1. Introduction
a. Motivation
Tornadoes that follow a trajectory noticeably different from that of their parent storms, hereby defined as deviant tornadoes, carry with them potentially noteworthy impacts. Deviant tornadoes, especially those that deviate northward or leftward with respect to the parent supercell, have been observed for several decades, particularly within the meticulous analyses of Dr. Tetsuya Theodore “Ted” Fujita. Fujita observed this phenomenon as early as 1957 with the Fargo, North Dakota, F5 tornado, which, after moving east-southeast and impacting the town, acquired a northeastward trajectory for the rest of its life (Fujita 1960). Other notable cases include the 1970 Lubbock, Texas, tornadic event, where both tornadoes were found to curve to the north, the 1980 Grand Island, Nebraska, “Night of the Twisters,” where several tornadoes assumed almost erratic trajectories, and even the 1974 Super Outbreak, where a large fraction of tornadoes especially close to the Ohio River Valley were noted to curve leftward with time (Fujita 1970, 1974; McDonald 2001).
More recently, multiple other high-impact cases have further motivated a need to understand deviant tornadoes. The Greensburg, Kansas, tornado of 4 May 2007 is one such example. Greensburg itself was included just within the northwestern edge of the first National Weather Service (NWS) tornado warning polygon; indeed, given the damage surveys done by Lemon and Umscheid (2008), the tornado would have passed east of town should it have continued on its initial trajectory, instead of deviating northward. A tornado on 15 May 2013 impacted the town of Cleburne, Texas, and similarly was included only on the northernmost edge of its NWS warning polygon. Though any impact appeared an unlikely occurrence given its initial southeastward track, this event proved the importance of the communication between the NWS and emergency management in relaying word of a sudden deviation due north (Cavanaugh et al. 2016, their Table A5). Perhaps most infamously, the El Reno, Oklahoma, tornado on 31 May 2013 killed eight people in vehicles, including the experienced TWISTEX severe weather research team of Timothy Samaras, Carl Young, and Paul Samaras, likely in part due to a lack of situational awareness of its ever-changing trajectory, from southeastward, to eastward, then north-northeastward (Wurman et al. 2014; Seimon et al. 2016). The north-northeastward turn went unanticipated by the NWS as well, prompting the office to issue a subsequent tornado warning covering areas left of the path of the previous warning. On this evidence, we argue that this problem reflects a substantial operational challenge.
The current polygon warning methodology fortunately does allow for some uncertainty in a tornado’s track; however, efforts are ongoing between the NWS and the National Severe Storms Laboratory (NSSL) to integrate the element of probability into warnings to better communicate this uncertainty. The next-generation Forecasting a Continuum of Environmental Threats (FACETs) paradigm employs Probabilistic Hazard Information (PHI), a “cone of uncertainty”-like approach similar to the current standard in hurricane prediction (Rothfusz et al. 2018), but assigns a continuous distribution of hazard probabilities that allows for the communication of a spectrum of likelihoods over an area. Compared to the current binary polygon approach, this probabilistic approach naturally aims to communicate the lower probabilities near the edges of a warning, such that a location near the northern edge may be relayed a warning of low probability of an imminent hazard, rather than a warning of an imminent hazard. In the case of a tornado, FACETs would necessarily require a forecast cone that anticipates its most likely future path, or else warning forecasters risk a potentially catastrophic event being communicated as low probability. Thus, understanding how to anticipate the paths of deviant tornadoes is imperative to forecasters.
NWS forecasters have been trained to adapt to deviating tornadoes. The Warning Decision Training Division (WDTD) Radar and Applications Course (RAC) encourages the forecaster to draw warning polygons in the direction of storm motion, then widen them as a buffer if the storm displays the propensity to produce deviant tornadoes (WDTD 2020). However, this approach is more reactive than proactive. A fuller understanding of the trajectory of tornadoes as disparate from that of the parent supercell may improve the ability to anticipate these deviations. Coincidentally, the introduction of FACETs, which is built to communicate such detailed information, provides a timely opportunity to improve tornado track prediction.
b. Background
The motion of supercell storms has been generally well examined, and is predictable with a substantial degree of accuracy today; this is largely the product of a succession of hodograph techniques (Maddox 1976; Davies and Johns 1993; Davies 1998; Rasmussen and Blanchard 1998; Bunkers et al. 2000, 2014; Bunkers 2018; Ramsay and Doswell 2005). The Bunkers “internal dynamics” method (hereafter B2K), today’s operational standard, predicts right-moving supercell motion with a mean error of 4.1 m s−1 (8.0 kt). This elegantly simple sum of the contributions of the mean wind and a fixed magnitude of deviation to the right (or left, for left-moving supercells) accounts for the average behavior of anomalous propagation as a response to mesocyclone dynamic pressure perturbations. Regardless of the motion of the supercell, however, past observations such as those from Fujita suggest that tornadoes can and do acquire motions different from those of their parent supercells.
The mechanisms behind deviant tornadoes have been the subject of occasional investigation. An early study by Agee et al. (1976) explored and classified patterns in the damage tracks of tornado families. They noted that a supercell storm can produce tornadoes in behaviors ranging from a single, longer-tracked circulation to a series of shorter-tracked “skipping” circulations that immediately deviate from the parent storm track, yielding roughly parallel damage paths. They hypothesized that these deviations could be a result of a “multiple vortex” structure within the parent supercell, where individual tornadoes rotate around the parent circulation. Indeed, this was noted in the 1990 Hesston, Kansas, tornado event, where an initial F5 tornado wrapped cyclonically around and merged into another developing F5 tornado during its dissipation stage (Davies et al. 1994). Similarly, this was noted more recently in the 2014 Pilger, Nebraska, tornado event, where an EF4 tornado wrapped cyclonically around another EF4 tornado, with the two paths crossing (https://www.weather.gov/oax/event_archive_20140616). Both of these cases would appear to be consistent with the orbital interaction hypothesis of the Agee model (Agee et al. 1976). However prevalent, though, this mechanism does not address the tendency for families of tornadoes to acquire a “preferred” consistent direction of deviation, such as which resulted in the parallel tracks noted in Agee et al. (1976).
Other potential mechanisms controlling the deviation of tornadoes were proposed as a result of the Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX). Comprehensive observations of a cyclic supercell on 8 June 1995 near McLean, Texas, sampled a number of tornadoes of different ratings and durations (Rasmussen et al. 1994). This allowed the collection of an array of storm-scale data corresponding to varying degrees of the storm’s capability to maintain a tornado. Subsequent mobile radar observations (Dowell and Bluestein 2002b) showed that tornadoes produced from this supercell had a tendency to move toward the left at the end of their life. This process began when the circulation in the low-level inflow to the tornado decreased, or if the convergence at the base of the parent updraft decreased, both of which were a product of the detachment of the tornado in the low levels from the main updraft centroid. In lieu of the word “occlusion,” signifying specifically the wrapping of colder air fully around a circulation, “detachment” is used here and in the remainder of this study to describe this process. Once the tornado detached from its initial location in the parent updraft centroid, it was “shed rearward” while taking on a deviant track at times nearly 90° left of the supercell’s motion; during this process, one tornado became separated from its parent updraft’s centroid by 7 km in only 14 min (Dowell and Bluestein 2002b). As each tornado moved further away from parent updraft’s centroid, it tended to narrow in size and decrease notably in rotational velocity.
Throughout the life-span of the McLean supercell, Dowell and Bluestein (2002b) noted that most tornadoes formed, then moved quickly out of the region with the theoretically best environment for tornado maintenance (where strong low-level circulation lies beneath a strong updraft). This tendency of motion away from that region was hypothesized to be related to horizontal advections by the low-level flow (a hypothesis also shared by Tanamachi et al. (2012) in radar observations of the Greensburg, Kansas, tornado). Indeed, the flow near the various McLean tornadoes analyzed at 500 m was related to their deviant motion. Similar results were obtained from observations of a tornadic supercell in Goshen County, Wyoming, on 5 June 2009 during the VORTEX2 project (French et al. 2014). After a ring of enhanced reflectivity surrounded the tornado, it became detached in the lowest 1.5 km and began to advect away from the updraft centroid, moving in a direction consistent with the 1.5-km mean wind. This deviation and ensuing dissipation, however, was delayed when the strength of the storm-relative rear-flank outflow increased (Dowell and Bluestein 2002b). In one case, a stronger outflow encouraged weaker storm-relative winds around the tornado, thus less tendency for it to immediately advect away from the parent updraft. This suggested that tornadoes were more apt to deviate northwestward when within weaker outflow, where southeasterly inflow winds were allowed to penetrate deeper into the left flank of the storm, a result corroborated by subsequent studies (Dowell and Bluestein 2002a; French et al. 2014). None of these studies disprove the prior conceptual model offered by Agee et al. (1976) that deviant tornadoes are a product of rotational motion about a parent mesocyclone. However, none of these studies offer sufficient evidence to further this conceptual model. We found it prudent, rather, to acknowledge the storm-relative advection hypothesis they did provide, since this suggests tornado deviation may be predictable using the hodograph.
Though we acknowledge the Agee et al. model and the advection of a tornado by the low-level storm-relative winds as two leading theories for the deviant motion of tornadoes, a number of other storm-scale factors may influence a tornado’s path. Most relevant to this study, any sufficiently dense downdraft and resulting internal momentum surge has the potential to steer a tornado. This includes the rear flank downdraft and any secondary surges, as well as any descending reflectivity cores (DRCs) (Rasmussen et al. 2006; Kennedy et al. 2007). Such momentum surges could either work to deviate the tornado particularly to the right or forward (Lee et al. 2012), or suppress an aforementioned advective tendency to deviate to the left or rearward (Dowell and Bluestein 2002b). We acknowledge that these carry a nontrivial role in tornado motion and, of particular note to this study, these may result in “failures” to deviate; however, since these are such transient storm-scale processes with little known inherent predictability by way of the environment, we will not delve further into the impact these have on leftward deviant tornadoes.
Throughout this study, several questions will be addressed: 1) is deviant motion predictably associated with the environmental low-level mean wind? If this is the case, which layer mean wind is most effective at predicting deviant tornado motion? 2) When does the hodograph fail to explain deviant motion? And last, 3) under which hodographs are deviant tornadoes most likely, and, in contrast, in which scenarios is information on the potential deviant motion of tornadoes least relevant to forecasters?
2. Data and methods
a. Case selection
A dataset of 102 cases of deviant tornadoes was developed, as no such sample existed, and this property of storms cannot be easily gleaned from existing datasets (this case list can be found in Table 1, which includes the date, start time, analysis time, rating, and warning performance of each tornado, as well as whether other deviant tornado cases existed with the same supercell). Cases were collected in two ways: 1) by finding local NWS damage track surveys that met the criteria of a leftward deviant tornado as one that turns noticeably left of its original trajectory over time, and 2) by searching the Storm Prediction Center Severe Weather Event Archive1 (https://www.spc.noaa.gov/exper/archive/events/) for any events that appeared to support deviant tornadoes based on the initial hypothesis of slow-moving, cyclic supercells amidst strong low-level advective flow. Any “suspect” cases were then examined using the Gibson Ridge Level II (GRLevel2) Analyst software (http://www.grlevelx.com/grlevel2/) for any possible leftward deviations in tornadic low-level mesocyclone trajectory. This full methodology is explained further in section 2c. Cases were limited to tornadoes observed during the years 2005–19, and produced by discrete supercells, using a 35-dBZ threshold in accordance with Smith et al. (2012). Each tornado examined must have been produced by a separate supercell, such that a greater variety of hodographs could be examined; however, two tornadoes from two separate supercells in a single day could be examined, as long as they were separated in time by 1 h or separated in space by 300 km. If a supercell produced more than one deviant tornado (which occurred in 41 of the 102 cases), the tornado was chosen that exhibited the majority of its path time marked by a deviation consistent in speed and direction. Each case needed to be examinable with archived WSR-88D radar data (Crum and Alberty 1993); for this study, this meant that the lowest-angle scan must be able to detect the entire life cycle of the tornado cyclone within 130 km (81 mi) of the radar. The 130-km threshold was chosen arbitrarily to ensure sufficient sampling of the near-surface tornado cyclone while also maximizing the number of examinable cases. Beyond this distance threshold, beamwidth was deemed unacceptable for accurately locating the cyclone center, and beam height unrepresentative of the tornado cyclone at the surface. This is especially due to studies like Dowell and Bluestein (2002b) that suggest considerable tilting of the tornado is possible in the lowest 2 km. Though the assumption that the circulation at any beam height represents the exact location of the near-surface tornado cyclone does not come without caveats, we acknowledge this in favor of attaining a sufficiently large sample size.
All tornadic low-level mesocyclones examined.
The deviant tornado cases encompassed a variety of locations around the United States (Fig. 1), and were most common in the southern/central Great Plains and High Plains. Though this sample of cases may not perfectly reflect the true distribution of deviant tornadoes across the United States, there is certainly evidence from this spatial distribution that NWS Weather Forecast Offices (WFOs) located in the central United States deal with deviant tornadoes on a more regular basis. Despite the overwhelming majority of cases in the Great Plains, however, 11 cases were found east of the Mississippi River, and one case along the West Coast, suggesting that, like most severe convective phenomena, deviant tornadoes can occur anywhere within the United States.
The locations of all 102 cases examined in this study, including one from Southern California (inset). These cases spanned the years 2005–19.
Citation: Weather and Forecasting 36, 1; 10.1175/WAF-D-20-0056.1
b. Hypothetical model of tornado deviation from the parent supercell
Evidence from studies in section 1b suggests that a tornado’s leftward deviation begins upon its detachment from the parent updraft centroid. This is used as a starting point in exploring the deviant motion of detached tornadoes. However, tornadoes can have multiple stages of widely ranging motions throughout their life span; a hypothetical model aiming to categorize these observed stages can be found in Fig. 2. Upon formation, some of the tornadoes examined in this study appeared to take on a trajectory further rightward of the pretornadic parent supercell’s initial motion. We define this as “rightward deviation.” The mechanisms behind this, other than those of internal momentum surges, are not explored further, and a count is not provided due to uncertainties as to whether this is a result of the deviation of the tornado or of the parent supercell. Most (but not all) tornadoes then exhibit a period of varying duration where they move with roughly the same speed and direction as the pretornadic parent supercell; we define this as “storm-following,” or simply, no deviation, as it is consistent with the parent supercell’s motion. In this study, all tornadoes then exhibit a period of varying duration where they take a deviant motion leftward or rearward of the parent supercell’s motion; we define this as “leftward deviation” for simplicity (but stress that this may also encompass rearward or other deviations). This deviation is likely a result of some component of any of the collective theories from section 1b, particularly the advective theory presented in Dowell and Bluestein (2002b) and the mesocyclone-orbiting theory presented in Agee et al. (1976). Last, some tornadoes appeared to take a further, continuously increasing deviation left (sometimes even “looping” back around) until dissipation; we define this as “chaotic deviation,” as the speed and direction throughout this period is highly variable. Though many forms of tornado motion are acknowledged above, “deviant” in this study refers only to the portion of the tornado’s life-span exhibiting leftward deviation, which we will show to be predictable using a hodograph via assuming the effects of storm-relative advection.
A hypothetical tornado path displaying three different types of deviation in addition to the nondeviant, storm-following segment, adapted from the path of the 4 May 2007 Greensburg, KS, tornado as surveyed by Lemon and Umscheid (2008).
Citation: Weather and Forecasting 36, 1; 10.1175/WAF-D-20-0056.1
c. Examination of WSR-88D data
Level II data from the closest WSR-88D to each tornado were downloaded and analyzed using GRLevel2. A tornadic vortex signature (TVS) (Brown et al. 1978), such as is detected automatically in operations (Mitchell et al. 1998), was determined manually from base velocity gate-to-gate shear in the lowest-tilt radar scan. When possible, the lowest-tilt normalized rotation (NROT) product was used; this normalizes gate-to-gate azimuthal shear by the area of the bins over which it was calculated, thus it can be used to find the location of maximum rotation assuming nonfaulty velocity data. Each case required two nonoverlapping time windows of study: first, the pretornadic phase, and second, the tornado’s life-span exhibiting leftward deviation. We assessed the supercell’s motion pretornado, not the tornado’s motion predeviation, because not only did many of the tornadoes become deviant nearly immediately upon formation (rendering there being no predeviation phase), but some tornadoes took an apparent right turn upon formation that deviated from the parent supercell motion as discussed earlier. For each case, regardless of damage path surveyed by the NWS, this study considers only the tornado’s associated lowest-tilt mesocyclone (hereafter the low-level mesocyclone) tracked using radar, since this is the primary mode of detection in today’s warning process. Thus, for any case, the study window may not match the actual duration of its tornado. The pretornadic phase of the parent supercell was defined to end the first scan when the low-level mesocyclone exhibited a perceptible deviation from its initial trajectory. The study window of the deviant tornado’s life span began the first radar scan before the tornadic signature exhibited a noticeable deviation from the recorded supercell motion in speed and/or direction, and ended the first scan that a tornadic signature was no longer detectable. The approximate speed and direction of both the supercell and tornado were obtained by examining the movement of their corresponding circulation centers, finding the distance and direction change from its starting point to its ending point. The start and end point were used in every case for consistency, and sufficed for determining motion since the paths of leftward deviant tornadoes tended to be markedly straight (as discussed in section 2e below).
d. Environment and tornado characteristics
The environmental vertical wind and thermodynamic profile for each case, proximal in both space and time of the deviant tornado, was obtained from either the 0-h Rapid Update Cycle (RUC) and Rapid Refresh (RAP) forecast model analyses (Benjamin et al. 2016), depending on their availability (for instance, the RAP was not operationally implemented until 1 May 2012). To be considered proximal in time, the analysis corresponded to the nearest hour to the end time of the tornado, as leftward deviation necessarily begins near the end of its life (time was rounded up such that a tornado ending at 2230 UTC would use the 2300 UTC RUC/RAP analysis hour). The RUC and RAP employ a 13-km grid spacing with 50 vertical levels; these dimensions have been considered adequate for sufficiently resolving vertical features as well as relevant spatial variability (Thompson et al. 2003; King and Kennedy 2019), while also not resolving convectively induced meso-β-scale features such as cold pools or convectively enhanced low-level wind fields that are more likely with convective allowing models with smaller grid spacing (Squitieri and Gallus 2020). To be considered proximal in space, the analysis data were obtained within 50 km of the tornado in a region that represented an “inflow sector” air mass, with the thermodynamic profile inspected to ensure it was free from convective contamination (Thompson et al. 2003).
A composite ground-relative hodograph (Fig. 3) was created to visualize the mean wind profile for all 102 deviant tornado cases, in order to form a conceptual model of what shear environments may be most conducive to deviant tornadoes and form a hypothesis on why they are most common in the Great Plains. The mean observed supercell motion is ≈246° (to the east/northeast) at 10.60 m s−1 (20.6 kt), with a mean deviant tornado motion of ≈173° (to the north) at 8.92 m s−1 (17.3 kt) (Tables 2 and 3 ). These motion vectors may be slightly different than the motion vectors on the composite hodograph, since the vectors on the hodograph were calculated using the mean u and υ (not the mean speed and mean direction). The interquartile range of observed tornado motions is smaller than that of observed storm motions. Deviant tornado-producing supercells move with a speed of under 14 m s−1 (≈27 kt) over 75% of the time. A further breakdown of supercell motion can be seen in Fig. 4, which reveals that the majority of supercells moved with some component to the northeast at less than 15 m s−1 (29.2 kt), though several cases did possess southeastward-moving supercells (which moved slower on average). The hodograph features a roughly due southeasterly surface wind at ≈5 m s−1 (just under 10 kt), veering to just past due south at over 15 m s−1 (≈30 kt) by 1 km. From 1 to 3 km, winds continue veering to the southwest with minimal increase in speed, with an additional veering and speed increase above this layer (but with large spread). Though the hodograph exhibits an almost 25 m s−1 (≈50 kt) bulk wind difference from 0 to 8 km, it also features a bulk wind difference of roughly the same magnitude from 1 to 8 km. The 0–1-km bulk wind difference was ≈13 m s−1 (≈25 kt), with large 0–3-km curvature. Little variance exists between the near-surface winds of the cases; however, substantial variance does exist throughout the rest of the hodograph, especially above 4 km; this suggests that there is no “specific” ground-relative hodograph shape conducive for deviant tornadoes.
A composite ground-relative hodograph of all cases examined. Segments are colored by height (labeled on hodograph). Error bars denote variance, such that 75% of the cases feature the given height within the respective area of the hodograph. The mean observed storm (tornado) motion is plotted as a red (magenta) dot, with 75% of cases within the large, transparent red (magenta) circle. Range rings are labeled in m s−1, with heights marked on each hodograph in km.
Citation: Weather and Forecasting 36, 1; 10.1175/WAF-D-20-0056.1
The distribution of speed and direction of the supercells which produced deviant tornadoes (all 102 cases); first quartile (Q1), median (Med), and third quartile (Q3).
The distribution of speed and direction of the leftward deviant portions of all tornadoes examined (all 102 cases); Q1, Med, and Q3 as in Table 2.
A wind rose of the direction and speed (m s−1) of the parent supercell motion vectors (i.e., the direction the supercell is moving toward) of all cases examined. The bars are colored by speed, and their length is proportional to the percentage of cases that possessed that supercell motion.
Citation: Weather and Forecasting 36, 1; 10.1175/WAF-D-20-0056.1
Of the 102 deviant tornadoes, the official ratings from official NWS surveys are broken down as follows: F/EF0: 20, F/EF1: 24, F/EF2: 21, F/EF3: 24, and F/EF4: 8 with the remainder F/EFU (unknown). This distribution, in which ≈52% of tornadoes are rated F/EF2 or higher, is remarkably dissimilar to estimates of the actual distribution of tornado ratings, in which only ≈14% of tornadoes are rated F/EF2+ (Anderson-Frey and Brooks 2019). This may be attributed in part to collection bias where higher-impact events were more readily found and more comprehensively surveyed than less-noteworthy events, while a more continuous monitoring of real-time events ensured fewer events were missed in 2018 and 2019. The distribution of the recorded ratings of the sample of tornadoes may also be explained in part by the hodograph. Though the aforementioned collection bias cannot be ignored, the high percentage of tornadoes rated significant (dealing F/EF2 damage or greater) is anomalous. We speculate that the composite hodograph shape is consistent with historical cases where tornadoes have reached a rating of F/EF2–F/EF3; indeed, long, “sickle-shaped” hodographs marked by strong low-level shear (thus substantial storm-relative helicity) and a “kink” in the low-levels have long been acknowledged to be conducive for significant tornadoes. These were first noted in cases dating back to 1981 by Thompson and Edwards (2000) (their Fig. 12), with subsequent work by Esterheld and Giuliano (2008) exploring the use of the “critical angle” in anticipating (strongly) tornadic storms.
An important distinction must be made that deviant tornadoes, though noted to be common with “cyclic” supercells, can occur with any supercell, even those with tendencies to produce only one tornado or very long-lived tornadoes rather than tornado families. Because cyclic may carry a variety of meanings, we approached this in a few ways. Of the 102 cases, 20 (≈20%) featured supercells that only produced one tornado, and thus were not cyclic in the sense that they only produced one tornado. Furthermore, in 28 of the 102 cases (≈27%), neither the mesocyclone cycle preceding nor following the examined tornado produced a tornado (thus not cyclic in the sense that the supercell did not produce consecutive tornadoes with each cycle). Last, however, in order to obtain a more reliable indicator of cyclic mesocyclone tendency (as explored by Adlerman and Droegemeier (2002)), we considered the longevity of the radar-detected tornado cyclones. As tornado longevity statistics are ill-defined, we consider a tornado cyclone to be long-lived if it lasts 45 min or longer [in similar fashion as Bunkers et al. (2006a) on supercell longevity, though tailored to the time scale of tornado warning duration (Brooks and Correia 2018)]. With this constraint, 18 of the 102 cases (≈18%) were particularly long-lived tornadoes associated with long-lived low-level mesocyclones (thus not cyclic in the sense that the supercell was characterized by rather steady-state mesocyclone maintenance rather than a rapid cycling tendency, as described by (Adlerman and Droegemeier 2002). Thus, however cyclic is defined, many deviant tornadoes do not require the supercell dynamics involved in cyclic supercells as was hypothesized in Agee et al. (1976).
e. National Weather Service tornado warning performance
The NWS tornado warning polygon performance was assessed for all cases where a tornado warning was issued (98 of 102 cases) using the diagram in Fig. 5. Assessment began at the start time of the deviant tornado study window. Because warning polygons spanned a variety of shapes and number of vertices, all polygons were normalized to four vertices; the four vertices were defined that best preserved the full size of the polygon. Though the shape of polygons often imply a directionality of the motion of the storm, many were either not oriented with the storm motion, or did not have a “long side.” As a result, we had to subjectively assign which dimension was oriented with the storm motion in these cases; this was done by selecting the dimension most parallel to the trajectory of storm motion. In the rare case where a coordinated warning polygon spanned a CWA boundary, a composite warning polygon was created. The polygon was used that was active at the onset of the tornado’s leftward deviation (if no polygon was active, the next polygon was used, or it was considered a “miss”). If this initial polygon expired before the detectable tornadic low-level mesocyclone dissipated, we had to assume the polygon was still in effect, and assigned it the performance it would have gotten if it were. In cases where two or more polygons were issued over the course of time from the onset of deviation to dissipation, if the tornado remained in the second polygon, it was still given the rating of the first polygon (no matter if the rating the second polygon would have achieved was lower, perhaps due to a continued leftward deviation). However, if the tornado moved out of the second polygon, it was still assigned a “poor” rating.
The methodology used for assessing NWS warning performance on deviant tornadoes. A hypothetical radar precipitation structure of a supercell with enhanced deviant tornado potential is shown in gray, with a hypothetical tornado warning polygon overlaid in red. Three of the many possible future trajectories of a tornado (gray inverted triangle) are displayed as arrows. Areas inside the warning polygon labeled by green (orange) checkmarks indicate areas the tornado may move into to generate an assessment of good (fair). Areas outside the warning polygon labeled by red X marks indicate areas the tornado may move into to generate an assessment of poor.
Citation: Weather and Forecasting 36, 1; 10.1175/WAF-D-20-0056.1
Because deviant tornadoes took on a variety of polygon-relative motions (including stationary or rearward), and polygons had a variety of shapes, performance was given one of these three ratings. 1) A rating of good meant that the low-level (lowest-tilt) radar-detected mesocyclone continued moving into the forward/right 75% of the warning polygon with respect to its motion. Since this area encompasses the majority of the warning, tornadoes should be expected (preferred) to remain in this area in most cases. 2) Fair meant that the low-level mesocyclone moved into the left/rear 25% of the polygon with respect to its motion from a location that was initially more central within the polygon (in other words, tornado motion left of or opposite the expected direction as inferred by the warning polygon). In this case, the warning polygon was occasionally corrected by the NWS to account for this deviation. 3) Poor meant that the low-level mesocyclone moved completely out of the left/rear edge of the polygon. In this case, an entirely new warning polygon was usually issued (in some cases this required multiple new warning polygons as the low-level mesocyclone continued to deviate from what was expected). The goal of this performance matrix was to assess the tendency of a leftward deviant tornado’s motion (i.e., if a leftward or rearward motion was unexpected by the forecaster). If so, the warning performance went down. This is why performance decreases to the left and rear. The right/forward area is still considered “good” because in these cases, a forecaster may have been anticipating a leftward deviation, but it did not occur. Though 75% of the spatial area of each tornado warning polygon was designated good, only 40 of 98 (≈40.8%) met this rating. The fair rating was given to 33 of 98 cases (≈33.7%), suggesting that a third of the detected tornadic circulations deviated into the left quarter of the polygon. Finally, 25 of the 98 cases (≈25.5%) were rated poor, thus a quarter of the polygons failed to contain the detected tornadic circulation once it deviated, with one or more corrections needed. As can be deduced, leftward deviant tornadoes are quite challenging for the warning forecaster.
The path tendencies of deviant tornadoes relative to the current tornado warning paradigm is illustrated in Fig. 6. The paths of the deviant portions of the tornadoes have very little curvature over the period where they are determined to be leftward-deviant, suggesting a consistent steering flow rather than an orbit about a mesocyclone. In the ground-relative sense, northwestward-deviating tornadoes apparently present the greatest difficulty to forecasters, as tornadoes moving in this direction were predominantly given fair or poor ratings. When the paths are rotated to the storm-relative sense such that they all emanate from a northeastward-moving storm, the majority of tornadoes that deviate near or out of their warning polygon move toward the front-left corner of the typical warning polygon (though a notable subset of tornadoes deviate toward and out of the rear of the polygon). Of course, limitations arise from comparing the tracks to the mean tornado warning polygon, especially since polygons may not always be oriented with storm motion to begin with. Regardless, this suggests that in general, tornado warning polygons—which ideally follow the path of a tornado—are substantially offset from the direction a deviant tornado actually takes (in rare cases, even nearly 180° offset). One may logically argue that pointing out this offset is not entirely fair, since warning polygons are designed to encapsulate an entire tornado path, not just the deviant portion. However, in 28 of the 102 cases (≈27%), the tornado was determined to be deviant immediately upon formation (in 36 of the 102 cases (≈35%), deviant in the first 5 min), thus in over a third of all cases, this offset does represent nearly the entire tornado path, and must be accounted for almost immediately upon tornado formation. This problem warrants further exploration into a technique that can forecast deviant tornadoes based on the environment.
The leftward deviant portions of all 102 tornadoes examined. These tracks are colored by NWS warning performance assessment, with green tracks indicating good performance, dark orange tracks indicating fair performance, red tracks indicating poor performance, and gray tracks indicating a miss (no tornado warning issued). On each panel, the composite mean storm-based tornado warning polygon (magenta) is displayed, along with the mean storm motion (black arrow). The paths of tornadoes were chosen to emanate from the center of the illustrative warning polygon, thus may not represent the true polygon-relative motion (especially in the ground-relative figure). (left) The ground-relative panel displays the north-relative motions of the leftward deviant tornadoes, while (right) the storm-relative panel displays the motions of the tornadoes relative to the mean storm motion. The mean polygon is assumed to be roughly oriented along the mean storm motion, though in each case the polygons will not always be oriented with storm motion, nor this exact size.
Citation: Weather and Forecasting 36, 1; 10.1175/WAF-D-20-0056.1
f. A new hodograph technique
The goal of this study is to devise a hodograph technique to predict the speed and direction in which tornadoes have the potential to deviate from their parent supercell. We chose to test the hypothesis that the motion of an occluded and leftward deviant tornado is influenced by varying degrees of both the motion it initially possessed predetachment and the motion it would attain if advected purely by the low-level mean wind. The deviant tornado motion (DTM) was thus defined as the mean of both the parent supercell motion vector and a low-level mean wind vector (with no weighting). The layer depth used to calculate the mean wind was changed in 50-m increments in order to find the mean wind that led to the DTM with the least median error from the observed tornado motion. In addition to using the observed parent supercell motion, a separate DTM was calculated using the internal dynamics (ID) right-moving storm motion method (Bunkers et al. 2000) from the given hodograph. This was done to ensure that DTM could be used both in real-time operations as well as in forecasts where actual storm motion is not known. The median error from the observed deviant tornado motion in meters per second, as well as the interquartile range of errors, was then calculated for each layer to identify the optimal low-level advective mean wind to use for DTM. Based on the errors obtained by the optimal low-level advective mean wind, we treated four cases as outliers (described in more detail in section 3), so the results represent 98 leftward deviant tornadoes.
3. Results
a. Optimal calculation of deviant tornado motion
The performance of DTM was evaluated for 98 leftward deviant tornadoes. To do so, it was compared to supercell motion (Fig. 7, Table 4) since no tornado motion metric exists currently. Though neither observed nor derived supercell motion metrics are designed to predict tornado motion, this comparison could be used to determine if a metric to do so would be advantageous. All subsequent errors are absolute errors from the observed tornado motion vector (and all positive in magnitude), thus do not take into account whether the estimated forward speed was slower or faster than the observed tornado. Assuming that all tornadoes travel with their observed parent storm motion yielded a median error of 7.18 m s−1 (14.0 kt) in predicting deviant tornado motion, with 75% of cases yielding an error of over 5.53 m s−1 (10.7 kt). Though it may seem advantageous to also consider the direction of the velocity vector in addition to its magnitude when assessing performance, it becomes an increasingly unrepresentative measure of error as storm motion approaches the origin and opposing tornado motion becomes more common, yielding errors up to 180° despite accurate placement of the DTM vector on the hodograph. Another approach would be to use the B2K method for parent storm motion. This yielded a median error of 10.03 m s−1 (19.5 kt), with 75% of cases yielding an error of over 7.58 m s−1 (14.7 kt).
Violin plots comparing the median error in predicting the observed deviant tornado motion via the proposed DTM method and storm motion (the only existing method), for both the observed (real time) and B2K (predictive) method of assessing supercell motion.
Citation: Weather and Forecasting 36, 1; 10.1175/WAF-D-20-0056.1
Error in predicting deviant tornado motion [m s−1 (kt)] for 1) observed right-moving storm motion (Obs RM), 2) DTMobs, 3) B2K-derived storm motion, and 4) DTMB2K; Q1, Med, and Q3 as in Table 2.
b. Advantage of deviant tornado motion over forecast storm motion
The two DTM methods were then compared to the only “existing” method of predicting deviant tornado motion (currently the B2K right-moving storm motion) using a 2D kernel density estimate (Fig. 8); again, the B2K vector was by no means designed to predict the motion of deviant tornadoes, but will be used here to determine whether such a metric would be useful. The tornadoes spanned a large range of the υ component, but little variability in the u component. DTMB2K, and especially DTMobs, showed relatively little variance from the observed tornado motion regardless of storm speed. This is especially true when compared with the B2K right-moving storm motion, where the observed tornado most commonly moves at a trajectory several knots to its north and west. While both DTM methods displayed considerable improvement over the B2K right-moving storm motion in predicting deviant tornado motion, we can conclude that the DTMobs, where observed storm motion is used instead of B2K, performs best. While it is common practice to use observed storm motion when available, this result should especially encourage its use.
The 2D kernel density estimate (kernel bandwidth 1.0) of the (left) u and (right) υ components (m s−1) of observed motion for all deviant tornadoes compared against (top) DTMobs, (middle) B2K DTM, and (bottom) B2K right-moving storm motion. Probability density is shaded, with a minimum cutoff value of 0.0001. Individual tornadoes plotted as grayscale circles, shaded lighter for increasing observed storm motion.
Citation: Weather and Forecasting 36, 1; 10.1175/WAF-D-20-0056.1
c. Understanding when to use deviant tornado motion
Forecasting the potential motion of deviant tornadoes is only necessary when deviant tornadoes are possible. To better understand when deviant tornadoes happen and when they do not, our definition of deviant as “noticeably” different from the parent supercell must be explored. There are two aspects necessary for deviant tornadoes as defined: deviation in the storm-relative sense, and deviation in the ground-relative sense. The median storm-relative deviation of tornadoes away from the parent supercell (again an absolute vector difference) was found to be 7.18 m s−1 (14.0 kt), with an interquartile range spanning only 3.99 m s−1 (7.8 kt) (Table 5). However, deviance as defined is a ground-relative perception, which also depends on storm motion. Figure 9 illustrates that although any two tornadoes may deviate away from their parent supercell with the same velocity in the storm-relative sense, an observer will perceive the actual path of the tornado from the slower-moving supercell to be more deviant. This is because its change in angular trajectory will be greater, and its change in forward speed will be proportionately larger.
The distribution of storm-relative deviation of leftward-deviant tornadoes from their parent supercell (all 102 cases); Q1, Med, and Q3 as in Table 2.
An illustration of the concept of tornado deviance for two hypothetical supercells. Two identical hodographs are presented (red and blue), but one produces a slow-moving supercell (red circle) while the other produces a fast-moving supercell (blue). Inverted triangles “A” (red) and “B” (blue) represent the hypothetical motion vectors of the leftward deviant tornadoes that result as a product of storm-relative advection. While both tornadoes take on the same storm-relative deviance, their resulting motion vectors and tracks show much different degrees of “deviance” (largely in direction) as perceived by an observer. Range rings are labeled in m s−1, with heights marked on each hodograph in km.
Citation: Weather and Forecasting 36, 1; 10.1175/WAF-D-20-0056.1
What this means to the forecaster is that, although tornadoes can deviate from their parent supercell regardless of storm speed, deviant tornadoes as we define them (“noticeably” deviant by an observer) are more apt to occur with slower-moving storms [reflected by the majority of cases examined featuring a storm motion slower than 15 m s−1 (≈30 kt)]. To get leftward deviant tornadoes with faster-moving supercells, then, increasingly long, looping hodographs are required. Such hodographs foster greater deviance in both storm-relative magnitude as well as ground-relative angular trajectory and speed. In contrast, a tornado is less likely to become deviant with a shorter, straighter hodograph and fast storm motion, even if it becomes detached and advected by the low-level storm-relative wind. Such hodographs not only minimize the storm-relative deviance brought about by advection, but also renders this deviance virtually imperceptible by an observer by minimizing changes in ground-relative angular trajectory and forward speed. When using DTM, the authors suggest that “noticeably” deviant tornadoes may occur anytime that storm motion is slow and/or hodographs are particularly long and looping. In contrast, DTM may not provide useful information when storm motion is fast and hodographs are particularly short and straight.
Although most of the examined tornadoes retained similar forward speeds upon deviating, this change in forward speed may also be negative. With fast storm motions and long, straight hodographs, a deviation that slows forward speed would theoretically take place instead of a noticeable angular deviation. With slow storm motions, some tornadoes, such as one near Bennington, Kansas, on 28 May 2013, may deviate to nearly stationary (analysis methodology was not changed in these cases). This would theoretically result from a storm motion that encourages the deviant tornado motion to lie near the center of the hodograph. These tornadoes may be perceived to display erratic behaviors as subtle accelerations in the storm-relative sense are fully realized in the ground-relative sense. The Bennington, Kansas, tornado displayed such a behavior, with a looped path described as “unpredictable” by Wurman et al. (2014). This tornado was also associated with close proximity to a surface boundary, which may have influenced the considerable error of 4.46 m s−1 obtained when using DTMobs, which surpasses the 75th percentile. Regardless of the mechanism behind these deviations, however, a motion close to the center of the hodograph will allow any “wobble” to take a different cardinal direction.
Of the 102 cases, 4 cases were classified as outliers with observed storm motion method errors greater than 7.75 m s−1 (≈15 kt); these were removed from calculations of DTM in order to best design the metric for the majority of cases, and are examined separately here for factors that may have influenced the predictability of DTM. The mean 100-hPa RUC/RAP mixed-layer CAPE for these cases was 2692 J kg−1, with 3 of 4 cases above the mean of 2162 J kg−1 of the other 98 cases (Table 6), as well as the median found in large samples of parameters associated with strong tornadoes (Johns et al. 1993). Furthermore, average lifted condensation level (LCL) height was 1425 m, with 3 of 4 cases above the mean of 959 m of the other 98 cases, as well as at or above the 1300 m guideline for high LCL environments found by Davies (2006) and the nontornadic guideline found by Thompson et al. (2003), their Table 2. Last, average downdraft CAPE (DCAPE) was 1425 J kg−1, with all cases above the mean (3 cases above the 3rd quartile) of the other 98 cases, and 3 of 4 cases above the 1000 J kg−1 guideline for values with the potential to encourage particularly strong downdrafts and damaging outflow winds (Gilmore and Wicker 1998). This suggests that environments featuring favorable values of parameters associated with particularly strong downdraft development (like those above) likely add substantial complications to the DTM methodology and limit predictability. As explored in the background, this is not surprising, since strong internal momentum surges have the potential to counter the impacts of advection or otherwise steer a tornado in a different direction (Dowell and Bluestein 2002b; Lee et al. 2012), and suggests that other approaches may be necessary to predict such behavior.
Thermodynamic parameters associated with the proximity environments for all 98 nonoutlier cases; Q1, Med, and Q3 as in Table 2.
4. Discussion
The average hodograph for deviant tornadoes must first be explored to better anticipate which synoptic setups are most conducive to them, and which locations are most susceptible to them. This hodograph features a slow northeastward-moving supercell coupled with a northward-moving tornado. The general adage among warning forecasters is that most tornadoes will tend to occlude to the north. But why? In the composite hodograph, this northward-moving tornado is made possible by its tendency to become advected by a relatively strong south/southeasterly low-level flow, under relatively weak flow aloft compared to typical environments supporting long-lived supercells (Bunkers et al. 2006b). While this long, looping hodograph structure places the storm motion vector at a substantial distance away from the low-level mean wind vector (thus encouraging deviant tornadoes from the storm-relative sense), the relatively weak flow aloft keeps storm motion slow (thus allowing deviant tornadoes from the ground-relative sense). This particular hodograph shape has been associated with nocturnal significant tornadoes in the Great Plains and manifests in part due to a relatively strong southerly low-level jet (Mead and Thompson 2011). Such a low-level jet can bexdiurnally driven, particularly from late spring into early summer, in the southern and central Great Plains (Hoecker 1963; Bonner 1968; Parish 2017). The prevalence of this low-level jet may be why the majority of deviant tornado cases were found in this region.
Next, we discuss the effectiveness of the DTM hodograph technique to predict the deviant motion of tornadoes. First, we reiterate that if a given tornado does not favorably occlude such that it acquires leftward deviation, DTM will not provide useful information. Furthermore, tornadoes can deviate (or fail to deviate) as a result of other mechanisms, particularly internal momentum surges, that may not be predictable using an environmental hodograph. This remains a potential subject of future work; we acknowledge that in reality, tornado deviation is a continuous process influenced by all of these mechanisms that are not accounted for with DTM. As mentioned previously, DTM may be particularly prone to error in environments supporting strong downdrafts (high CAPE, high DCAPE, and high LCL height), as well as near surface boundaries, though these scenarios require further research.
With that in mind, in this sample of 98 cases, DTM showed promising skill in predicting the motion of the portions of these tornadoes exhibiting leftward deviation. This suggests that tornadoes are indeed influenced by both the initial motion of the parent supercell and the mean wind in the lowest half-kilometer, in a way that manifests as a “tug-of-war” between a tornado’s initial motion and its tendency to move with the advective low-level flow. Such a result supports both hypotheses that this near-surface layer most impacts tornado deviations (Dowell and Bluestein 2002b; Tanamachi et al. 2012; French et al. 2014), as well as more recent findings that this layer carries particular weight in tornado maintenance (Coffer et al. 2019). Such a result also suggests that a more simplified conceptual model such as that by Agee et al. (1976), which attributes tornado deviations solely to a storm-scale rotation around a parent supercell, may have practical limitations. This is encouraging from an operational standpoint, since this means that an approximate trajectory of deviation can be predicted. We reiterate that deviant tornadoes can occur with or without a “cyclic” supercell. Though current training material emphasizes the importance of monitoring cyclic supercells for deviant tornadoes (WDTD 2020), our sample of deviant tornadoes includes several cases of only one tornado, as well as very long-lived tornadoes. Thus, we strongly recommend that the potential for deviant tornadoes be assessed from the hodograph, and not discounted in noncyclic supercells.
For use in forecasting, we again stress that DTM may prove most useful in environments with particularly long, looping hodographs, but DTM will only assist in assessing how deviant, and in what direction, a tornado has the potential to become once it detaches or “occludes.” This hodograph technique will not determine the likelihood of whether or not a leftward deviant tornado actually occurs, which may be considerably dependent on favorably weak internal downdrafts and other storm-scale processes. In practice, this may consist of recognizing the potential for deviant tornadoes, but also acknowledging that not every tornado may become deviant—perhaps none will at all.
Which DTM method is used (DTMobs or DTMB2K) will depend on whether the forecaster is forecasting or nowcasting. In the hours leading up to the event, the B2K method may foster awareness that tornadoes may take paths different from the B2K storm motion or simulated storm attributes from convective-allowing models. Later, when a tornadic supercell is ongoing, applying its observed motion to this simple hodograph technique (using a timely weather forecasting model, routine NWS sounding, proximity research sounding, WSR-88D velocity azimuth display (VAD) wind profile, etc.) will likely provide a better estimate of the potential trajectory a tornado could take once it detaches.
Last, we discuss potential improvements to the current tornado warning paradigm. Unlike most severe thunderstorm and flash flood warnings, the tornado warning attempts to relay the track of a feature typically less than 1 mi wide, which has also been noted throughout historic observations to possess “erratic” movements. On one hand, forecasters are encouraged to draw narrow polygons when possible in order to reduce false alarm rate. On the other hand, however, this practice may fall into the trap of failing to contain deviant tornadoes. Consequently, when uncertain, current practice is to draw polygons with ample space on both sides to account for deviations both leftward and rightward. Many polygons, upon issuance, may even include space behind the tornado, in the rare case it reverses direction.
An improved tornado warning paradigm can be achieved by acknowledging that a tornado’s potential trajectory can be different from that of its parent supercell, but also predictable, based on the results of this study. If this trajectory is estimated before an event unfolds, forecasters could better tailor tornado warnings to anticipate the deviant track a tornado may take (not the track of the parent supercell, which has been shown here to have a negative impact on warning verification). Anticipating this trajectory before issuing a warning is crucial, as over 35% of the examined leftward deviant tornadoes changed trajectory almost immediately upon formation. This methodology could ensure that polygons (or “cones of uncertainty”) are not substantially offset from the paths of deviant tornadoes, as they are currently. This methodology could also ensure that any extra space to the left and rear of a tornado’s trajectory are shaved off when it is known that it is unlikely to deviate leftward or rearward. Future studies could also look into the propensity of tornadoes to move rightward of the initial supercell motion (especially upon formation); this may provide further guidance as to when extra space to the right of a tornado’s trajectory could also be shaved off.
The above critiques may carry an even heavier weight for new probability-driven systems such as FACETs (Rothfusz et al. 2018). We have shown that tornadoes occasionally deviate into unwarned territory with the current polygon approach (a problem that will not go away should FACETs aim for similarly sized warnings). However, we have also shown that a large proportion of deviant tornadoes move toward the edge of the warning polygon, a location which, using a cone of uncertainty–like approach, ideally conveys a low probability of that hazard occurring.
5. Conclusions
The deviant motion of tornadoes, though only one challenge of severe convective warning operations, carries potentially considerable impacts. Examining 102 cases of deviant tornadoes, tornadoes dealing significant damage (F/EF2 or greater) accounted for around half of the dataset. With the detectable rotation signatures of over one quarter of the 102 tornadoes moving completely out of the initial NWS tornado warning polygon, there is no reason to believe that similar impacts could not result from future deviant tornadoes. In fact, since ≈59% of the examined tornadoes moved into a region accounting for less than 25% of the total area of the warning polygon, and the average storm-following warning is marked by a substantial offset from the average paths of these deviant tornadoes, the deviation of tornadoes into lower-probability zones could become a known problem in probability-driven warning paradigms such as FACETs. This may be significantly improved with a fuller understanding of tornado motion.
The deviant tornado motion hodograph technique presented here shows a promising approach for predicting the trajectories of occluded tornadoes, which appear to deviate with the contributions of both the initial parent storm motion and the advective low-level storm-relative wind in the lowest ≈500 m. This simple technique will be useful most often for slow-moving supercells within long, looping environmental hodographs, and is less relevant for fast-moving supercells within long, straight environmental hodograph structures. Deviant tornadoes occur most often with climatologically weak upper-level flow above a strong low-level jet, an environment most prevalent in the Great Plains region of the United States, where this may be of most use to forecasters. Since leveraging the hodograph allows for anticipating the potential for deviant tornado motion, this technique likely offers substantial improvement to this facet of the tornado warning process.
Acknowledgments
We would first like to acknowledge meteorologist Matt Ziebell and the National Weather Service Weather Forecast Office in Lubbock, Texas, for the inspiration behind examining deviant tornadoes. We would also like to acknowledge Dr. Matthew Bunkers of the National Weather Service Weather Forecast Office in Rapid City, South Dakota, for his invaluable encouragement, guidance, and contributions from the beginning to the finishing of this endeavor. Finally, we would like to acknowledge the extremely valuable contributions of Dr. Harold Brooks of the National Severe Storms Laboratory and the three reviewers, whose insightful comments allowed the impact of this study to be both stronger and better communicated. This research was supported by the Earth and Ecosystem Science Ph.D. program at Central Michigan University.
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The archive contains only start and end points of tornadoes, thus it was not used to verify deviant tornadoes.
