Unified model of radiance patterns under arbitrary sky conditions

The natural sky radiances are neither monotonic nor smooth functions of zenith/azimuth angle, primarily due to the presence of broken cloud arrays or single clouds scattered over the whole sky vault. In this paper we show how we have addressed the phenomena and developed a universal sky radiance model for a turbid, cloudy atmosphere. This model accommodates higher scattering orders, aerosol optics, surface albedo, and the statistically relevant contributions of single clouds. The radiance at ground depends on the bulk characteristics of cloud fields, such as spectral optical thickness, spectral reflectance, altitude, positions on the sky, sizes, and shapes. We have shown that single scattering approximation fails to reproduce the radiance in the circumsolar region when clouds block the direct solar beams. The single scattering concept also overestimates reflection by individual clouds. Incorporation of double scattering into a computational model generally makes the radiance patterns smooth and less steep at the edges of clouds as commonly occur in nature. The numerical demonstrations are based on UniSky Simulator (Kocifaj and Fecko, 2014) which allows for modeling of various cloud configurations and is available for public use.