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Modelling the spatio-temporal repartition of right-truncated data: an application to avalanche runout altitudes in Hautes-Savoie

  • A. Lavigne
  • N. Eckert
  • L. Bel
  • M. Deschâtres
  • E. Parent
Original Paper

Abstract

In this paper, we propose a novel approach for generating avalanche hazard maps based on the spatial dependence of avalanche runout altitudes. The right-truncated data are described with a Bayesian hierarchical model in which the spatio-temporal process is assumed to be the sum of independent spatial and temporal terms. Topography is roughly taken into account according to valley altitude and path exposition, and the spatial dependence is modelled with a Matérn covariance function. An application is performed to the Haute-Savoie region, French Alps. A spatial dependence in runout altitudes is identified, and an effective range of about 10 km is inferred. The temporal trend extracted highlights the increase of avalanche runout altitudes from 1955, attributed to both anthropogenic factors and climate warming. In a cross validation scheme, spatial predictions are provided on undocumented paths using kriging equations. All in all, although our model is unable to take into account small topographic features, it is a first-ever approach that produces very encouraging results. It could be enhanced in future work by incorporating a numerical physically-based code into the modelling.

Keywords

Bayesian hierarchical model Geostatistic Snow avalanche Truncated data 

Notes

Acknowledgments

The authors thank the ANR research program MOPERA (Modlisation probabiliste pour l’ Etude du Risque d’Avalanche http://www.avalanches.fr/mopera-projet/) for funding this work.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • A. Lavigne
    • 1
  • N. Eckert
    • 2
  • L. Bel
    • 3
  • M. Deschâtres
    • 2
  • E. Parent
    • 3
  1. 1.Université Lille 3 / LEM-CNRS (UMR 9221)Villeneuve d’AscqFrance
  2. 2.UR ETGR, Irstea / Université Grenoble AlpesSt Martin d’HèresFrance
  3. 3.UMR MIA-Paris, AgroParisTech, INRAUniversité Paris-SaclayParisFrance

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