This dissertation examines several questions in Martian surface processes relating to water or ice using a combination of geomorphology and modeling. I first examine sublimation of ice from new small mid-latitude craters with freshly exposed ice imaged by the High Resolution Imaging Science Experiment (HiRISE) camera. I discuss the theory of sublimation by free convection and describe a model that improves on the standard version used in the Mars literature. This model shows some differences from experimental data, but this appears to be because experimental conditions do not accurately capture the sublimation regime appropriate to the Martian surface. I use this sublimation model in concert with a thermal model and calculate sublimation rates at the sites of freshly exposed ice. Calculated sublimated thicknesses of one or more millimeters during the period when HiRISE images show ice imply that this ice is relatively pure, not pore-filling. The ice table thus revealed appears consistent with a model of the Martian subsurface in which relatively clean ice overlies pore-filling ice.Pingos are hills with cores of ice formed by freezing of liquid water under pressure. Possible pingos on Mars have been much discussed because they would have significant implications for Martian hydrological processes. I surveyed HiRISE images across a broad portion of the Martian surface searching for fractured mounds. Such features are candidate pingos, since pingos often develop surface fractures as they grow. A small number of Martian landforms, not previously identified, are morphologically consistent with pingos; however, landforms that appear related to these do show morphological differences from pingos. Other origins are possible, particularly since it is difficult to produce the requisite hydrologic conditions for pingo formation. Previously proposed pingos on Mars lack surface fracturing and are unlikely to be pingos.

Despite its ubiquity in planetary science, analogue-based reasoning largely has remained unbounded by guidelines of use. Establishing analogical guidelines and putting them to the test is the main aim of the thesis. Towards this end, I discuss the philosophical foundations of analogical reasoning in planetary geomorphology and posit rules of use that facilitate the evaluation of analogical hypotheses. Subsequently, I present four hypotheses concerning aeolian, fluvial and periglacial processes on Mars. Each of these hypotheses is evaluated in terms of the analogical rules presented. The fourth hypothesis is original to this thesis and suggests that a periglacial landscape comprising pingos and small-scale polygonal ground exists in an impact crater located in northwest Utopia Planitia.

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