Abstract: Slab avalanches reach a critical state and initiate by propagating shear fractures. This is a different mechanism than the classical prototype of SOC developed by Per Bak from sandpile avalanches. In the talk, I will discuss SOC from the perspective of slab avalanche initiation. The scaling law for self-similar criticality (SSC) is derived from the field measurements of slab thickness and other physical properties and the fact that alpine snow is a quasi-brittle (strain-softening) material which ultimately undergoes Mode II fracture initiation. Fracture mechanics principles imply that slab thickness is the fundamental scaling parameter. I show that the probability density function for the slab thickness scaling implies an inverse square relationship to Mode II fracture toughness (or inverse proportionality to fracture energy release rate).

The other requirement for SOC is that the frequency power spectrum for time series of avalanche arrivals exhibits 1/f noise i.e. the power spectrum decreases according to a power of the frequency: as frequency increases the power spectrum drops off. I illustrate this by times series of 20 years of avalanche records of mass arrivals from Bear Pass and Kootenay Pass, B.C. from many thousands of avalanches. The result is that the power spectrum from SSC (thickness scaling) and the power spectrum from the time series arrivals have the same analytical form (both evolve from log-normal probability density functions). From the perspective of mountain slope hazards these results are unique in two ways: 1. the equivalence of the power spectrum forms for SSC and the time series arrivals and 2. all the results are derived entirely from field measurements rather than resorting to computer models.

For debris flows, the time series requirement for SOC cannot be derived from field measurements since enough data would never be available. However, SSC can be attempted. I illustrate SSC from debris flow volume data for 87 events from the Queen Charlotte Islands. Using volume as a scaling parameter, I show that the probability density function for debris flow volume is a Type II extreme value distribution and scaling law for SSC has a different form than for snow avalanches (derived from a log-normal distribution). Conclusions about applicability of SOC for these two mountain hazards are given.