Constraining mean landslide occurrence rates for non-temporal landslide inventories using high-resolution elevation data

Constraining landslide occurrence rates can help to generate landslide hazard models that predict the spatial and temporal occurrence of landslides. However, most landslide inventories do not include any temporal data due to the difficulties of dating landslide deposits. Here we introduce a method for estimating the mean landslide occurrence rate of deep-seated rotational and translational slides derived solely from high-resolution (≤3 m) elevation data and globally available estimates of the diffusion coefficient for sediment flux. The method applies a linear diffusion model to the roughest landslide deposits until they reach a representative non-landslide roughness distribution. This estimates the time for a landslide deposit to be unrecognizable in high-resolution digital elevation data, which we term the mean lifetime of the landslide. Using the mean lifetime and number of landslides within an area of interest, we can estimate the mean occurrence rate of landslides over that domain. We validate this approach using a comprehensive temporal inventory of landslides in western Oregon created using age-roughness curves that are calibrated with high-resolution elevation data and radiocarbon data. We find good agreement between our diffusion method and the existing age-roughness-derived estimates, producing mean lifetimes of 4500 and 5200 years (4% difference), respectively. Hazard maps produced using the two methodologies generally agree, with the maximum differences in landslide probability reaching 0.1. Due to the relative abundance of high-resolution elevation data compared with age-dated landslides, our method could help constrain landslide occurrence rates in areas previously considered unfeasible.