Central to the model of the evolution of the martian hydrosphere by Clifford and Parker  is a permanent freezing of the planet at the end of the Noachian and recharge of the global groundwater system by basal melting of ice-rich polar deposits. Acquisition of MOLA data by Mars Global Surveyor provides a means of testing the model, since discharge of water onto the surface, after development of the cryosphere, is driven by the hydrostatic head created by the difference in elevation between the base of the polar-layered terrain and the discharge site. The new data show that, while most post- Noachian water-worn features are at a lower elevation than the base of the polar-layered terrains, as required by the model, there are exceptions. Prominent among these are possible lacustrine deposits within the canyons, tributaries to the canyons, and valleys on several volcanoes. These high-standing features can be reconciled with the model if volcanic melting of ice within the cryosphere is invoked as a source for water at high elevations. An alternative is that high pressures may have developed below the cryosphere as a result of water being trapped beneath the growing cryosphere and the impermeable basement. Yet another alternative is that, since the end of the Noachian, the groundwater system has been recharged by precipitation during occasional warm periods.