A variation in the α−β model which is a regression model that allows a deterministic prediction of the extreme runout to be expected in a given path, was applied for calculating avalanche runout in the Catalan Pyrenees. Present knowledge of major avalanche activity in this region and current mapping tools were used. The model was derived using a dataset of 97 ‘extreme’ avalanches that occurred from the end of 19th century to the beginning of 21st century. A multiple linear regression model was obtained using three independent variables: inclination of the avalanche path, horizontal length and area of the starting zone, with a good fit of the function (R2 = 0.81). A larger starting zone increases the runout and a larger length of the path reduces the runout. The new updated equation predicts avalanche runout for a return period of ~100 years. To study which terrain variables explain the extreme values of the avalanche dataset, a comparative analysis of variables that influence a longer or shorter runout was performed. The most extreme avalanches were treated. The size of the avalanche path and the aspect of the starting zone showed certain association between avalanches with longer or shorter runouts.

Particle size, particle speed and airflow speed have been measured in the powder snow clouds of avalanches to investigate the suspension and transportation processes of snow particles. The avalanches were artificially triggered at the Lautaret full-scale avalanche test-site (French Alps) where an ultrasonic anemometer and a snow particle counter were setup in an avalanche track for measurements. Relatively large particles were observed during passage of the avalanche head and then the size of the particles slightly decreased as the core of the avalanche passed the measurement station. The particle size distribution was well fitted by a gamma distribution function. A condition for suspension of particles within the cloud based on the ratio of vertical velocity fluctuation to particle settling velocity suggests that the large particles near the avalanche head are not lifted up by turbulent diffusion, but rather ejected by a process involving collisions between the avalanche flow and the rough snow surface. Particle speeds were lower than the airflow speed when large particles were present in the powder cloud.

We study the durations of the avalanches in the maximal avalanche decomposition of the Bak-Sneppen evolution model. We show that all the avalanches in this maximal decomposition have infinite expectation, but only ‘barely’, in the sense that if we made the appropriate threshold a tiny amount smaller (in a certain sense), then the avalanches would have finite expectation. The first of these results is somewhat surprising, since simulations suggest finite expectations.

Uniform sequential tree-building aggregation of n particles is analyzed together with the effect of the avalanche that takes place when a subtree rooted at a uniformly chosen vertex is removed. For large n, the expected subtree size is found to be ≃ logn both for the tree of size n and the tree that remains after an avalanche. Repeated breakage-restoration cycles are seen to give independent avalanches which attain size k(1 ≤ k ≤ n-1) with probability (k(k+1))-1 and restored trees that are recursive.