Bayesian Retrievals of Vertically Resolved Cloud Particle Size Distribution Properties

Retrievals of liquid cloud properties from remote sensing observations by necessity assume sufficient information is contained in the measurements, and in the prior knowledge of the cloudy state, to uniquely determine a solution. Bayesian algorithms produce a retrieval that consists of the joint probability distribution function (PDF) of cloud properties given the measurements and prior knowledge. The Bayesian posterior PDF provides the maximum likelihood estimate, the information content in specific measurements, the effect of observation and forward model uncertainties, and quantitative error estimates. It also provides a test of whether, and in which contexts, a set of observations is able to provide a unique solution. In this work, a Bayesian Markov chain Monte Carlo (MCMC) algorithm is used to sample the joint posterior PDF for retrieved cloud properties in shallow liquid clouds over the remote Southern Ocean. Combined active and passive observations from spaceborne W-band cloud radar and visible and near-infrared reflectance are used to retrieve the parameters of a gamma particle size distribution (PSD) for cloud droplets and drizzle. Combined active and passive measurements are able to distinguish between clouds with and without precipitation; however, unique retrieval of PSD properties requires specification of a scene-appropriate prior estimate. While much of the uncertainty in an unconstrained retrieval can be mitigated by use of information from 94-GHz passive brightness temperature measurements, simply increasing measurement accuracy does not render a unique solution. The results demonstrate the robustness of a Bayesian retrieval methodology and highlight the importance of an appropriately scene-consistent prior constraint in underdetermined remote sensing retrievals.