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We present a six-year global climatology of cloud properties, obtained from observations of the Atmospheric Infrared Sounder (AIRS) onboard the NASA Aqua satellite. Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) combined with CloudSat observations, both missions launched as part of the A-Train in 2006, provide a unique opportunity to evaluate the retrieved AIRS cloud properties such as cloud amount and height. In addition, they permit to explore the vertical structure of different cloud types. AIRS-LMD cloud detection agrees with CALIPSO about 85% over ocean and about 75% over land. Global cloud amount has been estimated from 66% to 74%, depending on the weighting of not cloudy AIRS footprints by partial cloud cover from 0 to 0.3. 42% of all clouds are high clouds, and about 42% of all clouds are single layer low-level clouds. The “radiative” cloud height determined by the AIRS-LMD retrieval corresponds well to the height of the maximum backscatter signal and of the “apparent middle” of the cloud. Whereas the real cloud thickness of high opaque clouds often fills the whole troposphere, their “apparent” cloud thickness (at which optical depth reaches about 5) is on average only 2.5 km. The real geometrical thickness of optically thin cirrus as identified by AIRS-LMD is identical to the “apparent” cloud thickness with an average of about 2.5 km in the tropics and midlatitudes. High clouds in the tropics have slightly more diffusive cloud tops than at higher latitudes. In general, the depth of the maximum backscatter signal increases nearly linearly with increasing “apparent” cloud thickness. For the same “apparent” cloud thickness optically thin cirrus show a maximum backscatter about 10% deeper inside the cloud than optically thicker clouds. We also show that only the geometrically thickest opaque clouds and (the probably surrounding anvil) cirrus penetrate the stratosphere in the tropics.