Abstract. The subglacial bed topography is critical for modelling the evolution of Thwaites Glacier in the Amundsen Sea Embayment (ASE), where rapid ice loss threatens the stability of the West Antarctic Ice Sheet. However, mapping of subglacial topography is subject to uncertainties of up to hundreds of metres, primarily due to large gaps of up to tens of kilometres in airborne ice-penetrating radar flight lines. Deterministic interpolation approaches do not reflect such spatial uncertainty.

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... ile traditional geostatistical simulations can model such uncertainty, they become difficult to apply because of the significant non-stationary spatial variation of topography over such large surface area. In this study, we develop a non-stationary multiple-point geostatistical (MPS) approach to interpolate large areas with irregular geophysical data and apply it to model the spatial uncertainty of entire ASE basal topography. We collect 166 high-quality topographic training images (TIs) of resolution 500 m to train the gap-filling of radar data gaps, thereby simulating realistic topography maps. The TIs are extensively sampled from deglaciated regions in the Arctic as well as Antarctica. To address the non-stationarity in topographic modelling, we introduce a Bayesian framework that models the posterior distribution of non-stationary TIs assigned to the local line data. Sampling from this distribution then provides candidate training images for local topographic modelling with uncertainty, constrained to radar flight line data. Compared to traditional MPS approaches that do not consider uncertain TI sampling, our approach results in a significant improvement in the topographic modelling quality and efficiency of the simulation algorithm. Finally, we simulate multiple realizations of high-resolution ASE topographic maps. We use the multiple realizations to investigate the impact of basal topography uncertainty on subglacial hydrological flow patterns.