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The North Sea Last Interglacial sea level is sensitive to the fingerprint of mass loss from polar ice sheets. However, the signal is complicated by the influence of glacial isostatic adjustment driven by Penultimate Glacial Period ice-sheet changes, and yet these ice-sheet geometries remain significantly uncertain. Here, we produce new reconstructions of the Eurasian ice sheet during the Penultimate Glacial Maximum (PGM) by employing large ensemble experiments from a simple ice-sheet model that depends solely on basal shear stress, ice extent, and topography. To explore the range of uncertainty in possible ice geometries, we use a parameterised shear-stress map as input that has been developed to incorporate bedrock characteristics and the influence of ice-sheet basal processes. We perform Bayesian uncertainty quantification, utilising Gaussian process emulation, to calibrate against global ice-sheet reconstructions of the Last Deglaciation and rule out combinations of input parameters that produce unrealistic ice sheets. The refined parameter space is then applied to the PGM to create an ensemble of constrained 3D Eurasian ice-sheet geometries. Our reconstructed PGM Eurasian ice-sheet volume is 48±8 m sea-level equivalent (SLE). We find that the Barents–Kara Sea region displays both the largest mean volume and volume uncertainty of 24±8 m SLE while the British–Irish sector volume of 1.7±0.2 m SLE is the smallest. Our new workflow may be applied to other locations and periods where ice-sheet histories have limited empirical data. [ABSTRACT FROM AUTHOR]