Dynamics of Ice Sheets and Glaciers

Greve, Ralf; Blatter, Heinz

doi:10.1007/978-3-642-03415-2

Cited by 390 publications

(550 citation statements)

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“…The problem addressed here is the one of an isothermal icesheet in SSA (Greve and Blatter, 2009). The two horizontal components of the stress balance in SSA with spatially uniform ice softness A are given by where v x and v y are the components in x and y direction of the horizontal velocity vector v, respectively, H is the ice thickness, h = H + b the ice-surface elevation with ice-base elevation b, ρ is the ice density, g the gravitational acceleration and n denotes Glen's flow-law exponent.…”

Section: Basic Equations For Similitude Analysismentioning

confidence: 99%

“…A value of m = 1/n = 1/3 is commonly assumed to represent sliding over rough bed (Schoof, 2007a;Joughin et al, 2009;Cuffey and Paterson, 2010). The evolution equation for the ice thickness, i.e., the ice thickness equation (ITE), which results out of mass conservation (Greve and Blatter, 2009) reads…”

Section: Basic Equations For Similitude Analysismentioning

confidence: 99%

“…1) is derived from the full Stokes equation using a single horizontal length scale L and timescale T , respectively (Greve and Blatter, 2009). Continuing this line of thought, we introduce the dimensionless ve-…”

Section: Two-dimensional Case With One Time and One Length Scalementioning

confidence: 99%

“…Here we apply the concept of similitude to the dynamics of idealized ice sheets based on the shallow-shelf approximation (SSA; Morland, 1987;MacAyeal, 1989;Greve and Blatter, 2009). In particular we assume isothermal ice and a spatially uniform basal friction coefficient, conditions that have been used to analyze ice-sheet dynamics in a number of previous studies (e.g., Dupont and Alley, 2005;Goldberg et al, 2009;Gudmundsson et al, 2012;Pattyn et al, 2013;AsayDavis et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

“…A dimensional analysis of the ice-dynamic equations is often carried out to compare the magnitudes of the different acting forces and thus to derive physically motivated approximations, as done when deriving the SSA from the full Stokes stress balance (MacAyeal, 1989;Greve and Blatter, 2009). The non-dimensionalized form of the SSA itself and the involved dimensionless coefficients that result from the introduction of typical scales for, e.g., ice-sheet thickness and velocity, have been used to consider asymptotic limits of SSA ice flow in previous work (Schoof, 2007a;Dupont and Alley, 2005;Tsai et al, 2015;Haseloff et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

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Similitude of ice dynamics against scaling of geometry and physical parameters

Feldmann

Levermann

2016

The Cryosphere

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Abstract. The concept of similitude is commonly employed in the fields of fluid dynamics and engineering but rarely used in cryospheric research. Here we apply this method to the problem of ice flow to examine the dynamic similitude of isothermal ice sheets in shallow-shelf approximation against the scaling of their geometry and physical parameters. Carrying out a dimensional analysis of the stress balance we obtain dimensionless numbers that characterize the flow. Requiring that these numbers remain the same under scaling we obtain conditions that relate the geometric scaling factors, the parameters for the ice softness, surface mass balance and basal friction as well as the ice-sheet intrinsic response time to each other. We demonstrate that these scaling laws are the same for both the (two-dimensional) flow-line case and the three-dimensional case. The theoretically predicted ice-sheet scaling behavior agrees with results from numerical simulations that we conduct in flow-line and three-dimensional conceptual setups. We further investigate analytically the implications of geometric scaling of ice sheets for their response time. With this study we provide a framework which, under several assumptions, allows for a fundamental comparison of the ice-dynamic behavior across different scales. It proves to be useful in the design of conceptual numerical model setups and could also be helpful for designing laboratory glacier experiments. The concept might also be applied to real-world systems, e.g., to examine the response times of glaciers, ice streams or ice sheets to climatic perturbations.

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Section: Basic Equations For Similitude Analysismentioning

confidence: 99%

Section: Basic Equations For Similitude Analysismentioning

confidence: 99%

Section: Two-dimensional Case With One Time and One Length Scalementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Similitude of ice dynamics against scaling of geometry and physical parameters

Feldmann

Levermann

2016

The Cryosphere

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Optimal initial conditions for coupling ice sheet models to Earth system models

2014

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We address complications in the coupling of a dynamic ice sheet model (ISM) and forcing from an Earth system model (ESM), which arise because of the unknown ISM initial conditions. Unless explicitly accounted for during ISM initialization, the ice sheet is far from thermomechanical equilibrium with the surface mass balance forcing from the ESM. Upon coupling to ESM forcing, the result is a shock and unphysical and undesirable transients in ice geometry and other state variables. Under the assumption of thermomechanical equilibrium, we present an approach for finding ISM initial conditions—characterized by optimization of the basal sliding coefficient and basal topography fields—that balance a best fit to surface velocity and basal topography observations against the minimization of unphysical transients when coupling to surface mass balance forcing. A quasi‐Newton method is used to solve the resulting large‐scale, partial differential equation‐constrained optimization problem, where the cost function gradients with respect to the parameter fields are computed using adjoints. After studying properties of our approach on a synthetic test problem, we apply the method toward obtaining optimal initial conditions for a model of the Greenland ice sheet. Our results show that, in the presence of uncertainties in the basal topography, ice thickness should also be treated as an optimization variable. While the focus here is on the coupling between an ISM and ESM‐derived surface mass balance, the method is easily extended to include optimal coupling to forcing from an ocean model through submarine melt rates.

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Supraglacial channel inception: Modeling and processes

2015

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Supraglacial drainage systems play a key role in glacial hydrology. Nevertheless, physical processes leading to spatial organization in supraglacial networks are still an open issue. In the present work we thus address from a quantitative point of view the question of what is the physics leading to widely observed patterns made up of evenly spaced channels. To this aim, we set up a novel mathematical model describing a condition antecedent channel formation, i.e., the down-glacier flow of a distributed meltwater film. We then perform a linear stability analysis to assess whether the ice-water interface undergoes a morphological instability compatible with observed patterns. The instability is detected, its features depending on glacier surface slope, ice friction factor, and water as well as ice thermal conditions. By contrast, in our model channel spacing is solely hydrodynamically driven and relies on the interplay between pressure perturbations, flow depth response, and Reynolds stresses. Geometrical features of the predicted pattern are quantitatively consistent with available field data. The hydrodynamic origin of supraglacial channel morphogenesis suggests that alluvial patterns might share the same physical controls.

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Dynamics of Ice Sheets and Glaciers

Cited by 390 publications

References 0 publications

Similitude of ice dynamics against scaling of geometry and physical parameters

Similitude of ice dynamics against scaling of geometry and physical parameters

Optimal initial conditions for coupling ice sheet models to Earth system models

Supraglacial channel inception: Modeling and processes

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