A Review of Applications of Extreme Value Theory to Environmental Risk Assessment

Assessing the risk of extreme environmental events is crucial for addressing the challenges brought forth by a world undergoing drastic climate change. The persistent increase in average global temperatures has induced a very strong impact on the environment, through an increase in the frequency and severity of devastating extreme events such as heatwaves or heavy rain storms. The consequences of such extreme events are far-reaching, affecting human lives through property damage and deaths. The field of statistical extreme value theory (EVT) encompasses the methodological tools developed to model such events, and the use of EVT in risk assessments is becoming increasingly pertinent. Predicting the likelihood and severity of future environmental extreme events allows us to prepare for future challenges imposed by our rapidly changing world and ultimately mitigate the risk of exposure to environmental extremes. This chapter revises the most important classical results and models of univariate EVT and reviews their use in applied settings. New contributions to the choice of the threshold in the peaks-over-threshold approach will be presented, alongside discussions of Bayesian, multivariate, and spatial approaches to modelling extreme environmental events. Emerging topics in the field of EVT, such as extensions of classical models, machine learning, and extremal causal inference, will be detailed alongside a review of their usage in recent environmental applications.