Landslide inventories and their statistical properties

Abstract

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.

Analysis of a landslide multi-date inventory in a complex mountain landscape: the Ubaye valley case study

“…Frequencymagnitude relationships for different locations and landslide types are frequently considered as a proxy for landslide magnitude (van den Eeckhaut et al, 2007;Florsheim and Nichols, 2013;Malamud et al, 2004;Schlögel et al, 2011;Guzzetti et al, 2006). In order to complete the quantitative analysis of the multi-date inventory, landslide temporal probability can also be assessed using a Poisson model.…”

“…Two size distribution models were proposed in the literature: (1) the Double Pareto distribution (Stark and Hovius, 2001) defined by a positive and a negative power scaling, and (2) the Inverse Gamma distribution (Malamud et al, 2004) defined by a power-law decay for medium and large landslides and an exponential rollover for small landslides. According to best-fit criteria on our data, we choose a maximum-likelihood fit of the simplified version of the double Pareto (DPS) distribution defined by Eq.…”

“…Inventory maps are either archive or geomorphological inventories (Guzzetti et al, 2000;Malamud et al, 2004). Archive inventories include landslides information obtained from the literature, or other archive sources (Reichenbach et al, 1998;Salvati et al, 2003).…”

Integrating rockfall risk assessment and countermeasure design by 3D modelling techniques

“…This requires knowing or assuming the relationship which describes the magnitude-frequency distribution of rockfall events in a given area characterised by specific geological and geomorphological features. For landslides, different magnitude-frequency relationships both in terms of area and volume have been used (Stark and Hovius, 2001;Guzzetti et al, 2002;Malamud et al, 2004). As to rockfalls, several authors (Hungr et al, 1999;Dussauge et al, 2003;Malamud et al, 2004) demonstrated that the magnitude-cumulative frequency (MCF) distribution of events in given volume classes j can be described by a power law in the form:…”

Probabilistic landslide hazard assessment using homogeneous susceptible units (HSU) along a national highway corridor in the northern Himalayas, India

“…Recently, several studies have been carried out to determine the probability of landslide magnitude (area or volume) using frequency-area or frequency-volume statistics of landslides (Malamud et al 2004). The probability of the landslide size, in terms of it affecting an area greater or equal than a given size, can be modelled using probability density functions, as suggested by Malamud et al (2004).…”