Modelling the spatial dependence of extreme PM2.5 events in Bengaluru using max-stable processes

Abstract

Urban air quality risk assessments typically treat monitoring stations as independent, systematically underestimating the probability that multiple locations simultaneously experience dangerous pollution levels. This study develops a spatial extreme value framework to quantify the joint tail dependence of fine particulate matter (PM2.5) across seven continuous ambient air quality monitoring stations (CAAQMS) in Bengaluru, India, using daily data from 2018 to 2026. A four-stage pipeline, comprising runs declustering, Generalised Pareto Distribution fitting with wind-speed covariate testing, semiparametric Fréchet marginal standardisation, and non-parametric extremal coefficient estimation via the F-madogram, is applied to all 21 station pairs. The stationary model is adequate at every station, indicating that local wind speed does not significantly modulate extreme pollution intensity. All station pairs exhibit substantial spatial dependence, with joint exceedance probabilities exceeding the independence benchmark by up to three orders of magnitude at severe pollution levels. The isotropic Brown–Resnick max-stable model fails to capture the observed dependence structure, revealing pronounced directional anisotropy: stations aligned along the north–south corridor show far stronger co-extreme behaviour than geographically closer stations oriented on other axes. The conditional risk analysis demonstrates that an extreme event at one station on the western corridor implies a probability of concurrent failure exceeding 78% at partner stations up to 10 km away, but substantially lower risk for off-corridor neighbours. These findings challenge the prevailing station-by-station paradigm for air quality management and indicate that pollution emergency response in Bengaluru should be organised along meteorological transport corridors rather than isotropic radial buffer zones.