基于Copula函数和蒙特卡洛法的黄河上游多站径流相关分析与随机模拟

Correlation analysis and stochastic simulation of multi-station runoff in the Upper Yellow River based on Copula Functions and Monte Carlo Method

摘要

【目的】径流具有随机性、非平稳性、时间连续性和空间异质性。考虑径流时空二维相关特征，建立了一种多站径流序列重构模型，能够模拟径流时空多变化场景。【方法】优选了合适的边缘分布和Copula函数，建立了相同站点不同时段、不同站点相同时段的径流相关关系，进而采用蒙特卡洛法中的逆变换抽样随机模拟多站径流序列。以黄河上游为例，开展了唐乃亥和兰州两大控制性水文站月尺度径流相关分析与随机模拟。【结果】结果表明，随着模拟次数增加，模拟径流序列与实测径流序列的一致性不断提高；当模拟次数为500次时，两站月径流平均相对误差最大为2.07%和3.28%;当模拟次数达到10 000次时，两站各月径流平均相对误差分别低于0.34%和0.37%。【结论】综上，基于Copula函数和蒙特卡洛法的径流序列重构模型能够推广应用于更多站点，为延长少资料区水文序列，建立多时空径流遭遇场景下具有水力与电力联系的水库群调度规则，以及流域水资源配置方案等提供可靠的数据支持。

Abstract

[Objective] Runoff exhibits characteristics of randomness, non-stationarity, temporal continuity, and spatial heterogeneity. This paper considers the spatiotemporal two-dimensional correlation characteristics of runoff and establishes a multi-station runoff sequence reconstruction model that can simulate various spatiotemporal scenarios of runoff. [Methods] This study optimally selected appropriate marginal distributions and Copula functions to establish the runoff correlations at the same station over different time periods, as well as across different stations at the same time period. Subsequently, the inverse transform sampling method from Monte Carlo simulations was used to randomly simulate multi-station runoff sequences. The method was applied to the Upper Yellow River, where correlation analysis and stochastic simulation of monthly runoff were conducted for the two control hydrological stations at Tangnaihai and Lanzhou. [Results] The results indicated that as the number of simulations increased, the consistency between the simulated and observed runoff series improved. When the number of simulations was 500, the maximum mean relative error(MRE) of monthly runoff at Tangnaihai and Lanzhou stations reached 2.07% and 3.28%, respectively. When the number of simulations reached 10,000, the MRE for all monthly runoff at both stations was lower than 0.34% and 0.37%, respectively. [Conclusion] The runoff series reconstruction model based on the Copula function and Monte Carlo method is applicable to more stations. It provides reliable data support for extending hydrological sequences in areas with sparse data, establishing operational rules for reservoir systems with hydraulic and electrical connections, and for formulating basin water resource allocation schemes under various spatiotemporal runoff scenarios.

关键词

黄河上游 / 边缘分布函数 / Copula函数 / 逆变换抽样 / 随机模拟 / 影响因素

Key words

upper Yellow River / marginal distribution function / Copula function / inverse transform sampling / stochastic simulation / influencing factors

基金资助

国家重点研发计划(2023YFC3206700)

国家自然科学基金项目(52479032)

国家自然科学基金项目(U2243232)