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We investigate atomic hydrogen (H) variability from the mesopause to the upper thermosphere, on time scales of solar cycle, seasonal, and diurnal, using measurements made by the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument on the Thermosphere Ionosphere Mesosphere Energetics Dynamics satellite, and simulations by the National Center for Atmospheric Research Whole Atmosphere Community Climate Model-eXtended (WACCM-X). In the mesopause region (85 to 95\ km), the seasonal and solar cycle variations of H simulated by WACCM-X are consistent with those from SABER observations: H density is higher in summer than in winter, and slightly higher at solar minimum than at solar maximum. However, mesopause region H density from the Mass-Spectrometer-Incoherent-Scatter (National Research Laboratory Mass-Spectrometer-Incoherent-Scatter 00 (NRLMSISE-00)) empirical model has reversed seasonal variation compared to WACCM-X and SABER. From the mesopause to the upper thermosphere, H density simulated by WACCM-X switches its solar cycle variation twice, and seasonal dependence once, and these changes of solar cycle and seasonal variability occur in the lower thermosphere (~95 to 130\ km), whereas H from NRLMSISE-00 does not change solar cycle and seasonal dependence from the mesopause through the thermosphere. In the upper thermosphere (above 150\ km), H density simulated by WACCM-X is higher at solar minimum than at solar maximum, higher in winter than in summer, and also higher during nighttime than daytime. The amplitudes of these variations are on the order of factors of ~10, ~2, and ~2, respectively. This is consistent with NRLMSISE-00.