Numerical modelling of subglacial water flow under a visco-elastic glacier-ice cover

We present a model for water flow at the base of a glacier implemented with the Elmer/Ice Open-Source Finite-Element Software. The model describes subglacial water flow in connection with the emptying of basal water bodies and the subglacial propagation of glacial outburst flood (jökulhlaup) fronts using a visco-elastic model for the overlying glacier combined with a turbulent thin-sheet model for water flow. The visco-elastic model is based on Maxwell-elements¹ combining linear elasticity with the non-linear viscous behaviour described by Glen's ice-flow law, and, by introducing a pressure variable, allowing for incompressibility of the material. The dynamics of the subglacial ice–water interface is implemented as fluid–structure interaction (FSI), utilizing artificial compressibility. The coupled visco-elastic, thin-sheet model aims to represent the propagation of rapidly- and slowly-rising subglacial floods², many of which are inferred from remote-sensing and in-situ observations to involve lifting of the glacier from its sole over large areas³. Dynamically similar subglacial ice–water interactions may be involved in widespread, propagating ice-velocity and surface-elevation disturbances that have been observed by remote sensing during subglacial drainage events in Greenland⁴ and Antarctica⁵, indicating that the dynamics of jökulhlaups may have wider implications for glacier dynamics in general. We will demonstrate the coupled model with simple synthetic examples. The visco-elastic model can simulate the observed geometry of ice-surface depressions formed by the collapse of basal water cupolas and conduits, for which we present simulation results with comparison to observed ice-surface depressions at Vatnajökull ice cap, Iceland.

References

¹Zwinger, T., Nield, G. A., Ruokolainen, J., and King, M. A.: A new open-source viscoelastic solid earth    deformation module implemented in Elmer (v8.4), Geosci. Model Dev., 13, 1155–1164 (2020).

² Jóhannesson, T. Propagation of a subglacial flood wave during the initiation of a jökulhlaup. Hydrol. Sci. J., 47, 417–434 (2002).

³ Magnússon, E., & 13 others. New insights into the development of slowly rising jökulhlaups from the Grímsvötn subglacial lake, Iceland, deduced from ICEYE SAR images and in-situ observations. EGU General Assembly 2024, EGU24-18204, https://doi.org/10.5194/egusphere-egu24-18204.

⁴ Maier, N., Andersen, J.K., Mouginot, J., Gimbert, F., & Gagliardini, O. Wintertime supraglacial  lake drainage cascade triggers large-scale ice flow response in Greenland. Geophys. Res.  Lett., 50(4), p.e2022GL10 (2023).

⁵Neckel, N., Franke, S., Helm, V., Drews, R., & Jansen, D. Evidence of cascading subglacial  water flow at Jutulstraumen Glacier (Antarctica) derived from Sentinel-1 and ICESat-2  measurements. Geophys. Res. Lett., 48(20), p.e2021GL094472 (2021).