PM2.5 as a proxy for aerosol optical depth in night sky brightness models

ABSTRACT Fine particulate matter (PM2.5) is routinely monitored at dense networks of air quality stations worldwide, whereas aerosol optical depth (AOD, $\tau$) is available only at sparse measurement sites. Since AOD is a key input parameter for night sky brightness (NSB) modelling, its limited spatial coverage introduces substantial uncertainty into skyglow predictions at most locations of interest. Although statistical relationships between AOD and PM2.5 have been studied extensively, existing models typically combine data acquired under varying atmospheric conditions, resulting in large uncertainty in the AOD–PM2.5 dependence and thus limited predictive power. We demonstrate that when relative humidity, particle size distribution, and physical properties of particles are properly accounted for, the AOD–PM2.5 relationship becomes well constrained. We derive an explicit analytical expression for the ratio $\tau$/PM2.5 based on Mie theory, standard log-normal size distribution parametrization, and established hygroscopic growth relations. We validate the model against Mie calculations for a large ensemble of stochastic aerosol populations, achieving a Pearson correlation coefficient of 0.998. Because the resulting formula is simple and all its parameters are physically interpretable and constrainable from routine meteorological observations, it provides a practical tool for accurate AOD estimation and consequently for improved NSB modelling in the vicinity of ground-based light sources.