Wind Shear and Reflectivity Gradient Effects on Doppler Radar Spectra

Abstract

The Doppler spectrum of radar echoes from scatterers is broadened by their motion perpendicular to the beam due to the finite beam width. This paper deals with the nature of the Doppler spectrum, its variance, and the associated autocorrelation function for the generalized case in which there is shear of the cross-beam motion and a gradient of the scatterers' reflectivity. The spectrum is generated numerically, while the variance and autocorrelation function are derived analytically. It is found for a linear vertical wind shear and an exponential variation of reflectivity with height that the variance of the Doppler spectrum may be increased by as much as 250% or decreased by as much as 72%, depending on whether the wind speed and reflectivity increase in the same or opposite directions, respectively. These variations result in changes from the Gaussian Doppler spectrum expected from a uniform crosswind and a Gaussian beam profile. The effects of vertical wind and reflectivity gradients increase with the linear vertical dimension of the radar beam, and thus with both the angular vertical beam width and range. For beams ≤3°, the variance is determined essentially by the horizontal crosswind and beam width at ranges out to about 20 km for all significant values of shear. At larger ranges, wind and reflectivity gradients become significant. Corresponding effects on the autocorrelation function are also computed.