1. Introduction
Two extreme tornado events occurred in the United States in May 2013. The first was an enhanced Fujita scale (EF)-5 tornado that devastated parts of Moore, Oklahoma, on 20 May, causing 24 fatalities and 377 injuries, and an estimated $2 billion (U.S. dollars) in damage. The second was an EF-3 tornado on 31 May, in the nearby community of El Reno, Oklahoma. Eight fatalities resulted from this estimated 2.6-mi (4.2 km) wide tornado, which is the largest documented tornado width to date [(National Climatic Data Center) NCDC 2013].
What these two extreme events have in common is their occurrence during a multiday period of tornado activity: based on the preliminary reports, the period containing the 20 May event consisted of 6 consecutive days of reported tornadoes, and the period containing the 31 May event consisted of 7 consecutive days.1 The May 2003 “extended tornado outbreak” (Hamill et al. 2005), in which 361 tornadoes (7 rated F4–F5) were reported during the 9-day period of 3–11 May 2003, is another notable example of such behavior. Other recent extreme events, including the EF-5 Joplin, Missouri, tornado on 22 May 2011, and the EF-4 Tuscaloosa, Alabama, tornado and associated tornado outbreak on 27 April 2011, also occurred during multiday periods of tornado activity.
The purpose of this article is to examine more thoroughly the climatological distribution of tornado-activity periods, and then to explore possible interrelationships between the length of the periods, tornado significance, and the characteristics of the meteorological forcing.
2. Data and methods
This study exploits the U.S. historical tornado database maintained by the National Oceanic and Atmospheric Administration (NOAA) Storm Prediction Center (SPC). The specific data used are the commencement time (as archived in central standard time) and calendar date of each reported tornado, and the damage-based tornado rating (F or EF scale). The time and date determine tornado days, which literally are calendar days when at least one (but possibly many more) tornado(es) is reported somewhere in the country. Tornado days are less susceptible to nonphysical biases to the tornado reporting (Changnon 1982), and have been used as a measure of tornado activity in several previous studies (e.g., Brooks et al. 2003; Trapp and Brooks 2013).
Tornado days are examined over 1983–2012. This coincides with North American Regional Reanalysis (NARR) data availability (see section 4), and also represents a relatively stable interval of the record: although the tornado-day data are not strictly stationary, the slope of the linear fit to this 30-yr time series is only 0.35 days yr−1.
The set of all tornado days during 1983–2012 is parsed to identify consecutive tornado days. The unique, nonoverlapping, consecutive-day groupings are referred to as periods, which have length ρ. Confidence intervals on the frequency of period lengths are determined from 10 000 bootstrap estimates of the frequency of each period, and estimated using the percentile method (e.g., Wilks 2006). To prevent the influence of possible spurious reports in the tornado day and thence period identifications, a three-report per day threshold is imposed for that day to be considered a tornado day. This is a somewhat arbitrary threshold, and tests of result sensitivity are presented below (see Table 1).
Results from tests of the sensitivity of the minimum number of tornado reports used to define a tornado day in the United States. The probabilities are evaluated using the sample space S′ of all tornado days during the period 1983–2012.
The tornado reports themselves are also considered, as are the damage-based ratings; both provide a metric to judge the significance of days and periods. Bearing in mind the usual caveats regarding the inflation of tornado reporting (e.g., Diffenbaugh et al. 2008; see also Trapp 2013), an individual day with more than 20 tornado reports is classified as an outbreak day (OB). There are other ways to quantify tornado outbreaks; this rather basic one follows from Galway (1975).
An additional caveat regards the enhancement made to the F-scale rating system (Fujita 1981) in 2007. In the enhanced, or EF-scale system (McDonald and Mehta 2006; Doswell et al. 2009), tornadoes are still (subjectively) rated based on the degree of damage, albeit with more detail. However, the attributed wind speeds per rating category are somewhat different than those in the original system; consequently, the specific wind speed information is not used here. Irrespective of the rating system, a tornado day is classified as significant (SIGTOR) given at least one tornado on that day with a rating of F/EF ≥ 3. Note that SIGTORs and OBs are not mutually exclusive, although there is a general tendency for outbreaks to contain one or more significant tornadoes.
3. Results
All tornado days during 1983–2012 can be divided into 1406 unique, nonoverlapping periods 
Frequency distribution of the length of all consecutive tornado-day periods in the United States during 1983–2012 as evaluated over the sample space S of the 1406 unique, nonoverlapping periods. Error bars represent 95% confidence intervals determined from 10 000 bootstrap estimates of the frequency of each period, and estimated using the percentile method.
Citation: Monthly Weather Review 142, 4; 10.1175/MWR-D-13-00347.1
Frequency distribution of the length of all consecutive tornado-day periods in the United States during 1983–2012 as evaluated over the sample space S of the 1406 unique, nonoverlapping periods. Error bars represent 95% confidence intervals determined from 10 000 bootstrap estimates of the frequency of each period, and estimated using the percentile method.
Citation: Monthly Weather Review 142, 4; 10.1175/MWR-D-13-00347.1
Frequency distribution of the length of all consecutive tornado-day periods in the United States during 1983–2012 as evaluated over the sample space S of the 1406 unique, nonoverlapping periods. Error bars represent 95% confidence intervals determined from 10 000 bootstrap estimates of the frequency of each period, and estimated using the percentile method.
Citation: Monthly Weather Review 142, 4; 10.1175/MWR-D-13-00347.1
The working hypothesis alluded to in section 1 is that SIGTORs and/or OBs are (more) likely to fall within multiday periods. The data show, in fact, that the conditional probability of period length 
As in Fig. 1, but for period length given at least one (a) OB and (b) SIGTOR during the period.
Citation: Monthly Weather Review 142, 4; 10.1175/MWR-D-13-00347.1
As in Fig. 1, but for period length given at least one (a) OB and (b) SIGTOR during the period.
Citation: Monthly Weather Review 142, 4; 10.1175/MWR-D-13-00347.1
As in Fig. 1, but for period length given at least one (a) OB and (b) SIGTOR during the period.
Citation: Monthly Weather Review 142, 4; 10.1175/MWR-D-13-00347.1
An alternative expression of these probabilities is provided by the sample space of all 3129 tornado days 
Frequency distribution of the (a) length of all consecutive tornado-day periods in the United States during 1983–2012, (b) period length given an OB, and (c) period length given a SIGTOR. The distributions are from the sample space S′ of the 3129 tornado days. The error bars are as in Fig. 1.
Citation: Monthly Weather Review 142, 4; 10.1175/MWR-D-13-00347.1
Frequency distribution of the (a) length of all consecutive tornado-day periods in the United States during 1983–2012, (b) period length given an OB, and (c) period length given a SIGTOR. The distributions are from the sample space S′ of the 3129 tornado days. The error bars are as in Fig. 1.
Citation: Monthly Weather Review 142, 4; 10.1175/MWR-D-13-00347.1
Frequency distribution of the (a) length of all consecutive tornado-day periods in the United States during 1983–2012, (b) period length given an OB, and (c) period length given a SIGTOR. The distributions are from the sample space S′ of the 3129 tornado days. The error bars are as in Fig. 1.
Citation: Monthly Weather Review 142, 4; 10.1175/MWR-D-13-00347.1
This basic conclusion about the working hypothesis is sensitive to the number of reports used to define a tornado day (see section 2). As might have been inferred, a higher report threshold effectively reduces the probability for multiday periods of tornado activity; it also reduces the probability for a significant tornado event during such a period (Table 1). The most literal definition of a tornado day—a minimum of one reported tornado on a given day—leads to the highest likelihood of an OB (by a factor of ~8.1) and/or SIGTOR (by a factor of ~4) during a multiday period. This bolsters the support for the hypothesis.
A common thread with the tornado events of May 2013 and indeed with other high-impact tornado events is that of their occurrence during the latter part, if not the end, of the multiday periods. To quantify this apparent tendency, the relative positions of SIGTORs and OBs during their respective periods are computed as 
Some final consideration is given to the seasonal cycle of tornado-day periods. As illustrated in Figs. 4a,c, multiday periods have a heavy bias toward the warm-season months of April–July, which reflects well the seasonal cycle of all tornado days. The 1–2-day periods, in contrast, are distributed more uniformly over the year, albeit with a noticeable local minima in May–June (Fig. 4b). There is some suggestion that 1–2-day periods are favored during transition seasons, when synoptic-scale eddies are relatively more frequent in the latitudinal belts most relevant to severe convective storms. The May–June peak of the multiday periods, on the other hand, connotes a contrasting behavior of the synoptic-scale forcing.
Mean seasonal cycle of (a) tornado-day periods of length ≥3 days, (b) tornado-day periods of length 1–2 days, and (c) all tornado days.
Citation: Monthly Weather Review 142, 4; 10.1175/MWR-D-13-00347.1
Mean seasonal cycle of (a) tornado-day periods of length ≥3 days, (b) tornado-day periods of length 1–2 days, and (c) all tornado days.
Citation: Monthly Weather Review 142, 4; 10.1175/MWR-D-13-00347.1
Mean seasonal cycle of (a) tornado-day periods of length ≥3 days, (b) tornado-day periods of length 1–2 days, and (c) all tornado days.
Citation: Monthly Weather Review 142, 4; 10.1175/MWR-D-13-00347.1
4. Connection to the meteorological forcing
As similarly envisioned by Drton et al. (2003) and Hamill et al. (2005), multiday periods of tornado activity are apt to be connected physically to a relatively slow-moving or even stationary synoptic-scale eddy, with a persistent surface cyclone and persistently strong flow in the lower and middle troposphere. While it is unlikely that all multiday periods have such a connection with what might be considered a “synoptically evident” situation (e.g., Doswell et al. 1993), the two events of 2013 introduced in section 1 do, as demonstrated by the following analysis of NARR data.
The analysis, in brief, results from an application of a low-pass Lanczos filter (see Duchon 1979) to 6-hourly NARR data over April–May–June (AMJ) during 2013, as well as for each year during 1983–2012. The spectral response of the 57-weight filter employed is such that 50% of the amplitude of frequencies corresponding to 3 days is retained, and nearly 100% (0%) of the amplitude of lower (higher) frequencies is retained. The filtered data are then averaged over a 30°–40°N latitudinal domain, and used to construct Hovmöller diagrams over AMJ and a longitudinal domain of 105°–80°W. For comparison, the unfiltered and unsmoothed AMJ 2013 tornado reports are presented in the same Hovmöller diagram.
Consider the medium- to low-frequency signal in sea level pressure during AMJ 2013, given in the Hovmöller diagram as a deviation from the 1983–2012 mean (Fig. 5a). Anomalously low pressure is found at longitudes ~105°W (eastern Colorado, eastern New Mexico) beginning on ~7 April, 14 April, 28 April, 18 May, and 27 May 2013; each one of these times save 28 April is part of an active tornado period. The 18 May feature evinces a very gradual west–east progression, while the 27 May feature supports the lee-cyclone persistence and associated longitudinally bound forcing during a several-day period. Figures 5b–d show that an analogous correspondence exists between AMJ 2013 tornado activity and the negatively anomalous geopotential height at 500 hPa, positively anomalous meridional winds at 850 hPa, and positively anomalous convective available potential energy (CAPE). Each of these lends credence to the envisioned connection.
Hovmöller diagrams of (a) sea level pressure (Pa), (b) 500-hPa heights (dam), (c) 850-hPa meridional winds (m s−1), and (d) convective available potential energy (J kg−1), for April–June 2013, presented as a deviation from the 1983–2012 mean. The data contributing to (a)–(d) originate from the North American Regional Reanalysis, are then low-pass filtered, and then averaged over a 30°–40°N latitudinal domain. Indicated as gray shaded contours in (a) are the April–June 2013 tornado reports (≥1, light gray; ≥5, dark gray), in the same time–longitude domain, and also averaged over 30°–40°N latitude. Indicated in (d) are contours of the magnitude of the surface–500-hPa wind shear vector (m s−1), also presented as a deviation from the 1983–2012 mean; only the 5 and 10 m s−1 contours are shown.
Citation: Monthly Weather Review 142, 4; 10.1175/MWR-D-13-00347.1
Hovmöller diagrams of (a) sea level pressure (Pa), (b) 500-hPa heights (dam), (c) 850-hPa meridional winds (m s−1), and (d) convective available potential energy (J kg−1), for April–June 2013, presented as a deviation from the 1983–2012 mean. The data contributing to (a)–(d) originate from the North American Regional Reanalysis, are then low-pass filtered, and then averaged over a 30°–40°N latitudinal domain. Indicated as gray shaded contours in (a) are the April–June 2013 tornado reports (≥1, light gray; ≥5, dark gray), in the same time–longitude domain, and also averaged over 30°–40°N latitude. Indicated in (d) are contours of the magnitude of the surface–500-hPa wind shear vector (m s−1), also presented as a deviation from the 1983–2012 mean; only the 5 and 10 m s−1 contours are shown.
Citation: Monthly Weather Review 142, 4; 10.1175/MWR-D-13-00347.1
Hovmöller diagrams of (a) sea level pressure (Pa), (b) 500-hPa heights (dam), (c) 850-hPa meridional winds (m s−1), and (d) convective available potential energy (J kg−1), for April–June 2013, presented as a deviation from the 1983–2012 mean. The data contributing to (a)–(d) originate from the North American Regional Reanalysis, are then low-pass filtered, and then averaged over a 30°–40°N latitudinal domain. Indicated as gray shaded contours in (a) are the April–June 2013 tornado reports (≥1, light gray; ≥5, dark gray), in the same time–longitude domain, and also averaged over 30°–40°N latitude. Indicated in (d) are contours of the magnitude of the surface–500-hPa wind shear vector (m s−1), also presented as a deviation from the 1983–2012 mean; only the 5 and 10 m s−1 contours are shown.
Citation: Monthly Weather Review 142, 4; 10.1175/MWR-D-13-00347.1
Besides revealing more explicitly when the atmosphere was supportive of organized, deep convection (e.g., Fig. 5d), this analysis also helps characterize the time scale of CAPE generation and sustenance relative to the time scale of CAPE consumption by such triggered convection (e.g., Emanuel 1994). It is speculated here that the containment of SIGTORs and/or OBs within—and more notably near the end of—these periods of positively anomalous CAPE is consistent with the idea that a multiple-day accumulation of CAPE would be more apt to lead to relatively more intense convective storms than would a single-day accumulation. Some additional speculations are provided in section 5.
5. Discussion
That tornado activity can extend over multiple days and be connected to the evolution of a synoptic-scale eddy is outwardly not very insightful. However, three questions and associated speculations are raised in this section that do in fact suggest the possibility of deeper insight, and accordingly help motivate future work.
a. Do convective feedbacks help promote multiday periods of tornado activity?
In the feedback loop described by Stensrud (1996), the diabatic heating of ongoing deep convection acts to deepen an associated surface cyclone and intensify its wind field. Horizontal advection of water vapor and temperature by the enhanced winds help replenish the moisture processed by the convection and otherwise help destabilize the proximal environment. The environment is thereafter supportive of subsequent deep convection and diabatic heating, affording another cycle of this feedback loop (see also Trapp 2013). The first speculation is that such a feedback helps anchor the synoptic-scale forcing so that CAPE is accumulated over a multiday period despite a daily convective cloud evolution. The CAPE release near the end of the period then has the potential to result in significantly severe convective storms.
b. Are these periods relatively more predictable?
The theoretical limit of deterministic predictability increases with the length scale of the phenomenon (Lorenz 1969), and inherently with its time scale. One implication is that the larger, more slowly evolving/moving synoptic-scale systems that appear to contribute to multiday tornado periods—and hence often to OBs and/or SIGTORs—may be relatively more predictable (e.g., Dalcher and Kalnay 1987). It is indeed noteworthy that the potential for severe convective storms in the southern Great Plains was recognized by the NOAA/Storm Prediction Center 5 days in advance of 20 May 2013, and 4 days in advance of 31 May 2013 (see online at http://www.spc.noaa.gov/products/exper/day4-8/archive/2013).
The second speculation is that the multiday events have even longer intervals of predictability. This would seem to be supported by the inherent predictability found in some warm-season multiday precipitation episodes (Carbone et al. 2002), although these persist in a time–space domain as a strong consequence of various mesoscale-convective processes, and the contextual predictability is days rather than the 1–2 weeks implied here.
c. To what extent can they be explained by internal climate variability?
Enhanced predictability will depend in part on the existence of persistent, low-frequency surface forcing, including that associated with anomalous tropical sea surface temperatures (e.g., Kalnay 2003). Such low-frequency surface forcing is often a manifestation of a mode of internal climate variability, which indeed has been implicated in tornado occurrence, most recently by Thompson and Roundy (2013), Barrett and Gensini (2013), and Lee at al. (2013). Each of these studies revealed remotely induced, regional-scale anomalies in dynamic and thermodynamic variables that have consistency with the synoptic-scale characteristics noted previously.
The final speculation, therefore, is that internal climate forcing is more likely to explain the multiday periods of tornado activity than the 1–2-day periods. The open questions include when/how one mode of internal forcing dominates over the others, and whether/how these are superposed onto external, anthropogenic climate forcing.
6. Conclusions
Motivated by the temporal behavior of recent high-end tornado events, a 30-yr historical record of tornadoes in the United States is examined for unique, nonoverlapping tornado-day periods with ≥3-day length. The conditional probability of such a multiday period given an OB (SIGTOR) is 0.74 (0.60). Alternative ways of expressing these conditional probabilities all lead to the conclusion that OBs and/or SIGTORs are relatively more likely to be contained within multiday periods of tornado activity.
Two additional conclusions arise from this analysis: 1) SIGTORs and OBs have a slightly higher likelihood of occurrence during the latter half of the multiday periods, and 2) multiday periods have a relatively higher likelihood of occurrence during the warm months of April–July. Future work will explore hypothesized connections with the synoptic-scale forcing and speculations about enhanced predictability.
Acknowledgments
The idea for this research began while the author was participating in the Mesoscale Predictability Experiment (MPEX), and therefore he acknowledges his MPEX support from the National Science Foundation (AGS-1230085). Drs. Sonia Lasher-Trapp, Rebecca Morss, and Mike Baldwin provided helpful comments on the direction of the research and on the manuscript. The two anonymous reviewers also provided useful suggestions and feedback.
REFERENCES
Barrett, B. S., and V. A. Gensini, 2013: Variability of central United States April–May tornado day likelihood by phase of the Madden–Julian Oscillation. Geophys. Res. Lett., 40, 2790–2795, doi:10.1002/grl.50522.
Brooks, H. E., C. A. Doswell III, and M. P. Kay, 2003: Climatological estimates of local daily tornado probability for the United States. Wea. Forecasting, 18, 626–640, doi:10.1175/1520-0434(2003)018<0626:CEOLDT>2.0.CO;2.
Carbone, R. E., J. D. Tuttle, D. A. Ahijevych, and S. B. Trier, 2002: Inferences of predictability associated with warm season precipitation episodes. J. Atmos. Sci., 59, 2033–2056, doi:10.1175/1520-0469(2002)059<2033:IOPAWW>2.0.CO;2.
Changnon, S. A., Jr., 1982: Trends in tornado frequencies: Fact or fallacy? Preprints, 12th Conf. on Severe Local Storms, Tulsa, OK, Amer. Meteor. Soc., 42–44.
Dalcher, A., and E. Kalnay, 1987: Error growth and predictability in operational ECMWF forecasts. Tellus, 39A, 474–491, doi:10.1111/j.1600-0870.1987.tb00322.x.
Diffenbaugh, N. S., R. J. Trapp, and H. E. Brooks, 2008: Does global warming influence tornado activity? Eos, Trans. Amer. Geophys. Union, 89, 553–554, doi:10.1029/2008EO530001.
Doswell, C. A., III, S. J. Weiss, and R. H. Johns, 1993: Tornado forecasting: A review. The Tornado: Its Structure, Dynamics, Prediction, and Hazards, Geophys. Monogr., Vol. 79, Amer. Geophys. Union, 161–172.
Doswell, C. A., III, H. E. Brooks, and N. Dotzek, 2009: On the implementation of the enhanced Fujita scale in the USA. Atmos. Res., 93, 554–563, doi:10.1016/j.atmosres.2008.11.003.
Drton, M., C. Marzban, P. Guttorp, and J. T. Schaefer, 2003: A Markov chain model of tornadic activity. Mon. Wea. Rev., 131, 2941–2953, doi:10.1175/1520-0493(2003)131<2941:AMCMOT>2.0.CO;2.
Duchon, C. E., 1979: Lanczos filtering in one and two dimensions. J. Appl. Meteor., 18, 1016–1022, doi:10.1175/1520-0450(1979)018<1016:LFIOAT>2.0.CO;2.
Emanuel, K. A., 1994: Atmospheric Convection. Oxford University Press, 592 pp.
Fujita, T. T., 1981: Tornadoes and downbursts in the context of generalized planetary scales. J. Atmos. Sci., 38, 1511–1534, doi:10.1175/1520-0469(1981)038<1511:TADITC>2.0.CO;2.
Galway, J. G., 1975: Relationship of tornado deaths to severe weather watch areas. Mon. Wea. Rev., 103, 737–741, doi:10.1175/1520-0493(1975)103<0737:ROTDTS>2.0.CO;2.
Hamill, T. M., R. S. Schneider, H. E. Brooks, G. S. Forbes, H. B. Bluestein, M. Steinberg, D. Melendez, and R. M. Dole, 2005: The May 2003 extended tornado outbreak. Bull. Amer. Meteor. Soc., 86, 531–542, doi:10.1175/BAMS-86-4-531.
Kalnay, E., 2003: Atmospheric Modeling, Data Assimilation, and Predictability. Cambridge University Press, 341 pp.
Lee, S.-K., R. Atlas, D. Enfield, C. Wang, and H. Liu, 2013: Is there an optimal ENSO pattern that enhances large-scale atmospheric processes conducive to tornado outbreaks in the United States? J. Climate, 26, 1626–1642, doi:10.1175/JCLI-D-12-00128.1.
Lorenz, E. N., 1969: The predictability of a flow which possesses many scales of motion. Tellus, 21, 289–307, doi:10.1111/j.2153-3490.1969.tb00444.x.
McDonald, J. R., and K. C. Mehta, 2006: A recommendation for an enhanced Fujita scale (EF-scale). Texas Tech University, Wind Science and Engineering Research Center, 111 pp. [Available online at http://www.depts.ttu.edu/nwi/Pubs/FScale/EFScale.pdf.]
NCDC, cited 2013: Storm events database. [Available online at http://www.ncdc.noaa.gov/stormevents/.]
Stensrud, D. J., 1996: Effects of persistent, midlatitude mesoscale regions of convection on the large-scale environment during the warm season. J. Atmos. Sci., 53, 3503–3527, doi:10.1175/1520-0469(1996)053<3503:EOPMMR>2.0.CO;2.
Thompson, D. B., and P. E. Roundy, 2013: The relationship between the Madden–Julian Oscillation and U.S. violent tornado outbreaks in the spring. Mon. Wea. Rev., 141, 2087–2095, doi:10.1175/MWR-D-12-00173.1.
Trapp, R. J., 2013: Mesoscale-Convective Processes in the Atmosphere. Cambridge University Press, 346 pp.
Trapp, R. J., and H. E. Brooks, 2013: Regional characterization of tornado activity. J. Appl. Meteor. Climatol., 52, 654–659, doi:10.1175/JAMC-D-12-0173.1.
Wilks, D. S., 2006: Statistical Methods in the Atmospheric Sciences. Academic Press, 627 pp.
Two of the days during this period had less than four tornadoes.
