Hierarchical Bayesian modelling for spatial analysis of the number of avalanche occurrences at the scale of the township N. Eckert a, ⁎ , E. Parent b , L. Bélanger a , S. Garcia a a UR ETNA, Cemagref Grenoble, BP 76, 38 402 Saint Martin d'Hères, France b Equipe MORSE, UMR 518 ENGREF/INRA/INAPG, 19 avenue du Maine, F-75732 Paris Cedex 15, France Received 31 August 2006; accepted 31 January 2007 Abstract The quantification of avalanche frequencies is necessary to compute snow avalanche return periods. In France, more than 5000 selected avalanche paths have been surveyed by forest rangers since the beginning of the 20th century. Few avalanches occur every year, but a spatial analysis makes it possible to overcome the sparseness of local data. An intermediate scale such as the township avoids errors in path localization and allows information to be transferred between neighboring paths. A statistical model inspired by spatial epidemiology is proposed. It associates a discrete Poisson model at the township scale and a latent autocorrelated field with neighboring relationships based on township boundaries. Spatial heterogeneity in avalanche frequencies is quantified and local noise is distinguished from the spatial structure. Model inference and predictive sampling are advantageously carried out in a hierarchical Bayesian modelling framework using Markov Chain Monte Carlo simulation methods. The illustrative example concerns the department of Savoie with 124 townships and 18,755 avalanches. The number of paths surveyed per township is used for data standardisation. Surprisingly, the spatial structure explains approximately 60% of the total variability of avalanche frequencies. Predictive values at the scale of the township range from 0.01 avalanches per year and path to 1.4 avalanches per year and path. Model validation, modelling hypotheses and possible extensions are discussed. © 2007 Elsevier B.V. All rights reserved. Keywords: Avalanche frequency; Township; Spatial field; Hierarchical Bayesian modelling 1. Introduction An increasing demographic pressure and recent catastrophic events (Glass et al., 2000; SLF Davos, 2000) have renewed interest in avalanche predetermina- tion in European countries. Predetermination means producing hazard maps where an annual probability of an event of given intensity occurring is computed for each avalanche path. Without avalanche frequencies, all prob- abilities that can be estimated using data are conditional to release. Predetermination of extreme avalanches therefore involves the quantification of both magnitude and frequency of possible damageable events so as to define reference hazards in terms of return periods (Ancey et al., 2004; Eckert et al., in press-a). Magnitude variations on a given path are discussed by many authors (Lied and Bakkehoi, 1980; McClung and Lied, 1987; Bozhinskiy et al., 2001; etc.) and are not investigated in this paper. Analysing avalanche frequen- cies is also obviously not new. The empirical estimation of the local avalanche frequency with reasonable con- fidence levels is possible on well-documented avalanche paths, but it turns out to be very difficult when few or no Cold Regions Science and Technology 50 (2007) 97 – 112 www.elsevier.com/locate/coldregions ⁎ Corresponding author. Tel.: +33 476762222, +33 476513803. E-mail address: nicolas.eckert@cemagref.fr (N. Eckert). 0165-232X/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.coldregions.2007.01.008