General theory of water flow at the base of a glacier or ice sheet

The theory of the flow of water at the base of a glacier is reviewed and extended. A detailed analysis is made of flow through Röthlisberger channels. (Röthlisberger channels are channels at the base of a glacier that are incised upward into the ice mass.) It is shown that, in general, a pressure gradient drives water melted from the bottom surface of a glacier away from Röthlisberger channels. Thus these channels are not good collectors of the water produced at the bottom surface of a glacier or ice sheet. If Nye channels exist (Nye channels are incised downward into the bedrock of a glacier bed), they should be important in the discharge of water at the base of a glacier. Nye tributary channels are expected to be spaced over several hundred meters apart. The analysis indicates that sheet flow is the main mechanism by which water melted from the bottom ice surface flows out of a glacier or ice sheet. The sheet flow described in this paper is a modification of that considered in our earlier papers. The thickness of the present sheets is not roughly uniform, but rather squeezes to negligible values at high‐pressure zones, where ice moves over the upstream side of obstacles and irregularities in the bed. The pressure of the water in the sheets is lower than the ice overburden pressure. The difference between the pressure in the sheets and the ice overburden pressure is estimated with the aid of the recent major refinements to glacier sliding theory made by J. F. Nye and by B. Kamb. (L. Lliboutry made the original suggestion that the pressure of the water at the base of a glacier is smaller than the ice overburden pressure.) Analysis indicates that a single Röthlisberger channel runs down the center of a glacier over a major fraction of its length. Pressure gradients, produced by the concave shape of the transverse bed profile, exist that drive water in the sheet toward this channel. However, in the upper parts of a glacier, this channel may take the form of a thick water layer of finite breadth.