78_wp, &
	1155	0.83_wp, 0.92_wp, 0.95_wp, 0.96_wp/)
	1156	ef(:,10) = (/ 0.039_wp, 0.3_wp, 0.46_wp, 0.69_wp, 0.81_wp, &
	1157	0.87_wp, 0.93_wp, 0.95_wp, 0.96_wp/)
	1158	ef(:,11) = (/ 0.095_wp, 0.33_wp, 0.51_wp, 0.72_wp, 0.82_wp, &
	1159	0.87_wp, 0.93_wp, 0.96_wp, 0.97_wp/)
	1160	ef(:,12) = (/ 0.098_wp, 0.36_wp, 0.51_wp, 0.73_wp, 0.83_wp, &
	1161	0.88_wp, 0.93_wp, 0.96_wp, 0.97_wp/)
	1162	ef(:,13) = (/ 0.1_wp, 0.36_wp, 0.52_wp, 0.74_wp, 0.83_wp, &
	1163	0.88_wp, 0.93_wp, 0.96_wp, 0.97_wp/)
	1164	ef(:,14) = (/ 0.17_wp, 0.4_wp, 0.54_wp, 0.72_wp, 0.83_wp, &
	1165	0.88_wp, 0.94_wp, 0.98_wp, 1.0_wp /)
	1166	ef(:,15) = (/ 0.15_wp, 0.37_wp, 0.52_wp, 0.74_wp, 0.82_wp, &
	1167	0.88_wp, 0.94_wp, 0.98_wp, 1.0_wp /)
	1168	ef(:,16) = (/ 0.11_wp, 0.34_wp, 0.49_wp, 0.71_wp, 0.83_wp, &
	1169	0.88_wp, 0.94_wp, 0.95_wp, 1.0_wp /)
	1170	ef(:,17) = (/ 0.08_wp, 0.29_wp, 0.45_wp, 0.68_wp, 0.8_wp, &
	1171	0.86_wp, 0.96_wp, 0.94_wp, 1.0_wp /)
	1172	ef(:,18) = (/ 0.04_wp, 0.22_wp, 0.39_wp, 0.62_wp, 0.75_wp, &
	1173	0.83_wp, 0.92_wp, 0.96_wp, 1.0_wp /)
	1174	ef(:,19) = (/ 0.02_wp, 0.16_wp, 0.33_wp, 0.55_wp, 0.71_wp, &
	1175	0.81_wp, 0.90_wp, 0.94_wp, 1.0_wp /)
[849]	1176
	1177	ENDIF
	1178
	1179	DO k = 1, 8
	1180	IF ( collected_r(k) <= mean_rm ) i = k
	1181	ENDDO
	1182
	1183	DO k = 1, 18
	1184	IF ( collector_r(k) <= rm ) j = k
	1185	ENDDO
	1186
[1359]	1187	IF ( rm < 10.0_wp ) THEN
	1188	e = 0.0_wp
	1189	ELSEIF ( mean_rm < 2.0_wp ) THEN
	1190	e = 0.001_wp
	1191	ELSEIF ( mean_rm >= 25.0_wp ) THEN
	1192	IF( j <= 2 ) e = 0.0_wp
	1193	IF( j == 3 ) e = 0.47_wp
	1194	IF( j == 4 ) e = 0.8_wp
	1195	IF( j == 5 ) e = 0.9_wp
	1196	IF( j >=6 ) e = 1.0_wp
	1197	ELSEIF ( rm >= 3000.0_wp ) THEN
	1198	IF( i == 1 ) e = 0.02_wp
	1199	IF( i == 2 ) e = 0.16_wp
	1200	IF( i == 3 ) e = 0.33_wp
	1201	IF( i == 4 ) e = 0.55_wp
	1202	IF( i == 5 ) e = 0.71_wp
	1203	IF( i == 6 ) e = 0.81_wp
	1204	IF( i == 7 ) e = 0.90_wp
	1205	IF( i >= 8 ) e = 0.94_wp
[849]	1206	ELSE
	1207	x = mean_rm - collected_r(i)
	1208	y = rm - collector_r(j)
	1209	dx = collected_r(i+1) - collected_r(i)
	1210	dy = collector_r(j+1) - collector_r(j)
	1211	aa = x2 + y2
	1212	bb = ( dx - x )2 + y2
	1213	cc = x2 + ( dy - y )2
	1214	dd = ( dx - x )2 + ( dy - y )2
	1215	gg = aa + bb + cc + dd
	1216
	1217	e = ( (gg-aa)ef(i,j) + (gg-bb)ef(i+1,j) + (gg-cc)*ef(i,j+1) + &
[1359]	1218	(gg-dd)ef(i+1,j+1) ) / (3.0_wp gg)
[849]	1219	ENDIF
	1220
	1221	END SUBROUTINE collision_efficiency_rogers
	1222
[825]	1223	END MODULE lpm_collision_kernels_mod

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