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Range-oversampling processing is a technique that can be used to lower the variance of radar-variable estimates, reduce radar update times, or a mixture of both. There are two main assumptions for using range-oversampling processing: accurate knowledge of the range correlation and uniform reflectivity in the radar resolution volume. The first assumption has been addressed in previous research; this work focuses on the uniform reflectivity assumption. Earlier research shows that significant reflectivity gradients can occur in storms; we utilized those results to develop realistic simulations of radar returns that include effects of reflectivity gradients in range. An important consideration when using range-oversampling processing is the resulting change in the range weighting function. The range weighting function can change for different types of range-oversampling processing, and some techniques, such as adaptive pseudowhitening, can lead to different range weighting functions at each range gate. To quantify the possible effects of differing range weighting functions in the presence of reflectivity gradients, we developed simulations to examine varying types of range-oversampling processing with two receiver filters: a matched receiver filter and a wider-bandwidth receiver filter (as recommended for use with range oversampling). Simulation results show that differences in range weighting functions are the only contributor to differences in radar reflectivity measurements. Results from real weather data demonstrate that the reflectivity gradients that occur in typical severe storms do not cause significant changes in reflectivity measurements and that the benefits from range-oversampling processing outweigh the possible isolated effects from large reflectivity gradients. [ABSTRACT FROM AUTHOR]

For weather radars, range-oversampling processing was proposed as an effective way either to reduce the variance of radar-variable estimates without increasing scan times or to reduce scan times without increasing the variance of estimates. Range oversampling entails acquiring the received signals at a rate L times as fast as the reciprocal of the pulse width (the conventional rate), where L is referred to as the range-oversampling factor. To accommodate the L-times-as-fast sampling, the original formulation of range-oversampling processing required a receiver filter with a bandwidth L times as wide as that of the matched filter (the conventional receiver filter). In this case, the noise at the output of the receiver filter can still be assumed to be white, resulting in a simplified formulation of the technique but also, and more important, in a more difficult practical implementation since the receiver filter in operational weather radars is typically matched to the transmitted pulse. In this work, we revisit the role of the receiver filter in the performance of rangeoversampling processing and show that using a receiver matched filter not only facilitates the implementation of range-oversampling processing but also results in the lowest variance of radar-variable estimates. [ABSTRACT FROM AUTHOR]

Since the dual-polarization upgrade of the Weather Surveillance Radar-1988 Doppler (WSR-88D), the polarimetric variables have become a fundamental tool for better interpretation and forecasting of hazardous weather events. Thus, improving their quality has been an important long-standing effort. In this paper, we introduce the hybrid-scan estimators (HSE), which use the available data in split cuts of operational volume coverage patterns (VCP) to provide better estimates of differential reflectivity, differential phase, and correlation coefficient. The HSE are designed to choose between the data provided by either one of the two scans in split cuts based on their expected statistical performance, resulting in the same or better data quality compared to the conventional estimators. The performance improvement realized with the HSE is characterized with simulations and illustrated with data from WSR-88D. While relatively simple, an operational implementation of the HSE could bring improvements to forecasters' data interpretation and algorithm performance, both of which rely on dual-polarization radar data. [ABSTRACT FROM AUTHOR]

Adaptive range oversampling processing can be used either to reduce the variance of radar-variable estimates without increasing scan times or to reduce scan times without increasing the variance of estimates. For example, an implementation of adaptive pseudowhitening on the National Weather Radar Testbed Phased-Array Radar (NWRT PAR) led to a twofold reduction in scan times. Conversely, a proposed implementation of adaptive pseudowhitening the U.S. Next Generation Weather Radar (NEXRAD) network would reduce the variance of dual-polarization estimates while keeping current scan times. However, the original version of adaptive pseudowhitening is not compatible with radar-variable estimators for which an explicit variance expression is not readily available. One such nontraditional estimator is the hybrid spectrum-width estimator, which is currently used in the NEXRAD network. In this paper, an extension of adaptive pseudowhitening is proposed that utilizes lookup tables (rather than analytical solutions based on explicit variance expressions) to obtain range oversampling transformations. After describing this lookup table (LUT) adaptive pseudowhitening technique, its performance is compared to that of the original version of adaptive pseudowhitening using traditional radar-variable estimators. LUT adaptive pseudowhitening is then applied to the hybrid spectrum-width estimator, and simulation results are confirmed with a qualitative analysis of radar data. [ABSTRACT FROM AUTHOR]

With more weather radars relying on low-power solid-state transmitters, pulse compression has become a necessary tool for achieving the sensitivity and range resolution that are typically required for weather observations. While pulse compression is well understood in the context of point-target radar applications, the design of pulse compression waveforms for weather radars is challenging because requirements for these types of systems traditionally assume the use of high-power transmitters and short conventional pulses. In this work, Weather Surveillance Radar-1988 Doppler (WSR-88D) antenna pattern requirements are used to illustrate how suitable requirements can be formulated for the radar range weighting function (RWF), which is determined by the transmitted waveform and any range-time signal processing. These new requirements set bounds on the RWF range sidelobes, which are unavoidable with pulse compression waveforms. Whereas nonlinear frequency modulation schemes are effective at reducing RWF sidelobes, they usually require a larger transmission bandwidth, which is a precious commodity. An optimization framework is proposed to obtain minimum-bandwidth pulse compression waveforms that meet the new RWF requirements while taking into account the effects of any range-time signal processing. Whereas pulse compression is used to meet sensitivity and range-resolution requirements, range-time signal processing may be needed to meet data-quality and/or update-time requirements. The optimization framework is tailored for three processing scenarios and corresponding pulse compression waveforms are produced for each. Simulations of weather data are used to illustrate the performance of these waveforms. [ABSTRACT FROM AUTHOR]

The staggered-pulse repetition time (SPRT) technique has been shown to be effective at mitigating range and velocity ambiguities; however, mitigation of ground clutter contamination for SPRT sequences has proven to be more challenging. Using the properties of the autocorrelation spectral density, the Clutter Environment Analysis using Adaptive Processing (CLEAN-AP) filter is extended to SPRT sequences for its implementation on the U.S. Next Generation Weather Radar (NEXRAD) network. The performance of the CLEAN-AP filter for SPRT sequences is characterized and illustrated with simulations and real data. The study shows that the proposed ground clutter filter meets NEXRAD operational performance requirements for ground clutter mitigation. [ABSTRACT FROM AUTHOR]

The autocorrelation spectral density (ASD) was introduced as a generalization of the classical periodogram-based power spectral density (PSD) and as an alternative tool for spectral analysis of uniformly sampled weather radar signals. In this paper, the ASD is applied to staggered pulse repetition time (PRT) sequences and is related to both the PSD and the ASD of the underlying uniform-PRT sequence. An unbiased autocorrelation estimator based on the ASD is introduced for use with staggered-PRT sequences when spectral processing is required. Finally, the strengths and limitations of the ASD for spectral analysis of staggered-PRT sequences are illustrated using simulated and real data. [ABSTRACT FROM AUTHOR]

WSR-88D superresolution data are produced with finer range and azimuth sampling and improved azimuthal resolution as a result of a narrower effective antenna beamwidth. These characteristics afford improved detectability of weaker and more distant tornadoes by providing an enhancement of the tornadic vortex signature, which is characterized by a large low-level azimuthal Doppler velocity difference. The effective-beamwidth reduction in superresolution data is achieved by applying a tapered data window to the samples in the dwell time; thus, it comes at the expense of increased variances for all radar-variable estimates. One way to overcome this detrimental effect is through the use of range oversampling processing, which has the potential to reduce the variance of superresolution data to match that of legacy-resolution data without increasing the acquisition time. However, range-oversampling processing typically broadens the radar range weighting function and thus degrades the range resolution. In this work, simulated Doppler velocities for vortexlike fields are used to quantify the effects of range-oversampling processing on the velocity signature of tornadoes when using WSR-88D superresolution data. The analysis shows that the benefits of range-oversampling processing in terms of improved data quality should outweigh the relatively small degradation to the range resolution and thus contribute to the tornado warning decision process by improving forecaster confidence in the radar data. [ABSTRACT FROM AUTHOR]

Radar returns from the ground, known as ground clutter, can contaminate weather signals, often resulting in severely biased meteorological estimates. If not removed, these contaminants may artificially inflate quantitative precipitation estimates and obscure polarimetric and Doppler signatures of weather. A ground-clutter filter is typically employed to mitigate this contamination and provide less biased meteorological-variable estimates. This paper introduces a novel adaptive filter based on the autocorrelation spectral density, which is capable of mitigating the adverse effects of ground clutter without unnecessarily degrading the quality of the meteorological data. The so-called Clutter Environment Analysis using Adaptive Processing (CLEAN-AP) filter adjusts its suppression characteristics in real time to match dynamic atmospheric environments and meets Next Generation Weather Radar (NEXRAD) clutter-suppression requirements. [ABSTRACT FROM AUTHOR]

One way to reduce the variance of meteorological-variable estimates on weather radars without increasing dwell times is by using range oversampling techniques. Such techniques could significantly improve the estimation of polarimetric variables, which typically require longer dwell times to achieve the desired data quality compared to the single-polarization spectral moments. In this paper, an efficient implementation of adaptive pseudowhitening that was developed for single-polarization radars is extended for dual polarization. Adaptive pseudowhitening maintains the performance of pure whitening at high signal-to-noise ratios and equals or outperforms the digital matched filter at low signal-to-noise ratios. This approach results in improvements for polarimetric-variable estimates that are consistent with the improvements for spectral-moment estimates described in previous work. The performance of the proposed technique is quantified using simulations that show that the variance of polarimetric-variable estimates can be reduced without modifying the scanning strategies. The proposed technique is applied to real weather data to validate the expected improvements that can be realized operationally. [ABSTRACT FROM AUTHOR]

Time-domain autocovariance processing is widely accepted as a computationally efficient method to estimate the first three spectral moments of Doppler weather radar signals (i.e., mean signal power, mean Doppler velocity, and spectrum width). However, when signals with different frequency content (e.g., ground clutter) contaminate the weather signal, spectral processing using the periodogram estimator of the power spectral density (PSD) is the preferred tool of analysis. After spectral processing (i.e., filtering), a PSD-based autocorrelation estimator is typically employed to produce unbiased estimates of the weather-signal spectral moments. However, the PSD does not convey explicit phase information, which has the potential to aid in the spectral analysis of radar signals. In this paper, the autocorrelation spectral density (ASD) is introduced for spectral analysis of weather-radar signals as a generalization of the classical PSD, and an ASD-based autocorrelation estimator is proposed to produce unbiased estimates of the weather-signal spectral moments. A significant advantage of the ASD over the PSD is that it provides explicit phase information that can be exploited to identify and remove certain types of contaminant signals. Thus, the ASD provides an alternative means for spectral analysis, which can lead to improved quality of meteorological data from weather radars. [ABSTRACT FROM AUTHOR]

As range-oversampling processing has become more practical for weather radars, implementation issues have become important to ensure the best possible performance. For example, all of the linear transformations that have been utilized for range-oversampling processing directly depend on the normalized range correlation matrix. Hence, accurately measuring the correlation in range time is essential to avoid reflectivity biases and to ensure the expected variance reduction. Although the range correlation should be relatively stable over time, hardware changes and drift due to changing environmental conditions can have measurable effects on the modified pulse. To reliably track changes in the range correlation, an automated real-time method is needed that does not interfere with normal data collection. A method is proposed that uses range-oversampled data from operational radar scans and that works with radar returns from both weather and ground clutter. In this paper, the method is described, tested using simulations, and validated with time series data. [ABSTRACT FROM AUTHOR]

A fundamental assumption for the application of range-oversampling techniques is that the correlation of oversampled signals in range is accurately known. In this paper, a theoretical framework is derived to quantify the effects of inaccurate range correlation measurements on the performance of such techniques, which include digital matched filtering and those based on decorrelation (whitening) transformations. It is demonstrated that significant reflectivity biases and increased variance of estimates can occur if the range correlation is not accurately measured. Simulations and real data are used to validate the theoretical results and to illustrate the detrimental effects of mismeasurements. Results from this work underline the need for reliable calibration in the context of range-oversampling processing, and they can be used to establish appropriate accuracy requirements for the measurement of the range correlation on modern weather radars. [ABSTRACT FROM AUTHOR]

The range-weighting function (RWF) determines how individual scatterer contributions are weighted as a function of range to produce the meteorological data associated with a single resolution volume. The RWF is commonly defined in terms of the transmitter pulse envelope and the receiver filter impulse response, and it determines the radar range resolution. However, the effective RWF also depends on the range-time processing involved in producing estimates of meteorological variables. This is a third contributor to the RWF that has become more significant in recent years as advanced range-time processing techniques have become feasible for real-time implementation on modern radar systems. In this work, a new formulation of the RWF for weather radars that incorporates the impact of signal processing is proposed. Following the derivation based on a general signal processing model, typical scenarios are used to illustrate the variety of RWFs that can result from different range-time signal processing techniques. Finally, the RWF is used to measure range resolution and the range correlation of meteorological data. [ABSTRACT FROM AUTHOR]

This paper describes a real-time implementation of adaptive range oversampling processing on the National Weather Radar Testbed phased-array radar. It is demonstrated that, compared to conventional matched-filter processing, range oversampling can be used to reduce scan update times by a factor of 2 while producing meteorological data with similar quality. Adaptive range oversampling uses moment-specific transformations to minimize the variance of meteorological variable estimates. An efficient algorithm is introduced that allows for seamless integration with other signal processing functions and reduces the computational burden. Through signal processing, a new dimension is added to the traditional trade-off triangle that includes the variance of estimates, spatial coverage, and update time. That is, by trading an increase in computational complexity, data with higher temporal resolution can be collected and the variance of estimates can be improved without affecting the spatial coverage. [ABSTRACT FROM AUTHOR]

Processing oversampled signals in range with a whitening transformation has been proposed as a means to reduce the variance of meteorological variable estimates on polarimetric Doppler weather radars. However, the original formulation to construct decorrelation transformations does not account for mismatches in the polarimetric channels, which results in abnormally biased polarimetric variable estimates if the two channels are not perfectly matched. This paper extends the initial formulation and demonstrates that, by properly accounting for the differences in the polarimetric channels, it is always possible to produce optimum estimates of all meteorological variables. Simulation analyses based on the reported characteristics of existing polarimetric radars are included to illustrate the performance of the proposed transformations. [ABSTRACT FROM AUTHOR]

The article considers the calculation of the Doppler effect for sound. The equation used in measuring the Doppler effect is described. The application of the Doppler-shifted frequency of free-falling sound to determine the acceleration of gravity is discussed. A review of the previous attempt to measure the acceleration of gravity is provided.

This paper describes the implementation of the staggered pulse repetition time (PRT) technique on NOAA's research and development WSR-88D in Norman, Oklahoma. The prototype algorithm incorporates a novel rule for the correct assignment of Doppler mean velocity that is needed to accommodate arbitrary stagger ratios. Description of the rule, consideration of errors, and choice of appropriate stagger ratios are presented. The staggered PRT algorithm is integrated with the standard processing on the WSR-88D, some details of which are included in the paper. A simple ground clutter canceller removes the pure complex time series mean (DC) component from autocovariance estimates; censoring of overlaid echoes and thresholding are equivalent to those used on the WSR-88D. Further, a cursory verification of statistical errors indicates good agreement with theoretical expectations. Although the staggered PRT algorithm operates in real time, it was advantageous to collect several events of staggered PRT time series data for further scrutiny. Results presented from one of the events demonstrate the potency of the staggered PRT to mitigate range and velocity ambiguities. [ABSTRACT FROM AUTHOR]

Pseudowhitening of oversampled signals in range is proposed as a method to improve the performance of spectral moment and polarimetric variable estimators on weather surveillance radars. In an attempt to overcome the noise sensitivity of the whitening transformation, a solution based on the minimum mean-square-error criterion is considered first; however, this transformation is less practical than whitening because it requires knowledge of the signal-to-noise ratio at every range location. Pseudowhitening techniques ae introduced as practical solutions that achieve a suboptimal compromise between variance reduction and noise sensitivity. Based on regularization methods for the solution of ill-conditioned problems, two pseudowhitening schemes are proposed: the clipped singular value decomposition transformation and the sharpening filter. By comparing their statistical performance with theoretical minimum bounds, it is shown that pseudowhitening-based estimators are almost optimal under practical conditions. Estimators based on pseudowhitening techniques avoid the pitfalls of their whitening-transformation-based counterparts and lead to more accurate radar products and/or rapid data acquisition for a much wider range of signal-to-noise ratios. [ABSTRACT FROM AUTHOR]

A radar antenna intercepts thermal radiation from various sources including the ground, the sun, the sky, precipitation, and man-made radiators. In the radar receiver, this external radiation produces noise that constructively adds to the receiver internal noise and results in the overall system noise. Consequently, the system noise power is dependent on the antenna position and needs to be estimated accurately. Inaccurate noise power measurements may lead to reduction of coverage if the noise power is overestimated or to radar data images cluttered by noise speckles if the noise power is underestimated. Moreover, when an erroneous noise power is used at low-to-moderate signal-to-noise ratios, estimators can produce biased meteorological variables. Therefore, to obtain the best quality of radar products, it is desirable to compute meteorological variables using the noise power measured at each antenna position. In this paper, an effective method is proposed to estimate the noise power in real time from measured powers at each radial. The technique uses a set of criteria to detect radar range resolution volumes that do not contain weather signals and uses those to estimate the noise power. The algorithm is evaluated using both simulated and real time series data; results show that the proposed technique accurately produces estimates of the system noise power. An operational implementation of this technique is expected to significantly improve the quality of weather radar products with a relatively small computational burden. [ABSTRACT FROM AUTHOR]

Demonstration of a method for improved Doppler spectral moment estimation is made on NOAA's research and development Weather Surveillance Radar-1988 Doppler (WSR-88D) in Norman, Oklahoma. Time series data have been recorded using a commercial processor and digital receiver whereby the sampling frequency is several times larger than the reciprocal of the transmitted pulse width. The in-phase and quadrature-phase components of oversampled weather signals are used to estimate the first three spectral moments by suitably combining weighted averages in range with usual processing at fixed range locations. The weights are chosen in such a manner that the resulting signals become uncorrelated. Consequently, the variance of estimates decreases significantly as is verified by this experiment. [ABSTRACT FROM AUTHOR]