1136 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 25

Tornado Detection Using a Neuro–Fuzzy System to Integrate Shear and Spectral Signatures

YADONG WANG,TIAN-YOU YU, AND MARK YEARY School of Electrical and Computer Engineering, University of Oklahoma, Norman, Oklahoma

ALAN SHAPIRO School of Meteorology, University of Oklahoma, Norman, Oklahoma

SHAMIM NEMATI Department of Mathematics, University of Oklahoma, Norman, Oklahoma

MICHAEL FOSTER AND DAVID L. ANDRA JR. National Weather Service, Norman, Oklahoma

MICHAEL JAIN National Severe Storms Laboratory, Norman, Oklahoma

(Manuscript received 25 April 2007, in final form 22 October 2007)

ABSTRACT

Tornado vortices observed from Doppler radars are often associated with strong azimuthal shear and Doppler spectra that are wide and flattened. The current operational tornado detection algorithm (TDA) primarily searches for shear signatures that are larger than the predefined thresholds. In this work, a tornado detection procedure based on a fuzzy logic system is developed to integrate tornadic signatures in both the velocity and spectral domains. A novel feature of the system is that it is further enhanced by a neural network to refine the membership functions through a feedback training process. The hybrid ap- proach herein, termed the neuro–fuzzy tornado detection algorithm (NFTDA), is initially verified using simulations and is subsequently tested on real data. The results demonstrate that NFTDA can detect tornadoes even when the shear signatures are degraded significantly so that they would create difficulties for typical vortex detection schemes. The performance of the NFTDA is assessed with level I time series data collected by the KOUN radar, a research Weather Surveillance Radar-1988 Doppler (WSR-88D) operated by the National Severe Storms Laboratory (NSSL), during two tornado outbreaks in central Oklahoma on 8 and 10 May 2003. In these cases, NFTDA and TDA provide good detections up to a range of 43 km. Moreover, NFTDA extends the detection range out to approximately 55 km, as the results indicate here, to detect a tornado of F0 magnitude on 10 May 2003.

1. Introduction later was suggested as an indicator of tornadoes (Fujita 1958). However, Forbes (1981) found that more than The subjective detection of potentially tornadic half of the tornadoes in his study did not exhibit appar- storms using hook-shaped returns in a radar’s display ent hook signatures and suggested that hook echoes was first documented by Stout and Huff (1953), and may not be a reliable indicator. A unique feature of strong azimuthal velocity difference at a constant range, termed the tornado vortex signature (TVS), was Corresponding author address: Yadong Wang, 202 W. Boyd, School of Electrical and Computer Engineering, University of first observed by Burgess et al. (1975) and Brown et al. Oklahoma, Norman, OK 73019. (1978) using a pulsed Doppler radar. The national net- E-mail: [email protected] work of Weather Surveillance Radar-1988 Doppler

DOI: 10.1175/2007JTECHA1022.1

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(WSR-88D) has been proven to improve the probabil- wide and flat features of the spectrum (Yeary et al. ity of detection (POD) and the warning lead time for 2007). tornadoes in the United States (Polger et al. 1994; Although each tornadic signature described above Bieringer and Ray 1996; Simmons and Sutter 2005). has the potential to facilitate tornado detection to some The basic idea of the current tornado detection algo- extent, it is possible to optimally integrate all of the rithm (TDA) is to search for strong and localized azi- available signatures to improve the detection based on muthal shear in the field of mean radial velocities (e.g., a single signature. A fuzzy logic methodology is ideal Crum and Alberty 1993; Mitchell et al. 1998). However, for addressing a complicated system that launches a because of the smoothing effect caused by the radar decision based on multiple inputs simultaneously. resolution volume, the shear signature can be signifi- Fuzzy logic–based systems have already been widely cantly degraded if the size of tornado is small and/or the applied to weather radar for hydrometeor classification tornado is located at far ranges (Brown and Lemon (e.g., Vivekanandan et al. 1999; Liu and Chandrasekar 1976). Recently, Brown et al. (2002) demonstrated that 2000; Zrnic´ et al. 2001). In this work, a fuzzy logic sys- the shear signature can be enhanced using half-degree tem is developed to integrate tornadic signatures in angular sampling despite the expense of slightly in- both the spectral and velocity domains. The system is creasing statistical errors in velocity data. Better tor- further enhanced by a feedback process provided nado signatures can be observed by mobile radars be- through a neural network and is termed the neuro– cause of their enhanced resolution in both temporal fuzzy tornado detection algorithm (NFTDA). and spatial domains (e.g., Bluestein et al. 2003; Wur- This paper is organized as follows. An overview of man and Alexander 2006; Bluestein et al. 2007b). A the characterization of tornado signatures is presented conical debris envelope, a low-reflectivity eye, and mul- in section 2. The NFTDA technique is developed in tiple semiconcentric bands of reflectivity surrounding section 3 and is followed by the simulation results in the eye have been observed using Doppler on Wheels section 4. The performance of NFTDA is further dem- (DOW) radar (Wurman and Gill 2000; Burgess et al. onstrated and evaluated using time series data collected 2002). In addition, Ryzhkov et al. (2005) have shown by the research WSR-88D (KOUN), operated by the that significant debris signatures can be observed in National Severe Storms Laboratory (NSSL), and com- tornadoes using an S-band polarimetric radar. Simi- pared to the operational TDA in section 5. Finally, a larly, anomalously low values of differential reflectivity summary and conclusions are given in section 6. ␳ ZDR, low cross-correlation coefficient h␷, and high- Z reflectivity were also observed by a mobile, dual- 2. An overview of tornado signature polarization X-band Doppler radar (Bluestein et al. characterization 2007a). Zrnic´ and Doviak (1975) have shown that tornado The TVS, which is exemplified by extreme values of spectra can have wide and bimodal signatures that set radial velocities with opposite signs over a small azi- them apart from other weather spectra. These distinct muthal distance, has been widely used as an indicator tornado spectral signatures (TSS) were subsequently for tornadoes (e.g., Burgess et al. 1975; Brown 1998; verified by a pulsed Doppler radar with a significant Brown et al. 2002). In the NSSL’s TDA, the velocity maximum unambiguous velocity of approximately 90 differences between adjacent gates are grouped to form msϪ1 (Zrnic´ et al. 1977; Zrnic´ and Istok 1980; Zrnic´ et a 3D feature based on multiple thresholds to facilitate al. 1985). Recent studies have shown that spectra simi- tornado detection (Mitchell et al. 1998). Moreover, TSS lar to white noise, but with significant signal power, with bimodal or white-noise-like features have been ob- can be observed in a tornadic region using numerical served from both real data and simulations (e.g., Zrnic´ simulations and data collected from WSR-88D with and Doviak 1975; Zrnic´ et al. 1985; Yu et al. 2007). It is operational setups (Yu et al. 2007). In that study, three noted that the Doppler spectrum represents a distribu- complementary parameters were introduced to quan- tion of weighted radial velocities within the radar reso- tify TSS, and these features were derived from high- lution volume, and the mean Doppler velocity is de- order spectral analysis and signal statistics. It was fined by their statistical average (i.e., the first moment). shown that the TSS still can be significant enough to It has been hypothesized in Yu et al. (2007) that the facilitate tornado detection at far ranges, even though TSS can retain enough information to facilitate tornado the shear signature may become difficult to identify. detection, while the TVS is degraded by the smoothing Moreover, the eigenvalues of the correlation matrix de- effect and becomes difficult to identify. Three feature rived from the raw time series data also have a distinct parameters were proposed by Yu et al. (2007) to char- distribution in the tornadic region resulting from the acterize the TSS. The first parameter is the spectrum

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width (␴␷), which is also known as the second spectral radar continuously over the entire tornadic event for moment. Although the spectrum width is an intuitive approximately1hon10May, but there were only two parameter used to describe the wide spectral feature, it volume scans of data on 8 May. The data from the is not sufficient to characterize the shape of a tornadic lowest two elevation angles (0.5° and 1.5°) were used to spectrum and is susceptible to a number of factors, such calculate the histograms, which were normalized by the as inaccurate estimate of noise level and radar settings total number of data used in the analysis. A tornadic (Fang et al. 2004). Moreover, large spectrum widths can case is defined by the gate where the velocity difference be observed in a nontornadic region where strong lin- of its adjacent azimuthal gates is larger than 20 m sϪ1 ear shear and/or low signal-to-noise ratio (SNR) are and within the tornado damage path. Regions outside present. Two additional feature parameters—the phase the damage path with an SNR larger than 20 dB are of the radially integrated bispectrum (PRIB; denoted defined as nontornadic cases. It is shown that the tor- ␴ ␴ ⌬ ␹ by P) and spectrum flatness s—were introduced to nadic cases are associated with large ␷, V, P, and R, ␴ characterize TSS in Yu et al. (2007). Because most but small s. It is interesting to point out that the dis- shape information of a pattern is retained in the phase tributions of tornadic and nontornadic cases are over- of its Fourier coefficients (Oppenheim and Lim 1981) lapped for all of the parameters. Thus, a parameter with and the commonly used power spectrum (the second- values in the overlapped region is not well defined for order spectrum) is phase blind, a third-order spectrum either tornadic or nontornadic cases (i.e., some degree termed “bispectrum” was introduced to extract the of fuzziness is involved). As a result, a simple thresh- phase information. In addition, the spectrum flatness, olding method may produce false results. Although the defined as the standard deviation of a Doppler spec- overlapping reign of ⌬V is not obvious in Fig. 1, with trum (dB), is used to identify a white-noise-like feature, 1.5% of nontornadic cases having ⌬V larger than 20 which is often observed if the radar’s maximum unam- msϪ1, the number of such cases is significantly larger biguous velocity is smaller than the maximum rota- than the tornadic cases, because the majority of the tional speed of a tornado vortex. Yu et al. (2007) have data are from nontornadic cases. As a result, many ␴ shown that significantly high P and low s values were false/miss detections may be obtained. Moreover, Yu et obtained from spectra in a tornadic region compared to al. (2007) have shown cases that PRIB and spectral those from nontornadic regions. Furthermore, Yeary et flatness can help to characterize the TSS while the sig- al. (2007) reported that a white-noise-like spectrum can natures of shear and spectrum width diminish. It is im- reflect on the distribution of the eigenvalues of the cor- portant to consider these complementary tornadic fea- relation matrix. It was found that regions of large eigen- tures simultaneously in a detection algorithm, and a ␹ ratios ( R), defined as the ratio of minimum to maxi- fuzzy logic is an ideal candidate. mum eigenvalues, are well correlated with wide and flat spectra in tornadic regions. 3. Neuro–fuzzy tornado detection algorithm Although the first tornado spectrum observed by a pulsed Doppler radar was in the mid-1970s (Zrnic´ and In this section, a fuzzy logic–based system is devel- Doviak 1975), the readily available number of cases oped for tornado detection. The choice of fuzzy logic with recorded tornadic spectra is limited. The paucity over other approaches, such as thresholding, decision of data is partially due to the massive storage require- trees, and neural networks in their pure form, is moti- ments and the computational expense to process all of vated by several considerations. First, as mentioned the raw time series data to obtain spectra in real time. previously, strong shear, a large spectrum width, a sig- The S-band KOUN radar has the capability to continu- nificant eigenratio, high PRIB, and a low value of spec- ously collect volumetric time series data for several tral flatness may be associated with a tornado vortex. hours. Although KOUN is dual polarized, only time The description of the degree of significance for each series from the horizontally polarized component were parameter is actually fuzzy in context, because terms collected for the cases of interest. like “strong,”“weak,”“large,” or “low” are used to In this work, a fuzzy logic system is developed to describe their significance. On the other hand, “crisp” integrate tornadic signatures, which include the velocity values are binary—these values either exceed or do not difference of adjacent azimuthal gates (⌬V), spectrum exceed a threshold. As such, the fuzzy parameters ac- width, spectral flatness, PRIB, and eigenratio. Statisti- tually contain more information than the crisp ones, cal analysis of these feature parameters is presented in and the intent here is to leverage this additional infor- Fig. 1 with data collected from two tornadic events on mation, which is otherwise typically neglected. In ret- 8 and 10 May 2003. rospect, thresholding approaches would be ideal if the The time series data were collected by the KOUN distributions of tornadic and nontornadic cases for any

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FIG. 1. Normalized histograms of (top left) spectrum width, (top middle) velocity difference, (top right) PRIB, (bottom left) eigenratio, and (bottom right) spectral flatness for tornadic and nontornadic cases.

of the parameters in Fig. 1 are disjointed; however, this a. Architecture of the fuzzy logic system is rarely the case for real scenarios. Second, a fuzzy A fuzzy logic system can be considered a nonlinear logic system can use all of the available features simul- mapping of feature parameters (i.e., inputs) to crisp taneously to reach a conclusion, while a decision tree outputs. In NFTDA the output is a binary detection of only uses a single parameter at each node and is exclu- the presence of a tornado. This fuzzy logic system con- sive for all other parameters. Moreover, fuzzy logic ar- sists of the following three subsystems: “fuzzification,” chitecture is more flexible than a decision tree for in- “rule inference,” and “defuzzification” (Mendel 1995). corporating additional parameters without readjusting In fuzzification, the five feature parameters (or crisp all the rules. Finally, a large amount of training data is input) of spectrum width, velocity difference, PRIB, typically required to build a robust neural network sys- eigenratio, and spectral flatness are converted to fuzzy tem in its pure form (Marzban and Stumpf 1996). In variables, by either an S-shaped curve or a Z-shaped contrast, a fuzzy logic system can be developed based curve membership function. An S-shaped membership on a set of rules that is obtained from a priori knowl- function of a crisp input x is defined by two breaking edge and/or is defined by experts. Nevertheless, the points (x and x ) in the following equation: self-learning capability provided by the neural network 1 2 is still attractive and is included here in this hybrid ap- Ͻ 0 x x1 proach to develop NFTDA. As such, the neural net- x Ϫ x 2 x ϩ x work is used to refine the rules to optimize system per- ͩ 1 ͪ Յ Ͻ 1 2 2 Ϫ x1 x formance. A similar approach of a neuro–fuzzy combi- x2 x1 2 F j͑x͒ ϭ , nation was developed by Liu and Chandrasekar (2000) i x Ϫ x 2 x ϩ x Ϫ ͩ 2 ͪ 1 2 Յ Ͻ Ά 1 2 x x2 for hydrometeor classification with polarimetric prod- Ϫ x2 x1 2 ucts. A schematic diagram of the NFTDA is depicted in 1 x Յ x Fig. 2, and a detailed description of NFTDA is pre- 2 sented in the following two subsections. ͑1͒

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FIG. 2. A schematic diagram of NFTDA is shown. A fuzzy logic system is designed to detect a tornado, while a neural network is incorporated to refine the membership functions through a self-learning process.

where i ϭ 1,2,...,5corresponds to the input param- b. Neural network for system optimization eter. The fuzzy variables for tornadic and nontornadic Y N cases are denoted by F i and F i , respectively, and j The membership function is one of the most impor- corresponds to either the tornadic (j ϭ Y) or nontor- tant components in a fuzzy logic system. It can be ob- nadic (j ϭ N) case. Note that a Z-shaped curve mem- tained from intuition, inference, rank ordering, neural bership function is also determined by two breaking networks, and/or inductive reasoning (e.g., Ross 2005). points, but with the value decreasing with the increas- In NFTDA, the shape of the membership functions was ing value of the crisp input. The membership functions determined using prior knowledge of the relationship of the NFTDA are shown in Fig. 3. between the feature parameters and fuzzy variables for The fuzzy variables are the inputs to the subsystem of both tornadoes and nontornadoes. For example, it is Y N rule inference with an output of T and T for tornadic expected that a tornado is likely to have strong ⌬␷, large ␴ ␹ ␴ and nontornadic cases, respectively, as shown in Fig. 2. ␷, high P, high R, and low s. Therefore, only an S- or The relationship between the input and output of rule Z-shaped membership function is employed. The two inference is described by fuzzy rules. The process of breaking points of the S-shaped membership function evaluating the strength of each rule is called rule in- of spectrum width for the tornadic case is exemplified ference. In NFTDA, the Mamdani system is selected in the upper-left panel of Fig. 3. The breaking points of for the rule inference (Ross 2005). The maximum prod- each membership function are initialized based on the uct (or correlation product) is used to set the rule results of statistical analysis in Fig. 1. Subsequently, the strength, which is defined as the product of the input breaking points are adjusted through a training process fuzzy variables. Finally, the output of the rule infer- using a neural network as depicted in Fig. 2. In the ence, which is still a fuzzy variable, is converted to a training process, all of the collected tornadic data are crisp output of a precise quantity through the sub- divided into two parts—one part is for training and the system of defuzzification. A maximum defuzzifier, de- other part is for testing. The data from two radar vol- fined as the maximum of T Y and T N, is implemented in ume scans (0341 and 0353 UTC 10 May 2003) at the NFTDA, and the final binary detection is made. In lowest elevation angle are used as a training dataset. other words, a positive detection of the presence of a Additional data generated from analytical simulations tornado is selected when T Y Ͼ T N; otherwise, it is a are used as supplemental training data. Each training nontornadic case. data point will be assigned one input state: either tor-

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FIG. 3. Membership functions for tornadic and nontornadic cases: (a) spectrum width, (b) velocity difference, (c) PRIB, (d) eigenratio, and (e) spectral flatness.

nado or nontornado. Corresponding detection results 1 km southwest of the center of a mesocyclone is simu- of this fuzzy logic system will be obtained based on lated. Both the tornado and mesocyclone are modeled present membership functions. If the detection results by a Rankine combined vortex model with a maximum do not match the input states, the membership func- tangential velocity of 50 and 15 m sϪ1, respectively. The tions will be modified by adjusting the breaking points. radius of the mesocyclone is 2 km and three different

The training process is achieved by minimizing the er- tornadoes’ radii (rt) are used in the simulation. More- ror between the known input states and the detection over, uniform reflectivity (Wood and Brown 1997; results through an iterative process (Liu and Chan- Brown 1998; Brown et al. 2002) is applied to the tor- drasekar 2000). Note that the membership functions nado and a broad Gaussian-shaped reflectivity is used shown in Fig. 3 were obtained after the training process for the mesocyclone. The level I time series data are was completed. ␪ simulated for a WSR-88D with a 1° beamwidth ( b) and a 250-m range resolution (⌬R). The maximum unam- Ϫ1 4. Simulation results biguous velocity is 35 m s . The mean Doppler veloc- ities and spectrum widths are estimated by the autoco- The NFTDA is tested and verified using simulated variance method (Doviak and Zrnic´ 1993). The spectral level I time series data of an idealized vortex (Rankine flatness, PRIB, and eigenratio are estimated by the vortex) generated from a radar simulator developed by methods described in Yu et al. (2007) and Yeary et al. Yu et al. (2007). Initially, a modeled Doppler spectrum (2007). is obtained from a superposition of weighted scatterers’ It has been shown that tornado’s shear and spectral velocities in the radar resolution volume. The weights signatures depend on several factors such as the range are determined by the reflectivity, antenna pattern, and between the tornado and radar, the size of the tornado, range-weighting function. If the scatterers’ radial veloc- and the relative location of a tornado in the radar’s ␷ ity exceeds the maximum unambiguous velocity ( a), it resolution volume (e.g., Zrnic´ et al. 1977; Brown et al. Ϫ␷ ␷ is aliased into the interval of [ a, a]. Consequently, 2002; Yu et al. 2007). In this work, the ratio of detec- ϭ the time series data are obtained from the inverse Fou- tion, defined as ROD Nd/Nt, is introduced to quantify rier transform of the modeled spectrum with a desirable the performance of NFTDA in the simulation, where Nt SNR. A detailed description of the simulator is pro- is the total number of tornadic cases generated for the

vided in Yu et al. (2007). In this work, a tornado located test and Nd is the number of cases detected. For each

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FIG. 4. Statistical analysis of the performance of NFTDA as a function of normalized range ⌬ ϭ ⌬ ϭ for R/rt 1.25, 2.5, and 5.0, where R 250 m is the range resolution. The abscissa is the

normalized range with r0 the distance from the radar to the center of the resolution volume, ␪ b the beamwidth, and rt the radius of the tornado. The NFTDA results are denoted by thick solid lines. The results from the detection based on a threshold of velocity difference of 20msϪ1 (TTD) are also provided for comparison and are denoted by the thin dashed lines.

realization 121 tornado locations in the radar resolution of 20 m sϪ1, one of the thresholds used in the NSSL’s volume are simulated with 11 ϫ 11 uniform grids in TDA (Mitchell et al. 1998), is provided in Fig. 4. Note azimuthal and range directions at a given range (i.e., that both the range and range resolution are normal- ϭ Nt 121). The radar resolution volume of interest is ized by the tornado’s radius so that the detection result centered at an azimuth of 0°. To calculate the velocity is scalable for radar with different beamwidths and difference, signals from two additional volumes cen- range resolutions. It is evident that NFTDA provides tered at azimuth angles of Ϫ1° and 1° are simulated at higher RODs than TTD, especially at far ranges for the each range. For each tornado location, the five feature three tornado sizes. For example, NFTDA and TTD parameters (velocity difference, spectrum width, spec- both have RODs of approximately 100% when the nor- ⌬ ϭ tral flatness, PRIB, and eigenratio) are obtained as the malized distance is smaller than 8.7 and R/rt 1.25 inputs of NFTDA. The ratio of detection can be (i.e., a relatively large tornado). When the range in- thought of as the POD for different tornado locations creases, ROD from TTD declines because of the dimin- within the radar resolution volume. The ROD as a ishing shear signatures. However, NFTDA still has high function of the normalized range is presented in Fig. 4 RODs because spectral signatures are still evident ⌬ for the three tornado sizes that are defined by R/rt, enough to facilitate the detection. Although the perfor- ϭ where rt 50, 100, and 200 m. mance of TTD can be improved by lowering the thresh- ␪ The normalized range is defined as r0 b/rt and is a old, false detections will likely increase. Note that measure of the transverse dimension of the radar reso- NFTDA has higher RODs than TTD under the condi-

lution volume relative to the tornado size, where r0 is tions of tornadoes associated with nonuniform reflec- the range from the radar to the center of resolution tivities, for example, doughnut-shaped reflectivity. In volume. Each data point represents the mean ROD practice, several factors can limit the performance of from 50 realizations, and each one has a different noise NFTDA, such as the degraded quality of the param- sequence added to the time series data. For the pur- eters caused by low SNRs and the fact that the radar poses of comparison, a tornado detection solely based actually samples the storms aloft resulting from the on the thresholding of velocity difference is also imple- earth curvature. mented and is termed the thresholding tornado detec- To better understand the strengths and weaknesses tion (TTD). The ROD from the TTD using a threshold of NFTDA, it is advantageous to investigate the regions

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⌬ ϭ FIG. 5. (a) A contour plot of the values of velocity difference for 121 tornado locations is shown for R/rt 5 ␪ ϭ and r0 b/rt 7. The regions where NFTDA and TTD have positive detections are depicted by white and black lines, respectively. (bottom) Spectra from three sample locations (A, B, and C) and the five parameters are shown from left to right. (b) In location A, both NFTDA and TTD have miss detections; (c) in location B, NFTDA has an accurate detection but TTD misses; (d) in location C, both NFTDA and TTD have good detections. where NFTDA and TTD detect and miss. One realiza- cause of the symmetry of the spectrum. Additionally, tion of the velocity difference for 121 tornado locations the magnitude of the mean Doppler velocity from ei- with the resolution volume, defined by 1° beamwidth, ther of the adjacent volumes centered at Ϫ1° or 1° 250-m resolution, and a normalized range of 7, is ex- should be relatively small because of the range depen- ⌬ ϭ emplified in the upper panel of Fig. 5 for R/rt 5. dence of the vortex velocities from a small tornado. For ϭ Note that the tornado is present for all 121 cases. a relatively large tornado (rt 200 m), a velocity dif- TTD has 20 positive detections, which results in an ference larger than 20 m sϪ1 is observed for all 121 ROD of 16.5%. It is interesting to point out that large tornado locations at the normalized distance of 7. velocity differences occur if a tornado is located closer Therefore, an ROD of 100% is obtained as shown in to the boundaries of a radar resolution volume in azi- Fig. 4. muth and toward the center of the radar resolution In contrast, the region of positive NFTDA detections volume in range. If an ideal tornado with a size smaller is denoted by white lines with an ROD of 73.5% in Fig. than the radar resolution volume is centered at an azi- 5. NFTDA misses the detection when the tornado is muth angle of Ϫ0.5° (i.e., the boundary of the radar located at the boundaries of a radar resolution volume beam) and the center of the gate, then the mean Dopp- in range. Spectra from the three locations, denoted by ler velocities from the two adjacent radar volumes in A, B, and C in the upper panel of Fig. 5, are depicted the azimuth (the one centered at 0° and the other one from left to right in the lower panels, respectively. At centered at Ϫ1°) have the same magnitude but opposite location A, both NFTDA and TTD miss the detection signs, because of the symmetry of the vortex and radar- of the tornado because neither the spectral nor the weighting functions. Thus, the maximum velocity dif- shear signature is significant enough. It is interesting to ference is obtained. If the tornado is located toward the point out that although the velocity difference at loca- center of the radar beam or the boundaries of a range tions A and B are similar and small, the spectrum from gate, the velocity difference decreases. For example, if location B is wider and more flattened than the one a small tornado is located at the center of the resolution from location A. As a result, prominent spectral fea- volume, the mean Doppler velocity is ideally zero be- tures assist the NFTDA to have a positive detection at

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FIG. 6. Comparisons of the detection results from TDA-KOUN and NFTDA-KOUN, which are denoted by blue triangles and red circles, respectively, for both tornadoes on 8 and 10 May 2003. Moreover, the TDA results from the operational WSR-88D at Twin Lakes, OK (TDA- KTLX), are depicted by black upward triangles. The location of both KOUN and KTLX is indicated by black asterisks. The time stamps from TDA-KOUN, NFTDA-KOUN, and TDA- KTLX are denoted by blue, red, and black boxes, respectively. The detection of hits from each approach is connected by a solid line to show the time continuity. Ground damage paths with Fujita scales are depicted by color-shaded contours.

B, which TTD misses. Both NFTDA and TTD have at 0329 UTC and had traveled 18 mi for approximately positive detections at location C, where the character- 37 min before dissipating. The maximum intensity of istic spectral and shear features are evident. this tornado was reported at F3 on the Fujita scale. The second tornado, which was estimated to be of F1 maxi- mum intensity, touched down approximately 4 mi south 5. Performance evaluations of Luther, Oklahoma, at 0406 UTC and had lasted for approximately 9 min with 3 mi of track. The final tor- a. Description of the experiments nado occurred between 0415 and 0424 UTC with a The performance of NFTDA is further assessed us- maximum intensity of F0. These tornadoes showed dis- ing two tornadic events in central Oklahoma on 8 and continuous tracks and collectively lasted approximately 10 May 2003. The tornado outbreaks on 10 May are of 56 min, which is similar to the multiple-cores mesocy- primary interest because continuous time series data clone described by Burgess et al. (1982) and Adlerman were collected by KOUN for the entire event. The Na- et al. (1999). The tornado damage path with the Fujita tional Climatic Data Center (NCDC) reported that scale from the ground survey is presented in the upper three tornadoes from the same supercell thunderstorm portion of Fig. 6. occurred in central Oklahoma from 0329 to 0425 UTC The damage path of the 8 May tornado is also in- 10 May 2003 (see information online at http:// cluded in the lower portion of the figure. The NCDC www.ncdc.noaa.gov). The first tornado touched down has reported that this tornado had a maximum intensity

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TABLE 1. Comparison of NFTDA-KOUN, TDA-KOUN, and TDA-KTLX for 8 and 10 May 2003 tornadoes. The time index of each volume scan for both KOUN and KTLX is given in the first column. The detection result and the range of detection are presented for the three methods

TDA-KOUN NFTDA-KOUN TDA-KTLX Time (UTC) Detection Range Detection Range Detection Range KOUN/KTLX result (km) result (km) result (km) 10 May 2003 0329/0329 Hit 35.188 Hit 35.625 Hit 27.358 False 33.336 False 28.968 0335/0334 Hit 38.892 Hit 37.625 Hit 27.358 False 46.352 0341/0339 Hit 38.892 Hit 39.625 Hit 25.749 0347/0349 Hit 40.744 Hit 40.625 Hit 25.749 False 42.596 False 27.358 0353/0354 Hit 42.596 Hit 42.625 Hit 25.749 False 33.336 False 27.358 0359/0359 Miss N/A Miss N/A Hit 27.358 False 28.968 0405/0404 Miss N/A Hit 48.125 Hit 27.358 False 30.577 0411/0409 False 46.30 Hit 52.625 Hit 28.968 0417/0419 Miss N/A Hit 55.375 Hit 32.165 8 May 2003 2230/2230 Miss N/A Hit 24.875 Hit 9.656 2236/2235 False 25.928 Hit 29.375 Hit 11.265 False 31.484 False 35.188 POD 55.6% 90.9% 100% FAR 61.5% 0% 33.3% CSI 29.4% 90.9% 75% of F4 and had traveled approximately 18 mi from 2210 results from the KTLX radar (denoted TDA-KTLX) to 2238 UTC. However, the collection of time series are used as another reference, because the maximum data by KOUN did not start until approximately 2230 distance between the KTLX and the 10 May tornadoes UTC, and therefore only two volume scans of the data is approximately 32 km, and it is expected that the are associated with the tornado. TDA will provide accurate and reliable detections for most cases at such relatively short ranges (Mitchell et b. Experimental results al. 1998). In addition to both objective references, we All of the feature parameters were calculated from carefully examine both spectral and shear signatures for the raw time series data collected by KOUN in Nor- each detection and consequently classify the results as man, Oklahoma. Subsequently, NFTDA was applied to “hit,”“miss,” or “false” detections; hit indicates that the data from the lowest elevation angle of 0.5° with the tornado is accurately detected, miss is assigned if no SNR larger than 20 dB. The output of NFTDA (de- tornado is detected when a tornado is present, and false noted NFTDA-KOUN) is a binary decision of whether is given if either the location of detection is not within the tornado is present or not. The NSSL’s TDA was the vicinity of the damage path or neither tornadic sig- also applied to the KOUN level II data and the detec- nature was observed. Note that the damage path could tion results are abbreviated by TDA-KOUN. For the be different from the location of radar detection, which verification of the detections from NFTDA-KOUN and can be caused by the tilt of the tornado, the width of the TDA-KOUN, the tornado damage path from the radar beam, and the limitation of the mechanical accu- ground survey is used as one of the objective refer- racy of the radar for determining the azimuth (Spehe- ences. However, the damage path may not be available ger 2006). Comparisons of the detections from in suburban areas and can be different from the real NFTDA-KOUN, TDA-KOUN, and TDA-KTLX for tornado location. The limitation of using the damage both 8 and 10 May tornadoes are summarized in Ta- path to verify the performance of the detection algo- ble 1. rithm is discussed in Witt et al. (1998). Moreover, TDA Note that only these TDA-KTLX detections with

Unauthenticated | Downloaded 09/30/21 01:56 PM UTC 1146 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 25 time indexes close to KOUN detections are included in produces three false detections. Furthermore, it is the table. shown in Fig. 6 and Table 1 that the TDA-KTLX has The comparisons of NFTDA-KOUN and TDA- hits for both 8 and 10 May cases, although a number of KOUN are divided into three time periods. In the first false detections can also be observed. The results from period, from 0329 to 0353 UTC, the tornado is detected both tornadic events suggest that TDA can accurately by both TDA-KOUN and NFTDA-KOUN. The maxi- detect tornadoes at close ranges, but it has limited per- mum range of detection during this period is approxi- formance if the tornado is weak and/or is located at far mately 42.6 km for both algorithms. All of the locations ranges. On the other hand, the NFTDA is robust and detected by NFTDA-KOUN agree well with the tor- can extend the tornado detection of the NSSL’s TDA nado damage path, as shown in Fig. 6, while there are up to approximately 55 km. few false detections from TDA-KOUN. The detections To quantify the performance, the scoring method de- from TDA-KOUN and NFTDA-KOUN are denoted scribed in Mitchell et al. (1998) was applied. The POD, by blue downward triangles and red filled circles, re- false-alarm ratio (FAR), and critical success index spectively. The false detection of TDA-KOUN can be (CSI) are defined by POD ϭ a/(a ϩ c), FAR ϭ b/(a ϩ caused by a number of factors, such as low SNR, ve- b), and CSI ϭ a/(a ϩ b ϩ c), where a, b, and c represent locity aliasing, and assigning issues in the algorithm. For hit, false, and miss, respectively. The scoring statistics example, the two false detections from TDA-KOUN— shown in Table 1 were calculated from all of the detec- one is at (4, 32) km from 0329 UTC and the other one tions shown in Fig. 6. For these two tornadic events, it is at (37, 25) km from 0335 UTC—were caused by low is evident that NFTDA-KOUN can improve the shear- SNR in these regions (between Ϫ8.3 and 7 dB). Note based TDA-KOUN to provide high POD, low FAR, that KOUN is located at the origin in Fig. 6. Another and high CSI. In addition, TDA-KTLX has a perfect false detection from 0353 UTC is located at (14, 42) km, POD of 100%, with maximum detection of approxi- where strong and localized azimuthal shears were ob- mately 32 km, while NFTDA-KOUN has a comparable served but were caused by velocity aliasing. In the sec- POD of 91%, with maximum detection of approxi- ond period, from 0405 UTC to the demise of the third mately 55 km. Moreover, NFTDA has the lowest FAR tornado at 0417 UTC, the TDA-KOUN has only one among the three approaches. detection at 0411 UTC, but it is approximately 6 km away from the damage path (i.e., a miss). On the other 6. Summary and conclusions hand, NFTDA-KOUN still provides robust and accu- rate detections that are consistent with the damage path Strong and localized azimuthal shears have been the throughout the entire period. The maximum detection primary feature for the operational and research tor- range of NFTDA-KOUN in this period is 55.375 km. nado detection algorithm of the WSR-88D. However, According to the NCDC, tornadoes were reported at the shear signature deteriorates with range because of F0–F1 scales during this period. In general, the velocity the smoothing effect by the increasing radar resolution differences are relatively small (Ͻ35 m sϪ1), and there- volume. In addition, tornado spectral signatures (TSSs) fore TDA-KOUN cannot provide reliable detections. were reported in the 1970s, and recently TSSs were On the other hand, NFTDA-KOUN has hits at 0411 characterized using spectrum width, bispectrum analy- and 0417 UTC because TSSs are still evident. The third sis, signal statistics, and eigenratios. In this work a novel time period is the single volume scan at 0359 UTC and algorithm based on fuzzy logic was developed to inte- neither algorithm has a hit, despite the presence of grate complementary information of spectral and shear damage on the ground. In this case, the maximum ve- signatures with the goal of improving tornado detec- locity difference is smaller than 28 m sϪ1. Additionally, tion. A fuzzy logic system is able to launch a decision spectra from the region of the damage path do not based on simultaneous multiple inputs with fuzzy de- exhibit white-noise-like features and they have rela- scriptions. The system is further enhanced by a training tively small spectrum widths. This can occur if the tor- process of a neural network. This hybrid approach is nado is weakening and the maximum rotational veloc- termed the neuro–fuzzy tornado detection algorithm ity of the vortex is smaller than the maximum unam- (NFTDA). biguous velocity. Nevertheless, NFTDA-KOUN still In this paper, the architecture of NFTDA was pre- has positive detections for data from two higher eleva- sented and discussed. The feasibility of NFTDA was tion angles of 1.5° and 2.5°. first tested using numerical simulations of Rankine vor- For the 8 May case, it is evident that NFTDA-KOUN tices of various sizes and distances from the radar. In has hits for both times (recall that KOUN data collec- addition, an intuitive tornado detection using a single tion did not begin until 2230 UTC), while TDA-KOUN threshold of azimuthal velocity difference (TTD) was

Unauthenticated | Downloaded 09/30/21 01:56 PM UTC JULY 2008 WANGETAL. 1147 implemented and used as a baseline for shear-based Pazmany, 2003: Mobile Doppler radar observations of a tor- TDA. A ratio of detection (ROD) was defined to quan- nado in a supercell near Bassett, Nebraska, on 5 June 1999. tify the POD for different tornado locations within the Part II: Tornado-vortex structure. Mon. Wea. Rev., 131, 2968–2984. radar resolution volume. Statistical analysis of ROD ——, M. M. French, R. L. Tanamachi, S. Frasier, K. Hardwick, F. has shown that both NFTDA and TTD have signifi- Juyent, and A. L. Pazmany, 2007a: Close-range observations cantly high ROD for large tornadoes at close ranges. of tornadoes in supercells made with a dual-polarization, X- However, for the cases for which a tornado is small band, mobile Doppler radar. Mon. Wea. Rev., 135, 1522– and/or located at far ranges, NFTDA has a higher 1543. Bluestein, H. B., C. C. Weiss, M. M. French, E. M. Holthaus, R. L. ROD than TTD because NFTDA can still leverage off Tananmachi, S. Frasier, and A. L. Pazmany, 2007b: The TSS to provide reliable detection. To further verify structure of tornadoes near Attica, Kansas, on 12 May 2004: NFTDA, it was compared with both research and op- High-resolution, mobile, Doppler radar observations. Mon. erational TDA for two tornadic events in Oklahoma on Wea. Rev., 135, 475–506. 8 and 10 May 2003. It is evident that NFTDA can ex- Brown, R. A., 1998: Nomogram for aiding the interpretation of tend the range of detection as suggested in the simula- tornadic vortex signatures measured by Doppler radar. Wea. Forecasting, 13, 505–512. tions. The POD, FAR, and CSI were subsequently de- ——, and L. R. Lemon, 1976: Single Doppler radar vortex recog- rived from these cases. Although the number of cases is nition. Part II: Tornadic vortex signatures. Preprints, 17th limited, the statistics of the scoring indicate that Conf. on Radar Meteorology, Seattle, WA, Amer. Meteor. NFTDA can significantly improve the conventional Soc., 104–109. TDA with enhanced POD and low FAR. More cases of ——, ——, and D. W. Burgess, 1978: Tornado detection by pulsed Doppler radar. Mon. Wea. Rev., 29–38. various conditions, including nonsupercell tornadoes, 106, ——, V. T. Wood, and D. Simians, 2002: Improved tornado de- are needed for a thorough and comprehensive analysis. tection using simulated and actual WSR-88D data with en- Furthermore, NFTDA is flexible enough to include hanced resolution. J. Atmos. Oceanic Technol., 19, 1759– additional feature parameters, such as differential re- 1771. flectivity and correlation coefficient, from a polarimet- Burgess, D. W., L. R. Lemon, and R. A. Brown, 1975: Tornado ric radar. NFTDA can also be easily adapted to other characteristics revealed by Doppler radar. Geophys. Res. Lett., 2, 183–184. radars without major modifications, such as the low- ——, V. T. Wood, and R. A. Brown, 1982: Mesocyclone evolution cost and low-power X-band radars developed by the statistics. Preprints, 12th Conf. on Severe Local Storms, San Center for Collaborative Adaptive Sensing of the At- Antonio, TX, Amer. Meteor. Soc., 422–424. mosphere (CASA). ——, M. A. Magsig, J. Wurman, D. C. Dowell, and Y. Richard- son, 2002: Radar observations of the 3 May 1999 Oklahoma Acknowledgments. This work was partially supported City tornado. Wea. Forecasting, 17, 456–471. by the DOC-NOAA NWS CSTAR program through Crum, T. D., and R. L. Alberty, 1993: The WSR-88D and the WSR-88D operational support facility. Bull. Amer. Meteor. Grant NA17RJ1227. In addition, this work was sup- Soc., 74, 1669–1687. ported in part by the National Science Foundation Doviak, R. J., and D. S. Zrnic´, 1993: Doppler Radar and Weather through ATM-0532107 and the Engineering Research Observations. Academic Press, 562 pp. Centers Program of the National Science Foundation Fang, M., R. J. Doviak, and V. Melniko, 2004: Spectrum width under NSF Cooperative Agreement EEC-0313747. measured by WSR-88D: Error sources and statistics of vari- Any opinions, findings, and conclusions or recommen- ous weather phenomena. J. Atmos. Oceanic Technol., 21, 888–904. dations expressed in this material are those of the au- Forbes, G. S., 1981: On the reliability of hook echoes as tornado thor(s) and do not necessarily reflect those of the Na- indicators. Mon. Wea. Rev., 109, 1457–1466. tional Science Foundation. The authors would also like Fujita, T., 1958: Mesoanalysis of the Illinois tornadoes of 9 April to thanks the NSSL staff for the collection of level I 1953. J. Meteor., 15, 288–296. data and the WFO in Norman for providing the ground Liu, H., and V. Chandrasekar, 2000: Classification of hydromete- damage survey. ors based on polarimetric radar measurements: Development of fuzzy logic and neuro-fuzzy system, and in situ verification. J. Atmos. Oceanic Technol., 17, 140–164. 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