## 1. Introduction

[2] UHF and VHF spaced-antenna (SA) radars have been used extensively to profile winds in the precipitation-free atmosphere [*Larsen and Röttger*, 1989]. These wind-profiling radars typically comprise a vertically directed transmitting beam and at least three spaced receiving antennas. Vertical wind along the transmitter beam can be calculated from the argument of the auto- or cross-correlation functions. The horizontal component of the wind, transverse to the radar beam, can be calculated from the magnitude of the auto- and cross-correlation functions of signals from pairs of receiving antennas. The accuracy of the vertical or along-beam wind component is reasonably well established [*Doviak and Zrnić*, 1993], but formulas to compute uncertainties of the horizontal or cross-beam wind component are not. *May* [1988] is the first to derive formulas to calculate precision when winds are estimated using the full correlation analysis (FCA) of *Briggs* [1984]. More recently, *Tahara et al.* [1997] and *Kawano et al.* [2002] have used simulations to determine the performance of SA and DBS wind profilers. In this paper we derive theoretical formulas to determine the precision of cross-beam winds calculated from SA data. These theoretical formulas are then compared with results obtained from simulations.

[3] *Doviak et al.* [1996] developed general formulas that relate the auto- and cross-correlation functions, for signals from pairs of spaced receiving antennas, to the statistical structure of the wind and refractive index field of the scattering medium. These general formulas for stochastic Bragg scatter reduce to relatively simple form if scatter is isotropic as it typically is for relatively short wavelength (i.e., λ < 1 m) radars. These simple forms are used to illustrate several methods for measuring cross-beam wind. Expressions for estimating the precision of wind estimates are developed using propagation of error calculations. For application examples, these expressions are used to estimate the theoretical performance of the UHF wind profiler developed by the National Center for Atmospheric Research (NCAR) [*Cohn et al.*, 1997, 2001], as well as the VHF profiler in Shigaraki, Japan [*Kawano et al.*, 2002]. The theory developed here assumes uniform wind, reflectivity, and isotropic turbulence throughout the radar's resolution volume, as well as infinite signal to noise ratio. Although the formulas are explicitly expressed in terms of profiling radar parameters, they can be applied to any SA radar measuring cross-beam wind.