Multiple year General Circulation Model (GCM) simulations that include a finite surface dust reservoir and an infinite surface dust reservoir are compared. While the infinite dust reservoir simulations produce a highly repeatable annual dust cycle, the finite surface dust reservoir simulations evolve quickly towards a low- dust condition. Once a region is swept clean of available surface dust, it reacquires only small amounts of dust during northern summer but it is repeatedly swept clean during each subsequent dust storm season (southern spring and summer). This argues against a finite dust reservoir as a mechanism for the interannual variability of global dust storms. Additionally, these results suggest that the regions of preferred wind stress lifting are deep dust reservoirs that are not depleted and resupplied on annual or decadal timescales. Therefore, the dust cycle must be closed on much longer timescales, possibly those associated with orbital variations.