
Statistical Avalanche Modelling Procedures
 Statistical models estimate extreme runout distances for simple topographies, based on a sample set of avalanche observations. Many of the models of this type were developed by members of SATSIE (Lied and Bakkehøi, 1980;
McClung and Lied, 1987; Keylock et al., 1999). Although they permit the estimation of the probable extent of extreme avalanches, they do not provide any information on velocities or impact pressures.
 Hence, they cannot be used to determine the optimal construction of avalanche dams or to produce avalanche hazard zones, which require information on both runout distance and pressures.
Traditional Dynamics Models
 The first widely used model for snow avalanche dynamics was developed by Voellmy in 1955. This model was onedimensional in nature and represented the avalanche as a sliding block of material that was affected by a Coulomb friction and a dynamic drag
that was proportional to the square of the velocity. The model required the specification of a reference point at which deceleration commenced.
 The need to specify a reference point was eliminated in the work of Perla et al. (1980). It should also be noted that Moskalev (1977) developed a model that was similar to that of Perla et al. independently.
 The original depthaveraged twoparameter models of the Voellmy type are today implemented within a hydrauliccontinuum framework and incorporate terms to deal with active/passive pressure conditions.
These models can predict runout distances, flow and deposit depths, velocities and pressures along the path. They have been developed in onedimensional (Natale et al., 1994), twodimensional (Naaim and Ancey, 1992) and pseudo two dimensional
(Bartelt et al., 1999) variants. A number of members of SATSIE undertook a comparison of these different model variants for several European avalanche paths as part of a previous ECfunded research project (Barbolini et al., 2000).
 All of these models require the specification of values for the friction parameters and because the physics of flowing snow is poorly understood, this cannot be achieved at present with reference to experimental data.
Thus, empirical calibration and operational experience are required instead. Suggested values can be found in procedures such as the "Swiss Guidelines" for model implementation written by Salm et al. (1990). However, these guidelines were written for the traditional versions of the Voellmy model and may
not be applicable to hydrauliccontinuum implementations. Please follow the first link below for an illustration of how
different friction parameters can result in the same runout distance but produce different deposit shapes. The second link shows an example simulation using the VARA model.
[ Effect of friction parameters on deposit shape. ]
[ An example of an avalanche dynamics simulation (760 Kb avi animation, which plays better under netscape). ]
 Another major problem with these traditional approaches is that no account is taken of flow regime transitions and mass change. This may be the main reason why the optimum parameters vary significantly from one avalanche to another. Model predictions are often quite sensitive to the parameter values
(Barbolini et al., 2000).
 It should be noted that approaches based on numerical and statistical modelling are not mutually exclusive. As part of the SAME project, Barbolini et al. (2000) reported on how a generalized modelling framework could use statistical models as a means of verifying numerical model output.
In addition, Keylock and Barbolini (2001), and Barbolini and Keylock (2002) show how statistical procedures can be used to integrate pressure estimations into a risk framework and how confidence intervals can be constructed
on the position of particular hazard zone boundaries.
Modelling the Avalanche Powder Cloud
 The models already discussed focus their attention on the flowing part of the avalanche. However, above this there is often a saltation layer and powder cloud. These layers may be of great importance for hazard zoning because the powder cloud, although much less dense, may travel farther and faster than the denser snow nearer the ground.
 Models for the powder cloud have been developed by SATSIE project members (Naaim et al., 1995; Issler, 1998). However, an important outstanding question is how these models can be coupled to a description of the flowing part of the avalanche. Such a scheme will probably need to resolve the conditions within the transitional saltation layer.
Pingpong ball experiments undertaken in Japan (McElwaine and Nishimura, 1998) have shown that the velocity of the flow scales with the number of particles and may give some clues as to how this layer behaves.
 Developing a fullycoupled avalanche model is also important for resolving issues such as the massbalance of the avalanche. For example, can a welldeveloped powder cloud and saltation layer moving ahead of the flowing part of the avalanche erode snow from the bed and starve the latter of mass? Under what conditions does the entrainment of snow into the flowing layer from the bed balance that lost into suspension?
It is clear that more sophisticated modelling approaches are needed to resolve these questions.
Alternative Approaches
 In the last fifteen years there has been a proliferation of approaches to modelling the dynamics of snow avalanches. Many of these are reviewed by Harbitz (1998). Perhaps the two most important for the flowing part of the avalanche are methods based on the
SavageHutter theory (Savage and Hutter, 1989; Gray et al., 1999) and the Norwegian approach (Norem et al., 1987) that models the avalanche with a CriminaleEricksonFilbey rheology. As part of the SATSIE project efforts will be made to determine the best way to develop the next generation of avalanche dynamics models. Both of these new approaches are important avenues to explore.
References
 Barbolini M., Gruber U., Keylock C.J., Naaim N. and Savi F. 2000. Application of statistical and hydrauliccontinuum densesnow avalanche models to 5 real European sites. Cold Regions Science and Technology, 31, 133149.
 Barbolini, M. and Keylock, C.J. 2002. A new method for avalanche hazard mapping using a combination of statistical and deterministic models, Natural Hazards and Earth System Sciences 2, 3/4, 239245
 Bartelt, P., Salm, B. and Gruber, U. 1999. Calculating densesnow avalanche runout using a Voellmyfluid model with active/passive longitudinal straining, Journal of Glaciology, 45, 150, 242254
 Gray J.M.N.T., Wieland W. and Hutter K. 1999. Gravitydriven free surface flow of granular avalanches over complex basal topography, Proceedings of the Royal Society of London, Series A, 455, 18411874.
 Harbitz C.B. (ed). 1998. EU Programme SAME: A survey of computational models for snow avalanche motion. NGI report no. 5812201. 127 pp.
 Issler, D. 1998. Modelling of snow entrainment and deposition in powder snow avalanches. Annals of Glaciology 26, 253258.
 Keylock C.J. and Barbolini M. 2001. Snow avalanche impact pressure/vulnerability relations for use in risk assessment, Canadian Geotechnical Journal, 38, 227238.
 Keylock C.J., McClung D.M. and Magnusson M.M. 1999. Avalanche risk by simulation. Journal of Glaciology, 45, 303314.
 Lied, K. and Bakkehøi, S. 1980. Empirical calculations of snowavalanche runout distance based on topographic parameters. Journal of Glaciology, 26, No. 94, 165177.
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 Moskalev, J.D. 1977. The dynamics of snow avalanches and avalanche calculations. Leningrad (in Russian). 232 pp.
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 Natale, L., Nettuno, L., and Savi, F. 1994. Numerical simulation of snow dense avalanche: an hydraulic approach. Proceedings of the 24th Annual Pittsburg International Conference on modelling and simulations, Pittsburg (IASTED 1994).
 Norem H., Irgens F. and Schieldrop B. 1987. A continuum model for calculating snow avalanche velocities, in Avalanche formation, movement and effects (proceedings of the Davos symposium, September 1986). IAHS publication no. 162, 363379
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 Salm, B., Burkard, A., and Gubler, H.U. 1990. Berechnung von Fliesslawinen; eine Anleitung für Praktiker mit Beispielen. Mitteilungen des Eidgenössischen Institutes für Schnee und Lawinenforschung, No. 47, Davos.
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