Stochastic investigation of hydrological extremes: influence of temporal variability and dependence

The understanding and modelling of hydrological extremes is a classic endeavor in hydrology and engineering, one which has received renewed interest during the past decades under climate change theory. Long before concerns regarding intensification of extremes became prominent, their inherent variability and uncertainty sufficed to make their understanding and modelling challenging. Stochastics, integrating probability, statistics, and the theory of stochastic processes, offer a uniquely appropriate and consistent framework to deal with the uncertain nature of extremes. While the marginal properties of extremes have been extensively studied in the literature, the same does not hold for their temporal properties, since extremes are traditionally treated as temporally independent. As a consequence, their temporal behaviours have been either largely overlooked, or approached via deterministic reasoning. Yet, there are both empirical and theoretical grounds that question the independence assumption, namely the fact that hydrological extremes originate from natural processes characterized by marked dependence at various scales. This Thesis aims to stochastically investigate and model the temporal variability and dependence of hydrological extremes from seasonal to climatic scales. The key innovation of the analysis is the identification of the temporal behaviours of the extremes and their stochastic linkage to the inherent properties of the parent hydrological process. Such an approach creates new perspectives on understanding the temporal dynamics of hydrological extremes that can significantly improve the perception of related risk over time and inform advanced mitigation practices. Two complementary objectives are pursued in this respect: (a) the characterization of their temporal properties, including the multi-scale dependence dynamics, from long-term hydrological records, and (b) the development of hydrologically relevant modelling frameworks that reproduce the observed extremal patterns. These objectives unfold at the following three scales: (i) the seasonal scale, pertaining to extreme rainfall seasonality and dependence dynamics of seasonal streamflow extremes, (ii) the annual scale, with respect to the propagation of long-term persistence, i.e. Hurst-Kolmogorov (HK) dynamics, from the parent process to the extremes and properties thereof, and last, (iii) the climatic-scale, regarding the theoretical and empirical basis of climatic projections of future rainfall.