A Chi Distribution Model of Hail Storm Damage

TL;DR

This paper develops a statistical model based on the chi distribution to describe hail storm damage patterns, incorporating storm movement and correlation, and applies it to radar data for damage estimation.

Contribution

It introduces a novel chi distribution-based damage model that accounts for storm movement and correlation, extending previous uncorrelated models.

Findings

The model accurately fits damage patterns observed in radar data.

Closed-form solutions for damage estimates are derived.

The model enhances damage prediction for insurance applications.

Abstract

This paper addresses the pattern of damage, and investigates its properties, of a theoretical hail storm which gathers in intensity before subsiding, and which travels linearly across the landscape at constant velocity. We start by assuming a simpler model, that of a storm which does not move, restricted to having an uncorrelated binormal distribution of damage. This model, expressed in the natural polar coordinates, leads to a 1-dimensional pattern of damage as a function of the marginal radial distance conforming to the $\chi$-distribution with two degrees of freedom. The model is then extended to the traveling form, allowing further for a correlation of the variables, extending, as well, to the multidimensional case. In its full florescence the model produces hyperellipsoidal hypersurfaces of equal intensity for the correlated multinormal assumption. We provide closed-form solutions for the totality of damages upon these hypersurfaces as proxies for the insurance claims to follow. Finally the model is applied to extensive datasets of hail events, as detected by the NEXRAD network of weather radars.