Modeling nonstationary surface-level ozone extremes through the lens of US air quality standards: A Bayesian hierarchical approach

Abstract

Surface-level ozone (O${\hspace{0.17em}}_3$) is a harmful air pollutant whose effects may be more deleterious when at its most extreme levels. Current US air quality standards are written in terms of the 3-year average of the 4th highest annual daily maximum 8-h O${\hspace{0.17em}}_3$ values; therefore, developing approaches based on extreme value theory may be useful. We develop a Bayesian hierarchical approach, where the $r$-largest order statistics are parametrized by the generalized extreme value (GEV) distribution, while a Gaussian process is employed to characterize how the GEV parameters depend on the O${\hspace{0.17em}}_3$ precursors, namely nitrous oxides (NO${\hspace{0.17em}}_x$) and volatile organic compounds (VOCs). The fitted model is then used to characterize the upper tail of the distribution of O${\hspace{0.17em}}_3$ and estimate O${\hspace{0.17em}}_3$ noncompliance probabilities. We illustrate the proposed method using data from an air quality station in Providence, Rhode Island (RI). The results suggest that the far upper tail of extreme O${\hspace{0.17em}}_3$ values is likely bounded, and the dependence of the upper tail distribution on NO${\hspace{0.17em}}_x$ and O${\hspace{0.17em}}_3$ is highly nonlinear, consistent with the known relationship, albeit not specifically for extreme values, in the existing scientific literature. A convolution-based approach is used to estimate noncompliance probabilities for several covariate scenarios. Our results indicate that estimated noncompliance probabilities in recent years are much lower than in the mid-1990s, primarily due to lower O${\hspace{0.17em}}_3$ precursor levels. However, the estimated noncompliance probabilities appear to rise sharply for hypothetical stricter O${\hspace{0.17em}}_3$ standards, even for the conditions observed in recent years.