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source: palm/trunk/SOURCE/lpm_collision_kernels.f90 @ 1323

Last change on this file since 1323 was 1323, checked in by raasch, 10 years ago
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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	! -----------------
[1321]	22	!
[1323]	23	!
[1321]	24	! Former revisions:
	25	! -----------------
	26	! $Id: lpm_collision_kernels.f90 1323 2014-03-20 17:09:54Z raasch $
	27	!
[1323]	28	! 1322 2014-03-20 16:38:49Z raasch
	29	! REAL constants defined as wp_kind
	30	!
[1321]	31	! 1320 2014-03-20 08:40:49Z
[1320]	32	! ONLY-attribute added to USE-statements,
	33	! kind-parameters added to all INTEGER and REAL declaration statements,
	34	! kinds are defined in new module kinds,
	35	! revision history before 2012 removed,
	36	! comment fields (!:) to be used for variable explanations added to
	37	! all variable declaration statements
[1008]	38	!
[1093]	39	! 1092 2013-02-02 11:24:22Z raasch
	40	! unused variables removed
	41	!
[1072]	42	! 1071 2012-11-29 16:54:55Z franke
	43	! Bugfix: collision efficiencies for Hall kernel should not be < 1.0E-20
	44	!
[1037]	45	! 1036 2012-10-22 13:43:42Z raasch
	46	! code put under GPL (PALM 3.9)
	47	!
[1008]	48	! 1007 2012-09-19 14:30:36Z franke
[1007]	49	! converted all units to SI units and replaced some parameters by corresponding
	50	! PALM parameters
	51	! Bugfix: factor in calculation of enhancement factor for collision efficencies
	52	! changed from 10. to 1.0
[829]	53	!
[850]	54	! 849 2012-03-15 10:35:09Z raasch
	55	! routine collision_efficiency_rogers added (moved from former advec_particles
	56	! to here)
	57	!
[836]	58	! 835 2012-02-22 11:21:19Z raasch $
	59	! Bugfix: array diss can be used only in case of Wang kernel
	60	!
[829]	61	! 828 2012-02-21 12:00:36Z raasch
[828]	62	! code has been completely reformatted, routine colker renamed
	63	! recalculate_kernel,
	64	! routine init_kernels added, radius is now communicated to the collision
	65	! routines by array radclass
[790]	66	!
[828]	67	! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4
	68	!
[826]	69	! 825 2012-02-19 03:03:44Z raasch
	70	! routine renamed from wang_kernel to lpm_collision_kernels,
	71	! turbulence_effects on collision replaced by wang_kernel
	72	!
[791]	73	! 790 2011-11-29 03:11:20Z raasch
	74	! initial revision
[790]	75	!
	76	! Description:
	77	! ------------
[828]	78	! This module calculates collision efficiencies either due to pure gravitational
	79	! effects (Hall kernel, see Hall, 1980: J. Atmos. Sci., 2486-2507) or
	80	! including the effects of (SGS) turbulence (Wang kernel, see Wang and
	81	! Grabowski, 2009: Atmos. Sci. Lett., 10, 1-8). The original code has been
	82	! provided by L.-P. Wang but is substantially reformatted and speed optimized
	83	! here.
	84	!
	85	! ATTENTION:
	86	! Physical quantities (like g, densities, etc.) used in this module still
	87	! have to be adjusted to those values used in the main PALM code.
	88	! Also, quantities in CGS-units should be converted to SI-units eventually.
[790]	89	!------------------------------------------------------------------------------!
	90
[1320]	91	USE constants, &
	92	ONLY: pi
	93
	94	USE kinds
	95
	96	USE particle_attributes, &
	97	ONLY: collision_kernel, dissipation_classes, particles, radius_classes
	98
[828]	99	USE pegrid
[790]	100
[828]	101
[790]	102	IMPLICIT NONE
	103
	104	PRIVATE
	105
[849]	106	PUBLIC ckernel, collision_efficiency_rogers, init_kernels, &
[1007]	107	rclass_lbound, rclass_ubound, recalculate_kernel
[790]	108
[1320]	109	REAL(wp) :: epsilon !:
	110	REAL(wp) :: eps2 !:
	111	REAL(wp) :: rclass_lbound !:
	112	REAL(wp) :: rclass_ubound !:
	113	REAL(wp) :: urms !:
	114	REAL(wp) :: urms2 !:
[790]	115
[1320]	116	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !:
	117	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !:
	118	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !:
	119
	120	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !:
	121	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !:
	122	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !:
	123	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !:
	124	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !:
	125
	126	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !:
[792]	127
[828]	128	SAVE
[792]	129
[790]	130	!
	131	!-- Public interfaces
[849]	132	INTERFACE collision_efficiency_rogers
	133	MODULE PROCEDURE collision_efficiency_rogers
	134	END INTERFACE collision_efficiency_rogers
	135
[828]	136	INTERFACE init_kernels
	137	MODULE PROCEDURE init_kernels
	138	END INTERFACE init_kernels
[790]	139
[828]	140	INTERFACE recalculate_kernel
	141	MODULE PROCEDURE recalculate_kernel
	142	END INTERFACE recalculate_kernel
[790]	143
	144
[828]	145	CONTAINS
[790]	146
[792]	147
[828]	148	SUBROUTINE init_kernels
	149	!------------------------------------------------------------------------------!
	150	! Initialization of the collision efficiency matrix with fixed radius and
	151	! dissipation classes, calculated at simulation start only.
	152	!------------------------------------------------------------------------------!
[792]	153
[828]	154	IMPLICIT NONE
[792]	155
[1320]	156	INTEGER(iwp) :: i !:
	157	INTEGER(iwp) :: j !:
	158	INTEGER(iwp) :: k !:
[790]	159
[828]	160
	161	!
	162	!-- Calculate collision efficiencies for fixed radius- and dissipation
	163	!-- classes
	164	IF ( collision_kernel(6:9) == 'fast' ) THEN
	165
	166	ALLOCATE( ckernel(1:radius_classes,1:radius_classes, &
	167	0:dissipation_classes), epsclass(1:dissipation_classes), &
	168	radclass(1:radius_classes) )
	169
	170	!
	171	!-- Calculate the radius class bounds with logarithmic distances
	172	!-- in the interval [1.0E-6, 2.0E-4] m
[1322]	173	rclass_lbound = LOG( 1.0E-6_wp )
	174	rclass_ubound = LOG( 2.0E-4_wp )
[828]	175	radclass(1) = 1.0E-6
	176	DO i = 2, radius_classes
	177	radclass(i) = EXP( rclass_lbound + &
	178	( rclass_ubound - rclass_lbound ) * ( i-1.0 ) /&
	179	( radius_classes - 1.0 ) )
	180	! IF ( myid == 0 ) THEN
	181	! PRINT, 'i=', i, ' r = ', radclass(i)1.0E6
	182	! ENDIF
	183	ENDDO
	184
	185	!
[1007]	186	!-- Set the class bounds for dissipation in interval [0.0, 0.1] m2/s3
[828]	187	DO i = 1, dissipation_classes
[1322]	188	epsclass(i) = 0.1 * REAL( i, KIND=wp ) / dissipation_classes
[828]	189	! IF ( myid == 0 ) THEN
	190	! PRINT*, 'i=', i, ' eps = ', epsclass(i)
	191	! ENDIF
	192	ENDDO
	193	!
	194	!-- Calculate collision efficiencies of the Wang/ayala kernel
	195	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
	196	ecf(1:radius_classes,1:radius_classes), &
	197	gck(1:radius_classes,1:radius_classes), &
	198	winf(1:radius_classes) )
	199
	200	DO k = 1, dissipation_classes
	201
	202	epsilon = epsclass(k)
[1322]	203	urms = 2.02 * ( epsilon / 0.04_wp )**( 1.0_wp / 3.0_wp )
[828]	204
	205	CALL turbsd
	206	CALL turb_enhance_eff
	207	CALL effic
	208
	209	DO j = 1, radius_classes
	210	DO i = 1, radius_classes
	211	ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j)
	212	ENDDO
	213	ENDDO
	214
	215	ENDDO
	216
	217	!
	218	!-- Calculate collision efficiencies of the Hall kernel
	219	ALLOCATE( hkernel(1:radius_classes,1:radius_classes), &
	220	hwratio(1:radius_classes,1:radius_classes) )
	221
	222	CALL fallg
	223	CALL effic
	224
	225	DO j = 1, radius_classes
	226	DO i = 1, radius_classes
	227	hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 &
	228	* ec(i,j) * ABS( winf(j) - winf(i) )
	229	ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0
	230	ENDDO
	231	ENDDO
	232
	233	!
	234	!-- Test output of efficiencies
	235	IF ( j == -1 ) THEN
	236
	237	PRINT, '** Hall kernel'
[1007]	238	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6, &
	239	i = 1,radius_classes )
[828]	240	DO j = 1, radius_classes
[1007]	241	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
	242	( hkernel(i,j), i = 1,radius_classes )
[828]	243	ENDDO
	244
	245	DO k = 1, dissipation_classes
	246	DO i = 1, radius_classes
	247	DO j = 1, radius_classes
	248	IF ( hkernel(i,j) == 0.0 ) THEN
	249	hwratio(i,j) = 9999999.9
	250	ELSE
	251	hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j)
	252	ENDIF
	253	ENDDO
	254	ENDDO
	255
	256	PRINT, '** epsilon = ', epsclass(k)
[1007]	257	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6, &
	258	i = 1,radius_classes )
[828]	259	DO j = 1, radius_classes
[1007]	260	! WRITE ( ,'(F4.0,1X,20(F4.2,1X))' ) radclass(j)1.0E6, &
	261	! ( ckernel(i,j,k), i = 1,radius_classes )
	262	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j)1.0E6, &
	263	( hwratio(i,j), i = 1,radius_classes )
[828]	264	ENDDO
	265	ENDDO
	266
	267	ENDIF
	268
	269	DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf )
	270
	271	ELSEIF( collision_kernel == 'hall' .OR. collision_kernel == 'wang' ) &
	272	THEN
	273	!
	274	!-- Initial settings for Hall- and Wang-Kernel
	275	!-- To be done: move here parts from turbsd, fallg, ecoll, etc.
	276	ENDIF
	277
	278	END SUBROUTINE init_kernels
	279
	280
[790]	281	!------------------------------------------------------------------------------!
[828]	282	! Calculation of collision kernels during each timestep and for each grid box
[790]	283	!------------------------------------------------------------------------------!
[828]	284	SUBROUTINE recalculate_kernel( i1, j1, k1 )
[790]	285
[1320]	286	USE arrays_3d, &
	287	ONLY: diss
[790]	288
[1320]	289	USE particle_attributes, &
	290	ONLY: prt_count, prt_start_index, radius_classes, wang_kernel
	291
[790]	292	IMPLICIT NONE
	293
[1320]	294	INTEGER(iwp) :: i !:
	295	INTEGER(iwp) :: i1 !:
	296	INTEGER(iwp) :: j !:
	297	INTEGER(iwp) :: j1 !:
	298	INTEGER(iwp) :: k1 !:
	299	INTEGER(iwp) :: pend !:
	300	INTEGER(iwp) :: pstart !:
[790]	301
	302
[828]	303	pstart = prt_start_index(k1,j1,i1)
	304	pend = prt_start_index(k1,j1,i1) + prt_count(k1,j1,i1) - 1
	305	radius_classes = prt_count(k1,j1,i1)
[792]	306
[828]	307	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
	308	radclass(1:radius_classes), winf(1:radius_classes) )
[790]	309
[828]	310	!
[1007]	311	!-- Store particle radii on the radclass array
	312	radclass(1:radius_classes) = particles(pstart:pend)%radius
[790]	313
[835]	314	IF ( wang_kernel ) THEN
[1007]	315	epsilon = diss(k1,j1,i1) ! dissipation rate in m2/s3
[835]	316	ELSE
	317	epsilon = 0.0
	318	ENDIF
[1322]	319	urms = 2.02 * ( epsilon / 0.04_wp )**( 0.33333333333_wp )
[790]	320
[1007]	321	IF ( wang_kernel .AND. epsilon > 1.0E-7 ) THEN
[828]	322	!
	323	!-- Call routines to calculate efficiencies for the Wang kernel
	324	ALLOCATE( gck(1:radius_classes,1:radius_classes), &
	325	ecf(1:radius_classes,1:radius_classes) )
[790]	326
[828]	327	CALL turbsd
	328	CALL turb_enhance_eff
	329	CALL effic
[790]	330
[828]	331	DO j = 1, radius_classes
	332	DO i = 1, radius_classes
	333	ckernel(pstart+i-1,pstart+j-1,1) = ec(i,j) * gck(i,j) * ecf(i,j)
[790]	334	ENDDO
[828]	335	ENDDO
[790]	336
[828]	337	DEALLOCATE( gck, ecf )
[790]	338
	339	ELSE
[828]	340	!
	341	!-- Call routines to calculate efficiencies for the Hall kernel
[790]	342	CALL fallg
	343	CALL effic
	344
[828]	345	DO j = 1, radius_classes
	346	DO i = 1, radius_classes
	347	ckernel(pstart+i-1,pstart+j-1,1) = pi * &
	348	( radclass(j) + radclass(i) )**2 &
	349	* ec(i,j) * ABS( winf(j) - winf(i) )
[790]	350	ENDDO
	351	ENDDO
	352
	353	ENDIF
	354
[828]	355	DEALLOCATE( ec, radclass, winf )
[790]	356
[828]	357	END SUBROUTINE recalculate_kernel
[790]	358
[828]	359
[790]	360	!------------------------------------------------------------------------------!
[828]	361	! Calculation of gck
	362	! This is from Aayala 2008b, page 37ff.
	363	! Necessary input parameters: water density, radii of droplets, air density,
	364	! air viscosity, turbulent dissipation rate, taylor microscale reynolds number,
	365	! gravitational acceleration --> to be replaced by PALM parameters
[790]	366	!------------------------------------------------------------------------------!
[792]	367	SUBROUTINE turbsd
[799]	368
[1320]	369	USE control_parameters, &
	370	ONLY: g, molecular_viscosity
	371
	372	USE particle_attributes, &
	373	ONLY: radius_classes
[790]	374
	375	IMPLICIT NONE
[1320]	376
	377	LOGICAL, SAVE :: first = .TRUE. !:
[790]	378
[1320]	379	INTEGER(iwp) :: i !:
	380	INTEGER(iwp) :: j !:
[790]	381
[1320]	382	REAL(wp) :: ao !:
	383	REAL(wp) :: ao_gr !:
	384	REAL(wp) :: bbb !:
	385	REAL(wp) :: be !:
	386	REAL(wp) :: b1 !:
	387	REAL(wp) :: b2 !:
	388	REAL(wp) :: ccc !:
	389	REAL(wp) :: c1 !:
	390	REAL(wp) :: c1_gr !:
	391	REAL(wp) :: c2 !:
	392	REAL(wp) :: d1 !:
	393	REAL(wp) :: d2 !:
	394	REAL(wp) :: eta !:
	395	REAL(wp) :: e1 !:
	396	REAL(wp) :: e2 !:
	397	REAL(wp) :: fao_gr !:
	398	REAL(wp) :: fr !:
	399	REAL(wp) :: grfin !:
	400	REAL(wp) :: lambda !:
	401	REAL(wp) :: lambda_re !:
	402	REAL(wp) :: lf !:
	403	REAL(wp) :: rc !:
	404	REAL(wp) :: rrp !:
	405	REAL(wp) :: sst !:
	406	REAL(wp) :: tauk !:
	407	REAL(wp) :: tl !:
	408	REAL(wp) :: t2 !:
	409	REAL(wp) :: tt !:
	410	REAL(wp) :: t1 !:
	411	REAL(wp) :: vk !:
	412	REAL(wp) :: vrms1xy !:
	413	REAL(wp) :: vrms2xy !:
	414	REAL(wp) :: v1 !:
	415	REAL(wp) :: v1v2xy !:
	416	REAL(wp) :: v1xysq !:
	417	REAL(wp) :: v2 !:
	418	REAL(wp) :: v2xysq !:
	419	REAL(wp) :: wrfin !:
	420	REAL(wp) :: wrgrav2 !:
	421	REAL(wp) :: wrtur2xy !:
	422	REAL(wp) :: xx !:
	423	REAL(wp) :: yy !:
	424	REAL(wp) :: z !:
[790]	425
[1320]	426	REAL(wp), DIMENSION(1:radius_classes) :: st !:
	427	REAL(wp), DIMENSION(1:radius_classes) :: tau !:
	428
[799]	429	!
[828]	430	!-- Initial assignment of constants
[799]	431	IF ( first ) THEN
[790]	432
[799]	433	first = .FALSE.
[790]	434
[1007]	435	ENDIF
[790]	436
[1322]	437	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon ) ! in m
	438	lambda_re = urms*2 SQRT( 15.0_wp / epsilon / molecular_viscosity )
[828]	439	tl = urms**2 / epsilon ! in s
[1007]	440	lf = 0.5 * urms**3 / epsilon ! in m
	441	tauk = SQRT( molecular_viscosity / epsilon ) ! in s
[1322]	442	eta = ( molecular_viscosity3 / epsilon )0.25_wp ! in m
[1007]	443	vk = eta / tauk
[790]	444
[828]	445	ao = ( 11.0 + 7.0 * lambda_re ) / ( 205.0 + lambda_re )
[1322]	446	tt = SQRT( 2.0 * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk ! in s
[799]	447
[1007]	448	CALL fallg ! gives winf in m/s
[790]	449
[828]	450	DO i = 1, radius_classes
[1007]	451	tau(i) = winf(i) / g ! in s
[828]	452	st(i) = tau(i) / tauk
[790]	453	ENDDO
	454
[828]	455	!
	456	!-- Calculate wr (from Aayala 2008b, page 38f)
	457	z = tt / tl
[1322]	458	be = SQRT( 2.0_wp ) * lambda / lf
[828]	459	bbb = SQRT( 1.0 - 2.0 * be**2 )
	460	d1 = ( 1.0 + bbb ) / ( 2.0 * bbb )
[1007]	461	e1 = lf * ( 1.0 + bbb ) * 0.5 ! in m
[828]	462	d2 = ( 1.0 - bbb ) * 0.5 / bbb
[1007]	463	e2 = lf * ( 1.0 - bbb ) * 0.5 ! in m
[828]	464	ccc = SQRT( 1.0 - 2.0 * z**2 )
	465	b1 = ( 1.0 + ccc ) * 0.5 / ccc
	466	c1 = tl * ( 1.0 + ccc ) * 0.5 ! in s
	467	b2 = ( 1.0 - ccc ) * 0.5 / ccc
	468	c2 = tl * ( 1.0 - ccc ) * 0.5 ! in s
[790]	469
[828]	470	DO i = 1, radius_classes
[790]	471
[1007]	472	v1 = winf(i) ! in m/s
[828]	473	t1 = tau(i) ! in s
[790]	474
[828]	475	DO j = 1, i
[1007]	476	rrp = radclass(i) + radclass(j)
	477	v2 = winf(j) ! in m/s
[828]	478	t2 = tau(j) ! in s
[790]	479
[1007]	480	v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) &
	481	- b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1)
	482	v1xysq = v1xysq * urms2 / t1 ! in m2/s**2
	483	vrms1xy = SQRT( v1xysq ) ! in m/s
[790]	484
[1007]	485	v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) &
	486	- b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2)
	487	v2xysq = v2xysq * urms2 / t2 ! in m2/s**2
	488	vrms2xy = SQRT( v2xysq ) ! in m/s
[790]	489
[828]	490	IF ( winf(i) >= winf(j) ) THEN
[799]	491	v1 = winf(i)
[790]	492	t1 = tau(i)
[799]	493	v2 = winf(j)
[790]	494	t2 = tau(j)
	495	ELSE
[799]	496	v1 = winf(j)
[790]	497	t1 = tau(j)
[799]	498	v2 = winf(i)
[790]	499	t2 = tau(i)
	500	ENDIF
	501
[828]	502	v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - &
	503	b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - &
	504	b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + &
	505	b2 * d2* zhi(c2,e2,v1,t1,v2,t2)
	506	fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 )
[1007]	507	v1v2xy = v1v2xy * fr * urms2 / tau(i) / tau(j) ! in m2/s**2
	508	wrtur2xy = vrms1xy2 + vrms2xy2 - 2.0 * v1v2xy ! in m2/s2
[828]	509	IF ( wrtur2xy < 0.0 ) wrtur2xy = 0.0
[1322]	510	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
	511	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) ) ! in m/s
[790]	512
[828]	513	!
	514	!-- Calculate gr
	515	IF ( st(j) > st(i) ) THEN
	516	sst = st(j)
[790]	517	ELSE
[828]	518	sst = st(i)
[790]	519	ENDIF
	520
[828]	521	xx = -0.1988 * sst*4 + 1.5275 sst*3 - 4.2942 sst**2 + &
	522	5.3406 * sst
	523	IF ( xx < 0.0 ) xx = 0.0
[1322]	524	yy = 0.1886 * EXP( 20.306_wp / lambda_re )
[790]	525
[1007]	526	c1_gr = xx / ( g / vk * tauk )**yy
[790]	527
[1322]	528	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
[828]	529	fao_gr = 20.115 * SQRT( ao_gr / lambda_re )
	530	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta ! in cm
[790]	531
[828]	532	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5 )
	533	IF ( grfin < 1.0 ) grfin = 1.0
[790]	534
[828]	535	gck(i,j) = 2.0 * pi * rrp*2 wrfin * grfin ! in cm**3/s
[790]	536	gck(j,i) = gck(i,j)
	537
	538	ENDDO
	539	ENDDO
	540
[828]	541	END SUBROUTINE turbsd
[790]	542
[828]	543
[790]	544	!------------------------------------------------------------------------------!
[1007]	545	! phi_w as a function
[790]	546	!------------------------------------------------------------------------------!
[1320]	547	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
[790]	548
	549	IMPLICIT NONE
	550
[1320]	551	REAL(wp) :: a !:
	552	REAL(wp) :: aa1 !:
	553	REAL(wp) :: b !:
	554	REAL(wp) :: tau0 !:
	555	REAL(wp) :: vsett !:
[790]	556
[828]	557	aa1 = 1.0 / tau0 + 1.0 / a + vsett / b
[1007]	558	phi_w = 1.0 / aa1 - 0.5 * vsett / b / aa1**2 ! in s
[790]	559
[1007]	560	END FUNCTION phi_w
[792]	561
[790]	562
	563	!------------------------------------------------------------------------------!
[1007]	564	! zhi as a function
[790]	565	!------------------------------------------------------------------------------!
[1320]	566	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
[790]	567
	568	IMPLICIT NONE
	569
[1320]	570	REAL(wp) :: a !:
	571	REAL(wp) :: aa1 !:
	572	REAL(wp) :: aa2 !:
	573	REAL(wp) :: aa3 !:
	574	REAL(wp) :: aa4 !:
	575	REAL(wp) :: aa5 !:
	576	REAL(wp) :: aa6 !:
	577	REAL(wp) :: b !:
	578	REAL(wp) :: tau1 !:
	579	REAL(wp) :: tau2 !:
	580	REAL(wp) :: vsett1 !:
	581	REAL(wp) :: vsett2 !:
[790]	582
[828]	583	aa1 = vsett2 / b - 1.0 / tau2 - 1.0 / a
	584	aa2 = vsett1 / b + 1.0 / tau1 + 1.0 / a
	585	aa3 = ( vsett1 - vsett2 ) / b + 1.0 / tau1 + 1.0 / tau2
	586	aa4 = ( vsett2 / b )2 - ( 1.0 / tau2 + 1.0 / a )2
	587	aa5 = vsett2 / b + 1.0 / tau2 + 1.0 / a
	588	aa6 = 1.0 / tau1 - 1.0 / a + ( 1.0 / tau2 + 1.0 / a) * vsett1 / vsett2
	589	zhi = (1.0 / aa1 - 1.0 / aa2 ) * ( vsett1 - vsett2 ) * 0.5 / b / aa3**2 &
	590	+ (4.0 / aa4 - 1.0 / aa52 - 1.0 / aa12 ) * vsett2 * 0.5 / b /aa6&
	591	+ (2.0 * ( b / aa2 - b / aa1 ) - vsett1 / aa22 + vsett2 / aa12 )&
	592	* 0.5 / b / aa3 ! in s**2
[799]	593
[828]	594	END FUNCTION zhi
[790]	595
[828]	596
[790]	597	!------------------------------------------------------------------------------!
[1007]	598	! Calculation of terminal velocity winf following Equations 10-138 to 10-145
	599	! from (Pruppacher and Klett, 1997)
[790]	600	!------------------------------------------------------------------------------!
[828]	601	SUBROUTINE fallg
[1320]	602
	603	USE cloud_parameters, &
	604	ONLY: rho_l
	605
	606	USE control_parameters, &
	607	ONLY: g
[790]	608
[1320]	609	USE particle_attributes, &
	610	ONLY: radius_classes
[790]	611
[1320]	612
[828]	613	IMPLICIT NONE
[790]	614
[1320]	615	INTEGER(iwp) :: i !:
	616	INTEGER(iwp) :: j !:
[790]	617
[1320]	618	LOGICAL, SAVE :: first = .TRUE. !:
[790]	619
[1320]	620	REAL(wp), SAVE :: cunh !:
	621	REAL(wp), SAVE :: eta !:
	622	REAL(wp), SAVE :: phy !:
	623	REAL(wp), SAVE :: py !:
	624	REAL(wp), SAVE :: rho_a !:
	625	REAL(wp), SAVE :: sigma !:
	626	REAL(wp), SAVE :: stb !:
	627	REAL(wp), SAVE :: stok !:
	628	REAL(wp), SAVE :: xlamb !:
[790]	629
[1320]	630	REAL(wp) :: bond !:
	631	REAL(wp) :: x !:
	632	REAL(wp) :: xrey !:
	633	REAL(wp) :: y !:
[799]	634
[1320]	635	REAL(wp), DIMENSION(1:7), SAVE :: b !:
	636	REAL(wp), DIMENSION(1:6), SAVE :: c !:
[799]	637
	638	!
[828]	639	!-- Initial assignment of constants
	640	IF ( first ) THEN
[799]	641
[828]	642	first = .FALSE.
	643	b = (/ -0.318657E1, 0.992696E0, -0.153193E-2, -0.987059E-3, &
	644	-0.578878E-3, 0.855176E-4, -0.327815E-5 /)
	645	c = (/ -0.500015E1, 0.523778E1, -0.204914E1, 0.475294E0, &
	646	-0.542819E-1, 0.238449E-2 /)
[790]	647
[1007]	648	!
	649	!-- Parameter values for p = 1013,25 hPa and T = 293,15 K
	650	eta = 1.818E-5 ! in kg/(m s)
	651	xlamb = 6.6E-8 ! in m
	652	rho_a = 1.204 ! in kg/m**3
	653	cunh = 1.26 * xlamb ! in m
	654	sigma = 0.07363 ! in kg/s**2
	655	stok = 2.0 * g * ( rho_l - rho_a ) / ( 9.0 * eta ) ! in 1/(m s)
	656	stb = 32.0 * rho_a * ( rho_l - rho_a) * g / (3.0 * eta * eta)
	657	phy = sigma*3 rho_a2 / ( eta4 * g * ( rho_l - rho_a ) )
[1322]	658	py = phy**( 1.0_wp / 6.0_wp )
[790]	659
[828]	660	ENDIF
[790]	661
[828]	662	DO j = 1, radius_classes
[790]	663
[1007]	664	IF ( radclass(j) <= 1.0E-5 ) THEN
[799]	665
[1007]	666	winf(j) = stok * ( radclass(j)*2 + cunh radclass(j) )
[790]	667
[1007]	668	ELSEIF ( radclass(j) > 1.0E-5 .AND. radclass(j) <= 5.35E-4 ) THEN
[790]	669
[828]	670	x = LOG( stb * radclass(j)**3 )
	671	y = 0.0
[790]	672
[828]	673	DO i = 1, 7
	674	y = y + b(i) * x**(i-1)
	675	ENDDO
[1007]	676	!
	677	!-- Note: this Eq. is wrong in (Pruppacher and Klett, 1997, p. 418)
	678	!-- for correct version see (Beard, 1976)
	679	xrey = ( 1.0 + cunh / radclass(j) ) * EXP( y )
[790]	680
[1007]	681	winf(j) = xrey * eta / ( 2.0 * rho_a * radclass(j) )
[790]	682
[1007]	683	ELSEIF ( radclass(j) > 5.35E-4 ) THEN
[790]	684
[1007]	685	IF ( radclass(j) > 0.0035 ) THEN
	686	bond = g * ( rho_l - rho_a ) * 0.0035**2 / sigma
[828]	687	ELSE
[1007]	688	bond = g * ( rho_l - rho_a ) * radclass(j)**2 / sigma
[828]	689	ENDIF
[790]	690
[1322]	691	x = LOG( 16.0 * bond * py / 3.0_wp )
[828]	692	y = 0.0
[790]	693
[828]	694	DO i = 1, 6
	695	y = y + c(i) * x**(i-1)
	696	ENDDO
[790]	697
[828]	698	xrey = py * EXP( y )
[790]	699
[1007]	700	IF ( radclass(j) > 0.0035 ) THEN
[1322]	701	winf(j) = xrey * eta / ( 2.0 * rho_a * 0.0035_wp )
[828]	702	ELSE
[1007]	703	winf(j) = xrey * eta / ( 2.0 * rho_a * radclass(j) )
[828]	704	ENDIF
[790]	705
[828]	706	ENDIF
[790]	707
[828]	708	ENDDO
[790]	709
[828]	710	END SUBROUTINE fallg
[790]	711
[828]	712
[790]	713	!------------------------------------------------------------------------------!
[1071]	714	! Calculation of collision efficiencies for the Hall kernel
[790]	715	!------------------------------------------------------------------------------!
[828]	716	SUBROUTINE effic
[1320]	717
	718	USE particle_attributes, &
	719	ONLY: radius_classes
[790]	720
[828]	721	IMPLICIT NONE
[790]	722
[1320]	723	INTEGER(iwp) :: i !:
	724	INTEGER(iwp) :: iq !:
	725	INTEGER(iwp) :: ir !:
	726	INTEGER(iwp) :: j !:
	727	INTEGER(iwp) :: k !:
[790]	728
[1320]	729	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !:
[790]	730
[1320]	731	LOGICAL, SAVE :: first = .TRUE. !:
[790]	732
[1320]	733	REAL(wp) :: ek !:
	734	REAL(wp) :: particle_radius !:
	735	REAL(wp) :: pp !:
	736	REAL(wp) :: qq !:
	737	REAL(wp) :: rq !:
[790]	738
[1320]	739	REAL(wp), DIMENSION(1:21), SAVE :: rat !:
	740
	741	REAL(wp), DIMENSION(1:15), SAVE :: r0 !:
	742
	743	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !:
[790]	744
[792]	745	!
[828]	746	!-- Initial assignment of constants
	747	IF ( first ) THEN
[790]	748
[792]	749	first = .FALSE.
[828]	750	r0 = (/ 6.0, 8.0, 10.0, 15.0, 20.0, 25.0, 30.0, 40.0, 50.0, 60., &
	751	70.0, 100.0, 150.0, 200.0, 300.0 /)
	752	rat = (/ 0.00, 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, &
	753	0.50, 0.55, 0.60, 0.65, 0.70, 0.75, 0.80, 0.85, 0.90, 0.95, &
	754	1.00 /)
[790]	755
[828]	756	ecoll(:,1) = (/0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, &
	757	0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001/)
	758	ecoll(:,2) = (/0.003, 0.003, 0.003, 0.004, 0.005, 0.005, 0.005, &
	759	0.010, 0.100, 0.050, 0.200, 0.500, 0.770, 0.870, 0.970/)
	760	ecoll(:,3) = (/0.007, 0.007, 0.007, 0.008, 0.009, 0.010, 0.010, &
	761	0.070, 0.400, 0.430, 0.580, 0.790, 0.930, 0.960, 1.000/)
	762	ecoll(:,4) = (/0.009, 0.009, 0.009, 0.012, 0.015, 0.010, 0.020, &
	763	0.280, 0.600, 0.640, 0.750, 0.910, 0.970, 0.980, 1.000/)
	764	ecoll(:,5) = (/0.014, 0.014, 0.014, 0.015, 0.016, 0.030, 0.060, &
	765	0.500, 0.700, 0.770, 0.840, 0.950, 0.970, 1.000, 1.000/)
	766	ecoll(:,6) = (/0.017, 0.017, 0.017, 0.020, 0.022, 0.060, 0.100, &
	767	0.620, 0.780, 0.840, 0.880, 0.950, 1.000, 1.000, 1.000/)
	768	ecoll(:,7) = (/0.030, 0.030, 0.024, 0.022, 0.032, 0.062, 0.200, &
	769	0.680, 0.830, 0.870, 0.900, 0.950, 1.000, 1.000, 1.000/)
	770	ecoll(:,8) = (/0.025, 0.025, 0.025, 0.036, 0.043, 0.130, 0.270, &
	771	0.740, 0.860, 0.890, 0.920, 1.000, 1.000, 1.000, 1.000/)
	772	ecoll(:,9) = (/0.027, 0.027, 0.027, 0.040, 0.052, 0.200, 0.400, &
	773	0.780, 0.880, 0.900, 0.940, 1.000, 1.000, 1.000, 1.000/)
	774	ecoll(:,10)= (/0.030, 0.030, 0.030, 0.047, 0.064, 0.250, 0.500, &
	775	0.800, 0.900, 0.910, 0.950, 1.000, 1.000, 1.000, 1.000/)
	776	ecoll(:,11)= (/0.040, 0.040, 0.033, 0.037, 0.068, 0.240, 0.550, &
	777	0.800, 0.900, 0.910, 0.950, 1.000, 1.000, 1.000, 1.000/)
	778	ecoll(:,12)= (/0.035, 0.035, 0.035, 0.055, 0.079, 0.290, 0.580, &
	779	0.800, 0.900, 0.910, 0.950, 1.000, 1.000, 1.000, 1.000/)
	780	ecoll(:,13)= (/0.037, 0.037, 0.037, 0.062, 0.082, 0.290, 0.590, &
	781	0.780, 0.900, 0.910, 0.950, 1.000, 1.000, 1.000, 1.000/)
	782	ecoll(:,14)= (/0.037, 0.037, 0.037, 0.060, 0.080, 0.290, 0.580, &
	783	0.770, 0.890, 0.910, 0.950, 1.000, 1.000, 1.000, 1.000/)
	784	ecoll(:,15)= (/0.037, 0.037, 0.037, 0.041, 0.075, 0.250, 0.540, &
	785	0.760, 0.880, 0.920, 0.950, 1.000, 1.000, 1.000, 1.000/)
	786	ecoll(:,16)= (/0.037, 0.037, 0.037, 0.052, 0.067, 0.250, 0.510, &
	787	0.770, 0.880, 0.930, 0.970, 1.000, 1.000, 1.000, 1.000/)
	788	ecoll(:,17)= (/0.037, 0.037, 0.037, 0.047, 0.057, 0.250, 0.490, &
	789	0.770, 0.890, 0.950, 1.000, 1.000, 1.000, 1.000, 1.000/)
	790	ecoll(:,18)= (/0.036, 0.036, 0.036, 0.042, 0.048, 0.230, 0.470, &
	791	0.780, 0.920, 1.000, 1.020, 1.020, 1.020, 1.020, 1.020/)
	792	ecoll(:,19)= (/0.040, 0.040, 0.035, 0.033, 0.040, 0.112, 0.450, &
	793	0.790, 1.010, 1.030, 1.040, 1.040, 1.040, 1.040, 1.040/)
	794	ecoll(:,20)= (/0.033, 0.033, 0.033, 0.033, 0.033, 0.119, 0.470, &
	795	0.950, 1.300, 1.700, 2.300, 2.300, 2.300, 2.300, 2.300/)
	796	ecoll(:,21)= (/0.027, 0.027, 0.027, 0.027, 0.027, 0.125, 0.520, &
	797	1.400, 2.300, 3.000, 4.000, 4.000, 4.000, 4.000, 4.000/)
	798	ENDIF
[790]	799
[792]	800	!
[828]	801	!-- Calculate the radius class index of particles with respect to array r
[1007]	802	!-- Radius has to be in Âµm
[828]	803	ALLOCATE( ira(1:radius_classes) )
	804	DO j = 1, radius_classes
[1322]	805	particle_radius = radclass(j) * 1.0E6_wp
[828]	806	DO k = 1, 15
	807	IF ( particle_radius < r0(k) ) THEN
	808	ira(j) = k
	809	EXIT
	810	ENDIF
	811	ENDDO
	812	IF ( particle_radius >= r0(15) ) ira(j) = 16
	813	ENDDO
[790]	814
[792]	815	!
[828]	816	!-- Two-dimensional linear interpolation of the collision efficiency.
	817	!-- Radius has to be in Âµm
	818	DO j = 1, radius_classes
	819	DO i = 1, j
[792]	820
[828]	821	ir = ira(j)
	822	rq = radclass(i) / radclass(j)
	823	iq = INT( rq * 20 ) + 1
	824	iq = MAX( iq , 2)
[792]	825
[828]	826	IF ( ir < 16 ) THEN
	827	IF ( ir >= 2 ) THEN
[1322]	828	pp = ( ( radclass(j) * 1.0E06_wp ) - r0(ir-1) ) / &
[828]	829	( r0(ir) - r0(ir-1) )
	830	qq = ( rq- rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	831	ec(j,i) = ( 1.0-pp ) * ( 1.0-qq ) * ecoll(ir-1,iq-1) &
	832	+ pp * ( 1.0-qq ) * ecoll(ir,iq-1) &
	833	+ qq * ( 1.0-pp ) * ecoll(ir-1,iq) &
	834	+ pp * qq * ecoll(ir,iq)
	835	ELSE
	836	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	837	ec(j,i) = (1.0-qq) * ecoll(1,iq-1) + qq * ecoll(1,iq)
	838	ENDIF
	839	ELSE
	840	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	841	ek = ( 1.0 - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
	842	ec(j,i) = MIN( ek, 1.0 )
[1071]	843	ENDIF
[792]	844
[1071]	845	IF ( ec(j,i) < 1.0E-20 ) ec(j,i) = 0.0
	846
[828]	847	ec(i,j) = ec(j,i)
[792]	848
[828]	849	ENDDO
	850	ENDDO
[792]	851
[828]	852	DEALLOCATE( ira )
[792]	853
[828]	854	END SUBROUTINE effic
[792]	855
	856
[790]	857	!------------------------------------------------------------------------------!
[828]	858	! Calculation of enhancement factor for collision efficencies due to turbulence
[790]	859	!------------------------------------------------------------------------------!
[828]	860	SUBROUTINE turb_enhance_eff
[790]	861
[1320]	862	USE particle_attributes, &
	863	ONLY: radius_classes
[790]	864
[828]	865	IMPLICIT NONE
[790]	866
[1320]	867	INTEGER(iwp) :: i !:
	868	INTEGER(iwp) :: iq !:
	869	INTEGER(iwp) :: ir !:
	870	INTEGER(iwp) :: j !:
	871	INTEGER(iwp) :: k !:
	872	INTEGER(iwp) :: kk !:
[790]	873
[1320]	874	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !:
	875
	876	LOGICAL, SAVE :: first = .TRUE. !:
[790]	877
[1320]	878	REAL(wp) :: particle_radius !:
	879	REAL(wp) :: pp !:
	880	REAL(wp) :: qq !:
	881	REAL(wp) :: rq !:
	882	REAL(wp) :: y1 !:
	883	REAL(wp) :: y2 !:
	884	REAL(wp) :: y3 !:
[790]	885
[1320]	886	REAL(wp), DIMENSION(1:11), SAVE :: rat !:
	887
	888	REAL(wp), DIMENSION(1:7), SAVE :: r0 !:
	889
	890	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !:
	891	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !:
[799]	892
	893	!
[828]	894	!-- Initial assignment of constants
	895	IF ( first ) THEN
[799]	896
[828]	897	first = .FALSE.
[799]	898
[828]	899	r0 = (/ 10.0, 20.0, 30.0, 40.0, 50.0, 60.0, 100.0 /)
	900	rat = (/ 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0 /)
	901	!
[1007]	902	!-- for 100 cm2/s3
[828]	903	ecoll_100(:,1) = (/1.74, 1.74, 1.773, 1.49, 1.207, 1.207, 1.0 /)
	904	ecoll_100(:,2) = (/1.46, 1.46, 1.421, 1.245, 1.069, 1.069, 1.0 /)
	905	ecoll_100(:,3) = (/1.32, 1.32, 1.245, 1.123, 1.000, 1.000, 1.0 /)
	906	ecoll_100(:,4) = (/1.250, 1.250, 1.148, 1.087, 1.025, 1.025, 1.0 /)
	907	ecoll_100(:,5) = (/1.186, 1.186, 1.066, 1.060, 1.056, 1.056, 1.0 /)
	908	ecoll_100(:,6) = (/1.045, 1.045, 1.000, 1.014, 1.028, 1.028, 1.0 /)
	909	ecoll_100(:,7) = (/1.070, 1.070, 1.030, 1.038, 1.046, 1.046, 1.0 /)
	910	ecoll_100(:,8) = (/1.000, 1.000, 1.054, 1.042, 1.029, 1.029, 1.0 /)
	911	ecoll_100(:,9) = (/1.223, 1.223, 1.117, 1.069, 1.021, 1.021, 1.0 /)
	912	ecoll_100(:,10)= (/1.570, 1.570, 1.244, 1.166, 1.088, 1.088, 1.0 /)
	913	ecoll_100(:,11)= (/20.3, 20.3, 14.6 , 8.61, 2.60, 2.60 , 1.0 /)
	914	!
[1007]	915	!-- for 400 cm2/s3
[828]	916	ecoll_400(:,1) = (/4.976, 4.976, 3.593, 2.519, 1.445, 1.445, 1.0 /)
	917	ecoll_400(:,2) = (/2.984, 2.984, 2.181, 1.691, 1.201, 1.201, 1.0 /)
	918	ecoll_400(:,3) = (/1.988, 1.988, 1.475, 1.313, 1.150, 1.150, 1.0 /)
	919	ecoll_400(:,4) = (/1.490, 1.490, 1.187, 1.156, 1.126, 1.126, 1.0 /)
	920	ecoll_400(:,5) = (/1.249, 1.249, 1.088, 1.090, 1.092, 1.092, 1.0 /)
	921	ecoll_400(:,6) = (/1.139, 1.139, 1.130, 1.091, 1.051, 1.051, 1.0 /)
	922	ecoll_400(:,7) = (/1.220, 1.220, 1.190, 1.138, 1.086, 1.086, 1.0 /)
	923	ecoll_400(:,8) = (/1.325, 1.325, 1.267, 1.165, 1.063, 1.063, 1.0 /)
	924	ecoll_400(:,9) = (/1.716, 1.716, 1.345, 1.223, 1.100, 1.100, 1.0 /)
	925	ecoll_400(:,10)= (/3.788, 3.788, 1.501, 1.311, 1.120, 1.120, 1.0 /)
	926	ecoll_400(:,11)= (/36.52, 36.52, 19.16, 22.80, 26.0, 26.0, 1.0 /)
[799]	927
[828]	928	ENDIF
[790]	929
[828]	930	!
	931	!-- Calculate the radius class index of particles with respect to array r0
[1007]	932	!-- Radius has to be in Âµm
[828]	933	ALLOCATE( ira(1:radius_classes) )
[790]	934
[828]	935	DO j = 1, radius_classes
[1322]	936	particle_radius = radclass(j) * 1.0E6_wp
[828]	937	DO k = 1, 7
	938	IF ( particle_radius < r0(k) ) THEN
	939	ira(j) = k
	940	EXIT
	941	ENDIF
	942	ENDDO
	943	IF ( particle_radius >= r0(7) ) ira(j) = 8
	944	ENDDO
[799]	945
	946	!
[828]	947	!-- Two-dimensional linear interpolation of the collision efficiencies
[1007]	948	!-- Radius has to be in Âµm
[828]	949	DO j = 1, radius_classes
	950	DO i = 1, j
[799]	951
[828]	952	ir = ira(j)
	953	rq = radclass(i) / radclass(j)
[799]	954
[828]	955	DO kk = 2, 11
	956	IF ( rq <= rat(kk) ) THEN
	957	iq = kk
	958	EXIT
	959	ENDIF
	960	ENDDO
[790]	961
[1007]	962	y1 = 0.0001 ! for 0 m2/s3
	963
[828]	964	IF ( ir < 8 ) THEN
	965	IF ( ir >= 2 ) THEN
[1007]	966	pp = ( radclass(j)*1.0E6 - r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
[828]	967	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	968	y2 = ( 1.0-pp ) * ( 1.0-qq ) * ecoll_100(ir-1,iq-1) + &
	969	pp * ( 1.0-qq ) * ecoll_100(ir,iq-1) + &
[1007]	970	qq * ( 1.0-pp ) * ecoll_100(ir-1,iq) + &
[828]	971	pp * qq * ecoll_100(ir,iq)
	972	y3 = ( 1.0-pp ) * ( 1.0-qq ) * ecoll_400(ir-1,iq-1) + &
	973	pp * ( 1.0-qq ) * ecoll_400(ir,iq-1) + &
	974	qq * ( 1.0-pp ) * ecoll_400(ir-1,iq) + &
	975	pp * qq * ecoll_400(ir,iq)
	976	ELSE
	977	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	978	y2 = ( 1.0-qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq)
	979	y3 = ( 1.0-qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq)
	980	ENDIF
	981	ELSE
	982	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	983	y2 = ( 1.0-qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq)
	984	y3 = ( 1.0-qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq)
	985	ENDIF
	986	!
[1007]	987	!-- Linear interpolation of dissipation rate in m2/s3
	988	IF ( epsilon <= 0.01 ) THEN
	989	ecf(j,i) = ( epsilon - 0.01 ) / ( 0.0 - 0.01 ) * y1 &
	990	+ ( epsilon - 0.0 ) / ( 0.01 - 0.0 ) * y2
	991	ELSEIF ( epsilon <= 0.06 ) THEN
	992	ecf(j,i) = ( epsilon - 0.04 ) / ( 0.01 - 0.04 ) * y2 &
	993	+ ( epsilon - 0.01 ) / ( 0.04 - 0.01 ) * y3
[828]	994	ELSE
[1007]	995	ecf(j,i) = ( 0.06 - 0.04 ) / ( 0.01 - 0.04 ) * y2 &
	996	+ ( 0.06 - 0.01 ) / ( 0.04 - 0.01 ) * y3
[828]	997	ENDIF
[790]	998
[828]	999	IF ( ecf(j,i) < 1.0 ) ecf(j,i) = 1.0
[790]	1000
[828]	1001	ecf(i,j) = ecf(j,i)
[790]	1002
[828]	1003	ENDDO
	1004	ENDDO
[790]	1005
[828]	1006	END SUBROUTINE turb_enhance_eff
[790]	1007
[849]	1008
	1009
	1010	SUBROUTINE collision_efficiency_rogers( mean_r, r, e)
	1011	!------------------------------------------------------------------------------!
	1012	! Collision efficiencies from table 8.2 in Rogers and Yau (1989, 3rd edition).
	1013	! Values are calculated from table by bilinear interpolation.
	1014	!------------------------------------------------------------------------------!
	1015
	1016	IMPLICIT NONE
	1017
[1320]	1018	INTEGER(iwp) :: i !:
	1019	INTEGER(iwp) :: j !:
	1020	INTEGER(iwp) :: k !:
[849]	1021
[1320]	1022	LOGICAL, SAVE :: first = .TRUE. !:
[849]	1023
[1320]	1024	REAL(wp) :: aa !:
	1025	REAL(wp) :: bb !:
	1026	REAL(wp) :: cc !:
	1027	REAL(wp) :: dd !:
	1028	REAL(wp) :: dx !:
	1029	REAL(wp) :: dy !:
	1030	REAL(wp) :: e !:
	1031	REAL(wp) :: gg !:
	1032	REAL(wp) :: mean_r !:
	1033	REAL(wp) :: mean_rm !:
	1034	REAL(wp) :: r !:
	1035	REAL(wp) :: rm !:
	1036	REAL(wp) :: x !:
	1037	REAL(wp) :: y !:
	1038
	1039	REAL(wp), DIMENSION(1:9), SAVE :: collected_r = 0.0 !:
	1040
	1041	REAL(wp), DIMENSION(1:19), SAVE :: collector_r = 0.0 !:
	1042
	1043	REAL(wp), DIMENSION(1:9,1:19), SAVE :: ef = 0.0 !:
[849]	1044
[1322]	1045	mean_rm = mean_r * 1.0E06_wp
	1046	rm = r * 1.0E06_wp
[849]	1047
	1048	IF ( first ) THEN
	1049
	1050	collected_r = (/ 2.0, 3.0, 4.0, 6.0, 8.0, 10.0, 15.0, 20.0, 25.0 /)
	1051	collector_r = (/ 10.0, 20.0, 30.0, 40.0, 50.0, 60.0, 80.0, 100.0, &
	1052	150.0, 200.0, 300.0, 400.0, 500.0, 600.0, 1000.0, &
	1053	1400.0, 1800.0, 2400.0, 3000.0 /)
	1054
	1055	ef(:,1) = (/0.017, 0.027, 0.037, 0.052, 0.052, 0.052, 0.052, 0.0, &
	1056	0.0 /)
	1057	ef(:,2) = (/0.001, 0.016, 0.027, 0.060, 0.12, 0.17, 0.17, 0.17, 0.0 /)
	1058	ef(:,3) = (/0.001, 0.001, 0.02, 0.13, 0.28, 0.37, 0.54, 0.55, 0.47/)
	1059	ef(:,4) = (/0.001, 0.001, 0.02, 0.23, 0.4, 0.55, 0.7, 0.75, 0.75/)
	1060	ef(:,5) = (/0.01, 0.01, 0.03, 0.3, 0.4, 0.58, 0.73, 0.75, 0.79/)
	1061	ef(:,6) = (/0.01, 0.01, 0.13, 0.38, 0.57, 0.68, 0.80, 0.86, 0.91/)
	1062	ef(:,7) = (/0.01, 0.085, 0.23, 0.52, 0.68, 0.76, 0.86, 0.92, 0.95/)
	1063	ef(:,8) = (/0.01, 0.14, 0.32, 0.60, 0.73, 0.81, 0.90, 0.94, 0.96/)
	1064	ef(:,9) = (/0.025, 0.25, 0.43, 0.66, 0.78, 0.83, 0.92, 0.95, 0.96/)
	1065	ef(:,10)= (/0.039, 0.3, 0.46, 0.69, 0.81, 0.87, 0.93, 0.95, 0.96/)
	1066	ef(:,11)= (/0.095, 0.33, 0.51, 0.72, 0.82, 0.87, 0.93, 0.96, 0.97/)
	1067	ef(:,12)= (/0.098, 0.36, 0.51, 0.73, 0.83, 0.88, 0.93, 0.96, 0.97/)
	1068	ef(:,13)= (/0.1, 0.36, 0.52, 0.74, 0.83, 0.88, 0.93, 0.96, 0.97/)
	1069	ef(:,14)= (/0.17, 0.4, 0.54, 0.72, 0.83, 0.88, 0.94, 0.98, 1.0 /)
	1070	ef(:,15)= (/0.15, 0.37, 0.52, 0.74, 0.82, 0.88, 0.94, 0.98, 1.0 /)
	1071	ef(:,16)= (/0.11, 0.34, 0.49, 0.71, 0.83, 0.88, 0.94, 0.95, 1.0 /)
	1072	ef(:,17)= (/0.08, 0.29, 0.45, 0.68, 0.8, 0.86, 0.96, 0.94, 1.0 /)
	1073	ef(:,18)= (/0.04, 0.22, 0.39, 0.62, 0.75, 0.83, 0.92, 0.96, 1.0 /)
	1074	ef(:,19)= (/0.02, 0.16, 0.33, 0.55, 0.71, 0.81, 0.90, 0.94, 1.0 /)
	1075
	1076	ENDIF
	1077
	1078	DO k = 1, 8
	1079	IF ( collected_r(k) <= mean_rm ) i = k
	1080	ENDDO
	1081
	1082	DO k = 1, 18
	1083	IF ( collector_r(k) <= rm ) j = k
	1084	ENDDO
	1085
	1086	IF ( rm < 10.0 ) THEN
	1087	e = 0.0
	1088	ELSEIF ( mean_rm < 2.0 ) THEN
	1089	e = 0.001
	1090	ELSEIF ( mean_rm >= 25.0 ) THEN
	1091	IF( j <= 2 ) e = 0.0
	1092	IF( j == 3 ) e = 0.47
	1093	IF( j == 4 ) e = 0.8
	1094	IF( j == 5 ) e = 0.9
	1095	IF( j >=6 ) e = 1.0
	1096	ELSEIF ( rm >= 3000.0 ) THEN
	1097	IF( i == 1 ) e = 0.02
	1098	IF( i == 2 ) e = 0.16
	1099	IF( i == 3 ) e = 0.33
	1100	IF( i == 4 ) e = 0.55
	1101	IF( i == 5 ) e = 0.71
	1102	IF( i == 6 ) e = 0.81
	1103	IF( i == 7 ) e = 0.90
	1104	IF( i >= 8 ) e = 0.94
	1105	ELSE
	1106	x = mean_rm - collected_r(i)
	1107	y = rm - collector_r(j)
	1108	dx = collected_r(i+1) - collected_r(i)
	1109	dy = collector_r(j+1) - collector_r(j)
	1110	aa = x2 + y2
	1111	bb = ( dx - x )2 + y2
	1112	cc = x2 + ( dy - y )2
	1113	dd = ( dx - x )2 + ( dy - y )2
	1114	gg = aa + bb + cc + dd
	1115
	1116	e = ( (gg-aa)ef(i,j) + (gg-bb)ef(i+1,j) + (gg-cc)*ef(i,j+1) + &
	1117	(gg-dd)ef(i+1,j+1) ) / (3.0gg)
	1118	ENDIF
	1119
	1120	END SUBROUTINE collision_efficiency_rogers
	1121
[825]	1122	END MODULE lpm_collision_kernels_mod

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