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

Abstract

The understanding and modelling of hydrological extremes is a classic endeavour in hydrology and engineering, one which has received renewed interest during the past decades under the anthropogenic climate change hypothesis. 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 both 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 the temporal properties and multi-scale dependence dynamics of extremes, 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, (ii) the annual, and (iii) the climatic. At the seasonal scale, the focus is placed both on daily rainfall and streamflow maxima. A novel characterization of extreme rainfall seasonality based on the Akaike model selection criterion is proposed to objectively identify extreme rainfall seasonality and infer the change in the distributional properties of seasonal rainfall extremes. The framework is successfully applied to the modelling of seasonal and annual properties of rainfall extremes from long-term rainfall records. Seasonal extremal dynamics are further explored with respect to identifying dependence dynamics of streamflow extremes, i.e. high and low flows, from a large sample of European rivers. Physical drivers enhancing seasonal dependence are sought, while in turn, the relevance of the latter for enhancing predictability of extremes is explored. At the annual scale, the Thesis investigates the propagation of persistence (long-range dependence), else known as Hurst-Kolmogorov (HK) dynamics, from the parent process to the occurrences of its extremes. Clustering of extremes is critical for hydrological design and risk management and challenges the popular assumption of independence of extremes. To this end, the less studied persistent properties of annual rainfall are first revisited employing a global rainfall database. Subsequently, extremal properties of persistent processes are investigated with a twofold goal (a) to infer the stochastic links between multi-scale clustering of extremes and HK dynamics, and (b) to develop a method to retrieve the latter, i.e. HK dynamics, from the former, i.e. the temporal extremal patterns. Shortcomings of existing methods for characterizing persistence from records of extremes are identified and a new probabilistic method for revealing multi-scale clustering of extremes and associated departures from independence is formulated. The framework is applied to real-world rainfall extremes from long-term records. The manifestations of dependence in hydrological extremes are exposed also with respect to their pre-asymptotic distributional properties. The literature on extreme value theory for dependent processes is reviewed and open questions concerning extremes of persistent processes are investigated through Monte Carlo simulations. Stochastic HK-type models are assessed in terms of capturing extremal dependence patterns, as revealed from long-term rainfall and streamflow observational records. At the climatic scale, the theoretical and empirical basis for the dominant practice of modelling rainfall trends is investigated. To this aim, a systematic prediction-oriented framework for evaluating trends is devised. The predictive performance of trend models is compared to the one of simpler mean models in terms of capturing out-of-sample, i.e. ‘future’, rainfall properties, including extremes. Conclusions are drawn from a rare dataset comprising 60 rainfall stations with more than 150 years of daily data, and are corroborated by theoretical findings for persistent processes.