Water temperature in englacial and supraglacial channels: Change along the flow and contribution to ice melting on the channel wall

The physics of water temperature change along a glacial water stream and its relation to ice melting rate on the channel walls are examined. The heat balance equation is based on the principles of energy conservation and an empirical relation of heat exchange between ice and flowing water. It is shown that the temperature of water exponentially approaches a nonzero value as flowing along a glacial channel. The channel meandering and noncircular cross-section were also taken into account. Typical values of the equilibrium water temperature are hundredths to a tenth of a degree depending on the channel size and slope, but the temperature can drastically increase when the channel has sediments. We compared our calculations to 1) a series of experiments with an artificial channel in ice and 2) data obtained from measurements at the Caucasus and Patagonia glaciers.