| Summary: | Ice sheets and glaciers constitute an enormous water storage, currently corresponding to a potential sea level rise of almost 70 meters if all ice was to melt completely. The ice sheets are dynamic components of the global climate system and numerical modeling is a useful tool that can help us understand and predict how the ice sheets develop. The most accurate model available for ice sheets is given by the Stokes equations, but to solve them for a real ice sheet on a relevant time scale would be way too computationally costly. Instead approximations of the Stokes equations are used such as the Shallow Ice Approximation (SIA). The SIA is valid for areas where the aspect ratio, the ice thickness divided by the horizontal extent of the ice, is small. In this project equations for temperature and surface evolution were implemented in a Matlab version of SIA. The model already had algorithms implemented for computation of stresses, velocities and pressures for an ice sheet with fixed geometry and temperature. Implementation of temperature and free surface equations also made the problem time-dependent. The result was evaluated by solving a simple test problem and comparing the solution to a full Stokes solution obtained with the code ElmerIce. The SIA solution was closer to the Stokes solution when the aspect ratio ε and slope α were decreased simultaneously such that ε=arctanα, but a similar improvement was also obtained when only the slope was decreased. The differences between the two solutions were satisfyingly small for both temperature, surface location and velocities for an aspect ratio of ε= 7.8 10−4 and ε=arctanα.
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