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1
GRIMA, C., I. KOCH, J. S. GREENBAUM, K. M. SODERLUND, D. D. BLANKENSHIP, D. A. YOUNG, D. M. SCHROEDER, and S. FITZSIMONS. "Surface and basal boundary conditions at the Southern McMurdo and Ross Ice Shelves, Antarctica." Journal of Glaciology 65, no. 252 (July 29, 2019): 675–88. http://dx.doi.org/10.1017/jog.2019.44.
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ABSTRACTWe derive the surface and basal radar reflectance and backscatter coefficients of the southern McMurdo Ice Shelf (SMIS) and part of the nearby Ross Ice Shelf (RIS), Antarctica, from radar statistical reconnaissance using a 60-MHZ airborne survey. The surface coefficients are further inverted in terms of snow density and roughness, providing a spatial distribution of the processes contributing to the surface boundary conditions. We disentangle the basal coefficients from surface transmission losses, and we provide the basal coherent content, an indicator of the boundary geometric disorder that is also self-corrected from englacial attenuation. The basal radar properties exhibit sharp gradients along specific iso-depths, suggesting an abrupt modification of the ice composition and geometric structure. We interpret this behavior as locations where the pressure-melting point is reached, outlining fields of freezing and melting ice. Basal steps are observed at both SMIS and RIS, suggesting a common geometric expression of widespread basal processes. This technique offers a simultaneous view of both the surface and basal boundary conditions to help investigate the ice-shelf stability, while its application to airborne data significantly improves coverage of the difficult-to-observe ice–ocean boundary. It also provides constraints on thermohaline circulation in ice shelves cavities, which are analogs for ice-covered ocean worlds.
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Testut, L., I. E. Tabacco, C. Bianchi, and F. Rémy. "Influence of geometrical boundary conditions on the estimation of rheological parameters." Annals of Glaciology 30 (2000): 102–6. http://dx.doi.org/10.3189/172756400781820877.
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AbstractImproved knowledge of geometrical boundary conditions, such as bedrock geometry and surface topography, can contribute significantly to glaciological studies including ice-sheet-flow modelling. Precise thickness and altimetric data allow an estimation of ice-flow direction, the balance velocity and the basal shear stress. These parameters are calculated along a 1160 km profile in East Antarctica using a relationship between shear stress, basal temperature, the Glen flow exponent and a parameter related to strain rate. Strong variations of the flow-law parameters and basal conditions are found to play a major role in the ice-flow pattern. Sliding, anisotropy and longitudinal stress strongly perturb the validity of the law, but their signature can be identified.
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Fowler, A. C. "Sub-Temperate Basal Sliding." Journal of Glaciology 32, no. 110 (1986): 3–5. http://dx.doi.org/10.1017/s0022143000006808.
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AbstractRecent observations of glacier sliding at temperatures below the melting point are discussed. It is pointed out that these observations can be simply explained by including solid friction in the sliding law. Furthermore, we re-emphasize the point that such sub-temperate sliding has an important effect on the basal boundary conditions which should be applied in model studies of ice sheets and glaciers.
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Fowler, A. C. "Sub-Temperate Basal Sliding." Journal of Glaciology 32, no. 110 (1986): 3–5. http://dx.doi.org/10.3189/s0022143000006808.
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AbstractRecent observations of glacier sliding at temperatures below the melting point are discussed. It is pointed out that these observations can be simply explained by including solid friction in the sliding law. Furthermore, we re-emphasize the point that such sub-temperate sliding has an important effect on the basal boundary conditions which should be applied in model studies of ice sheets and glaciers.
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Dukowicz, John K., Stephen F. Price, and William H. Lipscomb. "Incorporating arbitrary basal topography in the variational formulation of ice-sheet models." Journal of Glaciology 57, no. 203 (2011): 461–67. http://dx.doi.org/10.3189/002214311796905550.
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AbstractThere are many advantages to formulating an ice-sheet model in terms of a variational principle. In particular, this applies to the specification of boundary conditions, which might otherwise be problematic to implement. Here we focus primarily on the frictional basal sliding boundary condition in a non-Newtonian Stokes model. This type of boundary condition is particularly difficult because it is heterogeneous, requiring both a Dirichlet (no-penetration) condition normal to the bed, and a Neumann (frictional sliding) condition tangential to the bed. In general, Neumann conditions correspond to natural boundary conditions in a variational principle; that is, they arise naturally in the variational formulation and thus need not be explicitly specified. While the same is not necessarily true of Dirichlet conditions, it is possible to enforce a no-penetration condition using Lagrange multipliers within the variational principle so that the Dirichlet condition becomes a natural boundary condition. Thus, in the case of ice sheets, all relevant boundary conditions may be incorporated in the variational functional, making them particularly easy to discretize. For the Stokes model, the resulting basal boundary condition is valid for arbitrary topographic slopes. Here we apply the same methodology to the Blatter– Pattyn higher-order approximate model, which is ordinarily limited to small basal slopes by the smallaspect-ratio approximation. We introduce a modification that improves on the accuracy of the standard Blatter–Pattyn model for all values of the basal slope, as we demonstrate in the slow sliding regime for which analytical results are available. The remaining error is due to the effects of the small-aspect-ratio approximation in the Blatter–Pattyn model.
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GONG, YONGMEI, THOMAS ZWINGER, STEPHEN CORNFORD, RUPERT GLADSTONE, MARTINA SCHÄFER, and JOHN C. MOORE. "Importance of basal boundary conditions in transient simulations: case study of a surging marine-terminating glacier on Austfonna, Svalbard." Journal of Glaciology 63, no. 237 (December 20, 2016): 106–17. http://dx.doi.org/10.1017/jog.2016.121.
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ABSTRACTWe assess the importance of basal boundary conditions for transient simulations of Basin 3, Austfonna ice cap between January 1995 and December 2011 and for the surge starting in 2012 by carrying out simulations with the full-Stokes model Elmer/Ice and the vertically-integrated model BISICLES. Time-varying surface mass-balance data from the regional climate model HIRHAM5 are downscaled according to elevation. Basal friction coefficient is varied through time by interpolating between two data-constrained inversions of surface velocity fields, from 1995 and 2011. Evolution of the basal boundary condition appears to be much more important for mass discharge and the dynamic response of the fast flowing unit in Basin 3 than either model choice or the downscaling method for the surface mass balance. In addition, temporally linear extrapolation of the evolution of basal friction coefficient beyond the 2011 distribution could not reproduce the expansion of the acceleration observed in southern Basin 3 between January 2012 and June 2013. This implies that changes in basal friction patterns, and in turn basal processes that are not currently represented in either model, are among the most important factors for the 2012 acceleration.
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Kang, Il Mo, Myung Hun Kim, Youn Joong Kim, Hi-Soo Moon, and Yungoo Song. "Effect of layer structure boundary on the hectorite basal diffraction." Powder Diffraction 21, no. 1 (March 2006): 30–35. http://dx.doi.org/10.1154/1.2104534.
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This study examined basal peak irrationalities according to boundary conditions of the hectorite basal diffraction unit (BDU), which were recognized as the total assembly of 2:1 phyllosilicate layer plus interlayer material. The hectorite basal profiles were computer-simulated using the three kinds of BDU settings identified from the middle of octahedral sheets in the nearest neighbor (centrosymmetric model), the middle of interlayers in the nearest neighbor (centrosymmetric model), and a basal oxygen plane to the margin of interlayer in contact with the next phyllosilicate layer (non-centrosymmetric model). In the results of simulations, irrationality and asymmetry of the hectorite basal peaks relied straightforwardly on the BDU scattering modulations for the non-Bragg angles containing information on the synergic scattering events of phyllosilicate layer and interlayer material. Among the concerned BDU boundaries, the non-centrosymmetric model more effectively represented the real hectorite profile than the two previously reported centrosymmetric models.
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Barrette, P. D., N. K. Sinha, E. Stander, and B. Michel. "The effects of boundary conditions on the basal glide of ice crystals in compression." Journal of Materials Science 30, no. 1 (1995): 63–68. http://dx.doi.org/10.1007/bf00352132.
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Thoma, M., K. Grosfeld, C. Mayer, and F. Pattyn. "Interaction between ice sheet dynamics and subglacial lake circulation: a coupled modelling approach." Cryosphere Discussions 3, no. 3 (September 29, 2009): 805–29. http://dx.doi.org/10.5194/tcd-3-805-2009.
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Abstract. Subglacial lakes in Antarctica influence to a large extent the flow of the ice sheet. In this study we use an idealised lake geometry to study this impact. We employ a) an improved three-dimensional full Stokes ice flow model with a nonlinear rheology, b) a three-dimensional fluid dynamics model with eddy diffusion to simulate basal mass balance, and c) a newly developed coupler to exchange boundary conditions between individual models. Different boundary conditions are applied over grounded ice and floating ice. This results in significantly increased temperatures within the ice on top of the lake, compared to ice at the same depth outside the lake area. Basal melting of the ice sheet increases this lateral temperature gradient. Upstream the ice flow converges towards the lake and accelerates by about 10% whenever basal melting at the ice–lake boundary is present. Above and downstream of the lake, where the ice flow diverges, a velocity decrease of about 10% is simulated.
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Huybrechts, Philippe. "Basal temperature conditions of the Greenland ice sheet during the glacial cycles." Annals of Glaciology 23 (1996): 226–36. http://dx.doi.org/10.1017/s0260305500013483.
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A high-resolution, three-dimensional thermomechanical ice-sheet model, which includes isostasy, the possibility of ice-sheet expansion on the continental shelf and refined climatic parameterizations, was used to investigate the basal thermal regime of the Greenland ice sheet. The thermodynamic calculations take into account the usual terms of heat flow within the ice, a thermally active bedrock layer and all of the effects associated with changes in ice thickness and flow pattern. Basal temperature conditions are documented with respect to glacial–interracial shifts in climatic boundary conditions, both in steady state as during simulations over the last two glacial cycles using the GRIP δ 180 record. It is found that the basal temperature field shows a large sensitivity in steady-state experiments but that, during a glacial cycle, basal temperature variations are strongly damped, in particular in central areas. A comparison has been made with measured data from deep ice cores and the implications are discussed.
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Huybrechts, Philippe. "Basal temperature conditions of the Greenland ice sheet during the glacial cycles." Annals of Glaciology 23 (1996): 226–36. http://dx.doi.org/10.3189/s0260305500013483.
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A high-resolution, three-dimensional thermomechanical ice-sheet model, which includes isostasy, the possibility of ice-sheet expansion on the continental shelf and refined climatic parameterizations, was used to investigate the basal thermal regime of the Greenland ice sheet. The thermodynamic calculations take into account the usual terms of heat flow within the ice, a thermally active bedrock layer and all of the effects associated with changes in ice thickness and flow pattern. Basal temperature conditions are documented with respect to glacial–interracial shifts in climatic boundary conditions, both in steady state as during simulations over the last two glacial cycles using the GRIP δ180 record. It is found that the basal temperature field shows a large sensitivity in steady-state experiments but that, during a glacial cycle, basal temperature variations are strongly damped, in particular in central areas. A comparison has been made with measured data from deep ice cores and the implications are discussed.
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Thoma, M., K. Grosfeld, C. Mayer, and F. Pattyn. "Interaction between ice sheet dynamics and subglacial lake circulation: a coupled modelling approach." Cryosphere 4, no. 1 (January 8, 2010): 1–12. http://dx.doi.org/10.5194/tc-4-1-2010.
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Abstract. Subglacial lakes in Antarctica influence to a large extent the flow of the ice sheet. In this study we use an idealised lake geometry to study this impact. We employ a) an improved three-dimensional full-Stokes ice flow model with a nonlinear rheology, b) a three-dimensional fluid dynamics model with eddy diffusion to simulate the basal mass balance at the lake-ice interface, and c) a newly developed coupler to exchange boundary conditions between the two individual models. Different boundary conditions are applied over grounded ice and floating ice. This results in significantly increased temperatures within the ice on top of the lake, compared to ice at the same depth outside the lake area. Basal melting of the ice sheet increases this lateral temperature gradient. Upstream the ice flow converges towards the lake and accelerates by about 10% whenever basal melting at the ice-lake boundary is present. Above and downstream of the lake, where the ice flow diverges, a velocity decrease of about 10% is simulated.
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Tsai, Victor C., Andrew L. Stewart, and Andrew F. Thompson. "Marine ice-sheet profiles and stability under Coulomb basal conditions." Journal of Glaciology 61, no. 226 (2015): 205–15. http://dx.doi.org/10.3189/2015jog14j221.
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AbstractThe behavior of marine-terminating ice sheets, such as the West Antarctic ice sheet, is of interest due to the possibility of rapid grounding-line retreat and consequent catastrophic loss of ice. Critical to modeling this behavior is a choice of basal rheology, where the most popular approach is to relate the ice-sheet velocity to a power-law function of basal stress. Recent experiments, however, suggest that near-grounding line tills exhibit Coulomb friction behavior. Here we address how Coulomb conditions modify ice-sheet profiles and stability criteria. The basal rheology necessarily transitions to Coulomb friction near the grounding line, due to low effective stresses, leading to changes in ice-sheet properties within a narrow boundary layer. Ice-sheet profiles ‘taper off’ towards a flatter upper surface, compared with the power-law case, and basal stresses vanish at the grounding line, consistent with observations. In the Coulomb case, the grounding-line ice flux also depends more strongly on flotation ice thickness, which implies that ice sheets are more sensitive to climate perturbations. Furthermore, with Coulomb friction, the ice sheet grounds stably in shallower water than with a power-law rheology. This implies that smaller perturbations are required to push the grounding line into regions of negative bed slope, where it would become unstable. These results have important implications for ice-sheet stability in a warming climate.
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Grima, C., I. Koch, J. S. Greenbaum, K. M. Soderlund, D. D. Blankenship, D. A. Young, D. M. Schroeder, and S. Fitzsimons. "Surface and basal boundary conditions at the Southern McMurdo and Ross Ice Shelves, Antarctica – CORRIGENDUM." Journal of Glaciology 66, no. 256 (November 15, 2019): 348. http://dx.doi.org/10.1017/jog.2019.86.
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Lin, Zhu-Yuan, Yi-Shu Wang, Chao-Sheng Tang, Qing Cheng, Hao Zeng, Chun Liu, and Bin Shi. "Discrete element modelling of desiccation cracking in thin clay layer under different basal boundary conditions." Computers and Geotechnics 130 (February 2021): 103931. http://dx.doi.org/10.1016/j.compgeo.2020.103931.
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Blasco, Javier, Jorge Alvarez-Solas, Alexander Robinson, and Marisa Montoya. "Exploring the impact of atmospheric forcing and basal drag on the Antarctic Ice Sheet under Last Glacial Maximum conditions." Cryosphere 15, no. 1 (January 18, 2021): 215–31. http://dx.doi.org/10.5194/tc-15-215-2021.
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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.
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Habermann, M., M. Truffer, and D. Maxwell. "Changing basal conditions during the speed-up of Jakobshavn Isbræ, Greenland." Cryosphere Discussions 7, no. 3 (June 1, 2013): 2153–90. http://dx.doi.org/10.5194/tcd-7-2153-2013.
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Abstract. Ice-sheet outlet glaciers can undergo dynamic changes such as the rapid speed-up of Jakobshavn Isbræ following the disintegration of its floating ice tongue. These changes are associated with stress changes on the boundary of the ice mass. We investigate the basal conditions throughout a well-observed period of rapid change and evaluate parameterizations currently used in ice-sheet models. A Tikhonov inverse method with a Shallow Shelf Approximation forward model is used for diagnostic inversions for the years 1985, 2000, 2005, 2006 and 2008. Our ice softness, model norm, and regularization parameter choices are justified using the data-model misfit metric and the L-curve method. The sensitivity of the inversion results to these parameter choices is explored. We find a lowering of basal yield stress in the first 7 km of the 2008 grounding line and no significant changes higher upstream. The temporal evolution in the fast flow area is in broad agreement with a Mohr–Coulomb parameterization of basal shear stress, but with a till friction angle much lower than has been measured for till samples. The lowering of basal yield stress is significant within the uncertainties of the inversion, but it cannot be ruled out that there are other significant contributors to the acceleration of the glacier.
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Habermann, M., M. Truffer, and D. Maxwell. "Changing basal conditions during the speed-up of Jakobshavn Isbræ, Greenland." Cryosphere 7, no. 6 (November 7, 2013): 1679–92. http://dx.doi.org/10.5194/tc-7-1679-2013.
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Abstract. Ice-sheet outlet glaciers can undergo dynamic changes such as the rapid speed-up of Jakobshavn Isbræ following the disintegration of its floating ice tongue. These changes are associated with stress changes on the boundary of the ice mass. We invert for basal conditions from surface velocity data throughout a well-observed period of rapid change and evaluate parameterizations currently used in ice-sheet models. A Tikhonov inverse method with a shallow-shelf approximation forward model is used for diagnostic inversions for the years 1985, 2000, 2005, 2006 and 2008. Our ice-softness, model norm, and regularization parameter choices are justified using the data-model misfit metric and the L curve method. The sensitivity of the inversion results to these parameter choices is explored. We find a lowering of effective basal yield stress in the first 7 km upstream from the 2008 grounding line and no significant changes higher upstream. The temporal evolution in the fast flow area is in broad agreement with a Mohr–Coulomb parameterization of basal shear stress, but with a till friction angle much lower than has been measured for till samples. The lowering of effective basal yield stress is significant within the uncertainties of the inversion, but it cannot be ruled out that there are other significant contributors to the acceleration of the glacier.
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Van Liefferinge, B., and F. Pattyn. "Using ice-flow models to evaluate potential sites of million year-old ice in Antarctica." Climate of the Past Discussions 9, no. 3 (May 28, 2013): 2859–87. http://dx.doi.org/10.5194/cpd-9-2859-2013.
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Abstract. Finding suitable potential sites for an undisturbed record of million-year old ice in Antarctica requires a slow-moving ice sheet (preferably an ice divide) and basal conditions that are not disturbed by large topographic variations. Furthermore, ice should be thick and cold basal conditions should prevail, since basal melting would destroy the bottom layers. However, thick ice (needed to resolve the signal at sufficient high resolution) increases basal temperatures, which is a conflicting condition in view of finding a suitable drill site. In addition, slow moving areas in the center of ice sheets are also low-accumulation areas, and low accumulation reduces potential cooling of the ice through vertical advection. While boundary conditions such as ice thickness and accumulation rates are relatively well constraint, the major uncertainty in determining basal conditions resides in the geothermal heat flow (GHF) underneath the ice sheet. We explore uncertainties in existing GHF datasets and their effect on basal temperatures of the Antarctic ice sheet and propose an updated method based on Pattyn (2010) to improve existing GHF datasets in agreement with known basal temperatures and their gradients to reduce this uncertainty. Both complementary methods lead to a better comprehension of basal temperature sensitivity and a characterization of potential ice coring sites within these uncertainties.
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Akhmadullin, I. Sh. "Manifestation of Basal-Plane Anisotropy and Mechanical Boundary Conditions in Magnetic Birefringence of Sound in Hematite." Physics of the Solid State 47, no. 3 (2005): 523. http://dx.doi.org/10.1134/1.1884716.
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Shoemaker, E. M. "A Subglacial Boundary-layer Regelation Mechanism." Journal of Glaciology 36, no. 124 (1990): 263–68. http://dx.doi.org/10.3189/002214390793701309.
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AbstractHeat input to basal ice at subglacial low-pressure regions, such as exist on the lee side of bed bumps including regions of ice-bed separation, is shown to melt basal ice internally in a narrow boundary layer at most centimeters thick. Before ice at the ice-bed interface can begin to melt, the heat input Q must exceed a critical value Q*. Q* increases rapidly with an increase in the difference ΔΡ between the nominal (global) overburden pressure and the magnitude of the (local) normal stress acting between the ice and bed or ice and water pocket. Because of the non-linear nature of the flow law, the thickness of the boundary layer decreases rapidly with increasing ΔΡ. The ice in the boundary layer is likely to be soft with a high water content. Under certain conditions, a regelation cycle may exist between the boundary layer and the water in a subglacial cavity. The boundary layer is sufficiently narrow that the processes can reach steady state while ice traverses subglacial low-pressure regions of length the order of 0.01–0.1 m. The regelation phenomenon may preserve or aid the formation of narrow debris-rich ice layers at the base of temperate glaciers.
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Moore, Peter L., Neal R. Iverson, and Denis Cohen. "Ice flow across a warm-based/cold-based transition at a glacier margin." Annals of Glaciology 50, no. 52 (2009): 1–8. http://dx.doi.org/10.3189/172756409789624319.
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AbstractWhere polythermal glaciers have frozen margins that buttress otherwise temperate-based sliding ice, longitudinal compression can strongly influence ice-flow trajectory, and consequently sediment transport paths. Past efforts to model flow in the vicinity of a basal thermal transition (BTT) have generally relied on simplified boundary conditions or rheological idealizations, making these model results difficult to apply to real glacier termini. Herein, we present results of numerical simulations using a power-law rheology and with boundary conditions that better represent the frozen margin. Model results indicate that a transition to a non-sliding frozen margin causes a decline in surface velocity made possible by upward ice flow, implying either enhanced ablation for steady-state simulations or the formation of a surface bulge. Permitting ice loss by ablation combined with numerical smoothing of the basal slip transition subdues basal stress concentrations and thereby inhibits development of structural discontinuities such as thrust faults. Upward ice flow is accommodated by vertical extension up-glacier of the BTT. This strain regime can potentially account for key structural features in polythermal glacier termini without appealing to thrusting.
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Pocivavsek, Luka, Ann Junghans, Noureddine Zebda, Konstantin Birukov, and Jaroslaw Majewski. "Tuning endothelial monolayer adhesion: a neutron reflectivity study." American Journal of Physiology-Lung Cellular and Molecular Physiology 306, no. 1 (January 1, 2014): L1—L9. http://dx.doi.org/10.1152/ajplung.00160.2013.
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Endothelial cells, master gatekeepers of the cardiovascular system, line its inner boundary from the heart to distant capillaries constantly exposed to blood flow. Interendothelial signaling and the monolayers adhesion to the underlying collagen-rich basal lamina are key in physiology and disease. Using neutron scattering, we report the first ever interfacial structure of endothelial monolayers under dynamic flow conditions mimicking the cardiovascular system. Endothelial adhesion (defined as the separation distance ℓ between the basal cell membrane and solid boundary) is explained using developed interfacial potentials and intramembrane segregation of specific adhesion proteins. Our method provides a powerful tool for the biophysical study of cellular layer adhesion strength in living tissues.
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JIMÉNEZ, STEPHEN, and RAVINDRA DUDDU. "On the evaluation of the stress intensity factor in calving models using linear elastic fracture mechanics." Journal of Glaciology 64, no. 247 (September 10, 2018): 759–70. http://dx.doi.org/10.1017/jog.2018.64.
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ABSTRACTWe investigate the appropriateness of calving or crevasse models from the literature using linear elastic fracture mechanics (LEFM). To this end, we compare LEFM model-predicted stress intensity factors (SIFs) against numerically computed SIFs using the displacement correlation method in conjunction with the finite element method. We present several benchmark simulations wherein we calculate the SIF at the tips of water-filled surface and basal crevasses penetrating through rectangular ice slabs under different boundary conditions, including grounded and floating conditions. Our simulation results indicate that the basal boundary condition significantly influences the SIF at the crevasse tips. We find that the existing calving models using LEFM are not generally accurate for evaluating SIFs in grounded glaciers or floating ice shelves. We also illustrate that using the ‘single edge crack’ weight function in the LEFM formulations may be appropriate for predicting calving from floating ice shelves, owing to the low fracture toughness of ice; whereas, using the ‘double edge crack’ or ‘central through crack’ weight functions is more appropriate for predicting calving from grounded glaciers. To conclude, we recommend using the displacement correlation method for SIF evaluation in real glaciers and ice shelves with complex geometries and boundary conditions.
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Sargent, A., and J. L. Fastook. "Manufactured analytical solutions for isothermal full-Stokes ice sheet models." Cryosphere 4, no. 3 (August 18, 2010): 285–311. http://dx.doi.org/10.5194/tc-4-285-2010.
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Abstract. We present the detailed construction of a manufactured analytical solution to time-dependent and steady-state isothermal full-Stokes ice sheet problems. The solutions are constructed for two-dimensional flowline and three-dimensional full-Stokes ice sheet models with variable viscosity. The construction is done by choosing for the specified ice surface and bed a velocity distribution that satisfies both mass conservation and the kinematic boundary conditions. Then a compensatory stress term in the conservation of momentum equations and their boundary conditions is calculated to make the chosen velocity distributions as well as the chosen pressure field into exact solutions. By substituting different ice surface and bed geometry formulas into the derived solution formulas, analytical solutions for different geometries can be constructed. The boundary conditions can be specified as essential Dirichlet conditions or as periodic boundary conditions. By changing a parameter value, the analytical solutions allow investigation of algorithms for a different range of aspect ratios as well as for different, frozen or sliding, basal conditions. The analytical solutions can also be used to estimate the numerical error of the method in the case when the effects of the boundary conditions are eliminated, that is, when the exact solution values are specified as inflow and outflow boundary conditions.
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Sargent, A., and J. L. Fastook. "Manufactured analytical solutions for isothermal full-Stokes ice sheet models." Cryosphere Discussions 4, no. 2 (April 8, 2010): 495–560. http://dx.doi.org/10.5194/tcd-4-495-2010.
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Abstract. We present the detailed construction of an exact solution to time-dependent and steady-state isothermal full-Stokes ice sheet problems. The solutions are constructed for two-dimensional flowline and three-dimensional full-Stokes ice sheet models with variable viscosity. The construction is done by choosing for the specified ice surface and bed a velocity distribution that satisfies both mass conservation and the kinematic boundary conditions. Then a compensatory stress term in the conservation of momentum equations and their boundary conditions is calculated to make the chosen velocity distributions as well as the chosen pressure field into exact solutions. By substituting different ice surface and bed geometry formulas into the derived solution formulas, analytical solutions for different geometries can be constructed. The boundary conditions can be specified as essential Dirichlet conditions or as periodic boundary conditions. By changing a parameter value, the analytical solutions allow investigation of algorithms for a different range of aspect ratios as well as for different, frozen or sliding, basal conditions. The analytical solutions can also be used to estimate the numerical error of the method in the case when the effects of the boundary conditions are eliminated, that is, when the exact solution values are specified as inflow and outflow boundary conditions.
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Banerjee, Indranil, Santosh K. Ghosh, Hugh J. Abercrombie, and Edward H. Davies. "An integrated subsurface study of the Mannville–Colorado group boundary in the Cessford Field, Alberta." Canadian Journal of Earth Sciences 31, no. 3 (March 1, 1994): 489–504. http://dx.doi.org/10.1139/e94-044.
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The stratigraphic boundary separating the Mannville and the Colorado groups in Alberta, occupying incised valleys cut within the Upper Mannville strata, has previously been interpreted as an unconformity recording post-Mannville erosion followed by a late Albian marine transgression initiated by the deposition of the Joli Fou Shale and locally by the Basal Colorado Sandstone (both of the Colorado Group). Sedimentology, paleontology, organic and inorganic geochemistry, mineralogy, and petrography of strata above and below the unconformity or the sequence boundary have been studied in 106 samples from 37 wells within the Cessford Field covering an area of 3600 km2. Cores through the boundary show a distinct physical break represented by a scoured surface overlain by basal conglomerates. Paleontological data, based on dinoflagellates and foraminifers, show establishment of restricted marine conditions in the Basal Colorado times (initial transgression) and onset of open marine condition (maximum flooding) during the Joli Fou times. Although paleosol horizons have not been found near the boundary, influence of meteoric water in the Upper Mannville sandstones is inferred from development of spherulitic siderite and extensive early kaolinization of the feldspar, mica, and lithic grains. The absence of paleosol or fluvial strata within the incised valley fills suggests that the subaerial unconformity was modified by tidal erosion during the Joli Fou transgression.
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Brinkerhoff, Douglas J., Toby W. Meierbachtol, Jesse V. Johnson, and Joel T. Harper. "Sensitivity of the frozen/melted basal boundary to perturbations of basal traction and geothermal heat flux: Isunnguata Sermia, western Greenland." Annals of Glaciology 52, no. 59 (2011): 43–50. http://dx.doi.org/10.3189/172756411799096330.
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AbstractA full-stress, thermomechanically coupled, numerical model is used to explore the interaction between basal thermal conditions and motion of a terrestrially terminating section of the west Greenland ice sheet. The model domain is a two-dimensional flowline profile extending from the ice divide to the margin. We use data-assimilation techniques based on the adjoint model in order to optimize the basal traction field, minimizing the difference between modeled and observed surface velocities. We monitor the sensitivity of the frozen/melted boundary (FMB) to changes in prescribed geothermal heat flux and sliding speed by applying perturbations to each of these parameters. The FMB shows sensitivity to the prescribed geothermal heat flux below an upper threshold where a maximum portion of the bed is already melted. The position of the FMB is insensitive to perturbations applied to the basal traction field. This insensitivity is due to the short distances over which longitudinal stresses act in an ice sheet.
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Alley, Richard B. "Multiple Steady States in Ice-Water-Till Systems." Annals of Glaciology 14 (1990): 1–5. http://dx.doi.org/10.1017/s0260305500008132.
Full textAbstract:
An ice sheet with fixed boundary conditions may have two steady configurations, as shown by a new one-dimensional model including the physics and continuity of ice, water, and deforming subglacial till. In one steady state, a steep surface slope causes rapid internal ice shearing but forces basal water through subglacial aquifers, suppressing basal velocity; in the other steady state, a gentle surface slope causes only slow ice shearing but allows water to lubricate the ice-bed interface and cause rapid basal velocities. Small climatic forcing may cause large ice-sheet response during a switch between steady states.
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Alley, Richard B. "Multiple Steady States in Ice-Water-Till Systems." Annals of Glaciology 14 (1990): 1–5. http://dx.doi.org/10.3189/s0260305500008132.
Full textAbstract:
An ice sheet with fixed boundary conditions may have two steady configurations, as shown by a new one-dimensional model including the physics and continuity of ice, water, and deforming subglacial till. In one steady state, a steep surface slope causes rapid internal ice shearing but forces basal water through subglacial aquifers, suppressing basal velocity; in the other steady state, a gentle surface slope causes only slow ice shearing but allows water to lubricate the ice-bed interface and cause rapid basal velocities. Small climatic forcing may cause large ice-sheet response during a switch between steady states.
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Souchez, R., M. Lemmens, J. L. Tison, R. Lorrain, and L. Janssens. "Reconstruction of basal boundary conditions at the Greenland Ice Sheet margin from gas composition in the ice." Earth and Planetary Science Letters 118, no. 1-4 (July 1993): 327–33. http://dx.doi.org/10.1016/0012-821x(93)90176-a.
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Colinge, Jacques, and Heinz Blatter. "Stress and velocity fields in glaciers: Part I. Finite-difference schemes for higher-order glacier models." Journal of Glaciology 44, no. 148 (1998): 448–56. http://dx.doi.org/10.3189/s0022143000001969.
Full textAbstract:
AbstractThe set of force equations and stress strain-rate relations for ice masses can be solved with the method of lines and shooting the stress-free conditions at the free surface. Single- and multiple-shooting schemes with fixed point or Newton iterations for solving the stress equations including the deviatoric stress gradients are described and their performances arc discussed. The single-shooting Newton iteration proved to be the fastest seheme for typical valley glaciers, although its horizontal grid limitation is restrictive. Grid resolution can be improved substantially with a multiple-shooting scheme but computation time and storage requirements increase substantially. The Newton iteration allows the handling of mixed basal boundary conditions, partly basal velocity and partly basal shear traction being prescribed. A stick slip free gravity flow illustrates the performance of the scheme.
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Colinge, Jacques, and Heinz Blatter. "Stress and velocity fields in glaciers: Part I. Finite-difference schemes for higher-order glacier models." Journal of Glaciology 44, no. 148 (1998): 448–56. http://dx.doi.org/10.1017/s0022143000001969.
Full textAbstract:
AbstractThe set of force equations and stress strain-rate relations for ice masses can be solved with the method of lines and shooting the stress-free conditions at the free surface. Single- and multiple-shooting schemes with fixed point or Newton iterations for solving the stress equations including the deviatoric stress gradients are described and their performances arc discussed. The single-shooting Newton iteration proved to be the fastest seheme for typical valley glaciers, although its horizontal grid limitation is restrictive. Grid resolution can be improved substantially with a multiple-shooting scheme but computation time and storage requirements increase substantially. The Newton iteration allows the handling of mixed basal boundary conditions, partly basal velocity and partly basal shear traction being prescribed. A stick slip free gravity flow illustrates the performance of the scheme.
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Van Liefferinge, B., and F. Pattyn. "Using ice-flow models to evaluate potential sites of million year-old ice in Antarctica." Climate of the Past 9, no. 5 (October 18, 2013): 2335–45. http://dx.doi.org/10.5194/cp-9-2335-2013.
Full textAbstract:
Abstract. Finding suitable potential sites for an undisturbed record of million-year old ice in Antarctica requires slow-moving ice (preferably an ice divide) and basal conditions that are not disturbed by large topographic variations. Furthermore, ice should be thick and cold basal conditions should prevail, since basal melting would destroy the bottom layers. However, thick ice (needed to resolve the signal at sufficient high resolution) increases basal temperatures, which is a conflicting condition for finding a suitable drill site. In addition, slow moving areas in the center of ice sheets are also low-accumulation areas, and low accumulation reduces potential cooling of the ice through vertical advection. While boundary conditions such as ice thickness and accumulation rates are relatively well constrained, the major uncertainty in determining basal thermal conditions resides in the geothermal heat flow (GHF) underneath the ice sheet. We explore uncertainties in existing GHF data sets and their effect on basal temperatures of the Antarctic Ice Sheet, and propose an updated method based on Pattyn (2010) to improve existing GHF data sets in agreement with known basal temperatures and their gradients to reduce this uncertainty. Both complementary methods lead to a better comprehension of basal temperature sensitivity and a characterization of potential ice coring sites within these uncertainties. The combination of both modeling approaches show that the most likely oldest ice sites are situated near the divide areas (close to existing deep drilling sites, but in areas of smaller ice thickness) and across the Gamburtsev Subglacial Mountains.
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SCHOOF, CHRISTIAN. "Marine ice sheet dynamics. Part 2. A Stokes flow contact problem." Journal of Fluid Mechanics 679 (May 17, 2011): 122–55. http://dx.doi.org/10.1017/jfm.2011.129.
Full textAbstract:
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.
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Thorp, Peter W. "Surface profiles and basal shear stresses of outlet glaciers from a Late-glacial mountain ice field in western Scotland." Journal of Glaciology 37, no. 125 (1991): 77–88. http://dx.doi.org/10.1017/s0022143000042829.
Full textAbstract:
AbstractSurface and basal long profiles are reconstructed for 13 outlet glaciers that drained ice from a large ice field (80 km by 120 km) that formed in the western Grampians of Scotland during part of the Late-glacial period (c, 14000–10000years BP). Basal shear stresses are calculated at 5 km intervals along the central flowlines of the reconstructed outlet glaciers. Individual basal shear stresses for the outlet glaciers range from 10 to 204 kPa. Variations in calculated basal shear stresses within and between the glaciers are mainly explained by differences in bedrock topography, extending and compressional flow, and by differences in basal boundary conditions. Low basal shear stresses (<53kPa) calculated for the terminal zones of Creran, Menteith and Lomond glaciers are partly explained by the overriding of glaciomarine clays with inferred high pore-water pressures and a low yield strength that may have led to rapid basal sliding and thinning of the ice lobes.
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Thorp, Peter W. "Surface profiles and basal shear stresses of outlet glaciers from a Late-glacial mountain ice field in western Scotland." Journal of Glaciology 37, no. 125 (1991): 77–88. http://dx.doi.org/10.3189/s0022143000042829.
Full textAbstract:
Abstract Surface and basal long profiles are reconstructed for 13 outlet glaciers that drained ice from a large ice field (80 km by 120 km) that formed in the western Grampians of Scotland during part of the Late-glacial period (c, 14000–10000years BP). Basal shear stresses are calculated at 5 km intervals along the central flowlines of the reconstructed outlet glaciers. Individual basal shear stresses for the outlet glaciers range from 10 to 204 kPa. Variations in calculated basal shear stresses within and between the glaciers are mainly explained by differences in bedrock topography, extending and compressional flow, and by differences in basal boundary conditions. Low basal shear stresses (<53kPa) calculated for the terminal zones of Creran, Menteith and Lomond glaciers are partly explained by the overriding of glaciomarine clays with inferred high pore-water pressures and a low yield strength that may have led to rapid basal sliding and thinning of the ice lobes.
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Llorens, Maria-Gema, Albert Griera, Florian Steinbach, Paul D. Bons, Enrique Gomez-Rivas, Daniela Jansen, Jens Roessiger, Ricardo A. Lebensohn, and Ilka Weikusat. "Dynamic recrystallization during deformation of polycrystalline ice: insights from numerical simulations." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 375, no. 2086 (February 13, 2017): 20150346. http://dx.doi.org/10.1098/rsta.2015.0346.
Full textAbstract:
The flow of glaciers and polar ice sheets is controlled by the highly anisotropic rheology of ice crystals that have hexagonal symmetry (ice lh). To improve our knowledge of ice sheet dynamics, it is necessary to understand how dynamic recrystallization (DRX) controls ice microstructures and rheology at different boundary conditions that range from pure shear flattening at the top to simple shear near the base of the sheets. We present a series of two-dimensional numerical simulations that couple ice deformation with DRX of various intensities, paying special attention to the effect of boundary conditions. The simulations show how similar orientations of c -axis maxima with respect to the finite deformation direction develop regardless of the amount of DRX and applied boundary conditions. In pure shear this direction is parallel to the maximum compressional stress, while it rotates towards the shear direction in simple shear. This leads to strain hardening and increased activity of non-basal slip systems in pure shear and to strain softening in simple shear. Therefore, it is expected that ice is effectively weaker in the lower parts of the ice sheets than in the upper parts. Strain-rate localization occurs in all simulations, especially in simple shear cases. Recrystallization suppresses localization, which necessitates the activation of hard, non-basal slip systems. This article is part of the themed issue ‘Microdynamics of ice’.
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Raymond, Charles. "Shear margins in glaciers and ice sheets." Journal of Glaciology 42, no. 140 (1996): 90–102. http://dx.doi.org/10.1017/s0022143000030550.
Full textAbstract:
AbstractAnalytical and numerical techniques are used to examine the flow response of a sloped slab of power-law fluid (powern) subjected to basal boundary conditions that vary spatially across the flow direction, as for example near an ice-stream margin with planar basal topography. The primary assumption is that basal shear stress is proportional to the basal speed times a spatially variable slip resistance. The ratio of mean basal speed to the speed originating from shearing through the thickness. denoted asr, gives a measure of how slippery the bed is. The principal conclusion is that a localized disturbance in slip resistance affects the basal stress and speed in a zone spread over a greater width of the flow. In units of ice thicknessH, the spatial scale of spreading is proportional to a single dimensionless numberRn≡ (r/n+ 1)1/n+1derived fromnandr. The consequence for a shear zone above a sharp jump in slip resistance is that the shearing is spread out over a boundary layer with a width proportional toRn. For an ice stream caused by a band of low slip resistance with a half-width ofw H, the margins influence velocity and stress in the central part of the band depending onRnin comparison tow. Three regimes can be identified, which forn= 3 are quantified as follows: lowrdefined asR3< 0.1w, for which the central flow is essentially unaffected by the margins and the driving stress is supported entire by by basal drag; highrdefined asR3> 1w, for which the boundary layers from both sides bridge across the full flow width and the driving stress in the center is supported almost entirely by side drag; intermediater, for which the driving stress in the center is supported by a combination of basal and side drag. Shear zones that are narrower than predicted on the basis of this theory (≈R3) would require localized softening of the ice to explain the concentration of deformation at a shorter scale.
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Pollard, D., and R. M. DeConto. "A simple inverse method for the distribution of basal sliding coefficients under ice sheets, applied to Antarctica." Cryosphere 6, no. 5 (September 12, 2012): 953–71. http://dx.doi.org/10.5194/tc-6-953-2012.
Full textAbstract:
Abstract. Variations in intrinsic bed conditions that affect basal sliding, such as the distribution of deformable sediment versus hard bedrock, are important boundary conditions for large-scale ice-sheet models, but are hard to observe and remain largely uncertain below the modern Greenland and Antarctic ice sheets. Here a very simple model-based method is described for deducing the modern spatial distribution of basal sliding coefficients. The model is run forward in time, and the basal sliding coefficient at each grid point is periodically increased or decreased depending on whether the local ice surface elevation is too high or too low compared to observed in areas of unfrozen bed. The method considerably reduces large-scale errors in Antarctic ice elevation, from several 100s to several 10s of meters in most regions. Remaining ice elevation errors over mountain ranges such as the Transantarctics are further improved by parameterizing the possible effect of sub-grid topography in the basal sliding law, representing sliding in deep valleys. Results are compared with modern velocity data, and various sensitivity tests are described in Appendices.
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Kjøll, H. J., G. Viola, L. Menegon, and B. E. Sørensen. "Brittle–viscous deformation of vein quartz under fluid-rich low greenschist facies conditions." Solid Earth Discussions 7, no. 1 (January 23, 2015): 213–57. http://dx.doi.org/10.5194/sed-7-213-2015.
Full textAbstract:
Abstract. A coarse grained, statically crystallized quartz vein, embedded in a phyllonitic matrix, was studied by EBSD and optical microscopy to gain insights into the processes of strain localization in quartz deformed under low-grade conditions, broadly coincident with the frictional–viscous transition. The vein is from a high strain zone at the front of the Porsa Imbricate Stack in the Paleoproterozoic Repparfjord Tectonic Window in northern Norway. The vein was deformed under lower greenschist facies conditions during deformation along a large out-of-sequence phyllonitic thrust of Caledonian age. The host phyllonite formed at the expense of metabasalt wherein feldspar broke down to form interconnected layers of fine, synkinematic phyllosilicates. In the mechanically weak framework of the phyllonite, the studied quartz vein acted as a relatively rigid body deforming mainly by coaxial strain. Viscous deformation was initially accommodated by basal ⟨a⟩ slip of quartz during the development of a mesoscopic pervasive extensional crenulation cleavage. Under the prevailing boundary conditions, however, dislocation glide-accommodated deformation of quartz resulted inefficient and led to dislocation tangling and strain hardening of the vein. In response to hardening, to the progressive increase of fluid pressure and the increasing competence contrast between the vein and the weak foliated host phyllonite, quartz crystals began to deform frictionally along specific, optimally oriented lattice planes, creating microgouges along microfractures. These were, however, rapidly sealed by nucleation of new grains as transiently over pressured fluids penetrated the deforming system. The new nucleated grains grew initially by solution-precipitation and later by grain boundary migration. Due to the random initial orientation of the vein crystals, strain was accommodated differently in the individual crystals, leading to the development of remarkably different microstructures. Crystals oriented optimally for basal slip accommodated strain mainly viscously and experienced only minor fracturing. Instead, the crystals misoriented for basal slip hardened and deformed by pervasive domainal fracturing. This study indicates the importance of considering shear zones as dynamic systems wherein the activated deformation mechanisms vary transiently in response to the complex temporal and spatial evolution of the shear zone, often in a cyclic fashion.
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Wu, T., K. Jöhnk, B. Svendsen, and K. Hutter. "On the gravity-driven shear flow of an ice–till mixture." Annals of Glaciology 23 (1996): 124–28. http://dx.doi.org/10.1017/s0260305500013331.
Full textAbstract:
In this work, we formulate a model for the isothermal flow of a (basal) ice–till mixture that is overlain by a layer of pure ice. Such a model is relevant to the case of a glacier or ice sheet possessing a till at its base. To this end, ice is treated as usual as a constant true-density, very viscous fluid, while till, which is assumed to consist of sediment and bound (i.e. moving with the sediment) interstitial water, is also assumed in a first approximation to behave as such a fluid. Since the mixture is assumed isothermal, only the mass- and momentum-balance relations for till and ice need be considered. To complete the model, no-slip and stress-free boundary conditions are assumed at the base and free surface, respectively. By working with the former conditions, we neglect the process of entrainment of sediment into the basal layer, concentrating rather on its flow behaviour and thickness. The transition from the till–ice mixture layer to the overlaying pure ice layer is idealized in the model as a moving interface representing in the simplest case the till material boundary, at which jump-balance relations for till and ice apply. As in the basal layer, till and ice are assumed to interact mechanically at this interface. In the context of the thin-layer approximation, numerical solutions of the lowest-order form of the model show that it is predominantly the thickness of the basal (mixture) layer that is influenced by the ice–till momentum interaction.
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Wu, T., K. Jöhnk, B. Svendsen, and K. Hutter. "On the gravity-driven shear flow of an ice–till mixture." Annals of Glaciology 23 (1996): 124–28. http://dx.doi.org/10.3189/s0260305500013331.
Full textAbstract:
In this work, we formulate a model for the isothermal flow of a (basal) ice–till mixture that is overlain by a layer of pure ice. Such a model is relevant to the case of a glacier or ice sheet possessing a till at its base. To this end, ice is treated as usual as a constant true-density, very viscous fluid, while till, which is assumed to consist of sediment and bound (i.e. moving with the sediment) interstitial water, is also assumed in a first approximation to behave as such a fluid. Since the mixture is assumed isothermal, only the mass- and momentum-balance relations for till and ice need be considered. To complete the model, no-slip and stress-free boundary conditions are assumed at the base and free surface, respectively. By working with the former conditions, we neglect the process of entrainment of sediment into the basal layer, concentrating rather on its flow behaviour and thickness. The transition from the till–ice mixture layer to the overlaying pure ice layer is idealized in the model as a moving interface representing in the simplest case the till material boundary, at which jump-balance relations for till and ice apply. As in the basal layer, till and ice are assumed to interact mechanically at this interface. In the context of the thin-layer approximation, numerical solutions of the lowest-order form of the model show that it is predominantly the thickness of the basal (mixture) layer that is influenced by the ice–till momentum interaction.
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Albrecht, Torsten, Ricarda Winkelmann, and Anders Levermann. "Glacial-cycle simulations of the Antarctic Ice Sheet with the Parallel Ice Sheet Model (PISM) – Part 1: Boundary conditions and climatic forcing." Cryosphere 14, no. 2 (February 14, 2020): 599–632. http://dx.doi.org/10.5194/tc-14-599-2020.
Full textAbstract:
Abstract. Simulations of the glacial–interglacial history of the Antarctic Ice Sheet provide insights into dynamic threshold behavior and estimates of the ice sheet's contributions to global sea-level changes for the past, present and future. However, boundary conditions are weakly constrained, in particular at the interface of the ice sheet and the bedrock. Also climatic forcing covering the last glacial cycles is uncertain, as it is based on sparse proxy data. We use the Parallel Ice Sheet Model (PISM) to investigate the dynamic effects of different choices of input data, e.g., for modern basal heat flux or reconstructions of past changes of sea level and surface temperature. As computational resources are limited, glacial-cycle simulations are performed using a comparably coarse model grid of 16 km and various parameterizations, e.g., for basal sliding, iceberg calving, or for past variations in precipitation and ocean temperatures. In this study we evaluate the model's transient sensitivity to corresponding parameter choices and to different boundary conditions over the last two glacial cycles and provide estimates of involved uncertainties. We also discuss isolated and combined effects of climate and sea-level forcing. Hence, this study serves as a “cookbook” for the growing community of PISM users and paleo-ice sheet modelers in general. For each of the different model uncertainties with regard to climatic forcing, ice and Earth dynamics, and basal processes, we select one representative model parameter that captures relevant uncertainties and motivates corresponding parameter ranges that bound the observed ice volume at present. The four selected parameters are systematically varied in a parameter ensemble analysis, which is described in a companion paper.
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Siegert, M. J., N. Ross, H. Corr, B. Smith, T. Jordan, R. Bingham, F. Ferraccioli, D. Rippin, and A. Le Brocq. "Boundary conditions of an active West Antarctic subglacial lake: implications for storage of water beneath the ice sheet." Cryosphere Discussions 7, no. 3 (June 24, 2013): 2979–99. http://dx.doi.org/10.5194/tcd-7-2979-2013.
Full textAbstract:
Abstract. Repeat-pass IceSat altimetry has revealed 124 discrete surface height changes across the Antarctic Ice Sheet, interpreted to be caused by subglacial lake discharges (surface lowering) and inputs (surface uplift). Few of these active lakes have been confirmed by radio-echo sounding (RES) despite several attempts (notable exceptions are Lake Whillans and three in the Adventure Subglacial Trench). Here we present targeted RES and radar altimeter data from an "active lake" location within the upstream Institute Ice Stream, into which 0.12 km3 of water is calculated to have flowed between October 2003 and February 2008. We use a series of transects to establish an accurate appreciation of the influences of bed topography and ice-surface elevation on water storage potential. The location of surface height change is over the downslope flank of a distinct topographic hollow, where RES reveals no obvious evidence for deep (> 10 m) water. The regional hydropotential reveals a sink coincident with the surface change, however. Governed by the location of the hydrological sink, basal water will likely "drape" over existing topography in a manner dissimilar to subglacial lakes where flat strong specular RES reflections are measured. The inability of RES to detect the active lake means that more of the Antarctic ice sheet bed may contain stored water than is currently appreciated. Variation in ice surface elevation datasets leads to significant alteration in calculations of the local flow of basal water indicating the value of, and need for, high resolution RES datasets in both space and time to establish and characterise subglacial hydrological processes.
46
Raymond, Charles. "Shear margins in glaciers and ice sheets." Journal of Glaciology 42, no. 140 (1996): 90–102. http://dx.doi.org/10.3189/s0022143000030550.
Full textAbstract:
AbstractAnalytical and numerical techniques are used to examine the flow response of a sloped slab of power-law fluid (power n) subjected to basal boundary conditions that vary spatially across the flow direction, as for example near an ice-stream margin with planar basal topography. The primary assumption is that basal shear stress is proportional to the basal speed times a spatially variable slip resistance. The ratio of mean basal speed to the speed originating from shearing through the thickness. denoted as r, gives a measure of how slippery the bed is. The principal conclusion is that a localized disturbance in slip resistance affects the basal stress and speed in a zone spread over a greater width of the flow. In units of ice thickness H, the spatial scale of spreading is proportional to a single dimensionless number Rn ≡ (r/n+ 1)1/n+1 derived from n and r. The consequence for a shear zone above a sharp jump in slip resistance is that the shearing is spread out over a boundary layer with a width proportional to Rn. For an ice stream caused by a band of low slip resistance with a half-width of w H, the margins influence velocity and stress in the central part of the band depending on Rn in comparison to w. Three regimes can be identified, which for n = 3 are quantified as follows: low r defined as R3 < 0.1w, for which the central flow is essentially unaffected by the margins and the driving stress is supported entire by by basal drag; high r defined as R3 > 1w, for which the boundary layers from both sides bridge across the full flow width and the driving stress in the center is supported almost entirely by side drag; intermediate r, for which the driving stress in the center is supported by a combination of basal and side drag. Shear zones that are narrower than predicted on the basis of this theory (≈ R3) would require localized softening of the ice to explain the concentration of deformation at a shorter scale.
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Zhao, Chen, Rupert M. Gladstone, Roland C. Warner, Matt A. King, Thomas Zwinger, and Mathieu Morlighem. "Basal friction of Fleming Glacier, Antarctica – Part 1: Sensitivity of inversion to temperature and bedrock uncertainty." Cryosphere 12, no. 8 (August 15, 2018): 2637–52. http://dx.doi.org/10.5194/tc-12-2637-2018.
Full textAbstract:
Abstract. Many glaciers in the Antarctic Peninsula are now rapidly losing mass. Understanding of the dynamics of these fast-flowing glaciers, and their potential future behaviour, can be improved through ice sheet modelling studies. Inverse methods are commonly used in ice sheet models to infer the spatial distribution of a basal friction coefficient, which has a large effect on the basal velocity and ice deformation. Here we use the full-Stokes Elmer/Ice model to simulate the Wordie Ice Shelf–Fleming Glacier system in the southern Antarctic Peninsula. With an inverse method, we infer the pattern of the basal friction coefficient from surface velocities observed in 2008. We propose a multi-cycle spin-up scheme to reduce the influence of the assumed initial englacial temperature field on the final inversion. This is particularly important for glaciers like the Fleming Glacier, which have areas of strongly temperature-dependent deformational flow in the fast-flowing regions. Sensitivity tests using various bed elevation datasets, ice front positions and boundary conditions demonstrate the importance of high-accuracy ice thickness/bed geometry data and precise location of the ice front boundary.
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Pollard, D., and R. M. DeConto. "A simple inverse method for the distribution of basal sliding coefficients under ice sheets, applied to Antarctica." Cryosphere Discussions 6, no. 2 (April 12, 2012): 1405–44. http://dx.doi.org/10.5194/tcd-6-1405-2012.
Full textAbstract:
Abstract. Variations in intrinsic bed conditions that affect basal sliding, such as the distribution of deformable sediment versus hard bedrock, are important boundary conditions for large-scale ice-sheet models, but are hard to observe and remain largely uncertain below the modern Greenland and Antarctic ice sheets. Here a very simple model-based method is described for deducing the modern spatial distribution of basal sliding coefficients. The model is run forward in time, and the basal sliding coefficient at each grid point is periodically increased or decreased depending on whether the local ice surface elevation is too high or too low compared to observed, in areas of unfrozen bed. The method considerably reduces large-scale errors in Antarctic ice elevation, from several 100's to a few 10 m in most regions. Remaining ice elevation errors over mountain ranges such as the Transantarctics are further improved by parameterizing the possible effect of sub-grid topography in the basal sliding law, representing sliding in deep valleys. Results are briefly compared with previous work using relatively sophisticated control methods, and the method is applied to alternate topographies of the Recovery Glacier basin.
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Goldberg, Daniel N. "A variationally derived, depth-integrated approximation to a higher-order glaciological flow model." Journal of Glaciology 57, no. 201 (2011): 157–70. http://dx.doi.org/10.3189/002214311795306763.
Full textAbstract:
AbstractAn approximation to the first-order momentum balance with consistent boundary conditions is derived using variational methods. Longitudinal and lateral stresses are treated as depth-independent, but vertical velocity gradients are accounted for both in the nonlinear viscosity and in the treatment of basal stress, allowing for flow over a frozen bed. A numerical scheme is presented that is significantly less computationally expensive than that of a fully three-dimensional (3-D) solver. The numerical solver is subjected to the ISMIP-HOM experiments and experiments involving nonlinear sliding laws, and results are compared with those of 3-D models. The agreement with first-order surface velocities is favorable down to length scales of 10 km for flow over a flat bed with periodic basal traction, and ∼40 km for flow over periodic basal topography.
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Siegert, M. J., N. Ross, H. Corr, B. Smith, T. Jordan, R. G. Bingham, F. Ferraccioli, D. M. Rippin, and A. Le Brocq. "Boundary conditions of an active West Antarctic subglacial lake: implications for storage of water beneath the ice sheet." Cryosphere 8, no. 1 (January 3, 2014): 15–24. http://dx.doi.org/10.5194/tc-8-15-2014.
Full textAbstract:
Abstract. Repeat-pass ICESat altimetry has revealed 124 discrete surface height changes across the Antarctic Ice Sheet, interpreted to be caused by subglacial lake discharges (surface lowering) and inputs (surface uplift). Few of these active lakes have been confirmed by radio-echo sounding (RES) despite several attempts (notable exceptions are Lake Whillans and three in the Adventure Subglacial Trench). Here we present targeted RES and radar altimeter data from an "active lake" location within the upstream Institute Ice Stream, into which at least 0.12 km3 of water was previously calculated to have flowed between October 2003 and February 2008. We use a series of transects to establish an accurate depiction of the influences of bed topography and ice surface elevation on water storage potential. The location of surface height change is downstream of a subglacial hill on the flank of a distinct topographic hollow, where RES reveals no obvious evidence for deep (> 10 m) water. The regional hydropotential reveals a sink coincident with the surface change, however. Governed by the location of the hydrological sink, basal water will likely "drape" over topography in a manner dissimilar to subglacial lakes where flat strong specular RES reflections are measured. The inability of RES to detect the active lake means that more of the Antarctic ice sheet bed may contain stored water than is currently appreciated. Variation in ice surface elevation data sets leads to significant alteration in calculations of the local flow of basal water indicating the value of, and need for, high-resolution altimetry data in both space and time to establish and characterise subglacial hydrological processes.