Spherical particle populations: approximate analytic relationship between size distribution parameters and integral optical properties.

The absorption and scattering efficiencies of spherical particles in a certain size range can be approximated by a three-parameter formula. With this formula, an analytic relationship is developed between the extinction, scattering, or adsorption coefficient and the parameters of a log-normal size distribution. The technique permits approximate calculation of these coefficients from the mean radius, its standard deviation, and the total number concentration. By an inversion the size distribution parameters can be estimated from measurements of any of the coefficients at three wavelengths. The calculations require only hand calculators or slide rules. It is shown that use of the technique is justified for many cases of atmospheric aerosol particles and visible radiation.