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

Surface‐level ozone (O 3$$ {}_3 $$) 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 3$$ {}_3 $$ values; therefore, developing approaches based on extreme value theory may be useful. We develop a Bayesian hierarchical approach, where the r$$ r $$‐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 3$$ {}_3 $$ precursors, namely nitrous oxides (NO x$$ {}_x $$) and volatile organic compounds (VOCs). The fitted model is then used to characterize the upper tail of the distribution of O 3$$ {}_3 $$ and estimate O 3$$ {}_3 $$ 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 3$$ {}_3 $$ values is likely bounded, and the dependence of the upper tail distribution on NO x$$ {}_x $$ and O 3$$ {}_3 $$ 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 3$$ {}_3 $$ precursor levels. However, the estimated noncompliance probabilities appear to rise sharply for hypothetical stricter O 3$$ {}_3 $$ standards, even for the conditions observed in recent years.