Numerical recipes for landslide spatial prediction by using R-INLA: A step-by-step tutorial

The geomorphological community typically assesses the landslide susceptibility at the catch- ment or larger scales through spatial predictive models. However, the spatial information is conveyed only through the geographical distribution of the covariates. Spatial dependence, which allows capturing similarities at neighboring sites that are not directly explained by covariate information, is typically not accounted for in the landslides literature, whilst such spatial models have become commonplace in the geostatistical literature. Here we explain step by step how to rigorously model and predict activations of debris flow based on an adequate statistical model by using the R-INLA library from the statistical software R in the context of a real multiple landslide event. This chapter follows the analysis of Lombardo et al. (2018a) with a few modifications; it is written in a tutorial style to provide the geomor- phological community with a hands-on guide to replicate similar analyses in R. While our focus here is on implementation and computing, more details about the underlying statistical theory, modeling and estimation can be found in Lombardo et al. (2018a). Our modeling approach deviates fundamentally from the commonly-used regression models fitted to binary presence/absence data. Specifically, we use a Bayesian hierarchical Cox point process model to describe landslide counts at high resolution (i.e., at the pixel level), while capturing spatial dependence through a latent spatial effect defined at lower resolution over slope units. Our point process modeling approach allows us to derive the distribution of aggregated landslide counts for any areas of interest. Crucially, the latent spatial effect represents the unexplained but spatially structured component in the data when the linear or nonlinear effects of covariates are removed. Thus, in the case of sparse raingauge or seismic networks, we suggest using the latent spatial effect to uncover the trigger distribution over space. In particular, for landslides triggered by extreme precipitation, the meteorological stress can play a dominant role with respect to the covariates that are typically introduced in predictive models; therefore, accounting for the trigger in modeling may dramatically improve the performance of landslide prediction.