Ground-based Fabry-Perot observations of the hydrogen Balmer-alpha emission have been used since the late 1970s to investigate hydrogen in the geocorona, spanning the upper thermosphere and exosphere. Atomic hydrogen in this region is a byproduct of hydrogen-containing species below such as methane and water vapor. Models have predicted 50-75% increases in upper atmospheric hydrogen as a consequence of a doubling of tropospheric concentrations of methane, a primary greenhouse gas. The 11-year solar cycle is a dominant source of natural variability in the upper atmosphere and its effect on hydrogen distributions and emissions must be understood to investigate possible signs of longer-term climatic trends. We will discuss data from the present near-solar minimum winter compared with those from the previous near-solar minimum period of 1997, all taken with the same instrument, the Wisconsin H-alpha Mapper Fabry-Perot (Kitt Peak, AZ), and using the same nebular calibration source for absolute intensity calibration. The newer data are consistent with observations over the rise of the solar cycle with lower intensities observed during solar minimum compared with solar maximum conditions. We will also discuss preliminary comparisons with earlier data and the extra challenges associated with comparing data taken with different, though similarly designed instruments. The geocoronal hydrogen column emission observed by the Fabry-Perot is a function of the hydrogen density profile, the solar excitation flux, and radiative transfer including the contribution of multiple scattering below the Earth's shadow. We will discuss work in progress to use forward modeling to retrieve the hydrogen column abundance from the emission observations.