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

TL;DR

This paper generalizes the Posch ratio to relate zenith night sky radiance to horizontal irradiance, providing analytical tools and demonstrating its applicability for natural and light-polluted skies.

Contribution

It extends the Posch ratio concept to any linear radiance indicators and offers analytical expressions for nighttime sky components.

Findings

Posch ratio can estimate horizontal irradiance from zenith radiance.

The generalized ratio applies to natural and artificial light conditions.

Analytical expressions for moonlight, starlight, and artificial sources are provided.

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 Posch ratio, has been previously 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 nighttime 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.