Ice Sheet Modeling: Mass Balance Relationships for Map-plane Ice Sheet Reconstruction: Application to Tharsis Montes Glaciation

Introduction: Deposits on the flanks of the large Tharsis Montes volcanoes (Arsia, Pavonis, and Ascraeus Mons) have been recognized to be of glacial origin [1,2]. These Amazonian-aged deposits display three distinct facies, ridged, knobby, and smooth [3], each of which can be associated with different glacial processes [1]. The outermost ridged facies is thought to be the imprint of ice-margin drop moraines recording the fluctuations of a stable cold-based ice sheet. Inside this is the knobby facies, interpreted as a sublimation till deposited as the ice sheet sublimated during a period of major contraction of the ice sheet. Finally, contained within both of these is the smooth facies which may contain debris-covered glacial ice, similar to rock glaciers found in the Dry Valleys of Antarctica [1]. The deposits form fans trending to the northwest from each of the volcanoes and have been described elsewhere [1-4]. Steadystate flowband profiles have been shown to produce reasonable ice sheet configurations of a few hundred to a few thousand meters thickness. However, flowband modeling [5,6] makes estimates of volumes difficult, and steady-state modeling does not allow for the possibility that these ice sheets never attained full equilibrium configurations during the transient climatic conditions that accompany the large oscillations in obliquity that dominate the Martian climate [7]. Modeling: Postulated chronologies for ice sheet behavior are emerging as a better understanding of Mars climate change driven by major variation in the obliquity is seen as allowing for ice sheets to form near the equator at high elevations on the flanks of the large volcanoes [1]. Ice sheet models, coupled with reasonable assumptions about the climate, can obtain estimates for the volumes of these ice sheets, better constraining the water budget for the planet [5,6]. Ice sheet models usually involve an integrated momentum-conservation equation based on the flow law of ice [9] coupled with a mass-conservation, or continuity equations to yield a differential equation for ice extent and thickness as a function of time [10,11]. Mass Balance Distribution : Such an equation requires specification of the source of this mass at each point in the domain, the so-called mass balance. The mass balance consists of two parts, the annual accumulation (ice-equivalent snowfall, in m/yr) and the annual ablation (melting, sublimation, or other erosive processes that remove ice from the ice surface). The difference between these two is the net mass balance, which is the source (or sink if negative) in the continuity equation. On Earth the mass balance can be measured for existing ice sheets, but for reconstruction of paleo-ice sheets a parameterization in terms of elevation and location on the planet is usually used. The accumulation part of the mass balance is usually taken to be proportional to the saturation vapor pressure, a measure of how much water the atmosphere can hold. The saturation vapor pressure is an exponential function of temperature, with a cold atmosphere holding much less water, and hence able to produce much less snow. We would expect the Martian situation to be similar. On Earth, for most glaciers the ablation component is typically due to surface melting with liquid runoff from the ice sheet. This is calculated by imposing a seasonal amplitude onto the mean annual temperature at a location and counting