Ice Dynamics Preceding Catastrophic Disintegration of the Floating Part of Jakobshavn Isbrie, Greenland

The floating terminal of Jakobshavn Isbr ae, the fastest Greenland ice stream, has disintegrated since 2002, resulting in a doubling of ice velocity and rapidly lowering inland ice elevations. Conditions prior to disintegration were modeled using control theory in a plane-stress solution, and the Missoula model of ice-shelf flow. Both approaches pointed to a mechanism that inhibits ice flow and that is not captured by either approach. Jamming of flow, an inherent property of granular materials passing through a constriction (Jakobshavn Isfjord), is postulated as the mechanism. Rapid disintegration of heavily crevassed floating ice accompanies break-up of the ice jam.

Basal Melting Along the Floating Part of Byrd Glacier

A mass balance calculation was made for the floating part of Byrd Glacier, using 1978-79 ice elevation and velocity data, over the 45 km of Byrd Glacier from its grounding line to where it leaves its fjord and merges with the Ross Ice Shelf. Smoothed basal melting rates were relatively uniform over this distance and averaged 12 +/- 2 m yr(-1).

Relating Crevassing to Non-Linear Strain in the Floating Part of Jakobshavn Isbrae, West Greenland

Jakobshavn Isbrae is a major ice stream that drains the west-central Greenland ice sheet and becomes afloat in Jakobshavn Isfiord (69degreesN, 49degreesW), where it has maintained the world's fastest-known sustained velocity and calving rate (7 km a(-1)) for at least four decades. The floating portion is approximately 12 km long and 6 km wide. Surface elevations and motion vectors were determined photogrammetrically for about 500 crevasses on the floating ice, and adjacent grounded ice, using aerial photographs obtained 2 weeks apart in July 1985. Surface strain rates were computed from a mesh of 399 quadrilateral elements having velocity measurements at each corner. It is shown that heavy crevassing of floating ice invalidates the assumptions of linear strain theory that (i) surface strain in the floating ice is homogeneous in both space and time, (ii) the squares and products of strain components are nil, and (iii) first- and second-order rotation components are small compared to strain components. Therefore, strain rates and rotation rates were also computed using non-linear strain theory. The percentage difference between computed linear and non-linear second invariants of strain rate per element were greatest (mostly in the range 40-70%) where crevassing is greatest. Isopleths of strain rate parallel and transverse to flow and elevation isopleths relate crevassing to known and inferred pinning points.

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.

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.

On the Pulling Power of Ice Streams

Gravity wants to pull an ice sheet to the center of the Earth, but cannot because the Earth's crust is in the way, so ice is pushed out sideways instead. Or is it? The ice sheet "sees" nothing preventing it from spreading out except air, which is much less massive than ice. Therefore, does not ice rush forward to fill this relative vacuum; does not the relative vacuum suck ice into it, because Nature abhors a vacuum? If so, the ice sheet is not only pulled downward by gravity, it is also pulled outward by the relative vacuum. This pulling outward will be most rapid where the ice sheet encounters least resistance. The least resistance exists along the bed of ice streams, where ice-bed coupling is reduced by a basal water layer, especially if the ice stream becomes afloat and the floating part is relatively unconfined around its perimeter and unpinned to the sea floor. Ice streams are therefore fast currents of ice that develop near the margins of an ice sheet where these conditions exist. Because of these conditions, ice streams pull ice out of ice sheets and have pulling power equal to the longitudinal gravitational pulling force multiplied by the ice-stream velocity. These boundary conditions beneath and beyond ice streams can be quantified by a basal buoyancy factor that provides a life-cycle classification of ice streams into inception, growth, mature, declining and terminal stages, during which ice streams disintegrate the ice sheet. Surface profiles of ice streams are diagnostic of the stage in a life cycle and, hence, of the vitality of the ice sheet.

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.

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

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.

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.

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.

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.

Tidal Flexure of Jakobshavns Glacier, West Greenland

Jakobshavns Glacier, a floating outlet glacier on the West Greenland coast, was surveyed during July 1976. The vertical displacements of targets along two profiles perpendicular to the fjord wall bounding the north margin of the glacier were analyzed to determine the effect of flexure caused by tidal oscillations within the fjord. An analysis based on the assumption that vertical displacements of the glacier reflected pure elastic bending yielded the conclusion that the effective thickness of the ice (i.e., the thickness which remained unaffected by surface and basal cracking and which behaved as a continuum) was ∼160 m 2.6 km upglacier from the calving front and ∼110 m 0.6 km from the calving front. An analysis based on the more realistic assumption that observed bending reflected elastic and viscoplastic deformation yielded the conclusion that the average effective thickness of the ice was 316 ± 74 m (∼40% of the estimated 800-m total thickness) 2.6 km from the calving front and 160 ± 48 m (∼21% of the estimated 750-m total) 0.6 km from the calving front. A constitutive relationship appropriate for hard glide during flexure was used.

The Jakobshanvs Effect

The Jakobshavns Effect may have been a significant factor in hastening the collapse of palaeo ice sheets with the advent of climatic warming after 18,000 years ago and may precipitate partial collapse of the present‐day Greenland and Antarctic Ice Sheets following CO2‐induced climatic warming in the decades ahead. The Jakobshavns Effect is observed today on Jakobshavns Glacier, which is located at 69°10′N on the west coast of Greenland. The Jakobshavns Effect is a group of positive feedback mechanisms which allow Jakobshavns Glacier to literally pull ice out of the Greenland Ice Sheet at a rate exceeding 7 km/a across a floating terminus 800 m thick and 6 km wide. The pulling power results from an imbalance of horizontal hydrostatic forces in ice and water columns at the grounding line of the floating terminus. Positive feedback mechanisms that sustain the rapid ice discharge rate are ubiquitous surface crevassing, high summer rates of surface melting, extending creep flow, progressive basal uncoupling, progressive lateral uncoupling, and rapid iceberg calving.