A Scenario-Based Multi-Objective Framework for Hydrological Environmental-Flow Method Selection in the Upper Datong River

Hydrological methods are widely used for environmental-flow assessment in data-limited rivers, but different methods often produce divergent monthly thresholds, making method selection difficult under strong seasonal variability. This study develops a scenario-based multi-objective framework for selecting hydrological environmental-flow methods in the upper Datong River, a cold-region and semi-arid headwater tributary of the upper Yellow River. Using daily discharge records from the Gadatan hydrological station during 1956–2022, monthly environmental-flow thresholds were estimated using nine commonly applied hydrological methods. A four-dimensional RDVS framework was constructed to evaluate reliability, deficit intensity, naturalness deviation, and intra-annual rhythm distance. Pareto non-dominated screening and scenario-oriented ranking were then applied under three management scenarios: low-flow baseline protection, critical-period protection, and annual process consistency. The results show that low-flow months exhibit higher empirical variability and greater kurtosis and are associated with greater inter-method divergence. The Tennant method ranked first under the low-flow baseline scenario, whereas the intra-annual distribution method ranked first under both the critical-period and annual-consistency scenarios. The Texas method consistently entered the top three across all scenarios, indicating cross-scenario robustness. The targeted anomaly test and the annual-block bootstrap both supported the stability of the primary recommendations: the Tennant method ranked first in 94.0% of the S1 bootstrap replicates, whereas the intra-annual distribution method ranked first in 98.7% and 100.0% of the S2 and S3 replicates, respectively. Overall, the proposed framework transforms hydrological method comparison into a transparent, scenario-based, and reproducible selection process and provides a hydrology-based decision-support tool for screening candidate environmental-flow methods in data-limited rivers.