Estimation of the r-year river flood discharged using historical data by means of Extreme Value Theory.

Abstract

The understanding of the relationship between flood peaks magnitude and their frequency is a very important and crucial task in structural engineering and hydrology, since it provides fundamental information about the discharge’s magnitude which is used by engineers in the design process of appropriate structure to delimit river flood effects. Extreme value analysis is the branch of statistics that studies the behaviour of extreme values of a distribution and assess the probability of observing them. The aim of this dissertation is to estimate the r-year river flood discharged using historical data by means of Extreme Value Theory. The dissertation introduces Extreme Values Theory, emphasizing the idea of the general limit for extreme values, the Gumbel and GEV distributions and the graphical tools for extreme data analysis. The estimation is performed within a Bayesian data analysis method, focusing on two types of Markov Chain Monte Carlo methods: the Gibbs sampler and the Hamiltonian Monte Carlo algorithm. The application will focus on two gauging stations in the United Kingdom: Kingston, for the River Thames and Sheepmount, for the River Eden. The data used in this dissertation hail from the National River Flow Archive of the UK Centre for Ecology and Hydrology. In particular for the river Eden, historical data about large events from the past are available in the paper of Parkers B. and Demeritt D.