1. Introduction

The Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX; Rasmussen et al. 1994) was conducted during the spring of 1994 and 1995 in the southern Great Plains of the United States. The objectives of this validation experiment were driven by a set of hypotheses (see Rasmussen 1995) that concerned (i) the initiation of tornadic storms; (ii) low-level mesocyclogenesis, tornadogenesis, and the role(s) of mesoscale and stormscale boundaries in each; and (iii) the dynamics of tornadoes and their associated boundary layers.

VORTEX data presented herein provide additional observational basis for the sentiment expressed in Davies-Jones and Brooks (1993): “in perhaps the least known process, a tornado develops within the mesocyclone.” Indeed, several storms intercepted during VORTEX generated moderate to strong low-level mesocyclones that were sustained for a ≥15 min period,¹ and in other ways appeared “primed for tornadogenesis” (Brandes 1993), yet did not produce tornadoes. In other words, existence of a low-level mesocyclone was an insufficient condition for tornadogenesis. One may argue, then, that theories of low-level mesocyclogenesis (e.g., Rotunno and Klemp 1985; Davies-Jones and Brooks 1993; Brooks et al. 1993, 1994) fall short of explaining the details of tornadogenesis, as underscored by the idealized modeling results of Trapp and Fiedler (1995). Hence, another layer of complexity must be addressed by theories of tornadogenesis.

The aforementioned nontornadic storms are considered examples of “tornadogenesis failure,” an arguably subjective classification introduced here to provide a basis for comparison with tornadic storms and to help clarify tornadogenesis mechanisms. This concept of “failure” is attributed to Brooks et al. (1993), albeit in the context of low-level mesocyclogenesis. These authors identified failure modes in which a strong (vertical vorticity, ζ ∼ 0.01 s⁻¹) midlevel and/or low-level mesocyclone neither developed nor persisted in a numerically simulated storm; a failure mode was presumed to preclude the formation of a long-lived, significant tornado.² A proper balance between two opposing factors that govern rear-flank gust-front movement, namely the environmental inflow and the cold-air outflow, was found to be of critical importance in low-level mesocyclogenesis and sustenance [and in the sustenance of the parent storm itself; Weisman and Klemp (1982)].

The VORTEX observations imply a new challenge to operational forecasters in their efforts to discriminate, for warning purposes, storms that are likely to produce tornadoes from those that will not. A means to discriminate unambiguously between tornadic and nontornadic storms has yet to be demonstrated in the literature, hence motivating related research at the National Severe Storms Laboratory (NSSL) involving VORTEX data and complementary numerical modeling. This report provides the underpinning of some of that work by establishing existence of nontornadic low-level mesocyclones and attendant tornadogenesis failure during VORTEX.

A description of the datasets and analysis method used toward this end is provided in section 2. In section 3, evidence to support the classification of failure within three nontornadic storms is presented. A diagnostic comparison with three tornadic storms is used in section 4 to explore and provide additional clues on possible modes of failure. Some preliminary remarks on failure modes are discussed in section 5.

2. Data description

Airborne Doppler radar (ADR) observations, obtained by a helically scanning X-band radar mounted in the tail of one of the NOAA P-3 aircrafts, make up the primary data source. When employing either the fore–aft scanning technique or the all–fore, all–aft scanning technique, the P-3 is capable of gathering pseudo-dual-Doppler data during a flight leg (Jorgensen et al. 1996). A typical leg lasts ∼5 min and is flown at a distance of ∼10–20 km from the storm and at an altitude of ∼1 km above ground level. The P-3 aircrafts also are equipped with a lower-fuselage (LF)-mounted C-band conventional radar. This radar scans at a rate of two revolutions per min and collects reflectivity information at low elevation angles with respect to the quasi-horizontal plane containing the aircraft flight track. The Weather Surveillance Radar-1988 Doppler (WSR-88D) nearest to each storm supplements the LF and airborne Doppler radars. For reference, approximate distances of these radars from the mesocyclone center of each storm, at the time of tornado formation or failure, are listed in Table 1. Details of the ADR data analysis are provided in the appendix.

The criterion for VORTEX case consideration and selection is existence of pseudo-dual-Doppler data on the storm, at least 10–15 min prior to the time of its failure. To provide a basis for comparison with tornadic storms, failure is defined to be the lack of tornado formation within a strong (ζ ≥ 0.01 s⁻¹) low-level mesocyclone whose life cycle is ≥15 min, and furthermore within a storm possessing other characteristics shown to be associated with a transition to a tornadic phase (Klemp 1987; see section 3). The time of occurrence of peak low-level vertical vorticity, which in these cases corresponds to the time at which tornadogenesis appears imminent (from subjective visual and/or weather radar observations) and after which low-level vertical vorticity diminishes, is designated as time of tornadogenesis failure. A tornado is defined as in the Glossary of Meteorology. Although each instance of tornadogenesis failure is by definition a nontornadic event, it is not assumed herein that all nontornadic storms are instances of tornadogenesis failure; “nontornadic” carries with it no distinction about the existence of low-level rotation, which, on some scale larger than that of the tornado, is necessary for tornadogenesis.

WSR-88D data are used to identify times of maximum low-level rotational velocity and thus guide which ADR flight legs to analyze. Using calculations of vertical vorticity from the pseudo-dual-Doppler synthesized winds, tornadogenesis failure time is then verified, or adjusted if necessary. Additional analyses are produced at ∼5 and ∼10 min prior to failure time (hereinafter denoted as T5 and T10).

3. Observational evidence of tornadogenesis failure

It is prudent to recall first the pioneering efforts of Stout and Huff (1953), Browning and Donaldson (1963), Chisholm and Renick (1972), Marwitz (1972), and Lemon (1980). These researchers, among others [see the reviews by Donaldson (1990) and Burgess and Lemon (1990)], introduced supercell storm airflow models and radar-observable characteristics such as pendant and hook echoes from which rotation may be inferred;bounded weak echo regions (BWER) as a means to identify regions of strong updrafts; rotation (low-altitude convergence, storm-top divergence) signatures in mean Doppler velocity that depict mesocyclones (updrafts); and spatial correlations of a mesocyclone signature and BWER that indicate a rotating updraft.

Such characteristics have been used in descriptions of supercell storm life cycles. The stage that heralds tornado formation is of relevance in the present discussion. Brandes (1993), for example, described a “mature stage” as “that critical period in storm evolution at which the basic updraft and vertical vorticity patterns associated with supercells have evolved and the storm is primed for tornadogenesis.” A rudimentary hook echo, WER or BWER, rainy rear-flank downdraft and associated gust front, and an arc-shaped updraft that correlates spatially with vertical vorticity, are qualitative features that tend to be observed during and near the end of the mature stage. The formation of a tornadic vortex signature (TVS; Brown et al. 1978) aloft and within the mesocyclone also tends to precede tornadogenesis [though not necessarily in all cases; see Trapp and Davies-Jones (1997)]. In terms of kinematic quantities, the mature stage of the 8 June 1974 Harrah, Oklahoma, tornadic storm was characterized by ζ ∼ 1.5 × 10⁻² s⁻¹ and mean divergence of ∼−50 × 10⁻⁴ s⁻¹, at an altitude of 300 m (cf. Brandes 1993, his Figs. 6 and 7).

Other descriptions can be found as well. Lemon and Doswell (1979) detailed a “collapse phase” during which time “the strongest tornadoes and straight-line winds occur.” This is characterized by a dissipating BWER and the development of a divided mesocyclone structure, which are accompanied by the descent of the mesocyclone and rear-flank downdraft to the surface, and also the development of a TVS aloft. Klemp (1987) drew upon Lemon and Doswell’s discussion as well as numerical storm simulation results to describe a transition of a storm to its tornadic phase. This includes a rapid increase in low-level rotation. An adverse vertical pressure gradient owing to the relatively stronger low-level mesocyclone forces a downdraft that in turn leads to the onset of mesocyclone occlusion (see also Klemp and Rotunno 1983).

With these descriptions in mind, three VORTEX cases³ are considered herein as illustrations of tornadogenesis failure: the 29 April 1995 nontornadic storm near Sherman, Texas; the 12 May 1995 nontornadic storm near Hays, Kansas; and the 22 May 1995 nontornadic storm near Shamrock, Texas. To reiterate, a nontornadic storm that appears to evolve to a state ostensibly “primed for tornadogenesis,” and in particular, that possesses a moderate-to-strong mesocyclone in the lowest several hundred meters above ground, characterizes tornadogenesis failure.

Horizontal sections of reflectivity factor and storm-relative winds, at z = 1 km and analysis times T5 and T, are presented in Fig. 1.⁴ Each storm exhibits, to varying degrees of intensity, a low-level mesocyclone and a rainy downdraft to its rear. An associated rear-flank gust front arcs outward from the mesocyclone center; in no storm has the gust front advanced to promote a kinematic occlusion of the mesocyclone at time T. Quasi-vertical tail radar scans of the three storms depict the presence of a deep, echo-free vault, or BWER, and therefore extensive updraft (Fig. 2a). Significant hail (diameter > 4.5 cm) was reported in each case. WSR-88D data (see Table 1) confirm a spatial correlation of WER or BWER and mesocyclone, at some time during or preceding failure. Also, data collected from the Amarillo, Texas, WSR-88D (KAMA), for example, show the presence of a TVS at ∼2 km above the ground within the Shamrock mesocyclone (Fig. 2b). Lastly, observations of hook echoes from the LF radar at low altitude support existence of low-level mesocyclones (Fig. 2c). Within the context of the perceived understanding of tornadogenesis, these data provide ample evidence to support the characterization of tornadogenesis failure.

LF radar data provide some clues about the nature of each storm’s evolution and failure mode. In particular, scans of the Sherman storm (Fig. 2c) portray well this storm’s cyclic mesocyclogenesis, and exemplify the discussions of Burgess et al. (1982) and more recently, Adlerman et al. (1996). This cyclic behavior is consistent with the evolution of the “low-shear,” outflow-dominated case of Brooks et al. (1994), and also with the relatively high values of radar reflectivity within the Sherman mesocyclone core.

4. Diagnostic comparison

Three tornadic storms intercepted during VORTEX now are introduced for comparative purposes: the 29 May 1994 tornadic storm near Newcastle, Texas; the 17 April 1995 tornadic storm near Temple, Oklahoma; and the 16 May 1995 tornadic storm near Garden City, Kansas. An intensity estimate (Fujita 1981) of F3 was assigned to the Newcastle tornado, F1 to the Temple tornado, and F2 to the Garden City tornado.

Prima facie, the tornadic and nontornadic storms share many of the same traits (Fig. 3). To help identify differences, several kinematic quantities⁵ are computed using the radar reflectivity and three-dimensional wind analyses synthesized from the ADR. These are diagnostic, so as to show trends and “effect” rather than “cause,” yet hopefully provide further clues regarding the modes of failure. Computations using analyses that are plagued with missing data in crucial areas (e.g., in and around the mesocyclone) or that have the potential for relatively greater vertical velocity uncertainties due to large distances between radar and storm are omitted. Accounting for errors related to the radar system hardware, flow evolution and improperly corrected storm motion during pseudo-dual-Doppler data collection, improperly dealiased velocity data, and synthesis of Cartesian velocity components from pseudo-dual-Doppler radars separated by 40° in azimuth (see Jorgensen et al. 1996), the values presented below are estimated to have errors of approximately ±10%.

It is logical to begin with an evaluation of maximum low-level (0 < z ⩽ 1 km) vertical vorticity, ζ_max, which is graphed for each case at each of the three analysis times (Fig. 4). Although the general trend is an increase in ζ_max prior both to tornado formation and failure, the tornadic mesocyclones have greater vorticity at time T than do the nontornadic mesocyclones.

In Fig. 5a, r_c is plotted as a function of ζ_max at analysis time T. Clearly, the tornadic mesocyclones have smaller core radii and greater low-level vertical vorticity than do the nontornadic mesocyclones. This statement also holds true at analysis time T5 and is evident qualitatively in the storm-relative winds of the Garden City (tornadic) and Shamrock (nontornadic) storms analyzed at both times (Figs. 1c and 3c).

An intuitive and theoretically consistent result is shown when r_c is plotted as a function of the maximum, mean, low-level vertical vortex stretching, −ζδ (Fig. 5b). Here, δ is horizontal divergence, and the mean is constructed from all values within the nominal threshold of ζ > 1 × 10⁻² s⁻¹. The four cases suitable for this computation exhibit, at T, a well-behaved progression from large core radii and weaker vortex stretching in the nontornadic mesocyclones to smaller core radii and stronger stretching in the tornadic mesocyclones. Said another way, parcels that nearly conserve angular momentum penetrate closer to the central axis of the tornadic mesocyclones, resulting in large tangential velocities.

Correlations (or lack thereof) of vertical velocity and vertical vorticity corroborate the results in Fig. 5. Following Droegemeier et al. (1993), a correlation coefficient ρ(w, ζ) is defined at each level 0 < z ⩽ 1 km as

View Expanded

where 〈 〉 represents a horizontal average across a mesocyclone (defined by ζ > 1 × 10⁻² s⁻¹). Interestingly, the maximum low-level correlation decreases with time by more than 50% prior to tornado failure, yet changes very little prior to tornadogenesis (Fig. 6). This is indicative of a decoupling between low-level updraft and mesocyclone, and thus a cessation or disruption of vortex stretching.

An alternative means of diagnosing the genesis or failure in the six cases is provided through calculations of swirl ratio S (Davies-Jones 1973). This approach follows Brandes (1978) and Barnes (1978), who used swirl ratios computed with observed winds (by dual-Doppler radar and instrumented mesonet towers, respectively) to explain tornado development and subsequent behavior.

After Davies-Jones (1973), swirl ratio can be written as

View Expanded

where a = h/r₀ is the ratio of storm inflow depth (h) to nominal updraft radius (r₀). Inflow depth is approximated as in Barnes (1978) using the level of free convection (LFC) from a rawinsonde observation (raob) in the environment of each storm. As demonstrated in Fig. 7, r₀ is estimated using contoured fields of azimuthally averaged vertical velocity w and radial velocity V_r, where

V_ruθυθ.

Inflow angle

α⁻¹V_θV_r

is determined as in Brandes (1978) using azimuthally averaged tangential velocity [Eq. (1)] and radial velocity, evaluated at r₀ and h/2. Information regarding the raob for each case can be found in Table 2. Values of h, r₀, α, and S at analysis time T are listed in Table 3.

At time of tornado formation or failure, the three nontornadic storms have large swirl ratios and, with exception of the Garden City storm, the tornadic storms have smaller swirl ratios (Fig. 8). Results from laboratory model simulations as well as theory are invoked to show the consistency of large (smaller) swirl ratio with large (smaller) core radii found in the nontornadic (Newcastle and Temple tornadic) mesocyclones (see Figs. 5 and 8, and Table 3).

Turbulent vortices simulated in tornado chambers exhibit a functional dependence of core radius on swirl ratio (Davies-Jones 1973; Jischke and Parang 1974; Rotunno 1977). An inviscid, potential flow model of a stagnant core vortex aids the interpretation of the experimental data. Upon using Bernoulli’s theorem and applying a variational principle, it can be shown that

View Expanded

where r_cm is the minimum core radius, r₀ is the radius of the updraft hole [as in Eq. (3)], Q is the updraft volume flow rate, p_c is the constant pressure inside the stagnant core, p₀ is the constant pressure in the irrotational region outside the core, and ρ is the density (Lewellen 1976). For a fixed core pressure deficit, the core radius adjusts to its minimum value so as to maximize the volume flow rate, yet increases with increasing swirl ratio.

The stagnant vortex model does not apply at low swirl when vortices can be laminar upstream of an axial stagnation point and turbulent core (Davies-Jones 1973). However, the model and chamber experiments do well at explaining the fully turbulent vortices. In the Ward tornado chamber for example, a single, wide, fully turbulent vortex can exist in a steady state, for certain moderate values of S less than a critical swirl ratio (S*, which is dependent on the Reynolds number, R) (see Fig. 4d in Ward 1972). Snow (1982) describes this as a vortex at “intermediate swirl,” the core has broadened, yet (weak) rising motion still exists along the central axis (see his Fig. 8). To the extent that such a vortex is analogous to the three nontornadic, broadly rotating mesocyclones, one may state that the swirl in these cases destines the mesocyclones to resist tornado-scale vortex formation.

This statement comes with two caveats. First, unlike in the chamber and numerical models thereof, the swirl ratio associated with the parent thunderstorm is unsteady and therefore is a manifestation of storm-scale processes at a given time. Second, the chamber/numerical models inadequately treat (and ADR observations fail to resolve) Reynolds number–dependent boundary layer processes that play an important role in tornado dynamics (see, e.g., Snow 1982). This was stressed by one of the reviewers, who noted furthermore that if these processes are simulated sufficiently well, the models may reveal certain atmospheric values of R that allow strong radial inflow to develop in the surface layer and subsequently converge the otherwise nontornadic low-level mesocyclone of an intermediate swirl vortex into a tornado. In this regard, tornadogenesis failure is dependent on R as well as S. Ultimately, the discussion of failure must relate atmospheric conditions to particular values of S and perhaps R.

The Garden City storm and its thermodynamic environment foster the formation of a two-celled mesocyclonic vortex (i.e., downflow along the central axis, terminating in low-level radial outflow that turns vertical in an annular updraft at an outer radius) that apparently exceeds some critical swirl ratio. As in laboratory vortices at S ≥ S* and in multiple vortex tornadoes (Davies-Jones 1973; Jischke and Parang 1974; Church et al. 1979), a downdraft, presumably owing to a downward-directed vertical pressure gradient force, supplants upward motion along the Garden City mesocyclone’s central axis at times T10 (not shown) and T5 (Figs. 1c and 9). According to Rotunno (1984), the two-celled vortex is unstable to three-dimensional perturbations, and the instability is manifest greatest in azimuthal wavenumber two. These subsidiary vortices form in the annular updraft ring that surrounds the central downdraft (see Rotunno 1984, his Figs. 9 and 11).

Brandes (1978) and later Rotunno (1984) hypothesized that a subsidiary vortex in the two-celled mesocyclone of the 8 June 1974 Harrah, Oklahoma, storm contracted into the Harrah tornado. Wakimoto and Liu (1998) applied this theory to their analysis of the National Center for Atmospheric Research (NCAR) Electra Doppler radar data collected on the Garden City storm and tornado. Although the spatial and temporal data sampling of the NOAA P-3 data shown here are too large to afford a confirmation of Wakimoto and Liu’s conclusion, it is nevertheless supported by visual observations by VORTEX personnel of tornadogenesis near the periphery of the mesocyclone rather than in its center.

5. Remarks

Six storms intercepted during VORTEX were considered. Each of the three tornadic and three nontornadic storms generated and sustained a mesocyclone in the lowest several hundred meters above the ground. Significantly, this statement proves that mere existence of a low-level mesocyclone was insufficient for tornado formation in the nontornadic cases.

The percentage of low-level mesocyclones associated with tornadoes has yet to be presented in the formal literature; it is presumed to be greater than 30%–50% [the approximate number of tornadic midlevel mesocyclones; Burgess and Lemon (1990)], but less than 100%. Assuming that detection of a low-level mesocyclone (when possible) weighs heavily in Doppler-radar-based tornado warning decisions, these observations of nontornadic low-level mesocyclones introduce another uncertainty to the decision process, and complicate the tornadic/nontornadic storm discrimination problem.

It is possible to speculate on a number of tornadogenesis failure modes that can be addressed in future studies. Certainly, a storm that becomes “outflow-dominated” exemplifies one mode. As discussed in Brooks et al. (1993, 1994), the processes that give rise to low-level mesocyclogenesis also disrupt the subsequent intensification of associated low-level vorticity into a tornado-scale vortex. This means of failure presumably is quite time sensitive. Noting the analyses presented in sections 3 and 4, it is clear that not every nontornadic storm “fails” via mesocyclone undercut by cold-air outflow.

Recall the distinct modes of tornado formation within a single-celled mesocyclone, as described by Trapp and Davies-Jones (1997): (i) mode I, in which the embryonic tornado develops aloft within the parent mesocyclone, then gradually descends to the ground via a process known as the “dynamic pipe effect” (Leslie 1971); (ii) mode II, in which the embryonic tornado forms uniformly throughout a several kilometer depth or very near the ground, then contracts rapidly into a tornado. Both have corresponding failure modes. Mode I should fail if the vertical stability in the convective boundary layer is too large. The result is an embryonic tornado suspended above the ground. Mode II should fail if the primary meridional (radial–vertical) circulation associated with the updraft is too weak, particularly at low altitudes, to contract ambient rotation (the mesocyclone) into a tornado within tens of minutes. This also may be interpreted as a cause for the intermediate swirl vortex, which resists tornado-scale vortex formation (for certain values of Reynolds number, as discussed previously). The primary meridional circulation is driven in part by buoyancy forces, the vertical integral of which corresponds to the convective available potential energy (CAPE), and also by upward-directed vertical pressure gradient forces (VPGFs) owing to interactions between the updraft and ambient wind shear. Following recent results of McCaul and Weisman (1996), it is suspected that these favorable VPGFs and also the height of maximum positive buoyancy are more relevant to failure mode II than the value of CAPE alone.

The frequency with which tornadoes develop within two-celled mesocyclones is unclear, as is the frequency of two-celled mesocyclone formation itself. It is reiterated that the critical swirl ratio S*, the theoretical value at which two-celled vortices develop, is a function of Reynolds number and should vary from storm to storm. Inability of the storm to attain S* represents in some sense yet another mode of failure. Meteorological conditions in the near-storm, mesoscale environment (which perhaps include the effects of neighboring or preexisting storms) modulate this and the other failure modes in ways yet to be determined.

Much of the data collected during VORTEX lack the spatial and temporal resolution needed for a rigorous investigation of these and other conjectured failure modes. Thus it is premature at this time to attempt to assign a particular mode to a given storm. The investigative problem is, however, amenable in many ways to experiments with a numerical cloud model since tornadogenesis failure ultimately is related to meteorological conditions in the near-storm, mesoscale environment, as just mentioned. This likely will be the future direction of the research theme introduced here, in what can be considered a logical extension of the work of Brooks et al. (1994).