1 Introduction

Doppler weather radar data have high temporal and spatial resolutions and have been widely applied in operational forecasts and research on mesoscale weather phenomena (Anagnostou and Krajewski, 1999; Alfieri et al., 2010; Pan et al., 2010; Qin et al., 2014; Liu et al., 2016), presenting significant advantages compared with other observational data (Serafin and Wilson, 2000; Zheng et al., 2004; Xiao et al., 2008). For instance, radar data can be used to generate high-resolution quantitative precipitation estimations (Fulton et al., 1998; Qi and Zhang, 2017) and are often assimilated into numerical weather models for improving the prediction of convective systems (Jones et al., 2015; Ridal and Dahlbom, 2017). In radar data, however, there are not only meteorological echoes, but also non-meteorological echoes, such as ground clutters and isolated echoes that may comprise biological echoes, electronic interference, and so on (Steiner and Smith, 2002; Zhang et al., 2005). The occurrence of isolated non-meteorological echoes and ground clutters can often degrade the performance of applications of radar data in forecasting and research. Therefore, it is important to remove isolated non-meteorological echoes and ground clutters from radar data before they can be used.

Various techniques have been applied to identify and remove isolated non-meteorological echoes and ground clutters from radar data. For identifying isolated non-meteorological echoes, Fulton et al. (1998) simply defined them as gates with reflectivity exceeding a certain threshold (18 dBZ as default) and having no more than 1 in 8 surrounding neighbors above that threshold. Bergen and Albers (1988) and Krishnapuram and Keller (1993) presented a fuzzy logic based classification scheme to identify isolated points in a picture. Their scheme has been used in meteorological fields to identify isolated non-meteorological echoes, and was incorporated into the Weather Surveillance Radar-1988 Doppler (WSR-88D) system (Zhang et al., 2004) in the USA and the Severe Weather Automatic Nowcast (SWAN) system in China (Wu et al., 2013). Specifically, the method involves computing the percentage of gates with non-missing values in a box (window) and comparing the results with a given default threshold. If the percentage is less than the threshold, the center point (gate) of the box is regarded as an isolated echo. Although the method performs well in eliminating isolated non-meteorological echoes, it simultaneously removes the edges of meteorological echoes (Wu et al., 2013).

Many studies have also focused on methods to iden-tify ground clutters. For example, using the notion that ground clutters are characterized by near-zero Doppler velocities, Chrisman et al. (1995) developed an automated procedure to reduce or eliminate ground clutters using the radar-observed radial velocity. Unfortunately, however, the procedure also eliminates meteorological echoes with near-zero Doppler velocities, because they exhibit characteristics similar to those of ground clutters. In a later work, Fabry and Gadoury (2009) indicated that although the peak contribution from ground clutters is centered around zero velocity, ground clutters can extend to other velocities and even exceed those of meteorological echoes if they are strong. Meanwhile, Hubbert et al. (2009a) pointed out that the actual measured velocity from ground clutters can vary somewhat from zero and the spectrum width from the clutter can be widened (theoretically, it should be narrow) due to rotational scanning. Hence, such an approach would bias the resulting reflectivity. In radar-based quantitative precipitation estimation, Fulton et al. (1998) simply defined ground clutters as gates whose reflectivity exceed a fixed threshold (65 dBZ in default). Pamment and Conway (1998) devised a scheme to detect ground clutters by combining multiple independent observational data, such as surface observations, satellite images, and so on. However, it is difficult to apply this scheme in practice because of the sparse spatial and temporal resolutions of independent observations. Steiner and Smith (2002) used a decision tree comprised of the vertical extent of echoes, the spatial variability of reflectivity, and the vertical gradient of reflectivity, to identify ground clutters. However, this method also removes boundary layer features (e.g., gust fronts) and cannot handle strong, clear-air echoes, and the ground clutters appearing at two adjacent tilts because of the small vertical gradient of reflectivity. Kessinger et al. (2003) developed a detection algorithm for ground clutters based on fuzzy logic classification (depending on the echo variation on the vertical and azimuth-radial plane), which has since been introduced in the WSR-88D system in the USA. The algorithm has worked well for anomalous propagation and most ground clutters (Liu L. P. et al., 2007; Liu S.-Y. et al., 2008). However, a disadvantage is that it cannot identify the ground clutters presented at two adjacent tilts because they can induce small vertical gradients of reflectivity. Zhang et al. (2004) improved this algorithm by introducing a reference tilt with 3–4.5-km height, instead of an upper tilt, so that it can identify ground clutters appearing at two adjacent tilts. The method has also been introduced into the WSR-88D system in the USA (Zhang et al., 2004) and the SWAN system in China (Wu et al., 2013). Nevertheless, this improved method can only be used for the gates within a certain range from the radar, as the reference tilt is limited by the radar beam height of 4.5 km.

Recently, Hubbert et al. (2009a) constructed a new parameter [called “clutter phase alignment” (CPA)], based on the received base-band complex signal [referred to as the in-phase and quadrature-phase (I and Q) components] at the signal-processing level (i.e., level-I data). It is a good indicator in the identification of ground clutters. For example, the CPA is greater than 0.90 for the vast majority of ground clutters, whereas it is less than 0.5 for most weather echoes. Subsequently, Hubbert et al. (2009b) proposed a clutter mitigation decision (CMD) algorithm (a fuzzy logic recognition algorithm) using a combination of the CPA and other measures (such as the texture of reflectivity, the spatial variability of reflectivity, and so on). The CMD algorithm is designed to run in real time on operational radars and has been implemented in the updated WSR-88D Open Radar Product Generator (Hubbert et al., 2009b). Torres and Warde (2014) introduced a clutter environment analysis using adaptive processing (CLEAN-AP) filter, which is also based on the received base-band complex signals (I and Q) and can adjust its suppression characteristics in real time to match dynamic atmospheric environments. With the operational application of more advanced dual-polarization radars, polarimetric quantities such as the cross-correlation coefficient, the standard deviation of differential propagation phase measurements, differential reflectivity, etc., have been used to classify ground clutters and shown better results (Friedrich et al., 2006; Gourley et al., 2007; Rico-Ramirez and Cluckie, 2008; Lakshmanan et al., 2014).

The China New Generation Weather Radar (CINRAD) network consists of more than 170 radars comprising S-band (SA, SB, and SC types) and C-band (CB, CC, and CD types) instruments manufactured by three companies (Xu et al., 2017). These radars are now single-polarization radars (Su et al., 2018) and their received base-band complex signals (I and Q) at the signal-processing level are not stored in operation. Therefore, although the CMD algorithm (Hubbert et al., 2009b), CLEAN-AP filter (Torres and Warde, 2014), and methods based on polarimetric quantities (Friedrich et al., 2006; Gourley et al., 2007; Rico-Ramirez and Cluckie, 2008; Lakshmanan et al., 2014) have performed well in identifying ground clutters, they cannot be used in CINRAD (i.e., level-II data of single polarization) to eliminate ground clutters. Thus, for CINRAD data, the algorithms of Kessinger et al. (2003) and Zhang et al. (2004) are still a good choice for removing isolated non-meteorological echoes and ground clutters. However, as mentioned above, these methods can also remove the edges of meteorological echoes and cannot identify the ground clutters appearing at two adjacent tilts. Thus, our main goal here is to improve these algorithms such that they can remove isolated non-meteorological echoes whilst preserving the edges of meteorological echoes, as well as identify ground clutters (especially those appearing at two adjacent tilts) on the overall azimuth–range plane.

Following this introduction, the data and processing procedures are described in Section 2. The improved algorithms for identifying isolated echoes and ground clutters are presented in Sections 3 and 4, respectively. A statistical analysis is presented in Section 5, followed by conclusions in Section 6.

2 Data and processing

Three CINRADs located in Jiangxi Province (Fig. 1a) are used to test the methods of removing isolated non-meteorological echoes and ground clutters from radar base (i.e., level-II) data in this study. The locations of these three radars and altitude of their surroundings are shown in Fig. 1b. The radars located at Nanchang and Shangrao are S-band with type-A CINRADs (i.e., CINRAD/SA), which is a similar instrument to the WSR-88D radar. The one located at Ganzhou is an S-band with type-C CINRAD (i.e., CINRAD/SC), which is produced by 784 Factory in Chengdu, China. Up to 973 automatic rainfall observational stations around Nanchang are used to calculate the rainfall frequency from 0000 UTC 5 to 1600 UTC 14 March 2015. These data are obtained from the Meteorological Information Center of Jiangxi Province, China. The radar data are processed in polar coordinates (radar coordinates), but the corresponding displays are all in Cartesian coordinates. The method of horizontal interpolation with the nearest neighbor on the range–azimuth plane (Xiao et al., 2008) is selected to convert the radar data from polar to Cartesian coordinates with a resolution of 0.01° × 0.01°.

3 Isolated echoes 3.1 Original method

In the raw data observed by Doppler weather radar, there are sometimes many isolated non-meteorological echoes (i.e., noise), derived from sources such as insects, an aircraft, and so on. These isolated non-meteorological echoes obviously affect the application of radar data in estimating rainfall and monitoring weather, as well as data assimilation. Bergen and Albers (1988) and Krishnapuram and Keller (1993) presented a scheme based on fuzzy logic classification to identify isolated points in a picture, and the scheme was then applied in the quality control of radar data to remove isolated non-meteorological echoes (Zhang et al., 2004). The expression of the scheme is

${P_{\rm X}} = \frac{N}{{{N_{\rm {total}}}}}, $

(1)

where N is the number of grid points with valid reflectivity in a window (default 5 × 5, i.e., 5 radials and 5 azimuths) whose center is located at point X, and ${N_{\rm {total}}}$ is the total number of points within the window. When ${P_{\rm X}}$ is less than a threshold (default 0.75), the value at the center point X is regarded as an isolated echo (noise), and then replaced by a missing value. This method has been widely applied in removing reflectivity and radial velocity noises (Wang and Wan, 2006; Liu et al., 2008; Tang, 2011; Yang et al., 2011). It has also been introduced into radar operational or nowcasting systems, such as WRS-88D in the USA (Zhang et al., 2004) and SWAN in China (Wu et al., 2013) .

The reflectivity measurements at 0.5° elevation observed by Nanchang CINRAD/SA radar at 2203 UTC 18 June 2016 are selected to test the method (Fig. 2a), and the results show that the method can eliminate the isolated echoes remarkably well (Fig. 2b). However, the method also partially removes the margins of meteorological echoes, such as the encircled area in Fig. 2b. Wu et al. (2013) also pointed out this shortcoming of the me-thod. Intuitively, this deficiency is not particularly problematic in synoptic- and meso-α-scale meteorological echoes, because the area of the removed echoes is relatively small. However, in meso-β- and meso-γ-scale meteorological echoes (i.e., small-scale convective cells), the situation is quite different. Figure 3 depicts the primitive convective echoes observed by the Ganzhou CINRAD/SC radar and the convective echoes filtered by the current method. As shown in Fig. 3, the echo area is significantly reduced after the removal of isolated non-meteorological echoes based on the current method (Fig. 3b). The areas of all the convective cells (clouds A–F) are reduced by more than 30% (Table 1). Particularly, the area of cloud C decreases from 32 to 9 km² (a reduction of 72%), such that it is difficult to find in Fig. 3b. Moreover, the method can also remarkably decrease the coverage of radar echoes in nascent squall lines. This is because their shape is often long and narrow, meaning that the edge of echoes can be removed more effectively. For example, the area of the nascent squall line that occurred in northeastern Nanchang at 1003 UTC 10 June 2017 (Fig. 4a) decreases by about 30%, from 2189 to 1543 km². In particular, west of the squall line, the echo area decreases by about 50% (Fig. 4b). It is clear that the method has a shortcoming in that, when it eliminates isolated echoes, it partially removes the margins of meteorological echoes too. This situation is quite obvious in small-scale convective cells and squall lines with a long and narrow shape, because the edges of meteorological echoes account for a large proportion of the total echo area.

3.2 Improvements on the original method

What has caused the problem in the original method? In fact, when a window comprising 5 × 5 grid points is located at the edge of a storm, only half of all 25 grid points have valid radar reflectivity (Fig. 5a). The variable ${P_{\rm X}}$ is about 0.5, less than the threshold (0.75). Therefore, the echo at the window’s center point is regarded as an isolated echo and will be replaced by a missing value, destroying the edge of meteorological echoes. Although decreasing the threshold to below 0.5 could probably conserve the edge, it evidently decreases the ability to remove isolated non-meteorological echoes. Thus, in the new algorithm, a constraint parameter ${P_{\rm o}}$ that emphasizes whether an echo is isolated, is added to jointly determine (with ${P_{\rm X}}$ ) whether or not the echoes in the window are isolated. The variable ${P_{\rm o}}$ is expressed as

${P_{\rm o}} = \frac{{{N_{\rm {pv}}}}}{{{N_{\rm {pt}}}}}, $

(2)

where ${N_{\rm {pt}}}$ = 24 is the total number of connected periphe-ral grid points (i.e., the points along the dotted outmost square) around the window (Fig. 5b), and ${N_{\rm {pv}}}$ is the number of these connected peripheral grid points with valid reflectivity (i.e., those denoted by hollow circles in the storm area in Fig. 5b; N_pv = 11 in this case). Based on Eq. (2), a medium or large ${P_{\rm o}}$ indicates that the echoes in the window are connected with outside echoes, while a small ${P_{\rm o}}$ (approaching 0) reflects that the echoes in the window are disconnected with external ones. Therefore, a small ${P_{\rm o}}$ together with a small ${P_{\rm X}}$ indicates that all points, not only the center point, in the window should be marked as isolated echoes. Meanwhile, a small ${P_{\rm X}}$ accompanied with a large ${P_{\rm o}}$ (often occurring at the edge of echoes) or just a large ${P_{\rm X}}$ (often occurring at convective cells) corresponds to real meteorological echoes.

Theoretically, when echoes in the window are disconnected with external echoes (i.e., isolated echoes), ${P_{\rm o}}$ should equal to 0. In fact, however, in the area of dense isolated non-meteorological echoes (near the radar station), a few of the adjacent peripheral grid points around the window (the one in the dotted square in Fig. 5b) may have valid reflectivity, leading to ${P_{\rm o}}$ > 0. But what threshold of ${P_{\rm o}}$ ( ${N_{\rm {pv}}}$ ) is effective in identifying isolated non-meteorological echoes whilst preserving the edges of meteorological echoes? A large threshold can remove the edges of meteorological echoes, whereas a small thre-shold cannot eliminate isolated echoes effectively. It is worth noting that the improved algorithm can be used repeatedly to eliminate isolated echoes without removing the margins of meteorological echoes, because the constraint connected with external echoes limits the removal of meteorological echo margins. Therefore, a proper threshold could possibly be found by applying the improved algorithm several times to the raw data and observing the consequences. Figure 6 shows the echoes as a result of repeatedly applying (specifically, 5 times) the improved algorithm with ${P_{\rm o}}$ ≤ 0.125 (i.e., ${N_{\rm {pv}}}$ ≤ 3), ${P_{\rm o}}$ ≤ 0.167 (i.e., ${N_{\rm {pv}}}$ ≤ 4), ${P_{\rm o}}$ ≤ 0.208 (i.e., ${N_{\rm {pv}}}$ ≤ 5), and ${P_{\rm o}}$ ≤ 0.25 (i.e., ${N_{\rm {pv}}}$ ≤ 6), respectively. As shown in Fig. 6, some isolated echoes remain near the radar at ${P_{\rm o}}$ ≤ 0.125 (Fig. 6a), and some edges of meteorological echoes in cloud C have been removed at ${P_{\rm o}}$ ≤ 0.208 (Fig. 6c). More dramatically, when ${P_{\rm o}}$ ≤ 0. 25 (Fig. 6d), cloud C completely disappears, and some edges of clouds A and F have also been removed. This indicates that ${P_{\rm o}}$ ≤ 0.167 (i.e., ${N_{\rm {pv}}}$ ≤ 4) is a reasonable choice for removing isolated non-meteorological echoes as much as possible whilst preserving the edges of meteorological echoes.

Figures 2a, 3a, 4a, and 6a show that the intensity of most isolated non-meteorological echoes is less than 20 dBZ, and the echoes with reflectivity larger than 20 dBZ are considered as meteorological echoes. Therefore, the areas of echoes over 20 dBZ can imply the range of meteorological echoes. The rate of reduction of echoes over 20 dBZ is defined as

${P_{\rm r}} = 1 - \frac{{{A_{\rm a}}}}{{{A_{\rm b}}}}, $

(3)

where ${A_{\rm a}}$ ( ${A_{\rm b}}$ ) is the area of echoes over 20 dBZ after (before) the radar data are processed with the improved algorithm. The rate of reduction is used to further verify the threshold of ${P_{\rm o}}$ in the improved algorithm. Five cases are processed by using the improved algorithm with different thresholds of ${P_{\rm o}}$ (each case has 30 radar scans) as follows: three convective storms that occurred respectively during 0300–0600 UTC 25 August 2017 (Case 1), 0200–0500 UTC 15 May 2017 (Case 2), and 0400–0700 UTC 8 September 2017 (Case 3); a typhoon (Nesat) storm that occurred during 1100–1300 UTC 30 July 2017 (Case 4); and a synoptic-scale storm that occurred during 0200–0500 UTC 15 May 2017 (Case 5). The corresponding statistical analysis of P_r is shown in Table 2. The rate of reduction ${P_{\rm r}}$ increases with ${P_{\rm o}}$ and is lowest in the synoptic-scale storm (Case 5) due to the large horizontal continuity of reflectivity. When ${P_{\rm o}}$ increases to 0.208 (i.e., ${N_{\rm {pv}}}$ = 5), P_r in Cases 1–4 begins to rapidly increase, indicating that the edges of meteorological echoes have been noticeably removed. Interestingly, although P_r of echoes more than 20 dBZ is small in the synoptic-scale storm (Case 5) compared to the other 4 cases, it also increases to 0.1% at ${P_{\rm o}}$ ≤ 0.208 from approximately 0.0% at ${P_{\rm o}}$ < 0.208. These results indicate that the threshold of ${P_{\rm o}}$ should be less than 0.208 (i.e., ${N_{\rm {pv}}}$ < 5). On the other hand, the larger the threshold of ${P_{\rm o}}$ , the greater the removal of isolated non-meteorological echoes. Therefore, selecting 0.167 as the threshold of ${P_{\rm o}}$ (i.e., ${N_{\rm {pv}}}$ = 4) is most suitable for removing isolated non-meteorological echoes as much as possible whilst simultaneously preserving the meteorological echoes. The statistical results further suggest that ${P_{\rm o}}$ ≤ 0.167 is the best choice. The performance of the improved algorithm with ${P_{\rm o}}$ ≤ 0.167 in the reflectivity fields at 0.5° elevation for Nanchang radar at 2203 UTC 18 June 2016 (Fig. 7a) and 1003 UTC 10 June 2017 (Fig. 7b) shows that the results are largely free of isolated non-meteorological echoes whilst the edges of the meteorological echoes are almost entirely preserved (the original reflectivity fields are shown in Figs. 2a and 4a, respectively).

4 Ground clutters

Although the above improved algorithm is very useful for removing small, isolated non-meteorological echoes, it is impossible for it to eliminate ground clutters because ground clutters often occupy a relatively large area. However, ground clutters usually show worse spatial continuity than meteorological echoes, in both horizon-tal and vertical directions (especially the latter). Therefore, the difference in the spatial discontinuity between ground clutters and meteorological echoes can be used to identify and remove the ground clutters.

4.1 Original method

Meteorological echoes usually extend from the lower troposphere to the middle or upper troposphere, having a relatively deep vertical extent. Thus, the variation in reflectivity in the vertical direction is relative small (i.e., the vertical gradient of echoes is relatively small). In contrast, ground clutters often appear at only one or two elevation angles, with an abrupt change in intensity in the vertical direction. Based on this, the vertical discontinuity of reflectivity is widely used to filter out ground clutters (Steiner and Smith, 2002; Kessinger et al., 2003; Zhang et al., 2004; Wu et al., 2013). In the WSR-88D system in the USA (Kessinger et al., 2003), the vertical gradient of reflectivity with range weighting (RGDZ) is selected as the main variable for the identification and removal of ground clutters from its single-polarization, level-II radar data. The expression of RGDZ is

${\rm {RGDZ}} = W\left({Z - {Z_{\rm {up}}}} \right), $

(4)

where Z is the reflectivity value at the selected elevation angle, ${Z_{\rm {up}}}$ is the reflectivity at the upper elevation angle, and W is a weighting function with respect to the range. When the range is less than 40 km, W = 1; W decreases linearly from 1 to 0.5 with an increase in the range from 40 to 200 km. Then, W continues to decreases linearly from 0.5 at 200 km to 0 at 300 km (Kessinger et al., 2003). A large RGDZ implies existence of ground clutters, while a small RGDZ corresponds to meteorological echoes. The inclusion of W in the RGDZ expression is to allow for the presence of a stratiform precipitation system, which at long ranges from the radar will show a large vertical gradient of reflectivity owing to the shallow extension of this type of echo. The method works well for the ordinary ground clutter, because it often only appears at one elevation angle. However, sometimes a ground clutter will appear at two adjacent elevations, e.g., in a mountainous region close to the radar site. For instance, in this study, in the mountain region with peak altitude exceeding 1100 m, oriented from northeast to southwest and located about 30 km northwest from the Shangrao radar site, ground clutters appear at two adjacent elevations (2.4° and 3.4°) (Fig. 8). The distribution of the ground clutter at the 2.4° (3.4°) elevation angle is analogous to the shape of the terrain over 700 m (1100 m). Therefore, the value of RGDZ at the elevation of 2.4° is relatively small in the area with intense echoes at the elevation of 3.4°. In such a situation, the RGDZ value cannot be utilized to properly identify and remove the ground clutter.

To address this problem, Zhang et al. (2004) designed a new parameter, VDZ, which can be expressed as

${\rm{VDZ}} = \frac{{Z - {Z_{\rm {ref}}}}}{{{H_{\rm {ref}}} - H}}, $

(5)

where H is the height of the radar beam at the selected elevation angle; Z_ref and H_ref are the reflectivity and height at the upper reference elevation angle, respectively. The first upper elevation with radar beam height between 3 and 4.5 km will be treated as the reference elevation (i.e., 3 km ≤ H_ref ≤ 4.5 km). Thus, VDZ can remove ground clutters better than RGDZ under the condition of ground clutters appearing at two adjacent elevation angles. This promising performance of VDZ is the result of Z_ref not being a ground clutter (because H_ref is more than 3 km and ground clutters are often below 3 km). Similar to the situation with RGDZ, a large VDZ indicates existence of ground clutters, while a small VDZ corresponds to meteorological echoes. The VDZ parameter is applied in the WSR-88D radar operational system in the USA (Zhang et al., 2004) and the SWAN system in China (Wu et al., 2013).

Although VDZ has the advantage over RGDZ in terms of removing ground clutters, it is confined by the H_ref being less than 4.5 km. There are 9 elevation angles for the VCP21 mode (common mode) in the CINRAD SA/SC radar, and these elevation are 0.5°, 1.5°, 2.4°, 3.4°, 4.3°, 6.0°, 9.9°, 14.6°, and 19.5°. The corresponding range ( $R$ ) of different elevations at the height of 4.5 km can be calculated (Zhang et al., 2005) by

${({R^2} + R_{_W}^2 + 2R \cdot {R_{_W}} \cdot \sin \theta)^{1/2}}\,{\rm{ - }}\,{R_{_W}} \,= \, 4.5, $

(6)

where ${R_{_W}}$ = 8500 km (i.e., 4/3 earth’s radius) represents the effective earth radius, and $\theta $ is the elevation angle of the radar beam. In terms of Eq. (6), R at 1.5° and 2.4° elevation is about 130 and 95 km, respectively. This means that the VDZ can only be used at ranges less than 130 km (95 km) at 0.5° (1.5°) elevation. The maximum range for a valid VDZ is even shorter at higher elevations. This constraint severely limits the applicability of the VDZ. Besides, the presence of the denominator ${H_{\rm {ref}}} - H$ may also cause a smaller VDZ value in the region of ground clutter, leading to error in the removal of ground clutter. For example, supposing an instance of ground clutter with an intensity of 50 dBZ appears at about 45 km from the radar at 0.5° elevation (height of radar beam is approximately 0.5 km) and there is no effective reflectivity at its upper elevation angles. Therefore, its reference elevation and height are 4.3° and about 3.5 km, calculated by using Eq. (6), respectively. Then, the denominator ${H_{\rm {ref}}} - H$ is approximately 3 km and the VDZ is approximately 16.7 (50/3) dBZ, which is less than the threshold (20 dBZ) defined in Zhang et al. (2004), ultimately resulting in a failure to identify and remove the ground clutter. A few scattered instances of high-reflectivity clutter near the radar are left in the filtered reflectivity field (Fig. 8 in Zhang et al., 2004), which may also be a result of the presence of the denominator ${H_{\rm {ref}}} - H$ .

4.2 Improvements on the original method

The parameters RGDZ and VDZ have their own respective advantages and disadvantages. Based on their advantages, a new parameter, NDZ, can be constructed as follows:

${\rm{NDZ}} = \left\{ \begin{gathered} W\left({Z - {Z_{\rm {ref}}}} \right)\quad R \leqslant {R_{\max }} \\ W\left({Z - {Z_{\rm {up}}}} \right)\quad R > {R_{\max }} \\ \end{gathered} \right..$

(7)

Here, W is the same as the weighting function in Eq. (4), and ${R_{\max }}$ is the maximum range with a valid VDZ value (130 km at 0.5° elevation). The NDZ not only preserves the advantage of VDZ, but also makes up for its shortcomings by extending the useful ranges and removing the denominator. The distribution of NDZ at 2.4° elevation is shown in Fig. 9a. We find that the area (ground clutter) with large values (> 20 dBZ) of NDZ just overlaps the terrain with height exceeding 700 m and the area with reflectivity exceeding 40 dBZ inFig. 8a. The ground clutter in Fig. 8a is successfully identified and removed based on the NDZ parameter (Fig. 9b).

5 Statistical analysis

The removal of isolated echoes and ground clutters is performed by following two steps. First, under the condition of NDZ ≥ 20 dBZ, the ground clutter is removed from the radar base (level-II) data. Second, combining the two conditions ${P_{\rm{X}}}$ ≤ 0.75 [Eq. (1)] and ${P_{\rm{o}}}$ ≤ 0.167 [Eq. (2)], the isolated non-meteorological echoes are eliminated from the radar data. The reason to place the removal of ground clutters in the first step is that this process may generate new isolated echoes.

To further evaluate the performance of the improved algorithms in removing ground clutters and isolated non-meteorological echoes, the frequency images of original reflectivity over 20 dBZ at 0.5° evaluation, echo top (ET) height more than 3 km, precipitation more than 0.1 mm h^–1, and processed (using the improved algorithm) reflectivity over 20 dBZ at 0.5° elevation, are all generated from 0000 UTC 5 to 1600 UTC 14 March 2015 (232 scans with a 1-h temporal resolution; Fig. 10). This pe-riod encompasses a series of precipitation and clear-sky echoes. The frequency image has been used previously by Steenburgh et al. (2000) to describe the echoes induced or enhanced by the Great Salt Lake in the USA. In the frequency image of the raw reflectivity over 20 dBZ (Fig. 10a), most regions are filled by points with low frequency (less than 0.15). However, several scattered points with high frequencies (larger than 0.2, and even reaching 0.5) are apparent in the surroundings of Nanchang, as well as some flaky areas with high frequencies (larger than 0.2, and even reaching 0.8) near the mountains located to the west, north, and south of Nanchang. These regions with high frequency are evidently caused by isolated echoes (possibly from the tall buildings of Nanchang city) and ground clutters, because they are more stationary compared with meteorological echoes. The ET height can reflect the development of a storm and the intensity of the associated precipitation system (Bedka et al., 2015). Normally, the ET height of meteorological echoes is more than 3 km. Therefore, the frequency image of ET height more than 3 km (Fig. 10b) can to a large extent depict the distribution of meteorological echoes. As shown in Fig. 10b, the frequencies in the whole region are less than 0.2. Particularly, in the regions where the frequencies in Fig. 10a are more than 0.2, the frequencies of ET height are less than 0.15, or even 0.1. This further verifies that the regions with high frequency in Fig. 10a are created by non-meteorological echoes. The frequency distribution of precipitation with a 1-h temporal resolution (Fig. 10c) also illustrates this viewpoint, because there are no high frequencies in the regions shown in Fig. 10a. After removing the ground clutters and isolated non-meteorological echoes using the improved algorithms, in the frequency image of reflectivity over 20 dBZ at 0.5° elevation, there is no point with a frequency more than 0.2 (Fig. 10b) and the distribution of frequencies less than 0.15 coincides with that of unprocessed frequencies (Fig. 10a). It is clear that the improved algorithms perform well in removing the isolated non-meteorological echoes and ground clutters, whilst preserving the structure of storms at the same time. The areas with the highest frequency (> 0.15) are located over the mountain region in southern Nanchang inFig. 10d, but the areas with the highest frequency in Figs. 10b, c are not. This indicates that, although the improved algorithm for identifying ground clutters has performed well, it cannot completely remove all ground clutters. Note that in Figs. 10a, b, d, the areas with low frequency (< 0.05, and even 0.1) are mainly induced by the blocking of the radar beam at 0.5° elevation in the southeast of Nanchang.

The above analyses show that the high frequencies (> 0.2) inFig. 10a are mainly induced by isolated non-meteorological echoes and ground clutters (near mountain regions). Clearly, the ground clutters in the mountain regions characterized by high frequency are the important part of the observed echoes. Meanwhile, the isolated non-meteorological echoes in other regions with high frequency are also important. In order to quantitatively evaluate the performance of the improved algorithms, the ratio of removal of isolated non-meteorological echoes and ground clutters is defined as

${P_{\rm {rm}}} = 1 - \frac{{{A_{\rm {ha}}}}}{{{A_{\rm {hb}}}}}, $

(8)

where ${A_{\rm {ha}}}$ ( ${A_{\rm {hb}}}$ ) is the area of echoes over 20 dBZ in the high frequency (> 0.2) regions inFig. 10a after (before) applying the improved algorithms. If Eq. (8) is applied in mountain regions (other regions), ${P_{\rm {rm}}}$ indicates the ratio of removal of ground clutters (isolated non-meteorological echoes). The ratio of removal can quantitatively check how many instances of ground clutter (isolated non-meteorological echoes) have been detected and removed. The ratios of removal of ground clutters and isolated echoes from 0000 UTC 5 to 1600 UTC 14 March 2015 (232 scans) are shown in Fig. 11. We can see that the ratios vary with time. Specifically, under clear-sky conditions (ET height and rainfall close to 0), the ratios of removal of ground clutters and isolated non-meteorological echoes are large, at more than 0.95 (especially for isolated echoes, which even gets close to 1), indicating that the improved algorithms perform well and can iden-tify and remove over 95% of ground clutters and isola-ted meteorological echoes. In contrast, in rainy cases, the ratios for ground clutters and isolated non-meteorologi-cal echoes are small (< 0.2 at 2300 UTC 10 March 2015). This, however, does not indicate poor performance of the improved algorithms in removing isolated non-meteorological echoes and ground clutters under rainy conditions. In fact, the improved methods still perform well (Fig. 12). The reason for the small ratio of removal with good performance under rainy conditions is that there are few instances of non-meteorological echoes and ground clutter in the original reflectivity field (Fig. 12a). This is responsible for the fact that, under rainy conditions, the earth’s effective radius (which influences the radar beam height) is larger than that under clear-sky conditions, due to the small vertical gradient of specific humidity, thus inducing the increase in radar beam height and the disappearance of most instances of isolated non-meteorologi-cal echoes and ground clutter (Yu et al., 2006).

6 Conclusions

The present study proposes improvements to two algorithms commonly used for removing isolated non-meteorological echoes and ground clutters from single-polarization, level-II radar data. In view of the shortcomings of the original methods, which can remove the edges of meteorological echoes but cannot identify ground clutters appearing at two adjacent elevation angles, the current algorithms offer improvements in these respects. To remove isolated non-meteorological echoes as much as possible whilst preserving the edges of meteorological echoes, the improved algorithm introduces a constraint parameter, P_o, to determine whether a window of 5 × 5 grid points is in isolation. To identify the ground clutters appearing at two adjacent elevation angles without range limitation, the improved algorithm establishes a new vertical difference of reflectivity (NDZ) based on the parameters RGDZ and VDZ in the WSR-88D system. Correspondingly, a set of criteria are proposed for the improved algorithms to remove isolated non-meteorologi-cal echoes and ground clutters.

A statistical analysis of 5 cases (each with 30 scans, making a total of 150 scans) with different echo types (3 small-scale convection cases, 1 typhoon case, and 1 large-scale synoptic system case) demonstrates that a constraint parameter of P_o ≤ 0.167 is suitable for the improved algorithm to remove isolated non-meteorological echoes as much as possible whilst at the same time preserving the edges of meteorological echoes. The improved algorithms with P_o ≤ 0.167 and NDZ ≥ 20 dBZ are tested in 4 cases (3 for isolated non-meteorological echoes and 1 for ground clutter) and the statistics of 232 scans of radar data (temporal resolution of 1 h) measured at Nanchang from 0000 UTC 5 to 1600 UTC 14 March 2015. The results show that the improved algorithms not only remove most (> 95% under clear-sky conditions) of the isolated non-meteorological echoes and ground clutters (including that occurring at two adjacent elevation angles), but also preserve the structure of storms well.

Although the improved algorithms have shown promise in removing isolated non-meteorological echoes and ground clutters, certain residual non-meteorological echoes (especially for ground clutter) still exist, such as those in Figs. 10d, 11 (under clear-sky conditions, the ratios of removal of ground clutters are sometimes less than 100%). This indicates that there is still some room for the algorithms to be further improved. Particularly, other independent data, such as radar radial velocity, radar spectrum width, etc., should be introduced to jointly improve the algorithms even further.

Acknowledgments. We thank the two anonymous reviewers and the editor for their constructive comments, which have certainly helped improve the manuscript from its original version. Dr. Zhiqun Hu provided useful comments and suggestions regarding the received base-band complex signal at the signal-processing level.