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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.

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.

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.