Large volumes of glacial meltwater drain along the interface between the ice sheet and its bed, thereby influencing glacier dynamics. It is known from the geological record and modern glacial systems that channelized subglacial meltwater discharge generates high erosion rates, leading to the formation of overdeepenings and tunnel valleys, some over 500 m deep. It is therefore essential to constrain the depth of potential subglacial erosion under future ice sheets when searching for locations of high-level radioactive waste repository sites.The aim of this project is to quantify the meltwater-driven erosion under the past ice sheets in northern Germany and evaluate the erosion potential during future glaciations. To achieve this goal, we develop a next-generation dynamic numerical model simulating subglacial meltwater erosion on soft beds. In the first step, we built subsurface reservoir models at different scales and resolutions to examine the impact of model resolution on the subsequent erosion modelling. The 3D subsurface model approximately covers the area of the Northwest German Basin (40,000 km²), has a depth of 2000 m, and comprises lithostratigraphical units from the Permian Zechstein to the Pleistocene. The basin fill has a complex structure due to salt tectonics, and the main challenge was to generalize the complex lateral and vertical lithofacies/hydrofacies relationships.Two large-scale, low-resolution subsurface reservoir models were constructed. The first model does not include Quaternary deposits. This model was created to simulate the formation of Middle Pleistocene tunnel valleys and compare/validate the results with the Pleistocene record of the Northwest German Basin. The second large-scale subsurface model includes the Quaternary deposits and will be used to simulate subglacial erosion during future glaciations. A smaller high-resolution subsurface model, covering an area of about 2000 km², will then be used to test the effects of model size and model resolution on the simulation of subglacial erosion.

Estimating the erosive potential of future glaciations is important for assessing the long-term safety of nuclear waste repositories. Of special interest is the formation of tunnel-valleys, glacial erosional features over 500 m deep carved by meltwater channels beneath ice sheets and glaciers. We present a Python modeling framework to estimate tunnel-valley erosion using the erosion and deposition model of Walder & Fowler (1994) in combination with several open-source models and libraries for ice sheet modelling, flexural isostasy modelling, image pattern recognition, and meltwater routing. We showcase how the model works and performs on a synthetic fluvial pre-glacial landscape with a fixed simplified ice sheet configuration. The model works by routing both surface meltwater through simulated moulins in the ice sheet and basal meltwater on the hydraulic potential surface under the ice. The meltwater flow modulates the locations for initial channel incision, wherein the erosion and deposition will be calculated iteratively as the erosion and deposition rate depends on the channel cross-section. The preliminary results of this model show that a steady flux of meltwater from a deglaciating ice sheet can incise tunnel valleys tens of meters deep and several hundred meters wide over a period of hundreds of years. We anticipate incorporating features such as catastrophic lake drainage and an erosion parameter controlled by lithology into the model, as these mechanisms are believed to play a crucial role in the formation of large-scale tunnel valleys. Walder, J. S., & Fowler, A. (1994). Channelized subglacial drainage over a deformable bed. Journal of Glaciology, 40(134), 3–15. https://doi.org/10.3189/S002214300000375

Many of Antarctica’s ice streams reside on deformable beds. The description of their basalconditions is a major source of uncertainty in modeling studies attempting to predict theirresponse to a changing climate. The mechanics at the glacier bed, often divided into glaciersliding and deformation of the subglacial sediments (so-called till), depend on the subglacialwater pressure and thus on the subglacial drainage. To understand the drainage system atthe ice-till interface, past works modeled the stability of channels incised in the till (so-calledcanals). Such canals open due to erosion by water flow and close due to till creep and fluvialdeposition. Till rheology is a central point of discussion in these models.The original description by Walder and Fowler (1994) of canals assumed a viscous rheology ofthe subglacial till. Lab and field experiments show the subglacial till to be better described bya plastic rheology. A recent study by one of the co-authors of this contribution implemented aplastic rheology and showed that this leads to plastic behaviour of the canals’ closure, such asrapid canal collapse when their size is too large for prevailing effective pressure.In this contribution, we extend this latter model to parameterize the effect of till deformationinduced by glacier sliding on canal dynamics. Our results show the glacier sliding to drivecanal closure at all effective pressures. We describe this process with a closure rate that scaleslinearly with the basal sliding velocity and is increasing non-linearly with both the effectivepressure and the canals size.By controlling the canals’ closure, basal sliding thus impacts the drainage capacity, and inturn, the subglacial water pressure. Thus the positive relation between the basal sliding speedand canal closure could potentially be a mechanism leading to high sliding speeds, such asfound in ice streams.

Glacier flow has the potential to mobilize subglacial till, resulting in till deposition and subglacial landforms in glaciated areas. The subglacial till transport occurs when sedimentary beds are thawed and sufficiently weak relative to the glacial driving stress. As a consequence of till mobilization, soft-bedded and marine-terminating ice sheets are known to produce grounding-zone wedges. It has been hypothesized that these wedges may stabilize grounded ice in spite of rising sea level. In order to test this hypothesis, we develop a fully coupled framework for simulating ice flow, glacier hydrology, and till advection. Ice flow and hydrology is handled with PISM, the three-dimensional, thermomechanical, parallel ice sheet model (Bueler and Brown, 2009; Winkelmann et al 2011). Till advection is computed with the cohesive non-granular fluidity method with pore-water pressure, which is consistent with Coulomb-frictional mechanics and stress-dependent shear-zone thickness (Damsgaard et al., 2020). We apply the model to various bed geometries and forcing scenarios, and show how subglacial landforms evolve and grounding-zone wedges form. The grounding-zone wedges prove to contribute conditional stabilization to the ice sheet, and this mechanism could limit the marine-ice sheet instabilities that may occur on reverse sloping beds. References: Bueler, E. and Brown, J. 2009 “Shallow shelf approximation as a “sliding law” in a”. J. Geophys. Res. Earth Surf. 114(F3) Damsgaard, A., L. Goren and J. Suckale 2020 “Water pressure fluctuations control variability in sediment flux and slip dynamics beneath glaciers and ice streams”. Commun. Earth Environ. 1(66), 1–8. doi: 10.1038/s43247-020-00074-7 Winkelmann, R., M. A. Martin, M. Haseloff, T. Albrecht, E. Bueler, C. Khroulev and A. Levermann 2011 “The Potsdam Parallel Ice Sheet Model (PISM-PIK) - Part 1: Model description”. 5(3), 715–726. doi: 10.5194/tc-5-715-2011

Many subglacial environments consist of a fine‐grained, deformable sediment bed, known as till, hosting an active hydrological system that routes meltwater. Observations show that the till undergoes substantial shear deformation as a result of the motion of the overlying ice. The deformation of the till, coupled with the dynamics of the hydrological system, is further affected by the substantial strain rate variability in subglacial conditions resulting from spatial heterogeneity at the bed. However, it is not clear if the relatively low magnitudes of strain rates affect the bed structure or its hydrology. We study how laterally varying shear along the ice‐bed interface alters sediment porosity and affects the flux of meltwater through the pore spaces. We use a discrete element model consisting of a collection of spherical, elasto‐frictional grains with water‐saturated pore spaces to simulate the deformation of the granular bed. Our results show that a deforming granular layer exhibits substantial spatial variability in porosity in the pseudo‐static shear regime, where shear strain rates are relatively low. In particular, laterally varying shear at the shearing interface creates a narrow zone of elevated porosity which has increased susceptibility to plastic failure. Despite the changes in porosity, our analysis suggests that the pore pressure equilibrates near‐instantaneously relative to the deformation at critical state, inhibiting potential strain rate dependence of the deformation caused by bed hardening or weakening resulting from pore pressure changes. We relate shear variation to porosity evolution and drainage element formation in actively deforming subglacial tills.

Abstract The mechanical interactions between ice floes in the polar sea‐ice packs play an important role in the state and predictability of the sea‐ice cover. We use a Lagrangian‐based numerical model to investigate such floe‐floe interactions. Our simulations show that elastic and reversible deformation offers significant resistance to compression before ice floes yield with brittle failure. Compressional strength dramatically decreases once pressure ridges start to form, which implies that thicker sea ice is not necessarily stronger than thinner ice. The mechanical transition is not accounted for in most current sea‐ice models that describe ice strength by thickness alone. We propose a parameterization that describes failure mechanics from fracture toughness and Coulomb sliding, improving the representation of ridge building dynamics in particle‐based and continuum sea‐ice models.

The thickness of sea ice determines the ice cover resilience during melt periods. Ridging occurs when sea ice breaks and thickens through compression or shear. Current continuum sea-ice models parameterize this process, and assume that ice strength increases with ice thickness. However, the increasing resolution of climate models challenges the continuum assumption, making it relevant to consider the physical basis for ridging on the ice-floe scale. We perform high-resolution discrete element method simulations of compressional ice failure. Compression initiates with elastic deformation before plastic failure and ridging occurs. The elastic deformation is reversible, and offers significant resistance before the ice floes yield to brittle failure and create pressure ridges. Compressional strength decreases once plastic failure occurs, which implies that thicker sea ice is not necessarily stronger than thin ice. This mechanical transition is not considered in current models. We parameterize the observed behavior into a larger scale model, and show that the compressive mechanics strongly affect overall ice-pack strength and deformation distribution.

Many fast-flowing glaciers and ice streams move over beds consisting of reworked sediments and erosional products, commonly referred to as till. The complex interplay between ice, meltwater, and till at the subglacial bed connects several fundamental problems in glaciology including the debate about rapid mass loss from the ice sheets, the formation and evolution of subglacial landforms, and the storage and transport of subglacial water. In-situ measurements have probed the subglacial bed, but provide surprisingly variable and seemingly inconsistent evidence of the depth where deformation occurs, even at a given field site. These observations suggest that subglacial beds are inherently dynamic. The goal of this paper is to advance our understanding of the physical processes that contribute to the dynamics of subglacial beds as reflected in existing observations of basal deformation. We build on recent advances in modeling dense, granular flows to derive a new numerical model for water-saturated till. Our model demonstrates that changes in the force balance or temporal variations in water pressure can shift slip away from the ice-bed interface and far into the bed, causing episodes of significantly enhanced till transport because the entire till layer above the deep slip interface becomes mobilized. We compare our model results against observations of basal deformation from both mountain glacier and ice-stream settings in the past and present. We also present an analytical solution to assess the variability of till transport for different glacial settings and hydraulic properties.

Rapid ice loss is facilitated by sliding over beds consisting of reworked sediments and erosional products, commonly referred to as till. The dynamic interplay between ice and till reshapes the bed, creating landforms preserved from past glaciations. Leveraging the imprint left by past glaciations as constraints for projecting future deglaciation is hindered by our incomplete understanding of evolving basal slip. Here, we develop a continuum model of water-saturated, cohesive till to quantify the interplay between meltwater percolation and till mobilization that governs changes in the depth of basal slip under fast-moving ice. Our model explains the puzzling variability of observed slip depths by relating localized till deformation to perturbations in pore-water pressure. It demonstrates that variable slip depth is an inherent property of the ice-meltwater-till system, which could help understand why some paleo-landforms like grounding-zone wedges appear to have formed quickly relative to current till-transport rates. The disparity in predicted and observed till transport rates beneath flowing ice is partially explained by water pressure fluctuations which alter the rate and depth of slip in the sediments, according to a coupled ice-meltwater-till continuum model

Understanding the geomorphology left by waxing and waning of former glaciers and ice sheets during the late Quaternary has been the focus of much research. This has been hampered by the difficulty in dating such features. Luminescence has the potential to be applied to glacial sediments but requires signal resetting prior to burial in order to provide accurate ages. This paper explores the possibility that, rather than relying on light to reset the luminescence signal, glacial processes underneath ice might cause resetting. Experiments were conducted on a ring-shear machine set up to replicate subglacial conditions and simulate the shearing that can occur within subglacial sediments. Luminescence measurement at the single grain level indicates that a number (albeit small) of zero-dosed grains were produced and that these increased in abundance with distance travelled within the shearing zone. Observed changes in grain shape characteristics with increasing shear distance indicate the presence of localised high pressure grain-to-grain stresses caused by grain bridges. This appears to explain why some grains became zeroed whilst others retained their palaeodose. Based on the observed experimental trend, it is thought that localised grain stress is a viable luminescence resetting mechanism. As such relatively short shearing distances might be sufficient to reset a small proportion of the luminescence signal within subglacial sediments. Dating of previously avoided subglacial sediments may therefore be possible.

In a detailed study of mega-scale glacial lineations (MSGLs) left by a Weichselian palaeo-ice stream in Poland, Spagnolo et al. (2016) analysed multiple parameters of the land-forming till and concluded that it originated by a combination of lodgement and thin-skinned deformation whose cumulative effect was the formation of the MSGL field. To advance our understanding of till formation and deformation postulated by Spagnolo et al. (2016) we conducted a series of experiments on this till in a large ring-shear apparatus intended to mimic subglacial shearing to a total cumulative strain of 640. Undisturbed, oriented samples for micromorphological analyses were taken at displacement increments of 0, 9, 18, 36, 72, 144, 288, 576 and 1152 cm. Till microstructures mapped on thin sections across the zone of shearing gave intriguing and hitherto unmatched insights into the development and evolution of till properties during the shearing under controlled boundary conditions. The deformation signatures often varied non-systematically between the sampled increments. Threedimensional microtomographic scanning showed intervals of relatively stable till fabrics intervening with phases of fabric re-orientation towards new equilibria. Shear stresses during the deformation showed a distinct cyclicity possibly indicating formation and collapse of grain bridges. Collectively, we interpret the ring-shear data supported by discrete elements numerical modelling as a signature of permanent and largely unpredictable evolution of till structure with a general trend towards more ductile and less brittle deformation with increasing strain. These results bear on the reconstruction of past subglacial processes, deposits and landforms and we advocate extreme caution with interpreting the history of natural tills based on the micromorphological signatures alone.

Lagrangian models of sea-ice dynamics have several advantages over Eulerian continuum models. Spatial discretization on the ice-floe scale are natural for Lagrangian models and offer exact solutions for mechanical non-linearities with arbitrary sea-ice concentrations. This allows for improved model performance in ice-marginal zones. Furthermore, Lagrangian models can explicitly simulate jamming processes such as sea ice movement through narrow confinements. Granular jamming is a chaotic process that occurs when the right grains arrive at the right place at the right time, and the jamming likelihood over time can be described by a probabilistic model. While difficult to parameterize in continuum formulations, jamming emerges spontaneously in dense granular systems simulated in a Lagrangian framework. Here, we present a flexible discrete-element framework for approximating Lagrangian sea-ice mechanics at the ice-floe scale, forced by ocean and atmosphere velocity fields. Our goal is to evaluate the potential of simpler models than the traditional discrete-element methods for granular dynamics. We demonstrate that frictionless contact models based on compressive stiffness alone are unlikely to produce jamming, and describe two different approaches based on Coulomb-friction and cohesion which both result in increased bulk shear strength of the granular assemblage. The frictionless but cohesive contact model displays jamming behavior which is similar to the more complex model with Coulomb friction and ice-floe rotation at larger scales, and has significantly lower computational cost.

Ice streams are corridors of fast flowing ice that drain the interiors of the large Antarctic and Greenlandic ice sheets. The abrupt transition from the fast flowing ice of the streams to the almost stagnant ice to their side occurs along narrow shear margins, which experience intense internal deformation. This deformation can lead to warming and weakening of the ice, which makes shear margins prone to migration. Previous studies have suggested that efficient drainage of meltwater at the interface between the ice and the underlying weak sediment layer might control the stability of shear margins. However, weak sediment deformation is expected to be tightly coupled to meltwater drainage, and therefore the feedbacks between them are likely of great importance for ice stream stability, while they remain little understood. Here, we use a 3D model to capture the dynamic interactions between meltwater percolation and granular deformation. We solve for the granular mechanics using a discrete element algorithm, and compute the flow in the deforming porous media on a superimposed Eulerian grid. The model intends to represent the upper portion of the weak and unconsolidated sediment layer directly beneath the ice in the shear margin. We use it to study (1) how spatial variations in the shearing velocity affect meltwater percolation, and (2) to what degree the till grains are stable in the presence of horizontal gradients in water pressure. Our simulation results show that horizontal variations in shear velocity enhance the local porosity and permeability, leading to a potentially significant increase in the horizontal water transmissivity. Results further demonstrate that grain stability depends on the magnitude of the horizontal pressure gradient, and cascading events of grain mobilization precede bulk instability flows.

ABSTRACTFlow-frictional resistance at the base of glaciers and ice sheets is strongly linked to subglacial water pressure. Understanding the physical mechanisms that govern meltwater fluxes in subglacial channels is hence critical for constraining variations in ice flow. Previous mathematical descriptions of soft-bed subglacial channels assume a viscous till rheology, which is inconsistent with laboratory data and the majority of field studies. Here, we use a grain-scale numerical formulation coupled to pore-water dynamics to analyze the structural stability of channels carved into soft beds. Contrary to the soft-bed channel models assuming viscous till rheology, we show that the flanks of till channels can support substantial ice loads without creep closure of the channel, because the sediment has finite frictional strength. Increased normal stress on the channel flanks causes plastic failure of the sediment, and the channel rapidly shrinks to increase the ice-bed contact area. We derive a new parameterization for subglacial channelized flow on soft beds and show that channel dynamics are dominated by fluvial erosion and deposition processes with thresholds linked to the plastic rheology of subglacial tills. We infer that the described limits to channel size may cause subglacial drainage to arrange in networks of multiple closely spaced channels.