Further numerical simulations of subglacial bedform formation: Implications for interpreting palaeo-landscapes

Subglacial bedforms, repetitive landforms formed at the base of an ice-sheet or glacier as a result of the movement of subglacial sediments, are abundant in areas of former glaciation where they are often used to reconstruct past-ice flow conditions. Commonly referred to as one of the following morphotypes, the formation of drumlins, subglacial ribs and mega-scale glacial lineations (MSGL), has been the subject of scientific enquiry for over a century. Understanding subglacial bedform formation has important implications for reconstructions of palaeo ice-sheets, which require assumptions to be made regarding their genesis.

One explanation envisages subglacial bedforms as the result of instabilities in the coupled flow of ice, water, and till at the ice-bed interface. Here, we evaluate the progress of this hypothesis, commonly referred to as the instability theory of subglacial bedform formation. We present numerical solutions of the current version of the instability model, exploring the simulation outcomes for various constrained parameters. In our model, subglacial ribs and drumlins commonly arise, grow to a mature state, and persist. Drumlins are always preceded by subglacial ribs, perhaps explaining their commonly observed banded arrangements in the landscape. The transition from ribs to drumlins is rapid, with transitory intermediate quasi-circular forms - this perhaps explains why they are rarely observed. This evolutionary trajectory is one-way, with no simulations showing drumlins turning into ribs. This is most likely explained by the development of preferential pathways for water and sediment between drumlin ridges as the ice-bed interface evolves. Furthermore, we find that the numerical model is unable to produce MSGL, with previously reported MSGL-like features likely to be a consequence of periodic boundary conditions. This is despite analytical solutions to the model showing features with an MSGL-like wavelength. To resolve this, either a more sophisticated numerical toolkit is required, or the model requires further development.

Using these simulations as a basis of our discussion, we argue that whether the instability theory can be regarded as the fundamental cause of subglacial bedforms likely depends upon your viewpoint. For the mathematician, linear stability analysis of the model produces bedform wavelengths consistent with observations, so perhaps the problem is solved. For a numerical modeller, producing the missing MSGL remains a challenge. For sedimentologists, the model lacks the complexity to replicate the history of processes recorded within subglacial bedforms, and necessarily generalises deformational processes. Thus, many sedimentologically-based questions remain unanswered by this model. Finally, we argue that if subglacial bedforms arise from an instability, then inverting for glaciological conditions (e.g. velocity, thickness) based on the morphology of bedforms alone may be unachievable. The nature of instabilities means that small changes to the system will alter the final bedforms produced, and similar bedforms may occur through combinations of different conditions.