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

Beam broadening effects on the Doppler radar spectrum induced by along- and cross-radar-beam winds are theoretically investigated in this article. Analytical expression of beam broadening spectrum for a vertical beam subject to a constant vertical wind in the absence of horizontal wind is derived first. We find that the resultant beam broadening spectral shape is in an exponential form, rather than a Gaussian shape. The peak of the exponential spectrum corresponds to the true vertical wind velocity, and the spectral width σ is a function of vertical wind velocity ω and the half-power beam width χ_1/2 of the radar beam, in accordance with the expression σ=0.09wχ²_1/2. The beam broadening spectrum for a vertical radar beam subject to both vertical and horizontal winds is numerically studied, and the result shows that the spectral shape is distorted from the Gaussian form. The estimated vertical wind velocity of the distorted spectrum is very close to the true vertical wind velocity with a difference of less than 0.6% for a typical case. However, its spectral width is substantially greater than that of the conventional Gaussian spectrum broadened by horizontal wind only. The difference of the spectral widths Δσ (in unit of percentage) in the two, as a function of the half-power beam width and the ratio of vertical to horizontal wind velocities, can be well approximated by a parabolic equation. With this equation and the conventional Gaussian beam broadening spectral width caused by horizontal wind, the true width of the distorted beam broadening spectrum induced by vertical and horizontal winds can be inferred without complicated numerical computation. Through a transformation of wind velocity from vertical and horizontal winds into along-and cross-radar-bearn winds defined on the cross section of an oblique radar beam, the results obtained from the case of vertical radar beam can be directly applied to the case of the oblique beam. We show that in some special cases the beam broadening spectral widths of an oblique beam subject to both vertical and horizontal winds will be exceedingly narrower than those estimated by the existing formula, irrespective of the presence of strong horizontal wind velocity.