Atmospheric effects on radiometry from zenith of a plane with dark vertical protrusions

Abstract

Effects of an optically thin plane-parallel scattering atmosphere on radiometric imaging from the zenith of a specific surface-type are analyzed. The surface model was previously developed to describe arid steppe, where the sparse vegetation forms dark vertical protrusions from the bright soil-plane. The analysis is in terms of the surface reflectivity to the zenith r sub p for the direct beam, which is formulated as r sub p = r sub i exp (-s tan theta sub 0), where v sub i is the Lambert law reflectivity of the soil, the protrusions parameters s is the projection on a vertical plane of protrusions per unit area and theta sub 0 is the zenith angle. The surface reflectivity r sub p is approximately equal to that for the global irradiance (which is directly measured in the field) only for a narrow range of the solar zenith angles. The effects of the atmosphere when imaging large uniform areas of this type are comparable to those in imaging a Lambert surface with a reflectivity r sub p. Thus, the effects can be approximated by those in the case of a dark Lambert surface (analyzed previously), inasmuch as r sub p is smaller than the soil reflectivity r sub i for any off-zenith illumination. The surface becomes effectively darker with increasing solar zenith angle. Adjacency effects of a reflection from one area and scattering in the instantaneous field of view (object pixel) are analyzed as cross radiance and cross irradiance.