The applicability of asymptotic formulas for recovery of "optical" turbulence parameters from data of the lidar sensing. II. Results of the numerical calculations
V.V. Vorob’ev
A.M. Obukhov Institute of Atmospheric Physics Russian Academy of Sciences, Pyzhevsky per., 3, 119017, Moscow, Russia
Keywords: лидары, турбулентность, усиление обратного рассеяния, уравнения Вольтерра и Абеля, lidar, turbulence, backscattering enhancement, Volterra equations and Abel equations
Abstract
The applicability of the formulas obtained in the first part of the article [1] is investigated in a numerical experiment. It is shown that the geometric optics approximation is applicable only for short distances hundreds of times smaller than the corresponding length of the diffraction. Limitations, caused by the oscillations of the original integral equation kernel, lead to strong oscillations of the third derivative of the measured data. Relationships based on the asymptotic formula for a point receiver are insensitive to the oscillations of the measured data. The application of formulas for point receiver in the case of finite radius of receivers leads to smoothing inversed distributions and their shift relative to the given ones. Method of accounting for these factors is developed. The use the approximation of a point receiver together with smoothing the restored distributions leads to a partial loss in the restored data information about the turbulence spectrum. This makes it possible to simplify the solution of the inverse problem, reducing it to the calculation of the second order derivatives.
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