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- Author or Editor: Dúsan S. Zrnić x
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Abstract
Rainfall estimation from specific differential phases in meteorological situations with significant anomalous propagation (AP) is discussed. It is shown that the correlation coefficient between horizontally and vertically polarized backscatter signals and local variability of the total differential phase can be good identifiers of ground clutter–contaminated data. Further, it is suggested how to estimate rainfall in regions of ground clutter caused by AP.
Abstract
Rainfall estimation from specific differential phases in meteorological situations with significant anomalous propagation (AP) is discussed. It is shown that the correlation coefficient between horizontally and vertically polarized backscatter signals and local variability of the total differential phase can be good identifiers of ground clutter–contaminated data. Further, it is suggested how to estimate rainfall in regions of ground clutter caused by AP.
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.
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.
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.
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.
Abstract
This paper deals with the recovery of Doppler velocities in the presence of range overlaid echoes. Transmitted pulses are phase shifted to tag the echoes from scatterers, which are separated by the unambiguous range. A new systematic phase code and an algorithm for estimating the mean velocities of overlaid first- and second-trip signals are presented. The return samples are phase corrected to cohere the first- or the second-trip signal, leaving the other signal power spread in a deterministic manner across the Doppler spectrum. An algorithm has been developed to recover the velocity of the weaker signal even if the power ratio of overlaid signals is as large as 40 dB, for spectrum widths of 4 m s−1 or less, and an unambiguous velocity of 32 m s−1. Tests on simulated weather signals indicate that the method, employed in surveillance Doppler radars, can effectively double the unambiguous range without the sacrifice of the unambiguous velocity interval.
Abstract
This paper deals with the recovery of Doppler velocities in the presence of range overlaid echoes. Transmitted pulses are phase shifted to tag the echoes from scatterers, which are separated by the unambiguous range. A new systematic phase code and an algorithm for estimating the mean velocities of overlaid first- and second-trip signals are presented. The return samples are phase corrected to cohere the first- or the second-trip signal, leaving the other signal power spread in a deterministic manner across the Doppler spectrum. An algorithm has been developed to recover the velocity of the weaker signal even if the power ratio of overlaid signals is as large as 40 dB, for spectrum widths of 4 m s−1 or less, and an unambiguous velocity of 32 m s−1. Tests on simulated weather signals indicate that the method, employed in surveillance Doppler radars, can effectively double the unambiguous range without the sacrifice of the unambiguous velocity interval.
Abstract
This paper explores ground clutter filtering with a class of cancelers that use regression. Regression filters perform this task in a simple manner, resulting in similar or better performance than the fifth-order elliptic filter implemented in the WSR-88D. Assuming a slowly varying clutter signal, a suitable projection of the composite signal is used to notch a band of frequencies at either side of zero Doppler frequency. The complexity of this procedure is reduced by using a set of orthogonal polynomials. The frequency response of the resulting filter is related to the number of samples in each input block and the maximum order of approximating polynomials. Through simulations, it is demonstrated that the suppression characteristic of this filter is better than that of step-initialized infinite impulse response filters, whereby transients degrade the theoretical frequency response. The performance of regression filters is tested with an actual weather signal, and their efficiency in ground clutter canceling is demonstrated.
Abstract
This paper explores ground clutter filtering with a class of cancelers that use regression. Regression filters perform this task in a simple manner, resulting in similar or better performance than the fifth-order elliptic filter implemented in the WSR-88D. Assuming a slowly varying clutter signal, a suitable projection of the composite signal is used to notch a band of frequencies at either side of zero Doppler frequency. The complexity of this procedure is reduced by using a set of orthogonal polynomials. The frequency response of the resulting filter is related to the number of samples in each input block and the maximum order of approximating polynomials. Through simulations, it is demonstrated that the suppression characteristic of this filter is better than that of step-initialized infinite impulse response filters, whereby transients degrade the theoretical frequency response. The performance of regression filters is tested with an actual weather signal, and their efficiency in ground clutter canceling is demonstrated.
Abstract
Doppler radars offer unique data from which it is possible to estimate the turbulent eddy dissipation rates, ε. If the inertial subrange extends to lengths longer than the radar resolution volume size, ε can be obtained from the Doppler spectrum width. Spatial spectra of mean Doppler velocities can also yield ε estimates but only if a significant portion of the analysis length is contained within the inertial subrange. We compare dissipation rate estimates obtained with the two independent measurement techniques. At close range and vertical incidence, agreement between the two independent estimates of ε is within 10%. Furthermore, the slope of the spatial energy densities is very close to −5/3 predicted by Kolmogorov. The energy input is mainly from buoyancy-driven updrafts and the transition wavelength (about 3 km) between the input scale and the inertial subrange is consistent with the updraft-downdraft circulation cell, which is about 10 km. For a more distant storm at a range of 60 km, the filtering of mean velocities by the resolution volume precludes precise estimation of ε from spatial spectra of mean velocities.
Abstract
Doppler radars offer unique data from which it is possible to estimate the turbulent eddy dissipation rates, ε. If the inertial subrange extends to lengths longer than the radar resolution volume size, ε can be obtained from the Doppler spectrum width. Spatial spectra of mean Doppler velocities can also yield ε estimates but only if a significant portion of the analysis length is contained within the inertial subrange. We compare dissipation rate estimates obtained with the two independent measurement techniques. At close range and vertical incidence, agreement between the two independent estimates of ε is within 10%. Furthermore, the slope of the spatial energy densities is very close to −5/3 predicted by Kolmogorov. The energy input is mainly from buoyancy-driven updrafts and the transition wavelength (about 3 km) between the input scale and the inertial subrange is consistent with the updraft-downdraft circulation cell, which is about 10 km. For a more distant storm at a range of 60 km, the filtering of mean velocities by the resolution volume precludes precise estimation of ε from spatial spectra of mean velocities.
Abstract
A procedure to filter the ground clutter from a dual-polarized, staggered pulse repetition time (PRT) sequence and recover the complex spectral coefficients of the weather signal is presented. While magnitude spectra are sufficient for estimation of the spectral moments from staggered PRT sequences, computation of differential phase in dual-polarized radars requires recovery of the complex spectra. Herein a method is given to recover the complex spectral coefficients after the ground clutter is filtered. Under the condition of “narrow” spectra, it is possible to recover the differential phase, ΦDP, and the copolar correlation coefficient, ρ hv, accurately, in addition to the differential reflectivity, Z DR. The technique is tested on simulated time series and on actual radar data. The efficacy of the method is demonstrated on plan position indicator (PPI) plots of polarimetric variables.
Abstract
A procedure to filter the ground clutter from a dual-polarized, staggered pulse repetition time (PRT) sequence and recover the complex spectral coefficients of the weather signal is presented. While magnitude spectra are sufficient for estimation of the spectral moments from staggered PRT sequences, computation of differential phase in dual-polarized radars requires recovery of the complex spectra. Herein a method is given to recover the complex spectral coefficients after the ground clutter is filtered. Under the condition of “narrow” spectra, it is possible to recover the differential phase, ΦDP, and the copolar correlation coefficient, ρ hv, accurately, in addition to the differential reflectivity, Z DR. The technique is tested on simulated time series and on actual radar data. The efficacy of the method is demonstrated on plan position indicator (PPI) plots of polarimetric variables.
Abstract
Simultaneous transmission and reception of horizontally and vertically polarized waves is a preferable choice technique for dual-polarization weather radar. One of the consequences of such a choice is possible cross-coupling between orthogonally polarized waves. Cross-coupling depends on depolarizing properties of propagation media, and it is usually negligible in rain because the net mean canting angle of raindrops is close to zero.
Snow crystals at the tops of thunderstorm clouds are often canted in the presence of strong electric fields and produce noticeable cross-coupling between radar signals at horizontal and vertical polarizations if both signals are transmitted and received simultaneously. As a result, peculiar-looking radial signatures of differential reflectivity Z DR and differential phase ΦDP are commonly observed in the crystal regions of thunderstorms.
The paper presents examples of strong depolarization in oriented crystals from the data collected by the polarimetric prototype of the Weather Surveillance Radar-1988 Doppler (WSR-88D) and a theoretical model that explains the results of measurements. It is shown that the sign and magnitude of the Z DR and ΦDP signatures strongly depend on the orientation of crystals and a system differential phase on transmission.
Abstract
Simultaneous transmission and reception of horizontally and vertically polarized waves is a preferable choice technique for dual-polarization weather radar. One of the consequences of such a choice is possible cross-coupling between orthogonally polarized waves. Cross-coupling depends on depolarizing properties of propagation media, and it is usually negligible in rain because the net mean canting angle of raindrops is close to zero.
Snow crystals at the tops of thunderstorm clouds are often canted in the presence of strong electric fields and produce noticeable cross-coupling between radar signals at horizontal and vertical polarizations if both signals are transmitted and received simultaneously. As a result, peculiar-looking radial signatures of differential reflectivity Z DR and differential phase ΦDP are commonly observed in the crystal regions of thunderstorms.
The paper presents examples of strong depolarization in oriented crystals from the data collected by the polarimetric prototype of the Weather Surveillance Radar-1988 Doppler (WSR-88D) and a theoretical model that explains the results of measurements. It is shown that the sign and magnitude of the Z DR and ΦDP signatures strongly depend on the orientation of crystals and a system differential phase on transmission.
Abstract
The authors demonstrate that there are maximum measurable (saturation) spectrum widths for standard autocovariance techniques, the 0,1-lag autocovariance estimator and the 1,2-lag estimator. The maximal mean measurable spectrum widths from the two estimators depend on the number of samples and are substantially lower than the Nyquist velocity. Furthermore the maximal mean spectrum width of the 1,2-lag algorithm is approximately 2 times smaller than the maximum mean width of the 0,1-lag estimator. Simulated signals, solar noise, and weather signals are processed to verify theoretical predictions.
Abstract
The authors demonstrate that there are maximum measurable (saturation) spectrum widths for standard autocovariance techniques, the 0,1-lag autocovariance estimator and the 1,2-lag estimator. The maximal mean measurable spectrum widths from the two estimators depend on the number of samples and are substantially lower than the Nyquist velocity. Furthermore the maximal mean spectrum width of the 1,2-lag algorithm is approximately 2 times smaller than the maximum mean width of the 0,1-lag estimator. Simulated signals, solar noise, and weather signals are processed to verify theoretical predictions.
