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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.

Knowledge of the thickness, volume, and subglacial topography of glaciers is crucial for a range of glaciological, hydrological, and societal issues, including studies on climate-warming-induced glacier retreat and associated sea level rise. This is not in the least true for Svalbard, one of the fastest-warming places in the world. Here, we present new maps of the ice thickness and subglacial topography for every glacier on Svalbard. Using remotely sensed observations of surface height, ice velocity, rate of surface elevation change, and glacier boundaries in combination with a modelled mass balance product, we apply an inverse method that leverages state-of-the-art ice flow models to obtain the shape of the glacier bed. Specifically, we model large glaciers with the Parallel Ice Sheet Model (PISM) at 500 m resolution, while we resolve smaller mountain glaciers at 100 m resolution using the physics-informed deep-learning-based Instructed Glacier Model (IGM). Actively surging glaciers are modelled using a perfect-plasticity model. We find a total glacier volume (excluding the island Kvitøya) of 6800 ± 238 km3, corresponding to 16.3 ± 0.6 mm sea level equivalent. Validation against thickness observations shows high statistical agreement, and the combination of the three methods is found to reduce uncertainties. We discuss the remaining sources of errors, differences from previous ice thickness maps of the region, and future applications of our results.

X-ray based microdensitometry is conventionally used to produce climate-related tree-ring records. Micro X-ray fluorescence (µXRF) applications represent another growing area of interest and opportunities in dendrochronology. This paper demonstrates a method to correctly juxtapose and precisely synchronise the densitometry and µXRF profiles. Among µXRF variables, full fluorescence spectrum (FFS) corresponds distinctly well with the microdensitometry-based wood density variations. Accordingly, the FFS provides the most applicable variable to integrate the µXRF and density profiles. The method proposed here can be used to demonstrate the strength and sign of µXRF variables and wood density relations. Moreover, the µXRF based records can be readily compared to density variables, such as the latewood maximum density, which is demonstrated in this paper.

We present a new map of bed topography and ice thickness together with a corresponding ice volume estimate representative of the years ~2010 for all Scandinavian ice caps and glaciers. Starting from surface observations, we invert for ice thickness by iteratively running an innovative ice dynamics model on a distributed grid and updating bed topography until modelled and observed glacier dynamics as represented by their rate of surface elevation change (dh/dt) fields align. The ice flow model used is the instructed glacier model (Jouvet and Cordonnier, 2023, Journal of Glaciology 1–15), a generic physics-informed deep-learning emulator that models higher-order ice flow with high-computational efficiency. We calibrate the modelled thicknesses against >11 000 ice thickness observations, resulting in a final ice volume estimate of 302.7 km3 for Norway, 18.4 km3 for Sweden and 321.1 km3 for the whole of Scandinavia with an error estimate of ~ . The validation statistics computed indicate good agreement between modelled and observed thicknesses (RMSE = 55 m, Pearson's r = 0.87, bias = 0.8 m), outperforming all other ice thickness maps available for the region. The modelled bed shapes thus provide unprecedented detail in the subglacial topography, especially for ice caps where we produce the first maps that show ice-dynamically realistic flow features.

We present a novel thickness inversion approach that leverages satellite products and state-of-the-art ice flow models to produce distributed maps of sub-glacial topography consistent with the dynamic state of a given glacier. While the method can use any complexity of ice flow physics as represented in ice dynamical models, it is computationally cheap and does not require bed observations as input, enabling applications on both local and large scales. Using the mismatch between observed and modelled rates of surface elevation change dh/dt as the misfit functional, iterative point-wise updates to an initial guess of bed topography are made, while mismatches between observed and modelled velocities are used to simultaneously infer basal friction. The final product of the inversion is not only a map of ice thickness, but is also a fully spun-up glacier model that can be run forward without requiring any further model relaxation. Here we present the method and use an artificial ice cap built inside a numerical model to test it and conduct sensitivity experiments. Even under a range of perturbations, the method is stable and fast. We also apply the approach to the tidewater glacier Kronebreen on Svalbard and finally benchmark it on glaciers from the Ice Thickness Models Intercomparison eXperiment (ITMIX, Farinotti et al., 2017), where we find excellent performance. Ultimately, our method shown here represents a fast way of inferring ice thickness where the final output forms a consistent picture of model physics, input observations and bed topography.

Tree-ring records constitute excellent high-resolution data and provide valuable information for climate science and paleoclimatology. Tree-ring reconstructions of past temperature variations agree to show evidence for annual-to-centennial anomalies in past climate and place the industrial-era warming in the context of the late Holocene climate patterns and regimes. Despite their wide use in paleoclimate research, however, tree rings have also been deemed unsuitable as low-frequency indicators of past climate. The arising debate concerns whether the millennia-long tree-ring records show signals of orbital forcing due to the Milankovitch cycles. Here, we produce a summer-temperature reconstruction from tree-ring chronology running through mid- and late-Holocene times (since 5486 BCE) comprising minimum blue channel light intensity (BI). The BI reconstruction correlates with existing and new tree-ring chronologies built from maximum latewood density (MXD) and, unlike the MXD data, shows temperature trends on Milankovitch scales comparable to various types of sedimentary proxy across the circumpolar Arctic. Our results demonstrate an unrevealed potential of novel, unconventional tree-ring variables to contribute to geoscience and climate research by their capability to provide paleoclimate estimates from inter-annual scales up to those relevant to orbital forcing.

Retreat of marine outlet glaciers often initiates depletion of inland ice through dynamic adjustments of the upstream glacier. The local topography of a fjord may promote or inhibit such retreat, and therefore fjord geometry constitutes a critical control on ice sheet mass balance. To quantify the processes of ice-topography interactions and enhance the understanding of the dynamics involved, we analyze a multitude of topographic fjord settings and scenarios using the Ice-sheet and Sea-level System Model (ISSM). We systematically study glacier retreat through a variety of artificial fjord geometries and quantify the modeled dynamics directly in relation to topographic features. We find that retreat in an upstream-widening or upstream-deepening fjord does not necessarily promote retreat, as suggested by previous studies. Conversely, it may stabilize a glacier because converging ice flow towards a constriction enhances lateral and basal shear stress gradients. An upstream-narrowing or upstream-shoaling fjord, in turn, may promote retreat since fjord walls or bed provide little stability to the glacier where ice flow diverges. Furthermore, we identify distinct quantitative relationships directly linking grounding line discharge and retreat rate to fjord topography and transfer these results to a long-term study of the retreat of Jakobshavn Isbr AE. These findings offer new perspectives on ice-topography interactions and give guidance to an ad hoc assessment of future topographically induced ice loss based on knowledge of the upstream fjord geometry.