By Kristina Grolmusova, Jennifer L. Wadsworth and Thordis L. Thorarinsdottir<\/p>\n\n\n\n
Abstract<\/strong><\/p>\n\n\n\n We exploit the new framework of multivariate geometric extreme value theory<\/strong> for the statistical analysis of river flow extremes at multiple locations on a river network. Current methodologies<\/strong> within the geometric framework are limited to a relatively low number of dimensions<\/strong>. This is insufficient for the purposes of flood risk estimation, since the number of gauging stations on a river network is often of the order 10-20+. In order to create a parsimonious model in higher dimensions, we translate recent theoretical work on geometric extremal graphical models<\/strong> into statistical practice. We define the gauge function, a key object in geometric extremes, in a structured way using block graphs, which are a natural way of expressing the river network. We introduce both simple models<\/strong>, and more complex ones that can accommodate both simultaneous and non-simultaneous flows<\/strong>, and apply them to extreme flows at 10 locations<\/strong> on a river network around Preston<\/strong>, in north-west England. The models are shown to fit well<\/strong> and indicate strong extrapolation performance<\/strong>. We also introduce a correction coefficient<\/strong> for the geometric framework to address potential over- or under-estimation of marginal probabilities<\/strong>. The overall utility of our approach is illustrated through calculation of probabilities of simultaneous flooding at four locations on the network<\/strong>.<\/p>\n\n\n\n\n