Magnitude–frequency relations in debris flow

Debris flow occurs frequently in mountainous regions in China. Because of the difficulties involved in predicting and catching live debris flows, an assessment of the potential for debris flow is crucial in hazard mitigation. Magnitude–frequency (MF) relations are of special significance in such assessments. In previous studies, MF relations have been inferred by analyzing environmental factors and historical records and using empirical relations. This paper is concerned with the derivation of MF relations at regional and valley scales, using a large database of statistics. At the regional scale, it is represented by the distribution of the valley area, because the area is often taken to indicate the potential magnitude of debris flow. Statistics from over 5,000 debris flow valleys in various provinces in China show that a power law holds for the distribution, i.e., p(A) ∼ A −n , where p(A) is the percentage of valleys with area A and n varies with region and thus describes regional differences. At the valley scale, a case study focusing on Jiangjia Gully (JJG) was conducted, and the MF relations derived from it were expressed by the distributions of discharge and runoff (i.e., the total volume) of living debris flows observed over the last 40 years. The distributions can be expressed as exponential functions where the exponents vary with the events. These MF relations provide not only a potential quantitative reference for practical purposes but also hint at the intrinsic properties of the debris flow.