Garry K. C. Clarke

Origin and fate of Lake Vostok water frozen to the base of the East Antarctic ice sheet

The subglacial Lake Vostok may be a unique reservoir of genetic material and it may contain organisms with distinct adaptations, but it has yet to be explored directly. The lake and the overlying ice sheet are closely linked, as the ice-sheet thickness drives the lake circulation, while melting and freezing at the ice-sheet base will control the flux of water, biota and sediment through the lake. Here we present a reconstruction of the ice flow trajectories for the Vostok core site, using ice-penetrating radar data and Global Positioning System (GPS) measurements of surface ice velocity. We find that the ice sheet has a significant along-lake flow component, persistent since the Last Glacial Maximum. The rates at which ice is frozen (accreted) to the base of the ice sheet are greatest at the shorelines, and the accreted ice layer is subsequently transported out of the lake. Using these new flow field and velocity measurements, we estimate the time for ice to traverse Lake Vostok to be 16,000–20,000 years. We infer that most Vostok ice analysed to date was accreted to the ice sheet close to the western shoreline, and is therefore not representative of open lake conditions. From the amount of accreted lake water we estimate to be exported along the southern shoreline, the lake water residence time is about 13,300 years.

North American Ice Sheet reconstructions at the Last Glacial Maximum

Abstract The areal extent of the last glacial maximum (LGM) ice sheets is well known in North America, but there is no direct geological proxy for ice sheet thickness or volume. Uncertainties associated with glaciological and geophysical reconstructions give widely varying estimates of North American Ice Sheet (NAIS) volume at LGM. In an effort to quantify the uncertainty associated with glaciological reconstructions, we conducted a suite of 190 numerical simulations of the last glacial cycle in North America, prescribing different climatic, mass balance, glaciologic, and isostatic treatments for the least constrained model variables. LGM ice sheet reconstructions were evaluated using the well-established geologic record of ice sheet area and southern extent at LGM ( Dyke and Prest (1987) ). These constraints give a subset of 33 simulations that produce reasonable LGM ice cover in North America. Ice sheet dispositions and the associated parameter settings in this subset of tests provide insight into the plausible range of NAIS thickness, form, and mass balance regime at LGM. Ice volume in this subset of tests spans a range of 28.5–38.9×10 15 m 3 at LGM, with a predominant cluster at 32–36×10 15 m 3 . Taking floating ice and displaced continental water into account, this corresponds to 69–94 m eustatic sea level (msl). More than 75% of the accepted tests fall in the range 78–88 msl . We argue that this is a plausible estimate of the volume of water locked up in the NAIS at LGM.

Strain heating and creep instability in glaciers and ice sheets

Creep instability, the runaway increase of internal temperature and deformation rate, may affect the boundary condition at the base of glaciers and ice sheets and thus influence their flow and dimensions. We consider a simple slab model of heat transport in which three dimensionless parameters determine the relative importance of strain heating, ice advection normal to the surface, and boundary conditions. We find that an ice mass will be unstable if the strain-heating parameter exceeds a critical value which depends strongly on advection and boundary conditions. Critical values over the range of parameters appropriate to natural ice masses are presented. Accumulation (downward advection) or ablation (upward advection) affects the critical value by up to 5 orders of magnitude: ablation tends to reduce stability, and accumulation increases it. For an ice mass frozen to its bed, instability eventually raises the basal ice to melting point. This can restore thermal stability, but the ice mass will start to slide over its bed. If the strain-heating parameter exceeds a second, higher critical value, a layer of basal ice at melting point will form. We find that the conditions for instability are likely to exist in the accumulation and ablation zones of certain glaciers and ice sheets. However, times calculated for instability to develop are in the range 102–103 yr for glaciers and 103–104 yr for ice sheets. As these times exceed the normal residence time for ice in the ablation zone, it appears that instability is most likely to develop in the accumulation zone. This conclusion is reinforced by the fact that ablation increases the growth time for instability, whereas accumulation decreases it. The growth times quoted above are longer than the periods of most glacier surges, and thus creep instability is an unlikely surge mechanism. Unstable conditions may, however, obtain in East Antarctica and may have existed in the central part of ice age ice sheets. Surges of ice sheets triggered by creep instability may be possible.

A continuum mixture model of ice stream thermomechanics in the Laurentide Ice Sheet 1. Theory

We employ a continuum mixture framework to incorporate ice streams in a three-dimensional thermomechanical model of the Laurentide Ice Sheet. The ice mass is composed of a binary mixture of sheet ice, which deforms by viscous creep, and stream ice, which flows by sliding and/or sediment deformation at the bed. Dynamic and thermal evolutions are solved for each component in the mixture, with coupling rules to govern transfer between flow regimes. We describe two different transfer mechanisms: (1) creep exchange, the nourishment of ice streams by viscous creep inflow from the surrounding ice sheet, and (2) bed exchange, the activation, growth, and deactivation of ice streams, perpetrated by transfers of bed area between flow constituents. This paper develops the underlying mixture theory. We express the governing equations for mass, momentum, and energy balance in a form suitable for direct incorporation in existing numerical models of ice thermomechanics. A companion paper in this issue explores mixture and ice stream behavior in applications with the Laurentide Ice Sheet.

Black‐box modeling of the subglacial water system

Measurements of water pressure beneath Trapridge Glacier, Yukon Territory, Canada, yield the following generalizations about subglacial conditions in the studied region: (1) Even over short distances the subglacial water system is highly heterogeneous. (2) The subglacial water system consists of at least two distinct components which we refer to as the “connected” and “unconnected” water systems. (3) Regions of the glacier bed can switch back and forth from being part of the connected or part of the unconnected water system. (4) Large spatial pressure gradients can exist within the unconnected water system, and between the connected and unconnected systems. (5) Rapid pressure variations can occur in the unconnected water system. (6) Pressure variations in the unconnected water system do not match those in the connected system and can, in fact, be strongly anticorrelated with pressure variations in the connected system. If the water pressure variations in the connected system are viewed as a forcing and those in the unconnected system as a response to this forcing, the input-output relation between forcing and response can be efficiently represented as a low-order nonlinear ordinary differential equation. The response of the unconnected system to forcing from the connected system is governed by time constants having approximate magnitudes of ∼1.7 hours and ∼7.4 hours that we believe are associated with process rates for substrate compression and pore water diffusion, respectively.

Hydraulics of subglacial outburst floods: new insights from the Spring-Hutter formulation

Using a slightly modified form of the Spring-Hutter equations, glacial outburst floods are simulated from three classic sites, Hazard Lake, Yukon, Canada, Summit Lake, British Columbia, Canada, and Grimsvotn, Iceland, in order to calibrate the hydraulic roughness associated with subglacial conduits. Previous work has suggested that the Manning roughness of the conduits is remarkably high, but the new calibration yields substantially lower values that are representative of those for natural streams and rivers. The discrepancy can be traced to a poor assumption about the effectiveness of heat transfer at the conduit walls. The simulations reveal behaviour that cannot be interred from simplified theories: (1) During flood onset, water pressure over much of the conduit can exceed the confining pressure of surrounding ice. (2) Local values of fluid potential gradient can differ substantially from the value averaged over the length of the conduit, contradicting an assumption of simple theories. (3) As the flood progresses, the location of flow constrictions that effectively control the flood magnitude can jump rapidly over large distances. (4) Predicted water temperature at the conduit outlet exceeds that suggested by measurements of exit water temperature.

A continuum mixture model of ice stream thermomechanics in the Laurentide Ice Sheet 2. Application to the Hudson Strait Ice Stream

Episodic exportations of ice-rafted debris to the North Atlantic in the late Pleistocene suggest quasiperiodic ice streaming or surging activity on the northeastern margin of the Laurentide Ice Sheet. Much of this efflux of ice may originate from an ice stream issuing from Hudson Strait and tapping into core regions of the Laurentide in Hudson Bay, Labrador, and the Foxe Basin. Applying the continuum mixture theory outlined by Marshall and Clarke [this issue], we model the thermomechanical evolution of the Hudson Strait Ice Stream in a three-dimensional finite difference model of the Laurentide Ice Sheet. Our simulations focus on internal dynamics of the ice stream. Under thermal regulation of basal flow we find surge cycles of stream activity interspersed with quiescent periods where the ice stream is frozen to the bed. Modeled surge durations vary from 105 to 3260 years, while surge periodicities range from 585 to 22,410 years. With pervasively warm or cold internal temperature distributions in the ice, ice streams can also establish modes of permanent activity or inactivity under thermal regulation. Our most vigorous ice streams produce peak values of approximately 0.03 Sv of freshwater flux to the North Atlantic from basal meltwater and iceberg production. Associated ice stream velocities in this maximum case approach 6700 m yr -1 . The total ice volume mobilized in a single surge event is equivalent to a global sea level rise of 0.04m in the most tranquil surge and almost 0.6m in the most extreme case. These velocities and sea level impacts are an order of magnitude less than those predicted by MacAyeal [1993a,b], and only our most exuberant streams approach the iceberg flux estimates of Dowdeswell et al. [1995]. We propose that the sediment load of icebergs emanating from Hudson Strait in a surge event may exceed expectations from contemporary icebergs.

Geologic and topographic controls on fast flow in the Laurentide and Cordilleran Ice Sheets

Ice streams are fast flowing arteries which play a vital role in the dynamics and mass balance of present-day ice sheets. Although not fully understood, fast flow dynamics are intimately coupled with geologic, topographic, thermal, and hydrologic conditions of the underlying bed. These are difficult observables beneath contemporary ice sheets, hindering elucidation of the processes which govern ice streaxn behavior. For past ice sheets the problem is antithetic. Geologic evidence of former ice streams exists, but spatiM and temporal histories are uncertain; however, detailed knowledge of bed geology and topography is available in many places. We take advantage of this information to compile terrain characteristics relevant to fast flow dynamics in the Laurentide and Cordilleran Ice Sheets. Using seed points where fast flowing Wisconsinan ice has been geologically inferred, discriminant analysis of a suite of North American geologic and topographic properties yields a concise measure of ice-bed coupling strength. Our analysis suggests that the interior plains and continental shelf regions of North America have low basal coupling relative to areas of variable relief or exposed bedrock in the Cordillera and on the Canadian Shield. We conclude that the interior plains and continental shelves are both topographically and geologically predisposed to large-scale basal flows (i.e., ice streaxns or surge lobes). This result holds independent of whether the mechanism of fast flow is sediment deformation or decoupled sliding over the bed.

Review of subglacial hydro-mechanical coupling: Trapridge Glacier, Yukon Territory, Canada

Abstract The interaction of basal processes with the subglacial drainage system is a critical issue in understanding glacier dynamics. Since the recognition that many glaciers and ice masses overlie soft sediments rather than hard bedrock, much research has been undertaken to investigate how mechanical and hydrological conditions of a deformable substrate control the coupling at the ice–bed interface and thus affect fast ice flow and glacier surging. In research undertaken on Trapridge Glacier, a small surge-type glacier in the St. Elias Mountains, Yukon Territory, Canada, we have combined extensive field investigations using novel measurement techniques and theoretical modelling to study hydro-mechanical coupling processes. Measurements of subglacial water pressure indicate that the basal water system can be dramatically inhomogeneous, both spatially and temporally. Since ice–bed coupling is strongly influenced by subglacial water pressure, the stresses at the bed are also markedly heterogeneous and are expected to form a patchwork distribution which mimics the pressure distribution of the basal water system. This heterogeneity in the stress field at the ice–bed interface introduces a pronounced variability to the basal motion mechanics. As such, basal sliding and subglacial sediment deformation are not steady and continuous processes. Instead, the variability of the subglacial water system leads to a spatial and temporal interplay of increased ice–bed coupling at low water pressures at one site or time with ice–bed decoupling during rising water pressures at other sites or times. Thus, on the one hand there is downglacier shear deformation of the bed and accumulation of elastic strain in ice and sediment, while on the other hand there is enhanced slip-sliding of the glacier and upglacier shear motion of the bed due to an elastic relaxation of the sediment.

Abrupt glacier motion and reorganization of basal shear stress following the establishment of a connected drainage system

Three episodes of strong basal motion occurred at Trapridge Glacier, Yukon Territory, Canada, on 11 June 1995 following the establishment of a connected subglacial drainage system. Responses to these spring events are noted in the records for 42 instruments and were recorded throughout the ∼60 000 m study area. Strong basal motion during the events is indicated by ploughmeter, load-bolt and vertical-strain records, and abrupt pressure changes in several transducer records denote damage caused by extreme pressure pulses. These pressure pulses, generated by the abrupt basal motion, also resulted in the failure of seven pressure sensors. Records for pressure, turbidity and conductivity sensors indicate that basal drainage patterns did not change significantly during the events. Geophone records suggest that the episodes of basal motion were precipitated by the gradual failure of a sticky spot following hydraulic connection of part of the study area. This failure resulted in the transfer of basal stress to the unconnected region of the bed during the course of the events. No evidence for strong basal motion is seen in the instrument records for several weeks following the events, suggesting that the mechanical adjustments resulted in a stable configuration of basal stresses. This event illustrates how unstable situations can be quickly accommodated by mechanical adjustments at the glacier bed.