Comparison of modeled atmospheric hydrogen (H2) levels with observations is an important way of testing scientific understanding of H2 biogeochemistry. But the instrumental record is short and provides limited dynamic range with which to test assumptions about H2 cycling. Here, we compare twentieth century H2 levels reconstructed from polar firn air to the output from a historical run of the Geophysical Fluid Dynamics Laboratory Atmospheric Model 4.1 (GFDL-AM4.1). Simulated H2 exhibits reasonable agreement with the reconstruction. The twentieth century increase in H2 levels is consistent with rising atmospheric CH4 levels and changing emissions from fossil fuel combustion. However, the model fails to capture the reconstructed reversal in the interpolar H2 gradient between 1960 and 1990. We invert an 8-box model of the atmosphere to show that the reversal in the interpolar difference requires a large increase (decrease) in the simulated NH (SH) net source of H2 peaking circa 1980. Revisions to our estimates of historical biomass burning emissions, photochemical production, and/or anthropogenic emissions could help resolve the discrepancy. Our optimization implies a 15% increase in the strength of the soil sink in the NH mid to high latitudes from 1970 to 2000, which is qualitatively consistent with expectations based on changing soil moisture and temperature. We also show that smaller adjustments to the H2 budget would be needed to explain the reversal in the interpolar gradient if the H2 deposition lifetime were shorter than commonly accepted. A shorter lifetime may be supported by recently identified geological sources of H2.