Basal Boundary Conditions

For floating ice, the temperature boundary conditions are quite simple, with the surface temperatures prescribed by climatic values or measurements, and the basal temperatures prescribed by the pressure melting point of ice in contact with sea water.

For grounded ice the top boundary condition is the same, but the basal boundary condition is quite different. For grounded ice the basal boundary condition becomes one of specifying the flux of heat (the geothermal gradient) into the basal layer, along with the condition that this surface cannot exceed the pressure melting point.

This condition leads to three possibilities:

1. A melting bed
2. A freezing bed
3. A frozen bed.

The last case is the simplest, for a frozen bed the temperature is below the pressure melting point and the basal boundary condition is just specified heat flux (geothermal gradient).

The cases for melting and freezing beds are more complicated. In the case of a melting bed, the calculation will obtain a temperature that exceeds the pressure melting point. In such a case, the node involved must be constrained to be at the pressure melting point, and a basal gradient calculated. From this gradient, a heat flux can be calculated, and any excess heat required can be assumed to derive from the latent heat of ice melting at the bed. Hence we can calculate a melting rate for points on the bed that attain the pressure melting point.

For a freezing bed we again calculate a basal temperature using only a specified basal gradient. In this case the calculated temperature is below the pressure melting point, but in an area where we know water exists at the bed (presumably from some previous melting episode, but also possibly from basal transport of water across the bed). Again we must specify the temperature to be at the pressure melting point, and again calculate a basal gradient, whose difference from the geothermal gradient will be a measure of the freezing rate at that point on the bed. Freezing will continue to occur until all of the available water stored at the bed is frozen, after which this node can revert to the frozen bed case.