## 1. Introduction

When using Doppler weather radars to remotely sense weather phenomena, the selection of a single pulse repetition time (PRT) is often inadequate to provide unambiguous measurements of both range and Doppler velocity. That is, if the PRT is large enough to ensure complete range coverage (i.e., the maximum unambiguous range is larger than the maximum range of storms); then, velocity measurements are likely to become ambiguous (i.e., the maximum unambiguous velocity may be smaller than the maximum mean radial Doppler velocity of hydrometeors). Whereas choosing a sufficiently small PRT could ensure unambiguous velocity measurements, this would naturally result in range folded and range overlaid echoes due to an inadequate maximum unambiguous range. The U.S. National Weather Service (NWS) has adopted the staggered-PRT (SPRT) technique for future operational implementation on all NEXRAD’s S-band Weather Surveillance Radar-1988 Doppler (WSR-88D) radars (Warde et al. 2014) with a PRT ratio of 2/3 (Torres 2006). This PRT ratio achieves the best compromise between the extension of maximum unambiguous velocity and the quality of Doppler velocity data. That is, whereas staggered PRTs with larger ratios lead to larger maximum unambiguous velocities, the variance of Doppler velocity estimates also increases as the PRT ratio approaches unity (Zrnić and Mahapatra 1985). Still, one of the main challenges of developing an operational implementation of the SPRT technique has been the design of effective ground clutter filters, which is the focus of this paper.

One of the goals of weather signal design and processing is to retrieve uncontaminated radar variable estimates for weather echoes, which are typically obscured by different sources, such as echoes from the ground (referred to as ground clutter). Ground clutter mitigation is of prime concern when scanning at low elevation angles, where the radar beam is likely to intercept stationary objects. With uniformly sampled sequences (using a constant PRT), the characteristics of ground clutter (i.e., near-zero Doppler velocity with narrow spectrum width) are such that conventional high-pass filters can effectively mitigate the biasing effects of ground clutter contamination. Conversely, the use of periodic nonuniform sampling sequences, such as SPRT, makes the ground clutter mitigation problem more challenging. For SPRT sequences, it can be shown that conventional high-pass filters induce attenuating effects on signals with velocities around the integer multiples of *λ*/[2(*T*_{1} + *T*_{2})], where *λ* is the radar wavelength, and *T*_{1} and *T*_{2} are the PRTs in the staggered sequence (Banjanin and Zrnić 1991). Note that these velocities (zerolike velocities) alias to zero for a Nyquist velocity that corresponds to a PRT of *T*_{1} + *T*_{2} (i.e., the period of the SPRT sequence). Thus, direct application of a conventional ground clutter filter (GCF) designed for uniformly sampled sequences to SPRT sequences would negatively affect weather echoes with zerolike velocities. For example, a conventional GCF applied to a SPRT sequence with a 2/3 PRT ratio would not only attenuate the undesired ground clutter signal at zero velocity but would also attenuate weather signals with zerolike velocities at ±2*υ*_{a}/5 and ±4*υ*_{a}/5, where *υ*_{a} is the extended maximum unambiguous velocity given by *υ*_{a} = 2*λ*/4*T*_{1} = 3λ/4*T*_{2}. For this reason, specialized GCFs must be developed for effective operation with SPRT sequences.

Several ground clutter mitigation schemes have been proposed for SPRT sequences with varied degrees of success. Using time-domain processing, Anderson (1981) achieved limited clutter mitigation using block mean-level cancellers whereby the direct current (dc) component is removed from several subsets of the entire sequence. Improved clutter suppression was realized by Banjanin and Zrnić (1991) using time-varying filters that separate the SPRT sequence into two uniformly sampled subsequences with a sampling period of *T*_{1} + *T*_{2} (i.e., by taking every other sample), but these filters incurred both amplitude and phase distortions at the zerolike velocities. Torres et al. (1998) also found difficulties at the zerolike velocities when using regression filters. Biases induced by filtering at the zerolike velocities were greatly reduced using a parametric time domain method (PTDM; Moisseev et al. 2008); however, the required computational complexity and long dwell times preclude the operational use of the PTDM on the NEXRAD network. A less complex algorithm was proposed by Nguyen and Chandrasekar (2013), who converted the Gaussian model adaptive processing (GMAP) filter (Siggia and Passarelli 2004) into a time-domain filter; nevertheless, effective performance of this filter also requires longer dwell times than are typically used in NEXRAD operations. Finally, a novel spectral domain filter proposed by Sachidananda and Zrnić (2000) was shown to meet NEXRAD operational requirements for ground clutter mitigation of SPRT sequences with a 2/3 PRT ratio (Torres et al. 2009b, 2010a,b), but it lacked the flexibility to adapt to the clutter environment in real time.

Of equal importance to the design of an effective GCF is its judicious application (Chrisman et al. 1995)—that is, recognizing when to apply the GCF can be a very complex problem, especially in dynamic weather conditions. For example, frontal passages can cause changes in the refractive index of the atmosphere, bending the radar beam such that it increases contact with or overshoots ground clutter. These dynamic processes can give the appearance that the ground clutter shifts within or disappears from the radar volume very rapidly. This motivates the need for a dynamic application of the GCF that adapts to the clutter environment (i.e., to the amount of clutter contamination) by increasing or decreasing the amount of clutter suppression such that biases in radar-variable estimates are kept within acceptable limits. Fortunately, spectral examination of the received echoes provides a means to determine the presence of ground clutter contamination in real time. The so-called Clutter Environment Analysis using Adaptive Processing (CLEAN-AP)^{1} filter is capable of providing ground clutter mitigation that dynamically controls the clutter suppression level based on the amount of ground clutter contamination in the received signal (Torres and Warde 2014), but this has been demonstrated on only uniformly sampled sequences. In this work, we extend the CLEAN-AP filter to SPRT sequences and show that it meets NEXRAD operational requirements for clutter suppression.

The rest of the paper is organized as follows. In section 2, we review and modify the steps to extend the CLEAN-AP filter to SPRT sequences using the autocorrelation spectral density (ASD) developed by Torres and Warde (2017, hereafter Part I). The extension of the filter is tailored to replace the filtering steps of the basic SPRT algorithm described by Torres et al. (2004), which is applicable for any SPRT ratio; however, we concentrate on sequences with a 2/3 PRT ratio as proposed for the NEXRAD network. We analyze the performance of the SPRT CLEAN-AP filter in section 3 using simulations and apply it to two data cases collected with the KOUN radar in Norman, Oklahoma, in section 4. Section 5 concludes with a short summary and plans for future work.

## 2. The CLEAN-AP filter for staggered-PRT sequences

The CLEAN-AP filter can effectively handle SPRT sequences with a few modifications. To facilitate the discussion, the following assumptions are made without loss of generality. We assume that the SPRT sequence starts and ends with the short PRT (*T*_{1}) for a total of 2*M* + 1 pulses and that the positive integers *n*_{1} and *n*_{2} in the SPRT ratio (*T*_{1}/*T*_{2} = *n*_{1}/*n*_{2}) are coprime (i.e., positive integers that share no common factor except 1). The extended maximum unambiguous velocity (*υ*_{a}) is given by *n*_{1}*λ*/4*T*_{1} (or *n*_{2}*λ*/4*T*_{2}). The maximum unambiguous velocities and ranges corresponding to the individual PRTs are *υ*_{a1} = *λ*/4*T*_{1} and *r*_{a1} = *cT*_{1}/2 for *T*_{1}, and *υ*_{a2} = *λ*/4*T*_{2} and *r*_{a2} = *cT*_{2}/2 for *T*_{2}, where *c* is the speed of light. Furthermore, to accurately dealias the velocity estimate, we assume that the weather signal spectrum has compact support in any subinterval of length *λ*/2(*T*_{1} + *T*_{2}) within the extended Nyquist cointerval [this was discussed in Part I and is the same assumption in Sachidananda and Zrnić (2000)]. Last, we assume that storms are contained within *r*_{a2} so that overlaid echoes can be effectively handled by the SPRT algorithm (Warde and Torres 2009). The CLEAN-AP filter has four basic steps: data window selection, ASD computation, clutter-extent determination, and filtering (Torres and Warde 2014); these steps are described and extended for SPRT sequences next.

### a. Data window selection

An appropriate data window achieves a suitable compromise between clutter suppression and the variance of filtered radar variable estimates: whereas more tapered windows reduce the spectral leakage from strong ground clutter signals and result in improved ground clutter mitigation, they lead to larger variance of estimates. To estimate the required amount of tapering, the clutter-to-noise ratio (CNR) is roughly estimated from the direct-current (dc) power (a proxy for ground clutter power) and the noise power. Among the rectangular, von Hann, Blackman, and Blackman–Nuttall windows, the least tapered window that has sidelobes below the CNR estimate is selected.

In the preprocessing steps and at each range gate, the original SPRT sequence is decimated into three uniformly sampled subsequences of length *M* that begin with the first, second, and third sample, respectively, and skip every other sample. Mathematically, these subsequences are *n*_{s} = *n*_{1} + *n*_{2}, and *T*_{s} = *T*_{1} + *T*_{2}. These are denoted by *n*_{s}. With the assumptions stated above, note that *r*_{a1} and *r*_{a2} when estimating the CNR to select the data window. That is, for storms between *r*_{a1} and *r*_{a2}, returns from the short-PRT pulses overlay those from the long-PRT pulses; however, with the assumption that no storms are located beyond *r*_{a2}, returns from the long-PRT pulses never extend into those from the short-PRT pulses. Thus, to avoid overlaid echoes, only the first subsequence *r*_{a1} (Torres et al. 2004). Special filtering and processing considerations are required for computing radar variables past *r*_{a1}; these are well documented in the previous work (Torres et al. 2004; Warde and Torres 2009).

### b. ASD computation

*l*–

*l′*is the ASD lag, and

*F*

_{i}(

*i*=

*l*or

*l′*) is the discrete-time Fourier transform (DTFT) of the

*M*-sample signal subsequence after time shifting by

*iT*

_{s}and windowing with a power-preserving data window

*d*such that

*aliased*in the interval

*n*

_{s}times smaller than the Nyquist cointerval corresponding to

*T*

_{u}. Here,

*T*

_{u}is the PRT of the underlying uniform-PRT sequence from which the SPRT sequence is notionally obtained through decimation; that is

*T*

_{1}=

*n*

_{1}

*T*

_{u},

*T*

_{2}=

*n*

_{2}

*T*

_{u}, and

*T*

_{s}=

*n*

_{s}

*T*

_{u}.

*T*

_{1}+

*T*

_{2})] alias to zero Doppler in the SPRT ASD. Thus, a conventional GCF would remove these signals as if they were from ground clutter returns. However, for a weather signal with true mean Doppler velocity at one of the nonzero integer multiples of

*λ*/[2(

*T*

_{1}+

*T*

_{2})] (i.e., ±2

*υ*

_{a}/5 or ±4

*υ*

_{a}/5), the argument of the zeroth coefficient in the ASDs (3) and (4) is nonzero. Table 1 shows the expected arguments of the zeroth coefficient of the lag-2/5 and lag-3/5 ASDs for normalized true velocities (

*υ*/

*υ*

_{a}) of ±2/5 and ±4/5. Hence, the argument at the zeroth coefficient of (3) and/or (4) can be used to determine whether ground clutter contamination truly exists. Accordingly, we define a threshold of

*π*/

*n*

_{s}radians such that if the absolute value of the argument of the zeroth coefficient of the fractional-lag ASD exceeds it, then no clutter filtering is needed (i.e., the signal’s true velocity is away from zero) and the next two steps are skipped. Currently, we find that the use of (3) for this check is sufficient.

### c. Ground clutter extent determination

Given that (5) is simply the lag-1 ASD as described in Torres and Warde (2014), it can be used directly to determine the extent of ground clutter in all spectral densities—that is, the argument of the lag-1 ASD of a narrowband signal (such as ground clutter returns) locally “flattens,” whereas the argument of the lag-1 ASD of a wideband signal (such as weather) appears nearly unbiased. Thus, as done for uniform-PRT sequences, the argument of the lag-1 ASD can be compared against the so-called clutter model to determine the extent of ground clutter contamination. The “clutter model” is based on an ideal Gaussian spectrum with zero mean Doppler velocity and an adjustable spectrum width, which controls the filter’s maximum suppression. For this work, the spectrum width of the clutter model is set to 0.4 m s^{−1}, which matches the value used by the GMAP filter on the WSR-88D. A spectral coefficient is identified as clutter contamination if the corresponding lag-1 ASD coefficient has a magnitude above the spectral noise floor and an absolute argument less than the maximum value predicted by the clutter model [the reader is referred to Torres and Warde (2014) for more details about this process].

### d. Filtering

*T*

_{s}(

*k*

_{left}) and right (

*k*

_{right}) unfiltered spectral coefficients closest to the notch. A simple way to do this is to subtract or add 2

*π*to the phase difference

*π*radians:

*i*

_{min}corresponding to the element that has the minimum value. Then, the interpolation to obtain the argument of the filtered ASD (

*S*

_{f}) is

After filtering, the PSD- and ASD-based autocorrelations are computed and processing continues as outlined in Torres et al. (2004). That is, the arguments of the ASD-based autocorrelation estimates are used in the velocity difference transfer function to recover the dealiased Doppler velocity estimates, while the magnitudes of the PSD- and ASD-based autocorrelation estimates are used for power and spectrum width estimates. Although not explicitly discussed, the above-mentioned processing steps equally apply to a dual-polarimetric radar as described by Torres and Warde (2014).

## 3. Performance evaluation

Using 1000 Monte Carlo realizations, the performance of the CLEAN-AP filter is assessed using 65 samples of a SPRT sequence with *T*_{1} = 1 ms and *T*_{2} = 1.5 ms. Simulated weatherlike signals with a signal-to-noise ratio (SNR) of 20 dB, spectrum widths (*σ*_{υ}) of 1–4 m s^{−1}, and Doppler velocities spanning the Nyquist cointerval (−*υ*_{a} to *υ*_{a}, with *υ*_{a} = 50 m s^{−1}) are contaminated with simulated ground clutter signals with clutter-to-signal ratios (CSR) of −30 (no clutter) and 30 dB (moderate clutter), a spectrum width (*σ*_{c}) of 0.3 m s^{−1}, and zero Doppler velocity. The quality of the filter’s output is assessed in terms of biases and standard deviations of the radar variable estimates and compared against the requirements stated in the WSR-88D system specification. For operational use on the WSR-88D, SPRT is best suited for intermediate elevation angles, where ground clutter contamination is expected to be less severe and partially suppressed by lower antenna sidelobes. Thus, only 30 dB of clutter suppression is required (Sirmans 1992).

The WSR-88D reflectivity bias requirements for a no-clutter condition are 10, 2, and 1 dB for a *σ*_{υ} of 1, 2, and >3 m s^{−1}, respectively. Plotted in Fig. 1 are the reflectivity biases as a function of true velocity across the Nyquist cointerval (−50 to 50 m s^{−1}) for a CSR of −30 dB (i.e., no clutter contamination) and a *σ*_{υ} of 1 (black dotted line), 2 (black dash line), 3 (black solid line), and 4 (gray solid line) m s^{−1}. It is seen that reflectivity biases meet the WSR-88D requirements and are about −5.4, −1.5, and less than −0.9 dB for the benchmark conditions, respectively. Although there are no stated WSR-88D requirements for a reflectivity standard deviation, a 2-dB goal is typically adopted (Ice et al. 2004). In Fig. 2, the standard deviation of filtered reflectivity estimates is plotted for the same conditions as in Fig. 1. Although the 2-dB goal is achieved, the effects of the filter at the zerolike velocities (±20 and ±40 m s^{−1}) are evident.

Measured at a benchmark signal with a 20-dB SNR and a *σ*_{υ} of 4 m s^{−1}, the WSR-88D requirements for velocity and spectrum width biases and standard deviations are all 2 m s^{−1} for passband velocities above 2, 3, and 4 m s^{−1} and clutter suppression levels of 20, 28, and 50 dB, respectively. Plotted as a function of velocity in the extended Nyquist cointerval, Fig. 3 shows that the CLEAN-AP filter for SPRT sequences easily meets the velocity bias (left panel) and standard deviation (right panel) requirements for a clutter-free condition even at spectrum widths below the benchmark (4 m s^{−1}). Likewise, plotted as a function of true *σ*_{υ}, Fig. 4 shows that the filter easily meets the spectrum width of the WSR-88D requirements for bias (left panel) and standard deviation (right panel) for the benchmark conditions.

When clutter residue is present at the output of the filter, the WSR-88D requirements allow for an additional 1 dB in reflectivity bias (i.e., a total of a 2-dB bias) for a signal with a 20-dB SNR and spectrum widths at and above 4 m s^{−1}. This condition is reflected in Fig. 5, where power bias (left panel) and standard deviation (right panel) are seen to be below the 2-dB requirement for all velocities in the Nyquist cointerval and for an input CSR of 30 dB and a *σ*_{υ} of 4 m s^{−1}. Although well within requirements, localized increased negative reflectivity biases and elevated standard deviations are present at each zerolike velocity as well as at the true zero velocity. Note that the negative effects of the filter at velocities of 0, ±20, and ±40 m s^{−1} are more pronounced as the spectrum width becomes narrower, but they are maintained below ~2 m s^{−1} for both measures when spectrum widths are above ~2 m s^{−1}. Figure 6 confirms that the velocity bias (left panel) and standard deviation (right panel) for a CSR of 30 dB are within the 2 m s^{−1} requirements throughout the Nyquist cointerval. Note how the velocity bias is near zero around the zerolike velocities with localized increases (decreases) on the negative (positive) side of the zerolike velocities, which is the typical behavior around the stop band of a typical GCF. That is, a slight bias develops when a portion of the signal is removed by the filter, resulting in a bias that is away from the filter notch. The spectral reconstructive element of the CLEAN-AP filter attempts to recover the signal loss in the filter notch; thus, reduced biases are observed when the signal spans the filter notch. Nonetheless, increases in standard deviation (Fig. 6, right panel) are also observed at each of the stop bands around the zerolike velocities. Velocity dealiasing errors (referred to as catastrophic errors) can occur if errors in the individual velocity estimates (*υ*_{1} and/or *υ*_{2}) become large (Torres et al. 2009a). Similarly, the residual effects of ground clutter filtering can increase the statistical errors in these velocity estimates, as observed by the increase in standard deviation in Fig. 6. Figure 7 shows the percentage of catastrophic errors for a CSR of 30 dB (right panel). For no clutter contamination (not shown), there are no catastrophic errors associated with the filtering process; however, when ground clutter is present at a CSR of 30 dB, increases in catastrophic errors are observed. These errors occur near the zerolike velocities and are the largest near ±20 m s^{−1} and for a *σ*_{υ} of 1 m s^{−1} (as could have been predicted from the largest increase in standard deviation from Fig. 6 for these same velocities). At a CSR of 30 dB (Fig. 8), the spectrum width bias (left panel) and standard deviation (right panel) are shown to be within the 2 m s^{−1} requirements for true input spectrum width values from 1 to 8 m s^{−1}. In summary, these simulations confirm that the extension of the CLEAN-AP filter to SPRT sequences performs well and meets the WSR-88D operational requirements. Next, we illustrate this performance comparing NEXRAD standard acquisition modes (split-cut and batch modes) against SPRT in two data cases.

## 4. Application to WSR-88D data

Two data cases were collected with the KOUN radar, one on 4 March 2004 and one on 8 April 2012. In both cases, a constant-elevation revolution using a NEXRAD standard acquisition mode (the split-cut mode in the April 2012 case and the batch mode in the March 2004 case) was followed by another one that used the SPRT acquisition mode at the same elevation angle. For the April 2012 case, we compare the ground clutter filtering performance using the split-cut and SPRT acquisition modes. In the split-cut mode, the antenna completes two 360° revolutions at the same elevation angle and collects data using uniformly sampled sequences. The first revolution uses a long PRT to obtain range-unambiguous power measurements; the second revolution uses a short PRT to obtain Doppler-unambiguous velocity measurements. In this case, the long PRT is 3.1 ms with 15 samples per 1° ray, and the short PRT is 0.97 ms with 54 pulses per ray. Thus, the maximum unambiguous range is 464.7 km for reflectivity and 149.5 km for velocity. The SPRT sequence alternates PRTs of 1.74 and 2.61 ms with a PRT ratio of 2/3 for a total of 37 pulses for each 1° ray with a maximum unambiguous range of 391.2 km. Data collected with the split-cut mode are processed with the CLEAN-AP filter (Torres and Warde 2014); data collected with SPRT are processed with the modified CLEAN-AP filter as described in section 2. To test the filter performance under more difficult clutter contamination conditions, data were collected at a 0.5° elevation, which increases the diversity of range gates with a mix of ground clutter and weather returns. Plan position indicator (PPI) displays of unfiltered (left panels) and filtered (right panels) reflectivity for the SPRT (top panels) and split-cut (bottom panels) acquisition modes are shown in Fig. 9. For this case, convective storms are seen to be south of the radar and a clear-air environment is present near the radar. Most of the ground clutter contamination is seen to be within the clear-air environment. Whereas it can be qualitatively observed that the ground clutter near the radar (center of the PPI) is mitigated quite effectively using the CLEAN-AP filter either with uniform or staggered PRTs, it is difficult to quantitatively evaluate the performance of the filter from just examining the PPI images. To assess the filter performance, a regression of unfiltered-to-filtered reflectivity values is shown in Fig. 10. The color scale depicts the percentage of unfiltered reflectivity values that are associated with each filtered reflectivity value (from 0% in blue to 100% in maroon), where a logarithmic scale is chosen to highlight the filtered reflectivity values. It is seen that, with both the SPRT (left panel) and split-cut (right panel) acquisition modes, most values lie on a line where unfiltered and filtered reflectivity values are equal (especially at low unfiltered reflectivity values, where maroon is prominent). Mitigation of ground clutter can be seen as a light blue-green cloud emanating from about (5, −5) dB unfiltered–filtered reflectivity toward the right. The clutter suppression for both the SPRT and split-cut acquisition modes for this case is limited to about 55 dB, as shown by the white line. Velocities for this case are shown in Fig. 11 (displays are arranged as in Fig. 9) and clearly indicate that ground clutter is properly mitigated for both the SPRT and split-cut acquisition modes. That is, zero-velocity values in the unfiltered velocity images (left panels) associated with ground clutter are seen as smooth, homogenous velocity fields in the filtered velocity images (right panels). Although the maximum unambiguous velocity is nearly the same for the SPRT (32 m s^{−1}) and split-cut (28 m s^{−1}) acquisition modes, the unambiguous range is quite different: 391.5 km for the SPRT acquisition mode and 149.5 km for the split-cut acquisition mode. This is evident in the occurrence of unresolved overlaid echoes (purple color) in the split-cut images (bottom) that are not present in the SPRT images (top). For this case, the radial velocity of the storms exceeded the maximum unambiguous velocity for both the SPRT and split-cut acquisition modes and resulted in a couple of small patches of aliased velocities [positive velocities (red) in the region of predominantly negative velocities (green)] to the west and southwest of the radar. These aliased velocities could be easily corrected by a conventional velocity dealiasing algorithm (e.g., Jing and Wiener 1993; Zittel and Jing 2012).

Data for the March 2004 case uses the batch and SPRT acquisition modes at an elevation angle of 2.5°. In the batch acquisition mode, long- and short-PRT sequences alternate as the radar performs a single 360° revolution. Whereas the data acquisition is different, the roles of the long- and short-PRT data are similar as those in the split-cut mode. For this case, each dwell consists of 6 samples collected with a long PRT of 3.11 ms followed by 41 samples collected with a short PRT of 0.98 ms. The maximum unambiguous range is 466 km for reflectivity and 148 km for velocity with a maximum unambiguous velocity of 28.3 m s^{−1}. In this case, the SPRT dwell consists of a total of 39 samples collected with alternate PRTs of 1.23 and 1.84 ms for a 2/3 PRT ratio. For the SPRT acquisition mode, the maximum unambiguous range is 276 km, and the extended maximum unambiguous velocity is 45.1 m s^{−1}. Dwell times are nearly equal at ~58.8 ms in batch acquisition mode and ~59.6 ms in SPRT acquisition mode. For the batch acquisition mode, filtering is provided by a two-pulse canceller for the long-PRT samples and by the CLEAN-AP filter (Torres and Warde 2014) for the short-PRT samples. Data collected with SPRT are processed with the modified CLEAN-AP filter as described in section 2. In Fig. 12, unfiltered (left panels) and filtered (right panels) reflectivity PPI displays are shown for SPRT (top panels) and batch (bottom panels) acquisition modes. At an elevation of 2.5°, there is not much ground clutter contamination seen in the unfiltered reflectivity. However, a comparison shows that the SPRT reflectivity field is smoother (less variant) than the corresponding one for the batch mode. This can be attributed to a reduction in the variance of reflectivity estimates due to an increase in the number of independent samples. Note that the improved data quality for the SPRT mode compared to the batch mode also applies to all dual-polarization variables (not shown here) and is another significant operational benefit of using the SPRT mode in place of the batch mode. Figure 13 shows the unfiltered (left panels) and filtered (right panels) velocity PPI images for the SPRT (top panels) and batch (bottom panels) acquisition modes. The unfiltered velocity PPI images (left panels) more clearly show (qualitatively) where ground clutter contamination is located (zero-velocity values very near and to the northwest of the radar), which is effectively mitigated by filtering (right panels).

Still, the main benefit of using SPRT sequences is the ability to reduce velocity aliasing without increasing the likelihood of obscuration due to range folding. That is, SPRT allows for the use of longer PRTs (leading to a larger maximum unambiguous range) while providing a relatively simple means to unambiguously measure velocities in a Nyquist cointerval that is larger than either of those associated with the individual PRTs. A comparison of filtered Doppler velocity images obtained from batch (bottom-right panel) and SPRT (top-right panel) sequences in Fig. 13 exemplifies this benefit. Here, the maximum unambiguous velocity for the batch mode is only 28.3 m s^{−1} and the one for the SPRT mode is 45.1 m s^{−1}. Whereas the reduced maximum unambiguous velocity of the batch mode creates aliased velocities for this case, the extended maximum unambiguous velocity of the SPRT mode allows for unambiguous measurement of the entire velocity field. Additionally, the maximum unambiguous range for velocity estimates is 148 and 276 km for the batch and SPRT acquisition modes, respectively. Thus, whereas obscured (range overlaid) velocities (purple) northwest and southeast of radar are present in the velocity image obtained with the batch mode, no such obscuration is present in the corresponding image obtained with the SPRT acquisition mode.

## 5. Conclusions

In this paper, we extended the CLEAN-AP filter for staggered–pulse repetition time (SPRT) sequences by taking advantage of the properties of the autocorrelation spectral density (ASD). Whereas the filter modifications outlined in this paper may be applicable to sequences with other SPRT ratios, we focused our analysis on sequences with a 2/3 PRT ratio, as proposed for the NEXRAD network. Using simulations, the CLEAN-AP filter for SPRT sequences was shown to meet NEXRAD requirements for clutter suppression. Further, we illustrated the performance of the filter using two cases collected with the KOUN radar in Norman, Oklahoma, by comparing the SPRT acquisition mode to two standard NEXRAD acquisition modes: split cut and batch. The performance observed for these data cases confirmed the improvements that can be realized operationally when the batch acquisition mode is replaced with the SPRT acquisition mode. The SPRT algorithm, which incorporates the CLEAN-AP filter as described in this paper, is currently being evaluated by the National Weather Service Radar Operations Center for inclusion in a future upgrade of the NEXRAD network.

## Acknowledgments

Funding was provided by NOAA’s Office of Oceanic and Atmospheric Research under NOAA–University of Oklahoma Cooperative Agreement NA11OAR4320072, U.S. Department of Commerce.

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Torres, S., 2006: Range and velocity ambiguity mitigation on the WSR-88D: Performance of the staggered PRT algorithm.

*22nd Int. Conf. on Interactive Information and Processing Systems (IIPS) for Meteorology, Oceanography, and Hydrology,*Atlanta, GA, Amer. Meteor. Soc., 9.9. [Available online at https://ams.confex.com/ams/Annual2006/techprogram/paper_103695.htm.]Torres, S., and D. Warde, 2014: Ground clutter mitigation for weather radars using the autocorrelation spectral density.

,*J. Atmos. Oceanic Technol.***31**, 2049–2066, doi:10.1175/JTECH-D-13-00117.1.Torres, S., and D. Warde, 2017: Staggered-PRT sequences for Doppler weather radars. Part I: Spectral analysis using the autocorrelation spectral density.

,*J. Atmos. Oceanic Technol.***34**, 51–63, doi:10.1175/JTECH-D-16-0071.1.Torres, S., D. S. Zrnić, and R. J. Doviak, 1998: Ground clutter canceling with a regression filter. NSSL Interim Rep., 37 pp. [Available online at http://cimms.ou.edu/~torres/Documents/Report - Ground clutter canceling with a regression filter.pdf.]

Torres, S., Y. Dubel, and D. S. Zrnić, 2004: Design, implementation, and demonstration of a staggered PRT algorithm for the WSR-88D.

,*J. Atmos. Oceanic Technol.***21**, 1389–1399, doi:10.1175/1520-0426(2004)021<1389:DIADOA>2.0.CO;2.Torres, S., D. Zittel, and D. Saxion, 2009a: Update on deployment of staggered PRT for the NEXRAD network.

*25th Conf. on Int. Interactive Information and Processing Systems (IIPS) for Meteorology, Oceanography, and Hydrology*, Phoenix, AZ, Amer. Meteor. Soc., 11B.2. [Available online at https://ams.confex.com/ams/89annual/techprogram/paper_146154.htm.]Torres, S., D. Warde, and D. Zrnić, 2009b: Signal design and processing techniques for WSR-88D ambiguity resolution. Part 12: Staggered PRT updates and generalized phase codes, NOAA, 156 pp. [Available online at http://cimms.ou.edu/~torres/Documents/NSSL Ambiguity Report - Part 12.pdf.]

Torres, S., D. Warde, and D. Zrnić, 2010a: Signal design and processing techniques for WSR-88D ambiguity resolution. Part 13: Staggered PRT updates, NOAA, 142 pp. [Available online at http://cimms.ou.edu/~torres/Documents/NSSL Ambiguity Report - Part 13.pdf.]

Torres, S., D. Warde, B. Gallardo, K. Le, and D. Zrnić, 2010b: Signal design and processing techniques for WSR-88D ambiguity resolution. Part 14: Staggered PRT algorithm updates, the CLEAN-AP filter, and the hybrid spectrum width estimator, NOAA, 145 pp. [Available online at http://cimms.ou.edu/~torres/Documents/NSSL Ambiguity Report - Part 14.pdf.]

Warde, D., and S. Torres, 2009: Range overlaid staggered PRT.

*25th Conf. on Int. Interactive Information and Processing Systems (IIPS) for Meteorology, Oceanography, and Hydrology*, Phoenix, AZ, Amer. Meteor. Soc., P2.2. [Available online at https://ams.confex.com/ams/89annual/webprogram/Paper146269.html.]Warde, D., and S. Torres, 2014: The autocorrelation spectral density for Doppler-weather-radar signal analysis.

,*IEEE Trans. Geosci. Remote Sens.***52**, 508–518, doi:10.1109/TGRS.2013.2241775.Warde, D., S. Torres, R. Ice, and A. Heck, 2014: Deployment of the staggered PRT algorithm on the NEXRAD network.

*30th Conf. on Environmental Information Processing Technologies*, Atlanta, GA, Amer. Meteor. Soc., 5.4. [Available online at https://ams.confex.com/ams/94Annual/webprogram/Paper237155.html.]Zittel, W. D., and Z. Jing, 2012: Comparison of a 2-D velocity dealiasing algorithm to the legacy WSR-88D velocity dealiasing algorithm during Hurricane Irene.

*30th Conf. on Hurricanes*, Ponte Vedra Beach, FL, Amer. Meteor. Soc., 7C.7. [Available online at https://ams.confex.com/ams/30Hurricane/webprogram/Paper205076.html.]Zrnić, D., and P. Mahapatra, 1985: Two methods of ambiguity resolution in pulse Doppler weather radars.

,*IEEE Trans. Aerosp. Electron. Syst.***AES-21**, 470–483, doi:10.1109/TAES.1985.310635.

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CLEAN-AP 2009 Board of Regents of the University of Oklahoma.