The oceanic forcing of basal melt under floating ice shelves in Greenland and Antarctica is one of the major sources of uncertainty in climate icesheet modelling. We use a high-resolution, nonhydrostatic configuration of the Massachusetts Institute of Technology general circulation model(MITgcm) to investigate basal melt rates and melt-driven circulation in the Sherard Osborn Fjord under the floating tongue of Ryder Glacier,northwestern Greenland. The control model configuration, based on the first-ever observational survey by Ryder 2019 Expedition, yieldedmelt rates consistent with independent satellite estimates. A protocol of model sensitivity experiments quantified the response to oceanic thermalforcing due to warming Atlantic Water and to the buoyancy input from the subglacial discharge of surface fresh water. We found that the averagebasal melt rates show a nonlinear response to oceanic forcing in the lower range of ocean temperatures, while the response becomes indistinguishablefrom linear for higher ocean temperatures, which unifies the results from previous modelling studies of other marine-terminating glaciers. The meltrate response to subglacial discharge is sublinear, consistent with other studies. The melt rates and circulation below the ice tongue exhibit aspatial pattern that is determined by the ambient density stratification.

Ocean--driven submarine basal melt of the Greenland Ice Sheet remains a major source of uncertainty in climate projections of future sea-level rise based on ice sheet modelling. State-of-the-art parameterizations focus on properties of ocean waters reaching the marine terminating glaciers, processes at the ice--ocean interface and subglacial discharge. This study uses high resolution ocean simulations complemented by theory and observations to quantify two effects of fjord bathymetry (sills) on the thermal forcing with consequences for the basal melt. These effects are the recirculation of Glacially Modified Water due to hydraulic control at the sill (which we study in detail) and the cooling of the inflow due to the restriction of the deepest and warmest Atlantic Water inflow (which has been known before). For a fixed sill depth, an increase in subglacial discharge can make the exchange flow hydraulically controlled. Our results suggest that basal melt parameterizations should account for fjord bathymetry, and outline a road map to guide future parameterization developments.

Basal melt of marine terminating glaciers is a key uncertainty in predicting the future climate and the evolution of the Antarctic and Greenland ice sheets. Regional ocean circulation models use parameterizations that depend on the available heat to parameterize basal melt. The heat budget at the ice–ocean interface includes turbulent heat flux from the ocean below, latent heat for phase transition, and heat conduction into the ice. Here we review the estimation of heat conduction into the ice, which has been treated in various ways in modelling studies so far. We show that the formulation of Holland and Jenkins (1999) best captures the variety of temperature profiles measured in boreholes. Accounting for heat conduction into the ice reduces melt rates by up to 28 %.

We introduce a continuous Galerkin finite element discretization of the non-hydrostatic Boussinesq approximation of the Navier-Stokes equations, suitable for various applications such as coastal ocean dynamics and ice-ocean interactions, among others. In particular, we introduce a consistent modification of the gravity force term which enhances conservation properties for Galerkin methods without strictly enforcing the divergence-free condition. We show that this modification results in a sharp energy estimate, including both kinetic and potential energy. Additionally, we propose a new, symmetric, tensor-based viscosity operator that is especially suitable for modeling turbulence in stratified flow. The viscosity coefficients are constructed using a residual-based shock-capturing method and the method conserves angular momentum and dissipates kinetic energy. We validate our proposed method through numerical tests and use it to model the ocean circulation and basal melting beneath the ice tongue of the Ryder Glacier and the adjacent Sherard Osborn fjord in two dimensions on a fully unstructured mesh. Our results compare favorably with a standard numerical ocean model, showing better resolved turbulent flow features and reduced artificial diffusion. 

Effects of submarine glacier melt of the Greenland Ice Sheet remain amajor uncertainty in climate-model projections of future sea level rise.Development of submarine melt parameterizations have to a high degreerelied on ocean-circulation modelling of glacial fjords, designed toquantify effects such as ocean thermal forcing and fjord–glaciergeometry. Greenlandic fjords are relatively narrow, and it is frequentlyassumed that across-fjord flow variations are small enough to allowmarine melt to be quantified with two-dimensional ocean--circulationmodels. Here, we present three-dimensional model simulations showingthat the interplay between fjord-glacier geometry, side wall friction, andEarth's rotation makes the circulation in ice-shelf cavities three-dimensional even in narrow fjords. Remarkably, we find that Earth'srotation decreases the marine melt on a 10 km wide ice tongue by afactor of five compared to a non-rotating simulation. Our study promptsusing three-dimensional model configurations of Greenlandic fjords.