Comments on: Determination of Aerosol Size Distribution from Spectral Attenuation Measurements Ariel Cohen

Wave Propagation Laboratory, Environmental Research Laboratories, Boulder, Colorado 80302. Received 2 February 1972.

The use of light scattering (and extinction) measurements for the definition of the type and size range of the aerosols in the atmosphere had been described by Kerker1 as follows: "The practice has been to infer the particle size by methods which assume a high degree of a priori information and which involve a considerable amount of trial and error. The refractive index of

the particle is usually known as well as its shape and the general size range. Scattering patterns are calculated corresponding to the probable size distribution and the appropriate one is selected by comparison of the experimental with the theoretical results."

Although this had been stated in 1965, it still represents the state-of-the-art in the present time, i.e., see Ref. 2. (A suggested method that may reduce the required set of assumptions was recently presented by the author.3) Grassl4 suggests a method that he claims to eliminate some of the a priori assumptions mentioned above. A careful study of the work shows that, nevertheless, the following approximation and assumptions were being used:

(1) The refractive index of the aerosols is appproximately known (p. 2538, Ref. 4) and unique for the wavelength range 0.4-10.6μ (n = 1.5-0.02i).

(2) The general size range is 0.1-8μm (Table I, Ref. 4). (3) All particles are spherical. (4) The size range can be divided into seven subranges (see

Table I, Ref. 4) in respect to the particles' extinction cross sec­tions, and n(r) is constant within each subrange.

Grassl then suggests that the extinction could be measured in seven different wavelengths and by the use of an iteration tech­nique, the size distribution function n{r) can be resolved within 2-3% accuracy after sixty-nine iterations.

In this letter it is shown that the same assumptions can be used for the exact solution of n(r) involving no iterations at all. The extinction cross section Q*(r,n,λ) is calculated for each subsize range and for each wavelength by the equation

or

where

Thus, forty-nine coefficients for the extinction cross section are defined. (For better accuracy, one should add the corresponding molecular extinction to each coefficient.) The measurement of seven extinction values, kj, in seven different wavelengths, λj, leads to the matrix equation,

and ni(r) can be easily calculated—see Tables I and II. It would be well to note that Grassl's computational results

(Table III in Ref. 4) do not agree with the calculated results presented in Table II even to an approximation.

The main reason for the lack of agreement can be due to a dif­ferent set of coefficients (Table I) used by Grassl. It is believed that the use of the same set of coefficients that include molecular extinction would have lead to the same solution whether the method is exact or iterative. Any real difference in computa­tional results, based on the same set of coefficients, must be attributed to some uncertainties in Grassl's computation.

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Table I. Forty-nine Extinction Coefficients for Seven Average Sizes and Seven Wavelengthsa

a The refractive index n = 1.5 — 0.02i. (The values are in relative units.) In this example, molecular extinction was not taken into account.

Table I I . Calculated Size Distribution Function n(r), (Seven Values) for Grassl's Extinction Measurements (Table III in Ref. 4)°

a Computed values are normalized to 9.3 and 25.4 for r = 0.445 μm. b Smoothed solutions intended to avoid negative particle num­ber density are discussed, for example, by Dave.5

The research was accomplished while the author held a National Research Council Postdoctoral Resident Research Associateship supported by the National Oceanic and Atmospheric Administra­tion.

References 1. M. Kerker, "Multiple Scattering from Colloidal Spheres and

Cylinders," in Proceedings of the Second Interdisciplinary Conference on Electromagnetic Scattering (University of Massa­chusetts, Amherst, June 1965).

2. B. M. Herman, S. R. Browning, and J. A. Reagan, J. Atmos. Sci. 28, 763 (1971).

3. A. Cohen, "The Size Spectrum Determination of Spherical Aerosols by Light Scattering. Part I: Method", presented at the Air Pollution, Turbulence and Diffusion Symposium (December 1971) (published in the Proceedings of the Sym­posium Sandia Labs., Albuquerque, March 1972).

4. H. Grassl, Appl. Opt. 10, 2434 (1971).

5. J. V. Dave, Appl. Opt. 10, 2035 (1971).

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