Comparing methods for estimating basal velocity and internal deformation at the Grenzgletscher

The forward motion of glaciers and ice sheets results from two components: internal deformation and basal sliding, with the latter accounting almost entirely for the high speeds attained by ice streams. Even with direct access to the ice-bed interface (e.g., through a borehole), basal motion cannot be measured directly and must be derived through modelling. In this work, we compare three previously developed mathematical frameworks for deriving englacial and basal sliding velocities from borehole tilt observations. These methods address different tensional configurations: 1) pure plane strain, 2) plane strain with an ad-hoc extension component optimized for scenarios with a limited number of tiltmeters, and 3) plane strain with a combined extension-compression component, restricted to regions with negligible lateral drag. The velocity is reconstructed by measured variations in tilt angle along boreholes drilled to the bed. For synthetic tilt curves that are representative of a variety of tensional states, and for each of the modelling frameworks above, we assess the limitations and propagation of errors in the reconstructed velocity profiles and basal velocities. We further discuss the optimal number and location of borehole tiltmeters that minimize errors in the estimated sliding velocity. This work offers practical guidance on an upcoming borehole campaign at the Grenzgletscher, Switzerland, aimed at characterizing the onset of basal sliding at frozen/temperate basal transitions.