Introduction: The north polar ice cap on Mars has been mapped with the Mars Orbiter Laser Altimeter (MOLA) [1]. The surface of the ice cap rises about 2800 m above the surrounding surface. The appearance of the ice cap surface is dominated by an irregular spiral structure around two smooth centres. A large valley, Chasma Boreale, separates the two centres into a large elliptically shaped part which is centred at the pole, and a smaller part with a lengthy shape. The spiral structure appears as a results of a pattern of pronounced troughs and scarps at the surface. The steep, equator-facing scarps are dark due to a high dust concentration on the surface, while the more plane, pole-facing (or horizontal) terraces are light. The scarps have been related to a pattern of accumulation and ablation over the surface, with ablation along the dark, equator-facing scarps and accumulation along the light more plane terraces [2,3]. Assuming that the ice flows, a model was proposed, which explains the spiral structure as a result of the accumulation and ablation pattern over the ice cap, and qualitatively relates the scarps and the troughs to ice flow [3].

In this work, the ice flow in the northern cap is modelled. The flow model includes longitudinal stresses, and consider the effects from the ice temperature, which may be widely different from surface to bottom.

The ice flow model: On Earth, the ice sheets flow under their weight as a result of gravity. Accumulation in the central parts is accompanied by ablation in the marginal areas. On Mars, the gravity is smaller, the ice is colder and probably stiffer, and the accumulation and ablation is poorly constrained. If the ice cap is shrinking today, it might be stagnant. The geometry of the northern Martian ice cap is considered, and the deformation of the ice mass as a result of gravity is modelled by an ice flow model.

The ice flow model is axi-symmetrical, and models the ice flow along a line from the centre to the margin with a typical topography from MOLA data, i.e. with scarps and terraces becoming more pronounced as the margin is approached. The model assumes that the ice density is as water ice, and that the constitutive equation is given by the commonly applied flow law for water ice, Glens flow law (see Paterson, 1994). The ice thickness related to the area covered by the ice cap, is used to estimate the flow parameters. The model considers all stresses and include the effect from the temperature distribution through the ice, and calculates the ice flow. If the ice cap is close to steady state, the ice velocities along the surface are balanced by surface accumulation and ablation. Assuming steady state, particle trajectories are derived from the ice flow pattern.

Results: The resulting ice flow pattern is in agreement with the suggested flow pattern by Fisher (1993). The ice moves generally in the direction from the centre towards the margin. The longitudinal stresses are large enough to drag the lowest part of the ice past the pronounced scarps at the surface, even when the surface is north-facing. The scarps affect the ice flow down to the bottom. The ice velocities are highly enhanced in the vicinity of the scarps. If the ice cap is close to stea dy state this flow pattern must be accompanied by enhanced accumulation and ablation associated with the scarps.

References.

[1] Zuber, M. and others (1998). Science, 282, 2053-2060. [2] Howard, A.D. and others (1982). Icarus, 50, 161-215. [3] Fisher, D.A. (1993). Icarus, 105, 501-511.