The current Martian water cycle is extremely asymmetric, with large amounts of vapor subliming off a permanent north polar water ice cap in northern summer, but with no apparent major source of water vapor in the southern hemisphere. Detailed simulations of this process with a three-dimensional circulation model indicate that the summertime interhemispheric exchange (Hadley cell) is very much stronger than transport by eddies in other seasons. As a result, water ice would be distributed globally were it not for the buffering action of regolith soil adsorption which limits the net flux of water vapor off the north polar cap to amounts that are insignificant even on the scale of thousands of years. It has been suggested that the polar layered deposits are the result of exchange on these long time scales, driven by changes in Martian orbital parameters. We therefore are conducting simulations to test the effect of varied orbital parameters on the Martian water cycle. We find that when the perihelion summer pole is charged with a polar water ice cap, large quantities of water are quickly transfered to the aphelion summer pole, setting up an annual cycle that resembles the present one. Thus, the adsorptivity of the Martian regolith may be in the narrow range where it can limit net transport from the aphelion but not the perihelion pole.