Wind Shear and Reflectivity Gradient Effects on Doppler Radar Spectra: II

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  • 1 Dept. of the Geophysical Sciences, The University of Chicago
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Abstract

Other investigators have discussed the effects of wind and reflectivity gradients across the radar beam on Doppler measurements, but have either estimated their magnitude from a simple approximation or set them aside as negligible. This paper deals with the component of the shear vector along the beam. Exact solutions and simple approximations for both the mean and variance of the Doppler spectrum are derived for two types of reflectivity gradients combined with a linear velocity, gradient. In the case of an exponential reflectivity, gradient it is found that the “effective” beam (i.e., the reflectivity-weighed two-way illumination pattern) remains Gaussian with identical beamwidth to the real beam, but its mean is shifted to an angle ϕm on the high-reflectivity side of the actual beam. With a linear velocity profile in the ϕ direction, the approximate solution shows that the mean Doppler velocity, is then shifted to the scatterer velocity found at ϕm. This approximation is shown to be valid for most physically realizable conditions. Moreover, the spectra variance is found to be essentially independent of the reflectivity gradient and Lhermitte's simple approximation is also generally valid. Analogous results are obtained for a reflectivity profile varying as exp(cR2ϕ2) where R is range. The effects of reflectivity gradients on the beam-averaged echo power are also discussed.

Abstract

Other investigators have discussed the effects of wind and reflectivity gradients across the radar beam on Doppler measurements, but have either estimated their magnitude from a simple approximation or set them aside as negligible. This paper deals with the component of the shear vector along the beam. Exact solutions and simple approximations for both the mean and variance of the Doppler spectrum are derived for two types of reflectivity gradients combined with a linear velocity, gradient. In the case of an exponential reflectivity, gradient it is found that the “effective” beam (i.e., the reflectivity-weighed two-way illumination pattern) remains Gaussian with identical beamwidth to the real beam, but its mean is shifted to an angle ϕm on the high-reflectivity side of the actual beam. With a linear velocity profile in the ϕ direction, the approximate solution shows that the mean Doppler velocity, is then shifted to the scatterer velocity found at ϕm. This approximation is shown to be valid for most physically realizable conditions. Moreover, the spectra variance is found to be essentially independent of the reflectivity gradient and Lhermitte's simple approximation is also generally valid. Analogous results are obtained for a reflectivity profile varying as exp(cR2ϕ2) where R is range. The effects of reflectivity gradients on the beam-averaged echo power are also discussed.

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