9 December 1994 Estimation of spectrum of Doppler lidar signal in a turbulent atmosphere
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Abstract
One way of obtaining an information on wind velocity in the atmosphere from measurements by Doppler lidar is to estimate the power spectral density of the Doppler signal and its parameters, namely, the center of the spectrum and the width of the spectrum. The first of them is generally taken as the radial wind velocity component and the second one defines the radial velocity variance which contains information on the rate of turbulence energy dissipation. The accuracy of measurement of wind velocity and turbulence depends on the accuracy of estimation of the Doppler spectrum. The paper is dedicated to analysis of estimation of the power spectrum of the Doppler signal and the spectrum parameters. In contrary to previous works in this paper the non-Gaussian statistics of lidar signal due to atmospheric turbulence is taken into account. It is shown, that in consequence of non-Gaussian statistics the relative rms error of spectrum estimation exceeds unit if the measurement duration is far less than the period of correlation of wind velocity fluctuations and the length of sensing volume (Delta) z is far less than outer scale of turbulence LV((Delta) z/LV<<1). By the increase of (Delta) z the relative error can be reduced to the level determined by the number of statistical freedom degrees. The increase of dimension of the sensing volume leads also to decrease of the error of estimating both the center and width of the spectrum. The error of estimation of the width decreases with increasing the ratio (Delta) z/LV monotonously. The error of estimation of the spectrum center decreases up to the level determined by the signal-to-noise ratio and the time of measurement.
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Viktor A. Banakh, Igor N. Smalikho, Friedrich Koepp, Christian Werner, "Estimation of spectrum of Doppler lidar signal in a turbulent atmosphere", Proc. SPIE 2310, Lidar Techniques for Remote Sensing, (9 December 1994); doi: 10.1117/12.195866; https://doi.org/10.1117/12.195866
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