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.     

基于Copula函数的水体富营养化联合风险概率研究

为了分析小型人工湖水体富营养化指标联合风险发生的概率,基于Copula函数的基本原理,结合眉湖水体富营养化模型模拟结果,建立了水体富营养化指标的边缘分布及Copula函数联合概率分布.通过Copula函数拟合检验和拟合优度评价筛选出不同组合方式下最优的Copula函数,并根据最优的Copula函数计算出水体富营养化指标的二维和三维联合风险概率.结果表明,不同组合方式下水体富营养化指标达到不同富营养化状态时的联合风险概率区别较大;当Chl-a和COD都为轻度富营养时,二维联合风险概率最大为62.29%,说明这种组合方式下眉湖水体极易发生轻度富营养;当Chl-a和COD都为轻度富营养、TN为中度富营养时,三维联合风险概率最大为45.46%,说明这种组合方式下眉湖水体极易发生中度富营养;由于受到水体富营养化指标监测系列的影响,部分二维和三维联合风险概率较小甚至为零.     

洞庭湖流域高温热浪风险变化特征

洞庭湖流域是我国高温热浪事件多发地区之一,严重威胁人体健康及农业生产,研究高温热浪特征和风险,对当地防暑减灾具有重要指导意义。基于气象站点气温数据(1960~2013年),综合利用MK检验、概率模型和Copula概率模型,以年最长热浪长度(HWL)、热浪平均高温(HWT)、高温天数(HDL)和高温天内平均高温(HDT)为指数,系统分析了洞庭湖流域高温、热浪的时空规律及风险变化特征。结果表明,流域平均4项高温指数表现出先下降后上升的趋势。总体上,流域东部和东南部高温、热浪强度较大,西部和西南部强度较小, 另外,流域高温、热浪的风险和强度变化有一定的空间差异,但总体上升。此外,基于Copula的分析结果表明,洞庭湖流域东大部地区发生高强度热浪和长期高温的风险上升,而西南部以及南部部分地区有所下降。