Mars was warmer and wetter during the early to middle Noachian, before a hydrologic and climatic transition in the late Noachian led to a decrease in erosion rates, a change in valley network morphology, and a geochemical shift from phyllosilicate to sulfate formation that culminated in the formation of widespread sulfate-rich sedimentary deposits in Meridiani Planum and the surrounding Arabia Terra region. This secular evolution was overprinted by episodic and periodic variability, as recorded in the fluvial record, sedimentary layering, and erosional discontinuities. We investigate the temporal evolution of Martian groundwater hydrology during the Noachian and early Hesperian epochs using global-scale hydrological models. The results suggest that the more active hydrological cycle in the Noachian was a result of a greater total water inventory, causing a saturated near-surface and high precipitation rates. The late Noachian hydrologic, climatic, and geochemical transition can be explained by a fundamental shift in the hydrological regime driven by a net loss of water due to impact and solar wind erosion of the atmosphere. Following this transition, the water table retreated deep beneath the surface, except in isolated regions of focused groundwater upwelling and evaporation, producing the playa evaporites in Meridiani Planum and Arabia Terra. This long-term evolution was modulated by shorter-term climate forcing in the form of periodic and chaotic variations in the orbital parameters of Mars, resulting in changes in the volume of water sequestered in the polar caps and cryosphere. This shorter-term forcing can explain the observed periodic and bundled sedimentary layering, erosional unconformities, and evidence for a fluctuating water table at Meridiani Planum.