A methodological approach is proposed to provide an analytical (exponential-like) expression for the probability of occurrence of tornadoes as a function of the convective available potential energy and the wind shear (or, alternatively, the storm relative helicity). The resulting expression allows the probability of tornado occurrence to be calculated using variables that are computed by weather prediction and climate models, thus compensating for the lack of resolution needed to resolve these phenomena in numerical simulations.

Tornadoes are rapidly rotating columns of air

Our analysis is based on tornadoes that occurred in the USA (dataset provided by the Storm Prediction Center (SPC),

The univariate analysis of the (conditional) probability

The univariate analysis shows that all the four variables considered in our study (i.e. WMAX, WS

Univariate probability distribution for WMAX, WS

Concerning the bivariate analysis (i.e. considering the joint behaviour of pairs of predictors), in analogy with the univariate case, a

Considering the bivariate expression of

Bivariate probability distribution for

All parameters of the univariate fits in Fig.

Further investigations are required to ensure the validity of the expressions in Eqs. (

Possible explanations of the lack of compatibility between conditional probabilities obtained using the EU and USA datasets alone could be different tornado damage-reporting practices (leading to different counting and attributions of tornadoes to the EF/F scale) and different meteorological and/or morphological conditions in the two domains. In spite of these limitations, as well as the need for further investigations, the proposed statistical models suitably fit the conditional probabilities of tornado occurrence. In particular, Eq. (

The formulas of Eqs. (

The list of tornadoes in the USA can be freely downloaded at

The supplement related to this article is available online at:

RI has been responsible for data collecting, processing, and plotting; PL for the coordination of the study; MMM for the meteorological analysis; and GS for the statistical analysis and the computation of the probability of occurrence of tornadoes. All the authors wrote and contributed to the final manuscript.

At least one of the (co-)authors is a member of the editorial board of

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The authors gratefully acknowledge useful discussions and suggestions by Fabrizio Durante (University of Salento, Lecce, Italy. The work of Piero Lionello has been carried out with the partial financial support from ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data and Quantum Computing, funded by European Union – NextGenerationEU (CUP F83C22000740001). Moreover, we thank the support of the European COST Action CA17109 “DAMOCLES” (Understanding and Modeling Compound Climate and Weather Events) and the support of the Italian PRIN 2017 (Research Projects of National Interest) “Stochastic Models of Complex Systems” (2017JFFHSH). ESSL is acknowledged for providing European data, ECMWF for ERA5 reanalyses, and the Storm Prediction Center for US reports.

This work has been partially financially supported by ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data and Quantum Computing, funded by European Union – NextGenerationEU (CUP F83C22000740001).

This paper was edited by Maria-Carmen Llasat and reviewed by two anonymous referees.