Clear air turbulence (CAT) is a serious threat for civil aviation flights. In the years 2009 through 2015, with the support of the European Commission, as a part of the 7th Framework Program, the DELICAT project (DEmonstration of LIdar based Clear Air Turbulence detection) was implemented. In this project, an air-borne lidar was developed and built for an early detection of CAT. In August 2013, flight tests of the lidar were carried out. During the experiments, a large unique data set was collected; a copy of the data set is in the possession of the Obukhov Institute of Atmospheric Physics of Russian Academy of Sciences (IAP RAS). In the proposed project, we propose solving the following problems. We will develop a numerical model of the laser sounding of CAT, considering the effect of the laser beam propagation in a random medium, as well as the aerosol (Mie) and molecular (Rayleigh) scattering. The analysis of the existing observations indicates that, in most cases, the multiple scattering effects are negligible. The will allow us to develop the model on the basis of the multiple phase screen method. This model will produce realizations of the random signal for specific realization of the random refractivity and aerosol distribution fields. A modification of the multiple phase screen method will allow modeling a diverging laser beam. This will also allow modeling of the back-scattering enhancement (BSE). By varying the aerosol composition, it will be possible to model different degree of correlation and intensity ratio in co- and cross-polarization channels. The model of the laser sounding of CAT will help answering the question, whether aerosol is an impeding factor when using the BSE effect. We will develop a realistic model of the observation geometry variations. We will perform the primary processing of the whole available data set of the DELICAT observations. This will allow us to estimate the statistical properties of the measurement noise. We will analyze the DELICAT observations. We will fit the model parameters in order to reproduce, as close as possible, the statistical properties of the observations. This will help answering the questions, how accurately and timely it is possible to detect CAT parameters using two types of lidar systems: 1) system with two polarization channels, and 2) system based on the BSE effect.