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

Y.-H Chu

doi:10.5194/angeo-23-681-2005

Abstract

Abstract. 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 w and the half-power beam width θ1/2 of the radar beam, in accordance with the expression σ=0.09wθ1/22. 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-beam 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.

Highlights

It is well recognized that the background wind in the illuminating region of a Doppler radar with finite antenna beam width plays a crucial role in dominating the behavior of the Doppler spectrum for the radar returns generated from diffusive targets in the atmosphere, including turbulence-induced refractivity fluctuations and hydrometeors
We find that the shape of the beam broadening spectrum for a vertical radar beam subject to a vertical wind is in an exponential form, with a tail extending toward the lower Doppler frequency end, and its spectral width as a function of the product of the vertical wind velocity and the square of the half-power beam width which is considerably smaller than that caused by the horizontal wind
The difference between the mean Doppler velocity of the exponential spectrum and the true vertical wind velocity is the function of the antenna beam width only, while its spectral width is proportional to the product of the vertical wind velocity and the square of the radar half-power beam width

Summary

Introduction

It is well recognized that the background wind in the illuminating region of a Doppler radar with finite antenna beam width plays a crucial role in dominating the behavior of the Doppler spectrum for the radar returns generated from diffusive targets in the atmosphere, including turbulence-induced refractivity fluctuations and hydrometeors. The observed Doppler spectrum will be broadened owing to the radar returns consisting of the signals at various Doppler frequencies that correspond to the radial velocities of the targets located in the different positions in the scattering volume This broadening effect on the breadth of the Doppler spectrum caused by background wind and the antenna beam width is called the beam broadening effect and the resulting Doppler spectrum, without containing the information of atmospheric targets, is termed as the beam broadening spectrum (Hocking, 1983). The width of the beam broadening spectrum is a function of the antenna beam width and background wind velocity, and bears no relation to the characteristics of real atmospheric targets

Objectives

Findings

Discussion

Conclusion