Range and velocity ambiguities significantly impact weather radar measurements, particularly dual-polarization variables in simultaneous transmission mode. A key challenge is determining the unambiguous range interval from which returns originate, especially in the presence of overlaid returns that obscure polarimetric estimates. This article presents a novel dual-PRF processing algorithm that blends long- and short-PRT data to recover polarimetric variables in contaminated regions. Two approaches are proposed: designing pulse sequences that inherently produce similar quality of polarimetric variables or applying adaptive range-averaging techniques when pulse sequences cannot be modified. The performance is demonstrated through both time-series simulations and actual radar observations. Results from real data analysis show high consistency between data from the long- and short-PRT sequences, with Pearson correlation coefficients exceeding 0.81 for all polarimetric variables. These advancements improve the operational utility of dual-PRF Batch mode scanning, providing a practical solution for enhanced dual-polarization measurements in weather radar networks.

This addresses errors in [1]. A typographical error appears in several equations. The equation numbers are listed with the corresponding correction.

Pointed herein are differences between turbulence measurements by radars with conventional pencil bean antennas and electronically steering Phased Array Radar (PAR) antennas. Differences are caused by the shape and orientation of the beam cross section on phased array antenna. These depend on the pointing direction and everywhere except at broadside the beam cross section is approximately elliptical. A formalism applicable to pencil beams of circular cross section is extended to elliptic beam cross sections. For lateral dimensions of the radar resolution volume larger than its range extent an approximate formula is suggested for computing the eddy dissipation rate ε. A field of ε1/3indicative of turbulence affecting aircraft and obtained with a digital PAR is presented as well as values along a radial pointing at a 41.5° elevation.

A measurement procedure to determine transmitted differential phase between horizontally and vertically polarized radiation of a dual-polarization radar is presented. It is applicable to radars that transmit and receive Simultaneously Horizontally and Vertically (SHV) polarized waves. The method relies only on power measurements and leverages capabilities of polarimetric radars with independent transmitters per polarization to estimate differential phase on transmission. Measurements using this method by ground and airborne systems are conducted, and results are validated using a software-defined radio that provides true phase measurements. The differential phase estimate produced with the proposed method for the PX-1000 (X-band) radar is -105°, while that produced with the software-defined radio is -104.47° ±4.43°. The proposed method with a simple power sensor achieves a precision of ±2.5°.

It is shown that in the simultaneous dual-polarization radar mode, the differential phase ($\beta $) between the orthogonally polarized waves impinging on hail affects the polarimetric variables. This effect is caused by interference of the polarized waves scattered by nonspherical particles. The$\beta $impact is considered for dry hail and water-coated hailstones. For the hailstones’ canting angles oriented uniformly relative to the vertical, reflectivity and differential reflectivity do not depend on$\beta $, but the correlation coefficient between the polarized waves and phase upon scattering do. Tumbling of falling hailstones is considered using the Fisher distribution of the orientation angles. It is shown that the$\beta $impact enhances with increasing tumbling. The$\beta $impact should be considered in hail detection methods utilizing the correlation coefficient. The potential of using the differential phase upon scattering in hail detection and sizing is also discussed.

We use a commercially available full-wave electromagnetic (EM) tool to model scattering off rough hail. Through modeling various axis ratios and surface roughness, we systematically evaluate their effect on the polarimetric variables used for hail size discrimination. Our results produce the differential reflectivity and the copolar correlation coefficient typically not achieved using forward operators. We compare our results with available information in the literature. The inclusion of the additional shape parameter brings new insights into problems associated with the polarimetric variable for hailstone size gauging. Finally, using dual-polarization weather radars’ (WSR-88Ds’) observations of a hail storm on two opposite sides, we hypothesize that the source of negative differential reflectivity is wet oblate hail in the resonant size range.

This letter combines a time-domain modeling and simulation method for evaluating the impacts of system modules on polarimetric data quality of phased array weather radars with both theoretical analysis and actual measurements. In the presented phased array radar system simulator (PASIM), the distributed weather returns are modeled by randomly distributed scatterers, and Next-Generation Radar (NEXRAD) Level-II data or user-defined weather scenarios are utilized as weather truth fields. Based on a specially designed patch element, a dual-polarization phased array mobile demonstration system (Ten Panel Demonstrator or TPD) is simulated. In addition, the biases of differential reflectivity, copolar correlation coefficient, and differential phase along beam direction away from the broadside in principal plane and nonprincipal plane are used as data quality metrics. Moreover, theoretical analysis, system simulation, and actual TPD proof of concept measurements in a stratiform precipitation and a convective precipitation are presented, respectively, then similarities and discrepancies between simulations and measurements are compared and explained.

Future weather radar systems will need to provide rapid updates within a flexible multifunctional overall radar network. This naturally leads to the use of electronically scanned phased array antennas. However, the traditional multifaced planar antenna approaches suffer from having radiation patterns that are variant in both beam shape and polarization as a function of electronic scan angle; even with practically challenging angle-dependent polarization correction, this places limitations on how accurately weather can be measured. A cylindrical array with commutated beams, on the other hand, can theoretically provide patterns that are invariant with respect to azimuth scanning with very pure polarizations. This paper summarizes recent measurements of the cylindrical polarimetric phased array radar demonstrator, a system designed to explore the benefits and limitations of a cylindrical array approach to these future weather radar applications.

On phased-array radars, scanning is done by stepping the beam from one direction to the next direction and dwelling long enough at each direction to achieve acceptable errors of estimates. Combining data from the three directions is suggested to obtain superresolution similar to that available on the national network of weather radar (Weather Surveillance Radar-1988 Doppler or WSR-88D). Spectral analysis of such data is addressed, and it is demonstrated that the Doppler spectra of simply concatenated time series have very strong sidebands due to the discontinuity of the signals from the three beam positions. This artifact degrades the performance of the spectral clutter filters and other methods that rely on spectral processing to enhance the weather signal. Special adjustments of the signals at each range location before concatenating (splicing) are proposed to mitigate the effects of discontinuities in time and thus improve clutter filtering. The adjustment is such that the total information contained in the signal can be preserved in subsequent processing. Spectral quality of the concatenated signals is quantified via results from simulations. Samples of spectra obtained with the National Weather Radar Testbed are presented to substantiate the predictions. A ground clutter detector/filter accepted by the National Weather Service is applied to the conditioned time series data, and the ensuing fields of reflectivity factor and Doppler velocity are compared to the fields from which clutter had not been removed.

This letter proposes a design concept that can satisfy the requirements for weather observations with a multifunction polarimetric phased-array radar at about 1-min volume update time while meeting present aviation requirements.

To increase the scanning rate of phased-array radar by a factor of two or more, the contiguous transmission of two or more pulses toward two or more directions and simultaneous reception of weather echoes from those directions is employed. However, if there are strong gradients of reflectivity, mainlobe-to-sidelobe coupled echoes contaminate wanted mainlobe-to-mainlobe (m-m) coupled echoes and limit the accurate analysis of weather. To retrieve m-m echoes, a technique is derived that restores wanted m-m voltages for antenna sidelobe levels as high as -30 dB and the difference in echo power of 100 dB for two simultaneously sampled beam directions. The technique is demonstrated using data collected with the WSR-88D radar and simulating PAR operations.

We present a novel digital signal processing procedure, named eigenvalue signal processing (henceforth ESP), patented by the first author with Brookhaven Science Associates in 2013. The method enables the removal of the bias due to antenna coherent cross-channel coupling and is applicable in the LDR mode, the ATSR mode and the STSR orthogonal mode of weather radar measurements. In this paper, we focus on the LDR mode and consider copolar reflectivity at horizontal transmit (ZHH), cross-polar reflectivity at horizontal transmit (ZVH), linear depolarization ratio at horizontal transmit (LDRH) and degree of polarization at horizontal transmit (DOPH). The ESP (ESP) method is substantiated by an experiment carried out in November 2012 using C-band weather radar with a parabolic reflector located at the Selex ES-Gematronik facilities in Neuss, Germany. The experiment involved comparison of weather radar measurements taken 1.5 minutes apart in two hardware configurations, namely with cross-coupling on (cc-on) and cross-coupling off (cc-off). It is experimentally demonstrated that eigenvaluederived variables are invariant with respect to antenna coherent cross-channel coupling. This property had to be expected, since the eigenvalues of the Coherency matrix are SU(2) invariant.

We consider weather radar measurements at simultaneous transmission and simultaneous reception of horizontal and vertical polarizations and show that the degree of polarization at simultaneous transmit$(p_{s})$is related to differential reflectivity and copolar correlation coefficient at simultaneous transmit (namely,$Z_{\rm DR}^{s}$and$\rho_{hv}^{s}$). We evaluate the potential of degree of polarization at simultaneous transmit for weather radar applications. Ultimately, we explore the consequences of adjusting the transmit polarization state of dual-polarization weather radars to circular polarization.

This paper considers weather radar measurements at linear depolarization ratio (LDR) mode, consisting of transmission of horizontal polarization and simultaneous reception of the copolar (horizontal) and cross-polar (vertical) components of the returned wave. Such a system yields the coherency matrix, with four degrees of freedom. After a theoretical analysis of its structure and symmetries, we focus on three cross-polarization variables: LDR, cross-polar correlation coefficient at horizontal transmit (ρxh) , and degree of polarization at horizontal transmit (pH). The different properties of these variables with respect to backscattering and propagation are analyzed, together with the bias induced by antenna cross-channel coupling. It is demonstrated that the degree of polarization at horizontal transmit possesses attractive properties in terms of robustness to propagation effects and antenna cross-channel coupling.

We present a theoretical study of the bias in the copolar correlation coefficient caused by cross-polar radiation patterns and by unmatched horizontal and vertical copolar radiation patterns. The analysis of the bias induced by cross-polarization radiation is carried out for both modes of operation of polarimetric radars, designated as the simultaneous transmission and reception of horizontally and vertically polarized waves and the alternate transmission of horizontally and vertically polarized waves, respectively. The bias caused by unmatched horizontal and vertical copolar radiation patterns as a function of slight differences in pointing angles and beamwidths is also analyzed. In well-designed weather radars, for the purpose of hydrometeor classification, the overall acceptable bias in the copolar correlation coefficient should be less than about 0.01. The levels of cross-to-copolar gain ratios for acceptable performance are indicated. Ultimately, pointing angle and beamwidth tolerances are indicated for horizontal and vertical copolar antenna patterns.

This paper discusses ways to avoid and/or mitigate biases in polarimetric variables inherent to agile-beam planar phased-array radars. Two bias-avoiding schemes produce unbiased estimates of the polarimetric backscattering covariance matrix which are then combined into bias-free polarimetric variables. One concerns full polarimetric measurements and calls for adjusting the amplitudes and phases of the array elements so that the transmitted field equals that generated by a mechanically steered polarimetric weather radar antenna; this is followed by an additional adjustment of the received fields. The second scheme is also applicable to full polarimetric measurements but involves adjustments only of the received fields. Crucial to both schemes is decoupling of the Doppler effects from the terms of the covariance matrix. It is a significant part of the bias issue that had not been previously addressed. A scheme to reduce bias applicable to nondepolarizing media (i.e., diagonal backscattering matrix) is also addressed; it calls for multiplication of the fields received by each dipole as opposed to a combination of multiplication and addition required for full correction. The schemes are applied to the alternate transmission and simultaneous reception polarimetric mode and the simultaneous transmission and simultaneous reception mode.

It is becoming widely accepted that radar polarimetry provides accurate and informative weather measurements, while phased-array technology can shorten data updating time. In this paper, a theory of phased array radar (PAR) polarimetry is developed to establish the relation between electric fields at the antenna of the PAR and the fields in a resolution volume filled with hydrometeors. It is shown that polarimetric measurements with an electronically steered beam can cause measurement biases that are comparable to or even larger than the intrinsic polarimetric characteristics of hydrometeors. However, these biases are correctable if the transmitted electric fields are known. A correction to the measured scattering matrix that removes biases in meteorological variables is derived. The challenges and opportunities for weather sensing with a polarimetric PAR are discussed.

It is becoming widely accepted that radar polarimetry provides accurate and informative weather measurements, while phased array technology can shorten data updating time. In this paper, a theory of phased array radar polarimetry is developed, and the relationship between the wave field at the radar antenna coordinate and that at the hydrometeors is established, along with the correction matrix to the scattering matrix. The challenges and opportunities for the weather sensing are discussed.

An adaptive spectral technique for ground clutter and noise suppression in weather radar echoes is presented. This technique detects weak echoes that are masked by the residuals from ground clutter. The technique is demonstrated on two clear air cases observed with Doppler weather radar. After adaptive suppression of ground clutter and its residue, features appear over the Oklahoma City urban area where otherwise none could be seen. These are interpreted as birds' corridors between two lakes and along a river.

In this letter, we present a spectral technique for observation and analysis of scatterers' polarimetric attributes. This technique allows one to visualize the scatterers' spectral signatures as a function of azimuth, Doppler velocity, and polarimetric variable at the same time. Such visualization can be used to evaluate the participants of the detected motions, to understand what constitutes the polarimetric averages, and to provide resources for establishing intrinsic polarimetric values (functions) for different types of scatterers, which are necessary for the scatterers' classification algorithms. We demonstrate this technique on a clear-air case observed with the S-band polarimetric research radar in Norman, OK, on September 7, 2004. We discuss the preference for spectral density of backscatter differential phase versus other polarimetric spectral densities for the observations of clear air. The proposed visualization technique is not limited to observations of echoes in clear air and invites study of intrinsic properties for other types of scatterers.

In this paper, an investigation of the potential of rapid refractivity retrieval is presented. The retrieval technique utilizes radar phase measurements of ground clutter to derive near-surface refractivity, which has been commonly used as a proxy for humidity, given its close relation to vapor pressure. Surface humidity is an important meteorological parameter and has been known to play an important role in convective initiation. In this paper, the refractivity retrieval technique is exploited by using smaller numbers of samples for phase calculation, which is a fundamental process in refractivity retrieval. The impetus for this paper is to explore the possibility of rapid refractivity retrieval by exploiting the rapid beam-steering capability of a phased-array radar. Using the National Weather Radar Testbed in Norman, OK, a 64-pulse per radial raw-data set was collected for conventional refractivity processing. Then, subsets of the 64 samples were extracted to emulate shorter dwell periods and the corresponding more rapid experiments. The test cases that were considered are 2, 4, 8, 16, and 32 samples. Refractivity fields retrieved using smaller numbers of samples are compared against the reference field, which was obtained using the entire 64-sample data set. It will be shown that, statistically, significant refractivity fields can be obtained from as short as a two-sample dwell.

A new approach for the clear air velocity estimation in weather radar is presented. A combination of nonparametric with parametric spectral analysis allows us to identify and extract multiple processes caused by different scatterer types within a single radar resolution volume. An example of clear air observed using an S-band dual polarization radar is presented. Heretofore, migrating birds and wind-blown insects that are mixed within each resolution volume caused such data to be unusable for meteorological interpretation. In this paper, we construct power spectral densities of polarimetric variables. We use the polarimetric spectral densities to differentiate the scatterer types within the observed radar resolution volume. We demonstrate how our combination of non-parametric and parametric spectral analysis can be used to retrieve the true wind velocity in situations with severe contamination by biological scatterers.

Echoes detected by polarimetric weather radar in clear air contain signals from air and biological scatterers. Discriminating the various scatterer types from a composite echo is challenging due to variability in scatterres' quantity, azimuthal dependences of their polarimetric properties, and uneven mixing in resolution volumes. We use polarimetric spectral densities to estimate the volume content by constructing two dimensional (2D) histograms. The dimensions used to form image are Doppler velocity and polarimetric variable. The assimilation of these histograms in azimuth results in a 3D-azimuthal-spectral-histogram (3DASH). This representation allows us to use transparency for small occurrences to visualize the 3D-signatures of dominant content. The scatterer types have distinguishable signatures in 3DASH due to their diverse physical shapes, scattering properties, different headings, and speeds. 3DASH can help to understand what constitutes the polarimetric averages of the resolution volume. 3DASH can help provide resources for establishing intrinsic polarimetric values/functions for different types of biological scatterers, which are necessary for scatterer classification algorithms.

Several mechanisms are currently provided to alleviate effects of range overlaid echoes and velocity aliasing in the Weather Surveillance Radar-1988 Doppler (WSR-88D). However, due to limitations in these techniques, observation of severe weather phenomena is significantly impaired. This work presents results from a multi-year study at the National Severe Storms Laboratory dealing with methods to mitigate the effects of range and velocity ambiguities in the WSR-88D.

The polarimetric technique consists of simultaneous transmission and reception of Horizontally and Vertically polarized waves. Thus, transmitted polarization will be elliptical with equal horizontal and vertical components and arbitrary phase between the two. This scheme has been tested at NSSL on the NOAA research and development WSR-88D radar. Here reports on backscatter differential phase measurements with this radar. The radar also has a mode of transmitting horizontal polarization and receiving both the strong H and the weak V component (for short we refer to this mode as Linear Depolarization Ratio mode, LDR). Backscatter differential phase is considered a secondary polarimetric variable of lesser value for precipitation measurements than (the forward) specific differential phase or differential reflectivity. This is because backscatter differential phase is seldom significant. At 10 cm wavelength the only precipitation that can cause appreciable backscatter differential phase is hail. But it turns out that backscatter differential phase from other scatters provides two benefits. (1) it is suitable for discrimination between nonmeteorological scatters and precipitation and (2) it offers a way to calibrate (measure) the system differential phase. Of relevant and special importance is that, for some scatters, the measured total differential phase in the SHV scheme can differ from the value obtained in the sequential H, V scheme. The radar system contributes two distinct phases to the total differential phase. One is the differential phase in the transmission channel, the other is the differential phase in the receiver channel

Classification of meteorological and nonmeteorological radar echoes will be one of the key functions of the operational polarimetric NEXRAD radar. In this paper, basic principles of the classification for several cases are presented. The data were obtained from the polarimetric prototype of the NEXRAD radar.

The paper presents the scattering models of chaff that capture the essential polarimetric properties as well as some data to support the properties. Two simple scattering models are used to compute polarimetric variables. The models are Herzian dipole and thin wire antenna. The result shows that two models produce very similar results if the chaff length is half the radar wavelength or less.

The paper describes a technique to calibrate dual-polarization weather radar in the presence of a partial beam blockage. Radar reflectivity factor Z and differential reflectivity Z/sub DR/ can be calibrated using an idea of self-consistency among Z, Z/sub DR/, and specific differential phase K/sub DP/ for rain medium and polarization properties of dry snow and light rain.

The dataset analyzed is the first simultaneous in-situ and radar survey of phenomena associated with observed "columns" of differential reflectivity Z/sub dr/ and specific differential phase K/sub dp/ in a supercell storm. Further, no in situ measurements in regions of such enhanced Z/sub dr/ and K/sub dp/ have ever been reported. The measurements were made in an Oklahoma convective storm that formed in Kingfisher County, on May 17, 1995. Parcel and environmental freezing temperatures were near the 600 mb level (3.5 km AGL). Official observations of 2.5 cm hail were reported as well as a 40 m s/sup -1/ wind gust. Dual-polarization radar measurements were obtained with the NSSL's Cimarron radar. The in situ measurements are provided by the T-28 aircraft at a height of between 4.9 and 5.2 km (near 500 mb; about -5/spl deg/ C). These include temperature, vertical velocity and liquid water content (LWC), as well as hydrometeor size and concentration from the hail spectrometer and a foil impactor.

A method for estimation of Doppler 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 taken at a rate several times larger than the reciprocal of the transmitted pulse length. The aforementioned radar variables are estimated by suitably combining weighted averages of these oversampled signals in range with the usual processing of samples (spaced at pulse repetition time) at a fixed range location. The weights in range are chosen such that the oversampled signals become uncorrelated and consequently the variance of the estimates decreases significantly. Because the estimates' errors are inversely proportional to the volume scanning times, it follows that storms can be surveyed much faster than it is possible with current processing methods, or equivalently, for the current volume scanning time, the accuracy of the estimates can be greatly improved.

The authors present observations of biological scatterers with a polarimetric weather radar. The radar has a pencil beam, a high power, and a wavelength of 10 cm. It transmits horizontally and vertically polarized waves alternately. The available polarimetric variables are differential reflectivity, differential phase, and correlation coefficient between orthogonally polarized returns. Two types of biological scatterers, insects and birds, are contrasted. Observed polarimetric signatures of these are compared and explained with a simple scattering model. Finally, the authors discuss the implications of recognizing the biological scatterers' type and the size of birds.

Presents observations of the copolar correlation coefficient between horizontally and vertically polarized echoes |/spl rho//sub h/spl nu//(0)|. These were made with ground-based and airborne weather radars at nearly vertical incidence. A sharp decrease of |/spl rho//sub h/spl nu//(0)| occurs at the bright band bottom, and is attributed to a varying mixture of hydrometeors with diverse shape, size, and thermodynamic phase. The largest contribution to decorrelation seems to come from wet aggregates; this is substantiated by consideration of two simple models. One consists of randomly oriented wet prolate spheroids, and the other considers an ensemble of distorted spheres. Prolates with axis ratios of 3 or distorted spheres with rms roughness equal to 15% of the diameter decrease the correlation to 0.8 at S band. At Ku band and for the size range encountered in the bright band, the decrease is a function of equivalent diameter because scattering is in the Mie regime. |/spl rho//sub h/spl nu//(0)| measurement at 13.8 GHz and from the aircraft are the first ever. Also, differential phase and differential reflectivity at a 10/spl deg/ off nadir are the first of its kind. These last two variables showed a distinct signature in the bright band. This is significant because it might lead to applications on airborne or spaceborne platforms.>

The authors describe the physics of adverse weather, the basics of Doppler engineering, and a host of advanced sensing systems-some with the ability to autonomously identify and track storm conditions-for all stages of airplane travel. Three major new Doppler radar systems are discussed: the next generation weather radar, the terminal Doppler weather radar, and the airport surveillance radar with a dedicated weather channel. Other relatively simple new instruments for aviation weather support include the low level wind shear alert system, the Doppler wind profilers, the automated weather observation system, and the automated surface observation system. These systems are designed to perform higher level functions such as detection, characterization, and hazard potential estimation of aviation-significant weather phenomena, as well as their communication and display automatically.>

Several methods for canceling ground clutter in Doppler weather radars which operate with staggered pulse repetition times (PRTs) are investigated. A scheme is developed which consists of two filters that operate sequentially, so that the overall filter is time-varying, with periodically changing coefficients. This filter is analyzed theoretically and through simulations for a stagger ratio of 3/2, which extends the unambiguous velocity interval. The amplitude characteristic of the filter over this interval is very good, but the phase characteristic, which is nonlinear in a small part of the interval, requires that a special decision logic be used for velocity estimation.>

The measurement of clear-air turbulence with a Doppler radar is investigated. An autoregressive moving average (ARMA) model is proposed to improve the Doppler spectral width estimates. An iterative algorithm that has its origin in system identification is used for the estimation of the ARMA parameters. By taking advantage of a priori knowledge of the correlation matrix, which arises in the derivation of the governing equations of the ARMA parameters, the ARMA spectral estimate can be improved. This improvement is shown in terms of bias and variance of the spectral width estimate.>

A unified approach to three eigendecomposition-based methods for frequency estimation in the presence of noise is presented. These are the Tufts-Kumaresan (TK) method, the minimum-norm (MN) method, and the total-least-squares (TLS) method. It is shown that the MN method is a modified version of the TK method and the TLS method is a generalization of the MN methods. The TLS solution vector is expressed in matrix form, and an alternate way of computing it is presented. The MN methods exhibit some improvement over the TK method.>

Linear-prediction-based methods are applied to mean Doppler estimation of radar signals in the presence of ground clutter when only a small number of samples is available for processing. The authors show the ability of these methods to resolve weather signals from ground clutter in unfavourable conditions, i.e. when the clutter is stronger and its spectrum is narrower than the signal's. It is shown that the Prony method can be applied to this task. In addition, given the a priori information about ground clutter, the Prony method can be simplified to derive a convenient formula for mean Doppler frequency estimation in the presence of ground clutter. This estimator can be considered as a generalization of the pulse-pair (PP) estimator. Such a scheme can give satisfactory results in resolving weather signals from ground clutter for signal-to-noise ratios (SNR) above 20 dB. The eigendecomposition-based minimum-norm method is applied to lower the SNR threshold to 10 dB. The methods are compared with combinations of various ground clutter filters and the PP estimator.>

Signal-to-noise ratio (SNR) in the output of a zero-memory nonlinearity is defined and found when the input is a complex Gaussian process. The results are applied to an odd\nu \primeth law device and to an analog-to-digital (A/D) converter exhibiting both saturation and quantization.