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Results of glacier flow models and associated estimates of future sea level rise depend sensitively on the prescribed relation between shear stress and slip velocity at the glacier bed. Using a fully three‐dimensional numerical model of ice flow, we compute steady‐state sliding relations for where ice slips over a rock bed with three‐dimensional, periodic topography. In agreement with studies of two‐dimensional beds, water‐filled cavities that form down‐glacier from bedforms cause basal shear stress to peak at a threshold slip velocity and decrease at higher velocities (i.e., rate‐weakening drag). However, the shear stress magnitude and extent of rate‐weakening drag depend systematically on lateral topographic variations not considered previously. Moreover, steep up‐glacier‐facing slopes of bedforms can result in shear stress that increases monotonically over a wide range of slip velocity, helping to stabilize slip. These results highlight the potential variability of sliding relations and their likely sensitivity to the morphological diversity of glacier beds. Plain Language Summary: Parts of ice sheets that flow into the oceans and affect sea level can flow unusually fast by slipping over their beds. We use a computer to solve for the first time in three dimensions the equations that describe the flow of ice as it slips over a bumpy rock bed. We include the important tendency for glaciers to separate from rock and form water‐filled cavities down‐glacier from bumps. These calculations indicate that resistance to slip depends sensitively on the bump shape and spacing. Cavities can cause the bed to become more slippery the faster the ice slides, with this destabilizing effect being more severe for bumps that are laterally narrow and widely spaced. However, bumps with steeply sloping up‐glacier sides can reverse this effect and cause resistance to slip to increase over a wide range of increasing slip velocity. This diverse behavior highlights the need for estimates of glacier slip velocity to incorporate the actual topography of glacier beds. Key Points: Drag at rigid glacier beds during basal slip with ice‐bed separation depends sensitively on the three‐dimensional bedrock morphologyLateral spacing of bed obstacles affects the degree of rate‐weakening drag, in which drag decreases with increasing slip velocityBed obstacles with steep adverse slopes stabilize slip by causing drag to increase over a wide range of increasing slip velocity [ABSTRACT FROM AUTHOR]

Subglacial rock friction is an important control on the sliding dynamics and erosive potential of hard-bedded glaciers, yet it remains largely unconstrained. To explore the relative influence of basal melt rate, effective stress and ice temperature on frictional resistance, we conducted abrasion experiments in which limestone beds were slid beneath a fixed slab of ice laden with granitic rock fragments. Shear stress scales linearly with melt rate and cryostatic stress, confirming that both viscous drag and effective stress are first-order controls on the contact force in drained conditions. Furthermore, temperature gradients in the ice increase the contribution of viscous drag on basal shear stress. In all experiments, the relationship between melt rate and shear stress is best explained by a model that accounts for the effects of regelation and viscous creep on the bed-normal drag force. We interpret this to mean fluid flow around entrained clasts contributed to basal drag even at subfreezing temperatures. Incorporating premelting dynamics into the Watts/Hallet model for subglacial rock friction, we find that the predicted debris-bed drag decreases by approximately an order of magnitude, with a corresponding ~3.5 × increase in the transition radius. This is lower than we observe for ice slightly below the pressure melting point. [ABSTRACT FROM AUTHOR]

Theory and experiments indicate that ice–bed separation during glacier slip over 2-D hard beds causes basal shear stress to reach a maximum at a particular slip velocity and decrease at higher velocities. We use the sliding theory of Lliboutry (1968) to explore how friction between debris particles in sliding ice and a rock bed affects this relationship between shear stress and slip velocity. Particle–bed contact forces and associated debris friction increase with increasing slip velocity, owing to increased rates of ice convergence with up-glacier facing surfaces. However, debris friction on diminished areas of the bed counteracts this effect as cavities grow. Thus, friction from debris alone increases only slightly with slip velocity, and for sediment particles larger than ~60 mm in diameter, debris friction peaks and decreases with increasing slip velocity. The effect on the sliding relationship is to steepen its rising limb and shift its shear stress peak to a slightly higher velocity. These results, which exclude the effect of debris friction on cavity size and debris concentrations above ~15%, indicate that the effect of debris in ice is to increase basal shear stress but not significantly change the form of the sliding relationship. [ABSTRACT FROM AUTHOR]