On the temporal and spatial characteristics of tornado days in the United States

    On the temporal and spatial characteristics of tornado days in the United States Todd W. Moore PII: DOI: Reference:

S0169-8095(16)30459-8 doi:10.1016/j.atmosres.2016.10.007 ATMOS 3808

To appear in:

Atmospheric Research

Received date: Revised date: Accepted date:

30 June 2016 28 September 2016 12 October 2016

Please cite this article as: Moore, Todd W., On the temporal and spatial characteristics of tornado days in the United States, Atmospheric Research (2016), doi:10.1016/j.atmosres.2016.10.007

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ACCEPTED MANUSCRIPT

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Todd W. Moore*

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On the temporal and spatial characteristics of tornado days in the United States

Department of Geography and Environmental Planning, Towson University, Towson, Maryland

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21252, USA

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*Corresponding author: Todd W. Moore 8000 York Road Towson University Department of Geography and Environmental Planning Towson, MD 21252 Email: [email protected] Phone: 410-704-3973

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ACCEPTED MANUSCRIPT ABSTRACT More tornadoes are produced per year in the United States than in any other country,

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and these tornadoes have produced tremendous losses of life and property. Understanding

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how tornado activity will respond to climate change is important if we wish to prepare for

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future changes. Trends in various tornado and tornado day characteristics, including their annual frequencies, their temporal variability, and their spatial distributions, have been

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reported in the past few years. This study contributes to this body of literature by further

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analyzing the temporal and spatial characteristics of tornado days in the United States. The analyses performed in this study support previously reported findings in addition to providing

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new perspectives, including that the temporal trends are observed only in low-frequency and

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high-frequency tornado days and that the eastward shift in tornado activity is produced, in part,

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by the increasing number of high-frequency tornado days, which tend to occur to the east of the traditionally depicted tornado alley in the Great Plains. Keywords:

United States; tornado days; temporal trends in tornado days; spatial

distribution of tornado days; Mann-Kendall trend test; Taylor’s power law.

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ACCEPTED MANUSCRIPT 1. Introduction The United States (US) experiences an average of more than 1,000 tornadoes per year,

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which is more than any other country on Earth (NCEI, 2016b). Tornadoes in the US often result

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in losses of life and property. They were responsible for an average of 70 fatalities per year

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over the period 1986–2015; the average fatality count is 110 over the period 2006–2015 (NWS, 2016). They also caused an average annual loss of $982 million (US dollars) over the period

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1949–2006 (Changnon, 2009). These average values can be greatly exceeded, however, in

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extreme events when many tornadoes occur. For example, more than 100 tornadoes were produced on 27 April 2011 in the US across the states of Mississippi, Alabama, Georgia,

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Tennessee, and Virginia (NOAA, 2011; Knupp et al., 2014). These tornadoes were responsible

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for 316 fatalities and more than 2,700 injuries (NOAA, 2011; Knupp et al., 2014), and they,

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along with the others that occurred in April in the US, resulted in more than $11 billion (US dollars) in insured losses (Simmons and Sutter, 2012). Understanding the environmental conditions in which tornadoes occur, and when and where they occur, is imperative for mitigating their negative impacts. Over the years, research on the environment in which tornadoes occur (e.g., Doswell, 1987; Johns and Doswell, 1992; Doswell et al., 1996; Rasmussen, 2003; Doswell and Schultz, 2006; Grams et al., 2012; Garner, 2012, 2013; Mercer et al., 2012; Schultz et al., 2014; Sherburn and Parker, 2014) has highlighted various conditions, or ingredients (Doswell et al., 1996), that promote tornadogenesis. These include ample low-level humidity, high instability, high shear, and a lifting mechanism (e.g., lowlevel convergence or a front) (Doswell, 1987; Johns and Doswell, 1992). Thorough reviews of research on the environments in which tornadoes occur and tornado forecasting efforts are 3

ACCEPTED MANUSCRIPT provided by Galway (1985), Schaefer (1986), Galway (1992), Doswell et al. (1993), and Doswell (2007).

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The temporal and spatial distributions of tornadoes in the US have been documented in

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numerous climatological studies (e.g., Kelly et al., 1978; Brooks et al., 2003; Kis and Straka,

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2010). The National Oceanic and Atmospheric Administration’s (NOAA) National Centers for Environmental Information (NCEI) and Storm Prediction Center (SPC) also provide information

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about tornado climatology and tornado data (NCEI, 2016a, 2016b; SPC, 2016). This information

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and these data sources have been particularly useful to analyses of tornado hazard and to the development of tornado risk and vulnerability models (e.g., Boruff et al., 2003; Ashley et al.,

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2008; Dixon et al., 2011; Simmons and Sutter, 2011; Dixon and Moore, 2012; Widen et al.,

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2013; Ashley et al., 2014; Coleman and Dixon, 2014; Jagger et al., 2015; Rosencrants and

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Ashley, 2015; Shen and Hwang, 2015; Elsner et al., 2016; Romanić et al., 2016; StandoharAlfano and van de Lindt, 2015).

In addition to understanding the environmental conditions that were and are favorable for tornadoes, and their climatological distributions, it also is important to consider how they may change in response to global climate change. In multiple studies, the environmental conditions that are known to promote tornadoes have been modeled (i.e., they examined the tornado-favorable ingredients rather than tornadoes) to determine if atmospheric conditions in the future will be more or less favorable for them (e.g., Brooks et al., 2003; Trapp et al., 2009; Gensini and Ashley, 2011; Diffenbough et al., 2013; Robinson et al., 2013; Gensini and Mote, 2014; Gensini et al., 2014; Gensini and Mote, 2015; Seely and Romps, 2015; Tippett et al., 2015). This approach is taken because it is currently not possible to project whether tornadoes 4

ACCEPTED MANUSCRIPT will become more or less frequent, or more or less intense, in a warmer atmosphere with physics-based climate models because their spatial and temporal resolutions are too coarse

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(Tippett et al., 2015). Although uncertainty still exists, studies have reported that

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environmental conditions will likely favor more severe weather, and possibly tornadoes, in the

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future, largely because of an increase in atmospheric instability and low-level humidity. Recent empirical studies have searched for changes in the temporal and spatial

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distributions of tornadoes in the US. Some have shown that the annual numbers of tornadoes

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in the US have not increased (Brooks et al., 2014; Elsner et al., 2015; Tippett and Cohen, 2016; NCEI, 2016a), despite the projections for an increase in tornado-favorable environments

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(Diffenbough et al., 2013; Gensini and Mote, 2015; Seely and Romps, 2015; Tippett et al., 2015).

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Others have reported trends in tornado day frequencies and in various statistical characteristics

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of tornado activity. Brooks et al. (2014), for example, reported that the number of days per year with 1+ tornadoes declined since the 1970s, but that the number of days with more than 30 tornadoes increased. Elsner et al. (2015), similarly, reported that the number of days per year with 4+ tornadoes decreased whereas the number of days with 8+, 16+, and 32+ increased over time. They also found similar trends when looking at the annual probability of tornado days and the annual proportion of tornadoes occurring on days meeting these frequency thresholds. Tippett and Cohen (2016) reported an upward trend in the mean number of tornadoes per outbreak per year. Studies also have shown that several tornado metrics have become more variable over time. Brooks et al. (2014) reported an increase in the standard deviation of the ranks of monthly tornado frequency between 1954 and 2013. Tippett (2014) reported an increase, 5

ACCEPTED MANUSCRIPT primarily in the 2000s, in the volatility of annual tornado frequency, defined as the standard deviation of the difference between the annual tornado frequencies of successive years.

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Tippett and Cohen (2016) showed that the variance of the number of tornadoes per outbreak

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increased at a rate of 2.89% per year over the period 1954–2014.

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Temporal changes in the spatial distribution of tornadoes in the US also have been reported. Farney and Dixon (2014) plotted the annual average number of tornado days for the

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periods 1960–1989 and 1990–2011. Their plots show an increase in tornado day frequencies in

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the latter period throughout the Middle and Lower Mississippi, Ohio, and Tennessee River Valleys, and in a few places to the east of the Appalachian Mountains. Elsner et al. (2015)

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analyzed tornado density and found that tornadoes became more clustered in space over the

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period 1954–2013, leading to an increase in tornado density. Most recently, Agee et al. (2016)

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analyzed the spatial distribution of tornadoes in the periods 1954–1983 and 1984–2013 and reported a decrease in tornado activity in the latter period in Texas and Oklahoma and an increase to the east in Tennessee and Alabama. Understanding the environments in which tornadoes occur as well as their temporal and spatial distributions is important to many, including operational forecasters, emergency managers, and insurance companies. Continued study is needed to advance our understanding as new data become available. This is especially true in the context of climate change. This study builds upon the array of empirical studies on this topic by further analyzing the temporal and spatial trends of tornado days in the US.

2. Data and methods 6

ACCEPTED MANUSCRIPT 2.1. Data sources and processing Tornado reports were obtained from the SPC’s Severe Weather Database (SWD; SPC,

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2016). The SWD provides two tornado files. One has raw data and includes all state and county

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segments of a tornado track, meaning that a tornado could have multiple entries depending on

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the number of states and counties/parishes through which it tracked. The second includes only one entry per tornado, and therefore minimizes the overcount that results from long-tracked

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tornadoes that intersect multiple counties/parishes and/or states (there are 61,209 tornado

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entries in the raw database and 60,114 in the second). The second database (“Actual_tornadoes.csv” from SPC (2016)) is used in this study.

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The tornadoes in the database have multiple attributes, including information on their

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date, time, location, and estimated intensity. Intensity is estimated with the Fujita (F) or

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Enhanced Fujita (EF) Scale, both of which range from 0 (minimum damage) to 5 (maximum damage). The EF Scale replaced in the F Scale in 2007. An increasing trend in the number of (E)F0 tornadoes per year has been documented and attributed largely to non-meteorological factors such as changes in reporting practices and technology, whereas the (E)F1+ record is more stationary owing to the fact that stronger tornadoes have likely been observed and reported more consistently over time (Brooks and Doswell, 2001; Brooks, 2004; Doswell et al., 2005; Verbout et al., 2006; Kunkel et al., 2013). As a result, recent studies (e.g., Brooks et al., 2014; Elsner et al., 2015; Tippett and Cohen, 2016) have limited their analyses to (E)F1+ tornadoes. In line with these studies, only tornadoes rated (E)F1+ are analyzed here. The database was further narrowed by omitting tornadoes that occurred outside of the contiguous US; tornadoes in Hawaii (41), Alaska (4), and Puerto Rico (24) were excluded. 7

ACCEPTED MANUSCRIPT Beginning the analysis in 1974 reduces the under- and over-counts of F1 and F2 tornadoes, respectively, prior to 1974 (Agee and Childs, 2014). Other studies have shown that

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the number of tornadoes rated E(F)2+ declined after the 1970s when the National Weather

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Service began to systematically rate tornado intensity (Verbout et al., 2006; Edwards et al.,

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2013; Romanić et al., 2015). Multiple others have limited their analyses to tornado data from the 1970s and onward to reduce the effect of secular trends (e.g., Coleman and Dixon, 2014;

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Fuhrmann et al., 2014; Elsner et al., 2016; Standohar-Alfano and van de Lindt, 2016). Beginning

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the analysis in 1974 also enables future work that will combine environmental data from the North American Regional Reanalysis, which begins in 1974, with the datasets generated here.

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This future work will focus on the synoptic patterns and the kinematic and thermodynamic

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environments associated with low- and high-frequency tornado days.

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The analyses in this study are focused on tornado days, which are defined as days with 1+ tornadoes. Annual frequencies of tornado days were derived and recorded. Tornado days of different magnitudes also were derived and recorded on the basis of (1) exceedance thresholds, including 10+ tornadoes, 20+ tornadoes, 30+ tornadoes, and 50+ tornadoes, and (2) mutually exclusive groups, including 1–9 tornadoes, 10–19 tornadoes, 20–29 tornadoes, and 30+ tornadoes. 2.2. Methods of analysis Recent studies that reported trends in the frequencies and statistical metrics of tornado days have used generalized linear models, including ordinary least squares linear regression (Brooks et al., 2014; Elsner et al., 2015; Tippett and Cohen, 2016). In this study, I employ a previously-unused method, a combination the nonparametric Mann-Kendall test and Theil-Sen 8

ACCEPTED MANUSCRIPT slope estimate, to verify and further analyze trends in tornado day time series. These methods are appropriate given the asymmetry of the frequency distribution of tornado day magnitude

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(i.e., the number of tornadoes per day; Elsner et al., 2014), and they are commonly used to

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detect monotonic trends in the time series of extreme weather and climate events (e.g., Burn

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and Elnur, 2002; Webster et al., 2005; Kossin et al., 2007; Gocic and Trajkovic, 2013; Kunkel et al., 2013; Sonali and Kumar, 2013; Westra et al., 2013; Araghi et al., 2016; Bari et al., 2016;

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Pingale et al., 2016; Romanić et al., 2015). The trend statistics and parameters reported in this

Kendall, 1975).

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)

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The Mann-Kendall S is given by:

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study are the Mann-Kendall statistic (S) and the Theil-Sen slope estimate (β) (Mann, 1945;

(1)

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where Xa and Xb are the sequential data values of the time series in years a and b, n is the length of the time series, and: –

(2)

The variance of S is given by: (3) where m is the number of tied observations and t is the size of the ith tied value. The standardized Mann-Kendall test statistic (Z) is given by:

(4)

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ACCEPTED MANUSCRIPT The null hypothesis of the Mann-Kendall test is that there is no trend in a time series. For ǀZǀ ≥ Z1−(α/2), where α=0.05, the null hypothesis is rejected and the alternative hypothesis

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stating that a trend exists is accepted.

(5)

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The slopes of the trends (β) were determined with:

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Benefits of the Mann-Kendall test are that it does not make assumptions about the underlying distribution of a time series and it is robust to outliers, but it does assume that time

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series are serially independent (i.e., not auto-correlated). There were six auto-correlated time series in this study: (1) annual count of 1+ tornado days; (2) annual count of 1–9 tornado days;

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(3) annual count of (E)F1 tornadoes on 1–9 tornado days; (4) annual count of (E)F2 tornadoes

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on 1–9 tornado days; (5) annual count of (E)F1 tornadoes on 10–19 tornado days; (6) annual

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count of (E)F2 tornadoes on 10–19 tornado days. Following Burn and Elnur (2002) and Pingale et al. (2016), these time series were pre-whitened with the following: –

(6)

where Xt is the pre-whitened time series value in year t, xt is the original time series value in year t, and r is the lag-1 autocorrelation coefficient. The values of the lag-1 autocorrelation coefficients for the six aforementioned auto-correlated time series are as follows: r1=0.67; r2=0.69 ; r3=0.42 ; r4=0.38 ; r5=0.38 ; r6=0.37. The Mann-Kendall trend test and Theil-Sen slope methods were applied to, and trend parameters are provided for, the original and prewhitened series. To assess changes in the spatial distribution of tornado days, the start latitude and longitude coordinates provided in the tornado database were plotted. Various spatial statistics, 10

ACCEPTED MANUSCRIPT including the mean and median center and the standard deviational ellipses, were then generated to describe the central tendency and dispersion of the spatial distributions. These

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statistics were computed for the entire period of record and for multiple decades to determine

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if they changed over time. Previous studies also have examined changes in the spatial

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distribution of tornadoes using gridded tornado and tornado day frequencies and means. Farney and Dixon (2014), for example, analyzed the annual mean number of tornado days

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within 25-km miles of a given point and Agee et al. (2016) analyzed tornado and tornado day

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counts within a 2.5° × 2.5° grid. Both studies examined two periods of time (Farney and Dixon (2014) looked at 1960–1989 and 1990–2011; Agee et al. (2016) looked at 1954–1983 and 1984–

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2013), and both showed an increase in tornado activity in the Middle and Lower Mississippi,

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Ohio, and Tennessee River Valleys. The approach taken here compliments these previous

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studies by showing how the mean and median centers standard deviational ellipses changed in response to the changes in the spatial frequency distribution of tornado days.

3. Results and discussion

3.1. Temporal trends: Annual tornado frequency A linear trend fit to the annual frequency of (E)F1+ tornadoes between 1974 and 2015 suggests that the number of tornadoes per year has decreased (Fig. 1). Other recent studies (Brooks et al., 2014; Elsner et al., 2015; Tippett and Cohen, 2016) did not report significant trends in annual numbers of (E)F1+ tornadoes, but these studies extended to 1954. Rather, a 20–25 yr cycle is evident in the time series shown in these studies. A similar cycle also is evident in the quadratic polynomial curve shown in Fig. 1 over the shorter record examined 11

ACCEPTED MANUSCRIPT here. The quadratic polynomial shows a general decreasing trend from 1974 until the late 1990s, after which an increasing trend is observed. This pattern of variability implies that a

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linear trend may not be the best representation of the time series because it is dependent on

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the time interval, specifically where the interval lies within the cycle.

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Farney and Dixon (2014) also reported a similar 20–25 year cycle in the annual number of tornado days, but their analysis included (E)F0–5 tornadoes rather than only (E)F1+. As

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discussed next, other results presented here, and those presented by Brooks et al. (2014) and

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Elsner et al. (2015), do not show such a clear cycle in the annual number of tornado days when considering only (E)F1+ tornadoes.

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3.2. Temporal trends: Tornado days

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Trends in the annual number of tornado days meeting various exceedance thresholds

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are shown in Fig. 2. Similar to the annual number of tornadoes, but more evident, the number of tornado days per year has decreased since 1974 (Fig. 2a). Note that the 1+ tornado day time series is auto-correlated and that the trend parameters change when the test is run on the prewhitened time series (see Fig. 2 caption); the trend is no longer significant at α = 0.05, although it is significant at α = 0.10. This is opposed to the increase seen in the number of days with larger numbers of tornadoes (i.e., 20+ and 30+) (Fig. 2c and d). These trends are consistent with those reported by Brooks et al. (2014) and Elsner et al. (2015). In addition to exceedance thresholds, trends also were computed for mutually exclusive groupings of tornado days (Fig. 3). Parsing tornado days this way shows that statistically significant trends are observed only in the low-frequency (1–9 tornadoes) and high-frequency (30+ tornadoes) tornado days, with no significant trends observed in the mid-frequency (10–29 12

ACCEPTED MANUSCRIPT tornadoes) days. These same inferences can be made with mutually exclusive groups using the thresholds from Elsner et al. (2015) (Table 1). While not in disagreement with the trends

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reported in Brooks et al. (2014) and Elsner et al. (2015), the trends in Fig. 3 show more clearly

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that low-frequency tornado days are occurring less frequently while only the relatively high-

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frequency days are becoming more common.

The concurrent decrease and increase in low-frequency and high-frequency tornado

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days, respectively, led to an increase in the mean number of tornadoes per tornado day (Fig.

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4a), from 3.75 between 1975 and 1980 to 5.46 between 2010 and 2014 (Table 2). These concurrent changes also led to an increase in the relative variability of the number of tornadoes

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produced on tornado days (Fig. 4b; Table 2). The increased variability observed here is

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consistent with the variability of standard deviations reported by Brooks et al. (2014), with the

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increased volatility reported by Tippett (2014), and with the increased outbreak variance reported by Tippett and Cohen (2016). Recently, Guo et al. (2016) also reported an increasing trend in the variability of annual tornado occurrence in the Great Plains and Southeast Regions of the US, but a decreasing trend or no trend in other regions. Lastly, as a result of the changes seen here, primarily the increased probability of the high-frequency days, the asymmetry of the number of tornadoes per tornado day also increased over the period of study, but the trend is not statistically significant (Fig. 4c; Table2). Tippett and Cohen (2016) recently reported that the number of tornadoes per outbreak follows Taylor’s power law of fluctuation scaling over time. This implies that the variability of the number of tornadoes per outbreak is changing at a faster rate than the mean, and that the likelihood of extreme outbreaks is increasing faster than the trend in the mean. Some of the 13

ACCEPTED MANUSCRIPT results presented in this section show that that number of tornadoes per tornado day (as opposed to the number per outbreak that Tippett and Cohen (2016) presented) also exhibits

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this behavior. For example, the increase in the coefficient of variation (CV) (Fig. 4b), which is

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the ratio of the standard deviation to the mean, shows that the standard deviation increased

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faster than the mean over the period of record. The frequency of the 30+ days also increased slightly faster than the trend in the mean. Although both of the slopes (β) shown in Fig. 3d and

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4a are the same (i.e., 0.03), increasing their significant digits shows that the slope of the 30+

3.3. Temporal trends: Tornado intensity

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days series is 0.033 and the slope of the mean series is 0.027.

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Trends in the annual relative proportion of tornadoes per (E)F Scale are shown in Fig. 5

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and trend parameters are provided in Table 3. The percentage of annual tornadoes rated (E)F1

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increased in all groups over the period of study. The magnitudes of the trends ranged between a minimum of 0.2 % per year in the 1–9 tornado days (pre-whitened series) to 0.9 % per year in the 30+ tornado days. The percentage of (E)F2 and 3 tornadoes correspondingly decreased between 0.1 % and 0.5 % per year in all groups. The percentage of (E)F4 tornadoes also decreased over time, but the only trend that is statistically significant is with the 10–19 tornado days series. The shift toward lower intensity tornadoes according to the (E)F Scale is consistent with the hypothesis that the distribution of tornadoes will shift toward less intense events along with the projected increase and decrease in instability and shear, respectively, that will accompany climate change (Trapp et al., 2009; Brooks, 2013; Diffenbaugh et al., 2013). In addition to the temporal trends, another pattern seen in Fig. 5 is that the percentages of weaker (E)F1 tornadoes tend to decrease as the number of tornadoes per day increases, 14

ACCEPTED MANUSCRIPT whereas the percentages of stronger (E)F3+ tornadoes increase. For example, E(F)1 tornadoes accounted for 60–90 % of the tornadoes that occurred on days with 1–9 tornadoes, but they

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tended to account for ≤ 70 % of those that occurred on days when 30+ were produced.

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Oppositely, stronger E(F)3 tornadoes accounted for < 10 % of the tornadoes on days when 1–9

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were produced whereas they often accounted for ≥ 10 % of those that occurred on the 30+

have a higher proportion of stronger ones.

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3.4. Spatial distribution of tornado days

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days. The high-frequency days, therefore, not only have more tornadoes, they also tend to

The tornadoes that occurred on the lower-frequency days were widely distributed,

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mainly to the east of the continental divide (Fig. 6a and b). Tornadoes produced on the higher-

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frequency days, however, were distributed over somewhat smaller areas, and the centers of

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their distributions were shifted slightly eastward (Fig. 6c and d). The mean and median centers of the tornadoes produced on the 30+ tornado days, for example, are approximately 165 km and 224 km, respectively, to the east of those for the days with 1–9 tornadoes. The eastward shift is more pronounced when looking at days with 50+ tornadoes (Fig. 6d). Although some of the tornadoes on these days occurred in the Great Plains to the west, most tended around a north-south axis running generally from Lake Michigan down to Mississippi and Alabama. The spatial distributions of the tornado day groups shifted by various distances over the period of record (Fig. 7), with the shifts being more pronounced in the 10+ tornado groups (Fig. 7b–d). The mean and median centers of the last two decades (i.e., 1995–2004 and 2005–2014) shifted east of those of the first two decades (i.e., 1975–1984 and 1985–1994) with the exception of those for the 10–19 tornado days over the 2005–2014 period (Fig. 7b–d). 15

ACCEPTED MANUSCRIPT Moreover, those of the last three decades were shifted east of the first decade for the 10–19 and 20–29 tornado groups. The distances between the furthest west median center in the first

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two decades and the furthest east median center in the last two decades all exceed 200 km;

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this distance exceeds 400 km for the 30+ tornado days.

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Other studies (Farney and Dixon, 2014; Agee et al., 2016) also have provided evidence of an eastward shift in tornado activity over time. Most recently, Agee et al. (2016) reported an

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eastward shift in annual tornado activity in the US between the periods 1954–1983 and 1984–

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2013. The shifts seen here in the central tendencies are not as drastic as those reported by Agee et al. (2016), but these metrics are not expected to shift as much as the gridded

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frequencies reported by Agee et al. (2016). The distribution of the 30+ tornado days seen here,

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and especially the 50+ tornado days (Fig. 7d), generally coincides with the region of maximum

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tornado activity in northern Alabama and Tennessee in the 1984–2013 period shown by Agee et al. (2016). Given that the tornadoes that occur on the 30+ and 50+ day tend to occur in this region, and that these days are becoming more common (Fig. 3d; Fig. 6d; Table 4), it is not surprising that the frequency distribution of tornadoes shifted eastward. These shifts in observed data also are consistent with Gensini and Mote (2015), who recently projected that the largest increase in future severe weather will be across the Middle and Lower Mississippi, Ohio, and Tennessee River Valleys, especially through late spring and early summer.

4. Conclusion Temporal and spatial distributions of (E)F1+ tornadoes in the US over the period 1974– 2015 were analyzed in this study. Similar to others (Brooks et al., 2014; Elsner et al., 2015), the 16

ACCEPTED MANUSCRIPT results presented here show that the number of (E)F1+ tornado days has decreased since the mid-1970s whereas the number of high-frequency tornado days (30+ tornadoes) has increased.

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In addition to verifying these trends, this study also showed that the mid-frequency tornado

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days (i.e., those with 10–29 tornadoes) do not exhibit statistically significant trends.

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The concurrent and opposite trends in the low- and high-frequency tornado days have led to an increase in the mean and variability of the number of tornadoes per tornado day. The

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increasing trend in the CV observed here shows that the variability increased faster than the

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mean. This trend suggests that the number of tornadoes per tornado day exhibits Taylor’s power law of fluctuation scaling, similar to the number of tornadoes per outbreak as reported

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by Tippett and Cohen (2016). The temporal trend analyses performed here also show that the

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annual percentage of tornadoes rated (E)F1 have significantly increased, regardless of the

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number of tornadoes per tornado day, whereas some of the time series of the percentages of (E)F2+ tornadoes show significant declining trends. The tornadoes that occurred on lower-frequency days were more widely dispersed than those that occurred on higher-frequency days. Those that those that occurred on higherfrequency days tended to be focused further east than those that occurred on the lowerfrequency days. The central tendencies of the tornadoes tended to shift east between the first two and last two decades of the period of record. These observations are consistent with a recent study (Agee et al., 2016) that reported an eastward shift in tornado activity in the US. The temporal and spatial trends observed here in the 30+ tornado days partially explain why tornado activity might be shifting eastward―the 30+ tornado days tend to be concentrated in this region and they are becoming more common. 17

ACCEPTED MANUSCRIPT The results presented here along with those from other empirical studies suggest that the temporal and spatial statistical characteristics of tornadoes in the US are changing. It is

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possible that these changes are secular, and caused by changes in detection technology,

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observation and recording practices, and increases in the storm spotter network; the increases

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seen in the proportion of E(F)1 tornadoes could be related to the transition from F to EF Scale (Doswell et al., 2009; Edwards and Brooks, 2010). As noted by Brooks et al. (2014), however,

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non-meteorological factors (e.g., a trend related to an increase in tornado reporting over time)

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should influence the low- and high-frequency tornado days in the same direction, not opposite. Furthermore, recent studies have shown correlation between changes in tornado activity and

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2016).

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changes in environmental parameters, suggesting a physical forcing (Tippett, 2014; Lu et al.,

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More research is needed to further document these statistical changes and to explore possible changes to the environments in which the tornadoes are occurring. Tippett (2014), for example, analyzed changes in the volatility of the tornado environment index in addition to the volatility of the annual number of tornadoes to show that both changed over time. Although other studies reported no trends in the frequency of observed tornado-favorable conditions (Gensini and Ashley, 2011; Robinson et al., 2013), additional study is needed to determine if trends exist in other severe weather indices and parameters. The increased number of high-frequency tornado days, in particular, warrants further study. Tornado-favorable ingredients come together at various scales and with multiple convective modes (Edwards et al., 2012; Smith et al., 2012; Thompson et al., 2012). However, on the days with the most tornadoes, such as the high-frequency tornado days, these 18

ACCEPTED MANUSCRIPT conditions tend to co-occur in the presence of an extratropical cyclone (Doswell et al., 2012; Mercer et al., 2012; Schultz et al., 2014); the collocation of these factors with an extratropical

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cyclone is representative of Miller’s Type B tornado pattern (Miller, 1972) and is considered a

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synoptically evident pattern for tornado outbreaks (Doswell et al, 1993). Addition study should

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investigate whether environmental conditions associated with extratropical cyclones that

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produce tornadoes are changing.

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Acknowledgements

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References

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I thank the two anonymous reviewers for their constructive comments and suggests.

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< 0.01 < 0.01 0.08 0.46 < 0.01

−1.17 −0.36 −0.12 0.00 0.03

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−552 −424 −161 68 247

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β

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p-value

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Number of tornadoes 1–3 4–7 8–15 16–31 32+

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Table 1. Linear trend parameters for mutually exclusive groupings of tornado days. The MannKendall S statistic (S), p-value (p), and Theil-Sen slope estimate (β) are listed. Trends were run on the annual frequencies of the various tornado day groups over the period 1974–2015.

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Number of tornado days 739 726 583 611 558 528 515 473

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Time period 75–79 80–84 85–89 90–94 95–99 00–04 05–09 10–14

Number of tornadoes per tornado day Coefficient Mean Skewness of variation 3.75 1.18 3.50 3.97 1.25 3.38 3.44 1.25 4.12 4.04 1.54 4.49 4.12 1.40 4.10 4.08 1.54 3.94 4.75 1.43 3.36 5.46 1.93 6.66

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Table 2. Statistics describing the number of tornadoes per tornado day per 5-yr period. Note, 1974 and 2015 are omitted to keep 5-yr time periods.

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b

(E)F3

(E)F4

(E)F1

c

d

(E)F3

(E)F4

(E)F2

(E)F2

(E)F3

(E)F4

(E)F1

(E)F2

(E)F3

(E)F4

161

−121

−144

26

150

−132

−26

−48

0.03

0.02

0.08

0.03

0.71

<0.01

<0.01

0.63

0.35

<−0.001

0.006

−0.002

−0.002

0.000

0.009

−0.005

−0.001

<−0.001

376

−333

−312

−68

376

−322

−233

−198

p

<0.01

<0.01

<0.01

0.47

<0.01

<0.01

0.01

β

0.003

−0.002

<−0.001

<−0.001

0.005

−0.003

−0.001

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S

a

Pre-whitened trend: S = 218; p = 0.01; β = 0.002

b

Pre-whitened trend: S = −204; p = 0.02; β = −0.001

Pre-whitened trend: S = 278; p < 0.01; β = 0.003

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10–19 tornadoes

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1–9 tornadoes

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Table 3. Parameters for the trends in the annual number of tornadoes per (E)F Scale per mutually exclusive group of tornado day magnitude. The Mann-Kendall S statistic (S), p-value (p), and Theil-Sen slope estimate (β) are provided. Time series are shown in Fig. 5.

d

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Pre-whitened trend: S = −234; p < 0.01; β = −0.002

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Number of tornadoes 50 50 50 51 52 53 58 62 124 145

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Year 1990 1992 1995 2003 1992 2011 2011 2013 1974 2011

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Day 2 22 18 4 16 25 15 17 3 27

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Month 6 11 5 5 6 5 4 11 4 4

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Table 4. Top ten days with the most tornadoes over the period 1974–2015. Each of these days had 50+ tornadoes.

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Fig. 1. Time series of the annual frequency of (E)F1+ tornadoes between 1974 and 2015. The Mann-Kendall S statistic (S), p-value (p), and Theil-Sen slope estimate (β) are listed. The dashed black line shows the Theil-Sen trend line. A quadratic polynomial curve and equation are shown in gray, and a 5-yr moving mean is shown in solid black.

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Fig. 2. Trends in the annual number of tornado days with (a) 1+ tornadoes, (b) 10+ tornadoes, (c) 20+ tornadoes, and (d) 30+ tornadoes. The Mann-Kendall S statistic (S), p-value (p), and Theil-Sen slope estimate (β) are listed. The dashed black line shows the Theil-Sen trend line. The trend parameters in (a) change to S = −164, p = 0.07, β = −0.44 when the analysis is run on the pre-whitened time series. A 5-yr moving mean is shown in solid black.

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Fig. 3. Trends in the annual number of tornado days with (a) 1–9 tornadoes, (2) 10–19 tornadoes, (c) 20–29 tornadoes, and (d) 30+ tornadoes. The Mann-Kendall S statistic (S), pvalue (p), and Theil-Sen slope estimate (β) are listed. The dashed black line shows the Theil-Sen trend line. The trend parameters in (a) change to S = −176, p = 0.05, β = −0.44 when the analysis is run on the pre-whitened time series. A 5-yr moving mean is shown in solid black.

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Fig. 4. Trends in the (a) mean, (b) coefficient of variation, and (c) skewness of the number of tornadoes per tornado day per year. The Mann-Kendall S statistic (S), p-value (p), and Theil-Sen slope estimate (β) are listed. The dashed black line shows the Theil-Sen trend line. Fig. 5. Trends in the percentage of annual number of tornadoes per (E)F Scale that occurred on days with (a) 1–9 tornadoes, (b) 10–19 tornadoes, (c) 20–29 tornadoes, and (d) 30+ tornadoes. Time series for (E)F1–3 tornadoes are shown in (a)–(d); (E)F1–4 tornadoes are shown in (b)–(d); (E)F5 tornadoes are not shown. Dashed black Theil-Sen trend lines are shown for all trends that are significant at α ≤ 0.10.Trend parameters are provided in Table 3 and percentages aggregated to a 5-yr scale are provided in Table 4. Fig. 6. Spatial distribution of tornadoes occurring on days with (a) 1–9 tornadoes, (b) 10–19 tornadoes, (c) 20–29 tornadoes, and (d) 30+ tornadoes. Gray inverted triangles represent the start coordinates of individual tornadoes, black inverted triangles represent mean centers, black diamonds represent median centers, and black elliptical polygons represents one standard deviational ellipses. The darker gray inverted triangles in (d) represent tornadoes that occurred on days with 50+ tornadoes, and the black circle, black square, and dashed black elliptical polygon represent the mean center, median center, and one standard deviational ellipse of the 50+ tornado days, respectively. Fig. 7. Spatial distribution of the mean and median centers of the tornadoes that occurred on days with (a) 1–9 tornadoes, (b) 10–19 tornadoes, (c) 20–29 tornadoes, and (d) 30+ tornadoes. 33

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Low-frequency tornado days became less common between 1974 and 2015. High-frequency tornado days became more common between 1974 and 2015. The variability of the number of tornadoes per tornado day increased between 1974 and 2015 more than the mean number. Tornadoes that occur on high-frequency days tend to be located further east than those that occur on lower-frequency days.

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