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.

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 rely on an approximated heat budget at the ice-ocean interface that includes turbulent heat flux from the ocean below, latent heat for phase transition, and heat conduction into the ice in order to parameterize melt rates. Here we review the formulations of for the approximation of heat conduction into ice, utilizing three distinct observed ice temperature profiles. We show that the formulation accounting for constant vertical advection and vertical diffusion of heat into ice best represents the observed ice temperature profiles. Using idealized ocean simulations of a Greenlandic fjord and observed melt rates from Antarctica, we find a difference of up to 28 % (average of 12 %) in melt rates between the different approximations.

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 modeling. State-of-the-art parameterizations focus on the properties of the ocean water reaching the marine-terminating glaciers, processes at the ice-ocean interface and subglacial discharge to estimate submarine basal melt. This study uses 2-dimensional, nonrotating, 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 (reflux) 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. 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 relevant to narrow fjords.

Submarine glacier melt rates of the Greenland Ice Sheet remain a major uncertainty in climate model projections of future sea level rise. Development of submarine melt parameterizations have to a high degree relied on ocean circulation modelling of glacial fjords, designed to quantify effects such as ocean thermal forcing and fjordglacier geometry. Greenlandic fjords are relatively narrow, and it is frequently assumed that across-fjord flow variations are small enough to allow marine melt to be quantified with two-dimensional ocean–circulation models. Here, we present three–dimensional model simulations showing that the interplay between fjord–glacier geometry, side wall friction, and Earth’s rotation makes the circulation in ice–shelf cavities three–dimensional even in narrow fjords. Remarkably, we find that Earth’s rotation changes the flow pattern in the cavity below the ice shelf leading to a decrease in the marine melt on a 10 km wide ice shelf by a factor of five compared to a non–rotating simulation. Our study prompts using three–dimensional model configurations of Greenlandic fjords.

In this thesis, I investigate the complex interactions between the circulation and ice shelf melting in Greenlandic fjords, focusing particularly on ice shelves in North Greenland. The melting of ice shelves, driven by fjord circulation, is a major factor in the mass loss of ice sheets, which in turn contributes to global sea-level rise. Despite its importance, the processes that control marine ice shelf melt remain one of the largest contributors to uncertainty in climate and ice sheet models. This study aims to better understand the dynamics of these interactions by using high-resolution simulations from the Massachusetts Institute of Technology general circulation model (MITgcm) to explore the impact of oceanic forcing on marine melt and ocean circulation beneath the floating tongues of marine glaciers.

The research uses data from the 2019 Ryder Expedition, the first comprehensive survey of the region, to set up idealised model configurations for the Sherard Osborn Fjord and Ryder Glacier system. In this study, I examine how the warming of Atlantic Water, the injection of subglacial discharge, and the presence of fjord sills influence the fjord circulation and the resulting melt rates. One of the key findings is that melt rates exhibit a nonlinear response to oceanic temperature forcing for low ambient temperatures. This response becomes linear at higher temperatures. This behaviour combines results from previous studies, showing that glaciers experience a nonlinear dependence of melt on temperature forcing in colder conditions (such as at Antarctic ice shelves) and a linear dependence in warmer conditions, such as in Greenlandic fjords.

Additionally, in this study, I investigate the role of subglacial discharge, finding a sub-linear relationship between discharge volume and melt rates. The research also explores the spatial variability of melt rates under the ice shelf, driven by the ambient density stratification, which affects the ocean velocities at the ice shelf base. The presence of bathymetric features, such as fjord sills, can restrict the inflow of warm Atlantic Water and reduce overall melt rates by decreasing the temperature of water reaching the ice-ocean interface. I proceed to show the complex combined effect of variations in silldepth and variations in subglacial discharge volume.

During this work I assess different modelling approaches. I evaluate different approximations of the heat conduction into the ice in the parametrization commonly used to represent melting in ocean modelling. It further includes a comparison of results from MITgcm simulations with results from a novel finite element model. The latter offers advantages in representing complex seabed and ice shelf geometries and has the advantage of being able to locally refine the grid best represent regions of strong gradients, like the plume underneath ice shelves. The thesis also addresses the limitations of two-dimensional models. It shows that neglecting the effects of Earth’s rotation and the resulting across-fjord variability, even in narrow fjords, leads to an overestimation in shelf integrated melt by a factor of up to five. Three-dimensional models, although computationally more expensive, provide a more accurate representation of these processes, leading to more detailed representation of the melt rate underneath ice shelves.

The findings shown in this study have important implications for the modelling of ice shelves and the overall mass loss of the Greenland Ice Sheet and its contribution to global sea-level rise. By improving the understanding of the key processes driving marine melt in Greenlandic fjords, this research enhances the ability of climate models to include the effects of melting ice sheets. The insights gained from this work also provide a framework for further studies on ice-ocean interactions, particularly in the rapidly changing polar environments of fjords in Greenland.

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.