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source: palm/trunk/SOURCE/lpm_collision_kernels.f90 @ 1359

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

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