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

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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 rp for the direct beam, which is formulated as rp = ri exp(−s tan θ0), where ri 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 rP 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 rP . Thus, the effects can be approximated by those in the case of a dark Lambert surface (analysed previously), inasmuch as rP is smalleSr than the soil reflectivity ri 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.