1. Introduction
Dual-polarization radar provides the capability to discriminate between meteorological and nonmeteorological scatterers (e.g., Zrnić and Ryzhkov 1999), which has an important application for tornado detection. The random orientations, irregular shapes, and wide range of dielectric constants and sizes of lofted tornadic debris produce a unique polarimetric signature called the tornadic debris signature (TDS; Ryzhkov et al. 2002, 2005). These scattering characteristics produce a distinct TDS (Ryzhkov et al. 2002, 2005; Bluestein et al. 2007; Kumjian and Ryzhkov 2008; Snyder et al. 2010; Palmer et al. 2011; Bodine et al. 2011; Schwarz and Burgess 2011; Bunkers and Baxter 2011) characterized by high horizontal radar reflectivity factor (ZHH), low differential reflectivity (ZDR), and very low copolar cross-correlation coefficient (ρHV) values, which are typically collocated with the tornadic vortex signature (TVS; Brown et al. 1978).
In an examination of three tornado cases in central Oklahoma, Ryzhkov et al. (2005) showed that TDSs identified the locations of tornadoes (20–60 km from the radar) with an enhanced Fujita (EF) scale rating (McDonald et al. 2004; WSEC 2006) of 3 or higher using S-band radars. Their study determined preliminary criteria for tornado detection of ZHH > 45 dBZ, ZDR < 0.5 dB, and ρHV < 0.8. Ryzhkov et al. (2005) defined six parameters for the intensity of the TDS: the minimum and average ρHV value, minimum and average ZDR value, the number of 0.5 km × 0.5 km pixels where ρHV < 0.8 and ZHH > 45 dBZ, and the number of 0.5 km × 0.5 km pixels, where ZDR < 0.5 dB and ZHH > 45 dBZ. They found that the minimum and average values of ZDR and ρHV reached a minimum, and the number of pixels reached a maximum, during periods of peak damage severity for the three tornado cases.
The capability to identify tornadoes using the TDS has been examined in other studies. Kumjian and Ryzhkov (2008) examined TDSs associated with nine tornadoes of EF1 rating or higher at S and C bands, revealing that some weak tornadoes produce TDSs. However, they also noted that some weak tornadoes may not loft sufficient debris to produce a TDS. Precipitation entrainment also affects the TDS. Bluestein et al. (2007) observed that precipitation entrainment into the tornado may cause positive ZDR values, and Schwarz and Burgess (2011) observed that ρHV values in the TDS increased after precipitation was ingested during a storm merger. Using single-polarization Weather Surveillance Radar-1988 Doppler (WSR-88D) data, Bunkers and Baxter (2011) examined seven tornado cases rated between EF3 and EF5 and found ZHH values between 51 and 72 dBZ.
Though previous studies have shown the capability to use polarimetric radar to detect tornadoes, the application of the TDS to estimate near-real-time tornado damage severity has not yet been thoroughly examined. In this study, modified versions of the Ryzhkov et al. (2005) TDS parameters and new TDS parameters are examined using S-band polarimetric WSR-88D (Doviak et al. 2000) data from the Norman, Oklahoma (KOUN), radar. TDS parameters are compared to detailed damage surveys provided by the National Weather Service’s (NWS) Weather Forecast Office (WFO) in Norman. TDS parameters are tested on 14 tornado cases from the 10 May 2010 and 24 May 2011 tornado outbreaks, providing an analysis of the performance of TDS parameters for varied tornado intensities and sizes, distances from the radar, and different storm-scale environments. In addition to these 14 tornado cases, 7 tornado cases that did not produce TDSs are also documented.
Section 2 presents a description of the data from the KOUN polarimetric WSR-88D (Doviak et al. 2000), a brief overview of the tornado outbreaks and tornado damage surveys, and a description of the TDS parameters evaluated in the study. In section 3, detailed comparisons between two NWS damage surveys and TDS parameters are presented. Section 4 compares the highest and lowest values of TDS parameters for 14 tornado cases with the EF rating of each tornado. A discussion of potential factors impacting the TDS and the strengths and limitations of each TDS parameter is presented in section 5, followed by the conclusions in section 6.
2. Data and TDS parameter design
a. Data and damage survey overview
Data from the KOUN radar located in Norman are analyzed in this study. It is a prototype WSR-88D polarimetric (dual-pol) S-band radar with a 0.9° beamwidth and 250-m range resolution. Raw, level-II KOUN data from the 10 May 2010 and 24 May 2011 tornado outbreaks are examined in this study [different from the gridded data used in Ryzhkov et al. (2005)]. During both events, KOUN operated volume coverage pattern (VCP) 12 (Brown et al. 2005b), which includes the following elevation angles: 0.5°, 0.9°, 1.3°, 1.8°, 2.4°, 3.1°, 4.0°, 5.1°, 6.4°, 8.0°, 10.0°, 12.5°, 15.6°, and 19.5°. The 0.5°, 0.9°, and 1.3° elevation angles are oversampled at 0.5° resolution (Brown et al. 2005a), and the VCP requires 4 min 18 s to complete.
On 10 May 2010, 55 tornadoes struck portions of central and eastern Oklahoma. The two strongest tornadoes were rated EF4 and occurred near Norman. For a detailed discussion about the 10 May 2010 tornado outbreak and C-band observations of TDSs, the reader is referred to Palmer et al. (2011). On 24 May 2011, 12 tornadoes struck western and central Oklahoma, including two EF4 tornadoes and one EF5 tornado. Figure 1 shows the tornado damage paths on 10 May 2010 and 24 May 2011, which were plotted using data provided by the Norman NWS WFO. Of the tornadoes shown in Fig. 1, only the tornadoes occurring within 120 km of KOUN are investigated in this study.
Damage tracks for tornadoes 1–21 discussed in this study from 10 May 2010 and 24 May 2011. The dashed box in the top-left panel indicates the location of the inset panel given on the top-right. (bottom left) Tornadoes in south-central OK on 10 May 2010 and (bottom right) damage survey from 24 May 2011. The X and Y coordinates indicate the zonal and meridional distance from KOUN.
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-11-00158.1
In the present study, damage surveys based on the EF scale are compared to TDS parameters. The EF rating depends on the type of damage indicators along the damage path and the degree of damage (WSEC 2006). An important note is that the EF scale underestimates tornado wind speeds when the highest degree of damage for the damage indicators is observed. In rural areas, the upper bound of the wind speed that can be established from tree damage, farm buildings, or manufactured homes is much lower than engineered structures, which sometimes results in underestimated maximum wind speeds. Accordingly, some discrepancies between the along-path EF-scale rating and TDS parameters may be expected, even though both are dependent upon tornado damage. For example, consider a tornado producing isolated, EF4 damage to a well-constructed home and an identical tornado that remains in a rural area with no engineered structures. The TDS for a tornado producing EF4 damage to the residence may not differ significantly from the same tornado in a rural area with no engineered structures unless the debris lofted from the residence substantially changes the TDS. Moreover, the contribution of debris from the isolated residence may only affect a small portion of the TDS for a large-diameter tornado. Given that the differences in TDSs resulting from engineered structures and vegetation are not well understood, the differences in TDSs resulting from man-made structures and vegetation are unknown.
A reasonable hypothesis is that a more intense tornado may loft more tornadic debris than a weaker tornado. Hence, in the absence of engineered structures, the TDS may reflect changes in tornado intensity that cannot be deduced by the EF scale in the absence of engineered structures (e.g., a violent tornado lofting more vegetation than a weak tornado). Nonetheless, because near-surface, tornado-scale wind measurements were not available along the damage path, the focus of this study is to compare EF rating and damage path width to TDS parameters, not tornado intensity.
b. Threshold determination
Before TDS parameters are introduced, the determination of thresholds is discussed. Given that the dataset encompasses a relatively small number of cases, the presented thresholds may not be optimal for all tornado cases. Moreover, differences in population density or vegetation type may result in variations in lofted debris type, size, and concentration, and could affect which TDS threshold is optimal.
The purpose of the thresholds is to identify resolution volumes containing tornadic debris. To identify possible thresholds, all of the 0.5° KOUN data within 2 km of the 21 tornado cases were aggregated to examine the distributions of ZHH, ZDR, and ρHV within 2 km of these tornadoes. Bivariate histograms of ZDR and ρHV, and ZHH and ρHV, were produced using these data (Fig. 2). Bivariate histograms of ZDR and ρHV reveal a wide range of ZDR values for lower ρHV values, but a shift toward positive values for higher ρHV (Fig. 2a). The increase in ZDR as ρHV increases is likely due to an increasing contribution of precipitation within the resolution volume (Bluestein et al. 2007; Schwarz and Burgess 2011; Bodine et al. 2011). To determine an appropriate ρHV threshold (hereafter 
The log10 bivariate histograms showing (a) ZDR and ρHV and (b) ZHH and ρHV. The solid black line in (a) shows the median value of ZDR as a function of ρHV. The median ZDR increases above 0.5 dB (black, dashed line) at ρHV = 0.82.
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-11-00158.1
c. TDS parameters
This study investigates two categories of TDS parameters: lowest tilt and spatial TDS parameters. Lowest tilt TDS parameters examine the 10th or 90th percentiles of polarimetric variables at the lowest available elevation angle, which is 0.5° in the present study. The 10th percentile ρHV value, q0.1{ρHV}, is defined as the 10th percentile of ρHV values where 
A spatial resampling was applied to each of the lowest tilt TDS parameters using a nonparametric ordinary bootstrap resampling procedure (Efron 1979). A total of 1000 bootstrap resamples were taken to estimate the 95% confidence interval (CI). An important note is that the spatial correlation of polarimetric radar variables may result in an underestimate of CI. While a moving-tile resampling procedure was considered (e.g., Davison and Hinkley 1997), it was not possible to obtain a sufficiently large number of tiles to produce enough resamples for analysis times with smaller TDSs.
Modeling studies suggest that large debris element concentration decreases as a function of height (Dowell et al. 2005), so temporal changes in lowest tilt TDS parameters could reflect changes in sampling height rather than the temporal evolution of the tornado. Tornado observations at close ranges have observed that ZHH often decreases with height in tornadoes (e.g., Wurman et al. 1996; Wurman and Gill 2000; Bluestein et al. 2004; Wakimoto et al. 2011), so changes in range must be considered when applying the lowest tilt TDS parameters, particularly for tornadoes at close ranges. Nonetheless, because the highest concentration of debris elements is near the surface and lofted debris reaches the lowest tilt faster than higher tilts, the lowest tilt may yield the most important information about lofted tornadic debris and the severity of tornado damage.
The final TDS parameter is the maximum TDS height hmax, which is the maximum height where 
3. Detailed comparisons with damage surveys
a. Chickasha–Newcastle EF4 tornado
The 24 May 2011 Chickasha–Newcastle EF4 tornado forms in the southern part of Chickasha, Oklahoma at 2206 UTC. At 2208 UTC, the tornado produces EF0–EF1 damage (Fig. 3). Two resolution volumes with ZHH between 30 and 40 dBZ and ρHV < 0.85 are observed at 0.5° (about 580 m AGL), perhaps indicating some lofted light debris by the tornado (not shown). At 2212 UTC, the tornado produces EF1 and EF2 damage on the east side of Chickasha (Figs. 3 and 4). Figure 5 shows the 0.5°-elevation ZHH, υr, ρHV, and a TDS is seen at X = −41 km, Y = −23 km. The changes in TDS parameters correspond to an increase in tornado EF rating during this period (Fig. 6). We also see that q0.9{ZHH} increases (Figs. 6a,b), and q0.1{ρHV} and q0.1{ZDR} decrease for thresholds T1 (Figs. 6c,e). The higher 
Damage surveys complied by the Norman NWS WFO for the Chickasha–Newcastle and Washington–Goldsby tornadoes on 24 May 2011. The EF rating along the damage path is contoured, and the times and locations of the center of tornado vortex signature at 0.5° are shown by the white text and lines, respectively. The blue circle near the top right shows the location of KOUN. The boxes A, B, and C denote parts of the damage path shown in more detail in Fig. 4.
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-11-00158.1
Zoomed and rotated images of the Chickasha–Newcastle tornado damage path (A and B), and the Washington–Goldsby tornado damage path (C) on 24 May 2011. The image has been rotated so that the x axis is oriented southwest to northeast, and the y axis is oriented from southeast to northwest. The EF rating along the damage path is contoured, and the times and locations of the center of the tornado vortex signature at 0.5° are shown by the white text and gray dots, respectively. The white arrow points north.
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-11-00158.1
The 0.5°-elevation (top) ZHH, (middle) υr, and (bottom) ρHV at (left) 2212, (middle) 2225, and (right) 2238 UTC for the Chickasha–Newcastle tornado. The solid black lines shows the Chickasha tornado’s damage path and the thin black line is the radial at a 240° azimuth. The black arrow indicates the location of the TDS.
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-11-00158.1
TDS parameters q0.9{ZHH} for (a) T1 and (b) T2, q0.1{ρHV} for (c) T1 and (d) T2, and q0.1{ZDR} for (e) T1 and (f) T2, shown for the Chickasha EF4 tornado. The error bars show the 95% CI for each parameter based on 1000 bootstrap resamples. The black dash dotted line in (a) shows the height of the beam at the 0.5° elevation (m × 10).
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-11-00158.1
Shown for the Chickasha EF4 tornado are (a) 
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-11-00158.1
The tornado EF rating increases to EF4 and the damage path widens from 250 to 650 m between 2212 and 2216 UTC (Fig. 4). For thresholds T1 and T2, q0.9{ZHH} increases (no CI overlap), and q0.1{ZDR} and q0.1{ρHV} values decrease to their lowest values observed for the tornado (Fig. 6). While the CIs at 2212 and 2216 UTC overlap for q0.1{ρHV} and q0.1{ZDR}, the CIs do not overlap the mean over all resamples. Hence, a statistically significant difference remains likely. For both thresholds, 
The tornado produces EF3–EF4 damage over a 700–1000-m path between 2221 and 2229 UTC (Fig. 4). During this period, q0.9{ZHH} exhibits statistically significant increases for both T1 and T2 (Figs. 6a,b). For both T1 and T2, q0.1{ρHV} and q0.1{ZDR} remain very low, and statistically significant changes are not observed (Fig. 6c–f). The brief increase in q0.1{ZDR} occurs as a band of large drops wraps around the vortex at 2221 UTC (not shown), and may have increased ZDR values. At 2225 and 2229 UTC, a TDS based on threshold T1 is identified at the highest tilt, so the TDS volume and height shown are likely underestimated (Fig. 7b). At 2225 UTC, the maximum TDS height and volume for T1 are observed, 9.6 km and 44 km3, respectively. Figures 5 and 8 show ZHH, υr, and ρHV at 0.5°-, 3.2°-, 8.1°-, and 15.6°-elevation angles. A TDS occurs at each elevation angle, although the areal extent of the TDS decreases at the higher elevation angles. Using thresholds T2, the TDS volume reaches a maximum of 24 km3 (Fig. 7b). While the TDS extends through the highest tilt at 2229 UTC, the TDS volume of 19 km3 is likely a good estimate because the areal coverage of debris resolution volumes at 19.5° elevation angle is quite small compared to the lower tilts.
The (left) 3.2°-, (middle) 8.1°-, and (right) 15.6°-elevation (top) ZHH, (middle) υr, and (bottom) ρHV at 2225 UTC for the Chickasha tornado, which correspond to altitudes of 1.9, 4.6, and 7.8 km AGL at the center of the image. The thin black line is the radial at a 240° azimuth, the thick black lines are the damage path, and the black arrow indicates the location of the TDS.
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-11-00158.1
Between 2229 and 2234 UTC, the damage survey indicates a 3-km swath where the damage path narrowed to 300–400 m and primarily EF1 damage is observed (box B in Fig. 4). Between 2229 and 2234 UTC, the TDS height and volume for T2 both decrease, while the TDS height and volume for T1 remain unbounded (Figs. 6c,d). For this particular case, the less stringent thresholds T1 are less useful because they do not constrain the TDS height within the VCP. The 0.5° elevation scans occur at 2229 and 2234 UTC, so KOUN did not have observations at the 0.5° elevation during the brief period of reduced damage severity and extent. A statistically significant reduction in q0.9{ZHH} is observed at 2234 UTC compared to 2229 and 2238 UTC. Hence, a slight reduction in the q0.9{ZHH} at 2234 UTC could correspond to less debris lofted at 0.5° elevation (Figs. 6a,b).
The period of reduced damage severity and extent corresponds to a more pronounced decrease in TDS height and volume compared to q0.9{ZHH}. The TDS volume and height remain relatively low between 2234 and 2238 UTC (although still lofting debris above 2 km) after the tornado EF rating increases to 3 and 4 (Fig. 4). However, the reduced TDS height and volume may be attributed to the brief decrease in damage severity and extent and consequently less lofted debris through the storm, or a decrease in updraft intensity, which would decrease the vertical velocities of debris elements. Given that debris must be lofted to 5 km to affect the maximum height of the TDS, we suspect that decreased updraft intensity may play a role in lowering the TDS height and perhaps reducing the TDS volume.
The EF rating decreases from 4 to 1 between 2238 and 2247 UTC (Fig. 3). In addition, q0.9{ZHH} decreases (Figs. 6a,b) while q0.1{ρHV} and q0.1{ZDR} do not exhibit statistically significant changes. The spatial TDS parameters remain relatively constant or even increase in some cases (Fig. 7). During the 2238 UTC volume scan, debris fallout away from the tornado occurs within the rear-flank downdraft (RFD) with high ZHH (40–55 dBZ) and low ρHV (<0.8) (Fig. 5). The increased amount of debris at the lower tilts causes the areal coverage parameter to increase or remain constant (Fig. 7a), even though the severity of damage and amount of damage decrease. The large region of debris fallout may indicate a weakening of the updraft, as previously suggested. For thresholds T1 and T2, TDS volume and hmax exhibit a secondary maximum during the 2242 and 2247 UTC scans, although hmax is lower than the 6+ km maximum observed earlier (Figs. 7b,c). In this case, the vertical advection of lofted tornadic debris during the reintensification of the tornado and widening of the damage path between 2234 and 2238 UTC may cause this maximum in TDS height 5–10 min later. However, a weaker updraft could explain why the TDS height and volume remain lower than the previous period of EF3 and EF4 damage.
As the tornado dissipates between 2251 and 2259 UTC, most of the TDS parameters indicate a decrease in the amount of lofted tornadic debris. For both T1 and T2, 
b. Washington–Goldsby EF4 tornado
The 24 May 2011 Washington–Goldsby EF4 tornado forms 2 mi west of Bradley, Oklahoma, at 2226 UTC (Fig. 3). At 2225 UTC, while a TDS is not observed, ρHV values fall below the thresholds for T1 and T2 in the TVS (not shown), where ZHH is between 20 and 25 dBZ (Figs. 9a,b). While lower ρHV could result from a lower signal-to-noise ratio (SNR), much higher ρHV values (0.97–0.98) are observed at 20–25 dBZ within the hook echo (in regions with small drops). So, the lower ρHV values within the TVS could indicate some light debris being lofted at the onset of tornadogenesis.
As in Fig. 6, but for the Goldsby EF4 tornado. NT indicates that a tornado was not observed.
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-11-00158.1
The tornado produces EF0 damage at 2229 UTC consisting of small and large branch damage to hardwood trees (Fig. 3). The 0.5°-elevation ZHH, υr, and ρHV at 2229, 2238, and 2259 UTC are shown later (Fig. 11). At 2229 UTC, a TDS can be seen by high ZHH (>50 dBZ) and low ρHV. The values of q0.9{ZHH} increase to 48 and 50 dBZ, respectively, for T1 and T2 (Figs. 9a,b), and q0.1{ρHV} and q0.1{ZDR} indicate low ρHV and ZDR values that were not present in the previous volume scan (Figs. 9c–f). The spatial TDS parameters increase between 2225 and 2229 UTC (Fig. 10). Between 2229 and 2234 UTC, the tornado produces EF1 and EF2 damage and the width of the damage path is between 300 and 400 m (Figs. 3 and 4). At 2234 UTC, q0.9{ZHH} exhibits a statistically significant increase and q0.1{ρHV} and q0.1{ZDR} remain low but do not exhibit statistically significant changes (Fig. 9). Between 2229 and 2234 UTC, 
As in Fig. 7, but for the Goldsby EF4 tornado. NT indicates that a tornado was not observed.
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-11-00158.1
The tornado EF rating increases to 3 by 2238 UTC (Fig. 4). Between 2234 and 2238 UTC, statistically significant changes in the lowest tilt TDS parameters (Fig. 9) were not observed, and the TDS height and volume increase (Figs. 10b,c). Between 2238 and 2242 UTC, the tornado destroys a well-constructed residence leaving only the concrete slab (EF4 damage), and the damage path widens to 500–700 m (Fig. 4). Note that q0.9{ZHH} exhibits a statistically significant increase (Fig. 9a) and the TDS height and volume reach their maximum values throughout the tornado (Fig. 10). For thresholds T1 a TDS occurs at the highest elevation angle, so the TDS parameters may underestimate the TDS volume and height (in this case, ≥32 km3 and ≥8.3 km). For thresholds T2, the TDS height and volume are 16 km3 and 6.7 km, respectively, and the maximum TDS height is below the highest elevation angle.
Tornado damage severity and damage path width decrease between 2242 and 2247 UTC (Fig. 4). The tornado primarily produces EF1 and EF2 damage with some small regions of EF3 damage, and the width of the damage path narrows to 250–400 m. By 2247 UTC, the TDS height for threshold T1 remains unbounded, but the TDS height for threshold T2 falls from 8.3 to 3.2 km and the TDS volume decreases from 16 to 5 km3 (Fig. 11). The decrease in TDS height and volume could reflect the reduction in tornadic debris lofted and/or a weakening of the updraft. By the start of the 2247 UTC scan, the tornado reintensifies and produces EF4 damage. The CIs for q0.9{ZHH} overlap for T1 (but do not overlap the mean over all replicates) while the CIs for T2 do not overlap. Hence, a statistically significant decrease in q0.9{ZHH} is likely observed between 2242 and 2247 UTC (Figs. 9a,b).
The 0.5°-elevation (top) ZHH, (middle) υr, and (bottom) ρHV at (left) 2229, (middle) 2238, and (bottom) 2259 UTC for the Washington–Goldsby tornado. The thick black lines show the Washington–Goldsby tornado’s damage path, and the thin black line is the radial at a 180° and 210° azimuth. The black arrow indicates the location of the TDS.
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-11-00158.1
The tornado produces primarily EF3 damage between 2247 and 2251 UTC with some small regions of EF4 damage (Fig. 4). The width of the damage path fluctuates considerably, ranging from 150 to 600 m. During this period, the TDS volume (for T2) increases slightly (Figs. 10b,c). The q0.9{ZHH} parameter increases slightly to 66 dBZ for both T1 and T2 (Figs. 9a,b) while statistically significant changes in the other lowest tilt TDS parameters are not observed.
Between 2251 and 2255 UTC, a broader region of EF3 damage is observed and the damage path width ranges from 400 to 900 m (Fig. 4). The tornado was approaching KOUN from the south, and was located 13–18 km from KOUN between 2251 and 2255 UTC. Using threshold T1, the TDS height cannot be determined beginning at 2242 UTC through tornado dissipation. However, the more stringent threshold resolves that the TDS height decreases from 6 to 3 km between 2251 and 2259 UTC. During this same period, the TDS volume remains approximately constant while the tornado continues to produce EF2–EF4 damage. The decrease in TDS height with a constant TDS volume suggests that the debris is more concentrated at lower levels. This could result from a weakening storm-scale updraft, which would reduce the updraft’s ability to loft and suspend debris at the mid- and upper levels of the storm.
As the tornado weakens, q0.9{ZHH} decreases to 53 dBZ by 2259 UTC for T1 and T2 (Fig. 9a). However, q0.1{ρHV} shows statistically significant decreasing values for T1 (Figs. 9b–d). Just prior to dissipating, the tornado produces EF4 damage, which may account for the low ρHV and ZDR values. As the tornado dissipates, a broad large region of lofted debris descends from the weakening storm. Scientists at the National Weather Center observed pieces of insulation and leaves falling after the tornado dissipated. A broad region of lower ρHV and high ZHH (Fig. 11) over a 3.5 km2 region is observed between 2259 and 2304 UTC, causing increase in 
4. Evaluation of TDS parameters as tornado damage metrics
Table 1 lists 21 tornado cases investigated in this study, including 14 that produced a TDS. TDS parameters are computed for the 14 tornadoes that produced TDSs throughout the duration of the tornado, using the times provided by the National Weather Service damage surveys. Table 1 lists the 21 tornado cases investigated in the forthcoming analysis, including the seven missed detections (labeled ND). It is important to note that the total number of cases for the TDS parameter may not equal 14 for cases where fewer than 10 resolution volumes meet the specified thresholds, and thus the 10th or 90th percentiles could not be computed for some of the TDS parameters. Table 1 shows the location, date, EF rating, tornado times, and the range from KOUN. Tables 2 and 3 show the maximum or minimum values of TDS parameters for thresholds T1 and T2, respectively.
The location, tornado number, date, EF rating, times, and range from KOUN for the 21 tornado cases.
The location, tornado number, date, EF rating, q0.9{ZHH}, q0.1{ρHV}, q0.1{ZDR}, hmax, and Vmax for 21 tornado cases for thresholds T1. ND indicates that a TDS was not detected. The BT indicates that an insufficient number of resolution volumes met the threshold criteria so the lowest tilt TDS parameter could not be computed. The asterisk next to the TDS height and volume indicates that a TDS was observed at the highest tilt (19.5°) and, thus, is a minimum bound.
Two tornadoes were excluded owing to difficulties in separating the TDS from another tornado or temporal sampling limitations. The parent storm of the Chickaska–Newcastle EF4 tornado (tornado 19) produces a satellite tornado (tornado 3), which occurs within the TDS of the EF4 tornado. Hence, the contribution of this satellite tornado to the overall debris field is unknown, so it is excluded from the analysis. The southern Moore, Oklahoma, EF1 tornado (tornado 6) lasts only 1 min according the NWS damage survey, and radar scans remain above 2.4° elevation during this period. Neither a TDS nor a TVS are observed, so tornado 6 is excluded from the analysis.
In several cases, a TDS is not detected (Table 1). No TDSs are detected in EF0 cases, likely because the tornado must loft sufficient amounts of debris and the EF0 tornadoes were over 45 km from KOUN (tornadoes 1 and 2 in Fig. 1). The Healdton, Oklahoma, EF2 tornado (tornado 10) does not produce a TDS, although an EF3 tornado that occurred 12 min later produces a substantial TDS (tornado 13). Both tornadoes are located over 100 km from the radar, so lofted debris must reach at least 2 km to be sampled by the 0.5°-elevation scan.
The maximum and minimum values of lowest tilt TDS parameters reveal some interesting trends. For thresholds T1, the maximum q0.9{ZHH} for weak tornadoes are between 38 and 46 dBZ (Fig. 12a). Most strong tornadoes’ q0.9{ZHH} values are between 45 and 60 dBZ, and q0.9{ZHH} values exceed 55 dBZ for the five violent tornadoes. In stronger tornadoes, higher q0.9{ZHH} could result from the tornado lofting a greater number of debris elements, larger debris element sizes, or debris elements with high dielectric constants. The outlier case is the McLoud, Oklahoma, EF2 tornado (tornado 12). While q0.9{ZHH} was quite low (25.5 dBZ), higher ZHH values (>40 dBZ) satisfying T1 were observed at higher tilts. Because the tornado was relatively brief (4 min), the lowest tilt scan may not have observed the tornado’s debris field when the most severe damage was occurring.
Stacked bar graph of (a) q0.9{ZHH}, (b) q0.1{ρHV}, and (c) q0.1{ZDR} for thresholds T1. The number N indicates the number of cases meeting the required thresholds for each parameter. The light gray, dark gray, and black shadings indicate EF0 or EF1, EF2 or EF3, and EF4 or EF5 tornadoes, respectively. Note that while all 14 cases met the threshold T2 for 
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-11-00158.1
For the minimum q0.1{ρHV}, decreasing minimum values are observed as the tornado’s EF rating increases (Fig. 12b). Weak tornadoes had minimum q0.1{ρHV} values above 0.8, while strong and violent tornadoes had minimum q0.1{ρHV} values below 0.8. For the five violent tornado cases, minimum q0.1{ρHV} was below 0.5. For minimum q0.1{ZDR}, only two weak tornado cases met the threshold T1, but values were near zero or positive (Fig. 12c). For strong and violent tornadoes, the minimum q0.1{ZDR} values were primarily below 0 dB, and violent tornadoes were below −2 dB. Similar results are seen for threshold T2 (Figs. 13b,c). For extremely low ρHV values observed in violent tornadoes, the variance of ZDR appears to cause negative ZDR values. However, Ryzhkov et al. (2005) and Bluestein et al. (2007) observed regions of negative ZDR at S and X bands, and Bodine et al. (2011) observed a coherent region of negative ZDR in the outer debris ring of an EF4 tornado.
As in Fig. 12, but for thresholds T2. Note that while all 14 cases met the threshold T2 for 
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-11-00158.1
The maximum values of the spatial TDS parameters also reveal interesting trends as tornado damage severity increases. For thresholds T1 and T2, an increase in EF rating corresponds to higher TDS heights (Figs. 14a,c) and greater TDS volumes (Figs. 14b,d). The more stringent threshold T2 reduces the TDS height and TDS volume, decreasing the spread of values. For both thresholds, violent tornadoes exhibit much larger spread of TDS heights and volumes compared to weak and strong tornadoes, and in a few cases the TDS height and volume may be underestimated because the TDS extends to the highest elevation angle (Tables 2 and 3). In violent tornado cases, the maximum TDS height for T1 ranges from 4.8 to 12.4 km, and the TDS volume ranges from 11 to 51 km3. The 12.4-km TDS height and 51-km3 TDS volume occur after an EF5 tornado struck Piedmont, Oklahoma, where a broad region of EF4 damage occurs, numerous homes were destroyed, and unfortunately two fatalities also occurred (Table 2). As noted previously, the maximum in TDS height and volume for the Chickasha and Goldsby tornadoes occurs about 5–10 min after periods of sustained, widespread EF3 or EF4 damage.
Stacked bar graph of (a) TDS height and (b) TDS volume for thresholds T1, and (c) TDS height and (d) TDS volume for thresholds T2. The light gray, dark gray, and black shadings indicate EF0 or EF1, EF2 or EF3, and EF4 or EF5 tornadoes, respectively.
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-11-00158.1
5. Discussion
a. Storm-scale influences on TDS parameters
Precipitation and associated downdrafts may affect the TDS. When precipitation is entrained into the TDS, ρHV values within the TDS increase (Schwarz and Burgess 2011; Bodine et al. 2011). An increase in ρHV would occur if the debris concentration remained the same but the concentration of raindrops increased in the resolution volume. If resolution volume initially possessed a ρHV value at or just below the 
This study reveals that in some cases large amounts of tornadic debris are transported quite high into the storm. As suggested by Dowell et al. (2005), centrifuged tornadic debris may be recycled by the storm-scale updraft. As expected, the TDS is much wider than the actual damage path at the surface in the Chickasha and Goldsby tornadoes due to debris centrifuging (e.g., Snow 1984; Dowell et al. 2005). For the Chickasha and Goldsby tornadoes, the most significant tornado damage occurs along the right side of the tornado relative to its motion, where ground-relative wind speeds are enhanced by storm motion. Lofted debris is centrifuged and advected cyclonically, producing a broader and more uniform TDS. Even though debris has been centrifuged from the tornado, centrifuged debris remains beneath the low-level mesocyclone and sufficiently small and low terminal velocity debris is “recycled” and transported vertically into the updraft.
b. TDS parameter utility
Given that the TDS parameters use different elevation angles, the time required to loft debris to the height of different elevation angles will vary (depending on updraft strength and debris fall speeds). Hence, the TDS parameters will exhibit some delay between when damage occurs and when a change in the TDS parameters are observed. The lowest tilt TDS parameters should have the smallest lag times. For example, debris lofted at 20 m s−1 would reach a typical 0.5° beam height of 200–600 m in 10–30 s. Accordingly, debris will take longer to reach the higher tilts. Thus, the delay for the TDS height and volume may be greater compared to the lowest tilt TDS parameters.
An important limitation of the lowest tilt TDS parameters is that these parameters could reflect changes in sampling height (due to changes in range) rather than changes in tornadic debris. However, the two cases presented (both tornadoes approaching the radar) show good correlation between the damage surveys and changes in q0.9{ZHH} during tornado intensification and dissipation. In a case with the tornado moving away from the radar, the Norman–Lake Thunderbird tornado (tornado 18) exhibits increasing q0.9{ZHH} values during tornado intensification and maximum values during the period of EF4 damage east of Lake Thunderbird (not shown). Hence, for these cases, changes in the debris field appear to be more important than changes in sampling height. Nonetheless, more cases are needed to better understand how changes in beam height affect the lowest tilt TDS parameters.
Spatial TDS parameters provide an indication of the amount of tornado damage occurring and the updraft intensity. Given that the TDS volume depends on the spatial coverage of the TDS throughout the storm, it provides a diagnostic tool for examining the amount of debris lofted by the tornado. The Chickasha EF4 tornado exhibits higher maximum TDS volumes compared to the Goldsby EF4 tornado, which could result from the wider damage path of the Chickasha EF4 tornado and, consequently, more lofted debris. Nonetheless, the TDS volume also depends on the strength of the storm-scale updraft and whether or not the updraft can suspend tornadic debris. The maximum TDS height may possess a greater sensitivity to the intensity of the storm-scale updraft than the TDS volume because the areal coverage of the TDS decreases with height (see Fig. 8). The primary limitation of the TDS volume and height parameters is the lag time between when tornadic debris is lofted and when tornadic debris reaches the TDS height. In this study, the maximum TDS volume or height occurs about 5–10 min after the most significant damage occurs at the surface. Hence, these parameters should be viewed as a cumulative measure of tornadic debris over the preceding 5–10-min period.
c. Discrepancies between damage survey and TDS parameters
Interesting differences are evident between the Goldsby EF rating and the TDS parameters during its intensification. At 2229 UTC, the damage survey indicates only EF0 damage while q0.9{ZHH} and q0.1{ρHV} are 48 dBZ and 0.56, respectively (Fig. 9). Comparing these values to the maximum or minimum values for other tornadoes (Fig. 12), such values are characteristic of higher-EF-rated tornado cases presented herein. Moreover, for other EF0 tornadoes no TDS is observed (Tables 2 and 3), suggesting not enough debris is lofted to produce a TDS. A possible explanation for this discrepancy is that the EF scale underestimated tornado intensity, and a more intense tornado was present and lofted more tornadic debris. By 2234 UTC, the threshold T1 TDS height and volume are 5 km and 10 km3, respectively (Fig. 10). These values are more consistent with the TDS height and volumes observed for other violent tornado cases rather than a tornado producing EF1 or EF2 damage (Fig. 13). Thus, the EF scale may still underestimate tornado intensity at 2234 UTC. The first engineered structure listed as a damage indicator in the survey is at 2234 UTC, so an underestimation of tornado intensity is certainly possible. Moreover, the differences in TDS height and volume may reflect a stronger low-level updraft present, resulting in the more rapid vertical transport of debris.
The Chickasha and Goldsby tornadoes primarily affected rural areas with some small to medium-sized towns. However, the primary source of scatterers in rural areas appears to be vegetation. Along the Chickasha and Goldsby tornado damage paths, hardwood trees provided a source of debris elements. An important note is that in regions with little vegetation or few man-made structures, tornadoes may have lower ZHH and higher ρHV values than areas with higher population density or more vegetation cover. Hence, TDS parameters may not perform as well in areas with little vegetation or engineered structures.
6. Conclusions
This study investigates the potential of using polarimetric radar to estimate tornado damage severity and spatial extent. The study uses modified TDS parameters developed by Ryzhkov et al. (2005) and develops other new TDS parameters for estimating tornado damage. Using two detailed damage surveys conducted by the Norman NWS WFO, comparisons between TDS parameters and damage surveys are presented. Then, TDS parameters are computed for 14 tornado cases in central Oklahoma and the EF rating is compared to maximum or minimum TDS parameter values.
The TDS parameters tend to be correlated with the damage surveys. During tornado intensification, q0.9{ZHH} and spatial TDS parameters increase and q0.1{ρHV} and q0.1{ZDR} decrease. During tornado dissipation, q0.9{ZHH} decreases while the other lowest tilt TDS parameters sometimes show a trend. The application of TDS parameters during tornado dissipation is complicated by debris fallout, which may increase the areal coverage of the TDS at the lowest tilt. The maxima or minima of TDS parameter values also show potential for assessing the amount and severity of tornado damage. Maximum q0.9{ZHH}, TDS height, and TDS volume increase and minimum q0.1{ZDR} and q0.1{ρHV} decrease as tornado damage severity increases. Because the damage surveys from the other cases were not as detailed, it is unknown if the maximum or minimum TDS parameter values coincide with the peak damage intensity for most cases. The peak values of the TDS volume and height tend to occur after significant amounts of tornadic debris have been lofted over a 5–10-min period.
This paper illustrates the potential for estimating tornado damage using polarimetric radar. The information provided by the TDS parameters could help forecasters identify changing trends in tornado damage severity, and estimate the severity and extent of tornado damage in near–real time. This new information could allow forecasters to issue more specific statements about tornado damage severity through special weather statements or tornado emergencies, and disseminate this information to the public, emergency managers, and the media. The TDS parameters are not intended to predict when a violent tornado will occur and the TDS should not be relied on for issuing tornado warnings. However, they could enable forecasters to gauge tornado damage severity, particularly when spotter reports are unavailable (e.g., for rain-wrapped tornadoes or at night) or when low-level velocity data are not available (e.g., at long ranges). The TDS parameters can provide near-real-time information about the severity of tornado damage to emergency managers and first responders to ensure that their efforts are immediately directed to the most severely affected areas.
The study also raises several intriguing scientific questions about tornadic debris and supercell dynamics. Numerous studies have documented tornadic debris sedimentation in the RFD, forward-flank downdraft and also observed tornadic debris fallout over 100 km from the storm (e.g., Snow et al. 1995; Magsig and Snow 1998). In the present study, a broad region of tornadic debris fallout is observed within the RFD, possibly caused by debris fallout after updraft weakening or small fall speeds of light debris (e.g., leaves, insulation). If the updraft weakened, was the weaker updraft caused by storm-scale processes or could tornadic debris loading throughout the updraft be a contributing factor? We speculate that both factors could be important in the present case. Finally, the rapid, vertical advection of tornadic debris in violent tornado cases suggests the presence of a very strong, low-level updraft (also Oklahoma City and Lake Thunderbird EF4 tornadoes, tornadoes 17 and 18, not shown) compared to weaker tornadoes. If so, how does a strong, low-level updraft contribute to tornado intensification and maintenance?
To further investigate the potential for nowcasting tornado damage using TDS parameters, future studies should examine more tornado cases, including cases in different geographic areas and cases with detailed damage surveys. More cases are needed to determine if a near-real-time classification of tornado damage severity can be developed. To better understand the relationship between the amount of lofted debris and tornado intensity, studies combining polarimetric WSR-88D data with mobile radar observations should be pursued. Future studies could also investigate the relationship between TDS height and volume and storm-scale updraft intensity using polarimetric radar and rapid-scan, dual-Doppler data. The current upgrade to the WSR-88D network with dual-polarization will provide the opportunity to expand this research to a much larger dataset and different geographic areas, and would allow the implementation of TDS parameters as a tool for providing near-real-time information on tornado damage and severity.
Acknowledgments
The authors greatly appreciate the detailed damage surveys provided Greg Stumpf, Gabe Garfield, and Doug Speheger, and others who contributed to the 10 May 2010 and 24 May 2011 damage surveys. The detail provided in these damage surveys was critical for making comparisons between the observed damage and polarimetric radar observations. Discussions with Chris Schwarz, Daniel Betten, Conrad Ziegler, Jim Kurdzo, Steve Ansari, and Clark Payne were also helpful in this analysis. The authors are also thankful to Paul Schlatter and Les Lemon for reviewing an early draft of the manuscript. The authors also appreciate comments from three anonymous reviewers, which were particularly helpful in improving statistical aspects of the paper and comparisons of the EF scale to TDS parameters.
REFERENCES
Bluestein, H. B., Weiss C. C. , and Pazmany A. L. , 2004: The vertical structure of a tornado near Happy, Texas, on 5 May 2002: High-resolution, mobile, W-band, Doppler radar observations. Mon. Wea. Rev., 132, 2325–2337.
Bluestein, H. B., French M. M. , Tanamachi R. L. , Frasier S. , Hardwick K. , Junyent F. , and Pazmany A. , 2007: Close-range observations of tornadoes in supercells made with a dual-polarization, X-band, mobile Doppler radar. Mon. Wea. Rev., 135, 1522–1543.
Bodine, D., Kumjian M. R. , Smith A. J. , Palmer R. D. , Ryzhkov A. V. , and Heinselman P. L. , 2011: High-resolution polarimetric observations of an EF4 tornado on 10 May 2010 from OU-PRIME. Preprints, 35th Conf. on Radar Meteorology, Pittsburgh, PA, Amer. Meteor. Soc., 3B.4. [Available online at https://ams.confex.com/ams/91Annual/webprogram/Paper182431.html.]
Brown, R. A., Lemon L. R. , and Burgess D. W. , 1978: Tornado detection by pulsed Doppler radar. Mon. Wea. Rev., 106, 29–38.
Brown, R. A., Flickinger B. A. , Forren E. , Schultz D. M. , Sirmans D. , Spencer P. L. , Wood V. T. , and Ziegler C. L. , 2005a: Improved detection of severe storms using experimental fine-resolution WSR-88D measurements. Wea. Forecasting, 20, 3–14.
Brown, R. A., Steadham R. M. , Flickinger B. A. , Lee R. R. , Sirmans D. , and Wood V. T. , 2005b: New WSR-88D volume coverage pattern 12: Results of field tests. Wea. Forecasting, 20, 385–393.
Bunkers, M. J., and Baxter M. A. , 2011: Radar tornadic debris signatures on 27 April 2011. Electron. J. Oper. Meteor., 12 (7), 1–6.
Davison, A. C., and Hinkley D. V. , 1997: Bootstrap Methods and Their Application. Cambridge University Press, 582 pp.
Doviak, R. J., Bringi V. , Ryzhkov A. , Zahrai A. , and Zrnić D. , 2000: Considerations for polarimetric upgrades to operational WSR-88D radars. J. Atmos. Oceanic Technol., 17, 257–278.
Dowell, D. C., Alexander C. R. , Wurman J. M. , and Wicker L. J. , 2005: Centrifuging of hydrometeors and debris in tornadoes: Radar-reflectivity patterns and wind-measurement errors. Mon. Wea. Rev., 133, 1501–1524.
Efron, B., 1979: Bootstrap methods: Another look at the jackknife. Ann. Stat., 7, 1–26.
Kumjian, M. R., and Ryzhkov A. V. , 2008: Polarimetric signatures in supercell thunderstorms. J. Appl. Meteor. Climatol., 47, 1940–1961.
Magsig, M. A., and Snow J. T. , 1998: Long-distance debris transport by tornadic thunderstorms. Part I: The 7 May 1995 supercell thunderstorm. Mon. Wea. Rev., 126, 1430–1449.
McDonald, J. R., Forbes G. S. , and Marshall T. P. , 2004: The enhanced Fujita (EF) scale. Preprints, 22nd Conf. on Severe Local Storms, Hyannis, MA, Amer. Meteor. Soc., 3B.2. [Available online at http://ams.confex.com/ams/pdfpapers/81090.pdf.]
Palmer, R. D., and Coauthors, 2011: The 10 May 2010 tornado outbreak in central Oklahoma: Potential for new science with high-resolution polarimetric radar. Bull. Amer. Meteor. Soc., 92, 871–891.
Picca, J., and Ryzhkov A. , 2012: A dual-wavelength polarimetric analysis of the 16 May 2010 Oklahoma City extreme hailstorm. Mon. Wea. Rev., 140, 1385–1403.
Ryzhkov, A., Burgess D. , Zrnić D. , Smith T. , and Giangrande S. , 2002: Polarimetric analysis of a 3 May 1999 tornado. Preprints, 21th Conf. on Severe Local Storms, San Antonio, TX, Amer. Meteor. Soc., 14.2. [Available online at http://ams.confex.com/ams/pdfpapers/47348.pdf.]
Ryzhkov, A., Schuur T. J. , Burgess D. W. , and Zrnić D. S. , 2005: Polarimetric tornado detection. J. Appl. Meteor., 44, 557–570.
Schwarz, C. M., and Burgess D. W. , 2011: Supercell polarimetric signatures at X-band: Data from VORTEX2. Preprints, 35th Conf. on Radar Meteorology, Pittsburgh, PA, Amer. Meteor. Soc., 7B.4. [Available online at https://ams.confex.com/ams/35Radar/webprogram/Paper191298.html.]
Snow, J. T., 1984: On the formation of particle sheaths in columnar vortices. J. Atmos. Sci., 41, 2477–2491.
Snow, J. T., Wyatt A. L. , McCarthy A. K. , and Bishop E. K. , 1995: Fallout of debris from tornadic thunderstorms: A historical perspective and two examples from VORTEX. Bull. Amer. Meteor. Soc., 76, 1777–1790.
Snyder, J. C., Bluestein H. B. , Zhang G. , and Frasier S. J. , 2010: Attenuation correction and hydrometeor classification of high-resolution, X-band, dual-polarized mobile radar measurements in severe convective storms. J. Atmos. Oceanic Technol., 27, 1979–2001.
Wakimoto, R. M., Atkins N. T. , and Wurman J. , 2011: The LaGrange tornado during VORTEX2. Part I: Photogrammetric analysis of the tornado combined with single-Doppler radar data. Mon. Wea. Rev., 139, 2233–2258.
WSEC, 2006: A recommendation for an enhanced Fujita scale (EF-scale). Wind Science and Engineering Center Tech. Rep., Texas Tech University, 15 pp + 3 appendixes. [Available online at http://www.depts.ttu.edu/weweb/EFScale.pdf.]
Wurman, J., and Gill S. , 2000: Finescale radar observations of the Dimmitt, Texas (2 June 1995), tornado. Mon. Wea. Rev., 128, 2135–2164.
Wurman, J., Straka J. M. , and Rasmussen E. N. , 1996: Fine-scale Doppler radar observations of tornadoes. Science, 272, 1774–1777.
Zrnić, D. S., and Ryzhkov A. V. , 1999: Polarimetry for weather surveillance radars. Bull. Amer. Meteor. Soc., 80, 389–406.
