A model for spatio‐temporal clustering using multinomial probit regression: application to avalanche counts

Abstract

Although modeling complex environmental spatio‐temporal processes, separability between time and space effects is often assumed as a first approach, even though it may be unrealistic. Hence, the development of adapted non‐separable spatio‐temporal models is a challenging issue. In this work, we are interested in modeling avalanche counts over the whole French Alps, a large area that exhibits zones characterized by distinct climatic behaviors. We have at our disposal a data set of 405, 63‐year series of avalanche counts, one series for one township. We assume the series can be divided into several spatial clusters presenting specific temporal trends. On the latent layer of a hierarchical negative binomial‐lognormal structure, the clusters are characterized by independent temporal evolutions, modeled using smoothing splines. The clusters arise as the result of a multinomial probit regression, with spatial coordinates used as covariates. Inference is performed within the Bayesian hierarchical framework. The number of clusters is assessed using cross validation. The best score is obtained for a three‐cluster model, but other configurations also share some evidence. The first cluster is located in the east of the French Alps, whereas the others are located together in the west part of the French Alps. The three contrasted temporal trends corresponding to the three clusters result from regional climate change effects, interacting with a strong altitudinal control and data limitation. The proposed model could be used for analyzing various other climatic and environmental data sets. Copyright © 2012 John Wiley & Sons, Ltd.

Impact du réchauffement climatique sur l'activité avalancheuse et multiplication des avalanches humides dans les Alpes françaises

“…Le « recul des avalanches » ensuite observé, accompagné d'une diminution de la proportion des avalanches avec aérosol s'inscrit quant à lui dans une période de réchauffement marqué. Enfin, depuis quelques années (2000) Ce schéma global masque en réalité des évolutions différenciées contrôlées par l'altitude [Lavigne et al, 2012 ;2015]. A basse altitude, la réduction d'activité depuis 1980 environ a été drastique, en lien avec la forte réduction de l'enneigement induite par le réchauffement climatique.…”

Adding Expert Contributions to the Spatiotemporal Modelling of Avalanche Activity Under Different Climatic Influences

“…In Lavigne et al . (), based on the hypothesis that avalanche frequency temporal trends should be different in the two subregions, a model‐based clustering approach was designed. In Eckert et al .…”

“…In the French Alps, data coming from a systematic survey of avalanche events which began at the beginning of the 20th century is available. However, even though adapted probabilistic models are now well developed (Eckert et al ., , ; Eckert, Parent, Kies and Bays, ; Lavigne et al ., ), complementary expertise is needed to account for the specific complexity of the entire region.…”

Dynamics of glide avalanches and snow gliding

“…[ Beniston , ; Adam et al , ; Bebi et al , ; Keiler et al , ; Stoffel and Huggel , ]. Climate change is therefore likely to influence the occurrence of damage due to avalanches; however, the exact trend remains undecided and will be highly dependent on the region concerned [ Lavigne et al , ; Castebrunet et al , ; McClung , ]. Some studies have concluded that there is no clear correlation between the frequency of extreme events and climatic conditions [ Schneebeli et al , ; Eckert et al , ], whereas others have provided evidence that the runout distance of extreme avalanches has decreased since the mid‐1970s [ Eckert et al , ].…”