Large-Scale Dynamics of Ice Sheets

Abstract

With the constitutive equations given in Sects. 4.3 and 4.4, we are now able to formulate the mechanical and thermodynamical field equations for the flow of ice in an ice sheet. Figure 5.1 shows the typical geometry (cross section) of a grounded ice sheet with attached floating ice shelf (the latter will be treated in Chap. 6), as well as its interactions with the atmosphere (snowfall, melting), the lithosphere (geothermal heat flux, isostasy) and the ocean (melting, calving). Also, a Cartesian coordinate system is introduced, where x and y lie in the horizontal plane, and z is positive upward. These coordinates are naturally associated with the set of basis vectors {ex, ey, ez}. The free surface (ice-atmosphere interface) is given by the function z = h(x, y, t), the ice base by z = b(x, y, t) and the lithosphere surface by z = zl(x, y, t).