Spatial Cascading of Extreme Water–Sediment Imbalance Risks in a Heavily Regulated River Reach: A Copula-CoVaR Framework

The Inner Mongolia reach of the Yellow River faces compound “low flow, high sediment” extremes under reservoir regulation, threatening flood and ice-flood safety in ways that traditional mean-based or correlation-based methods fail to quantify. This study integrates POT-GPD extreme value theory with a vine copula-CoVaR framework using daily data (1951–2023) from four stations. The financial CoVaR concept was adapted to rivers through three hydrological modifications: a 5-day hydrodynamic lag, redefinition of the baseline to the downstream unconditional VaR, and semi-parametric tail modeling. Bootstrap confidence intervals (n = 1000) and a sensitivity analysis to the upstream–downstream lag (τ = 3–7 days) and the period cutoff (1984–1990) were used to assess robustness. Bayangol exhibits the highest Expected Shortfall (ES95 = 0.0329 kg·s·m−6). The Bayangol → Toudaoguai path is the only persistent positive risk transmission link, with ΔCoVaR showing a directionally consistent increase of 253% from the natural period (1951–1986) to the regulated period (1987–2023); by contrast, ΔCoVaR from Dengkou to Toudaoguai remains near zero or negative when assessed under the conventional bivariate framework. A three-dimensional vine copula analysis, conducted independently for the pre- and post-reservoir periods, reveals a qualitative reversal of compound extreme spillover that is masked when the two periods are pooled. While the bivariate analysis identifies Bayangol → Toudaoguai as the only persistent positive spillover route at the annual scale, the 3D vine analysis unpacks the compound extreme mechanism at the daily scale. Under the joint compound extreme condition (upstream Q and S each ≥ Q90), the conditional VaR95 of downstream sediment concentration shifts from systematically negative in P1 (ΔVaR95 = −4.75 kg·m−3 at the 90th-percentile threshold, indicating natural attenuation) to systematically positive in P2′ (ΔVaR95 = +4.70 kg·m−3, +86.9% relative increase, indicating amplification). The same reversal is observed for the tail mean (ΔES95), is preserved across four compound extreme thresholds (Q75–Q90), and is robust to the choice of period cutoff (28/28 cases reverse across seven candidate cutoffs). Bidirectional counterfactual simulations indicate that the copula shift from tail independence (Clayton) to tail dependence (Gaussian) alone elevates extreme concurrence probability by 58% (from 2.21% to 3.49%), while marginal distribution changes contribute negligibly (≤0.1 percentage points). Structural deterioration of water–sediment coordination therefore dominates risk amplification. The copula-CoVaR framework offers a candidate tool that requires further validation with large samples for tail risk assessment in heavily regulated fluvial systems.