Spatial Patterns in Mass Balance of the Siple Coast and Amundsen Sea Sectors, West Antarctica

Local rates of change in ice-sheet thickness were calculated at IS sites in West Antarctica using the submergence velocity technique. This method entails a comparison of the vertical velocity of the ice sheet, measured using repeat global positioning system surveys of markers, and local long-term rates of snow accumulation obtained using firn-core stratigraphy. Any significant difference between these two quantities represents a thickness change with time. Measurements were conducted at sites located similar to 100-200 km apart along US ITASE traverse routes, and at several isolated locations. All but one of the sites are distributed in the Siple Coast and the Amundsen Sea basin along contours of constant elevation, along flowlines, across ice divides and close to regions of enhanced flow. Calculated rates of thickness change are different from site to site. Most of the large rates of change in ice thickness (similar to 10 cm a(-1) or larger) are observed in or close to regions of rapid flow, and are probably related to ice-dynamics effects. Near-steady-state conditions are calculated mostly at sites in the slow-moving ice-sheet interior and near the main West Antarctic ice divide. These results are consistent with regional estimates of ice-sheet change derived from remote-sensing measurements at similar locations in West Antarctica.

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.

Local Rates of Ice-Sheet Thickness Change in Greenland

The rate of ice-sheet thickness change is calculated for 10 sites in Greenland by comparing measured values of ice vertical velocity and snow-accumulation rate. Vertical velocities are derived from repeat surveys of markers using precision global positioning system techniques, and accumulation rates are determined from stratigraphic analysis of firn cores. The results apply to time-scales covered by the firn-core records, which in most cases are a few decades. A spectrum of thickness-change rates is obtained, ranging from substantial thinning to slow thickening. The sites where ice-sheet thinning is indicated are located near the ice-sheet margin or in outlet glacier catchments. Interior and high-elevation sites are predominantly in balance or thickening slowly. Uncertainties in the rates of thickness change are dominated by errors in the determination of accumulation rates. The results of this work are broadly comparable with regional estimates of mass balance obtained from the analysis of catchment input vs discharge.

Geometrical Force Balance in Glaciology

The analytical force balance traditionally used in glaciology relates gravitational forcing to ice surface slope for sheet flow and to ice basal buoyancy for shelf flow. It is unable to represent stream flow as a transition from sheet flow to shelf flow by having gravitational forcing gradually passing from being driven by surface slope to being driven by basal buoyancy downslope along the length of an ice steam. This is a serious defect, because ice streams discharge up to 90% of ice from ice sheets into the sea. The defect is overcome by using a geometrical force balance that includes basal buoyancy, represented by the ratio of basal water pressure to ice overburden pressure, as a source of gravitational forcing. When combined with the mass balance, the geometrical force balance provides a holistic approach to ice flow in which resistance to gravitational flow must be summed upstream from the calving front of an ice shelf. This is not done in the analytical force balance, and it provides the ice-thinning rate required by gravitational collapse of ice sheets as interior ice is downdrawn by ice streams.