Inverting for Antarctic subglacial topography using variability in satellite remote-sensing observations of the ice surface

As global temperatures rise, melting of the Antarctic Ice Sheet will lead to increasing global sea levels, but we do not currently have good constraints on the speed of future sea-level rise. A lack of knowledge about the subglacial topography of the ice sheets is a key cause of this uncertainty, as small variations in subglacial topography can have a significant influence on the rates of ice loss in numerical ice-sheet models. Our current understanding of subglacial topography comes from airborne and ground-based geophysical observations, which are expensive and time consuming to collect, and there are very few regions where the 1-2 km resolution required by ice-sheet models is achieved. When interpolation methods such as kriging, mass conservation and flow-line diffusion are applied to fill the gaps, they can miss influential mesoscale (2-30 km) subglacial features. In this thesis, I use a mathematical description of the relationship between surface and subglacial topography in flowing ice, alongside high-resolution observations of ice surface topography and velocities to invert for Antarctic subglacial topography and slipperiness. I develop a method for doing this which I term Ice Flow Perturbation Analysis (IFPA). Initially, I use synthetic models of subglacial topography to explore the range of landforms which can be resolved with this approach. I apply the IFPA method to Thwaites Glacier in West Antarctica in order to compare the results with high-resolution ice-penetrating radar measurements, and to select appropriate parameter values. I also apply the IFPA method to Pine Island Glacier in West Antarctica, and show that IFPA can resolve landforms which are not present in topographic maps which have interpolated between geophysical survey lines using flow-line diffusion. Finally, I use an updated version of the IFPA methodology to look at subglacial topography across the entire Antarctic continent. The new topography map reveals new features at the bed, and fills in the details for partially-surveyed features, providing an enriched understanding of the geometry and geomorphology of the subglacial landscape. Overall, this thesis demonstrates the value of the Ice Flow Perturbation Analysis method for mapping the subglacial topography beneath ice sheets using high-resolution satellite datasets, particularly in regions which have not yet been the focus for geophysical surveying. I emphasise the utility of the IFPA map for studying subglacial geometry and interpreting landforms, and hope that future work will enable maps produced with IFPA to incorporate more of the existing geophysical observations. When applied alongside other methods which estimate ice thickness, bed topography maps from IFPA should lead to better-constrained projections of future sea-level rise.