Estimating linear radiance indicators from the zenith night-sky brightness: on the Posch ratio for natural and light-polluted skies

Abstract

Estimating the horizontal irradiance from measurements of the zenith night-sky radiance is a useful operation for basic and applied studies in observatory site assessment, atmospheric optics, and environmental sciences. The ratio between these two quantities, also known as the Posch ratio, has previously been studied for some canonical cases and reported for a few observational sites. In this work we (a) generalize the Posch ratio concept, extending it to any pair of radiance-related linear indicators, (b) describe its main algebraic properties, and (c) provide analytical expressions and numerical evaluations for its three basic night-time components (moonlight, starlight and other astrophysical light sources, and artificial light). We show that the horizontal irradiance (or any other linear radiance indicator) is generally correlated with the zenith radiance, enabling its estimation from zenith measurements if some a priori information on the atmospheric state is available.

Modeling the artificial night sky brightness at short distances from streetlights

“…When multiple sources are at play, surrounded by extended reflecting surfaces, the resulting observed radiance can be computed by adding the individual emitter patch contributions, resorting to the whole conceptual and calculation toolbox provided by linear systems theory, as described in detail elsewhere [2,[27][28][29]37]. The same can be said of the computation of integral indicators like, e.g., the average sky radiance or the horizontal irradiance [30,38]. The use of a single-scattering approach is justified for our problem under most practically interesting atmospheric conditions, since the short source-detector distances here considered translate into a low probability of double scattering events.…”