Correction to Variations of Ice Bed Coupling Beneath and Beyond Ice Streams: The Force Balance

A geometrical force balance that links stresses to ice bed coupling along a flow band of an ice sheet was developed in 1988 for longitudinal tension in ice streams and published 4 years later. It remains a work in progress. Now gravitational forces balanced by forces producing tensile, compressive, basal shear, and side shear stresses are all linked to ice bed coupling by the floating fraction phi of ice that produces the concave surface of ice streams. These lead inexorably to a simple formula showing how phi varies along these flow bands where surface and bed topography are known: phi = h(O)/h(I) with h(O) being ice thickness h(I) at x = 0 for x horizontal and positive upslope from grounded ice margins. This captures the basic fact in glaciology: the height of ice depends on how strongly ice couples to the bed. It shows how far a high convex ice sheet (phi = 0) has gone in collapsing into a low flat ice shelf (phi = 1). Here phi captures ice bed coupling under an ice stream and h(O) captures ice bed coupling beyond ice streams.

Variations of Ice Bed Coupling Beneath and Beyond Ice Streams: The Force Balance

A geometrical force balance that links stresses to ice bed coupling along a flow band of an ice sheet was developed in 1988 for longitudinal tension in ice streams and published 4 years later. It remains a work in progress. Now gravitational forces balanced by forces producing tensile, compressive, basal shear, and side shear stresses are all linked to ice bed coupling by the floating fraction phi of ice that produces the concave surface of ice streams. These lead inexorably to a simple formula showing how phi varies along these flow bands where surface and bed topography are known: phi = h(O)/h(I) with h(O) being ice thickness h(I) at x = 0 for x horizontal and positive upslope from grounded ice margins. This captures the basic fact in glaciology: the height of ice depends on how strongly ice couples to the bed. It shows how far a high convex ice sheet (phi = 0) has gone in collapsing into a low flat ice shelf (phi = 1). Here phi captures ice bed coupling under an ice stream and h(O) captures ice bed coupling beyond ice streams.

Ice-Bed Coupling Beneath and Beyond Ice Streams: Byrd Glacier, Antarctica

Ice sheet thickness is determined mainly by the strength of ice-bed coupling that controls holistic transitions from slow sheet flow to fast streamflow to buttressing shelf flow. Byrd Glacier has the largest ice drainage system in Antarctica and is the fastest ice stream entering Ross Ice Shelf. In 2004 two large subglacial lakes at the head of Byrd Glacier suddenly drained and increased the terminal ice velocity of Byrd Glacier from 820 m yr(-1) to 900 m yr(-1). This resulted in partial ice-bed recoupling above the lakes and partial decoupling along Byrd Glacier. An attempt to quantify this behavior is made using flowband and flowline models in which the controlling variable for ice height above the bed is the floating fraction phi of ice along the flowband and flowline. Changes in phi before and after drainage are obtained from available data, but more reliable data in the map plane are required before Byrd Glacier can be modeled adequately. A holistic sliding velocity is derived that depends on phi, with contributions from ice shearing over coupled beds and ice stretching over uncoupled beds, as is done in state-of-the-art sliding theories.

Evidence for a Frozen Bed, Byrd Glacier, Antarctica

Ice thickness, computed within the fjord region of Byrd Glacier on the assumptions that Byrd Glacier is in mass-balance equilibrium and that ice velocity is entirely due to basal sliding, are on average 400 m less than measured ice thicknesses along a radio-echo profile. We consider four explanations for these differences: (1) active glacier ice is separated from a zone of stagnant ice near the base of the glacier by a shear zone at depth; (2) basal melting rates are some 8 m/yr; (3) internal shear occurs with no basal sliding in much of the region above the grounding zone; or (4) internal creep and basal sliding contribute to the flow velocity in varying proportions above the grounding zone. Large gradients of surface strain rate seem to invalidate the first explanation. Computed values of basal shear stress (140 to 200 kPa) provide insufficient frictional heat to melt the ice demanded by the second explanation. Both the third and fourth explanations were examined by making simplifying assumptions that prevented a truly quantitative evaluation of their merit. Nevertheless, there is no escaping the qualitative conclusion that internal shear contributes strongly to surface velocities measured on Byrd Glacier, as is postulated in both these explanations.

Thermal Conditions at the Bed of the Laurentide Ice Sheet in Maine During Deglaciation: Implications for Esker Formation

The University of Maine Ice Sheet Model was used to study basal conditions during retreat of the Laurentide ice sheet in Maine. Within 150 km of the margin, basal melt rates average similar to 5 mm a(-1) during retreat. They decline over the next 100km, so areas of frozen bed develop in northern Maine during retreat. By integrating the melt rate over the drainage area typically subtended by an esker, we obtained a discharge at the margin of similar to 1.2 m(3) s(-1). While such a discharge could have moved the material in the Katahdin esker, it was likely too low to build the esker in the time available. Additional water from the glacier surface was required. Temperature gradients in the basal ice increase rapidly with distance from the margin. By conducting upward into the ice all of the additional viscous heat produced by any perturbation that increases the depth of flow in a flat conduit in a distributed drainage system, these gradients inhibit the formation of sharply arched conduits in which an esker can form. This may explain why eskers commonly seem to form near the margin and are typically segmented, with later segments overlapping onto earlier ones.