Integrated Phase Function Research Articles

Two-Stream Theory of Reflectance of Snow

Spectral reflectance of snow under diffuse illumination is studied using the two-stream approximation of the radiative transfer equation. The scattering and absorption parameters of the radiative transfer equation-the single scattering albedo, the optical depth, and the integrated phase function are obtained from the grain size and density of snow. Analytical expressions for the intensity within the snowpack, the reflectance, and the asymptotic flux extinction coefficient, are given. Good agreement is shown between the theory and available experimental data on visible and near-infrared reflectance, and the asymptotic flux extinction coefficient. The theory may also be used to explain the observed effect of aging on the snow reflectance.

Radiative transfer: Terrestrial clouds

The terrestrial atmospheric physicist is interested in radiative transfer in clouds from two distinct points of view: firstly, the profound and as yet imperfectly understood effects of clouds on the atmospheric radiation balance and secondly the inference of cloud characteristics (size, drop size, dispersion, etc.) through measurements of the angular or wavelength dependence of radiation scattered by clouds. The work to be reported here relates to the second aspect, the inference of cloud characteristics from scattered radiation and has excluded wavelengths at which emission becomes important. Numerical results (by the doubling method) for conservative or almost-conservative scattering show that the single-scattering phase function is almost entirely “forgotten” in the multiply scattered radiation from clouds of sizable optical depths; even the crudest estimate of the particle size distribution requires a quite accurate knowledge of the integrated phase function for the distribution, and the conclusion seems inescapable that effectively no information about the size distribution can be obtained from multiply scattered radiation at wavelengths which are not absorbed. At absorbed wavelengths the single scattering albedo and the asymmetry are size dependent and the outlook for useful inferences seems less bleak but still quite restricted. To illustrate the degree of variation resulting from changes in cloud structure, reflection spectra have been calculated out to 3 μ for three situations in which meteorologists or cloud physicists have special interest. These are (1) the conversion of a non-freezing cloud from a non-raining state to a raining state; (2) the contrast between a maritime water cloud, continental water cloud and a thick urban fog; (3) the glaciation of a cloud. The results show a measurable change in reflection spectrum in the case of the gross changes in situations (2) and (3) but the differences in situation (1) are quite slight.