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10
11<center><b><font size=+1>Algorithm and computation of aerosols phase functions</font></b>
12<p><i>by A.N. Rublev</i>
13<p><font size=-1>(Internal Note IAE-5715/16 of Russian Research Center
14" Kurchatov Institute ", Moscow, 51 pp., 1994).</font>
15<p><b>Extended abstract</b></center>
16
17<p>Aerosols are known to influence the propagation of the solar radiation
18in the atmosphere. Aerosols emission sources are numerous: e.g. dust storms,
19fuel combustion (soot), ocean sprays, etc... Stratospheric aerosols and
20tropospheric anthropogenic aerosols which play an essential role in climate
21forcing (Charlson et al.<sup>1</sup>) can be generated by atmospheric chemical
22reactions with sulfates, sulfuric acid and nitric acid. The volcanic eruptions
23are one of the important atmospheric aerosol generators, for example the
24eruption of the volcano Pinatubo, Philippines, June 1991 resulted in the
25emission 20 Mts of SO<sub>2</sub> (Gregs et al.<sup>2</sup>) which is a
26main source of sulfuric acid aerosol fraction.
27<p>Despite the large number of different aerosol sources, only some selected
28basic aerosol components have been considered in the development of various
29aerosol models (WMO publication<sup>3</sup>). Principal aerosol models
30(<i>e.g. continental, urban, maritime, stratospheric, volcanic, upper atmosphere,
31and cloudy</i>) and their basic components (<i>e.g. dust, water-soluble
32particles, soot, salt particles (oceanic), sulfuric acid solution droplets,
33volcanic ash, and water</i>) are listed in Table 1 (from Ref. 3) with the
34following entries:
35<ul>
36<li>
37the aerosol model name (first column) and the related basic aerosol components
38(second column);</li>
39</ul>
40
41<ul>
42<li>
43the aerosol fraction by volume in % (third column), and the related aerosol
44relative concentration&nbsp;<img SRC="/icons-geisa/alexei_n1n2.gif" height=41 width=25 align=CENTER>(fourth
45column), where <i><font size=+1>N<sub>i</sub></font></i> is the number
46of particles of the i-th component, and N is total number of particles
47in a given aerosol sample.</li>
48</ul>
49Main expressions for the aerosol integrated optical properties as given
50by Deirmendjian<sup>4</sup> are:
51<div align=right>• the scattering coefficient:&nbsp;<img SRC="/icons-geisa/alexei_eq1.gif" height=50 width=224 align=ABSCENTER>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
52(1)
53<p>• the extinction coefficient:&nbsp;<img SRC="/icons-geisa/alexei_eq2.gif" height=50 width=225 align=ABSCENTER>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
54(2)</div>
55&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; • the scattering phase function corresponding
56to the scattering angle
57<i><font face="Symbol"><font size=+1>q</font></font></i>:
58<div align=right><img SRC="/icons-geisa/alexei_eq3.gif" height=50 width=190 align=ABSCENTER>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
59(3)</div>
60&nbsp;
61<div align=right>
62<br>• the single scattering albedo:&nbsp;<img SRC="/icons-geisa/alexei_eq4.gif" height=45 width=81 align=ABSCENTER>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
63(4)
64<p>• the asymmetry factor:&nbsp;<img SRC="/icons-geisa/alexei_eq5.gif" height=51 width=154 align=ABSCENTER>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
65(5)
66<p>• the normalization factor:&nbsp;<img SRC="/icons-geisa/alexei_eq6.gif" height=51 width=124 align=ABSCENTER>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
67(6)</div>
68where:
69<br><img SRC="/icons-geisa/alexei_k_2pi.gif" height=43 width=54 align=ABSCENTER>
70<br><i><font size=+1>x=kr </font></i>is the dimensionless size of the particles
71with radius <i><font size=+1>r</font></i>
72<br><i><font size=+1>m=p-iq</font></i><font face="Arial"> </font>is the
73complex index of refraction with the real (<i><font size=+1>p</font></i>)
74and imaginary (<i><font size=+1>q</font></i>) parts
75<br><i><font size=+1>n(x)</font></i>-is the aerosol particle size distribution
76function (i.e., <i><font size=+1>n(x)d(x)</font></i> is the number of particles
77per cm<sup>3</sup> with dimensionless radii <i><font size=+1>x</font></i>
78in the interval <i><font size=+1>dx</font></i> so that&nbsp;<img SRC="/icons-geisa/alexei_integ.gif" height=50 width=90 align=CENTER>is
79the total number of particles per cm<sup>3</sup>);
80<br><i>K<sub><font size=+1>sc</font></sub></i>(<i><font size=+1>x,m</font></i>)and
81<i>K<sub><font size=+1>ex</font></sub></i>(<i><font size=+1>x,m)</font></i>
82are dimensionless efficiency factors for scattering and extinction, respectively
83(Ref. 4)
84<br><i><font size=+1>i(x,m,<font face="Symbol">q</font>)</font></i> is
85the scattering intensity for non-polarized radiation (Ref. 4):<img SRC="/icons-geisa/alexei_i.gif" height=44 width=156 align=ABSCENTER>
86, where
87<i><font size=+1>S<sub>1</sub>, S<sub>2</sub></font></i> are dimensionless
88complex functions (see Ref. 4, 5 for explicit formulas) which give the
89complex amplitudes&nbsp;<img SRC="/icons-geisa/alexei_as.gif" height=24 width=44 align=ABSCENTER>of
90the scattered wave in terms of the complex amplitudes&nbsp;<img SRC="/icons-geisa/alexei_ai.gif" height=24 width=43 align=ABSCENTER>of
91the incident radiation resolved along the transverse and parallel directions
92with respect to the scattering plane, respectively (Ref. 5):
93<center>
94<p><img SRC="/icons-geisa/alexei_matr.gif" height=51 width=144 align=CENTER></center>
95
96<p>is a linear interpolation of the phase function <i><font size=+1>I<sub><font face="Symbol">q</font></sub>.</font></i>.
97<br>Eqs. (1-5) determine optical properties of the aerosols to be considered
98in non-polarized radiative transfer problems. In particular, the optical
99thickness <i><font face="Symbol"><font size=+1>t(l)</font></font></i> at
100the wavelength <i><font face="Symbol"><font size=+1>l</font></font></i>
101of an atmosphere including aerosols is expressed as the sum: <i><font face="Symbol"><font size=+1>t(l)=t</font></font><sub>gas</sub><font face="Symbol"><font size=+1>(l)+t</font></font><sub>aer</sub><font face="Symbol"><font size=+1>(l)</font></font></i>,
102<p>where <i><font face="Symbol"><font size=+1>t</font></font><sub>gas</sub></i>
103is the atmospheric gases optical thickness calculated using, for example,
104well-known spectroscopic " line-by-line " methods;
105<p><i><font face="Symbol"><font size=+1>t</font></font><sub>aer</sub></i>
106is the aerosol optical thickness calculated for an arbitrary non-homogeneous
107path <i><font size=+1>L</font></i>:
108<center>
109<p><img SRC="/icons-geisa/alexei_thick.gif" height=41 width=132 align=ABSCENTER></center>
110<i><font size=+1><font face="Symbol">s</font><sub>ex</sub></font><sub>(x;</sub><font size=+1><font face="Symbol">l</font>)</font></i>
111is the aerosol extinction coefficient at a point <i><font size=+1>x</font></i>
112of the path <i><font size=+1>L</font></i>.
113<br>It should be outlined, that the normalization factor of Eq.(6) (<img SRC="/icons-geisa/alexei_kn.gif" height=22 width=48 align=ABSCENTER>)
114has been calculated to check the reliability of the linear interpolation
115of the phase function of Eq.(3) used in the calculations of Eq. (5). It
116is aimed at the determination of a required number of angular mesh points
117providing an accurate interpolation of the phase function according to
118the following criterion: the closer K<sub>n</sub> is to 1, the better is
119the interpolation (see last column of Table 2 as an example). In Rublev’s
120paper 204 angular mesh points (from 0 to 180 degrees) are used in the calculations.
121<br>The Mie theory (see, for example, Deirmendjian<sup>4</sup>, Van de
122Hulst<sup>6</sup>) based algorithm has been developed and a related computer
123code as well, providing a reliable accuracy for computations of the above
124mentioned aerosol optical properties (estimated relative error <font face="Symbol">&pound;</font>
1250.3%).
126<p><i>Main results presented in the publication are (see Table 2 as an
127example):</i>
128<p>• Tables in the Appendix to the paper provide the computed values of
129the phase function for the principal aerosol models and their basic components
130as listed in Table 1. The calculations were made for 8 wavelengths in the
131UV, visible and IR regions, with an estimated relative error <font face="Symbol">&pound;</font>
1320.3%.
133<p>• The principal optical properties of the basic aerosol components (column
1342 of Table 1: soot, dust, water-soluble particles, etc...), namely&nbsp;<img SRC="/icons-geisa/alexei_sigmaext.gif" height=22 width=48 align=ABSCENTER>-
135the extinction coefficient (km<sup>-1</sup>) for a particle number concentration
136<i><font size=+1>N</font></i>=1
137particle per 1 cm<sup>3</sup>; <i><font face="Symbol"><font size=+1>w</font></font></i>-
138the single scattering albedo; <i><font size=+1>g</font></i>- the asymmetry
139factor; <i><font size=+1>K<sub>n</sub></font></i>- the normalization factor
140and its values at 204 angles.
141<p>• The same as above defined optical properties for non-cloudy basic
142aerosol models (column 1 of Table 1: continental, maritime, urban, etc...).
143As an example, results of the calculations for the urban aerosol model
144with basic components from Table 1 (water-soluble, soot, dust) are shown
145in Table 2.
146<p>• The optical properties for a cloudy aerosol model with a particle
147number concentration <i><font size=+1>N<sub>0</sub></font></i>=353.678
148cm<sup>-3</sup> corresponding to a typical cloud water content <i><font size=+1>W</font></i>=0.3
149g m<sup>-3 </sup>(Ref. 7), with the modified Gamma function n(r) (Ref.
1506, 7) as a particle size distribution function:
151<div align=right><img SRC="/icons-geisa/alexei_eq7.gif" height=45 width=220 align=ABSCENTER>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
152(7)</div>
153with the following values of parameters (Ref. 4): <i><font face="Symbol"><font size=+1>a</font></font></i>=2;
154<i><font size=+1>r<sub>0</sub></font></i>=1.5
155<font face="Symbol">m</font>m.
156<p>The software package AERCOMP (FORTRAN code) allowing the determination
157of the optical properties of more complex aerosol models has been developed.
158In particular, using optical properties of basic aerosol components, one
159can calculate (applying linear interpolation on wavelengths and cosines
160of scattering angels) the optical properties for more complex, composite
161aerosol models. Table 2 is an example of outputs of this program.
162<center>
163<p><b>References</b></center>
164
165<dir>
166<dir>
167<ol>
168<li>
169Charslon R.J., S.E. Schwartz, J.M. Hales, R.D. Cess, J.A. Coakley, Jr.,
170J.E. Hansen, and D.J. Hofman, " Climate forcing by anthropogenic aerosols
171", <i>Science</i>, <b>255</b>, 423-430 (1992)</li>
172
173<li>
174Gregs J.S., et al., " Global tracking of the SO<sub>2</sub> clouds from
175the June 1991 month Pinatubo eruptions " <i>Geophys. Res. Letters</i>,
176<b>19</b>,
177151-154 (1992)</li>
178
179<li>
180World Meteorology Organization (WMO) publication: "<i>A preliminary cloudless
181standard atmosphere for radiation computation</i>", WCP-112, WMO/TD-NO.
18224 (1986)</li>
183
184<li>
185Deirmendjian D., <i>Electromagnetic Scattering on Spherical Polydispersions</i>.
186Elsevier, 290 pp. (1969)</li>
187
188<li>
189Twomey S. <i>Atmospheric aerosols</i>. Elsevier, 302 pp. (1977)</li>
190
191<li>
192Van de Hulst, H.C., <i>Light scattering by small particles</i>, 470 pp.,
193New York : Dover Publications, 1981.</li>
194
195<li>
196<i>Handbook: Clouds and cloudy atmosphere.</i> Leningrad, " Gidrometeoizdat
197", 649 p., 1989 (in Russian).</li>
198</ol>
199</dir>
200</dir>
201
202<center><b>Table 1. Principal aerosol models.</b>
203<p>(from Ref. 3)</center>
204
205<p><br>
206<center><table BORDER CELLSPACING=2 CELLPADDING=4 WIDTH="642" >
207<tr>
208<td VALIGN=TOP WIDTH="34%">
209<center><b>Aerosol model</b></center>
210</td>
211
212<td VALIGN=TOP WIDTH="34%">
213<center><b>Basic aerosol components and their designation</b></center>
214</td>
215
216<td VALIGN=TOP COLSPAN="2" WIDTH="33%">
217<center><b>Relative content</b></center>
218
219<p><b>volume (%) N<sub>i</sub>/N <sup>*)</sup></b></td>
220</tr>
221
222<tr>
223<td VALIGN=TOP WIDTH="34%">
224<center>Continental</center>
225</td>
226
227<td VALIGN=TOP WIDTH="34%">
228<center>dust (Dust-Like)
229<p>water-soluble (W-S)
230<p>soot (Soot)</center>
231</td>
232
233<td VALIGN=TOP WIDTH="17%">
234<center>70
235<p>29
236<p>1</center>
237</td>
238
239<td VALIGN=TOP WIDTH="16%">
240<center>2.26278E-06
241<p>9.37437E-01
242<p>6.25607E-02</center>
243</td>
244</tr>
245
246<tr>
247<td VALIGN=TOP WIDTH="34%">
248<center>Urban</center>
249</td>
250
251<td VALIGN=TOP WIDTH="34%">
252<center>water-soluble (W-S)
253<p>soot (Soot)
254<p>dust (Dust-Like)</center>
255</td>
256
257<td VALIGN=TOP WIDTH="17%">
258<center>61
259<p>22
260<p>17</center>
261</td>
262
263<td VALIGN=TOP WIDTH="16%">
264<center>5.88931E-01
265<p>4.11069E-01
266<p>1.64128E-07</center>
267</td>
268</tr>
269
270<tr>
271<td VALIGN=TOP WIDTH="34%">
272<center>Maritime</center>
273</td>
274
275<td VALIGN=TOP WIDTH="34%">
276<center>oceanic (Ocean)
277<p>water-soluble (W-S)</center>
278</td>
279
280<td VALIGN=TOP WIDTH="17%">
281<center>95
282<p>5</center>
283</td>
284
285<td VALIGN=TOP WIDTH="16%">
286<center>4.29942E-04
287<p>9.99573E-01</center>
288</td>
289</tr>
290
291<tr>
292<td VALIGN=TOP WIDTH="34%">
293<center>Stratospheric</center>
294</td>
295
296<td VALIGN=TOP WIDTH="34%">
297<center>sulfuric acid (75% H<sub>2</sub>SO<sub>4</sub>)</center>
298</td>
299
300<td VALIGN=TOP WIDTH="17%">
301<center>100</center>
302</td>
303
304<td VALIGN=TOP WIDTH="16%">
305<center>1.0</center>
306</td>
307</tr>
308
309<tr>
310<td VALIGN=TOP WIDTH="34%">
311<center>Volcanic</center>
312</td>
313
314<td VALIGN=TOP WIDTH="34%">
315<center>volcanic ash (V-Ash)</center>
316</td>
317
318<td VALIGN=TOP WIDTH="17%">
319<center>100</center>
320</td>
321
322<td VALIGN=TOP WIDTH="16%">
323<center>1.0</center>
324</td>
325</tr>
326
327<tr>
328<td VALIGN=TOP WIDTH="34%">
329<center>Upper Atmosphere</center>
330</td>
331
332<td VALIGN=TOP WIDTH="34%">
333<center>sulfuric acid (75% H<sub>2</sub>SO<sub>4</sub>)</center>
334</td>
335
336<td VALIGN=TOP WIDTH="17%">
337<center>100</center>
338</td>
339
340<td VALIGN=TOP WIDTH="16%">
341<center>1.0</center>
342</td>
343</tr>
344
345<tr>
346<td VALIGN=TOP WIDTH="34%">
347<center>Cloudy&nbsp;</center>
348</td>
349
350<td VALIGN=TOP WIDTH="34%">
351<center>water</center>
352</td>
353
354<td VALIGN=TOP WIDTH="17%">
355<center>100</center>
356</td>
357
358<td VALIGN=TOP WIDTH="16%">
359<center>1.0</center>
360</td>
361</tr>
362</table></center>
363
364<dir>
365<dir><sup>*)</sup> N<sub>i</sub>- number of particles of i-component; N-
366total number of particles in an aerosol sample.
367<center>
368<p><b>Table 2. Integrated optical properties of the urban aerosol model
369(a non-cloudy model).</b></center>
370</dir>
371</dir>
372
373<center><table BORDER COLS=6 WIDTH="80%" >
374<tr>
375<td ALIGN=CENTER VALIGN=CENTER WIDTH="20%">
376<center><i>&nbsp;Num</i></center>
377</td>
378
379<td>
380<center>&nbsp;<font face="Symbol">l(m</font>m)</center>
381</td>
382
383<td>
384<center><font face="Symbol">s</font><i><sub>ex</sub></i>(km<sup>-1</sup>)&nbsp;</center>
385</td>
386
387<td>
388<center><font face="Symbol">w</font></center>
389</td>
390
391<td>
392<center><font face="Symbol">m</font></center>
393</td>
394
395<td>
396<center><i>K<sub>n</sub></i></center>
397</td>
398</tr>
399
400<tr>
401<td>
402<center>1
403<br>2
404<br>3
405<br>4</center>
406</td>
407
408<td ALIGN=CENTER VALIGN=TOP>
409<center>0.200
410<br>0.250
411<br>0.300
412<br>0.337</center>
413</td>
414
415<td ALIGN=CENTER VALIGN=TOP>
416<center>&nbsp;0.13889E-05
417<br>0.12610E-05
418<br>0.11042E-05
419<br>0.98538E-06</center>
420</td>
421
422<td ALIGN=CENTER VALIGN=TOP>
423<center>0.53439E+00
424<br>0.59215E+00
425<br>0.65632E+00
426<br>0.66404E+00</center>
427</td>
428
429<td ALIGN=CENTER VALIGN=TOP>
430<center>&nbsp;0.68971E+00
431<br>0.64587E+00
432<br>0.61527E+00
433<br>0.60741E+00</center>
434</td>
435
436<td ALIGN=CENTER VALIGN=TOP>
437<center>&nbsp;1.001
438<br>1.000
439<br>1.000
440<br>1.000</center>
441</td>
442</tr>
443</table></center>
444
445<br>&nbsp;
446<dir>
447<dir><i>Num</i>- line number;
448<br><i><font face="Symbol">l</font></i> - wavelength in micrometers;
449<br><font face="Symbol">s</font><i><sub>ex </sub></i>- extinction coefficient
450in km<sup>-1</sup>;
451<br><i><font face="Symbol">w</font></i>- single scattering albedo;
452<br><i><font face="Symbol">m</font></i>- asymmetry factor;
453<br><i>K<sub>a</sub></i>- normalization factor.
454<br>&nbsp;
455<p><br>
456<center>
457</dir>
458</dir>
459</body>
460</html>
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