Richard J. Lataitis

Cross correlations and cross spectra for spaced antenna wind profilers: 1. Theoretical analysis

The presented theory ties the properties of a turbulently advected scattering medium to the cross correlation and cross spectrum of signals in a general configuration of receiving and transmitting antennas. The correlation length of Bragg scatterers and antenna diameter are the significant parameters determining the diffraction patterns correlation length. We examine how vertical anisotropy of the scattering medium affects the diffraction patterns correlation length. We demonstrate that the cross spectrum can be formulated in terms of a pair of spectral sampling functions (a one-dimensional Doppler and a three-dimensional wavenumber function), and closed form solutions are obtained. We give the conditions under which the scattering mediums statistical properties can be represented by a Gaussian correlation or spectral model, and the distance over which the diffraction pattern simply advects without significant change. We show that the diffraction pattern of a pair of scatterers can translate at the speed of the scatterers, not twice their speed as is commonly thought.

Wander of an optical beam in the turbulent atmosphere

A simple, analytic, geometrical optics expression for the variance of the beam displacements caused by propagation through weak refractive turbulence described by the Kolmogorov spectrum is presented. The analytical formula includes the effect of the divergence or convergence of the initial beam. The formula is compared with numerical results obtained from a more complicated expression including effects of diffraction and strong path-integrated turbulence. The simple geometrical optics expression holds for apertures larger than the Fresnel zone size and larger than the ratio of the square of the Fresnel zone to the phase coherence length.

Cross correlations and cross spectra for spaced antenna wind profilers: 2. Algorithms to estimate wind and turbulence

In part 1 of this paper we developed analytic relationships linking the cross correlation and cross spectrum of the echoes from a spaced antenna system to the properties of a horizontally isotropic scattering medium (e.g., clear-air refractive index irregularities) and the background flow (e.g., laminar or isotropic turbulent flow). Using these analytic expressions, in the present paper, part 2, we construct algorithms (for both the time domain and frequency domain) for extracting unbiased wind and turbulence estimates. We derive a condition under which one can ignore turbulence when computing winds from the time delay to the peak of the cross-correlation functions. We show profiles of the horizontal wind and turbulence based on these algorithms using data from the unique 33-cm wavelength spaced antenna wind profiler developed by the National Center for Atmospheric Research.

Removing Ground and Intermittent Clutter Contamination from Wind Profiler Signals Using Wavelet Transforms

Abstract New algorithms for removing ground and intermittent clutter contamination from wind profiler data are presented. The techniques use wavelet transforms to “filter” the contribution of clutter to the wind profiler signals. Examples of typical clutter contamination using simulated and actual signals are presented. The corresponding Doppler spectra before and after wavelet filtering are compared. The authors find that wavelet filtering can reduce the clutter-to-clear-air signal power by as much as 40 dB, even when the clutter and clear-air peaks cannot be resolved in the Doppler spectrum. The enhancement in clear-air signal detectability in the presence of clutter is due to the more efficient separation of clutter and clear-air energy in the wavelet domain.

Validation of a UHF spaced antenna wind profiler for high‐resolution boundary layer observations

In this paper we apply a spaced antenna technique derived from the recent work of Doviak et al. [1996a] and Holloway et al. [this issue] to wind measurement with a small UHF boundary layer profiler. We discuss the implementation of the technique, averaging and quality control strategies, and some advantages and limitations of spaced antenna methods over conventional Doppler beam swinging wind profilers in the boundary layer. Such advantages include a relaxation of the assumption of a horizontally uniform wind field and the possibility of high temporal resolution wind profiles. In this regard we present velocity measurements derived from this UHF system with time resolution of about 30 s and compare these measurements with in situ sonic anemometer data taken on a 300-m tower. Finally, we present an example of a high-resolution time-height cross section of atmospheric winds. This example, collected in stratiform precipitation, shows the intriguing situation of a wind speed maximum (jet) which closely follows the height of the melting layer over several hours even as this height changes by several hundred meters.

Angle-of-arrival fluctuations of a reflected beam in atmospheric turbulence

The statistics of the angle-of-arrival fluctuations are studied for the case of a laser beam reflected from a curved surface in a uniformly turbulent atmosphere. The variance for the direct beam and for the reflected beam and the covariance for the two beams are calculated for arbitrary divergence of the illumination and radius of curvature of the reflector. Experimental results support the conclusions that the reflected-beam angle-of-arrival fluctuations are very sensitive to small deviations from perfect collimation and that the correlation of the fluctuations in the direct and reflected beams is high.

Space and Time Filtering of Remotely Sensed Velocity Turbulence

Abstract It is well known that the width of a clear-air Doppler radar spectrum can be used to estimate the small-scale variability of the wind. To do this accurately requires that all contributions to the spectral width be accounted for. Recently, an approximate formula for correcting Doppler spectral widths for spatial and temporal filtering effects was proposed. The formula assumes independent additive contributions to the spectral width from the inherent volume averaging of the radar-sampling volume and the finite measurement interval. In the present paper the approximate formula is compared to an exact triple-integral formulation in which the spatial and temporal effects are shown to be coupled in a nonlinear fashion. The required integrations are evaluated numerically and are carried out over the full range of scales in wavenumber space, in contrast to earlier work, where truncated forms of isotropic, inertial-subrange spectral forms were used to obtain a simple, closed-form expression. Comparisons s...

Signal power for radio acoustic sounding of temperature: The effects of horizontal winds, turbulence, and vertical temperature gradients

A simple expression for the expected average signal power of a radio acoustic sounding system (RASS) comprising a monostatic pulsed Doppler radar and a continuous-wave broadbeam acoustic source is developed. The effects of horizontal winds, atmospheric turbulence, and vertical temperature gradients are included. Under ideal conditions (i.e., in the absence of winds, turbulence, and gradients) the received signal power is a maximum and, for a broadband acoustic source, is predicted to be proportional to the radar range resolution and inversely proportional to the acoustic bandwidth and square of the range R. Turbulence-induced distortion of the acoustic wave fronts yields the expected R−26/5 range dependence, provided winds are light. This result is based on the assumption that the turbulence strength does not vary with range. For the more realistic case of turbulence concentrated primarily within the boundary layer (R ≲ 1 km) a much weaker range dependence at longer ranges is predicted. A flattening of the acoustic wave fronts by temperature gradients typical of unstable midday conditions results in an R−6 range dependence, provided winds are light. Turbulence effects are predicted to dominate at shorter ranges (R ≲ 8 km) and gradient effects at longer ranges. The expected compensation of power loss associated with the wind-induced lateral displacement of the acoustic wave fronts by the turbulence- and gradient-induced broadening of the displaced RASS focal spot is also predicted.

An alternative method for inferring winds from spaced‐antenna radar measurements

One variation of the spaced-antenna technique for measuring atmospheric winds using a pulse Doppler radar is based on a calculation of the complex temporal cross-correlation function for the backscattered fields detected by a pair of spaced receiving antennas. The delay to the peak of the cross-correlation amplitude, adjusted for the temporal evolution of the backscattered field pattern through an extended analysis, is related to the so-called trace velocity along the antenna pair baseline, with two nonparallel baselines yielding the full horizontal wind vector. We suggest an alternative method for inferring the horizontal wind from the temporal cross correlation. We demonstrate that the slope of the cross-correlation amplitude at zero lag, normalized by the level of the cross-correlation amplitude at zero lag, is directly proportional to the component of the wind velocity along the antenna pair baseline. We illustrate that this measure of the horizontal wind is insensitive to the temporal evolution of the backscattered field pattern. Therefore no extended analysis is needed to estimate the horizontal wind vector. The advantage of this approach is that it is a very simple and direct method of retrieving the horizontal wind. Our theory indicates that for many cases of interest the proportionality constant relating the normalized slope to the wind component along the antenna pair baseline depends only on the transmitting and receiving antenna diameters and on the separation between the receiving antennas. This constant can be calculated, or the system can be calibrated against a rawinsonde retrieval. A disadvantage to the slope technique is that it is somewhat sensitive to the degree of vertical anisotropy of the scattering medium. We loosely define the degree of vertical anisotropy r as the ratio of the vertical to horizontal correlation length of refractive index irregularities having a spatial scale of the order of the Bragg wavelength λ/2, where λ is the radar wavelength. In the neutral atmosphere, r typically satisfies 0 < r ≤ 1. We find that for a horizontally isotropic, Kolmogorov-type refractive index spectrum with λ/2 < L0z, where L0z is the vertical outer scale, the slope method is useful provided r is greater than the effective system beam width λ/De, where De is an effective system antenna diameter (approximately equal to the transmitter antenna diameter). We note that this same restriction ensures that the correlation scale of the backscattered field (i.e., the pattern scale) is solely a function of the antenna diameters. The slope method is therefore limited to scattering from isotropic to moderately anisotropic turbulence (i.e., λ/De < r ≤ 1) provided λ/2 < L0z and is perhaps best suited for wind profiling in the atmospheric boundary layer. A comparison of horizontal winds obtained by applying the slope technique to data from a 915-MHz spaced-antenna radar and winds from a rawinsonde retrieval showed good agreement.

Optimal Generation of Radar Wind Profiler Spectra

Abstract Radar wind profilers (RWPs) sense the mean and turbulent motion of the clear air through Doppler shifts induced along several (3–5) upward-looking beams. RWP signals, like all radars signals, are often contaminated. The contamination is clearly evident in the associated Doppler spectra, and automatic routines designed to extract meteorological quantities from these spectra often yield inaccurate results. Much of the observed contamination is due to an aliasing of higher frequency signals into the clear-air portion of the spectrum and a broadening of the spectral contaminants caused by the relatively short time series used to generate Doppler spectra. In the past, this source of contamination could not be avoided because of limitations on the size and speed of RWP processing computers. Today’s computers, however, are able to process larger amounts of data at greatly increased speeds. Here it is shown how standard and well-known spectral processing methods can be applied to significantly longer tim...