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Beam broadening effects on the Doppler radar spectrum induced by along- andcross-radar-beam winds are theoretically investigated in this article.Analytical expression of beam broadening spectrum for a vertical beamsubject to a constant vertical wind in the absence of horizontal wind isderived first. We find that the resultant beam broadening spectral shape isin an exponential form, rather than a Gaussian shape. The peak of theexponential spectrum corresponds to the true vertical wind velocity, and thespectral width σ is a function of vertical wind velocity w and thehalf-power beam width θ1/2 of the radar beam, in accordance with theexpression σ=0.09wθ1/22. The beam broadeningspectrum for a vertical radar beam subject to both vertical and horizontalwinds is numerically studied, and the result shows that the spectral shapeis distorted from the Gaussian form. The estimated vertical wind velocity ofthe distorted spectrum is very close to the true vertical wind velocity witha difference of less than 0.6% for a typical case. However, its spectralwidth is substantially greater than that of the conventional Gaussianspectrum broadened by horizontal wind only. The difference of the spectralwidths Δσ (in unit of percentage) in the two, as a functionof the half-power beam width and the ratio of vertical to horizontal windvelocities, can be well approximated by a parabolic equation. With thisequation and the conventional Gaussian beam broadening spectral width causedby horizontal wind, the true width of the distorted beam broadening spectruminduced by vertical and horizontal winds can be inferred without complicatednumerical computation. Through a transformation of wind velocity fromvertical and horizontal winds into along- and cross-radar-beam winds definedon the cross section of an oblique radar beam, the results obtained from thecase of vertical radar beam can be directly applied to the case of the obliquebeam. We show that in some special cases the beam broadening spectral widthsof an oblique beam subject to both vertical and horizontal winds will beexceedingly narrower than those estimated by the existing formula, irrespectiveof the presence of strong horizontal wind velocity

Effects of along- and cross-radar-beam winds on Doppler radar spectrum