Overcast sky luminance is dependent on the physical state of the atmosphere below cloud level

Abstract

An approximate formula for sky luminance under overcast conditions taking into account different pollution content of the atmosphere is determined. The homogeneous cloud layer is considered to be a constant source of light, while the undercloud atmosphere is taken as a single scattering medium. The final mathematical expressions depend on turbidity and scattering ability of the undercloud atmosphere as well as on the altitude of the clouds. Such a parameterised model is therefore easily scalable and well adjusted to the actual meteorological situation (contrary to empirical models in current use). The derived analytical formula is suitable for engineering practice to perform rapid simulations of sky luminance.