**Advertisement**

ABSTRACT

The three-body scatter signature (TBSS) is a radar artifact that appears downrange from a high-radar-reflectivity core in a thunderstorm as a result of the presence of hailstones. It is useful to identify the *H*, 2) differential reflectivity Z*DR*, 3) copolar cross-correlation coefficient ?*hv*, 4) along-beam standard deviation of horizontal radar reflectivity factor SD(Z*H*), and 5) along-beam standard deviation of differential phase SD(F*DP*). These membership functions are added to an HCA to identify TBSSs. Testing is conducted on radar data collected by dual-polarization-upgraded operational WSR-88Ds from multiple severe-weather events, and results show that automatic identification of the

1. Introduction

The three-body scatter signature (TBSS) was a term coined by Zrnic (1987) to describe a region of radar reflectivity aligned radially downrange from a highly reflective echo core (Lemon 1998). The

Zrnic (1987) attributed

Thus, it is important to note that

Operationally,

Polarimetric signatures associated with

Polarimetric radar measurements have been utilized in classifying radar echoes for different hydrometeors and nonmeteorological targets in hydrometeor classification algorithms (HCAs; Straka and Zrnic 1993). HCAs were first studied by Straka and Zrnic (1993) and have become more sophisticated in recent years (e.g., Zrnic and Ryzhkov 1999; Vivekanandan et al. 1999; Liu and Chandrasekar 2000; Zrnic et al. 2001; Lim et al. 2005;

The goal of this study is to utilize polarimetric radar measurements to automatically identify (i.e., classify) the radar echoes associated with

2. Development of the

a. Introduction of the modified HCA

In this study, a modified version of the P09 HCA is developed. This HCA is chosen because a version of it is implemented on the WSR-88D network. Three major simplifications are made to the original algorithm. First, specific differential phase KDP is not used in the algorithm. In P09, KDP (for radar reflectivity Z , 40 dBZ) is obtained from a slope of a least squares fit of heavily filtered differential phase FDP (averaging of 25 successive samples). In this study, it was found thatFDP is incredibly chaotic and noisy within a

Therefore, in our algorithm, the five variables utilized for the discrimination of hydrometeor types are 1) ZH; 2) ZDR; 3) rhv; 4) a texture parameter, SD(ZH); and 5) another texture parameter, SD(FDP). The texture fields are calculated for each gate by calculating the standard deviation along the radial using five gates (i.e., the current gate, and the two gates before and after the current gate along the radial). The standard deviations are calculated by dividing by the total number of observations n (i.e., 5) and not by n - 1.

Certain classes are restricted based upon the heights that bound the melting layer. P09 used the melting-layer detection algorithm developed at the

All the membership functions, weights, and hard thresholds are the same as in P09. In P09 the membership functions are fitted to trapezoidal functions with a maximum value of 1 and a minimal value of 0. The trapezoidal functions are described by four parameters: x1, x2, x3, and x4. The weights, which are determined subjectively, characterize the discriminating efficiency of each variable with respect to each class.

For each radar gate, an aggregation valueAi for the ith class (i = 1, 2, . . . , 10) of radar echoes is calculated. As in P09, Ai is defined as

(

where P(i)(Vj) is the trapezoidal membership function for the jth variable for the ith class and Wij is a weight between 0 and 1 assigned to the ith class and jth variable. The classification of the radar echo is determined by which class has the largest aggregation value. The final step is a nine-point smoothing of the raw classifications to account for errors in the HCA output. In this smoothing technique, the mode of the raw classes of the current gate plus the surrounding eight gates (nine total gates) determines the smooth value of the current gate.

Figure 2 provides examples of classification results with the modified P09 HCA that does not have a

The next step is to add a new class of

The following specific steps for developing the enhanced HCA that includes

b. Data and statistics of radar variables in TBSSs

The experimental KOUNWSR-88D, located inNorman,

Approximately 20min of data between 2334 and

Table 1 is a statistical summary for the radar variables extracted and/or calculated from the 50 TBSSs. Columns 1-5 describe the five variables that are used to develop membership functions for the

The ZH (Fig. 4a), SD(ZH) (Fig. 4d), SD(FDP) (Fig. 4e), and spectrum width (Fig. 5b) all have positively skewed distributions. The skewness is greatest on the SD(ZH) distribution at;3.2319. This is followed by skewnesses of 1.2767, 0.8778, and 0.5284 for SD(FDP), ZH, and spectrum width, respectively. Visual inspections of the distributions validate these calculations. Recall that Lemon (1998) found that the

The ZDR distribution (Fig. 4b) demonstrates a significant limitation of the level-2 radar data. The ZDR is capped at 7.9375 dB. The reason behind this assertion is that 310 out of 2975 (;10%) gates have a value of exactly 7.9375 dB. It is statistically unlikely that 10% of the radar gates have this value because the precision of ZDR is to four decimal points. The maximum ZDR value was evident in all level-2 data from the cases in this study. If the radar data could provide greater ZDR values, the distribution may have been normally distributed (i.e., a skewness near zero). There is a bias toward positive measurements for ZDR (i.e., mean ZDR of 2.32 dB and median of 2.06 dB). However, 27% of the ZDR measurements are also negative.

Because of the difference in scattering patterns of the horizontally and vertically polarized waves, the bistatic ZDR varies depending on the size of the hailstones. Figure 6 shows sample calculations of ZDR as a function of scattering angle using Mie theory (Bohren and Huffman 1983) (

A similar issue that affects the ZDR distribution is present in the rhv distribution (Fig. 4c). Theminimumrhv value in the level-2 radar data is 0.2083. In this case, 165 out 2975 gates have a value of exactly 0.2083. As with the ZDR, the minimum rhv value was evident in all level-2 data from the cases in this study. If radar data could provide smaller rhv values, the rhv distribution may have been normally distributed.

The rhv distribution matches previous observations by Hubbert and Bringi (2000) that 95% of the rhv measurements are below 0.80. The low rhv in the polarimetric

The radial velocity distribution (Fig. 5a) has a skewness of 20.4716, which indicates the distribution is slightly negatively skewed. It is noteworthy that out of 2975 radar gates, not a single gate has a positive or zero radial velocity measurement. The measured radial velocity associated with the

c. Determination of membership functions and hard thresholds

After subjectively analyzing the membership functions of P09, and taking into account the distributions for all the variables, the following criteria from the collected data are used to determine the four parameters in the five trapezoidal membership functions: x1, 0.5 percentile; x2, 20th percentile; x3, 80th percentile; and x4, 99.5th percentile.

As a result, 60%of the radar data collected would have amembership value of 1, and 39%of the radar datawould have amembership value between 0 and 1. The remaining 1%of the radar data collected would have a membership value of 0. The minimum and maximum are excluded from the calculation of x1 and x4, respectively, to account for outliers in the dataset. The physical origin of these outliers could be mixed targets and estimation errors in the radar variables. These parameters are also rounded to what is considered reasonable precision for each variable (e.g., rhv rounded to the nearest hundredth). Note that these criteria can easily be modified if necessary.

These criteria are modified for the ZDR and rhv membership functions. As noted earlier, themaximum ZDR in the level-2 radar data is 7.9375 dB, and the minimum rhv is 0.2083. Theoretically, it is safe to assume that higher ZDR and lower rhv values would have been present. Therefore, if x4 5 8 dB for the ZDR membership function (i.e., 99.5th percentile), the membership value would be artificially too low (i.e., nearly zero) in the case where ZDR was 7.9375 dB. A similar situation would be present if x1 5 0.21 for the rhv membership function. Assuming a Gaussian distribution and adding a buffer, the standard score calculation results in a ZDR value of approximately 12 dB at the 99.5th percentile. As a result, the ZDR membership function for the

Next, the weights for the different classes are determined. Recall the weights characterize the discriminating efficiency of each variable with respect to the class. P09 subjectively determined theseweights. The weights in their scheme had values of 0, 0.2, 0.4, 0.6, 0.8, or 1.0. Each variable's weight was different for each of the 10 classes. For the

Finally, any constraints to restrict the class are determined. P09 called these constraints ''hard thresholds.'' No restrictions are placed on the

The scattering path's angle of incidence with respect to the ground ur will determine the distance r that the signal will travel from point C to the ground (Fig. 1). The shortest path (i.e., the fastest time of arrival) will be for vertical paths directly belowthe large hydrometeors (ur5 908), as noted by an h in Fig. 1. Therefore, the

Because the

One other hard threshold was considered, based upon a radar variable that was not used in the fuzzy logic portion of the HCA-radial velocity. Radial velocity was a variable used as a hard threshold in P09 HCA for the ground clutter and anomalous propagation class. They had a hard threshold that no ground clutter or anomalous propagation would be allowed if the radial velocity was .1ms21. Recall that no zero or positive radial velocity measurements are present in the distribution (Fig. 5b). Therefore, it was considered to include a constraint that no

3. Analysis and results

The enhanced HCA is tested on five different significant hail events that occurred between

In addition to the enhanced HCA classifications, radar reflectivity factor and rhv are shown for each case study. These radar variables were picked because it is easiest to visually confirmthe presence of a

The enhanced HCA is also tested on the KOUN radar data that were collected on

In the HCA output (Fig. 7d), a few

The second event the enhanced HCA is tested on occurred on

In the HCA output (Fig. 9d), there is a slight discontinuity in the

The third event the enhanced HCA is tested on occurred the next day on 1April 2012. Radar data collected by the KBMX WSR-88D near

In this example, a few

The fourth event the modified HCA is tested on occurred on

In this case, a few

The final event the HCA is tested on occurred on

In the HCA output, there is possible overidentification of

4. Summary and conclusions

The three-body scatter signature, or

The current S-band WSR-88D network that is in operational use in

The results of the

Acknowledgments. The authors thank

REFERENCES

Bohren, C. F., and

Hubbert, J. C., and

Kumjian, M.,

Lemon, L. R., 1998: The radar ''three-body scatter spike'': An operational large-hail signature. Wea. Forecasting, 13, 327-340, doi:10.1175/1520-0434(1998)013,0327:TRTBSS.2.0.CO;2.

Lim, S., V. Chandrasekar, and

Lindley, T.T., and

Liu, H., and V. Chandrasekar, 2000: Classification of hydrometeors based on polarimetric radar measurements: Development of fuzzy logic and neuro-fuzzy systems, and in situ verification. J.

Marzano, F. S., D. Scaranari,

Oye, R.,

Picca, J., and A. Ryzhkov, 2012: A dual-wavelength polarimetric analysis of the

Ryzhkov, A. V.,

Schuur, T. J.,

SPC, cited 2013: Storm reports. Storm Prediction Center. [Available online at http://www.spc.noaa.gov/climo/.]

Straka,

Vivekanandan, J.,

Wilson, J.W., andD.Reum, 1986: ''The hail spike'': Reflectivity and velocity signature. Preprints, 23rd Conf. on RadarMeteorology,

_____, and _____, 1988: The flare echo: Reflectivity and velocity signature. J.

Zrnic, D. S., 1987: Three-body scattering produces precipitation signature of special diagnostic value. Radio Sci., 22, 76-86, doi:10.1029/ RS022i001p00076.

_____, and

_____,_____,

(Manuscript received

Corresponding author address:

E-mail: vmahale@ou.edu