## Coupling thermal and mechanical models

Because the viscosity parameter, B, is dependent on temperature and, conversely, the temperature distribution depends on the flow field through the advective terms in the energy balance equation, a complete model of a polar glacier or ice sheet must include calculations of both the flow field and the temperature distribution. It is not practical to combine these two calculations, so they must be done iteratively. First a flow field is determined, given an assumed or previously calculated temperature field. Then the temperature distribution is modeled and used as input to the next flow calculation. Time stands still during this iterative procedure. Once convergence is achieved, so the difference between successive solutions from one iteration to the next is within prescribed limits, the surface profile can be updated by multiplying the calculated surface velocities and prescribed mass balance rate by the time step. An updated temperature boundary condition at the surface can then be specified, and a new calculation started.

When energy balance and momentum balance models are coupled in this way, the result is commonly called a thermomechanical model.

Results from ten thermomechanical models were compared in a second phase of the EISMINT study (Payne et al., 2000). The ice sheet modeled was again circular, and all models predicted a central zone in which the ice sheet was frozen to the bed surrounded by an outer zone in which the base was at the pressure melting point. This time, however, results of the comparison were somewhat less consistent, inasmuch as the area of the inner cold zone varied among the models from 13% to 42% of the total area. Furthermore, when the surface temperature at the center of the ice sheet was -50 °C, an instability appeared in all but one of the models. This instability is believed to be related to the positive feedback from velocity to frictional heat generation and thence to temperature. The models were otherwise consistent in their predictions of the area, volume, thickness at the divide, and basal temperature at the divide.

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