Millennial-scale migration of the frozen/melted basal boundary, western Greenland ice sheet

The geometry and thermal structure of western Greenland ice sheet are known to have undergone relatively substantial change over the Holocene. Evolution of the frozen and melted fractions of the bed associated with the ice-sheet retreat over this time frame remains unclear. We address this question using a thermo-mechanically coupled flowline model to simulate a 11 ka period of ice-sheet retreat in west central Greenland. Results indicate an episode of ~100 km of terminus retreat corresponded to ~16 km of upstream frozen/melted basal boundary migration. The majority of migration of the frozen area is associated with the enhancement of the frictional and strain heating fields, which are accentuated toward the retreating ice margin. The thermally active bedrock layer acts as a heat sink, tending to slow contraction of frozen-bed conditions. Since the bedrock heat flux in our region is relatively low compared to other regions of the ice sheet, the frozen region is relatively greater and therefore more susceptible to marginward changes in the frictional and strain heating fields. Migration of melted regions thus depends on both geometric changes and the antecedent thermal state of the bedrock and ice, both of which vary considerably around the ice sheet.

Thermodynamics of a fast-moving Greenlandic outlet glacier revealed by fiber-optic distributed temperature sensing

Measurements of ice temperature provide crucial constraints on ice viscosity and the thermodynamic processes occurring within a glacier. However, such measurements are presently limited by a small number of relatively coarse-spatial-resolution borehole records, especially for ice sheets. Here, we advance our understanding of glacier thermodynamics with an exceptionally high-vertical-resolution (~0.65 m), distributed-fiber-optic temperature-sensing profile from a 1043-m borehole drilled to the base of Sermeq Kujalleq (Store Glacier), Greenland. We report substantial but isolated strain heating within interglacial-phase ice at 208 to 242 m depth together with strongly heterogeneous ice deformation in glacial-phase ice below 889 m. We also observe a high-strain interface between glacial- and interglacial-phase ice and a 73-m-thick temperate basal layer, interpreted as locally formed and important for the glacier’s fast motion. These findings demonstrate notable spatial heterogeneity, both vertically and at the catchment scale, in the conditions facilitating the fast motion of marine-terminating glaciers in Greenland.

Basal conditions at Engabreen, Norway, inferred from surface measurements and inverse modelling

ABSTRACTEngabreen is an outlet glacier of the Svartisen Ice Cap located in Northern Norway. It is a unique glacier due to the Svartisen Subglacial Laboratory which allows direct access to the glacier bed. In this study, we combine both sub- and supraglacial observations with ice-flow modelling in order to investigate conditions at the bed of Engabreen both spatially and temporally. We use the full-Stokes model Elmer/Ice and satellite-based surface-velocity maps from 2010 and 2014 to infer patterns of basal friction. Direct measurements of basal sliding and deformation of lower layers of the ice are used to adjust the ice viscosity and provide essential input to the setup of our model and influence the interpretation of the results. We find a clear seasonal cycle in the subglacial conditions at the higher elevation region of the study area and discuss this in relation to the subglacial hydrological system. Our results also reveal an area with an overdeepening where basal friction is significantly lower than elsewhere on the glacier all year round. We attribute this to either water pooling at the base, or saturated sediments and increased strain heating at this location which softens the ice further.

Heat sources within the Greenland Ice Sheet: dissipation, temperate paleo-firn and cryo-hydrologic warming

Ice temperature profiles from the Greenland Ice Sheet contain information on the deformation history, past climates and recent warming. We present full-depth temperature profiles from two drill sites on a flow line passing through Swiss Camp, West Greenland. Numerical modeling reveals that ice temperatures are considerably higher than would be expected from heat diffusion and dissipation alone. The possible causes for this extra heat are evaluated using a Lagrangian heat flow model. The model results reveal that the observations can be explained with a combination of different processes: enhanced dissipation (strain heating) in ice-age ice, temperate paleo-firn, and cryo-hydrologic warming in deep crevasses.

Excess heat in the Greenland Ice Sheet: dissipation, temperate paleo-firn and cryo-hydrologic warming

Ice temperature profiles from the Greenland Ice Sheet contain information on the deformation history, past climates and recent warming. We present full-depth temperature profiles from two drill sites on a flowline passing through Swiss Camp, West Greenland. Numerical modeling reveals that ice temperatures are considerably higher than would be expected from heat diffusion and dissipation alone. The possible causes for this excess heat are evaluated using a Lagrangian heat flow model. The model results reveal that the observations can be explained with a combination of different processes: enhanced dissipation (strain heating) in ice-age ice, temperate paleo-firn, and cryo-hydrologic warming in deep crevasses.

Exact solutions to the thermomechanically coupled shallow-ice approximation: effective tools for verification

We describe exact solutions to the thermomechanically coupled shallow-ice approximation in three spatial dimensions. Although artificially constructed, these solutions are very useful for testing numerical methods. In fact, they allow us to verify a finite-difference scheme, that is, to show that the results of our numerical scheme converge to the correct continuum values as the grid is refined in three dimensions. Comparison of numerical results with exact solutions has helped us to precisely quantify and understand some of the numerical errors we are making. Our verified numerical scheme shows the basal temperature spokes which arose in the EISMINT (European Ice Sheet Modelling INiTiative) II intercomparison (Payne and others, 2000). A careful analysis describes these warm spokes as numerical errors which occur when the derivative of the strain-heating term with respect to the temperature is large. On the other hand, the appearance of basal temperature spokes in a verified numerical scheme strongly suggests that they are a feature of the EISMINT II experiment F continuum problem. In fact, they are clear evidence of an unstable equilibrium point of the continuum problem. This paper is a sequel to Bueler and others (2005) which addresses exact solutions and verification in the isothermal case.

RECOVERY CHARACTERISTIC FOR SHAPE MEMORY EFFECT UNDER THE CONDITION OF HEATING WITH CONSTRAINT STRAIN

A new constitutive equation is proposed based on the series combined model, considering the generation of slip deformation, due to the recovery stress in heating under constraint strain, as well as external stress in loading. The martensite volume fractions in the constitutive equation were distinguished into three kinds: un-reoriented martensite, reoriented martensite and plastic damaged martensite. And the critical stress for the slip deformation, generated through the reverse transformation, in a constraint strain-heating process, was clarified experimentally and introduced into the constitutive equation. Moreover, the validity of our constitutive equation has been confirmed by experimentation conducted under various constraint strain-heating conditions in the recovery process.