This dissertation is an investigation into how measurements of backscatter and extinction from lidar can be interpreted to gain information about other aerosol properties by determining uncertainties of aerosol size distributions and refractive indexes. A derivation of aerosol optical properties from particle size distributions and their resulting effect on lidar signals is shown. Procedures for retrieving optical properties from lidar signals are shown and an analysis of the dependency of optical coefficient retrieval error on true value is performed. Methods of retrieving aerosol size distributions including linear basis representation and parameterization are discussed. A graphical uncertainty analysis is discussed and applied to analyzing the effects on uncertainty when extinction measurements are included to a three-wavelength backscatter measurement set in an assumed index of refraction model. The problems associated with using a mono-modal model in the presence of a bimodal aerosol distribution are analyzed.

The Bayesian inverse method is introduced and a reverse Monte Carlo method based on conditional probability is used to illustrate discrepancies from a conventional forward Monte Carlo method. An analytic formula for the color ratio retrieval error probability density function (PDF) is derived for computing the posterior PDF. Discrepancies between posterior cumulative distribution functions (CDFs) and estimated CDFs from forward Monte Carlo methods using Bayesian and non-Bayesian retrieval methods are demonstrated and quantified for an array of scenarios. General differences in marginal and measurement-conditional error PDFs are formulated. Posterior PDFs are used to derive credible sets of aerosol distribution parameters including complex index of refraction from synthetic optical coefficient measurements.

A plan for using posterior PDFs for uncertainty analysis in high dimensional aerosol models based on the Metropolis-Hastings Markov chain Monte Carlo algorithm is presented. Preliminary results of its application in the parameterized model are shown and compared with analytic posterior CDFs.