## Balance velocity

The general pattern of flow in a glacier is determined by the net budget. Consider an idealized glacier which, over a period of years, is in a steady state so its thickness (or surface profile) does not change. Then, at some distance, x, from the divide, the mean horizontal velocity averaged over depth is:

where h(x) is the glacier thickness, and for convenience, the units of bn are taken to be meters of ice per year (Figure 5.1). This equation is an expression of the principle of conservation of mass in an incompressible medium. As much mass must be moved out of the control volume, V, by flow, u h(x), as enters it by accumulation on the surface, /bn(x) dx. The velocity u is called the balance velocity.

Balance velocities on the Antarctic ice sheet are shown in Figure 5.2. To calculate these velocities, Huybrechts et al. (2000) used detailed maps of the surface and bed elevations to obtain ice thicknesses at nearly

80 000 points of a grid. They then used the surface elevations to calculate surface slopes, and hence directions of ice flow. This allowed the calculation of balance velocities, using a two-dimensional form of Equation (5.1) to take convergence and divergence of flow into consideration. Ice divides show up well on the map as regions of essentially zero velocity. Note also the general increase in velocity toward the coast, and the focusing of flow into relatively narrow zones near the coast. Because most of the ice loss from Antarctica is by calving, there is no decrease in velocity near the coast as there would be if ice were lost by melting in an ablation zone of appreciable width.

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