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 analysed. 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_p for the direct beam, which is formulated as r_p = r_i exp(−s tan θ₀), where r_i is the Lambert-law reflectivity of the soil, the protrusion parameter 5 is the projection on a vertical plane of protrusions per unit area and θ⁰ is the zenith angle. The surface reflectivity r_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_P . Thus, the effects can be approximated by those in the case of a dark Lambert surface (analysed previously), inasmuch as r_P is smalleSr than the soil reflectivity r_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 analysed as cross radiance and cross irradiance, The analysis is only for the case of a small object pixel embedded in a different terrain, extending to infinity as a uniform area. The effects of the cross radiance (which are dominant) are found to be smaller than those over a Lambert plane for the same surroundings-to-object-pixel contrast and atmospheric conditions. However, the adjacency effects are highly variable, because the effective contrast for our plane with dark protrusions is a function of not only the surface parameters but also of the solar zenith angle and the atmospheric conditions.