An Accurate Analytic Approximation for Light Scattering by Non-absorbing Spherical Aerosol Particles

Description

The scattering of light by particles in the atmosphere is a ubiquitous and important phenomenon, with applications to numerous fields of science and technology. The problem of scattering of electromagnetic radiation by a uniform spherical particle was solved by the method of Mie and Debye as a series of terms depending on the size parameter, x=2πr/λ, and the complex index of refraction, m; however, this solution does not provide insight into the dependence of the scattering on the radius of the particle, the wavelength, or the index of refraction, or how the scattering varies with relative humidity. Here an analytic approximation for the scattering efficiency of a non-absorbing spherical particle is presented that is accurate over a wide range of particle sizes of atmospheric importance and which readily displays the dependences of the scattering efficiency on particle radius, index of refraction, and wavelength. For an aerosol for which the particle size distribution is parameterized as a gamma function, this approximation also yields analytical results for the scattering coefficient and for the Angstrom exponent, with the dependences of scattering properties on wavelength and index of refraction clearly displayed. This approximation provides insight into the dependence of light scattering properties on factors such as relative humidity, readily enables conversion of scattering from one index of refraction to another, and demonstrates the conditions under which the aerosol index (the product of the aerosol optical depth and the Angstrom exponent) is a useful proxy for the number of cloud condensation nuclei.