基于Copula函数的日含沙量随机模拟

Stochastic Simulation of Daily Sediment Concentration Process Based on Copula Function

考虑相邻两日含沙量之间的相关关系,建立了基于Copula函数的日含沙量随机模拟模型。并针对日含沙量模拟时段较多,日含沙量边缘分布难以统一确定的特点,采用正态分位数变换对实测日含沙量资料进行了标准正态化处理。以屏山水文站日含沙量为研究对象,采用该模型对其日含沙量过程进行随机模拟,并将模拟结果与分期平稳AR模型模拟结果进行对比。结果表明,所建立的模型能较好保持实测日含沙量资料的统计特性,计算精度较高,各统计参数的通过率均在98%以上,最大平均相对误差4.22%,且在偏态性和非线性相关关系方面要优于分期平稳AR模型,说明本模型可用于日含沙量过程的长序列随机模拟。

This paper presents a stochastic model for modeling daily suspended sediment concentrations (SSCs), with the use of Copula function of accounting for temporal correlation. It first normalizes the daily SSCs observations by using the normalized quantile transform method to enhance the marginal distribution selection of SSCs. Next, the bivariate Archimedean copulas are used to construct the joint distributions of adjacent daily SSCs. Finally, the developed stochastic model is applied to generate long-term daily SSCs sequences of the Pingshan station on Jinsha River. The widely used autoregressive (AR) model results are also used as references, which shows that the proposed stochastic model can preserve the statistical characteristics of the historical daily SSCs with a high level of accuracy. The differences of statistical values between simulated and observed series are small. Above 98% of average relative errors of statistics are less than 10%, and the maximum is 4.22%. In addition, the proposed model performed better than the AR model in preserving the skewness and lag-1 correlation. This study suggests that the proposed Copula-based model is able to generate long-term daily SSCs data, which may have significant ramifications to water resources management.