Md. Alexandrov et Aa. Lacis, A new three-parameter cloud/aerosol particle size distribution based on the generalized inverse Gaussian density function, APPL MATH C, 116(1-2), 2000, pp. 153-165
We describe a three-parameter cloud/aerosol size distribution based on the
generalized inverse Gaussian density function that provides a simple and co
nvenient recipe for characterizing aerosol radiative properties. The featur
e that makes this distribution attractive is that all of its moments can be
calculated analytically providing simple formulas for the effective radius
and variance and relating these to other important quantities such as the
particle number and mass densities. Another advantage of this distribution
is the smooth exponential cut-off not only for large particles sizes but al
so in small particles regime which prevents the singularity that occurs at
zero size for large effective variances for distributions like the popular
gamma distribution. Unlike most size distributions in current use the propo
sed Functional form has a third-parameter (order) which Provides greater fl
exibility in representing different distributional shapes. Analytical expre
ssions for the moments of the generalized inverse Gaussian distribution in
the generic case contain ratios of modified Bessel functions, however for h
alf-integer orders these expressions are simple ratios of polynomials. As a
practical example we compare extinction efficiency factors acid asymmetry
parameters computed for several different orders of the proposed distributi
on function. (C) 2000 Published by Elsevier Science Inc. All rights reserve
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