We present a fitted model of sky dome radiance and attenuation for realistic terrestrial atmospheres. Using scatterer distribution data from atmospheric measurement data, our model considerably improves on the visual realism of existing analytical clear sky models, as well as of interactive methods that are based on approximating atmospheric light transport. We also provide features not found in fitted models so far: radiance patterns for post-sunset conditions, in-scattered radiance and attenuation values for finite viewing distances, an observer altitude resolved model that includes downward-looking viewing directions, as well as polarisation information. We introduce a fully spherical model for in-scattered radiance that replaces the family of hemispherical functions originally introduced by Perez et al., and which was extended for several subsequent analytical models: our model relies on reference image compression via tensor decomposition instead.

We present a physically-based analytical model of the daytime sky. Based on the results of a first-principles brute force simulation of radiative transfer in the atmosphere, we use the same general approach of fitting basis function coefficients to radiance data as the Perez and Preetham models do. However, we make several modifications to this process, which together significantly improve the rendition of sunsets and high atmospheric turbidity setups -- known weak points of the Preetham model. Additionally, our model accounts for ground albedo, and handles each spectral component independently. The latter property makes it easily extensible to the near ultraviolet range of the spectrum, so that the daylight appearance of surfaces that include optical brighteners can be properly predicted. Due to its similar mathematical properties, the new model can be used as a drop-in replacement of the Preetham model.