Weighted likelihood copula modeling of extreme rainfall events in Connecticut

Copulas have recently emerged as a practical method for multivariate modeling. To date, only limited amount of work has been done to apply copula-based modeling in the context of extreme rainfall analysis, and no work exists on modeling multiple characteristics of rainfall events from data at resolutions finer than hourly. In this study, trivariate copula-based modeling is applied to annual extreme rainfall events constructed from 15-min time series precipitation data at 12 stations within the state of Connecticut. Three characteristics (volume, duration, and peak intensity) are modeled by a multivariate distribution specified by three marginal distributions and a dependence structure via copula. A major issue in this application is that, because the 15-min precipitation data are only available fairly recently, the sample size at most stations is small, ranging from 10 to 33 years. For each station, we estimate the model parameters by maximizing a weighted likelihood, which assigns weight to data at stations nearby, borrowing strengths from them. The weights are assigned by a kernel function whose bandwidth is chosen by cross-validation in terms of predictive loglikelihood. The fitted model and sampling algorithms provide new knowledge on design storms and risk assessment in Connecticut.