scholarly journals Application of a Polythermal Three-Dimensional Ice Sheet Model to the Greenland Ice Sheet: Response to Steady-State and Transient Climate Scenarios

1997 ◽  
Vol 10 (5) ◽  
pp. 901-918 ◽  
Author(s):  
Ralf Greve
Keyword(s):  
Steady State ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Climate Scenarios

scholarly journals Basal temperature conditions of the Greenland ice sheet during the glacial cycles

1996 ◽  
Vol 23 ◽  
pp. 226-236 ◽  
Author(s):  
Philippe Huybrechts
Keyword(s):  
Steady State ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Ice Cores ◽  
Ice Thickness ◽  
Glacial Cycle ◽  
Glacial Cycles ◽  
Temperature Conditions ◽  
Strongly Damped

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.

scholarly journals A Plasticity Theory Approach to the Steady-State Shape of a Three-Dimensional Ice Sheet

1982 ◽  
Vol 28 (100) ◽  
pp. 431-455 ◽  
Author(s):  
Niels Reeh
Keyword(s):  
Steady State ◽  
Flow Pattern ◽  
Bottom Topography ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Theory Approach ◽  
Ice Streams ◽  
Perfectly Plastic ◽  
Set Up

AbstractThe differential equation determining the elevations of a perfectly plastic three-dimensional steady-state ice sheet is set up. Analytical solutions of the equation are obtained in two simple case, (1) an ice sheet on a horizontal base with an arbitrary edge curve, and (2) an ice sheet on a plane sloping base with a rectilinear ice margin. The solutions are discussed, particularly with reference to the development of ice divides and ice streams.For arbitrary base and ice-margin geometries, solutions are obtained by means of the method of characteristics, which reduces the problem to solving simultaneously three ordinary first-order differential equations. The integration, which is performed by numerical methods, is generally commenced at the ice margin, where the necessary boundary conditions are known.The method has been applied to model the elevation contours and the flow pattern of the central Greenland ice sheet, using the bottom topography revealed by radio echo soundings and the present ice margin geometry. The result is in surprisingly good agreement with our knowledge of the ice-sheet topography and flow pattern, all significant ice divides and ice streams being reproduced. This suggests, that the method can be applied to model the shape and flow pattern of ice sheets under glacial conditions, using information about former ice-margin positions.

scholarly journals Basal temperature conditions of the Greenland ice sheet during the glacial cycles

1996 ◽  
Vol 23 ◽  
pp. 226-236 ◽  
Author(s):  
Philippe Huybrechts
Keyword(s):  
Steady State ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Ice Cores ◽  
Ice Thickness ◽  
Glacial Cycle ◽  
Glacial Cycles ◽  
Temperature Conditions ◽  
Strongly Damped

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.

scholarly journals A Plasticity Theory Approach to the Steady-State Shape of a Three-Dimensional Ice Sheet

1982 ◽  
Vol 28 (100) ◽  
pp. 431-455 ◽  
Author(s):  
Niels Reeh
Keyword(s):  
Steady State ◽  
Flow Pattern ◽  
Bottom Topography ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Theory Approach ◽  
Ice Streams ◽  
Perfectly Plastic ◽  
Set Up

AbstractThe differential equation determining the elevations of a perfectly plastic three-dimensional steady-state ice sheet is set up. Analytical solutions of the equation are obtained in two simple case, (1) an ice sheet on a horizontal base with an arbitrary edge curve, and (2) an ice sheet on a plane sloping base with a rectilinear ice margin. The solutions are discussed, particularly with reference to the development of ice divides and ice streams.For arbitrary base and ice-margin geometries, solutions are obtained by means of the method of characteristics, which reduces the problem to solving simultaneously three ordinary first-order differential equations. The integration, which is performed by numerical methods, is generally commenced at the ice margin, where the necessary boundary conditions are known.The method has been applied to model the elevation contours and the flow pattern of the central Greenland ice sheet, using the bottom topography revealed by radio echo soundings and the present ice margin geometry. The result is in surprisingly good agreement with our knowledge of the ice-sheet topography and flow pattern, all significant ice divides and ice streams being reproduced. This suggests, that the method can be applied to model the shape and flow pattern of ice sheets under glacial conditions, using information about former ice-margin positions.

scholarly journals The Age-Depth Profile in the Upper Part of a Steady-State Ice Sheet

1989 ◽  
Vol 35 (121) ◽  
pp. 406-417 ◽  
Author(s):  
Niels Reeh
Keyword(s):  
Steady State ◽  
Layer Thickness ◽  
Flow Line ◽  
Numerical Models ◽  
Accumulation Rate ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Ice Thickness ◽  
Western Slope ◽  
Simple Models

AbstractSimple analytical models are developed in order to study how up-stream variations in accumulation rate and ice thickness, and horizontal convergence/ divergence of the flow influence the age and annual layer-thickness profiles in a steady-state ice sheet. Generally, a decrease/increase of the accumulation rate and an increase/decrease of the ice thickness in the up-stream direction (i.e. opposite to the flow direction) results in older/younger ice at a given depth in the ice sheet than would result if the up-stream accumulation rate and ice thickness were constant along the flow line.Convergence/divergence of the up-stream flow will decrease/increase the effect of the accumulation-rate and ice-thickness gradients, whereas convergence/divergence has no influence at all on the age and layer-thickness profiles if the up-stream accumulation rate and ice thickness are constant along the flow line.A modified column-flow model, i.e. a model for which the strain-rate profile (or, equivalently, the horizontal velocity profile) is constant down to the depth corresponding to the Holocene/Wisconsinan transition 10 750 year BP., seems to work well for dating the ice back to 10 000–11 000 year B P. at sites in the slope regions of the Greenland ice sheet. For example, the model predicts the experimentally determined age profile at Dye 3 on the south Greenland ice sheet with a relative root-mean-square error of only 3% back to c. 10 700 year B.P. As illustrated by the Milcent location on the western slope of the central Greenland ice sheet, neglecting up-stream accumulation-rate and ice-thickness gradients, may lead to dating errors as large as 3000–000 years for c. 10 000 year old ice.However, even if these gradients are taken into account, the simple model fails to give acceptable ages for 10 000 year old ice at locations on slightly sloping ice ridges with strongly divergent flow, as for example the Camp Century location. The main reason for this failure is that the site of origin of the ice cannot be determined accurately enough by the simple models, if the flow is strongly divergent.With this exception, the simple models are well suited for dating the ice at locations where the available data or the required accuracy do not justify application of elaborate numerical models. The formulae derived for the age-depth profiles can easily be worked out on a pocket calculator, and in many cases will be a sensible alternative to using numerical flow models.

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 The sensitivity of the Greenland Ice Sheet to glacial–interglacial oceanic forcing

2018 ◽  
Vol 14 (4) ◽  
pp. 455-472 ◽  
Author(s):  
Ilaria Tabone ◽  
Javier Blasco ◽  
Alexander Robinson ◽  
Jorge Alvarez-Solas ◽  
Marisa Montoya
Keyword(s):  
Sea Level ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
High Sensitivity ◽  
Glacial Cycles ◽  
The Past ◽  
Primary Driver ◽  
Oceanic Forcing ◽  
Atmospheric Variations

Abstract. Observations suggest that during the last decades the Greenland Ice Sheet (GrIS) has experienced a gradually accelerating mass loss, in part due to the observed speed-up of several of Greenland's marine-terminating glaciers. Recent studies directly attribute this to warming North Atlantic temperatures, which have triggered melting of the outlet glaciers of the GrIS, grounding-line retreat and enhanced ice discharge into the ocean, contributing to an acceleration of sea-level rise. Reconstructions suggest that the influence of the ocean has been of primary importance in the past as well. This was the case not only in interglacial periods, when warmer climates led to a rapid retreat of the GrIS to land above sea level, but also in glacial periods, when the GrIS expanded as far as the continental shelf break and was thus more directly exposed to oceanic changes. However, the GrIS response to palaeo-oceanic variations has yet to be investigated in detail from a mechanistic modelling perspective. In this work, the evolution of the GrIS over the past two glacial cycles is studied using a three-dimensional hybrid ice-sheet–shelf model. We assess the effect of the variation of oceanic temperatures on the GrIS evolution on glacial–interglacial timescales through changes in submarine melting. The results show a very high sensitivity of the GrIS to changing oceanic conditions. Oceanic forcing is found to be a primary driver of GrIS expansion in glacial times and of retreat in interglacial periods. If switched off, palaeo-atmospheric variations alone are not able to yield a reliable glacial configuration of the GrIS. This work therefore suggests that considering the ocean as an active forcing should become standard practice in palaeo-ice-sheet modelling.

scholarly journals Bathymetry of Northwest Greenland Using “Ocean Melting Greenland” (OMG) High-Resolution Airborne Gravity and Other Data

2019 ◽  
Vol 11 (2) ◽  
pp. 131 ◽  
Author(s):  
Lu An ◽  
Eric Rignot ◽  
Romain Millan ◽  
Kirsty Tinto ◽  
Josh Willis
Keyword(s):  
High Resolution ◽  
Continental Shelf ◽  
Gravity Data ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Three Dimensions ◽  
Airborne Gravity ◽  
Lack Of Information ◽  
Sea Bed

Marine-terminating glaciers dominate the evolution of the Greenland Ice Sheet (GrIS) and its contribution to sea-level rise. Widespread glacier acceleration has been linked to the warming of ocean waters around the periphery of Greenland but a lack of information on the bathymetry of the continental shelf and glacial fjords has limited our ability to understand how subsurface, warm, salty ocean waters of Atlantic origin (AW) reach the glaciers and melt them from below. Here, we employ high-resolution, airborne gravity data (AIRGrav) in combination with multibeam echo sounding (MBES) data, to infer the bathymetry of the coastal areas of Northwest Greenland for NASA’s Ocean Melting Greenland (OMG) mission. High-resolution, AIRGrav data acquired on a 2 km spacing, 150 m ground clearance, with 1.5 mGal crossover error, is inverted in three dimensions to map the bathymetry. To constrain the inversion away from MBES data, we compare two methods: one based on the Direct Current (DC) shift of the gravity field (absolute minus observed gravity) and another based on the density of the bedrock. We evaluate and compare the two methods in areas with complete MBES coverage. We find the lowest standard error in bed elevation (±60 m) using the DC shift method. When applied to the entire coast of Northwest Greenland, the three-dimensional inversion reveals a complex network of connected sea bed channels, not known previously, that provide natural and varied pathways for AW to reach the glaciers across the continental shelf. The study demonstrates that the gravity approach offers an efficient and practical alternative to extensive ship mapping in ice-filled waters to obtain information critical to understanding and modeling ice-ocean interaction along ice sheet margins.

Simulations of dated radiostratigraphy for the Greenland ice sheet

2020 ◽  
Author(s):  
Andreas Born ◽  
Alexander Robinson
Keyword(s):  
Degrees Of Freedom ◽  
Vertical Structure ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Climate Forcing ◽  
Lagrangian Description ◽  
Glacial Cycle ◽  
Dynamic Constraints ◽  
The Last Glacial

<p>As layers of accumulated snow compact into ice and start to flow under its own weight, their deformations are recorded in the vertical structure of the glacier. Therefore, the isochronal stratigraphy of the Greenland ice sheet provides comprehensive dynamic constraints, which, with adequate methods, can be used to calibrate ice sheet models and greatly improve their accuracy.<br><br>We present the first three-dimensional ice sheet model that explicitly resolves isochrones. Individual layers of accumulation do not exchange mass with each other as the flow of ice deforms them, resembling the Lagrangian description of flow in the vertical dimension, while lateral flow within each layer is Eulerian. Direct comparison with dated radiostratigraphy is used to filter an ensemble of simulations of the Greenland ice sheet. The abundant information implied by the shape of the three-dimensional layering enables us to constrain a large number of degrees of freedom. The mismatch in the thickness of certain isochrones is used to calibrate the climate forcing of different periods of the last glacial cycle.</p>

A Parallel Computational Model for Three-Dimensional, Thermo-Mechanical Stokes Flow Simulations of Glaciers and Ice Sheets

2014 ◽  
Vol 16 (4) ◽  
pp. 1056-1080 ◽  
Author(s):  
Wei Leng ◽  
Lili Ju ◽  
Max Gunzburger ◽  
Stephen Price
Keyword(s):  
Finite Element ◽  
Computational Model ◽  
Stokes Flow ◽  
Stokes Problem ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Iterative Solution ◽  
Element Model ◽  
High Order

AbstractThis paper focuses on the development of an efficient, three-dimensional, thermo-mechanical, nonlinear-Stokes flow computational model for ice sheet simulation. The model is based on the parallel finite element model developed in [14] which features high-order accurate finite element discretizations on variable resolution grids. Here, we add an improved iterative solution method for treating the nonlinearity of the Stokes problem, a new high-order accurate finite element solver for the temperature equation, and a new conservative finite volume solver for handling mass conservation. The result is an accurate and efficient numerical model for thermo-mechanical glacier and ice-sheet simulations. We demonstrate the improved efficiency of the Stokes solver using the ISMIP-HOM Benchmark experiments and a realistic test case for the Greenland ice-sheet. We also apply our model to the EISMINT-II benchmark experiments and demonstrate stable thermo-mechanical ice sheet evolution on both structured and unstructured meshes. Notably, we find no evidence for the “cold spoke” instabilities observed for these same experiments when using finite difference, shallow-ice approximation models on structured grids.

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