Widespread occurrences of valley networks on Mars provide geomorphic evidence for an active hydrologic cycle. To constrain the climatic conditions capable of forming the valley networks, a hydrological model was used to analyze the valley incision depth and volume of eroded valleys. Because the absolute magnitudes of precipitation, runoff, and evaporation are uncertain, we have used the ratio of these quantities (the X-ratio) to express climatic conditions. The spatial distribution and strength of the correlations between (1) the estimated depth and volume of eroded material and (2) estimated flood magnitude and valley gradients were investigated as a function of the assumed X-ratio. We also conducted an analysis of conditions required to have appreciable discharge in selected valley networks, which provided the most definitive constraint on Martian paleoclimate. The other methods show a relatively weak dependency of incision depths and volumes upon the assumed X-ratio. The multiple regression analyses indicate that incision depth is strongly influenced by gradient and weakly related to modeled flood discharge. The factors determining relative depth of incision depend partly on the type of channel bed. However, postflow modification of the valley networks by mass wasting, cratering, aeolian infilling, and ice-related processes precludes direct determination of bed morphology. Our hydrological analyses suggest that climatic conditions on early Mars were at least as moist as those that occurred in the Great Basin region of the U.S. when large lakes were present during the Pleistocene in terms of the balance of runoff and lake evaporation.
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