On the relation between zenith sky brightness and horizontal illuminance

The effects of artificial light at night are an emergent research topic for astronomers, physicists, engineers and biologists around the world. This leads to a need for measurements of the night sky brightness (= diffuse luminance of the night sky) and nocturnal illuminance. Currently, the most sensitive light meters measure the zenith sky brightness in magV/arcsec or – less frequently – in cd m−2. However, the horizontal illuminance resulting only from the night sky is an important source of information that is difficult to obtain with common instruments. Here we present a set of approximations to convert the zenith luminance into horizontal illuminance. Three different approximations are presented for three idealized atmospheric conditions: homogeneous sky brightness, an isotropically scattering atmosphere and a turbid atmosphere. We also apply the resulting conversion formulae to experimental data on night sky luminance, obtained during the past three years.