POWER LAW MODELS FOR ROCKFALL FREQUENCY-MAGNITUDE DISTRIBUTIONS: REVIEW AND IDENTIFICATION OF FACTORS THAT INFLUENCE THE SCALING EXPONENT

Fitting a power law to a rockfall frequency-magnitude distribution is a common tool for summarizing the shape of the distribution. The slope of the power law (i.e., the scaling exponent) has implications for the relative contribution of small and large rockfall volumes to overall activity and provides the basis for comparisons among inventories, estimation of recurrence intervals, and study of geomorphic processes. While the frequency-magnitude relationship is often used to summarize rockfall inventories, uncertainty remains regarding which variables control the shape of the distribution by affecting either rockfall processes directly (i.e., physical and environmental factors) or our measurement of the rockfall processes (i.e., systematic factors related to the methods chosen). In addition, the current literature lacks concise summaries of background on the frequency-magnitude distribution for rockfalls and power law fitting. To help address these knowledge gaps, we first briefly review the rockfall frequency literature to collect the basic concepts, methods, and applications of the rockfall frequency-magnitude curve in one place. Following this, we present a new meta-analysis of 46 rockfall inventories using Analysis of Variance and Regression to test the influences of 11 independent physical and systematic factors on the slope of the power law. Notable relationships with the scaling exponent were observed for rockmass condition, geology, and maximum inventory volume. Other factors, such as climate, data collection frequency, and data collection method also appear to have some influence on the scaling exponent, though the evidence from this study is more nuanced. In line with previous work, this study reinforces the importance of sampling large volumes for obtaining an accurate distribution, along with the tradeoffs present among spatial resolution, temporal resolution, and temporal extent when developing rockfall inventories. We conclude with discussion of the implications of these results for future rockfall studies.