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A novel statistical method for the retrieval of atmospheric temperature and moisture profiles has been developed and evaluated with simulated clear-air and observed partially cloudy sounding data from the Atmospheric InfraRed Sounder (AIRS) and the Advanced Microwave Sounding Unit (AMSU). The algorithm is implemented in two stages. First, a projected principal components (PPC) transform is used to reduce the dimensionality of and optimally extract geophysical profile information from the cloud-cleared infrared radiance data. Second, a multilayer feedforward neural network (NN) is used to estimate the desired geophysical parameters from the PPCs. For the first time, NN temperature and moisture retrievals are presented using actual microwave and hyperspectral infrared observations of cloudy atmospheres, over both ocean and land (with variable terrain elevation), and at all sensor scan angles. The performance of the NN retrieval method (henceforth referred to as the PPC/NN method) was evaluated using global Earth Observing System Aqua orbits colocated with European Center for Medium-range Weather Forecasting fields for seven days throughout 2002 and 2003. Over 350,000 partially cloudy footprints were used in the study, and retrieval performance was compared with the AIRS Science Team Level-2 retrieval algorithm (version 3). Performance compares favorably with that obtained with simulated clear-air observations from the NOAA88b radiosonde set of approximately 7500 profiles. The PPC/NN method requires significantly less computation than traditional variational retrieval methods, while achieving comparable performance.