Application of Mathematical Statistics to Assess the Avalanche Danger Level in the Ile Alatau Mountains

Abstract— The Institute of Geography and Water Safety adapted the world experience in assessing the avalanche danger level to the conditions of Kazakhstan. This work is based on the five-point scale method of danger level classification recommended by the WSL Institute for Snow and Avalanche Research (SLF). The methods of mathematical statistics are used to analyze data on weather conditions and avalanches. The analysis identified the main statistical parameters of data series. The cluster analysis revealed five similar groups (clusters) in the distribution of snow water equivalent and air temperature and three clusters in the distribution of precipitation amounts. The spectral analysis showed that the duration of avalanche periods is basically 2–3 days. The distribution of the number of days with different levels of avalanche danger, total volumes of avalanches and heavy precipitation obeys the Pareto law. The results are statistically significant according to the Kolmogorov–Smirnov test ( \(\alpha = 10\) %, \(p < 0.01\) ).