Abstract
The mathematical requirements for a self-organized critical system include scale invariance both with respect to the characteristic sizes of the events and the power spectrum in the frequency domain based on time arrival. Sandpile avalanches and other types of avalanches have been analyzed from the perspective of common characteristics of critical systems. However, snow avalanches have not been completely analyzed, particularly in the frequency domain. Snow avalanches constitute a natural hazard and they are of much more practical importance than other types of avalanches so far analyzed. In this chapter, I consider the mathematical criteria for scale invariance in both the size and frequency domain for snow avalanches based entirely on analysis of field measurements.
In combination, the mathematical results suggest that neither the size distribution, the time arrival nor waiting time between avalanche events conform to that of a critical system as defined for self-organized criticality or thermodynamics. If snow avalanches are to conform to a critical system in geophysics then a revision of the mathematical requirements or definition is called for. However, time series of events show that snow avalanche arrivals consist of clusters, intermittancies and bursts with rapid changes over short time intervals interrupted by periods of stasis. The data and analysis combined with field observations suggest that a system of snow avalanches paths exhibits the characteristics of a non-critical, punctuated equilibrium system.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bak, P. (1996), How nature works, the science of self-organized criticality, Springer-Verlag New York Inc., New York, U.S.A., 212 pp.
Bak, P., Tang, C. and K. Wiesenfeld (1987), Self-organized criticality: An explanation of 1/fnoise, Physical Review Letters, 59, 381-384.
Bažant, Z.P. and J. Planas (1998), Fracture and size effect in concrete and other quasibrittle materials, CRC Press, Boca Raton, USA, 616 pp.
Bažant, Z.P., G. Zi and D.McClung (2003), Size effect and fracture mechanics of the triggering of dry snow slab avalanches, J. Geophys. Res., Vol. 108,No. B2, 2119, doi:10.1029/2002JB001884.
Birkeland, K.W. and C.C. Landry (2002), Power laws and snow avalanches, Geophys. Res. Lett, 29(11), 49-1–49-3.
Benjamin, J.R. and C. A. Cornell (1970), Probability, statistics and decision for civil engineers, McGraw- Hill Inc, New York, U.S.A., 684 pp.
Ito, K. (1995), Punctuated equilibrium model of biological evolution is also a self-organized critical model of earthquakes, Phys. Rev. E(52): 3232.
Jensen, H.J. (1998) Self-organized criticality, emergent complex behaviour in physical and biological systems, Cambridge Lecture Notes in Physics 10, Cambridge University Press, Cambridge, U.K., 153 pp.
Korvin, G. (1992), Fractal models in the earth sciences, Elsevier, Amsterdam, 396 pp.
McClung, D.M. (1979), Shear fracture precipitated by strain-softening as a mechanism of dry slab avalanche release, J. Geophys. Res., 84(B7), 3519-3526.
McClung, D.M. (1999), The encounter probability for mountain slope hazards, Canadian Geotechnical Journal, Vol. 36, No. 6, 1195 -1196.
McClung, D.M. (2002(a)), The elements of applied avalanche forecasting part I: the human issues, Natural Hazards, Vol. 26, No. 2, 111-129.
McClung, D.M. (2002(b)), The elements of applied avalanche forecasting part II: the physical issues and rules of applied avalanche forecasting, Natural Hazards, Vol. 26, No. 2, 131-146.
McClung, D.M. (2003(a)) Size scaling for dry snow slab release, J. Geophys. Res., Vol. 108, No. B10, 2465, doi:1029/2002JB002298.
McClung, D.M. (2003 (b)) Time arrival of slab avalanche masses, J. Geophys. Res. Vol. 108, No. B10, 2466, doi:10.1029/2002JB002299.
McClung, D.M. (2003(c)) Magnitude and frequency of avalanches in relation to terrain and forest cover, Arctic, Antarctic and Alpine Res. Vol. 35, No.1, 82-90.
McClung, D.M. (2005), Dry slab avalanche shear fracture properties from field measurements, J. Geophys.Res., 110, F04005, doi:10.1029/2005JF000291.
McClung, D. and P. Schaerer (2006), The Avalanche Handbook, 3rdEdition, The Mountaineers Books, Seattle, Wash., 342 pp.
McCormick, N.J. (1981), Reliability and risk analysis, methods and nuclear power applications, Academic Press, Inc., Boston, U.S.A., 446 pp.
Montroll, E.W. and M.F. Shlesinger (1983), Maximum entropy formalism, fractals, scaling phenolmena, and 1 /f noise: a tale of tails, Journal of Statistical Physics, Vol. 32, No.2, 209-230.
Schroeder, M. (1990), Fractals, chaos, power laws, minutes from an infinite paradise, W.H. Freeman and Company, New York, 429 pp.
Shlesinger, M.F. and B.D. Hughes (1981), Analogs of renormalization group transformations in random processes, Physica 109A, 597-608.
Van der Ziel, A. (1950), On the noise spectra of semi-conductor noise and flicker effectPhysica XVI, no. 4, 359-372.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer Science+Business Media, LLC
About this paper
Cite this paper
McClung, D. (2007). Snow Avalanches as a Non-critical, Punctuated Equilibrium System. In: Nonlinear Dynamics in Geosciences. Springer, New York, NY. https://doi.org/10.1007/978-0-387-34918-3_24
Download citation
DOI: https://doi.org/10.1007/978-0-387-34918-3_24
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-34917-6
Online ISBN: 978-0-387-34918-3
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)