1. Introduction
Distinguishing tornadic supercell environments from those associated with nontornadic supercells is among the most daunting challenges currently facing severe storms forecasters. A number of early studies attempted to define the environments capable of supporting tornado-producing thunderstorms, many of which were undoubtedly supercell thunderstorms (e.g., Darkow 1968, 1969; Maddox 1976; Darkow and McCann 1977). This work was followed by studies that investigated differences between the environments that support weak versus strong tornadoes (e.g., Davies-Jones et al. 1990; Davies and Johns 1993; Johns et al. 1993) and, perhaps more importantly, tornadic versus nontornadic supercells (e.g., Rasmussen and Wilhelmson 1983; Brooks et al. 1994a; Davies 1998, 2002; Rasmussen and Blanchard 1998; Markowski et al. 1998; Thompson 1998; Edwards and Thompson 2000; Thompson and Edwards 2000; Brooks and Craven 2002; Craven et al. 2002). The sheer abundance of studies cited above in just the last few years is a testament to the considerable attention given to the problem of discriminating between tornadic and nontornadic supercell environments.
In this note we present the results of a study of characteristics of tornadic and nontornadic supercell hodographs derived from 40-km Rapid Update Cycle (RUC; Benjamin et al. 2002) analyses.1 One motivation for this study is the relatively recent availability and widespread use of hourly conditions from analysis systems that initialize numerical weather prediction models (e.g., the RUC, which has been used herein). Although analyses are sensitive to the accuracy of short-term forecasts made by a numerical model, there are some advantages to using model analysis data. The primary advantage is the superior temporal and spatial resolution compared to that of the upper-air observing network. Furthermore, storm-scale modifications of the model vertical wind profiles by the supercells (Brooks et al. 1994a; Weisman et al. 1998) are expected to be less significant in an operational model that does not explicitly resolve convection.2 Thus, the troublesome issue of defining what constitutes a suitable “proximity” sounding (Brooks et al. 1994a) is somewhat circumvented. The availability of thermodynamic and wind profile information at a large number of grid points and times also facilitates the assembly of a large number of cases in far less time than if only observed soundings within relatively close proximity to an event were acceptable. The fact that a large sample can be acquired within only a few years (versus decades to obtain a sample of observed proximity soundings having similar size) has the additional advantage that the results are largely immune to the variations in severe weather reporting present on larger timescales [e.g., inconsistent tornado intensity ratings (Brooks and Craven 2002) and a steady rise in the annual number of tornado reports since World War II (Bruening et al. 2002)].
We also are motivated by the need for a comparison of hodograph characteristics between tornadic and nontornadic supercell environments over the entire troposphere. Several investigators have examined mean wind profiles associated with tornadic supercells (e.g., Darkow 1969; Maddox 1976; Darkow and McCann 1977; Kerr and Darkow 1996),3 but these have not yet been systematically compared to mean wind profiles associated with nontornadic supercells (the null events). Some other studies have compared tornadic and nontornadic wind profile characteristics (e.g., Brooks et al. 1994a; Rasmussen and Blanchard 1998; Thompson 1998), but only at a few levels, and only for a relatively limited number of parameters.
The present study examines vertical profiles of wind speed, wind shear, horizontal vorticity orientation, helicity, and hodograph shape from the surface to the upper troposphere, based on a relatively large sample of both tornadic and nontornadic supercell cases obtained during a 3-yr period. It will be shown that vertical wind profile characteristics differ most noticeably in the lowest 1 km. Furthermore, differences between the vertical wind profiles of tornadic and nontornadic supercells above 1 km are generally not statistically significant, and where they are, the differences are probably too small to be reliably detected by the present sounding and wind profiler network.
2. Data and analysis methods
Vertical wind profiles derived from hourly RUC analyses were obtained near 413 supercells nationwide from 1999 to 2001 (Thompson et al. 2003). Supercells were defined as storms displaying one or more characteristic radar reflectivity structures [e.g., hook echoes, inflow notches (Lemon 1977)] and azimuthal wind shear4 exceeding 2 × 10−3 s−1 for at least 30 min. Wind profiles were interpolated to the location of the surface observing station nearest to the event at the hour nearest to the event.5 All soundings were within 30 min and 40 km of the supercells. Attempts were made to exclude supercells processing potentially buoyant air from above the boundary layer (“elevated supercells”) by requiring that model proximity soundings have surface-based convective available potential energy (CAPE). Additional details about how soundings were chosen for each supercell event are described by Thompson et al. (2003).
Only right-moving (cyclonically rotating) supercells were included in the analysis. Supercells were classified as nontornadic (NT; 215 cases), “weakly tornadic” (WT; associated with F0–F1 tornadoes; 144 cases), and “significantly tornadic” (ST; associated with F2–F5 tornadoes; 54 cases). For each class of supercells, vertical profiles of mean and standard deviation values for a number of parameters related to environmental wind speed and wind shear were computed. No smoothing was applied to the vertical wind profiles, nor to the profiles of derived parameters. Vertical derivatives were estimated using second-order, centered finite differences, except at the ground. All variable definitions are consistent with those used by Davies-Jones (1984). Their relationship to the hodograph can be viewed in Fig. 1.
Figures 2 and 3 contain profiles of the zonal (u) and meridional (υ) wind components for each of the three supercell classes. Figures 4–7 contain profiles of ground-relative wind speed |v|, storm-relative wind speed |v − c|, vertical wind shear magnitude |dv/dz|, and negative hodograph curvature −dϕ/dz (positive values indicate clockwise turning of the shear vector, dv/dz), respectively, where v(z) = [u(z), υ(z)] is the environmental horizontal wind vector, c is the observed storm motion, and ϕ(z) describes the orientation of the wind shear.
Figures 8–11 contain profiles of crosswise vorticity ωc (=d|v − c|/dz), streamwise vorticity ωs (=−|v − c|dψ/dz), ground-relative helicity (GRH) density v · ω, and storm-relative helicity (SRH) density (v − c) · ω, respectively. The GRH (SRH) density is the integrand of GRH (SRH); thus, the area to the left of the v · ω [(v − c) · ω] profiles represents GRH (SRH), and the v · ω[(v − c) · ω] profiles provide information about the vertical distribution of GRH (SRH).6
Two-sample t tests were conducted to obtain a measure of the robustness of the differences between the mean vertical profiles of the various parameters. Light gray shading in Figs. 2–11 denotes layers in which the mean ST value differs from the NT value at the 95% significance level. Dark gray shading denotes layers in which the mean ST value differs from the NT and WT value at the 95% significance level.
Mean hodographs were constructed for each of the three classes of supercells (Fig. 12), using the data displayed in Figs. 2 and 3. No transformations of the hodographs were performed prior to averaging, as has been done in some past studies (e.g., Darkow and McCann 1977; Kerr and Darkow 1996). Other calculations were completed (not shown) in which, prior to averaging the hodographs, the 0–6-km mean wind was removed, followed by a rotation of the hodograph so that the bulk Richardson number shear vector (the vector difference between the mean winds in the 0–500-m and 0–6-km layers) was oriented from west to east. These results did not differ significantly from those presented herein, largely due to the large-scale vertical wind shear being approximately westerly in the majority of supercell environments.
3. Results
In this section, some of the interesting differences and similarities among the ST, WT, and NT supercell classes are summarized.
Ground-relative wind speeds are larger in ST environments than in WT and NT environments. On average, speeds in ST environments are 5 (4) m s−1 larger than speeds in NT (WT) environments (Fig. 4). These differences are considerably larger and more statistically robust in the lower to middle troposphere than the storm-relative wind speed differences, to be discussed below. We speculate that the larger ground-relative winds may give rise to larger low-level vertical wind shear due to friction near the ground (simulations conducted with a free-slip lower boundary yield identical results as the hodograph is translated with respect to the origin). Or perhaps larger ground-relative wind speeds imply stronger larger-scale dynamical forcing, and something about this type of atmosphere (yet undiscovered) is favorable for ST supercells. Strong tornadoes have long been associated with anomalously fast low-level and upper-level jets and large surface pressure gradients (Johns and Doswell 1992). Furthermore, we find it interesting that the υ wind component is decidely larger in ST environments (Fig. 3) compared to WT and especially NT environments, on average. This may imply that ST environments tend to be associated with more amplified synoptic-scale (short wave) troughs compared to NT and WT environments, which also is consistent with the aforementioned observation that strong tornadoes have long been associated with relatively strong synoptic-scale dynamics.
Storm-relative wind speeds are similar through the lower to middle troposphere in ST, WT, and NT environments. Storm-relative wind speed differences were <2 m s−1 below approximately 10 km, above which storm-relative wind speeds were 2–4 m s−1 weaker in ST environments compared to NT environments (Fig. 5). Although the storm-relative wind differences between NT and ST environments are statistically significant in the 2.7–5.7-km layer and above 10.4 km, it is believed that the differences are not what could be termed meteorologically significant; that is, differences are less than what could be expected to be detected observationally in a real-time setting (storm motion estimates alone probably are associated with >2 m s−1 velocity uncertainty, given the range of motions typically obtained depending on whether the echo centroid, mesocyclone, or bounded weak-echo region is tracked). Thompson (1998) found, using Eta Model analyses, that surface storm-relative wind speeds were similar (within ∼2 m s−1), on average, in nontornadic and tornadic supercell environments, consistent with the results obtained herein. However, he also found that the storm-relative wind speeds were similar at 250 mb, and at 500 mb, more significant differences (∼4 m s−1) between nontornadic and tornadic supercell environments were obtained. These middle- to upper-tropospheric differences, compared to the present study, might be reconciled by noting the smaller sample used by Thompson (1998), as well as the relatively large standard deviations of 500- and 250-mb storm-relative wind speeds (>4 and >8 m s−1, respectively) in tornadic and nontornadic environments. On the other hand, the simulation findings of Brooks et al. (1994b) are more difficult to reconcile with the midlevel storm-relative flow similarities obtained herein (Fig. 5), if one assumes that the likelihood of a tornado being produced by a supercell generally increases with the intensity of mesocyclone rotation near the surface. Brooks et al. found that the strength of midlevel storm-relative winds (which they altered by modifying the midlevel vertical wind shear) had a substantial influence on the distribution of precipitation within supercells, the development of low-level temperature gradients, and ultimately the production of rotation near the surface. Based on their findings, one might have expected that more significant differences in midlevel storm-relative wind speeds would have been obtained among the ST, WT, and NT supercell classes.
Vertical wind shear magnitude, streamwise vorticity, and SRH density (and therefore its integral SRH) in ST environments are significantly larger than in WT and NT environments in the lowest 1 km. The differences are largest at the surface, and in the lowest 500 m, these parameters are twice as large in ST environments than in both WT and NT environments (Figs. 6, 9, and 11). Above 1 km, these parameters generally are not significantly different. These results are consistent with the Markowski et al. (1998) findings of substantially larger SRH in the lowest 1 km in tornadic versus nontornadic supercell environments. We note, however, that although the 0–1-km SRH contains the differences, the 0–3-km SRH (Davies-Jones et al. 1990) does not mask them; that is, the SRH in the 1–3-km layer is similar in all supercell environments.7 McCaul and Weisman (2001) also arrived at a similar conclusion regarding the importance of the vertical wind shear near the surface. Furthermore, GRH density (and therefore its integral GRH) is substantially larger in ST cases compared to WT and NT cases in roughly the 500–1500-m layer (Fig. 10), perhaps implying stronger warm advection in ST environments (this depends on the degree of ageostrophy in ST versus WT/NT environments). These differences, along with the differences in |dv/dz| in the lowest 1 km, are perhaps especially noteworthy because they are insensitive to storm motion.
No robust differences in hodograph curvature exist among the three supercell classes. Statistically significant differences (which are arguably meteorologically insignificant, especially upon viewing Fig. 12) between ST and NT curvature exist only in a couple of shallow layers (both are <300 m deep) (Fig. 7). Note that −dϕ/dz has particularly large standard deviations reflecting the fact that it is related to a second derivative of the vertical wind profile and hence is error prone.
The differences between WT and NT environments typically are quite small and generally are not statistically significant. For example, |dv/dz| differences between NT and WT supercells are not statistically significant at any level. (Significance levels between NT and WT supercells are not indicated with shading in Figs. 4–11, in order to make the figures more readable.) This perhaps is not terribly surprising; even on storm scales observed during recent field experiments using mobile in situ sensors and radar, many kinematic traits of WT and NT supercells have been virtually indistinguishable (e.g., Blanchard and Straka 1998; Trapp 1999; Wakimoto and Cai 2000; Markowski et al. 2002). In layers in which statistically significant differences in hodograph parameters are observed between WT and NT environments, the differences between the WT and NT profiles usually are smaller than the differences between ST and WT profiles.
The shapes of the mean hodographs are virtually indistinguishable above 1 km. The most obvious hodograph differences (Fig. 12) are the locations with respect to the origin (a manifestation of the |v| differences) and the length of the hodograph below 1 km, which leads to the |dv/dz|, ωs, and (v − c) · ω differences noted above. The storm motions with respect to the hodographs only differ slightly, with the differences almost entirely due to the hodograph differences below 1 km [i.e., if one uses a Galilean invariant empirical storm motion predictor, such as the Rasmussen and Blanchard (1998) or Bunkers et al. (2000) techniques, the storm motions are equally well anticipated for all three mean hodographs for most practical purposes].
4. Final remarks
In summary, ST environments are associated with larger ground-relative wind speeds in the lower and middle troposphere, vertical wind shear in the lowest 1 km, and streamwise vorticity and SRH in the lowest 1 km compared to WT and NT environments, on average. Vertical wind profiles associated with ST, WT, and NT environments, on average, are relatively similar in terms of storm-relative wind speeds in the lower and middle troposphere, hodograph curvature at most levels, and crosswise vorticity at most levels.
The reader should be cautioned that there is considerable variability in the vertical profiles of the hodograph parameters. Standard deviations of many of the parameters are nearly as large as the parameters themselves.
Some remaining questions to ponder include the following:
- To what extent, if any, is the finding of vertical wind shear and streamwise vorticity differences in the lowest 1 km between ST and NT/WT environments due to the interaction of ST storms with low-level baroclinic boundaries?
- Could there be any relationship between the observed wind profile differences and rear-flank downdraft thermodynamic properties, which recently have been found to differ between tornadic and nontornadic supercells?
- When wind profile characteristics such as those investigated herein are combined with thermodynamic profile characteristics, how much improvement can be gained in our ability to distinguish between supercell types? Which combinations of parameters are best?
- Should storm-relative wind speeds continue to be assessed in an operational setting to discriminate between tornadic and nontornadic supercells?8
Given the wind profile similarities above 1 km, there is little wonder why operationally discriminating between tornadic and nontornadic environments has been so difficult. It is believed that it may be worthwhile to develop new technologies capable of better sampling the vertical wind profile in the lowest 500–1000 m, and with much improved horizontal resolution compared to the current wind profiler demonstration network. We also believe it would be worthwhile for future numerical simulation studies to concentrate on the effects of hodograph differences in this layer, perhaps in a manner similar to that of Wicker (1996), with a realistic inclusion of surface drag. The majority of past parameter space studies probably did not have adequate vertical resolution near the ground (two to three grid points in the lowest kilometer) to explore the sensitivity of storms to near-ground wind profile changes.
We are thankful for comments provided by Mr. Steve Weiss, Mr. Barry Schwartz, Mr. Matt Bunkers, Dr. Brain Klimowski, Dr. Bob Davies-Jones, Dr. Erik Rasmussen, Dr. Jerry Straka, Dr. Yvette Richardson, and an anonymous reviewer.
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Diagram of a hodograph [u(z), υ(z)] depicting the storm motion vector c, storm-relative wind vector v − c, vertical wind shear vector dv/dz, environmental horizontal vorticity vector ω, and the relationships between v − c and ψ, and dv/dz and ϕ. The vectors p(z) = (cosψ, sinψ) and q(z) = (−sinψ, cosψ) are unit vectors parallel and normal to the left of the storm-relative wind, respectively, and ψ(z) describes the orientation of the storm-relative wind. Adapted from Davies-Jones (1984).
Citation: Weather and Forecasting 18, 6; 10.1175/1520-0434(2003)018<1262:COVWPN>2.0.CO;2
(left) Mean vertical profiles of zonal wind speed, u. Height above ground level is in km on the ordinate, and abscissa units are m s−1. Solid profiles are associated with ST environments, dashed profiles are associated with WT environments, and dotted profiles are associated with NT environments. Light gray shading denotes layers in which the mean ST value differs from the NT value at the 95% significance level. Dark gray shading denotes layers in which the mean ST value differs from the NT and WT values at the 95% significance level. (right) Std dev profiles for the parameters displayed on the left. Units are the same as on the left, as are the lines used to denote supercell type.
Citation: Weather and Forecasting 18, 6; 10.1175/1520-0434(2003)018<1262:COVWPN>2.0.CO;2
As in Fig. 2 except that (left) mean vertical profiles of meridional wind speed, υ, and (right) its std dev are displayed.
Citation: Weather and Forecasting 18, 6; 10.1175/1520-0434(2003)018<1262:COVWPN>2.0.CO;2
As in Fig. 2 except that (left) mean vertical profiles of ground-relative wind speed, |v|, and (right) its std dev are displayed.
Citation: Weather and Forecasting 18, 6; 10.1175/1520-0434(2003)018<1262:COVWPN>2.0.CO;2
As in Fig. 2 except that (left) mean vertical profiles of storm-relative wind speed, |v − c|, and (right) its std dev are displayed.
Citation: Weather and Forecasting 18, 6; 10.1175/1520-0434(2003)018<1262:COVWPN>2.0.CO;2
As in Fig. 2 except that (left) mean vertical profiles of vertical wind shear magnitude, |dv/dz|, and (right) its std dev are displayed. Abscissa units are s−1.
Citation: Weather and Forecasting 18, 6; 10.1175/1520-0434(2003)018<1262:COVWPN>2.0.CO;2
As in Fig. 2 except that (left) mean vertical profiles of negative hodograph curvature, −dϕ/dz, and (right) its std dev are displayed. Abscissa units are rad m−1.
Citation: Weather and Forecasting 18, 6; 10.1175/1520-0434(2003)018<1262:COVWPN>2.0.CO;2
As in Fig. 2 except that (left) mean vertical profiles of crosswise vorticity, ωc, and (right) its std dev are displayed. Abscissa units are s−1.
Citation: Weather and Forecasting 18, 6; 10.1175/1520-0434(2003)018<1262:COVWPN>2.0.CO;2
As in Fig. 2 except that (left) mean vertical profiles of streamwise vorticity, ωs, and (right) its std dev are displayed. Abscissa units are s−1.
Citation: Weather and Forecasting 18, 6; 10.1175/1520-0434(2003)018<1262:COVWPN>2.0.CO;2
As in Fig. 2 except that (left) mean vertical profiles of GRH density, v · ω, and (right) its std dev are displayed. Abscissa units are m s−2.
Citation: Weather and Forecasting 18, 6; 10.1175/1520-0434(2003)018<1262:COVWPN>2.0.CO;2
As in Fig. 2 except that (left) mean vertical profiles of SRH density, (v − c) · ω, and (right) its std dev are displayed. Abscissa units are m s−2.
Citation: Weather and Forecasting 18, 6; 10.1175/1520-0434(2003)018<1262:COVWPN>2.0.CO;2
Mean hodographs for significantly tornadic, weakly tornadic, and nontornadic environments (solid, dashed, and dotted lines are used as in Figs. 2–11). Markings are placed along the traces at 1-km intervals. The circled S, W, and N indicate the mean storm motions for the ST, WT, and NT supercell classes, respectively. Units on the speed rings are m s−1.
Citation: Weather and Forecasting 18, 6; 10.1175/1520-0434(2003)018<1262:COVWPN>2.0.CO;2
A companion paper in this issue by Thompson et al. (2003) examines aspects of the thermodynamic profiles.
None of the soundings in the dataset were obtained at grid points at which the RUC convective parameterization was activated.
The datasets used by these investigators probably included some tornadoes not associated with supercell thunderstorms, although it is probably safe to assume that tornadoes associated with supercell thunderstorms dominated their climatologies.
This shear criterion is similar to that used by the National Severe Storms Laboratory's Mesocyclone Detection Algorithm (Stumpf et al. 1998).
Although interpolation was not required for the study, the vagaries of the software used to archive the model soundings facilitated the collection of profiles that had been bilinearly interpolated to a surface observing station.
The GRH associated with the geostrophic wind is proportional to temperature advection.
One of the reasons Davies-Jones et al. (1990) chose the 0–3-km layer for SRH calculations was the scarcity of low-level data points from wind profilers and soundings.
Clearly we do not advocate neglecting low-level storm-relative wind velocities, because low-level streamwise vorticity and SRH are sensitive to storm-relative wind direction changes with height.
