Comparison of spaced‐antenna baseline wind estimators: Theoretical and simulated results

Abstract

[1] Formulas for the theoretical precision of cross-beam winds measured with spacedantenna profilers are developed and compared with results obtained from simulations for conditions of high signal-to-noise-ratios. These formulas relate the precision of wind measurement to radar and atmospheric parameters. Formulas for Briggs' Full Correlation Analysis, the Intersection method, and the Slope-at-Zero-Lag method are each presented for two implementations-estimating parameters for assumed Gaussian shaped correlation functions, and a direct finite difference method where this assumption is not necessary. For each wind measurement method and implementation, these formulas are used to evaluate, as an example, the theoretical performance of MAPR, NCAR's 915 MHz, Multiple Antenna Profiling Radar. The theory is also compared with the standard error obtained from simulations presented by Kawano et al. [2002] for the MU radar in Shigaraki, Japan. Comparisons show that the Intersection and Briggs' FCA methods are identical and provide the best performance.

Performance of correlation estimators for spaced‐antenna wind measurement in the presence of noise

“…The two‐lag CCR estimator for cross‐beam wind measurements is analogous to the pulse pair estimator for radial wind measurements [ Doviak and Zrnic , 1993]. Doviak et al [2004] show that, under the condition T se ≪ τ c , and in the absence of noise, the two‐lag CCR estimator is identical to the slope‐at‐zero‐lag (SZL) estimator described by Lataitis et al [1995]. It can be expected that the estimates obtained from a fitted line have smaller errors than those obtained by simply using data at ± T se .…”

“…Because parameters τ p and τ x in can only be estimated, the baseline wind estimate is expressed as Doviak et al [2004] show that the correlation between the estimates p and x can be ignored in computing the standard deviation of the D‐FCA baseline wind estimates. Thus the SD [ ox ] for baseline wind estimates obtained from the D‐FCA is, …”

“…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.…”

“…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.…”

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

“…for different baselines B ij , the effect of the variance of τ c on τ (ij ) p was assumed negligible, following the results of Doviak et al (2004). The model calculations become unwieldy as τ (ij ) i becomes much larger than τ (ij ) p +τ c , where τ c is the square root of the second moment of the Gaussian function.…”