Extremes in the hydrological cycle: A metastatistical framework applied to extreme coastal flooding and droughts

The study of extremes, maxima and minima of random variables, has a long history in applied hydrology for engineering purposes. The magnitude and the frequency of extreme events are described by the right-most part of a probability distribution, usually referred as tail. Therefore, the task for hydrologists is to extract as much information as possible from the data set to assess the tail behavior correctly and reduce the uncertainty in the estimates. Traditionally, the most widely used probabilistic methods are based on the asymptotic results of the Extreme Value (EV) theory, which is commonly applied using block maxima or via peak-over-threshold analysis. However, despite its theoretical basis, a number of scientific contributions highlights the limits of these traditional approaches. In particular, classical EV methods are considered to waste much of the available observational information, which is reflected into increased estimation uncertainty for quantiles that are large with respect to the observed largest values. This notion is leading to the development of alternative modeling approaches that make a better use of the observations. Among these methods, non-asymptotic models, i.e. statistical models which do not assume the block maximum to arise from a large number of ordinary values, promise to lead to more robust estimates of high quantiles. In particular, this dissertation estimates the probability of extremely large events using a non-asymptotic approach based on the Metastatistical Extreme Value Distribution, MEVD, and its simplified versions, including SMEV, or Simplified Metastatistical Extreme Value distribution. A comparative assessment of the predictive performance of the proposed non-asymptotic model and conventional approaches based on the three-parameter Generalized Extreme Value distribution, GEV, is the focus here. The present work, therefore, investigates the potential of MEVD-based approaches to characterize the probabilistic structure of the tail distribution that governs opposing phenomena such as coastal flooding and drought occurrence. In fact, the proposed general model (i.e., fewer a-priori assumptions on the properties of the event occurrence process and efficient use of the data) yields a reduction of estimation uncertainty in the quantification of extremely rare quantiles. Even though the studied extreme events are different from a process perspective, the results confirm the advantages and flexibility of these novel extreme value distributions.