ALBERT

Description: The interaction between ice shelves and the ocean is an important process for the development of marine ice sheets. However, it is difficult to model in full detail due to the high computational cost of coupled ice–ocean simulations, so that simplified basal-melt parameterizations are required. In this work, a new analytical expression for basal melt is derived from the theory of buoyant meltwater plumes moving upward under the ice shelf and driving the overturning circulation within the ice-shelf cavity. The governing equations are nondimensionalized in the case of an ice shelf with constant basal slope and uniform ambient ocean conditions. An asymptotic analysis of these equations in terms of small slopes and small thermal driving, assumed typical for Antarctic ice shelves, leads to an equation that can be solved analytically for the dimensionless melt rate. This analytical expression describes a universal melt-rate curve onto which the scaled results of the original plume model collapse. Its key features are a positive melt peak close to the grounding line and a transition to refreezing further away. Comparing the analytical expression with numerical solutions of the plume model generally shows a close agreement between the two, even for more general cases than the idealized geometry considered in the derivation. The results show how the melt rates adapt naturally to changes in the geometry and ambient ocean temperature. The new expression can readily be used for improving ice-sheet models that currently still lack a sufficiently realistic description of basal melt.

Description: Basal melting below ice shelves is a major factor in the decline of the Antarctic ice sheet, which can contribute significantly to possible future sea-level rise. Therefore, it is important to have an adequate description of the basal melt rates for use in ice-dynamical models. Most current ice models use rather simple parametrizations based on the local balance of heat between ice and ocean. In this work, however, we use a recently derived parametrization of the melt rates based on a buoyant meltwater plume travelling upward beneath an ice shelf. This plume parametrization combines a nonlinear ocean temperature sensitivity with an inherent geometry dependence, which is mainly described by the grounding-line depth zgl and the local slope α of the ice-shelf base. For the first time, this type of parametrization is evaluated on a two-dimensional grid covering the entire Antarctic continent. In order to apply the essentially one-dimensional parametrization to realistic ice-shelf geometries, we present an algorithm that determines effective values for zgl and α for any point beneath an ice shelf. Furthermore, since detailed knowledge of temperatures and flow patterns in the ice-shelf cavities is sparse or absent, we construct an effective ocean temperature field from observational data with the purpose of matching (area-averaged) melt rates from the model with observed present-day melt rates. The result is a realistic map of basal melt rates around Antarctica, not only in terms of average values, but also in terms of the spatial pattern, with high melt rates typically occurring near the grounding line. The plume parametrization and the effective temperature field are therefore promising tools for future simulations of the Antarctic ice sheet.

Description: Basal melting below ice shelves is a major factor in mass loss from the Antarctic Ice Sheet, which can contribute significantly to possible future sea-level rise. Therefore, it is important to have an adequate description of the basal melt rates for use in ice-dynamical models. Most current ice models use rather simple parametrizations based on the local balance of heat between ice and ocean. In this work, however, we use a recently derived parametrization of the melt rates based on a buoyant meltwater plume travelling upward beneath an ice shelf. This plume parametrization combines a non-linear ocean temperature sensitivity with an inherent geometry dependence, which is mainly described by the grounding-line depth and the local slope of the ice-shelf base. For the first time, this type of parametrization is evaluated on a two-dimensional grid covering the entire Antarctic continent. In order to apply the essentially one-dimensional parametrization to realistic ice-shelf geometries, we present an algorithm that determines effective values for the grounding-line depth and basal slope in any point beneath an ice shelf. Furthermore, since detailed knowledge of temperatures and circulation patterns in the ice-shelf cavities is sparse or absent, we construct an effective ocean temperature field from observational data with the purpose of matching (area-averaged) melt rates from the model with observed present-day melt rates. Our results qualitatively replicate large-scale observed features in basal melt rates around Antarctica, not only in terms of average values, but also in terms of the spatial pattern, with high melt rates typically occurring near the grounding line. The plume parametrization and the effective temperature field presented here are therefore promising tools for future simulations of the Antarctic Ice Sheet requiring a more realistic oceanic forcing.