基于Archimedean Copula函数的流域降雨-径流关系变异分析

降雨径流关系是工程水文学领域中一个重要的应用问题,利用Copula函数在捕捉多变量间相依结构的灵活性这一优点,引入Archimedean Copula函数构建流域降雨-径流联合分布,诊断流域降雨-径流关系变异。以泾河流域为例,确定了降雨、径流分别服从Gumbel分布与对数正态分布,Copula函数检验结果表明,泾河流域降雨径流关系变异发生在1996年,并以降雨-径流关系变异点为分割点,将降雨、径流序列分割为1960~1996与1997~2010年两个阶段,分析表明两个时段降雨-径流关系发生较大变化,相同降雨情况下1997~2010年产流量相对1960~1996年减小30%以上,年降水量越小,产流量减小幅度越大,当年降水量为500mm时,减小幅度达到37.59%,并结合人类活动对照等分析,验证了Copula函数诊断流域降雨径流关系变异结果的合理性与准确性。

Detection of variations in precipitation-runoff relationship based on Archimedean Copula

Precipitation-runoff relationship is a core issue in engineering hydrology. Copula functions have advantages and flexibility in capturing dependences between variables. This study adopted an Archimedean Copula function to construct such a distribution relationship and detect its abrupt variation points based on the monthly and yearly scales of precipitation and runoff. The Jinghe river basin features precipitation and runoff following the Gamma and logarithmic normal distributions respectively, and according to Copula function analysis its abrupt point on precipitation-runoff relationship occurred in 1996. At the abrupt point, we divided the time series into two parts for the periods 1960~1996 and 1997~2010. Then, the analysis shows that a significant change in the relationship occurred, i.e. a reduction of 30% in water yield during 1997~2010 relative to 1960~1996 in the same conditions of precipitation. And the less precipitation, the greater reduction in water yield, with its maximum of 37.59% at P=500mm. This abrupt variation point on precipitation-runoff relationship calculated by Copula function is demonstrated by considering the variation in human activities, etc.