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Abstract Basal sliding of glaciers and ice sheets remains a source of uncertainty in simulating the long‐term evolution of ice masses. In particular, the response of ice flow to changes in driving stress depends strongly on the value of the exponent m in nonlinear friction laws (e.g., Weertman's law), which is poorly constrained by observations. Here we constrain the friction law at a natural scale on Argentière Glacier (French Alps, hard‐bed), taking advantage of well‐resolved observations of glacier mass balance, geometry and basal sliding over time spans that include large changes in driving stress. By combining three different independent methods based on (a) surface velocity inversion, (b) transient length change modeling, and (c) direct local sliding measurements, we consistently find a value of m = 3.1 ± 0.3. We suggest that Weertman's law is suitable for modeling the long‐term evolution of hard‐bedded glaciers and ice sheets.

The driving mechanisms of glacier fast flow and the cyclical instability inherent in ice streams and surging glaciers are not fully understood. Current theories suggest fast flow is driven by glacier sliding and basal deformation facilitated by water at the ice–bed interface and/or the presence of weak till. However, the wettability of sediments and the physics driving these sediment–water interactions have yet to be fully explored. Here, we review recent work on superhydrophobicity, hydrophobic soils and lubricated surfaces, and bring together aspects of materials science, biophysics and geoscience, to propose three modes by which a subglacial environment could become super slippery. Those modes are via (i) hydrophobic chemistry, (ii) microbial biofilms or (iii) the incorporation of oil. We then hypothesise how ice flow on super slippery sediments would result in enhanced sliding and deformation by introducing or increasing a lubricated interface and/or creating zones of sediment weakness and instability. We propose that future research should further explore this potential paradigm to soft bed deformation and sliding.

Ice streams are bands of fast-flowing ice in ice sheets. We investigate their formation as an example of spontaneous pattern formation, based on positive feedbacks between dissipation and basal sliding. Our focus is on temperature-dependent subtemperate sliding, where faster sliding leads to enhanced dissipation and hence warmer temperatures, weakening the bed further, and on a similar feedback driven by basal melt water production. Using a novel thermomechanical model, we show that formation of a steady pattern of fast and slow flow can occur through the downstream amplification of noise in basal conditions. This process can lead to the establishment of a clearly defined ice stream separated from slowly flowing, cold-based ice ridges by narrow shear margins. Our model is also able to predict the downstream widening of ice streams due to dissipation and heat transport in these margins. We also show that downward advection of cold ice induced by accelerated sliding is the primary stabilizing mechanism that can suppress ice steam formation altogether, and give an approximate, analytical criterion for pattern formation.

A hydrologically coupled flowband model of 'higher order' ice dynamics is used to explore perturbations in response to supraglacial water drainage and subglacial flooding. The subglacial drainage system includes interacting 'fast' and 'slow' drainage elements. The fast drainage system is assumed to be composed of ice-walled conduits and the slow system of a macroporous water sheet. Under high subglacial water pressures, flexure of the overlying ice is modelled using elastic beam theory. A regularized Coulomb friction law describes basal boundary conditions that enable hydrologically driven acceleration. We demonstrate the modelled interactions between hydrology and ice dynamics by means of three observationally inspired examples: (i) simulations of meltwater drainage at an Alpine-type glacier produce seasonal and diurnal variability, and exhibit drainage evolution characteristic of the so-called 'spring transition'; (ii) horizontal and vertical diurnal accelerations are modelled in response to summer meltwater input at a Greenland-type outlet glacier; and (iii) short-lived perturbations to basal water pressure and ice-flow speed are modelled in response to the prescribed drainage of a supraglacial lake. Our model supports the suggestion that a channelized drainage system can form beneath the margins of the Greenland ice sheet, and may contribute to reducing the dynamic impact of floods derived from supraglacial lakes.

Basal sliding is one of the most important components in the dynamics of fast-flowing glaciers, but remains poorly understood on a theoretical level. In this paper, the problem of glacier sliding with cavitation over hard beds is addressed in detail. First, a bound on drag generated by the bed is derived for arbitrary bed geometries. This bound shows that the commonly used sliding law, τb = CumbNn, cannot apply to beds with bounded slopes. In order to resolve the issue of a realistic sliding law, we consider the classical Nye-Kamb sliding problem, extended to cover the case of cavitation but neglecting regelation. Based on an analogy with contact problems in elasticity, we develop a method which allows solutions to be constructed for any finite number of cavities per bed period. The method is then used to find sliding laws for irregular hard beds, and to test previously developed theories for calculating the drag generated by beds on which obstacles of many different sizes are present. It is found that the maximum drag attained is controlled by those bed obstacles which have the steepest slopes.

The influence of hydrologic transience and heterogeneity on basal motion is an often‐neglected aspect of numerical ice‐flow models. We present a flow‐band model of glacier dynamics with a Coulomb friction sliding law that is coupled to a model of the basal drainage system by means of subglacial water pressure. The ice‐flow model contains “higher‐order” stress gradients from the Stokes flow approximation originally conceived by Blatter (1995). The resulting system of nonlinear equations is solved using a modified Picard iteration that is shown to improve the rate of convergence. A parameterization of lateral shearing is included to account for the effects of three‐dimensional geometry. We find that lateral drag has a discernible effect on glacier speed even when glacier width exceeds glacier length. Variations in flow‐band width are shown to have a greater influence on flow line speed than either different valley cross‐sectional shapes or the presence or absence of glacier sliding along valley walls. Modeled profiles of subglacial water pressure depart significantly from pressures prescribed as a uniform fraction of overburden, thus producing profiles of glacier sliding that are distinctly different from those that would be described by a sliding law controlled by overburden pressures. Simulations of hydraulically driven glacier acceleration highlight the value of including a representation of basal hydrology in models aiming for improved predictive capability of glacier dynamics.

Long‐term records of the flow patterns and dynamics of surge‐type glaciers improve our understanding of their underlying dynamic processes, and are critical to better resolve their contribution to a changing cryosphere. We adapt a modeling approach designed to emulate glacier surging and fold kinematics using the full Stokes ice‐flow model Elmer/Ice to simulate surging of the Dusty Glacier, located in the St. Elias Mountains, Canada. We combine distributed mass‐balance and numerical ice‐flow models to reconstruct the fold kinematics of the 2001–2003 surge of the Dusty Glacier by comparing model results to Landsat‐7 and Sentinel‐2 imagery, and assess the sensitivity of centennial‐scale modeled glacier structure to different mass balance and sliding parameterizations. This study demonstrates the feasibility of using the approach to reconstruct the surface structure kinematics of a surge‐type glacier in nature, highlighting its potential application to other surge‐type glaciers and regions. Plain Language Summary Glaciers can exhibit irregular flow patterns that complicate predictions of their evolution over the coming decades and centuries. We present a method for reproducing iconic surface structures known as folded medial moraines using glaciological modeling. These moraines are wavy flow patterns found on surge‐type glaciers, highlighted by sediment deposited onto the ice that traces their path. By reconstructing these patterns, the underlying climate and sliding conditions that contributed to the glacier's past flow can be identified. Improving our knowledge of these conditions can help improve glacier flow models. We demonstrate that our methodology successfully reconstructs the flow patterns present on a large surge‐type glacier in Yukon, Canada, and explore its past flow history, and possible future, based on these results. Key Points We use a distributed mass‐balance model and Elmer/Ice to reconstruct the 2001–2003 surge kinematics of the Dusty Glacier, Yukon, Canada We explore the centennial‐scale sensitivity of glacier surface fold geometry to mass balance and sliding parameterizations This study is a proof‐of‐concept for further model reconstructions of the past dynamics of surge‐type glaciers

Glacier slip is usually described using steady-state sliding laws that relate drag, slip velocity and effective pressure, but where subglacial conditions vary rapidly transient effects may influence slip dynamics. Here we use results from a set of laboratory experiments to examine the transient response of glacier slip over a hard bed to velocity perturbations. The drag and cavity evolution from lab experiments are used to parameterize a rate-and-state drag model that is applied to observations of surface velocity and ice-bed separation from the Greenland ice sheet. The drag model successfully predicts observed lags between changes in ice-bed separation and sliding speed. These lags result from the time (or displacement) required for cavities to evolve from one steady-state condition to another. In comparing drag estimates resulting from applying rate-and-state and steady-state slip laws to transient data, we find the peaks in drag are out of phase. This suggests that in locations where subglacial conditions vary on timescales shorter than those needed for cavity adjustment transient slip processes control basal drag.

Changes in water pressure at the beds of glaciers greatly modify their sliding rate, affecting rates of ice mass loss and sea level change. However, there is still no agreement about the physics of subglacial sliding or how water affects it. Here, we present a new simplified physical model for the effect of transient subglacial hydrology on basal ice velocity. This model assumes that a fraction of the glacier bed is connected by an active hydrologic system that, when averaged over an appropriate scale, is governed by two parameters with limited spatial variability. The sliding model is reminiscent of Budd's empirical sliding law but with fundamental differences including a dependence on the fractional area of the active hydrologic system. With periodic surface meltwater forcing, the model displays classic diffusion-wave behavior, with a downstream time lag and decay of subglacial water pressure perturbations. Testing the model against Greenland observations suggests that, despite its simplicity, it captures key features of observed proglacial discharges and ice velocities with reasonable physical parameter values. Given these encouraging findings, including this sliding model in predictive ice-sheet models may improve their ability to predict time-evolving velocities and associated sea level change and reduce the related uncertainties.

Water pressure beneath glaciers influences ice velocity. Subglacial hydrology models are helpful for gaining insight into basal conditions, but models depend on unconstrained parameters, and a current challenge is reproducing elevated water pressures in winter. We eliminate terms related to englacial storage, opening by sliding, and melt due to changes in the pressure-melting-point temperature, to create a minimalist version of the Subglacial Hydrology And Kinetic, Transient Interactions (SHAKTI) model, and apply this model to Helheim Glacier in east Greenland to explore the winter base state of the subglacial drainage system. Our results suggest that meltwater produced at the bed alone supports active winter drainage with large areas of elevated water pressure and preferential drainage pathways, using a continuum approach that allows for transitions between flow regimes. Transmissivity varies spatially over several orders of magnitude from 10−4 to 103 m2s−1, with regions of weak transmissivity representing poorly connected regions of the system. Bed topography controls the location of primary drainage pathways, and high basal melt rates occur along the steep valley walls. Frictional heat from sliding is a dominant source of basal melt; different approaches for calculating basal shear stress produce significantly different basal melt rates and subglacial discharge.