Identification and Removal of Non-meteorological Echoes in Dual-polarization Radar Data Based on a Fuzzy Logic Algorithm

Received 27 September 2014; revised 31 December 2014; accepted 19 January 2015

The weather radar is commonly used to estimate rainfall at high spatial and temporal resolution over large regions. However, radar moment data are contaminated by non-meteorological echo (NME) such as ground clutter, anomalous propagation (AP), chaff etc. (Smith et al., 1996) showed that AP echoes lead to systematic overestimation of rainfall. In addition, chaff echo can lead to radar precipitation on clear days. Thus, quality control of radar data is essential for improving radar quantitative precipitation estimation.

Several methods have been used to identify and remove NME: (1) average ground echo mask; (2) time domain filter; (3) frequency domain filter; and (4) moment-based suppression using the temporal and spatial variability of moment data. Moment-based suppression is widely known and accepted for operational application with various statistical techniques (e.g. neural network, Bayes classifier, and fuzzy logic).

The neural network is one of the most commonly used techniques in identifying NME (Haykin and Deng, 1991; Grecu and Krajewski, 2000; Krajewski and Vignal, 2001; Lakshmanan et al., 2007). (Grecu and Krajewski, 2000) proposed the use of neural networks to identify AP echoes by applying the spatial fluctuation of the reflectivity. (Moszkowicz et al., 1994) suggested the Bayes classifier to detect NME by applying discriminating functions of Bayesian theorem. (Rico-Ramirez and Cluckie, 2008) compared the Bayes classifier with the fuzzy classifier for C-band dual-polarization radar data. Their Bayes classifier gave a slightly better performance than the fuzzy classifier. Recently, (Nicol et al., 2011) showed that ground clutter identification is likely to benefit from measurements of the power ratio or clutter phase alignment even when dual-polarization parameters are available in the Bayes classifier.

Fuzzy logic algorithms have been widely used for the mitigation of NME due to their simplicity. (Cho et al., 2006) derived the normalized frequency distributions of three feature parameters (vertical gradient of reflectivity, standard deviation of reflectivity, and absolute value of radial velocity) to define the characteristics of ground clutter echo, AP echo, and precipitation echo (PRE). Membership functions (MFs) and their weights are derived from these characteristics for given parameter and reflectivity intervals. Their algorithm identifies NME using the total membership value calculated from each MF and weight. The performance of their algorithm is comparable with that from a polarimetric approach. (Berenguer et al., 2006) also used a fuzzy logic algorithm that employs the echo top, vertical gradient of reflectivity, spin change (Steiner and Smith, 2002), and texture of reflectivity.

Many ground clutter detection algorithms based on dual-polarimetric radar data have also been developed using fuzzy logic algorithms. (Gourley et al., 2007) used an algorithm that derives the MFs of the correlation coefficient, standard deviation of differential reflectivity, and standard deviation of differential phase using Gaussian kernel density estimation proposed by (Silverman, 1981) for C-band dual-polarization radar data. They evaluated the performance using accumulation maps from PRE and NME. In addition, the clutter mitigation decision (CMD) combines three discriminants (clutter phase alignment, texture of reflectivity, and spin) using the fuzzy logic algorithm to identify NME (Hubbert et al., 2009a, 2009b) and then applies an adaptive frequency domain filter. The hydrometeor classification algorithm (HCA), which discriminates hydrometeor type as well as ground clutter, also uses a fuzzy logic classifier (Liu and Chandrasekar, 2000; Park et al., 2009; Mahale et al., 2014).

Recently, several ground clutter filters using spectral parameters have been demonstrated in the radar research community. (Warde and Torres, 2014) developed CLEAN-AP (Clutter Environment Analysis using Adaptive Processing) using the phase of the auto-correlation spectral density. It shows better results than CMD (Torres et al., 2012). STEP (Spectrum-Time Estimation and Processing) can improve the quality of polarimetric radar data using three novel algorithms: Spectrum Clutter Identification (SCI), bi-Gaussian clutter filter, and multi-lag moment estimation (Cao et al., 2012). The SCI algorithm has four discriminants (spectral power distribution, spectral phase fluctuations, spatial texture of echo power, and spatial texture of spectrum width) based on the Bayesian method (Li et al., 2013). (Li et al., 2014) also detected ground clutter using a Bayesian classifier for polarimetric radar.

The Ministry of Land, Infrastructure and Transport (MOLIT) has been operating the Mount Sobaek S-band polarimetric radar, situated in complex terrain, since November 2011. In this paper, a moment-based fuzzy logic algorithm is developed by optimizing the MFs and weights for Mount Sobaek dual-polarization radar measurements. Our approach is similar to (Cho et al., 2006), except for the fuzzy parameters. However, their approach is adapted into dual-polarization data. In addition, this radar does not archive unfiltered polarimetric parameters and only unfiltered reflectivity is obtained. Thus, the algorithm is further adapted to resolve issues with an absence of unfiltered polarimetric measurements. The detection accuracy of the proposed method is evaluated using accumulated rainfall, POD, FAR, and CSR.

The data used are summarized in section 2 and the methodology is discussed in section 3. Section 4 presents the results of determining the MFs and weights, as well as validation of the proposed algorithm.

Moment data from the Mount Sobaek S-band dual polarization radar are used. This radar has been operated by MOLIT since 15 November 2011. The peak power of the Klystron transmitter is 750 kW. The Mount Sobaek radar operates a full volume scan composed of six elevation angles (-0.5^°, -0.1^°, 0.3^°, 0.7^°, 1.0^°, 1.3^°) in a simultaneous transmitter and receiver (STAR) mode. The unambiguous range is 150 km in the rain mode. The gate size is 125 m and the pulse repetition frequency is 1000 Hz.

The radar produces unfiltered reflectivity (DZ), filtered reflectivity (CZ), Doppler velocity (V_r, spectrum width, differential reflectivity (Z _DR), correlation coefficient (ρ _HV), differential phase (Φ _DP), specific differential phase (K _DP), and signal quality index (SQI). Figure 1 shows plan position indicator (PPI) images of all radar parameters for the precipitation case at the elevation angle of -0.5^° at 0802 LST (local standard time) 6 July 2012. The signal processor of the radar provides one unfiltered parameter, DZ only, and all other parameters are filtered by a Gaussian model adaptive processing (GMAP; Siggia and Passarelli Jr., 2004) clutter filter in the signal processor. Thus, other parameters show areas of "no data" when compared with DZ data.

Figure 1.  PPI images of radar parameters at 0802 LST 6 July 2012 and average ground echo map of Mount Sobaek radar at an elevation angle of -0.5^°.

Two different data sets are used in this study: one for building MFs and weights, and the other for validating the proposed algorithm. The MFs and weights are obtained from seven NME events (377 volume scans) and four PRE events (375 volume scans), listed in Table 1. The NME events include ground clutter, clear air, and chaff echoes. The precipitation events are composed of widespread rain and monsoon fronts. The validation of the fuzzy logic algorithm is performed for three dominant echo types (chaff, clear air, and precipitation), shown in Table 2. The selection of the various events is due to the increase in diversity in the feature parameters.

The MFs and weights of the Mount Sobaek radar are necessary to detect NME. The MFs and weights are determined by the same procedure described in (Cho et al., 2006). Radar moment data are divided into two areas (the NME and PRE areas) based on the average ground echo map. Then, the probability density functions (PDFs) of the five fuzzy parameters are derived for the two areas to define the characteristics of the NME and PRE. Finally, the MFs and weights are derived from these PDFs.

The average ground echo map is produced by the mean reflectivity of ground clutter echoes during 0345-0445 LST 8 July 2012. This period is composed of 25 volume scans and is representative of the normal propagation of the radar beam. No precipitation and clouds are present. The derived average ground echo map at the elevation angle of -0.5^° shows significant ground echoes in northwest, south, and southeast areas, where several mountain ranges are located (Fig. 1). The NME and PRE areas are classified using this average ground echo map as reference. For the PRE events in Table 1, the PRE area is limited to pixels where DZ<0 dBZ in the average ground echo map. On the other hand, the NME area is determined for the NME events (Table 1) with the condition of DZ≥5 dBZ in the average ground echo map.

For the selected NME and PRE areas, five fuzzy parameters (FPs) are calculated. They are: the standard deviation of reflectivity [SD(DZ)]; the standard deviation of differential reflectivity [SD(Z _DR)]; the standard deviation of the correlation coefficient [SD(ρ _HV)]; the standard deviation of differential phase [SD(Φ _DP)]; and the correlation coefficient (ρ _HV). The standard deviation of a given variable (V: DZ, Z _DR, Φ _DP, and ρ _HV) is defined as follows:

\begin{equation} {\rm SD}(V_{\rm c})=\sqrt{\dfrac{1}{n}\sum_{i={\rm c}-2}^{{\rm c}+2}(V_i-V_{\rm c})^2} .(1) \end{equation}

Here, the c is the gate number at which the SD is calculated. The i indicates the gate number.

The PDFs of the five FPs are then calculated with five reflectivity intervals for both the NME and PRE areas. The four intervals of reflectivity (DZ) are:

\(0\le\rm DZ<10\); 10≤ DZ<20; 20≤ DZ<30; \(30\le\rm DZ\).

For given fuzzy parameters (FP_i) and reflectivity intervals (DZ_i), the MF is derived using the PDFs of the NME and PRE with the following equation:

\begin{equation} {\rm MF}({\rm FP}_{\rm i},{\rm DZ}_{\rm j})=\dfrac{{\rm PDF}_{\rm NME}({\rm FP}_{\rm i},{\rm DZ}_{\rm j})}{{\rm PDF}_{\rm NME}({\rm FP}_{\rm i},{\rm DZ}_{\rm j}) +{\rm PDF}_{\rm PRE}({\rm FP}_{\rm i},{\rm DZ}_{\rm j})} . (2)\end{equation}

Here,the FP stands for SD(DZ), SD(Z _DR), SD(ρ _HV), SD(Φ _DP), and ρ _HV.

The MFs of the fuzzy parameters are combined with weights to derive the total membership value as Eq. (3). The total membership value is the same concept as in another study using a fuzzy logic algorithm (Cho et al., 2006):

\begin{equation} {\rm MF}_{\rm total}=\sum W({\rm FP}_{\rm i},{\rm DZ}_{\rm j}){\rm MF}({\rm FP}_{\rm i},{\rm DZ}_{\rm j}) . (3)\end{equation}

Here, W indicates the weight, which is derived below:

\begin{eqnarray} W({\rm FP}_{\rm i},{\rm DZ}_{\rm j})&=&\dfrac{1}{A_{{\rm FP}_{\rm i},{\rm DZ}_{\rm j}}}\times \dfrac{1}{S} ,(4)\\ S&=&\dfrac{1}{A_{\rm SD(DZ)}}+\dfrac{1}{A_{{\rm SD}(Z_{\rm DR})}}+\dfrac{1}{A_{{\rm SD}(\rho_{\rm HV})}}+\quad\nonumber\\ &&\dfrac{1}{A_{{\rm SD}(\Phi_{\rm DP})}}+\dfrac{1}{A_{\rho_{\rm HV}}} ,(5) \end{eqnarray}

where the A indicates the overlapping area of PDF _NME[FP _i, DZ _j] and PDF _PRE[FP _i, DZ _j]. A point of intersection between PDF _NME[FP _i, DZ _j] and PDF _PRE[FP _i, DZ _j] is determined. The overlapping area is then calculated by adding smaller values between normalized PDF _NME[FP _i, DZ _j] and PDF _NME[FP _i, DZ _j] on both sides of the point. Thus, the FP _i with the large overlapping area is considered as a less significant parameter in the detection of NME.

The five fuzzy parameters are calculated from radar moment data at each gate. The fuzzy membership values of fuzzy parameters are calculated by predetermined MFs and are combined with weights as in Eq. (3) to lead to the total fuzzy membership value (MF _total). When MF _total is larger than the threshold (= 0.5), the pixel is identified as the NME, and vice versa for the PRE.

Figure 2.  PDF of the standard deviation of (a) DZ, (b) Z _DR, (c) ρ _HV, and (d) Φ _DP, and the PDF of (e) ρ _HV. Solid lines represent the PDF of NME. Dotted lines represent the PDF of PRE.

Figure 3.  The MFs of five fuzzy parameters for Mount Sobaek radar.

Figure 4.  PPI images of the standard deviation of DZ, Z _DR, ρ _HV, Φ _DP and ρ _HV at an elevation angle of -0.5^° at 0802 LST 6 July 2012.

Figure 5.  PPI images of the membership values of the five fuzzy parameters and of the total membership value at an elevation angle of -0.5^° at 0802 LST 6 July 2012.

Figure 6.  PPI images of average reflectivity at an elevation angle of -0.5^° from 0802 to 0859 LST 6 July 2012 (a) before applying the threshold and (b) after applying the threshold. (c) Fraction of removed pixels to overall pixels as a function of the difference between DZ and CZ before applying the threshold.

Figure 7.  Rainfall accumulations derived from (a, d, g) DZ and (b, e, h) CZ, and (c, f, i) the reflectivity (FZ) of the proposed algorithm at different elevation angles. Each row represents the same elevation angle. EL1, 2 and 3 represent elevation angles of -0.5^°, -0.1^° and 0.3^°, respectively.

Since all parameters of Mount Sobaek radar except DZ are filtered, the derived FP does not fully represent the characteristics of NME. Thus, the performance of the algorithm can be significantly undermined. To avoid this problem, the difference between DZ and CZ is additionally applied to eliminate residual NME. The difference between DZ and CZ reflects the degree of contamination from ground clutter. The larger the difference, the more contaminations PRE will receive. The threshold of 5 dBZ is used to further remove echoes from PRE in this study.

For the selected NME and PRE areas from pure NME and pure PRE events in Table 1, the PDFs of NME and PRE are calculated for five fuzzy parameters with reflectivity intervals (Fig. 2). Figure 2a shows that the SD(DZ) of the PRE is within 5 dB. The higher the values of the reflectivity interval, the broader and the more skewed the distribution of NME. The PDFs of SD(Z _DR) show a distinctive discrepancy between PRE and NME. The PDF _PRE[SD(Z _DR)] appears mostly at SD(Z _DR) ≤2 dB, except for \(0\le\rm DZ<10\) dBZ (Fig. 2b). The higher value of SD(Z _DR) for 0≤ DZ<10 dBZ is due to the edge of precipitation echoes. The PDF _PRE[SD(ρ _HV)] shows a smaller value [SD(ρ _HV)<0.2] (Fig. 2c). The most distinctive separation is shown in the PDFs of SD(Φ _DP) (Fig. 2d). The PDF _PRE[SD(Φ _DP)] mostly appears at SD(Φ _DP)<10^°. When DZ ≥30 dBZ, the overlap area between the PDFs of NME and PRE is almost negligible. The higher the value of the reflectivity interval, the larger the value of ρ _HV. (Fig. 2e). The PDFs clearly show that the SD of the three dual-polarimetric variables will play a key role in identifying NME. In particular, the SD(Φ _DP) is the most important indicator at higher DZ.

Figure 3 shows the MFs of each fuzzy parameter that are calculated from the PDFs of NME and PRE. Each line represents the MF of different reflectivity intervals. The MFs become broader and less steep as the reflectivity decreases, except for SD(Z _DR). For example, when SD(ρ _HV) = 0.1, MF = 0.9 in DZ ≥30 dBZ, whereas MF = 0.65 in 0≤ DZ<10 dBZ. This indicates the MFs are good indicators at higher DZ rather than smaller DZ.

Table 3 shows the weights of the five fuzzy parameters derived from the overlapping area of the PDFs of NME and PRE. When DZ≥ 30 dBZ, SD(Z _DR) and SD(Φ _DP) have higher weights, whereas the weight of ρ _HV is the lowest. The SD(Φ _DP) shows higher values of weights at overall ranges of DZ intervals. The SD(Z _DR) is also an important feature parameter for the classification of NME.

To detect NME for a selected case, the five fuzzy parameters are first calculated from the radar moment data. The NME and PRE are distinctive in the PPI images of the fuzzy parameters, especially SD(DZ) and SD(Z _DR) (Fig. 4). In particular, the high value of SD(DZ) and SD(Z _DR) is distinctive in the areas of normal ground echoes, while these areas are not present in the other parameters. This is due to the GMAP filtering of power spectra near zero Doppler velocity. In addition, the values of SD(ρ _HV) and SD(Φ _DP) are larger in the residual areas of normal ground echoes. This indicates that the GMAP filtering is not sufficient to completely eliminate the contamination of ground echoes. Furthermore, the partial beam blocking areas are clearly identified with the SD(ρ _HV) and SD(Φ _DP).

The value of MFs for each parameter are shown in Fig. 5. When MF = 1.0 (0.0), a favorable condition is indicated for NME (PRE). The membership value of SD(DZ) in the areas of normal ground clutter is close to 1.0, while the membership value for PRE is below 0.6 (Fig. 5a). The NME and PRE areas are clearly discernible in the membership value of SD(Z _DR) (Fig. 5b). The membership values of SD(Φ _DP) show smaller areas of high MF (Fig. 5d). In addition, the value of MF in the areas of partial beam blocking is small, indicating less of an effect of beam blocking in Φ _DP. The values of SD(ρ _HV) and ρ _HV better represent the partial beam blockage areas and ground clutter compared with SD(Φ _DP). In particular, the high values are shown in the rays along the southwest direction when the value of ρ _HV is low. The total membership value is higher in the areas of partial beam blocking, residual clutter, and edges. The MF _total in most PRE areas has a value as small as 0.1.

In the dual-polarization fuzzy logic algorithm, the unfiltered parameter (DZ) and filtered parameters (Z _DR, ρ _HV, and Φ _DP) are used. Figure 6a is the PPI image of hourly average reflectivity at the elevation angle of -0.5^° from 0802 to 0859 LST 6 July 2012. After applying the fuzzy logic algorithm, ground clutter echoes above 40 dBZ still remain in areas of residual clutter due to filtered dual-polarimetric parameters (Fig. 6a). This is more prominent for areas of mixed ground echoes and precipitation. After applying GMAP filtering, the NME characteristics of dual-polarimetric parameters become weaker and less distinctive.

Figure 6c shows the fraction of removed pixels to overall pixels as a function of the difference between DZ and CZ. The minimum fraction exists at DZ-CZ=0 dB. As the values of DZ-CZ increase, the fraction also increases, up to DZ-CZ=25 dB. This indicates that mixed areas of clutter and precipitation echoes are not properly removed with such high values of DZ-CZ. The fraction is then less than 1 at DZ-CZ= 25-50 dB. This may be due to residual clutter and precipitation echoes at near zero Doppler velocity. The threshold of 5 dB is further applied to eliminate residual clutters. If the difference between DZ and CZ in a pixel is higher than the threshold, the pixel is removed as NME. After applying the threshold, all residual ground clutter echoes shown in Fig. 6a are removed (see Fig. 6b). This removed area is similar to the ground echo map above 40 dBZ in Fig. 1. In addition, the average reflectivities in the zero isodop area, indicated by the red dashed line in Fig. 6b, are also decreased by about 10 dBZ. This is unavoidable due to the use of the DZ-CZ threshold.

4.4.1. Verification with rainfall accumulation

The performance of the dual-polarization fuzzy logic algorithm is validated using rainfall accumulation. The following rainfall estimator is used for each PPI:

\begin{equation} R({\rm DZ})=1.7\times 10^{-2}{\rm DZ}^{0.71} . (6)\end{equation}

Then, total rainfall accumulations are obtained for the entire period. The total rainfall amount from the original DZ and CZ, and the DZ after applying the fuzzy algorithm, are compared.

Mount Sobaek radar produces filtered dual-polarization data using GMAP. This frequency domain filter has a weakness in that all echoes are filtered regardless of their echo types. These filtered data are significantly biased and can lead to systematic bias in rainfall accumulation. Moreover, the broad clutter spectrum cannot be completely filtered. These drawbacks are shown in the verification using rainfall accumulation.

The performance of the dual-polarization fuzzy classifier is validated using rainfall accumulation from 0100 to 1300 LST 22 October 2012 (Fig. 7). The first column shows accumulated rainfall derived from unfiltered reflectivity (DZ); the second shows that calculated from filtered reflectivity (CZ); and the last column from DZ after applying the dual-polarization fuzzy classifier (FZ). High rainfall above 200 mm associated with ground clutter echoes exists in the rainfall accumulation derived from DZ at all elevation angles. Most of these contaminated pixels are removed in both the rainfall accumulations derived from CZ and FZ. However, R(CZ) and R(FZ) show several different features in terms of residual ground clutter, rainfall amount, bright band, and second trip echo. The features are easily discernable in Fig. 7 and Fig 8. High rainfall areas (>100 km), shown in red dashed circles (Fig. 7), are residual ground clutter echoes that cannot be removed by GMAP, but they are properly removed by FZ (black dashed circles).

In addition, the rainfall accumulation of R(FZ) shows higher values than that of R(CZ). Figure 8 shows differences among different accumulations. The difference in rain accumulation is larger over precipitation areas in R(DZ)-R(CZ) than in R(DZ)-R(FZ). This is due to the over-filtering of precipitation echoes by GMAP, whereas the precipitation areas are properly presented in FZ. The relatively larger values of the difference in the northwest and southeast directions (Fig. 8) are due to filtering of precipitation echoes near zero velocity. The dashed circle areas in the right panel show over-deduction of precipitation by FZ. Detailed examination reveals that these areas are due to the second trip echoes (not shown). The SQI values in the second trip echo area are low. The dual-polarization parameters of second trip echo are already removed by the SQI threshold before applying our algorithm in several cases. For this reason, if the measurements of dual-polarization variables are void in these areas, then FZ is removed. Thus, FZ can be used to remove second trip echoes. In addition, the proposed algorithm can reduce the overestimated rainfall due to bright band at >100 km for the reason that ρ _HV is low and SD(ρ _HV) is high in the melting layer. The rain accumulation in Figs. 7g and h clearly shows overestimation at far ranges, as shown by the rings close to the 150 km. This overestimation is not shown in Fig 7i and the large value of R(DZ)-R(FZ) in the same area supports this argument.

Figure 8.  Difference in rainfall accumulation between (left) R(DZ) and R(CZ) and (right) R(DZ) and R(FZ) at different elevation angles. Each row represents the same elevation angle. EL1, 2 and 3 represent elevation angles of -0.5^°, -0.1^° and 0.3^°, respectively.

4.4.2. Verification with skill score

The detection accuracy of the fuzzy logic algorithm is evaluated using the POD and FAR:

\begin{eqnarray} {\rm POD}&=&\dfrac{H}{H+M} ,(7)\\ {\rm FAR}&=&\dfrac{F}{H+F} . (8)\end{eqnarray}

The POD and FAR are derived based on the contingency table shown in Table 4. For the PRE events, the hit (H) is defined as the PRE echoes with SQI >0.7 in actual measurements and DZ <10 dBZ in the average ground echo map. The miss (M) is the eliminated pixel by the fuzzy logic algorithm with the same condition as in H. The false (F) is the remaining pixel in the NME area after applying the fuzzy algorithm. For NME events, the M is the area of DZ<10 dBZ in the average ground echo map that is not detected by the algorithm. The H is the detected area in the algorithm. Thus, the POD in NME evaluates the removal efficiency of ground clutter, chaff, and AP echoes. For the NME events, the F cannot be calculated because the precipitation pixels do not exist.

Validation is also performed as functions of CSR for the PRE events only. The CSR is defined as

\begin{equation} {\rm CSR}=10\lg\left(\dfrac{T_0-C_0}{C_0}\right)\approx 10\lg\left(\dfrac{{\rm DZ-CZ}}{\rm CZ}\right) , (9)\end{equation}

where T₀ is the unfiltered signal power and C₀ is the filtered signal power. Since the real-time moment data do not provide T₀ and C₀, the CSR is approximated with DZ and CZ. For a given CSR, the fraction (F) of removed pixels to overall pixels is calculated by:

\begin{equation} {\it F}=\dfrac{P_{\rm re}}{P_{\rm all}} .(10) \end{equation}

The term P _all represents the overall number of pixels with radar echoes and P _re is the number of removed pixels among them.

The validation of the dual-polarization fuzzy classifier is performed for the events in Table 2. Figure 9a shows the PODs as a function of reflectivity thresholds. The average POD for the clear echo and chaff echo events is about 1.00. The average POD for the PRE events is 0.7-0.85. This slightly lower POD is due to the exclusion of mixed areas of ground clutter and precipitation and the removal of edge regions. The average FAR for the PRE events decreases from 0.06 to 0.02 with reflectivity thresholds. In the case of ground clutter, chaff and precipitation echo, NMEs are properly removed by our algorithm (Fig. 10). The spatial variations of Z _DR and Φ _DP in the chaff echo are large and ρ _HV is less than 0.8.

Figure 9.  (a) Average PODs for non-meteorological echo events (squares) and precipitation echo events (triangles), and average FAR for precipitation echo events (crosses). (b) Fraction of removed pixels to overall pixels as functions of the CSR threshold for precipitation echo cases.

Figure 10.  PPI images of original reflectivity (DZ), reflectivity after applying the algorithm (FZ), Doppler velocity (V _r), and dual-polarization parameters (Z _DR, Φ _DP, and ρ _HV).

The fraction of removed pixels to overall pixels is shown in Fig. 9b as a function of CSR. The fraction is about 0.5 at CSR = 0 dB. As the CSR increases, more pixels are removed. When the echoes are more contaminated, they are easily eliminated.

A moment-based fuzzy logic algorithm is developed to identify and remove NME by optimizing membership functions and weights for Mount Sobaek dual-polarization radar data. We use five fuzzy parameters [SD(DZ), SD(Z _DR), SD(ρ _HV), SD(Φ _DP), and ρ _HV] and reflectivity intervals from selected NME and PRE cases for determination of MFs and weights. For the selected NME and PRE areas, the PDFs of NME and PRE clearly show that the five fuzzy parameters show discernible features to identify NME, especially Φ _DP. The MFs and weights are derived using the PDFs of the NME and PRE. The MFs become broader and less steep as the reflectivity interval decreases. The SD(Φ _DP) shows higher values of weights at overall ranges of DZ intervals. The SD(Φ _DP) is an important feature parameter for classification of NME. The fuzzy membership values at each pixel are calculated using predetermined MFs and are combined with weights to lead to the total membership value. When the total membership value is higher than 0.5, this pixel is identified and removed as NME.

After applying the fuzzy logic algorithm, ground clutter echoes still remain in areas of mixed ground and precipitation echoes. This is due to the absence of unfiltered dual-polarimetric measurements provided from Mount Sobaek radar. The signal processor of Mount Sobaek radar provides one unfiltered parameter only. All the others, including dual-polarization parameters are filtered. After GMAP filtering, the NME characteristics of dual-polarimetric measurements become weaker or are removed. Thus, the dual-polarimetric fuzzy parameters cannot be identified as NME after applying the fuzzy logic algorithm. To avoid this problem, our algorithm further applies the threshold of difference between DZ and CZ. The DZ-CZ indicates the degree of contamination from ground clutter. Average reflectivity after applying the threshold (5 dB) shows that residual ground clutter echoes.

The performance of the fuzzy logic algorithm is evaluated using accumulated rainfall, POD, FAR, and CSR. In the comparison of rainfall accumulation, the proposed algorithm has several different results to GMAP filtering of Mount Sobaek radar. The GMAP filters all echoes regardless of echo type. Thus, significant underestimation appears in high rainfall areas compared with the proposed algorithm. Moreover, residual ground clutter echoes still remain and cause high rainfall that cannot be removed by GMAP due to the broad clutter spectrum. These areas are properly removed by R(FZ). In addition, the proposed algorithm can reduce the overestimated rainfall due to bright band and second trip echoes. Values of high SD(ρ _HV) and low ρ _HV in the bright band can be detected in the proposed algorithm. Moreover, removal of second trip echo is possible using the SQI threshold. The average POD for NME (PRE) events is about 1.00 (0.76). The average FAR for PRE events is 0.05, and decreases as a function of the reflectivity threshold. The fraction of removed pixels to overall pixels increases as a function of CSR and reaches F=1 at CSR = 4 dB.