AbstractA two‐dimensional form of cross‐covariance function between the radar radial‐ and tangential‐components (with respect to the direction of radar beam) of background wind errors is derived. Like the previously derived auto‐covariance function for the radial component, this cross‐covariance function is homogeneous but non‐isotropic in the horizontal. The auto‐ and cross‐covariance functions are used with the statistical interpolation technique to perform a vector wind analysis from Doppler radial‐velocity observations on a conical surface of low‐elevation radar‐scans. The structures of the two covariance functions are compared and interpreted in terms of the influence of a single‐point radial‐velocity observation on the analysed vector wind field. The utility and value of these covariance functions are demonstrated through analysis experiments that use either simulated radial‐velocity data from idealized flows or real radar observations. The results of the statistical interpolation scheme utilizing the proposed covariance functions are shown to be superior to the results of traditional VAD technique. The proposed technique can actually be considered a generalization of the traditional VAD technique. Copyright © 2006 Royal Meteorological Society