Detailed Assessment of Multiple‐Scattering Effects on Night‐Sky Brightness Modeling in Turbid Environments: The Impact of Truncation and Convergence Errors

Abstract

Detailed modeling of the night‐sky brightness (NSB) is needed to pinpoint environmental impacts caused by artificial light at night. This becomes progressively more intricate with longer distances to emission sources or under high atmospheric turbidity. In such cases, the multiple‐scattering processes that affect light propagation become increasingly critical. To detect and quantify the potential errors caused by popular approximations like single or double scattering in current models, a rigorous multiple‐scattering model is used here. It integrates an advanced method of resolution based on the successive orders of scattering that can provide analytical “exact” solutions. With this tool, it is found that simplistic approaches lead to numerical predictions violating physics principles, resulting in incorrect outcomes that can have profound implications in a large variety of research areas. To avoid this, it is proposed to force the convergence of the modeled radiance to its true value through a carefully controlled process, by which the contribution from the remaining higher‐scattering terms to the modeled radiative property is kept below the specified error tolerance. For green light, it is found that, for a turbid atmosphere with an aerosol optical depth larger than 0.3 and an asymmetry parameter exceeding 0.7, four scattering orders are needed to compute the zenith radiance 60‐km away from the light source within an experimental error tolerance of 10%.