Modeling dependence between extreme rainfall and storm surge to estimate coastal flooding risk

Accounting for dependence between extreme rainfall and storm surge can be critical for correctly estimating coastal flood risk. Several statistical methods are available for modeling such extremal dependence, but the comparative performance of these methods for quantifying the exceedance probability of rare coastal floods is unknown. This paper compares three classes of statistical methods—threshold-excess, point process, and conditional—in terms of their ability to quantify flood risk. The threshold-excess method offers approximately unbiased estimates for dependence parameters, but its application for quantifying flood risk is limited because it is unable to handle situations where only one of the two variables is extreme. In contrast, the point process method (with the logistic and negative logistic models) and the conditional method describe the full distribution of extremes, but they overestimate and underestimate the dependence strength, respectively. We conclude that the point process method is the most suitable approach for modeling dependence between extreme rainfall and storm surge when the dependence is relatively strong, while none of the three methods produces satisfactory results for bivariate extremes with very weak dependence. It is therefore important to take the bias of each method into account when applying them to flood estimation problems. A case study is used to demonstrate the three statistical methods and illustrate the implication of dependence to flood risk.