Retrieval of cloud parameters from the multiple scattered lidar signals

The conventional lidar technique is elaborated to measure parameteres of the atmospheric aerosols where the single scattering approximation is valid. This technique fails to measure the size distribution and the number density profile of the cloud particles because of the great optical density of clouds where the process of multiple scattering of the lidar signal becomes predominant. The process of multiple scattering essentially smoothes out the information on the cloud parameters and the inverse problem looks rather hopeless. The information on the cloud parameters is not lost so quickly in the multiple scattering process due to the small angular scattering when the particles sizes are greater than the lidar wavelength. In this case, the inverse problem can be successfully considered and applied for the moderate optical depths. To use the advantage of the small-angular scattering, in this paper the multiple scattered radiation is divided into two parts: the small-angular or multiple diffracted part and the residue or the quasi-isotropical part. The division procedure is strict and the proper radiative transfer equations for the both terms are written down. The equation for MDP is solved analytically using the known small-angular approximation of the radiative transfer equation. The simple analytical expression obtained for the small-angular distribution of the lidar signals is used to construct an analytical algorithm to retrieve the particle size distribution or the number density profile of those cloud particles which are greater than the wavelength. The obtained lidar algorithm can be the basis of the quantitative theory. To extract the multiple diffracted part from the whole experimentally measured lidar signal, the numerical calculations of the lidar signal based on the Monte-Carlo method have been made