Flood risk assessment is essential for flood control and disaster mitigation in arid and semi-arid river basins, where conventional univariate and bivariate frequency analyses struggle to capture nonlinear dependence among flood variables and often underestimate extreme synergistic risks. This study focuses on the Wulanmulun River Basin in Inner Mongolia and employs long-term observations from the Zuanlongwan and Wangdaohengta hydrological stations. A trivariate D-vine Copula model was constructed to jointly characterize peak discharge, total flood volume, and water level. Optimal vine structures differ between the stations (Qp–H–W and W–Qp–H) and outperform traditional Copula models in representing extreme joint risks. The ternary joint return periods reveal two distinct flood risk transmission modes, “jump” and “accumulation”, and joint exceedance probabilities under low, medium, high, and ultra-high-risk scenarios are 6.4%, 31.95%, 37.64%, and 5.75% at Zuanlongwan, and 4.7%, 35.24%, 45.78%, and 0.53% at Wangdaohengta, indicating concentration in medium-to-high risk ranges. The validation at Longtouguai Station showed an error RSME of 0.0630 and an R2 of 0.905, confirming the reliability of the model framework. These results indicate that the proposed framework can effectively capture multivariate flood dependencies and provide a scientific basis for flood control design, risk zoning, and emergency management of small and medium rivers in arid and semi-arid regions.
Sun et al. (Sun,) studied this question.