[1] A hydrologic routing model has been applied to the Noachian cratered highlands of Mars to establish the climatic conditions required to maintain exit breached lakes on early Mars and the likely fraction of the upland surface that would have hosted lakes whether they overflowed or not. The climatic conditions were expressed as a ratio of net evaporative loss from lakes to the surface runoff from uplands (the "X ratio"). Simulations were conducted using 16 different X ratios. The lake area, volume, and number of overflowing lakes decrease as climate becomes drier (larger X ratio). The modal frequency of the X ratio for the overflow of highland basins with eroded exit breaches was 5.0, which is comparable to that of the Great Basin region in the western United States during the Last Glacial Maximum (LGM). This indicates that lakes on early Mars were likely to have been at least as extensive as those in the Great Basin region during the LGM.

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[1] Drainage networks on Titan, Earth, and Mars provide the only known examples of non-volcanic fluvial activity in our solar system. The drainage networks on Titan are apparently the result of a methane-ethane cycle similar to Earth's water cycle. The scarcity of impact craters and the uneven distribution of fluvial dissection on Titan suggest that the surface may be relatively young. The purpose of this study is to assess the importance of erosion relative to other plausible mechanisms of resurfacing such as tectonic deformation, cryovolcanism, or deposition of aerosols. We present a new method, based on a measure of drainage network shape known as the width function, to estimate cumulative erosion into an initially rough surface. We calibrate this method with a numerical landscape evolution model, and successfully test the method by applying it to river networks on Earth with different exhumation histories. To estimate erosional exhumation on Titan, we mapped fluvial networks in all Synthetic Aperture Radar swaths obtained by the Cassini spacecraft through T71. Application of our method to the most completely imaged drainage networks indicates that for two of four regions analyzed, Titan's fluvial networks have produced only minor erosional modification of the surface. For the best-constrained region in the northern high latitudes, we find that fluvial networks reflect spatially averaged erosion of more than 0.4% but less than 9% of the initial topographic relief. This result implies either a recent, non-fluvial resurfacing event or long-term fluvial incision rates that are slow relative to the rate of resurfacing.

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