B. D. Malamud^{1} and D. L. Turcotte^{2}
^{1}Department of Geography, King's College London, Strand, London, WC2R 2LS, UK

^{2}Department of Geology, University of California, Davis, CA 95616, USA

Received: 30 Dec 2011 – Published in Atmos. Chem. Phys. Discuss.: 07 Mar 2012

Revised: 09 Aug 2012 – Accepted: 15 Aug 2012 – Published: 20 Sep 2012

Abstract. The standard measures of the intensity of a tornado in the USA and many other countries are the Fujita and Enhanced Fujita scales. These scales are based on the damage that a tornado causes. Another measure of the strength of a tornado is its path length of touchdown, *L*. In this study we consider severe tornadoes, which we define as *L*≥10 km, in the continental USA (USA Storm Prediction Center Severe Weather Database). We find that for the period 1982–2011, for individual severe tornadoes (*L*≥10 km): (i) There is a strong linear scaling between the number of severe tornadoes in a year and their total path length in that year. (ii) The cumulative frequency path length data suggests that, not taking into account any changing trends over time, we would expect in a given year (on average) one severe tornado with a path length *L*≥115 km and in a decade (on average) one severe tornado with a path length *L*≥215 km. (iii) The noncumulative frequency-length statistics of severe tornado touchdown path lengths, 20<*L*<200 km, is well approximated by an inverse power-law relationship with exponent near 3. We then take the total path length of severe tornadoes in a convective day (12:00–12:00 UTC), *L*_{D}, as a measure of the strength of a 24-h USA tornado outbreak. We find that: (i) For 1982–2011, the number of severe tornadoes in a USA convective day outbreak has a strong power-law relationship (exponent 0.80) on the convective day total path length, *L*_{D}. (ii) For 1952–2011, the cumulative frequency path length data for severe tornado outbreaks suggests that we would expect in a given year (on average) one daily severe tornado outbreak with total path length *L*_{D}≥480 km and in a decade (on average) one daily severe tornado outbreak with a total path length *L*_{D}≥1200 km. (iii) For 1982–2011, the noncumulative frequency-length statistics of tornado outbreaks, 10<*L*_{D}<1000 km d^{−1}, is well approximated by an inverse power-law relationship with exponent near 1.8. Finally, we consider the frequency path-length scaling of severe tornadoes (*L*≥10 km) during two tornado outbreaks, 27 April 2011 (67 severe tornadoes) and 25 May 2011 (16 severe tornadoes), and find similar statistical distributions with robust scaling. We believe that our robust scaling results provide evidence that touchdown path lengths can be used as quantitative measures of the systematic properties of severe tornadoes and severe tornado outbreaks.

**Citation:**
Malamud, B. D. and Turcotte, D. L.: Statistics of severe tornadoes and severe tornado outbreaks, Atmos. Chem. Phys., 12, 8459-8473, doi:10.5194/acp-12-8459-2012, 2012.