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

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.

Keywords

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