Snow Avalanches as a Non-critical, Punctuated Equilibrium System

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.