Illuminance and Luminance under Overcast Skies

Abstract

The illuminance of a horizontal surface at the ground below an overcast sky is computed. The transmittance, T, of visible light is given as a function of the cloud optical thickness, h/L, of the sun’s zenith distance, Z, and of the reflectance, a, of the underlying surface. For some cloud thicknesses, T varies markedly with Z. Also, for thick clouds, T is several times larger over a fresh snow cover than it is over snow-free ground.A formula for luminance distribution, B(θ), of a heavily overcast sky is presented. This formula agrees fairly well with existing measurements made over snow-free terrain; however, it further suggests that B(θ) will become much more uniform when a fresh snowfall uniformly covers the ground.