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Richard J. Doviak

Abstract

Several methods used to estimate rainfall rate R are surveyed. The distribution N(D) of drop sizes is of central importance in determining the reflectivity factor Z, attenuation rate K, and R. With single-parameter measurement techniques either of the remotely sensed parameters Z or K can he used to estimate R when gross assumptions on N(D) can be made. If N(D) can be described by a two-parameter distribution, dual measurement techniques can better estimate R without invoking these coarse assumptions. A review is made of three techniques whereby two variables might be measured. 1) dual wavelength in which Z and K are remotely measured, 2) dual polarization in which reflectivity is measured with two orthogonal polarizations, and 3) raingage-radar combinations whereby in situ point measurements of R and radar measurement of Z or R are combined to obtain a better assessment of rain over areas between gages.

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Ming Fang and Richard J. Doviak

Abstract

Contrary to accepted usage, the second central moment of the Doppler spectrum is not the sum of the second central moments of individual spectral broadening mechanisms. A rigorous theoretical derivation of the spectrum width observed with short dwell times reveals that the sum cannot strictly be taken for the variances associated with various spectral broadening mechanisms and that an added-term coupling shear with turbulence is needed. Furthermore, shear and antenna rotation are coupled. The theoretical expressions derived herein apply to radars with fixed or scanning beams.

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Richard J. Doviak and Runsheng Ge

Abstract

Doppler radar and a 444 m tall instrumented tower provide a detailed view of the kinematic and thermodynamic structure of a solitary gust. A study of the data fields, and comparison with theoretical and laboratory work leads to the conclusion that the gust is an internal solitary wave of permanent form launched by a thunderstorm outflow onto an inversion layer formed by the passage of an earlier storm. Comparisons with results from fluid experiments and numerical models are made and the similarities are striking. Both observations show turbulent breakdown at the rear of the wave. The ease with which solitary waves can be generated in experiments gives reason to believe that these nonlinear waves might be of considerable interest in the context of geophysical fluid dynamics.

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Guifu Zhang and Richard J. Doviak

Abstract

The theory of measuring crossbeam wind, shear, and turbulence within the radar’s resolution volume V6 is described. Spaced-antenna weather radar interferometry is formulated for such measurements using phased-array weather radar. The formulation for a spaced-antenna interferometer (SAI) includes shear of the mean wind, allows turbulence to be anisotropic, and allows receiving beams to have elliptical cross sections. Auto- and cross-correlation functions are derived based on wave scattering by randomly distributed particles. Antenna separation, mean wind, shear, and turbulence all contribute to signal decorrelation. Crossbeam wind cannot be separated from shear, and thus crossbeam wind measurements are biased by shear. It is shown that SAI measures an apparent crossbeam wind (i.e., the angular shear of the radial wind component). Whereas the apparent crossbeam wind and turbulence within V6 cannot be separated using monostatic Doppler techniques, angular shear and turbulence can be separated using the SAI.

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Guifu Zhang and Richard J. Doviak

Abstract

The theory of spaced-antenna interferometry (SAI) is formulated to detect and locate deterministic objects and reflectivity inhomogeneities embedded within the phased-array weather radar’s resolution volume V 6 and to improve weather radar performance. An analogy is made between monopulse tracking and SAI. The cross-correlation function and its power spectrum are derived based on wave scattering by a large deterministic object and clusters of randomly distributed precipitation particles. It is shown that nonuniform beam filling leads to an effective narrower beam and an increase in cross-correlation coefficient at zero lag. Hence, an individual object or a subvolume inhomogeneity can be detected and located by SAI. This capability further enhances the potential applications of phased-array weather radar used as a multimission system.

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Michael J. Istok and Richard J. Doviak

Abstract

A technique to separate ordered flow in a tornadic thunderstorm from the random velocities associated with turbulence is described. The relative importance of the ordered flow shear and turbulence in the broadening of the Doppler velocity spectrum is evaluated by least-squares fitting an assumed linear model of radial velocities to measured ones over an angular analysis domain (about 3° in azimuth and 3° in elevation). Fields and cumulative probabilities of Doppler spectral widths associated with turbulence and velocity shear, of root-mean-square (rms) velocity residuals, and of the turbulent kinetic energy dissipation rates ε are presented. In order to estimate ε from measurements of Doppler spectral width, the outer scale of the inertial subrange of turbulence must be at least three times larger than the size of the radar's resolution volume. Wind fields synthesized from the Doppler data of two radars are related to the turbulent kinetic energy dissipation rate and rms velocity residual fields. The observed relationship between wind gradients, rms residuals, and dissipation rates suggests the expected cascade of turbulent kinetic energy as it moves from the largest length scales down to the smallest.

Within this storm, turbulence contributed much more to spectral broadening than ordered flow shear. However, in a very small portion of the storm, shear and nonturbulent eddies are responsible for nearly all spectral broadening. Fifty percent of the volume of this tornadic storm had ε larger than 0.1 m2 s−3.

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Ming Fang, Richard J. Doviak, and Valery Melnikov

Abstract

Spectrum widths, one of the three moments measured and displayed by the Weather Surveillance Radar-1988 Doppler (WSR-88D), are categorized for various weather conditions showing both expected and unexpected results. Weather phenomena are classified into seven categories based on radar observations, and the statistics of the censored spectrum width fields for each of the categories are obtained. Daytime fair weather without birds, stratiform rain and snow, and isolated tornadic storms produce weather signals that have the smallest volumetric median values of spectrum widths (i.e., < 2 m s−1). Surprisingly, the median spectrum width values in the isolated tornadic storms are as low (i.e., <2 m s−1) as in the fair weather (without the presence of echoes from birds). The median spectrum width value from fair weather regions contaminated with bird echoes is larger (i.e., 3.0 m s−1). The largest median spectrum width values, ranging from 4.0 to 5.4 m s−1, are associated with embedded areal squall lines. Clusters of severe storms and storms along broken squall lines appear to have median spectrum width values between these two regimes. Spectrum width fields are also shown to be more prone to errors than fields of reflectivity and velocity. Errors mainly result from overlaid echoes, improper automatic gain control (AGC) settings, low signal-to-noise ratios, and incorrect estimates of noise power. Thus spectrum width data fields require extensive censoring. The most persistent errors appear to be those related to overlaid weather signals and low signal-to-noise ratios.

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Valery M. Melnikov and Richard J. Doviak

Abstract

Weather radar observations of stratiform precipitation often reveal regions having very large measured Doppler spectrum widths, exceeding 7, and sometimes 10, m s−1. These widths are larger than those typically found in thunderstorms; widths larger than 4 m s−1 are associated with moderate or severe turbulence in thunderstorms. In this work, stratiform precipitation has been found to have layers of widths larger than 4 m s−1 in more than 80% of cases studied, wherein the shear of the wind on scales that are large compared to the dimensions of the radar resolution volume is the dominant contributor to spectrum width. Analyzed data show that if width ≤7 m s−1, and if the layers are not wavy or patchy, these layers have weak turbulence. On the other hand, regions having widths >4 m s−1 in patches or in wavelike structures are likely to have moderate to severe turbulence with the potential to be a hazard to safe flight. To separate the contributions to spectrum width from wind shear and turbulence and to evaluate the errors in turbulence estimates, data have been collected with elevation increments much less than a beamwidth. Despite beamwidth limitations, the small elevation increments reveal impressive structures in the fields. For example, the “cat’s eye” structure associated with Kelvin–Helmholtz waves is clearly exhibited in the fields of spectrum width observed at low-elevation angles, but not in the reflectivity or velocity fields. Reflectivity fields in stratiform precipitation are featureless compared to spectrum width fields.

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Dusan S. Zrnic and Richard J. Doviak

Abstract

Doppler velocity spectra of a combined Rankine model vortex are computed by assuming a Gaussian antenna pattern, various vortex sizes, pulse volume depths, and reflectivity profiles. Both very narrow and very broad antenna beamwidths may produce bimodal spectra. Most often, the theoretically derived spectra exhibit a rapid power decrease for spectral components near maximum velocity which agrees with an experimental observation previously reported.

In spring 1973, NSSL's 10 cm, high-resolution Doppler radar scanned the vicinity of a large tornado that devastated Union City, Okla. Digital radar samples were recorded and Fourier-analyzed to derive power spectra for sample volumes spaced about the vortex location. Power spectra were examined for white noise type signatures that indicated vortex rotation contained within the radar sample volume. Spectra were simulated using radar and tornado cyclone parameters matched to those existing during the observations to determine spectral features for comparison with those recorded by the pulse-Doppler radar. The reflectivity throughout and around the funnel was uniform and spectra compared well. Although the precise vortex center location could not be deduced its position was consistent with tornado position determined from film documentation. In the gates containing vortex signatures spectral standard deviations were consistently maximal.

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Richard J. Doviak and Claude M. Weil

Abstract

Recent operation of the Valley Forge-Wallops Island bistatic radar link during two days characterized by light rain and drizzle provided some detailed, bistatically derived information on atmospheric structure in the vicinity of Wallops Island. Data are presented that give unambiguous evidence of the simultaneous bistatic and monostatic radar detection of the melting layer. The height of the melting layer, as measured in the bistatic mode, has been confirmed by both radar backscatter measurements and radiosonde data. Methods used in interpreting forward-scatter data are discussed and approximate values for the layer thickness and reflectivity are derived.

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