On the use of TCEV and Kappa four-parameter distributions for at-site flood frequency analysis

Main task of Flood Frequency Analysis (FFA) is the estimation of a design flood for a given site fitting a probability distribution to a record of peak flows. This allows to compute parameters and quantiles estimates, achievable with different approaches (e.g. frequentist and Bayesian methodologies). Although appears a conceptually simple procedure, several approaches were proposed for its implementation. As a consequence, a wide debate started up in hydrology on merits and limits of each method, making FFA an attractive topic for scientists. Furthermore, regardless of strategies adopted for achieving parameters and quantiles estimates, as well as the choice of the best fitting model, the correct evaluation of uncertainty in flood frequency estimates should be considered an important step for undertaking an aware decision strategy. At-site flood frequency analysis is one of more direct methods for making inference from data. Several probability distributions are traditionally fitted for this type of analysis, such as Gumbel, log-Normal, Generalized Extreme Value (GEV) and log-Pearson type 3 (LP3). However, these distributions are typically characterized by two or three parameters, leaving the use of distributions with more parameters only for regional applications. This is the case of Two Components Extreme Value (TCEV) and Kappa distributions, which belong to the class of four-parameter distributions. These distributions are characterized by a distinct theoretical background, which reflects on their analytical properties. With respect to at-site analysis, while some investigations for properties of Kappa were conducted, similar studies for TCEV were neglected, probably due to the supposed relevant degree of uncertainty that should affect related estimates. In this thesis the applicability of a Bayesian approach for at-site estimation of parameters and quantiles of TCEV and Kappa distribution is tested. In particular, in order to achieve a complete vision about this topic, the theoretical background of extreme value distributions was revisited, with a focus on their role in interpreting floods phenomenology. One of the main contributions of this work can be considered the development of a Bayesian procedure for providing inferential conclusions about Kappa and TCEV, with an explicit quantification on connected uncertainty and, in the case of this latter distribution, a new measure for discerning the presence of two different populations into a sample was introduced. As case study, Eastern and Northern Australia was selected, due to high variability of climate and floods regime in this area. In this way, several underlying mechanisms of floods generation are expected to be analyzed, and abilities of TCEV and Kappa in fitting gauged data was tested. Results of application showed that in most cases, for sites located below the latitude of 23° south, TCEV distribution provide an excellent fit to at-site data, when compared to LP3 and GEV distributions. Furthermore, better performances were detected also in terms of uncertainty for high quantiles. Results are explainable with the climate-driven floods regime that affect the region. Finally, a single Italian case study was investigated, on the basis of several studies that documented two different mechanisms of runoff generation: as expected, in accordance with its theoretical formulation, TCEV provided a relevant ability in fitting at-site data.