Theoretical Calving Rates from Glaciers Along Ice Walls Grounded in Water of Variable Depths

Calving has been studied for glaciers ranging from slow polar glaciers that calve on dry land, such as on Deception Island (63.0-degrees-S, 60.6-degrees-W) in Antarctica, through temperate Alaskan tide-water glaciers, to fast outlet glaciers that float in fiords and calve in deep water, such as Jakobshavns Isbrae (69.2-degrees-N, 49.9-degrees-W) in Greenland. Calving from grounded ice walls and floating ice shelves is the main ablation mechanism for the Antarctic and Greenland ice sheets, as it was along marine and lacustrine margins of former Pleistocene ice sheets, and is for tide-water and polar glaciers. Yet, the theory of ice calving is underdeveloped because of inherent dangers in obtaining field data to test and constrain calving models. An attempt is made to develop a calving theory for ice walls grounded in water of variable depth, and to relate slab calving from ice walls to tabular calving from ice shelves. A calving law is derived in which calving rates from ice walls are controled by bending creep behind the ice wall, and depend on wall height h, forward bending angle-theta, crevasse distance c behind the ice wall and depth d of water in front of the ice wall. Reasonable agreement with calving rates reported by Brown and others (1982) for Alaskan tide-water glaciers is obtained when c depends on wall height, wall height above water and water depth. More data are needed to determine which of these dependencies is correct. A calving ratio c/h is introduced to understand the transition from slab calving to tabular calving as water deepens and the calving glacier becomes afloat.

Crevassing and Calving of Glacial Ice

Calving of ice is a relatively new area of research in the still young field of glaciology. In the short time that calving has been studied, it has been mainly treated as an afterthought, with the predominant mode of thinking being that it will happen so to concern oneself with why is not important. Many studies dealt with observations of calving front positions over time vs. ice velocity in an attempt to quantify the calving rate as the difference between the two, while others have attempted to deduce some empirical relationship between calving rate and variables such as water depth or temperature. This study instead addresses the question of why, where, and when ice will first become crevassed, which is an obviously necessary condition for a later calving event to occur. Previous work examining the causes of calving used ideas put forth from a variety of fields, including civil engineering, materials science, and results from basic physics and mechanics. These theories are re-examined here and presented as part of a larger whole. Important results from the field of fracture mechanics are utilized frequently, and these results can be used as a predictor of ice behavior and intrinsic properties of ice, as well as properties like back stresses induced by local pinning points and resistive shears along glacial ice boundaries. A theory of fracture for a material experiencing creep is also presented with applications to ice shelves and crevasse penetration. Finally, a speculative theory regarding large scale iceberg formation is presented. It is meant mainly as an impetus to further discussion on the topic, with the hope that a model relating crevasse geometries to flow parameters can result in crevasse spacings that could produce the tabular icebergs which are so newsworthy. The primary focus of this thesis is to move away from the "after the fact" studies that are so common in calving research, and instead devote energy to determining what creates the conditions that drive the calving of ice in the first place.

Bending Shear: The Rate-Controlling Mechanism for Calving Ice Walls

Bending shear was observed to produce nearly vertical shear bands in a calving ice wall standing on dry land on Deception Island (Iat. 63.0 oS., long. 60.6 W.), and slabs calved straight downward when shear rupture occurred along these shear bands (Hughes, 1989). A formula for the calving rate was developed from the Deception Island data, and we have attempted to justify generalizing this formula to include ice walls standing along beaches or in water. These are environments in which a wave-washed groove develops along the base of the ice wall or along a water line above the base. The rate of wave erosion provides an alternative mechanism for controlling the calving rate in these environments. We have determined that the rate at which bending creep produces nearly vertical shear bands, along which shear r upture occurs, controls the calving rate in all environments. Shear rupture occurs at a calving shear stress of about I bar. Our results justify using the calving formula to compute the calving rate of ice walls in computer models of ice-sheet dynamics. This is especially important in simulating retreat of Northern Hemisphere ice sheets during the last deglaciation, when marine and lacustrine environments were common along retreating ice margins. These margins would have been ice walls standing along beaches or in water, because floating ice shelves are not expected in the ablation zone of retreating ice sheets.

West Antarctic Ice Streams

Solar heat is the acknowledged driving force for climatic change. However, ice sheets are also capable of causing climatic change. This property of ice sheets derives from the facts that ice and rock are crystalline whereas the oceans and atmosphere are fluids and that ice sheets are massive enough to depress the earth's crust well below sea level. These features allow time constants for glacial flow and isostatic compensation to be much larger than those for ocean and atmospheric circulation and therefore somewhat independent of the solar variations that control this circulation. This review examines the nature of dynamic processes in ice streams that give ice sheets their degree of independent behavior and emphasizes the consequences of viscoplastic instability inherent in anisotropic polycrystalline solids such as glacial ice. Viscoplastic instability and subglacial topography are responsible for the formation of ice streams near ice sheet margins grounded below sea level. As a result the West Antarctic marine ice sheet is inherently unstable and can be rapidly carved away by calving bays which migrate up surging ice streams. Analyses of tidal flexure along floating ice stream margins, stress and velocity fields in ice streams, and ice stream boundary conditions are presented and used to interpret ERTS 1 photomosaics for West Antarctica in terms of characteristic ice sheet crevasse patterns that can be used to monitor ice stream surges and to study calving bay dynamics.

Sudden Increase in Tidal Response Linked to Calving and Acceleration at a Large Greenland Outlet Glacier

Large calving events at Greenland's largest outlet glaciers are associated with glacial earthquakes and near instantaneous increases in glacier flow speed. At some glaciers and ice streams, flow is also modulated in a regular way by ocean tidal forcing at the terminus. At Helheim Glacier, analysis of geodetic data shows decimeter-level periodic position variations in response to tidal forcing. However, we also observe transient increases of more than 100% in the glacier's responsiveness to such tidal forcing following glacial-earthquake calving events. The timing and amplitude of the changes correlate strongly with the step-like increases in glacier speed and longitudinal strain rate associated with glacial earthquakes. The enhanced response to the ocean tides may be explained by a temporary disruption of the subglacial drainage system and a concomitant reduction of the friction at the ice-bedrock interface, and suggests a new means by which geodetic data may be used to infer glacier properties. Citation: de Juan, J., et al. (2010), Sudden increase in tidal response linked to calving and acceleration at a large Greenland outlet glacier, Geophys. Res. Lett., 37, L12501, doi: 10.1029/2010GL043289.

Fracture and Back Stress Along the Byrd Glacier Flowband on the Ross Ice Shelf

East Antarctic ice discharged by Byrd Glacier continues as a flowband to the calving front of the Ross Ice Shelf. Flow across the grounding line changes from compressive to extensive as it leaves the fjord through the Transantarctic Mountains occupied by Byrd Glacier. Magnitudes of the longitudinal compressive stress that suppress opening of transverse tensile cracks are calculated for the flowband. As compressive back stresses diminish, initial depths and subsequent growth of these cracks, and their spacing, are calculated using theories of elastic and ductile fracture mechanics. Cracks are initially about one millimeter wide, with approximately 30 in depths and 20 in spacings for a back stress of 83 kPa at a distance of 50 kin beyond the fjord, where floating ice is 600 in thick. When these crevasses penetrate the whole ice thickness, they release tabular icebergs 20 kin to 100 kin wide, spaced parallel to the calving front of the Ross Ice Shelf

Multi-Decadal Record of Ice Dynamics on Daugaard Jensen Gletscher, East Greenland, from Satellite Imagery and Terrestrial Measurements

The history of ice velocity and calving front position of Daugaard Jensen Gletscher, a large outlet glacier in East Greenland, is reconstructed from field measurements, aerial photography and satellite imagery for the period 1950-2001. The calving terminus of the glacier has remained in approximately the same position over the past similar to 50 years. There is no evidence of a change in ice motion between 1968 and 2001, based on a comparison of velocities derived from terrestrial surveying and feature tracking using sequential satellite images. Estimates of flux near the entrance to the fjord vs snow accumulation in the interior catchment show that Daugaard Jensen Gletscher has a small negative mass balance. This result is consistent with other mass-balance estimates for the inland region of the glacier.

Calving Giant Icebergs: Old Principles, New Applications

Earth-orbiting satellites can now monitor calving of large icebergs from ice shelves bordering the marine West Antarctic Ice Sheet, and recent calving events have stimulated interest in calving mechanisms. To advance this interest pioneering work in brittle and ductile fracture mechanics is reviewed, leading to a new application to calving of giant icebergs from Antarctic ice shelves. The aim is to view iceberg calving as more than terminal events for Antarctic ice when glaciologists lose interest. Instead calving launches Antarctic ice into the larger dynamic system of Earth's climate machine. This encourages a holistic approach to glaciology.

Glacier Calving: A Numerical Model of Forces in the Calving-Speed/Water-Depth Relation

Empirical data suggest that the race of calving of grounded glaciers terminating in water is directly proportional to the water depth. Important controls on calving may be the extent to which a calving face tends to become oversteepened by differential flow within the ice and the extent to which bending moments promote extrusion and bottom crevassing at the base of a calving face. Numerical modelling suggests that the tendency to become oversteepened increases roughly linearly with water depth. In addition, extending longitudinal deviatoric stresses at the base of a calving face increase with water depth. These processes provide a possible physical explanation for the observed calving-rate/water-depth relation.

Buckling Rate and Overhang Development at a Calving Face

Using the finite-element we have modeled the stress field near the calving face of an idealized tidewater glacier under a variety of assumptions about submarine calving-face height, subaerial calving-face height, and ice rheology These simulations all suggest that a speed maximum should be present at the calving face near the waterline. In experiments without crevassing, the decrease in horizontal velocity above this maximum culminates in a zone of longitudinal compression at the surface somewhat Up-glacier from the face. This zone of compression appears to be a consequence of the non-linear rheology of ice. It disappears when a linear rheology is assumed. Explorations of the near-surface stress field indicate that when pervasive crevassing of the surface ice is accounted for in the simulations (by rheological softening), the zone of compressive strain rates does not develop. Variations in the pattern of horizontal velocity with glacier thickness support the contention that calving rates should increase with water depth at the calving face. In addition, the height of the subaerial calving face may have an importance that is not visible ill Current field data owing to the lack of variation in height of such faces in nature. Glaciers with lower calving faces may not have sufficient tensile stress to calve actively, while tensile stresses in simulated higher faces are sufficiently high that such faces will be unlikely to build in nature.

Spatial and Temporal Melt Variability at Helheim Glacier, East Greenland, and Its Effect on Ice Dynamics

Understanding the behavior of large outlet glaciers draining the Greenland Ice Sheet is critical for assessing the impact of climate change on sea level rise. The flow of marine-terminating outlet glaciers is partly governed by calving-related processes taking place at the terminus but is also influenced by the drainage of surface runoff to the bed through moulins, cracks, and other pathways. To investigate the extent of the latter effect, we develop a distributed surface-energy-balance model for Helheim Glacier, East Greenland, to calculate surface melt and thereby estimate runoff. The model is driven by data from an automatic weather station operated on the glacier during the summers of 2007 and 2008, and calibrated with independent measurements of ablation. Modeled melt varies over the deployment period by as much as 68% relative to the mean, with melt rates approximately 77% higher on the lower reaches of the glacier trunk than on the upper glacier. We compare melt variations during the summer season to estimates of surface velocity derived from global positioning system surveys. Near the front of the glacier, there is a significant correlation (on >95% levels) between variations in runoff (estimated from surface melt) and variations in velocity, with a 1 day delay in velocity relative to melt. Although the velocity changes are small compared to accelerations previously observed following some calving events, our findings suggest that the flow speed of Helheim Glacier is sensitive to changes in runoff. The response is most significant in the heavily crevassed, fast-moving region near the calving front. The delay in the peak of the cross-correlation function implies a transit time of 12-36 h for surface runoff to reach the bed.

Antarctic Volcanic Flux Ratios from Law Dome Ice Cores

Explosive volcanic eruptions can inject large quantities of sulphur dioxide into the stratosphere. The aerosols that result from oxidation of the sulphur dioxide can produce significant cooling of the troposphere by reflecting or absorbing solar radiation. It is possible to obtain an estimate of the relative stratospheric sulphur aerosol concentration produced by different volcanoes by comparing sulphuric acid fluxes determined by analysis of polar ice cores. Here, we use a non-sea-salt sulphate time series derived from three well-dated Law Dome ice cores to investigate sulphuric acid flux ratios for major eruptions over the period AD 1301-1995. We use additional data from other cores to investigate systematic spatial variability in the ratios. Only for the Kuwae eruption (Law Dome ice date AD 1459.5) was the H2SO4 flux larger than that deposited by Tambora (Law Dome ice date AD 1816.7).

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.

Late Pleistocene Interactions of East and West Antarctic Ice-Flow Regimes: Evidence from the McMurdo Ice Shelf

We present new interpretations of deglaciation in McMurdo Sound and the western Ross Sea, with observationally based reconstructions of interactions between East and West Antarctic ice at the last glacial maximum (LGM), 16 000, 12 000, 8000 and 4000 sp. At the LGM? East Antarctic ice from Mulock Glacier split, one branch turned westward south of Ross Island but the other branch rounded Ross Island before flowing southwest into McMurdo Sound. This flow regime, constrained by an ice saddle north of Ross Island, is consistent with the reconstruction of Stuiver and others (1981a). After the LGM, grounding-line retreat was most rapid in areas with greatest water depth, especially along the Victoria Land coast. By 12 000 sp, the ice-now regime in McMurdo Sound changed to through-flowing Mulock Glacier ice, with lesser contributions from Koettlitz, Blue and Ferrar Glaciers, because the former ice saddle north of Ross Island was replaced by a dome. The modern flew regime was established similar to 4000 BP. Ice derived from high elevations on the Polar Plateau but now stranded on the McMurdo Ice Shelf, and the pattern of the Transantarctic Mountains erratics support our reconstructions of Mulock Glacier ice rounding Minna Bluff but with all ice from Skelton Glacier ablating south of the bluff. They are inconsistent with Drewry's (1979) LGM reconstruction that includes Skelton Glacier ice in the McMurdo-Sound through-flow. Drewry's (1979) model closely approximates our results for 12 000-4000 BP. Ice-sheet modeling holds promise for determining whether deglaciation proceeded by grounding-line retreat of an ice sheet that was largely stagnant, because it never approached equilibrium flowline profiles after the Ross Ice Shelf, grounded, or of a dynamic ice sheet with flowline profiles kept low by active ice streams that extended northward from present-day outlet glaciers after the Ross Ice Shelf grounded.

The Most Extensive Holocene Advance in the Stauning Alper, East Greenland, Occurred in the Little Ice Age

We present glacial geologic and chronologic data concerning the Holocene ice extent in the Stauning Alper of East Greenland. The retreat of ice from the late-glacial position back into the mountains was accomplished by at least 11 000 cal years B.P. The only recorded advance after this time occurred during the past few centuries (the Little Ice Age). Therefore, we postulate that the Little Ice Age event represents the maximum Holocene ice extent in this part of East Greenland.