A new method for the estimation of avalanche distance exceeded probabilities

A crucial point in any methodology for avalanche hazard assessment is the evaluation of avalanche distance exceeded probability, i.e., the annual probability that any assigned location along a given path is reached or exceeded by an avalanche. Typically this problem is faced by estimating the snow volume in the starting zone that is likely to accumulate on average every (T) over bar years by statistical analysis of snowfall record, and then using this volume as input to an appropriately calibrated avalanche dynamics model to determine the runout distances for this design event. This methodology identifies the areas that can be affected by an avalanche for the considered value of the return period (i.e. the average interval of time for a certain event to repeat itself), (T) over bar. However, it does not allow us to evaluate the actual avalanche encounter probability for any given point in the runout zone. In the present work this probability is computed by numerical integration of the expression P(x) = integral(0)(infinity) P*(V) f (V) dV, where f is the probability density function (PDF) of the avalanche release volume V, and P* is the probability of the point x being reached or passed by an avalanche if the release volume is V; this latter probability is calculated by avalanche dynamics simulations. The procedure is implemented using a one-dimensional hydraulic-continuum avalanche dynamic model, calibrated on data from different Italian Alpine ranges, and is applied to a real world hazard mapping problem.