Distribution Of Echo Power Research Articles

High-range resolution spectral analysis of precipitation through range imaging of the Chung-Li VHF radar

Abstract. Multi-frequency range imaging (RIM) has been operated in the Chung-Li very high-frequency (VHF) radar, located on the campus of National Central University, Taiwan, since 2008. RIM processes the echo signals with a group of closely spaced transmitting frequencies through appropriate inversion methods to obtain high-resolution distribution of echo power in the range direction. This is beneficial to the investigation of the small-scale structure embedded in dynamic atmosphere. Five transmitting frequencies were employed in the radar experiment for observation of the precipitating atmosphere during the period between 21 and 23 August 2013. Using the Capon and Fourier methods, the radar echoes were synthesized to retrieve the temporal signals at a smaller range step than the original range resolution defined by the pulse width, and such retrieved temporal signals were then processed in the Doppler frequency domain to identify the atmosphere and precipitation echoes. An analysis called conditional averaging was further executed for echo power, Doppler velocity, and spectral width to verify the potential capabilities of the retrieval processing in resolving small-scale precipitation and atmosphere structures. Point-by-point correction of range delay combined with compensation of range-weighting function effect has been performed during the retrieval of temporal signals to improve the continuity of power spectra at gate boundaries, making the small-scale structures in the power spectra more natural and reasonable. We examined stratiform and convective precipitation and demonstrated their different structured characteristics by means of the Capon-processed results. The new element in this study is the implementation of RIM on spectral analysis, especially for precipitation echoes.

Rapid variations in echo power maps of VHF radar backscatter from the lower atmosphere

For the first time, echo power maps of aspect-sensitive VHF backscatter are shown, with good time and spatial resolutions, for angles 0°–7° from zenith. Sequences of power maps show large changes in appearance over timescales of a few minutes and height intervals of a few hundred metres. Often, individual power maps are consistent with tilted and distorted specular-type scattering layers, rather than anisotropic turbulence, and the direction of maximum echo power is sometimes several degrees off-vertical. Nevertheless, after time-averaging the variable echo-power patterns, the average pattern can become almost circular and centred on zenith, as has been assumed in the past. Echo power maps measured in strong windshear beneath the jet stream show a skewing of the echo power distribution. However, some power maps in the lower stratosphere, despite stronger wind shear, appear more constrained and their maximum echo power remains closer to zenith.

<i>Letter to the Editor</i>: Complete maps of the aspect sensitivity of VHF atmospheric radar echoes

Abstract. Using the MU radar at Shigaraki, Japan (34.85°N, 136.10°E), we measure the power distribution pattern of VHF radar echoes from the mid-troposphere. The large number of radar beam-pointing directions (320) allows the mapping of echo power from 0° to 40° from zenith, and also the dependence on azimuth, which has not been achieved before at VHF wavelengths. The results show how vertical shear of the horizontal wind is associated with a definite skewing of the VHF echo power distribution, for beam angles as far as 30° or more from zenith, so that aspect sensitivity cannot be assumed negligible at any beam-pointing angle that most existing VHF radars are able to use. Consequently, the use of VHF echo power to calculate intensity of atmospheric turbulence, which assumes only isotropic backscatter at large beam zenith angles, will sometimes not be valid.Key words. Meteorology and atmospheric dynamics (middle atmosphere dynamics; turbulence; instruments and techniques)

An investigation of tilted aspect‐sensitive scatterers in the lower atmosphere using the MU and Aberystwyth VHF radars

This study investigates subtle variations of the zenith and azimuth dependence of VHF‐radar echo power in the troposphere and lower stratosphere. Using the middle and upper atmosphere (MU) and Aberystwyth radars, we reanalyze data from two areas of the literature on tilted aspect‐sensitive scatterers, linking results from the spatial interferometry (SI) and Doppler beam‐swinging (DBS) techniques. Whereas wind profilers commonly use three or five radar beams, we examine a MU radar data set with 64 beam positions, so that maps of echo power distribution can be plotted as far as 5° from zenith. The power distribution pattern is often skewed, with the azimuth of maximum power being closely related to the wind shear caused by, for example, inertia‐gravity waves in the lower stratosphere. The results imply that inertia‐gravity wave motions are closely coupled to the smaller‐scale wind field, causing patches of Kelvin‐Helmholtz instability and/or steepening of other shorter‐period gravity waves. These effects can alter the distribution of the tilts of aspect‐sensitive scatterers and explain the skewed echo power patterns. The deviations of vertical‐beam incidence angle measured by SI are found to be inappropriate for off‐vertical beams, and it also appears impossible for basic DBS systems to be used for measuring vertical‐beam incidence angles. Further tests of mountain wave data are consistent with the tilted layer model and help to confirm that the azimuth of gravity waves may be calculated using radar echo‐power imbalances.

Complete maps of the aspect sensitivity of VHF atmospheric radar echoes

Using the MU radar at Shigaraki, Japan (34.85∞N, 136.10∞E), we measure the power distribution pattern of VHF radar echoes from the mid-troposphere. The large number of radar beam-pointing directions (320) allows the mapping of echo power from 0∞ to 40∞ from zenith, and also the dependence on azimuth, which has not been achieved before at VHF wavelengths. The results show how vertical shear of the horizontal wind is associated with a definite skewing of the VHF echo power distribution, for beam angles as far as 30∞ or more from zenith, so that aspect sensitivity cannot be assumed negligible at any beam-pointing angle that most existing VHF radars are able to use. Consequently, the use of VHF echo power to calculate intensity of atmospheric turbulence, which assumes only isotropic backscatter at large beam zenith angles, will sometimes not be valid.

On the relationship between aspect sensitivity and spatial interferometric in-beam incidence angles

Using data from the Middle and Upper Atmosphere Radar, we present a study of the subtle characteristics of the echo power distribution caused by aspect sensitivity at VHF wavelengths. This is accomplished by using 64 beam positions in order to create a high-resolution map of the echo power distribution close to zenith. It is shown that the maximum in the power distribution can be tilted away from vertical by as much as 1 °. Further, azimuthal scans of echo power show a wave-like structure possibly caused by the tilt of the echo power distribution. Justifications based on the characteristics of typical isentropic surfaces are used to explain an asymmetry between the zonal and meridional components of the tilt of the echo power distribution. Finally, the use of spatial interferometry to estimate the angular tilt of the echo power distribution is shown to be valid. In previous studies, it was assumed that the in-beam incidence angles, measured using spatial interferometry, are equivalent to the angular location of the peak in the echo power distribution. In the present work, we show this assumption is reasonable.

Radar Contributions to Asteroid Astrometry and Dynamics

Almost every radar observation of asteroids has measured some characteristics of the distribution of echo power in time delay (range) and Doppler frequency (radial velocity). Such measurements, which are orthogonal to optical plane-of-sky angular astrometry, are also done in the well-known, “absolute” reference frame of the planetary ephemerides, often with fractional precision that is much finer than can be achieved with other kinds of groundbased observations; they therefore can dramatically refine orbits and ephemerides. This statement is most true for near-Earth asteroids (NEAs), which constitute the most prolifically observed radar targets and are likely to be observed in increasing abundance as instrumental capabilities improve and CCD-based, NEA search programs expand. Moreover, studies of closely approaching NEAs benefit tremendously from the inverse fourthpower dependence of echo strength on target distance. For these reasons, I devote the bulk of this paper to NEAs

Radar contributions to asteroid astrometry and dynamics

Almost every radar observation of asteroids has measured some characteristics of the distribution of echo power in time delay (range) and Doppler frequency (radial velocity). Such measurements, which are orthogonal to optical plane-of-sky angular astrometry, are also done in the well-known, “absolute” reference frame of the planetary ephemerides, often with fractional precision that is much finer than can be achieved with other kinds of groundbased observations; they therefore can dramatically refine orbits and ephemerides. This statement is most true for near-Earth asteroids (NEAs), which constitute the most prolifically observed radar targets and are likely to be observed in increasing abundance as instrumental capabilities improve and CCD-based, NEA search programs expand. Moreover, studies of closely approaching NEAs benefit tremendously from the inverse fourth-power dependence of echo strength on target distance. For these reasons, I devote the bulk of this paper to NEAs.

Radar Astrometry of Asteroids, Comets and Planetary Satellites

Groundbased radar has considerable astrometric potential for asteroids, comets and natural satellites that enter the detectability windows of available telescopes. For very closely approaching asteroids and comets, measurements of the distribution of echo power in time delay (range) and Doppler frequency (radial velocity) can achieve a fractional precision between 10−5 and 10−9, and consequently are invaluable for refining orbits and prediction ephemerides. Even for mainbelt asteroids and the more readily detectable planetary satellites whose orbits are very well known, radar can collapse range uncertainties from a few target radii to a few percent of a target radius, with direct implications for the navigation of spacecraft on flyby or rendezvous trajectories.

Planetary radar astronomy

Radar is a powerful technique that has furnished otherwise unavailable information about solar system bodies for three decades. The advantages of radar in planetary astronomy result from (1) the observer's control of all the attributes of the coherent signal used to illuminate the target, especially the wave form's time/frequency modulation and polarization; (2) the ability of radar to resolve objects spatially via measurements of the distribution of echo power in time delay and Doppler frequency; (3) the pronounced degree to which delay-Doppler measurements constrain orbits and spin vectors; and (4) centimeter-to-meter wavelengths, which easily penetrate optically opaque planetary clouds and cometary comae, permit investigation of near-surface macrostructure and bulk density, and are sensitive to high concentrations of metal or, in certain situations, ice. Planetary radar astronomy has primarily involved observations with Earth-based radar telescopes, but also includes some experiments with a spaceborne transmitter or receiver. In addition to providing a wealth of information about the geological and dynamical properties of asteroids, comets, the inner planets, and natural satellites, radar experiments have established the scale of the solar system, have contributed significantly to the accuracy of planetary ephemerides, and have helped to constrain theories of gravitation. This review outlines radar astronomical techniques and describes principal observational results.

Radar interferometry technique: Three‐dimensional wind measurement theory

Generalizing radar interferometry to three‐dimensional space, we present a model which predicts the variation with respect to frequency of the phase of the cross‐spectrum obtained between two separate antennas. The slope of this variation is proportional to the cosine of the angle between the horizontal wind and the interferometer baseline, and inversely proportional to the horizontal wind amplitude. The zero‐frequency phase depends on the horizontal wind speed and direction, on the vertical wind velocity, and on the anisotropy of the backscattered power with respect to the zenith. The model also allows us to predict qualitatively the effects of specularity, beam shape, and random turbulence on the phase versus frequency variation. Assuming a spaced receiver setup with three baselines rotated by 120°, we present an implementation scheme of the radar interferometry technique which yields a three‐dimensional wind estimate and a parameter characterizing the anisotropy of the echo power distribution. Finally, we argue that the radar interferometry horizontal wind measurements will suffer from limitations similar to those of the so‐called apparent velocity as both techniques are related by Fourier transform, and that the vertical wind component will be unbiaised by anisotropy in the backscattered power.

Radar interferometry technique and anisotropy of the echo power distribution: First results

The theory of radar interferometry developed in the companion paper [ Van Baelen and Richmond, this issue] is applied to a set of measurements obtained with the middle and upper atmosphere (MU) radar in order to demonstrate the technique and to test the theory. The variations with respect to Doppler frequency of the coherencies and phases of the signals cross‐correlated between receiver pairs depend on the amplitude and direction of the wind in the manner predicted by the theory. The horizontal wind derived by the interferometric technique agrees quite well with the so‐called apparent velocity obtained by cross‐correlating signals in the time domain from different receiver pairs, and under our experimental conditions the latter estimate has been determined to be a good representation of the true wind, in spite of slight tendencies to overestimate the wind amplitude. The vertical wind derived by the interferometric technique shows significant differences with the Doppler wind obtained from a vertically pointing antenna, but these differences disappear when the Doppler wind is corrected for the off‐zenith distribution of the received power. An examination of the mean angle‐of‐arrival of the received signal reveals that there is a tendency for the angle to approach, though not attain, perpendicularity with the three‐dimensional wind vector, and perhaps also to tend to be perpendicular to isentropes in the crosswind direction. A postset beam steering analysis of several examples of data illustrates the behavior of the angular distribution of received power in time and space. When the signal‐to‐noise ratio is large, there is a tendency for the power to be fairly isotropic with respect to zenith angle, but highly distorted patterns can be encountered when the signal is weaker. There appears to be a tendency for the patterns to vary relatively slowly over time, but strong variations in altitude are observed in passing from one 300‐m range gate to the next. The direction of most intense received power does not necessarily correspond to the direction of mean angle‐of‐arrival of the signal as determined by interferometry.

Doppler radar imaging of spherical planetary surfaces

A new approach to making radar reflectivity images of spherical planetary objects uses echo spectra acquired as a function of rotational phase and at an arbitrary number of subradar latitudes. If only equatorial views are used then the image will have a north‐south ambiguity. If non‐equatorial views are used then unambiguous images are possible. The technique is tailored for depolarized or diffuse (nonspecular) polarized backscatter and works best when the limb darkening is minimal. In developing the Doppler‐radar imaging system, the target's reflectivity distribution is expanded in a truncated spherical harmonic series and the distribution of echo power in rotational phase and Doppler frequency is obtained as a linear, analytic function of the series coefficients. To estimate the coefficients from an observed phase‐Doppler distribution, the inversion is cast as a least‐squares problem and solved using singular value decomposition. The result is a linear imaging system whose capabilities and sensitivity to such factors as subradar latitude coverage and signal‐to‐noise ratio are easily explored with simulations. Doppler‐radar imaging can be used with existing radar telescopes to map the diffuse component of echoes from the inner planets and to make north‐south ambiguous reflectivity maps of the icy Galilean satellites. SNRs needed for Doppler‐radar imaging of the largest asteroids, Io, and Titan would be accessible upon implementation of upgrades proposed for the Arecibo telescope.

Weather Radar Signal Processing and Recording at the National Severe Storms Laboratory

The radar data system at the National Severe Storms Laboratory presents weather radar return power data with a significant reduction in the variations that arise from the relative motion of discrete precipitation elements. The system provides intensity-contoured plan position indicator (PPI) displays for visual inspection and photographic archival, and digital records in azimuth-range coordinates for use in computers and for narrow-band transmission to remote locations. Digital records can also be reproduced in the PPI format. The spatial distribution of echo power perceived during each two degrees of antenna azimuthal revolution, is represented as ten levels of return power intensity at intervals of 2°×1 nmi. Spatial reticulation is of the same order as limits of resolution inherent in the radar beamwidth and pulse length, and the system output thus retains most of the information on precipitation rate distributions contained in the unprocessed video signals. Averaging over two pulse lengths and the equivalence of ten pulse periods provides approximately Gaussian-distributed estimates of mean intensity with a standard error of 1 dB, less than one-fifth of the uncertainty of point-sampled unprocessed video. The system is used routinely at NSSL with a 10-cm WSR-57 radar, a type widely used by the Weather Bureau, and could be adapted to any weather radar system.