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Alexander Ryzhkov
and
Dusan Zrnić

Abstract

This paper examines some effects of drop size distribution and shape on the rainfall-rate estimates obtained from the specific differential phase. An algorithm that uses exclusively the specific differential phase is presented, and performance of this algorithm is examined by applying it to 15 storm events in Oklahoma that include heavy and light rainfalls. Radar-derived cumulative rainfall is compared to total rain measured by gauges in a dense gauge network in Oklahoma for each of the events.

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Dusan Zrnic
and
Michael Istok

Abstract

Doppler spectra of a tornado were collected with a radar having a large unambiguous velocity range, ±91 m s−1. Thus for the first time a presentation of nonaliased spectra was possible, showing direct measurement of radial velocities. By fitting the tornado model spectrum to data, the radius of maximum winds and tornado center location are deduced. Tornado spectral signature is defined as a double peak, symmetric with respect to the mean wind spectrum. Histograms of maximum measured wind speeds (from spectrum skirts) for two tornadic storms are obtained, and the histograms of velocity difference (between the left and right spectrum skirt) suggest that smaller scale turbulence (<500 m) is principally responsible for spectrum broadness.

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Robert Rabin
and
Dusan Zrnic

Abstract

The VAD technique is applied to unevenly spaced data obtained with two nearby Doppler weather radars in the optically clear atmosphere. Assuming that the power of higher order harmonies can be neglected, a least-squares fit method obtains the zeroth and first harmonies. The VAD results are compared with a detailed dual Doppler-radar analysis of a nearby area. The divergence found by both methods is explained in terms of the synoptic weather situation. The value of single Doppler weather radar is demonstrated in determining subsynoptic vertical winds in clear air. Inherent errors are briefly discussed.

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Dúsan S. Zrnić

Abstract

The concept of the polarimetric scattering matrix applicable to hydrometeors is reviewed to indicate the total number of measurands that is possible from a radar system with two orthogonal linear polarizations. It is shown how to obtain this complete set of polarimetric measurands together with Doppler spectral moments through a single receiver by proper choice of polarization in a transmit-receive sequence pair.

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Dusan Zrnić
and
David Schvartzman

Abstract

We review cubic phase codes for mitigating ambiguities in range and velocity before introducing two specific codes. The two have periodicities of 5 and 7 samples for both the transmitted and the modulation code sequences. The short periods are suitable for generating codes of arbitrary length starting with about 15. We abbreviate the two codes with L5 and L7 and describe generation of the codes starting with kernels (i.e., minimum length sequences that repeat to generate the codes of desired lengths). The L5 modulation code produces 5 spectral replicas of the coded signal and the L7 produces 7. We apply the L7 code to a sinusoid and reveal spectra of the modulated signals from several ambiguous range intervals. Through simulation, we show application to weatherlike signals and construct examples whereby two weather signals and ground clutter are overlaid. Using theory, we define the operating region of the codes in the signal parameter space. The region covers a wide range of overlaid returned powers and spectrum widths; it is obtained from simulations involving the L codes and the SZ(8/64) code. The technique is effective in distinguishing the returns from two trip regions separated by no more than L − 2 ambiguous range intervals and reconstructing the corresponding spectral moments. The L5 and L7 codes protect from trip returns up to the fifth and seventh, making them suitable for short-wavelength (3 and 5 cm) radars as their PRTs must be relatively short to accommodate the expected spread of velocities in storms.

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Alexander Ryzhkov
and
Dusan Zrnic

Abstract

Effects of beamfilling nonuniformities on the differential phase and rainfall estimation that use specific differential phase are examined. Two physical models are considered: an isolated rain cell with azimuthal dimensions comparable to the beamwidth and a sharp rain boundary approximating a squall line. The model results are compared to observations. An extension of the analysis to include observations of the melting layer is made. From this analysis emerges an interpretation of the radial profile of differential phase that varies from previous explanations. The current interpretation might be favored due to its simplicity and reliance on accepted physical properties of the melting layer.

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John W. Conway
and
Dušan S. Zrnić

Abstract

The origin and importance to embryo and hail production of a region of drops advected above the freezing level in the updraft of a severe Colorado hailstorm is examined using radar polarization measurements in conjunction with dual-Doppler and trajectory analysis. These drops, which give a distinct radar signature termed the “differential reflectivity column,” originate from 1) melted hydrometeors that fall from the back-sheared anvil, through the embryo curtain, and are recirculated into the storm updraft, and 2) in situ drop growth within the updraft. Some of the drops refreeze and likely produce frozen-drop hailstone embryos.

Numerous hailstone trajectories are found to cross either through, or over, the drop column where the hailstones undergo a significant growth phase. Two separate hailstone fallout regions are identified. Some hailstones in the northern fallout region show anticyclonic trajectories and in situ updraft and column growth. Others grow while crossing the top of the vault. Hailstones in the southern region exhibit growth while passing cyclonically through the column or over the vault.

A new method to determine hydrometeor fall speeds from radar polarization measurements for use with dual-Doppler analysis is introduced.

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Glenn R. Smythe
and
Dusan S. Zrnic

Abstract

A technique for tracking patterns of radial velocity and reflectivity data obtained with a single-Doppler radar is described. Application of the technique to two different scans of the same spatial region may lead to the extraction of a field of “wind” vectors with both radial and azimuthal components. This is accomplished by displacing, in range and azimuth, small volumes or “boxes” of data from the earlier scan and then correlating them with boxes of equal dimensions from the later scan. The displacements at which correlation coefficients maximize are assumed to be due to the advection of patterns existing at scales up to the “box” dimensions.

Correlation coefficients of radial velocities are shown, for the clear air cases analyzed, to be higher than those of reflectivity [dB(Z)]. “Winds” retrieved by correlating velocities and reflectivities independently are compared with each other and with winds synthesized from dual-Doppler radar data. Winds from radial velocity correlations agree better with the dual-Doppler winds than do winds from reflectivity correlations. Convective rolls spaced ∼5 km apart are revealed in the planetary boundary layer.

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R. J. Doviak
and
Dusan Zrnić

Abstract

Probert-Jones' radar equation assumes receiver bandwidth large compared to the reciprocal of the transmitted pulse width τ. The advent of coherent radars with precise transmitter frequencies allows consideration of receiver bandwidth “matched” to and sometimes smaller than τ−1 in order to enhance measurement signal-to-noise ratio.

An extension to the radar equation has been made to show explicitly the dependence of echo power on the product of transmitter pulse width and receiver bandwidth. When receiver bandwidth is less than twice τ−1, there is significant loss in echo power. This should be accounted for when estimating reflectivities.

Considerable improvement in Doppler velocity estimation can often be obtained by matching range resolution to the angular one and this has implications of practical importance when moderately sensitive dual-Doppler radars are used to map the mesoscale wind in clear air.

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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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