Correlated Geometric Scaling of Tornado Damage Paths in the SPC Database (1950–2024)

Abstract. We investigate the large-scale geometric organisation of tornado damage paths using the NOAA Storm Prediction Center (SPC) tornado database over the period 1950–2024. The analysis focuses primarily on the correlated geometry of tornado path length and width independently of any energetic weighting procedure.

A robust anisotropic scaling relation is identified between tornado path width W and path length L,

W ∼ L^α, α ≈ 0.43,

indicating that longer tornadoes undergo systematic sublinear lateral broadening during propagation. This correlated geometric growth naturally induces a hierarchy for the geometry-only observable

A = LW,

which obeys the scaling law

A ∼ L^1+α ≈ L^1.43.

Complementary cumulative distribution functions reveal broad heavy-tailed statistics spanning several decades in scale. Finite-size scaling analysis further demonstrates that the geometric hierarchy remains remarkably stable across independent historical periods despite major observational transitions associated with Doppler-radar deployment and evolving survey practices.

Higher-order conditional moments remain predominantly affine and are shown to be fully consistent with the measured width–length scaling relation. Null-model comparisons demonstrate that the observed hierarchy cannot be explained solely by broad marginal distributions or simple algebraic construction effects, but instead reflects genuine correlations linking tornado length and width across scales.

Although the present analysis remains fundamentally statistical, the results suggest that tornado damage geometry may reflect the large-scale statistical imprint of persistent coherent vortex organisation embedded within strongly nonlinear convective dynamics.