Statistical Techniques for Debris-Flow Frequency–Magnitude Analyses

Debris flows are a curse where they interfere with the built environment because of their poor predictability, their long runout and high impact forces. This has prompted a vast body of research and hundreds of thousands of structures have been erected worldwide to cope with the corresponding debris-flow risk. Debris-flow science has bloomed over the past decades in response to urban encroachment in steep terrain. In most jurisdictions, a design event is chosen based on a specific return period or annual exceedance probability. In other cases, quantitative risk assessments for loss of life and/or economic losses guide the type and scale of structure (see Strouth et al., this volume). Sometimes, the decision is based purely on cost–benefit analysis amalgamating the other two techniques. Finally, decisions are made based on a finite budget to be spent to achieve maximum risk reduction. Irrespective of which method guides the mitigation efforts, an understanding of debris-flow frequency-magnitude relationships is valuable, and failure to incorporate such relationships has ripple effects for the risk assessment and design of mitigation works. In this chapter, we present various statistical techniques at the disposal of the practitioner, discuss their respective benefits and describe three case studies. As for most predictive geophysical phenomena, we argue for model ensembles rather than reliance on a single approach. Uniting expert judgment with empirical/statistical methods appears the winning bet for deciphering how often and how big debris flows may become.