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source: palm/trunk/SOURCE/lpm_collision_kernels.f90 @ 1350

Last change on this file since 1350 was 1347, checked in by heinze, 11 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	! -----------------
[1347]	22	!
	23	!
[1321]	24	! Former revisions:
	25	! -----------------
	26	! $Id: lpm_collision_kernels.f90 1347 2014-03-27 13:23:00Z maronga $
	27	!
[1347]	28	! 1346 2014-03-27 13:18:20Z heinze
	29	! Bugfix: REAL constants provided with KIND-attribute especially in call of
	30	! intrinsic function like MAX, MIN, SIGN
	31	!
[1323]	32	! 1322 2014-03-20 16:38:49Z raasch
	33	! REAL constants defined as wp_kind
	34	!
[1321]	35	! 1320 2014-03-20 08:40:49Z
[1320]	36	! ONLY-attribute added to USE-statements,
	37	! kind-parameters added to all INTEGER and REAL declaration statements,
	38	! kinds are defined in new module kinds,
	39	! revision history before 2012 removed,
	40	! comment fields (!:) to be used for variable explanations added to
	41	! all variable declaration statements
[1008]	42	!
[1093]	43	! 1092 2013-02-02 11:24:22Z raasch
	44	! unused variables removed
	45	!
[1072]	46	! 1071 2012-11-29 16:54:55Z franke
	47	! Bugfix: collision efficiencies for Hall kernel should not be < 1.0E-20
	48	!
[1037]	49	! 1036 2012-10-22 13:43:42Z raasch
	50	! code put under GPL (PALM 3.9)
	51	!
[1008]	52	! 1007 2012-09-19 14:30:36Z franke
[1007]	53	! converted all units to SI units and replaced some parameters by corresponding
	54	! PALM parameters
	55	! Bugfix: factor in calculation of enhancement factor for collision efficencies
	56	! changed from 10. to 1.0
[829]	57	!
[850]	58	! 849 2012-03-15 10:35:09Z raasch
	59	! routine collision_efficiency_rogers added (moved from former advec_particles
	60	! to here)
	61	!
[836]	62	! 835 2012-02-22 11:21:19Z raasch $
	63	! Bugfix: array diss can be used only in case of Wang kernel
	64	!
[829]	65	! 828 2012-02-21 12:00:36Z raasch
[828]	66	! code has been completely reformatted, routine colker renamed
	67	! recalculate_kernel,
	68	! routine init_kernels added, radius is now communicated to the collision
	69	! routines by array radclass
[790]	70	!
[828]	71	! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4
	72	!
[826]	73	! 825 2012-02-19 03:03:44Z raasch
	74	! routine renamed from wang_kernel to lpm_collision_kernels,
	75	! turbulence_effects on collision replaced by wang_kernel
	76	!
[791]	77	! 790 2011-11-29 03:11:20Z raasch
	78	! initial revision
[790]	79	!
	80	! Description:
	81	! ------------
[828]	82	! This module calculates collision efficiencies either due to pure gravitational
	83	! effects (Hall kernel, see Hall, 1980: J. Atmos. Sci., 2486-2507) or
	84	! including the effects of (SGS) turbulence (Wang kernel, see Wang and
	85	! Grabowski, 2009: Atmos. Sci. Lett., 10, 1-8). The original code has been
	86	! provided by L.-P. Wang but is substantially reformatted and speed optimized
	87	! here.
	88	!
	89	! ATTENTION:
	90	! Physical quantities (like g, densities, etc.) used in this module still
	91	! have to be adjusted to those values used in the main PALM code.
	92	! Also, quantities in CGS-units should be converted to SI-units eventually.
[790]	93	!------------------------------------------------------------------------------!
	94
[1320]	95	USE constants, &
	96	ONLY: pi
	97
	98	USE kinds
	99
	100	USE particle_attributes, &
	101	ONLY: collision_kernel, dissipation_classes, particles, radius_classes
	102
[828]	103	USE pegrid
[790]	104
[828]	105
[790]	106	IMPLICIT NONE
	107
	108	PRIVATE
	109
[849]	110	PUBLIC ckernel, collision_efficiency_rogers, init_kernels, &
[1007]	111	rclass_lbound, rclass_ubound, recalculate_kernel
[790]	112
[1320]	113	REAL(wp) :: epsilon !:
	114	REAL(wp) :: eps2 !:
	115	REAL(wp) :: rclass_lbound !:
	116	REAL(wp) :: rclass_ubound !:
	117	REAL(wp) :: urms !:
	118	REAL(wp) :: urms2 !:
[790]	119
[1320]	120	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !:
	121	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !:
	122	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !:
	123
	124	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !:
	125	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !:
	126	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !:
	127	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !:
	128	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !:
	129
	130	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !:
[792]	131
[828]	132	SAVE
[792]	133
[790]	134	!
	135	!-- Public interfaces
[849]	136	INTERFACE collision_efficiency_rogers
	137	MODULE PROCEDURE collision_efficiency_rogers
	138	END INTERFACE collision_efficiency_rogers
	139
[828]	140	INTERFACE init_kernels
	141	MODULE PROCEDURE init_kernels
	142	END INTERFACE init_kernels
[790]	143
[828]	144	INTERFACE recalculate_kernel
	145	MODULE PROCEDURE recalculate_kernel
	146	END INTERFACE recalculate_kernel
[790]	147
	148
[828]	149	CONTAINS
[790]	150
[792]	151
[828]	152	SUBROUTINE init_kernels
	153	!------------------------------------------------------------------------------!
	154	! Initialization of the collision efficiency matrix with fixed radius and
	155	! dissipation classes, calculated at simulation start only.
	156	!------------------------------------------------------------------------------!
[792]	157
[828]	158	IMPLICIT NONE
[792]	159
[1320]	160	INTEGER(iwp) :: i !:
	161	INTEGER(iwp) :: j !:
	162	INTEGER(iwp) :: k !:
[790]	163
[828]	164
	165	!
	166	!-- Calculate collision efficiencies for fixed radius- and dissipation
	167	!-- classes
	168	IF ( collision_kernel(6:9) == 'fast' ) THEN
	169
	170	ALLOCATE( ckernel(1:radius_classes,1:radius_classes, &
	171	0:dissipation_classes), epsclass(1:dissipation_classes), &
	172	radclass(1:radius_classes) )
	173
	174	!
	175	!-- Calculate the radius class bounds with logarithmic distances
	176	!-- in the interval [1.0E-6, 2.0E-4] m
[1322]	177	rclass_lbound = LOG( 1.0E-6_wp )
	178	rclass_ubound = LOG( 2.0E-4_wp )
[828]	179	radclass(1) = 1.0E-6
	180	DO i = 2, radius_classes
	181	radclass(i) = EXP( rclass_lbound + &
	182	( rclass_ubound - rclass_lbound ) * ( i-1.0 ) /&
	183	( radius_classes - 1.0 ) )
	184	! IF ( myid == 0 ) THEN
	185	! PRINT, 'i=', i, ' r = ', radclass(i)1.0E6
	186	! ENDIF
	187	ENDDO
	188
	189	!
[1007]	190	!-- Set the class bounds for dissipation in interval [0.0, 0.1] m2/s3
[828]	191	DO i = 1, dissipation_classes
[1322]	192	epsclass(i) = 0.1 * REAL( i, KIND=wp ) / dissipation_classes
[828]	193	! IF ( myid == 0 ) THEN
	194	! PRINT*, 'i=', i, ' eps = ', epsclass(i)
	195	! ENDIF
	196	ENDDO
	197	!
	198	!-- Calculate collision efficiencies of the Wang/ayala kernel
	199	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
	200	ecf(1:radius_classes,1:radius_classes), &
	201	gck(1:radius_classes,1:radius_classes), &
	202	winf(1:radius_classes) )
	203
	204	DO k = 1, dissipation_classes
	205
	206	epsilon = epsclass(k)
[1322]	207	urms = 2.02 * ( epsilon / 0.04_wp )**( 1.0_wp / 3.0_wp )
[828]	208
	209	CALL turbsd
	210	CALL turb_enhance_eff
	211	CALL effic
	212
	213	DO j = 1, radius_classes
	214	DO i = 1, radius_classes
	215	ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j)
	216	ENDDO
	217	ENDDO
	218
	219	ENDDO
	220
	221	!
	222	!-- Calculate collision efficiencies of the Hall kernel
	223	ALLOCATE( hkernel(1:radius_classes,1:radius_classes), &
	224	hwratio(1:radius_classes,1:radius_classes) )
	225
	226	CALL fallg
	227	CALL effic
	228
	229	DO j = 1, radius_classes
	230	DO i = 1, radius_classes
	231	hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 &
	232	* ec(i,j) * ABS( winf(j) - winf(i) )
	233	ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0
	234	ENDDO
	235	ENDDO
	236
	237	!
	238	!-- Test output of efficiencies
	239	IF ( j == -1 ) THEN
	240
	241	PRINT, '** Hall kernel'
[1007]	242	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6, &
	243	i = 1,radius_classes )
[828]	244	DO j = 1, radius_classes
[1007]	245	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
	246	( hkernel(i,j), i = 1,radius_classes )
[828]	247	ENDDO
	248
	249	DO k = 1, dissipation_classes
	250	DO i = 1, radius_classes
	251	DO j = 1, radius_classes
	252	IF ( hkernel(i,j) == 0.0 ) THEN
	253	hwratio(i,j) = 9999999.9
	254	ELSE
	255	hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j)
	256	ENDIF
	257	ENDDO
	258	ENDDO
	259
	260	PRINT, '** epsilon = ', epsclass(k)
[1007]	261	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6, &
	262	i = 1,radius_classes )
[828]	263	DO j = 1, radius_classes
[1007]	264	! WRITE ( ,'(F4.0,1X,20(F4.2,1X))' ) radclass(j)1.0E6, &
	265	! ( ckernel(i,j,k), i = 1,radius_classes )
	266	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j)1.0E6, &
	267	( hwratio(i,j), i = 1,radius_classes )
[828]	268	ENDDO
	269	ENDDO
	270
	271	ENDIF
	272
	273	DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf )
	274
	275	ELSEIF( collision_kernel == 'hall' .OR. collision_kernel == 'wang' ) &
	276	THEN
	277	!
	278	!-- Initial settings for Hall- and Wang-Kernel
	279	!-- To be done: move here parts from turbsd, fallg, ecoll, etc.
	280	ENDIF
	281
	282	END SUBROUTINE init_kernels
	283
	284
[790]	285	!------------------------------------------------------------------------------!
[828]	286	! Calculation of collision kernels during each timestep and for each grid box
[790]	287	!------------------------------------------------------------------------------!
[828]	288	SUBROUTINE recalculate_kernel( i1, j1, k1 )
[790]	289
[1320]	290	USE arrays_3d, &
	291	ONLY: diss
[790]	292
[1320]	293	USE particle_attributes, &
	294	ONLY: prt_count, prt_start_index, radius_classes, wang_kernel
	295
[790]	296	IMPLICIT NONE
	297
[1320]	298	INTEGER(iwp) :: i !:
	299	INTEGER(iwp) :: i1 !:
	300	INTEGER(iwp) :: j !:
	301	INTEGER(iwp) :: j1 !:
	302	INTEGER(iwp) :: k1 !:
	303	INTEGER(iwp) :: pend !:
	304	INTEGER(iwp) :: pstart !:
[790]	305
	306
[828]	307	pstart = prt_start_index(k1,j1,i1)
	308	pend = prt_start_index(k1,j1,i1) + prt_count(k1,j1,i1) - 1
	309	radius_classes = prt_count(k1,j1,i1)
[792]	310
[828]	311	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
	312	radclass(1:radius_classes), winf(1:radius_classes) )
[790]	313
[828]	314	!
[1007]	315	!-- Store particle radii on the radclass array
	316	radclass(1:radius_classes) = particles(pstart:pend)%radius
[790]	317
[835]	318	IF ( wang_kernel ) THEN
[1007]	319	epsilon = diss(k1,j1,i1) ! dissipation rate in m2/s3
[835]	320	ELSE
	321	epsilon = 0.0
	322	ENDIF
[1322]	323	urms = 2.02 * ( epsilon / 0.04_wp )**( 0.33333333333_wp )
[790]	324
[1007]	325	IF ( wang_kernel .AND. epsilon > 1.0E-7 ) THEN
[828]	326	!
	327	!-- Call routines to calculate efficiencies for the Wang kernel
	328	ALLOCATE( gck(1:radius_classes,1:radius_classes), &
	329	ecf(1:radius_classes,1:radius_classes) )
[790]	330
[828]	331	CALL turbsd
	332	CALL turb_enhance_eff
	333	CALL effic
[790]	334
[828]	335	DO j = 1, radius_classes
	336	DO i = 1, radius_classes
	337	ckernel(pstart+i-1,pstart+j-1,1) = ec(i,j) * gck(i,j) * ecf(i,j)
[790]	338	ENDDO
[828]	339	ENDDO
[790]	340
[828]	341	DEALLOCATE( gck, ecf )
[790]	342
	343	ELSE
[828]	344	!
	345	!-- Call routines to calculate efficiencies for the Hall kernel
[790]	346	CALL fallg
	347	CALL effic
	348
[828]	349	DO j = 1, radius_classes
	350	DO i = 1, radius_classes
	351	ckernel(pstart+i-1,pstart+j-1,1) = pi * &
	352	( radclass(j) + radclass(i) )**2 &
	353	* ec(i,j) * ABS( winf(j) - winf(i) )
[790]	354	ENDDO
	355	ENDDO
	356
	357	ENDIF
	358
[828]	359	DEALLOCATE( ec, radclass, winf )
[790]	360
[828]	361	END SUBROUTINE recalculate_kernel
[790]	362
[828]	363
[790]	364	!------------------------------------------------------------------------------!
[828]	365	! Calculation of gck
	366	! This is from Aayala 2008b, page 37ff.
	367	! Necessary input parameters: water density, radii of droplets, air density,
	368	! air viscosity, turbulent dissipation rate, taylor microscale reynolds number,
	369	! gravitational acceleration --> to be replaced by PALM parameters
[790]	370	!------------------------------------------------------------------------------!
[792]	371	SUBROUTINE turbsd
[799]	372
[1320]	373	USE control_parameters, &
	374	ONLY: g, molecular_viscosity
	375
	376	USE particle_attributes, &
	377	ONLY: radius_classes
[790]	378
	379	IMPLICIT NONE
[1320]	380
	381	LOGICAL, SAVE :: first = .TRUE. !:
[790]	382
[1320]	383	INTEGER(iwp) :: i !:
	384	INTEGER(iwp) :: j !:
[790]	385
[1320]	386	REAL(wp) :: ao !:
	387	REAL(wp) :: ao_gr !:
	388	REAL(wp) :: bbb !:
	389	REAL(wp) :: be !:
	390	REAL(wp) :: b1 !:
	391	REAL(wp) :: b2 !:
	392	REAL(wp) :: ccc !:
	393	REAL(wp) :: c1 !:
	394	REAL(wp) :: c1_gr !:
	395	REAL(wp) :: c2 !:
	396	REAL(wp) :: d1 !:
	397	REAL(wp) :: d2 !:
	398	REAL(wp) :: eta !:
	399	REAL(wp) :: e1 !:
	400	REAL(wp) :: e2 !:
	401	REAL(wp) :: fao_gr !:
	402	REAL(wp) :: fr !:
	403	REAL(wp) :: grfin !:
	404	REAL(wp) :: lambda !:
	405	REAL(wp) :: lambda_re !:
	406	REAL(wp) :: lf !:
	407	REAL(wp) :: rc !:
	408	REAL(wp) :: rrp !:
	409	REAL(wp) :: sst !:
	410	REAL(wp) :: tauk !:
	411	REAL(wp) :: tl !:
	412	REAL(wp) :: t2 !:
	413	REAL(wp) :: tt !:
	414	REAL(wp) :: t1 !:
	415	REAL(wp) :: vk !:
	416	REAL(wp) :: vrms1xy !:
	417	REAL(wp) :: vrms2xy !:
	418	REAL(wp) :: v1 !:
	419	REAL(wp) :: v1v2xy !:
	420	REAL(wp) :: v1xysq !:
	421	REAL(wp) :: v2 !:
	422	REAL(wp) :: v2xysq !:
	423	REAL(wp) :: wrfin !:
	424	REAL(wp) :: wrgrav2 !:
	425	REAL(wp) :: wrtur2xy !:
	426	REAL(wp) :: xx !:
	427	REAL(wp) :: yy !:
	428	REAL(wp) :: z !:
[790]	429
[1320]	430	REAL(wp), DIMENSION(1:radius_classes) :: st !:
	431	REAL(wp), DIMENSION(1:radius_classes) :: tau !:
	432
[799]	433	!
[828]	434	!-- Initial assignment of constants
[799]	435	IF ( first ) THEN
[790]	436
[799]	437	first = .FALSE.
[790]	438
[1007]	439	ENDIF
[790]	440
[1322]	441	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon ) ! in m
	442	lambda_re = urms*2 SQRT( 15.0_wp / epsilon / molecular_viscosity )
[828]	443	tl = urms**2 / epsilon ! in s
[1007]	444	lf = 0.5 * urms**3 / epsilon ! in m
	445	tauk = SQRT( molecular_viscosity / epsilon ) ! in s
[1322]	446	eta = ( molecular_viscosity3 / epsilon )0.25_wp ! in m
[1007]	447	vk = eta / tauk
[790]	448
[828]	449	ao = ( 11.0 + 7.0 * lambda_re ) / ( 205.0 + lambda_re )
[1322]	450	tt = SQRT( 2.0 * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk ! in s
[799]	451
[1007]	452	CALL fallg ! gives winf in m/s
[790]	453
[828]	454	DO i = 1, radius_classes
[1007]	455	tau(i) = winf(i) / g ! in s
[828]	456	st(i) = tau(i) / tauk
[790]	457	ENDDO
	458
[828]	459	!
	460	!-- Calculate wr (from Aayala 2008b, page 38f)
	461	z = tt / tl
[1322]	462	be = SQRT( 2.0_wp ) * lambda / lf
[828]	463	bbb = SQRT( 1.0 - 2.0 * be**2 )
	464	d1 = ( 1.0 + bbb ) / ( 2.0 * bbb )
[1007]	465	e1 = lf * ( 1.0 + bbb ) * 0.5 ! in m
[828]	466	d2 = ( 1.0 - bbb ) * 0.5 / bbb
[1007]	467	e2 = lf * ( 1.0 - bbb ) * 0.5 ! in m
[828]	468	ccc = SQRT( 1.0 - 2.0 * z**2 )
	469	b1 = ( 1.0 + ccc ) * 0.5 / ccc
	470	c1 = tl * ( 1.0 + ccc ) * 0.5 ! in s
	471	b2 = ( 1.0 - ccc ) * 0.5 / ccc
	472	c2 = tl * ( 1.0 - ccc ) * 0.5 ! in s
[790]	473
[828]	474	DO i = 1, radius_classes
[790]	475
[1007]	476	v1 = winf(i) ! in m/s
[828]	477	t1 = tau(i) ! in s
[790]	478
[828]	479	DO j = 1, i
[1007]	480	rrp = radclass(i) + radclass(j)
	481	v2 = winf(j) ! in m/s
[828]	482	t2 = tau(j) ! in s
[790]	483
[1007]	484	v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) &
	485	- b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1)
	486	v1xysq = v1xysq * urms2 / t1 ! in m2/s**2
	487	vrms1xy = SQRT( v1xysq ) ! in m/s
[790]	488
[1007]	489	v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) &
	490	- b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2)
	491	v2xysq = v2xysq * urms2 / t2 ! in m2/s**2
	492	vrms2xy = SQRT( v2xysq ) ! in m/s
[790]	493
[828]	494	IF ( winf(i) >= winf(j) ) THEN
[799]	495	v1 = winf(i)
[790]	496	t1 = tau(i)
[799]	497	v2 = winf(j)
[790]	498	t2 = tau(j)
	499	ELSE
[799]	500	v1 = winf(j)
[790]	501	t1 = tau(j)
[799]	502	v2 = winf(i)
[790]	503	t2 = tau(i)
	504	ENDIF
	505
[828]	506	v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - &
	507	b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - &
	508	b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + &
	509	b2 * d2* zhi(c2,e2,v1,t1,v2,t2)
	510	fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 )
[1007]	511	v1v2xy = v1v2xy * fr * urms2 / tau(i) / tau(j) ! in m2/s**2
	512	wrtur2xy = vrms1xy2 + vrms2xy2 - 2.0 * v1v2xy ! in m2/s2
[828]	513	IF ( wrtur2xy < 0.0 ) wrtur2xy = 0.0
[1322]	514	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
	515	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) ) ! in m/s
[790]	516
[828]	517	!
	518	!-- Calculate gr
	519	IF ( st(j) > st(i) ) THEN
	520	sst = st(j)
[790]	521	ELSE
[828]	522	sst = st(i)
[790]	523	ENDIF
	524
[828]	525	xx = -0.1988 * sst*4 + 1.5275 sst*3 - 4.2942 sst**2 + &
	526	5.3406 * sst
	527	IF ( xx < 0.0 ) xx = 0.0
[1322]	528	yy = 0.1886 * EXP( 20.306_wp / lambda_re )
[790]	529
[1007]	530	c1_gr = xx / ( g / vk * tauk )**yy
[790]	531
[1322]	532	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
[828]	533	fao_gr = 20.115 * SQRT( ao_gr / lambda_re )
	534	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta ! in cm
[790]	535
[828]	536	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5 )
	537	IF ( grfin < 1.0 ) grfin = 1.0
[790]	538
[828]	539	gck(i,j) = 2.0 * pi * rrp*2 wrfin * grfin ! in cm**3/s
[790]	540	gck(j,i) = gck(i,j)
	541
	542	ENDDO
	543	ENDDO
	544
[828]	545	END SUBROUTINE turbsd
[790]	546
[828]	547
[790]	548	!------------------------------------------------------------------------------!
[1007]	549	! phi_w as a function
[790]	550	!------------------------------------------------------------------------------!
[1320]	551	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
[790]	552
	553	IMPLICIT NONE
	554
[1320]	555	REAL(wp) :: a !:
	556	REAL(wp) :: aa1 !:
	557	REAL(wp) :: b !:
	558	REAL(wp) :: tau0 !:
	559	REAL(wp) :: vsett !:
[790]	560
[828]	561	aa1 = 1.0 / tau0 + 1.0 / a + vsett / b
[1007]	562	phi_w = 1.0 / aa1 - 0.5 * vsett / b / aa1**2 ! in s
[790]	563
[1007]	564	END FUNCTION phi_w
[792]	565
[790]	566
	567	!------------------------------------------------------------------------------!
[1007]	568	! zhi as a function
[790]	569	!------------------------------------------------------------------------------!
[1320]	570	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
[790]	571
	572	IMPLICIT NONE
	573
[1320]	574	REAL(wp) :: a !:
	575	REAL(wp) :: aa1 !:
	576	REAL(wp) :: aa2 !:
	577	REAL(wp) :: aa3 !:
	578	REAL(wp) :: aa4 !:
	579	REAL(wp) :: aa5 !:
	580	REAL(wp) :: aa6 !:
	581	REAL(wp) :: b !:
	582	REAL(wp) :: tau1 !:
	583	REAL(wp) :: tau2 !:
	584	REAL(wp) :: vsett1 !:
	585	REAL(wp) :: vsett2 !:
[790]	586
[828]	587	aa1 = vsett2 / b - 1.0 / tau2 - 1.0 / a
	588	aa2 = vsett1 / b + 1.0 / tau1 + 1.0 / a
	589	aa3 = ( vsett1 - vsett2 ) / b + 1.0 / tau1 + 1.0 / tau2
	590	aa4 = ( vsett2 / b )2 - ( 1.0 / tau2 + 1.0 / a )2
	591	aa5 = vsett2 / b + 1.0 / tau2 + 1.0 / a
	592	aa6 = 1.0 / tau1 - 1.0 / a + ( 1.0 / tau2 + 1.0 / a) * vsett1 / vsett2
	593	zhi = (1.0 / aa1 - 1.0 / aa2 ) * ( vsett1 - vsett2 ) * 0.5 / b / aa3**2 &
	594	+ (4.0 / aa4 - 1.0 / aa52 - 1.0 / aa12 ) * vsett2 * 0.5 / b /aa6&
	595	+ (2.0 * ( b / aa2 - b / aa1 ) - vsett1 / aa22 + vsett2 / aa12 )&
	596	* 0.5 / b / aa3 ! in s**2
[799]	597
[828]	598	END FUNCTION zhi
[790]	599
[828]	600
[790]	601	!------------------------------------------------------------------------------!
[1007]	602	! Calculation of terminal velocity winf following Equations 10-138 to 10-145
	603	! from (Pruppacher and Klett, 1997)
[790]	604	!------------------------------------------------------------------------------!
[828]	605	SUBROUTINE fallg
[1320]	606
	607	USE cloud_parameters, &
	608	ONLY: rho_l
	609
	610	USE control_parameters, &
	611	ONLY: g
[790]	612
[1320]	613	USE particle_attributes, &
	614	ONLY: radius_classes
[790]	615
[1320]	616
[828]	617	IMPLICIT NONE
[790]	618
[1320]	619	INTEGER(iwp) :: i !:
	620	INTEGER(iwp) :: j !:
[790]	621
[1320]	622	LOGICAL, SAVE :: first = .TRUE. !:
[790]	623
[1320]	624	REAL(wp), SAVE :: cunh !:
	625	REAL(wp), SAVE :: eta !:
	626	REAL(wp), SAVE :: phy !:
	627	REAL(wp), SAVE :: py !:
	628	REAL(wp), SAVE :: rho_a !:
	629	REAL(wp), SAVE :: sigma !:
	630	REAL(wp), SAVE :: stb !:
	631	REAL(wp), SAVE :: stok !:
	632	REAL(wp), SAVE :: xlamb !:
[790]	633
[1320]	634	REAL(wp) :: bond !:
	635	REAL(wp) :: x !:
	636	REAL(wp) :: xrey !:
	637	REAL(wp) :: y !:
[799]	638
[1320]	639	REAL(wp), DIMENSION(1:7), SAVE :: b !:
	640	REAL(wp), DIMENSION(1:6), SAVE :: c !:
[799]	641
	642	!
[828]	643	!-- Initial assignment of constants
	644	IF ( first ) THEN
[799]	645
[828]	646	first = .FALSE.
	647	b = (/ -0.318657E1, 0.992696E0, -0.153193E-2, -0.987059E-3, &
	648	-0.578878E-3, 0.855176E-4, -0.327815E-5 /)
	649	c = (/ -0.500015E1, 0.523778E1, -0.204914E1, 0.475294E0, &
	650	-0.542819E-1, 0.238449E-2 /)
[790]	651
[1007]	652	!
	653	!-- Parameter values for p = 1013,25 hPa and T = 293,15 K
	654	eta = 1.818E-5 ! in kg/(m s)
	655	xlamb = 6.6E-8 ! in m
	656	rho_a = 1.204 ! in kg/m**3
	657	cunh = 1.26 * xlamb ! in m
	658	sigma = 0.07363 ! in kg/s**2
	659	stok = 2.0 * g * ( rho_l - rho_a ) / ( 9.0 * eta ) ! in 1/(m s)
	660	stb = 32.0 * rho_a * ( rho_l - rho_a) * g / (3.0 * eta * eta)
	661	phy = sigma*3 rho_a2 / ( eta4 * g * ( rho_l - rho_a ) )
[1322]	662	py = phy**( 1.0_wp / 6.0_wp )
[790]	663
[828]	664	ENDIF
[790]	665
[828]	666	DO j = 1, radius_classes
[790]	667
[1007]	668	IF ( radclass(j) <= 1.0E-5 ) THEN
[799]	669
[1007]	670	winf(j) = stok * ( radclass(j)*2 + cunh radclass(j) )
[790]	671
[1007]	672	ELSEIF ( radclass(j) > 1.0E-5 .AND. radclass(j) <= 5.35E-4 ) THEN
[790]	673
[828]	674	x = LOG( stb * radclass(j)**3 )
	675	y = 0.0
[790]	676
[828]	677	DO i = 1, 7
	678	y = y + b(i) * x**(i-1)
	679	ENDDO
[1007]	680	!
	681	!-- Note: this Eq. is wrong in (Pruppacher and Klett, 1997, p. 418)
	682	!-- for correct version see (Beard, 1976)
	683	xrey = ( 1.0 + cunh / radclass(j) ) * EXP( y )
[790]	684
[1007]	685	winf(j) = xrey * eta / ( 2.0 * rho_a * radclass(j) )
[790]	686
[1007]	687	ELSEIF ( radclass(j) > 5.35E-4 ) THEN
[790]	688
[1007]	689	IF ( radclass(j) > 0.0035 ) THEN
	690	bond = g * ( rho_l - rho_a ) * 0.0035**2 / sigma
[828]	691	ELSE
[1007]	692	bond = g * ( rho_l - rho_a ) * radclass(j)**2 / sigma
[828]	693	ENDIF
[790]	694
[1322]	695	x = LOG( 16.0 * bond * py / 3.0_wp )
[828]	696	y = 0.0
[790]	697
[828]	698	DO i = 1, 6
	699	y = y + c(i) * x**(i-1)
	700	ENDDO
[790]	701
[828]	702	xrey = py * EXP( y )
[790]	703
[1007]	704	IF ( radclass(j) > 0.0035 ) THEN
[1322]	705	winf(j) = xrey * eta / ( 2.0 * rho_a * 0.0035_wp )
[828]	706	ELSE
[1007]	707	winf(j) = xrey * eta / ( 2.0 * rho_a * radclass(j) )
[828]	708	ENDIF
[790]	709
[828]	710	ENDIF
[790]	711
[828]	712	ENDDO
[790]	713
[828]	714	END SUBROUTINE fallg
[790]	715
[828]	716
[790]	717	!------------------------------------------------------------------------------!
[1071]	718	! Calculation of collision efficiencies for the Hall kernel
[790]	719	!------------------------------------------------------------------------------!
[828]	720	SUBROUTINE effic
[1320]	721
	722	USE particle_attributes, &
	723	ONLY: radius_classes
[790]	724
[828]	725	IMPLICIT NONE
[790]	726
[1320]	727	INTEGER(iwp) :: i !:
	728	INTEGER(iwp) :: iq !:
	729	INTEGER(iwp) :: ir !:
	730	INTEGER(iwp) :: j !:
	731	INTEGER(iwp) :: k !:
[790]	732
[1320]	733	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !:
[790]	734
[1320]	735	LOGICAL, SAVE :: first = .TRUE. !:
[790]	736
[1320]	737	REAL(wp) :: ek !:
	738	REAL(wp) :: particle_radius !:
	739	REAL(wp) :: pp !:
	740	REAL(wp) :: qq !:
	741	REAL(wp) :: rq !:
[790]	742
[1320]	743	REAL(wp), DIMENSION(1:21), SAVE :: rat !:
	744
	745	REAL(wp), DIMENSION(1:15), SAVE :: r0 !:
	746
	747	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !:
[790]	748
[792]	749	!
[828]	750	!-- Initial assignment of constants
	751	IF ( first ) THEN
[790]	752
[792]	753	first = .FALSE.
[828]	754	r0 = (/ 6.0, 8.0, 10.0, 15.0, 20.0, 25.0, 30.0, 40.0, 50.0, 60., &
	755	70.0, 100.0, 150.0, 200.0, 300.0 /)
	756	rat = (/ 0.00, 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, &
	757	0.50, 0.55, 0.60, 0.65, 0.70, 0.75, 0.80, 0.85, 0.90, 0.95, &
	758	1.00 /)
[790]	759
[828]	760	ecoll(:,1) = (/0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, &
	761	0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001/)
	762	ecoll(:,2) = (/0.003, 0.003, 0.003, 0.004, 0.005, 0.005, 0.005, &
	763	0.010, 0.100, 0.050, 0.200, 0.500, 0.770, 0.870, 0.970/)
	764	ecoll(:,3) = (/0.007, 0.007, 0.007, 0.008, 0.009, 0.010, 0.010, &
	765	0.070, 0.400, 0.430, 0.580, 0.790, 0.930, 0.960, 1.000/)
	766	ecoll(:,4) = (/0.009, 0.009, 0.009, 0.012, 0.015, 0.010, 0.020, &
	767	0.280, 0.600, 0.640, 0.750, 0.910, 0.970, 0.980, 1.000/)
	768	ecoll(:,5) = (/0.014, 0.014, 0.014, 0.015, 0.016, 0.030, 0.060, &
	769	0.500, 0.700, 0.770, 0.840, 0.950, 0.970, 1.000, 1.000/)
	770	ecoll(:,6) = (/0.017, 0.017, 0.017, 0.020, 0.022, 0.060, 0.100, &
	771	0.620, 0.780, 0.840, 0.880, 0.950, 1.000, 1.000, 1.000/)
	772	ecoll(:,7) = (/0.030, 0.030, 0.024, 0.022, 0.032, 0.062, 0.200, &
	773	0.680, 0.830, 0.870, 0.900, 0.950, 1.000, 1.000, 1.000/)
	774	ecoll(:,8) = (/0.025, 0.025, 0.025, 0.036, 0.043, 0.130, 0.270, &
	775	0.740, 0.860, 0.890, 0.920, 1.000, 1.000, 1.000, 1.000/)
	776	ecoll(:,9) = (/0.027, 0.027, 0.027, 0.040, 0.052, 0.200, 0.400, &
	777	0.780, 0.880, 0.900, 0.940, 1.000, 1.000, 1.000, 1.000/)
	778	ecoll(:,10)= (/0.030, 0.030, 0.030, 0.047, 0.064, 0.250, 0.500, &
	779	0.800, 0.900, 0.910, 0.950, 1.000, 1.000, 1.000, 1.000/)
	780	ecoll(:,11)= (/0.040, 0.040, 0.033, 0.037, 0.068, 0.240, 0.550, &
	781	0.800, 0.900, 0.910, 0.950, 1.000, 1.000, 1.000, 1.000/)
	782	ecoll(:,12)= (/0.035, 0.035, 0.035, 0.055, 0.079, 0.290, 0.580, &
	783	0.800, 0.900, 0.910, 0.950, 1.000, 1.000, 1.000, 1.000/)
	784	ecoll(:,13)= (/0.037, 0.037, 0.037, 0.062, 0.082, 0.290, 0.590, &
	785	0.780, 0.900, 0.910, 0.950, 1.000, 1.000, 1.000, 1.000/)
	786	ecoll(:,14)= (/0.037, 0.037, 0.037, 0.060, 0.080, 0.290, 0.580, &
	787	0.770, 0.890, 0.910, 0.950, 1.000, 1.000, 1.000, 1.000/)
	788	ecoll(:,15)= (/0.037, 0.037, 0.037, 0.041, 0.075, 0.250, 0.540, &
	789	0.760, 0.880, 0.920, 0.950, 1.000, 1.000, 1.000, 1.000/)
	790	ecoll(:,16)= (/0.037, 0.037, 0.037, 0.052, 0.067, 0.250, 0.510, &
	791	0.770, 0.880, 0.930, 0.970, 1.000, 1.000, 1.000, 1.000/)
	792	ecoll(:,17)= (/0.037, 0.037, 0.037, 0.047, 0.057, 0.250, 0.490, &
	793	0.770, 0.890, 0.950, 1.000, 1.000, 1.000, 1.000, 1.000/)
	794	ecoll(:,18)= (/0.036, 0.036, 0.036, 0.042, 0.048, 0.230, 0.470, &
	795	0.780, 0.920, 1.000, 1.020, 1.020, 1.020, 1.020, 1.020/)
	796	ecoll(:,19)= (/0.040, 0.040, 0.035, 0.033, 0.040, 0.112, 0.450, &
	797	0.790, 1.010, 1.030, 1.040, 1.040, 1.040, 1.040, 1.040/)
	798	ecoll(:,20)= (/0.033, 0.033, 0.033, 0.033, 0.033, 0.119, 0.470, &
	799	0.950, 1.300, 1.700, 2.300, 2.300, 2.300, 2.300, 2.300/)
	800	ecoll(:,21)= (/0.027, 0.027, 0.027, 0.027, 0.027, 0.125, 0.520, &
	801	1.400, 2.300, 3.000, 4.000, 4.000, 4.000, 4.000, 4.000/)
	802	ENDIF
[790]	803
[792]	804	!
[828]	805	!-- Calculate the radius class index of particles with respect to array r
[1007]	806	!-- Radius has to be in Âµm
[828]	807	ALLOCATE( ira(1:radius_classes) )
	808	DO j = 1, radius_classes
[1322]	809	particle_radius = radclass(j) * 1.0E6_wp
[828]	810	DO k = 1, 15
	811	IF ( particle_radius < r0(k) ) THEN
	812	ira(j) = k
	813	EXIT
	814	ENDIF
	815	ENDDO
	816	IF ( particle_radius >= r0(15) ) ira(j) = 16
	817	ENDDO
[790]	818
[792]	819	!
[828]	820	!-- Two-dimensional linear interpolation of the collision efficiency.
	821	!-- Radius has to be in Âµm
	822	DO j = 1, radius_classes
	823	DO i = 1, j
[792]	824
[828]	825	ir = ira(j)
	826	rq = radclass(i) / radclass(j)
	827	iq = INT( rq * 20 ) + 1
	828	iq = MAX( iq , 2)
[792]	829
[828]	830	IF ( ir < 16 ) THEN
	831	IF ( ir >= 2 ) THEN
[1322]	832	pp = ( ( radclass(j) * 1.0E06_wp ) - r0(ir-1) ) / &
[828]	833	( r0(ir) - r0(ir-1) )
	834	qq = ( rq- rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	835	ec(j,i) = ( 1.0-pp ) * ( 1.0-qq ) * ecoll(ir-1,iq-1) &
	836	+ pp * ( 1.0-qq ) * ecoll(ir,iq-1) &
	837	+ qq * ( 1.0-pp ) * ecoll(ir-1,iq) &
	838	+ pp * qq * ecoll(ir,iq)
	839	ELSE
	840	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	841	ec(j,i) = (1.0-qq) * ecoll(1,iq-1) + qq * ecoll(1,iq)
	842	ENDIF
	843	ELSE
	844	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	845	ek = ( 1.0 - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
[1346]	846	ec(j,i) = MIN( ek, 1.0_wp )
[1071]	847	ENDIF
[792]	848
[1071]	849	IF ( ec(j,i) < 1.0E-20 ) ec(j,i) = 0.0
	850
[828]	851	ec(i,j) = ec(j,i)
[792]	852
[828]	853	ENDDO
	854	ENDDO
[792]	855
[828]	856	DEALLOCATE( ira )
[792]	857
[828]	858	END SUBROUTINE effic
[792]	859
	860
[790]	861	!------------------------------------------------------------------------------!
[828]	862	! Calculation of enhancement factor for collision efficencies due to turbulence
[790]	863	!------------------------------------------------------------------------------!
[828]	864	SUBROUTINE turb_enhance_eff
[790]	865
[1320]	866	USE particle_attributes, &
	867	ONLY: radius_classes
[790]	868
[828]	869	IMPLICIT NONE
[790]	870
[1320]	871	INTEGER(iwp) :: i !:
	872	INTEGER(iwp) :: iq !:
	873	INTEGER(iwp) :: ir !:
	874	INTEGER(iwp) :: j !:
	875	INTEGER(iwp) :: k !:
	876	INTEGER(iwp) :: kk !:
[790]	877
[1320]	878	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !:
	879
	880	LOGICAL, SAVE :: first = .TRUE. !:
[790]	881
[1320]	882	REAL(wp) :: particle_radius !:
	883	REAL(wp) :: pp !:
	884	REAL(wp) :: qq !:
	885	REAL(wp) :: rq !:
	886	REAL(wp) :: y1 !:
	887	REAL(wp) :: y2 !:
	888	REAL(wp) :: y3 !:
[790]	889
[1320]	890	REAL(wp), DIMENSION(1:11), SAVE :: rat !:
	891
	892	REAL(wp), DIMENSION(1:7), SAVE :: r0 !:
	893
	894	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !:
	895	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !:
[799]	896
	897	!
[828]	898	!-- Initial assignment of constants
	899	IF ( first ) THEN
[799]	900
[828]	901	first = .FALSE.
[799]	902
[828]	903	r0 = (/ 10.0, 20.0, 30.0, 40.0, 50.0, 60.0, 100.0 /)
	904	rat = (/ 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0 /)
	905	!
[1007]	906	!-- for 100 cm2/s3
[828]	907	ecoll_100(:,1) = (/1.74, 1.74, 1.773, 1.49, 1.207, 1.207, 1.0 /)
	908	ecoll_100(:,2) = (/1.46, 1.46, 1.421, 1.245, 1.069, 1.069, 1.0 /)
	909	ecoll_100(:,3) = (/1.32, 1.32, 1.245, 1.123, 1.000, 1.000, 1.0 /)
	910	ecoll_100(:,4) = (/1.250, 1.250, 1.148, 1.087, 1.025, 1.025, 1.0 /)
	911	ecoll_100(:,5) = (/1.186, 1.186, 1.066, 1.060, 1.056, 1.056, 1.0 /)
	912	ecoll_100(:,6) = (/1.045, 1.045, 1.000, 1.014, 1.028, 1.028, 1.0 /)
	913	ecoll_100(:,7) = (/1.070, 1.070, 1.030, 1.038, 1.046, 1.046, 1.0 /)
	914	ecoll_100(:,8) = (/1.000, 1.000, 1.054, 1.042, 1.029, 1.029, 1.0 /)
	915	ecoll_100(:,9) = (/1.223, 1.223, 1.117, 1.069, 1.021, 1.021, 1.0 /)
	916	ecoll_100(:,10)= (/1.570, 1.570, 1.244, 1.166, 1.088, 1.088, 1.0 /)
	917	ecoll_100(:,11)= (/20.3, 20.3, 14.6 , 8.61, 2.60, 2.60 , 1.0 /)
	918	!
[1007]	919	!-- for 400 cm2/s3
[828]	920	ecoll_400(:,1) = (/4.976, 4.976, 3.593, 2.519, 1.445, 1.445, 1.0 /)
	921	ecoll_400(:,2) = (/2.984, 2.984, 2.181, 1.691, 1.201, 1.201, 1.0 /)
	922	ecoll_400(:,3) = (/1.988, 1.988, 1.475, 1.313, 1.150, 1.150, 1.0 /)
	923	ecoll_400(:,4) = (/1.490, 1.490, 1.187, 1.156, 1.126, 1.126, 1.0 /)
	924	ecoll_400(:,5) = (/1.249, 1.249, 1.088, 1.090, 1.092, 1.092, 1.0 /)
	925	ecoll_400(:,6) = (/1.139, 1.139, 1.130, 1.091, 1.051, 1.051, 1.0 /)
	926	ecoll_400(:,7) = (/1.220, 1.220, 1.190, 1.138, 1.086, 1.086, 1.0 /)
	927	ecoll_400(:,8) = (/1.325, 1.325, 1.267, 1.165, 1.063, 1.063, 1.0 /)
	928	ecoll_400(:,9) = (/1.716, 1.716, 1.345, 1.223, 1.100, 1.100, 1.0 /)
	929	ecoll_400(:,10)= (/3.788, 3.788, 1.501, 1.311, 1.120, 1.120, 1.0 /)
	930	ecoll_400(:,11)= (/36.52, 36.52, 19.16, 22.80, 26.0, 26.0, 1.0 /)
[799]	931
[828]	932	ENDIF
[790]	933
[828]	934	!
	935	!-- Calculate the radius class index of particles with respect to array r0
[1007]	936	!-- Radius has to be in Âµm
[828]	937	ALLOCATE( ira(1:radius_classes) )
[790]	938
[828]	939	DO j = 1, radius_classes
[1322]	940	particle_radius = radclass(j) * 1.0E6_wp
[828]	941	DO k = 1, 7
	942	IF ( particle_radius < r0(k) ) THEN
	943	ira(j) = k
	944	EXIT
	945	ENDIF
	946	ENDDO
	947	IF ( particle_radius >= r0(7) ) ira(j) = 8
	948	ENDDO
[799]	949
	950	!
[828]	951	!-- Two-dimensional linear interpolation of the collision efficiencies
[1007]	952	!-- Radius has to be in Âµm
[828]	953	DO j = 1, radius_classes
	954	DO i = 1, j
[799]	955
[828]	956	ir = ira(j)
	957	rq = radclass(i) / radclass(j)
[799]	958
[828]	959	DO kk = 2, 11
	960	IF ( rq <= rat(kk) ) THEN
	961	iq = kk
	962	EXIT
	963	ENDIF
	964	ENDDO
[790]	965
[1007]	966	y1 = 0.0001 ! for 0 m2/s3
	967
[828]	968	IF ( ir < 8 ) THEN
	969	IF ( ir >= 2 ) THEN
[1007]	970	pp = ( radclass(j)*1.0E6 - r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
[828]	971	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	972	y2 = ( 1.0-pp ) * ( 1.0-qq ) * ecoll_100(ir-1,iq-1) + &
	973	pp * ( 1.0-qq ) * ecoll_100(ir,iq-1) + &
[1007]	974	qq * ( 1.0-pp ) * ecoll_100(ir-1,iq) + &
[828]	975	pp * qq * ecoll_100(ir,iq)
	976	y3 = ( 1.0-pp ) * ( 1.0-qq ) * ecoll_400(ir-1,iq-1) + &
	977	pp * ( 1.0-qq ) * ecoll_400(ir,iq-1) + &
	978	qq * ( 1.0-pp ) * ecoll_400(ir-1,iq) + &
	979	pp * qq * ecoll_400(ir,iq)
	980	ELSE
	981	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	982	y2 = ( 1.0-qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq)
	983	y3 = ( 1.0-qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq)
	984	ENDIF
	985	ELSE
	986	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	987	y2 = ( 1.0-qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq)
	988	y3 = ( 1.0-qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq)
	989	ENDIF
	990	!
[1007]	991	!-- Linear interpolation of dissipation rate in m2/s3
	992	IF ( epsilon <= 0.01 ) THEN
	993	ecf(j,i) = ( epsilon - 0.01 ) / ( 0.0 - 0.01 ) * y1 &
	994	+ ( epsilon - 0.0 ) / ( 0.01 - 0.0 ) * y2
	995	ELSEIF ( epsilon <= 0.06 ) THEN
	996	ecf(j,i) = ( epsilon - 0.04 ) / ( 0.01 - 0.04 ) * y2 &
	997	+ ( epsilon - 0.01 ) / ( 0.04 - 0.01 ) * y3
[828]	998	ELSE
[1007]	999	ecf(j,i) = ( 0.06 - 0.04 ) / ( 0.01 - 0.04 ) * y2 &
	1000	+ ( 0.06 - 0.01 ) / ( 0.04 - 0.01 ) * y3
[828]	1001	ENDIF
[790]	1002
[828]	1003	IF ( ecf(j,i) < 1.0 ) ecf(j,i) = 1.0
[790]	1004
[828]	1005	ecf(i,j) = ecf(j,i)
[790]	1006
[828]	1007	ENDDO
	1008	ENDDO
[790]	1009
[828]	1010	END SUBROUTINE turb_enhance_eff
[790]	1011
[849]	1012
	1013
	1014	SUBROUTINE collision_efficiency_rogers( mean_r, r, e)
	1015	!------------------------------------------------------------------------------!
	1016	! Collision efficiencies from table 8.2 in Rogers and Yau (1989, 3rd edition).
	1017	! Values are calculated from table by bilinear interpolation.
	1018	!------------------------------------------------------------------------------!
	1019
	1020	IMPLICIT NONE
	1021
[1320]	1022	INTEGER(iwp) :: i !:
	1023	INTEGER(iwp) :: j !:
	1024	INTEGER(iwp) :: k !:
[849]	1025
[1320]	1026	LOGICAL, SAVE :: first = .TRUE. !:
[849]	1027
[1320]	1028	REAL(wp) :: aa !:
	1029	REAL(wp) :: bb !:
	1030	REAL(wp) :: cc !:
	1031	REAL(wp) :: dd !:
	1032	REAL(wp) :: dx !:
	1033	REAL(wp) :: dy !:
	1034	REAL(wp) :: e !:
	1035	REAL(wp) :: gg !:
	1036	REAL(wp) :: mean_r !:
	1037	REAL(wp) :: mean_rm !:
	1038	REAL(wp) :: r !:
	1039	REAL(wp) :: rm !:
	1040	REAL(wp) :: x !:
	1041	REAL(wp) :: y !:
	1042
	1043	REAL(wp), DIMENSION(1:9), SAVE :: collected_r = 0.0 !:
	1044
	1045	REAL(wp), DIMENSION(1:19), SAVE :: collector_r = 0.0 !:
	1046
	1047	REAL(wp), DIMENSION(1:9,1:19), SAVE :: ef = 0.0 !:
[849]	1048
[1322]	1049	mean_rm = mean_r * 1.0E06_wp
	1050	rm = r * 1.0E06_wp
[849]	1051
	1052	IF ( first ) THEN
	1053
	1054	collected_r = (/ 2.0, 3.0, 4.0, 6.0, 8.0, 10.0, 15.0, 20.0, 25.0 /)
	1055	collector_r = (/ 10.0, 20.0, 30.0, 40.0, 50.0, 60.0, 80.0, 100.0, &
	1056	150.0, 200.0, 300.0, 400.0, 500.0, 600.0, 1000.0, &
	1057	1400.0, 1800.0, 2400.0, 3000.0 /)
	1058
	1059	ef(:,1) = (/0.017, 0.027, 0.037, 0.052, 0.052, 0.052, 0.052, 0.0, &
	1060	0.0 /)
	1061	ef(:,2) = (/0.001, 0.016, 0.027, 0.060, 0.12, 0.17, 0.17, 0.17, 0.0 /)
	1062	ef(:,3) = (/0.001, 0.001, 0.02, 0.13, 0.28, 0.37, 0.54, 0.55, 0.47/)
	1063	ef(:,4) = (/0.001, 0.001, 0.02, 0.23, 0.4, 0.55, 0.7, 0.75, 0.75/)
	1064	ef(:,5) = (/0.01, 0.01, 0.03, 0.3, 0.4, 0.58, 0.73, 0.75, 0.79/)
	1065	ef(:,6) = (/0.01, 0.01, 0.13, 0.38, 0.57, 0.68, 0.80, 0.86, 0.91/)
	1066	ef(:,7) = (/0.01, 0.085, 0.23, 0.52, 0.68, 0.76, 0.86, 0.92, 0.95/)
	1067	ef(:,8) = (/0.01, 0.14, 0.32, 0.60, 0.73, 0.81, 0.90, 0.94, 0.96/)
	1068	ef(:,9) = (/0.025, 0.25, 0.43, 0.66, 0.78, 0.83, 0.92, 0.95, 0.96/)
	1069	ef(:,10)= (/0.039, 0.3, 0.46, 0.69, 0.81, 0.87, 0.93, 0.95, 0.96/)
	1070	ef(:,11)= (/0.095, 0.33, 0.51, 0.72, 0.82, 0.87, 0.93, 0.96, 0.97/)
	1071	ef(:,12)= (/0.098, 0.36, 0.51, 0.73, 0.83, 0.88, 0.93, 0.96, 0.97/)
	1072	ef(:,13)= (/0.1, 0.36, 0.52, 0.74, 0.83, 0.88, 0.93, 0.96, 0.97/)
	1073	ef(:,14)= (/0.17, 0.4, 0.54, 0.72, 0.83, 0.88, 0.94, 0.98, 1.0 /)
	1074	ef(:,15)= (/0.15, 0.37, 0.52, 0.74, 0.82, 0.88, 0.94, 0.98, 1.0 /)
	1075	ef(:,16)= (/0.11, 0.34, 0.49, 0.71, 0.83, 0.88, 0.94, 0.95, 1.0 /)
	1076	ef(:,17)= (/0.08, 0.29, 0.45, 0.68, 0.8, 0.86, 0.96, 0.94, 1.0 /)
	1077	ef(:,18)= (/0.04, 0.22, 0.39, 0.62, 0.75, 0.83, 0.92, 0.96, 1.0 /)
	1078	ef(:,19)= (/0.02, 0.16, 0.33, 0.55, 0.71, 0.81, 0.90, 0.94, 1.0 /)
	1079
	1080	ENDIF
	1081
	1082	DO k = 1, 8
	1083	IF ( collected_r(k) <= mean_rm ) i = k
	1084	ENDDO
	1085
	1086	DO k = 1, 18
	1087	IF ( collector_r(k) <= rm ) j = k
	1088	ENDDO
	1089
	1090	IF ( rm < 10.0 ) THEN
	1091	e = 0.0
	1092	ELSEIF ( mean_rm < 2.0 ) THEN
	1093	e = 0.001
	1094	ELSEIF ( mean_rm >= 25.0 ) THEN
	1095	IF( j <= 2 ) e = 0.0
	1096	IF( j == 3 ) e = 0.47
	1097	IF( j == 4 ) e = 0.8
	1098	IF( j == 5 ) e = 0.9
	1099	IF( j >=6 ) e = 1.0
	1100	ELSEIF ( rm >= 3000.0 ) THEN
	1101	IF( i == 1 ) e = 0.02
	1102	IF( i == 2 ) e = 0.16
	1103	IF( i == 3 ) e = 0.33
	1104	IF( i == 4 ) e = 0.55
	1105	IF( i == 5 ) e = 0.71
	1106	IF( i == 6 ) e = 0.81
	1107	IF( i == 7 ) e = 0.90
	1108	IF( i >= 8 ) e = 0.94
	1109	ELSE
	1110	x = mean_rm - collected_r(i)
	1111	y = rm - collector_r(j)
	1112	dx = collected_r(i+1) - collected_r(i)
	1113	dy = collector_r(j+1) - collector_r(j)
	1114	aa = x2 + y2
	1115	bb = ( dx - x )2 + y2
	1116	cc = x2 + ( dy - y )2
	1117	dd = ( dx - x )2 + ( dy - y )2
	1118	gg = aa + bb + cc + dd
	1119
	1120	e = ( (gg-aa)ef(i,j) + (gg-bb)ef(i+1,j) + (gg-cc)*ef(i,j+1) + &
	1121	(gg-dd)ef(i+1,j+1) ) / (3.0gg)
	1122	ENDIF
	1123
	1124	END SUBROUTINE collision_efficiency_rogers
	1125
[825]	1126	END MODULE lpm_collision_kernels_mod

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