## 1. Introduction

The Center for Collaborative Adaptive Sensing of the Atmosphere (CASA), an engineering research center (ERC) established by the National Science Foundation (NSF) deployed its first generation network of four low-power, short-range, X-band, dual-polarized Doppler weather radars known as Networked Radar System (NETRAD; Chandrasekar and Jayasumana 2001; D. McLaughlin 2002, unpublished manuscript). The short-range CASA radars have range overlay and velocity folding problems with conventional pulse-pair processing. The first test bed of X-band radar systems (developed within the ERC) is deployed in central Oklahoma Integrated Project 1 (IP1). The IP1 radar network consists of four polarimetric weather radar nodes at Cyril (KCYR), Chickasha (KSAO), Rush Springs (KRSP), and Lawton (KLWE). The major challenges associated with the deployment of such a networked of short range of radar has been described by Chandrasekar et al. (2004) and Junyent and Chandrasekar (2009) describe the design and characterization of such radar networks. The X-band radars with conventional uniform pulsing will have low unambiguous velocity, and increasing the PRF will result in multiple trip overlays because storms can extend over a large distance. In addition, the radar systems deployed use a 2° beamwidth antenna and are intended to make observation close to the ground. The radar observations with such a system will be severely contaminated by ground clutter (Junyent et al. 2010). It is important to address the abovementioned issues when designing waveforms and associated processing algorithms.

The main objective of designing waveforms is to provide spectral moments and polarimetric variables with desired accuracy and to mitigate the effect of clutter and range–velocity ambiguity. Traditionally, operational radars have operated with simple uniform PRF waveforms with infinite impulse response/finite impulse response (IIR/FIR) clutter filter and pulse-pair processing (Groginsky and Glover 1980; Doviak and Zrnić 1993; Bringi and Chandrasekar 2001). Specific waveforms and processing methodologies have been proposed to mitigate range–velocity ambiguities and ground clutter contamination. Phase coding technique to mitigate range overlaid (Siggia 1983; Sachidananda and Zrnic 1999) and staggered waveforms for velocity unfolding (Zrnic and Mahapatra 1985; Holleman and Beekhuis 2003; Joe and May 2003; Cho 2005b) have been proposed and evaluated individually. Similarly clutter filtering has been proposed and tested (Groginsky and Glover 1980; Sachidananda and Zrnic 2000; Siggia and Passarelli 2004; Cho 2005a) with primary emphasis being only on clutter filtering. However, waveforms and processing methodologies that jointly implement phase coding, dual-PRF, and ground clutter filtering into an operational system using adaptive spectral processing has seldom been used operationally. The advent of modern signal processing techniques and computational power enables us to use complex waveforms and advanced processing to meet the challenging requirements.

This paper presents waveform design and signal processing methodologies that jointly consider clutter suppression, ambiguity mitigation, operational requirements and hardware requirements for CASA’s IP1 radars. Section 2 presents the challenges associated with waveform design for X band. The hardware and operational requirements for CASA’s IP1 radar network are presented in section 3. The performance of waveforms at X band for clutter suppression is described in section 4. Section 5 describes the dual-PRF waveform for ambiguity mitigation and performance of dual pulse repetition frequency waveform in the presence of clutter and a novel spatial filter to minimize the errors in unfolding velocities. Section 6 presents the results from the waveform implemented in the operational IP1 radar network. A description of the waveforms, the real-time environment and performance is presented in section 6. The paper concludes with a summary in section 7.

## 2. Waveform design perspective

The objective of waveform design for Doppler weather radars is to provide a waveform that minimizes errors and ambiguity in Doppler spectral moment estimates. The following sections describe the issues that are considered when designing waveforms for Doppler weather radars.

### a. Range–velocity ambiguity

*r*

_{max}) and maximum unambiguous velocity (

*υ*

_{max}) given by

*λ*is radar wavelength and

*c*is the velocity of light. The

*r*

_{max}

*υ*

_{max}limit reduces by a factor of three when the wavelength is changed from S band to X band. There is always a tradeoff between

*r*

_{max}and

*υ*

_{max}(range–velocity ambiguity). Precipitation particles can be distributed over a large area and the dynamic range of the radar reflectivity can be as high as 80 dB, which results in range overlay. Velocity measurements can span ±50 m s

^{−1}in severe storms resulting in velocity folding. Networked radar systems deployed by CASA are primarily for targeted applications such as tornado detection, flash flood monitoring, and hydrological applications. Such applications will have range overlay and velocity folding problems with conventional pulse-pair processing. The IP1 test bed with smaller X-band radar systems developed within CASA (Junyent et al. 2010) is a facility to demonstrate networked radar operations for targeted applications. Figure 1 shows the range–velocity limitation of an X-band radar compared to S-band radar. The X-band radars have a low unambiguous velocity because of their short wavelength, and increasing the PRF will result in multiple trip overlays since storms can extend over a large distance. It can be observed that range–velocity ambiguity is more severe for X-band radars compared to the conventional S band. For example, a commonly used 1-ms pulse repetition time at S band results in an unambiguous velocity of only 7.5 m s

^{−1}at X band compared to the 25 m s

^{−1}at S band.

Several range–velocity ambiguity mitigation schemes have been proposed in the past. Staggered PRT pulsing can be used to increase the unambiguous velocity Zrnic and Mahapatra (1985), and Golestani et al. (1995) extends this concept for dual-polarized radars. Random phase coding of the transmitted pulse was proposed by (Siggia 1983) to mitigate range overlay, and a systematic phase code and associated processing was suggested in Sachidananda and Zrnic (1999). A systematic phase code has been known to give better performance than random phase codes but requires a phase-controlled amplifier klystron, traveling wave tube (TWT) or solid-state transmitter. All the above methods have been tested with S- and C-band radars.

### b. Ground clutter

The CASA concept advocates radars designed for targeted applications at short ranges. A dense network of short-range radars mitigates the problem of Earth’s curvature and provides finer resolution with smaller antennas when compared to their S-band counterparts. However, radar observations at short ranges are contaminated by ground clutter. Ground clutter contamination is the radar return from nonmeteorological targets that bias the reflectivity and velocity estimates. Ground clutter at close range could come from side lobes or main lobe of the antenna, depending on the radar altitude or the phenomena being observed. Specifically, when designing radars for short-range operation there should be emphasis on clutter mitigation. At close ranges, the equivalent radar reflectivity due to clutter can easily be in the 40–60-dB*Z* range; whereas, the phenomena being observed, such as light rain or tornadoes, may have echoes in the range of 20–40 dB*Z*. Therefore, the waveform must consider clutter mitigation along with range–velocity ambiguity.

## 3. Design considerations

Waveforms for the individual radar nodes are based on IP1 operational requirements, such as scan speeds, volume coverage pattern, and system–hardware limitations (imposed by budgetary–market constraints), in addition to their ability to mitigate range–velocity ambiguities and suppress ground clutter echoes. The waveform considered for X-band implementation includes phase coding and multi-PRF capabilities using spectral processing. The advent of high-speed digital processors and extensive computational power with the capability of real-time spectral processing makes such waveforms viable for operational use. The number of waveforms for the radar is constrained by the hardware and system requirements. The following sections describe the requirements for the IP1 radars that impose constraints on the IP1 radar waveform.

### a. Operation requirements

The main goal of CASA is to provide an efficient system for hazardous weather detection and prediction using a collaborative network of radars operating in a closed loop with end users. The radars are intended to provide short-range coverage with a range of 40 km for each node. To efficiently detect different weather phenomenon, each radar must provide data that satisfies the recommended data specifications. Each low-powered radar must provide a sensitivity of at least 10 dB*Z* at 30 km (with no signal attenuation due to propagation) with an accuracy of 1 dB (SRD 2005). The accuracy of reflectivity has to be within 1 dB for the error in rainfall rate to be within 15% (Bringi and Chandrasekar 2001). The radars must also provide a Nyquist velocity of at least 25 m s^{−1} when operating in the Doppler mode with an accuracy of 1 m s^{−1} (SRD 2005). The accuracy of both reflectivity and velocity mentioned above will be applicable in the absence of clutter filtering. In addition to the basic requirements, there are several spatial and temporal aspects in the data specifications based on weather detection algorithms. One of the main requirement based on detection algorithms is the need for an azimuthal sampling resolution of 1° (SRD 2005), which is a little over half the beamwidth (oversampling in azimuth). Brown et al. (2002) suggested the use of azimuthal oversampling for improved tornado detection. The azimuthal sampling resolution directly places a constraint on the dwell time and scan speed.

The system “heartbeat” of CASA’s first-generation radar network is 40 s. The heartbeat is the time duration in which the entire networked radar system updates its current state. The decision to assign new tasks for scanning are made every heartbeat based on observations. One of the essential tasks is to provide two low elevation angle sweeps (360°) within a heartbeat. To provide two low elevation angle sweeps within the heartbeat, the scan speed of the radar nodes needs to be very high (in excess of 15° s^{−1}). The radar operates in a surveillance mode to assess the overall weather pattern and updates the feature repository. The captured features of the weather event are used to generate new radar scan strategies.

### b. Hardware requirements

To make a network of radars affordable, one of the drivers is to work with smaller less expensive radars, which dictates the hardware requirements. The first-generation CASA radar systems are magnetron-based with limited agility on duty cycle and supported waveforms. Junyent et al. (2010) gives a complete description of the radar system along with its features. The specifications of the radar system are listed in Table 1. The transmitter can deliver a maximum peak power of 25 kW at a duty cycle of 0.1%. Hence, only a PRF of 1.5 kHz can be used at the peak power of 25 kW. The transmitter can be tuned below its maximum peak power allowing one to increase the duty cycle, which is used to accommodate the higher PRF bursts. For example, a 3.3-dB reduction in peak power will enable the transmitter to pulse at a PRF of 3.2 kHz. A direct result of lowering the peak power to accommodate higher PRF is the loss in sensitivity. However, the maximum PRF that can be achieved is still limited by the duty cycle and any high PRF pulse train that is beyond the rated duty cycle has to be compensated by operating with a lower PRF. In addition to loss in sensitivity, there will be significant frequency drifts in the magnetron due to temperature fluctuations if the PRF is very high. There is also a limitation on the ability to phase code the transmit pulses because a magnetron based system has a random startup phase. Therefore, random phase coding is the only scheme that can be implemented.

## 4. Ground clutter filtering

Ground clutter echo is the signal back scattered from fixed targets such as terrain, buildings, trees, and nonmeteorological targets. The ground clutter echo from antenna side lobes or main lobe has zero mean Doppler velocity. This property is used to filter or eliminate the contamination caused by ground clutter. Ground clutter filtering is performed by applying a notch filter centered at zero Doppler velocity. Elliptic filters have been traditionally used for clutter filtering. The advent of high-speed digital processors enables clutter filtering in spectral domain. Siggia and Passarelli (2004) suggested an adaptive spectral filtering technique called Gaussian model adaptive processing (GMAP) to filter ground clutter. In this paper, an adaptive spectral domain filter similar to GMAP is used to suppress ground clutter. The following paragraph provides a brief description of the assumption and methodology for clutter filtering in the spectral domain.

The spectral clutter-filtering algorithm operates on the two polarization channels jointly and does not process the horizontal polarization channel and vertical polarization channel independently. The assumptions made for the processing are as follows:

- Both clutter and weather spectral density functions are Gaussian (Doviak and Zrnić 1993; Bringi and Chandrasekar 2001). The clutter contaminated weather echo can be modeled with a spectral density given bywhere
= [*μ**S*_{0c},*σ*,_{c}*S*_{0},*υ*,_{m}*σ*,_{υ}*N*_{0}]^{T}and the spectrum is written as a function of the magnitude of the Doppler velocity. In Eq. (2),*υ**S*_{0c}is the signal power of clutter echo,*σ*is the Doppler spectral width of clutter echo,_{c}*S*_{0}is the signal power of weather echo,*υ*is the mean Doppler velocity of weather echo,_{m}*σ*is the Doppler spectral width of weather echo, and_{υ}*N*_{0}is the noise power density. Clutter signal has a very narrow Doppler spectrum width (0.2–0.3 m s

^{−1}) and is centered on zero Doppler velocity.The spectral width of weather is greater than spectral width of clutter.

The distribution of copolar correlation for clutter is fairly wide; |

*ρ*_{hυ}(0)| is very low for side-lobe clutter while it can be very high for main-lobe clutter (Moisseev et al. 2002; Zrnic et al. 2006).The copolar correlation of precipitation is very high (0.99 or greater).

The noise power density

*N*_{0}is the superposition of system noise floor and noise contribution because of phase noise.

A window function is applied to the received signal in both H and V polarization channels. The complex spectral coefficients are computed using the DFT and the periodogram estimate of the spectral density in both channels is estimated.

The spectral noise floor in both the polarization channel is obtained from the sorted power spectral coefficients.

The clutter power is computed from the samples around zero Doppler velocity

The Gaussian clutter model is fit based on the clutter power and an a priori clutter spectral width

The Gaussian clutter model along with the spectral noise floor in each polarization channel is used to determine the width of the spectral clipper.

The spectral clipper and noise floor from both polarization channels are used to notch the complex spectral coefficients in each polarization channel. The widest spectral clipper is applied to the complex spectral coefficients and identical filters are applied to the H and V channels, respectively.

The polarimetric variables are computed from the filtered complex spectral coefficients.

A Gaussian weather spectral density is recursively fit to the remaining power spectral density points and the notched power spectral coefficients are interpolated with the fitted model.

The Doppler spectral moments are estimated from the interpolated power spectral density. The reflectivity is obtained from the zeroth spectral moment and calibration constants.

Figure 2 illustrates the clutter filtering process for a clutter-to-signal ratio (CSR) of 20 dB (CSR is a measure of clutter contamination) with a clutter spectral width *σ _{c}* = 0.3 m s

^{−1}. A Gaussian clutter model is obtained from the received signal, and this model is used to notch the clutter spectral coefficients. The notched region is recursively interpolated with a Gaussian spectral density fitted to the remaining signal to obtain the filtered signal. The interpolation performed only on the power spectral density and not the complex spectral coefficients. The governing model for interpolation is only for power spectrum and not the phase spectrum.

The joint processing of the H and V channels in step vi is the critical step in the processing of dual-polarization radar. The Doppler spectral moments are obtained from the interpolated power spectral density in the H channel and are not affected by the processing in the V channel. However, the polarimetric variables are relative measurements obtained from the complex spectral coefficients in the H and V channels. Therefore, it is important to perform identical processing in each channel. Nonidentical filtering in the H and V channels will introduce decorrelation between the channels that, in turn, increases the variance of the polarimetric variables. To ensure identical filtering in the H and V channels the same filter is used to remove clutter spectral coefficients and noise. The width of the notch filter is the widest width obtained from the clutter model for the H and V channels.

The ability to suppress clutter and estimate the Doppler moments and polarimetric variables are dependent on various factors such as system phase noise and desired accuracy. The impact of phase noise and number of pulses is studied by simulating weather and clutter signal with varying properties. The polarimetric signals are simulated based on procedure described by Chandrasekar et al. (1986). In this paper, the measure of clutter contamination used is the CSR.

*δθ*is the phase noise of the system in radians. For example,

*δθ*= 0.25° results in SNR

*= 47.20 dB. The impact of phase noise on clutter suppression ability is evaluated by varying CSR and estimating the errors in the Doppler moments and polarimetric variables. To eliminate the effect of low SNR simulations are performed for SNR varying from 10 to 20 dB. The errors are averaged for SNR varying from 10 to 20 dB. The standard deviation is estimated for varying CSR with phase noise as a parameter. The mean Doppler velocity is selected to be half the Nyquist velocity so that clutter suppression ability is only affected by phase noise. The standard deviations of power and mean Doppler velocity as a function of CSR are shown in Fig. 3 for*

_{e}*N*= 64 and

*σ*= 2 m s

_{υ}^{−1}at a nominal PRF = 2 kHz operating at X band. It can be observed that a system without any phase noise is capable of suppressing clutter up to 50 dB with acceptable accuracy while the clutter suppression degrades as phase noise increases from 0.25° to 0.50°. CSR = 43 dB can be achieved for a system with 0.25° where the standard deviation of power is less than 2 dB and standard deviation of mean Doppler velocity is less than 2 m s

^{−1}. However, the clutter suppression ability is lower when the accuracy of polarimetric variables is considered. The standard deviation of

*Z*

_{dr}and

*ϕ*

_{dp}are shown as a function of CSR with phase noise as a parameter in Fig. 4. Clutter suppression up to 50 dB can be achieved in the absence of phase noise but only CSR = 35 dB can be achieved for a system with 0.25° where the standard deviation of

*Z*

_{dr}is less than 0.6 dB and standard deviation of

*ϕ*

_{dp}is less than 5°. It can be observed in Figs. 3 and 4 that the clutter suppression ability drops to about 35 dB for Doppler moments and about 30 dB for polarimetric variables when the phase noise is increased to

*δθ*= 0.5°. The system phase noise plays an important role in clutter suppression ability and forms one of the key design parameters for pulsed Doppler weather radars.

## 5. Dual-PRF waveform

Staggered PRT and staggered-PRF techniques for extending the unambiguous velocity have been known for more than two decades and are available on several operational Doppler weather radars, especially longer wavelength radar systems. The long-standing problem with staggered PRT waveforms has been effective clutter filtering (Sachidananda and Zrnic 2000). Sachidananda and Zrnic (2002) proposed a spectral method for ground clutter filtering for staggered PRT and this technique was demonstrated for Weather Surveillance Radar-1988 Doppler (WSR-88D) using the KOUN radar (Torres et al. 2004). However, this technique is not suitable at X band because the reduction in wavelength from S band to X band dramatically reduces the operating Doppler spectrum range (Nyquist bandwidth) of the staggered PRT waveform. Moisseev et al. (2008) suggested a time–domain parametric method for effective clutter filtering for staggered PRT and this method is suitable for implementation at X band. However, the time–domain parametric method is computationally intensive and is currently not a viable option for real-time operations. A staggered PRF provides an alternative approach to mitigate the range–velocity ambiguity while still enabling effective clutter filtering.

*κ*= 2:3 can be represented by

*p*and

_{h}*p*are indicator function representation of the transmitted waveform as described by Bringi and Chandrasekar (2001). The subscripts

_{υ}*h*and

*v*represent the transmit polarization state. The 1’s indicate the time instant when a pulse is transmitted and 0’s indicate that no pulse is fired. Any arbitrary waveform can be represented using this generalized representation. Consider a waveform with

*κ*= 2:3 with two different pulse spacings

*T*

_{1}= 2

*T*and

_{u}*T*

_{2}= 3

*T*where

_{u}*T*is a fundamental pulse repetition time. The autocorrelation estimates,

_{u}*R̂*

_{1}at lag

*T*

_{1}and

*R̂*

_{2}at lag

*T*

_{2}are obtained from pulse-pair estimates. The mean velocity estimate and the maximum unambiguous velocity are estimated as

*T*, the larger the unambiguous velocity. However, the maximum unambiguous velocity is limited by the accuracy of the estimator in (5) because the errors in

_{u}*υ̂*are inversely proportional to

*T*. The best accuracy in the estimate of mean Doppler velocity is obtained for a stagger ratio

_{u}*κ*= 2:3 (Zrnic and Mahapatra 1985). However, the accuracy of velocity estimated from (5) is much higher than the accuracy of velocity estimated from

*R̂*

_{1}and

*R̂*

_{2}. The Doppler velocities from the two autocovariance estimates are obtained as below:

*υ*

_{1}and

*υ*

_{2}occur at different Doppler velocities. Therefore, a comparison of the two velocities can be used to obtain unfolded velocities. The

*υ*

_{1}−

*υ*

_{2}velocity difference remains unique within the interval ±

*υ*for a stagger ratio

_{a}*κ*= 2:3 (Nathanson 1969). The unfolded velocity is obtained as

*α*is the velocity correction term. The velocity correction term is obtained based on the

*υ*

_{1}−

*υ*

_{2}velocity difference and is given in Table 2.

Figure 5 shows a scatterplot of unfolded velocity versus true velocity for *σ _{υ}* = 4 m s

^{−1}with two different dual-PRF waveforms. Waveform 1 uses PRF

_{1}= 2.4 kHz with

*N*

_{1}= 54 and PRF

_{2}= 1.6 kHz with

*N*

_{2}= 40. Waveform-1 provides an unambiguous velocity

*υ*= 38.3 m s

_{a}^{−1}. Waveform 2 uses PRF

_{1}= 3.0 kHz with

*N*

_{1}= 64 and PRF

_{2}= 2.0 kHz with

*N*

_{2}= 56. Waveform 2 provides an unambiguous velocity

*υ*= 47.8 m s

_{a}^{−1}. Both waveform 1 and waveform 2 can provide an integration period of 1° at a scan speed of 21° s

^{−1}. It can be observed in Fig. 5 that the unfolding based on

*υ*

_{1}−

*υ*

_{2}velocity difference provides satisfactory results. However, the presence of ground clutter and clutter filtering will result in higher errors in the unfolded velocities.

*σ*= 1, 2, 3 m s

_{υ}^{−1}, and it can be observed that the unfolding errors are high at the Nyquist folding velocities of PRF

_{1}= 2.4 kHz and PRF

_{2}= 1.6 kHz in waveform 1, and at Nyquist folding velocities of PRF

_{1}= 3.0 kHz and PRF

_{2}= 2.0 kHz, in waveform 2. The velocity unfolding errors are larger than 5% at the Nyquist folding velocities. The presence of measurement errors in the estimated velocities at each PRF may results in

*υ*

_{1}−

*υ*

_{2}velocity difference that produce outliers in the unfolded velocity field. Such outliers have been reported in Holleman and Beekhuis (2003) and Joe and May (2003), and spatial filtering has been suggested to remove the outliers. In this section a phasor median filter (PMF) is utilized to remove outliers in the velocity field. The PMF is based on multichannel median filtering proposed by Astola et al. (1990) for nonlinear filtering of images. A phasor field is obtained from the unfolded velocity estimates as

*υ̂*is the measured velocity and

*W*= (

*;*

_{i}*i*= 1, 2, 3, … ,

*n*

^{2}) be the phasors within an

*n*×

*n*processing window in the range–azimuth dimension. The absolute distance associated with the sample

*is given by*

_{i}*D*is the aggregated vector distances. The output of the PMF is given by

_{i}*σ*(

*υ*) that corresponds to measurement error in Doppler velocity is added to the radial velocities at each PRF. The unfolding of velocities is performed on the observation with noise added to it. The velocity unfolding error is computed by comparing the unfolded velocities with the true velocities. The velocity unfolding error obtained from raw unfolded velocities, velocity filtered with PMF of order

*n*and velocity filtered with a simple median filter (MF) of order

*n*is shown in Fig. 7. The unfolding error in Fig. 7 is plotted as a function of

*σ*(

*υ*) and it can be observed that the raw unfolded estimates can have very high errors for

*σ*(

*υ*) ≥ 2.5 m s

^{−1}while the errors are small (≤5%) when spatial filters are used. The performance of PMF and MF are comparable in the region where

*σ*(

*υ*) ≤ 4 m s

^{−1}. However, the performance of PMF is better than MF when there are large errors in the Doppler velocity field.

## 6. Waveform for first generation CASA radars

Based on the requirements for the first generation CASA radar network a dual-PRF waveform has been recommended for operations. The waveform consists of two PRFs with *N*_{1} = 40 pulses at PRF_{1} = 1.6 kHz and *N*_{2} = 54 pulses at PRF_{2} = 2.4 kHz. This dual-PRF waveform as shown in Fig. 8 has been operational on the IP1 radar network. The waveform is processed with full spectral processing to enable spectral clutter filtering and overlay echo suppression. The dual-PRF measurements are used to unfold the velocity and the naturally occurring random phase coding with magnetron radars is used for range overlay suppression.

### a. Real-time environment and data

The data acquisition system is an field-programmable gate array (FPGA) system with Ethernet-based data interfaces to the real-time signal processor. The real-time signal processing is performed on a general purpose server running a Linux operating system. The servers currently used in CASA’s first-generation radars use a single Intel Quad core Xeon processor with a clock speed of 2.33 GHz and 3 GB of RAM. The calibration and timing information are inputs to the signal processor to process staggered waveforms and provide calibrated products. A more detailed description of the hardware, data acquisition system, and operations is presented in Junyent et al. (2010). The standard waveform operating in the IP1 radar is a dual-PRF waveform using PRF_{1} = 2.4 kHz, *N*_{1} = 54, PRF_{2} = 1.6 kHz, and *N*_{2} = 40 with antenna scan speed of 21° s^{−1}. Spectral processing for clutter filtering and overlaid echo suppression is performed on the received signal with each PRF block. The dwell time of each PRF block results in an azimuthal interval of 0.5°. The spectral processing outputs from each of the PRF blocks are averaged.

The signal processor has been constantly operated without failure for several years. Extensive datasets have been archived during operations. Figure 9 and Fig. 10 illustrate the Doppler moments and polarimetric variables estimated in the KSAO radar obtained with spectral processing and dual PRF A range height indicator (RHI) scan performed at an azimuth of 0° from 0°–30° during a widespread shower event on 1934:18 UTC 4 May 2009 is shown in Fig. 9 and Fig. 10. Figures 9a,b shows the filtered reflectivity and Doppler velocity along with the unfiltered products. The suppression of ground clutter closer to the ground can easily be observed. However, there is residual clutter in regions where the ground clutter signal is very strong. The filtered *Z*_{dr} and |*ρ*_{hυ}(0)| along with the unfiltered data are shown in Figs. 10a,b. There is a slight increase in |*ρ*_{hυ}(0)| that occurs after filtering because noise spectral coefficients are notched, which results in slightly improving the copolar correlation coefficient. The difference in filtered and unfiltered *Z*_{dr} is not very apparent in the RHI plots. However, the plot is useful to demonstrate that the adaptive nature of the filtering does not degrade *Z*_{dr} where there is no clutter. A scatterplot of *Z*_{dr} is used to compare the filtered and unfiltered *Z*_{dr}. A scatterplot of *Z _{h}* versus

*Z*

_{dr}from RHI data collected with KSAO radar at different azimuths during widespread showers from 1924 to 1934 UTC 4 May 2009 is shown in Fig. 11. The scatterplot is shown for both unfiltered and filtered data. The data points selected in the scatterplots are based on a reflectivity threshold

*Z*≥ 10 dB

_{h}*Z*and copolar correlation coefficient |

*ρ*

_{hυ}(0)| ≥ 0.99. The impact of clutter and filtering can be observed in Fig. 11 where the strong clutter signals provides very noise

*Z*

_{dr}data for reflectivities greater than 30 dB

*Z*. The outliers in the filtered data can be attributed to the residual clutter.

### b. Clutter suppression in IP1

Ground clutter suppression is one of the critical aspects for IP1 radars because the antenna beamwidth is 2° that results severe clutter contamination at lower elevation angles. The ground clutter signals can be side-lobe clutter and main-lobe clutter. Traditionally, clutter maps are used to identify the clutter region and clutter filter is applied only as indicated by clutter maps. However, no clutter map is used in IP1 radar and the filter is applied in all regions. Figure 12 shows the observations with and without clutter filtering. The phenomenon shown in Fig. 12a is a hook echo observed from the Lawton radar at 0037:42 UTC 9 May 2007. Hook echoes are associated with tornadoes in storms. It can be observed that the spectral clutter filtering suppresses the strong ground clutter closer to the hook echo. The circulation feature is more clear after spectral filtering as shown in Fig. 12b.

Ground clutter suppression has been traditionally viewed in terms of its impact on the spectral moments. However, in a networked radar environment the estimated moments are used to adaptively steer the antenna. The adaptive steering of the antenna will not have the optimal volume coverage pattern if there is a lot false detection because of clutter. Therefore, in addition to providing filtered spectral moments, the spectral clutter filter also minimizes the false detection for adaptive scanning, which is critical for networked radar operations.

To evaluate clutter suppression in the IP1 radar network the clutter suppressed is decomposed into two types. That is to say the amount of clutter suppressed when there is no meteorological signal and the amount of clutter suppressed when there is weather echo present along with clutter. To achieve this goal an estimate of the SNR is used to classify the CSR measurements. The SNR and CSR were estimated in the spectral domain. The SNR is not the total received signal power-to-noise ratio. However, the SNR is estimated in the spectral domain specifically for meteorological signal. The clutter power, signal power and noise power are estimated during the filtering process. These powers are used to compute SNR and CSR. Figure 13 shows the cumulative distribution function (CDF) of CSR where the CDFs shown in the plot are for the dataset listed in Table 3. The CDF of CSR when meteorological signal is present is shown in Fig. 13a, and CSR when no meteorological signal is present is shown in Fig. 13b. An SNR threshold greater than 3 dB was used to identify meteorological signal. The CDFs shown are for 10 datasets collected with the IP1 radar nodes during experiments conducted in 2007 and 2008. Table 3 lists the clutter suppressed for the specified date. The clutter suppression is obtained as the 99% value of CSR from the CDF for each date. The dataset corresponding to each date can be from more than one radar, as shown in second column of Table 3. The clutter suppressed when the received signal is purely clutter is much higher than when weather echo is contaminated by clutter. The total SNR of the signal is limited by the phase noise of the system, which implies that the signal plus clutter power is limited by the phase noise. Therefore, the clutter suppression observed with the system is about 33 dB based on the observation from IP1 CSR data.

### c. Overlay echo suppression in IP1

*ψ*). The received signal is phase corrected (cohered) to account for the switching phase. Only the selected trip, say the first trip signal is cohered, the second trip is then phase-modulated by the phase sequence

_{k}*ϕ*=

_{k}*ψ*

_{k−1}−

*ψ*. Let

_{k}*V*

_{1}(

*k*) and

*V*

_{2}(

*k*) be the two distinct weather echoes from the first and second trip, respectively. The received signal after recohering for the first trip echo can be written as

*ϕ*=

_{k}*ψ*

_{k−1}−

*ψ*is called the modulation code. The second trip signal

_{k}*V*

_{2}(

*k*) is phase-modulated by the polyphase sequence

*e*. In real operational scenarios there can be third and fourth trip signals, and these signals are also phase modulated by

^{jϕk}*ψ*

_{k−2}−

*ψ*and

_{k}*ψ*

_{k−3}−

*ψ*, respectively, but only second trip signal will be considered in this section. The modulation code alters the spectral distribution of the overlaid second trip signal,

_{k}*V*

_{2}(

*k*). The exact nature of this change in spectral distribution depends on the modulation code

*ϕ*.

_{k}

*υ*_{1}and

*υ*_{2}be the first and second trip signal vectors, respectively. The cohered received signal can be written as

**= diag[exp(**

*ϕ**jϕ*)] matrix. In the frequency domain, with DFT on both sides of (14),

_{k}**Φ**is a circulant matrix whose first row is the discrete Fourier transform of

*ϕ*. The spectral distribution of

_{k}**Φ**determines the nature of

**ΦV**

_{2}. For example, if

**Φ**is uniformly distributed (i.e.,

*ϕ*is a random phase sequence) in the Nyquist bandwidth then the second trip echo,

_{k}

*υ*_{2}is whitened and appears as noise. Random phase coding of transmitted pulses was proposed by Siggia (1983). Random phase coding occurs naturally with magnetron transmitters. Many of the weather radars deployed around the world use magnetron transmitter and random phase coding can be used to suppress range-overlaid echoes. Alternatively,

**Φ**can selected such that the spectral distribution

**Φ**has only a finite number of non-zero spectral coefficients resulting in weighted replicas of

**V**

_{2}in the Nyquist bandwidth;

**Φ**with finite number of nonzero spectral lines are obtained from systematic phase sequences or systematic phase codes. Systematic phase sequences have been proposed and evaluated for range ambiguity mitigation (Sachidananda and Zrnic 1999; Bharadwaj and Chandrasekar 2007).

The IP1 radar use magnetron transmitter that forces the use of random phase coding that naturally occurs with magnetron. Figure 14 shows the observations of reflectivity with and without overlaid echo suppression for a precipitating region with light rain. The phenomenon shown in Fig. 14 is observed from the Cyril radar at 0037:42 UTC 9 February 2007. The presence of overlaid echoes can lead to biases in precipitation estimation. The presence of overlaid echo is very clearly observed in Fig. 14 without any spectral processing to remove second trip echoes while the filtered reflectivity has both ground clutter as well as overlaid echoes filtered. In addition to biasing precipitation estimates, overlaid echoes lead to serious problem in adaptive scanning systems that rely on precipitation detection such as the MCandC in CASA’s IP1 radar network. The presence of overlaid echoes will lead to precipitation detection where there is no echo. Therefore, it is very important to mitigate and filter the overlaid echoes to enable adaptive scanning. The use of random phase coding to suppress overlaid echoes has been operation in CASA’s IP1 radars. Figure 15 shows the CDF of overlaid echo suppressed. The CDFs shown are for 10 datasets collected with the IP1 radar nodes during experiments conducted in 2007 and 2008. Table 4 lists the overlaid echo suppressed for the specified date. The amount of suppression is measured as the 99% value of overlaid echo suppression from the CDF for each date. The dataset corresponding to each date can be from more than one radar, as shown in second column of Table 4.

### d. Velocity dealiasing in IP1

The dual-PRF waveform has been used in the IP1 radar network to dealias radial velocities. Figure 16 shows the reflectivity observations from a hook echo observed from Cyril. The dataset was collected on 2115:39 UTC 10 February 2009 at an elevation of 3.0°. The radial velocity at the individual PRFs is shown in Fig. 17a. The velocity aliasing effect is clearly observed as radial streaks. The estimated radial velocities are dealiased by comparing the difference of the adjacent radial velocity from the same range gate. The measure velocities at the individual PRFs are less than 13 and 20 m s^{−1} for the long and short PRT bursts. The dealiased velocities are shown in Fig. 17b and it can be observed that velocities greater than 20 m s^{−1} are retrieved. This can be observed around the 0-degree azimuth from 10 to 15 km in range. However, dual-PRF dealiasing does have unfolding errors and this can be observed in Fig. 17b. Such error have been reported in literature and can be corrected for by using spatial filtering as described in section 5. Figure 18 shows a comparison of the spatially filtered Doppler velocity field and the raw unfolded velocity obtained from the dual-PRF waveform. The data shown in Fig. 18 is an example obtained from IP1 operations from Cyril radar at 0050:15 UTC 24 March 2009. Figure 18a shows the attenuation corrected reflectivity obtained after spectral filtering. Figure 18b shows the raw unfolded velocity obtained and the speckle noise in the velocity field easily observed. This noise in the velocity field occurs as a result of incorrect unfolding and this error in unfolding is because of increased variance after spectral filtering. Figure 18c shows the filtered velocity field after nonlinear filtering using PMF. There is a reduction in the speckle noise in the velocity field after the application of PMF. The order of PMF chosen in this case is *n* = 5. It is important to select *n* depending on the desired level of smoothing of the velocity field.

## 7. Summary

This paper described the design, implementation, and demonstration of waveform design and signal processing for staggered waveforms with simulations as well as on CASA’s IP1 radars operating at X band. The challenges associated with designing waveforms for an X-band radar system were described and mainly included issues relating to range-velocity ambiguity and ground clutter suppression. In addition to range–velocity ambiguity and clutter filtering the waveforms design needs to take into considerations operational requirements and hardware limitations. The important factors affecting the waveform design for precipitation radars is the resulting dwell time based on scan speeds and the agility of the transmitter to implement complex waveforms.

Spectral processing is used for ground clutter suppression. The proposed spectral filter uses an adaptive notch filter and recursive interpolation to minimize the impact of notch filtering. The recursive interpolation is beneficial for estimating the Doppler spectral moments. However, no interpolation is required for the complex spectral coefficient to estimate the polarimetric variables. It is critical that identical notch filters and noise filters be applied in both the horizontal polarization and vertical polarization channels. The clutter suppression ability is governed by the phase noise of the system and the number of pulses in the dwell time. A phase noise of 0.25° will provide adequate clutter suppression. The number of pulses is determined by the accuracy requirement and the operational scan speeds. A design space with the number of pulses, Doppler spectral moments and polarimetric variables has been presented in this paper at X band.

Dual-PRF waveform is suggested to mitigate the ambiguity in measurements. A simple unfolding algorithm for dealiasing the velocities is described, and its performance in the presence errors due to ground clutter filtering was described. The outliers or high errors in velocity mostly lie near the Nyquist folding velocities of the waveform. The outliers due to incorrect unfolding can be minimized by applying spatial filters. A phasor median filter was presented to reduce the unfolding errors and a simulation study showed better performance of PMF compared to traditional median filters when errors in Doppler velocity estimates are high. The PMF is suggested for filtering outliers from the spatial velocity field prior to applying any detection algorithms.

Waveforms based on ambiguity mitigation and clutter filtering enables the selection of waveforms for operational use. However, both operational requirement and hardware requirements ultimately play a major role in the selection of the waveform. First, faster scanning operational requirement for the IP1 radars reduces the dwell time thereby reducing the number of pulses that can be used for integration. Second, cheaper and low-power magnetron transmitters with very limited agility in terms of duty cycle that were used in CASA’s IP1 radars reduced the possible waveforms for implementation. A dual-PRF waveform with *N*_{1} = 40 pulses at PRF_{1} = 1.6 kHz and *N*_{2} = 54 pulses at PRF_{2} = 2.4 kHz has been implemented in operational use. The random phase coding of magnetron has been used to mitigate range-overlaid echoes. The operations range of IP1 radars is 40 km and hence, random phase coding was not used to extend the operating range but only to suppress range overlaid echoes. The dual-PRF waveform provides azimuth integration period of 1° at a scan speed of 21° s^{−1}. The clutter suppression ability and overlaid echo suppression based on operations of the IP1 radar has been described along with the application of dual-PRF unfolding for increasing the unambiguous velocity. A clutter suppression of about 30 dB and overlaid echo suppression of about 23 dB has been observed with the IP1 radars. The PMF filter along with staggered PRF waveforms provides a viable means to measure very high velocities at X band.

## Acknowledgments

This work was supported primarily by the Engineering Research Centers Program of the National Science Foundation under NSF Award Number 0313747. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect those of the National Science Foundation.

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Clutter filtering with Gaussian spectral density fits.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Clutter filtering with Gaussian spectral density fits.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Clutter filtering with Gaussian spectral density fits.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Standard deviation of power and mean Doppler velocity as a function of clutter-to-signal ratio for a weather signal with *N* = 64 samples, *σ _{υ}* = 2 m s

^{−1}, and SNR = 10–20 dB. The weather echo is located at half the Nyquist velocity at PRF = 2 kHz.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Standard deviation of power and mean Doppler velocity as a function of clutter-to-signal ratio for a weather signal with *N* = 64 samples, *σ _{υ}* = 2 m s

^{−1}, and SNR = 10–20 dB. The weather echo is located at half the Nyquist velocity at PRF = 2 kHz.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Standard deviation of power and mean Doppler velocity as a function of clutter-to-signal ratio for a weather signal with *N* = 64 samples, *σ _{υ}* = 2 m s

^{−1}, and SNR = 10–20 dB. The weather echo is located at half the Nyquist velocity at PRF = 2 kHz.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Standard deviation of (left) *Z*_{dr} and (right) *ϕ*_{dp} as a function of clutter-to-signal ratio for a weather signal with *N* = 64 samples, *σ _{υ}* = 2 m s

^{−1}, and SNR = 10–20 dB. The weather echo is located at half the Nyquist velocity at PRF = 2 kHz.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Standard deviation of (left) *Z*_{dr} and (right) *ϕ*_{dp} as a function of clutter-to-signal ratio for a weather signal with *N* = 64 samples, *σ _{υ}* = 2 m s

^{−1}, and SNR = 10–20 dB. The weather echo is located at half the Nyquist velocity at PRF = 2 kHz.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Standard deviation of (left) *Z*_{dr} and (right) *ϕ*_{dp} as a function of clutter-to-signal ratio for a weather signal with *N* = 64 samples, *σ _{υ}* = 2 m s

^{−1}, and SNR = 10–20 dB. The weather echo is located at half the Nyquist velocity at PRF = 2 kHz.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Scatterplot of unfolded Doppler velocity vs the true Doppler velocity for *σ _{υ}* = 4 m s

^{−1}for two different dual-PRF waveform at X band.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Scatterplot of unfolded Doppler velocity vs the true Doppler velocity for *σ _{υ}* = 4 m s

^{−1}for two different dual-PRF waveform at X band.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Scatterplot of unfolded Doppler velocity vs the true Doppler velocity for *σ _{υ}* = 4 m s

^{−1}for two different dual-PRF waveform at X band.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Unfolding error rate as a function of mean Doppler velocity for CSR = 25 dB and phase noise *δθ* = 0.25°. (left) Waveform 1: PRF_{1} = 2.4 kHz, *N*_{1} = 54, PRF_{2} = 1.6 kHz, *N*_{2} = 40, and *υ _{a}* = 38.3 m s

^{−1}. (right) Waveform 2 = PRF

_{1}= 3.0 kHz,

*N*

_{1}= 64, PRF

_{2}= 2.0 kHz,

*N*

_{2}= 56 and

*υ*= 47.8 m s

_{a}^{−1}.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Unfolding error rate as a function of mean Doppler velocity for CSR = 25 dB and phase noise *δθ* = 0.25°. (left) Waveform 1: PRF_{1} = 2.4 kHz, *N*_{1} = 54, PRF_{2} = 1.6 kHz, *N*_{2} = 40, and *υ _{a}* = 38.3 m s

^{−1}. (right) Waveform 2 = PRF

_{1}= 3.0 kHz,

*N*

_{1}= 64, PRF

_{2}= 2.0 kHz,

*N*

_{2}= 56 and

*υ*= 47.8 m s

_{a}^{−1}.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Unfolding error rate as a function of mean Doppler velocity for CSR = 25 dB and phase noise *δθ* = 0.25°. (left) Waveform 1: PRF_{1} = 2.4 kHz, *N*_{1} = 54, PRF_{2} = 1.6 kHz, *N*_{2} = 40, and *υ _{a}* = 38.3 m s

^{−1}. (right) Waveform 2 = PRF

_{1}= 3.0 kHz,

*N*

_{1}= 64, PRF

_{2}= 2.0 kHz,

*N*

_{2}= 56 and

*υ*= 47.8 m s

_{a}^{−1}.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Unfolding error rate as a function of variance of mean Doppler velocity for raw unfolded velocity, phasor median filter, and median filter data. (left) Waveform 1: PRF_{1} = 2.4 kHz, *N*_{1} = 54, PRF_{2} = 1.6 kHz, *N*_{2} = 40, and *υ _{a}* = 38.3 m s

^{−1}. (right) Waveform 2 = PRF

_{1}= 3.0 kHz,

*N*

_{1}= 64, PRF

_{2}= 2.0 kHz,

*N*

_{2}= 56, and

*υ*= 47.8 m s

_{a}^{−1}.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Unfolding error rate as a function of variance of mean Doppler velocity for raw unfolded velocity, phasor median filter, and median filter data. (left) Waveform 1: PRF_{1} = 2.4 kHz, *N*_{1} = 54, PRF_{2} = 1.6 kHz, *N*_{2} = 40, and *υ _{a}* = 38.3 m s

^{−1}. (right) Waveform 2 = PRF

_{1}= 3.0 kHz,

*N*

_{1}= 64, PRF

_{2}= 2.0 kHz,

*N*

_{2}= 56, and

*υ*= 47.8 m s

_{a}^{−1}.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Unfolding error rate as a function of variance of mean Doppler velocity for raw unfolded velocity, phasor median filter, and median filter data. (left) Waveform 1: PRF_{1} = 2.4 kHz, *N*_{1} = 54, PRF_{2} = 1.6 kHz, *N*_{2} = 40, and *υ _{a}* = 38.3 m s

^{−1}. (right) Waveform 2 = PRF

_{1}= 3.0 kHz,

*N*

_{1}= 64, PRF

_{2}= 2.0 kHz,

*N*

_{2}= 56, and

*υ*= 47.8 m s

_{a}^{−1}.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Illustration of dual-PRF waveform implemented in CASA IP1 radars.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Illustration of dual-PRF waveform implemented in CASA IP1 radars.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Illustration of dual-PRF waveform implemented in CASA IP1 radars.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

RHI plots of dual-PRF data collected with Chickasha radar on 1934:18 UTC 4 May 2009: the unfiltered and filtered (a) reflectivity and (b) mean Doppler velocity.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

RHI plots of dual-PRF data collected with Chickasha radar on 1934:18 UTC 4 May 2009: the unfiltered and filtered (a) reflectivity and (b) mean Doppler velocity.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

RHI plots of dual-PRF data collected with Chickasha radar on 1934:18 UTC 4 May 2009: the unfiltered and filtered (a) reflectivity and (b) mean Doppler velocity.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

RHI plots of dual-PRF data collected with Chickasha radar at 1934:18 UTC 4 May 2009: the unfiltered and filtered (a) *Z*_{dr} and (b) |*ρ*_{hυ}(0)|.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

RHI plots of dual-PRF data collected with Chickasha radar at 1934:18 UTC 4 May 2009: the unfiltered and filtered (a) *Z*_{dr} and (b) |*ρ*_{hυ}(0)|.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

RHI plots of dual-PRF data collected with Chickasha radar at 1934:18 UTC 4 May 2009: the unfiltered and filtered (a) *Z*_{dr} and (b) |*ρ*_{hυ}(0)|.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Scatterplot of *Z _{h}* vs

*Z*

_{dr}from RHI data collected with KSAO radar at different azimuths during a widespread showers at 1924–1934 UTC 4 May 2009. The scatterplot is done for data with (left) unfiltered and (right) filtered data. The data points selected in the scatterplots are based on a reflectivity threshold

*Z*≥ 10 dB

_{h}*Z*and copolar correlation coefficient |

*ρ*

_{hυ}(0)| ≥ 0.99.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Scatterplot of *Z _{h}* vs

*Z*

_{dr}from RHI data collected with KSAO radar at different azimuths during a widespread showers at 1924–1934 UTC 4 May 2009. The scatterplot is done for data with (left) unfiltered and (right) filtered data. The data points selected in the scatterplots are based on a reflectivity threshold

*Z*≥ 10 dB

_{h}*Z*and copolar correlation coefficient |

*ρ*

_{hυ}(0)| ≥ 0.99.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Scatterplot of *Z _{h}* vs

*Z*

_{dr}from RHI data collected with KSAO radar at different azimuths during a widespread showers at 1924–1934 UTC 4 May 2009. The scatterplot is done for data with (left) unfiltered and (right) filtered data. The data points selected in the scatterplots are based on a reflectivity threshold

*Z*≥ 10 dB

_{h}*Z*and copolar correlation coefficient |

*ρ*

_{hυ}(0)| ≥ 0.99.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Plan position indicator (PPI) plots of dual-PRF data collected with Cyril radar at 0037:42 UTC 9 May 2007: the unfiltered and filtered (a) reflectivity and (b) velocity.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Plan position indicator (PPI) plots of dual-PRF data collected with Cyril radar at 0037:42 UTC 9 May 2007: the unfiltered and filtered (a) reflectivity and (b) velocity.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Plan position indicator (PPI) plots of dual-PRF data collected with Cyril radar at 0037:42 UTC 9 May 2007: the unfiltered and filtered (a) reflectivity and (b) velocity.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Cumulative distribution function of clutter suppressed (a) with weather signal and (b) without weather echo. The cumulative distribution functions plotted is for 10 datasets collected with the IP1 radar network. Each line in the plot is the CDF for the dataset listed in Table 3.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Cumulative distribution function of clutter suppressed (a) with weather signal and (b) without weather echo. The cumulative distribution functions plotted is for 10 datasets collected with the IP1 radar network. Each line in the plot is the CDF for the dataset listed in Table 3.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Cumulative distribution function of clutter suppressed (a) with weather signal and (b) without weather echo. The cumulative distribution functions plotted is for 10 datasets collected with the IP1 radar network. Each line in the plot is the CDF for the dataset listed in Table 3.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Reflectivity of a precipitation cell contaminated with ground clutter and overlaid echoes. (a) Unfiltered reflectivity and (b) filtered reflectivity. Data collected from Cyril at 2115:08 UTC 10 Feb 2009 with a dual-PRF waveform.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Reflectivity of a precipitation cell contaminated with ground clutter and overlaid echoes. (a) Unfiltered reflectivity and (b) filtered reflectivity. Data collected from Cyril at 2115:08 UTC 10 Feb 2009 with a dual-PRF waveform.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Reflectivity of a precipitation cell contaminated with ground clutter and overlaid echoes. (a) Unfiltered reflectivity and (b) filtered reflectivity. Data collected from Cyril at 2115:08 UTC 10 Feb 2009 with a dual-PRF waveform.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Cumulative distribution function of overlaid echo suppressed. The cumulative distribution functions plotted is for 10 datasets collected with the IP1 radar network.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Cumulative distribution function of overlaid echo suppressed. The cumulative distribution functions plotted is for 10 datasets collected with the IP1 radar network.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Cumulative distribution function of overlaid echo suppressed. The cumulative distribution functions plotted is for 10 datasets collected with the IP1 radar network.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Reflectivity of a precipitation cell forming a hook echo. Data collected from Cyril on 2115:39 UTC 10 Feb 2009 with a dual-PRF waveform.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Reflectivity of a precipitation cell forming a hook echo. Data collected from Cyril on 2115:39 UTC 10 Feb 2009 with a dual-PRF waveform.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Reflectivity of a precipitation cell forming a hook echo. Data collected from Cyril on 2115:39 UTC 10 Feb 2009 with a dual-PRF waveform.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Doppler velocity of a precipitation cell forming a hook echo: (a) folded velocity and (b) unfolded velocity. Data collected from Cyril at 2115:39 UTC 10 Feb 2009 with a dual-PRF waveform.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Doppler velocity of a precipitation cell forming a hook echo: (a) folded velocity and (b) unfolded velocity. Data collected from Cyril at 2115:39 UTC 10 Feb 2009 with a dual-PRF waveform.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

Doppler velocity of a precipitation cell forming a hook echo: (a) folded velocity and (b) unfolded velocity. Data collected from Cyril at 2115:39 UTC 10 Feb 2009 with a dual-PRF waveform.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

PPI plots of dual-PRF data collected with Cyril radar on 0050:15 UTC 24 Mar 2009: (a) The filtered reflectivity, (b) raw unfolded velocity, and (c) PMF-filtered velocity. Data collected at elevation angle of 1°.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

PPI plots of dual-PRF data collected with Cyril radar on 0050:15 UTC 24 Mar 2009: (a) The filtered reflectivity, (b) raw unfolded velocity, and (c) PMF-filtered velocity. Data collected at elevation angle of 1°.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

PPI plots of dual-PRF data collected with Cyril radar on 0050:15 UTC 24 Mar 2009: (a) The filtered reflectivity, (b) raw unfolded velocity, and (c) PMF-filtered velocity. Data collected at elevation angle of 1°.

Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1415.1

IP1 radar node design characteristics.

Dual-PRF unfolding for a stagger ratio of 2/3.

Ground clutter suppression.

Overlaid echo suppression.