Approximation Formulas to Calculate Infrared Extinction by an Aerosol Having a Junge Size Distribution

Abstract

The exact Mie curves for the extinction efficiency factor Qe as a function of the normalized size parameter ?=2α(n?1) are approximated by eight continuous linear segments. These linear approximations for Qe are used to obtain an analytical approximation formula for the extinction coefficient ke in the infrared of an aerosol having a Junge size distribution, described by dN/dr=Ar?v. This formula expresses ke as an explicit function of v, propagation wavelength ? and the real part n and the imaginary part k of the complex index of refraction. For ?, v, n and k in the ranges 1 ?m ≤?≤11?m, 3.6≤v≤4.4, 1.2≤n1.65 and 0≤k≤0.15, the values of ke calculated from the approximation formula agree to within 5% with those obtained by numerical integration using the exact Mie theory formulas for Qe. An analytical approximation formula for ke as a function of relative humidity is derived based on the assumption that the relationship between particle size r in humid air and particle size rd in dry air can be described by r/rd=Φ(S, where S is the saturation ratio.