The controls on basal temperature are not simple. Temperate glaciers (those entirely at the pressure melting point) commonly form in regions of high snowfall with mean annual temperatures near or even above freezing (Porter, 1977), especially in maritime climates. Farther inland, glacier existence usually requires mean annual air temperatures and near-surface ice temperatures below freezing over at least part of the glacier (the accumulation zone). Heat then is supplied to the glacier bed by geothermal flow and by viscous dissipation ("friction") of ice flow. Heat is removed by upward conduction through the ice to its cold surface; the rate of conduction is affected by vertical and lateral ice flow. The balance of these processes determines the basal temperature (see review in Paterson, 1981, Ch. 10).

Consider first the central region of a large ice sheet, such as the Laurentide, Fennoscandian, or the modern Antarctic and Greenland ice sheets. Near the center, flow velocities are low and viscous dissipation is small compared to geothermal heating. When the ice sheet is sufficiently large and thick (more than a few hundred kilometers in diameter, >1000 m thick) to affect atmospheric circulation significantly, surface temperature and accumulation will decrease with increasing ice-sheet elevation. Surface air temperature will decrease approximately at the atmospheric lapse rate (≈1° C/100 m). Precipitation usually will be limited by the ability of the cold air to transport water vapor onto the ice sheet; in modern East Antarctica, accumulation varies exponentially with temperature (Robin, 1977).

In the absence of ice flow, the insulating ability of ice would cause the difference between bed and surface temperatures to increase by about 2° C/100 m of ice thickness, whereas surface temperatures cool only about 1° C/100 m; the result would be rapid bed warming with increase of ice thickness and thawed beds beneath all but the thinnest glaciers. However, flow processes cause surface ice to move down into an ice sheet in accumulation areas. (Ice spreads and thins under the gravitational stresses caused by its weight and surface slope; new snowfall balances this thinning in a steady ice sheet and exceeds it in a growing ice sheet.) This ice motion advects the surface cold downward and chills the bed.

This vertical advection effect scales approximately with (b/h)1/2, where b is accumulation rate and h is ice thickness (Robin, 1955). A thin, high-accumulation ice sheet has a cold bed in the central regions, but its behavior becomes more like that of a stagnant ice layer as the ice thickness increases and the accumulation rate drops. For likely conditions in the center of a continental ice sheet initiated in a subfreezing climate, the bed will remain frozen until the ice thickness exceeds ≈ 3000 m.

The 3500-m-thick East Antarctic ice sheet is underlain by a wet bed in places (Oswald and Robin, 1973) but almost as great a thickness of ice in Greenland shows widespread freezing to its bed (Radok et al., 1982; Robin, 1983). The bed of the West Antarctic ice sheet is largely thawed; however, it occurs in a recently active tectonic region, which probably has high geothermal flux (Alley and Bentley, 1988), and rests on low bedrock (typically 500 to 2000 m below sea level; Drewry, 1983), allowing thick ice to have a low, warm surface. By simple analogy and by physical reasoning, it is likely that the Laurentide and Fennoscandian ice sheets were frozen to their beds in central regions until their sizes increased close to their maximum values (Hooke, 1977; Sugden, 1977).

If basal melting occurs beneath the central part of an ice sheet, it will be slow. A typical geothermal flux will melt about 5 mm/yr of ice in the absence of heat conduction into the ice; beneath cold ice, a melt rate <1 mm/yr will be more typical.

An ice sheet thins away from its center, which from the discussion above would tend to cool the bed, and colder ice formed at higher elevation is transported to lower regions with higher surface temperatures by ice flow, also cooling the bed. However, flow velocities and viscous dissipation increase outward, tending to warm the bed. Local details of bed topography, geothermal flux, accumulation rate, and other factors are likely to be more important in controlling basal temperature than any "typical" variation along flow, although zones of net basal freeze-on of meltwater (e.g., Byrd Station in West Antarctica; Gow et al., 1979) or frozen bed will occur downstream of thawed regions in many cases.

At some point near the ice-sheet margin, flow tends to funnel into fast-moving, often relatively thin ice streams or outlet glaciers. These channelized flows may occur between regions of bare rock outcrop, but often occur between thin ice ridges nourished by local accumulation but not by flow from upstream. Viscous dissipation in ice streams is strong, typically melting O(10 to 100 mm/yr) [O(x) signifies "of the order of magnitude of x"]; interstream ridges are likely to be frozen to their beds. This situation can give rise to selective linear erosion, with the ice stream carving a channel between ridges experiencing little or no erosion (Sugden, 1978).

Surface melting on ice sheets is limited to warm areas at lower elevations and latitudes. Following the onset of melting, meltwater initially drains into surface snow and refreezes. Sufficient melting will cause surface runoff. Such runoff can drain to the bed if the ice is sufficiently thin, warm, and crevassed. At present, surface melting is common and supplies water to the bed on many mountain glaciers, but this is restricted to a relatively narrow band around the coast of Greenland and is almost absent in Antarctica. Where surface melting occurs it generally dominates the glacier water budget; rates of O(1 m/yr) are common.

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