Controls on the magnitude-frequency scaling of an inventory of secular landslides
Linking landslide size and frequency is important at both human and geological timescales for quantifying both landslide hazards and the effectiveness of landslides in the removal of sediment from evolving landscapes. The statistical behaviour of the magnitude-frequency of landslide inventories is usually compiled following a particular triggering event such as an earthquake or storm, and their statistical behaviour is often characterised by a power-law relationship with a small landslide rollover. The occurrence of landslides is expected to be influenced by the material properties of rock and/or regolith in which failure occurs. Here we explore the statistical behaviour and the controls of a secular landslide inventory (SLI) (i.e. events occurring over an indefinite geological time period) consisting of mapped landslide deposits and their underlying lithology (bedrock or superficial) across the United Kingdom. The magnitude-frequency distribution of this secular inventory exhibits an inflected power-law relationship, well approximated by either an inverse gamma or double Pareto model. The scaling exponent for the power-law scaling of medium to large landslides is α = −1.71 ± 0.02. The small-event rollover occurs at a significantly higher magnitude (1.0–7.0 × 10 −3 km 2) than observed in single-event landslide records (~ 4 × 10 −3 km 2). We interpret this as evidence of landscape annealing, from which we infer that the SLI underestimates the frequency of small landslides. This is supported by a subset of data where a complete landslide inventory was recently mapped. Large landslides also appear to be under-represented relative to model predictions. There are several possible reasons for this, including an incomplete data set, an incomplete landscape (i.e. relatively steep slopes are under-represented), and/or temporal transience in landslide activity during emergence from the last glacial maximum toward a generally more stable late-Holocene state. The proposed process of landscape annealing and the possibility of a transient hillslope response have the consequence that it is not possible to use the statistical properties of the current SLI database to rigorously constrain probabilities of future landslides in the UK.