The zeroth (reflectivity) and first (radial velocity) moments of the Doppler spectrum observed with the Doppler weather radar have been used extensively by operational and research meteorologists for various purposes. Compared to reflectivity and velocity fields, the squared root of the second central moment, or spectrum width, has had limited application. Shear and turbulence are two major meteorological contributors to the broadening of the spectrum width. Because turbulence in the atmosphere closely relates to the aviation safety, many researchers focus on relating the measured spectrum width to the turbulence intensity in the atmosphere. However, although more than half century has passed since turbulence was recognized as one of major contributors to the spectrum width, this effort seems still not very successful. A theoretical research shows that there is an additional zero mean random variable term that couples mean wind shear and turbulence in the Doppler radar spectrum width equation. This random variable, labeled the "coupled term", has been neglected heretofore in the literature. Herein, the variance of the squared spectrum width ascribed to this coupled term is determined from data collected with a WSR-88D in two snow storms; it can exceed 1 m4 s-4. Thus, this coupled term can be a significant contributor to the variance of the spectrum width and must be considered when using spectrum width to deduce turbulence.
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