  Modeling the hemispherical night sky brightness of anthropogenic origin is a
demanding computational challenge, due to the intensive calculations required
to produce all-sky maps with fine angular resolution including high-order
scattering effects. We present in this Letter a physically consistent,
semi-analytic two-parameter model of the all-sky radiance produced by an
artificial light source that encodes efficiently the spectral radiance in all
directions of the sky above the observer. The two parameters of this function
are derived from the state of the atmosphere, the distance to the observer, and
the source's angular and spectral emission pattern. The anthropogenic all-sky
radiance at any place on Earth can be easily calculated by adding up the
contributions of the surrounding artificial sources, using the information
available from nighttime satellite imagery and ground-truth lighting
inventories. This opens the way for the elaboration of a global world map of
the artificial all-sky brightness.
