Importance of calculating subglacial heat flow in 3D

Geothermal heat flow has been recognized as a key boundary condition for understanding the evolution of ice sheets. While there has been, to a certain degree, consensus on the regional variations in Antarctica, local scale variations are of increasing interest as even small variations can lead to the presence of subglacial melt.

Local variations, on top of the regional variations stemming from the lithospheric architecture, depend on a variety of parameters, e.g. variation of thermal conductivity and radiogenic heat production, but also the geometry of the ice-bed interface.

Local variations in thermal parameters can be predicted by combining joint inversion of geophysical data sets with machine learning approaches, especially when Antarctica is linked to tectonically neighbouring areas, where extensive databases on all of these parameters exist, e.g. Australia.

Still, geothermal heat flow is mostly calculated by solving the steady-state heat equation in 1D. Here, we apply finite-element modelling based on the pyGIMLI environment to solve the steady steady-state heat equation in 2D and 3D to estimate how much this affects subglacial heat flow.

Our case examples in East Antarctica show that variations in topography and sedimentary layer thickness can both locally change subglacial heat flow up to at least ∼10%, in an effect known as thermal refraction. Exploring the role of variations in radiogenic heat production shows, that this contribution to subglacial heat flow is decreased compared to 1D models, as these are dampened by the system. In contrast, the results of 2D and 3D modelling generally agree, indicating that 2D calculations along profiles are a reasonable approach.

These results have an important implication, when coupling ice temperature and solid earth temperature models, as a basic 1D approach is not well suited, and coupling should be done ideally in 3D, or at least in 2D for selected profiles.