## 1. Introduction

[2] The SA technique measures both the radial and cross-beam wind components within the radar's resolution volume, and thus potentially provides wind data with higher resolution than Doppler beam swinging (DBS) methods (i.e., a variant of the velocity azimuth display, VAD, technique first proposed by *Lhermitte and Atlas* [1961]). The DBS method is today the most widely used wind profiling method [*Strauch et al.*, 1984]. The theory of the SA technique developed by *Briggs et al.* [1950] is based on the motion of the interference pattern formed from waves scattered by random perturbations in the propagation medium (i.e., due to variations in electron density, refractive index perturbations, etc.). The most commonly used data analysis method for the SA technique is Briggs' full correlation analysis (FCA) [*Briggs et al.*, 1950; *Briggs*, 1984], in which the wind is estimated from both the auto- and cross-correlation functions while accounting for random changes in the interference pattern as it moves across pairs of receiving antennas.

[3] Theoretical and experimental studies of the performance of wind profilers are required to determine the limits of measurement accuracy and resolution of these remote sensing techniques to retrieve wind data. The performance of the Doppler method for wind measurement has been thoroughly studied and evaluated [*Doviak and Zrnic*, 1993]. The spaced antenna method, however, still requires a rigorous theoretical basis and experimental evaluation, even though the cross-correlation function has been derived based on wave scattering [*Doviak et al.*, 1996], and various wind estimators have been proposed [*Holloway et al.*, 1997]. A theoretical comparison, supported by simulations, of various estimators under the condition of large signal-to-noise-ratio (SNR) has been made by *Doviak et al.* [2004]. However, the performance of these wind estimators in the presence of noise has not been evaluated. The purpose of this paper is to extend the theory and simulations [*Zhang et al.*, 2003] to evaluate the performance of SA wind profilers under low SNR conditions. In the simulations, we follow the technique described by *May* [1988], and use a SNR = 0 dB for all our examples.

[4] The accuracy of an FCA estimator was first studied by *May* [1988], but his analysis is based upon an approximate formula for the standard deviation (*SD*) of the cross-correlation coefficient estimates. Other cross-beam wind estimators are (1) the cross- to auto-correlation-ratio (CACR) and (2) intersection (INT) methods [*Holloway et al.*, 1997], and (3) the slope-at-zero-lag (SZL) method [*Lataitis et al.*, 1995]. The theoretical accuracy of the baseline wind estimated with the latter two of these three estimators is derived by *Doviak et al.* [2004], who compare them with the theoretical accuracy obtained with the FCA estimator. The theoretical accuracies are also compared with those derived from simulations. A cross-correlation-ratio (CCR) method was recently proposed to measure cross-beam wind without the need for the auto-correlation function, and *Zhang et al.* [2003] compared its performance to that obtained with the FCA estimator. Except for *May*'s [1988] work, all the other theoretical error analyses for SA cross-beam wind estimates were performed under the assumption of infinite SNR. In practice, however, noise is usually an important component of the correlation functions and power spectra [*May et al.*, 1989; *Holdsworth*, 1999]. In this paper we focus our attention on the effects that additive white noise has on the FCA and CCR estimators examined by *Zhang et al.* [2003]. Although the focus of this paper is on the accuracy of the baseline wind component, the results can be applied to assess the errors in wind speed and direction, using the procedure of *Doviak et al.* [1976], to asses those errors in estimating the correlation lengths of refractive index perturbations (G. Hassenpflug et al., Standard deviation of refractive index perturbation correlation length estimates in spaced antenna observations, submitted to *Radio Science*, 2003), and to improve radar sensitivity of weak weather echoes in the presence of noise. Since FCA and CCR are unbiased estimators for small fluctuation of correlation estimates, we concentrate on standard deviations of wind estimates in this paper.

[5] The paper is organized as follows: In section 2, we provide a general background of the SA technique for wind estimation. In section 3, we present theoretical results for the *SD* of wind estimates in the presence of noise, and make comparisons with results from numerical simulations. In section 4, these results are then compared with root mean squared (rms) deviations obtain from data collected with NCAR's Multiple Antenna Profiling Radar (MAPR [*Brown et al.*, 1999; *Cohn et al.*, 1997, 2001]). Finally, we summarize results of SA wind estimation in the presence of noise, and discuss ways to reduce wind estimation errors.