Forward modeling of ice topography on Mars to infer basal shear stress conditions

Understanding the history of ice caps on Mars could reveal important information about Martian geologic and climatic history. To do this, an ice reconstruction model is needed that operates over complex topography and can be constrained with a limited number of free parameters. In this study we developed a threshold-sliding model for ice cap morphology based on the classic model of Nye later incorporated into the models of Reeh and colleagues. We have updated the Nye-Reeh model with a new numerical algorithm. Although the model was originally developed to model perfectly plastic deformation, it is applicable to any ice body that deforms when a threshold basal shear stress is exceeded. The model requires three inputs: a digital elevation model of bed topography, a "mask" grid that defines the position of the ice terminus, and a function defining the threshold basal shear stress. To test the robustness of the model, the morphology of the Greenland ice sheet is reconstructed using an empirical equation between threshold basal shear stress and ice surface slope. The model is then used to reconstruct the morphology of ice draping impact craters on the margins of the south polar layered deposits using an inferred constant basal shear stress of ∼0.6 bar for the majority of the examples. This inferred basal shear stress value is almost 1/3 of the average basal shear stress calculated for the Greenland ice sheet. What causes this lower basal shear stress value on Mars is unclear but could involve the strain-weakening behavior of ice.