## 1. Introduction

[2] Wind profilers have been used successfully for nearly four decades to study structure and dynamics of the atmosphere since the 1970s [*Woodman and Guilen*, 1974; *Larsen and Röttger*, 1982; *Balsley and Gage*, 1982]. A large variety of atmospheric parameters and phenomena in MST (meso-, strato-, tropo-sphere) region are measured and observed by using wind profilers at different frequencies, including gravity and planetary waves, tropopause, layer thickness, bright band structure, terminal velocity and drop size distribution of hydrometeor, meteor events, turbulence strengths, atmospheric stability, wind velocity, eddy dissipation rates, etc. [*Ecklund et al.*, 1979; *Hocking*, 1997]. The atmospheric parameters are commonly estimated from three lowest moments of observed Doppler spectrum (e.g., power, radial velocity and spectral width) in accordance with theoretical relationships. However, a number of factors may broaden or narrow the Doppler spectra, including turbulence activity, wind field, aspect sensitivity of backscatter and integration effect of wave modulation. Therefore, the estimations of the true atmospheric parameters are complicated by such unwanted contributions.

[3] The beam broadening effect on the observed Doppler spectra have long been the topic of interest in the Doppler radar community. This effect is especially important for wind profilers which have large beamwidths. Even using polarimetric weather radar with relatively narrow beamwidth, the data quality of atmospheric information still deteriorates with range [*Ryzhkov*, 2007]. Therefore large measurement errors may be induced by finite range and angular resolution [e.g., *Sato and Fukao*, 1982; *Hocking*, 1983; *Fukao et al.*, 1988; *May et al.*, 1988; *Meischner*, 2004]. Further, *Candusso and Crochet* [2001] have addressed the problem of overlapping and wind velocity profilers smearing due to beam broadening. Besides, the effect of non-uniform reflectivity cannot be ignored [*Fukao et al.*, 1988; *Chu and Wang*, 2003].

[4] A number of theoretical expressions of the beam broadening spectral widths for different atmospheric targets have been developed. For example, *Chu and Wang* [2007] estimated the velocity fluctuation and spatial distribution of ionospheric field-aligned irregularities in sporadic *E* region after removing the beam broadening contribution from observed spectral width. *Hocking* [1983] established a method to estimate the root mean square velocity of clear-air, in which some spectral broadening effects are considered, such as beam broadening, shear broadening and finite pulse lengths. With this method, the turbulent eddy dissipation rate can be obtained from the corrected spectral width. The results are in good agreement with those obtained using backscattered power method for a common data set [*Cohn*, 1995]. *Wakasugi et al.* [1986] proposed a deconvolution algorithm to remove clear-air turbulence and beam broadening effects from the observed precipitation Doppler spectrum to estimate the raindrop size distribution. In addition, *Nastrom and Eaton* [1997] derived an expression to estimate quantitative contribution of gravity wave to spectral width such that the wave effect can be removed from the observation data.

[5] Beam broadening effect has a profound influence on the measured Doppler spectrum, mainly governed by mean background wind [*Chu*, 2002, 2005]. This broadening effects for various targets have been investigated for years, and there is no general agreement on the quantitative estimation of the resultant spectral moments. *Nastrom* [1997] proposed an analytic formula of spectral width caused by finite beamwidth and vertical shear of the horizontal wind. *Chu* [2002] derived theoretical beam broadening spectrum as a function of three-dimensional wind vector and antenna beamwidth. Moreover, *Nastrom and Tsuda* [2001] reported that the observed spectral widths are smaller for the beams parallel to horizontal wind than those perpendicular to horizontal wind. This feature was attributed to non-uniform distribution of scatters in the azimuth direction. In this article, an attempt is made to investigate the beam broadening spectral width induced by not only three-dimensional wind vector but also vertical wind shear of horizontal wind. In section 2, a numerical simulation model of beam broadening spectrum is established. The study of the beam broadening effect due to wind vector is presented in section 3, in which a comparison between the analytic expression and numerical simulation is made. The wind shear effect on the beam broadening spectrum is investigated in section 4. Conclusions are drawn in section 5.