Objective definition of rainfall intensity–duration thresholds for the initiation of post-fire debris flows in southern California

Rainfall intensity–duration (ID) thresholds are commonly used to predict the temporal occurrence of debris flows and shallow landslides. Typically, thresholds are subjectively defined as the upper limit of peak rainstorm intensities that do not produce debris flows and landslides, or as the lower limit of peak rainstorm intensities that initiate debris flows and landslides. In addition, peak rainstorm intensities are often used to define thresholds, as data regarding the precise timing of debris flows and associated rainfall intensities are usually not available, and rainfall characteristics are often estimated from distant gauging locations. Here, we attempt to improve the performance of existing threshold-based predictions of post-fire debris-flow occurrence by utilizing data on the precise timing of debris flows relative to rainfall intensity, and develop an objective method to define the threshold intensities. We objectively defined the thresholds by maximizing the number of correct predictions of debris flow occurrence while minimizing the rate of both Type I (false positive) and Type II (false negative) errors. We identified that (1) there were statistically significant differences between peak storm and triggering intensities, (2) the objectively defined threshold model presents a better balance between predictive success, false alarms and failed alarms than previous subjectively defined thresholds, (3) thresholds based on measurements of rainfall intensity over shorter duration (≤60 min) are better predictors of post-fire debris-flow initiation than longer duration thresholds, and (4) the objectively defined thresholds were exceeded prior to the recorded time of debris flow at frequencies similar to or better than subjective thresholds. Our findings highlight the need to better constrain the timing and processes of initiation of landslides and debris flows for future threshold studies. In addition, the methods used to define rainfall thresholds in this study represent a computationally simple means of deriving critical values for other studies of nonlinear phenomena characterized by thresholds.