The Truncated Geometric Approximation and the Size Distribution of Small Atmospheric Particles

This paper describes a simple relationship between the slope of particulate optical depth as a function of wavelength and the size distribution of spherical particles. It is based on approximating extinction using a truncated geometric optics relationship and is applicable when optical depth decreases with wavelength. The new relationship suggests that extinction versus wavelength measurements are most sensitive to particles that are comparable in size to the wavelength. When optical depth is expressed as a power-law function of wavelength, the resulting particle size distribution is also a power-law function of size, with the two exponents reproducing the well-known relationship between the Ångström and Junge exponents. Examples of applying the new relationship are shown using both numerical calculations based on Mie theory and measurements from the Aerosol Robotic Network (AERONET) sun photometer at NASA Goddard Space Flight Center (GSFC). Since the truncated geometric approximation makes no assumptions per se concerning the form of the particle size distribution, it may find application in supplementing solar aureole profile measurements in retrieving the size distributions of particles in thin clouds—for example, cirrus—or when they are present.