A numerical model reconstruction was made of the northeastern Laurentide Ice Sheet in the Baffin Island - Foxe Basin region using geophysical, terrestrial, and marine geologic evidence for initial and boundary conditions. The simulated ice sheet consists of a Foxe Dome with additional smaller Hall and Amadjuak domes and a Penny Ice Divide. A specific objective was to determine boundary conditions that would allow advance of a marine-based low surface slope ice stream into and out of Cumberland Sound, a major marine embayment in the uplifted rim of the eastern Canadian Arctic (up to 1200 m deep), while maintaining ice free or nonsliding (e.g., cold-based) thin ice on adjacent plateaus of Cumberland Peninsula; this scenario accommodates interpretations based on terrestrial and marine studies in this region. After an initial ice-sheet configuration is placed on the eastern Arctic terrain, basal sliding is allowed in specified regions. Basal sliding below sea level and between the Foxe Dome and Cumberland Sound and a reasonable but critical initial ice sheet volume and dome surface elevation are needed to obtain advance along and out of Cumberland Sound. Rapid flow into Hudson Strait and along Cumberland Sound causes drawdown and a change in ice-sheet configuration. Although more Foxe Dome ice flows into western Hudson Strait than Cumberland Sound in the simulations, the latter may still have been an important conduit connecting the interior of the northeastern Laurentide Ice Sheet to the Labrador Sea, thereby affecting regional ice sheet dynamics, specifically ice surface elevations and flow paths.

A simple interpretation of the traditional definitions of glacier and ice sheet response time (e.g., thickness divided by mass balance rate, ) suggests that larger glaciers respond more slowly than small glaciers to a perturbation in climate. However, with reasonable choices for mass balance behavior, a scaling analysis shows that the response time of valley glaciers decreases as a function of increasing size when other variables are held constant. In essence, this is because larger valley glaciers push further into the ablation zone, and ablation increases more rapidly than the thickness (so that gets smaller). Ice sheets have different mass balance regimes than valley glaciers, and as they grow larger, the ablation does not increase faster than the thickness. Therefore, as ice sheets grow in surface area, the response time increases. For both ice sheets and valley glaciers, the response time also depends on a mass balance index, which is defined as the slope of the balance curve as a function of horizontal distance along the glacier surface (rather than elevation). The response time decreases as the balance index increases, so for valley glaciers, an increase in the balance index and an increase in glacier size have opposite effects on the response time. The balance index is typically larger for smaller valley glaciers. Therefore a small glacier will typically respond faster than a large glacier, but this quicker response is because of mass balance considerations and not because of the dynamic characteristics of the glacier arising from its small size, as often assumed.

Numerical experiments were made using a time‐dependent nonlinear finite element model of glacier flow to seek confirmation of theoretical predictions made in the companion to this paper [Bahr et al., this issue]. The theoretical analysis indicates that under conditions of equal gradients in mass balance along the glacier surface ( ), other variables being held constant, response time to mass balance perturbations will decrease as glacier size increases. This behavior is confirmed by the numerical model experiments, which are performed on a suite of 23 radially symmetric ice caps with sizes ranging over ∼4 orders of magnitude. The shape and mass balance profiles of the ice caps are defined so that is constant over all ice caps, and for uniform perturbations in mass balance, the modeled response times are faster for larger ice caps. The model results also confirm a volume/area scaling relationship established in the theoretical discussion and confirm the equivalence between two measures of response time, one arising from the present theory and the other a conventional expression of response time. The apparent discrepancy between the present results and preexisting theory is discussed, and it is shown that the results are compatible.

This paper presents a boundary element formulation for 3-D linear and viscoelastic bodies subjected to the body force of gravity. The Laplace transformation is first used to suppress the time variable, and solutions of displacements and stresses are found in the transformed domain. The time domain solutions are then found by an accurate and efficient numerical inversion method which requires only real calculations for all quantities. Input and output data, and solutions in the transformed and time domains are connected through an Interactive Data Language code written by the authors. While particular solutions of stresses and displacements related to the body force of gravity (which is applied at time t = 0 and is kept constant) are derived, the Green's functions in the Laplace domain are obtained through the correspondence principle. The new formulation has been implemented into an existing 3-D BEM program, and several numerical examples involving 3-D viscoelastic bodies are presented. Although the discussion in this paper focuses on Maxwell viscoelastic and isotropic media, other linear isotropic and even anisotropic viscoelastic models can also be incorporated, without difficulty, into the 3-D viscoelastic BEM program.

A time‐dependent finite element model was used to reconstruct the advance of ice from a late Glacial dome on northern Quebec/Labrador across Hudson Strait to Meta Incognita Peninsula (Baffin Island) and subsequently to the 9.9–9.6 ka 14C Gold Cove position on Hall Peninsula. Terrestrial geological and geophysical information from Quebec and Labrador was used to constrain initial and boundary conditions, and the model results are compared with terrestrial geological information from Baffin Island and considered in the context of the marine event DC‐0 and the Younger Dryas cooling. We conclude that advance across Hudson Strait from Ungava Bay to Baffin Island is possible using realistic glacier physics under a variety of reasonable boundary conditions. Production of ice flux from a dome centered on northeastern Quebec and Labrador sufficient to deliver geologically inferred ice thickness at Gold Cove (Hall Peninsula) appears to require extensive penetration of sliding south from Ungava Bay. The discharge of ice into the ocean associated with advance and retreat across Hudson Strait does not peak at a time coincident with the start of the Younger Dryas and is less than minimum values proposed to influence North Atlantic thermohaline circulation; nevertheless, a significant fraction of freshwater input to the North Atlantic may have been provided abruptly and at a critical time by this event.

The interaction between crevassing and far-field stresses at a glacier surface determines in part the distribution, orientation, surface density, and extent of propagation of crevasses. These properties characterizing crevassing of a glacier surface are important parameters when modeling iceberg calving from glacier terminii, since they describe the initial geometry of pre-existing cracks entering the calving front. Crack-by-crack modeling of fracture at a calving terminus is too complex a task to be modeled in full detail, however, and some means of selecting the crevasse features most significant in the stress field is desired. We present a Boundary Element Analysis of the stress field surrounding a group of cracks at the surface of a linear elastic half-space and the part of the stress field arising from crack interactions alone. This stress field shows the extent to which individual crack stress fields interact, and gives a measure of the radius of interaction of clacks. We find that typical crevasses in a glacier surface, formed in extension, cease to affect the stress field of neighboring crevasses if the crevasses are separated by a distance greater than three to four times the crevasse depth. This agrees well with limited observations of crevasse depth and spacing, and with a separate theoretical analysis based on stress intensity factors, The calculation gives an explanation of observed crevasse depth/spacing observations and provides a means for determining representative distributions of crevasse depths and spacings in a model based in part on calculations of far-field stresses.