One hundred forty four crater basins with closed drainage have been mapped within the Martian Noachian highlands that have influent but no outflow channels. The influent streambeds to these basins are characterized by steep gradients and elevation head losses on average of 1 km. These closed basins and influent fluvial channels provide a foundation to investigate the processes under which water was transferred among the early Martian atmosphere and groundwater reservoirs. Channel gradients reflect basin-controlled water table conditions, and the channel head losses suggest sustained drawdowns within the basins due to evaporation and/or sublimation-induced pumping of groundwater. Finite element modeling of groundwater flow permits estimation of minimum rates for evaporation/sublimation for a reasonable set of boundary conditions and hydraulic conductivities, and suggests a Noachian environment with a minimum of 10--20 cm/yr of evaporation and/or sublimation. The flow models are unable to be reconciled with channel gradients without introduction of local precipitation. Acceptable solutions are found with a minimum of 1--2 cm/yr of groundwater recharge. ¿ 1998 American Geophysical Union