基于Copula函数的多源径流预报误差联合分布研究

Joint Distribution of Prediction Errors of Multi-Source Runoff Based on Copula Function

摘要: 为了准确量化梯级水库群多源径流汇入的预报误差，提高优化调度方案的制作精度，采用正态分布、t分布、logistic分布和stable分布，分别对梯级水库群多源汇入径流的预报误差进行分布拟合优选，借助Copula函数具有耦合不同类型边缘分布函数的优势，构建多源径流预报误差的联合分布。锦屏一级与官地水库构成的梯级水库群的应用结果表明：锦屏一级入库的径流预报误差服从t分布，九龙河区间入流的径流预报误差服从logistic分布；采用Clayton copula函数构建的联合分布拟合效果最好，随机模拟产生的预报误差模拟值与实际值相差不大，验证了该方法的可行性，可以为水库群调度提供一定的参考依据。

Abstract: In order to accurately quantify forecasting error of the cascade reservoirs with multi-source inflows and improve the accuracy of the optimal scheduling scheme, the four distribution curves of normal distribution, t-distribution, logistic distribution and stable distribution are used to fit the error series, and the Copula function is used to construct joint distribution of multi-source runoff prediction errors. Application results of Jinping and Guandi Reservoirs show that the runoff forecast error of Jinping reservoir obeys the t-distribution, the runoff forecast error of the Jiulonghe interval inflow obeys the logistic distribution, and the joint distribution of the Clayton Copula function is the best. The simulation error generated by stochastic simulation is not much different from the actual value. The feasibility of the method is verified, which can provide a reference for reservoir group scheduling.