Light-pollution model for cloudy and cloudless night skies with ground-based light sources.

The scalable theoretical model of light pollution for ground sources is presented. The model is successfully employed for simulation of angular behavior of the spectral and integral sky radiance and/or luminance during nighttime. There is no restriction on the number of ground-based light sources or on the spatial distribution of these sources in the vicinity of the measuring point (i.e., both distances and azimuth angles of the light sources are configurable). The model is applicable for real finite-dimensional surface sources with defined spectral and angular radiating properties contrary to frequently used point-source approximations. The influence of the atmosphere on the transmitted radiation is formulated in terms of aerosol and molecular optical properties. Altitude and spectral reflectance of a cloud layer are the main factors introduced for simulation of cloudy and/or overcast conditions. The derived equations are translated into numerically fast code, and it is possible to repeat the entire set of calculations in real time. The parametric character of the model enables its efficient usage by illuminating engineers and/or astronomers in the study of various light-pollution situations. Some examples of numerical runs in the form of graphical results are presented.