A two-dimensional form of error covariance function is derived for the radial component of the background vector wind projected onto the direction of radar beam at a low elevation under the assumption that the background wind error is a Gaussian random vector field and this random field is homogeneous and isotropic on the conic surface of radar scans. The derived covariance function can be used directly by optimal interpolation of radar observed radial winds on the conic surface, although the true optimality of the analysis depends on the underlying assumption. The derived covariance function can be also used as an influence function for a radial-wind analysis with zero background. The utilities of the derived covariance function are demonstrated by numerical experiments. Examples will also be presented to highlight the recent progress in using flow-dependent forms of error covariance estimated by ensemble Kalman filters to improve radar wind analyses.