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.

中文翻译：

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基于 Copula 的双变量重现期分析及其对水文设计事件的启示

在单变量频率分析中，事件的重现期与其特征值具有一一对应关系，水工建筑物对水文事件所表达的水文载荷的响应是单调的。因此，水工建筑物的设计准则可以等效地用水文事件的重现期来表示，因此，基于设计事件的设计参数评估在实际工程中得到了广泛应用。然而，水文事件重现期与水工结构响应之间的单调对应关系在多变量背景下并不存在，联合重现期越大的水文负荷并不总是产生越不安全的响应。对水文事件重现期概念的误解，水文设计事件的估计通常发生在多变量频率分析中。本研究从理论上推导了不同类型的联合重现期、联合重现期及其边际重现期、双变量极端事件的发生及其重现期之间的关系，并对理论框架进行了检验。案例结果有助于理解双变量水文事件重现期，结果表明设计准则不能等效地用水文负荷联合重现期来表示，水工建筑物的设计参数不应由多变量水文设计确定事件。本研究从理论上推导了不同类型的联合重现期、联合重现期及其边际重现期、双变量极端事件的发生及其重现期之间的关系，并对理论框架进行了检验。案例结果有助于理解双变量水文事件重现期，结果表明设计准则不能等效地用水文负荷联合重现期来表示，水工建筑物的设计参数不应由多变量水文设计确定事件。本研究从理论上推导了不同类型的联合重现期、联合重现期及其边际重现期、双变量极端事件的发生及其重现期之间的关系，并对理论框架进行了检验。案例结果有助于理解双变量水文事件重现期，结果表明设计准则不能等效地用水文负荷联合重现期来表示，水工建筑物的设计参数不应由多变量水文设计确定事件。