Superstatistical Analysis of PDFs and autocorrelation functions for air pollution concentrations in the UK

Abstract

Conventional statistical models often struggle to fully capture the complex spatio-temporal dynamics, intermittent fluctuations, and heavy-tailed distributions characteristic of real-world air pollution data. Furthermore, existing literature frequently focuses on extreme events, overlooking the persistence of low-pollution states and temporal memory effects. To address these gaps, we apply superstatistical frameworks from non-equilibrium statistical physics to analyse a comprehensive five-year dataset (2020-2025) of hourly air pollutant concentrations across the United Kingdom. Excellent fits of experimentally measured distributions are obtained from our theoretical models. We observe large heterogeneities of the best fitting parameters depending on the locations where the measurements are performed. These parameters form characteristic patterns in the 3-dimensional parameter space and depend on the type of pollutant considered, as well as on the environmental conditions (high traffic, industrial, or rural surroundings). We also investigate autocorrelation functions and provide evidence for differences in day-time and night-time decays of the autocorrelation function. Our investigation mainly focuses onto the dynamics of NO, NO2, PM2.5, PM10, but we also report on some anomalous distributions observed for O3.