scholarly journals A three-dimensional ice-sheet flow solution

2009 ◽  
Vol 55 (191) ◽  
pp. 473-480 ◽  
Author(s):  
L.W. Morland
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Surface Profile ◽  
Temperature Dependent ◽  
Spatial Variables ◽  
Equation Problem ◽  
Dependent Rate ◽  
Horizontal Velocity Component ◽  
Spatial Coordinates

AbstractAn accurate three-dimensional reduced model (shallow-ice approximation) flow with velocity depending on all three spatial coordinates is constructed for the commonly adopted isotropic viscous law with temperature-dependent rate factor. The solution is for steady flow with a prescribed temperature distribution, but can be extended to flow with a coupled energy balance, and to unsteady flow. The accuracy hinges on the reduction to a two-point ordinary differential equation problem for the surface profile, on an unknown span, for which established accurate numerical methods are available. This is achieved by setting one horizontal velocity component in elliptic cylindrical coordinates to zero, but the other two components depend on all three spatial variables. While not of direct physical interest, such an ‘exact’ solution is valuable as a test solution for the large-scale numerical codes commonly used in ice-sheet modelling, which have not yet been subjected to such a comparison.

scholarly journals Contribution to the Movement and the form of Ice Sheets in the Arctic and Antarctic

1961 ◽  
Vol 3 (30) ◽  
pp. 1133-1151 ◽  
Author(s):  
R. Haefeli
Keyword(s):  
Average Rate ◽  
Ice Sheet ◽  
Surface Profile ◽  
Greenland Ice Sheet ◽  
Present Theory ◽  
The Arctic ◽  
Small Influence ◽  
Horizontal Velocity Component ◽  
Flow Law ◽  
Set Up

AbstractStarting from Glen’s flow law for ice and from a series of assumptions based in part on observations in Greenland and in the Jungfraujoch, the velocity distribution (horizontal velocity component) and surface configuration is derived for a strip-shaped ice sheet in a stationary state. For the choice n = 3 − 4 of the exponent in the power-law flow relation, there is extensive agreement between the theoretically calculated surface profile and the east-west profile measured through “Station Centrale” by Expéditions Polaires Françaises. The corresponding theoretical solution for a circular ice sheet is also given. As a first application of this theory, an attempt is made to calculate the average rate of accumulation in Antarctica from its surface profile (assumed circular in plan) and from the flow-law parameters derived from the Greenland Ice Sheet. It is also shown that a change in accumulation has only a small influence on the total ice thickness of an ice sheet. A method of calculating approximately the age of ice in an ice sheet, based on the foregoing theory, is illustrated by applying it to the Greenland Ice Sheet. After comparing the present theory with that of Nye, a general expression for the surface profile of an ice sheet with constant accumulation is set up and discussed by means of comparison with two profiles through Antarctica.

scholarly journals A Three-Dimensional Polar Ice-Sheet Model

1977 ◽  
Vol 18 (80) ◽  
pp. 373-389 ◽  
Author(s):  
D. Jenssen
Keyword(s):  
Three Dimensional ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Phase Changes ◽  
Three Dimensions ◽  
Dimensional Model ◽  
Polar Ice ◽  
Three Dimensional Model ◽  
Temperature Dependent ◽  
Mass Depletion

AbstractA three-dimensional model of the temperature and velocity distribution within any arbitrary-shaped ice mass is described. There is a mutual interaction in the model between the flow of the ice and its thermodynamics, since the flow law used in the model is temperature-dependent.Ice growth in three dimensions is governed by mass accumulation through precipitation, by mass depletion through loss of ice over the ocean, and by continuity requirements. Phase changes at the base of the ice are accounted for. The model has been applied in art exploratory manner to the Greenland ice sheet. Changes in the ice shape and temperature are presented and discussed. The basic shortcoming of the model as here presented appears primarily due to the coarse finite-difference mesh used, and to an unsophisticated approach to modelling the boundary ice.

scholarly journals Ice sheet flow with thermally activated sliding. Part 2: the stability of subtemperate regions

2019 ◽  
Vol 475 (2231) ◽  
pp. 20190411
Author(s):  
E. Mantelli ◽  
C. Schoof
Keyword(s):  
Melting Point ◽  
Large Scale ◽  
Thermal Structure ◽  
Ice Sheet ◽  
Temperature Dependent ◽  
Length Scales ◽  
Thermally Activated ◽  
Potential Alternative ◽  
The Stability ◽  
Alternative Structure

The onset of sliding in ice sheets may not take the form of a sharp boundary between regions at the melting point, in which sliding is permitted, and regions below that temperature, in which there is no slip. Such a hard switch leads to the paradox of the bed naturally wanting to refreeze as soon as sliding has commenced. A potential alternative structure is a region of subtemperate sliding. Here temperatures are marginally below the melting point and sliding velocities slower than they would if the bed was fully temperate. Rather than being controlled by a standard sliding law, sliding velocities are then constrained by the need to maintain energy balance. This thermal structure arises in temperature-dependent sliding laws in the limit of strong sensitivity to temperature. Here, we analyse the stability of such subtemperate regions, showing that they are subject to a set of instabilities that occur at all length scales between ice thickness and ice sheet length. The fate of these instabilities is to cause the formation of patches of frozen bed, raising the possibility of highly complicated cold-to-temperate transitions with spatial structures at short length scales that cannot be resolved in large-scale ice sheet simulation codes.

scholarly journals A Three-Dimensional Polar Ice-Sheet Model

1977 ◽  
Vol 18 (80) ◽  
pp. 373-389 ◽  
Author(s):  
D. Jenssen
Keyword(s):  
Three Dimensional ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Phase Changes ◽  
Three Dimensions ◽  
Dimensional Model ◽  
Polar Ice ◽  
Three Dimensional Model ◽  
Temperature Dependent ◽  
Mass Depletion

Abstract A three-dimensional model of the temperature and velocity distribution within any arbitrary-shaped ice mass is described. There is a mutual interaction in the model between the flow of the ice and its thermodynamics, since the flow law used in the model is temperature-dependent. Ice growth in three dimensions is governed by mass accumulation through precipitation, by mass depletion through loss of ice over the ocean, and by continuity requirements. Phase changes at the base of the ice are accounted for. The model has been applied in art exploratory manner to the Greenland ice sheet. Changes in the ice shape and temperature are presented and discussed. The basic shortcoming of the model as here presented appears primarily due to the coarse finite-difference mesh used, and to an unsophisticated approach to modelling the boundary ice.

scholarly journals Impacts of pre-initial conditions on anisotropic separate universe simulations: a boosted tidal response in the epoch of reionization

2020 ◽  
Vol 500 (1) ◽  
pp. 1018-1028
Author(s):  
Shogo Masaki ◽  
Takahiro Nishimichi ◽  
Masahiro Takada
Keyword(s):  
Structure Formation ◽  
Large Scale ◽  
Particle Distribution ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Initial Anisotropy ◽  
Anisotropic Expansion ◽  
Local Background ◽  
Systematic Effects ◽  
Spatial Coordinates

ABSTRACT To generate initial conditions for cosmological N-body simulations, one needs to prepare a uniform distribution of simulation particles, the so-called pre-initial condition (pre-IC). The standard method to construct the pre-IC is to place the particles on the lattice grids evenly spaced in the three-dimensional spatial coordinates. However, even after the initial displacement of each particle according to cosmological perturbations, the particle distribution remains to display an artificial anisotropy. Such an artefact causes systematic effects in simulations at later time until the evolved particle distribution sufficiently erases the initial anisotropy. In this paper, we study the impacts of the pre-IC on the anisotropic separate universe simulation, where the effect of large-scale tidal field on structure formation is taken into account using the anisotropic expansion in a local background (simulation volume). To quantify the impacts, we compare the simulations employing the standard grid pre-IC and the glass one, where the latter is supposed to suppress the initial anisotropy. We show that the artificial features in the grid pre-IC simulations are seen until z ∼ 9, while the glass pre-IC simulations appear to be stable and accurate over the range of scales we study. From these results we find that a coupling of the large-scale tidal field with matter clustering is enhanced compared to the leading-order prediction of perturbation theory in the quasi-non-linear regime in the redshift range 5 ≲ z ≲ 15, indicating the importance of tidal field on structure formation at such high redshifts, e.g. during the epoch of reionization.

scholarly journals Contribution to the Movement and the form of Ice Sheets in the Arctic and Antarctic

1961 ◽  
Vol 3 (30) ◽  
pp. 1133-1151 ◽  
Author(s):  
R. Haefeli
Keyword(s):  
Average Rate ◽  
Ice Sheet ◽  
Surface Profile ◽  
Greenland Ice Sheet ◽  
Present Theory ◽  
The Arctic ◽  
Small Influence ◽  
Horizontal Velocity Component ◽  
Flow Law ◽  
Set Up

Abstract Starting from Glen’s flow law for ice and from a series of assumptions based in part on observations in Greenland and in the Jungfraujoch, the velocity distribution (horizontal velocity component) and surface configuration is derived for a strip-shaped ice sheet in a stationary state. For the choice n = 3 − 4 of the exponent in the power-law flow relation, there is extensive agreement between the theoretically calculated surface profile and the east-west profile measured through “Station Centrale” by Expéditions Polaires Françaises. The corresponding theoretical solution for a circular ice sheet is also given. As a first application of this theory, an attempt is made to calculate the average rate of accumulation in Antarctica from its surface profile (assumed circular in plan) and from the flow-law parameters derived from the Greenland Ice Sheet. It is also shown that a change in accumulation has only a small influence on the total ice thickness of an ice sheet. A method of calculating approximately the age of ice in an ice sheet, based on the foregoing theory, is illustrated by applying it to the Greenland Ice Sheet. After comparing the present theory with that of Nye, a general expression for the surface profile of an ice sheet with constant accumulation is set up and discussed by means of comparison with two profiles through Antarctica.

scholarly journals Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation

2008 ◽  
Vol 2 (2) ◽  
pp. 77-93 ◽  
Author(s):  
G. H. Gudmundsson
Keyword(s):  
Analytical Solutions ◽  
Boundary Data ◽  
Small Amplitude ◽  
Large Scale ◽  
Stokes Equations ◽  
Ice Sheet ◽  
Surface Profile ◽  
Phase Speed ◽  
Simple Description ◽  
Ice Stream

Abstract. New analytical solutions describing the effects of small-amplitude perturbations in boundary data on flow in the shallow-ice-stream approximation are presented. These solutions are valid for a non-linear Weertman-type sliding law and for Newtonian ice rheology. Comparison is made with corresponding solutions of the shallow-ice-sheet approximation, and with solutions of the full Stokes equations. The shallow-ice-stream approximation is commonly used to describe large-scale ice stream flow over a weak bed, while the shallow-ice-sheet approximation forms the basis of most current large-scale ice sheet models. It is found that the shallow-ice-stream approximation overestimates the effects of bed topography perturbations on surface profile for wavelengths less than about 5 to 10 ice thicknesses, the exact number depending on values of surface slope and slip ratio. For high slip ratios, the shallow-ice-stream approximation gives a very simple description of the relationship between bed and surface topography, with the corresponding transfer amplitudes being close to unity for any given wavelength. The shallow-ice-stream estimates for the timescales that govern the transient response of ice streams to external perturbations are considerably more accurate than those based on the shallow-ice-sheet approximation. In particular, in contrast to the shallow-ice-sheet approximation, the shallow-ice-stream approximation correctly reproduces the short-wavelength limit of the kinematic phase speed given by solving a linearised version of the full Stokes system. In accordance with the full Stokes solutions, the shallow-ice-sheet approximation predicts surface fields to react weakly to spatial variations in basal slipperiness with wavelengths less than about 10 to 20 ice thicknesses.

The Laurentide ice sheet through the last glacial cycle: the topology of drift lineations as a key to the dynamic behaviour of former ice sheets

1990 ◽  
Vol 81 (4) ◽  
pp. 327-347 ◽  
Author(s):  
G. S. Boulton ◽  
C. D. Clark
Keyword(s):  
Atmospheric Circulation ◽  
Large Scale ◽  
Three Dimensional ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Aerial Photographs ◽  
Laurentide Ice Sheet ◽  
Glacial Cycle ◽  
Sheet Flow ◽  
Integrative Framework

ABSTRACTStudy of satellite images from most of the area of the Canadian mainland once covered by the Laurentide ice sheet reveals a complex pattern of superimposed drift lineations. They are believed to have formed subglacially and parallel to ice flow. Aerial photographs reveal patterns of superimposition which permit the sequence of lineation patterns to be identified. The sequential lineation patterns are interpreted as evidence of shifting patterns of flow in an evolving ice sheet. Flow stages are recognised which reflect roughly synchronous integrated patterns of ice sheet flow. Comparison with stratigraphic sections in the Hudson Bay Lowlands suggests that all the principal stages may have formed during the last, Wisconsinan, glacial cycle. Analogy between Flow stage lineation patterns and the form and flow patterns of modern ice sheets permits reconstruction of patterns of ice divides and centres of mass which moved by 1000–2000 km during the glacial period. There is evidence that during the early Wisconsinan, ice sheet formation in Keewatin may have been independent of that in Labrador–Quebec, and that these two ice masses joined to form a major early Wisconsinan ice sheet. Subsequently the western dome decayed whilst the eastern dome remained relatively stable. A western dome then re-formed, and fused with the eastern dome to form the late Wisconsinan ice sheet before final decay.Because of strong coupling between three-dimensional ice sheet geometry and atmospheric circulation, it is suggested that the major changes of geometry must have been associated with large scale atmospheric circulation changes.Lineation patterns suggest very little erosional/depositional activity in ice divide regions, and can be used to reconstruct large scale patterns of erosion/deposition.The sequence of flow stages through time provides an integrative framework allowing sparse stratigraphic data to be used most efficiently in reconstructing ice sheet history in time and space.

scholarly journals Large-scale ice-sheet modelling as a means of dating deep ice cores in Greenland

1997 ◽  
Vol 43 (144) ◽  
pp. 307-310 ◽  
Author(s):  
Ralf Greve
Keyword(s):  
Surface Temperature ◽  
Large Scale ◽  
Piecewise Linear ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Ice Cores ◽  
Temperature History ◽  
Geothermal Heat ◽  
Annual Layer

Abstract The three-dimensional ice-sheet model SICOPOLIS is used to simulate the dynamic/thermody namic behaviour of the entire Greenland ice sheet from 250 000 a BP until today. External forcing consists of a surface-temperature history constructed from δ18O data of the GRIP core, a snowfall history coupled linearly to that of the surface temperature, a piecewise linear sea-level scenario and a constant geothermal heat flux. The simulated Greenland ice sheet is investigated in the vicinity of Summit, the position where the maximum elevation is taken, and where the two drill sites GRIP and GISP2 are situated 28km apart from each other. In this region, the agreement between modelled and observed topography and ice temperature turns out to be very good. Computed age-depth profiles for GRIP and GISP2 are presented, which can he used to complete the dating of these cores in the deeper regions where annual-layer counting is not possible. However, artificial diffusion influences the computed ages in a near-basal boundary layer of approximately 15% of the ice thickness, so that the age at the bottom of the cores cannot be predicted yet.

scholarly journals Deglaciation of the Northern Hemisphere at the onset of the Eemian and Holocene

1999 ◽  
Vol 28 ◽  
pp. 1-8 ◽  
Author(s):  
Ralf Greve ◽  
Karl-Heinz Wyrwoll ◽  
Anton Eisenhauer
Keyword(s):  
Northern Hemisphere ◽  
Large Scale ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Ice Cores ◽  
Point Of View ◽  
Simulation Code ◽  
Ice Volume ◽  
Global Ice Volume ◽  
Ice Sheet Dynamics

AbstractHigh resolution (TIMS) U-series dating of sea-level events obtained from coral-reef complexes suggests that global deglaciation from the Saale (penultimate) glacial to the Eem Interglacial (marine δ18O stages 6/5) may have occurred earlier in relation to Milankovitch insolation forcing than that from the Wisconsinan glacial to the Holocene Interglacial (marine δ18O stages 2/1). However, the interpretation of these data has been problematic because of the possibility of isotope exchange. In order to investigate whether these different lead—lag relations between Milankovitch forcing and ice volume are feasible from the point of view of large-scale ice-sheet dynamics and thermodynamics, the three-dimensional polythermal ice-sheet model SICOPOLIS (Simulation Code for Poly- thermal Ice Sheets) is applied to the entire Northern Hemisphere (which gives the major contribution to global ice-volume changes due to the relative stability of the Antarctic ice sheet) and simulations through the last two climatic cycles are conducted. The simulations cover the interval from 250 kyr BP until today and are driven by surface-temperature reconstructions of deep ice cores (GRIP, Vostok) and simple parameterizations for the change of precipitation with time. Discussion of the results is focused on the Saale/Eem and the Wisconsinan/Holocene transitions. The amount and rate of deglaciation are in good agreement with the SPECMAP record for both cases, and the evidence of the data for an early start of the Eem Interglacial is supported.

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