Landslide inventories and their statistical properties

Landslides are generally associated with a trigger, such as an earthquake, a rapid snowmelt or a large storm. The landslide event can include a single landslide or many thousands. The frequency-area (or volume) distribution of a landslide event quantifies the number of landslides that occur at different sizes. We examine three well-documented landslide events, from Italy, Guatemala and the USA, each with a different triggering mechanism, and find that the landslide areas for all three are well approximated by the same three-parameter inverse-gamma distribution. For small landslide areas this distribution has an exponential 'roll-over' and for medium and large landslide areas decays as a power-law with exponent -2-40. One implication of this landslide distribution is that the mean area of landslides in the distribution is independent of the size of the event. We also introduce a landslide-event magnitude scale m(L) = log(N-LT), with N-LT the total number of landslides associated with a trigger. If a landslide-event inventory is incomplete (i.e. smaller landslides are not included), the partial inventory can be compared with our landslide probability distribution, and the corresponding landslide-event magnitude inferred. This technique can be applied to inventories of historical landslides, inferring the total number of landslides that occurred over geologic time, and how many of these have been erased by erosion, vegetation, and human activity. We have also considered three rockfall-dominated inventories, and find that the frequency-size distributions differ substantially from those associated with other landslide types. We suggest that our proposed frequency-size distribution for landslides (excluding rockfalls) will be useful in quantifying the severity of landslide events and the contribution of landslides to erosion.