A new three-parameter cloud/aerosol particle size distribution based on the generalized inverse Gaussian density function

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 d.