## Abstract

Tornado debris signatures (TDS) exhibited in polarimetric measurements have the potential to facilitate tornado detection. The upgrade of the network of S-band Weather Surveillance Radar-1988 Doppler (WSR-88D) to dual polarization was completed recently. Therefore, it is timely to develop a tornado detection algorithm that capitalizes on TDS and integrates with other existing signatures observed in the velocity (shear signature) and Doppler spectrum (spectral signature) fields. In this work, the analysis indicates that TDS are not always present with shear and spectral signatures. A neuro-fuzzy tornado detection algorithm (NFTDA) using the Sugeno fuzzy inference system is developed to consider the strength of different tornado signatures that are characterized by operationally available data of differential reflectivity, cross-correlation coefficient, velocity difference, and spectrum width with the goal of reliable and robust detection. The performance is further optimized using a training procedure based on a neural network. The performance of NFTDA is evaluated using polarimetric WSR-88D data from 17 tornadoes with enhanced Fujita (EF) scale ratings ranging from EF-0 to EF-4 and distance from 16 to 133 km to the radar. NFTDA performs well with the probability of detection (POD), false alarm ratio (FAR), and critical success index (CSI) of 86%, 11%, and 78%, respectively. Moreover, a computationally efficient method is introduced to analyze the sensitivity of the tornado signatures. It is demonstrated that even though TDS play a less important role than the other two signatures, TDS can help improve the detection, especially during the later stage of a tornado, when the shear and spectral signatures become weaker.

## 1. Introduction

The tornado detection algorithm (TDA) developed by the National Severe Storms Laboratory (NSSL) was reported to provide higher probability of detection (POD) and critical success index (CSI) than the Weather Surveillance Radar-1988 Doppler (WSR-88D) Tornadic Vortex Signature (88D TVS) algorithm at the expense of increased false alarm rate (FAR) (Mitchell et al. 1998). Both algorithms search for strong and localized azimuthal shear in the velocity field and their performance is limited when a tornado is small and/or far range from the radar, due to smoothing from the radar resolution volume (Brown and Lemon 1976; Mitchell et al. 1998; Brown et al. 2002; Toth et al. 2013). Tornado spectral signatures (TSS) observed by S-band pulsed Doppler radar, manifested by a wide and flat spectrum shape, were first reported by Zrnić (1975) and further characterized using signal statistics, high-order spectral analysis, and eigenvalue analysis by Yeary et al. (2007) and Yu et al. (2007). It was shown that TSS can still be maintained at far range where the shear signature deteriorates. With the nationwide upgrade of WSR-88D to dual-polarization, polarimetric variables of cross-correlation coefficient , differential reflectivity , and differential phase become available for all WSR-88Ds. These polarimetric variables can provide extra information about scatterers’ size, shape, and orientation. The fuzzy logic–based hydrometeor classification algorithms (HCA) utilizing polarimetric variables were therefore developed (Vivekanandan et al. 1999; Liu and Chandrasekar 2000; Park et al. 2009). Tornadic debris signatures (TDS) observed by polarimetric radar are characterized by near-zero and anomalously low (Ryzhkov et al. 2002, 2005; Kumjian and Ryzhkov 2008; Bodine et al. 2013). TDS can be caused by randomly oriented debris with large sizes, irregular shapes, and a low degree of common alignment (Ryzhkov et al. 2005). TDS are generally apparent from tornadoes stronger than the enhanced Fujita (EF) scale (Edwards et al. 2013) of EF-3, but they sometimes can be observed from weaker tornadoes of EF-1 scale (Kumjian and Ryzhkov 2008). Similar polarimetric signatures can also be observed by polarimetric radars at shorter wavelength at X band (Bluestein et al. 2007; Snyder et al. 2013; Wurman et al. 2014) and C band (Kumjian and Ryzhkov 2008; Palmer et al. 2011). A C-band tornado detection algorithm including TDS was described in Palmer et al. (2011). It was found that TDS can be clearly captured by S-band polarimetric radar, and their potential in tornado detection became prominent especially after the polarimetric variables become available for WSR-88Ds. However, to our knowledge, there is no operation S-band polarimetric tornado detection algorithm, and it is timely to develop such an algorithm.

Inspired by TSS, a neuro-fuzzy tornado detection algorithm (NFTDA) was developed to intelligently combine shear and multiple spectral signatures (spectrum width, spectral flatness, higher-order spectra, and eigenvalue ratio) using a fuzzy inference system (Wang et al. 2008), and is denoted by NFTDA08 in the current work. The performance of NFTDA08 was evaluated using level 1 (I and Q) data collected by the research WSR-88D (KOUN) operated by NSSL during two tornadic events in 2003. Compared to the operational TDA, NFTDA08 can provide significantly improved detections verified by higher POD and CSI, lower FAR, and extended maximum detection range (Wang et al. 2008). In spite of the enhanced performance provided by NFTDA08, two issues needed to be addressed. The first issue is that the operational application of NFTDA08 is limited because only one of the four spectral features, spectrum width, is readily available from the WSR-88D base product, while the other features require further processing of level 1 time series data. The second issue is that TDS need to be considered in the detection, given their apparent benefits. However, before TDS can be included in the fuzzy inference system for detection, it is important to determine whether TDS are present simultaneously with other signatures. For example, NFTDA08 implicitly assumes that all the shear and spectral signatures need to be relatively strong to detect tornadoes. Specifically, the method of multiplication (logic AND) is used in the rule inference (Ross 2004) of NFTDA08. As shown later in section 2a TDS might not be present at the same time as other signatures. In this work, an adaptive NFTDA was developed to address these two issues with additional improvements. NFTDA is significantly different from NFTDA08, except for sharing the standard architecture of the neuro-fuzzy system. This will be discussed in more detail in section 2b.

This paper is organized as follows. The characteristics of tornado signatures are briefly reviewed and demonstrated in section 2a. Section 2b introduces the new adaptive neuro-fuzzy inference system, in which the Sugeno-type fuzzy rule inference is applied. For the first time, tornadic spectral, shear, and debris signatures observed by S-band polarimetric WSR-88D radars are integrated with a fuzzy logic framework to facilitate tornado detection. In section 3, the performance of proposed NFTDA is evaluated with 17 tornado events and the impact of TDS on NFTDA is investigated and demonstrated. Finally, a summary and conclusions are given in section 4.

## 2. NFTDA

### a. Overview of tornadic shear, spectral, and debris signatures

The tornado’s shear, spectral, and debris signatures are characterized by velocity difference , spectrum width , differential reflectivity , and cross-correlation coefficient . These four variables were found to effectively capture tornado signatures and were implemented or potentially implemented in tornado detection (Mitchell et al. 1998; Ryzhkov et al. 2005; Wang et al. 2008; Palmer et al. 2011). Although a couple of other variables derived from base data, such as the texture of reflectivity and differential phase, were implemented in the classification of hydrometeors (Park et al. 2009), they do not exhibit any apparent tornadic signatures and therefore are not considered in NFTDA. It should be noted that implemented in the current work is not corrected for attenuation. Based on our knowledge, current attenuation correction approaches on the field are mainly based on the integration of , and the water medium (such as raindrops) along the path is assumed. Since the tornado debris is different from water, any -based correction approach is not suitable for this study. In this work, data from polarimetric WSR-88D radars are “superresolution” data with half-degree azimuthal sampling and 250-m gate spacing. The half-degree azimuthal sampling is obtained by first collecting samples from 1° overlapping radials every half degree and subsequently applying a von Hann or Blackman window function (Torres and Curtis 2007). As a result, a smaller effective beamwidth of 1.02° (i.e., finer angular resolution) is achieved, which is 74% of the legacy resolution with an effective beamwidth of 1.38° (Torres and Curtis 2007). Brown et al. (2002) have shown that mesocyclone and tornado vortex signatures can be better captured using superresolution data. The derived from radial velocities in two adjacent azimuths was first used in NSSL’s TDA (Mitchell et al. 1998) and was further implemented in NFTDA08. The is defined in the following equation:

where is the radial velocity at *i*th azimuth angle and *j*th range gate. Moreover, the base reflectivity is also implemented in the current work, although it is not a direct input of fuzzy logic. To decrease the computational cost, the reflectivity is used as a threshold, and only those range gates with reflectivity larger than 30 dB*Z* are applied with fuzzy logic. The 30-dB*Z* reflectivity threshold is based on the analysis of all the available tornado cases.

It is of interest to investigate the strength of a tornado’s shear, spectral, and debris signatures during its different stages. Nine tornado events were used in this analysis, in which four tornadoes were from 2 March 2012 in central Alabama with maximum ratings of EF-3, and five tornadoes were from 14 to 15 April 2012 in Kansas with maximum ratings of EF-4. The selected tornado events are indicated by asterisks in Tables 1 and 2. These nine cases were all observed by the two polarimetric WSR-88Ds (KBMX and KICT), and more details are provided in section 3. The other eight tornadoes listed in Table 2 were not included in this analysis because either each had a relatively short lifetime (less than 20 min) or each was located at relatively far range (>130 km). However, they were still used in the performance evaluation in section 3.

In the analysis, the tornado locations were determined by carefully examining the radar variables and tornado damage path obtained from the National Weather Service (NWS) Weather Forecast Office (WFO). A simple criterion was used to categorize the radar data into one of the three tornado stages of “beginning,” “maturity,” and “ending.” This criterion is based on the combination of tornado report (from NWS WFO), tornado damage path, and the radar data. Specifically, the volume scan of radar data from the time closest to the reported touchdown time was first examined. If clear tornado signatures (such as shear, spectral, and debris signature) were identified from the location adjacent to the beginning part of the damage path, this volume scan data are designated as from the beginning stage. Otherwise, the next volume scan radar data will be examined. Using the same approach, the data from the ending stage were designated based on the ending part of the damage path and the reported tornado disappearing time. Those volume scans in between the beginning and ending stages are designated as from the maturity stage. It was found that not all the tornado signatures are present simultaneously during these three stages, that is, strong , large , low , and close to zero . For most of the time, only partial tornado signatures are apparently present. This is exemplified in Fig. 1, where the azimuthal profile of , , , and at three adjacent gates from the beginning (at 2353 UTC) and ending (0020 UTC) stages of the Beechwood tornado are denoted by red and black lines, respectively. Based on the report from NWS WFO in Birmingham, Alabama, the Beechwood tornado (rated as EF-1) was observed to touch down at 2353 UTC 2 March 2012. Large velocity difference and spectrum width are evident at the beginning stage of this tornado and are consistent at the three adjacent ranges (118, 118.25, and 118.50 km). The maximum velocity difference is as large as 38 m s^{−1}, which is larger than the largest threshold (35 m s^{−1}) implemented in TDA (Mitchell et al. 1998). The maximum spectrum width is approximately 15 m s^{−1}, and such a large value is normally generated by tornadic vortex (Yu et al. 2007). However, TDS are relatively weak at the beginning stage of this tornado. Specifically, both and show relatively large values. Values of above 0.98 and above 1 dB are within the ranges of typical meteorological scatterers as opposed to debris. One hypothesis is that at initial stage, the tornado may only produce limited debris, and no obvious polarimetric signatures can be generated yet. On the contrary, during the ending stage of the tornado (0020 UTC), the shear and spectral signatures become weaker, but TDS are still evident. Specifically, the maximum velocity difference is only approximately 14 m s^{−1} at range of 110.75 km and is less than 10 m s^{−1} at the other two ranges. Such velocity difference is smaller than the minimum threshold in TDA (11 m s^{−1}) and will lead to missed detection (Mitchell et al. 1998). A large spectrum width of approximately 15 m s^{−1} was produced only at one range gate (at 110.50 km and an azimuth of 166.5°), while most of others are smaller than 10 m s^{−1}. On the other hand, evident TDS can be identified, such as a low of approximately 0.8 and a of close to 0 dB at azimuth of 166.5° and range of 110.50 km. Such low values of and are within the ranges produced by tornado debris (Ryzhkov et al. 2005; Kumjian and Ryzhkov 2008). It is speculated that even though a tornado might weaken, shrink, and possibly lose its structure at the ending stage, the debris aloft could still produce relatively apparent TDS (Schultz et al. 2012).

The scatterplots of , , and against from these nine tornadoes are presented in Fig. 2, where variables from the beginning, maturity, and ending stages are denoted by red, gray, and blue dots, respectively. For most of these nine cases, large velocity difference and spectrum width but relatively weak polarimetric debris signatures are observed at the beginning stage of the tornado. The mean values of , , , and of these nine tornadoes are 38.5 m s^{−1}, 13.0 m s^{−1}, 0.94, and 1.55 dB, respectively. On the other hand, smaller velocity difference and spectrum width but better polarimetric debris signatures are observed at the ending stage of these tornadoes. The mean values of , , , and are 14.8 m s^{−1}, 10.3 m s^{−1}, 0.79, and 0.67 dB, respectively. Moreover, it can also be observed that at the maturity stage of a tornado, tornado signatures in , , , and are not always present simultaneously. The strength of these signatures also depends on the intensity of the tornado, the range between the radar and tornado, etc. Therefore, these signatures cannot be integrated together by simply using the logic of “AND” as in NFTDA08. In this work, a new rule inference (i.e., Sugeno) method is introduced in the neuro-fuzzy system to address this issue.

### b. Architecture of adaptive neuro-fuzzy tornado detection algorithm

#### 1) Flowchart of NFTDA

The flowchart of NFTDA is provided in Fig. 3, including three subsystems of fuzzification, rule inference, and defuzzification; a neural network training process; and a quality control (QC) procedure. Generally speaking, the inputs of NFTDA (i.e., ) include velocity difference, spectrum width, differential reflectivity, and cross-correlation coefficient. In the fuzzification, each input is converted to a fuzzy membership degree, whose value ranges from 0 to 1, using a Gaussian membership function (MF) of , where , for both tornado and nontornado cases. Note and are mean and standard deviation (SD) of the Gaussian MF for the *i*th variable for tornado and nontornado cases, respectively. Although other continuous and piecewise differentiable functions, such as the commonly used trapezoidal-shaped, triangular-shaped, and bell-shaped memberships, are also qualified candidates, the Gaussian membership function is selected because of its relatively simple formula (with only two variables of mean and standard deviation). Subsequently, the strength of each rule is evaluated from the fuzzy membership degrees. In NFTDA08, the tornado’s shear and multiple spectral signatures are considered to be present simultaneously to facilitate tornado detection, and therefore the multiplication of fuzzy membership degrees (logic AND) is used in the rule inference. However, it is shown in section 2a that debris, spectral, and shear signatures may not always occur at the same time. The performance of tornado detection would be significantly limited if the multiplication were to be used in the rule inference. The Sugeno fuzzy inference system introduced by Sugeno (1985) can still provide reasonable detection in this situation. Specifically, the rule inference in the Sugeno fuzzy system consists of two layers as indicated in Fig. 3. In the first layer, the firing strengths of the rules for tornado and nontornado are still obtained by the multiplication of and :

In the second layer, the outputs of rule inference ( and ) are calculated from the normalized firing strengths and weighted sum of the crisp inputs, as shown in the following equations.

where the normalized firing strengths for tornado and nontornado cases are obtained by and , respectively; and , are the weights for crisp inputs; and and are constants. In defuzzification, a crisp output is produced based on the sum of the two outputs from rule inference . If *O* is larger than a predefined threshold, then a positive detection of the presence of a tornado is assigned; otherwise, the detection result is nontornado. For a Sugeno type of fuzzy system, if some of the tornado signatures (such as shear, spectral, and debris signatures) are weak, then the outputs of the first layer ( or ) in rule inference can be extremely small because of the multiplication of small membership degrees. But the weighted average in the second layer can still be significantly large due to the presence of other existing signatures. As a result, the output of rule inference *O* can still be large enough to produce positive detection. Moreover, the mathematical characteristics such as the significance of each input variable in the Sugeno fuzzy system can be easily assessed and will be discussed in section 2b(2).

Another attractive feature of NFTDA is the training procedure based on a neural network. The means and SDs of the Gaussian MFs in the fuzzification, the weights ( and ) in the rule inference, and the threshold in the defuzzification can be optimized from a relatively small set of training data. This unique feature also makes NFTDA to be extremely flexible for studying different numbers of input variables. For example, in section 3, NFTDA with inputs of only velocity difference and spectrum width is implemented to demonstrate the impact of polarimetric signatures, which can be achieved easily by retraining the system.

The output of the neuro-fuzzy system is radar range gates with potential identification. Subsequently, a QC is performed to eliminate false detections that do not meet the range continuity or are associated with nontornado shear. Specifically, only those detected gates with at least two adjacent neighbor(s) in the range direction will be kept to form clusters of horizontal (2D) detections. The aspect ratio of each 2D cluster, which is defined by the ratio of the cluster’s radial extent to its azimuthal extent (Mitchell et al. 1998), is examined. If the aspect ratio exceeds a predefined threshold (4 in this work), this cluster is determined as nontornadic and discarded, because such elongated shear feature is typically observed in gust front or squall line. Furthermore, the subtractive clustering method (SCM), an extension of the mountain clustering method proposed by Yager and Filev (1994), was used to determine the center of the cluster, which is designated to be the tornado location. Unlike other clustering methods, such as the fuzzy *c*-means (FCM) technique, which finds the cluster center with a predefined cluster number, SCM can estimate the number of clusters and determine their centers simultaneously. In SCM, each range gate is initially assumed to be a potential center. The likelihood of each data point that would be the cluster center is calculated based on the density of the surrounding data points. The density is the number of data in a region of a circle (the center is the initial point, and the radius is 0.5). The point with the highest potential is set as the first cluster center, and all the other data points in the vicinity (as determined by a predefined radius) are removed. This process is iterated until all of the data are within a radius of a cluster center. This advantage of SCM is especially important when more than one tornado is present in a volume scan.

#### 2) Sensitivity of input variables

The significance of the four variables in the detection algorithm is a critical topic and needs further investigation. For example, heuristic methods have been developed for this purpose (e.g., Sugeno and Yasukawa 1993; Jang 1996; Chiu 1996), where the importance of input variables can be assessed by excluding them in a sequential manner and comparing the corresponding algorithm performance. However, the computational cost can hinder the feasibility of these methods. A computationally efficient method proposed by Gaweda et al. (2001) is introduced in this work to determine the significance of each input variable by calculating the normalized sensitivity as shown in the following equation:

where *k* represents “Y” and “N” as demonstrated in Fig. 3, and the is the weight used in the rule inference. Moreover, defines the interval of the *i*th input variables and is the interval for the output of the rule inference. The significance of a variable is defined by the maximum sensitivity, as shown in the following equation (Gaweda et al. 2001):

where *i* is for , , , and . The input variable with the largest *ϑ* is the most important variable in NFTDA. The sensitivities of these four variables in NFTDA will be discussed in section 3.

## 3. Performance evaluation

### a. Experiment description and evaluation scheme

A total of 17 tornado events, listed in Tables 1 and 2, were used to evaluate the performance of NFTDA. These 17 tornadoes are from two major outbreaks in central Kansas on 14 and 15 April 2012, and central Alabama on 2 March 2012. All the selected tornado cases meet the following three criteria: (i) the tornado’s lifetime is more than 5 min; (ii) the quality of the radar data is good—that is, no missing detections caused by blockage, missing data, or corrupted data; and (iii) all the tornadoes are located within 150 km from the radar, as suggested by Mitchell et al. (1998). All the WSR-88D level 2 base data were acquired from the NCDC website (http://www.ncdc.noaa.gov/nexradinv/). Six variables of reflectivity, radial velocity, spectrum width, differential reflectivity, differential phase, and cross-correlation coefficient are included in level 2 data. Different from level 3 data, only limited initial processing is applied on level 2 data, and no clutter removal and velocity dealiasing are applied on level 2 data.

Tornado damage paths obtained from the NWS were used to validate the detection results from NFTDA. A detection is defined as “hit” when the detected location is within the close vicinity (<1.5 km) of the tornado damage path and defined as “false” otherwise. In addition, a missed detection is assigned if a tornado is present but the algorithm produces no detections. Note that there could be displacement between the damage path and the location of radar detections, which can be caused by the tilt of the tornado, the width of the radar beam, the limitation of the mechanical accuracy of the radar for determining the azimuth, and the limitation of the ground damage path survey (Speheger and Smith 2006). Following the time scoring method proposed by Witt et al. (1998), the NFTDA was applied within the time window that starts from 15 min prior to the time of the tornado was first reported to 5 min after the ending time. Three scores of POD, FAR, and CSI are used to quantify the performance, where , , and , where *H*, *F*, and *M* represent hit, false, and miss detections, respectively.

In this work, two volume scans of data from the Beechwood tornado (at 2356 UTC) and the Verbena–Nixburg tornado (at 0412 UTC) were selected as the training data and the remaining data were used to evaluate the algorithm. These two volumes scans were selected because the tornado’s shear, spectral, and debris signatures were clearly observed, and the location of these signatures matched well with the tornado damage track. In the training dataset, the radar variables of , , , and from the tornado locations (a total of 9 gates) were designated as “tornado cases,” and other nontornado locations (a total of 1940 gates) were designated as “nontornado cases.” The MFs of NFTDA were initialized loosely based on the mean and SD of the training data, and further adjusted by the neural network with a combination of gradient method and least squares estimation (Jang 1993). The training procedure was considered to be accomplished if the error, defined as the difference between the designated result in training data and NFTDA output (with the latest MFs and weights), reaches a predefined minimum value, or the maximum number of iterations is reached (Jang 1993). The initial (blue lines) and trained (red lines) MFs for each input are presented in Fig. 4. It could be found that there are apparent differences between the initial and trained MFs, especially for . During the neural network training process, the adjustments on MFs and weights are accomplished according to the combination of all the input variables. For one obtained single MF, it does not best represent the distribution of this variable compared to the initial MF, but the integrated output can minimize the error—that is the reason for using trained MFs, which have better performance, rather than the initial MFs. Therefore, it should be noted that the obtained MFs are largely empirical as a result of the combined inputs and do not necessarily have a good physical interpretation.

The well-trained NFTDA, denoted as NFTDA^{4}, was tested on these 17 tornado events, and the superscript “4” means four the input variables of , , , and were implemented. The significance of each parameter in the NFTDA^{4} was calculated by using Eqs. (4) and (5) introduced in section 2b. It is interesting to point out that the Doppler variables of ( = 8.2) and ( = 6.8) play more important roles than ( = 6.5) and ( = 3.3) in the NFTDA^{4}. This result suggests that using only and is not sufficient for accurate tornado detection, but they might provide some important assistance. To demonstrate the benefit of TDS in NFTDA, the NFTDA using only two inputs of and (denoted as NFTDA^{2}) was implemented and optimized using the same training data. The performance of NFTDA using multiplication rule inference (Wang et al. 2008) is also examined in this work and is denoted as NFTDA08-dual. Different from the original NFTDA08, where shear and TSS were implemented, the NFTDA08-dual integrates four input variables (, , , and ) with multiplication rule inference (Wang et al. 2008). Other TSS are not included because they are derived from level 1 data and are not available for most of the WSR-88Ds. The NFTDA08-dual was trained with the same dataset as NFTDA^{4} and NFTDA^{2}. The detection results and the damage path are presented in Figs. 5 and 7 for Alabama and Kansas tornadoes, respectively. The tornado’s maximum EF ratings are also indicated. The detection results from NFTDA^{4}, NFTDA^{2}, and NFTDA08-dual are denoted by red circles, blue triangles, and black stars, respectively. Detailed investigations of the performance of NFTDA^{4}, NFTDA^{2}, and NFTDA08-dual are provided in the following.

### b. Tornado events in Alabama on 2 March 2012

Several supercell thunderstorms developed along a strong cold front in central Alabama on 2 March 2012, where a total of nine tornadoes were reported to have touched down with the maximum EF3 rating. Four of them were selected in the evaluation, and the other five tornadoes were excluded because they occurred too far away from the radar. According to the report from NWS WFO in Birmingham, these four tornadoes in total traveled approximately 99.5 mi on the ground for a period of 117 min and caused one fatality and two injuries. The county map and tornado damage path are presented in Fig. 5, where the tornado damage paths were obtained from the NWS official website (http://www.srh.noaa.gov/bmx/?n=event_03022012). It should be noted that Fig. 5 (also see Fig. 7 below) were plotted in Cartesian coordination, and the azimuth angles and ranges according to KBMX and KICT were converted into distances in the zonal and meridional directions. The polarimetric WSR-88D located in Birmingham (KBMX) recorded these four tornadoes with superresolution. The maximum range for these cases is between KBMX and the Eagle Creek tornado of approximately 127 km. The performances of the well-trained NFTDA^{4}, NFTDA^{2}, and NFTDA08-dual are first compared using these four tornadoes. Generally, NFTDA^{4} produces accurate detections that are consistent with the tornado damage path. Zero missed detection and one false detection (from the Little Oakmulgee Creek tornado) lead to that the POD, FAR, and CSI for these four tornadoes are 100%, 3%, and 96.4%, respectively. The NFTDA^{2} can accurately detect the tornadoes for most of the time, but it produces two missed detections and five false detections located about 100 km north of KBMX. To clearly show the right detections along the tornado path, these five false detections are not included in Fig. 5. The resulting POD, FAR, and CSI decrease to 92%, 17%, and 78%, respectively. The NFTDA08-dual implements the multiplication in the rule inference, which produced the worst POD (74%), FAR (13%), and CSI (67%).

An example of , , , and fields from the Eagle Creek tornado at 0508 UTC is presented in Fig. 6, where the detected tornado location from NFTDA^{4} is depicted by white asterisks. A circle centered at the tornado location with a radius of 1.5 km is also included. The tornado was located 118 km away from KBMX, and was classified as EF-0 to EF-1 at 0508 UTC. The detection results from NFTDA^{4}, NFTDA^{2}, and NFTDA08-dual are hit, miss, and miss, respectively. For this particular case, the size of the cross range of the radar beam is larger than 2 km, and the shear signature is significantly smoothed ( m s^{−1}). In other words, a missed detection likely results from the conventional shear-based TDA. Similarly, NFTDA^{2} and NFTDA08-dual do not detect the tornado due to the small velocity difference, despite a reasonably large of 11.5 m s^{−1}. On the other hand, NFTDA^{4} captures the apparently low in this region to produce an accurate detection.

### c. Tornado events in Kansas on 14 April 2012

Based on the WFO’s survey in Wichita (http://www.crh.noaa.gov/images/ict/pdf/apr14th_torlist.pdf) and Dodge city (http://www.crh.noaa.gov/news/display_cmsstory.php?wfo=ddc&storyid=81881&source=2), Kansas, a total of 24 tornadoes were reported that touched down during 14–15 April 2012, and the most severe one was classified as an EF-4 tornado (http://www.crh.noaa.gov/images/ict/pdf/apr14th_torlist.pdf). Among these 24 tornadoes, 13 of them observed by KICT in Wichita were selected in this work based on the three selection criteria discussed previously. The total estimated time of these 13 tornadoes on the ground is 281 min, and the total traveled length is 198.65 miles. The WSR-88D (KICT) located in Wichita is the closest polarimetric radar to these tornado events and is used in the evaluation. Similar to the tornado events in Alabama, the tornadoes’ details, such as track name, touchdown time, and the maximum EF scale, etc., are listed in Table 2.

Generally, NFTDA08-dual, NFTDA^{2}, and NFTDA^{4} can detect most tornadoes with ratings of EF-3 and stronger even at far distance, such as the St. John–Hudson tornado at approximately of 133 km and the Rice/Ellsworth/Saline 1 (RC/EW/SA 1) tornado at approximately 124 km. For the two weakest tornadoes, that of Saline 5 (EF-0) and Butler 4 (EF-0), all the algorithms produced miss detections. After examining the radar fields from these two cases, none of the tornado signatures was identified. Moreover, according to the WFO’s survey, these two tornadoes did not produce any damage, but there were several power flashes. It is suspected that these two cases might be associated with a very weak tornado or no tornado. On the contrary, although the Ellsworth 1 tornado is classified as an EF-0–EF-1 tornado, significant vortex, spectral, and polarimetric signatures were observed. Four and six false detections were found from the RC/EW/SA 1 and Mcpherson 2 tornadoes from NFTDA^{4}, respectively. From Fig. 7, it could be found that false detections from RC/EW/SA 1 are mainly from an adjacent region of the tornado RC/EW/SA 1 (on the northern part of RC/EW/SA 1). Significant velocity, spectral, and polarimetric signatures could be found from this region. The false detections from McPherson 2 are mainly from the region between −100 and −50 in the zonal direction, and between −100 and −75 in the meridional direction. Significant velocity, spectral, and polarimetric signatures could also be found from this region. Moreover, an EF-1 tornado (tornado Harper1) touched down about 20 min later in this region. The reasons for causing the false detections in these two tornadoes are unclear. However, it was found that these false detections are from the same region (continued spatially) and are also present in the continued volume scans. Other unreported tornadoes could be the reason for causing the detections, but further verification is needed. The overall POD, FAR, and CSI with NFTDA^{4}, NFTDA^{2}, and NFTDA08-dual from this event are summarized in Table 2. It is evident that TDS can enhance the performance of NFTDA with higher POD and CSI, and lower FAR.

## 4. Summary and conclusions

In the current work, tornadic vortex, spectral, and debris signatures were investigated using operationally available base data from recently upgraded polarimetric WSR-88D. A tornado is expected to produce large velocity difference in azimuth (vortex or shear signature), larger spectrum width (spectral signature), and low differential reflectivity and cross-correlation coefficient (polarimetric signature). It was found that, during the “beginning,” “maturity,” and “ending” stages of a tornado, not all the signatures can be clearly observed simultaneously. To integrate all four of these variables with reliable performance, a Sugeno-type neuro-fuzzy tornado detection algorithm (NFTDA) was developed. The performance of NFTDA was evaluated using 17 tornado events during 2012. Compared to NFTDA08, where multiplication was applied in the rule inference, three major modifications were performed. First, in order to enhance the practical value of the algorithm and capitalize on the polarimetric variables, the NFTDA only takes in operationally available base data of radial velocity, spectrum width, differential reflectivity, and cross-correlation coefficient. Second, two layers of rule inference were used in the Sugeno-type fuzzy system to address the different strengths of the signatures. Third, the quality controls and subtractive clustering method were incorporated to enhance the performance. Compared to the NFTDA08, the current NFTDA is more robust even if one or a few input parameters are weak. Moreover, the significance of the input parameters in the current NFTDA can be easily evaluated by calculating the normalized sensitivity coefficient. Generally, the velocity difference and spectrum width play more important roles than the polarimetric signatures. Nevertheless, it was demonstrated that polarimetric signatures can help to improve tornado detection. Based on the 17 tornadoes, the NFTDA with all four input parameters produce high POD (86%) and CSI (78%), and low FAR (11%).

## Acknowledgments

The authors thank Mr. Robb Lawson from the NWS WFO in Wichita, Kansas, for providing the tornado damage path. Funding was partially provided by NOAA/Office of Oceanic and Atmospheric Research under NOAA–University of Oklahoma Cooperative Agreement NA11OAR4320072, U.S. Department of Commerce. This work is partially supported by Toshiba, Japan.

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