Lidars are powerful remote sensing instruments, which illuminate targets with a pulsed laser source and measure the backscattered power at wavelengths of interest. Lidars play a crucial role in the study of the atmosphere as they allow, in principle, to retrieve information on the optical and microphysical characteristics of the atmospheric aerosol, including pollution, clouds, dust and other types of substances.
In this work, we consider the problem of retrieving the aerosol number size distribution, i.e. the distribution of particles radii, from the reconstructed optical parameters, i.e. extinction and backscattering coefficients, obtained by Lidar measurements. Solving this problem essentially corresponds to solving an inverse problem governed by the Mie scattering equations. We propose an innovative method developed within a cooperation program between the Lidar group at Università di Napoli “Federico II”, the MIDA group at Università di Genova, CNR-SPIN and ALA srl. The proposed method is based on the Bayesian approach to ill-posed inverse problems. We assume that the number size distribution is the superposition of a small number of log-normal distributions, and is therefore described by a small number of parameters (mode, width and height of each component). Because of the non-linearity of the problem, we approximate the posterior distribution for the parameters of interest using a Metropolis-Hastings Markov Chain Monte Carlo algorithm. A validation on synthetic data indicates that the algorithm is effective in reconstructing unimodal and bimodal distributions; three-modal distributions are more challenging and need careful use of a priori information. Validation on experimental data is in due course.