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.

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.

Surface "Waves" on Byrd Glacier, Antarctica

Byrd Glacier has one of the largest ice catchment areas in Antarctica, delivers more ice to the Ross Ice Shelf than any other ice stream, and is the fastest of these ice streams. A force balance, combined with a mass balance, demonstrates that stream flow in Byrd Glacier is transitional from sheet flow in East Antarctica to shelf flow in the Ross Ice Shelf. The longitudinal pulling stress, calculated along an ice flowband from the force balance, is linked to variations of ice thickness, to the ratio of the basal water pressure to the ice overburden pressure where Byrd Glacier is grounded, and is reduced by an ice-shelf buttressing stress where Byrd Glacier is floating. Longitudinal tension peaks at pressure-ratio maxima in grounded ice and close to minima in the ratio of the pulling stress to the buttressing stress in floating ice. The longitudinal spacing of these tension peaks is rather uniform and, for grounded ice, the peaks occur at maxima in surface slope that have no clear relation to the bed slope. This implies that the maxima in surface slope constitute a "wave train" that is related to regular variations in ice-bed coupling, not primarily to bed topography. It is unclear whether these surface "waves" are "standing waves" or are migrating either upslope or downslope, possibly causing the grounding line to either retreat or advance. Deciding which is the case will require obtaining bed topography in the map plane, a new map of surface topography, and more sophisticated modeling that includes ice flow linked to subglacial hydrology in the map plane.

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.

Mass Balance and Accumulation Rate Across Siple Dome, West Antarctica

Snow-accumulation rates and rates of ice-thickness change (mass balance) are studied at several sites on Siple Dome, West Antarctica. Accumulation rates are derived from analyses of gross beta radioactivity in shallow firn cores located along a 60 km transect spanning both flanks and the crest of the dome. There is a north-south gradient in snow-accumulation rate across the dome that is consistent with earlier radar mapping of internal stratigraphy. Orographic processes probably control this distribution. Mass balance is inferred from the difference between global positioning system (GPS)-derived vertical velocities and snow-accumulation rates for sites close to the firn-core locations. Results indicate that there is virtually no net thickness change at four of the five sites. The exception is at the northernmost site where a small amount of thinning is detected, that appears to be inconsistent with other studies. A possible cause of this anomalous thinning is recent retreat of the grounding line of Ice Stream D.

State of the Antarctic and Southern Ocean Climate System

This paper reviews developments in our understanding of the state of the Antarctic and Southern Ocean climate and its relation to the global climate system over the last few millennia. Climate over this and earlier periods has not been stable, as evidenced by the occurrence of abrupt changes in atmospheric circulation and temperature recorded in Antarctic ice core proxies for past climate. Two of the most prominent abrupt climate change events are characterized by intensification of the circumpolar westerlies (also known as the Southern Annular Mode) between similar to 6000 and 5000 years ago and since 1200-1000 years ago. Following the last of these is a period of major trans-Antarctic reorganization of atmospheric circulation and temperature between A. D. 1700 and 1850. The two earlier Antarctic abrupt climate change events appear linked to but predate by several centuries even more abrupt climate change in the North Atlantic, and the end of the more recent event is coincident with reorganization of atmospheric circulation in the North Pacific. Improved understanding of such events and of the associations between abrupt climate change events recorded in both hemispheres is critical to predicting the impact and timing of future abrupt climate change events potentially forced by anthropogenic changes in greenhouse gases and aerosols. Special attention is given to the climate of the past 200 years, which was recorded by a network of recently available shallow firn cores, and to that of the past 50 years, which was monitored by the continuous instrumental record. Significant regional climate changes have taken place in the Antarctic during the past 50 years. Atmospheric temperatures have increased markedly over the Antarctic Peninsula, linked to nearby ocean warming and intensification of the circumpolar westerlies. Glaciers are retreating on the peninsula, in Patagonia, on the sub-Antarctic islands, and in West Antarctica adjacent to the peninsula. The penetration of marine air masses has become more pronounced over parts of West Antarctica. Above the surface, the Antarctic troposphere has warmed during winter while the stratosphere has cooled year-round. The upper kilometer of the circumpolar Southern Ocean has warmed, Antarctic Bottom Water across a wide sector off East Antarctica has freshened, and the densest bottom water in the Weddell Sea has warmed. In contrast to these regional climate changes, over most of Antarctica, near-surface temperature and snowfall have not increased significantly during at least the past 50 years, and proxy data suggest that the atmospheric circulation over the interior has remained in a similar state for at least the past 200 years. Furthermore, the total sea ice cover around Antarctica has exhibited no significant overall change since reliable satellite monitoring began in the late 1970s, despite large but compensating regional changes. The inhomogeneity of Antarctic climate in space and time implies that recent Antarctic climate changes are due on the one hand to a combination of strong multidecadal variability and anthropogenic effects and, as demonstrated by the paleoclimate record, on the other hand to multidecadal to millennial scale and longer natural variability forced through changes in orbital insolation, greenhouse gases, solar variability, ice dynamics, and aerosols. Model projections suggest that over the 21st century the Antarctic interior will warm by 3.4 degrees +/- 1 degrees C, and sea ice extent will decrease by similar to 30%. Ice sheet models are not yet adequate enough to answer pressing questins about the effect of projected warming on mass balance and sea level. Considering the potentially major impacts of a warming climate on Antarctica, vigorous efforts are needed to better understand all aspects of the highly coupled Antarctic climate system as well as its influence on the Earth's climate and oceans.