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A Bayesian algorithm to retrieve profiles of cloud ice water content (IWC), ice particle size (Dme), and relative humidity from millimeter-wave/submillimeter-wave radiometers is presented. The first part of the algorithm prepares an a priori file with cumulative distribution functions (CDFs) and empirical orthogonal functions (EOFs) of profiles of temperature, relative humidity, three ice particle parameters (IWC, Dme, distribution width), and two liquid cloud parameters. The a priori CDFs and EOFs are derived from CloudSat radar reflectivity profiles and associated ECMWF temperature and relative humidity profiles combined with three cloud microphysical probability distributions obtained from in situ cloud probes. The second part of the algorithm uses the CDF/EOF file to perform a Bayesian retrieval with a hybrid technique that uses Monte Carlo integration (MCI) or, when too few MCI cases match the observations, uses optimization to maximize the posterior probability function. The very computationally intensive Markov chain Monte Carlo (MCMC) method also may be chosen as a solution method. The radiative transfer model assumes mixtures of several shapes of randomly oriented ice particles, and here random aggregates of spheres, dendrites, and hexagonal plates are used for tropical convection. A new physical model of stochastic dendritic snowflake aggregation is developed. The retrieval algorithm is applied to data from the Compact Scanning Submillimeter-wave Imaging Radiometer (CoSSIR) flown on the ER-2 aircraft during the Tropical Composition, Cloud and Climate Coupling (TC4) experiment in 2007. Example retrievals with error bars are shown for nadir profiles of IWC, Dme, and relative humidity, and nadir and conical scan swath retrievals of ice water path and average Dme. The ice cloud retrievals are evaluated by retrieving integrated 94 GHz backscattering from CoSSIR for comparison with the Cloud Radar System (CRS) flown on the same aircraft. The rms difference in integrated backscattering is around 3 dB over a 30 dB range. A comparison of CoSSIR retrieved and CRS measured reflectivity shows that CoSSIR has the ability to retrieve low-resolution ice cloud profiles in the upper troposphere

Ice hydrometeor profile retrieval algorithm for high-frequency microwave radiometers: application to the CoSSIR instrument during TC4