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

Abstract

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.

Atmospheric radar imaging using multiple‐receiver and multiple‐frequency techniques

“…For the case of volume scattering, the brightness spectrum has a more general form with a dependence ofR' -R and can be further represented in terms of the turbulence spatial spectrum and wind velocity [e.g., Liu and Pan, 1993; Doviak et al, 1996]. In such a case, the brightness spectrum can be thought of as a uniformly distributed function within the resolution volume.…”

MF and HF radar techniques for investigating the dynamics and structure of the 50 to 110 km height region: a review

“…Other analysis approaches to SA data are described by Lataitis et al (1995), Doviak et al (1996), and Holloway et al (1997). Lataitis et al (1995) showed 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.…”

“…This would correspond to wind profiling in the atmospheric boundary layer. Doviak et al (1996) and Holloway et al (1997) further considered the application of spaced antenna technique in situations of more isotropic turbulence, a condition more likely to hold only as generally true in the troposphere when using upper VHF, UHF, or higher frequencies. For example, in a typical study, Tsuda et al (1997) found significant aspect sensitivity at lower VHF in the troposphere and lower stratosphere when using the MU radar in Japan.…”

MU radar spaced antenna observations with varying apertures: Scatterer and antenna contributions to the ground diffraction pattern

“…The first is related to homogeneity, namely, that perturbations in the refractive index are uniformly distributed within the radar resolution volume. For uniform reflectivity of such a layer, homogeneous turbulence results in an expected normalized power spectrum equal to the velocity distribution [Doviak and Zrnik, 1993], so that if the radar transmitting beam is Gaussian, then uniform horizontal wind results in a Gaussian power spectrum, and consequently a Gaussian correlation function. Secondly, the sampling function of the radar [Doviak et al, 1996] is narrow with respect to the scatterer spectrum, at least in the vertical wavenumber domain.…”

“…The structure of the turbulent medium can therefore not be measured. A different development, such as that by Doviak et al [1996] and Holloway et al [1997aHolloway et al [ , 1997b, is based on a description of the physical process of scattering in the antenna beam volume Liu et al [1990], and relates the spatial spectrum of the scatterers to the cross-correlation of the diffraction pattern of the scattered field, and hence to the crosscorrelation of signals received at spaced antennas. An estimation method based on the latter enables measurement not only the horizontal wind field and the lateral diffraction pattern scales as seen at the receiver antennas, RADIO SCIENCE, VOL.…”