  Determining the all-sky radiance distribution produced by artificial light
sources is a computationally demanding task that generally requires an
intensive calculation load. We develop in this work an analytic formulation
that provides the all-sky radiance distribution produced by an artificial light
source as an explicit and analytic function of the observation direction,
depending on two single parameters that characterize the overall effects of the
atmosphere. One of these parameters is related to the effective attenuation of
the light beams, whereas the other accounts for the overall asymmetry of the
combined scattering processes in molecules and aerosols. By means of this
formulation a wide range of all-sky radiance distributions can be efficiently
and accurately calculated in a short time. This substantial reduction in the
number of required parameters, in comparison with other currently used
approaches, is expected to facilitate the development of new applications in
the field of light pollution research.
