A note on the water budget of temperate glaciers

In this note, the total dissipative melting in temperate glaciers is studied. The analysis is based on the notion that the dissipation is determined by the loss of potential energy due to the downward motion of mass (ice, snow, meltwater and rain). A mathematical formulation of the dissipation is developed and applied to a simple glacier geometry. In the next step, meltwater production resulting from enhanced ice motion during a glacier surge is calculated. The amount of melt energy available follows directly from the lowering of the centre of gravity of the glacier. To illustrate the concept, schematic calculations are presented for a number of glaciers with different geometric characteristics. Typical dissipative melt rates, expressed as water-layer depth averaged over the glacier, range from a few centimetres per year for smaller glaciers to half a metre per year for Franz Josef Glacier, one of the most active glaciers in the world (in terms of mass turnover). The total generation of meltwater during a surge is typically half a metre. For Variegated Glacier a value of 70 cm is found, for Kongsvegen 20 cm. These values refer to water layer depth averaged over the entire glacier. The melt \textit{rate} depends on the duration of the surge. It is generally an order of magnitude greater than water production by `normal' dissipation. On the other hand, the additional basal melt rate during a surge is comparable in magnitude with the water input from meltwater and precipitation. This suggests that enhanced melting during a surge does not grossly change the total water budget of a glacier. Basal water generated by enhanced sliding is an important ingredient in many theories of glacier surges. It provides a positive feedback mechanism that actually makes the surge happen. The results found here suggest that this can only work if water generated by enhanced sliding accumulates in a part of the glacier base where surface meltwater and rain have no or very limited access. This finding seems compatible with the fact that, on many glaciers, surges are initiated in the lower accumulation zone