Constructing rainfall thresholds for debris flow initiation based on critical discharge and S-hydrograph

Debris flows caused by channel bed erosion present major hazards affecting life, livelihoods, and the built environment in mountainous regions. An efficient way to decrease hazard impact is through reliable hazard forecasts and appropriate early-warning strategies. Rainfall thresholds are fundamental in achieving reliable hazard forecasts. However, a lack of rainfall records often impedes the empirical establishment of such thresholds. This paper constructs rainfall intensity-duration thresholds based on process-based critical runoff discharge for the initiation of debris flows and a mathematical approximation among peak discharge, rainfall intensity and duration. Simulations of conditions that triggered debris flow and non-debris flow events allowed determination of the lower and upper limits of critical discharge for debris flow initiation. In turn, these critical discharge limits are compared with four estimates derived from process-based approaches to test which approach best delimit the critical conditions. Hydrological simulations derive S-hydrographs for recorded rainfall events. Further analysis of the S-hydrographs results in a mathematical approximation of peak discharge as a function of rainfall intensity and duration and the establishment of the minimum rainfall required to produce a particular peak discharge. The minimum rainfall threshold to trigger an event can be calculated by setting the process-based critical discharge as the peak dis charge. In turn, this enables the establishment of a conventional rainfall I-D threshold for debris flow initiation. This process-based approach enables the construction of valley-specific I-D thresholds in data-poor areas and provides a promising pathway to improve the reliability of debris flow hazard forecasts and early warnings.