Predicting the Severity of Tornado Events by Learning a Statistical Manifold for Tornado Property Losses

Abstract

We examine the relationship between property losses caused by tornadoes and their physical parameters, namely the tornado path length and width, using data reported by the National Oceanic and Atmospheric Administration in the United States. We observe that the statistics of property losses cannot be described by a single distribution but rather by a two-dimensional statistical manifold of distributions that may re ect two di erent mechanisms of property loss compensations. Assessing the di erence between distributions of losses caused by tornadoes using Kolmogorov-Smirnov's distance, we construct the 2-D manifold using the method of multi-dimensional scaling. Then we de ne a curvature coe cient that characterizes the contraction and expansion of the derived manifold to explain the complex dynamics of the probability distributions of losses. The regions with expansions identify the ranges of physical parameters for which the extreme tornado events may occur, which helps in assessing compensation strategies.