Geostatistical methods for improved quantification of ice mass bed topography

Contribution to global mean sea level rise by ice sheets, ice caps and glaciers is accelerating. The total volume of water stored globally in terrestrial ice is estimated by a multitude of methods but principally by the interpolation of icethickness data. For the ice sheets and large Arctic ice caps, ice thickness is predominantly measured by airborne radio-echo sounding surveys which use radio waves to detect the bed of the surveyed ice mass. While such surveys are now extensive, large portions of ice masses are generally unsurveyed due to their size. In order to quantify ice thickness and subsequently ice volume over the entirety of an ice mass, interpolation of the input measurements is used. Throughout this whole process, uncertainties arise. Initially, from the radio-echo sounding (RES) survey and subsequently, in the interpolation. Compounding this is the absence of ground-truthing for measurements and interpolations due to the inaccessibility of ice mass beds. Hence, there is a requirement to find alternative means of quantifying uncertainty in ice thickness measurements and subsequently derived bed topography, and analyses made from these data to reduce the uncertainty in sea level change projections. This thesis develops and applies methods which aim to reduce uncertainty in ice thickness and bed topography datasets. Using high-resolution elevation data, this study exploits the likely similarity between currently ice-covered topography and formerly glaciated topography in the Arctic to generate datasets which provide alternative validation for ice mass bed topography. For the first time topographic error in RES surveying is quantified and corrections are formulated for treating future and historic ice thickness and bed topography data. Additionally, the propagation of these uncertainties through interpolations of bed topography is quantified and reduced, focussing on the Greenland Ice Sheet. Finally, the full suite of methods is applied to ice caps in the Canadian Arctic to generate, for the first time, ice cap wide topography for ice caps in the region that hold approximately a third of the freshwater outside of the continental ice sheets. By quantifying and reducing uncertainty in datasets of bed topography and ice thickness this thesis assesses the perceived stability of the continental ice sheets and large ice Arctic ice caps. From this, the implications of this for near and far term global mean sea-level rise are investigated