Glacier longitudinal profiles in regions of active uplift

Headley, Rachel; Roe, Gerard H.; Hallet, Bernard

doi:10.1016/j.epsl.2011.11.010

Cited by 15 publications

(22 citation statements)

References 63 publications

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“…Here the glacier mass balance is assumed to be linearly dependent on the position along the glacier ( x , measured in a downstream direction) via the mass balance gradient β x and in relation to the horizontal position of the equilibrium line, E x . This is consistent with the approach of Headley et al (). The mass balance can then be integrated from the summit of the glacier to estimate ice flux q at any point x along the glacier:

q = \int_{0}^{x} - β_{x} ((), x - E_{x}) normald x

…”

Section: Shallow Ice Solution For Glacial Equilibrium Profilessupporting

confidence: 93%

“…Note that the scaling exponents for d h /d x and H derived from our model differ from those given by Headley et al (). For example, Headley et al () report a linear relationship between U and d h /d x in a sliding‐dominated scenario with n = 3 and l = 1 and an exponent of 0.5 for l = 2, while the exponent derived here is 0.6 for n = 3 and l = 1, and 0.3 for l = 2. Similarly, the scaling exponent of H with U is −1 ( l = 1) or −0.5 ( l = 2) according to Headley et al (), but −0.4 ( l = 1) or −0.2 ( l = 2) in this study.…”

Section: Scaling Relations In a Glacial Topographic Steady Statecontrasting

confidence: 87%

“…In the first case, erosion rate and sliding velocity are uniform, while in the latter case

ė

and u s vary as they have to match U . Headley et al () provide similar scenarios but without the feedback between glacier mass balance and ice surface elevation.…”

Section: Discontinuities and Valley Widthmentioning

confidence: 99%

“…This contradicts the nature of the glacier mass balance gradient as a climatic variable which depends on temperature and precipitation and should thus be independent from tectonic influences, at least as long as orographic effects are neglected. To overcome these issues, we extend our study beyond the work of Headley et al () and consider glacier mass balance as a function of altitude instead of distance along the glacier. For this, it is convenient to introduce a glacier mass balance gradient over elevation, β = d B /d z , where B is the glacier mass balance.…”

Section: Shallow Ice Solution For Glacial Equilibrium Profilesmentioning

confidence: 99%

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Glacial Steady State Topography Controlled by the Coupled Influence of Tectonics and Climate

et al. 2018

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Glaciers and rivers are the main agents of mountain erosion. While in the fluvial realm empirical relationships and their mathematical description, such as the stream power law, improved the understanding of fundamental controls on landscape evolution, simple constraints on glacial topography and governing scaling relations are widely lacking. We present a steady state solution for longitudinal profiles along eroding glaciers in a coupled system that includes tectonics and climate. We combined the shallow ice approximation and a glacial erosion rule to calculate ice surface and bed topography from prescribed glacier mass balance gradient and rock uplift rate. Our approach is inspired by the classic application of the stream power law for describing a fluvial steady state but with the striking difference that, in the glacial realm, glacier mass balance is added as an altitude‐dependent variable. From our analyses we find that ice surface slope and glacial relief scale with uplift rate with scaling exponents indicating that glacial relief is less sensitive to uplift rate than relief in most fluvial landscapes. Basic scaling relations controlled by either basal sliding or internal deformation follow a power law with the exponent depending on the exponents for the glacial erosion rule and Glen's flow law. In a mixed scenario of sliding and deformation, complicated scaling relations with variable exponents emerge. Furthermore, a cutoff in glacier mass balance or cold ice in high elevations can lead to substantially larger scaling exponents which may provide an explanation for high relief in high latitudes.

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q = \int_{0}^{x} - β_{x} ((), x - E_{x}) normald x

…”

Section: Shallow Ice Solution For Glacial Equilibrium Profilessupporting

confidence: 93%

Section: Scaling Relations In a Glacial Topographic Steady Statecontrasting

confidence: 87%

“…In the first case, erosion rate and sliding velocity are uniform, while in the latter case

ė

and u s vary as they have to match U . Headley et al () provide similar scenarios but without the feedback between glacier mass balance and ice surface elevation.…”

Section: Discontinuities and Valley Widthmentioning

confidence: 99%

Section: Shallow Ice Solution For Glacial Equilibrium Profilesmentioning

confidence: 99%

See 2 more Smart Citations

Glacial Steady State Topography Controlled by the Coupled Influence of Tectonics and Climate

et al. 2018

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“…The pattern of fluid flow both within and at the base of a glacier can be a complex THM process by itself. Problems associated with the mechanics of glaciers (Weertman, 1972;Marshall, 2005), the motion of glaciers (Fowler, 1981(Fowler, , 2011Morland, 1987;Picasso et al, 2004;Gomez et al, 2013;Stucki and Schlunegger, 2013;Ahlkrona et al, 2013;Thoma et al, 2014), the constitutive properties of ice and ice-rock interfaces (Picasso et al, 2004;Marshall, 2005;Headley et al, 2012;Tezaur et al, 2015), the contact with the bedrock and the evolution of their shapes (dell'Isola and Hutter, 1998;Picasso et al, 2004;Dietrich et al, 2010;Headley et al, 2012;Nielsen et al, 2012;Pollard and deConto, 2012;Gomez et al, 2013;Stucki and Schlunegger, 2013;Steffen et al, 2006;de Boer et al, 2014) have been studied. The glacier dynamics on a centennial timescale due to climatic warming was studied by Hambrey et al (2005).…”

Section: The Initial Boundary Value Problemmentioning

confidence: 99%

Thermo-hydro-mechanical processes in fractured rock formations during a glacial advance

2015

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Abstract. The paper examines the coupled thermo-hydromechanical (THM) processes that develop in a fractured rock region within a fluid-saturated rock mass due to loads imposed by an advancing glacier. This scenario needs to be examined in order to assess the suitability of potential sites for the location of deep geologic repositories for the storage of high-level nuclear waste. The THM processes are examined using a computational multiphysics approach that takes into account thermo-poroelasticity of the intact geological formation and the presence of a system of sessile but hydraulically interacting fractures (fracture zones). The modelling considers coupled thermo-hydro-mechanical effects in both the intact rock and the fracture zones due to contact normal stresses and fluid pressure at the base of the advancing glacier. Computational modelling provides an assessment of the role of fractures in modifying the pore pressure generation within the entire rock mass.

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Topographic signatures of progressive glacial landscape transformation

Liebl

Robl

Egholm

et al. 2021

Earth Surf Processes Landf

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SummaryThe Pleistocene glaciations left a distinct topographic footprint in mountain ranges worldwide. The geometric signature of glacial topography has been quantified in various ways, but the temporal development of landscape metrics has not been traced in a landscape evolution model so far. However, such information is needed to interpret the degree of glacial imprint in terms of the integrated signal of temporal and spatial variations in erosion as a function of glacial occupation time.We apply a surface process model for cold‐climate conditions to an initially fluvial mountain range. By exploring evolving topographic patterns in model time series, we determine locations where topographic changes reach a maximum and where the initial landscape persists. The signal of glacial erosion, expressed by the overdeepening of valleys and the steepening of valley flanks, develops first at the glacier front and migrates upstream with ongoing glacial erosion. This leads to an increase of mean channel slope and its variance. Above steep flanks and head‐walls, however, the observed mean channel slope remains similar to the mean channel slope of the initial fluvial topography. This leads to a characteristic turning point in the channel slope–elevation distribution above the equilibrium line altitude, where a transition from increasing to decreasing channel slope with elevation occurs. We identify this turning point and a high channel slope variance as diagnostic features to quantify glacial imprint.Such features are abundant in glacially imprinted mid‐latitude mountain ranges such as the Eastern Alps. By analysing differently glaciated parts of the mountain range, we observe a decreasing clarity of this diagnostic morphometric property with decreasing glacial occupation. However, catchments of the unglaciated eastern fringe of the Alps also feature turning points in their channel slope–elevation distributions, but in contrast to the glaciated domain, the variance of channel slope is small at all elevation levels.

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Glacier longitudinal profiles in regions of active uplift

Cited by 15 publications

References 63 publications

Glacial Steady State Topography Controlled by the Coupled Influence of Tectonics and Climate

Glacial Steady State Topography Controlled by the Coupled Influence of Tectonics and Climate

Thermo-hydro-mechanical processes in fractured rock formations during a glacial advance

Topographic signatures of progressive glacial landscape transformation

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