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 m
2 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.
Keywords Debris slides - Debris flows - Cellular automata - Magnitude–frequency - Landslides