The Kellerville Tornado during VORTEX: Damage Survey and Doppler Radar Analyses

Transcription

1 VOLUME 131 MONTHLY WEATHER REVIEW OCTOBER 2003 The Kellerville Tornado during VORTEX: Damage Survey and Doppler Radar Analyses ROGER M. WAKIMOTO AND HANNE V. MURPHEY Department of Atmospheric Sciences, University of California, Los Angeles, Los Angeles, California DAVID C. DOWELL Advanced Study Program, National Center for Atmospheric Research,* Boulder, Colorado HOWARD B. BLUESTEIN School of Meteorology, University of Oklahoma, Norman, Oklahoma (Manuscript received 11 September 2002, in final form 7 February 2003) ABSTRACT A detailed aerial and ground survey of a long-track ( 50 km) F5 tornado is presented. The survey revealed that the tornado exhibited unusual nonlinear movements at two different locations. One portion of the track was associated with a pronounced sinusoidal pattern while another location was characterized by a cusplike pattern. For the first time, high-resolution dual-doppler wind measurements can be used to evaluate mechanisms for such deviations from a linear tornado path. The analyses of data collected with Electra Doppler Radar (ELDORA) suggest that these departures are trochoidal marks produced as the tornado was revolving within the larger-scale mesocyclone. Retrieved perturbation pressures indicate that the mesocyclone departed significantly from a cyclostrophically balanced state during these deviations. The maximum vorticity associated with the mesocyclone at low levels was shown to be an unreliable indicator of the tornado s intensity. Vertical cross sections of wind, vertical vorticity, radar reflectivity, and perturbation pressure were photogrammetrically superimposed onto two pictures of the tornado. This merger of data provides a unique view of the structural relationship between the hook echo and the mesocyclone. One of the important conclusions was the lack of a definitive relationship between the widths and strengths of the mesocyclone and the tornado. 1. Introduction Documentation of the damage caused by tornadoes (Fujita 1981; Doswell and Burgess 1988) has been a critical component in the development of the operational tornado warning process. Surveys of damage tracks have provided the ground truth for verification that is needed when one identifies possible precursors in Doppler radar data of tornadogenesis (e.g., Brandes 1978; Brown et al. 1978). Indeed, Bluestein and Golden (1993) have emphasized that the need for surveys is even more important now as the new generation of operational Doppler radars are being used by the National Weather Service (NWS). Detailed aerial and ground surveys of damage caused * The National Center for Atmospheric Research is sponsored by the National Science Foundation. Corresponding author address: Dr. Roger M. Wakimoto, Dept. of Atmospheric Sciences, UCLA, Los Angeles, CA roger@atmos.ucla.edu by tornadoes have also been instrumental in advancing our understanding of these intense circulations. Pronounced cycloidal marks evident within the damage tracks were one of the early findings from aerial surveys (e.g., van Tassel 1955; Prosser 1964; Fujita 1981). Fujita (1971) discounted the prevailing theory that these were scour marks caused by debris being dragged along the ground by the tornado. Instead, he hypothesized based on ground surveys that these marks were caused by suction vortices rotating around a common core. Another intriguing discovery revealed in early damage surveys was the nonlinear nature of some of the tornado tracks (e.g., Hall and Brewer 1959). This was frequently illustrated by the distinct right or left turns of the track near the latter stages of the tornado s life cycle (Fujita et al. 1970; Fujita 1974; Agee et al. 1976; Bluestein 1983). There are, however, well-documented cases of tornadoes making unusual and large deviations in their movements even though there were no obvious changes in the parent storm s overall propagation (e.g., Brown and Knupp 1980; Fujita 1992). Wakimoto and Atkins (1996) documented the path of an intense tor American Meteorological Society 2197

2 2198 MONTHLY WEATHER REVIEW VOLUME 131 nado near Newcastle, Texas, that initially tracked to the west before making a sharp U-turn. The prevailing theory for explaining the turns, bends, and cusplike tornado paths documented by poststorm surveys is that the trochoidal track 1 is a result of the tornado revolving within a larger-scale mesocyclone circulation (Fujita 1963; Agee et al. 1976; Brown and Knupp 1980). There had been no data collected to date, however, to confirm this possible mechanism. The introduction of Doppler radars, which collected data at low levels, provided researchers with the first quantitative information that improved our understanding of the tornado s kinematic structure as a function of time and its relationship to the damage it produces (e.g., Brown et al. 1978; Zrnic and Istok 1980; Burgess et al. 1993). Zrnic and Istok (1980) presented single-doppler analyses that suggested that a tornado was rotating cyclonically around the center of a parent circulation. Unfortunately, no visual information on the funnel or detailed damage survey was provided to confirm this movement. A major improvement in the spatial resolution of radar data occurred when the platforms became mobile (Bluestein et al. 2001). The close range of the mobile platforms to the tornado provided unprecedented information on the hook-echo structure and the rotational couplet as seen in radar reflectivity and Doppler velocity analyses, respectively (e.g., Bluestein and Unruh 1989; Bluestein et al. 1993; Wakimoto et al. 1996; Bluestein and Pazmany 2000; Wurman and Gill 2000; Burgess et al. 2002). The images collected by these mobile radars have been striking. Echo-free or weak-echo eyes within the hook, first noted by Fujita (1958, 1965), and spiral bands of radar reflectivity were shown to be ubiquitous (e.g., Bluestein and Pazmany 2000; Wurman and Gill 2000). The reduced sampling volume meant that the measured maximum wind speeds were approaching the values within the tornado rather than being highly filtered (e.g., Bluestein et al. 1993). Comparisons of these wind speeds with the F-scale rating of the damage were found to be reasonably consistent (Bluestein et al. 1993; Bluestein and Pazmany 2000; Wurman and Gill 2000; Burgess et al. 2002). These findings are surprising given the danger of associating F-scale assessments based on damage to equivalent wind speed estimates (Doswell and Burgess 1988). The study by Burgess et al. (2002) was important since the single-doppler information was compared to an unusually detailed damage survey. Indeed, the survey was comparable to those produced by Fujita (1989, 1993). 1 The terms cycloid and trochoid have been used in the literature to describe these damage marks on the ground. Cycloid is the curve that is generated by a point on the circumference of a circle as it rolls along a straight line, while trochoid is the curve generated by a point on the radius of a circle as the circle rolls along a straight line. The latter term is used in the present study since a cycloid can be considered a special case of a trochoid. Since single-doppler velocities only provide the radial component of motion, there have been several attempts to relate dual-doppler radar syntheses to tornado damage surveys. Unfortunately, these syntheses have either been too coarse (e.g., Brandes 1978, 1981; Johnson et al. 1987; Dowell and Bluestein 1997; Ziegler et al. 2001) or the tornado was too small (Wakimoto and Liu 1998). In addition, except for the case analyzed by Wakimoto and Liu (1998), these studies were typically not accompanied by comprehensive damage surveys (e.g., Bluestein et al. 1997). On 8 June 1995, a tornadic supercell formed over the Texas panhandle and produced a family of tornadoes during the Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX; Rasmussen et al. 1994). High-resolution airborne Doppler radar data were collected on this storm by the National Center for Atmospheric Research (NCAR) Electra Doppler Radar (ELDORA). A total of three major tornadoes were scanned by ELDORA over a nearly 2-h period. One of the tornadoes was associated with a large funnel cloud and was rated by one of the authors as F5 in intensity. This is one of the best-documented cases of the process known as cyclic tornadogenesis (Rasmussen et al. 1982) and is believed to be the only dual-doppler case of a long-track tornado (Dowell and Bluestein 2002a,b). Another important aspect of this case is the extensive ground and aerial survey that was performed on two of the tornado tracks in the days immediately after the event. In particular, this paper focuses on the detailed damage track of the F5 tornado (hereafter referred to as the Kellerville tornado). The Kellerville tornado was one of most violent tornadoes ever surveyed and exhibited unusual nonlinear movements in its track in at least two locations. A prominent cusplike pattern was apparent in one section of the track. Another portion of the damage path exhibited a pronounced sine-wave pattern that has not been previously documented in the literature. Unlike past studies, high-resolution wind syntheses based on the data collected by ELDORA provide an opportunity to explain the unusual movements in its track. The Kellerville tornado was photographed at several locations during its lifetime. Two of the photographs were analyzed using photogrammetric techniques. The dimensions and the visual characteristics of the funnel are presented. More importantly, these photographs are merged with the dual-doppler data so that the structural relationship between the tornado with the hook echo and mesocyclone are revealed. Although this type of analysis was presented on a nonsupercell tornado (Wakimoto and Martner 1992), a similar presentation with a supercell tornado has not been attempted. Section 2 documents the tornado paths, ELDORA flight track, and the data analysis methodology. The results of a detailed damage survey are shown in section 3. Section 4 presents a comprehensive comparison of the high-resolution Doppler syntheses with the damage track. The com-

3 OCTOBER 2003 WAKIMOTO ET AL FIG. 1. Damage tracks of the three major tornadoes (Alanreed, McLean, and Kellerville) spawned by the McLean supercell. The damage survey of the Alanreed and Kellerville tornadoes is based on an extensive aerial and ground survey over a 3-day period. F-scale ratings are labeled along the tracks. The flight track of the Electra is shown by the dashed black line. Times are in UTC. The black dots represent the locations of two photo sites. The gray rectangular box is enlarged in a series of analyses shown in Fig. 3. Gray lines represent some of the major roads in the area. bined analysis of the ELDORA data and the photographs of the Kellerville tornado is discussed in section 5. A summary and discussion are presented in section Tornado paths, ELDORA tracks, and data analysis methodology The storm [referred to as the McLean storm by Dowell and Bluestein (2002a)] that spawned the Kellerville tornado was one of several supercells that formed on the afternoon of 8 June. This storm produced three major tornadoes during its lifetime (Fig. 1). The Alanreed and Kellerville tornado tracks were reconstructed based on an extensive aerial and ground survey conducted over a period of 3 days. The latter track was 50 km in length. Time did not permit a detailed damage survey of the McLean tornado, but the position of the track was determined. Dowell and Bluestein (2002a,b) documented two additional tornadoes that had short lifetimes and were weak. These tornadoes were not resolved by the Doppler analysis, so they are not included in the figure, although they are shown in Dowell and Bluestein (2002a). Approximate F-scale ratings are labeled along the track. Most of the tornado damage occurred over open country so only a few structures were damaged. The first author used his experience based on many previous surveys to assign F numbers based on scour marks in the ground, tree and vegetation damage, and damage to nearby structures if they existed. The assessment also relied on the guidelines provided by Fujita (1992) documenting approximate F-scale ratings based on damage to vegetation (see his Fig ). While there could be some questions raised as to the absolute magnitude of the assigned F-scale rating, the relative ratings of weak versus strong areas of damage are accurate. The final assignment of a maximum rating of 5 on the Fujita scale for the Kellerville tornado was based on similar damage observed during past surveys of F4 and F5 tornadoes. Vegetation in the F5 region was completely scoured,

4 2200 MONTHLY WEATHER REVIEW VOLUME 131 FIG. 2. Time series of the McLean supercell echo based on data collected by ELDORA at select intervals superimposed onto the tornado damage tracks. The tracks of the tornadoes are shaded gray and outlined by dashed black lines. The thin black line represents the flight track of the Electra. The echoes are plotted for a height of 1.6 km AGL and the values of the isopleths are shown in the upper-left-hand corner. The echo times labeled on the figure correspond to the flyby patterns of the Electra. leaving exposed soil (see Fujita 1992). The Alanreed tornado was rated F3. In comparison, an independent survey by the NWS led to ratings of F4 and F2 for the Kellerville and Alanreed tornadoes, respectively (NCDC 1995). The dashed line in Fig. 1 represents the flight track of the Electra aircraft flown southeast of the storm. Each pass was 5 6-min long, comparable to previous airborne studies of supercells (e.g., Wakimoto et al. 1998). The flight level for the Electra was nominally 300 m above ground level (AGL; hereafter all heights are AGL). A time series of the supercell echo at select intervals superimposed onto the tornado tracks is shown in Fig. 2. The storm moved to the northeast, and a well-defined hook echo centered on the damage path can be identified in several of the plots. The overall storm movement was from 220 at 8.5 m s 1. Also apparent is a weak-echo hole within the hook, a characteristic feature of highresolution radar reflectivity data of tornadoes (e.g., Fujita 1981; Wakimoto and Martner 1992; Wakimoto and Liu 1998; Bluestein and Pazmany 2000; Wurman and Gill 2000). Unfortunately, no ELDORA data were collected after 0015 UTC, at which time the Kellerville tornado was approximately at the midpoint of its damage path. The Electra encountered severe turbulence at this point and the mission was terminated. The ELDORA is an airborne Doppler radar platform that collects detailed observations in the along-track direction by using a fast rotation rate of the antenna. The unambiguous range of velocities is also large in order to minimize the ambiguities that are often associated with the high wind speeds in severe convective storms. The interested reader is referred to Hildebrand et al. (1994) and Wakimoto et al. (1996) for more information on the radar design and capabilities of ELDORA. The reflectivity and Doppler velocity data recorded by ELDORA are the same as those used in the study by Dowell and Bluestein (2002a,b); the editing methodology is discussed in their paper. Observations were separated by 300 m in the along-track direction and 1.44 in the direction of the sweeps. In the analysis domain, the maximum vertical sampling was approxi-

5 OCTOBER 2003 WAKIMOTO ET AL mately every 450 m at a distance of 18 km from the aircraft. The syntheses presented in this paper were at ranges less than this value. As a result, the reflectivity and Doppler velocity data were interpolated onto a Cartesian grid with horizontal and vertical grid spacings of 300 and 400 m, respectively, using Reorder software (Oye et al. 1995). This interpolation represents a slight reduction in the spacing chosen by Dowell and Bluestein (2002a) since one of the major goals of the present study was to compare the highest-resolution wind syntheses to the damage surveys. The lowest grid level was located at 400 m. The individual radar scans for each pass by the Mc- Lean storm were time space adjusted using a velocity of the mesocyclone for that volume as objectively determined by Dowell and Bluestein (2002a). A Cressman filter (Cressman 1959) was used in the interpolation process with a radius of influence of 300 and 400 m in the horizontal and vertical, respectively. A sensitivity test using a radius of influence of 600 and 800 m did not significantly change the Doppler wind syntheses. The data were synthesized within Custom Editing and Display of Reduced Information in Cartesian Space Software (CEDRIC; Mohr et al. 1986). The hydrometeor fall speeds based on radar reflectivity were estimated from the relationship established by Joss and Waldvogel (1970) with a correction for the effects of air density (Foote and du Toit 1969). A three-step Leise filter (Leise 1982) was applied to the synthesis that significantly damps wavelengths up to 3.6 km and removes wavelengths of 2.4 km or less. Although the Kellerville tornado was associated with a large funnel early in its life cycle (funnel diameter of 1 km based on photogrammetric calculations), the Doppler wind synthesis does not resolve the tornado circulation. 2 Instead, the circulation is representative of the larger-scale mesocyclone. The mesocyclone is defined by vertical vorticity greater than 0.01 s 1 in this study, consistent with benchmarks established by Davies-Jones et al. (2001). The diameter of the mesocyclone was close to the minimum resolved wavelength using a three-step filter. Therefore, it is possible that reported decreases in tangential wind speeds and vertical vorticity could be related to decreases in vortex size rather than reflect actual kinematic changes. Wind syntheses were also generated using a two-step Leise filter in order to assess the extent of this potential problem. The two-step filter dampens wavelengths up to 1.8 km and removes those less than 1.2 km, dimensions that should minimize the effects described above. Differences between these two wind syntheses are discussed in section 4 when relevant. The vertical velocities were obtained from the an- 2 It should be noted that some tornado-scale features are resolved in the raw ELDORA scans since the vortex was large and close to the radar. However, the three-dimensional wind fields associated with the tornado cannot be synthesized because the spatial resolution is not consistent in all directions. elastic continuity equation by upward integration of the horizontal convergence field. An estimate of the vertical velocity below the lowest grid level is based on the scheme proposed by Nelson and Brown (1987). The integration was terminated at the 4.8-km level because accrued errors above this level would have been large. Since the emphasis in the present study is on the lowlevel wind fields, the neglect of the kinematics in the upper regions of the storm is not considered serious. Additional details of the expected standard deviations of the vertical velocity fields can be found in Wakimoto et al. (1998) and Wakimoto and Cai (2000). The reader is cautioned that airborne Doppler radar data cannot accurately resolve the horizontal divergence field within tens of meters of the ground. This layer could be critical to understanding the kinematic structure of the mesocyclone. Gal-Chen (1978) first proposed the use of three-dimensional winds synthesized from multi-doppler radar analyses to retrieve the total perturbation pressure (p ) and density patterns using a least squares method in a horizontal plane. The retrieval treats the pressure and temperature as unknown variables and solves the Poisson equation derived from the anelastic momentum equation. While this method retrieves individual horizontal cross sections of perturbation pressure, it does not reveal its vertical structure. Roux (1985, 1988), Roux and Sun (1990), and Roux et al. (1993) were able to modify Gal-Chen s method in order to retrieve the full three-dimensional perturbation pressure. This was accomplished by deriving a thermodynamic equation that relates the advection of temperature to the latent heat released through condensation or absorbed through melting and evaporation while neglecting other diabatic heat sources and sinks. It is assumed that saturated and unsaturated conditions occur during the production and removal of precipitation, respectively. The Roux technique, including the tendency term, is used in the present study. The reference frame is relative to the motion of the low-level mesocyclone. A momentum check was performed to assess the quality of the retrievals. The values ranged from 0.13 to 0.25 for all of the analysis volumes, well within the acceptable range defined by Gal-Chen and Kropfli (1984). The time gap between syntheses was 5 6 min. The retrievals presented in this paper were compared with the steady-state solutions (not shown) in order to assess whether these time gaps were too large to accurately estimate the tendency term. There were very small differences in the patterns and the individual values of the isopleths, suggesting that this effect was minimal. In addition, both forward and backward time steps (i.e., the next and previous syntheses times, respectively) were used when approximating the tendency. The pressure retrievals using either time step were nearly the same.

6 2202 MONTHLY WEATHER REVIEW VOLUME Damage survey A comprehensive damage survey of the McLean and Kellerville tornadoes was performed during June A ground survey was conducted on the first two days and was followed by an aerial survey using a small aircraft on the third day. Nearly 500 photographs of damage were taken from the aircraft. Photogrammetric analyses of these photographs combined with the ground surveys were used to plot the tornado track (Fig. 3). The black arrows represent the direction of tree fall and scattered debris from nearby structures. There were numerous ground swath marks (indicated by the semicircular lines on the figure) near the center of the track that were presumably caused by suction vortices rotating around the tornado core. The entire damage path of the Kellerville tornado is not shown in Fig. 3. The figure only highlights the portion of the track that can be compared with the ELDORA analyses. Isopleths of the F-scale values are drawn on the figure. The damage extends over a large region at the beginning of the tornado track and rapidly narrows to 1-km width near the overlapping regions (Figs. 3a,b). The most intense damage (F4 F5) was noted 6 km from the beginning of the track. The locations of two sites where photographs of the tornado were taken are shown in Fig. 1. The photos were photogrammetrically analyzed in order to determine the width of the funnel cloud. The viewing angles and radial distances from the photographer and the funnel diameters near the ground are shown in Figs. 3b and 3c. There is good agreement between the funnel diameter and the F0 isopleths at these two locations. This agreement may be serendipitous, however, since it is known that the visual characteristics of the funnel at low levels may (e.g., Golden and Purcell 1978) or may not (e.g., Bluestein et al. 1993, 1997) be a good indicator of the width of the damage path at the ground. There are two locations shown in Figs. 3b and 3c where the Kellerville tornado departed substantially from a straight line. One segment of the tornado path was characterized by a sinusoidal pattern (Figs. 3b, 4a). This type of tornadic footprint has not been previously documented in the literature. There appear to be at least three cycles of the wave whose amplitude was estimated to be 250 m with values ranging from 200 to 300 m (Fig. 4a). The wavelength was not constant but was, based on photogrammetric measurements, on average 900 m (values ranging from m). Another prominent deviation from a linear track can be seen in Figs. 3c and 4b. A pronounced cusplike feature is evident in the damage map and two aerial photographs. The tornado was moving to the north before the cusp in Fig. 4b. Subsequently, the tornado tracked to the northeast after exiting the cusp. Fujita et al. (1970, 1976) and Agee et al. (1977) documented a trochoidal mark in damage caused by a suction vortex rotating around the central core of a tornado called a stepping spot. This mark occurred when the tornado s translation velocity equaled the rotational velocity of the suction vortex around the center of the tornado. The path of the tornado shown in Figs. 3c and 4b is similar to a stepping spot but on a much larger scale. Brown and Knupp (1980) suggested that the cusp pattern observed during their study could have been caused by the tornado revolving around the mesocyclone of a supercell but they quickly discounted it as a plausible theory. Instead, they hypothesized that a strengthening mesolow, through the alteration of the storm-scale airflow, caused the tornado to deviate from a linear path. Zrnic and Istok (1980) provided single-doppler data suggesting that a tornado was rotating cyclonically around a parent circulation. The trochoidal pattern that provides the best fit to the observed tornado track is shown by the gray dashed line in Fig. 3c. The radius from the center of a circulation to produce this trochoid is 580 m. 4. Doppler radar syntheses a. 2336: :40 UTC The first ELDORA pass after the Kellerville tornado developed was at 2336: :40 UTC (Fig. 5). The tornado was 3 km from the beginning of the track at this time and was producing damage that was rated F3. A well-defined hook echo with a weak-echo eye and a velocity differential greater than 100 m s 1 across the rotational couplet are apparent (Figs. 5a,b). The mesocyclone, defined as the region where vertical vorticity exceeded 0.01 s 1, was 4 km in diameter with a peak value of s 1 (Fig. 5c). There is a slight asymmetry evident in the radial velocity (Fig. 5b), suggesting a displacement between the tornado and mesocyclone circulation center (see Brown and Wood FIG. 3. Enlarged (and rotated) plot of the Kellerville tornado track encompassed by the gray box shown in Fig. 1. (a) (c) Overlapping analyses starting at the beginning of the track [shown in (a)] and progressing northeastward. The black dashed line represents the boundary encompassing F0 damage. The black lines represent isopleths of higher F-scale damage, with the light and dark gray shading representing intensities exceeding F3 and F4, respectively. The black arrows represent the direction of fallen trees and structural damage. Thin black lines that are semicircular within the tornado track represent suction vortex marks in the ground. The large black crosses denote the locations of the low-level mesocyclone based on Doppler wind synthesis from ELDORA. The black circles in (b) and (c) represent the diameter of the funnel cloud based on two photographs. The locations of the photo sites are shown in Fig. 1. The gray dashed line shown in (c) represents the trochoid that best fits the damage track at that location. Two aerial photographs of the damage track are shown in (b) and (c). The area along the track covered by the photo is shown by the black arrows. Light gray lines denote the major roads.

7 OCTOBER 2003 WAKIMOTO ET AL. 2203

8 2204 MONTHLY WEATHER REVIEW VOLUME 131 FIG. 4. Aerial pictures of two segments of the Kellerville tornado track. (a) A sinusoidal pattern in the tornado path. Photograph looking northeast down the path of the tornado track. Another photograph of this section of the track is shown in Fig. 3b. (b) Close-up view of the cusp mark in the tornado track. Another photograph of this pattern is shown in Fig. 3c. 1991). However, the dual-doppler wind syntheses, which were used to position the latter, and the rotational couplet in the raw fore and aft scans of the tail Doppler velocity, used to position the former, did not support a displacement. The location of the rear-flank gust front is apparent in Fig. 5c by the convergent wind field and the band of updrafts that curls cyclonically around the northern sector of the mesocyclone. The main rear-flank downdraft is located west and southwest of the mesocyclone, and a weaker downdraft is positioned south of the circulation. In order to understand the relationship between the wind syntheses and the damage track, the former, at the lowest grid level (400 m), was carefully superimposed onto the latter (Fig. 6). Past studies have used relatively coarse dual-doppler analyses or single-doppler information. Using the latter data, only certain kinematic quantities, such as vertical vorticity, could be estimated under the restrictive assumption of axisymmetric flow. As previously mentioned, the resolved circulation presented in Figs. 5 and 6 cannot be interpreted as the tornado, owing to the characteristics of the raw observations and the imposed filtering, but it should be representative of the mesocyclone. The tornado is large at this formative stage ( 2 km wide), as indicated by the F0 contours, and the mesocyclone is nearly twice the diameter of the tornado. The center of the tornado is indicated by the letter T in the figure. The centers of the tornado and mesocyclone circulations are nearly collocated at this time. The mesocyclone is accompanied by a mesolow of nearly the same dimension with a maximum perturbation pressure deficit exceeding 9 mb (Fig. 6c). The center of the mesolow is collocated with the center of the tornado circulation. A qualitative inspection of the isobars of p (Fig. 6c) suggests that the storm-relative flow is in quasi-cyclostrophic balance. This hypothesis was tested by retrieving the cyclostrophic component of the perturbation pressure ( p cyclo ) using the procedure outlined by Liu et al. (1997) and Cai and Wakimoto (2001). Subsequently, the field of p cyclo (not shown) was subtracted from the total perturbation pressure (p ) and the results were plotted in Fig. 6d. The small values of p p cyclo provide quan- titative evidence that the low-level mesocyclone was in approximate cyclostrophic balance during this period. b. 2343: :02 UTC The subsequent radar scans occurred when the Kellerville tornado was near its peak damage intensity of F4 F5 (Fig. 3b). The tornado damage path had narrowed significantly at this time (Figs. 3a,b). A weakecho eye is still apparent in the radar reflectivity image (Fig. 7a). The Doppler velocity differential has increased and is now greater than 110 m s 1, consistent with the increase in the damage intensity associated with the tornado (Fig. 7b). Interestingly, the maximum vertical vorticity of the mesocyclone has decreased to s 1. This decrease, however, is an artifact of the filtering routine. The synthesis using a two-step Lei-

9 OCTOBER 2003 WAKIMOTO ET AL FIG. 5. Storm-relative winds at 800 m AGL at 2336: :40 UTC superimposed onto (a) radar reflectivity, (b) radar reflectivity and objectively analyzed single-doppler velocities (positive and negative values are drawn as solid and dashed black lines, respectively), and (c) vertical vorticity (positive and negative values are drawn as solid and dashed black lines, respectively) and vertical velocity (positive and negative values are drawn as gray and dashed gray lines, respectively). Radar reflectivity is drawn as gray lines, with values greater than 40 dbz shaded gray. Vertical velocities greater than 15 m s 1 are shaded gray. The s 1 contour of vorticity has been added to the vorticity plot and is shown by the dashed dot black line. The viewing angle of the Doppler radar is shown by the black arrow in (b). se filter (not shown) reveals an increase in the maximum vertical vorticity. It is important to note that in all subsequent analysis times presented in this section, the twoand three-step wind syntheses provide a consistent description of the changes in the kinematic structure of the low-level mesocyclone. This finding is highlighted in a plot of maximum vertical vorticity versus F-scale rating shown in Fig. 8. The plot includes the vorticity estimates from the two- and three-step Leise filters of the Doppler wind syntheses. The flow at low levels, presented in Fig. 7c, shows the downdraft and updraft air spiraling cyclonically around the center of the circulation, which is typical of many past radar and numerical simulations of supercell storms (e.g., Lemon and Doswell 1979; Dowell and Bluestein 2002a). The comparison of the Doppler syntheses with the damage track at this time is shown in Fig. 9. No weak-echo eye is apparent in the radar reflectivity data at 400 m shown in Fig. 9a (also supported in the vertical cross sections to be shown later). Note

10 2206 MONTHLY WEATHER REVIEW VOLUME 131 FIG. 6. Storm-relative winds at 400 m AGL at 2336: :42 UTC superimposed onto (a) radar reflectivity (radar reflectivity is drawn as gray lines with values greater than 40 dbz shaded gray), (b) vertical vorticity (positive and negative values are drawn as solid and dashed black lines, respectively) and vertical velocity (positive and negative values are drawn as gray and dashed gray lines, respectively), (c) perturbation pressure (positive and negative values are drawn as dashed black and solid lines, respectively), and (d) total perturbation pressure minus the cyclostrophic component of the perturbation pressure (positive and negative values are drawn as dashed black and solid lines, respectively). The thick gray line represents the s 1 isopleth of vertical vorticity, and the short-dashed line denotes the F0 isopleth of the tornado track. The s 1 contour of vorticity has been added to the vorticity plot (c) and is shown by the dashed dot black line. The black dot, cross, and the letters T and L denote the location of the storm-relative circulation center, the maximum vertical vorticity, tornado, and the center of the mesolow, respectively. The storm-relative wind vectors are plotted every 600 m (i.e., half of the resolution that is available). that the vorticity field suggests that the values between 40 and s 1 demarcate the approximate location of the F0 damage. 3 Equivalent values were difficult to determine from Fig. 6b since the mesocyclone 3 Vorticity calculations are independent of the reference frame, but damage at the surface also depends on the motion of the tornado (i.e., surface damage is a result of rotation plus translation). Accordingly, the numbers quoted here may not be generally applicable. was not centered on the tornado track. The width of the mesolow has decreased in Fig. 9c compared to that in Fig. 6c and the central pressure has increased by 4 mb [(the latter is to be expected since the maximum vertical vorticity has decreased; e.g., see Rotunno and Klemp 1982)]. The center of the storm-relative circulation, central low pressure, maximum vorticity, and the tornado center are all collocated in Fig. 9, similar to the results shown in Fig. 6. The isopleths of p p cyclo

11 OCTOBER 2003 WAKIMOTO ET AL FIG. 7. Same as Fig. 5 except for 2343: :02 UTC. The black line denotes the position of the vertical cross section shown in Fig. 17. The black line denotes the track of the Electra. suggest that the mesocyclone is still in approximate cyclostrophic balance (Fig. 9d). Note the large deviation that is associated with positive perturbation pressures on the right-hand side of analysis in Fig. 9d. These positive values are within the convergence zone along the gust front and result from the fluid extension terms in the perturbation pressure equation. c. 2349: :32 UTC The Kellerville tornado was narrowing and intensifying as it moved to the northeast during the earlier analysis times discussed in sections 2a and 2b. The period UTC was characterized by a major change in the orientation of the damage path. Although the tornado was still rated F4 F5 in damage intensity (Fig. 3b), it began to deviate from a linear path. This deviation was manifested as a pronounced sinusoidal wave pattern developed in the track (Figs. 3b, 4a). The aerial photographs revealed that the amplitude and wavelength of the pattern were 250 and 900 m, respectively. Past studies have only been able to make anecdotal comments concerning these unusual tornado tracks since supporting data were unavailable. The single-doppler velocity differential has decreased compared to that at earlier times to less than 80 ms 1 (Fig. 10b) even though the tornado s intensity has not diminished based on the surface damage (Fig. 3b). This result may be related to the discrete sampling that can change the magnitudes of the peak Doppler velocity values depending on the location of the mesocyclone relative to the radar beams (Wood and Brown 1997).

12 2208 MONTHLY WEATHER REVIEW VOLUME 131 FIG. 8. Estimated F-scale rating vs maximum vertical vorticity in the low-level mesocyclone for the Doppler wind syntheses using a two- and a three-step Leise filter. The maximum vertical vorticity has also decreased (Fig. 10c), but this should not be related to the discrete sampling limitations since the imposed Leise filtering on the wind field should negate the sensitivity of the positions of small point maxima and minima in single- Doppler velocities relative to the location of the radar beam. This weakening of the mesocyclone is also apparent in Fig. 11b since the peak vertical vorticity at 400 m decreased to s 1. In fact, the same approximate decrease in maximum vertical vorticity was observed at the lowest three levels of the syntheses. The analyses presented in Figs. 10 and 11 illustrate that the strength of the mesocyclone may not be correlated with the tornado s intensity based on the surface damage. As previously mentioned, the wind synthesis using a twostep Leise filter also supports a decrease in the maximum vorticity within the low-level mesocyclone. It is known that strong and violent tornadoes may develop at the time of the maximum mesocyclone strength (e.g., Burgess et al. 1993); however, changes in the mesocyclone intensity may not accurately reflect changes in the tornado s intensity. It is also apparent that the strength of the mesocyclone as quantitatively measured by the vertical vorticity is also a relatively poor indicator of the width of the tornado damage. The southern extent of the F0 damage in Fig. 11b is near the s 1 isopleth, a much lower value than was suggested in Fig. 9b, even though there was no apparent change in the tornado s motion. The mesolow has also continued to fill and has only one closed contour encompassing the minimum perturbation pressure (Fig. 11c). In addition to the general weakening of the circulation at this time, the structure has undergone a dramatic change. The relationship of the storm-relative flow to the mesolow suggests that the mesocyclone circulation departs from the nearly cyclostrophically balanced state that was evident in the earlier syntheses. This is supported by a larger range of p p cyclo isopleths, shown in Fig. 11d. Unlike the earlier times, there are now displacements between the circulation center, tornado, vorticity maximum, and center of the mesolow (Fig. 11). The storm-relative circulation is located to the north while the tornado is located to the south, embedded within the westerly flow of the mesocyclone and positioned in the center of the damage path. The minimum central pressure is near the maximum vorticity owing to the dominance of the fluid shear terms in the diagnostic perturbation pressure equation (not shown). The prevailing hypothesis advanced to explain the unusual twists and turns in a damage track based on past surveys was that the tornadic circulation was revolving within the larger-scale mesocyclone circulation (i.e., a trochoid). A schematic that illustrates this process is shown in Fig. 12a. This figure presents examples of trochoidal marks depending on the rotational speed of a hypothetical tornado around a larger mesocyclone propagating at different speeds. In order to test the trochoid hypothesis, it was decided to use the vorticity field as a proxy for the mesocyclone circulation since it is Galilean invariant (unlike the storm-relative wind field) and is commonly used to define the mesocyclone circulation (e.g., Davies-Jones et al. 2001). The location of the tornado was known based on the raw vertical scans recorded by the tail radars. The distance between the vorticity maximum and the tornado center was determined to be 310 m based on the analysis shown in Fig. 11. This distance compares favorably with the observed amplitude of 250 m measured in the track (Figs. 3b, 4a). The trochoid hypothesis, however, does not fully explain the sinusoidal damage track. A trochoid cannot produce a pattern with ridges and troughs that are symmetric. As shown at the top of Fig. 12a, the ridges will be associated with greater curvature than the troughs. In contrast, the damage track shown in the aerial photographs closely approximates a sinusoidal pattern. The reason for the observed departure from an ideal trochoid is not known. d. 2354: :56 UTC The tornado was near the end of the sinusoidal damage pattern at UTC (Figs. 13, 14). The rotational couplet has weakened in Fig. 13b compared to that in Fig. 10b, consistent with the damage rating falling into the F3 F4 range at this location of the tornado path. The maximum vertical vorticity displayed in Figs. 13c and 14c, however, has increased in magnitude from the previous pass (by s 1 ), again suggesting that changes in the mesocyclone s kinematic properties are not well correlated with the damage produced by a tornado. The increase in vorticity is consistent with the convergence as indicated by the rotated Doppler veloc-

13 OCTOBER 2003 WAKIMOTO ET AL FIG. 9. Same as Fig. 6 except for 2343: :02 UTC. The dashed black circle represents the diameter of the Kellerville funnel cloud based on a photograph shown in Fig. 17. ity field seen in Fig. 13b (see Brown and Wood 1991). It is possible that the characteristics of the mesocyclone at 400 m are not an appropriate indicator of flow near the ground; however, most Weather Surveillance Radar Dopplers (WSR-88Ds) used for tornado warnings are unlikely to see conditions lower than those presented in this study. Accordingly, the present findings have important operational implications; that is, changes in the intensity of the mesocyclone circulation as viewed by the WSR-88Ds may not be an accurate surrogate for the tornado circulation. It is seen in Fig. 14c that the flow is returning to a more cyclostrophically balanced state with two closed isobars enclosing the minimum pressure and the flow nearly parallel to the isobars. This trend is also supported by the trough of the isopleths of p p cyclo through the mesocyclone (Fig. 14d). This balanced state exists over a smaller region than was exhibited in Figs. 6c and 9c. The mesolow continues the trend of filling even though the maximum vorticity has increased. The tornado, storm-relative circulation center, and maximum vertical vorticity are once again collocated, while the low perturbation pressure is displaced slightly to the northeast. The maximum vorticity and the tornado are slightly displaced, which is consistent with the tornado approaching the end of the sinusoidal damage pattern and the track becoming linear once more. e. 0001: :09 UTC The tornado continued to weaken (damage intensity rated F3) and narrow by the next analysis time (

14 2210 MONTHLY WEATHER REVIEW VOLUME 131 FIG. 10. Same as Fig. 5 except for 2349: :32 UTC. UTC) based on the damage survey (Fig. 3) and a photograph of the funnel, respectively. The observed diameter of the funnel at this time was approximately half of the width noted at 2344 UTC and was consistent with the width of the damage as shown by the black circle in Fig. 3c. The results of the analysis of the ELDORA data from 0001 to 0003 UTC are presented in Fig. 15. The reduced damage intensity noted in Fig. 3c is supported by the smaller velocity differential in the couplet, suggesting that the tornado has weakened (Fig. 15). The vorticity associated with the mesocyclone (Fig. 15c) also decreased when compared to the analysis at UTC. The synthesis at the lowest grid level superimposed onto the damage track is shown in Fig. 16. The mesolow continues its trend to fill, with the minimum perturbation pressure deficit now less than 3 mb (Fig. 16c). There is no closed isobar, and the circulation again departs from a cyclostrophically balanced state (Fig. 16d), similar to the results presented in section 4c. The circulation center, tornado, maximum in vorticity, and minimum in perturbation pressure are in disparate locations in Fig. 16, in contrast to the results shown at UTC in section 4a. Indeed, the storm-relative circulation center is 3 km north of the tornado, and the position of the maximum in vorticity is 640 m from the tornado. Immediately after the synthesis time, a dramatic deviation in the tornado track occurred (Figs. 3c, 4b). The damage track of the Kellerville tornado had a cusplike pattern that was similar to the trochoid that is produced when the rotation around a circulation is

15 OCTOBER 2003 WAKIMOTO ET AL FIG. 11. Same as Fig. 6 except for 2349: :32 UTC. FIG. 12. Illustration of (a) basic trochoidal marks as a function of the rotational velocity of a hypothetical tornado around the mesocyclone and the motion of the mesocyclone and (b) a track if the tornado was rotating around the mesocyclone at the same speed as the translation velocity of the mesocyclone.

16 2212 MONTHLY WEATHER REVIEW VOLUME 131 FIG. 13. Same as Fig. 5 except for 2354: :56 UTC. equal to the translation speed of the circulation, as illustrated by the second-from-the-top drawing in Fig. 12a. Similar bends/turns in tornado tracks have been documented before in the literature (e.g., Brown and Knupp 1980; Fujita 1992), but no supporting data were available. The trochoid that provides the best fit to the Kellerville damage track is shown by the dashed gray line in Fig. 3c. The 580-m radius of the trochoid is nearly the same as the 640-m distance between the tornado and vorticity maximum. To further test the trochoid hypothesis, we estimated the movement of the parent mesocyclone and calculated the tangential wind speed associated with the mesocyclone at the location of the tornado. The mesocyclone was moving at 10.4 m s 1 from during the synthesis time. We averaged (over nine grid points) the winds in the location of the tornado and then subtracted the observed mesocyclone motion from the average. The result, representing the rotational velocity of the mesocyclone in the vicinity of the tornado, was 10 m s 1 from 238. The close agreement between the two speeds suggests that if the tornado were moving with the mean low-level flow in its surroundings (Dowell and Bluestein 2002b), it would have followed a trochoidal path with a cusplike pattern (Fig. 12). In summary, the nontrochoidal segments of the track occur when the tornado is located near or at the center of the mesocyclone. Radial displacements of the tornado from this center produce conditions supporting a trochoidal path. It should be noted that, owing to the coars-

17 OCTOBER 2003 WAKIMOTO ET AL FIG. 14. Same as Fig. 6 except for 2354: :56 UTC. er resolution of the data, the distances resolved in this study would not have been possible in many of the past dual-doppler studies of supercells. 5. Relationship of the Kellerville tornado with the hook echo and mesocyclone In using Doppler radar to define the airflow near and within a tornado, it is important that the visual characteristics of the tornado are known in order to remove possible ambiguities in interpreting the Doppler velocity fields. The most important characteristics are the tornado s width and its relationship to the radar beamwidth (e.g., Brown et al. 1978). The diameter of the tornado can be determined either by photogrammetry or from surface damage markings. The surface damage provides valid dimensions only for the bottom of the tornado. Unfortunately, this combination of photography and radar data has rarely been achieved in the literature. Bluestein et al. (1993) were able to provide detailed Doppler wind spectra on several tornadoes and document, with schematics, the ratio of the beamwidth to tornado diameter. Wurman and Gill (2000) presented high-resolution Doppler velocity information on the high-reflectivity ring based on radar reflectivity, but the relationship of the ring to the tornado was not known since no photographs of the funnel were shown. Wurman (2002) showed multiple rotational couplets embedded within a large tornado that were suggestive of suction vortices; however, only the debris ring was presented as a surrogate to the tornado width. Wakimoto and Atkins (1996) examined the mesocyclone and the visual characteristics of a wall cloud and tornado, but only single-doppler velocities were shown. Wakimoto

18 2214 MONTHLY WEATHER REVIEW VOLUME 131 FIG. 15. Same as Fig. 5 except for 0001: :09 UTC. The black line denotes the position of the vertical cross section shown in Fig. 19. The black line denotes the track of the Electra. and Martner (1992) presented analyses that revealed the relationship between the hook echo and the synthesized wind field with the appearance of a tornado funnel. However, the tornado was spawned by a storm that was not a supercell; that is, it was a nonsupercell tornado (e.g., Wakimoto and Wilson 1989). Therefore, the tornado was not accompanied by a parent mesocyclone. The Kellerville tornado provided an opportunity to create analyses similar to the ones by Wakimoto and Martner (1992) since two photographs, mentioned earlier in this paper, were taken of the condensation funnel at the same time that ELDORA was scanning the storm. The pictures were photogrammetrically analyzed so that vertical cross sections of the ELDORA wind synthesis and radar reflectivity could be superimposed on the images. a. 2343: :02 UTC B. Haynie was near the Kellerville tornado (southeast at a distance of 4.5 km) when he shot a dramatic picture of the funnel when the width was 1 km. This photograph was presented in Wakimoto et al. (1996, see their Fig. 11). Haynie s position is shown by the black dot in Fig. 1 and the viewing angle is enlarged in Fig. 3b. The tornado was rated between F4 and F5 at this time. In order to perform a photogrammetric analysis of Haynie s picture, a survey to locate the photographer s exact position was undertaken approximately one week after the event. Once the site was located, precise azimuth angles to targets on the horizon were determined, and the effective focal length and the tilt angle of the

19 OCTOBER 2003 WAKIMOTO ET AL FIG. 16. Same as Fig. 6 except for 0001: :09 UTC. camera lens were calculated. Subsequently, an azimuth and elevation-angle grid was constructed and superimposed onto the photograph. Knowledge of the photo site and the angle grid is required to produce vertical cross sections of the ELDORA syntheses that can be projected onto the picture. This technique has been used by Kingsmill and Wakimoto (1991), Wakimoto and Martner (1992), and Wakimoto et al. (1994) to augment the interpretation of the radar syntheses of convective phenomena. A general discussion of the photogrammetry can be found in Abrams (1952) and Holle (1986). The vertical cross sections in Fig. 17 demonstrate the storm structure within a slice through the weak-echo region of the tornado. The size of the radar beamwidth is drawn on the figure and the along-track data spacing was 300 m. The eye extended over a large depth and was associated with minimum radar reflectivity values 20 dbz. An enlarged view of this analysis focused on the tornado is shown in Fig. 18a. The stippled area in Fig. 17a denotes reflectivities of 45 dbz, which are located on the periphery of the funnel cloud. This feature might be considered part of the high-reflectivity ring that has been documented by Bluestein and Pazmany (2000) and Wurman and Gill (2000); however, it is embedded within a downdraft region and there does not appear to be any visual debris identifiable in the photograph. Weak downdrafts along the rear flank are evident to the left of the tornado (Figs. 17a,c), and the storm-scale updraft/downdraft interface near the surface is located at the center of the tornado (see also Fig. 18a). Strong updrafts are pervasive within the weak-echo eye of the

20 2216 MONTHLY WEATHER REVIEW VOLUME 131 FIG. 17. Vertical cross section through the Kellerville tornado at 2344:00 UTC superimposed onto a photograph: (a) radar reflectivity, (b) vertical vorticity, (c) vertical velocities and horizontal wind vectors, and (d) perturbation pressure. Storm relative winds are shown. Wind vectors are plotted with the following notation: barb 5ms 1, and half-barb 2.5ms 1. The location of the vertical cross section is shown by the black line in Fig. 7. The length scale in (a) is valid at the distance of the tornado. The radar beamwidth is also indicated in (a). The stippled area in (a) represents values 45 dbz. Photo taken by B. Haynie. hook and a trough of echo on the right-hand side of the figure. This trough is an extension of the weak-echo vault (Fig. 7a). Figures 17b and 18b present a unique view of the tornado embedded within the vertical vorticity field associated with the mesocyclone. The mesocyclone was 3 4 times larger than the visible funnel at this time. The maximum in vorticity ( s 1 ) can be seen near the surface and aloft. Also apparent in Figs. 7c and 17b is the anticyclonic vorticity to the rear of the rear-flank gust front, which is a feature often noted in this region (e.g., Klemp and Rotunno 1983). The vertical velocities and a profile of the horizontal winds are shown in Fig. 17c (and enlarged in Fig. 18c). The storm-scale updraft/downdraft interface and the strong horizontal shear across the funnel cloud are apparent in

21 OCTOBER 2003 WAKIMOTO ET AL FIG. 17. (Continued) these figures. The easterly and northeasterly inflows entering and rising on the north side of the mesocyclone are shown. The westerly flow spiraling cyclonically and descending south of the tornado (confined at low levels) is also apparent. The vertical structure of the mesolow is presented in Fig. 17d. The largest pressure deficits are evident near the ground and aloft, which is expected since the vertical vorticity was the strongest at these levels. The downward-directed vertical pressure gradient (not shown but can be estimated qualitatively from Fig. 17d) is largely responsible for forcing the downdrafts south of the tornado (e.g., Brandes 1984). Retrieved thermodynamic fields (not shown) reveal that positively buoyant air was the dominant forcing for the updrafts above the level of free convection (LFC). The updrafts below the LFC were dynamically forced by the upward-directed perturbation pressure gradient force. b. 0001: :09 UTC Another opportunity to compare the visual characteristics of the tornado with the radar synthesis occurred during the pass from 0001 to 0003 UTC. A photograph

22 2218 MONTHLY WEATHER REVIEW VOLUME 131 was taken from the cockpit of the Electra at 0002:18 UTC as the aircraft flew to the west past the storm (see Figs. 1,2). The diameter of the funnel cloud according to the photogrammetric analysis was shown in Fig. 3c and was approximately half of the width noted at 2344 UTC. The damage caused by the tornado, however, was still severe, with a maximum rating of F3. As previously mentioned, the tornado was located along the southern periphery of the mesocyclone at this time (Fig. 16b). This displacement explains the trochoidal pattern noted in the damage path in Fig. 3c based on the evidence presented in section 4. The method of photogrammetric analysis of this picture was different from that of the photo discussed in the previous section. This slight modification was needed since the photo was taken from an airborne platform. The camera imprinted the photograph with the time to the second. This time was then used to determine the location of the aircraft based on the GPS latitude and longitude recorded at flight level. Vanishing points were identified using roads in the picture to determine azimuth angles. The vanishing points can also be used to determine the nadir of the aircraft. This calculated nadir is then used as a cross-check to the GPS latitude and longitude. The effective focal length and tilt angle were calculated. The latter required a small correction factor, owing to the height of the aircraft above the ground. The funnel is 460 m in width near the low levels, and a pronounced debris cloud is apparent in the images shown in Fig. 19. The weak-echo eye is no longer apparent in the vertical cross section (Fig. 19a). The updrafts, as depicted in the wind field and Fig. 19c, are weaker over the tornadic region when compared to those in Fig. 17. The horizontal plots in Fig. 15c reveal that the overall updrafts are stronger; however, they are displaced to the east of the mesocyclone. The maximum vorticity and the gradients of vorticity (Fig. 19b) are weaker when compared to those evident in Fig. 17b, but the width of the mesocyclone is the same. Accordingly, the ratio of the width of the mesocyclone to the tornado funnel has increased and is now between The plots shown in Figs. 17b and 19b highlight the gap in our current understanding of the relationship between the strength and size of the mesocyclone and the tornado. FIG. 18. Enlarged vertical cross section through the Kellerville tornado at 2344:00 UTC superimposed onto a photograph: (a) radar reflectivity and storm-relative winds, (b) vertical vorticity and stormrelative winds, and (c) vertical velocities and horizontal wind vectors. Wind vectors are plotted with the following notation: barb 5m s 1, and half-barb 2.5 m s 1. The location of the vertical cross section is shown by the black line in Fig. 7. The length scale in (a) is valid at the distance of the tornado. The radar beamwidth is also indicated in (a). Photo taken by B. Haynie. 6. Summary and discussion A major outbreak of tornadoes occurred on 8 June 1995 during VORTEX. One of the tornadoes on this day, referred to as the Kellerville tornado, was rated F5 in damage intensity and produced a track that was 50 km long. A detailed aerial and ground survey of the tornado s path was conducted over a 3-day period. Two sections of the track exhibited unusual nonlinear swaths. One portion of the track was associated with a pronounced sinusoidal pattern that has not been previously documented in the literature. Another location was char-

23 OCTOBER 2003 WAKIMOTO ET AL FIG. 19. Same as Fig. 17 except for 0002:18 UTC. The location of the vertical cross section is shown by the black line in Fig. 15. The length scale in (a) is valid at the distance of the tornado. The radar beamwidth is also indicated in (a). acterized by a cusplike pattern. Theories to explain these movements proposed in past studies lacked supporting data. Fortunately, the current study was enhanced by the availability of high-resolution Doppler radar data collected by ELDORA. The ELDORA syntheses suggest that the nonlinear tracks are trochoidal marks produced as the tornado revolved about the center of the largerscale mesocyclone circulation. This hypothesis, however, does not fully explain the sinusoidal track since a trochoid does not exhibit symmetric ridges and troughs, which were evident in the aerial survey of the damage track. Another finding was that the storm-relative winds within the mesocyclone departed from a cyclostrophically balanced state during the times when the tornado deviated from the linear path. The physical reason for this relationship is not clearly understood at this time. The tornado circulation was not resolved in the wind synthesis because of the characteristics of the raw data and the imposed Leise filtering, although the position of the tornado was determined from the raw vertical scans of the tail radar. Instead, the resolved circulation was representative of the mesocyclone. The characteristics of the mesocyclone at 400 m were shown to be an unreliable indicator of the tornado s maximum intensity (as estimated from the F scale). No relationship could be found between a threshold vorticity value and the F0 isopleth that defined the outer limits of the damage caused by the tornado. It is possible that the characteristics of the mesocyclone at a height of 400 m are not an appropriate indicator of flow near the ground; however, most WSR-88Ds used for tornado warnings are unlikely to detect conditions lower than those presented in this study. These results are important in light of recent work suggesting a stronger relationship between tornado strength and the strength of the largerscale mesocyclone circulation (Burgess et al. 2002). It is possible that the collection of a larger database of measured winds in the lowest m might suggest better agreement between the tornado and mesocyclone intensities. Airborne radars cannot resolve winds at these low levels. In this regard, a future objective would be to target a tornado with both airborne and groundbased mobile radars. To date, this has yet to be accomplished. Two photographs were taken of the Kellerville tornado during the time that ELDORA was scanning the storm. These pictures were merged with the vertical cross sections of the ELDORA syntheses using photogrammetric techniques. These analyses revealed the structural relationship among the visual characteristics of the tornado, the hook echo, and the mesocyclone. One of the important conclusions was the lack of a definitive relationship between the widths of the mesocyclone and the tornado. This finding was also supported by ELDORA analyses at other times that were compared with the detailed damage survey of the tornado track. The factors that control this relationship constitute a long-standing issue that has not been given much attention in the literature. Acknowledgments. The authors would like to thank Bruce Haynie for providing the tornado photograph used in Figs. 17 and 18. The authors also wish to acknowledge Nolan Atkins and Ching-Hwang Liu, who participated in the survey of the tornadoes on 8 June 1995 and determined the location of the photograph taken by Bruce Haynie. Comments from the reviewers improved an earlier version of this manuscript. Research results presented in this paper were supported by the National Science Foundation under Grants ATM and (through RMW) and ATM (through HBB).