Snow Avalanches as a Non-critical, Punctuated Equilibrium System
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.
KeywordsScale Invariance Rock Avalanche Snow Avalanche Weak Layer Avalanche Event
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- Bak, P. (1996), How nature works, the science of self-organized criticality, Springer-Verlag New York Inc., New York, U.S.A., 212 pp.Google Scholar
- Bažant, Z.P. and J. Planas (1998), Fracture and size effect in concrete and other quasibrittle materials, CRC Press, Boca Raton, USA, 616 pp.Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- Korvin, G. (1992), Fractal models in the earth sciences, Elsevier, Amsterdam, 396 pp.Google Scholar
- 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.Google Scholar
- McClung, D. and P. Schaerer (2006), The Avalanche Handbook, 3rdEdition, The Mountaineers Books, Seattle, Wash., 342 pp.Google Scholar
- McCormick, N.J. (1981), Reliability and risk analysis, methods and nuclear power applications, Academic Press, Inc., Boston, U.S.A., 446 pp.Google Scholar
- Schroeder, M. (1990), Fractals, chaos, power laws, minutes from an infinite paradise, W.H. Freeman and Company, New York, 429 pp.Google Scholar
- Shlesinger, M.F. and B.D. Hughes (1981), Analogs of renormalization group transformations in random processes, Physica 109A, 597-608.Google Scholar
- Van der Ziel, A. (1950), On the noise spectra of semi-conductor noise and flicker effectPhysica XVI, no. 4, 359-372.Google Scholar