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Mountain glaciers and ice caps distinct from the ice sheets in Greenland and Antarctica, here-after “glaciers”, are melting and retreating around the World. Improving projections of glacier change and assessing associated Earth system impacts requires accurate knowledge of the bed topography beneath the ice. However, direct observations of the glacier bed exist for only a small fraction of the >200,000 glaciers globally. Thus, computational inversion methods are needed to infer bed properties from more accessible surface data. This thesis presents the development of a glacier bed and ice thickness inversion method and its applications on regional and global scales.

The newly developed inverse method is computationally efficient, robust, model agnostic and compatible with complex ice-flow physics on distributed grids. Tests on synthetic and real glaciers demonstrated strong performance, with benchmarks ranking it among the best available methods. The first regional application produced detailed bed topographies for Scandinavia, constraining total glacier volume to 0.32×10³ km³, equivalent to 0.8 mm of global mean sea-level rise if melted. A subsequent application to all glaciers in Svalbard — where glacier dynamics are more complex — estimated a volume of 6.80×10³ km³ (16.3 mm sea-level equivalent) and achieved improved agreement with observations compared to earlier studies. Finally, a global application yielded a total glacier volume of 149.41×10³ km³ (316.1 mm sea-level equivalent). While the global total aligns with previous estimates, notable regional differences were identified. Beyond ice volume, the global study produced physically realistic bed topographies and mapped >50,000 potential future lakes in presently glacier-covered terrain, totaling 3,138 km³ in volume (2% of global glacier volume) and >40,000 km² in area.

Methodologically, this thesis advances large-scale glacier thickness inversions, and presents the first global-scale application of higher-order ice-flow physics on distributed grids, enabled by physics-informed deep learning and parallelized code optimized for Graphic Processing Units. Practically, the regional and global ice volume estimates provide key data for adaptation and mitigation strategies in response to glacier mass loss and sea-level rise, while the derived bed maps support future research across the Earth sciences and improved projections of glacier change.