Though sources of retrieval error are known to be large, it is commonly assumed that ice cloud property retrievals are well constrained so that a look up table or optimal estimation approach can be used to provide a unique solution. However, because of nonlinearities in radiative transfer models, the error characteristics of retrieved ice cloud properties are generally not well known. An alternative formulation, which represents information from prior knowledge, observations, and the forward model probabilistically, allows for an accurate assessment of the solution space and provides information about the nature of uncertainties in the retrieval. In this paper, one such technique, the Markov chain Monte Carlo (MCMC) approach, is used to sample the PDF of retrieved ice water path and ice particle effective radius, and to explore the characteristics of the ice cloud property retrieval solution. MCMC is first used to explore the well-known sensitivity of infrared cloud property retrievals to errors in cloud top height and geometric thickness. The method is then used to explore the effect of changes to the assumed ice crystal shape, as well as the effect of reduction in observation error, particle settling, and different error probability distributions.

It is found that, though the effects of uncertainty in cloud top height are not insignificant, it is uncertainty in the ice crystal shape that contributes most to the uncertainty in the retrieval. In addition, in the absence of information to constrain crystal shape, multiple potential solutions exist. Reduction of observation error and the assumption of particle settling serve to change the preferred combination of crystal shapes in the volume, but do not eliminate the potential for a multimode result. Application of MCMC to a scene reveals that both the nature and magnitude of retrieval errors exhibit a strong dependence on cloud optical depth. Solution PDFs of both IWP and effective radius depart from the traditionally-assumed Gaussian shape for any given pixel across the scene, and often exhibit multiple modes.