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In this paper, we introduce the results of the statistical analysis of atmospheric characteristics at the site of the Big Telescope Alt-azimuthal (BTA) of the Special Astrophysical Observatory (SAO) of the Russian Academy of Science (RAS). The BTA is the largest optical telescope in Eurasia and is located near Mt Pastukhova in the northern part of the Caucasus Mountains, at an altitude of 2070 m above sea level. The atmosphere of the Earth is a major challenge for observing and it limits the quality of astronomical images obtained by ground-based telescopes. The study of the atmosphere above astronomical observatories is important for the planning of observing time, for the optimization of instrument performance and for the development of adaptive optics systems. We discuss the results of a study of the meteorological conditions at the BTA site: total cloud cover, wind speed at the pressure level of 200 hPa, vertical motions, vertical profiles of the wind speed employing data from the ERA-Interim and National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) re-analysis data bases.