Evidence of chaos in slab avalanching

Abstract

We present evidence that slab avalanching is a chaotic process. We studied a set of 8062 avalanches running on more than 140 paths at Mammoth Mountain, CA between November 1982 and May 2002. Cumulative crown size distributions over the entire mountain and on individual paths are scale invariant and appear to form a multifractal set; chaotic systems often exhibit such statistics. We examine avalanche control data from 416 days on a single path over the same 20-year period and reconstruct the phase space portrait and resulting attractor for crown size. Three independent tests indicate the time series is deterministic: plateauing of the correlation dimension with increasing embedding dimension, the correlation dimension of the attractor compared against the correlation dimensions of surrogate sets of random data and a measure of trajectory alignments for neighboring points in phase space. These tests, coupled with non-periodic and non-intersecting phase space trajectories, suggest the attractor is a strange attractor and that slab avalanching is a chaotic process. We examine and reject two likely non-chaotic sources of crown size scaling: new snow layering and topography. We discuss three factors that might contribute to chaotic avalanche behavior: scaling, the deposition and evolution of snow layers and the mechanics of slab release. If slab avalanching is a chaotic process, then subresolution processes and system sensitivity to initial conditions preclude purely physical models of long-term slab evolution and release.