Cross‐correlation ratio method to estimate cross‐beam wind and comparison with a full correlation analysis

Abstract

[1] Cross-beam wind is usually estimated using a full correlation analysis (FCA) method applied to signals from spaced antennas. In this paper we present a cross-correlation ratio (CCR) method for wind measurements. The CCR method is illustrated using theory, and data obtained with the National Center for Atmospheric Research's multiple antenna profiling radar. The standard errors of estimated cross-beam wind using CCR and a FCA are studied based on a rigorous analysis of the variance of the cross-correlation estimates. The results of the analysis are compared with previous works. It is shown that the current method is easy to implement and has smaller error for receiving antenna spacing small compared to the transmitting antenna dimensions.

Variance of wind estimates using spaced antenna techniques with the MU radar

“…The results hold for anisotropic conditions and are derived from the FCA analysis method of Doviak et al (1996) and Holloway et al (1997a), using cross-correlation function magnitude estimation, as per Zhang et al (2003). The results are equally applicable to the Briggs method of FCA.…”

“…Secondly, the variance of this parameter is derived by applying the standard theory of error propagation, taking all covariance terms into account. The covariances of the different ACF and CCF magnitudes at arbitrary time lags are derived using the method of Zhang et al (2003). In such a manner, we obtain expressions for the variance of refractive index irregularity horizontal correlation lengths, ellipse orientation, and wind components.…”

“…Assuming Gaussian forms for un-normalized correlation functions, we use the method described in Zhang et al (2003) to derive the 10 variances and 45 covariances of unnormalized cross-correlation function magnitudes necessary to solve for wind components in a general SA configuration, with the restriction described in Sect. 1.…”

“…However, simplifications are often made to the case of isotropic scattering, and furthermore, analyses of parameter estimate variance have been largely limited to simulations and analytical considerations of alongbaseline wind components (Tahara and Yamamoto, 1997;Kawano et al, 2002;Zhang et al, 2003).…”

“…We describe the variance of horizontal wind components in terms of the un-normalized cross-correlation function CCF and auto-correlation function ACF magnitudes, following the example of Zhang et al (2003). Characteristics of the atmospheric refractive index irregularities, such as backscattered power, correlation length and correlation time, and the radar parameters, such as baseline length, wavelength and transmitting and receiving antenna beam-width, determine the CCF magnitudes, and these magnitudes, in turn, determine the CCF magnitude variance and hence the estimated parameter (e.g.…”