Abstract

Between 2003 and 2015, there were 5343 outbreak tornadoes and 9389 isolated tornadoes reported in the continental United States. Here, the near-storm environmental parameter-space distributions of these two categories are compared via kernel density estimation, and the seasonal, diurnal, and geographical features of near-storm environments of these two sets of events are compared via self-organizing maps (SOMs). Outbreak tornadoes in a given geographical region tend to be characterized by greater 0–1-km storm-relative helicity and 0–6-km vector shear magnitude than isolated tornadoes in the same geographical region and also have considerably higher tornado warning-based probability of detection (POD) than isolated tornadoes. A SOM of isolated tornadoes highlights that isolated tornadoes with higher POD also tend to feature higher values of the significant tornado parameter (STP), regardless of the specific shape of the area of STP. For a SOM of outbreak tornadoes, when two outbreak environments with similarly high magnitudes but different patterns of STP are compared, the difference is primarily geographical, with one environment dominated by Great Plains and Midwest outbreaks and another dominated by outbreaks in the southeastern United States. Two specific tornado outbreaks are featured, and the events are placed into their climatological context with more nuance than typical single proximity sounding-based approaches would allow.

1. Introduction

Tornado outbreaks often result in major loss of life and property, but a clear and consistent definition of the term “tornado outbreak” has remained elusive. The classical definition of a tornado outbreak is generally agreed to involve multiple tornadoes that are likely linked to the same synoptic-scale storm system. The specifics, however, vary considerably; after some early attempts at creating general definitions of tornado outbreaks, the research community has acknowledged that one-size-fits-all definitions should likely be set aside in favor of varying the definition depending on the stated objectives and foci of the study in question (Doswell et al. 2006).

There have been a variety of definitions of tornado outbreaks in the decades of research on the topic, with criteria ranging from intensity and damage (Flora 1953; Wolford 1960) to spatial (Galway 1975, 1977) and temporal proximity (Doswell et al. 2006). These definitions have been used to 1) identify and rank severe weather outbreak days (Shafer et al. 2010; Shafer and Doswell 2011), 2) distinguish objectively between tornadic and nontornadic severe weather outbreak days through the use of principal component analysis (PCA) on numerical weather prediction output (Mercer et al. 2009, 2012), 3) distinguish between the physical characteristics of extratropical cyclones in which tornadic outbreaks occurred and those in which they did not occur (Tochimoto and Niino 2016), and 4) determine how the annual mean number of tornadoes per outbreak has changed over time (Tippett and Cohen 2016).

While much of the tornado outbreak research to date has focused on comparisons of tornadic versus nontornadic severe weather outbreaks, the work that follows examines the differences between environments in which tornado outbreaks occurred and the environments in which tornadoes did occur, but without an accompanying outbreak of many other tornadoes in the vicinity. This research will also provide a novel look at how outbreak and isolated tornado near-storm environments differ by geographical region within the United States. By making use of a large, comprehensive set of tornado events across the continental United States, and by establishing a definition of outbreak and isolated tornadoes consistent with our goal of comparing the near-storm environments in which both types of tornadoes generally occur, we seek to apply an established statistical toolkit (cf. Anderson-Frey et al. 2016, 2017) to enrich and clarify elements of the tornado outbreak climatology.

In section 2, the dataset is introduced and outbreak tornadoes are defined. Section 3 introduces the analytical methods that will be used to compare the environments in which outbreak and isolated tornadoes occurred, while sections 4 and 5 apply these methods to the tornado event dataset. Section 6 briefly examines two tornado outbreaks within the context of this analysis. Finally, section 7 summarizes the results of this study.

2. Data and definitions

The tornado event dataset is the same as that featured in Anderson-Frey et al. (2016, 2017): the study period of 2003–15 comprises 14 732 tornado events. The tornado event dataset is created by filtering county tornado segment data and keeping the highest (E)F-scale rating within an hour and a 40 × 40 km2 area (Smith et al. 2012). Note that this filtering means that multiple tornadoes that occur both within an hour and a 40 × 40 km2 area will be counted as one tornado event. Environmental data corresponding to each of these tornado events is obtained by taking archived mesoanalysis gridded data from the grid box containing the start location of the reported tornado (Smith et al. 2012); the background for the mesoanalyses is obtained from the Rapid Update Cycle model (RUC; Benjamin et al. 2004) for January 2003–April 2012, or the Rapid Refresh model (RAP; Benjamin et al. 2016) for later dates. The SPC has also compiled a manual convective mode classification (Smith et al. 2012) that assigns a convective mode [e.g., quasi-linear convective system (QLCS), right-moving supercell (RMS), cluster] to each tornado event. Note that these convective modes are only available for 1 January 2003–30 June 2013. See Thompson et al. (2012) and Anderson-Frey et al. (2016) for discussions of the strengths and limitations of the dataset; in any imperfect proximity sounding matching approach, caution must be taken to keep in mind the gridpoint spacing. The assumption here is that biases will be minimized by the large size of the dataset (Thompson et al. 2003, 2012).

In the discussion that follows, day is defined as the period between local sunrise and 2 h before local sunset, the early evening transition (EET) is defined as the period between 2 h before and 2 h after local sunset, and night is defined as the period between 2 h after local sunset and local sunrise. Season is defined in the meteorological sense: spring (MAM), summer (JJA), fall (SON), and winter (DJF). Figure 1 shows the geographical regions in the United States used for the following research. Although the division of regions is subjective and does not strictly follow the National Weather Service (NWS) regional divisions, it is based on a combination of previous literature (e.g., Brooks et al. 2003) and qualitative grouping of areas with similar storm types or environmental characteristics.

In the results and discussion that follow, the term “event” describes a single tornado, regardless of its outbreak or isolated status. The term “outbreak” refers to a series of tornadoes grouped together according to the definition to be established in this section. The term “outbreak tornado” is used to describe an individual tornado that has occurred during an outbreak. A distinction can thus be made between the tornadoes that are flagged as part of an outbreak (“outbreak tornadoes”) and the tornadoes that are flagged as isolated events (“isolated tornadoes”).

It is clear that this research will require a specific definition of a tornado outbreak. To begin, we establish “clusters” of tornadoes based on intensity and temporal proximity: subsequent tornadoes in a cluster must be no more than 6 h apart [we tested 8, 6, 3, 2, and 1 h with little difference in the final number of outbreak events], and there must be at least 10 tornadoes rated (E)F1+ within each cluster. For each of these clusters, a two-dimensional kernel density estimation (KDE; a simple smoothing method that replaces each data point with a Gaussian “kernel”) is performed [following the methodology of Shafer and Doswell (2011), we use a bandwidth of 1 for latitude/longitude values and a density threshold of 0.001]. Each cluster is split into outbreaks based on the KDE groupings. These outbreaks are then rechecked for the presence of at least 10 (E)F1+ tornadoes and no more than 6 h between subsequent tornadoes. Each of the events in the 2003–15 tornado event dataset is assigned a flag as outbreak or isolated (i.e., not belonging to an outbreak as defined by the previous criteria).

The final result is thus 5343 events identified as belonging to 134 separate outbreaks, and 9389 tornadoes identified as belonging to the isolated category.

Figure 2a shows the geographical distribution of outbreak tornadoes. Tornado outbreaks are generally most prominent in the Great Plains, Northern Plains, Midwest, and South regions (as confirmed by the plot of tornado outbreak centroids in Fig. 2b); the tornadoes in the West and Northeast region are almost all isolated.

Note that while detrending is often necessary to account for nonmeteorological factors leading to an increase in the number of nontornadic severe weather outbreaks, Doswell et al. (2006) found that it is unnecessary for tornadic outbreaks. To verify, given that this dataset is outside the temporal scope of Doswell et al.’s (2006) analysis, we performed a linear regression on the annual mean number of tornado reports within a given cluster; the result was a regression line with a slope of 0.0185, an intercept of −30.744, and an r2 value of 0.0038. Given the very small positive trend, we believe a lack of detrending on this dataset is justified.

3. Analytical methods

The significant tornado parameter (STP; Thompson et al. 2003) is a composite parameter that incorporates several atmospheric variables that together discriminate fairly well (Thompson et al. 2012) between the near-storm environments of nontornadic (but significantly severe) supercells and significantly tornadic supercells (i.e., those supercells capable of supporting tornadoes with ratings ≥ EF2). The variables in question include mixed-layer convective available potential energy (MLCAPE), 0–6-km vector shear magnitude (SHR6), mixed-layer lifting condensation level (MLLCL), and 0–1-km storm-relative helicity (SRH1). Hence,

 
formula

Individually, the MLCAPE–SHR6 and MLLCL–SRH1 parameter spaces can provide additional insights into the distribution of tornadic near-storm environments (Anderson-Frey et al. 2016, 2017). This version of STP is used in lieu of the effective-layer STP because effective-layer parameters were not available for the entirety of the dataset’s time scale.

Parameter spaces for outbreak and isolated tornadoes can be obtained by simply plotting each tornado on a scatterplot in which the ordinate is SHR6 (SRH1) and the abscissa is MLCAPE (MLLCL), but with several thousand points to plot, at-a-glance comparisons and analysis become difficult. Instead, we make use of KDE, which facilitates comparison between the parameter-space distributions of outbreak and isolated tornadoes. Further details on the use of KDE for tornadic near-storm environmental studies can be found in Anderson-Frey et al. (2016). Statistical significance is discussed in the following section with respect to the difference between mean values of a given variable (e.g., differences in MLCAPE between the isolated and outbreak datasets). These differences are calculated using a 10 000-sample bootstrap with a p value = 0.05.

Self-organizing maps (SOMs; Kohonen 1982), while commonly used in broader climatological studies (Liu and Weisberg 2011), have only recently begun to be utilized in severe weather research (Nowotarski and Jensen 2013; Anderson-Frey et al. 2017; Nowotarski and Jones 2018). A SOM enables clustering of near-storm environments based not on point (proximity sounding like) data, but on the two-dimensional patterns of atmospheric variables; each cluster can then be investigated in order to identify, for instance, environmental patterns with particularly high occurrences of outbreak tornadoes. Further details on the use of SOMs for this tornadic near-storm environmental study can be found in the  appendix.

4. KDE analysis of tornado outbreaks

The KDE method lends itself well to an analysis of the parts of the parameter space in which tornado outbreaks occur versus the parts of the parameter space in which more isolated tornadoes occur. There are clear differences in the statistics of the outbreak tornadoes and the isolated tornadoes; mean values of MLCAPE, SHR6, MLLCL, SRH1, and STP are listed in Table 1 for outbreak tornadoes and isolated tornadoes, along with the probability of detection (POD; the percentage of all tornadoes for which an associated warning had a positive lead time) for each category. In terms of bulk values of variables, outbreak tornadoes and isolated tornadoes show little difference in MLCAPE (1233 vs 1260 J kg−1; this difference is the only one not statistically significant with a p value of 0.05), but outbreak tornadoes tend to have greater SHR6 (29 vs 21 m s−1), lower MLLCL heights (835 vs 1041 m), and greater SRH1 (348 vs 164 m2 s−2). The STP is thus higher on average for outbreak tornadoes (2.6 vs 0.9). Probability of detection is considerably higher for outbreak tornadoes (80%) than for isolated tornadoes (59%). Note that the false alarm ratio cannot be calculated due to the lack of warning data (choosing which warnings, including false alarm warnings, are associated with outbreaks is beyond the scope of this work) and that POD data in isolation must be analyzed with caution.

Outbreak tornadoes are also, on average, significantly more likely to cause casualties; 11% (4%) of outbreak (isolated) tornadoes result in injuries, and 5% (1%) result in deaths. The percentage of outbreak tornadoes that have a QLCS storm mode (12%) is virtually the same as the percentage of isolated tornadoes that have a QLCS storm mode (11%), and outbreak tornadoes are more likely to be RMS tornadoes than isolated tornadoes are (81% vs 65%).

A glance at Fig. 2 shows that outbreak tornadoes are more common in the South (42% of outbreak tornadoes) than the Great Plains (24% of outbreak tornadoes), the Midwest (25% of outbreak tornadoes), and the Northern Plains (8% of outbreak tornadoes); on the other hand, a higher percentage of isolated tornadoes occur in the Great Plains (34%) than in the South (25%). Outbreak tornadoes rarely occur in the Northeast or the West, whereas those regions make up 5% and 3%, respectively, of isolated tornadoes. Outbreak tornadoes are much more common in the spring (58% of outbreak tornadoes) than in any other season, whereas isolated tornadoes are slightly more likely to occur in the summer (43% of isolated tornadoes) than in the spring (37% of isolated tornadoes). Nocturnal tornadoes make up a higher percentage of outbreak tornadoes (26%) than they do of isolated tornadoes (11%).

Figure 3 shows the KDE distributions of the outbreak tornadoes and the isolated tornadoes; as suggested by the values in Table 1, there is little difference in the distribution of MLCAPE values, but outbreak tornadoes tend toward greater SHR6 than isolated tornadoes (Fig. 3a). Likewise, outbreak tornadoes are characterized by lower MLLCL heights across a smaller range of values, as well as considerably higher SRH1 values than isolated tornadoes (Fig. 3b).

It is important to recognize, however, that based on the geographical distribution of tornado events (Fig. 2), one might expect that the parameter-space distribution of the outbreak tornadoes would strongly resemble the Great Plains, Northern Plains, Midwest, and South environments, while the isolated tornadoes would have slightly more weight from the distributions of the Northeast and West environments, although those regions are still a small percentage of the total.

To discuss these regional differences, Fig. 4 shows the outbreak and isolated parameter-space distributions for the Great Plains, Northern Plains, Midwest, and South regions. In the Great Plains (Figs. 4a,b), overall MLCAPE values are higher than the Midwest and the South for both categories, MLLCL heights are lower for outbreak than for isolated tornadoes, and outbreak tornadoes are characterized by higher SHR6 and SRH1 values than isolated tornadoes. The Northern Plains (Figs. 4c,d) have fairly similar distributions to those in the Great Plains, whereas the Midwest (Figs. 4e,f) has the 90% (outer) contour for outbreak tornadoes spreading across a narrower range of values of MLCAPE than the isolated tornadoes; overall, though, MLLCL heights again extend into higher values for isolated tornadoes, while outbreak tornadoes have higher values of SHR6 and SRH1. Outbreak tornadoes in the South (Figs. 4g,h) generally have slightly higher values of MLCAPE than isolated tornadoes; in addition, there are again the characteristic higher SHR6 and SRH1 values for outbreak tornadoes than for isolated tornadoes.

Figure 5 depicts box-and-whisker plots of STP values for outbreak and isolated tornadoes. Note that, while there is some overlap between the two categories, isolated tornadoes (Fig. 5, left) generally occur for lower values of STP than outbreak tornadoes (Fig. 5, right); that is, taken as a whole, the tornadoes in this dataset that occurred during a tornado outbreak also tended to occur in more favorable environments based on STP.

The POD (Table 1) is considerably higher for outbreak tornadoes (80%) than for isolated tornadoes (59%); Fig. 6 depicts the distribution of POD values across the parameter spaces for each category by binning events within grid squares of dimensions = 4 m s−1 (MLLCL = 75 m) and SHR6 = 2 m s−1 (SRH1 = 30 m2 s−2) for the MLCAPE–SHR6 (MLLCL–SRH1) parameter space, where is as defined in the caption for Fig. 3. Within each bin, the number of warned events is counted and divided by the total number of events in the bin (i.e., POD is calculated within each bin). The higher overall values of POD for the outbreak tornadoes (Figs. 6a,c) are apparent; the pattern in POD is also more apparent for outbreak tornadoes than for isolated tornadoes, with higher values of POD generally corresponding to more tornado-favorable values of MLCAPE, SHR6, and SRH1.

5. SOM analysis of tornado outbreaks

A SOM provides an instructive method of analyzing the two-dimensional patterns of favorable environments surrounding outbreak tornadoes. This method involves creating 480 × 480 km2 maps of STP centered on the location of each event in question. The SOM will, using this stack of maps as input, produce a user-specified number (in this case, a 3 × 3 grid) of statistically distinct prototypical environments (called nodes in what follows), around which the full set of events can be clustered. Details of this methodology are described in Nowotarski and Jensen (2013), Anderson-Frey et al. (2017), and the  appendix. Note that SOMs are primarily a data visualization technique, and care must be taken to treat these plots as exploratory rather than inferential.

a. Isolated tornado environments

To begin, Fig. 7 is a SOM for isolated tornadoes (i.e., those tornadoes that do not meet the outbreak criteria defined in previous sections). Figure 8a plots the POD for each node, and each node’s cluster is split into its geographical region (Fig. 8b), its time of day (Fig. 8c), its season (Fig. 8d), its (E)F-scale rating (Fig. 8e), and its parent storm morphology (Fig. 8f; note that only RMS and QLCS storms are featured).

Generally speaking, POD is highest (Fig. 8a) for those nodes with the highest overall values of STP: node 7 has the highest STP and also a 100% POD, whereas node 3 has the lowest STP and only a 46% POD. This general trend (POD increasing with overall STP) seems to hold regardless of the specific two-dimensional distribution of STP values: nodes 1, 4, and 8 feature similar values of STP (Fig. 7) and also have similar values of POD (80%, 80%, and 81%, respectively). Incidentally, node 7 also has the highest percentage of tornadoes that resulted in injuries (14%), whereas node 3 has the lowest (3%).

Node 7, with its extreme values of STP and perfect POD, is composed entirely of tornadoes that occurred in the Great Plains (Fig. 8b), during the spring (Fig. 8d), and from an RMS parent storm (Fig. 8f). None of these tornadoes occurred during the day, with a total of 71% occurring overnight (Fig. 8c). While the other nodes, on average, were composed of only 0.4% (E)F3+ tornadoes, 14% of the tornadoes sorted into node 7 were rated (E)F3 or greater; (E)F1 tornadoes are also almost twice as common as (E)F0 tornadoes in this node (57% vs 29%, respectively; Fig. 8e). The pattern of node 7, with extremely high STP values all around the tornado but especially to the northeast of it, is hence reflective of particularly violent isolated RMS tornadoes that tend to occur in the Great Plains, during the springtime, and primarily at night.

The node with the most dramatic contrast to node 7 is the much more marginal node 3 (Fig. 7), with a mean STP below 1 at all points surrounding the tornado. These tornadic environments occur mainly in the Great Plains and the South (Fig. 8b), but a full 5% also occur in the West. This is also the only node in which the majority of events (62%) occur during the day (Fig. 8c) and in which a full half of the events (50%) occur during the summer (Fig. 8d). The (E)F0 tornadoes are by far the most common in this node (76%; Fig. 8e), and many of the parent storms for this node are neither RMS nor QLCS storms (Fig. 8f). These weak events occur outside the bounds of “textbook” tornado risk, where conditions are marginal.

Between the two extremes, nodes 4 and 8 (Fig. 7) feature moderate values of STP of approximately the same magnitude; node 4 has its most favorable conditions in a broad area to the south of the tornado, whereas node 8’s most favorable conditions generally exist to the east of the tornado. Having already determined that these two environments have similar PODs (Fig. 8a), what other features differentiate them? As it turns out, node 8 more closely resembles the high-STP/high-POD node 7 than node 4 does; node 8 has a higher percentage of Great Plains tornadoes (49%, vs 34% for node 4; Fig. 8b), a higher percentage of springtime tornadoes (51%, vs 39% for node 4; Fig. 8d), a higher percentage of (E)F3+ tornadoes (9%, vs 4% for node 4; Fig. 8e), and a slightly higher percentage of RMS tornadoes (90%, vs 86% for node 4; Fig. 8f). On the other hand, node 4 does have a higher percentage of nocturnal tornadoes (35%, vs 12% for node 8) and South tornadoes (21%, vs 12% for node 8). Both nodes 4 and 8 depict isolated tornado environments that have fairly high PODs, but the former, with a north–south STP gradient that resembles a warm front, features a higher percentage of South and nocturnal tornadoes, and the latter, with an east–west gradient more evocative of a dryline scenario, features a higher percentage of springtime Great Plains RMS tornadoes.

Overall, the SOM approach used here has allowed us to characterize typical environments in which isolated tornadoes occur: better-warned isolated tornadoes (in terms of POD) also tend to feature higher values of STP; this pattern holds regardless of the specific shape of the area of STP, although two environments with similar magnitudes of STP and different distributions are generally the result of different parent environments, in terms of geography, time of day, season, intensity, and morphology.

b. Outbreak tornado environments

To contrast the isolated tornadic environments summarized in Figs. 7 and 8, the next step is to create a SOM for outbreak tornadoes, the results of which are shown in Figs. 9 and 10.

The contrast between the outbreak nodes of Fig. 9 and the isolated nodes of Fig. 7 is immediately apparent: the magnitudes of STP are considerably higher for outbreaks. Even the outbreaks’ most marginal node (node 3; Fig. 9) features values of STP greater than 1. Recall, too, that the POD for outbreak tornadoes (80%) is on average considerably higher than that for isolated tornadoes (59%). This difference is in line with work such as that by Brotzge and Erickson (2009), who found in their analysis of 2000–04 tornado events that the POD for days in which fewer than 5 tornadoes occurred in a given day was only 62%, whereas 10 or more tornadoes in a given day had a POD of 90%; POD generally increased with the number of tornado events in a given day.

Similar to the isolated tornadoes, outbreak tornado nodes also generally have higher POD associated with higher STP (Fig. 10a), although the relationship is not monotonic: node 7 has a slightly higher maximum value of STP (12.4) than node 8 (11.7), but node 8 has a higher value of POD (97%, vs 89% for node 7). Even node 3, which features the most marginal values of STP overall, has a POD of 70%, which is still higher than three of the nodes for isolated tornadoes (Fig. 8a). The range of POD values is also smaller for the outbreak nodes (where the difference between lowest and highest node PODs is 27%) than for the isolated nodes (where the difference is 54%); outbreak tornadoes, as a group, are warned rather well in terms of POD, whereas the POD for isolated tornadoes varies more dramatically based on environment.

Nodes 7 and 8 both feature high values of STP; for node 7, the most favorable conditions are generally to the northwest of the tornado, whereas for node 8, these conditions are to the southeast (Fig. 9). These two nodes are similar in most particulars: few daytime events (Fig. 10c), majority springtime events (Fig. 10d), and relatively high percentages of (E)F3+ tornadoes (Fig. 10e) and tornadoes with RMS parent storms (Fig. 10f). The biggest difference appears to be geographical: node 8, with its higher POD values (97%, vs 89% for node 7), is mainly composed of Great Plains (47%) and Midwest (34%) events, whereas node 7 is composed primarily of South events (72%).

Recall that the most marginal node of the isolated tornado SOM featured primarily summer tornadoes (Fig. 8d); in contrast, node 3, the most marginal node of the outbreak tornado SOM, has a broad spread of primarily springtime (39%), fall (32%), and even winter tornadoes (20%; Fig. 10d). Node 3 of the outbreak SOM is also primarily a South event (45%; Fig. 10d), and features a low percentage of (E)F3+ tornadoes (4%; Fig. 10e). This node has the highest percentage of QLCS tornadoes (Fig. 10f) when compared with any other node in either the outbreak or isolated tornado SOMs.

Six percent (11%) of outbreak tornadoes result in at least one death (injury); contrast this with 1% (7%) of isolated tornadoes. Node 8, with its high values of STP, is the most deadly outbreak environment depicted here, with 15% of all events resulting in at least one fatality. Perhaps surprisingly, node 4 has the second-highest percentage of deadly tornadoes (10%), despite its relatively low STP values. Node 7, despite having comparable STP values and a lower POD than node 8, has a considerably lower percentage of deadly tornadoes (4%), emphasizing that fatality rates do not line up perfectly with POD and that many other factors (e.g., warning communication, building codes, warning fatigue) may come into play when reducing fatalities.

6. Case studies

To apply the results of the previous research to specific cases, this section considers two major tornado outbreaks during the period in question: these outbreaks will be defined as in the previous sections to include at least 10 (E)F1+ tornadoes within the same KDE grouping with no more than 6 h between subsequent tornadoes in the outbreak.

a. 27 April 2011

The 27 April 2011 tornado outbreak (Fig. 11), as defined using the aforementioned method, consisted of 275 tornadoes, occurring between 1815 UTC 26 April and 2123 UTC 28 April 2011. Over these two days, tornadoes were identified in 17 states; of these tornadoes, 231 were in the South, 20 were in the Northeast, 16 were in the Great Plains, and 8 were in the Midwest. Ninety-two tornadoes occurred during the day, 90 during the EET, and 93 at night. These tornadoes alone were associated with 2347 injuries and 240 fatalities. The mean (median) warning lead time for these tornadoes was 20.0 (20.0) min, with a POD of 88%. Eighty percent of the tornadoes in this outbreak were RMS tornadoes.

A time series summary of the tornado (E)F-scale ratings and morphology is provided in Knupp et al.’s (2014) thorough review of the outbreak (their Fig. 3). The event consists of two distinct types of storms: morning/midday QLCS and afternoon supercells (Knupp et al. 2014).

On average, the 275 tornadoes composing this event occurred in environments with a mean value of 1278 J kg−1 MLCAPE, 34 m s−1 SHR6, 821 m MLLCL, and 512 m2 s−2 SRH1; Fig. 12 shows the tornadoes of this outbreak overlaid on the KDE plots of the MLCAPE–SHR6 and the MLLCL–SRH1 parameter-space diagrams for all outbreak tornadoes in the 2003–15 dataset. Note that the QLCS tornado events within this outbreak (blue markers in Fig. 12a) are generally limited to <1000 J kg−1 of MLCAPE, whereas RMS tornado events extend well beyond that threshold. Similarly, QLCS tornado events tend toward values of SRH1 that are greater than 400 m2 s−2 (Fig. 12b), while RMS tornado events extend across a broader range of SRH1 values.

To compare the environment in which the 27 April 2011 outbreak occurred with the composite environments created by the SOMs, Fig. 13 is a plot of mean STP values for each of the 480 km × 480 km areas surrounding the 275 tornado events within the outbreak, and further split into tornadoes with RMS parent storms (Fig. 13b) and tornadoes with QLCS parent storms (Fig. 13c). The environment associated with this outbreak is characterized by relatively high values of STP to the southwest of the tornado, but note that this pattern is most prevalent among the RMS tornadoes and is considerably less dramatic for QLCS tornadoes within the outbreak.

The mean plots in Fig. 13 can be compared via Euclidean distance (i.e., straight-line distance between corresponding points) with the nodes of the SOM plot for outbreak tornadoes (Fig. 9). Using these criteria, the mean plot of the 27 April 2011 outbreak (Fig. 13a) matches most closely with node 1 (Euclidean distance of 13.8); this node is characterized by relatively broad areas of moderate STP, featuring more favorable environments to the southeast of the tornado. Node 1 of the SOM has a nearly equal distribution of events between the South (33%), the Great Plains (27%), and the Midwest (29%; Fig. 10b).

Note, however, that the 27 April 2011 outbreak can be split into the early-day QLCS tornadoes and the later-day RMS tornadoes; the RMS tornadoes in Fig. 13b match most closely with node 5 (Euclidean distance of 15.1; a map in which moderate values of STP are spread fairly symmetrically around the tornado), whereas the QLCS tornadoes in Fig. 13c match node 6 (Euclidean distance of 8.1; a map in which marginal values of STP are to the east of the tornado). Node 6 of the SOM does indeed have a higher percentage of QLCS tornadoes than node 5 (8% vs 4%, respectively; Fig. 10f), and node 5 is more characteristic of tornadoes in the South than node 1 (Fig. 10b), the initial match for this event when taken as a whole. The contrast between the broader spread of the STP in node 5 and the sharper gradient in node 6 (Fig. 9) suggests the different patterns of the favorable environments in which these storms occurred.

These comparisons show that the complexity even within a given event—a long-duration outbreak like this one encompasses several different environmental regimes—can be captured by considering how the individual tornadoes’ environments map to the nodes of a SOM.

b. 10 May 2010

The 10 May 2010 tornado outbreak (Fig. 14) consisted of 42 tornado events, running from 1827 UTC 10 May 2010 to 0142 UTC 11 May 2010. These tornadoes occurred exclusively in Kansas and Oklahoma (both in the Great Plains region); 31 occurred during the daytime and 11 occurred during the EET, and three fatalities and 94 injuries were associated with these 42 tornadoes. The mean (median) warning lead time for these tornadoes was 19.9 (18.1) min, with a POD of 83%. Eighty-eight percent of the tornadoes in this outbreak were RMS tornadoes.

This outbreak event is characterized by mean MLCAPE of 2482 J kg−1, mean SHR6 of 38 m s−1, mean MLLCL of 921 m, and mean SRH1 of 446 m2 s−2. When compared with the mean values of these variables for the 27 April 2011 outbreak, these results already depict a typical difference between tornado environments in the Great Plains and the South: MLCAPE is higher and SRH1 is lower for the Great Plains outbreak than for the outbreak in the South. The details are depicted in Fig. 15, which overlays the tornadoes of this outbreak onto the KDE plots of the MLCAPE–SHR6 and the MLLCL–SRH1 parameter-space diagrams for all outbreak tornadoes in the 2003–15 dataset. The tornadoes in this outbreak tend to occur for higher SHR6 and, occasionally, higher SRH1 than the typical distribution of tornado outbreak environments.

The 10 May 2010 outbreak mean STP environment (Fig. 16) has moderate to high values of STP along a relatively thin corridor running north–south through the location of the tornado. Comparing this outbreak to the SOM plot for all outbreak tornadoes (Fig. 9), the 10 May 2010 tornado outbreak matches most closely with node 1 (Euclidean distance of 20.3), which is an environment in which favorable values of STP occur to the southeast of the tornado. This is a node characterized by a high percentage of springtime (Fig. 10b), daytime or EET (Fig. 10c), and RMS tornadoes (Fig. 10f).

7. Summary of findings

For the purposes of this study, tornado outbreaks were defined as being a series of spatially clustered tornado events, of which 10 or more are rated (E)F1+, with each subsequent tornado within the outbreak occurring no more than 6 h apart. These tornado outbreaks are most common in the Great Plains, Northern Plains, Midwest, and South regions.

We identified 5343 tornado events in 134 separate outbreaks and analyzed these storms in comparison to 9389 tornado events belonging to more isolated occurrences. The average outbreak tornado is characterized by greater SRH1 and lower MLLCL heights than isolated tornadoes. When divided by geographic region, outbreak tornadoes in the Great Plains, the Northern Plains, the South, and the Midwest all have higher values of SHR6 and SRH1 than isolated tornadoes, but in the South there is also a difference in MLCAPE, with outbreak tornadoes having higher values than isolated tornadoes on average; in comparison, Tochimoto and Niino (2016) found that both SRH and CAPE were higher for outbreak cyclones than for nonoutbreak cyclones, but geographical differences in these variables were not analyzed. Outbreak tornadoes are more likely to occur in the spring than during any other season, while isolated tornadoes are split more evenly between spring and summer, and nocturnal tornadoes make up 26% of outbreak tornadoes and only 11% of isolated tornadoes. POD is higher for outbreak tornadoes (80%) than for isolated tornadoes (59%), in line with Brotzge and Erickson’s (2009) finding that higher numbers of tornadoes on a given day resulted in higher overall PODs on that day. The POD for outbreak tornadoes also shows a more consistent relationship to values of CAPE and SHR6, with higher values of POD corresponding to relatively tornado-favorable parameter values.

The SOM of all isolated tornadoes reveals that the POD relies more strongly on the magnitude of the STP value surrounding the tornado than its spatial pattern. The SOM of outbreak tornadoes shows that tornado outbreak environments with similar magnitudes but different distributions of STP are mostly differentiated by their geographical makeup; Great Plains and Midwest tornado outbreaks dominate an environment in which high values of STP are to the east of the tornado, whereas South tornado outbreaks dominate an environment in which those favorable conditions are to the northwest of the tornado. A lower magnitude of STP values does not necessarily correlate with low-casualty outbreaks; one of the outbreak SOM nodes (node 4) showed a relatively modest stretch of moderate STP values and still resulted in high rates of injury (20%) and death (10%). A relatively low-STP outbreak pattern was identified (node 3), corresponding to spring and cool-season South, Midwest, and Great Plains tornado outbreaks. Although tornado outbreaks can occur even in relatively low-STP conditions, they are disproportionately more likely to occur when STP values are high; the low-STP environments are simply more common.

Two particular tornado outbreaks were discussed briefly (27 April 2011 and 10 May 2010), and both were compared to the KDE plots and SOM plots of the near-storm environments characteristic of outbreak tornadoes. This approach showcases the potential for the use of these methods to characterize outbreak tornadoes through the use of parameters such as the STP in the near-storm environment, thus providing a more nuanced picture of the tornado outbreak climatology.

Acknowledgments

The authors are grateful for the assistance of Brenton MacAloney in obtaining the verification data. This work has benefited tremendously from helpful discussions with George Young, Martin Tingley, Israel Jirak, Russ Schneider, Harold Brooks, Richard Grumm, the forecasters at the NWS State College Weather Forecast Office, Steven Weiss, Bill Bunting, Roger Edwards, and Paul Markowski, as well as the mesoscale research group at Penn State University. This paper was greatly improved by the comments of Matthew Bunkers and three anonymous reviewers. AKAF is supported through NSERC Postgraduate Scholarship PGSD3-462554-2012, and AKAF and YPR’s time is supported by NOAA CSTAR Program Award NA14NWS4680015 and NOAA VORTEX-SE Award NA17OAR4590189.

APPENDIX

Self-Organizing Map Formulation

A SOM is here being used as a visualization technique via a clustering approach to make qualitative and quantitative comparisons between common two-dimensional patterns of STP that emerge in isolated and outbreak tornado environments. The SOM is built using Matlab’s neural network clustering toolkit.

An important evaluation tool in comparing clusters of data is the silhouette coefficient (SC), which makes use of the mean intracluster distance (IC), and the mean distance between a sample and the nearest cluster that it is not a part of (NC). Note that “distance” here refers to the Euclidean distance. The silhouette coefficient is defined as follows:

 
formula

The first step in constructing a SOM is also the only user-specified part of its construction: determining the final number of clusters. The SOM size of 3 × 3 was chosen from among a subset of possible sizes (5 × 5, 4 × 4, 3 × 2, 2 × 3, and 2 × 2) based on (i) quantitatively, its positive silhouette coefficient (with a mean of 0.24) that is on average higher than those of the other potential sizes, and (ii) qualitatively, its ability to depict several different environments without arbitrarily separating environments that look similar at a glance. The qualitative aspect of this selection process is essential, as the intended audience (forecasters) must be able to distinguish between environmental nodes; if two nodes are statistically different but cannot be distinguished in a practical way, the value of their separation is dubious at best.

As training data input for the outbreak (isolated) SOM, we provide 5343 (9389) maps of STP, for which each map consists of 13 × 13 gridpoint STP values from the RUC/RAP analysis, with each 13 × 13 grid centered on the grid point nearest the location of tornado touchdown. The SOM is then constructed by first producing nine 13 × 13 randomly generated maps. Each of the training maps is compared to these nine “nodes,” and the nodes are nudged toward those training maps based on their proximity (via Euclidean distance) to the training map in question. After all training data have nudged the nodes, the training step is repeated; this process continues 200 times, at which point the nodes have settled into a stable configuration.

The specific process used here also includes a preference for assigning the same number of events to each node, although this preference is evidently not a guarantee (i.e., clear cutoffs in clusters will trump the same-size preference). Given the importance in this application of describing environments in which outbreaks occur with high STP (an uncommon event) and low STP (a more common event), this imbalance in the number of events in each node was judged to be acceptable.

When training is complete, the training data are then matched up with their nearest-match nodes (again based on Euclidean distance), resulting in nine clusters of data. The mean map of each cluster is what is depicted in the SOM plots of this work.

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Footnotes

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