A dynamic warning system for single-gully debris flows in Beijing mountain areas: model construction and performance verification

Debris flows in Beijing's mountainous areas feature sudden occurrence and high destructiveness, posing severe threats to residents' lives and property. Conventional early warning models based only on regional rainfall thresholds or static susceptibility suffer from low spatial resolution, high false alarm rates, and poor timeliness. This study develops a mechanism-inspired statistical dynamic early warning model for single-gully debris flows using multi-dimensional controlling factors and historical disaster data (2016–2022). The model establishes a composite geological index from four core indicators and a rainfall index using maximum hourly rainfall intensity and event-based cumulative rainfall. A power-law nonlinear coupling relationship is optimized via grid search, and a four-level graded warning system is constructed. Validated by three extreme rainfall events (2023–2025), the model achieves a Probability of Detection exceeding 97%, a false alarm rate below 5%, a critical success index above 0.80, and an average warning lead time of 1.2–1.5 hours. It has been implemented in the Beijing Geological Hazard Monitoring and Early Warning System for real-time operation. This work enables a shift from regional to refined single-gully warning, providing technical support for disaster mitigation and a transferable framework for similar urban mountainous regions worldwide.