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We develop a two-dimensional, plan-view formulation of ice-shelf flow and viscoelastic ice-shelf flexure. This formulation combines, for the first time, the shallow-shelf approximation for horizontal ice-shelf flow (and shallow-stream approximation for flow on lubricated beds such as where ice rises and rumples form), with the treatment of a thin-plate flexure. We demonstrate the treatment by performing two finite-element simulations: one of the relict pedestalled lake features that exist on some debris-covered ice shelves due to strong heterogeneity in surface ablation, and the other of ice rumpling in the grounding zone of an ice rise. The proposed treatment opens new venues to investigate physical processes that require coupling between the longitudinal deformation and vertical flexure, for instance, the effects of surface melting and supraglacial lakes on ice shelves, interactions with the sea swell, and many others. [ABSTRACT FROM AUTHOR]

Diurnal depth cycles of decimeter scale are observed in a supraglacial lake on the McMurdo Ice Shelf, Antarctica. We evaluate two possible causes: (1) tidal tilt of the ice shelf in response to the underlying ocean tide, and (2) meltwater input variation. We find the latter to be the most likely explanation of our observations. However, we do not rule out tidal tilt as a source of centimeter scale variations, and point to the possibility that other, larger supraglacial lake systems, particularly those on ice shelves that experience higher amplitude tidal tilts, such as in the Weddell Sea, may have depth cycles driven by ocean tide. The broader significance of diurnal cycles in meltwater depth is that, under circumstances where the ice shelf is thin, tidal-tilt amplitudes are high, and meltwater runoff rates are large, there may be associated flexure stresses that can contribute to ice-shelf fracture and destabilization. For the McMurdo Ice Shelf (~20–50 m thickness, ~ 1 m tidal amplitude and ~10 cm water-depth variations), these stresses amount to several 10's of kPa. [ABSTRACT FROM AUTHOR]