基于Copula函数的嘉陵江流域水沙丰枯遭遇关系探究

Exploration of Water and Sediment Abundance Encounter Relationship in Jialing River Basin Based on Copula Function

为了深入了解嘉陵江水沙关系的变化规律。基于嘉陵江出口北碚水文站1965-2022年的年径流量和年输沙量资料,利用Mann-Kendall检验法、双累积曲线法并结合物理成因法诊断水沙关系的变异点,通过AIC、BIC、RMSE对径流量和输沙量的边缘分布函数和Copula函数进行优选,确定最优Copula函数并建立嘉陵江流域水沙联合分布模型,运用模型对流域内水沙丰枯遭遇概率、联合和同现重现期进行计算,进而对比分析水沙单变量和联合变量设计值。结果表明:①水沙关系在1989年发生突变,变异前的水沙相关性强于变异后的水沙相关性;②1965-1989年阶段水沙序列最优边缘分布都为Logn,最优水沙联合分布模型为Gumbel Copula模型。1990-2022年阶段径流量和输沙量的最优边缘分布分别为Gamma、GP,最优水沙联合分布模型为Frank Copula模型;③2个阶段水沙序列同步概率分别是59.77%、61.14%,均大于异步概率,且出现极端情况“水丰沙枯”、“水枯沙丰”类型的概率极低,表明水沙概率存在较大的相关性,来水来沙条件相对稳定;④联合变量设计值大于单变量设计值,通过两变量联合分布计算的径流量和输沙量设计值更加可靠。水沙联合重现期集中在2年附近,同现重现期绝大部分小于50年。通过探讨嘉陵江流域来水来沙联合变化特征,可为流域的水沙调控、防灾减灾等工作提供参考。

In order to gain a deeper understanding of the changing law of water-sand relationship in the Jialing River,based on the annual runoff and sediment load data of Beibei Hydrological Station at the outlet of the Jialing River from 1965 to 2022,the Mann-Kendall test,double cumulative curve method and the physical genesis method were used to diagnose the variation points of water and sediment relationship,and the marginal distribution function and Copula function of the runoff and sediment load were preferred through the AIC,BIC,and RMSE,and the optimal Copula function was determined,and the water-sediment joint distribution model of the Jialing River basin was established.The established model was then used to calculate the probability of water and sediment abundance and depletion encounter,joint and co-occurring recurrence periods in the basin,and then to compare and analyse the univariate and joint variables design values of water and sediment.The results show that:①The water and sediment relationship changed abruptly in 1989,and the water and sediment correlation before the change was stronger than that after the change.②The optimal marginal distributions of the water and sediment series in 1965-1989 are Logn,and the optimal joint distribution model of water and sediment is the Gumbel Copula model,while the optimal marginal distributions of runoff and sediment in 1990-2022 are Gamma and GP respectively,and the optimal joint distribution model of water and sediment is the Frank Copula model.③The synchronous probability of the two stages of water and sediment sequences is 59.77%and 61.14%respectively,both of which are greater than the asynchronous probability,and the probability of occurrence of the extreme cases of“abundant water and sediment depletion”and“depleted water and sediment abundance”is extremely low,which indicates that there is a large correlation between the probability of water and sediment,and the water and sediment conditions are relatively stable.④The design value of the joint variable is larger than the univariate one,and the design value of runoff and sediment load calculated by the joint distribution of the two variables is more reliable.The joint recurrence period of water and sediment is concentrated near 2 years,and the majority of the co-occurrence recurrence period is less than 50 years.By exploring the characteristics of the joint change of water and sand in the Jialing River basin,this study can provide a reference for water and sand regulation,disaster prevention and mitigation in the basin.