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 pattern's correlation length. We examine how vertical anisotropy of the scattering medium affects the diffraction pattern's 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 medium's 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.

Abstract. 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.

Abstract. 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. IntroductionIn the past decade a growing number of "clear-air" wind profilers have been used to probe the troposphere and lower stratosphere. Spaced antenna (SA) techniques are an alternative to the more common DBS technique. They use a single vertically directed transmitted beam, and the diffraction pattern formed by energy backscattered from the atmosphere is received using three or more spatially separated receiving antennas. Although not specifically developed for this purpose, SA measurement techniques can relax the assumption of uniform wind because the vector wind is measured within one radar pulse volume rather than at several separated volumes. Another potential benefit of SA techniques is that less time may be needed for the measurement 1279

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.

No abstract