Abstract

An equilibrium glacier is one that has constant dimensions, since the average net accumulation per budget year above the annual firn limit exactly equals the amount of bare ice lost each year by ablation below the firn limit; the flow of ice maintains the glacier in exact balance over a period of years. Three basic equations that apply to an equilibrium glacier are:  
formula
The first equation gives the mass of ice Q1 moving through any cross section in the accumulation area in terms of the mass of snow H at any point X along the glacier at the end of the summer season. The second equation gives the mass of ice Q2 moving through any cross section in the ablation region in terms of the mass of ice Q* passing through the firn line and the ablation H' of bare ice per year. The third equation shows how the average velocity of flow forumla depends upon the mass of ice Q through a cross section of area S and ice of density ρ.

These equations must be solved by numerical approximations for an actual glacier, but they may be solved exactly for idealized glaciers of many shapes; this has been done for eight idealized examples. The results show that the velocity of flow is usually greatest near the annual firn limit and very small near the head and the terminus.

The theory predicts longitudinal expansion in the accumulation area and longitudinal contraction in the ablation area. Transverse surface profiles of equilibrium glaciers are generally higher in the center than at the edges in the ablation area, but in the accumulation area the transverse profiles are generally dish-shaped.

Large rates of ablation require large velocities of flow in order to maintain equilibrium. This concept is used to explain some of the phenomena often observed near ice-dammed lakes.

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