Theoretical stability of ice shelf basal crevasses with a vertical temperature profile

Abstract

Abstract 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.