Feedback Mechanisms between Heterogeneous Geothermal Heat Fluxes and the Dynamic Ice Sheet Reinforce the Formation of Tunnel Valleys

The large variety of subglacial landforms observed on Earth are due to a complex interplay between the overlying ice sheet and the solid Earth below. While the ice cover thermally isolates the subglacial region, hence shields it from any influence by variations in the atmosphere, spatially varying geothermal heat fluxes from below may lead to the formation or reinforcement of existing subglacial landform patterns, such as tunnel valleys. An observed spatial correlation between tunnel valleys and underlying salt structures in the North German Basin is often explained mechanically. In this work, we alternatively focus on the role of heat transfer for the formation of tunnel valleys, which has not been holistically investigated until now. As salt has a higher thermal conductivity than the surrounding rocks, a local concentration of geothermal energy above salt structures may lead to increased subglacial melting rates of the overlying ice sheet. In particular, it is our goal to investigate to which extent the resulting meltwater discharge and corresponding erosion has the potential to reinforce tunnel valley formation. For our analysis, we develop a coupled computational strategy capable of determining the interplay between the temperature distribution within the heterogeneous subsurface including heat transport and ground water flow, and the overlying ice sheet. Modelling the interfacial heat flux from the subsurface into the ice sheet then allows us to infer on subglacial melt rates, which can be further assessed with respect to their role in the formation of tunnel valleys. In this contribution, we present results of a scaling analysis that takes into account the ice sheet with its internal horizontal and vertical velocity fields, the subsurface and the subglacial interfacial area. We furthermore describe a 1D computational strategy to combine the heat transport including subglacial phase change into a coupled process model allowing for investigating feedback mechanisms. Finally, we discuss strategies how this can be integrated into a full dimensional computational subsurface model, such as SHEMAT-Suite. Preliminary results for two tunnel valleys overlying salt structures in the German North Sea show that the local concentration of geothermal energy solely basing on heat conduction is only slightly augmented. The role of hydrothermal flow processes still remains to be quantified. We can therefore conclude that the geothermal distribution has a complementary effect to mechanical processes together leading to the formation of tunnel valleys.