Basal crevasses threaten the stability of ice shelves through the potential to form rifts and calve icebergs. Furthermore, it is important to determine the dependence of crevasse stability on temperature due to large vertical temperature variations on ice shelves. In this work, considering the vertical temperature profile through ice viscosity, we compare (1) the theoretical crack depths and (2) the threshold stress causing the transition from basal crevasses to full thickness fractures in several fracture theories. In the Zero Stress approximation, the depth-integrated force at the crevassed and non-crevassed location are unbalanced, violating the volume-integrated Stokes equation. By incorporating a Horizontal Force Balance (HFB) argument, recent work showed analytically that the threshold stress for rift initiation is only half of that predicted by the Zero Stress approximation. We generalize the HFB theory to show that while the temperature profile influences crack depths, the threshold rifting stress is insensitive to temperature. We compare with observations and find that HFB best matches observed rifts. Using HFB instead of Zero Stress for cracks in an ice-sheet model would substantially enlarge the predicted fracture depth, reduce the threshold rifting stress and potentially increase the projected rate of ice shelf mass loss.
The one‐dimensional steady state analytical solution of the energy conservation equation obtained by Robin (1955, https://doi.org/10.3189/002214355793702028) is frequently used in glaciology. This solution assumes a linear change in surface velocity from a minimum value equal to minus the mass balance at the surface to zero at the bed. Here we show that this assumption of a linear velocity profile leads to large errors in the calculated temperature profile and especially in basal temperature. By prescribing a nonlinear power function of elevation above the bed for the vertical velocity profile arising from use of the Shallow Ice Approximation, we derive a new analytical solution for temperature. We show that the solution produces temperature profiles identical to numerical temperature solutions with the Shallow Ice Approximation vertical velocity near ice divides. We quantify the importance of strain heating and demonstrate that integrating the strain heating and adding it to the geothermal heat flux at the bed is a reasonable approximation for the interior regions. Our analytical solution does not include horizontal advection components, so we compare our solution with numerical solutions of a two‐dimensional advection‐diffusion model and assess the applicability and errors of the analytical solution away from the ice divide. We show that several parameters and assumptions impact the spatial extent of applicability of the new solution including surface mass balance rate and surface temperature lapse rate. We delineate regions of Greenland and Antarctica within which the analytical solution at any depth is likely within 2 K of the actual temperatures with horizontal advection.
more » « less- PAR ID:
- 10459302
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Journal of Geophysical Research: Earth Surface
- Volume:
- 124
- Issue:
- 2
- ISSN:
- 2169-9003
- Page Range / eLocation ID:
- p. 271-286
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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