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The Atmospheric Infrared Sounder (AIRS) onboard the National Aeronautics and Space Administration's Earth Observing System's (EOS) Aqua spacecraft, with its high spectral resolution and radiometric accuracy, provides atmospheric vertical temperature and moisture sounding information with high vertical resolution and accuracy for numerical weather prediction (NWP). Due to its relatively coarse spatial resolution (13.5 km at nadir), the chance for an AIRS footprint to be completely cloud free is small. However, the Moderate Resolution Imaging Spectroradiometer (MODIS), also on the Aqua satellite, provides colocated clear radiances at several spectrally broad infrared (IR) bands with 1-km spatial resolution; many AIRS cloudy footprints contain clear MODIS pixels. An optimal cloud-correction or cloud-clearing (CC) algorithm, an extension of the traditional single-band N* technique, is developed. The technique retrieves the hyperspectral infrared sounder clear column radiances from the combined multiband imager IR clear radiance observations with high spatial resolution and the hyperspectral IR sounder cloudy radiances on a single-footprint basis. The concurrent AIRS and MODIS data are used to verify the algorithm. The AIRS cloud-removed or cloud-cleared radiance spectrum is convolved to all the possible MODIS IR spectral bands with spectral response functions (SRFs). The convoluted cloud-cleared brightness temperatures (BTs) are compared with MODIS clear BT observations within AIRS cloud-cleared footprints passing our quality tests. The bias and the standard deviation between the convoluted BTs and MODIS clear BT observations is less than 0.25 and 0.5 K, respectively, over both water and land for most MODIS IR spectral bands. The AIRS cloud-cleared BT spectrum is also compared with its nearby clear BT spectrum, the difference, accounting the effects due to scene nonuniformity, is reasonable according to the analysis. The multiband optimal cloud-clearing is also compared with the traditional single-band N* cloud-clearing; the performance enhancement of the optimal cloud-clearing over the single-band traditional N* cloud-clearing is demonstrated and discussed. It is found that more than 30% of the AIRS cloudy (partly and overcast- ) footprints in this study have been successfully cloud-cleared using the optimal cloud-clearing method, revealing the potential application of this method to the operational processing of hyperspectral IR sounder cloudy radiance measurements when the collocated imager IR data are available. The use of a high spatial resolution imager, along with information from a high spectral resolution sounder for cloud-clearing, is analogous to instruments planned for the next-generation Geostationary Operational Environmental Satellite (GOES-R) instruments-the Advanced Baseline Imager and the Hyperspectral Environmental Suite. Since no microwave instruments are being planned for GOES-R, the cloud-clearing methodology demonstrated in this paper will become the most practical approach for obtaining the reliable clear-column radiances.