Vorticity Evolution Leading to Tornadogenesis and Tornadogenesis Failure in Simulated Supercells

MARCH 2014 N A Y L O R A N D G I L M O R E 1201

JASON NAYLOR AND MATTHEW S. GILMORE Department of Atmospheric Sciences, University of North Dakota, Grand Forks, North Dakota

(Manuscript received 19 July 2013, in ﬁnal form 30 September 2013)

ABSTRACT

A three-dimensional idealized cloud model was used to study the storm-scale differences between simulated supercells that produce tornado-like vortices and those that do not. Each simulation was initialized with a different Rapid Update Cycle, version 2 (RUC-2), sounding that was associated with tornadic and nontornadic supercells in nature. The focus is an analysis of vorticity along backward-integrated trajectories leading up to tornadogenesis (19 simulations) and tornadogenesis failure (14 simulations). In so doing, the differences between the nontornadic and tornadic cases can be explored in relation to their associated environmental sounding. Backward-integrated trajectories seeded in the near-surface circulation indicate that the largest differences in vertical vorticity production between the tornadic and nontornadic simulations occur in parcels that descend to the surface from aloft (i.e., descending). Thus, the results from this study support the hypothesis that descending air in the rear of the storm is crucial to tornadogenesis. In the tornadic simulations, the descending parcels experience more negative vertical vorticity production during descent and larger tilting of horizontal vorticity into positive vertical vorticity after reaching the surface, owing to stronger horizontal gradients of vertical velocity. The larger vertical velocities experienced by the trajectories just prior to tornadogenesis in the tornadic simulations are associated with environmental soundings of larger CAPE, smaller convective inhibition (CIN), and larger 0–1-km storm-relative environmental helicity. Furthermore, in contrast with what might be expected from previous works, trajectories entering the incipient tornadic circulations are more negatively buoyant than those entering the nontornadic circulations.

1. Introduction d tilting of horizontal vorticity that was baroclinically generated (i.e., vorticity generated by the storm’s own Although tornadoes have been studied extensively horizontal density gradients), over the last 50 years, many unanswered questions re- d tilting of horizontal vorticity associated with the main regarding the storm-scale processes responsible vertical wind shear of the environment (also known for their development. Numerical modeling studies have as barotropic vorticity), or repeatedly shown that supercells do not develop low- d transport of vertical vorticity to the surface. level rotation until downdrafts reach the surface (e.g., Klemp and Rotunno 1983; Davies-Jones and Brooks More than one of these processes contributes to the 1993; Walko 1993; Trapp and Fiedler 1995; Wicker and rotation within the low-level mesocyclone (Klemp and Wilhelmson 1995, hereafter WW95; Adlerman et al. Rotunno 1983; Davies-Jones and Brooks 1993; A99; 1999, hereafter A99). While these studies agree that Markowski et al. 2008); however, the relative impor- downdrafts are critically important, they do not agree tance of these processes to tornadogenesis appears to on the exact mechanisms that produce low-level vor- vary among cases. First, modeling studies by Davies- ticity. These works have concluded that downdrafts can Jones and Brooks (1993) and Grasso and Cotton (1995) produce positive (cyclonic) near-surface vertical vor- found that the largest source of vertical vorticity in the ticity via the low-level mesocyclone is baroclinically generated and tilted into the vertical in air that descends cyclonically Corresponding author address: Jason Naylor, NorthWest Research around the updraft. Second, Markowski et al. (2003) and Associates, 3380 Mitchell Lane, Boulder, CO 80301. Davies-Jones (2008) demonstrated that tornadogenesis E-mail: [email protected] could occur only through the transport of vertical vorticity

DOI: 10.1175/JAS-D-13-0219.1

Ó 2014 American Meteorological Society Unauthenticated | Downloaded 10/06/21 04:52 AM UTC 1202 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 71 to the surface via downdrafts and curtains of rain that wrap tornadic and nontornadic supercells. Trapp (1999) com- cyclonically around the low-level mesocyclone. Third, pared six supercells (three nontornadic and three torna- the Brandes (1984) observational study and WW95 nu- dic) observed during the Verification of the Origins of merical study concluded that the primary source of cyclonic Rotation in Tornadoes Experiment (VORTEX) and vertical vorticity was via tilting and stretching of horizontal found that while the nontornadic supercells experi- vorticity originally generated along the forward-flank gust enced less stretching of vertical vorticity and less low- front, and that descending parcels either did not strongly level convergence, the supercells were similar in other contribute to low-level vertical vorticity or, as in WW95, respects—including the presence of low-level mesocy- contributed adversely to vorticity of the opposite sign. clones and rear-flank gust fronts. Using a similar da- Much of the research involving nontornadic storms taset from VORTEX, Markowski et al. (2008) found has only focused on understanding differences in the that both tornadic and nontornadic supercells exhibit near-storm environments (NSEs) of tornadic and non- vortex line ‘‘arches’’ that straddle the hook echo— tornadic storms (e.g., Darkow 1969; Maddox 1976; Davies suggesting that near-surface rotation development in and Johns 1993; Brooks et al. 1994; Rasmussen and both types of supercells was aided by baroclinic vorticity Blanchard 1998; Thompson et al. 2003, 2012; Togstad generation in the rear-flank downdraft. Wakimoto and et al. 2011). For example, it is now known that tornadic Cai (2000) found that while a nontornadic supercell had supercells occur more often in NSEs with large values of ‘‘more extensive’’ precipitation (as indicated by radar storm-relative environmental helicity, large CAPE, low reflectivity) in the rear flank, stronger inflow, and stron- LCL heights (Rasmussen and Blanchard 1998; Thompson ger updrafts along the rear flank compared to a tornadic et al. 2003, 2012), and small convective inhibition (CIN) supercell, the nontornadic supercell had an order-of- (Thompson et al. 2012). However, there are still many magnitude less horizontal vorticity in the NSE despite questions regarding the storm-scale differences between both storms having an occlusion downdraft and horseshoe- tornadic and nontornadic supercells and how these dif- shaped updraft–downdraft signatures. Ziegler et al. (2001) ferences may be influenced by the NSE. concluded that a tornadic supercell had strong, low- One storm-scale feature that may help discriminate level stretching of cyclonic vertical vorticity associated between tornadic and nontornadic storms is the buoy- with a preexisting boundary layer vortex, while a nearby ancy of the low-level storm outflow. Observational studies nontornadic storm was characterized by negative stretch- have also shown that the evaporatively chilled storm ing. While the aforementioned studies show that tornadic outflow in significantly tornadic supercells often has and nontornadic storms share many structural similari- smaller negative buoyancy (not as cold/dense) relative ties, differences in vorticity production may explain why to the prestorm NSE compared to nontornadic super- some storms were tornadic and others were not. How- cells (e.g., Markowski et al. 2002; Shabbott and Markowski ever, the small number of cases and different analysis 2006; Grzych et al. 2007). Simulations by Markowski strategies makes it difficult to generalize differences in et al. (2003) using a model with a 2D axisymmetric co- vorticity production. ordinate system show that downdrafts with more nega- The main goal of the current study is to advance the tively buoyant air cannot be lifted by the updraft, thus current understanding of tornadogenesis by simulating disrupting near-surface convergence and stretching of numerous tornadic1 and nontornadic storms to deter- vertical vorticity. Markowski et al. (2011) computed mine the source(s) of vorticity-rich air at low levels, trajectories using dual-Doppler wind retrievals in three identify the processes that result in tornadogenesis and nontornadic supercells and found that the air entering tornadogenesis failure, and relate these to the NSE. the near-surface circulation only ascends a short dis- Idealized simulations were initialized with proximity tance before abruptly descending again, implying either soundings representative of the NSEs of tornadic and 1) the parcels in the nontornadic cases are too negatively nontornadic supercells. It is believed that the study buoyant to be lifted by the updraft or 2) the low-level herein contains the largest number of tornado-resolving vertical pressure gradient force is insufficient to lift the parcels. The findings from these studies suggest that barotropic vorticity is important to tornadogenesis and 1 Herein, when terms such as ‘‘tornado,’’ ‘‘tornadic,’’ ‘‘non- if the downdraft is too ‘‘cold,’’ this might inhibit torna- tornadic,’’ ‘‘tornadogenesis,’’ or ‘‘tornadogenesis failure’’ are used dogenesis despite stronger implied baroclinic production. to reference phenomena occurring within the hook echoes of However, none of these studies presented a detailed simulated supercells, it should be understood that they are used to describe the presence (or lack) of tornado-like vortices in those analysis of vorticity evolution. simulations. These vortices are missing the complete physics that In fact, only a handful of studies have investigated are present in real-world tornadoes (such as centrifuging and fric- differences in near-surface vorticity production between tional interaction with the ground).

Unauthenticated | Downloaded 10/06/21 04:52 AM UTC MARCH 2014 N A Y L O R A N D G I L M O R E 1203 simulations to date. The sample is large enough to sta- spheroid placed in the center of the domain for the first tistically compare the characteristics between the two 900 s of simulation.2 During this time, the vertical ve- groups: 19 tornadic and 14 nontornadic. locity at a particular grid point inside this spheroid was The idealized model that was used represents the NSE specified by as horizontally homogeneous with a single profile of ( p vertical wind shear and CAPE. This follows many prior w cos2 b ,if0# b # 1 5 max 2 supercell modeling studies that have studied the NSE in wmag (1) relation to the resulting storm type and behavior (e.g., 0, if b . 1 Klemp and Wilhelmson 1978; Weisman and Klemp 1982). 5 1 3 a 3 2 Previous observational and modeling studies have shown wt wt21 dts max(wmag wt21, 0), (2) or suggested that nonhomogeneous features (i.e., preexisting baroclinic regions and vertical vorticity) can also where b is the distance from the center of the spheroid influence low-level rotation and tornado potential in normalized by its radius, a is the acceleration constant 2 supercells (e.g., Maddox et al. 1980; Markowski et al. (0.5 s 1), dts is the small model time step (0.167 s), and 1998; Atkins et al. 1999; Fierro et al. 2006; Richardson the max function ensures that nudging was not applied 21 et al. 2007). By excluding these nonhomogeneous fea- once the vertical velocity exceeds wmax (10 m s ). Up- tures, the ability (or inability) of a modeled storm to draft nudging was used because the traditional ‘‘warm produce a tornado can be limited to the NSE. However, bubble’’ technique is much less effective for realistic aspects of the model itself, such as grid spacing or the soundings with capping inversions [also see Naylor and microphysics parameterization (through its impact on Gilmore (2012a)]. the cold pool and baroclinic horizontal vorticity pro- Each simulation was initialized with one sounding— duction; e.g., Snook and Xue 2008 and Dawson et al. originally selected by Thompson et al. (2003, 2007) from 2010), may influence tornadogenesis, but such simula- a Rapid Update Cycle, version 2 (RUC-2), model grid tion sensitivities to model characteristics are beyond the point within 40 km spatially and 30 min temporally of an scope of the current study. observed supercell. This current study specifically focuses on soundings that were associated with mature supercells—of which there are 113 significantly tornadic 2. Methodology and 454 nontornadic. Because many of the significantly Idealized simulations were carried out using version tornadic RUC-2 soundings have large-magnitude shear 14 of Cloud Model 1 (CM1; Bryan and Fritsch 2002) layers (shear Richardson number less than 0.25) the with default settings unless otherwise noted herein. All eddy mixing from the initial base-state environment was simulations have isotropic 100-m grid spacing and were removed from the total eddy mixing tendency for each run for 2 h of simulation time. The Klemp–Wilhelmson model variable. This practice is necessary in idealized time-splitting scheme was used, with a large time step of cloud models when using realistic soundings to ensure 1 s and a small time step of 0.167 s. The computational that the initial base-state environment is preserved in domain was 120 km 3 120 km 3 20 km with a moving regions away from active convection (L. Wicker 2013, grid determined by the 0–6-km mean wind of the input personal communication). sounding. Precipitation processes were represented by a. Automated and manual supercell identification the single-moment, 6-class bulk microphysics scheme from Gilmore et al. (2004)—with default settings for all Simulated supercells were identified objectively at variables, including intercepts and graupel/hail den- 1-km grid spacing by the presence of 2–5-km integrated 2 22 sity. The subgrid turbulence parameterization was updraft helicity (UH2–5) greater than 180 m s fol- based on Smagorinsky (1963). Lateral boundaries were lowing Naylor et al. (2012b). At 100-m grid spacing, . gravity wave radiating, and an additional Rayleigh damper simulations were flagged for further analysis if UH2–5 2 was used within 10 km of the domain edge to eliminate 900 m2 s 2 (extrapolated from coarser gridspacing re- partial reflection. The rigid upper and lower boundaries sults of Naylor et al. 2012b). Cases were excluded from were free slip and a standard Rayleigh damping layer further analysis if they did not meet the criteria contin- was applied above height z 5 16 km to damp vertically ually for at least 1 h. For those cases that passed the propagating gravity waves and minimize their reflection thresholds, supercell existence was confirmed subjectively off the upper boundary. The Coriolis force was neglected. Convection was initiated using the updraft nudging technique described by Naylor and Gilmore (2012a). 2 Naylor and Gilmore (2012a) found that a nudging duration of Nudging was applied over a 10 km 3 10 km 3 3km 900-s optimized average simulated supercell longevity.

Unauthenticated | Downloaded 10/06/21 04:52 AM UTC 1204 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 71 every 5 min using a manual procedure previously used in and only at grid points where the pressure perturbation radar observations of supercells (defined and described was less than 23 hPa (between z 5 100 and 500 m). In in Naylor et al. 2012b). Only supercells that lasted at the interest of computational expense, an upper limit of least 1 h were considered for further analysis of torna- 100 trajectory parcels was set for each simulation. The dogenesis and tornadogenesis failure. pressure-drop threshold of 23 hPa was used to ensure that plenty of trajectories surround even the weak tor- b. Automated surface mesocyclone and tornado nadic vortices (and indeed in every tornadic simulation, detection the maximum number of trajectories was initialized). Because of the large number of simulations in this Trajectories were traced backward 900 s (consistent with study herein, a manual analysis to determine if, when, previous studies utilizing trajectories to determine the and where tornadogenesis occurs in the simulations source region of air parcels—e.g., A99), using model would have been extremely tedious and time consuming. history files generated at 5-s intervals. Dahl et al. (2012) To circumvent this difficulty, an automated tornado- showed that this temporal resolution is sufficient to detection algorithm was developed and tested. Following compute accurate backward trajectories. Naylor and Gilmore (2012b), a tornado was said to be In the nontornadic simulations, a 1 km 3 1km 3 present in the simulation at the first instance that the 0.4 km box was centered on the location of maximum 0– following three criteria are met:3 (i) the pressure drop 1-km updraft helicity, and trajectories were seeded at from the center of the vortex to the radius of maximum equidistant points inside this box having vertical vor- 2 winds was 24.5 hPa or less, (ii) the horizontal wind ticity greater than 0.05 s 1 between the same range of 2 speed at the radius of max winds was at least 30 m s 1, altitudes as in the tornadic cases (z 5 100–500 m). The and (iii) vertical vorticity z in the center of the vortex was box was defined such that it was large enough to en- 2 at least 0.1 s 1. For more information, refer to Naylor compass the primary circulation on the scale of a tor- and Gilmore (2012b). nado (if one were to form), and the vorticity criteria was In the nontornadic simulations, tornadogenesis failure used to remove points that fall outside the primary cir- was said to occur in supercells that did not meet the tor- culation. In many of the nontornadic simulations, only nadogenesis criteria at the time of maximum low-level 50–75 trajectories were seeded, since some parcels within mesocyclone strength—defined herein by the maximum the box failed to meet the threshold value of vertical value of 0–1-km updraft helicity. This method ensured vorticity. that vertical vorticity and updraft were collocated. Also, Parcel positions were calculated using a fourth-order, since multiple circulation centers occurred along the multistep Runge–Kutta technique—the same as used by leading gust front of many the simulated storms, moni- Lee and Wilhelmson (1997). After each step along the toring trends in updraft helicity better revealed intensity integration, the scalar and wind vector properties of the changes for the low-level mesocyclone than would vor- parcel were determined using trilinear interpolation ticity alone. Other studies have used the time of peak from the surrounding eight grid points. In addition, vertical vorticity in the near-surface mesocyclone be- vorticity tendencies along the trajectories were calcu- neath the bounded weak-echo region (Trapp 1999) or lated using first-order discretizations of the following have paired vorticity information with small values of equations from Klemp and Rotunno (1983): Okubo–Weiss number (associated with decreased pres- dz ›w sure, large vertical vorticity, and small deformation) to 5 v $ w 1 z H H › , (3) pinpoint the circulation center (Markowski et al. 2011). dt z dv ^ c. Initialization and backward integration of H 5 v $y 1 $ 3 Bk, (4) trajectories dt H

A trajectory analysis was performed for each of the where vH is the horizontal component of the vorticity tornadic and nontornadic simulations. In the tornadic vector, v is the total vorticity vector, w is the vertical simulations, trajectories were seeded at the time of velocity, B is buoyancy, and yH is the horizontal com- tornadogenesis (ﬁrst triggering of the tornado-detection ponent of velocity. The terms on the rhs of (3) represent algorithm) at equidistant points inside a 1 km 3 1km3 the generation of vertical vorticity through the tilting of 0.4 km box centered on the location of minimum pressure horizontal vorticity and stretching of existing vertical vorticity, respectively. In the absence of existing vertical vorticity, positive tilting produces cyclonic vertical vor- 3 These criteria are consistent with a tornado that is approxi- ticity (and ‘‘negative tilting’’ produces anticyclonic ver- mated by a Rankine vortex. tical vorticity). The stretching term acts to increase (or

Unauthenticated | Downloaded 10/06/21 04:52 AM UTC MARCH 2014 N A Y L O R A N D G I L M O R E 1205 decrease, depending on the sign of the vertical accel- 3. Results eration) the magnitude of the anticyclonic or cyclonic To identify soundings that would produce sustained rotation. Equation (4) represents the production of simulated supercells and to reduce the computational horizontal vorticity. The first term on the rhs of (4) is expense of the simulations, all 113 significantly tornadic the production of horizontal vorticity through the and 454 nontornadic RUC-2 proximity soundings were stretching of existing horizontal vorticity and tilting of first simulated with a low-resolution model configura- vertical vorticity into the horizontal while the second tion (1-km horizontal and 250-m vertical grid spacing). term represents baroclinic generation. Additional terms With this low-resolution configuration, 60 of 113 (53%) in (3) and (4) such as solenoidal generation of vertical simulations initialized with significantly tornadic sound- vorticity—which vanishes owing to use of the Boussinesq ings and 155 of 454 (34%) of simulations initialized with approximation—and turbulent mixing are neglected, nontornadic supercell soundings produced supercells following prior studies (e.g., Klemp and Rotunno 1983; lasting at least 1 h in duration. WW95; A99). Those neglected vorticity processes within When the 60-member subset of significantly tornadic the trajectory analysis cause differences in vorticity RUC-2 soundings was resimulated with 100-m grid generation–dissipation compared to the actual model. spacing, 30 (50%) of the simulations produced super- The inclusion of turbulent mixing would have decreased cells lasting at least 1 h—19 (63%) of which produced a the vorticity magnitude along trajectories by only a small tornado that was associated with the main mesocyclone amount (e.g., Brandes 1984). of the supercell. When a randomly selected 40-member At each point along the trajectory, the terms in (3) and subset of the 155 nontornadic RUC-2 soundings was (4) were calculated. Once the trajectories were traced resimulated with 100-m grid spacing, 24 (60%) pro- backward by 900 s, they were separated into the fol- duced long-lived supercells—14 (58%) of which were lowing categories: nontornadic. The forthcoming analysis focuses only on 1) Descending: trajectories that experience a net de- these 14 nontornadic simulations initialized with non- scent to the surface from a height of z $ 1 km. tornadic RUC-2 soundings (herein NON) and the 19 2) Ascending: trajectories that originate near the sur- tornadic simulations initialized with significantly tor- face, many traveling along the forward-flank gust nadic RUC-2 soundings (herein TOR). front, and steadily rise as they approach the near- surface circulation. Trajectory analysis After the trajectories were sorted into these cate- An overview of the backward trajectory paths ini- gories, net values of the terms in (3) and (4) along each tialized within the TOR simulations at the time of tor- category of trajectory were computed for each indi- nadogenesis (Fig. 1) and NON simulations at the time of vidual case. For instance, ‘‘net tilting in rising trajecto- tornadogenesis failure (Fig. 2) reveals three distinct ries’’ in each simulation was calculated by integrating types of circulations: those fed primarily by rising air the tilting term in the vertical vorticity equation over the parcels, those fed primarily by descending air parcels, length of each trajectory (900 s) and averaging over all and those that contain both rising and descending air trajectories in the ‘‘rising’’ category. Then these cate- parcels. The circulations composed primarily of rising gorical averages were separately averaged over all tor- parcels are the rarest, with only two cases—both of nadic and nontornadic cases. which were tornadic (Fig. 1; T15 and T16). The tornadoes in these two cases developed early in the simula- d. Forward integration of trajectories tions, prior to the development of a strong cold pool, and In both the tornadic and nontornadic simulations, may have been influenced by the convective initiation forward trajectories were also calculated to observe procedure. These cases are included for completeness. the maximum vertical extent of these parcels and to In both the TOR and NON simulations (cf. Figs. 1 and investigate the influence of outflow thermodynamics 2), the rising parcels generally originate at low levels, on tornadogenesis and tornadogenesis failure. Tra- downshear of the near-surface mesocyclone, and move jectory seeding criteria and locations were the same parallel to the forward-flank gust front (not shown) as as for backward-integrated trajectories so that the they approach the circulation. The descending parcels same parcels were being followed. Forward-trajectory typically approach the near-surface circulation from the calculations used the same time step (1 s) and time right, often wrapping cyclonically around the midlevel resolution (history files every 5 s), except they were mesocyclone similar to the schematic from Klemp (1987). computed forward for 1200 s instead of backward for Rising parcels contribute similarly to the low-level 900 s. circulation in both the TOR and NON simulations by

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FIG. 1. Overview of the 19 tornadic simulations showing the 30-dBZ contour of simulated radar reﬂectivity (thick black) and air parcel trajectory paths integrated backward for 15 min from the ﬁrst tornado position (green: ascending; blue: descending).

tilting baroclinically generated horizontal vorticity and NON simulations. Unlike the rising parcels, the descend- amplifying it via stretching. The average rising parcel’s ing parcels in the TOR simulations have larger average net z generation via tilting over the 900-s integrated back net tilting than those in the NON simulations (Fig. 3c). trajectories is very similar (Fig. 3a) but the average net z Similar to the rising parcels, stretching in the descending generation via stretching of vertical vorticity (Fig. 3b) is parcels is also larger in the TOR simulations (Fig. 3d). greater in the TOR cases; however, most of the differ- However, while Fig. 3 shows that there are differences in ence is found at the very end of the trajectories (not total vorticity production between descending parcels in shown), when tornadogenesis is imminent. Because ris- the TOR and NON simulations, it does not provide in- ing parcels contribute similarly between the TOR and formation about when these differences occur. NON simulations, they do not appear to discriminate To better illustrate how differences in vorticity pro- between tornadogenesis and tornadogenesis failure. duction between the TOR and NON simulations evolve Descending parcels, however, do reveal some impor- with time, and to help identify the point(s) along the tant differences that discriminate between the TOR and descending trajectories where these differences are

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FIG. 2. As in Fig. 1, but for the 14 nontornadic simulations integrated backward from the time of tornadogenesis failure. greatest, a single composite descending trajectory was tornadic circulation (or low-level mesocyclone in the created for both the TOR and NON simulations (an NON simulations). Vorticity production terms were individual composite trajectory for each simulation is analyzed during a 400-s window centered on tshift 5 0s examined later in this section). This was done by aver- and all further plots dealing with descending trajectories aging the vorticity production properties along all de- use the time-shifted data. The shifting required in in- scending trajectories from all cases at each trajectory dividual cases typically varied by 6100 s. It is important time step. Substantial differences in the average net to note that after shifting the trajectories, all parcels (in vorticity production between the TOR and NON simu- all cases) are descending at tshift 52200 s and that the lations were evident (not shown); however, this technique tornadogenesis/tornadogenesis failure time is usually

‘‘smeared’’ the data since the trajectories do not all arrive slightly after tshift 5 200 s. It should also be noted that at the ‘‘surface’’ (i.e., the lowest scalar level; z 5 100 m) at when individual cases are examined, the trajectories the same time. behave similarly to these TOR-average and NON- To adjust for this smearing, the individual descending average plots. trajectories among all NON cases (and separately among As the parcels descend, negative z is produced in both all TOR cases) were shifted forward or backward in time the TOR and NON simulations (Fig. 5a). In both com- and synchronized to arrive at z 5 100 m simultaneously posite trajectories, a minimum in z occurs at approxi- before averaging. This time is referred to herein as tshift 5 mately tshift 5250 s—which is 50 s before the parcels 0 s. A schematic of the shifting process is shown in Fig. 4. ﬁrst descend below z 5 100 m (i.e., tshift 5 0 s)—and the Also shown in Fig. 4 is the typical behavior of descending magnitude of this minimum is larger in the TOR com- trajectory parcels (in both the TOR and NON simula- posite. In both composites, this minimum in z occurs just tions). That is, parcels descend from aloft, travel hori- after a minimum in z production via vH tilting (Fig. 5b) zontally near the surface, and then ascend into the and at approximately the same time as a maximum in z

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FIG. 3. Box-and-whisker plots showing the average net vorticity generation in the (a),(b) rising trajectory parcels and (c),(d) descending trajectory parcels of the TOR (black) and NON (gray) simulations due to (a),(c) tilting of horizontal vorticity and (b),(d) stretching of vertical vorticity. The average value (for one case) represents an integration of the vorticity production over the length of the 15-min trajectory and averaging over all rising trajectories in that case.

21 production via stretching (Fig. 5c), with the peaks being tshift 5250 s (versus 26ms in the NON composite; of larger magnitude in the TOR composite. The mini- Fig. 5h) and thus would experience a stronger decel- mum in z production owing to vH tilting between tshift 5 eration as they approach the surface. Hence, the stretching 2200 and 250 s is associated with increases in jvHj of z is larger in the TOR composite at this time be- (Fig. 5d), increasing horizontal gradients of vertical cause ›w/›z and z are both more negative in the TOR velocity (Fig. 5e), increasing baroclinic generation of composite. vH (Fig. 5f), and tilting of z into vH plus horizontal As tshift approaches zero, the differences in vorticity stretching of vH (Fig. 5g). Between tshift 52100 and magnitude and vorticity production between the two 250 s, baroclinic generation is the dominant vH pro- composites become smaller. However, both composites duction term at more than 2 times larger than the pro- show strong increases in jvHj and the production of vH duction of vH via the sum of tilting of z and horizontal (Figs. 5d,g). Also, note that the maximum in baroclinic stretching of vH (Fig. 5g). generation of vH in both composites (Fig. 5f) immedi- Between tshift 5250 and 0 s, z increases toward zero in ately precedes the sharp increase in jvHj (Fig. 5d) and both the TOR and NON composites (Fig. 5a). This in- the ﬁvefold increase in production of vH via the tilting of crease is associated with increases in tilting of vH and z into vH and stretching of vH (Fig. 5g). positive z stretching (Figs. 5b,c). If z is negative (and As the parcels slowly descend below z 5 100 m be- decreasing in magnitude) and stretching of z is positive, tween tshift 5 0 and 150 s, z continues increasing (but then ›w/›z must also be negative. In a descending parcel remains negative and close to zero) in both the TOR and that is approaching the surface, ›w/›z is negative as the NON composites, with the values being very similar. parcel decelerates between tshift 5250 and 0 s. In the Stretching production is positive (Fig. 5c) and tilting TOR composite, average downdrafts are stronger, with production of z is positive in both composites (Fig. 5b). 2 a minimum average value of 28ms 1 occurring around Tilting and stretching production of z are both larger in

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spread in vorticity production terms for the individual cases in the TOR and NON categories. Figure 7 shows box-and-whisker plots of several of the ﬁelds from Fig. 5 at select times. As the parcels descend to the surface, there are signiﬁcant differences in z between the TOR and NON simulations (Fig. 7a). There are also sub-

stantial differences in jvHj (Fig. 7b), the tilting of vH (Fig. 7c), and the magnitude of horizontal gradients in vertical velocity (Fig. 7d). As the parcels reach z 5 100 m, and shortly thereafter, differences between NON and TOR for all ﬁelds shown in Fig. 7 become small. As the parcels approach the low-level circulation near

tshift 5 200 s, the differences between the TOR and NON simulations begin to increase, particularly the produc-

tion of z via the tilting of vH (Fig. 7c), which itself is a function of the horizontal gradients in vertical velocity (Fig. 7d). Also, note that after t 5 0 s, the individual TOR simulations show a larger spread in z than do the NON simulations (Fig. 7a). This larger spread explains the apparent ‘‘noise’’ in some of the TOR trajectory ﬁgures (i.e., Figs. 5c,g and 6). The results thus far have demonstrated that TOR- averaged parcels, as well as parcels in the individual TOR simulations, typically arrive at the surface (z 5

100 m) with larger jvHj than the NON simulations. As the parcels then travel toward the near-surface circula-

tion, the TOR parcels experience stronger tilting of vH FIG. 4. Schematic showing three descending trajectories (gray, z jv j 5 into (owing to larger H and stronger gradients in black, and dark gray) that arrive at the lowest model level (z v 100 m) at (a) slightly different times and (b) simultaneously owing vertical velocity) and stronger stretching of both H and to shifting them in time. z. These results suggest that the low-level updraft is stronger in the TOR simulations. TOR. The magnitude of the horizontal vorticity vector Adding to this hypothesis, analysis of forward tra- jvHj continues to increase in both the TOR and NON jectories seeded in the near-surface circulation shows composites (Fig. 5d), but more rapidly in TOR, pri- that, on average, parcels in the TOR simulations are marily owing to production of vH via the tilting of z and lifted to higher altitudes than those in the NON sim- stretching of vH (Fig. 5g), which is about 4–5 times larger ulations (Figs. 8a,c). The differences become even than baroclinic generation of vH at this time (Fig. 5f). more apparent when relating trajectory height to en- The production of vH is separated even further into the vironmental LFC height (Figs. 8b,d). Only three stretching of existing vH and the tilting of z into vH (16%) of the TOR cases have an average parcel height (Fig. 6). The stretching term dominates positive pro- that is well below LFC height, while eight (57%) of duction of vH at all times analyzed, while the tilting the NON simulations do. For the soundings used in term is negative. this study, LFC height is strongly correlated to CIN

At approximately tshift 5100 s, differences in z pro- (not shown). duction between the TOR and NON composites become To determine if the differences in low-level updraft larger. Both composites show increases in z (Fig. 5a) strength between the TOR and NON simulations were and its production terms—tilting (Fig. 5b) and stretching related to differences in parcel buoyancy, perturbations

(Fig. 5c)—after tshift 5 100 s; however, the rate of increase of pseudoequivalent potential temperature uep were in these ﬁelds is much larger in the TOR composite. The calculated in a 1 km 3 1 km box centered on the location larger tilting in the TOR composite is associated with of the tornado in the TOR simulations and on the lo- greater vH (Fig. 5d) and larger horizontal gradients in cation of maximum 0–1-km UH in the NON simulations vertical velocity (Fig. 5e). at the trajectory initialization time (Fig. 9). Perturba-

Figure 5 illustrates average differences between the tions are relative to the surface value of uep in the NSE TOR and NON simulations but does not show the and uep was calculated following Bolton (1980). The

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FIG. 5. Composite trajectories for the TOR (solid line) and NON (dashed line) simulations showing time series of (a) vertical vorticity, (b) tilting of horizontal vorticity into the vertical, (c) stretching of vertical vorticity, (d) magnitude of the horizontal vorticity vector, (e) magnitude of the horizontal gradient in vertical velocity, (f) baroclinic generation of horizontal vorticity, (g) tilting of vertical vorticity into horizontal vorticity plus stretching of horizontal vorticity, and (h) vertical velocity. The x axis is relative to the time when descending parcels ﬁrst descend below z 5 100 m. results from this analysis show that the majority of the had much-larger-magnitude deﬁcits (i.e., much smaller

NON simulations had small-magnitude uep deﬁcits (i.e., than the base-state environment) at the time of torna- similar to base state environment) at the time of tornadogenesis. This result refutes the notion that updrafts in dogenesis failure, whereas many of the TOR simulations the NON simulations are weaker because of excessive

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4. Discussion In this study, it was shown that differences in vorticity processes between the TOR and NON simulations are largest in descending parcels. In the TOR simulations, parcels produce more negative z while they descend than do parcels in the NON simulations. It appears that as the parcels in both categories reach the surface, this negative z developed during descent is reduced in

magnitude via compression while vH steadily increases. The parcels then travel horizontally and, as they rise, vH is tilted back into the vertical by strong horizontal gradients in vertical velocity. Thus, it seems that the main differences between the TOR and NON simulations is

FIG. 6. Composite trajectories for the TOR (solid lines) and that the TOR simulations have larger horizontal vor- NON (dashed lines) simulations showing time series of the increase ticity after they reach the surface—due in part to larger in horizontal vorticity with time due to stretching of existing hor- initial (i.e., environmental) horizontal vorticity and also izontal vorticity (black lines) and tilting of vertical vorticity into more baroclinic generation—which is tilted in the ver- horizontal vorticity (gray lines). tical by stronger low-level updrafts. Certainly, these variations in vorticity production are negative buoyancy of the low-level outflow at the time of due to differences in the initial environments of the tornadogenesis failure. Rather, the NON storms typi- TOR and NON simulations. Thompson et al. (2003) cally have more buoyant outflow surrounding the non- showed that two of the most statistically significant tornadic vortex. differences between the significantly tornadic and

FIG. 7. Box-and-whisker plots of selected terms from Fig. 5 at various times along the trajectory for TOR (black) and NON (gray) simulations: (a) vertical vorticity, (b) magnitude of horizontal vorticity, (c) production of vertical vorticity via tilting of horizontal vorticity, and (d) magnitude of the horizontal gradient of vertical velocity.

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FIG. 8. (a),(c) Average maximum height of forward trajectories for the TOR and NON cases and (b),(d) ratio of maximum trajectory height to environmental LFC height.

nontornadic proximity soundings were mixed-layer section 3 show that the largest-magnitude uep deficits CAPE and 0–1-km storm relative helicity (SREH). actually occurred in the TOR simulations. Since CAPE Thompson et al. (2003) found that both of these quanti- is substantially larger in the TOR simulations, it seems ties were smaller in the nontornadic soundings. The same reasonable to expect that these simulations will also is true for the subset of soundings used in this study, as the have stronger downdrafts (e.g., Srivastava 1987) and soundings come from Thompson et al. (2003), albeit with more precipitation production (e.g., Weisman and Klemp substantially less overlap (Fig. 10). Nearly every TOR 1982)—hence, more evaporational cooling and melting. simulation had larger CAPE than the NON simulations Additionally, the NON simulations have more CIN on (Fig. 10a). Thus, it should not be surprising that the average, which has been shown by Naylor et al. (2012a) to horizontal gradients of vertical velocity were larger in reduce uep deficits in the cold pool. the TOR simulations, since CAPE is proportional to There are several possible reasons why the cold-pool vertical velocity (e.g., Weisman and Klemp 1982). Ad- characteristics of these simulations, and the associated ditionally, the NON simulations had larger-magnitude tornado behavior, seemingly disagree with past studies. CIN (Fig. 10b), which has been shown to be able to re- Markowski et al. (2002)—the first study to link torna- duce the strength of the low-level updraft and downdraft dogenesis to cold-pool characteristics—showed that the (Naylor et al. 2012a). largest differences in cold pools are between signifi- The discrepancies in CAPE and CIN between the cantly tornadic and nontornadic supercell, whereas in TOR and NON simulations are also likely to influence this current study, no distinction is made between weak outflow thermodynamics. Numerous studies have sug- tornadoes and significant tornadoes. However, Naylor gested that the cold pools in nontornadic supercells are and Gilmore (2012b) did show that many of the TOR more negatively buoyant (i.e., larger-magnitude uep def- simulations presented in this current study do produce icits) than tornadic supercells. However, the results in long-lived tornadoes or tornado families. Alternatively,

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FIG. 9. Maximum and minimum perturbations of uep for the TOR (crosses) and NON (circles) simulations. Perturbations are relative to the surface value in the base-state environment. The calculation was performed over a 1 km 3 1 km box centered on the circulation at the time of tornadogenesis or tornadogenesis failure. observations of cold-pool temperature in past studies may not have been taken precisely at the time of tornadogenesis or tornadogenesis failure and/or may suffer from errors in the steady-state assumption necessary for the time-to-space conversion of measurements. Many of these studies state that cold-pool measurements were taken ‘‘within 5 min’’ of tornadogenesis or tornadogenesis failure (i.e., Markowski et al. 2002; Grzych et al. 2007). Since some of the observations were taken after tornadogenesis occurred, perhaps the ‘‘warm’’ outflow air observed near significant tornados is a result of the tornado and not a precursor to its formation, as has been observed in numerical supercell simulations performed by the second author [e.g., animation in slide 15 of Gilmore et al. (2006)]. In fact, some recent studies have shown evidence of the importance of strong cold pools to tornadogenesis and tornado maintenance. In an analysis of the Bowdle, South Dakota, cyclic tornadic storm, Finley et al. (2010) found that the initial, nontornadic mesocyclone in that storm had much larger uep in and around the low-level mesocyclone than the subsequent tornadic mesocyclone. Marquis et al. (2012) concluded that a cold, secondary rear-flank downdraft FIG. 10. Box-and-whisker plots of (a) mixed-layer CAPE, (RFD) surge assisted with tornado maintenance by en- (b) mixed-layer CIN, and (c) 0–1-km SREH from the initial hancing the baroclinic generation of horizontal vorticity. soundings used in the TOR and NON simulations. CAPE and Straka et al. (2007) and Markowski et al. (2008) have CIN are calculated using a 500-m mixed-layer parcel and the also discussed the possible importance of baroclinic virtual temperature correction from Doswell and Rasmussen vorticity generation in parcels near the rear of the storm, (1994). Storm motion in SREH calculations follows Bunkers et al. (2000). although neither discussed the cold-pool properties of the analyzed storms in those studies. It is also possible that the subset of nontornadic soundings in this study did not adequately represent the

Unauthenticated | Downloaded 10/06/21 04:52 AM UTC 1214 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 71 range of CAPE values typical of nontornadic storms in nature. The CAPE in nearly every NON simulation was less than the median value when computed using the full Thompson et al. (2003, 2007) dataset. As mentioned previously, it is reasonable to expect the storms in smaller CAPE environments to have weaker downdrafts than do the TOR cases with larger CAPE. If nontornadic storms observed during field campaigns— such as those documented by Markowski et al. (2002) and Grzych et al. (2007)—were also associated with larger CAPE and/or smaller CIN, then they may represent a different mode of tornadogenesis failure not observed in this current study. Last, limitations in the microphysics parameterization may have led to enhanced cold pools in the TOR simulations. Kumjian (2011) found that hydrometeor drop FIG. 11. Scatterplot of 0–1-km SREH vs average minimum ver- size distributions have large spatial variability in and tical vorticity in descending parcels from the TOR (circles) and around the hook echo of supercells, including regions NON (crosses) simulations. dominated by large raindrops. Such distributions are more common in storms occurring in environments with large SREH (Kumjian and Ryzhkov 2008, 2009), which between descending parcels in the TOR and NON would make them more likely in tornadic supercells simulations. Davies-Jones and Brooks (1993) state that than nontornadic. However, this type of drop size dis- tilting of horizontal vorticity produces downdrafts with tribution is not possible with the simple microphysics anticyclonic vorticity (i.e., negative z) when the hori- scheme used in this study herein. The single-moment zontal vorticity is purely streamwise and zero net z when scheme used here resets the drop size distribution to an the flow is purely crosswise, owing to symmetry. Al- inverse exponential form after each time step. This re- though Davies–Jones and Brooks only discuss these two sults in the artificial insertion of numerous small rain- extremes, it seems reasonable that there is a continual drops, which easily evaporate (e.g., Dawson et al. 2010). increase in net anticyclonic vorticity production as the This added evaporation might enhance downdrafts and flow becomes more streamwise—which is proportional baroclinic vorticity generation, and bring lower-uep air to SREH. In fact, Fig. 11 does indicate a somewhat to the surface than would otherwise have occurred. linear association between SREH and negative z in de- It seems that both barotropically and baroclinically scending parcels. There are, however, numerous points generated horizontal vorticity were important in the that do not follow a simple linear fit, likely because the TOR simulations. The larger barotropic vorticity in magnitude of vertical vorticity in descending parcels these cases (i.e., larger SREH; Fig. 10c) not only results also depends on the amount of vorticity stretching that in larger initial vorticity along the trajectories, but it occurs, which itself is related to other environmental should also produce a larger vertical pressure gradient parameters such as CAPE, precipitable water, and pos- force that strengthens low-level updrafts (e.g., Rotunno sibly CIN. Despite the outliers, the larger SREH in the and Klemp 1982; Brooks and Wilhelmson 1993; McCaul TOR simulations seems to result in larger negative z as and Weisman 1996, 2001)—thus enhancing horizontal the parcels descend, which then tilts into the horizontal as gradients of vertical velocity that influence stretching it reaches the surface and increases the magnitude of and tilting. However, based on the analysis presented, it horizontal vorticity. is unclear whether the differences in horizontal gradi- There is also evidence suggesting that baroclinic ents of vertical velocity between the TOR and NON generation is extremely important to the evolution of simulations are primarily due to the differences in vorticity in the descending parcels. Peaks in baroclinic buoyancy (i.e., CAPE and CIN) or the shear-induced generation occurred in conjunction with peaks in tilting low-level vertical pressure gradient force (i.e., related to of z and increases in horizontal vorticity in the de- SREH). A pressure decomposition analysis would cer- scending parcels of both the TOR and NON simulations. tainly shed light on this issue and is planned for a future In addition, baroclinic generation was an order of mag- study. nitude larger than the production of horizontal vorticity The larger barotropic vorticity in the TOR simulations via tilting–stretching throughout a large portion of parcel may also explain differences in negative z production descent. However, after reaching ground, horizontal

Unauthenticated | Downloaded 10/06/21 04:52 AM UTC MARCH 2014 N A Y L O R A N D G I L M O R E 1215 stretching of vH becomes much more important than were compared to 19 tornadic simulations. In comparing baroclinic generation. the tornadic and nontornadic simulations, the following Overall, vorticity production in the TOR simulations points are summarized: agrees quite well with previous studies. Parcels that d Vertical vorticity production in rising parcels was descend from aloft primarily generate negative vertical similar. The tornadic simulations experienced larger vorticity as they descend (e.g., Brandes 1984; Davies- vertical vorticity production via stretching of horizon- Jones and Brooks 1993; WW95; A99). During descent, tal vorticity, with the largest differences occurring less tilting is negative, while stretching is positive (WW95; than 60 s prior to tornadogenesis or tornadogenesis A99). As parcels approach the surface, baroclinic gen- failure. Thus, the larger stretching in the tornadic sim- eration of horizontal vorticity increases (Davies-Jones ulations is likely because tornadogenesis is imminent. and Brooks 1993; WW95; A99; Straka et al. 2007; d Vertical vorticity production in descending parcels Markowski et al. 2008). Only after the parcels reach the was noticeably different. Tilting of horizontal vorticity surface do they acquire positive z (in agreement with was much larger in magnitude in the tornadic simula- WW95). One impact of the current study is the re- tions, with stronger negative tilting occurring during producibility of these prior results across a wide variety descent and stronger positive tilting as the downdraft of soundings (with capping inversions) and with the trajectories approached the circulation. same model setup and the contrast in behavior between d During parcel descent, peaks in anticyclonic vorticity the TOR environments against the NON environments. occurred in association with peaks in negative tilting, Finally, we note that differences between the TOR positive stretching, and baroclinic generation, all of and NON environments in this study herein agree which were larger in the tornadic simulations. qualitatively with the findings from previous supercell d After the descending parcels reach the surface, the climatology studies (e.g., CAPE and SREH are good larger tilting of horizontal vorticity in the tornadic discriminators between tornadic and nontornadic envi- simulations can be attributed to larger horizontal ronments; Rasmussen and Blanchard 1998; Thompson vorticity and stronger horizontal gradients of vertical et al. 2003). However, those studies found large overlap velocity. in the CAPE and SREH values typical of tornadic and d Vertical vorticity became positive in descending par- nontornadic storms, whereas the study herein found cels only after they reached the surface (on average). very little overlap (cf. Fig. 10). This difference may re- The increase in vertical vorticity after descent was veal the inherent difficulty in forecasting tornadogenesis stronger in the tornadic simulations, owing to larger in real-world storms. That is, aspects not considered horizontal vorticity and stronger horizontal gradients here that are intrinsically included in observational cli- in vertical velocity. matology studies may also be influential (e.g., horizontal d On average, forward-integrated trajectories reached boundaries and/or gradients of CAPE and shear, varying higher average altitudes in the tornadic simulations. In surface roughness length and land use types, geograph- most of the nontornadic simulations, the trajectories ically dependent aerosol distributions, etc.). However, were, on average, unable to reach the environmental when these factors are removed—as was done in the LFC height. current study—the impact of the NSE becomes much d The strongest cold pools in the vicinity of the low-level clearer. mesocyclone were associated with the tornadic simulations. Most of the nontornadic simulations had cold 5. Summary and conclusions pools with small deficits of pseudoequivalent potential temperature. In the study herein, an idealized cloud model was used to investigate storm-scale mechanisms important for In conclusion, the largest differences between the tornadogenesis and tornadogenesis failure. Simulations tornadic and nontornadic supercells are related to vor- were initialized with supercell proximity soundings ticity production in parcels that descend from aloft. The associated with significantly tornadic ($F2 or lasting tornadic (nontornadic) simulations produce more (less) longer than 5 min) and nontornadic supercells. These anticyclonic vertical vorticity during parcel descent, which soundings were taken from the RUC-2 model by is generated by larger (smaller) tilting of horizontal Thompson et al. (2003, 2007). A subset of the tornadic vorticity and stretching of existing vertical vorticity. As and nontornadic RUC-2 soundings was simulated at the parcels reach the surface, they are tilted back into 100-m resolution in order to compare vorticity pro- the horizontal. After the parcels reach the surface, the duction terms in simulations with tornadic and non- magnitude of the horizontal vorticity is larger (smaller) tornadic supercells. Then, 14 nontornadic supercells in the tornadic (nontornadic) simulations owing to the

Unauthenticated | Downloaded 10/06/21 04:52 AM UTC 1216 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 71 larger (smaller) initial barotropic horizontal vorticity, Brandes, E. A., 1984: Vertical vorticity generation and mesocy- larger (smaller) baroclinic generation during descent, clone sustenance in tornadic thunderstorms: The observa- and larger (smaller) stretching of horizontal vorticity. tional evidence. Mon. Wea. Rev., 112, 2253–2269. Brooks, H. E., and R. B. Wilhelmson, 1993: Hodograph curvature As the parcels travel horizontally toward the low-level and updraft intensity in numerically modeled supercells. circulation, this horizontal vorticity is then tilted into J. Atmos. Sci., 50, 1824–1833. the vertical direction and stretched, with both of these ——, C. A. Doswell III, and J. Cooper, 1994: On the environments processes being larger in the tornadic simulations be- of tornadic and nontornadic mesocyclones. Wea. Forecasting, cause of stronger updrafts. 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L., 1969: An analysis of over sixty tornado proximity Future work will involve investigating the processes soundings. Preprints, Sixth Conf. on Severe Local Storms, responsible for tornado maintenance and demise by Chicago, IL, Amer. Meteor. Soc., 218–221. Davies, J. M., and R. H. Johns, 1993: Some wind and instability analyzing vorticity budgets and thermodynamics for the parameters associated with strong and violent tornadoes: trajectories arriving in the simulated tornadoes through- 1. Wind shear and helicity. The Tornado: Its Structure, Dy- out their lifetime. In addition, several of the tornadic namics, Prediction, and Hazards, Geophys. Monogr., Vol. 79, simulations produced cyclic tornadogenesis. These sec- Amer. Geophys. Union, 573–582. ondary tornadoes could be analyzed to determine if the Davies-Jones, R. P., 2008: Can a descending rain curtain in a su- processes related to initial tornadogenesis differ from percell instigate tornadogenesis barotropically? J. Atmos. 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Unauthenticated | Downloaded 10/06/21 04:52 AM UTC 3568 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 71

CORRIGENDUM

JASON NAYLOR AND MATTHEW S. GILMORE Department of Atmospheric Sciences, University of North Dakota, Grand Forks, North Dakota

The caption for Fig. 9 in Naylor and Gilmore (2014) incorrectly identifies the symbols in the figure. The figure with its correct caption is presented below. We regret any in- convenience this error may have caused.

FIG. 9. Maximum and minimum perturbations of uep for the TOR (circles) and NON (crosses) simulations. Perturbations are relative to the surface value in the base-state environment. The calculation was performed over a 1 km 3 1 km box centered on the circulation at the time of tornadogenesis or tornadogenesis failure.

Acknowledgments. The authors thank Dr. Paul Markowski for bringing this error to their attention.

REFERENCE

Naylor, J., and M. S. Gilmore, 2014: Vorticity evolution leading to tornadogenesis and tornadogenesis failure in simulated supercells. J. Atmos. Sci., 71, 1201–1217, doi:10.1175/JAS-D-13-0219.1.

Corresponding author address: Jason Naylor, NorthWest Research Associates, 3380 Mitchell Lane, Boulder, CO 80301. E-mail: [email protected]

DOI: 10.1175/JAS-D-14-0204.1

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