variation partitioning environment space time rcode rscript

We found that Mod5 performed better than the others. 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.

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 also show that the intensity is strongly related to the aggregated landslide area per SU. 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. Ultimately, our most complex model (Mod5) contextually features all these relations. By contrast, our fourth model (Mod4) accounts for the latent temporal dependence, separately for each SU, disregarding neighboring influences. 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. In particular, our third model (Mod3) also accounts for latent spatial dependencies among neighboring SUs. The second model (Mod2) is analogous, but it allows for time-interval-specific regression constants. 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. Our “baseline” model (Mod1) carries the spatial information only through the covariates mentioned above. We used this complex space-time information to prepare five models of increasing complexity. We further counted how many of the 3,379 landslides in the multi-temporal inventory affect each SU and grouped them into six periods. 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. In each SU, we computed the mean and standard deviation of 16 morphometric covariates derived from a 10 m × 10 m digital elevation model. We subdivided the 79 km 2 area into 889 slope units (SUs). 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. 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 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. 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.

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.

This information may prove useful to design landslide mitigation strategies, and to reduce landslide risk and societal and economic losses. 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. Landslides are nearly ubiquitous phenomena and pose severe threats to people, properties, and the environment in many areas.

Variation partitioning environment space time rcode rscript