Absorption of cosmic rays by atmospheric mass varies temporally due to a redistribution of atmospheric pressure by ice sheets during glaciations, the compression and expansion of the atmosphere due to cooling and warming, and changes in katabatic winds near large ice masses. These atmospheric processes can result in changes in production rates of cosmogenic nuclides which, when integrated over long exposure durations may result in 0% to >5% adjustments in site production rates depending on location. Combining a CCM3 model with imbedded ice sheets for 20 ka, we show that production rates changes (relative to today) are greatest at high elevations (6--7% at 5 km altitude) due to atmospheric compression from decreased temperature. Production rates at specific times for sites near ice sheet margins can be reduced more than 10% due to a combination of katabatic winds draining off the ice sheet margins and atmospheric cooling. Nunatak settings may be significantly affected by the climate effect due to persistent glacial atmospheric conditions. Atmospheric variability may explain some of the disparities among cosmogenic nuclide production rate calibrations.