Masters lecture in Statistics -  Árni Víðir Jóhannesson

Master's student: Árni Víðir Jóhannesson
Title: A spatial Bayesian hierarchical model for flood frequency analysis
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Faculty: Faculty of Physical Sciences
Advisor: Birgir Hrafnkelsson, Professor at the Faculty of Physical Sciences

Other member of the master committee: Anna Helga Jónsdóttir,  Assistant Professor at the Faculty of Physical Sciences.

Examiner: Egil Ferkingstad, Research scientist at deCODE genetics

Abstract

The goal of this thesis is to model data on annual maximum series of peak flow from 553 catchments across the UK. An accurate estimate of extreme floods is of interest in many circumstances, especially concerning vital civil infrastructure. For this purpose, a latent Gaussian model with a multivariate link function for the location, scale and shape parameters of the data density is proposed for flood frequency analysis. The observations are assumed to follow the generalised extreme value (GEV) distribution. The model is inferred using the Bayesian methodology, and due to the large dimension of the data, an approximation is made to make the inference computationally feasible. Structured additive regression models are proposed for the three parameters of the data density. These regression models all contain fixed linear effects for catchment descriptors, e.g., catchment area and average annual rainfall. Two spatial components, for the location and scale parameters, are introduced in order to explain some of the otherwise unexplained variability introduced by the geographical locations of the catchments. Using this model, the quantiles of the data are investigated so that predictions can be made for the return level of an extreme flood. 

The results show that latent Gaussian models are a viable option for flood frequency analysis. The quantile plots for the return periods of floods show promising results, and a model of this form could prove to be useful. The results show that the spatial components for the location and scale parameter of the data density are both of importance and neither should be ignored.