Collocated active and passive remote sensing measurements collected at U.S. Department of Energy Atmospheric Radiation Measurement Program sites enable simultaneous retrieval of cloud and precipitation properties and air motion. Previous studies indicate the parameters of a bimodal cloud particle size distribution can be effectively constrained using a combination of passive microwave radiometer and radar observations; however, aspects of the particle size distribution and particle shape are

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... ically assumed to be known. In addition, many retrievals assume the observation and retrieval error statistics have Gaussian distributions and use least squares minimization techniques to find a solution. In truth, the retrieval error characteristics are largely unknown. Markov chain Monte Carlo (MCMC) methods can be used to produce a robust estimate of the probability distribution of a retrieved quantity that is nonlinearly related to the measurements and that has non-Gaussian error statistics. In this work, an MCMC algorithm is used to explore the error characteristics of cloud property retrievals from surface-based W-band radar and low-frequency microwave radiometer observations for a case of orographic snowfall. In this particular case, it is found that a combination of passive microwave radiometer measurements with radar reflectivity and Doppler velocity is sufficient to constrain the liquid and ice particle size distributions, but only if the width parameter of the assumed gamma particle size distribution and mass-dimensional relationships are specified. If the width parameter and mass-dimensional relationships are allowed to vary realistically, a unique retrieval of the liquid and ice particle size distribution for this orographic snowfall case is rendered far more problematic.