Dynamic Threshold Determination Method for Triggering Critical Rainfall in Mountainous Debris Flow

The initiation of debris flows in mountainous areas is dynamically influenced by multiple factors, including rainfall intensity, duration, and antecedent rainfall conditions. Traditional static threshold methods struggle to adapt to these dynamic environmental conditions. To address this issue, this paper proposes a dynamic threshold determination method for the critical rainfall triggering debris flows in mountainous regions. Firstly, high-risk areas are identified based on the frequency ratio model, and the effective rainfall is quantified using the Crozier model. Subsequently, a combination of dynamic variables, such as soil saturation and safety factor, is constructed, and the Jensen–Shannon (JS) divergence is introduced for sensitivity screening to select the most relevant variables. These optimized variables are then fed into an LSTM-TCN (Long Short-Term Memory-Temporal Convolutional Network) framework to extract temporal features and predict the probability of debris flow occurrence time. Finally, real-time threshold determination is achieved by integrating the absolute rainfall energy with a dynamic threshold model. Test results demonstrate that this method can effectively quantify the dynamic nature of rainfall across different regions, screen key variables, and achieve threshold determination with high coverage (average of 0.978) and precise interval width (average of 0.023). This approach provides a more accurate and adaptive means of predicting and managing debris flow risks in mountainous areas, enhancing our ability to respond to these natural hazards in a timely and effective manner.