Brief communication: Towards a universal formula for the probability of tornadoes

Nat. Hazards Earth Syst. Sci., 23, 2443–2448, 2023 https://doi.org/10.5194/nhess-23-2443-2023 © Author(s) 2023. This work is distributed under the Creative Commons Attribution 4.0 License. Brief communication: Towards a universal formula for the probability of tornadoes Roberto Ingrosso1 , Piero Lionello2 , Mario Marcello Miglietta3 , and Gianfausto Salvadori4 1 Department of Earth and Atmospheric Sciences, University of Quebec in Montréal, 201 av. duPresident Kennedy, Montréal, H3C 3P8, Canada 2 Dipartimento di Scienze e Tecnologie Biologiche ed Ambientali, Università del Salento, via per Monteroni 165, Lecce, 73100, Italy 3 ISAC-CNR, Istituto di Scienze dell’Atmosfera e del Clima, Consiglio Nazionale delle Ricerche, corso Stati Uniti 4, Padua, 35127, Italy 4 Dipartimento di Matematica e Fisica, Università del Salento, Provinciale Lecce-Arnesano, P.O. Box 193, Lecce, 73100, Italy Correspondence: Piero Lionello () Received: 6 February 2023 – Discussion started: 7 February 2023 Revised: 19 May 2023 – Accepted: 1 June 2023 – Published: 11 July 2023 Abstract. 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. 1 Introduction Tornadoes are rapidly rotating columns of air (American Meteorological Society, 2020), extending vertically from the surface to the base of a cumuliform cloud, and represent one of the most severe weather phenomena in terms of victims and damage. Considering only the USA, every year about 500 tornadoes (Kunkel et al., 2013) of intensity EF1 (enhanced Fujita scale; Fujita, 1971; Potter, 2007) or stronger occur, producing an average of 125 victims and huge devastation (Ashley, 2007). Numerical simulations of the very fine spatial and temporal scale of tornadoes (typically with a diameter of less than 2 km and a duration of less than 1000 s) require resolutions that are orders of magnitude smaller than those currently available in operational weather prediction and climate models (Yokota et al., 2018). Further, the chaotic dynamics of these vortices limit their deterministic prediction (Markowski, 2020). Consequently, climatological studies focused on the identification of the environmental conditions favourable to tornado-spawning severe convective storms. Several thermodynamic and kinematic meteorological parameters have been analysed, either individually or considering combined instability indices, to identify the conditions most favourable to the genesis of tornadoes (Brooks et al., 2003; Romero et al., 2007; Taszarek et al., 2018, 2020; Ingrosso et al., 2020; Bagaglini et al., 2021). This approach is consistent with the basic idea that tornadoes result from a multi-stage process, which takes into account that the tilting of the horizontal vorticity near the ground by a violent updraught plays a basic role (Rotunno, 2013; Davies-Jones, 2015). Such a conceptual model is used here as a background framework for introducing an analytical formula for the probability of tornado occurrence. A previous study defined a tornado index limited to the USA based on a Poisson regression between the observed U.S. climatology of tornadoes and monthly averaged environmental parameters from reanalysis (Tippett et al., 2012). Other studies limited their conclusions to the identification of the conditions that are associated with mesoscale convective hazards (Brooks, 2013; Diffenbaugh et al., 2013). The expression that we propose in this study is meant to provide a tool for supporting tornado warning in operational weather predictions and estimating changes in the frequency of tornado occurrence in climate projections. Published by Copernicus Publications on behalf of the European Geosciences Union. 2444 2 Data and methods Our analysis is based on tornadoes that occurred in the USA (dataset provided by the Storm Prediction Center (SPC), https://www.spc.noaa.gov/wcm/#dat, last access: 4 June 2023) and in Europe (dataset provided by the European Severe Weather Database (ESWD), https://www.essl. org, last access: 4 June 2023, managed by the European Severe Storm Laboratory (ESSL); Dotzek et al., 2009). We considered only tornadoes of category 2 or higher (F2+), following the idea that weak events might have an uncertain signature in the environmental conditions and their reporting in official databases is less accurate. A total number of 3073 tornadoes have been considered in this study (2632 for the USA and 441 for Europe; see the Supplement for density plots) during the period 2000–2018. Unfortunately, our dataset does not allow us to differentiate supercellular tornadoes from landspouts in most cases. The hourly fields of ERA5 (ECMWF Reanalysis 5; Hersbach et al., 2020) are used to establish a statistical link between the occurrence of tornadoes and a set of meteorological variables, allowing a straightforward physical interpretation of the results: the updraught maximum parcel vertical velocity (WMAX), which depends on the convective available potential energy (CAPE), the mid-level wind shear (WS700 ), the low-level storm relative helicity (SRH900 ), and the lifting condensation level (LCL; Kaltenböck et al., 2009). The Supplement reports the expressions defining the variables used in this study. The values of these variables have been extracted in the period 2000–2018 in all cells where at least one tornado occurred, considering the hourly reanalysis fields at 25 km resolution. The values corresponding to the occurrence of tornadoes have been selected considering the time step closest to the recorded time of the tornado onset in the database. The univariate analysis of the (conditional) probability P of tornado occurrence is carried out by partitioning the observed range spanned by each variable into 17 equiprobable sub-intervals (bins). Such a number has been chosen as a compromise between the need of a number of bins sufficient for robust regressions and of a number of observations in each bin sufficient for a robust statistical analysis. An empirical estimate of the probability of tornado occurrence, conditional to the fact that the value of the variable lies in a given bin, is computed as the relative frequency of tornadoes in the bin. Its uncertainty is estimated via a suitable bootstrap (Monte Carlo) procedure. An analytical expression of y = log10 P is found by a simple linear regression for WS700 , SRH900 , and LCL, as well as by a non-linear regression for WMAX (see the Supplement). Notice that first the climatology of the variable of interest is calculated via the partiti (...truncated)