## Blowing harder and more often

The frequency of tornado outbreaks (clusters of tornadoes) and the number of extremely powerful tornado events have been increasing over nearly the past half-century in the United States. Tippett *et al.* found that tornado outbreaks have become more common since the 1970s. This increase seems to have been driven by consistent changes in the meteorological environment that make tornadoes more likely to form. However, the changes are not necessarily those that one would expect from climate change, which makes it difficult to predict whether this trend will continue.

*Science*, this issue p. 1419

## Abstract

Tornadoes and severe thunderstorms kill people and damage property every year. Estimated U.S. insured losses due to severe thunderstorms in the first half of 2016 were $8.5 billion (US). The largest U.S. effects of tornadoes result from tornado outbreaks, which are sequences of tornadoes that occur in close succession. Here, using extreme value analysis, we find that the frequency of U.S. outbreaks with many tornadoes is increasing and that it is increasing faster for more extreme outbreaks. We model this behavior by extreme value distributions with parameters that are linear functions of time or of some indicators of multidecadal climatic variability. Extreme meteorological environments associated with severe thunderstorms show consistent upward trends, but the trends do not resemble those currently expected to result from global warming.

In the United States, tornado outbreaks have substantial effects on human lives and property. Tornado outbreaks are sequences of six or more tornadoes that are rated F1 and greater on the Fujita scale or rated EF1 and greater on the Enhanced Fujita scale and that occur in close succession (*1*, *2*). About 79% of tornado fatalities during the period 1972 to 2010 occurred in outbreaks (*1*), and 35 people died in U.S. tornado outbreaks in 2015. No significant trends have been found in either the annual number of reliably reported tornadoes (*3*) or of outbreaks (*1*). However, recent studies indicate increased variability in large normalized economic and insured losses from U.S. thunderstorms (*4*), increases in the annual number of days on which many tornadoes occur (*3*, *5*), and increases in the annual mean and variance of the number of tornadoes per outbreak (*6*). Here, using extreme value analysis, we find that the frequency of U.S. outbreaks with many tornadoes is increasing and that it is increasing faster for more extreme outbreaks. We model this behavior by extreme value distributions with parameters that are linear functions of time or of some indicators of multidecadal climatic variability. Extreme meteorological environments associated with severe thunderstorms show consistent upward trends, but the trends do not resemble those currently expected to result from global warming.

Linear trends in the percentiles of the number of tornadoes per outbreak (Fig. 1A) are positive, statistically significant, and increase exponentially faster with percentile probability (Fig. 1B). This behavior is consistent with the positive trends in mean and variance (*6*), which suggested that the distribution of the number of tornadoes per outbreak is shifting to the right (increasing mean) and that higher percentiles of the distribution are shifting faster than the mean (increasing variance). The increase of percentile trends with percentile probability is consistent with trends in the frequency of tornado days with many tornadoes increasing with threshold (*5*).

Nonstationary generalized extreme value (GEV) distributions with trends in their parameters do not reproduce the observed upward trend in the slopes of percentiles as a function of percentile probability (supplementary materials and fig. S1). Therefore, we use the Generalized Pareto (GP) approach with a threshold of 12 E/F1+ tornadoes [(*2*) and fig. S2]. We refer to outbreaks with 12 or more E/F1+ tornadoes as “extreme outbreaks” (*2*). There were 435 extreme outbreaks from 1965 through 2015, no statistically significant trends in the annual number of extreme outbreaks (*P *= 0.66) (Fig. 2A), and no statistically significant autocorrelation in the numbers of tornadoes per extreme outbreak (fig. S2C). The GP distributions found here have shape parameter around 0.3 (finite mean and variance) and are lighter-tailed distributions than was found considering tornadoes per day (rather than outbreaks) and a threshold of one (Pareto shape parameter of 0.61, infinite mean and variance) (*7*).

The percentiles of the number of tornadoes per extreme outbreak (Fig. 2B) also have upward trends that are statistically significant (above the 30th percentile) and depend approximately exponentially on the percentile probability (Fig. 2C). Allowing a trend as a function of time in the GP threshold *u* would give percentile trends (slopes) that are the same for all percentiles, contrary to observation. Permitting a linear trend as a function of time in the scale improves the fit to the data statistically significantly. According to this model, the scale parameter and the percentiles increase linearly with time (Table 1), and higher percentiles increase faster. The standardized quantile-quantile plot in fig. S3 shows fairly good agreement between the data and the GP distribution, with a linear trend in its scale parameter as a function of time. Data quantiles exceed those of the model at high percentiles (standardized model quantile values of 3 to 4 in fig. S3), meaning that the model predicts that outbreaks with many tornadoes would occur more often than is observed. The difference between model and data quantiles falls within the range expected from sampling variability (fig. S3). We cannot reject the model on this basis.

The slopes of the percentiles of the GP distribution with a linear trend in its scale parameter are approximately exponential in the percentile probability and match well those estimated by quantile regression (Fig. 2C). The trends from quantile regression and from the nonstationary GP distribution deviate from exponential dependence on the percentile probability near the end points of 0% and 100% probability. Adding a trend to the scale parameter ξ results in a marginally statistically significant (*P* = 0.04) (Table 1) upward trend that is statistically insignificant when the largest value (in 2011) is withheld (*P* = 0.1) (table S2). The scale trends change little when the outbreak value from 2011 is withheld (table S2). Return levels for 2-, 5-, and 25-year return periods are shown in Fig. 2D along with 90% bootstrap confidence intervals (5000 bootstrap samples with bias correction and acceleration). The estimated number of tornadoes in the 5-year most extreme outbreak roughly doubles from 40 in 1965 to nearly 80 in 2015.

The outbreak trends in the tornado report database may reflect changes in reporting rather than real properties of tornadoes (*8*). The environments associated with tornadoes and severe thunderstorms provide valuable evidence that is independent of report data for assessing the variability of severe convective storms (*4*, *9*–*13*). We use a two-part environmental proxy for the number of tornadoes per outbreak (*2*, *6*). Here, we define extreme environments as those with values of the outbreak proxy greater than 12, matching the extreme outbreak definition. The proxy is computed using reanalysis data (*2*) and depends on two factors, convective available potential energy (CAPE) and a measure of vertical wind shear, storm relative helicity (SRH). Modeling studies project that CAPE will increase in future warmer climates (*14*, *15*), and Elsner *et al*. (*5*) hypothesized that climate change and increases in CAPE could already be leading to more active areas of severe convection on days with tornadoes.

However, we find no statistically significant trends in the percentiles of CAPE conditional on extreme environments (Fig. 3A) nor in the percentiles of CAPE conditional on CAPE > 1 J kg^{−1} (not shown). On the other hand, there are statistically significant upward trends in the percentiles of SRH conditional on extreme environments (Fig. 3B), and these trends are the source of the trends in the percentiles of the outbreak number proxy (Fig. 3C). The linear growth rates (slopes) of the proxy for the number of tornadoes per extreme outbreak are approximately exponential in the percentile probabilities, like those for the number of tornadoes in extreme outbreaks, and have roughly the same range of values. Percentiles of environments (not extreme) conditional on the environmental occurrence proxy show the same qualitative behavior (fig. S5). Therefore, we cannot at present associate previously identified features of a warmer climate with the observed changes in our environmental proxy and, by extension, with the changes in tornado outbreak statistics.

The observed trends in the statistics of outbreaks and extreme environments may be related to low-frequency climate variability other than climate change. Multidecadal variability in U.S. tornado activity has been compared with sea surface temperature (SST)–forced variability (*16*). We explore the connection between multidecadal climate signals and outbreak statistics using a nonstationary GP distribution whose scale parameter is a linear function of the climate signal rather than time.

The Atlantic Multidecadal Oscillation (AMO) (*17*) affects North American climate, is characterized by variations in North Atlantic SST, and can be explained as an oceanic response to mid-latitude atmospheric forcing (*18*). The AMO shows multidecadal variability, increasing from about 1970 though the mid-2000s (fig. S4A). The GP distribution whose scale parameter is a linear function of the AMO index fits the data significantly better than the stationary GP distribution but not better than a linear time trend (Table 1).

Another important pattern of climate variability is the Pacific Decadal Oscillation (PDO) (*19*) (fig. S4B). The GP distribution whose scale parameter is a linear function of the PDO index does not fit the data significantly better than the stationary GP distribution (Table 1).

Contiguous U.S. (CONUS) annual average temperature is increasing, and that change has prompted investigations of changes in the U.S. tornado climatology (*20*). Taking the GP scale parameter to depend linearly on CONUS temperature gives a significantly better fit to the data than does the stationary GP distribution but not a better fit than the GP distribution with a scale parameter that depends linearly on either time or the AMO index (Table 1).

Many changes in U.S. tornado report statistics have been ascribed to changes in reporting practices, technology, and other nonmeteorological factors (*8*). However, recent findings point to increases in the number of tornadoes per event, whether events are defined as days when tornadoes occur (*3*, *5*) or as tornado outbreaks (*6*). Here, we found statistically significant upward trends in the higher percentiles of the number of tornadoes per outbreak. We modeled these trends using extreme value distributions with a time-varying scale parameter. Similar behavior in an environmental proxy suggested that the behavior of the tornado reports is not due simply to changes in reporting practice or technology.

Climate change has been proposed as contributing to changes in tornado statistics (*5*, *20*). Climate model projections indicate that CAPE, one of the factors in our environmental proxy, will increase in a warmer climate, leading to more frequent environments favorable to severe thunderstorms in the United States (*14*, *15*). However, the proxy trends here are not due to increasing CAPE but instead due to trends in SRH, a quantity related to vertical wind shear that was previously identified as a factor in increased year-to-year variability of U.S. tornado numbers (*11*). Therefore, we cannot at present associate the observed changes in our environmental proxy and, by extension, the changes in tornado outbreak statistics, with previously identified features of a warmer climate. This conclusion is, of course, subject to revision by the discovery of other implications of a warmer climate for severe thunderstorm environments.

The question of which climatic factors have driven the observed changes in tornado activity has important implications for the future. If global warming is changing tornado activity, then we might expect to see either continued increases in the number of tornadoes per outbreak or at least no return to earlier levels. On the other hand, if multidecadal variability, anthropogenic or natural, is responsible, then a return toward earlier levels might be possible in the future. Further clouding the future, many of the outbreak measures (annual maximum and higher percentiles of the number of tornadoes per outbreak) reached their lowest values in more than a decade in 2015. As a final caveat, inferring tornadic actively solely from the environment has considerable uncertainty even in the current climate and at least as much in projected climates (*21*).

## Supplementary Materials

www.sciencemag.org/content/354/6318/1419/suppl/DC1

Materials and Methods

Figs. S1 to S5

Tables S1 and S2

## References and Notes

**Acknowledgments:**The authors thank A. Rhimes and K. McKinnon for suggestions on the use of quantile regression with count data. We thank two reviewers who provided constructive and helpful comments. M.K.T. and C.L. were partially supported by a Columbia University Research Initiatives for Science and Engineering (RISE) award; Office of Naval Research awards N00014-12-1-0911 and N00014-16-1-2073; NOAA’s Climate Program Office’s Modeling, Analysis, Predictions, and Projections program award NA14OAR4310185; and the Willis Research Network. J.E.C. was partially supported by U.S. National Science Foundation grant DMS-1225529 and thanks P. K. Rogerson for assistance during this work. The views expressed herein are those of the authors and do not necessarily reflect the views of any of the sponsoring agencies. The study was led by M.K.T.; calculations were carried out and the manuscript was drafted by M.K.T. C.L. prepared the environmental data. All authors were involved with designing the research, analyzing the results, and revising and editing the manuscript. All the authors declare no competing interests. Correspondence and material requests should be addressed to M.K.T. U.S. tornado report data come from NOAA’s Storm Prediction Center www.spc.noaa.gov/wcm. North American Regional Reanalysis data are provided by the NOAA/Office of Oceanic and Atmospheric Research/Earth System Research Laboratory Physical Sciences Division, Boulder, Colorado, USA, from their website at www.esrl.noaa.gov/psd and the Data Support Section of the Computational and Information Systems Laboratory at the National Center for Atmospheric Research (NCAR). NCAR is supported by grants from the National Science Foundation.