A Bayesian approach for the retrieval of atmospheric particle properties from lidar data with uncertainty quantification

We consider the inverse problem of recovering the particle size distribution of atmospheric aerosol from backscattering and extiction coefficients at three wavelengths, as attainable using ground lidar measurements. We set up a Bayesian model composed of a collection of fixed-dimensional models, and devise a sequential Monte Carlo algorithm to sample its posterior distribution, allowing for automated model selection. As the target distribution is a complex, often multimodal distribution, we first assess the degree of reliability of the sampling procedure. We then go on to characterize the ill-posedness in terms of multimodality of the posterior distribution, in order to verify the presence of multiple alternative scenarios that are compatible with the measured data. We finally assess the accuracy of the reconstruction for practical use. Our results show that the proposed approach can successfully retrieve the particle size distribution from lidar data even under complex circumstances, and reliably characterize the uncertainty that inevitably arises due to the nature of the data.