A new subglacial sediment deformation discharge rule

Movement of glaciers over (soft) sediment beds can deform the underlying sediment, transporting it in the direction of glacier flow. This subglacial sediment discharge can vary spatially, leading to net erosion in some areas and deposition in others—stripping some areas free of sediment, while others accumulate thick deposits—thereby forming a diverse array of subglacial landforms. The sediment discharge rules currently employed in landscape evolution models lack an empirical basis, which limits their predictive capabilities. We propose a new sediment discharge rule informed by highly controlled laboratory ring shear experiments, in which sediment discharge was directly measured. In these experiments, a water-saturated sediment layer was placed beneath a rotating ring of ice that was spun at varying slip speeds and effective stresses (N, defined as overburden stress minus water pressure), while sediment deformation was monitored. Sediment did not deform below a threshold speed, which depended on N and the material properties of the sediment. Past this threshold, deformation occurred with a near linear dependence between sediment discharge and ice slip speed, along with a non-monotonic dependence of sediment discharge on N. Specifically, sediment discharge increased with N up to approximately 60 kPa, after which it decreased. This non monotonic relationship arose from the coupling of the viscous ice sole with the sediment bed and the development of force chains within the deforming sediment layer. Considering these different mechanical attributes, we derive a sediment discharge rule that is both simple to implement and physically grounded, depending on effective stress, slip speed and the material properties of the sediment. This new relationship captures a range of dynamic behaviors at low N and can explain observed patterns of subglacial landform formation.