On the applicability of asymptotic formulas of retrieving “optical” turbulence parameters from pulse lidar sounding data: II–results of numerical simulation

Abstract

The applicability of formulas derived in the first part of this work has been studied in a numerical experiment. The geometrical optics approximation is shown to be applicable only on short paths whose length is less than the corresponding diffraction lengths by a factor of hundreds. The restrictions are caused by oscillations of the kernel of the initial integral equation. They lead to strong oscillations of the third derivative of the measured data. The formulas based on the asymptotic formula of the kernel for a point receiver are slightly sensitive to oscillations of the measured data. Applying the formulas for a point receiver in the case of receivers with a finite radius smoothes the retrieved distributions and shifts them with respect to the given ones. A technique of taking these factors into account in the process of retrieving has been proposed. Together with smoothing of the retrieved distributions, applying the point receiver approximation leads to partial loss of the information about the turbulence spectrum in the retrieved data. This allows one to simplify the retrieval procedure by reducing it to calculating usual derivatives of the second order.