Doppler weather radar has been widely used in both research and operational fields to advance our understanding of storm dynamics and improve warning of severe and hazardous weather. The three fundamental radar products, reflectivity, mean radial velocity, and spectrum width, are derived from the zeroth, first, and second moments of a Doppler spectrum, respectively, and can be estimated using autocovariance method (or commonly referred as pulse-pair processing) or spectral method. Moreover, in the autocovariance method a Gaussian-shape Doppler spectrum is assumed. A Doppler spectrum represents the distribution of weighted radial velocities and is a result of the interplay among radar weighting function, reflectivity, and velocity distribution within the radar volume. Asymmetric and non-Gaussian spectra can introduce biases in the estimation of mean radial velocity and spectrum width. Moreover, if more than one dynamical process is present within the radar volume, the three spectral moments are not sufficient to characterize these processes.

Doppler spectra from a tornadic supercell observed by the research WSR-88D (KOUN) in Norman, Oklahoma will be presented. Many cases of asymmetric and non-Gaussian spectra can be observed within the storm. A dual-Gaussian model was developed to fit the observed spectra. The results suggest that the dual-Gaussian model can better characterize the observed Doppler spectrum compared with those obtained by spectral analysis or autocovariance method. Moreover, for the regions where both storm motion and environmental inflow are presented within the radar volume, the dual-Gaussian model can accurately capture both processes, while the conventional methods provide biased velocity estimates. Statistical analysis of the dual-Gaussian approach will be performed using numerical simulations.