Climatic Change

, Volume 101, Issue 3–4, pp 515–553 | Cite as

A spatio-temporal modelling framework for assessing the fluctuations of avalanche occurrence resulting from climate change: application to 60 years of data in the northern French Alps

Article

Abstract

Based on a previous township-scale model, a spatio-temporal framework is proposed to study the fluctuations of avalanche occurrence possibly resulting from climate change. The regional annual component is isolated from the total variability using a two-factor nonlinear analysis of variance. Moreover, relying on a Conditional AutoRegressive sub-model for the spatial effects, the structured time trend is distinguished from the random noise with different time series sub-models including autocorrelative, periodic and change-point models. The hierarchical structure obtained takes into account the uncertainty related to the estimation of the annual component for the quantification of the time trend. Bayesian inference is performed using Monte Carlo simulations. This allows a comparison of the different time series models and the prediction of future activity in an explicit unsteady context. Application to the northern French Alps illustrates the information provided by the model’s different components, mainly the spatial and temporal terms as well as the spatio-temporal fluctuation of the relative risk. For instance, it shows no strong modifications in mean avalanche activity or in the number of winters of low or high activity over the last 60 years. This suggests that climate change has recently had little impact on the avalanching rhythm in this region. However, significant temporal patterns are highlighted: a complex combination of abrupt changes and pseudo-periodic cycles of approximately 15 years. For anticipating the future response of snow avalanches to climate change, correlating them with fluctuations of the constraining climatic factors is now necessary.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akaike H (1981) Likelihood of a model and information criteria. J Econom 16:3–14CrossRefGoogle Scholar
  2. Ancey C (2005) Impact du réchauffement climatique. Technical report. Available online at http://www.toraval.fr/rechauffement.php
  3. Ancey C, Rapin F, Martin E, Coleou C et al (2000) L’avalanche de Péclerey du 9 février 1999. Houille Blanche 5:45–53CrossRefGoogle Scholar
  4. Bader S, Kunz P (2000) Climate risks—The challenge for Alpine Region - PNR31. Ed. by Zürich: vdf Hochschuverlag AG an der ETH. Zürich, 291 ppGoogle Scholar
  5. Banerjee S, Carlin B, Gelfand AE (2003) Hierarchical modeling and analysis for spatial data. Chapman & Hall, 472 ppGoogle Scholar
  6. Barbolini M, Keylock CJ (2002) A new method for avalanche hazard mapping using a combination of statistical and deterministic models. Nat Hazards Earth Syst Sci 2:239–245CrossRefGoogle Scholar
  7. Bayes T (1763) Essay towards solving a problem in the doctrine of chances. Philos Trans R Soc Lond 53:370–418; 54:296–325CrossRefGoogle Scholar
  8. Bélanger L, Cassayre Y (2004) Projects for past avalanche observation and zoning in France, after 1999 catastrophic avalanches. In: Proceedings of the international snow science workshop, Jackson Hole, Wyoming, 19–24 September 2004, pp 416–422Google Scholar
  9. Beniston M (1997) Variations of snow depth and duration in the Swiss Alps over the last 50 years: links to changes in large-scale climatic forcings. Clim Change 36(3–4):281–300CrossRefGoogle Scholar
  10. Beniston M (2005) Warm winter spells in the Swiss Alps: strong heat waves in a cold season? A study focusing on climate obsrvations at the Saentis high mountain site. Geophys Res Lett 32:L01812. doi:10.1029/2004GL021478 CrossRefGoogle Scholar
  11. Berger JO (1985) Statistical decision theory and Bayesian analysis, 2nd edn. Springer, 617 ppGoogle Scholar
  12. Bernier J (1993) Statistical detection of changes in geophysical series. In: Engineering risk and reliability in a changing physical environment. Proc. NATO Advanced Study Institute, Deauville, France, 24 May–4 June 1993Google Scholar
  13. Besag J, York J, Mollié A (1991) Bayesian image restoration, with two applications in spatial statistics. Ann Inst Stat Math 43:1–59 (with discussion)CrossRefGoogle Scholar
  14. Best N, Richardson S, Thomson A (2004) A comparison of Bayesian spatial models for disease mapping. Stat Methods Med Res 14(1):35–59CrossRefGoogle Scholar
  15. Bloomfield P (1992) Trends in global temperature. Clim Change 21(1):1–16CrossRefGoogle Scholar
  16. Bocchiola D, Medagliani M, Rosso R (2006) Regional snow depth frequency curves for avalanche hazard mapping in central Italian Alps. Cold Reg Sci Technol 46(3):204–222CrossRefGoogle Scholar
  17. Booth NB, Smith AFM (1982) A Bayesian approach to retrospective identification of change-points. J Econom 19(1):7–22CrossRefGoogle Scholar
  18. Box GEP, Jenkins GM (1976) Time series analysis: forecasting and control. Holden-Day series in time series analysis. San Francisco, 575 ppGoogle Scholar
  19. Brooks SP (1998) Markov Chain Monte Carlo Method and its application. Statistician 47(1):69–100Google Scholar
  20. Brooks SP, Gelman A (1998) General methods for monitoring convergence of iterative simulations. J Comput Graph Stat 7(4):434–455CrossRefGoogle Scholar
  21. Cappé O, Moulines E, Rydèn T (2005) Inference in Hidden Markov models. Springer, 678 ppGoogle Scholar
  22. Carlin JB, Chib S (1995) Bayesian model choice via Markov chain Monte Carlo methods. J R Stat Soc Ser B 57:473–484Google Scholar
  23. Carlin BP, Gelfand AE, Smith AFM (1992) Hierarchical Bayesian analysis of changepoint problems. Appl Stat 41(2):389–405CrossRefGoogle Scholar
  24. Cemagref ETNA (2000) Commune de Chamonix Mont Blanc, projet de Centre de secours principal près des Pélerins, étude du risque d’avalanche. Rapport d’expertise, F. Rapin coordGoogle Scholar
  25. Cemagref ETNA (2008) Détection de certains événements manquants de l’EPA. 5p. Rapport technique à la DPPR. Available online at http://www.avalanches.fr/
  26. Clark JS (2005) Why environmental scientists are becoming bayesians. Ecol Lett 8:2–14CrossRefGoogle Scholar
  27. Clark JS, Gelfand A (2006) Computational statistics: hierarchical Bayes and MCMC methods in the environmental. Oxford University Press, 205 ppGoogle Scholar
  28. Cosse JM, Vauterin P, Belanger L, Garcia S (2005) Regards croisés sur l’épisode neigeux de janvier 2004 dans les Hautes Alpes. Neige et Avalanches 109Google Scholar
  29. Diaz J (1982) Bayesian detection of a change of scale parameter in sequences of independent gamma random variables. J Econom 19(1):23–29CrossRefGoogle Scholar
  30. Diongue S, Eckert N (2006) Caractérisation des crues avalancheuses affectant les départements français. Rapport Cemagref ETNA diffusé aux services RTM. 16p. Available online at http://www.avalanches.fr/
  31. Dullinger S, Dirnböck T, Grabherr G (2004) Modelling climate change-driven treeline shifts: relative effects of temperature increase, dispersal and invisibility. J Ecol 92(2):241–252CrossRefGoogle Scholar
  32. Eckert N, Garcia S, Bélanger L (2006) Bilan 2005/06 de l’Enquête Permanente sur les Avalanches. Neiges et Avalanches 116:6–9Google Scholar
  33. Eckert N, Parent E, Belanger L et al (2007a) Hierarchical modelling for spatial analysis of the number of avalanche occurrences at the scale of the township. Cold Reg Sci Technol 50:97–112CrossRefGoogle Scholar
  34. Eckert N, Parent E, Richard D (2007b) Revisiting statistical–topographical methods for avalanche predetermination: Bayesian modelling for runout distance predictive distribution. Cold Reg Sci Technol 49:88–107CrossRefGoogle Scholar
  35. Eckert N, Parent E, Naaim M, Richard D (2008a) Bayesian stochastic modelling for avalanche predetermination: from a general system framework to return period computations. Stoch Environ Res Risk Assess 22:185–206CrossRefGoogle Scholar
  36. Eckert N, Parent E, Faug T, Naaim M (2008b) Optimal design under uncertainty of a passive defense structure against snow avalanches: from a general Bayesian framework to a simple analytical model. Nat Hazards Earth Syst Sci 8:1067–1081CrossRefGoogle Scholar
  37. Elliott P, Wakefield J, Best N, Briggs D (2000) Spatial epidemiology, methods and applications. Oxford, 475 ppGoogle Scholar
  38. Elsasser H, Buerki R (2002) Climate change as a threat to tourism in the Alps. Clim Res 20:253–257CrossRefGoogle Scholar
  39. Etienne D (2006) Situations météorologiques synoptiques et risques d’avalanche. L’exemple de Vallorcine. Master 2 Evaluation et Gestion de l’Environnement et des Paysages de Montagne. Université Joseph Fourier—Institut de Géographie Alpine, Grenoble, France, 84 pp. Available online at http://www.avalanches.fr/ Google Scholar
  40. Fortin V, Perreault L, Salas JD (2004) Retrospective analysis and forecasting of streamflows using a shifting level model. J Hydrol 296:135–163CrossRefGoogle Scholar
  41. Fuhrer J, Beniston M, Fischlin A, Frei C, Goyette S, Jasper K, Pfister C (2006) Climate risks and their impact on agriculture and forests in Switzerland. Clim Change 79(1–2):79–106CrossRefGoogle Scholar
  42. Garcia S, Belanger L (2002) Analyse de la régularité des observations de l’Enquête Permanente sur les Avalanches. DESS Ingéniérie Mathématique. Université Joseph Fourrier, Grenoble, France, 101 pp. Available online at http://www.avalanches.fr/ Google Scholar
  43. Gassner M, Brabec B (2002) Nearest neighbour models for local and regional avalanche forecasting. Nat Hazards Earth Syst Sci 2:247–253CrossRefGoogle Scholar
  44. Gaucherel C, Campillo F, Misson L, Guiot G, Boreux JJ (2008) Parameterization of a process-based tree-growth model: comparison of optimization, MCMC and particle filtering algorithms. Environ Model Softw 23(10–11):1280–1288CrossRefGoogle Scholar
  45. Gelman A, Carlin JB, Stern HS, Rubin DB (1995) Bayesian data analysis. Chapman & Hall, 526 ppGoogle Scholar
  46. Geman S, Geman D (1984) Stochastic relaxation, Gibbs Distribution and the Bayesian Restoration of Images. IEEE Trans Pattern Anal Mach Intell Pami-6(6):721–741CrossRefGoogle Scholar
  47. Germain D, Filion L, Hétu B (2009) Snow avalanche regime and climatic conditions in the Chic-Choc Range, eastern Canada. Clim Change 91(1–2):141–167. doi:10.1007/s10584-008-9439-4 CrossRefGoogle Scholar
  48. Ghinoi A, Chang CJ (2005) STARTER: a statistical GIS-based model for the prediction of snow avalanche susceptibility using terrain features—application to Alta Val Badia, Italian Dolomites. Geomorphology 66:305–325CrossRefGoogle Scholar
  49. Gilks WR, Richardson S, Spiegelhalter DJ (2001) Markov Chain Monte Carlo in Practice. Chapman & Hall, 486 ppGoogle Scholar
  50. Hägeli P, McClung D (2003) Avalanche characteristics of a transitional snow climate-Columbia Mountains, British Columbia, Canada. Cold Reg Sci Technol 37(3):255–276CrossRefGoogle Scholar
  51. Hägeli P, McClung D (2007) Expanding the snow-climate classification with avalanche-relevant information: initial description of avalanche winter regimes for southwestern Canada. J Glaciol 53(181):266–276CrossRefGoogle Scholar
  52. Hebertson EG, Jenkins MJ (2003) Historic climate factors associated with major avalanche years on the Wasatch Plateau, Utah. Cold Reg Sci Technol 37(3):315–332CrossRefGoogle Scholar
  53. Hendrikx J, Owens I, Carran W, Carran A (2005) Avalanche activity in an extreme maritime climate: the application of classification trees for forecasting. Cold Reg Sci Technol 43(1–2):104–116CrossRefGoogle Scholar
  54. Hurrell JW (1995) Decadal trends in the North Atlantic Oscillation: regional temperatures and precipitation. Science 4 269(5224):676–679CrossRefGoogle Scholar
  55. Hurrell JW, Van Loon H (1997) Decadal variations in climate associated with the North Atlantic Oscillation. Clim Change 36(3–4):301–326CrossRefGoogle Scholar
  56. Jaedicke C, Bakkehoi S (2007) Climate database for avalanche consulting and warning in Norway. Cold Reg Sci Technol 47(1–2):171–179CrossRefGoogle Scholar
  57. Jamard AL, Garcia S, Bélanger L (2002) L’enquête permanente sur les Avalanches (EPA). Statistique descriptive générale des événements et des sites. DESS Ingéniérie Mathématique option Statistique. Université Joseph Fourrier, Grenoble, France, 101 pp. Available online at http://www.avalanches.fr/ Google Scholar
  58. Jomelli V, Pech P (2004) Effects of the little ice age on avalanche boulder tongues in the French Alps (Massif des Ecrins). Earth Surf Process Landf 29:553–564CrossRefGoogle Scholar
  59. Jomelli V, Pech P, Chochillon C, Brunstein D (2004) Geomorphic variations of debris flows and recent climatic change in the French Alps. Clim Change 64(1–2):77–102CrossRefGoogle Scholar
  60. Jomelli V, Delval C, Grancher D et al (2007) Probabilistic analysis of recent snow avalanche activity and climate in the French Alps. Cold Reg Sci Technol 47:180–192CrossRefGoogle Scholar
  61. Kass RE, Raftery AE (1995) Bayes factors. J Am Stat Assoc 90:773–795CrossRefGoogle Scholar
  62. Keller F, Goyette S, Beniston M (2005) Sensitivity analysis of snow cover to climate change scenarios and their impact on plant habitats in alpine terrain. Clim Change 72(3):299–319CrossRefGoogle Scholar
  63. Keylock CJ (2003) The North Atlantic Oscillation and snow avalanching in Iceland. Geophys Res Lett 30(5):1254. doi:10.1029/2002GL016272 CrossRefGoogle Scholar
  64. Keylock CJ, McClung D, Magnusson M (1999) Avalanche risk mapping by simulation. J Glaciol 45(150):303–314Google Scholar
  65. Kies R (2007) Modélisation spatiale et spatio-temporelle des occurrences avalancheuses à partir des données historiques contenues dans l’Enquête Permanente sur les Avalanches. Rapport de stage de master professionnel Ingénierie Statistique. Université Joseph Fourrier, Grenoble, France, 59 pp. Available online at http://www.avalanches.fr/
  66. Laternser M, Schneebeli M (2002) Temporal trend and spatial distribution of avalanche activity during the last 50 years in Switzerland. Nat Hazards 27:201–230CrossRefGoogle Scholar
  67. Lazar B, Williams M (2008) Climate change in western ski areas: potential changes in the timing of wet avalanches and snow quality for the Aspen ski area in the years 2030 and 2100. Cold Reg Sci Technol 51(2–3):219–228CrossRefGoogle Scholar
  68. Maggioni M (2005) Avalanche release Areas and their influence on uncertainty in avalanche hazard mapping. PhD thesis, University of ZurichGoogle Scholar
  69. Maggioni M, Gruber U (2003) The influence of topographic parameters on avalanche release and frequency. Cold Reg Sci Technol 37:407–419CrossRefGoogle Scholar
  70. Marchal L, Belanger L, Garcia S (2003) Corrélations météorologiques avec l’EPA (Enquête Permanente sur les Avalanches). Rapport IUP GMI option Mathématiques Appliquées et Industrielles. Université Joseph Fourier, Grenoble, France, 69 pp. Available online at http://www.avalanches.fr/
  71. Martin E, Giraud G, Lejeune Y, Boudart G (2001) Impact of climate change on avalanche hazard. Ann Glaciol 32:163–167CrossRefGoogle Scholar
  72. Marty C (2008) Regime shift of snow days in Switzerland. Geophys Res Lett 35:L12501. doi:10.1029/2008GL033998 CrossRefGoogle Scholar
  73. McClung D, Tweedy J (1994) Numerical avalanche prediction: Kootenay Pass, British Columbia, Canada. J Glaciol 40(135):350–358Google Scholar
  74. McCollister C, Birkeland K, Hansen K et al (2003) Exploring multi-scale spatial patterns in historical avalanche data, Jackson Hole Mountain Resort, Wyoming. Cold Reg Sci Technol 37:299–313CrossRefGoogle Scholar
  75. Mearns L, Rosenzweig C, Goldberg R (1997) Mean and variance change in climate scenarios: methods, agricultural applications, and measures of uncertainty. Clim Change 35(4):367–396CrossRefGoogle Scholar
  76. Menzefricke U (1981) A Bayesian analysis of a change in the precision of a sequence of independent normal random variables at an unknown time point. Appl Stat 30:141–146CrossRefGoogle Scholar
  77. Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machine. J Chem Phys 21:1087–1091CrossRefGoogle Scholar
  78. Meunier M, Ancey C (2004) Towards a conceptual approach to predetermining high-return-period avalanche run-out distances. J Glaciol 50–169:268–278CrossRefGoogle Scholar
  79. Meunier M, Ancey C, Naaim M (2001) Mise au point d’une méthode de prédétermination statistique des cotes d’arrêt d’avalanches. Houille Blanche 67:92–98CrossRefGoogle Scholar
  80. Michener WK, Blood ER, Bildstein KL, Brinson MM, Gardner LR (1997) Climate change, hurricanes and tropical storms, and rising sea level in coastal wetlands. Ecol Appl 7(3):770–801CrossRefGoogle Scholar
  81. Mock CJ, Birkeland KW (2000) Snow avalanche climatology of the western United States mountain ranges. Bull Am Meteorol Soc 81(1):2367–2392CrossRefGoogle Scholar
  82. Mollié A (1996) Bayesian mapping of disease. In: Gilks WR, Richardson S, Spiegelhalter DJ (eds) Markov Chain Monte Carlo in practice, 2nd edn (2001). Chapman & Hall, London, pp 359–379Google Scholar
  83. Mougin P (1922) Les avalanches en Savoie. Ministère de l’Agriculture, Direction Générale des Eaux et Forêts, Service des Grandes Forces Hydrauliques, Paris, pp 175–317Google Scholar
  84. Naaim M, Naaim-Bouvet F, Faug T, Bouchet A (2004) Dense snow avalanche modelling: flow, erosion, deposition and obstacle effects. Cold Reg Sci Technol 39:193–204CrossRefGoogle Scholar
  85. Oerlemans J, Fortuin JPF (1992) Sensitivity of glaciers and small ice caps to greenhouse warming. Science 258(5079):115–117CrossRefGoogle Scholar
  86. ONERC (2008) Changements climatiques dans les Alpes: Impacs et risques naturels. Rapport technique N°1, 86 pp. Available online at http://www.risknat.org/docs/Technical%20Report%20N%B01.pdf
  87. Parent E, Bernier J (2007) Le raisonnement bayésien: modélisation et inférence. Springer, 380 ppGoogle Scholar
  88. Paul P (2002) Reconstitution d’anomalies de paramètres climatiques et de fréquences de catastrophes naturelles (crues, sécheresses, tempêtes) au cours des 500 dernières années en Europe Centrale. Houille Blanche 6/7:111–114CrossRefGoogle Scholar
  89. Perreault L, Bernier J, Bobée B, Parent E (2000a) Bayesian change-point analysis in hydrometeorological time series. Part 1. The normal model revisited. J Hydrol 235(3–4):221–241CrossRefGoogle Scholar
  90. Perreault L, Bernier J, Bobée B, Parent E (2000b) Bayesian change-point analysis in hydrometeorological time series. Part 2. Comparison of change-point models and forecasting. J Hydrol 235(3–4):242–263CrossRefGoogle Scholar
  91. Perreault L, Bernier J, Bobée B, Parent E, Slivitzky M (2000c) Retrospective multivariate Bayesian change-point analysis: a simultaneous single change in the mean of several hydrological sequences. Stoch Environ Res Risk Assess 14(4):243–261CrossRefGoogle Scholar
  92. Pickands J (1975) Statistical inference using extreme order statistics. Ann Stat 3:11–130Google Scholar
  93. ProClim (1999) De pareils hivers à avalanches sont-ils encore normaux? Climate-Press, no 5, 2 pp. Available online at http://www.proclim.ch/Products/ClimatePress/ClimatePress05F.pdf
  94. Rao A, Tirtotjondro W (1996) Investigation of changes in characteristics of hydrological time series by Bayesian methods. Stoch Environ Res Risk Assess 10(4):295–317Google Scholar
  95. Renard B, Lang M, Bois P et al (2006) Evolution des extrêmes hydrométriques en France à partir des donnés observées. Congrès SHF “Valeurs extrêmes de débit...”. Lyon. Mars 2006, pp 21–27Google Scholar
  96. Salas JD, Boes DC (1980) Shifting Level modelling of hydrologic series. Adv Water Resour 3(2):59–63CrossRefGoogle Scholar
  97. Schneebeli M, Laternser M, Ammann W (1997) Destructive snow avalanches and climate change in the Swiss Alps. Eclogae Geol Helv 90:457–461Google Scholar
  98. Seiler W (2006) Klimawandel im der alpenraum auswirkungen und herausforderung. Les changements climatiques dans l’espace alpin: tendances, retombées et défis. In: Deuxième manifestation thématique “Changement du climat dans l’espace alpin—Effets et défis”. 31ème réunion du Comité permanent, Galtür, Autriche, pp 7–19. Available online at http://www.cenat.ch/ressources/planat_product_fr_786.pdf
  99. SLF Davos (2000) Der Lawinenwinter 1999. Ereignisanlyse, 588 ppGoogle Scholar
  100. Smith AFM (1975) A Bayesian approach to inference about a change-point in a sequence of random variables. Biometrika 62(2):407–416CrossRefGoogle Scholar
  101. Spiegelhalter DJ, Thomas DJ, Best A (2000) WinBUGS version 1.3 user manual. MRC Biostatistics Unit. Available online at http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/contents.shtml
  102. Spiegelhalter DJ, Best N, Carlin B, Van der Linde A (2002) Bayesian measures of model complexity and fit (with discussion). J R Stat Soc Ser B 64:583–640CrossRefGoogle Scholar
  103. Tanner MH (1992) Tools for statistical inference: observed data and data augmentation methods. SpringerGoogle Scholar
  104. Tapsoba D, Haché M, Perreault L, Bobée B (2003) Bayesian rainfall variability analysis in West Africa along cross sections in space–time grid boxes. J Climate 17(5):1069–1082CrossRefGoogle Scholar
  105. Theurillat JP, Guisan A (2001) Potential impact of climate change on vegetation in the European Alps: a review. Clim Change 50(1–2):77–109CrossRefGoogle Scholar
  106. Thomas A, Best N, Lunn D et al (2004) GeoBUGS version 1.2 user manual. Available online at http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/contents.shtml
  107. Vincent C (2002) Influence of climate change over the 20th century on four French glacier mass balances. J Geophys Res 109(D19):4375. doi:10.1029/2001JD000832 CrossRefGoogle Scholar
  108. Voellmy A (1955) Über die Zerstörungskraft von Lawinen. Schweiz Bauztg Jahrg 73(12):159–162, 212–217, 246–249, 280–285Google Scholar
  109. Von Storch H, Zwiers FW (2002) Statistical analysis in climate research. Cambridge University Press, 494 ppGoogle Scholar
  110. Webster PJ, Holland GJ, Curry JA, Chang HR (2005) Changes in tropical cyclone number, duration, and intensity in a warming environment. Science 16 309(5742):1844–1846CrossRefGoogle Scholar
  111. Wikle C (2003) Hierarchical Bayesian models for predicting the spread of ecological processes. Ecology 84:1382–1394CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.UR ETNASaint Martin d’HèresFrance
  2. 2.Equipe MORSE, UMR 518 AgroParisTech/INRAParis cedex 15France

Personalised recommendations