The validity of asymptotic formulas for recovery of "optical" turbulence parameters from data of the lidar sensing. I. Equations
V.V. Vorob’ev
A.M. Obukhov Institute of Atmospheric Physics Russian Academy of Sciences, Pyzhevsky per., 3, 119017, Moscow, Russia
Keywords: турбулентность, лидары, усиление обратного рассеяния, уравнения Вольтерра и Абеля, lidar, turbulence, backscattering enhancement, Volterra equations and Abel equations
Abstract
Asymptotic solutions of the problem of reconstructing the distribution of the structural characteristics of the refractive index fluctuations from the measurement data of the backscatter enhancement effect are derived. Solutions are expressed through fractional derivatives of the backscattering gain in the case of small aperture receiver, or through the ordinary derivatives in the case of receivers with a large aperture. The properties of the integral equation kernel are studied in detail, from which the asymptotic formulas follow. Attention is drawn to the fact that the kernel is oscillating in general. Kernel oscillations little impact the value of the backscattering enhancement, but their impact can be significant on the derivatives of this factor.
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