Ice-sheet dynamics

Glacial flow rate in the Antarctic ice sheet

Ice sheet dynamics describe the motion within large bodies of ice, such those currently on Greenland and Antarctica. Ice motion is dominated by the movement of glaciers, whose activity is controlled by two main factors: the temperature and strength of their bases. A number of processes alter these two factors, resulting in cyclic surges of activity interspersed with longer periods of inactivity, on both hourly and Template:Wict time scales.

Flow dynamics

Ice behaves as a brittle solid until its thickness exceeds about 50 meters (160 ft), after which the pressure causes plastic flow, and the glacier deforms by creep.

Glaciers may also move by basal sliding, where the base of the glacier is lubricated by meltwater, allowing the glacier to slide over the terrain on which it sits.

Meltwater may be provided by pressure-induced melting, friction or geothermal heat.

The top 50 meters of the glacier form the fracture zone, where ice moves as a single unit. Cracks form as the glacier moves over irregular terrain, which may penetrate the full depth of the fracture zone.

Glacial bottom processes

The stress-strain relationship of plastic flow (teal section): a small increase in stress creates an exponentially greater increase in strain, which equates to deformation speed.

Most of the important processes controlling glacial motion occur in the ice-bed contact—even though it is only a few metres thick. Glaciers will move by sliding when the basal shear stress drops below the shear resulting from the glacier's weight.

τ_D = ρgh sin α

where τ_D is the driving stress, and α the angle of repose.

τ_B is the basal shear stress, a function of bed temperature and softness.

τ_F, the shear stress, is the lower of τ_B and τ_D. It controls the rate of plastic flow, as per the figure (inset, right).

For a given glacier, the two variables are τ_D, which varies with h, the depth of the glacier, and τ_B, the basal shear stress.

Basal shear stress

The basal shear stress is a function of three factors: the bed's temperature, roughness and softness.

Whether a bed is hard or soft depends on the porosity and pore pressure; higher porosity decreases the sediment strength (thus increases the shear stress τ_B). If the sediment strength falls far below τ_D, movement of the glaicer will be accommodated by motion in the sediments, as opposed to sliding.

Rates of ice sheet thinning in Greenland

Porosity may vary through a range of methods.

• Movement of the overlying glacier may cause the bed to undergo Template:Wict; the resulting shape change reorganises blocks. This reorganises closely packed blocks (A little like neatly folded, tightly packed clothes in a suitcase) into a messy jumble (just as clothes never fit back in when thrown in in a disordered fashion). This increases the porosity. Unless water is added, this will necessarily reduce the pore pressure (as the pore fluids have more space to occupy).
• Pressure may cause compaction and consolidation of underlying sediments. Since water is relatively incompressible, this is easier when the pore space is filled with vapour; any water must be removed to permit compression. In soils, this is an irreversible process.
• Sediment degradation by abrasion and fracture decreases the size of particles, which tends to decrease pore space, although the motion of the particles may disorder the sediment, with the opposite effect. These processes also generate heat, whose importance will be discussed later.

A soft bed, with high porosity and low pore fluid pressure, allows the glacier to move by sediment sliding: the base of the glacier may even remain frozen to the bed, where the underlying sediment slips underneath it like a tube of toothpaste. A hard bed cannot deform in this way; therefore the only way for hard-based glaciers to move is by basal sliding, where meltwater forms between the ice and the bed itself.

Bed softness may vary in space or time, and changes dramatically from glacier to glacier. An important factor is the underlying geology; glacial speeds tend to differ more when they change bedrock than when the gradient changes.

As well as affecting the sediment stress, fluid pressure (p_w) can affect the friction between the glacier and the bed. High fluid pressure provides a buoyancy force upwards on the glacier, reducing the friction at its base. The fluid pressure is compared to the ice overburden pressure, p_i, given by ρgh. Under fast-flowing ice streams, these two pressures will be approximately equal, with an effective pressure (p_i - p_w) of 30 kPa; i.e. all of the weight of the ice is supported by the underlying water, and the glacier is afloat.

Factors controlling the flow of ice

A number of factors can affect bed temperature, which is intimately associated with basal meltwater. The melting point of water decreases under pressure, meaning that water melts at a higher temperature under thicker glaciers. This acts as a "double whammy", because thicker glaciers have a lower heat conductance, meaning that the basal temperature is also likely to be higher.

Bed temperature tends to vary in a cyclic fashion. A cool bed has a high strength, reducing the speed of the glacier. This increases the rate of accumulation, since newly fallen snow is not transported away. Consequently, the glacier thickens, with three consequences: firstly, the bed is better insulated, allowing greater retention of geothermal heat. Secondly, the increased pressure can facilitate melting. Most importantly, τ_D is increased. These factors will combine to accelerate the glacier. The increased velocity will further increase the heating caused by friction, with ensuing melting - which causes a positive feedback, increasing ice speed to a faster flow rate still: west Antarctic glaciers are known to reach velocities of up to a kilometre per year. Eventually, the ice sill be surging fast enough that it begins to thin, as accumulation cannot keep up with the transport. This thinning will increase the conductive heat loss, slowing the glacier and causing freezing. This freezing will slow the glacier further, often until it is stationary, whence the cycle can begin again.

Supraglacial lakes represent another possible supply of liquid water to the base of glaciers, so can play an important role in accelerating glacial motion. Lakes of a diameter greater than ~300 m are capable of creating a fluid-filled crevasse to the glacier/bed interface. When these crevasses form, the entirety of the lake's (relatively warm) contents can reach the base of the glacier in as little as 2-18 hours - lubricating the bed and causing the glacier to surge.

Finally, bed roughness can act to slow glacial motion. The roughness of the bed is a measure of how many boulders and obstacles protrude into the overlying ice. Ice flows around these obstacles by melting under the high pressure on their lee sides; the resultant meltwater is then forced down a steep pressure gradient into the cavity arising in their stoss, where it re-freezes. Cavitation on the stoss side increases this pressure gradient, which assists flow.

Pipe and sheet flow

The flow of water under the glacial surface can have a large effect on the motion of the glacier itself. Subglacial lakes contain significant amounts of water, which can move fast: cubic kilometres can be transported between lakes over the course of a couple of years.

This motion is thought to occur in two main modes: pipe flow involves liquid water moving through pipe-like conduits, like a sub-glacial river; sheet flow involves motion of water in a thin layer. A switch between the two flow conditions may be associated with surging behaviour. Indeed, the loss of sub-glacial water supply has been linked with the shut-down of ice movement in the Kamb ice stream. The subglacial motion of water is expressed in the surface topography of ice sheets, which slump down into vacated subglacial lakes.

Boundary conditions

The interface between an ice stream and the ocean is a significant control of the rate of flow.

The collapse of the Larsen B ice shelf had profound effects on the velocities of its sfeeder glaciers.

Ice shelves - thick layers of ice floating on the sea - can stabilise the glaciers that feed them. These tend to have accumulation on their tops, may experience melting on their bases, and calve icebergs at their periphery. The catastrophic collapse of the Larsen B ice shelf in the space of three weeks during February 2002 yielded some unexpected observations. The glaciers that had fed the ice sheet (Crane, Jorum, Green, Hektoria - see image) increased substantially in velocity. This cannot have been due to seasonal variability, as glaciers flowing into the remnants of the ice shelf (Flask, Leppard) did not accelerate.

Ice shelves have a dominant control in Antarctica, but are less important in Greenland, where the ice sheet meets the sea in fjords. Here, melting at the glaciers' bases is the dominant ice removal process, resulting in loss of mass at the edges of the ice sheet as icebergs are calved in the fjords.

Tidal effects are also important; the influence of a 1 m tidal oscillation can be felt as much as 100 km from the sea. On an hour-to-hour basis, surges of ice motion can be modulated by tidal activity. During larger spring tides, an ice stream will remain almost stationary for hours at a time, before a surge of around a foot in under an hour, just after the peak high tide; a stationary period then takes hold until another surge towards the middle or end of the falling tide. At neap tides, this interaction is less pronounced, without tides surges would occur more randomly, approximately every 12 hours.

Ice shelves are also sensitive to basal melting. In Antarctica, this is driven by heat fed to the shelf by the circumpolar deep water current, which is 3 °C above the ice's melting point.

As well as heat, the sea can also exchange salt with the oceans. The effect of latent heat, resulting from melting of ice or freezing of sea water, also has a role to play. The effects of these, and variability in snowfall and base sea level combined, account for around 80 mm a^-1 variability in ice shelf thickness. In contrast, the ice shelf in Pine Island Bay is thinning at 5.5 m a^-1. Clearly the influence of tides, combined with processes affecting the strength of the glacier's bed, are far more significant than these oceanic effects.

Effects of climate change on ice sheet dynamics

The implications of the current climate change on ice sheets are difficult to constrain. It is clear that increasing temperatures are resulting in reduced ice volumes globally. Due to increased precipitation, the mass of parts of the Antarctic ice sheet may currently be increasing, but the total mass balance is unclear.