Marine ice sheet dynamics. Part 2. A Stokes flow contact problem

2011 ◽  
Vol 679 ◽  
pp. 122-155 ◽  
Author(s):  
CHRISTIAN SCHOOF
Keyword(s):  
Contact Problem ◽  
Boundary Conditions ◽  
Boundary Layers ◽  
Contact Line ◽  
Stokes Flow ◽  
Flow Model ◽  
Layer Structure ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Continuous Transition

We develop an asymptotic theory for marine ice sheets from a first-principles Stokes flow contact problem, in which different boundary conditions apply to areas where ice is in contact with bedrock and inviscid sea water, along with suitable inequalities on normal stress and boundary location constraining contact and non-contact zones. Under suitable assumptions about basal slip in the contact areas, the boundary-layer structure for this problem replicates the boundary layers previously identified for marine ice sheets from depth-integrated models and confirms the results of these previous models: the interior of the grounded ice sheet can be modelled as a standard free-surface lubrication flow, while coupling with the membrane-like floating ice shelf leads to two boundary conditions on this lubrication flow model at the contact line. These boundary conditions determine ice thickness and ice flux at the contact line and allow the lubrication flow model with a contact line to be solved as a moving boundary problem. In addition, we find that the continuous transition of vertical velocity from grounded to floating ice requires the presence of two previously unidentified boundary layers. One of these takes the form of a viscous beam, in which a wave-like surface feature leads to a continuous transition in surface slope from grounded to floating ice, while the other provides boundary conditions on this viscous beam at the contact line.

scholarly journals Coupled ice sheet–climate modeling under glacial and pre-industrial boundary conditions

2014 ◽  
Vol 10 (5) ◽  
pp. 1817-1836 ◽  
Author(s):  
F. A. Ziemen ◽  
C. B. Rodehacke ◽  
U. Mikolajewicz
Keyword(s):  
Boundary Conditions ◽  
General Circulation ◽  
Climate Modeling ◽  
Ice Sheets ◽  
Ice Sheet ◽  
General Circulation Models ◽  
Quasi Equilibrium ◽  
Ice Streams ◽  
Ice Stream ◽  
First Results

Abstract. In the standard Paleoclimate Modelling Intercomparison Project (PMIP) experiments, the Last Glacial Maximum (LGM) is modeled in quasi-equilibrium with atmosphere–ocean–vegetation general circulation models (AOVGCMs) with prescribed ice sheets. This can lead to inconsistencies between the modeled climate and ice sheets. One way to avoid this problem would be to model the ice sheets explicitly. Here, we present the first results from coupled ice sheet–climate simulations for the pre-industrial times and the LGM. Our setup consists of the AOVGCM ECHAM5/MPIOM/LPJ bidirectionally coupled with the Parallel Ice Sheet Model (PISM) covering the Northern Hemisphere. The results of the pre-industrial and LGM simulations agree reasonably well with reconstructions and observations. This shows that the model system adequately represents large, non-linear climate perturbations. A large part of the drainage of the ice sheets occurs in ice streams. Most modeled ice stream systems show recurring surges as internal oscillations. The Hudson Strait Ice Stream surges with an ice volume equivalent to about 5 m sea level and a recurrence interval of about 7000 yr. This is in agreement with basic expectations for Heinrich events. Under LGM boundary conditions, different ice sheet configurations imply different locations of deep water formation.

scholarly journals Lateral boundary conditions for a local anisotropic ice-flow model

2002 ◽  
Vol 35 ◽  
pp. 503-509 ◽  
Author(s):  
Olivier Gagliardini ◽  
Jacques Meyssonnier
Keyword(s):  
Boundary Conditions ◽  
Flow Model ◽  
Ice Sheet ◽  
Lateral Boundary ◽  
Local Flow ◽  
Ice Flow ◽  
Lateral Boundary Conditions ◽  
Potential Applications ◽  
Two Dimensional Flow ◽  
Spatial Domains

AbstractA local two-dimensional flow model which accounts for the anisotropic behaviour of polar ice and the evolution of its strain-induced anisotropy is briefly reviewed. Due to its complexity, it is not yet possible to use this model to simulate the flow of a whole ice sheet, and its potential applications are presently restricted to limited spatial domains around existing drilling sites. In order to calculate the local flow of ice, boundary conditions must be applied on the lateral edges of the studied domain. Since these limits correspond to fictitious sections of the ice sheet, the type of boundary condition to adopt is not obvious. In the present paper, different kinds of boundary conditions of the Dirichlet type, applied at the lateral boundary of an idealized ice sheet of simplified geometry, are discussed. This will serve as a first step towards the coupling of the local flow model with a global ice-sheet flow model.

scholarly journals Experimental Determination of the Buckling Loads of Floating Ice Sheets

1983 ◽  
Vol 4 ◽  
pp. 260-265 ◽  
Author(s):  
D. S. Sodhi ◽  
F. D. Haynes ◽  
K. Kato ◽  
K. Hirayama
Keyword(s):  
Experimental Data ◽  
Boundary Conditions ◽  
Experimental Determination ◽  
Characteristic Length ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Experimental Results ◽  
Buckling Loads ◽  
Data Points

Experiments were performed to determine the forces required to buckle a floating ice sheet pushing against structures of different widths. The characteristic length of each ice sheet was determined to enable a comparison to be made between the theoretical and experimental results.Most of the experimental data points are within the range of the theoretical values of normalized buckling loads for frictionless and hinged boundary conditions, which represent the extreme situations for ice-structure contact. Thus, the agreement between the theoretical and experimental buckling loads is considered to be good. Photographs of the buckled ice sheets show a resemblance to the theoretical mode of buckling.

scholarly journals Experimental Determination of the Buckling Loads of Floating Ice Sheets

1983 ◽  
Vol 4 ◽  
pp. 260-265 ◽  
Author(s):  
D. S. Sodhi ◽  
F. D. Haynes ◽  
K. Kato ◽  
K. Hirayama
Keyword(s):  
Experimental Data ◽  
Boundary Conditions ◽  
Experimental Determination ◽  
Characteristic Length ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Experimental Results ◽  
Buckling Loads ◽  
Data Points

Experiments were performed to determine the forces required to buckle a floating ice sheet pushing against structures of different widths. The characteristic length of each ice sheet was determined to enable a comparison to be made between the theoretical and experimental results. Most of the experimental data points are within the range of the theoretical values of normalized buckling loads for frictionless and hinged boundary conditions, which represent the extreme situations for ice-structure contact. Thus, the agreement between the theoretical and experimental buckling loads is considered to be good. Photographs of the buckled ice sheets show a resemblance to the theoretical mode of buckling.

scholarly journals Exploring the impact of atmospheric forcing and basal drag on the Antarctic Ice Sheet under Last Glacial Maximum conditions

2021 ◽  
Vol 15 (1) ◽  
pp. 215-231
Author(s):  
Javier Blasco ◽  
Jorge Alvarez-Solas ◽  
Alexander Robinson ◽  
Marisa Montoya
Keyword(s):  
Boundary Conditions ◽  
Continental Shelf ◽  
Last Glacial Maximum ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Shelf Break ◽  
Ice Volume ◽  
Basal Friction ◽  
The Antarctic ◽  
Continental Shelf Break

Abstract. Little is known about the distribution of ice in the Antarctic Ice Sheet (AIS) during the Last Glacial Maximum (LGM). Whereas marine and terrestrial geological data indicate that the grounded ice advanced to a position close to the continental-shelf break, the total ice volume is unclear. Glacial boundary conditions are potentially important sources of uncertainty, in particular basal friction and climatic boundary conditions. Basal friction exerts a strong control on the large-scale dynamics of the ice sheet and thus affects its size and is not well constrained. Glacial climatic boundary conditions determine the net accumulation and ice temperature and are also poorly known. Here we explore the effect of the uncertainty in both features on the total simulated ice storage of the AIS at the LGM. For this purpose we use a hybrid ice sheet shelf model that is forced with different basal drag choices and glacial background climatic conditions obtained from the LGM ensemble climate simulations of the third phase of the Paleoclimate Modelling Intercomparison Project (PMIP3). Overall, we find that the spread in the simulated ice volume for the tested basal drag parameterizations is about the same range as for the different general circulation model (GCM) forcings (4 to 6 m sea level equivalent). For a wide range of plausible basal friction configurations, the simulated ice dynamics vary widely but all simulations produce fully extended ice sheets towards the continental-shelf break. More dynamically active ice sheets correspond to lower ice volumes, while they remain consistent with the available constraints on ice extent. Thus, this work points to the possibility of an AIS with very active ice streams during the LGM. In addition, we find that the surface boundary temperature field plays a crucial role in determining the ice extent through its effect on viscosity. For ice sheets of a similar extent and comparable dynamics, we find that the precipitation field determines the total AIS volume. However, precipitation is highly uncertain. Climatic fields simulated by climate models show more precipitation in coastal regions than a spatially uniform anomaly, which can lead to larger ice volumes. Our results strongly support using these paleoclimatic fields to simulate and study the LGM and potentially other time periods like the last interglacial. However, their accuracy must be assessed as well, as differences between climate model forcing lead to a large spread in the simulated ice volume and extension.

Impact of ice sheet reconstructions on the deglacial climate in iLOVECLIM

2021 ◽  
Author(s):  
Nathaelle Bouttes ◽  
Didier Roche ◽  
Fanny Lhardy ◽  
Aurelien Quiquet ◽  
Didier Paillard ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Last Deglaciation ◽  
Antarctic Ice Sheet ◽  
Intermediate Complexity ◽  
Climate Evolution ◽  
The Last Deglaciation ◽  
The Antarctic ◽  
The Impact

<p>The last deglaciation is a time of large climate transition from a cold Last Glacial Maximum at 21,000 years BP with extensive ice sheets, to the warmer Holocene 9,000 years BP onwards with reduced ice sheets. Despite more and more proxy data documenting this transition, the evolution of climate is not fully understood and difficult to simulate. The PMIP4 protocol (Ivanovic et al., 2016) has indicated which boundary conditions to use in model simulations during this transition. The common boundary conditions should enable consistent multi model and model-data comparisons. While the greenhouse gas concentration evolution and orbital forcing are well known and easy to prescribe, the evolution of ice sheets is less well constrained and several choices can be made by modelling groups. First, two ice sheet reconstructions are available: ICE-6G (Peltier et al., 2015) and GLAC-1D (Tarasov et al., 2014). On top of topographic changes, it is left to modelling groups to decide whether to account for the associated bathymetry and land-sea mask changes, which is technically more demanding. These choices could potentially lead to differences in the climate evolution, making model comparisons more complicated.</p><p>We use the iLOVECLIM model of intermediate complexity (Goosse et al., 2010) to evaluate the impact of different ice sheet reconstructions and the effect of bathymetry changes on the global climate evolution during the Last deglaciation. We test the two ice sheet reconstructions (ICE-6G and GLAC-1D), and have implemented changes of bathymetry and land-sea mask. In addition, we also evaluate the impact of accounting for the Antarctic ice sheet evolution compared to the Northern ice sheets only.</p><p>We show that despite showing the same long-term changes, the two reconstructions lead to different evolutions. The bathymetry plays a role, although only few changes take place before ~14ka. Finally, the impact of the Antarctic ice sheet is important during the deglaciation and should not be neglected.</p><p>References</p><p>Goosse, H., et al., Description of the Earth system model of intermediate complexity LOVECLIM version 1.2, Geosci. Model Dev., 3, 603–633, https://doi.org/10.5194/gmd-3-603-2010, 2010</p><p>Ivanovic, R. F., et al., Transient climate simulations of the deglaciation 21–9 thousand years before present (version 1) – PMIP4 Core experiment design and boundary conditions, Geosci. Model Dev., 9, 2563–2587, https://doi.org/10.5194/gmd-9-2563-2016, 2016</p><p>Peltier, W. R., Argus, D. F., and Drummond, R., Space geodesy constrains ice age terminal deglaciation: The global ICE-6G_C (VM5a) model, J. Geophys. Res.-Sol. Ea., 120, 450–487, doi:10.1002/2014JB011176, 2015</p><p>Tarasov,L.,  et al., The global GLAC-1c deglaciation chronology, melwater pulse 1-a, and a question of missing ice, IGS Symposium on Contribution of Glaciers and Ice Sheets to Sea-Level Change, 2014</p>

scholarly journals The asymptotic equivalence of fixed heat flux and fixed temperature thermal boundary conditions for rapidly rotating convection

2015 ◽  
Vol 784 ◽  
Author(s):  
Michael A. Calkins ◽  
Kevin Hale ◽  
Keith Julien ◽  
David Nieves ◽  
Derek Driggs ◽  
...  
Keyword(s):  
Heat Flux ◽  
Boundary Conditions ◽  
Boundary Layers ◽  
Layer Structure ◽  
Plane Layer ◽  
Order System ◽  
Leading Order ◽  
Fixed Temperature ◽  
Rotating Convection ◽  
Thermal Boundary Conditions

The influence of fixed temperature and fixed heat flux thermal boundary conditions on rapidly rotating convection in the plane layer geometry is investigated for the case of stress-free mechanical boundary conditions. It is shown that whereas the leading-order system satisfies fixed temperature boundary conditions implicitly, a double boundary layer structure is necessary to satisfy the fixed heat flux thermal boundary conditions. The boundary layers consist of a classical Ekman layer adjacent to the solid boundaries that adjust viscous stresses to zero, and a layer in thermal wind balance just outside the Ekman layers that adjusts the normal derivative of the temperature fluctuation to zero. The influence of these boundary layers on the interior geostrophically balanced convection is shown to be asymptotically weak, however. Upon defining a simple rescaling of the thermal variables, the leading-order reduced system of governing equations is therefore equivalent for both boundary conditions. These results imply that any horizontal thermal variation along the boundaries that varies on the scale of the convection has no leading-order influence on the interior convection, thus providing insight into geophysical and astrophysical flows where stress-free mechanical boundary conditions are often assumed.

scholarly journals Exploring the impact of atmospheric forcing and basal boundary conditions on the simulation of the Antarctic ice sheet at the Last Glacial Maximum

2020 ◽  
Author(s):  
Javier Blasco ◽  
Jorge Alvarez-Solas ◽  
Alexander Robinson ◽  
Marisa Montoya
Keyword(s):  
Boundary Conditions ◽  
Continental Shelf ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Ice Volume ◽  
Basal Friction ◽  
The Antarctic ◽  
Continental Shelf Break ◽  
The Last Glacial Maximum ◽  
The Last Glacial

Abstract. Little is known about the distribution of ice in the Antarctic ice sheet (AIS) during the Last Glacial Maximum (LGM). Whereas marine and terrestrial geological data indicate that the grounded ice advanced to a position close to the continental-shelf break, the total ice volume is unclear. Glacial boundary conditions are potentially important sources of uncertainty, in particular basal friction and climatic boundary conditions. Basal friction exerts a strong control on the large-scale dynamics of the ice sheet and thus affects its size, and is not well constrained. Glacial climatic boundary conditions determine the net accumulation and ice temperature, and are also poorly known. Here we explore the effect of the uncertainty in both features on the total simulated ice storage of the AIS at the LGM. For this purpose we use a hybrid ice-sheet-shelf model that is forced with different basal-drag choices and glacial background climatic conditions obtained from the LGM ensemble climate simulations of the third phase of the Paleoclimate Modelling Intercomparison Project (PMIP3). For a wide range of plausible basal friction configurations, the simulated ice dynamics vary widely but all simulations produce fully extended ice sheets towards the continental-shelf break. More dynamically active ice sheets correspond to lower ice volumes, while they remain consistent with the available constraints on ice extent. Thus, this work points to the possibility of an AIS with very active ice streams during the LGM. In addition, we find that the surface boundary temperature field plays a crucial role in determining the ice extent through its effect on viscosity. For ice sheets of a similar extent and comparable dynamics, we find that the precipitation field determines the total AIS volume. However, precipitation is deeply uncertain. Climatic fields simulated by climate models show more precipitation in coastal regions than a spatially uniform anomaly, which can lead to larger ice volumes. We strongly support using these paleoclimatic fields to simulate and study the LGM and potentially other time periods like the Last Interglacial. However, their accuracy must be assessed as well, as differences between climate model forcing lead to a range in the simulated ice volume and extension of about 6 m sea-level equivalent and one million km2.

scholarly journals Snapshots of the Greenland ice sheet configuration in the Pliocene to early Pleistocene

2011 ◽  
Vol 57 (205) ◽  
pp. 871-880 ◽  
Author(s):  
Anne M. Solgaard ◽  
Niels Reeh ◽  
Peter Japsen ◽  
Tove Nielsen
Keyword(s):  
Flow Model ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Early Pleistocene ◽  
Pleistocene Glaciations ◽  
Ice Flow ◽  
Late Pliocene ◽  
Ice Caps ◽  
Climate Reconstructions

AbstractThe geometry of the ice sheets during the Pliocene to early Pleistocene is not well constrained. Here we apply an ice-flow model in the study of the Greenland ice sheet (GIS) during three extreme intervals of this period constrained by geological observations and climate reconstructions. We study the extent of the GIS during the Mid-Pliocene Warmth (3.3–3.0 Ma), its advance across the continental shelf during the late Pliocene to early Pleistocene glaciations (3.0–2.4 Ma) as implied by offshore geological studies, and the transition from glacial to interglacial conditions around 2.4 Ma as deduced from the deposits of the Kap København Formation, North Greenland. Our experiments show that no coherent ice sheet is likely to have existed in Greenland during the Mid-Pliocene Warmth and that only local ice caps may have been present in the coastal mountains of East Greenland. Our results illustrate the variability of the GIS during the Pliocene to early Pleistocene and underline the importance of including independent estimates of the GIS in studies of climate during this period. We conclude that the GIS did not exist throughout the Pliocene to early Pleistocene, and that it melted during interglacials even during the late Pliocene climate deterioration.

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