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

A Chi Distribution Model of Hail Storm Damage