Exploring the magnitude–frequency distribution: a cellular automata model for landslides

Abstract

Landslide magnitude–frequency curves allow for the probabilistic characterization of regional landslide hazard. There is evidence that landslides exhibit self-organized criticality including the tendency to follow a power law over part of the magnitude–frequency distribution. Landslide distributions, however, also typically exhibit poor agreement with the power law at smaller sizes in a flattening of the slope known as rollover. Understanding the basis for this difference is critical if we are to accurately predict landslide hazard, risk or landscape denudation over large areas. One possible argument is that the magnitude–frequency distribution is dominated by physiographic controls whereby landslides tend to a larger size, and larger landslides are landscape limited according to a power law. We explore the physiographic argument using first a simple deterministic model and then a cellular automata model for watersheds in coastal British Columbia. The results compare favorably to actual landslide data: modeled landslides bifurcate at local elevation highs, deposit mass preferentially where the local slopes decrease, find routes in confined valley or channel networks, and, when sufficiently large, overwhelm the local topography. The magnitude–frequency distribution of both the actual landslides and the cellular automata model follow a power law for magnitudes higher than 10,000–20,000 m2 and show a flattening of the slope for smaller magnitudes. Based on the results of both models, we argue that magnitude–frequency distributions, including both the rollover and the power law components, are a result of actual physiographic limitations related to slope, slope distance, and the distribution of mass within landslides. The cellular automata model uses simple empirically based rules that can be gathered for regions worldwide.