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Sebastián M. Torres

Abstract

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.

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Sebastián M. Torres and David Schvartzman

Abstract

We propose a simulation framework that can be used to design and evaluate the performance of adaptive scanning algorithms on different phased-array weather radar designs. The simulator is proposed as tool to 1) compare the performance of different adaptive scanning algorithms on the same weather event, 2) evaluate the performance of a given adaptive scanning algorithm on several weather events, and 3) evaluate the performance of a given adaptive scanning algorithm on a given weather event using different radar designs. We illustrate the capabilities of the proposed framework to design and evaluate the performance of adaptive algorithms aimed at reducing the update time using adaptive scanning. The example concept of operations is based on a fast low-fidelity surveillance scan and a high-fidelity adaptive scan. The flexibility of the proposed simulation framework is tested using two phased-array-radar designs and three complementary adaptive scanning algorithms: focused observations, beam clustering, and dwell tailoring. Based on a significant weather event observed by an operational NEXRAD radar, our experimental results consist of radar data that were simulated as if the same event had been observed by arbitrary combinations of radar systems and adaptive scanning configurations. Results show that simulated fields of radar data capture the main data-quality impacts from the use of adaptive scanning and can be used to obtain quantitative metrics and for qualitative comparison and evaluation by forecasters. That is, the proposed simulator could provide an effective interface with meteorologists and could support the development of concepts of operations that are based on adaptive scanning to meet the evolutionary observational needs of the U.S. National Weather Service.

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Christopher D. Curtis and Sebastián M. Torres

Abstract

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.

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Sebastián M. Torres and Christopher D. Curtis

Abstract

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 range-oversampling 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.

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Christopher D. Curtis and Sebastián M. Torres

Abstract

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.

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Sebastián M. Torres and Christopher D. Curtis

Abstract

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.

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Sebastian M. Torres and Dušan S. Zrnić

Abstract

A method to reduce errors in estimates of polarimetric variables beyond those achievable with standard estimators is suggested. It consists of oversampling echo signals in range, applying linear transformations to decorrelate these samples, processing in time the sequences at fixed range locations to obtain various second-order moments, averaging in range these moments, and, finally, combining them into polarimetric variables. The polarimetric variables considered are differential reflectivity, differential phase, and the copolar correlation coefficient between the horizontally and vertically polarized echoes. Simulations and analytical formulas confirm a reduction in variance proportional to the number of samples within the pulse compared to standard processing of signals behind a matched filter. This reduction is possible, however, if the signal-to-noise ratios (SNRs) are larger than a critical value. Plots of the critical SNRs for various estimates as functions of Doppler spectrum width and other parameters are provided.

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Sebastián M. Torres and Christopher D. Curtis

Abstract

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.

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Sebastián M. Torres and Dušan S. Zrnić

Abstract

A method for estimation of spectral moments on pulsed weather radars is presented. This scheme operates on oversampled echoes in range; that is, samples of in-phase and quadrature-phase components are collected at a rate several times larger than the reciprocal of the transmitted pulse length. The spectral moments are estimated by suitably combining weighted averages of these oversampled signals in range with usual processing of samples (spaced at the pulse repetition time) at a fixed range location. The weights in range are derived from a whitening transformation; hence, the oversampled signals become uncorrelated and, consequently, the variance of the estimates decreases significantly. Because the estimate errors are inversely proportional to the volume scanning times, it follows that storms can be surveyed much faster than is possible with current processing methods, or equivalently, for the current volume scanning time, accuracy of the estimates can be greatly improved. This significant improvement is achievable at large signal-to-noise ratios.

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Christopher D. Curtis and Sebastián M. Torres

Abstract

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.

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