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Avalanche risk evaluation and protective dam optimal design using extreme value statistics


In snow avalanche long-term forecasting, existing risk-based methods remain difficult to use in a real engineering context. In this work, we expand a quasi analytical decisional model to obtain simple formulae to quantify risk and to perform the optimal design of an avalanche dam in a quick and efficient way. Specifically, the exponential runout model is replaced by the Generalized Pareto distribution (GPD), which has theoretical justifications that promote its use for modelling the different possible runout tail behaviours. Regarding the defence structure/flow interaction, a simple law based on kinetic energy dissipation is compared with a law based on the volume stored upstream of the dam, whose flexibility allows us to cope with various types of snow. We show how a detailed sensitivity study can be conducted, leading to intervals and bounds for risk estimates and optimal design values. Application to a typical case study from the French Alps, highlights potential operational difficulties and how they can be tackled. For instance, the highest sensitivity to the runout tail type and interaction law is found at abscissas of legal importance for hazard zoning (return periods of 10–1000 a), a crucial result for practical purposes.

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This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (, which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Correspondence: Philomène Favier <>
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Abraham, C and Cadre, B (2004) Asymptotic global robustness in Bayesian decision theory. Ann. Stat., 32, 13411366 (doi: 10.1214/009053604000000562)
Ancey, C (2012) Are there “dragon-kings” events (i.e. genuine outliers) among extreme avalanches? Eur. Phys. J.: Spec. Top., 205(1), 117129 (doi: 10.1140/epjst/e2012-01565-7)
Arnalds, D, Jonasson, K and Sigurdsson, S (2004) Avalanche hazard zoning in iceland based on individual risk. Ann. Glaciol., 38(1), 285290 (doi: 10.3189/172756404781814816)
Barbolini, M, Natale, L and Savi, F (2002) Effects of release conditions uncertainty on avalanche hazard mapping. Nat. Hazards, 25, 225244, ISSN 0921-030X (doi: 10.1023/A:1014851705520)
Barbolini, M, Cappabianca, F and Savi, F (2004a) Risk assessment in avalanche-prone areas. Ann. Glaciol., 38, 115122, ISSN 0260-3055 (doi: 10.3189/172756404781815103)
Barbolini, M, Cappabianca, F and Sailer, R (2004b) Empirical estimate of vulnerability relations for use in snow avalanche risk assessment. In Brebbia, CA ed. Risk analysis IV, Brebbia C, WIT Press, Southampton, 533–542
Bartelt, P, Salm, L and Gruberl, U (1999) Calculating dense-snow avalanche runout using a Voellmy-fluid model with active/passive longitudinal straining. J. Glaciol., 45(150), 242254 (doi: 10.3189/002214399793377301)
Bernier, J (2003) Decisions and attitude of decision makers facing hydrological risk. Hydrol. Sci. J., 48(3), 301316 (doi: 10.1623/hysj.48.3.301.45284)
Bertrand, D, Naaim, M and Brun, M (2010) Physical vulnerability of reinforced concrete buildings impacted by snow avalanches. Nat. Hazard Earth Syst. Sci., 10(7), 15311545, ISSN 1561-8633 (doi: 10.5194/nhess-10-1531-2010)
Blanchet, J and Davison, A (2011) Spatial modeling of extreme snow depth. Ann. Appl. Stat., 5(3), 16991725 (doi: 10.1214/11-AOAS464)
Bründl, M, Romang, H, Bishof, N and Rheinberger, C (2009) The risk concept and its application in natural hazard risk management in Switzerland. Nat. Hazard Earth Syst. Sci., 9, 801813
Cappabianca, F, Barbolini, M and Natale, L (2008) Snow avalanche risk assessment and mapping: a new method based on a combination of statistical analysis, avalanche dynamics simulation and empirically based vulnerability relations integrated in a GIS platform. Cold Reg. Sci. Technol., 54(3, Sp. Iss. SI), 193205, ISSN 0165-232X (doi: 10.1016/j.coldregions.2008.06.005)
Coles, S (2001) An introduction to statistical modeling of extreme values. Springer, London
Eckert, N, Parent, E and Richard, D (2007) Revisiting statistical-topographical methods for avalanche predetermination: Bayesian modelling for runout distance predictive distribution. Cold Reg. Sci. Technol., 49, 88107 (doi: 10.1016/j.coldregions.2007.01.005)
Eckert, N, Parent, E, Faug, T and Naaim, M (2008) Optimal design under uncertainty of a passive defense structure against snow avalanches: from a general Bayesian framework to a simple analytical model. Nat. Hazard Earth Syst. Sci., 8(5), 10671081, ISSN 1561-8633
Eckert, N, Parent, E, Faug, T and Naaim, M (2009) Bayesian optimal design of an avalanche dam using a multivariate numerical avalanche model. Stoch. Environ. Res. Risk Assess., 23(8), 11231141 (doi: 10.1007/s00477-008-0287-6)
Eckert, N and 5 others (2010a) Cross-comparison of meteorological and avalanche data for characterising avalanche cycles: the example of December 2008 in the eastern part of the French Alps. Cold Reg. Sci. Technol., 64(2), 119136 (doi: 10.1016/j.coldregions.2010.08.009)
Eckert, N, Naaim, M and Parent, E (2010b) Long-term avalanche hazard assessment with Bayesian depth averaged propagation model. J. Glaciol., 56, 563583 (doi: 10.3189/002214310793146331)
Eckert, N, Gaume, J and Castebrunet, H (2011) Using spatial and spatial-extreme statistics to characterize snow avalanche cycles. Procedia Environ, Sci., 7, 224229 (doi: 10.1016/j.proenv.2011.07.039)
Eckert, N and 6 others (2012) Quantitative risk and optimal design approaches in the snow avalanche field: review and extensions. Cold Reg. Sci. Technol., 79–80, 119 (doi: 10.1016/j.coldregions.2012.03.003)
Embrechts, P, Klüppelberg, C and Mikosch, T (1997) Modelling extremal events for insurance and finance. Springer Verlag, Berlin
Faug, T (2004) Simulation sur modèle réduit de l'influence d'un obstacle sur un écoulement à surface libre Application aux ouvrages de protection contre les avalanches de neige . (PhD thesis, Université Joseph Fourier, Grenoble)
Faug, T, Naaim, M, Bertrand, D, Lachamp, P and Naaim-Bouvet, F (2003) Varying dam height to shorten the run-out of dense avalanche flows: developing a scaling law from laboratory experiments. Surv. Geophys., 24(5/6), 555568
Faug, T, Naaim, M and Naaim-Bouvet, F (2004) An equation for spreading length, centre of mass and maximum run-outs shortenings of avalanche flows by obstacle. Cold Reg. Sci. Technol., 39(2/3), 141151 (doi: 10.1016/j.coldregions.2004.04.002)
Faug, T, Gauer, P, Lied, K and Naaim, M (2008) Overrun length of avalanches overtopping catching dams: cross-comparison of small-scale laboratory experiments and observations from full-scale avalanches. J. Geophys. Res. F: Earth Surf., 113(3) (doi: 10.1029/2007JF000854)
Favier, P, Bertrand, D, Eckert, N and Naaim, M (2014a) A reliability assessment of physical vulnerability of reinforced concrete walls loaded by snow avalanches. Nat. Hazard Earth Syst. Sci., 14, 689704 (doi: 10.5194/nhess-14-689-2014)
Favier, P, Eckert, N, Bertrand, D and Naaim, M (2014b) Sensitivity of avalanche risk to vulnerability relations. Cold Reg. Sci. Technol., 108, 163177 (doi: 10.1016/j.coldregions.2014.08.009)
Fuchs, S and Mc Alpin, MC (2005) The net benefit of public expenditures on avalanche defense structures in the municipality of Davos, Switzerland. Nat. Hazard Earth Syst. Sci., 5, 893–301
Fuchs, S, Thoeni, M, McAlpin, MC, Gruber, U and Bründl, M (2007) Avalanche hazard mitigation strategies assessed by cost effectiveness analyses and cost benefit analyses – evidence from Davos, Switzerland. Nat. Hazards, 41(1), 113129, ISSN 0921-030X (doi: 10.1007/s11069-006-9031-z)
Gauer, P, Kronholm, K, Lied, K, Kristensen, K and Bakkehøi, S (2010) Can we learn more from the data underlying the statistical α-α model with respect to the dynamical behavior of avalanches? Cold Reg. Sci. Technol., 62(1), 4254 (doi: 10.1016/j.coldregions.2010.02.001)
Gaume, J, Chambon, G, Eckert, N and Naaim, M (2012) Relative influence of mechanical and meteorological factors on avalanche release depth distributions: an application to French Alps. Geophys. Res. Lett., 39(12) (doi: 10.1029/2012GL051917)
Gaume, J, Eckert, N, Chambon, G, Naaim, M and Bel, L (2013) Mapping extreme snowfalls in the French Alps using max-stable processes. Water Resour. Res., 49(2), 10791098 (doi: 10.1002/wrcr.20083)
Hendrikx, J and Owens, I (2008) Modified avalanche risk equations to account for waiting traffic on avalanche prone roads. Cold Reg. Sci. Technol., 51(2–3), 214218 (doi: 10.1016/j.coldregions.2007.04.011)
Jónasson, K, Sigurðsson, ST and Arnalds, D (1999) Estimation of avalanche risk. Report No. R99001-URO. Veðurstofu Íslands, Reykjavík
Jordaan, I (2005) Decisions under uncertainty. Probabilistic analysis for engineering decisions. Cambridge University Press, Cambridge
Katz, R, Parlange, M and Naveau, P (2002) Statistics of extremes in hydrology. Adv. Water Resour., 25(8–12), 12871304 (doi: 10.1016/S0309-1708(02)00056-8)
Keylock, C (2005) An alternative form for the statistical distribution of extreme avalanche runout distances. Cold Reg. Sci. Technol., 42(3), 185193, ISSN 0165-232X (doi: 10.1016/j.coldregions.2005.01.004)
Keylock, C and Barbolini, M (2001) Snow avalanche impact pressure – vulnerability relations for use in risk assessment. Can. Geotech. J., 38(2), 227238 (doi: 10.1139/cgj-38-2-227)
Keylock, C, McClung, D and Magnusson, M (1999) Avalanche risk mapping by simulation. J. Glaciol., 45(150), 303314
Leadbetter, M, Lindgren, G and Rootzén, H (1983) Extremes and related properties of random sequences and processes
Lied, K and Bakkehoi, S (1980) Empirical calculations of snow-avalanche run-out distance based on topographic parameters. J. Glaciol., 26(94), 165177, ISSN 0022-1430
Margreth, S and Romang, H (2010) Effectiveness of mitigation measures against natural hazards. Cold Reg. Sci. Technol., 64(2), 199207 (doi: 10.1016/j.coldregions.2010.04.013)
Margreth, S, Stoffel, L and Wilhelm, C (2003) Winter opening of high alpine pass roads-analysis and case studies from the Swiss Alps. Cold Reg. Sci. Technol., 37(3), 467482 (doi: 10.1016/S0165-232X(03)00085-5)
Mavrouli, CJO (2010) Vulnerability of simple reinforced concrete buildings to damage by rockfalls. Landslides, 7(2), 169180 (doi: 10.1007/s10346-010-0200-5)
McClung, D (2000) Extreme avalanche runout in space and time. Can. Geotech. J., 37(1), 161170
McClung, D and Lied, K (1987) Statistical and geometrical definition of snow avalanche runout. Cold Reg. Sci. Technol., 13(2), 107119, ISSN 0165-232X
McClung, DM (2001) Extreme avalanche runout: a comparison of empirical models. Can. Geotech. J., 38, 12541265, ISSN 0008-3674 (doi: 10.1139/cgj-38-6-1254)
Merz, B, Kreibich, H, Schwarze, R and Thieken, A (2010) Review article “assessment of economic flood damage”. Nat. Hazard Earth Syst. Sci., 10(8), 16971724 (doi: 10.5194/nhess-10-1697-2010)
Meunier, M and Ancey, C (2004) Towards a conceptual approach to predetermining long-return-period avalanche run-out distances. J. Glaciol., 50(169), 268278
Naaim, M, Naaim-Bouvet, F, Faug, T and Bouchet, A (2004) Dense snow avalanche modeling: flow, erosion, deposition and obstacle effects. Cold Reg. Sci. Technol., 39(2), 193204 (doi: 10.3189/2013JoG12J205)
Naaim, M, Faug, T, Naaim, F and Eckert, N (2010) Return period calculation and passive structure design at the taconnaz avalanche path, france. Ann. Glaciol., 51(54), 8997 (doi: 10.3189/172756410791386517)
Naaim, M, Durand, Y, Eckert, N and Chambon, G (2013) Dense avalanche friction coefficients : influence of physical properties of snow. J. Glaciol., 59, 771782 (doi: 10.3189/2013JoG12J205)
Naveau, P, Toreti, A, Smith, I and Xoplaki, E (2014) A fast nonparametric spatio-temporal regression scheme for generalized pareto distributed heavy precipitation. Water Resour. Res., 50(5), 40114017 (doi: 10.1002/2014WR015431)
Nolde, N and Joe, H (2013) A Bayesian extreme value analysis of debris flows. Water Resour. Res., 49(10), 70097022 (doi: 10.1002/wrcr.20494)
Papathoma-Köhle, M, Kappes, M, Keiler, M and Glade, T (2010) Physical vulnerability assessment for alpine hazards: state of the art and future needs. Nat. Hazards, 58(2), 645680 (doi: 10.1007/s11069-010-9632-4)
Parent, E and Bernier, J (2003a) Bayesian pot modeling for historical data. J. Hydrol., 274(1–4), 95108, ISSN 0022-1694 (doi: 10.1016/S0022-1394(02)00396-7)
Parent, E and Bernier, J (2003b) Encoding prior experts judgments to improve risk analysis of extreme hydrological events via pot modeling. J. Hydrol., 283(1–4), 118 (doi: 10.1016/S0022-1694(03)00080-5)
Pickands, J (1975) Statistical inference using extreme order statistics. Ann. Stat., 3(1), 119131, ISSN 00905364
Raiffa, H (1968) Decision analysis: introductory lectures on choices under uncertainty. Addison-Wesley, Reading, MA
Resnick, S (1987) Extreme values, point processes and regular variation. Springer, New York
Rheinberger, C, Bründl, M and Rhyner, J (2009) Dealing with the white death: avalanche risk management for traffic routes. Risk Anal., 29(1), 7694 (doi: 10.1111/j.1539-6924.2008.01127.x)
Rietsch, T, Naveau, P, Gilardi, N and Guillou, A (2013) Network design for heavy rainfall analysis. J. Geophys. Res. D: Atmospheres, 118(23), 1307513086 (doi: 10.1002/2013JD020867)
Salm, B, Burkard, A and Gubler, H (1990) Berechnung von fliesslawinen, eine anleitung für praktiker mit beispielen. Technical Report No. 47. Eidgenössisches Institut für Schnee -und Lawinenforschung, Davos
Schläppy, R and 7 others (2014) Validation of extreme snow avalanches and related return periods derived from a statistical dynamical model using tree-ring techniques. Cold Reg. Sci. Technol., 99, 1226 (doi: 10.1016/j.coldregions.2013.12.001)
Sielenou, P, Eckert, N and Naveau, P (2016) A limiting distribution for maxima of discrete stationary triangular arrays with an application to risk due to avalanches. Extremes, 19(1), 2540 (doi: 10.1007/s10687-015-0234-0)
Van Danzig, D (1956) Economic decision problems for flood prevention. Econometrica, 24, 276287
Von Neumann, J and Morgenstern, O (1953) Theory of games and economic behaviour. Princeton University Press, Princeton, NJ
Wilhelm, C (1997) Wirtschaftlichkeit im lawinenschutz. methodik und erhebungen zur beurteilung von schutzmassnahmen mittels quantitativer risikoanalyse und ökonomischer bewertung. Mitt.Eidgenöss. Inst. Schnee- Lawinenforsch, 203, 288293
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