Theory of the optical properties of snow

Abstract

The optical properties of a snowpack are calculated, giving relations between the asymptotic flux extinction coefficient and albedo under diffuse illumination on the one hand and the density, grain size, and wavelength, on the other. A geometrical optics calculation of the properties of a single grain is used with approximate solutions of the radiative transfer problem. Most of the scattering is the result of change in direction of the light beam upon transmission through the grain, rather than reflection. The asymptotic flux extinction coefficient is directly proportional to the snowpack density and inversely proportional to the square root of the grain size. The albedo under diffuse illumination is independent of density and proportional to the square root of the grain size. The derived relations agree with experimental data to within 20% for the flux extinction coefficient and to better than 2% for the albedo without using adjustable parameters. Higher values of the flux extinction coefficient will be measured if the snow is confined within a finite cylinder with absorbing sides. An analysis of this effect is given.