Copula-Based Bivariate Return Period Analysis and Its Implication to Hydrological Design Event

In univariate frequency analysis, the return period of an event has a one-to-one correspondence with its characteristic value, and the response of the hydraulic structure to hydrological load expressed by the hydrological event is monotonic. Thus, the design criteria of the hydraulic structure can be equivalently represented by the return period of the hydrological event, and consequently, design event-based design parameters evaluated have been widely used in practical engineering. However, the monotonic correspondence between the return period of the hydrological event and the response of the hydraulic structure does not exist in the multivariate context, and hydrological load with a larger joint return period does not always produce a more unsafe response. Misunderstandings of concepts of return periods of hydrological event, and estimation of hydrological design events usually take place in multivariate frequency analysis. This study theoretically derives the relations between different types of joint return periods, joint return period and its marginal return periods, the occurrence of bivariate extreme events and their return periods, and then the theoretical framework is tested. Results from the case contribute to the understanding of bivariate return periods of hydrological event, and the results demonstrate that design criteria cannot be equivalently represented by joint return periods of hydrological load, and design parameters of the hydraulic structure should not be determined by multivariate hydrological design events.