Space-time landslide predictive modelling

Landslides are nearly ubiquitous phenomena and pose severe threats to people, properties, and the environment in many areas. Investigators have for long attempted to estimate landslide hazard in an effort to determine where, when (or how frequently), and how large (or how destructive) landslides are expected to be in an area. This information may prove useful to design landslide mitigation strategies, and to reduce landslide risk and societal and economic losses. In the geomorphology literature, most of the attempts at predicting the occurrence of populations of landslides by adopting statistical approaches are based on the empirical observation that landslides occur as a result of multiple, interacting, conditioning and triggering factors. Based on this observation, and under the assumption that at the spatial and temporal scales of our investigation individual landslides are discrete "point" events in the landscape, we propose a Bayesian modelling framework for the prediction of the spatio-temporal occurrence of landslides of the slide type caused by weather triggers. We build our modelling effort on a Log-Gaussian Cox Process (LGCP) by assuming that individual landslides in an area are the result of a point process described by an unknown intensity function. The modelling framework has two stochastic components: (i) a Poisson component, which models the observed (random) landslide count in each terrain subdivision for a given landslide "intensity", i.e., the expected number of landslides per terrain subdivision (which may be transformed into a corresponding landslide "susceptibility"); and (ii) a Gaussian component, used to account for the spatial distribution of the local environmental conditions that influence landslide occurrence, and for the spatio-temporal distribution of "unobserved" latent environmental controls on landslide occurrence. We tested our prediction framework in the Collazzone area, Umbria, Central Italy, for which a detailed multi-temporal landslide inventory covering the period from before 1941 to 2014 is available together with lithological and bedding data. We subdivided the 79 km2 area into 889 slope units (SUs). In each SU, we computed the mean and standard deviation of 16 morphometric covariates derived from a 10 m × 10 m digital elevation model. For 13 lithological and bedding attitude covariates obtained from a 1:10,000 scale geological map, we computed the proportion of each thematic class intersecting the given SU. We further counted how many of the 3,379 landslides in the multi-temporal inventory affect each SU and grouped them into six periods. We used this complex space-time information to prepare five models of increasing complexity. Our "baseline" model (Mod1) carries the spatial information only through the covariates mentioned above. It does not include any additional information about the spatial and temporal structure of the data, and it is therefore equivalent to the predominantly used landslide susceptibility model in the literature. The second model (Mod2) is analogous, but it allows for time-interval-specific regression constants. Our next two models are more complex. In particular, our third model (Mod3) also accounts for latent spatial dependencies among neighboring SUs. These are inferred for each of the six time intervals, to explain variations in the landslide intensity and susceptibility not explained by the thematic covariates. By contrast, our fourth model (Mod4) accounts for the latent temporal dependence, separately for each SU, disregarding neighboring influences. Ultimately, our most complex model (Mod5) contextually features all these relations. It contains the information carried by morphometric and thematic covariates, six time-interval-specific regression constants, and it also accounts for the latent temporal effects between consecutive slope instabilities at specific SUs as well as the latent spatial effects between adjacent SUs. We also show that the intensity is strongly related to the aggregated landslide area per SU. Because of this, our most complex model largely fulfills the definition of landslide hazard commonly accepted in the literature, at least for this study area. We quantified the spatial predictive performance of each of the five models using a 10-fold cross-validation procedure, and the temporal predictive performance using a leave-one-out cross-validation procedure. We found that Mod5 performed better than the others. We then used it to test a novel strategy to classify the model results in terms of both landslide intensity and susceptibility, which provides more information than traditional susceptibility zonations for land planning and management--hereafter we use the term "traditional" simply to refer to the majority of modelling procedures in the literature. We discuss the advantages and limitations of the new modelling framework, and its potential application in other areas, making specific and general hazard and geomorphological considerations. We also give a perspective on possible developments in landslide prediction modelling and zoning. We expect our novel approach to the spatio-temporal prediction of landslides to enhance the currently limited ability to evaluate landslide hazard and its temporal and spatial variations. We further expect it to lead to better projections of future landslides, and to improve our collective understanding of the evolution of complex landscapes dominated by mass-wasting processes under multiple geophysical and weather triggers.