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We have several perennial rivers in my country that originate out of high altitude alpine glacier melt. I can understand snow or glacier melting in the summer to increase the flows but it is observed that flows do not come to a complete halt during peak winter as well even though temperatures maybe below freezing point. Upon investigation it was revealed that a process called calving(presumably pressure differences) is responsible for glacier breakdown but wikipedia claims that the mathematics of this process is still in development. Is it possible to get an expert answer on this phenomenon ?

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Liquid water can be stored in several ways in a glacier and the glacier environment. As ice and snow melts water can be temporarily stored stored in crevasses in the glacier or as equivalent to ground water in the permeable firn and snow pack on the glacier. Such water is slowly released, although sudden releases are also known, during the frozen season. In addition, sediments under and around the glacier also store ground water which is released during the frozen period. Altogether, this is known as "base flow" in hydrology. depending on the size and evacuation rates, the flow can persists throughout a winter season.

There are factors that influence this behaviour. The general case described above concerns so-called temperate glaciers. Glaciers at very high elevations and latitudes may be completely below the freezing point. There may also be permafrost in surroundings. Under such circumstances the storage volume can be very small and winter flow may cease altogether after some time.

A small fraction of water can also be generated by melting from geothermal heat. If the glacier is temperate at the bed the heat flux will provide energy to generate melt. A simple calculation based on typical continental geothermal heat fluxes show that the energy is sufficient to melt millimetres to a centimetre of basal ice. Consider that this melting occurs during the course for a year and the volume of water will be the melt rate multiplied by the basal ice-ground contact area of the glacier and the numbers will show that the runoff will be minuscule. Hence such contributions are generally not comparable to those produced by the "base flow" from ground and glacier aquifers.

The following paper provides a thorough description of storage of water in glaciers:

Jansson, P., Hock, R. and Schneider, T., 2003. The concept of glacier storage -- A review. Journal of Hydrology. 282 (1-4), 116-129.

A large volume of literature on glacier hydrology and runoff can be found in Journal of Glaciology.

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Not claiming to be an expert, but I think the process you're referring to is called pressure melt. This effect occurs when the pressure at the bottom of the glacier is high enough to either shift the melting point slightly (melting point decreases by 0.7$\,^{\circ}$C per km of ice according to this link, which provides some more background information on processes and conditions inside glaciers), which combined with frictional energy from the constant movement of the glacier, and, in some regions, geothermal energy causes a constant supply of liquid water. Since these discharges are usually concentrated under the ice (also the principle behind the formation of eskers), leading to large discharges at a few emergence points with enough energy to prevent them from freezing over.

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    $\begingroup$ Unfortunately, pressure melting does not necessarily lead to net melting since the resulting water under pressure will have a temperature that will result in freezing once the pressure is released. Pressure melting is an important factor for melt-refreeze processes. So I am afraid this process is basically negligible in the context of the question. $\endgroup$ Commented Dec 29, 2014 at 12:01

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