scholarly journals Well-posed boundary conditions for limited-domain models of transient ice flow near an ice divide

2012 ◽  
Vol 58 (211) ◽  
pp. 1008-1020 ◽  
Author(s):  
Michelle R. Koutnik ◽  
Edwin D. Waddington
Keyword(s):  
Boundary Conditions ◽  
Ice Core ◽  
Ice Sheet ◽  
Temporal Variations ◽  
Impulse Response Functions ◽  
Ice Flow ◽  
Domain Boundaries ◽  
Ill Posed ◽  
Domain Models ◽  
Well Posed

AbstractWhen an ice-flow model is constrained by data that exist over only a section of an ice sheet, it is computationally advantageous to limit the model domain to only that section. For example, a limited domain near an ice-core site might cross an ice divide, and have no termini. Accurately calculating ice-sheet evolution in response to spatial and temporal variations in climate and ice flow depends on accurately calculating the transient ice flux crossing the limited-domain boundaries. In the absence of information from outside the limited domain, this is an ill-posed problem. Boundary conditions based only on information from inside the limited domain can produce ice-sheet evolution incompatible with the full ice sheet within which we suppose it to exist. We use impulse-response functions to provide boundary values that are informed by the external ice sheet, without conventionally 'nesting' the limited domain in a full ice-sheet model. Evolution within a limited domain can then be consistent with evolution of boundary conditions is designed for future use in affected the limited domain can be inferred from the full ice sheet. Our treatment of limited-domain an inverse problem in which external changes that data from within the limited domain.

scholarly journals Elastostatics of Bernoulli–Euler Beams Resting on Displacement-Driven Nonlocal Foundation

Nanomaterials ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 573
Author(s):  
Marzia Sara Vaccaro ◽  
Francesco Paolo Pinnola ◽  
Francesco Marotti de Sciarra ◽  
Raffaele Barretta
Keyword(s):  
Boundary Conditions ◽  
Structural Engineering ◽  
Beam Deflection ◽  
Soil Reaction ◽  
Differential Problem ◽  
Reaction Field ◽  
Ill Posed ◽  
Elastic Responses ◽  
Benchmark Solutions ◽  
Well Posed

The simplest elasticity model of the foundation underlying a slender beam under flexure was conceived by Winkler, requiring local proportionality between soil reactions and beam deflection. Such an approach leads to well-posed elastostatic and elastodynamic problems, but as highlighted by Wieghardt, it provides elastic responses that are not technically significant for a wide variety of engineering applications. Thus, Winkler’s model was replaced by Wieghardt himself by assuming that the beam deflection is the convolution integral between soil reaction field and an averaging kernel. Due to conflict between constitutive and kinematic compatibility requirements, the corresponding elastic problem of an inflected beam resting on a Wieghardt foundation is ill-posed. Modifications of the original Wieghardt model were proposed by introducing fictitious boundary concentrated forces of constitutive type, which are physically questionable, being significantly influenced on prescribed kinematic boundary conditions. Inherent difficulties and issues are overcome in the present research using a displacement-driven nonlocal integral strategy obtained by swapping the input and output fields involved in Wieghardt’s original formulation. That is, nonlocal soil reaction fields are the output of integral convolutions of beam deflection fields with an averaging kernel. Equipping the displacement-driven nonlocal integral law with the bi-exponential averaging kernel, an equivalent nonlocal differential problem, supplemented with non-standard constitutive boundary conditions involving nonlocal soil reactions, is established. As a key implication, the integrodifferential equations governing the elastostatic problem of an inflected elastic slender beam resting on a displacement-driven nonlocal integral foundation are replaced with much simpler differential equations supplemented with kinematic, static, and new constitutive boundary conditions. The proposed nonlocal approach is illustrated by examining and analytically solving exemplar problems of structural engineering. Benchmark solutions for numerical analyses are also detected.

scholarly journals Site information and initial results from deep ice drilling on Law Dome, Antarctica

1997 ◽  
Vol 43 (143) ◽  
pp. 3-10 ◽  
Author(s):  
V.I. Morgan ◽  
C.W. Wookey ◽  
J. Li ◽  
T.D. van Ommen ◽  
W. Skinner ◽  
...  
Keyword(s):  
Ice Core ◽  
Ice Sheet ◽  
High Accumulation ◽  
Ice Flow ◽  
Ice Cap ◽  
Basal Ice ◽  
Inland Ice ◽  
The Last Glacial Maximum ◽  
Initial Results ◽  
The Last Glacial

AbstractThe aim of deep ice drilling on Law Dome, Antarctica, has been to exploit the special characteristics of Law Dome summit, i.e. low temperature and high accumulation near an ice divide, to obtain a high-resolution ice core for climatic/environmental studies of the Holocene and the Last Glacial Maximum (LGM). Drilling was completed in February 1993, when basal ice containing small fragments of rock was reached at a depth of 1196 m. Accurate ice dating, obtained by counting annual layers revealed by fine-detail δ18О, peroxide and electrical-conductivity measurements, is continuous down to 399 m, corresponding to a date of AD 1304. Sulphate concentration measurements, made around depths where conductivity tracing indicates volcanic fallout, allow confirmation of the dating (for Agung in 1963 and Tambora in 1815) or estimates of the eruption date from the ice dating (for the Kuwae, Vanuatu, eruption ~1457). The lower part of the core is dated by extrapolating the layer-counting using a simple model of the ice flow. At the LGM, ice-fabric measurements show a large decrease (250 to 14 mm2) in crystal size and a narrow maximum in c-axis vertically. The main zone of strong single-pole fabrics however, is located higher up in a broad zone around 900 m. Oxygen-isotope (δ18O) measurements show Holocene ice down to 1113 m, the LGM at 1133 m and warm (δ18O) about the same as Holocene) ice near the base of the ice sheet. The LGM/Holocene δ18O shift of 7.0‰, only ~1‰ larger than for Vostok, indicates that Law Dome remained an independent ice cap and was not overridden by the inland ice sheet in the Glacial.

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 Bed topography and subglacial landforms in the onset region of the Northeast Greenland Ice Stream

2020 ◽  
Vol 61 (81) ◽  
pp. 143-153 ◽  
Author(s):  
Steven Franke ◽  
Daniela Jansen ◽  
Tobias Binder ◽  
Nils Dörr ◽  
Veit Helm ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Ultra Wideband ◽  
Ice Flow ◽  
Detailed Model ◽  
Dynamic Component ◽  
Bed Topography ◽  
Ice Stream ◽  
Topography Model

AbstractThe Northeast Greenland Ice Stream (NEGIS) is an important dynamic component for the total mass balance of the Greenland ice sheet, as it reaches up to the central divide and drains 12% of the ice sheet. The geometric boundary conditions and in particular the nature of the subglacial bed of the NEGIS are essential to understand its ice flow dynamics. We present a record of more than 8000 km of radar survey lines of multi-channel, ultra-wideband radio echo sounding data covering an area of 24 000 km2, centered on the drill site for the East Greenland Ice-core Project (EGRIP), in the upper part of the NEGIS catchment. Our data yield a new detailed model of ice-thickness distribution and basal topography in the region. The enhanced resolution of our bed topography model shows features which we interpret to be caused by erosional activity, potentially over several glacial–interglacial cycles. Off-nadir reflections from the ice–bed interface in the center of the ice stream indicate a streamlined bed with elongated subglacial landforms. Our new bed topography model will help to improve the basal boundary conditions of NEGIS prescribed for ice flow models and thus foster an improved understanding of the ice-dynamic setting.

scholarly journals Ice-sheet flow conditions deduced from mechanical tests of ice core

1999 ◽  
Vol 29 ◽  
pp. 179-183 ◽  
Author(s):  
Atsushi Miyamoto ◽  
Hideki Narita ◽  
Takeo Hondoh ◽  
Hitoshi Shoji ◽  
Kunio Kawada ◽  
...  
Keyword(s):  
Uniaxial Compression ◽  
Enhancement Factor ◽  
Flow Behavior ◽  
Ice Core ◽  
Ice Sheet ◽  
Constant Strain Rate ◽  
Uniaxial Compression Test ◽  
Ice Flow ◽  
Schmid Factor ◽  
Flow Enhancement

AbstractUniaxial compression tests were performed on samples of the Greenland Ice Gore Project (GRIP) deep ice core, both in the field and later in a cold-room laboratory, in order to understand the ice-flow behavior of large ice sheets. Experiments were conducted under conditions of constant strain rate (type A) and constant load (type B). Fifty-four uniaxial-compression test specimens from 1327-2922 m were selected. Each test specimen (25 mm x 25 mm x 90 mm) was prepared with its uniaxial stress axis inclined 45° from the core axis in order to examine the flow behavior of strong single-maximum ice-core samples with basal planes parallel to the horizontal plane of the ice sheet. The ice-flow enhancement factors show a gradual increase with depth down to approximately 2000 m. These results can be interpreted in terms of an increase in the fourth-order Schmid factor. Below 2000 m depth, the flow-enhancement factor increases to about 20-30 with a relatively high variability When the Schmid factor was > 0.46, the enhancement factor obtained was higher than expected from the .-axis concentrations measured. The higher values of flow-enhancement factor were obtained from specimens with a cloudy band structure. It was revealed that cloudy bands affect ice-deformation processes, but the details remain unclear.

scholarly journals Ice flow between the Greenland Ice Core Project and Greenland Ice Sheet Project 2 boreholes in central Greenland

1997 ◽  
Vol 102 (C12) ◽  
pp. 26851-26859 ◽  
Author(s):  
C. Schøtt Hvidberg ◽  
D. Dahl-Jensen ◽  
E. D. Waddington
Keyword(s):  
Ice Core ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Ice Flow ◽  
Core Project

scholarly journals EXTRACTION OF ICE SHEET LAYERS FROM TWO INTERSECTED RADAR ECHOGRAMS NEAR NEEM ICE CORE IN GREENLAND

2016 ◽  
Vol XLI-B7 ◽  
pp. 585-591 ◽  
Author(s):  
S. Xiong ◽  
J.-P. Muller
Keyword(s):  
Ice Core ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Electromagnetic Properties ◽  
Flow Mode ◽  
Internal Layers ◽  
Ice Flow ◽  
The North ◽  
Radar Echo ◽  
Echo Sounder

Accumulation of snow and ice over time result in ice sheet layers. These can be remotely sensed where there is a contrast in electromagnetic properties, which reflect variations of the ice density, acidity and fabric orientation. Internal ice layers are assumed to be isochronous, deep beneath the ice surface, and parallel to the direction of ice flow. The distribution of internal layers is related to ice sheet dynamics, such as the basal melt rate, basal elevation variation and changes in ice flow mode, which are important parameters to model the ice sheet. Radar echo sounder is an effective instrument used to study the sedimentology of the Earth and planets. Ice Penetrating Radar (IPR) is specific kind of radar echo sounder, which extends studies of ice sheets from surface to subsurface to deep internal ice sheets depending on the frequency utilised. In this study, we examine a study site where folded ice occurs in the internal ice sheet south of the North Greenland Eemian ice drilling (NEEM) station, where two intersected radar echograms acquired by the Multi-channel Coherent Radar Depth Sounder (MCoRDS) employed in the NASA’s Operation IceBridge (OIB) mission imaged this folded ice. We propose a slice processing flow based on a Radon Transform to trace and extract these two sets of curved ice sheet layers, which can then be viewed in 3-D, demonstrating the 3-D structure of the ice folds.

scholarly journals Ice Flow Along an I.A.G.P. Flow Line and Interpretation of Data From an Ice Core in Terre Adélie, Antarctica

1979 ◽  
Vol 24 (90) ◽  
pp. 103-115 ◽  
Author(s):  
D. Raynaud ◽  
C. Lorius ◽  
W. F. Budd ◽  
N. W. Young
Keyword(s):  
Flow Line ◽  
Ice Core ◽  
Ice Sheet ◽  
Sheet Thickness ◽  
Gas Content ◽  
Ice Flow ◽  
The Core ◽  
The Past ◽  
Terre Adélie ◽  
Inland Ice

AbstractAn ice core has been obtained to the bedrock about 300 m deep in Terre Adélie, 5 km inland from the coast. Stable isotopes and gas content have been measured over the length of the core. The results have been interpreted in terms of the temperature and elevation of origin of the ice further inland on the ice sheet from the data obtained along an 800 km traverse towards Dome “C”, and from Dome “C”, at an elevation of about 3 200 m. The flow of the ice from Dome “C“ to the coast has been modelled to determine the ages and particle trajectories of the ice for present conditions.It has been found that the upper isotope and gas-content values in the core can be matched with the present regime using a base for ice flow above the present bed which is suggested by moraine in the ice core. The ice in the layer from the 200 m depth, where the age is apparently more than 5 000 years, to the 250 m depth, appears to have originated from conditions which differ substantially from those existing on the present inland ice-sheet surface. The results give an indication of a colder climate and greater ice-sheet thickness in the past.

scholarly journals Where to find 1.5 million yr old ice for the IPICS "Oldest-Ice" ice core

2013 ◽  
Vol 9 (6) ◽  
pp. 2489-2505 ◽  
Author(s):  
H. Fischer ◽  
J. Severinghaus ◽  
E. Brook ◽  
E. Wolff ◽  
M. Albert ◽  
...  
Keyword(s):  
Heat Flux ◽  
Ice Core ◽  
Ice Sheet ◽  
Ice Thickness ◽  
Geothermal Heat ◽  
Ice Flow ◽  
Antarctic Ice Sheet ◽  
Quaternary Climate ◽  
Drill Site ◽  
Heat Flow Model

Abstract. The recovery of a 1.5 million yr long ice core from Antarctica represents a keystone of our understanding of Quaternary climate, the progression of glaciation over this time period and the role of greenhouse gas cycles in this progression. Here we tackle the question of where such ice may still be found in the Antarctic ice sheet. We can show that such old ice is most likely to exist in the plateau area of the East Antarctic ice sheet (EAIS) without stratigraphic disturbance and should be able to be recovered after careful pre-site selection studies. Based on a simple ice and heat flow model and glaciological observations, we conclude that positions in the vicinity of major domes and saddle position on the East Antarctic Plateau will most likely have such old ice in store and represent the best study areas for dedicated reconnaissance studies in the near future. In contrast to previous ice core drill site selections, however, we strongly suggest significantly reduced ice thickness to avoid bottom melting. For example for the geothermal heat flux and accumulation conditions at Dome C, an ice thickness lower than but close to about 2500 m would be required to find 1.5 Myr old ice (i.e., more than 700 m less than at the current EPICA Dome C drill site). Within this constraint, the resolution of an Oldest-Ice record and the distance of such old ice to the bedrock should be maximized to avoid ice flow disturbances, for example, by finding locations with minimum geothermal heat flux. As the geothermal heat flux is largely unknown for the EAIS, this parameter has to be carefully determined beforehand. In addition, detailed bedrock topography and ice flow history has to be reconstructed for candidates of an Oldest-Ice ice coring site. Finally, we argue strongly for rapid access drilling before any full, deep ice coring activity commences to bring datable samples to the surface and to allow an age check of the oldest ice.

Modelling ice rise englacial temperature profiles to constrain past ice-sheet dynamics

2020 ◽  
Author(s):  
Aleksandr Montelli ◽  
Jonathan Kingslake
Keyword(s):  
Heat Flux ◽  
Boundary Conditions ◽  
Ross Sea ◽  
Accumulation Rate ◽  
Ice Sheet ◽  
Temperature Profiles ◽  
Measured Temperature ◽  
Ice Dynamics ◽  
Ice Flow ◽  
Thickness Change

<p>Present-day englacial temperatures are the product of the millennial-scale histories of ice flow and thermal boundary conditions experienced by an ice sheet. Vertical englacial temperature profiles extracted from boreholes drilled at ice divides record past ice dynamics and changing external forcings. Bindschadler (1990) estimated the timing of grounding of Crary Ice Rise, Ross Sea, by minimizing the mismatch between modelled and measured temperature profiles. This approach has huge potential if future boreholes are drilled at Antarctic ice rises in locations suspected of undergoing significant dynamics change. Yet, the uncertainties inherent in this approach must be carefully assessed to target and maximize the utility of borehole drilling. Here, using a 1D vertical heat flux model, we simulate the evolution of temperature as a function of depth in six locations with slow-flowing, cold-based ice in the Weddell and Ross Sea sectors of the West Antarctic Ice Sheet. The locations were chosen using output from the Parallel Ice Sheet Model (PISM) as which are most likely to have ungrounded and regrounded during the last deglaciation (i.e., through last 20 k.y.). We use the shallow ice approximation assuming horizontally isothermal ice and no basal sliding. Several parameters, accounting for timing and duration of grounding/ungrounding events, surface temperature evolution, accumulation rate, ice-thickness change, geothermal heat flux and vertical velocity, are varied to generate a range of different temperature profile outputs. Uncertainties associated with each parameter are then evaluated using a Monte-Carlo approach, yielding a statistical account of model sensitivity to key variables. We highlight that the precision needed to infer timing of grounding increases with the duration of grounded ice flow. Results presented here can help in choosing future ice drilling sites, and provide useful constraints on inferring past forcings and changing boundary conditions from in-situ temperature-depth measurements.</p>

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