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

摘要

In univariate frequency analysis, the return period of an event has a one-to-one correspondencewith its characteristic value, and the response of the hydraulic structure to hydrological load expressed by thehydrological event is monotonic. Thus, the design criteria of the hydraulic structure can be equivalently representedby the return period of the hydrological event, and consequently, design event-based design parametersevaluated have been widely used in practical engineering. However, the monotonic correspondence between thereturn period of the hydrological event and the response of the hydraulic structure does not exist in the multivariatecontext, and hydrological load with a larger joint return period does not always produce a more unsaferesponse. Misunderstandings of concepts of return periods of hydrological event, and estimation of hydrologicaldesign events usually take place in multivariate frequency analysis. This study theoretically derives the relationsbetween different types of joint return periods, joint return period and its marginal return periods, theoccurrence 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 theresults demonstrate that design criteria cannot be equivalently represented by joint return periods of hydrologicalload, and design parameters of the hydraulic structure should not be determined by multivariate hydrologicaldesign events.