Trivariate Frequency Analysis of Extreme Sediment Events of Compound Floods Based on Vine Copula: A Case Study of the Middle Yellow River in China: Fid-Bau Portal

Trivariate Frequency Analysis of Extreme Sediment Events of Compound Floods Based on Vine Copula: A Case Study of the Middle Yellow River in China

Zhao, Fangzheng / Yi, Peng / Wang, Yuanjian / Wan, Xinyu / Wang, Sen / Song, Chen / Xue, Yuting

Abstract

Extreme flood events, laden with significant sediment loads, pose substantial risks to reservoir flood control and sediment deposition management. A multivariate frequency analysis incorporating peak sediment concentration (SSC), peak flood discharge ( $Q$ ), and 5-day maximum flood volume ( $V$ ) during the flood serves as a critical foundation for determining the return periods of such extreme events. Currently, the frequency analysis of extreme sediment events at a flood scale predominantly relies on traditional copula functions. However, these conventional copulas, constrained by a single parameter, are inadequate for capturing the intricate correlations among variables, thus impeding the attainment of satisfactory model performance. To address this gap, the present study introduces a vine copula–based approach for the multivariate frequency analysis of extreme sediment-flood events, focusing on modeling the joint behavior of SSC, $Q$ , and $V$ , and simulating the variation in the joint return periods of compound sediment-flood events. Utilizing the Tongguan Station on the Yellow River in China as a case study for model application, the results indicate that (1) the vine copula model exhibits superior performance compared with traditional copula models, with evaluation metrics root-mean square error (RMSE), $R^{2}$ , and Akaike information criterion (AIC) values of 0.038, 0.972, and $- 447.7$ , respectively, compared with 0.045, 0.957, and $- 423.2$ , providing a more precise description of the joint distribution of $SSC - Q - V$ ; (2) in both bivariate and trivariate joint return period scenarios, an increase in any variable among SSC, $Q$ , or $V$ leads to a rise in their joint return period; in conditional return period scenarios, an increase in any variable results in a decrease in the conditional return period of the remaining variables in combination with that variable; and (3) a specific joint return period corresponds to multiple $SSC - Q - V$ events, and the joint return period for trivariate joint return “AND” scenarios being greater than that for univariate return periods. The research findings provide model support for risk assessment of extreme flood-sediment events and water-sediment regulation schemes.