Modelling extreme rain accumulation with an application to the 2011 Lake Champlain flood

Abstract

A simple strategy is proposed to model total accumulation in non-overlapping clusters of extreme values from a stationary series of daily precipitation. Assuming that each cluster contains at least one value above a high threshold, the cluster sum S is expressed as the ratio S=M/P of the cluster maximum M and a random scaling factor P ∈ (0,1]. The joint distribution for the pair (M,P) is then specified by coupling marginal distributions for M and P with a copula. Although the excess distribution of M is well approximated by a generalized Pareto distribution, it is argued that, conditionally on P<1, a scaled beta distribution may already be sufficiently rich to capture the behaviour of P. An appropriate copula for the pair (M,P) can also be selected by standard rank-based techniques. This approach is used to analyse rainfall data from Burlington, Vermont, and to estimate the return period of the spring 2011 precipitation accumulation which was a key factor in that year's devastating flood in the Richelieu Valley Basin in Québec, Canada.