Controls on the size distributions of shallow landslides

Rainfall-triggered shallow landslides are destructive hazards and play an important role in landscape processes. A theory explaining the size distributions of such features remains elusive. Prior work connects size distributions to topography, but field-mapped inventories reveal pronounced similarities in the form, mode, and spread of distributions from diverse landscapes. We analyze nearly identical distributions occurring in the Oregon Coast Range and the English Lake District, two regions of strikingly different topography, lithology, and vegetation. Similarity in minimum sizes at these sites is partly explained by theory that accounts for the interplay of mechanical soil strength controls resisting failure. Maximum sizes, however, are not explained by current theory. We develop a generalized framework to account for the entire size distribution by unifying a mechanistic slope stability model with a flexible spatial-statistical description for the variability of hillslope strength. Using hillslope-scale numerical experiments, we find that landslides can occur not only in individual low strength areas but also across multiple smaller patches that coalesce. We show that reproducing observed size distributions requires spatial strength variations to be strongly localized, of large amplitude, and a consequence of multiple interacting factors. Such constraints can act together with the mechanical determinants of landslide initiation to produce size distributions of broadly similar character in widely different landscapes, as found in our examples. We propose that size distributions reflect the systematic scale dependence of the spatially averaged strength. Our results highlight the critical need to constrain the form, amplitude, and wavelength of spatial variability in material strength properties of hillslopes.