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Five years of atmospheric temperature data, collected with an Fe Boltzmann lidar by the University of Colorado group from 2011 to 2015 at Arrival Heights, are used to characterize the vertical wavelengths, periods, vertical phase speeds, frequency spectra, and vertical wave number spectra of stratospheric gravity waves from 30 to 50 km altitudes. Over 1000 dominant gravity wave events are identified from the data. The seasonal spectral distributions of vertical wavelengths, periods, and vertical phase speeds in summer, winter, and spring/fall are found obeying a lognormal distribution. Both the downward and upward phase progression gravity waves are observed by the lidar, and the fractions of gravity waves with downward phase progression increase from summer similar to 59% to winter similar to 70%. The seasonal and monthly mean vertical wavelengths and periods exhibit clear seasonal cycles with vertical wavelength growing from summer similar to 5.5 km to winter similar to 8.5 km, and period increasing from summer similar to 4.5 h to winter similar to 6 h. Statistically significant linear correlations are found between the monthly mean vertical wavelengths/periods and the mean zonal wind velocities from 30 to 50 km. Assuming horizontal phase speeds independent of month, the monthly mean horizontal wavelengths, intrinsic periods, and group velocities are estimated for stratospheric gravity waves. The slopes of wave frequency spectra change from similar to 1.9 at 30-60 km to similar to 1.45 around 60-65 km. The vertical wave number spectra show the power spectral density at vertical wavelengths of 5-20 km decreasing from winter maximum to summer minimum. Several aforementioned features are observed for the first time in Antarctica.

Plain Language Summary Generated by buoyancy force, gravity waves are one of the most ubiquitous and important atmospheric waves. They transport momentum and energy over the globe, affect the atmospheric circulation and chemical reactions, generate turbulence, and mix the air. The missing gravity wave drag especially in the Antarctic stratosphere is regarded as one possible mechanism for the long-lasting "cold-pole" problem in most climate models, and the challenge came from the sparsity of polar gravity wave observations. Five years of Fe Boltzmann lidar observations at McMurdo, Antarctica, provide a unique opportunity to meet this challenge and reveal numerous gravity wave properties for the first time in Antarctica. From these observational facts, the science points in the paper lead to a better understanding of the potential wave sources and provide information for gravity wave parameterization, a key point for atmospheric models to be right. In addition, a new method is rigorously developed to infer the intrinsic period, horizontal phase speed, and wavelength from the nearly linear relation of gravity wave parameters with the mean background winds. Overall, a complete picture of gravity waves in the polar stratosphere resolvable from lidar starts to emerge and would greatly impact the whole atmosphere community.