Frequency-magnitude distribution of debris flows compiled from global data, and comparison with post-fire debris flows in the western U.S.

Forecasting debris flow hazard is challenging due to the episodic occurrence of debris flows in response to stochastic precipitation and, in some areas, wildfires. In order to facilitate hazard assessment, we have gathered available records of debris flow volumes into the first comprehensive global catalog of debris flows (n=988). We also present results of field collection of recent debris flows (n=77) in the northern Rocky Mountains, where debris flow frequency increases following wildfire. As a first step in parameterizing hazard models, we use frequency-magnitude distributions and empirical cumulative distribution functions (ECDFs) to compare volumes of post-fire debris flows to non-fire-related debris flows. The ECDF of post-fire debris flow volumes is significantly different (at 95% confidence) from that of non-fire-related debris flows, suggesting that the post-fire distribution is composed of a higher proportion of small events than that of non-fire-related debris flows. The slope of the frequency-magnitude distribution of post-fire debris flows is steeper than that of non-fire-related debris flows, corroborating evidence that small post-fire debris flows occur with a higher relative frequency than non-fire-related debris flows. Taken together, the statistical analyses suggest that post-fire debris flows come from a different population than non-fire-related debris flows, and their hazard must be modeled separately. We propose two possible non-exclusive explanations for the fact that the post-fire environment produces a higher proportion of small debris flows: 1) following fires, smaller storms or effective drainage areas can trigger debris flows due to increased runoff and/or decreases in root strength, resulting in smaller volumes and increased probability of failure, and 2) fire increases the probability and frequency of debris flows, causing their distribution to shift toward smaller events due to limitations in sediment supply.