Equilibrium-reflectance model for clear or cloudy atmosphere

Aspects of an earlier equilibrium-radiance model atmosphere for the visible spectrum are extended to the partially cloudy case. Data indicate that in the real atmosphere for some partly cloudy days (60% of the measured paths during one field trip), the point-function equilibrium radiance for a given path of sight is reasonably constant with altitudes up to 6 km for cloud-free path segments. In order for equilibrium radiance to be constant, all path segments must be cloud free and the entire path must be either sunlit or shadowed from the Sun. In an even higher percentage of the partly cloudy and overcast cases (80% during one field trip), the point-function equilibrium reflectance for a path of sight is found to be reasonably constant with altitude. In order for equilibrium reflectance to be constant, all path segments must be cloud free but the path may be partially sunlit and partially shadowed from the Sun. As a result of equilibrium-reflectance constancy, the contrast transmittance for a path of sight with cloud-free path segments in the troposphere can be expressed in the sky–ground-ratio reflectance form.