Modelling Extreme Rain Accumulation with an Application to the 2011 Lake Champlain Flood

Abstract

Summary 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.