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source: palm/trunk/SOURCE/lpm_collision_kernels.f90 @ 1519

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

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