Size scaling of large landslides from incomplete inventories

Abstract. Landslide inventories have become cornerstones for estimating the relationship between the frequency and size of slope failures, thus informing appraisals of hillslope stability, erosion, and commensurate hazard. Numerous studies have reported how larger landslides are systematically rarer than smaller ones, drawing on probability distributions fitted to mapped landslide areas or volumes. In these models, much uncertainty concerns the larger landslides (defined here as affecting areas ≥ 0.1 km2) that are rarely sampled and often projected by extrapolating beyond the observed size range in a given study area. Relying instead on size-scaling estimates from other inventories is problematic because landslide detection and mapping, data quality, resolution, sample size, model choice, and fitting method can vary. To overcome these constraints, we use a Bayesian multi-level model with a generalised Pareto likelihood to provide a single, objective, and consistent comparison grounded in extreme value theory. We explore whether and how scaling parameters vary between 37 inventories that, although incomplete, bring together 8627 large landslides. Despite the broad range of mapping protocols and lengths of record, as well as differing topographic, geological, and climatic settings, the posterior power-law exponents remain indistinguishable between most inventories. Likewise, the size statistics fail to separate known earthquakes from rainfall triggers and event-based triggers from multi-temporal catalogues. Instead, our model identifies several inventories with outlier scaling statistics that reflect intentional censoring during mapping. Our results thus caution against a universal or solely mechanistic interpretation of the scaling parameters, at least in the context of large landslides.