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source: palm/trunk/SOURCE/lpm_collision_kernels.f90 @ 1682

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

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