Estimation of radial wind velocity for the non-Gaussian statistics of the Doppler lidar signal in the turbulent atmosphere

In this paper we present the detailed investigation of estimation of radial wind velocity for the non-Gaussian Doppler lidar signals in the turbulent atmosphere. It is shown that the Doppler lidar signal is the non-Gaussian random process with Gaussian conditional statistical characteristics. The correlation of wind velocity fluctuations in the scattering volume is the reason of the differences of the Doppler lidar signal statistics from the Gaussian one. For the Doppler lidar signal which is the sum of large number random variables, we can not use the central limit theorem for the study of signal statistics because positions of particles are not independently in the turbulent atmosphere. The procedure based on statistical analysis and perturbation theory leads to series for the Doppler shift estimation which is a sum of the regular component, conditional Gaussian and non-Gaussian fluctuation components. The comparison indicates that for limiting cases equation of radial wind velocity estimation coincides with the research results obtained using different theoretical approaches. The standard deviation of the measurement uncertainty of mean radial wind velocity increases with increase of the energy of turbulence. The conditional non-Gaussian component of standard deviation increases with increase of the energy of turbulence and the conditional Gaussian component depends weakly on state of atmospheric turbulence. At night, when the weak turbulence is observed, the non-Gaussian component is approximately equal to zero and the behavior of standard deviation is determined by conditional Gaussian fluctuations. In the afternoon, when the energy of turbulence increases, the conditional Gaussian and non-Gaussian components are of the same order.