Copula-based frequency analysis of overflow and flooding in urban drainage systems

•We highlight the importance of rainfall dependence structure in sewer system evaluation.•The best marginal distribution fitting does not necessarily produce the best copula fitting.•Copula selection should be based on several measures e.g. statistics and graphics.•The dependence structure has more significant impacts on flood and CSO than marginal distributions.•Different copulas have different effects on the probabilities of flood and overflow.

SummaryThe performance evaluation of urban drainage systems is essentially based on accurate characterisation of rainfall events, where a particular challenge is development of the joint distributions of dependent rainfall variables such as duration and depth. In this study, the copula method is used to separate the dependence structure of rainfall variables from their marginal distributions and the different impacts of dependence structure and marginal distributions on system performance are analysed. Three one-parameter Archimedean copulas, including Clayton, Gumbel, and Frank families, are fitted and compared for different combinations of marginal distributions that cannot be rejected by statistical tests. The fitted copulas are used, through the Monte Carlo simulation method, to generate synthetic rainfall events for system performance analysis in terms of sewer flooding and Combined Sewer Overflow (CSO) discharges. The copula method is demonstrated using an urban drainage system in the UK, and the cumulative probability distributions of maximum flood depth at critical nodes and CSO discharge volume are calculated. The results obtained in this study highlight the importance of taking into account the dependence structure of rainfall variables in the context of urban drainage system evaluation and also reveal the different impacts of dependence structure and marginal distributions on the probabilities of sewer flooding and CSO volume.