1. Introduction
Although tornadoes have been studied extensively over the last 50 years, many unanswered questions remain regarding the storm-scale processes responsible for their development. Numerical modeling studies have repeatedly shown that supercells do not develop low-level rotation until downdrafts reach the surface (e.g., Klemp and Rotunno 1983; Davies-Jones and Brooks 1993; Walko 1993; Trapp and Fiedler 1995; Wicker and Wilhelmson 1995, hereafter WW95; Adlerman et al. 1999, hereafter A99). While these studies agree that downdrafts are critically important, they do not agree on the exact mechanisms that produce low-level vorticity. These works have concluded that downdrafts can produce positive (cyclonic) near-surface vertical vorticity via the
tilting of horizontal vorticity that was baroclinically generated (i.e., vorticity generated by the storm’s own horizontal density gradients),
tilting of horizontal vorticity associated with the vertical wind shear of the environment (also known as barotropic vorticity), or
transport of vertical vorticity to the surface.
Much of the research involving nontornadic storms has only focused on understanding differences in the near-storm environments (NSEs) of tornadic and nontornadic storms (e.g., Darkow 1969; Maddox 1976; Davies and Johns 1993; Brooks et al. 1994; Rasmussen and Blanchard 1998; Thompson et al. 2003, 2012; Togstad et al. 2011). For example, it is now known that tornadic supercells occur more often in NSEs with large values of storm-relative environmental helicity, large CAPE, low LCL heights (Rasmussen and Blanchard 1998; Thompson et al. 2003, 2012), and small convective inhibition (CIN) (Thompson et al. 2012). However, there are still many questions regarding the storm-scale differences between tornadic and nontornadic supercells and how these differences may be influenced by the NSE.
One storm-scale feature that may help discriminate between tornadic and nontornadic storms is the buoyancy of the low-level storm outflow. Observational studies have also shown that the evaporatively chilled storm outflow in significantly tornadic supercells often has smaller negative buoyancy (not as cold/dense) relative to the prestorm NSE compared to nontornadic supercells (e.g., Markowski et al. 2002; Shabbott and Markowski 2006; Grzych et al. 2007). Simulations by Markowski et al. (2003) using a model with a 2D axisymmetric coordinate system show that downdrafts with more negatively buoyant air cannot be lifted by the updraft, thus disrupting near-surface convergence and stretching of vertical vorticity. Markowski et al. (2011) computed trajectories using dual-Doppler wind retrievals in three nontornadic supercells and found that the air entering the near-surface circulation only ascends a short distance before abruptly descending again, implying either 1) the parcels in the nontornadic cases are too negatively buoyant to be lifted by the updraft or 2) the low-level vertical pressure gradient force is insufficient to lift the parcels. The findings from these studies suggest that barotropic vorticity is important to tornadogenesis and if the downdraft is too “cold,” this might inhibit tornadogenesis despite stronger implied baroclinic production. However, none of these studies presented a detailed analysis of vorticity evolution.
In fact, only a handful of studies have investigated differences in near-surface vorticity production between tornadic and nontornadic supercells. Trapp (1999) compared six supercells (three nontornadic and three tornadic) observed during the Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX) and found that while the nontornadic supercells experienced less stretching of vertical vorticity and less low-level convergence, the supercells were similar in other respects—including the presence of low-level mesocyclones and rear-flank gust fronts. Using a similar dataset from VORTEX, Markowski et al. (2008) found that both tornadic and nontornadic supercells exhibit vortex line “arches” that straddle the hook echo—suggesting that near-surface rotation development in both types of supercells was aided by baroclinic vorticity generation in the rear-flank downdraft. Wakimoto and Cai (2000) found that while a nontornadic supercell had “more extensive” precipitation (as indicated by radar reflectivity) in the rear flank, stronger inflow, and stronger updrafts along the rear flank compared to a tornadic supercell, the nontornadic supercell had an order-of-magnitude less horizontal vorticity in the NSE despite both storms having an occlusion downdraft and horseshoe-shaped updraft–downdraft signatures. Ziegler et al. (2001) concluded that a tornadic supercell had strong, low-level stretching of cyclonic vertical vorticity associated with a preexisting boundary layer vortex, while a nearby nontornadic storm was characterized by negative stretching. While the aforementioned studies show that tornadic and nontornadic storms share many structural similarities, differences in vorticity production may explain why some storms were tornadic and others were not. However, the small number of cases and different analysis strategies makes it difficult to generalize differences in vorticity production.
The main goal of the current study is to advance the current understanding of tornadogenesis by simulating numerous tornadic1 and nontornadic storms to determine the source(s) of vorticity-rich air at low levels, identify the processes that result in tornadogenesis and tornadogenesis failure, and relate these to the NSE. Idealized simulations were initialized with proximity soundings representative of the NSEs of tornadic and nontornadic supercells. It is believed that the study herein contains the largest number of tornado-resolving simulations to date. The sample is large enough to statistically compare the characteristics between the two groups: 19 tornadic and 14 nontornadic.
The idealized model that was used represents the NSE as horizontally homogeneous with a single profile of vertical wind shear and CAPE. This follows many prior supercell modeling studies that have studied the NSE in relation to the resulting storm type and behavior (e.g., Klemp and Wilhelmson 1978; Weisman and Klemp 1982). Previous observational and modeling studies have shown or suggested that nonhomogeneous features (i.e., preexisting baroclinic regions and vertical vorticity) can also influence low-level rotation and tornado potential in supercells (e.g., Maddox et al. 1980; Markowski et al. 1998; Atkins et al. 1999; Fierro et al. 2006; Richardson et al. 2007). By excluding these nonhomogeneous features, the ability (or inability) of a modeled storm to produce a tornado can be limited to the NSE. However, aspects of the model itself, such as grid spacing or the microphysics parameterization (through its impact on the cold pool and baroclinic horizontal vorticity production; e.g., Snook and Xue 2008 and Dawson et al. 2010), may influence tornadogenesis, but such simulation sensitivities to model characteristics are beyond the scope of the current study.
2. Methodology
Idealized simulations were carried out using version 14 of Cloud Model 1 (CM1; Bryan and Fritsch 2002) with default settings unless otherwise noted herein. All simulations have isotropic 100-m grid spacing and were run for 2 h of simulation time. The Klemp–Wilhelmson time-splitting scheme was used, with a large time step of 1 s and a small time step of 0.167 s. The computational domain was 120 km × 120 km × 20 km with a moving grid determined by the 0–6-km mean wind of the input sounding. Precipitation processes were represented by the single-moment, 6-class bulk microphysics scheme from Gilmore et al. (2004)—with default settings for all variables, including intercepts and graupel/hail density. The subgrid turbulence parameterization was based on Smagorinsky (1963). Lateral boundaries were gravity wave radiating, and an additional Rayleigh damper was used within 10 km of the domain edge to eliminate partial reflection. The rigid upper and lower boundaries were free slip and a standard Rayleigh damping layer was applied above height z = 16 km to damp vertically propagating gravity waves and minimize their reflection off the upper boundary. The Coriolis force was neglected.
Each simulation was initialized with one sounding—originally selected by Thompson et al. (2003, 2007) from a Rapid Update Cycle, version 2 (RUC-2), model grid point within 40 km spatially and 30 min temporally of an observed supercell. This current study specifically focuses on soundings that were associated with mature supercells—of which there are 113 significantly tornadic and 454 nontornadic. Because many of the significantly tornadic RUC-2 soundings have large-magnitude shear layers (shear Richardson number less than 0.25) the eddy mixing from the initial base-state environment was removed from the total eddy mixing tendency for each model variable. This practice is necessary in idealized cloud models when using realistic soundings to ensure that the initial base-state environment is preserved in regions away from active convection (L. Wicker 2013, personal communication).
a. Automated and manual supercell identification
Simulated supercells were identified objectively at 1-km grid spacing by the presence of 2–5-km integrated updraft helicity (UH2–5) greater than 180 m2 s−2 following Naylor et al. (2012b). At 100-m grid spacing, simulations were flagged for further analysis if UH2–5 > 900 m2 s−2 (extrapolated from coarser gridspacing results of Naylor et al. 2012b). Cases were excluded from further analysis if they did not meet the criteria continually for at least 1 h. For those cases that passed the thresholds, supercell existence was confirmed subjectively every 5 min using a manual procedure previously used in radar observations of supercells (defined and described in Naylor et al. 2012b). Only supercells that lasted at least 1 h were considered for further analysis of tornadogenesis and tornadogenesis failure.
b. Automated surface mesocyclone and tornado detection
Because of the large number of simulations in this study herein, a manual analysis to determine if, when, and where tornadogenesis occurs in the simulations would have been extremely tedious and time consuming. To circumvent this difficulty, an automated tornado-detection algorithm was developed and tested. Following Naylor and Gilmore (2012b), a tornado was said to be present in the simulation at the first instance that the following three criteria are met:3 (i) the pressure drop from the center of the vortex to the radius of maximum winds was −4.5 hPa or less, (ii) the horizontal wind speed at the radius of max winds was at least 30 m s−1, and (iii) vertical vorticity ζ in the center of the vortex was at least 0.1 s−1. For more information, refer to Naylor and Gilmore (2012b).
In the nontornadic simulations, tornadogenesis failure was said to occur in supercells that did not meet the tornadogenesis criteria at the time of maximum low-level mesocyclone strength—defined herein by the maximum value of 0–1-km updraft helicity. This method ensured that vertical vorticity and updraft were collocated. Also, since multiple circulation centers occurred along the leading gust front of many the simulated storms, monitoring trends in updraft helicity better revealed intensity changes for the low-level mesocyclone than would vorticity alone. Other studies have used the time of peak vertical vorticity in the near-surface mesocyclone beneath the bounded weak-echo region (Trapp 1999) or have paired vorticity information with small values of Okubo–Weiss number (associated with decreased pressure, large vertical vorticity, and small deformation) to pinpoint the circulation center (Markowski et al. 2011).
c. Initialization and backward integration of trajectories
A trajectory analysis was performed for each of the tornadic and nontornadic simulations. In the tornadic simulations, trajectories were seeded at the time of tornadogenesis (first triggering of the tornado-detection algorithm) at equidistant points inside a 1 km × 1 km × 0.4 km box centered on the location of minimum pressure and only at grid points where the pressure perturbation was less than −3 hPa (between z = 100 and 500 m). In the interest of computational expense, an upper limit of 100 trajectory parcels was set for each simulation. The pressure-drop threshold of −3 hPa was used to ensure that plenty of trajectories surround even the weak tornadic vortices (and indeed in every tornadic simulation, the maximum number of trajectories was initialized). Trajectories were traced backward 900 s (consistent with previous studies utilizing trajectories to determine the source region of air parcels—e.g., A99), using model history files generated at 5-s intervals. Dahl et al. (2012) showed that this temporal resolution is sufficient to compute accurate backward trajectories.
In the nontornadic simulations, a 1 km × 1 km × 0.4 km box was centered on the location of maximum 0–1-km updraft helicity, and trajectories were seeded at equidistant points inside this box having vertical vorticity greater than 0.05 s−1 between the same range of altitudes as in the tornadic cases (z = 100–500 m). The box was defined such that it was large enough to encompass the primary circulation on the scale of a tornado (if one were to form), and the vorticity criteria was used to remove points that fall outside the primary circulation. In many of the nontornadic simulations, only 50–75 trajectories were seeded, since some parcels within the box failed to meet the threshold value of vertical vorticity.
At each point along the trajectory, the terms in (3) and (4) were calculated. Once the trajectories were traced backward by 900 s, they were separated into the following categories:
Descending: trajectories that experience a net descent to the surface from a height of z ≥ 1 km.
Ascending: trajectories that originate near the surface, many traveling along the forward-flank gust front, and steadily rise as they approach the near-surface circulation.
After the trajectories were sorted into these categories, net values of the terms in (3) and (4) along each category of trajectory were computed for each individual case. For instance, “net tilting in rising trajectories” in each simulation was calculated by integrating the tilting term in the vertical vorticity equation over the length of each trajectory (900 s) and averaging over all trajectories in the “rising” category. Then these categorical averages were separately averaged over all tornadic and nontornadic cases.
d. Forward integration of trajectories
In both the tornadic and nontornadic simulations, forward trajectories were also calculated to observe the maximum vertical extent of these parcels and to investigate the influence of outflow thermodynamics on tornadogenesis and tornadogenesis failure. Trajectory seeding criteria and locations were the same as for backward-integrated trajectories so that the same parcels were being followed. Forward-trajectory calculations used the same time step (1 s) and time resolution (history files every 5 s), except they were computed forward for 1200 s instead of backward for 900 s.
3. Results
To identify soundings that would produce sustained simulated supercells and to reduce the computational expense of the simulations, all 113 significantly tornadic and 454 nontornadic RUC-2 proximity soundings were first simulated with a low-resolution model configuration (1-km horizontal and 250-m vertical grid spacing). With this low-resolution configuration, 60 of 113 (53%) simulations initialized with significantly tornadic soundings and 155 of 454 (34%) of simulations initialized with nontornadic supercell soundings produced supercells lasting at least 1 h in duration.
When the 60-member subset of significantly tornadic RUC-2 soundings was resimulated with 100-m grid spacing, 30 (50%) of the simulations produced supercells lasting at least 1 h—19 (63%) of which produced a tornado that was associated with the main mesocyclone of the supercell. When a randomly selected 40-member subset of the 155 nontornadic RUC-2 soundings was resimulated with 100-m grid spacing, 24 (60%) produced long-lived supercells—14 (58%) of which were nontornadic. The forthcoming analysis focuses only on these 14 nontornadic simulations initialized with nontornadic RUC-2 soundings (herein NON) and the 19 tornadic simulations initialized with significantly tornadic RUC-2 soundings (herein TOR).
Trajectory analysis
An overview of the backward trajectory paths initialized within the TOR simulations at the time of tornadogenesis (Fig. 1) and NON simulations at the time of tornadogenesis failure (Fig. 2) reveals three distinct types of circulations: those fed primarily by rising air parcels, those fed primarily by descending air parcels, and those that contain both rising and descending air parcels. The circulations composed primarily of rising parcels are the rarest, with only two cases—both of which were tornadic (Fig. 1; T15 and T16). The tornadoes in these two cases developed early in the simulations, prior to the development of a strong cold pool, and may have been influenced by the convective initiation procedure. These cases are included for completeness. In both the TOR and NON simulations (cf. Figs. 1 and 2), the rising parcels generally originate at low levels, downshear of the near-surface mesocyclone, and move parallel to the forward-flank gust front (not shown) as they approach the circulation. The descending parcels typically approach the near-surface circulation from the right, often wrapping cyclonically around the midlevel mesocyclone similar to the schematic from Klemp (1987).
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).
Citation: Journal of the Atmospheric Sciences 71, 3; 10.1175/JAS-D-13-0219.1
As in Fig. 1, but for the 14 nontornadic simulations integrated backward from the time of tornadogenesis failure.
Citation: Journal of the Atmospheric Sciences 71, 3; 10.1175/JAS-D-13-0219.1
Rising parcels contribute similarly to the low-level circulation in both the TOR and NON simulations by tilting baroclinically generated horizontal vorticity and amplifying it via stretching. The average rising parcel’s net ζ generation via tilting over the 900-s integrated back trajectories is very similar (Fig. 3a) but the average net ζ generation via stretching of vertical vorticity (Fig. 3b) is greater in the TOR cases; however, most of the difference is found at the very end of the trajectories (not shown), when tornadogenesis is imminent. Because rising parcels contribute similarly between the TOR and NON simulations, they do not appear to discriminate between tornadogenesis and tornadogenesis failure.
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.
Citation: Journal of the Atmospheric Sciences 71, 3; 10.1175/JAS-D-13-0219.1
Descending parcels, however, do reveal some important differences that discriminate between the TOR and NON simulations. Unlike the rising parcels, the descending parcels in the TOR simulations have larger average net tilting than those in the NON simulations (Fig. 3c). Similar to the rising parcels, stretching in the descending parcels is also larger in the TOR simulations (Fig. 3d). However, while Fig. 3 shows that there are differences in total vorticity production between descending parcels in the TOR and NON simulations, it does not provide information about when these differences occur.
To better illustrate how differences in vorticity production between the TOR and NON simulations evolve with time, and to help identify the point(s) along the descending trajectories where these differences are greatest, a single composite descending trajectory was created for both the TOR and NON simulations (an individual composite trajectory for each simulation is examined later in this section). This was done by averaging the vorticity production properties along all descending trajectories from all cases at each trajectory time step. Substantial differences in the average net vorticity production between the TOR and NON simulations were evident (not shown); however, this technique “smeared” the data since the trajectories do not all arrive at the “surface” (i.e., the lowest scalar level; z = 100 m) at the same time.
To adjust for this smearing, the individual descending trajectories among all NON cases (and separately among all TOR cases) were shifted forward or backward in time and synchronized to arrive at z = 100 m simultaneously before averaging. This time is referred to herein as tshift = 0 s. A schematic of the shifting process is shown in Fig. 4. Also shown in Fig. 4 is the typical behavior of descending trajectory parcels (in both the TOR and NON simulations). That is, parcels descend from aloft, travel horizontally near the surface, and then ascend into the tornadic circulation (or low-level mesocyclone in the NON simulations). Vorticity production terms were analyzed during a 400-s window centered on tshift = 0 s and all further plots dealing with descending trajectories use the time-shifted data. The shifting required in individual cases typically varied by ±100 s. It is important to note that after shifting the trajectories, all parcels (in all cases) are descending at tshift = −200 s and that the tornadogenesis/tornadogenesis failure time is usually slightly after tshift = 200 s. It should also be noted that when individual cases are examined, the trajectories behave similarly to these TOR-average and NON-average plots.
Schematic showing three descending trajectories (gray, black, and dark gray) that arrive at the lowest model level (z = 100 m) at (a) slightly different times and (b) simultaneously owing to shifting them in time.
Citation: Journal of the Atmospheric Sciences 71, 3; 10.1175/JAS-D-13-0219.1
As the parcels descend, negative ζ is produced in both the TOR and NON simulations (Fig. 5a). In both composite trajectories, a minimum in ζ occurs at approximately tshift = −50 s—which is 50 s before the parcels first descend below z = 100 m (i.e., tshift = 0 s)—and the magnitude of this minimum is larger in the TOR composite. In both composites, this minimum in ζ occurs just after a minimum in ζ production via ωH tilting (Fig. 5b) and at approximately the same time as a maximum in ζ production via stretching (Fig. 5c), with the peaks being of larger magnitude in the TOR composite. The minimum in ζ production owing to ωH tilting between tshift = −200 and −50 s is associated with increases in |ωH| (Fig. 5d), increasing horizontal gradients of vertical velocity (Fig. 5e), increasing baroclinic generation of ωH (Fig. 5f), and tilting of ζ into ωH plus horizontal stretching of ωH (Fig. 5g). Between tshift = −100 and −50 s, baroclinic generation is the dominant ωH production term at more than 2 times larger than the production of ωH via the sum of tilting of ζ and horizontal stretching of ωH (Fig. 5g).
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 = 100 m.
Citation: Journal of the Atmospheric Sciences 71, 3; 10.1175/JAS-D-13-0219.1
Between tshift = −50 and 0 s, ζ increases toward zero in both the TOR and NON composites (Fig. 5a). This increase is associated with increases in tilting of ωH and positive ζ stretching (Figs. 5b,c). If ζ is negative (and decreasing in magnitude) and stretching of ζ is positive, then 
As tshift approaches zero, the differences in vorticity magnitude and vorticity production between the two composites become smaller. However, both composites show strong increases in |ωH| and the production of ωH (Figs. 5d,g). Also, note that the maximum in baroclinic generation of ωH in both composites (Fig. 5f) immediately precedes the sharp increase in |ωH| (Fig. 5d) and the fivefold increase in production of ωH via the tilting of ζ into ωH and stretching of ωH (Fig. 5g).
As the parcels slowly descend below z = 100 m between tshift = 0 and +50 s, ζ continues increasing (but remains negative and close to zero) in both the TOR and NON composites, with the values being very similar. Stretching production is positive (Fig. 5c) and tilting production of ζ is positive in both composites (Fig. 5b). Tilting and stretching production of ζ are both larger in TOR. The magnitude of the horizontal vorticity vector |ωH| continues to increase in both the TOR and NON composites (Fig. 5d), but more rapidly in TOR, primarily owing to production of ωH via the tilting of ζ and stretching of ωH (Fig. 5g), which is about 4–5 times larger than baroclinic generation of ωH at this time (Fig. 5f). The production of ωH is separated even further into the stretching of existing ωH and the tilting of ζ into ωH (Fig. 6). The stretching term dominates positive production of ωH at all times analyzed, while the tilting term is negative.
Composite trajectories for the TOR (solid lines) and NON (dashed lines) simulations showing time series of the increase in horizontal vorticity with time due to stretching of existing horizontal vorticity (black lines) and tilting of vertical vorticity into horizontal vorticity (gray lines).
Citation: Journal of the Atmospheric Sciences 71, 3; 10.1175/JAS-D-13-0219.1
At approximately tshift =100 s, differences in ζ production between the TOR and NON composites become larger. Both composites show increases in ζ (Fig. 5a) and its production terms—tilting (Fig. 5b) and stretching (Fig. 5c)—after tshift = 100 s; however, the rate of increase in these fields is much larger in the TOR composite. The larger tilting in the TOR composite is associated with greater ωH (Fig. 5d) and larger horizontal gradients in vertical velocity (Fig. 5e).
Figure 5 illustrates average differences between the TOR and NON simulations but does not show the 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 ζ between the TOR and NON simulations (Fig. 7a). There are also substantial differences in |ωH| (Fig. 7b), the tilting of ωH (Fig. 7c), and the magnitude of horizontal gradients in vertical velocity (Fig. 7d). As the parcels reach z = 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 = 200 s, the differences between the TOR and NON simulations begin to increase, particularly the production of ζ via the tilting of ωH (Fig. 7c), which itself is a function of the horizontal gradients in vertical velocity (Fig. 7d). Also, note that after t = 0 s, the individual TOR simulations show a larger spread in ζ 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).
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.
Citation: Journal of the Atmospheric Sciences 71, 3; 10.1175/JAS-D-13-0219.1
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 = 100 m) with larger |ωH| than the NON simulations. As the parcels then travel toward the near-surface circulation, the TOR parcels experience stronger tilting of ωH into ζ (owing to larger |ωH| and stronger gradients in vertical velocity) and stronger stretching of both ωH and ζ. These results suggest that the low-level updraft is stronger in the TOR simulations.
Adding to this hypothesis, analysis of forward trajectories seeded in the near-surface circulation shows that, on average, parcels in the TOR simulations are lifted to higher altitudes than those in the NON simulations (Figs. 8a,c). The differences become even more apparent when relating trajectory height to environmental LFC height (Figs. 8b,d). Only three (16%) of the TOR cases have an average parcel height that is well below LFC height, while eight (57%) of the NON simulations do. For the soundings used in this study, LFC height is strongly correlated to CIN (not shown).
(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.
Citation: Journal of the Atmospheric Sciences 71, 3; 10.1175/JAS-D-13-0219.1
To determine if the differences in low-level updraft strength between the TOR and NON simulations were related to differences in parcel buoyancy, perturbations of pseudoequivalent potential temperature θep were calculated in a 1 km × 1 km box centered on the location of the tornado in the TOR simulations and on the location of maximum 0–1-km UH in the NON simulations at the trajectory initialization time (Fig. 9). Perturbations are relative to the surface value of θep in the NSE and θep was calculated following Bolton (1980). The results from this analysis show that the majority of the NON simulations had small-magnitude θep deficits (i.e., similar to base state environment) at the time of tornadogenesis failure, whereas many of the TOR simulations had much-larger-magnitude deficits (i.e., much smaller than the base-state environment) at the time of tornadogenesis. This result refutes the notion that updrafts in the NON simulations are weaker because of excessive negative buoyancy of the low-level outflow at the time of tornadogenesis failure. Rather, the NON storms typically have more buoyant outflow surrounding the nontornadic vortex.
Maximum and minimum perturbations of θep 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 × 1 km box centered on the circulation at the time of tornadogenesis or tornadogenesis failure.
Citation: Journal of the Atmospheric Sciences 71, 3; 10.1175/JAS-D-13-0219.1
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 ζ while they descend than do parcels in the NON simulations. It appears that as the parcels in both categories reach the surface, this negative ζ developed during descent is reduced in magnitude via compression while ωH steadily increases. The parcels then travel horizontally and, as they rise, ωH 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 that the TOR simulations have larger horizontal vorticity after they reach the surface—due in part to larger initial (i.e., environmental) horizontal vorticity and also more baroclinic generation—which is tilted in the vertical by stronger low-level updrafts.
Certainly, these variations in vorticity production are due to differences in the initial environments of the TOR and NON simulations. Thompson et al. (2003) showed that two of the most statistically significant differences between the significantly tornadic and nontornadic proximity soundings were mixed-layer CAPE and 0–1-km storm relative helicity (SREH). Thompson et al. (2003) found that both of these quantities were smaller in the nontornadic soundings. The same is true for the subset of soundings used in this study, as the soundings come from Thompson et al. (2003), albeit with substantially less overlap (Fig. 10). Nearly every TOR simulation had larger CAPE than the NON simulations (Fig. 10a). Thus, it should not be surprising that the horizontal gradients of vertical velocity were larger in the TOR simulations, since CAPE is proportional to vertical velocity (e.g., Weisman and Klemp 1982). Additionally, the NON simulations had larger-magnitude CIN (Fig. 10b), which has been shown to be able to reduce the strength of the low-level updraft and downdraft (Naylor et al. 2012a).
Box-and-whisker plots of (a) mixed-layer CAPE, (b) mixed-layer CIN, and (c) 0–1-km SREH from the initial soundings used in the TOR and NON simulations. CAPE and CIN are calculated using a 500-m mixed-layer parcel and the virtual temperature correction from Doswell and Rasmussen (1994). Storm motion in SREH calculations follows Bunkers et al. (2000).
Citation: Journal of the Atmospheric Sciences 71, 3; 10.1175/JAS-D-13-0219.1
The discrepancies in CAPE and CIN between the TOR and NON simulations are also likely to influence outflow thermodynamics. Numerous studies have suggested that the cold pools in nontornadic supercells are more negatively buoyant (i.e., larger-magnitude θep deficits) than tornadic supercells. However, the results in section 3 show that the largest-magnitude θep deficits actually occurred in the TOR simulations. Since CAPE is substantially larger in the TOR simulations, it seems reasonable to expect that these simulations will also have stronger downdrafts (e.g., Srivastava 1987) and more precipitation production (e.g., Weisman and Klemp 1982)—hence, more evaporational cooling and melting. Additionally, the NON simulations have more CIN on average, which has been shown by Naylor et al. (2012a) to reduce θep deficits in the cold pool.
There are several possible reasons why the cold-pool characteristics of these simulations, and the associated tornado behavior, seemingly disagree with past studies. Markowski et al. (2002)—the first study to link tornadogenesis to cold-pool characteristics—showed that the largest differences in cold pools are between significantly tornadic and nontornadic supercell, whereas in this current study, no distinction is made between weak tornadoes and significant tornadoes. However, Naylor and Gilmore (2012b) did show that many of the TOR simulations presented in this current study do produce long-lived tornadoes or tornado families. Alternatively, 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 θep in and around the low-level mesocyclone than the subsequent tornadic mesocyclone. Marquis et al. (2012) concluded that a cold, secondary rear-flank downdraft (RFD) surge assisted with tornado maintenance by enhancing the baroclinic generation of horizontal vorticity. Straka et al. (2007) and Markowski et al. (2008) have also discussed the possible importance of baroclinic vorticity generation in parcels near the rear of the storm, 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 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 size distributions have large spatial variability in and around the hook echo of supercells, including regions dominated by large raindrops. Such distributions are more common in storms occurring in environments with large SREH (Kumjian and Ryzhkov 2008, 2009), which would make them more likely in tornadic supercells than nontornadic. However, this type of drop size distribution is not possible with the simple microphysics scheme used in this study herein. The single-moment scheme used here resets the drop size distribution to an inverse exponential form after each time step. This results in the artificial insertion of numerous small raindrops, which easily evaporate (e.g., Dawson et al. 2010). This added evaporation might enhance downdrafts and baroclinic vorticity generation, and bring lower-θep air to the surface than would otherwise have occurred.
It seems that both barotropically and baroclinically generated horizontal vorticity were important in the TOR simulations. The larger barotropic vorticity in these cases (i.e., larger SREH; Fig. 10c) not only results in larger initial vorticity along the trajectories, but it should also produce a larger vertical pressure gradient force that strengthens low-level updrafts (e.g., Rotunno and Klemp 1982; Brooks and Wilhelmson 1993; McCaul and Weisman 1996, 2001)—thus enhancing horizontal gradients of vertical velocity that influence stretching and tilting. However, based on the analysis presented, it is unclear whether the differences in horizontal gradients of vertical velocity between the TOR and NON simulations are primarily due to the differences in buoyancy (i.e., CAPE and CIN) or the shear-induced low-level vertical pressure gradient force (i.e., related to SREH). A pressure decomposition analysis would certainly shed light on this issue and is planned for a future study.
The larger barotropic vorticity in the TOR simulations may also explain differences in negative ζ production between descending parcels in the TOR and NON simulations. Davies-Jones and Brooks (1993) state that tilting of horizontal vorticity produces downdrafts with anticyclonic vorticity (i.e., negative ζ) when the horizontal vorticity is purely streamwise and zero net ζ when the flow is purely crosswise, owing to symmetry. Although Davies–Jones and Brooks only discuss these two extremes, it seems reasonable that there is a continual increase in net anticyclonic vorticity production as the flow becomes more streamwise—which is proportional to SREH. In fact, Fig. 11 does indicate a somewhat linear association between SREH and negative ζ in descending parcels. There are, however, numerous points that do not follow a simple linear fit, likely because the magnitude of vertical vorticity in descending parcels also depends on the amount of vorticity stretching that occurs, which itself is related to other environmental parameters such as CAPE, precipitable water, and possibly CIN. Despite the outliers, the larger SREH in the TOR simulations seems to result in larger negative ζ as the parcels descend, which then tilts into the horizontal as it reaches the surface and increases the magnitude of horizontal vorticity.
Scatterplot of 0–1-km SREH vs average minimum vertical vorticity in descending parcels from the TOR (circles) and NON (crosses) simulations.
Citation: Journal of the Atmospheric Sciences 71, 3; 10.1175/JAS-D-13-0219.1
There is also evidence suggesting that baroclinic generation is extremely important to the evolution of vorticity in the descending parcels. Peaks in baroclinic generation occurred in conjunction with peaks in tilting of ζ and increases in horizontal vorticity in the descending parcels of both the TOR and NON simulations. In addition, baroclinic generation was an order of magnitude larger than the production of horizontal vorticity via tilting–stretching throughout a large portion of parcel descent. However, after reaching ground, horizontal stretching of ωH becomes much more important than baroclinic generation.
Overall, vorticity production in the TOR simulations agrees quite well with previous studies. Parcels that descend from aloft primarily generate negative vertical vorticity as they descend (e.g., Brandes 1984; Davies-Jones and Brooks 1993; WW95; A99). During descent, tilting is negative, while stretching is positive (WW95; A99). As parcels approach the surface, baroclinic generation of horizontal vorticity increases (Davies-Jones and Brooks 1993; WW95; A99; Straka et al. 2007; Markowski et al. 2008). Only after the parcels reach the surface do they acquire positive ζ (in agreement with WW95). One impact of the current study is the reproducibility of these prior results across a wide variety of soundings (with capping inversions) and with the same model setup and the contrast in behavior between the TOR environments against the NON environments.
Finally, we note that differences between the TOR and NON environments in this study herein agree qualitatively with the findings from previous supercell climatology studies (e.g., CAPE and SREH are good discriminators between tornadic and nontornadic environments; Rasmussen and Blanchard 1998; Thompson et al. 2003). However, those studies found large overlap in the CAPE and SREH values typical of tornadic and nontornadic storms, whereas the study herein found very little overlap (cf. Fig. 10). This difference may reveal the inherent difficulty in forecasting tornadogenesis in real-world storms. That is, aspects not considered here that are intrinsically included in observational climatology studies may also be influential (e.g., horizontal boundaries and/or gradients of CAPE and shear, varying surface roughness length and land use types, geographically dependent aerosol distributions, etc.). However, when these factors are removed—as was done in the current study—the impact of the NSE becomes much clearer.
5. Summary and conclusions
In the study herein, an idealized cloud model was used to investigate storm-scale mechanisms important for tornadogenesis and tornadogenesis failure. Simulations were initialized with supercell proximity soundings associated with significantly tornadic (≥F2 or lasting longer than 5 min) and nontornadic supercells. These soundings were taken from the RUC-2 model by Thompson et al. (2003, 2007). A subset of the tornadic and nontornadic RUC-2 soundings was simulated at 100-m resolution in order to compare vorticity production terms in simulations with tornadic and nontornadic supercells. Then, 14 nontornadic supercells were compared to 19 tornadic simulations. In comparing the tornadic and nontornadic simulations, the following points are summarized:
Vertical vorticity production in rising parcels was similar. The tornadic simulations experienced larger vertical vorticity production via stretching of horizontal vorticity, with the largest differences occurring less than 60 s prior to tornadogenesis or tornadogenesis failure. Thus, the larger stretching in the tornadic simulations is likely because tornadogenesis is imminent.
Vertical vorticity production in descending parcels was noticeably different. Tilting of horizontal vorticity was much larger in magnitude in the tornadic simulations, with stronger negative tilting occurring during descent and stronger positive tilting as the downdraft trajectories approached the circulation.
During parcel descent, peaks in anticyclonic vorticity occurred in association with peaks in negative tilting, positive stretching, and baroclinic generation, all of which were larger in the tornadic simulations.
After the descending parcels reach the surface, the larger tilting of horizontal vorticity in the tornadic simulations can be attributed to larger horizontal vorticity and stronger horizontal gradients of vertical velocity.
Vertical vorticity became positive in descending parcels only after they reached the surface (on average). The increase in vertical vorticity after descent was stronger in the tornadic simulations, owing to larger horizontal vorticity and stronger horizontal gradients in vertical velocity.
On average, forward-integrated trajectories reached higher average altitudes in the tornadic simulations. In most of the nontornadic simulations, the trajectories were, on average, unable to reach the environmental LFC height.
The strongest cold pools in the vicinity of the low-level mesocyclone were associated with the tornadic simulations. Most of the nontornadic simulations had cold pools with small deficits of pseudoequivalent potential temperature.
In conclusion, the largest differences between the tornadic and nontornadic supercells are related to vorticity production in parcels that descend from aloft. The tornadic (nontornadic) simulations produce more (less) anticyclonic vertical vorticity during parcel descent, which is generated by larger (smaller) tilting of horizontal vorticity and stretching of existing vertical vorticity. As the parcels reach the surface, they are tilted back into the horizontal. After the parcels reach the surface, the magnitude of the horizontal vorticity is larger (smaller) in the tornadic (nontornadic) simulations owing to the larger (smaller) initial barotropic horizontal vorticity, larger (smaller) baroclinic generation during descent, and larger (smaller) stretching of horizontal vorticity. As the parcels travel horizontally toward the low-level circulation, this horizontal vorticity is then tilted into the vertical direction and stretched, with both of these processes being larger in the tornadic simulations because of stronger updrafts. The stronger (weaker) updrafts in the tornadic (nontornadic) simulations appear to be a result of larger (smaller) values of environmental CAPE and 0–1-km SREH as well as smaller (larger) CIN and not the buoyancy of the parcels near ground that are entering the circulation at the time of tornadogenesis (tornadogenesis failure). Tornadogenesis failure in the NON cases in these simulations is due to weaker overall vorticity production (compared to the TOR cases).
Future work will involve investigating the processes responsible for tornado maintenance and demise by analyzing vorticity budgets and thermodynamics for the trajectories arriving in the simulated tornadoes throughout their lifetime. In addition, several of the tornadic simulations produced cyclic tornadogenesis. These secondary tornadoes could be analyzed to determine if the processes related to initial tornadogenesis differ from subsequent tornadogenesis events. It would also be interesting to examine the tornadic supercell simulations that resulted from the use of nontornadic RUC-2 soundings and vice versa.
Acknowledgments
This work was supported by NSF Grant AGS-0843269 and completed in partial fulfillment of the Ph.D. dissertation by the first author. Computational resources were provided by the National Institute for Computational Sciences (NICS) through XSEDE Allocation TG-ATM100048. The trajectory code was developed by David Wojtowicz under NSF Grant ATM-92-14098 as modified by Jon Siwek and Stuart Levy at the National Center for Supercomputing Applications (NCSA). Rich Thompson and Roger Edwards provided the RUC-2 sounding database. We thank three anonymous reviewers for their helpful comments in reviewing an earlier version of this work. NorthWest Research Associates provided support to the first author during the revision process.
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Herein, when terms such as “tornado,” “tornadic,” “nontornadic,” “tornadogenesis,” or “tornadogenesis failure” are used to reference phenomena occurring within the hook echoes of simulated supercells, it should be understood that they are used to describe the presence (or lack) of tornado-like vortices in those simulations. These vortices are missing the complete physics that are present in real-world tornadoes (such as centrifuging and frictional interaction with the ground).
Naylor and Gilmore (2012a) found that a nudging duration of 900-s optimized average simulated supercell longevity.
These criteria are consistent with a tornado that is approximated by a Rankine vortex.