Extreme Value Theory: Lessons Learned for Changing Rainfall and Extreme Hurricanes

The evaluation of extreme events in many natural phenomena is key to the definition of design events for engineering applications. Traditional approaches are based on the Generalized Extreme Value distribution, known to be the asymptotic extreme value distribution for a large class of random variables. However, its foundational assumptions are often overlooked, and significantly limit the application of the theory and its ability to use the available observations. I will review the hypotheses of the classical extreme value theory, illustrate its application, and examine its limitations. I then introduce and illustrate the application of a Metastatistical Extreme Value Distribution (MEVD), which relaxes some key limitations of the traditional Extreme Value Theory. In essence the MEVD is derived from ensemble averaging yearly distributions of annual maxima and, by averaging over distributions of a large number of “ordinary” events makes use of all the available information. I will exemplify this general approach by applying it to daily rainfall, flood peak discharges in the continental US, and Atlantic Hurricane intensities. I will show that the MEV approach reduces the uncertainty in the estimation of high-quantile extremes in all these applications of engineering relevance. I will then use the MEVD and IPCC scenarios to project the probability of occurrence of extreme Atlantic hurricanes, which is seen to likely double before the end of the century. I conclude that the MEVD constitutes a significant advance over the traditional extreme value theory and that it is particularly suited for non-stationary natural processes