基于核密度估计和Copula函数的降水径流丰枯组合概率研究

Research of combined probability of rainfall-runoff based on kernel density estimation and Copula function

本文从规避水文风险角度出发,将非参数核密度估计方法与Copula函数相结合,利用核密度估计方法确定水文变量的边缘分布,利用Copula函数计算不同变量之间的联合分布,并应用于南水北调中线一期工程水源地丹江口水库不同分期降雨径流的概率计算与丰枯风险分析。研究结果表明:该流域汛期降雨与径流的组合概率中,丰平枯等级一致的总概率为76%,而非汛期降雨与径流丰平枯等级一致的总概率仅为53.3%。与汛期相比,非汛期降雨与径流等级不一致的概率明显升高。当汛期径流等级为丰时,非汛期径流等级为丰的条件概率达到60.1%;当汛期径流等级为平时,非汛期径流等级为丰、平、枯的条件概率相差不大;当汛期径流等级为枯时,非汛期径流等级为枯的条件概率达到59.8%。

In order to reduce the hydrological risks,kernel density estimation method was used to deter？mine the marginal distribution,and copula function was used to construct a joint distribution for differentvariables in this paper. Danjiangkou reservoir is served as the water source for the first stage in the middleroute of South-to-North Water Transfer Project. We calculated the probability of rainfall-runoff process indifferent periods,and analyzed the risk of flood and drought in the upper catchment of Danjiangkou reservoir. The results of the combined probability of rainfall and runoff show that the total probability is 76%when the high,median and low levels of precipitation are consistent with runoff during the flood periodand this value is merely 53.3% during the non-flood period. The levels of precipitation are obviously moreinconstistent with runoff during the non-flood period,compared with the flood period. Th conditional proba？bility that the runoff could reach the hight level is 60.1% during the non- flood period when there isahigh lvele of runoff during the flood period. The conditional probabilities of three possible results are similar during the non-flood period when there is a median level of runoff during the flood period. When thereis a low level of runoff during the flood period,the conditional probability is 59.8%. There is the same lovel of runoff during the non-flood period. The methods and results that are presented in this paper couldprovidea reference for operation of inter-basin water transfer projescts.