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source: palm/trunk/SOURCE/lpm_collision_kernels.f90 @ 1661

Last change on this file since 1661 was 1520, checked in by hoffmann, 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	! -----------------
[1520]	22	!
[1347]	23	!
[1321]	24	! Former revisions:
	25	! -----------------
	26	! $Id: lpm_collision_kernels.f90 1520 2015-01-08 10:27:21Z raasch $
	27	!
[1520]	28	! 1519 2015-01-08 10:20:42Z hoffmann
	29	! Bugfix: Using the new particle structure, particles are not sorted by size.
	30	! Hence, computation of collision efficiencies must ensure that the ratio of
	31	! two colliding droplets is < 1.
	32	!
[1360]	33	! 1359 2014-04-11 17:15:14Z hoffmann
	34	! New particle structure integrated.
	35	! Kind definition added to all floating point numbers.
	36	!
[1347]	37	! 1346 2014-03-27 13:18:20Z heinze
	38	! Bugfix: REAL constants provided with KIND-attribute especially in call of
	39	! intrinsic function like MAX, MIN, SIGN
	40	!
[1323]	41	! 1322 2014-03-20 16:38:49Z raasch
	42	! REAL constants defined as wp_kind
	43	!
[1321]	44	! 1320 2014-03-20 08:40:49Z
[1320]	45	! ONLY-attribute added to USE-statements,
	46	! kind-parameters added to all INTEGER and REAL declaration statements,
	47	! kinds are defined in new module kinds,
	48	! revision history before 2012 removed,
	49	! comment fields (!:) to be used for variable explanations added to
	50	! all variable declaration statements
[1008]	51	!
[1093]	52	! 1092 2013-02-02 11:24:22Z raasch
	53	! unused variables removed
	54	!
[1072]	55	! 1071 2012-11-29 16:54:55Z franke
	56	! Bugfix: collision efficiencies for Hall kernel should not be < 1.0E-20
	57	!
[1037]	58	! 1036 2012-10-22 13:43:42Z raasch
	59	! code put under GPL (PALM 3.9)
	60	!
[1008]	61	! 1007 2012-09-19 14:30:36Z franke
[1007]	62	! converted all units to SI units and replaced some parameters by corresponding
	63	! PALM parameters
	64	! Bugfix: factor in calculation of enhancement factor for collision efficencies
	65	! changed from 10. to 1.0
[829]	66	!
[850]	67	! 849 2012-03-15 10:35:09Z raasch
	68	! routine collision_efficiency_rogers added (moved from former advec_particles
	69	! to here)
	70	!
[836]	71	! 835 2012-02-22 11:21:19Z raasch $
	72	! Bugfix: array diss can be used only in case of Wang kernel
	73	!
[829]	74	! 828 2012-02-21 12:00:36Z raasch
[828]	75	! code has been completely reformatted, routine colker renamed
	76	! recalculate_kernel,
	77	! routine init_kernels added, radius is now communicated to the collision
	78	! routines by array radclass
[790]	79	!
[828]	80	! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4
	81	!
[826]	82	! 825 2012-02-19 03:03:44Z raasch
	83	! routine renamed from wang_kernel to lpm_collision_kernels,
	84	! turbulence_effects on collision replaced by wang_kernel
	85	!
[791]	86	! 790 2011-11-29 03:11:20Z raasch
	87	! initial revision
[790]	88	!
	89	! Description:
	90	! ------------
[828]	91	! This module calculates collision efficiencies either due to pure gravitational
	92	! effects (Hall kernel, see Hall, 1980: J. Atmos. Sci., 2486-2507) or
	93	! including the effects of (SGS) turbulence (Wang kernel, see Wang and
	94	! Grabowski, 2009: Atmos. Sci. Lett., 10, 1-8). The original code has been
	95	! provided by L.-P. Wang but is substantially reformatted and speed optimized
	96	! here.
	97	!
	98	! ATTENTION:
	99	! Physical quantities (like g, densities, etc.) used in this module still
	100	! have to be adjusted to those values used in the main PALM code.
	101	! Also, quantities in CGS-units should be converted to SI-units eventually.
[790]	102	!------------------------------------------------------------------------------!
	103
[1320]	104	USE constants, &
	105	ONLY: pi
	106
	107	USE kinds
	108
	109	USE particle_attributes, &
	110	ONLY: collision_kernel, dissipation_classes, particles, radius_classes
	111
[828]	112	USE pegrid
[790]	113
[828]	114
[790]	115	IMPLICIT NONE
	116
	117	PRIVATE
	118
[849]	119	PUBLIC ckernel, collision_efficiency_rogers, init_kernels, &
[1007]	120	rclass_lbound, rclass_ubound, recalculate_kernel
[790]	121
[1320]	122	REAL(wp) :: epsilon !:
	123	REAL(wp) :: eps2 !:
	124	REAL(wp) :: rclass_lbound !:
	125	REAL(wp) :: rclass_ubound !:
	126	REAL(wp) :: urms !:
	127	REAL(wp) :: urms2 !:
[790]	128
[1320]	129	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !:
	130	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !:
	131	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !:
	132
	133	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !:
	134	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !:
	135	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !:
	136	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !:
	137	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !:
	138
	139	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !:
[792]	140
[828]	141	SAVE
[792]	142
[790]	143	!
	144	!-- Public interfaces
[849]	145	INTERFACE collision_efficiency_rogers
	146	MODULE PROCEDURE collision_efficiency_rogers
	147	END INTERFACE collision_efficiency_rogers
	148
[828]	149	INTERFACE init_kernels
	150	MODULE PROCEDURE init_kernels
	151	END INTERFACE init_kernels
[790]	152
[828]	153	INTERFACE recalculate_kernel
	154	MODULE PROCEDURE recalculate_kernel
	155	END INTERFACE recalculate_kernel
[790]	156
	157
[828]	158	CONTAINS
[790]	159
[792]	160
[828]	161	SUBROUTINE init_kernels
	162	!------------------------------------------------------------------------------!
	163	! Initialization of the collision efficiency matrix with fixed radius and
	164	! dissipation classes, calculated at simulation start only.
	165	!------------------------------------------------------------------------------!
[792]	166
[828]	167	IMPLICIT NONE
[792]	168
[1320]	169	INTEGER(iwp) :: i !:
	170	INTEGER(iwp) :: j !:
	171	INTEGER(iwp) :: k !:
[790]	172
[828]	173
	174	!
	175	!-- Calculate collision efficiencies for fixed radius- and dissipation
	176	!-- classes
	177	IF ( collision_kernel(6:9) == 'fast' ) THEN
	178
	179	ALLOCATE( ckernel(1:radius_classes,1:radius_classes, &
	180	0:dissipation_classes), epsclass(1:dissipation_classes), &
	181	radclass(1:radius_classes) )
	182
	183	!
	184	!-- Calculate the radius class bounds with logarithmic distances
	185	!-- in the interval [1.0E-6, 2.0E-4] m
[1322]	186	rclass_lbound = LOG( 1.0E-6_wp )
	187	rclass_ubound = LOG( 2.0E-4_wp )
[1359]	188	radclass(1) = 1.0E-6_wp
[828]	189	DO i = 2, radius_classes
	190	radclass(i) = EXP( rclass_lbound + &
[1359]	191	( rclass_ubound - rclass_lbound ) * &
	192	( i - 1.0_wp ) / ( radius_classes - 1.0_wp ) )
[828]	193	ENDDO
	194
	195	!
[1007]	196	!-- Set the class bounds for dissipation in interval [0.0, 0.1] m2/s3
[828]	197	DO i = 1, dissipation_classes
[1359]	198	epsclass(i) = 0.1_wp * REAL( i, KIND=wp ) / dissipation_classes
[828]	199	ENDDO
	200	!
	201	!-- Calculate collision efficiencies of the Wang/ayala kernel
	202	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
	203	ecf(1:radius_classes,1:radius_classes), &
	204	gck(1:radius_classes,1:radius_classes), &
	205	winf(1:radius_classes) )
	206
	207	DO k = 1, dissipation_classes
	208
	209	epsilon = epsclass(k)
[1359]	210	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 1.0_wp / 3.0_wp )
[828]	211
	212	CALL turbsd
	213	CALL turb_enhance_eff
	214	CALL effic
	215
	216	DO j = 1, radius_classes
	217	DO i = 1, radius_classes
	218	ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j)
	219	ENDDO
	220	ENDDO
	221
	222	ENDDO
	223
	224	!
	225	!-- Calculate collision efficiencies of the Hall kernel
	226	ALLOCATE( hkernel(1:radius_classes,1:radius_classes), &
	227	hwratio(1:radius_classes,1:radius_classes) )
	228
	229	CALL fallg
	230	CALL effic
	231
	232	DO j = 1, radius_classes
	233	DO i = 1, radius_classes
	234	hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 &
	235	* ec(i,j) * ABS( winf(j) - winf(i) )
	236	ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0
	237	ENDDO
	238	ENDDO
	239
	240	!
	241	!-- Test output of efficiencies
	242	IF ( j == -1 ) THEN
	243
	244	PRINT, '** Hall kernel'
[1359]	245	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6_wp, &
[1007]	246	i = 1,radius_classes )
[828]	247	DO j = 1, radius_classes
[1007]	248	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
	249	( hkernel(i,j), i = 1,radius_classes )
[828]	250	ENDDO
	251
	252	DO k = 1, dissipation_classes
	253	DO i = 1, radius_classes
	254	DO j = 1, radius_classes
[1359]	255	IF ( hkernel(i,j) == 0.0_wp ) THEN
	256	hwratio(i,j) = 9999999.9_wp
[828]	257	ELSE
	258	hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j)
	259	ENDIF
	260	ENDDO
	261	ENDDO
	262
	263	PRINT, '** epsilon = ', epsclass(k)
[1359]	264	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i) 1.0E6_wp, &
[1007]	265	i = 1,radius_classes )
[828]	266	DO j = 1, radius_classes
[1359]	267	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j) 1.0E6_wp, &
[1007]	268	( hwratio(i,j), i = 1,radius_classes )
[828]	269	ENDDO
	270	ENDDO
	271
	272	ENDIF
	273
	274	DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf )
	275
	276	ELSEIF( collision_kernel == 'hall' .OR. collision_kernel == 'wang' ) &
	277	THEN
	278	!
	279	!-- Initial settings for Hall- and Wang-Kernel
	280	!-- To be done: move here parts from turbsd, fallg, ecoll, etc.
	281	ENDIF
	282
	283	END SUBROUTINE init_kernels
	284
	285
[790]	286	!------------------------------------------------------------------------------!
[828]	287	! Calculation of collision kernels during each timestep and for each grid box
[790]	288	!------------------------------------------------------------------------------!
[828]	289	SUBROUTINE recalculate_kernel( i1, j1, k1 )
[790]	290
[1320]	291	USE arrays_3d, &
	292	ONLY: diss
[790]	293
[1320]	294	USE particle_attributes, &
[1359]	295	ONLY: prt_count, radius_classes, wang_kernel
[1320]	296
[790]	297	IMPLICIT NONE
	298
[1320]	299	INTEGER(iwp) :: i !:
	300	INTEGER(iwp) :: i1 !:
	301	INTEGER(iwp) :: j !:
	302	INTEGER(iwp) :: j1 !:
	303	INTEGER(iwp) :: k1 !:
	304	INTEGER(iwp) :: pend !:
	305	INTEGER(iwp) :: pstart !:
[790]	306
	307
[1359]	308	pstart = 1
	309	pend = prt_count(k1,j1,i1)
[828]	310	radius_classes = prt_count(k1,j1,i1)
[792]	311
[828]	312	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
	313	radclass(1:radius_classes), winf(1:radius_classes) )
[790]	314
[828]	315	!
[1007]	316	!-- Store particle radii on the radclass array
	317	radclass(1:radius_classes) = particles(pstart:pend)%radius
[790]	318
[835]	319	IF ( wang_kernel ) THEN
[1007]	320	epsilon = diss(k1,j1,i1) ! dissipation rate in m2/s3
[835]	321	ELSE
[1359]	322	epsilon = 0.0_wp
[835]	323	ENDIF
[1359]	324	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 0.33333333333_wp )
[790]	325
[1359]	326	IF ( wang_kernel .AND. epsilon > 1.0E-7_wp ) THEN
[828]	327	!
	328	!-- Call routines to calculate efficiencies for the Wang kernel
	329	ALLOCATE( gck(1:radius_classes,1:radius_classes), &
	330	ecf(1:radius_classes,1:radius_classes) )
[790]	331
[828]	332	CALL turbsd
	333	CALL turb_enhance_eff
	334	CALL effic
[790]	335
[828]	336	DO j = 1, radius_classes
	337	DO i = 1, radius_classes
	338	ckernel(pstart+i-1,pstart+j-1,1) = ec(i,j) * gck(i,j) * ecf(i,j)
[790]	339	ENDDO
[828]	340	ENDDO
[790]	341
[828]	342	DEALLOCATE( gck, ecf )
[790]	343
	344	ELSE
[828]	345	!
	346	!-- Call routines to calculate efficiencies for the Hall kernel
[790]	347	CALL fallg
	348	CALL effic
	349
[828]	350	DO j = 1, radius_classes
	351	DO i = 1, radius_classes
	352	ckernel(pstart+i-1,pstart+j-1,1) = pi * &
	353	( radclass(j) + radclass(i) )**2 &
	354	* ec(i,j) * ABS( winf(j) - winf(i) )
[790]	355	ENDDO
	356	ENDDO
	357
	358	ENDIF
	359
[828]	360	DEALLOCATE( ec, radclass, winf )
[790]	361
[828]	362	END SUBROUTINE recalculate_kernel
[790]	363
[828]	364
[790]	365	!------------------------------------------------------------------------------!
[828]	366	! Calculation of gck
	367	! This is from Aayala 2008b, page 37ff.
	368	! Necessary input parameters: water density, radii of droplets, air density,
	369	! air viscosity, turbulent dissipation rate, taylor microscale reynolds number,
	370	! gravitational acceleration --> to be replaced by PALM parameters
[790]	371	!------------------------------------------------------------------------------!
[792]	372	SUBROUTINE turbsd
[799]	373
[1320]	374	USE control_parameters, &
	375	ONLY: g, molecular_viscosity
	376
	377	USE particle_attributes, &
	378	ONLY: radius_classes
[790]	379
	380	IMPLICIT NONE
[1320]	381
	382	LOGICAL, SAVE :: first = .TRUE. !:
[790]	383
[1320]	384	INTEGER(iwp) :: i !:
	385	INTEGER(iwp) :: j !:
[790]	386
[1320]	387	REAL(wp) :: ao !:
	388	REAL(wp) :: ao_gr !:
	389	REAL(wp) :: bbb !:
	390	REAL(wp) :: be !:
	391	REAL(wp) :: b1 !:
	392	REAL(wp) :: b2 !:
	393	REAL(wp) :: ccc !:
	394	REAL(wp) :: c1 !:
	395	REAL(wp) :: c1_gr !:
	396	REAL(wp) :: c2 !:
	397	REAL(wp) :: d1 !:
	398	REAL(wp) :: d2 !:
	399	REAL(wp) :: eta !:
	400	REAL(wp) :: e1 !:
	401	REAL(wp) :: e2 !:
	402	REAL(wp) :: fao_gr !:
	403	REAL(wp) :: fr !:
	404	REAL(wp) :: grfin !:
	405	REAL(wp) :: lambda !:
	406	REAL(wp) :: lambda_re !:
	407	REAL(wp) :: lf !:
	408	REAL(wp) :: rc !:
	409	REAL(wp) :: rrp !:
	410	REAL(wp) :: sst !:
	411	REAL(wp) :: tauk !:
	412	REAL(wp) :: tl !:
	413	REAL(wp) :: t2 !:
	414	REAL(wp) :: tt !:
	415	REAL(wp) :: t1 !:
	416	REAL(wp) :: vk !:
	417	REAL(wp) :: vrms1xy !:
	418	REAL(wp) :: vrms2xy !:
	419	REAL(wp) :: v1 !:
	420	REAL(wp) :: v1v2xy !:
	421	REAL(wp) :: v1xysq !:
	422	REAL(wp) :: v2 !:
	423	REAL(wp) :: v2xysq !:
	424	REAL(wp) :: wrfin !:
	425	REAL(wp) :: wrgrav2 !:
	426	REAL(wp) :: wrtur2xy !:
	427	REAL(wp) :: xx !:
	428	REAL(wp) :: yy !:
	429	REAL(wp) :: z !:
[790]	430
[1320]	431	REAL(wp), DIMENSION(1:radius_classes) :: st !:
	432	REAL(wp), DIMENSION(1:radius_classes) :: tau !:
	433
[799]	434	!
[828]	435	!-- Initial assignment of constants
[799]	436	IF ( first ) THEN
[790]	437
[799]	438	first = .FALSE.
[790]	439
[1007]	440	ENDIF
[790]	441
[1322]	442	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon ) ! in m
	443	lambda_re = urms*2 SQRT( 15.0_wp / epsilon / molecular_viscosity )
[828]	444	tl = urms**2 / epsilon ! in s
[1359]	445	lf = 0.5_wp * urms**3 / epsilon ! in m
[1007]	446	tauk = SQRT( molecular_viscosity / epsilon ) ! in s
[1322]	447	eta = ( molecular_viscosity3 / epsilon )0.25_wp ! in m
[1007]	448	vk = eta / tauk
[790]	449
[1359]	450	ao = ( 11.0_wp + 7.0_wp * lambda_re ) / ( 205.0_wp + lambda_re )
	451	tt = SQRT( 2.0_wp * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk ! in s
[799]	452
[1007]	453	CALL fallg ! gives winf in m/s
[790]	454
[828]	455	DO i = 1, radius_classes
[1007]	456	tau(i) = winf(i) / g ! in s
[828]	457	st(i) = tau(i) / tauk
[790]	458	ENDDO
	459
[828]	460	!
	461	!-- Calculate wr (from Aayala 2008b, page 38f)
	462	z = tt / tl
[1322]	463	be = SQRT( 2.0_wp ) * lambda / lf
[1359]	464	bbb = SQRT( 1.0_wp - 2.0_wp * be**2 )
	465	d1 = ( 1.0_wp + bbb ) / ( 2.0_wp * bbb )
	466	e1 = lf * ( 1.0_wp + bbb ) * 0.5_wp ! in m
	467	d2 = ( 1.0_wp - bbb ) * 0.5_wp / bbb
	468	e2 = lf * ( 1.0_wp - bbb ) * 0.5_wp ! in m
	469	ccc = SQRT( 1.0_wp - 2.0_wp * z**2 )
	470	b1 = ( 1.0_wp + ccc ) * 0.5_wp / ccc
	471	c1 = tl * ( 1.0_wp + ccc ) * 0.5_wp ! in s
	472	b2 = ( 1.0_wp - ccc ) * 0.5_wp / ccc
	473	c2 = tl * ( 1.0_wp - ccc ) * 0.5_wp ! in s
[790]	474
[828]	475	DO i = 1, radius_classes
[790]	476
[1007]	477	v1 = winf(i) ! in m/s
[828]	478	t1 = tau(i) ! in s
[790]	479
[828]	480	DO j = 1, i
[1007]	481	rrp = radclass(i) + radclass(j)
	482	v2 = winf(j) ! in m/s
[828]	483	t2 = tau(j) ! in s
[790]	484
[1007]	485	v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) &
	486	- b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1)
	487	v1xysq = v1xysq * urms2 / t1 ! in m2/s**2
	488	vrms1xy = SQRT( v1xysq ) ! in m/s
[790]	489
[1007]	490	v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) &
	491	- b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2)
	492	v2xysq = v2xysq * urms2 / t2 ! in m2/s**2
	493	vrms2xy = SQRT( v2xysq ) ! in m/s
[790]	494
[828]	495	IF ( winf(i) >= winf(j) ) THEN
[799]	496	v1 = winf(i)
[790]	497	t1 = tau(i)
[799]	498	v2 = winf(j)
[790]	499	t2 = tau(j)
	500	ELSE
[799]	501	v1 = winf(j)
[790]	502	t1 = tau(j)
[799]	503	v2 = winf(i)
[790]	504	t2 = tau(i)
	505	ENDIF
	506
[828]	507	v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - &
	508	b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - &
	509	b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + &
	510	b2 * d2* zhi(c2,e2,v1,t1,v2,t2)
	511	fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 )
[1359]	512	v1v2xy = v1v2xy * fr * urms2 / tau(i) / tau(j) ! in m2/s**2
	513	wrtur2xy = vrms1xy2 + vrms2xy2 - 2.0_wp * v1v2xy ! in m2/s2
	514	IF ( wrtur2xy < 0.0_wp ) wrtur2xy = 0.0_wp
[1322]	515	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
	516	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) ) ! in m/s
[790]	517
[828]	518	!
	519	!-- Calculate gr
	520	IF ( st(j) > st(i) ) THEN
	521	sst = st(j)
[790]	522	ELSE
[828]	523	sst = st(i)
[790]	524	ENDIF
	525
[1359]	526	xx = -0.1988_wp * sst*4 + 1.5275_wp sst*3 - 4.2942_wp &
	527	sst*2 + 5.3406_wp sst
	528	IF ( xx < 0.0_wp ) xx = 0.0_wp
	529	yy = 0.1886_wp * EXP( 20.306_wp / lambda_re )
[790]	530
[1007]	531	c1_gr = xx / ( g / vk * tauk )**yy
[790]	532
[1322]	533	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
[1359]	534	fao_gr = 20.115_wp * SQRT( ao_gr / lambda_re )
[828]	535	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta ! in cm
[790]	536
[1359]	537	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5_wp )
	538	IF ( grfin < 1.0_wp ) grfin = 1.0_wp
[790]	539
[1359]	540	gck(i,j) = 2.0_wp * pi * rrp*2 wrfin * grfin ! in cm**3/s
[790]	541	gck(j,i) = gck(i,j)
	542
	543	ENDDO
	544	ENDDO
	545
[828]	546	END SUBROUTINE turbsd
[790]	547
[828]	548
[790]	549	!------------------------------------------------------------------------------!
[1007]	550	! phi_w as a function
[790]	551	!------------------------------------------------------------------------------!
[1320]	552	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
[790]	553
	554	IMPLICIT NONE
	555
[1320]	556	REAL(wp) :: a !:
	557	REAL(wp) :: aa1 !:
	558	REAL(wp) :: b !:
	559	REAL(wp) :: tau0 !:
	560	REAL(wp) :: vsett !:
[790]	561
[1359]	562	aa1 = 1.0_wp / tau0 + 1.0_wp / a + vsett / b
	563	phi_w = 1.0_wp / aa1 - 0.5_wp * vsett / b / aa1**2 ! in s
[790]	564
[1007]	565	END FUNCTION phi_w
[792]	566
[790]	567
	568	!------------------------------------------------------------------------------!
[1007]	569	! zhi as a function
[790]	570	!------------------------------------------------------------------------------!
[1320]	571	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
[790]	572
	573	IMPLICIT NONE
	574
[1320]	575	REAL(wp) :: a !:
	576	REAL(wp) :: aa1 !:
	577	REAL(wp) :: aa2 !:
	578	REAL(wp) :: aa3 !:
	579	REAL(wp) :: aa4 !:
	580	REAL(wp) :: aa5 !:
	581	REAL(wp) :: aa6 !:
	582	REAL(wp) :: b !:
	583	REAL(wp) :: tau1 !:
	584	REAL(wp) :: tau2 !:
	585	REAL(wp) :: vsett1 !:
	586	REAL(wp) :: vsett2 !:
[790]	587
[1359]	588	aa1 = vsett2 / b - 1.0_wp / tau2 - 1.0_wp / a
	589	aa2 = vsett1 / b + 1.0_wp / tau1 + 1.0_wp / a
	590	aa3 = ( vsett1 - vsett2 ) / b + 1.0_wp / tau1 + 1.0_wp / tau2
	591	aa4 = ( vsett2 / b )2 - ( 1.0_wp / tau2 + 1.0_wp / a )2
	592	aa5 = vsett2 / b + 1.0_wp / tau2 + 1.0_wp / a
	593	aa6 = 1.0_wp / tau1 - 1.0_wp / a + ( 1.0_wp / tau2 + 1.0_wp / a) * &
	594	vsett1 / vsett2
	595	zhi = (1.0_wp / aa1 - 1.0_wp / aa2 ) * ( vsett1 - vsett2 ) * 0.5_wp / &
	596	b / aa32 + ( 4.0_wp / aa4 - 1.0_wp / aa52 - 1.0_wp / aa1**2 ) &
	597	* vsett2 * 0.5_wp / b /aa6 + ( 2.0_wp * ( b / aa2 - b / aa1 ) - &
	598	vsett1 / aa22 + vsett2 / aa12 ) * 0.5_wp / b / aa3 ! in s**2
[799]	599
[828]	600	END FUNCTION zhi
[790]	601
[828]	602
[790]	603	!------------------------------------------------------------------------------!
[1007]	604	! Calculation of terminal velocity winf following Equations 10-138 to 10-145
	605	! from (Pruppacher and Klett, 1997)
[790]	606	!------------------------------------------------------------------------------!
[828]	607	SUBROUTINE fallg
[1320]	608
	609	USE cloud_parameters, &
	610	ONLY: rho_l
	611
	612	USE control_parameters, &
	613	ONLY: g
[790]	614
[1320]	615	USE particle_attributes, &
	616	ONLY: radius_classes
[790]	617
[1320]	618
[828]	619	IMPLICIT NONE
[790]	620
[1320]	621	INTEGER(iwp) :: i !:
	622	INTEGER(iwp) :: j !:
[790]	623
[1320]	624	LOGICAL, SAVE :: first = .TRUE. !:
[790]	625
[1320]	626	REAL(wp), SAVE :: cunh !:
	627	REAL(wp), SAVE :: eta !:
	628	REAL(wp), SAVE :: phy !:
	629	REAL(wp), SAVE :: py !:
	630	REAL(wp), SAVE :: rho_a !:
	631	REAL(wp), SAVE :: sigma !:
	632	REAL(wp), SAVE :: stb !:
	633	REAL(wp), SAVE :: stok !:
	634	REAL(wp), SAVE :: xlamb !:
[790]	635
[1320]	636	REAL(wp) :: bond !:
	637	REAL(wp) :: x !:
	638	REAL(wp) :: xrey !:
	639	REAL(wp) :: y !:
[799]	640
[1320]	641	REAL(wp), DIMENSION(1:7), SAVE :: b !:
	642	REAL(wp), DIMENSION(1:6), SAVE :: c !:
[799]	643
	644	!
[828]	645	!-- Initial assignment of constants
	646	IF ( first ) THEN
[799]	647
[828]	648	first = .FALSE.
[1359]	649	b = (/ -0.318657E1_wp, 0.992696E0_wp, -0.153193E-2_wp, &
	650	-0.987059E-3_wp, -0.578878E-3_wp, 0.855176E-4_wp, &
	651	-0.327815E-5_wp /)
	652	c = (/ -0.500015E1_wp, 0.523778E1_wp, -0.204914E1_wp, &
	653	0.475294E0_wp, -0.542819E-1_wp, 0.238449E-2_wp /)
[790]	654
[1007]	655	!
	656	!-- Parameter values for p = 1013,25 hPa and T = 293,15 K
[1359]	657	eta = 1.818E-5_wp ! in kg/(m s)
	658	xlamb = 6.6E-8_wp ! in m
	659	rho_a = 1.204_wp ! in kg/m**3
	660	cunh = 1.26_wp * xlamb ! in m
	661	sigma = 0.07363_wp ! in kg/s**2
	662	stok = 2.0_wp * g * ( rho_l - rho_a ) / ( 9.0_wp * eta ) ! in 1/(m s)
	663	stb = 32.0_wp * rho_a * ( rho_l - rho_a) * g / (3.0_wp * eta * eta)
[1007]	664	phy = sigma*3 rho_a2 / ( eta4 * g * ( rho_l - rho_a ) )
[1322]	665	py = phy**( 1.0_wp / 6.0_wp )
[790]	666
[828]	667	ENDIF
[790]	668
[828]	669	DO j = 1, radius_classes
[790]	670
[1359]	671	IF ( radclass(j) <= 1.0E-5_wp ) THEN
[799]	672
[1007]	673	winf(j) = stok * ( radclass(j)*2 + cunh radclass(j) )
[790]	674
[1359]	675	ELSEIF ( radclass(j) > 1.0E-5_wp .AND. radclass(j) <= 5.35E-4_wp ) THEN
[790]	676
[828]	677	x = LOG( stb * radclass(j)**3 )
[1359]	678	y = 0.0_wp
[790]	679
[828]	680	DO i = 1, 7
	681	y = y + b(i) * x**(i-1)
	682	ENDDO
[1007]	683	!
	684	!-- Note: this Eq. is wrong in (Pruppacher and Klett, 1997, p. 418)
	685	!-- for correct version see (Beard, 1976)
[1359]	686	xrey = ( 1.0_wp + cunh / radclass(j) ) * EXP( y )
[790]	687
[1359]	688	winf(j) = xrey * eta / ( 2.0_wp * rho_a * radclass(j) )
[790]	689
[1359]	690	ELSEIF ( radclass(j) > 5.35E-4_wp ) THEN
[790]	691
[1359]	692	IF ( radclass(j) > 0.0035_wp ) THEN
	693	bond = g * ( rho_l - rho_a ) * 0.0035_wp**2 / sigma
[828]	694	ELSE
[1007]	695	bond = g * ( rho_l - rho_a ) * radclass(j)**2 / sigma
[828]	696	ENDIF
[790]	697
[1359]	698	x = LOG( 16.0_wp * bond * py / 3.0_wp )
	699	y = 0.0_wp
[790]	700
[828]	701	DO i = 1, 6
	702	y = y + c(i) * x**(i-1)
	703	ENDDO
[790]	704
[828]	705	xrey = py * EXP( y )
[790]	706
[1359]	707	IF ( radclass(j) > 0.0035_wp ) THEN
	708	winf(j) = xrey * eta / ( 2.0_wp * rho_a * 0.0035_wp )
[828]	709	ELSE
[1359]	710	winf(j) = xrey * eta / ( 2.0_wp * rho_a * radclass(j) )
[828]	711	ENDIF
[790]	712
[828]	713	ENDIF
[790]	714
[828]	715	ENDDO
[790]	716
[828]	717	END SUBROUTINE fallg
[790]	718
[828]	719
[790]	720	!------------------------------------------------------------------------------!
[1071]	721	! Calculation of collision efficiencies for the Hall kernel
[790]	722	!------------------------------------------------------------------------------!
[828]	723	SUBROUTINE effic
[1320]	724
	725	USE particle_attributes, &
	726	ONLY: radius_classes
[790]	727
[828]	728	IMPLICIT NONE
[790]	729
[1320]	730	INTEGER(iwp) :: i !:
	731	INTEGER(iwp) :: iq !:
	732	INTEGER(iwp) :: ir !:
	733	INTEGER(iwp) :: j !:
	734	INTEGER(iwp) :: k !:
[790]	735
[1320]	736	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !:
[790]	737
[1320]	738	LOGICAL, SAVE :: first = .TRUE. !:
[790]	739
[1320]	740	REAL(wp) :: ek !:
	741	REAL(wp) :: particle_radius !:
	742	REAL(wp) :: pp !:
	743	REAL(wp) :: qq !:
	744	REAL(wp) :: rq !:
[790]	745
[1320]	746	REAL(wp), DIMENSION(1:21), SAVE :: rat !:
	747
	748	REAL(wp), DIMENSION(1:15), SAVE :: r0 !:
	749
	750	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !:
[790]	751
[792]	752	!
[828]	753	!-- Initial assignment of constants
	754	IF ( first ) THEN
[790]	755
[792]	756	first = .FALSE.
[1359]	757	r0 = (/ 6.0_wp, 8.0_wp, 10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp, &
	758	30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, 70.0_wp, 100.0_wp, &
	759	150.0_wp, 200.0_wp, 300.0_wp /)
[790]	760
[1359]	761	rat = (/ 0.00_wp, 0.05_wp, 0.10_wp, 0.15_wp, 0.20_wp, 0.25_wp, &
	762	0.30_wp, 0.35_wp, 0.40_wp, 0.45_wp, 0.50_wp, 0.55_wp, &
	763	0.60_wp, 0.65_wp, 0.70_wp, 0.75_wp, 0.80_wp, 0.85_wp, &
	764	0.90_wp, 0.95_wp, 1.00_wp /)
	765
	766	ecoll(:,1) = (/ 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
	767	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
	768	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp /)
	769	ecoll(:,2) = (/ 0.003_wp, 0.003_wp, 0.003_wp, 0.004_wp, 0.005_wp, &
	770	0.005_wp, 0.005_wp, 0.010_wp, 0.100_wp, 0.050_wp, &
	771	0.200_wp, 0.500_wp, 0.770_wp, 0.870_wp, 0.970_wp /)
	772	ecoll(:,3) = (/ 0.007_wp, 0.007_wp, 0.007_wp, 0.008_wp, 0.009_wp, &
	773	0.010_wp, 0.010_wp, 0.070_wp, 0.400_wp, 0.430_wp, &
	774	0.580_wp, 0.790_wp, 0.930_wp, 0.960_wp, 1.000_wp /)
	775	ecoll(:,4) = (/ 0.009_wp, 0.009_wp, 0.009_wp, 0.012_wp, 0.015_wp, &
	776	0.010_wp, 0.020_wp, 0.280_wp, 0.600_wp, 0.640_wp, &
	777	0.750_wp, 0.910_wp, 0.970_wp, 0.980_wp, 1.000_wp /)
	778	ecoll(:,5) = (/ 0.014_wp, 0.014_wp, 0.014_wp, 0.015_wp, 0.016_wp, &
	779	0.030_wp, 0.060_wp, 0.500_wp, 0.700_wp, 0.770_wp, &
	780	0.840_wp, 0.950_wp, 0.970_wp, 1.000_wp, 1.000_wp /)
	781	ecoll(:,6) = (/ 0.017_wp, 0.017_wp, 0.017_wp, 0.020_wp, 0.022_wp, &
	782	0.060_wp, 0.100_wp, 0.620_wp, 0.780_wp, 0.840_wp, &
	783	0.880_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	784	ecoll(:,7) = (/ 0.030_wp, 0.030_wp, 0.024_wp, 0.022_wp, 0.032_wp, &
	785	0.062_wp, 0.200_wp, 0.680_wp, 0.830_wp, 0.870_wp, &
	786	0.900_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	787	ecoll(:,8) = (/ 0.025_wp, 0.025_wp, 0.025_wp, 0.036_wp, 0.043_wp, &
	788	0.130_wp, 0.270_wp, 0.740_wp, 0.860_wp, 0.890_wp, &
	789	0.920_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	790	ecoll(:,9) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.040_wp, 0.052_wp, &
	791	0.200_wp, 0.400_wp, 0.780_wp, 0.880_wp, 0.900_wp, &
	792	0.940_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	793	ecoll(:,10) = (/ 0.030_wp, 0.030_wp, 0.030_wp, 0.047_wp, 0.064_wp, &
	794	0.250_wp, 0.500_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
	795	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	796	ecoll(:,11) = (/ 0.040_wp, 0.040_wp, 0.033_wp, 0.037_wp, 0.068_wp, &
	797	0.240_wp, 0.550_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
	798	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	799	ecoll(:,12) = (/ 0.035_wp, 0.035_wp, 0.035_wp, 0.055_wp, 0.079_wp, &
	800	0.290_wp, 0.580_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
	801	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	802	ecoll(:,13) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.062_wp, 0.082_wp, &
	803	0.290_wp, 0.590_wp, 0.780_wp, 0.900_wp, 0.910_wp, &
	804	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	805	ecoll(:,14) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.060_wp, 0.080_wp, &
	806	0.290_wp, 0.580_wp, 0.770_wp, 0.890_wp, 0.910_wp, &
	807	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	808	ecoll(:,15) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.041_wp, 0.075_wp, &
	809	0.250_wp, 0.540_wp, 0.760_wp, 0.880_wp, 0.920_wp, &
	810	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	811	ecoll(:,16) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.052_wp, 0.067_wp, &
	812	0.250_wp, 0.510_wp, 0.770_wp, 0.880_wp, 0.930_wp, &
	813	0.970_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	814	ecoll(:,17) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.047_wp, 0.057_wp, &
	815	0.250_wp, 0.490_wp, 0.770_wp, 0.890_wp, 0.950_wp, &
	816	1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
	817	ecoll(:,18) = (/ 0.036_wp, 0.036_wp, 0.036_wp, 0.042_wp, 0.048_wp, &
	818	0.230_wp, 0.470_wp, 0.780_wp, 0.920_wp, 1.000_wp, &
	819	1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp /)
	820	ecoll(:,19) = (/ 0.040_wp, 0.040_wp, 0.035_wp, 0.033_wp, 0.040_wp, &
	821	0.112_wp, 0.450_wp, 0.790_wp, 1.010_wp, 1.030_wp, &
	822	1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp /)
	823	ecoll(:,20) = (/ 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, &
	824	0.119_wp, 0.470_wp, 0.950_wp, 1.300_wp, 1.700_wp, &
	825	2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp /)
	826	ecoll(:,21) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, &
	827	0.125_wp, 0.520_wp, 1.400_wp, 2.300_wp, 3.000_wp, &
	828	4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp /)
[828]	829	ENDIF
[790]	830
[792]	831	!
[828]	832	!-- Calculate the radius class index of particles with respect to array r
[1007]	833	!-- Radius has to be in Âµm
[828]	834	ALLOCATE( ira(1:radius_classes) )
	835	DO j = 1, radius_classes
[1322]	836	particle_radius = radclass(j) * 1.0E6_wp
[828]	837	DO k = 1, 15
	838	IF ( particle_radius < r0(k) ) THEN
	839	ira(j) = k
	840	EXIT
	841	ENDIF
	842	ENDDO
	843	IF ( particle_radius >= r0(15) ) ira(j) = 16
	844	ENDDO
[790]	845
[792]	846	!
[828]	847	!-- Two-dimensional linear interpolation of the collision efficiency.
	848	!-- Radius has to be in Âµm
	849	DO j = 1, radius_classes
	850	DO i = 1, j
[792]	851
[828]	852	ir = ira(j)
[1519]	853	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
[828]	854	iq = INT( rq * 20 ) + 1
	855	iq = MAX( iq , 2)
[792]	856
[828]	857	IF ( ir < 16 ) THEN
	858	IF ( ir >= 2 ) THEN
[1322]	859	pp = ( ( radclass(j) * 1.0E06_wp ) - r0(ir-1) ) / &
[828]	860	( r0(ir) - r0(ir-1) )
[1359]	861	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	862	ec(j,i) = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) &
	863	* ecoll(ir-1,iq-1) &
	864	+ pp * ( 1.0_wp - qq ) * ecoll(ir,iq-1) &
	865	+ qq * ( 1.0_wp - pp ) * ecoll(ir-1,iq) &
[828]	866	+ pp * qq * ecoll(ir,iq)
	867	ELSE
	868	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	869	ec(j,i) = ( 1.0_wp - qq ) * ecoll(1,iq-1) + qq * ecoll(1,iq)
[828]	870	ENDIF
	871	ELSE
	872	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	873	ek = ( 1.0_wp - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
[1346]	874	ec(j,i) = MIN( ek, 1.0_wp )
[1071]	875	ENDIF
[792]	876
[1359]	877	IF ( ec(j,i) < 1.0E-20_wp ) ec(j,i) = 0.0_wp
[1071]	878
[828]	879	ec(i,j) = ec(j,i)
[792]	880
[828]	881	ENDDO
	882	ENDDO
[792]	883
[828]	884	DEALLOCATE( ira )
[792]	885
[828]	886	END SUBROUTINE effic
[792]	887
	888
[790]	889	!------------------------------------------------------------------------------!
[828]	890	! Calculation of enhancement factor for collision efficencies due to turbulence
[790]	891	!------------------------------------------------------------------------------!
[828]	892	SUBROUTINE turb_enhance_eff
[790]	893
[1320]	894	USE particle_attributes, &
	895	ONLY: radius_classes
[790]	896
[828]	897	IMPLICIT NONE
[790]	898
[1320]	899	INTEGER(iwp) :: i !:
	900	INTEGER(iwp) :: iq !:
	901	INTEGER(iwp) :: ir !:
	902	INTEGER(iwp) :: j !:
	903	INTEGER(iwp) :: k !:
	904	INTEGER(iwp) :: kk !:
[790]	905
[1320]	906	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !:
	907
	908	LOGICAL, SAVE :: first = .TRUE. !:
[790]	909
[1320]	910	REAL(wp) :: particle_radius !:
	911	REAL(wp) :: pp !:
	912	REAL(wp) :: qq !:
	913	REAL(wp) :: rq !:
	914	REAL(wp) :: y1 !:
	915	REAL(wp) :: y2 !:
	916	REAL(wp) :: y3 !:
[790]	917
[1320]	918	REAL(wp), DIMENSION(1:11), SAVE :: rat !:
	919
	920	REAL(wp), DIMENSION(1:7), SAVE :: r0 !:
	921
	922	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !:
	923	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !:
[799]	924
	925	!
[828]	926	!-- Initial assignment of constants
	927	IF ( first ) THEN
[799]	928
[828]	929	first = .FALSE.
[799]	930
[1359]	931	r0 = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, &
	932	100.0_wp /)
	933
	934	rat = (/ 0.0_wp, 0.1_wp, 0.2_wp, 0.3_wp, 0.4_wp, 0.5_wp, 0.6_wp, &
	935	0.7_wp, 0.8_wp, 0.9_wp, 1.0_wp /)
[828]	936	!
[1007]	937	!-- for 100 cm2/s3
[1359]	938	ecoll_100(:,1) = (/ 1.74_wp, 1.74_wp, 1.773_wp, 1.49_wp, &
	939	1.207_wp, 1.207_wp, 1.0_wp /)
	940	ecoll_100(:,2) = (/ 1.46_wp, 1.46_wp, 1.421_wp, 1.245_wp, &
	941	1.069_wp, 1.069_wp, 1.0_wp /)
	942	ecoll_100(:,3) = (/ 1.32_wp, 1.32_wp, 1.245_wp, 1.123_wp, &
	943	1.000_wp, 1.000_wp, 1.0_wp /)
	944	ecoll_100(:,4) = (/ 1.250_wp, 1.250_wp, 1.148_wp, 1.087_wp, &
	945	1.025_wp, 1.025_wp, 1.0_wp /)
	946	ecoll_100(:,5) = (/ 1.186_wp, 1.186_wp, 1.066_wp, 1.060_wp, &
	947	1.056_wp, 1.056_wp, 1.0_wp /)
	948	ecoll_100(:,6) = (/ 1.045_wp, 1.045_wp, 1.000_wp, 1.014_wp, &
	949	1.028_wp, 1.028_wp, 1.0_wp /)
	950	ecoll_100(:,7) = (/ 1.070_wp, 1.070_wp, 1.030_wp, 1.038_wp, &
	951	1.046_wp, 1.046_wp, 1.0_wp /)
	952	ecoll_100(:,8) = (/ 1.000_wp, 1.000_wp, 1.054_wp, 1.042_wp, &
	953	1.029_wp, 1.029_wp, 1.0_wp /)
	954	ecoll_100(:,9) = (/ 1.223_wp, 1.223_wp, 1.117_wp, 1.069_wp, &
	955	1.021_wp, 1.021_wp, 1.0_wp /)
	956	ecoll_100(:,10) = (/ 1.570_wp, 1.570_wp, 1.244_wp, 1.166_wp, &
	957	1.088_wp, 1.088_wp, 1.0_wp /)
	958	ecoll_100(:,11) = (/ 20.3_wp, 20.3_wp, 14.6_wp, 8.61_wp, &
	959	2.60_wp, 2.60_wp, 1.0_wp /)
[828]	960	!
[1007]	961	!-- for 400 cm2/s3
[1359]	962	ecoll_400(:,1) = (/ 4.976_wp, 4.976_wp, 3.593_wp, 2.519_wp, &
	963	1.445_wp, 1.445_wp, 1.0_wp /)
	964	ecoll_400(:,2) = (/ 2.984_wp, 2.984_wp, 2.181_wp, 1.691_wp, &
	965	1.201_wp, 1.201_wp, 1.0_wp /)
	966	ecoll_400(:,3) = (/ 1.988_wp, 1.988_wp, 1.475_wp, 1.313_wp, &
	967	1.150_wp, 1.150_wp, 1.0_wp /)
	968	ecoll_400(:,4) = (/ 1.490_wp, 1.490_wp, 1.187_wp, 1.156_wp, &
	969	1.126_wp, 1.126_wp, 1.0_wp /)
	970	ecoll_400(:,5) = (/ 1.249_wp, 1.249_wp, 1.088_wp, 1.090_wp, &
	971	1.092_wp, 1.092_wp, 1.0_wp /)
	972	ecoll_400(:,6) = (/ 1.139_wp, 1.139_wp, 1.130_wp, 1.091_wp, &
	973	1.051_wp, 1.051_wp, 1.0_wp /)
	974	ecoll_400(:,7) = (/ 1.220_wp, 1.220_wp, 1.190_wp, 1.138_wp, &
	975	1.086_wp, 1.086_wp, 1.0_wp /)
	976	ecoll_400(:,8) = (/ 1.325_wp, 1.325_wp, 1.267_wp, 1.165_wp, &
	977	1.063_wp, 1.063_wp, 1.0_wp /)
	978	ecoll_400(:,9) = (/ 1.716_wp, 1.716_wp, 1.345_wp, 1.223_wp, &
	979	1.100_wp, 1.100_wp, 1.0_wp /)
	980	ecoll_400(:,10) = (/ 3.788_wp, 3.788_wp, 1.501_wp, 1.311_wp, &
	981	1.120_wp, 1.120_wp, 1.0_wp /)
	982	ecoll_400(:,11) = (/ 36.52_wp, 36.52_wp, 19.16_wp, 22.80_wp, &
	983	26.0_wp, 26.0_wp, 1.0_wp /)
[799]	984
[828]	985	ENDIF
[790]	986
[828]	987	!
	988	!-- Calculate the radius class index of particles with respect to array r0
[1007]	989	!-- Radius has to be in Âµm
[828]	990	ALLOCATE( ira(1:radius_classes) )
[790]	991
[828]	992	DO j = 1, radius_classes
[1322]	993	particle_radius = radclass(j) * 1.0E6_wp
[828]	994	DO k = 1, 7
	995	IF ( particle_radius < r0(k) ) THEN
	996	ira(j) = k
	997	EXIT
	998	ENDIF
	999	ENDDO
	1000	IF ( particle_radius >= r0(7) ) ira(j) = 8
	1001	ENDDO
[799]	1002
	1003	!
[828]	1004	!-- Two-dimensional linear interpolation of the collision efficiencies
[1007]	1005	!-- Radius has to be in Âµm
[828]	1006	DO j = 1, radius_classes
	1007	DO i = 1, j
[799]	1008
[828]	1009	ir = ira(j)
[1519]	1010	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
[799]	1011
[828]	1012	DO kk = 2, 11
	1013	IF ( rq <= rat(kk) ) THEN
	1014	iq = kk
	1015	EXIT
	1016	ENDIF
	1017	ENDDO
[790]	1018
[1359]	1019	y1 = 0.0001_wp ! for 0 m2/s3
[1007]	1020
[828]	1021	IF ( ir < 8 ) THEN
	1022	IF ( ir >= 2 ) THEN
[1359]	1023	pp = ( radclass(j)*1.0E6_wp - r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
[828]	1024	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	1025	y2 = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) * ecoll_100(ir-1,iq-1) + &
	1026	pp * ( 1.0_wp - qq ) * ecoll_100(ir,iq-1) + &
	1027	qq * ( 1.0_wp - pp ) * ecoll_100(ir-1,iq) + &
	1028	pp * qq * ecoll_100(ir,iq)
	1029	y3 = ( 1.0-pp ) * ( 1.0_wp - qq ) * ecoll_400(ir-1,iq-1) + &
	1030	pp * ( 1.0_wp - qq ) * ecoll_400(ir,iq-1) + &
	1031	qq * ( 1.0_wp - pp ) * ecoll_400(ir-1,iq) + &
	1032	pp * qq * ecoll_400(ir,iq)
[828]	1033	ELSE
	1034	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	1035	y2 = ( 1.0_wp - qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq)
	1036	y3 = ( 1.0_wp - qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq)
[828]	1037	ENDIF
	1038	ELSE
	1039	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	1040	y2 = ( 1.0_wp - qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq)
	1041	y3 = ( 1.0_wp - qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq)
[828]	1042	ENDIF
	1043	!
[1007]	1044	!-- Linear interpolation of dissipation rate in m2/s3
[1359]	1045	IF ( epsilon <= 0.01_wp ) THEN
	1046	ecf(j,i) = ( epsilon - 0.01_wp ) / ( 0.0_wp - 0.01_wp ) * y1 &
	1047	+ ( epsilon - 0.0_wp ) / ( 0.01_wp - 0.0_wp ) * y2
	1048	ELSEIF ( epsilon <= 0.06_wp ) THEN
	1049	ecf(j,i) = ( epsilon - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	1050	+ ( epsilon - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	1051	ELSE
[1359]	1052	ecf(j,i) = ( 0.06_wp - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	1053	+ ( 0.06_wp - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	1054	ENDIF
[790]	1055
[1359]	1056	IF ( ecf(j,i) < 1.0_wp ) ecf(j,i) = 1.0_wp
[790]	1057
[828]	1058	ecf(i,j) = ecf(j,i)
[790]	1059
[828]	1060	ENDDO
	1061	ENDDO
[790]	1062
[828]	1063	END SUBROUTINE turb_enhance_eff
[790]	1064
[849]	1065
	1066
	1067	SUBROUTINE collision_efficiency_rogers( mean_r, r, e)
	1068	!------------------------------------------------------------------------------!
	1069	! Collision efficiencies from table 8.2 in Rogers and Yau (1989, 3rd edition).
	1070	! Values are calculated from table by bilinear interpolation.
	1071	!------------------------------------------------------------------------------!
	1072
	1073	IMPLICIT NONE
	1074
[1320]	1075	INTEGER(iwp) :: i !:
	1076	INTEGER(iwp) :: j !:
	1077	INTEGER(iwp) :: k !:
[849]	1078
[1320]	1079	LOGICAL, SAVE :: first = .TRUE. !:
[849]	1080
[1320]	1081	REAL(wp) :: aa !:
	1082	REAL(wp) :: bb !:
	1083	REAL(wp) :: cc !:
	1084	REAL(wp) :: dd !:
	1085	REAL(wp) :: dx !:
	1086	REAL(wp) :: dy !:
	1087	REAL(wp) :: e !:
	1088	REAL(wp) :: gg !:
	1089	REAL(wp) :: mean_r !:
	1090	REAL(wp) :: mean_rm !:
	1091	REAL(wp) :: r !:
	1092	REAL(wp) :: rm !:
	1093	REAL(wp) :: x !:
	1094	REAL(wp) :: y !:
	1095
[1359]	1096	REAL(wp), DIMENSION(1:9), SAVE :: collected_r = 0.0_wp !:
[1320]	1097
[1359]	1098	REAL(wp), DIMENSION(1:19), SAVE :: collector_r = 0.0_wp !:
[1320]	1099
[1359]	1100	REAL(wp), DIMENSION(1:9,1:19), SAVE :: ef = 0.0_wp !:
[849]	1101
[1322]	1102	mean_rm = mean_r * 1.0E06_wp
	1103	rm = r * 1.0E06_wp
[849]	1104
	1105	IF ( first ) THEN
	1106
[1359]	1107	collected_r = (/ 2.0_wp, 3.0_wp, 4.0_wp, 6.0_wp, 8.0_wp, &
	1108	10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp /)
	1109	collector_r = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, &
	1110	60.0_wp, 80.0_wp, 100.0_wp, 150.0_wp, 200.0_wp, &
	1111	300.0_wp, 400.0_wp, 500.0_wp, 600.0_wp, 1000.0_wp, &
	1112	1400.0_wp, 1800.0_wp, 2400.0_wp, 3000.0_wp /)
[849]	1113
[1359]	1114	ef(:,1) = (/ 0.017_wp, 0.027_wp, 0.037_wp, 0.052_wp, 0.052_wp, &
	1115	0.052_wp, 0.052_wp, 0.0_wp, 0.0_wp /)
	1116	ef(:,2) = (/ 0.001_wp, 0.016_wp, 0.027_wp, 0.060_wp, 0.12_wp, &
	1117	0.17_wp, 0.17_wp, 0.17_wp, 0.0_wp /)
	1118	ef(:,3) = (/ 0.001_wp, 0.001_wp, 0.02_wp, 0.13_wp, 0.28_wp, &
	1119	0.37_wp, 0.54_wp, 0.55_wp, 0.47_wp/)
	1120	ef(:,4) = (/ 0.001_wp, 0.001_wp, 0.02_wp, 0.23_wp, 0.4_wp, &
	1121	0.55_wp, 0.7_wp, 0.75_wp, 0.75_wp/)
	1122	ef(:,5) = (/ 0.01_wp, 0.01_wp, 0.03_wp, 0.3_wp, 0.4_wp, &
	1123	0.58_wp, 0.73_wp, 0.75_wp, 0.79_wp/)
	1124	ef(:,6) = (/ 0.01_wp, 0.01_wp, 0.13_wp, 0.38_wp, 0.57_wp, &
	1125	0.68_wp, 0.80_wp, 0.86_wp, 0.91_wp/)
	1126	ef(:,7) = (/ 0.01_wp, 0.085_wp, 0.23_wp, 0.52_wp, 0.68_wp, &
	1127	0.76_wp, 0.86_wp, 0.92_wp, 0.95_wp/)
	1128	ef(:,8) = (/ 0.01_wp, 0.14_wp, 0.32_wp, 0.60_wp, 0.73_wp, &
	1129	0.81_wp, 0.90_wp, 0.94_wp, 0.96_wp/)
	1130	ef(:,9) = (/ 0.025_wp, 0.25_wp, 0.43_wp, 0.66_wp, 0.78_wp, &
	1131	0.83_wp, 0.92_wp, 0.95_wp, 0.96_wp/)
	1132	ef(:,10) = (/ 0.039_wp, 0.3_wp, 0.46_wp, 0.69_wp, 0.81_wp, &
	1133	0.87_wp, 0.93_wp, 0.95_wp, 0.96_wp/)
	1134	ef(:,11) = (/ 0.095_wp, 0.33_wp, 0.51_wp, 0.72_wp, 0.82_wp, &
	1135	0.87_wp, 0.93_wp, 0.96_wp, 0.97_wp/)
	1136	ef(:,12) = (/ 0.098_wp, 0.36_wp, 0.51_wp, 0.73_wp, 0.83_wp, &
	1137	0.88_wp, 0.93_wp, 0.96_wp, 0.97_wp/)
	1138	ef(:,13) = (/ 0.1_wp, 0.36_wp, 0.52_wp, 0.74_wp, 0.83_wp, &
	1139	0.88_wp, 0.93_wp, 0.96_wp, 0.97_wp/)
	1140	ef(:,14) = (/ 0.17_wp, 0.4_wp, 0.54_wp, 0.72_wp, 0.83_wp, &
	1141	0.88_wp, 0.94_wp, 0.98_wp, 1.0_wp /)
	1142	ef(:,15) = (/ 0.15_wp, 0.37_wp, 0.52_wp, 0.74_wp, 0.82_wp, &
	1143	0.88_wp, 0.94_wp, 0.98_wp, 1.0_wp /)
	1144	ef(:,16) = (/ 0.11_wp, 0.34_wp, 0.49_wp, 0.71_wp, 0.83_wp, &
	1145	0.88_wp, 0.94_wp, 0.95_wp, 1.0_wp /)
	1146	ef(:,17) = (/ 0.08_wp, 0.29_wp, 0.45_wp, 0.68_wp, 0.8_wp, &
	1147	0.86_wp, 0.96_wp, 0.94_wp, 1.0_wp /)
	1148	ef(:,18) = (/ 0.04_wp, 0.22_wp, 0.39_wp, 0.62_wp, 0.75_wp, &
	1149	0.83_wp, 0.92_wp, 0.96_wp, 1.0_wp /)
	1150	ef(:,19) = (/ 0.02_wp, 0.16_wp, 0.33_wp, 0.55_wp, 0.71_wp, &
	1151	0.81_wp, 0.90_wp, 0.94_wp, 1.0_wp /)
[849]	1152
	1153	ENDIF
	1154
	1155	DO k = 1, 8
	1156	IF ( collected_r(k) <= mean_rm ) i = k
	1157	ENDDO
	1158
	1159	DO k = 1, 18
	1160	IF ( collector_r(k) <= rm ) j = k
	1161	ENDDO
	1162
[1359]	1163	IF ( rm < 10.0_wp ) THEN
	1164	e = 0.0_wp
	1165	ELSEIF ( mean_rm < 2.0_wp ) THEN
	1166	e = 0.001_wp
	1167	ELSEIF ( mean_rm >= 25.0_wp ) THEN
	1168	IF( j <= 2 ) e = 0.0_wp
	1169	IF( j == 3 ) e = 0.47_wp
	1170	IF( j == 4 ) e = 0.8_wp
	1171	IF( j == 5 ) e = 0.9_wp
	1172	IF( j >=6 ) e = 1.0_wp
	1173	ELSEIF ( rm >= 3000.0_wp ) THEN
	1174	IF( i == 1 ) e = 0.02_wp
	1175	IF( i == 2 ) e = 0.16_wp
	1176	IF( i == 3 ) e = 0.33_wp
	1177	IF( i == 4 ) e = 0.55_wp
	1178	IF( i == 5 ) e = 0.71_wp
	1179	IF( i == 6 ) e = 0.81_wp
	1180	IF( i == 7 ) e = 0.90_wp
	1181	IF( i >= 8 ) e = 0.94_wp
[849]	1182	ELSE
	1183	x = mean_rm - collected_r(i)
	1184	y = rm - collector_r(j)
	1185	dx = collected_r(i+1) - collected_r(i)
	1186	dy = collector_r(j+1) - collector_r(j)
	1187	aa = x2 + y2
	1188	bb = ( dx - x )2 + y2
	1189	cc = x2 + ( dy - y )2
	1190	dd = ( dx - x )2 + ( dy - y )2
	1191	gg = aa + bb + cc + dd
	1192
	1193	e = ( (gg-aa)ef(i,j) + (gg-bb)ef(i+1,j) + (gg-cc)*ef(i,j+1) + &
[1359]	1194	(gg-dd)ef(i+1,j+1) ) / (3.0_wp gg)
[849]	1195	ENDIF
	1196
	1197	END SUBROUTINE collision_efficiency_rogers
	1198
[825]	1199	END MODULE lpm_collision_kernels_mod

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