1. Introduction

Typically, only standard, 12-hourly National Weather Service (NWS) rawinsonde, 5-min NWS WSR-88D Doppler radar velocity azimuth displays (VAD), and 6-min to hourly profiler upper-air data are available to evaluate wind-derived parameters for severe storm forecasts. Unfortunately, profiler data generally are poor quality in the lower levels [0–1.5 km above ground level (AGL); Richardson 1993; D. Burgess and F. Carr 1997, personal communication] and VAD data are poor in the upper levels (D. Burgess and D. Zrnić 1997, personal communication), which limits use of these platforms. Moreover, rawinsondes also have to be interpreted with care as they may travel more than 100 km before reaching the tropopause.

In forecasting the most severe convective storms, which also tend to be those that are long lasting and rotating, parameters such as the bulk Richardson number (Weisman and Klemp 1982, 1984), 0–4-km shear (Rasmussen and Wilhelmson 1983), and storm-relative environmental helicity (SREH, described in the next section; Davies-Jones 1984, 1993; Lilly 1986a,b; Davies-Jones et al. 1990; Davies and Johns 1993; Johns et al. 1993) have been used. These parameters gained acceptance in practical applications in part through theoretical (Davies-Jones 1984; Lilly 1986a,b), numerical model (Brooks and Wilhelmson 1990; Brooks et al. 1993; Droegemeier et al. 1993), and observational (Leftwich 1990; Davies and Johns 1993; Johns et al. 1993; Hales and Vescio 1996) studies. Some of these studies demonstrated a high positive correlation between vertical vorticity and updrafts in convective storms occurring in environments with particular wind speed and direction morphology. As is well documented throughout the literature, storms developing in environments with large values of low-level shear and/or SREH are known to have a propensity for violent weather phenomena such as large hail, strong winds, and tornadoes.

Davies-Jones et al. (1990) and Davies-Jones (1993) showed changes of SREH by an order of magnitude on spatial scales of less than 100 km and temporal scales of less than 3 h (Fig. 1; from Davies-Jones 1993) in severe convective storm environments. Davies-Jones further suggested that rapid local changes in SREH could make tornado forecasting difficult. It is important to note that significant tornadoes have been highly associated with large values of resolved helicity (Rasmussen 1998, manuscript submitted to Wea. Forecasting) as shown in Table 1 (from Rasmussen 1998, manuscript submitted to Wea. Forecasting). This has also been shown in other studies [e.g., Davies-Jones 1993; Davies and Johns 1993 and Johns et al. 1993; though it is not known if this is always the case, such as when convective available potential energy (CAPE) is very large; e.g., CAPE > 4000 J kg⁻¹]. It also is important to note that it is possible that only certain supercells in a given environment become tornadic by moving into regions with large values of helicity that might be unresolved owing to large variability in helicity (Richardson et al. 1998, manuscript submitted to Mon. Wea. Rev.) and as documented herein and by Davies-Jones et al. (1990) and Davies-Jones (1993). In other studies, Rasmussen and Wilhelmson (1983) and Maddox (1993) noted diurnal variations of 0–4-km shear and SREH, respectively, over the Great Plains of the United States. Maddox further suggested that the variations might be associated with diurnal oscillations of the low-level jet, which might play an important role in nocturnal tornado outbreaks. Finally, Brooks et al. (1994) demonstrated dramatic changes in SREH in the near environments of storms and that these owed to changes caused by inflow enhancement by the storms.

During 1994 and 1995 the Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX; Rasmussen et al. 1994) took place over the south-central Plains with the goal of gaining a better understanding of tornadoes and their near environments. Additional upper-air information was available from nine Cross-chain Loran Atmospheric Sounding System-type (CLASS; Lauritsen et al. 1987; Rust et al. 1990) sounding facilities (Rasmussen et al. 1994) and 3-hourly rawinsondes from selected NWS sites. In this paper it is shown that the inclusion of additional upper-air data collected by VORTEX in the analyses of the regular NWS upper-air data indicates more variability in helicity (in at least the tornadic environments investigated thus far) from that possibly detectable from the regularly available NWS upper-air wind data. Moreover, the results demonstrate that helicity varies over spatial and temporal scales that are essentially impossible to feasibly measure (and probably to numerically predict) with current technology. It is not known yet if this variability exists in more quiescent atmospheres or is found more often in association with atmospheres supportive of severe storms. Given this, the understanding of the possible causes and effects of this variability is difficult to define and therefore the severe weather forecast problem is probably compounded. Note that it is not the intent of this paper to explain these causes and effects in the cases studied, since the data collected thus far are too limited to draw firm conclusions, as has been the case for most previous similar studies.

In the past it has been common to use the term SREH. The use of the word “environment” makes the definition of SREH ambiguous, thus the term storm-relative helicity (SRH) is adopted, in general, hereafter. In this paper a description of SRH is presented in section 2; four case studies are presented in section 3 to demonstrate SRH variability; a discussion and summary of the present work and a mention of possible future work are presented in section 4.

2. Storm-relative helicity

The essence of SRH is described in some detail below. In addition the magnitude of the terms describing the generation of streamwise vorticity (from which SRH is derived) are put into perspective before describing the case studies. Helicity is a quantity derived from the streamwise vorticity (vorticity vector aligned with the velocity vector; Davies-Jones 1984). In a storm-relative framework, storm-relative helicity is

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where v − c is the storm-relative wind (environmental wind vector v minus the storm motion vector c), and ω_h is the horizontal vorticity vector defined here as

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with u, υ, and w the wind components and x, y, and z the components of the Cartesian coordinate system.

Assuming we are in the low levels (0–3 km) of an environment that would support rotating storms, a typical value that might be expected for Δw/Δx or Δw/Δy might be 1 m s⁻¹/10⁴ m or about 10⁻⁴ s⁻¹ (conceivably this could be as large as 10⁻³ s⁻¹ at a boundary). In comparison, Δu/Δz or Δυ/Δz might be 10 m s⁻¹/10³ m or about 10⁻² s⁻¹ or possibly larger. Thus, the equation for ω_h probably can be approximated as

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which shows that the horizontal vorticity vector is dominated by the vertical shear of the horizontal wind. The streamwise horizontal vorticity is defined as (v − c)·ω_h. The integral in (1) is over the storm inflow depth H, often chosen to be 3 km AGL, approximately the level of free convection (Davies-Jones 1984). (Hereafter 0–3-km helicity is implied everywhere helicity is discussed.) SRH can be graphically computed as minus twice the area swept out by the storm-relative wind between 0 and H on a hodograph (Davies-Jones et al. 1990). By standard geometric convention, the area is negative (positive) if swept out clockwise (counterclockwise).

Storm-relative helicity is defined by the vertical integral of the dot product of the storm-relative wind and streamwise vorticity. The streamwise vorticity equation in natural coordinates can be written as

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where ω_s is the streamwise component of vorticity; ω_n is the crosswise component of vorticity; ω_z is the vertical component of vorticity; υ is the flow along a streamline (scale defined by notation U); B = gΔθ_υ/θ_υ is buoyancy [where B is buoyancy, g is gravity, θ_υ is virtual potential temperature (no precipitation), and Δθ_υ is virtual potential temperature perturbation]; s is the streamwise direction, n is the crosswise (normal, and positive to the left of the flow, by convention) direction (scale of s and n defined by notation L), z is the vertical component (scale defined by notation H); and F is friction (molecular-scale friction is assumed to be negligible). From a scale analysis of this equation, assuming the case of the environment on the storm scale (L = 10⁴ m, H = 10³ m, U = 10 m s⁻¹, Δθ_r = 5°C, ω_s,n = 1.0 × 10⁻² s⁻¹, ω_z = 1.0 × 10⁻³ s⁻¹ to 1.0 × 10⁻⁴ s⁻¹), there is some confidence that dominant production mechanisms for SRH are most likely to be baroclinic generation and horizontal stretching with an order of magnitude of about 10⁻³ s⁻¹. The vertical derivative term is about an order of magnitude smaller. Assuming an eddy mixing coefficient of about 100 m² s⁻¹ in a well-mixed boundary layer, the eddy mixing term is smaller by a magnitude or more than that for the buoyancy and stretching terms. This would permit streamwise vorticity generated by a thermal boundary to exist possibly several hours after the buoyancy gradient dissipated.

The importance of boundaries in the problem described in this paper is baroclinic generation of vorticity related to temperature gradients (e.g., Klemp and Rotunno 1983; Rotunno et al. 1988). As temperature, or more accurately, buoyancy gradients often form in regions with a base motion normal to the gradient vector (i.e., flow parallel to the boundary; e.g., Maddox et al. 1980; Rotunno 1993; Richardson et al. 1998, manuscript submitted to Mon. Wea. Rev.), the baroclinically generated horizontal vorticity usually will be substantially streamwise:

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(as opposed to crosswise). Furthermore, longer residence times of a parcel in a barocline lead to greater amounts of horizontal vorticity. Values of horizontal vorticities associated with boundaries of 10⁻³ s⁻¹–10⁻² s⁻¹ probably are common (e.g., simple scale analysis; using Δθ_υ = 1°C–10°C and L = 10⁴ m, see also Richardson et al. 1998, manuscript submitted to Mon. Wea. Rev.). The boundaries that might be considered include fronts on the synoptic scale or mesoscale, active or decaying thunderstorm outflows, sea breezes or inland sea breezes, or other boundaries (e.g., Purdom 1976, 1993;Maddox et al. 1980; Weaver and Nelson 1982; Rotunno and Klemp 1982; Weisman and Klemp 1984; Klemp and Rotunno 1983; Rotunno et al. 1988; Ziegler et al. 1995)

Finally, SRH may vary substantially near storms owing to the updraft of a storm. The low-level winds may be altered and strengthened as the parcel approaches an updraft that might stretch preexisting horizontal vorticity. The rate at which streamwise horizontal vorticity is increased owing to inflow accelerations/stretching is

View Expanded

where ω_s, υ, and s are as defined before. For a parcel that accelerates 10 m s⁻¹ over a 40 km distance toward an updraft, ω_s can double in 45 min. According to Davies-Jones and Brooks (1993), cloud model results show that as the streamwise component is increased through stretching, SRH also will increase. Similarly, Bluestein et al. (1988) observed accelerations from 10–19 m s⁻¹ in the surface to 2-km-AGL layer between the wall cloud and a point 125 km distant from the updraft base. SRH approximately tripled along the path to that updraft. It should be noted that horizontal stretching of streamwise vorticity occurs with all storms if SRH is present, not just tornadic ones.

3. Case studies

The analyses presented herein include upper-air data from standard NWS rawinsonde sites and times as well as data from nine CLASS rawinsondes (four fixed and five mobile). Also available were 3-hourly NWS rawinsonde data in the forecast target region. Surface data included that available from the NWS, Oklahoma Mesonet (Brock et al. 1995), ARM-CART sites (e.g., see Rasmussen et al. 1995), profiler sites, and 12 mobile mesonets (e.g., Straka et al. 1996; Rasmussen et al. 1994, 1995). Errors for NWS and M-CLASS winds are less than 1 m s⁻¹ (e.g., Rasmussen et al. 1995), whereas those for profilers and VADs are about 1 m s⁻¹ (D. Zrnić 1997, personal communication). The mobile mesonet errors are similar to those for the Oklahoma Mesonet (Brock et al. 1995; Straka et al. 1996). A summary of the errors associated with all of the VORTEX instruments is provided in Rasmussen et al. (1995).

In preparing the upper-air data, the NWS and M-CLASS rawinsonde winds were sampled to give the same resolution as that of the profiler data to avoid resolution biases (i.e., the NWS soundings contain more information). Values of SRH and the shear between the lowest mean 500-m wind and the 6-km wind were plotted on mesoscale maps and insets in regions where tornadic storms occurred. Storm motions for SRH were based on (a) 60% of the 0–4 km shear vector and 8 m s⁻¹ to the right of it (Rasmussen 1998, manuscript submitted to Wea. Forecasting) for mesoscale maps, and (b) the average supercell motions observed on the inset maps. Since these values may not always be appropriate for each storm, sensitivity tests were performed to see how values of SRH might vary. The values can be considered accurate to within ±10–30 m² s⁻². Finally it is noted that values of SRH were not contoured. As will become apparent, doing so would be nearly impossible owing to the huge variability observed in many areas, and the fact that there are too few data points to make meaningful analyses.

4. Discussion and summary

It has been documented herein that SRH can have substantial variability in space (<100 km) and time (<3 h) where tornadoes occurred for at least the VORTEX cases investigated thus far. Variability in nontornadic and nonsupercell environments is not known for comparison. The values of SRH seem to be highly dependent on winds in the lowest levels [<1–2 km AGL; not shown for brevity’s sake; however, this can be seen in works by Davies-Jones et al. (1990) and Davies-Jones (1993)] of the atmosphere. It is believed, based on the variability of the values of SRH that were plotted here and in other studies, that there were almost certainly larger and smaller values near the various storms that developed, including those that became tornadic. The implications of this are discussed below. Another part of this work showed that the shear between the lowest mean 500-m wind and the 6-km wind was relatively uniform in all the cases in both time and space. In some cases the strongest shear was in regions where the most intense storms occurred; however, this was not a general conclusion. From this work the following implications are suggested:

• Important SRH variations often will not be detected. The conventional NWS upper-air observing network does not allow for adequate sampling of variations in severe convective storm environments. It is possible that careful monitoring of VAD and profilers might offer some additional guidance; however, even these are distributed over coarse scales (about 150–300 km). In the future, as more commercial aircraft are equipped to report real-time soundings of meteorological variables, including wind, potentially valuable forecast information may be available. This information will also augment calculations of low-level shear.

• Important SRH enhancement can be anticipated near boundaries using conventional data. If SRH is to be a useful forecast parameter, forecasters must be sensitive to the potential for highly variable SRH in regions where deep convection is occurring and boundaries are being generated. The application of a single value of SRH in a forecast in many cases may be inappropriate. Boundaries may supply additional buoyancy-generated streamwise vorticity in environments where only marginal values of SRH for severe storms are indicated.

• Models will be of some assistance when and if they can resolve the important temporal and spatial scales for individual cases. Mesoscale models are forever increasing resolution (now typically 30–80 km and expected to rapidly increase to 5–10 km), which should provide some guidance in primarily an “outlook” scenario for SRH fields. In the nowcasting arena, storm-scale prediction models (regular use of resolutions of 1–3 km will become a reality in the next five years or so) could conceivably provide some idea of variability that might indicate which storms may be important to monitor but this has yet to be demonstrated, and the limitations of these models have yet to be evaluated and established. For this to become a reality, storm initiation and evolution will need to be accurately forecast. To this date, even in high-resolution (10–50 km) mesoscale models, shear and SRH predicted in other cases tend to be smooth (e.g., Stensrud et al. 1997) compared to what was observed during VORTEX. Higher-resolution models can predict considerable varibility (sometimes as much as observed) but meaningful comparison remains an important issue in accurate storm-scale numerical weather prediction and related problems.

• SRH variability may explain, in part, why some storms are tornadic and others are not in seemingly similar environments. A truly enigmatic observation that has been made by almost every astute severe storm observationalist and forecaster is why one storm produces a tornado and a nearby one does not. Based on the work presented, as well as in some high-resolution (2–5-km resolution) modeling studies known to the authors, it has been shown repeatedly that SRH can be exceedingly variable. If environments with larger values of SRH are truly the ones that produce supercell tornadoes, and SRH is so variable, it might not be surprising that there is so much variability in which storms produce tornadoes. This concept needs to be more carefully investigated by examining cases where many storms produce tornadoes versus those in which only a few produce tornadoes to see if SRH was fairly uniform or highly variable in space. Also, the meaning or relevance of a threshold of SRH for supercell torndoes needs to be more clearly defined, and how to use SRH with other important storm predictors needs to be determined.

• Future work concerning the variability of SRH will involve a complete investigation of all tornadic and nontornadic supercell cases using data available from VORTEX and possibly some previous experiments (e.g., Davies-Jones et al. 1990; and Davies-Jones 1993). Furthermore, it would be interesting to know if the large heterogeneity of SRH noted for tornadic storm cases (many of which had at least one or more boundaries from one or more origins) is found in more quiescent environments. Finally, the usefulness and feasability of mesoscale and storm-scale numerical weather prediction models in resolving accurately in time and space the apparently observed heterogeneity in SRH in severe storm environments needs to be demonstrated.