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Abstract
Quasi‐linear convective system (QLCS) mesovortices produce a non‐trivial fraction of tornadoes across the United States each year. Tornadoes from QLCS mesovortices evolve rapidly on time scales less than that observed by conventional weather radars. In this study, a well‐calibrated, dual‐polarization phased array radar (PAR) is used to examine three tornadic mesovortices in the 27 February 2023 QLCS in central Oklahoma, with rapid volumetric scanning strategies that included dense elevation angles. Through examining dual‐polarization profiles and three‐dimensional wind estimates around the mesovortices, we show that the mesovortices examined were associated with (a) downdrafts prior to tornadogenesis, (b) increased convergence along the QLCS gust front ahead of the downdrafts, and (c) dual‐polarization profiles that suggest evaporation and precipitation drove the downdrafts. This study represents the first time a dual‐polarization PAR has been used to document tornadic QLCS mesovortices.
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Introduction
Quasi-linear convective systems (QLCSs) produce about one-fifth of tornadoes documented annually in the United States (Ashley et al., 2019). QLCSs are considered a class of mesoscale convective systems (MCSs; e.g., Houze, 2004) and are often characterized by a leading convective line and trailing stratiform region (e.g., Biggerstaff & Houze, 1991). Although many conceptual models represent MCSs and QLCSs and their environmental parameters such as environmental wind shear as quasi-two-dimensional, the leading-edge convective line is characterized by local vertical draft heteorogeneities. Such heterogeneities can be integral to QLCS mesovortex dynamics, which are often responsible for both severe wind hazards and tornadoes (Flournoy & Coniglio, 2019; Goodnight et al., 2022; Miller et al., 2020; Wheatley & Trapp, 2008).
QLCS mesovortices and their tornadoes are thought to form by a number of different processes. For example, many studies have shown that the tilting (by updrafts or downdrafts) of baroclinic vorticity along the cold pool interface is an integral redistribution mechanism of vertical vorticity (Atkins & St. Laurent, 2009; Flournoy & Coniglio, 2019; Trapp & Weisman, 2003; Wheatley & Trapp, 2008). Secondary sources of vorticity have been noted in downdrafts descending within the rear inflow jet behind the cold pool front (e.g., Atkins & St. Laurent, 2009; Flournoy & Coniglio, 2019). No matter the source of vorticity, an often key feature of mesovortices is a local gust front surge (Atkins & St. Laurent, 2009; Flournoy & Coniglio, 2019; Schaumann & Przybylinski, 2012; Trapp & Weisman, 2003; Xu et al., 2015) that yields enhanced convergence and/or enhanced tilting of vorticity along the gust front edge. Downdrafts behind the cold pool near the developing tornadic mesovortex are often considered responsible for the local surge. Recent work from McDonald and Weiss (2021) suggests that such regions may be characterized by local minima in virtual potential temperature, thereby locally enhancing baroclinity. Few detailed observations have been collected to date to examine the relationship between vertical draft and/or thermodynamic processes, however.
Many studies point to downdrafts as being an integral part of QLCS mesovortexgenesis and/or intensification. For example, Flournoy and Coniglio (2019) showed parcels originating from the rear-inflow jet (e.g., Smull & Houze, 1987) descending rapidly toward the surface over periods 5 min, resembling the concept of a local downdraft linked to a gust front surge in the vicinity of mesovortices. Measuring such processes is quite challenging observationally. Conventional, rotating, parabolic antenna weather radars such as the Weather Surveillance Radar- 1988 Dopplers (WSR-88Ds; Crum & Alberty, 1993; Doviak et al., 2000) collect radar volumes every 4.5–6 min, suggesting that WSR-88Ds may not fully resolve such features in time (Lyza et al., 2019). However, phased array radar (PAR) can collect full radar volumes in 1–2 min, depending on how a scan strategy is designed. Using a single-polarization PAR, Newman and Heinselman (2012) characterized tornadic mesovortices in central Oklahoma and showed that increasing mid-level convergence (implying a downdraft in the low levels) was followed by enhanced low level outflow (i.e., a surge). Unfortunately, no dual-polarization PAR studies, which can be used to evaluate both the kinematic and microphysical evolution of QLCS mesovortices, exist. This study leverages the NOAA National Severe Storm Laboratory (NSSL) Advanced Technology Demonstrator (ATD) to document three tornadic mesovorites on 27 February 2023. Specifically, we seek to leverage rapid-update, dual-polarization PAR data to understand (a) if downdrafts may be responsible for localized surges in the convective line as suggested mostly by modeling studies (e.g., Atkins & St. Laurent, 2009; Flournoy & Coniglio, 2019; Schaumann & Przybylinski, 2012; Trapp & Weisman, 2003; Xu et al., 2015) and (b) the microphysical drivers that may be inherent to these downdrafts (e.g., French et al., 2015; McDonald & Weiss, 2021).
Data and Methods
The Advanced Technology Demonstrator (ATD)
The NSSL ATD is a dual-polarization PAR that operates at S-band wavelength (10-cm). It is built to examine the benefits of dual-polarization PAR, particularly as the NOAA National Weather Service considers the next generation of weather radar. A historic difficulty with dual-polarization PAR is taking into account the cross-polarization biases induced in dual-polarization variables (Palmer et al., 2022). However, research at NSSL has yielded robust dual-polarization calibration techniques that have been implemented on the ATD (Ivic, 2022). The ATD is positioned atop a rotating platform so that its face, comprised of 76 panels with a total of 4,864 individual elements, can be rotated in a desired direction. The ATD is designed to mimic one side of a four-faced PAR and has a 90 field of view. At broadside (i.e., the direction normal to the antenna face), the ATD has a 1.6 half-power two-way beamwidth and swells to 2.1°± 45° azimuth from broadside.
The 27 February 2023 QLCS
On 26–27 February (UTC dates), a line of severe thunderstorms entered western Oklahoma. The ATD began observing the QLCS at 27 February 0025 UTC. In total, it produced 13 tornadoes across Oklahoma (see ). The ATD observed the parent mesovortices of many of the tornadoes in its 90 field of view (e.g., Figures 1a and 1b). Three mesovortices that produced tornadoes near Gracemont, Minco, and Tuttle, OK, respectively, were particularly well-sampled by ATD and are the subjects of this study. Each mesovortex was tracked in space and time at each 0.5 elevation update from the ATD by computing the linear-least-squares azimuthal derivative of Doppler velocity described in Mahalik et al. (2019), also commonly referred to as “AzShear.” AzShear, as discussed in Mahalik et al. (2019), scales to approximately one-half of the vertical vorticity (for an axisymmetric vortex) and is a commonly used metric to track mesocyclones and mesovortices (e.g., Alford et al., 2023; Flournoy et al., 2022; Lyza et al., 2022; Sandmæl et al., 2023). In this case, each mesovortex center was tracked subjectively to ensure that spurious maxima in AzShear did not bias the results. We report the centers at each time in the Supporting Information S1.
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Dual-Polarization Data
Dual-polarization data were collected by ATD throughout the event. A scanning strategy similar to the WSR-88D Volume Coverage Pattern 212 (but with additional elevation angles sampled) was designed for use by the ATD to collect a full volume scan in 2 min (see the inset text in Figure 1c). We note that the ATD can collect volumes on the order of 1 min, but the intent of this particular collection was to examine dense vertical coverage with rapid, 2-min volume updates. Rather than examine the dual-polarization data in plan views, we employ a four-quadrant time-height series, similar to the four-quadrant analysis in French et al. (2015), to examine the mean dual-polarization characteristics through the following steps:
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The speed and direction of a mesovortex observed at 0.5 elevation was computed for each radar volume time. The 0.5 elevation mesovortex position was recorded for each 0.5 elevation (Figure 1c) in each radar volume. The forward-difference change in position of the mesovortex between the first and second 0.5 elevation scans was then used to compute the east-west u and north-south v components of mesovortex motion.
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In this study, we use the mesovortex position on the 0.5 radar elevation surface as the frame of reference. Since the complete radar volume takes 2 min to complete, the position of the mesovortex must be taken into account as each radar elevation is collected. To do so, the u and v component of motion derived in the previous step is used to approximate the mesovortex position at the time the elevation scan in the radar volume was collected.
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All dual-polarization data at each radar volume time were then rotated into a mesovortex-motion-relative direction such that 0 points along the mesovortex motion vector and the angle increases clockwise.
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Finally, the mean value of each dual-polarization variable was computed for each quadrant (0–90, 90–180, 180–270, and 270–360) relative to mesovortex position at each radar elevation. Only data on each elevation surface within a 5-km radius of the mesovortex center were used. Reducing the radius around the mesovortex yielded similar, but increasingly noisy results. We note that even within 5 km of the mesovortex center, the radar gate height will change slightly along the radar elevation surface. Thus, we computed the mean height for each quadrant as well to find a representative height.
The result at each radar time is a vertical profile of each radar variable for each mesovortex-relative quadrant, ultimately yielding a time-height series for each radar variable relative to the approximate location of the mesovortex center on the 0.5 elevation surface.
Estimating Vertical Motion
In this study, we also use ATD data to estimate vertical motion. Unfortunately, dual- or multi-Doppler radar analysis (e.g., Armijo, 1969; Potvin et al., 2012) is not possible. We instead employed a technique that allows an estimate of vertical motion by combining a representative pre-QLCS environment with ATD observations. The Spline Analysis at Mesoscale Utilizing Radar and Aircraft Instrumentation (SAMURAI; Bell et al., 2012) is a variational cost function technique that yields a “maximum likelihood estimate of the atmosphere.” SAMURAI, unlike other objective analysis techniques, allows for greater flexibility in including a priori background estimates of the atmosphere to constrain the final wind field solution derived from observations (in this case, ATD observations).
Using SAMURAI to retrieve vertical motion is not without uncertainty, particularly in the novel, single-Doppler approach used here. A single-Doppler ATD solution (with a background constraint) yields vertical wind fields that are heavily weighted toward the component of divergence observed by the ATD. We caution the reader that the placements of updrafts and downdrafts are meaningful, but their magnitudes are underestimated. We also compute horizontal divergence from the retrieved horizontal wind components, which are (again) heavily weighted toward the Doppler observations. As described further in the Supporting Information S1, the wind fields serve as proxies for the true wind field. This approach is similar to assessing the raw, single-Doppler-observed winds as in Newman and Heinselman (2012), but in a three-dimensional SAMURAI framework. We show an error analysis in the Supporting Information S1, indicating this single-Doppler approach applied to a QLCS is reasonable, but we suggest additional error analysis be undertaken if the technique is applied to other convective modes. We attempted a multi-radar solution using the central Oklahoma WSR-88Ds and found that the comparatively poor volumetric time resolution inhibited the SAMURAI analyses. Details of the SAMURAI domain are included in the Supporting Information S1.
Results
On the Enhanced Fujita (EF) scale, the Gracemont, Minco, and Tuttle mesovortices each produced tornadoes rated EF0, EF0, and EF1 at 0232, 0252, and 0257 UTC, respectively. In this section, we examine the dual-polarization data with particular attention paid to characteristics prior to tornadogenesis. We focus our dual-polarization analysis on differential radar reflectivity () and specific differential phase (). We remind readers that is the difference between horizontal and vertical polarized radar reflectivity and is characteristic of the shape of larger particles (e.g., raindrops). is the range derivative of the differential phase (the difference between the phase of the horizontal and vertical polarized waves) and is related to the particle concentration (e.g., total amount of liquid water). We refer the reader to (Kumjian, 2013) for a review of dual-polarization radar variables.
Four-Quadrant Analysis
In Figure 2, the four-quadrant analyses for all three mesovortices is shown. Figures 2a and 2b show the evolution of and , respectively, associated with the Gracemont mesovortex. On the left side of the mesovortex (i.e., the 270–360 and 180–270 quadrants) generally decreases prior to and after tornadogenesis (0232 UTC), particularly 2-km altitude. On the right side of the mesovortex, there is an increase in from 2 dB at 0225 UTC to 3 dB at 0231 UTC at 1.5-km altitude. In terms of on the left side of the mesovortex, the highest values (near 4) are noted in the 270–360 quadrant near and just after tornadogenesis at 3–4-km altitude and decrease below. In contrast, comparatively low magnitudes of in the 180–270 quadrant are noted. On the right side of the mesovortex, increases from at 0225 UTC to 1.5–3 from 0227 to 0231 UTC in the 90–180 quadrant. After tornadogenesis, decreases in the 90–180 quadrant. However, near and after tornadogenesis, increases in the 0–90 quadrant and is higher in the 0–90 than in the 90–180 quadrant. We note that the highest values of tend to be near 2–3-km altitude on the right side of the mesovortex. Below the maximum, increases closer to the surface.
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In the Minco mesovortex (Figures 2c and 2d), some differences in and compared to the Gracemont mesovortex are noted. For example, approaches 2.5 dB at 0245–0247 UTC in the 180–270 quadrant, but then decreases in the minutes leading up to tornadogenesis. In the 0–90 quadrant, does not increase near tornadogenesis as it did in the Gracemont mesovortex. However, there are similarities between the two such as 2.5 dB observed below 2 km in the 90–180 quadrant until tornadogenesis. Additionally, an increase in from near 3 at 0239 UTC to 4 at 0243 UTC is noted in the 90–180 quadrant, preceding tornadogenesis at 0251 UTC. also remains higher in the 0–90 quadrant after tornadogenesis than the 90–180 quadrant. Like in the Gracemont mesovortex, the highest on the right side of the mesovortex tends to be co-located or above the maximum in altitude.
The general and temporal evolution of the Tuttle mesovortex (Figures 2e and 2f) is similar to that of the Minco mesovortex. In the 180–270 quadrants, is near 2.5 dB at 0247 UTC and generally decreases up to tornadogenesis. likewise decreases from a maximum above 4 at 0247 to <2°km−1 immediately before tornadogenesis. However, in the 90–180 quadrant, higher values (2.5–3 of ) are maintained to near tornadogenesis. In the 0–90 quadrant, high magnitudes of are noted at 0255 UTC just before tornadogenesis and decrease in the few minutes following tornadogenesis. Similar to the previous two vortices, we note that the maxima in on the right side of the Tuttle mesovortex tend to be above the surface (near or just below 2-km altitude). tends to be nearly steady or decrease slightly below the maximum.
We further discuss the significance of the temporal and vertical structure of the dual-polarization data in Section 4.
Vertical Velocity Estimates
We further examine the relationship between the maxima detailed in Section 3.1 and near-mesovortex kinematics. Using the SAMURAI-based analyses of vertical motion discussed in Section 2.4, we show surfaces of vertical velocity on the SAMURAI grid within 5 km of the center of the Tuttle mesovortex prior to and near tornadogenesis in Figure 3. We focus here on the Tuttle vortex, as it was best observed by the ATD, but show similar analyses in Figures S2 and S3 in Supporting Information S1 for the other mesovortices.
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At the earliest possible time at which the mesovortex could be identified (Figure 3a), a downdraft to the southwest of the mesovortex is analyzed in the SAMURAI wind fields. A local maximum in is approximately co-located with the downdraft. To the east of the mesovortex, an updraft maximum approximately oriented north-south can be seen and is associated with the leading edge of the cold pool (similar to conceptual models of MCSs and QLCSs; Biggerstaff & Houze, 1991; Houze, 2004). Approximately 6 min prior to the Tuttle tornado, the downdraft and maximum were located to the southwest of the Tuttle mesovortex. To the east of the maximum, convergence increased at 0.5-km altitude. Two minutes prior to tornadogenesis, further separation of the maximum and the downdraft location is noted, such that the maximum is displaced to the east of the downdraft core. Likewise, the convergence maximum at 0.5-km altitude appears to remain farther displaced east ahead of the maximum. At tornadogenesis, the maximum in is displaced to the south. Following tornadogenesis, the maximum is displaced east of the mesovortex center and quickly decreases in magnitude, similar to the results of the four-quadrant analyses in Figure 2.
We also examined similar analyses for the Gracemont and Minco mesovortices in Figures S2 and S3 in Supporting Information S1, respectively. In the Gracemont vortex, the most substantial differences were that (a) convergence only slightly increased to the southeast of the mesovortex just before and near tornadogenesis and (b) the downdraft magnitude was muted. Both are likely explained by the significant undersampling of the low-level wind field of the Gracemont mesovortex at far range. In the Minco mesovortex, the convergence maximum is displaced further east than the Tuttle mesovortex at 2 min prior to tornadogenesis, but does appear to “wrap” into the near-center of the mesovortex. Although there are differences in the , vertical draft, and gust front convergence evolution among the three mesovorties examined prior to their producing tornadoes, we note several important similarities between them:
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Prior to tornadogenesis in all three vortices, there exist vertically coherent maxima (generally upwards of 4 ) to the south and southwest of the mesovortices. As time progresses, decreases to the southwest and increases to the southeast, similar to the results of Figure 2.
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The maxima are associated with a local minimum in vertical velocity at the earliest observed time, which may be considered mesovortex-genesis as we were unable to further track a mesovortex backward in time.
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Following mesovortex-genesis, low level convergence increases along the gust front. The increase was noted to the south, southeast, and/or near the center of the mesovortex near tornadogenesis (and near the time at which the mesovortex was strongest).
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In the Minco and Tuttle mesovortices (the best observed mesovortices) downdrafts persisted from mesovortex-genesis through tornadogenesis, but weakened near tornadogenesis as they became displaced from the maxima.
The evolution has important similarities to previous studies, which we further explore in Section 4.
Discussion
Summary
This manuscript used the NSSL, dual-polarization, ATD PAR to document the evolution of three tornadic mesovorties with 2-min radar volume updates. We employed a four-quadrant, mesovortex-following analysis to show that tends to increase in the 90–180 quadrants (meaning behind and to the right of the mesovortex) prior to tornadogenesis (Figure 2). Near and after tornadogenesis, the highest was noted in the 0–90 quadrants. On the right side of the vortices, tends to be maximized 1–3-km altitude and decrease toward the surface. tends to increase or slightly decrease below the maximum. We further explored the relationship between vertical motion and the low level maxima near the mesovortices and found that at the earliest observed time at which a mesovortex could be identified, a vertically coherent maximum was co-located with a minimum in vertical motion. Near tornadogenesis, tended to decrease to the south and southwest of the mesovortices.
Mesovortex Evolution
As previously noted, high in the 90–180 quadrant tends to precede tornadogenesis and decreases near or after tornadogenesis. The same trends were also noted in our examination of the combined kinematic- analysis in Figure 3. Such evolution is akin to the evolution of mid- and low level core evolution discussed in Kuster et al. (2024). Maximum values approaching 5 are noted at times in Figure 3, suggesting significant water droplet concentrations (and possibly water-coated hail) precede tornadogenesis and are associated with mesovortex-genesis. As such, water-loaded downdrafts exist behind and to the right of the mesovortices and appear to precede low level enhancements in 0.5-km altitude convergence (Figure 3). Many model-based studies have suggested that precipitation-loaded downdrafts may be a factor in locally enhancing convergence along the gust front and may be important in mesovortex and/or tornadogenesis (Atkins & St. Laurent, 2009; Flournoy & Coniglio, 2019; Trapp & Weisman, 2003; Xu et al., 2015). However, few observations have been collected with sufficient temporal and spatial (primarily vertical) resolution to validate these typically model-based conclusions. Our observational results here support such a conceptual evolution and provide additional context to the operational-oriented dual-polarization signatures documented in Kuster et al. (2024).
We likewise noted that tended to be maximized to the right of the vortices at between 1 and 3-km altitude and decrease toward the surface with the exception of the profiles in the 90–180 quadrant in Figure 2d where tended to remain steady or increase. , on the other hand, tended to increase toward the surface in the Gracemont and Minco vortices and remained steady or slightly decrease in the Tuttle mesovortex. We also note that reflectivity (Figure S1 in Supporting Information S1) tended to decrease near the surface below the maximum between 1 and 3-km altitude. Precipitation processes in a vertical column may be gleaned from dual-polarization data following Kumjian et al. (2022, their Table 1), which notes that decreases in reflectivity and and increases or small decreases in toward the surface can imply evaporation. Small droplet evaporation tends to reduce and reflectivity, which yields a drop size distribution skewed more in favor of large droplets and increases (or slight decreases) in . As noted by Kumjian et al. (2022), the presence of a “dominant” precipitation process does not exclude another (e.g., breakup). However, based on the relatively small changes in toward the surface coupled with decreases in reflectivity and often , we find the presence of evaporation in the downdrafts examined here to be plausible. Given the near co-location between the maxima and downdrafts, we expect that downdrafts in this case are associated with enhanced evaporation. McDonald and Weiss (2021) notes that local cooling may give rise to enhanced baroclinically generated vorticity being transported into a mesovortex. Note that the presence of evaporation does not necessarily imply that substantial cooling is present due to the influence of environmental saturation, nor is this process ubiquitous across all QLCS mesovortex cases. Quantifying the full baroclinic effects of evaporation, if any, on mesovortices and their associated tornadoes observationally will require further study.
We also note that there is substantial overlap between 2 dB and 3.5 on the right side of the mesovortices at the bottom of the profiles (Figure 2). At S-band, 2 dB tends to imply the presence of large droplets and 2–3 tends to imply significant water drop concentrations, suggesting that a broad drop size distribution is likely (i.e., both small and large droplets). Such substantial quantities of and can imply melting hail/graupel and enhanced precipitation loading, respectively, which are considered buoyant effects. A precipitation-loaded downdraft, which leads to enhanced near-gust front convergence, as demonstrated in Figure 3, is consistent with many studies cited here.
Previous studies of supercell rear flank downdrafts such as French et al. (2015) indicate a wide variety of drop size distributions. It was posed in French et al. (2015) that regions with large concentrations of small drops (i.e., high ) may suggest more limited evaporation, which is typically favorable for supercell tornadoes. Although evaporation signatures are observed, near the surface remains rather high. High regions with low drop concentrations in the rear flank downdraft implies greater evaporation, which potentially limits tornadoes in supercells. Arguments by Kumjian (2011) suggest that regions with both high and high may suggest that drops are transported quickly downward by dynamically induced downdrafts such that the evaporation of small drops is limited. Although we cannot directly differentiate the dynamic versus thermodynamic drivers inherent to the downdrafts observed in this study, our findings suggest that both thermodynamic and dynamic downdraft mechanisms are likely.
Broader Impacts
QLCS mesovortices and their tornadoes are notoriously difficult to forecast due to their rapid evolution and often shallow depths. Using dual-polarization signatures to monitor tornadic potential in QLCS mesovortices has received recent attention (Kuster et al., 2024), which showed that tornadic mesovortices tend to be associated with stronger maxima (“ cores”) near and below the melting level than non-tornadic mesovortices. This study provides additional insight into the microphysical and kinematic processes associated with tornadic mesovortices and “ cores” discussed in Kuster et al. (2024) and other studies. In the former sub-section, we noted some uncertainties in our results, including the relationship between evaporation and local cold pool enhancements as well as the broader application of our results across other QLCSs. The recent Propagation, Evolution, and Rotation in Linear Storms (PERiLS) project (Kosiba et al., 2024) collected a wide variety of dual-polarization radar, sounding, profiling, and in situ drop size distribution information that will likely be useful to examine such topics.
Finally, we note that this study represents the first time a dual-polarization PAR has been used to examine tornadic mesovortices in a QLCS. PAR is a replacement option under consideration for the operational WSR-88D network (Alford, Kuster, Schuur, et al., 2025; Alford et al., 2024; NOAA, 2022). Again, the ATD was built to mimic one side of a four-panel PAR concept. Using the ATD to observe the mesovortices examined here suggests that PAR is better able to capture the full, three-dimensional, volumetric evolution of QLCS mesovortices with 2-min temporal resolution compared to WSR-88D scanning strategies which take much longer. Although the WSR-88Ds can revisit 0.5 elevations several times within a single radar volume to capture up to 90-s low level updates, the total volume update time is extended to do so. However, we show that the dual-polarization signatures associated with tornadic mesovortex evolution are not limited to the lowest radar elevation, but rather evolve quickly in time over several kilometer depths. Thus, the benefits of rapid-update volumes afforded by dual-polarization PAR are emphasized in this study.
Acknowledgments
This work was supported by the Phased Array Radar Program at the NOAA National Severe Storms Laboratory. Funding for R.M. was provided by NOAA/Office of Oceanic and Atmospheric Research under NOAA-University of Oklahoma Cooperative Agreement NA21OAR4320204, U.S. Department of Commerce. We thank Dr. Tony Lyza, Dr. Anthony Reinhart, and Dr.Larry Hopper for their comments that improved this work. We also wish to acknowledge the two anonymous reviewers for their comments that improved this manuscript.
Conflict of Interest
The authors declare no conflicts of interest relevant to this study.
Data Availability Statement
The ATD data leveraged in this study are available from .
The analysis code created for this study are housed at and archived, along with the SAMURAI analyses, at Alford, Kuster, and Miller (2025).
Figures 1a, 1b, and 2; Figure S1 in Supporting Information S1 were made using Matplotlib version 3.4.3 (Caswell et al., 2021).
Figure 3; Figures S2 and S3 in Supporting Information S1 were generated using Plotly version 5.22.0 available from .
SAMURAI is documented in Bell et al. (2012) and available from .
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