Investigation of Doppler spectra from a tornadic supercell thunderstorm: Are they Gaussian?

The Doppler spectrum of weather signals can reveal the power-weighted radial velocity distribution within the radar resolution volume and has gained increasing attention in recent years. The three fundamental radar parameters, reflectivity, mean radial velocity, and spectrum width, are defined from the three spectral moments and can be estimated either by spectral methods in the frequency domain or the autocovariance method in the time domain. For a Gaussian-shaped Doppler spectrum, the first three moments (zero, first, and second moments) are sufficient to fully characterize the spectrum. However, to our knowledge, there are only limited studies to systematically investigate and verify the Gaussian assumption using modern Doppler weather radar. For non-Gaussian or asymmetric spectra, the mean radial velocity and spectrum width estimated by the autocovariance method can be biased. In this work, Doppler spectra from a tornadic supercell thunderstorm collected by the research WSR-88D (KOUN) in Norman, Oklahoma are examined. Many interesting spectra (ex, non-Gaussian, skewed, flat top, etc.) are observed and will be shown. Simple models in relation to the storm dynamics are proposed to explain the observed spectrum shape. Moreover, mean squared error between the observed and fitted spectra and higher moments such as the skewness and kurtosis are introduced to quantify the deviation from Gaussianarity within the storm.