A Velocity Dealiasing Scheme for C-band Weather Radar Systems

In addition to providing data for weather watches and warnings and quantifying rainfall, radar observations are increasingly being used in the initialization of numerical weather prediction (NWP) models. All these applications require robust quality control and putting the data into a format that allows product algorithms to be reliably used. Two major issues are the removal of noise and clutter, and correcting Doppler radar velocity data that have been aliased. Ray and Ziegler (1977) introduced a one dimensional dealiasing scheme along the radial direction. Since then, there have been many improvements for operational use. He et al. (2012a, 2012b) provide an overview of the literature and the progress in developing dealiasing algorithms. Most of the focus with dealiasing has been for S-band radars because of their widespread operational use in the USA. Owing to the C-band radar’s shorter wavelength (~5 cm), those algorithms must be strengthened to address a problem that is approximately twice as difficult. Techniques related to the challenges of unfolding C-band Doppler radar velocities have included (James and Houze, 2001) and some powerful dual pulse repetition frequency (PRF) approaches (e.g., Doviak1976; Holleman and Beaekhuis, 2001).

The extent of unambiguous velocities (Nyquist cointerval) relates to the transmitted wavelength (λ) and PRF sent out by a radar. This is given by(-Vmax,Vmax), where

V_max=(PRF)λ/4, (1)

which is called the “Nyquist velocity” and is the maximum observed velocity. If the frequency shifts of the observations exceed ±PRF/2, the observed velocities will be aliased and appear within ±Vmax. The true velocity (V_T) may be different to the observed velocity(V_o), but the relationship between these two velocities is:

V_T=V_o+2nV_max,n=0,1,2, … (2)

China has a radar network named CINRAD (China Next Generation Weather Radar). This network contains a total of 158 Doppler radars comprising 85 S-band and 73 C-band radars (Fig. 1). Most of the C-band radar stations are located in the interior and in central and western China, while S-band radar stations are located along the coast and near the Yangtze River. The CINRAD system is responsible for observing wind, precipitation and hail in near real-time.

Figure 1.  The location of all the CINRAD stations in China. Circles represent S-band radars, while triangles are the C-band radar stations.

With the shorter wavelength, the radial velocity observation of C-band radars has more velocity folding. More reliable and robust dealiasing methods should be developed to unfold C-band velocity data with smaller Nyquist intervals. Eilts and Smith (1990) produced a 2D Velocity Dealiasing Algorithm (VDA), which is fundamentally based on minimizing velocity gradients along a radial for NEXRAD (Next-Generation Radar) velocity data. This dealiasing method is still in use to de-alias NEXRAD radial velocity data in order to produce operationally useful products in the United States. (He et al., 2012a) modified the NEXRAD algorithm to develop the S-CIDA algorithm, which improved the dealiasing results with S-band CINRAD data. Here, with a proposed new algorithm-C-band CINRAD Dealiasing Algorithm (C-CIDA), we extend the modifications further to improve the dealiasing performance for C-band data.

The following new modifications are directly, or extensions of, those described by He et al. (2012a, 2012b). Where there are changes related to the characteristics of the C-band data, the modifications are noted. A schematic diagram of the algorithm, along with which modules are new or modified, is shown in Fig. 2.

Figure 2.  Schematic diagram of module function and sequence of implementation. Provisional conditions and other details have been omitted. The modules shaded gray are the newly added modules for C-CIDA, as compared with S-CIDA.

Unwanted data such as noisy data and clutter may be caused by second trip echo, ground clutter and low returned power or antenna imperfections. Here, we refer to all such data as noise. The noisy velocity data are removed in two steps. First, the radial velocities are removed when the corresponding reflectivity is less than 16 dBZ and the spectrum width is larger than 2 m s^-1. After this step, sporadic noise may still be found, typified by large spectrum widths and large reflectivities, often at the edge of a distant echo (Fig. 3b). Inadequate returned echo power is the most probable cause. According to the radar equation, the echo power is inversely proportional to the square of distance between the radar and the reflectivity at the scatter’s location. Thus, the data with the corresponding spectrum width are greater than 1.5 m s^-1 and the reflectivities less than aR are remove (R is the distance between the radar station and each velocity). The value of a=0.25 km^-1 (with R expressed in km) was obtained by examining a matrix of values for what provided the most filtering of unwanted values with the minimum sacrifice of what appeared to be good data. For example, velocities removed from the spectrum width were greater than 1.5 m s^-1 and the reflectivity was less than 25 dBZ at the 100-km range. After these two steps, the noisy data far away from the radar station are almost removed, as seen in Fig. 3c. It is acknowledged that some “good” data will be removed while operating noise removal. However, it is a better strategy to lose some (as little as possible) good data to avoid the consequences of retaining noisy data (He et al., 2012b).

Figure 3.  Radar radial velocity at an elevation angle of 1.5°from Baicheng Station (C-band) at 1158 UTC 1 Jul 2007: (a) raw velocity; (b) noise removal after Step 1 in Module 1; (c) noise removal after Step 2 in Module 1. The x-axis is the distance away from the radar in the west-east direction, while the y-axis is the distance away from the radar in the south-north direction.

A reference radial is one that exhibits little or no aliasing. The most likely position for this to occur is where the wind direction is almost orthogonal to the direction the antenna is pointing. Also, the average value of the absolute value of that radial’s Doppler velocity will be at a minimum. The concept of one reference radial was first proposed by (Zhang and Wang, 2006). The checking extended 180° both clockwise and counterclockwise from the reference radial. There are occasions when this approach leads to a progression of errors, most likely from 90° to 180°. Two independently determined reference radials restrict the application to 90° sectors. When two reference radials are not reliably available there exists the option to obtain a mean wind externally (such as rawinsonde), or from a velocity-azimuth display (VAD) scan.

Generally, there is a companion reference radial approximately 180° from the first reference radial. (He et al., 2012b) used one reference radial for S-band radar data. However, for the C-band case, two reference radials are selected instead of one. This is because, for the same wind field, the number of aliased velocities is nearly doubled, and the added complexities in the observed wind field increase the probability of unfolding mistakes. This was not a problem with S-band radars for all the cases examined, but more mistakes were apparent with the C-band data because of the Nyquist interval being one half that of S-band radars. There are occasions when only one radial is needed, but the use of two is never detrimental.

Figure 4 illustrates the process for reference radial selection using a dataset from a typhoon observed by the Wenzhou radar station at 1045 UTC 29 July 2008, which was also used by (He et al., 2012a) for the S-band algorithm. The dataset was converted to what a C-band radar would have obtained. In Fig. 4, the sum of the absolute values of the radial velocities for each radial are plotted separately for S-band and C-band radars. Before plotting, the sums were normalized to the maximum value found for any of the radials. For the case of the S-band radar, two minima were found representing the azimuths where the wind direction was closest to being orthogonal to the radar beam; only one was used, as this was always sufficient. In the C-band radar case, four minima were found, with the additional two coming from azimuths where there was extensive folding and therefore small aliased velocities.

Figure 4.  The normalized average of the absolute values of measured velocities at all the valid gates along each radial in S-band data (black solid curve) and C-band data (black dashed curve). The gray solid curve is the total number of valid gates along each radial. The gray dotted line is the average of all the valid gates, and the gray horizontal solid line indicates the average of all the valid gates multiplied by two-thirds. The azimuth radial number starts from the radial to the north of the radar.

To be a reference radial, four criteria must be met. First, they are minima in the curve of the normalized average of the absolute values of the measured velocities at all the valid gates along each radial. Second, these two initial reference radials should be separated by approximately 180° (He et al., 2012b). The reference radial was chosen with the larger average velocity and more valid gates in the radials indicated by the black circle on the left on the black solid curve (Fig. 4). Because of the smaller Nyquist interval of C-band radar, more than two radials may meet the first criterion in C-band radial velocity data when observing the same weather situation, and only a couple of radials are separated by nearly 180° (unless there are multiple folds). The third criterion is that the reference radial must have the biggest difference between minima in the curve and the adjacent maxima. The radials indicated in Fig. 4 by two black circles on the black dashed curve can be chosen as reference radials. The fourth criterion is that the number of data points for the radial with the minimum sum must contain at least two-thirds of the average number (the gray dotted line) of valid gates in all the radials in all azimuths (the gray solid horizontal line in Fig. 4).

The location of the reference radials with regard to the radial velocity observation is illustrated in Fig. 5g. The algorithm starts from the two almost co-linear radials to de-alias both in the clockwise and counterclockwise direction. Radial-by-radial dealiasing in each direction goes through 90°. This strategy also restricts the dealiasing errors inside a 90° arc. If only one reference radial exists because of lots of missing data, the algorithm still starts from the radials next to this reference radial and goes through 180° in both the clockwise and counterclockwise directions.

As in (He et al., 2012a), after reference radials are found, the unfolding is done much in the same way as described by Eilts and Smith (1990) and modified by (Zhang and Wang, 2006), except that instead of a 180° sector, a 90° sector is employed when it is possible to identify two reference radials. The initial unfolding (Eilts and Smith, 1990) relies largely on minimizing the difference between a previous reliably correct velocity in a gate and the next gate in the radial.

The possibility of errant velocities still exists. These may be due to side lobes, non-hydrometeors, statistical uncertainty, electronic stability, signal processing etc. (Rossa, 2005). Any such error can lead to failures in the algorithm. In this module, the errors are identified by comparing each velocity with the average velocity of all the valid gates in the previous 10 radials and the 20 closest gates in each radial (He et al., 2012a).

For a quasi-linear wind field, the valid velocities along each radial can be assumed to meet a linear relationship. First, assume all valid radial velocities along each radial satisfy the relationship

V_T=a_mR+b_m, (3)

where V_T is approximated by V_O from Eq. (2) and R is the distance between the radar station and each velocity. The coefficients a_m and b_m for mth radial can be solved by a least squares equation. So, each reference velocity for each gate can be calculated by Eq. (3). Then, each velocity point is de-aliased to be within a Nyquist co-interval centered on each reference velocity value.

The observed radial velocity is the real wind velocity projected in the radial direction. Thus, in each semicircular field, between the initial radials, all the velocities with the same distance away from the radar station in the azimuth direction often almost meet a quadratic relationship (as a proxy of the cosine function between -πand π). All the velocities in each semicircle can be de-aliased by a quadratic least squares fitting method in a manner similar to Module 5 in the azimuth direction. This is similar to (Mapes and Lin, 2005), who basically used a histogram similar to (Ray and Ziegler, 1977), except that they used a sine wave for the azimuth as the basis function instead of the mean for fitting the radial one-by-one.

This module is only applicable for hurricanes and typhoons. It has long been known that wind speeds increase with proximity to the eye of the hurricane or typhoon. With the addition of altitude, the wind velocity increases to a maximum value at about 750 hPa, and thereafter decreases with increasing height. Furthermore, the maximum speed appears at around 23 km east of the hurricane or typhoon center (Hawkins and Rubsam, 1968). Thus, the observed radial velocities in hurricane or typhoon cases generally change almost linearly in the radial direction at low elevations (no larger than 6.0°) because the pulses sent out from radars do not spread deep into the atmosphere at such angles. Meanwhile, the velocities at higher elevation angles are more closely approximated by a quadratic relationship in each radial, as the radar beam passes through the areas of maximum velocity at higher elevations. Elevations greater than 6.0° can be corrected again by solving the quadratic least squares fitting method (as in Module 6) in each radial in the typhoon case. Implanting the quadratic least squares fitting method three times in the radial direction leads to the best results at high tilt angles.

The SOLO II (Oye et al., 1995) software package developed by the National Center for Atmospheric Research (NCAR) is the most widely used interactive data-editing tool. It works by illustrating each sweep of radar observation data and enabling the user to manually de-alias radial velocities, remove ground clutter, manipulate variables, and so on. The subjectively edited and manually generated velocity field de-aliased by SOLO II can be considered as the “true” velocity field. The “true” field can then be used as a reference for testing the dealiasing results from an automatic scheme for CINRAD C-band data.

The velocity dealiasing algorithm was tested on radar data from four different weather systems: one widespread rain case and three convective cases. These storms were observed by the Datong and Xi’an radar stations—both CINRAD C-band Doppler radars. Radial velocities extended out to 200 km. Depending on the PRF sent out from the radar, the Nyquist velocity ranged from 14 to 16 m s^-1. In the following sections, some examples dealiasing results are presented. Comparisons of the results from the proposed C-CIDA algorithm and the Next Generation Weather Radar (NEXRAD) algorithm are also reported.

The NEXRAD dealiasing algorithm for S-band radar data performed poorly with C-band radar data with the smaller Nyquist velocity beause of the multiple aliasing in the data. However, using the proposed C-CIDA algorithm, with two initial reference radials that divided the velocity field into four parts for dealiasing purposes, satisfactory results were obtained.

Figure 5 displays the raw observed velocity filed at the elevation angle of 0.5° at 1557 UTC 8 August 2007 for a wide spread rain case as observed at Xi’an radar station. There were two velocity areas to the northeast and northwest of the radar station in the 50-100 km range where the velocities were aliased. The “truth”, i.e., manually de-aliased and generated, is shown in Fig. 5b. The de-aliased results based on the NEXRAD algorithm are shown in Fig. 5c. Some aliased velocities that existed near the range-folding areas created a piece of incorrect dealiasing northeast of the radar. However, the C-CIDA algorithm successfully de-aliased all the aliased areas (Figs. 5d-g). The linear least squares error check in the radial direction and quadratic least squares error check in the azimuth direction (Modules 5 and 6) corrected the field that the NEXRAD algorithm did not have. The two reference radials (black lines) discussed in section 2.2 (Module 2) and illustrated in Fig. 5g were used. With these as the starting locations, the new algorithm examines the velocities at 90° in both the clockwise and counterclockwise directions.

Figure 5.  Radar radial velocity at an elevation angle of 0.5° from Xi’an Station at 1557 UTC 8 Aug 2007: (a) raw velocity; (b) reference velocity; (c) de-aliased by the NEXRAD algorithm; (d) dealiased by the C-CIDA algorithm from Module 1-3; (e) de-aliased by the C-CIDA algorithm from Module 1-4; (f) dealiased by the C-CIDA algorithm from Module 1-5; and (g) de-aliased by the C-CIDA algorithm from Module 1-6. The black lines in (g) indicate the initial reference radials searched by the C-CIDA algorithm. The Nyquist for this case is 13.99 m s^-1. The x-axis is the distance away from the radar in the west-east direction, while the y-axis is the distance away from the radar in the south-north direction.

Dealiasing algorithms often fail easily when there are real discontinuities and areas of missing data in the radial velocity field. Figure 6 illustrates the 1.5° velocity field at 1139 UTC 25 July 2006 for a strong convective storm as observed at Xi’an station. As a result of a large area of missing data, the algorithm could identify just one initial reference radial at each elevation angle of this volume scan. The original 208° radial line (Fig. 6d) is the reference radial at an elevation angle of 1.5°. The NEXRAD algorithm failed in the area northeast of the radar (Fig. 6c). The C-CIDA algorithm gave a better result in this area, but some problems still persisted at the edge of the maximum observation distance in the area east of the radar. Because of the remaining noisy data and small number of velocity samples with the same distance away from the radar, the quadratic least squares error check in the azimuth direction could not determine accurate coefficients for some ranges.

Figure 6.  Radar radial velocity on 1.5° elevation angle from Xi’an station at 1139 UTC 25 July 2006. (a) raw velocity, (b) reference velocity, (c) dealiased by NEXRAD algorithm, and (d) dealiased by C-CIDA algorithm. The black line in (d) indicates the initial reference radial searched by C-CIDA algorithm. The Nyquist velocity for this case was 13.99 m s^-1. The x-axis is the distance away from the radar in the west-east direction, while the y-axis is the distance away from the radar in the south-north direction.

It is always a challenge for any algorithm when de-aliasing the double-folding radial velocity field. There was no double-folding phenomenon in all the cases we tested. However, it is still necessary to examine the capability of dealiasing the double-folding field by the new C-band algorithm. An idealized radar velocity field observed from southerly wind with a speed of 50 m s^-1 is shown in Fig. 7a, and Fig. 7b is the synthetic C-band radar (with the Nyquist of 20 m s^-1) velocity field from Fig. 7a. Two large areas in the north and south of the radar are double-folded. Figure 7c provides the dealiasing result by the proposed C-band algorithm, which is almost the same as the “true” velocity field (Fig. 7a).

Figure 7.  Statistical results of POD (gray solid bar), FAR (black solid bar, indicated by right y-axis) and CSI (gray dashed bar) of radar data observed in different weather situations and de-aliased by different algorithms. Key: T (S-band) = S-band typhoon data; SL (S-band) = S-band squall line data; HR (S-band) = S-band widespread rain data; ST (C-band) = synthetic C-band typhoon data; SC (C-band) = C-band strong convective storm data; S-CIDA = S-band CINRAD improved dealiasing algorithm; C-CIDA = C-band CINRAD improved dealiasing algorithm; POD = probability of detection; FAR = false alarm rate; CSI = critical success index.

Using C-band radar data from China, the C-CIDA algorithm was applied to the radial velocity field from one widespread rain case and three strong convective cases. As a measure of success, we employed a series of metrics defined as follows (He et al., 2012a): POD (probability of detection) = N/M; FAR (false alarm rate) = P/M; and CSI (critical success index) = N/(N+P+Q), where M is the total number of aliased gates in each case, N is the total number of correctly de-aliased gates in each case, P is the total number of incorrectly de-aliased gates in each case, and Q is the total number of missed dealiased gates in each case. The effectiveness of the algorithm and the details of the datasets used are given in Table 1 for each storm type and dataset.

With these metrics, we assessed how the algorithm performed for the different types of storms and how the new algorithm performed in comparison with previous algorithms when applied to data as it would be “seen” by a C-band Doppler radar. In Table 1, we see that the proposed algorithm performed better for cases 1 and 3 than cases 2 and 4. This is because cases 1 and 3 had two initial reference radials at each elevation angle, while cases 2 and 4 had just one. When using only one reference radial in cases 1 and 3, the POD, FAR and CSI changed to 93.8% and 94.7%, 9.65% and 7.8%, and 85.54% and 87.86% for cases 1 and 3, respectively (Table 2).

The first number of each pair is for case 1 and the second is for case 3. This illustrates the advantage of using two reference radials when they are available. One possible alternative for the selection of a reference radial is to use a VAD scan to derive a mean wind field, analogous to a guess field. Algorithm challenges will always exist in all cases where there are large natural velocity gradients, discontinuities or range-folding, and isolated echoes. Overall, the C-CIDA algorithm performed well with the CINRAD C-band data, with the average results from Table 1 being 96.65% of the aliased velocity observations being successfully corrected, and only 3.98% of the velocities not being correctly dealiased.

Figure 8 shows a histogram of POD (gray solid bar), FAR (black solid bar) and CSI (gray dashed bar) of radar data observed from different weather situations de-aliased by different dealiasing algorithms. All data were collected in China using the C-band and S-band radar network. In all cases, the “correct” result was obtained by careful human manual editing. The first to third group of bars in Fig. 8 represent the (S-band, large Nyquist interval) S-CIDA dealiasing results from the typhoon, squall line and widespread rain cases given in He et al. (2012a). These data were collected by S-band radars with a Nyquist interval of 26 m s^-1 at low elevations and 32 m s^-1 at high elevations. The fourth group of bars is the dealiasing results of synthetic C-band typhoon cases, which were transformed from CINRAD S-band data (same as the data in the first group) to what a C-band radar would have observed. The last group of bars represents the results of four strong convective cases, as listed in Table 1, which were de-aliased by the C-CIDA algorithm. It was expected that the data collected with a larger Nyquist interval would be more successful in correcting aliasing than an algorithm that had to correct data collected with a reduced Nyquist interval, and the results confirmed this expectation. It can be seen that the de-aliased results for the widespread rain and typhoon cases were better than the results for the strong convective and squall line cases. Furthermore, the de-aliased results of CINRAD S-band data by S-CIDA (He et al., 2012a) were better than those for the CINRAD C-band data by the C-CIDA algorithm proposed in the present work.

Figure 9 presents a comparison between results from C- and S-band radars (with attendant difference in Nyquist intervals) utilizing different dealiasing algorithms. The S-band data here are the same as the data listed in Table 1 of He et al. (2012a), and the C-band data are the four strong convective cases listed in Table 1. The dealiasing results of S-band data (the second group of bars in Fig. 9) de-aliased by the S-CIDA algorithm were superior to the results de-aliased by the NEXRAD algorithm. However, the dealiasing results of the four C-band cases in the present study, de-aliased by the S-CIDA algorithm, were not as good as when C-CIDA was applied. The C-CIDA algorithm can help to increase the POD and CSI of C-band data and decrease the FAR, and was also more successful than the NEXRAD algorithm for these C-band cases. Figure 10 shows how each module successively improves the scoring matrix for all the elevation angles in case 1. In all three metrics (POD, FAR and CSI) there is clear improvement with the addition of each module.

Figure 8.  Statistical results of POD (gray solid bar), FAR (black solid bar, indicated by right y-axis) and CSI (gray dashed bar) of different band radar data de-aliased by different algorithms. Key: NEXRAD = NEXRAD algorithm; S-CIDA = S-band CINRAD improved dealiasing algorithm; C-CIDA = C-band CINRAD improved dealiasing algorithm; S = S-band data; C = C-band data; POD = probability of detection; FAR = false alarm rate; CSI = critical success index.

Figure 9.  Illustration of the impact of applying successive modules on the unfolding scores for all the elevations in Case 1. Notice that the POD steadily rises, as does the CSI, while the FAR declines.

Figure 10.  Illustration of the impact of applying successive modules on the unfolding scores for all the elevations in case 1. Notice that the Probability of Detection steadily rises as does the Critical Success Index, while the False Alarm Rate declines.

An improved dealiasing scheme for application with C-band radar data has been presented in the present paper. Algorithms for S-band radars, such as those proposed by (He et al., 2012a) and others, are prone to failure with data from C-band radars because of the smaller Nyquist interval common with C-band radars. The C-band data used in the present study had a Nyquist velocity of about 14-16 m s^-1, about one half that which is common for S-band Doppler radars. The proposed scheme includes seven modules to remove noisy data, a method to find the starting reference radials, and ways to identify and correct aliased velocities.

The proposed dealiasing scheme was applied to C-band data collected in China for four different weather cases. The performance improved in every case over using the existing NEXRAD and other algorithms developed for S-band application. The algorithm correctly de-aliased 96.65% of the aliased radial velocities when compared with manually dealiasingaliased results. We found that 3.98% of the velocities did not get dealiased or were incorrectly changed because velocities were near missing data, range-folded data or noise that did not get removed. This was an improvement of several percent over any algorithm developed for application with S-band radars.