A Bayesian parametric approach to the retrieval of the atmospheric number size distribution from lidar data

We consider the problem of reconstructing the number size distribution (or particle size distribution) in the atmosphere from lidar measurements of the extinction and backscattering coefficients. We assume that the number size distribution can be modeled as a superposition of log-normal distributions, each one defined by three parameters: mode, width and height. We use a Bayesian model and a Monte Carlo algorithm to estimate these parameters. We test the developed method on synthetic data generated by distributions containing one or two modes and perturbed by Gaussian noise as well as on three datasets obtained from AERONET. We show that the proposed algorithm provides good results when the right number of modes is selected. In general, an overestimate of the number of modes provides better results than an underestimate. In all cases, the PM1, PM2.5 and PM10 concentrations are reconstructed with tolerable deviations.