David L. Egholm

Lifespan of mountain ranges scaled by feedbacks between landsliding and erosion by rivers

An important challenge in geomorphology is the reconciliation of the high fluvial incision rates observed in tectonically active mountain ranges with the long-term preservation of significant mountain-range relief in ancient, tectonically inactive orogenic belts. River bedrock erosion and sediment transport are widely recognized to be the principal controls on the lifespan of mountain ranges. But the factors controlling the rate of erosion and the reasons why they seem to vary significantly as a function of tectonic activity remain controversial. Here we use computational simulations to show that the key to understanding variations in the rate of erosion between tectonically active and inactive mountain ranges may relate to a bidirectional coupling between bedrock river incision and landslides. Whereas fluvial incision steepens surrounding hillslopes and increases landslide frequency, landsliding affects fluvial erosion rates in two fundamentally distinct ways. On the one hand, large landslides overwhelm the river transport capacity and cause upstream build up of sediment that protects the river bed from further erosion. On the other hand, in delivering abrasive agents to the streams, landslides help accelerate fluvial erosion. Our models illustrate how this coupling has fundamentally different implications for rates of fluvial incision in active and inactive mountain ranges. The coupling therefore provides a plausible physical explanation for the preservation of significant mountain-range relief in old orogenic belts, up to several hundred million years after tectonic activity has effectively ceased.

Glaciations in response to climate variations preconditioned by evolving topography

Landscapes modified by glacial erosion show a distinct distribution of surface area with elevation (hypsometry). In particular, the height of these regions is influenced by climatic gradients controlling the altitude where glacial and periglacial processes are the most active, and as a result, surface area is focused just below the snowline altitude. Yet the effect of this distinct glacial hypsometric signature on glacial extent and therefore on continued glacial erosion has not previously been examined. Here we show how this topographic configuration influences the climatic sensitivity of Alpine glaciers, and how the development of a glacial hypsometric distribution influences the intensity of glaciations on timescales of more than a few glacial cycles. We find that the relationship between variations in climate and the resulting variation in areal extent of glaciation changes drastically with the degree of glacial modification in the landscape. First, in landscapes with novel glaciations, a nearly linear relationship between climate and glacial area exists. Second, in previously glaciated landscapes with extensive area at a similar elevation, highly nonlinear and rapid glacial expansions occur with minimal climate forcing, once the snowline reaches the hypsometric maximum. Our results also show that erosion associated with glaciations before the mid-Pleistocene transition at around 950,000 years ago probably preconditioned the landscape—producing glacial landforms and hypsometric maxima—such that ongoing cooling led to a significant change in glacial extent and erosion, resulting in more extensive glaciations and valley deepening in the late Pleistocene epoch. We thus provide a mechanism that explains previous observations from exposure dating and low-temperature thermochronology in the European Alps, and suggest that there is a strong topographic control on the most recent Quaternary period glaciations.

The mechanics of clay smearing along faults

A clay- or shale-rich fault gouge can significantly reduce fault permeability. Therefore, predictions of the volume of clay or shale that may be smeared along a fault trace are important for estimating the fluid connectivity of groundwater and hydrocarbon reservoir systems. Here, we show how fault smears develop spontaneously in layered soil systems with varying friction coefficients, and we present a quantitative dynamic model for such behavior. The model is based on Mohr-Coulomb failure theory, and using discrete element computations, we demonstrate how the model framework can predict the fault smear potential from soil friction angles and layer thicknesses.

A new strategy for discrete element numerical models: 2. Sandbox applications

[1] Here we present a series of numerical experiments using a new formulation of the discrete element method (DEM) that improves performance in modeling faults and shear zones. In the new method, named the stress-based discrete element method (SDEM), which is introduced in the companion paper by Egholm, stress tensors are stored at each circular particle. Further, SDEM includes rotational resistivity of particles and elastoplastic constitutive rules for governing particle deformation. When combining these new features, the SDEM is capable of reproducing the friction properties of rocks and soils, without the need for the ad hoc calibration routines normally associated with DEM. In contrast to the conventional DEM, the friction properties of a SDEM particle system are in agreement with the Mohr-Coulomb constitutive model with friction angles specified on a particle level. ‘‘Benchmark’’ sandbox models show that unlike most commonly used numerical methods, SDEM faults and shear zones develop at angles in agreement with general observations from structural geology and analogue modeling studies. Citation: Egholm, D. L., M. Sandiford, O. R. Clausen, and S. B. Nielsen (2007), A new strategy for discrete element numerical models: 2. Sandbox applications, J. Geophys. Res., 112, B05204, doi:10.1029/2006JB004558.

Discrete element modeling of subglacial sediment deformation

[1] The Discrete Element Method (DEM) is used in this study to explore the highly nonlinear dynamics of a granular bed when exposed to stress conditions comparable to those at the bed of warm-based glaciers. Complementary to analog experiments, the numerical approach allows a detailed analysis of the material dynamics and the shear zone development during progressive shear strain. The geometry of the heterogeneous stress network is visible in the form of force-carrying grain bridges and adjacent, volumetrically dominant, inactive zones. We demonstrate how the shear zone thickness and dilation depend on the level of normal (overburden) stress, and we show how high normal stress can mobilize material to great depths. The particle rotational axes tend to align with progressive shear strain, with rotations both along and reverse to the shear direction. The results from successive laboratory ring-shear experiments on simple granular materials are compared to results from similar numerical experiments. The simulated DEM material and all tested laboratory materials deform by an elastoplastic rheology under the applied effective normal stress. These results demonstrate that the DEM is a viable alternative to continuum models for small-scale analysis of sediment deformation. It can be used to simulate the macromechanical behavior of simple granular sediments, and it provides an opportunity to study how microstructures in subglacial sediments are formed during progressive shear strain.

Glacial isostatic uplift of the European Alps

Following the last glacial maximum (LGM), the demise of continental ice sheets induced crustal rebound in tectonically stable regions of North America and Scandinavia that is still ongoing. Unlike the ice sheets, the Alpine ice cap developed in an orogen where the measured uplift is potentially attributed to tectonic shortening, lithospheric delamination and unloading due to deglaciation and erosion. Here we show that ∼90% of the geodetically measured rock uplift in the Alps can be explained by the Earth’s viscoelastic response to LGM deglaciation. We modelled rock uplift by reconstructing the Alpine ice cap, while accounting for postglacial erosion, sediment deposition and spatial variations in lithospheric rigidity. Clusters of excessive uplift in the Rhône Valley and in the Eastern Alps delineate regions potentially affected by mantle processes, crustal heterogeneity and active tectonics. Our study shows that even small LGM ice caps can dominate present-day rock uplift in tectonically active regions.

Glacial landscape evolution by subglacial quarrying: A multiscale computational approach

Quarrying of bedrock is a primary agent of subglacial erosion. Although the mechanical theory behind the process has been studied for decades, it has proven difficult to formulate the governing principles so that large-scale landscape evolution models can be used to integrate erosion over time. The existing mechanical theory thus stands largely untested in its ability to explain post-glacial topography. In this study we relate the physics of quarrying to long-term landscape evolution with a multi-scale approach that connects meter-scale cavities to kilometer-scale glacial landscapes. By averaging the quarrying rate across many small-scale bedrock steps, we quantify how regional trends in basal sliding speed, effective pressure, and bed slope affect the rate of erosion. A sensitivity test indicates that a power-law formulated in terms of these three variables provides an acceptable basis for quantifying regional-scale rates of quarrying. Our results highlight the strong influence of effective pressure, which intensifies quarrying by increasing the volume of the bed that is stressed by the ice and thereby the probability of rock failure. The resulting pressure dependency points to subglacial hydrology as a primary factor for influencing rates of quarrying and hence for shaping the bedrock topography under warm-based glaciers. When applied in a landscape evolution model, the erosion law for quarrying produces recognizable large-scale glacial landforms: U-shaped valleys, hanging valleys and overdeepenings. The landforms produced are very similar to those predicted by more standard sliding-based erosion laws, but overall quarrying is more focused in valleys, and less effective at higher elevations.

One million years of glaciation and denudation history in west Greenland

The influence of major Quaternary climatic changes on growth and decay of the Greenland Ice Sheet, and associated erosional impact on the landscapes, is virtually unknown beyond the last deglaciation. Here we quantify exposure and denudation histories in west Greenland by applying a novel Markov-Chain Monte Carlo modelling approach to all available paired cosmogenic 10Be-26Al bedrock data from Greenland. We find that long-term denudation rates in west Greenland range from >50 m Myr−1 in low-lying areas to ∼2 m Myr−1 at high elevations, hereby quantifying systematic variations in denudation rate among different glacial landforms caused by variations in ice thickness across the landscape. We furthermore show that the present day ice-free areas only were ice covered ca. 45% of the past 1 million years, and even less at high-elevation sites, implying that the Greenland Ice Sheet for much of the time was of similar size or even smaller than today.

Basal shear stress under alpine glaciers: insights from experiments using the iSOSIA and Elmer/Ice models

Shear stress at the base of glaciers exerts a significant control on basal sliding and hence also glacial erosion in arctic and high-altitude areas. However, the inaccessible nature of glacial beds complicates empirical studies of basal shear stress, and little is therefore known of its spatial and temporal distribution. In this study we seek to improve our understanding of basal shear stress using a higher-order numerical ice model (iSOSIA). In order to test the validity of the higher-order model, we first compare the detailed distribution of basal shear stress in iSOSIA and in a three-dimensional full-Stokes model (Elmer/Ice). We find that iSOSIA and Elmer/Ice predict similar first-order stress and velocity patterns, and that differences are restricted to local variations at length scales of the order of the grid resolution. In addition, we find that subglacial shear stress is relatively uniform and insensitive to subtle changes in local topographic relief. Following the initial comparison studies, we use iSOSIA to investigate changes in basal shear stress as a result of landscape evolution by glacial erosion. The experiments with landscape evolution show that subglacial shear stress decreases as glacial erosion transforms preglacial V-shaped valleys into U-shaped troughs. These findings support the hypothesis that glacial erosion is most efficient in the early stages of glacial landscape development.

Ice‐flow dynamics forced by water‐pressure variations in subglacial granular beds

Glaciers and ice streams can move by deforming underlying water-saturated sediments, and the nonlinear mechanics of these materials are often invoked as the main reason for initiation, persistence, and shut-down of fast-flowing ice streams. Existing models have failed to fully explain the internal mechanical processes driving transitions from stability to slip. We performed computational experiments that show how rearrangements of load-bearing force chains within the granular sediments drive the mechanical transitions. Cyclic variations in pore-water pressure give rise to rate-dependent creeping motion at stress levels below the point of failure, while disruption of the force-chain network induces fast rate-independent flow above it. This finding contrasts previous descriptions of subglacial sediment mechanics, which either assume rate-dependence regardless of mechanical state or unconditional stability before the sediment yield point. Our new micro-mechanical computational approach is capable of reproducing important transitions between these two end-member models, and can explain multimodal velocity patterns observed in glaciers, landslides and slow-moving tremor zones.