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Subglacial water modulates glacier-bed friction and therefore is of fundamental importance when characterising the dynamics of ice masses. The state of subglacial pore water, whether liquid or frozen, is associated with differences in electrical resistivity that span several orders of magnitude; hence, liquid water can be inferred from electrical resistivity depth profiles. Such profiles can be obtained from inversions of transient (time-domain) electromagnetic (TEM) soundings, but these are often non-unique. Here, we adapt an existing Bayesian transdimensional algorithm (Multimodal Layered Transdimensional Inversion – MuLTI) to the inversion of TEM data using independent depth constraints to provide statistical properties and uncertainty analysis of the resistivity profile with depth. The method was applied to ground-based TEM data acquired on the terminus of the Norwegian glacier, Midtdalsbreen, with depth constraints provided by co-located ground-penetrating radar data. Our inversion shows that the glacier bed is directly underlain by material of resistivity 10 2 Ω m ± 1000 %, with thickness 5–40 m, in turn underlain by a highly conductive basement (10 0 Ω m ± 15 %). High-resistivity material, 5×104 Ω m ± 25 %, exists at the front of the glacier. All uncertainties are defined by the interquartile range of the posterior resistivity distribution. Combining these resistivity profiles with those from co-located seismic shear-wave velocity inversions to further reduce ambiguity in the hydrogeological interpretation of the subsurface, we propose a new 3-D interpretation in which the Midtdalsbreen subglacial material is partitioned into partially frozen sediment, frozen sediment/permafrost and weathered/fractured bedrock with saline water. [ABSTRACT FROM AUTHOR]