Doppler radar spectral width broadening due to beamwidth and wind shear

The spectral width observed by Doppler radars can be due to several e€ects including the atmospheric turbulence within the radar sample volume plus e€ects associated with the background ̄ow and the radar geometry and con®guration. This study re-examines simple models for the e€ects due to ®nite beamwidth and vertical shear of the horizontal wind. Analytic solutions of 1and 2-dimensional models are presented. Comparisons of the simple 2-dimensional model with numerical integrations of a 3-dimensional model with a symmetrical Gaussian beam show that the 2-dimensional model is usually adequate. The solution of the 2dimensional model gives a formula that can be applied easily to large data sets. Analysis of the analytic solutions of the 2-dimensional model for o€-vertical beams reveals a term that has not been included in mathematical formulas for spectral broadening in the past. This term arises from the simultaneous e€ects of the changing geometry due to curvature within a ®nite beamwidth and the vertical wind shear. The magnitude of this e€ect can be comparable to that of the wellknown e€ects of beam-broadening and wind shear, and since it can have either algebraic sign, it can signi®cantly reduce (or increase) the expected spectral broadening, although under typical conditions it is smaller than the beam-broadening e€ect. The predictions of this simple model are found to be consistent with observations from the VHF radar at White Sands Missile Range, NM.