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Recent geological and geophysical data suggest that a 1 km thick ice shelf extended over the glacial Arctic Ocean during Marine Isotope Stage 6, about 140 000 years ago. Here, we theoretically analyse the development and equilibrium features of such an ice shelf, using scaling analyses and a one-dimensional ice-sheet-ice-shelf model. We find that the dynamically most consistent scenario is an ice shelf with a nearly uniform thickness that covers the entire Arctic Ocean. Further, the ice shelf has two regions with distinctly different dynamics: a vast interior region covering the central Arctic Ocean and an exit region towards the Fram Strait. In the interior region, which is effectively dammed by the Fram Strait constriction, there are strong back stresses and the mean ice-shelf thickness is controlled primarily by the horizontally integrated mass balance. A narrow transition zone is found near the continental grounding line, in which the ice-shelf thickness decreases offshore and approaches the mean basin thickness. If the surface accumulation and mass flow from the continental ice masses are sufficiently large, the ice-shelf thickness grows to the point where the ice shelf grounds on the Lomonosov Ridge. As this occurs, the back stress increases in the Amerasian Basin and the ice-shelf thickness becomes larger there than in the Eurasian Basin towards the Fram Strait. Using a one-dimensional ice-dynamic model, the stability of equilibrium ice-shelf configurations without and with grounding on the Lomonosov Ridge are examined. We find that the grounded ice-shelf configuration should be stable if the two Lomonosov Ridge grounding lines are located on the opposites sides of the ridge crest, implying that the downstream grounding line is located on a downward sloping bed. This result shares similarities with the classical result on marine ice-sheet stability of Weertman, but due to interactions between the Amerasian and Eurasian ice-shelf segments the mass flux at the downstream grounding line decreases rather than increases with ice thickness

Ice-shelf damming in the glacial Arctic Ocean: dynamical regimes of a basin-covering kilometre-thick ice shelf