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

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%. Light emitted from artificial sources at night can propagate over long distances. Consequences include the disruption of natural conditions and negative impacts on some atmospheric remote-sensing techniques, especially ground-based astronomical observations, and various biological processes. In particular, the light emitted by many artificial light sources and scattered away in the atmosphere might show a complex structure because of, for example, air pollution. Multiple scattering processes, combined with the heterogeneous distribution of finite-sized ground-based light sources, result in difficulties to predict the diffuse light field accurately. In this work, an advanced multiple-scattering model is used to identify apparent mistakes in previous models of the literature, and quantify their consequences on the propagation of artificial light throughout the night-time environment, as a function of the local aerosol conditions. More generally, any shortcoming in the modeling of night-sky brightness (NSB) leads to serious errors downstream, with wide-ranging implications for the interdisciplinary light pollution research community. The present findings are critical because a number of conclusions based on current prediction models might be faulty. As a remedy, a convergence method is proposed so that the modeled radiance (or irradiance) can approach realistic values by adequately selecting the number of higher scattering orders. This method is also tailored to guarantee appropriate results when they are compared to experimental measurements having significant uncertainty. The present findings and new developments are expected to result in comprehensive improvements in the way nighttime lighting can be more adequately modeled in the future. Night-sky brightness from distant light sources is greatly impacted by multiple scattering in turbid atmospheresCurrent modeling tools potentially misinterpret outcomes due to convergence errors and incorrect treatment of multiple scatteringImpacts of truncation errors on radiance and irradiance under various aerosol conditions and experimental scenarios are quantified