Size and frequency of large landslides from different incomplete inventories

Landslide catalogues have grown such that they allow for increasingly robust estimates of the size scaling of slope failures. Relationships between landslide volume, area, and their relative abundance provide useful insight into quantitative models of hillslope stability, hazard and risk, and landscape evolution. Numerous studies concur that smaller landslides are systematically more frequent than larger ones, and fitted various probability distributions to mapped landslide areas or volumes to capture this inverse relationship. However, especially the larger and commensurately rarer landslides (defined here as affecting footprint areas ≥0.1 km²) tend to eldude these statistical analyses. Thus, it remains unclear as to how an extrapolation of models derived from smaller landslides is valid beyond the size range identified for a given study area. Similarly, it can be problematic to use scaling statistics from other inventories because of likely differing methods of landslide detection and mapping, data quality, resolution, sample size, model choice, and fitting. We propose a multi-level Bayesian Generalised Pareto model as common ground for consistently estimating and comparing size distributions of large slope failures from different catalogues. The model remediates the problem of small sample size and makes use of all available data from thousands of landslides across several dozens of databases. The underlying peak-over-threshold approach is firmly rooted in extreme-value theory and offers a statistical reference against which any physical interpretations of landslide scaling statistics can be compared. We find that, despite a broad set of mapping protocols and lengths of record, and differing topographic, geological, and climatic conditions, the posterior power-law exponents remain indistinguishable between most inventories. The same goes for known earthquake from rainfall triggers, and event-based from multi-temporal catalogues. However, our model identifies several inventories with outlier scaling statistics that more likely result from censoring effects during the mapping or compilation process. We thus caution against a universal or solely mechanistic interpretation of scaling parameters, at least concerning large landslides. Some of this physical meaning might get diluted, mixed, or even lost in empirical data that combine confounding controls.