Tornado damage ratings estimated with cumulative logistic regression

James B Elsner, Zoe Schroder Searcy 

Empirical studies have led to improvements in evaluating and quantifying the tornado threat. However more work is needed to put the research onto a solid statistical foundation. Here the authors begin to build this foundation by introducing and then demonstrating a statistical model to estimate damage rating probabilities. A goal is to alert researchers to available statistical technology for improving severe weather warnings. The model is cumulative logistic regression and the parameters are determined using Bayesian inference. The model is demonstrated by estimating damage rating probabilities from values of known environmental factors on days with many tornadoes in the United States. Controlling for distance-to-nearest town/city, which serves as a proxy variable for damage target density, the model quantifies the chance that a particular tornado will be assigned any damage rating given specific environmental conditions. Under otherwise average conditions the model estimates a 65% chance that a tornado occurring in a city or town will be rated EF0 when bulk shear is weak (10 m/s). This probability drops to 38% when the bulk shear is strong (40 m/s). The model quantifies the corresponding increases in the chance of the same tornado receiving higher damage ratings. Quantifying changes to the probability distribution on the ordered damage rating categories is a natural application of cumulative logistic regression.