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source: palm/trunk/SOURCE/lpm_collision_kernels.f90 @ 1359

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

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