The characterization of landslide size distributions

Landslide size distributions generally exhibit power-law scaling over a limited scale range. The range is set by the mapping resolution, by the number of observed events, and by the slope failure process itself. This property of self-similarity is an important insight into the physics of hillslope failure. Typically, however, a large proportion of the landslide data does not fit a simple power law. These data are always ignored in order to characterize the scaling. We show that landslide data sets from New Zealand and Taiwan exhibit two scaling regimes, separated by a crossover scale that is purely an artefact of mapping resolution. Below this scale the landslide data are undersampled. We propose a general model for the size distribution of observed landslides which can account for the whole population of mapped slope failures. The model quantifies the undersampling of smaller landslides and provides an improved estimation of the power-la cv scaling of larger landslides. Estimates of this scaling suggest that the area disturbed by landsliding, and perhaps the landslide sediment yield, are essentially dependent on the frequency of smaller landslides. Higher resolution landslide maps will be required in order to quantify these fluxes. Our results also indicate that the probability of extreme landslide events is less than previous studies would predict.