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 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 Reconstruction of the Glacial Ice Covers of Greenland and the Canadian Arctic Islands by Three-Dimensional, Perfectly Plastic Ice-Sheet Modelling

1984 ◽  
Vol 5 ◽  
pp. 115-121 ◽  
Author(s):  
N. Reeh
Keyword(s):  
Flow Pattern ◽  
Bottom Topography ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Canadian Arctic ◽  
Ice Cover ◽  
Glacial Ice ◽  
North West ◽  
Ice Caps ◽  
Perfectly Plastic

A three-dimensional perfectly plastic ice-sheet model, developed for determining the surface elevations and the flow pattern of an ice sheet with given bottom topography and ice-margin positions, is applied to the reconstruction of the glacial ice covers of Greenland and the Canadian Arctic islands. In the northern regions, two different reconstructions have been performed with ice margins along the present 600 and 200 m sea-depth contours, respectively. In central Greenland, the ice margin is considered to be at the outermost ice-margin deposits on the coastal shelf to the west, and at the present 200 m sea-depth contour to the east.The main conclusions to be drawn from the reconstructions are: (1). The flow pattern of the glacial ice cover of Greenland shows a great resemblance to the present one, the central ice divide being displaced less than 50 km from its present position and being no more than 200 m higher than today. (2). The main ice divide of the ice sheet covering the Canadian Arctic islands (the Innuitian ice sheet) was located over the highlands of eastern Ellesmere Island with local domes positioned over the present ice caps, indicating that even the deep ice of Wisconsin age in these ice caps is of local origin. This is also the case for the Devon Island ice cap. (3). Even in the not very likely case of a rather extensive glacial ice cover in north-west Greenland, the ice-flow pattern upstream of the Camp Century deep drill site would not have changed radically compared to the present flow pattern. Thus it is concluded that even advanced ice margins in late-Wisconsin time could at most have resulted in an elevation of the deposition site of the late-Wisconsin ice at Camp Century 600 m higher than at present. The consequences of this conclusion are discussed.

scholarly journals Reconstruction of the Glacial Ice Covers of Greenland and the Canadian Arctic Islands by Three-Dimensional, Perfectly Plastic Ice-Sheet Modelling

1984 ◽  
Vol 5 ◽  
pp. 115-121 ◽  
Author(s):  
N. Reeh
Keyword(s):  
Flow Pattern ◽  
Bottom Topography ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Canadian Arctic ◽  
Ice Cover ◽  
Glacial Ice ◽  
North West ◽  
Ice Caps ◽  
Perfectly Plastic

A three-dimensional perfectly plastic ice-sheet model, developed for determining the surface elevations and the flow pattern of an ice sheet with given bottom topography and ice-margin positions, is applied to the reconstruction of the glacial ice covers of Greenland and the Canadian Arctic islands. In the northern regions, two different reconstructions have been performed with ice margins along the present 600 and 200 m sea-depth contours, respectively. In central Greenland, the ice margin is considered to be at the outermost ice-margin deposits on the coastal shelf to the west, and at the present 200 m sea-depth contour to the east.The main conclusions to be drawn from the reconstructions are: (1). The flow pattern of the glacial ice cover of Greenland shows a great resemblance to the present one, the central ice divide being displaced less than 50 km from its present position and being no more than 200 m higher than today. (2). The main ice divide of the ice sheet covering the Canadian Arctic islands (the Innuitian ice sheet) was located over the highlands of eastern Ellesmere Island with local domes positioned over the present ice caps, indicating that even the deep ice of Wisconsin age in these ice caps is of local origin. This is also the case for the Devon Island ice cap. (3). Even in the not very likely case of a rather extensive glacial ice cover in north-west Greenland, the ice-flow pattern upstream of the Camp Century deep drill site would not have changed radically compared to the present flow pattern. Thus it is concluded that even advanced ice margins in late-Wisconsin time could at most have resulted in an elevation of the deposition site of the late-Wisconsin ice at Camp Century 600 m higher than at present. The consequences of this conclusion are discussed.

scholarly journals Surface Contours and Flow Pattern of a Perfectly Plastic Three-Dimensional Ice Sheet With Arbitrary Bottom and Edge Topography

1979 ◽  
Vol 24 (90) ◽  
pp. 511-512
Author(s):  
Niels Reeh
Keyword(s):  
Differential Equation ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Ice Streams ◽  
Line Segments ◽  
Perfectly Plastic ◽  
Straight Line ◽  
Sloping Bed ◽  
Set Up ◽  
Arbitrary Curve

Abstract The 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 cases, viz. (1) an ice sheet on a horizontal base with an arbitrary curve as edge and (2) an ice sheet ona plane but sloping bed, with an edge composed of straight-line segments. The solutions are discussed in particular with reference to the development of ice divides and ice streams.

scholarly journals Surface Contours and Flow Pattern of a Perfectly Plastic Three-Dimensional Ice Sheet With Arbitrary Bottom and Edge Topography

1979 ◽  
Vol 24 (90) ◽  
pp. 511-512
Author(s):  
Niels Reeh
Keyword(s):  
Differential Equation ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Ice Streams ◽  
Line Segments ◽  
Perfectly Plastic ◽  
Straight Line ◽  
Sloping Bed ◽  
Set Up ◽  
Arbitrary Curve

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 cases, viz. (1) an ice sheet on a horizontal base with an arbitrary curve as edge and (2) an ice sheet ona plane but sloping bed, with an edge composed of straight-line segments. The solutions are discussed in particular with reference to the development of ice divides and ice streams.

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 ICESHEET 1.0: a program to produce paleo-ice sheet reconstructions with minimal assumptions

2016 ◽  
Vol 9 (5) ◽  
pp. 1673-1682 ◽  
Author(s):  
Evan J. Gowan ◽  
Paul Tregoning ◽  
Anthony Purcell ◽  
James Lea ◽  
Oscar J. Fransner ◽  
...  
Keyword(s):  
Steady State ◽  
Barents Sea ◽  
Global Climate ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Computational Time ◽  
Climate Modelling ◽  
Ice Dynamics ◽  
Perfectly Plastic ◽  
Input Parameters

Abstract. We describe a program that produces paleo-ice sheet reconstructions using an assumption of steady-state, perfectly plastic ice flow behaviour. It incorporates three input parameters: ice margin, basal shear stress and basal topography. Though it is unlikely that paleo-ice sheets were ever in complete steady-state conditions, this method can produce an ice sheet without relying on complicated and unconstrained parameters such as climate and ice dynamics. This makes it advantageous to use in glacial-isostatic adjustment ice sheet modelling, which are often used as input parameters in global climate modelling simulations. We test this program by applying it to the modern Greenland Ice Sheet and Last Glacial Maximum Barents Sea Ice Sheet and demonstrate the optimal parameters that balance computational time and accuracy.

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 ICESHEET 1.0: A program to produce paleo-ice sheet models with minimal assumptions

2016 ◽  
Author(s):  
E. J. Gowan ◽  
P. Tregoning ◽  
A. Purcell ◽  
J. Lea ◽  
O. J. Fransner ◽  
...  
Keyword(s):  
Steady State ◽  
Barents Sea ◽  
Global Climate ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Computational Time ◽  
Climate Modelling ◽  
Ice Dynamics ◽  
Perfectly Plastic ◽  
Input Parameters

Abstract. We describe a program that produces paleo-ice sheet models using an assumption of steady state, perfectly plastic ice flow behaviour. It incorporates three input parameters: ice margin, basal shear stress and basal topography. Though it is unlikely that paleo-ice sheets were ever in complete steady-state conditions, this method can produce an ice sheet without relying on complicated and unconstrained parameters such as climate and ice dynamics. This makes it advantageous to use in glacial-isostatic adjustment ice sheet models, which are often used as input parameters in global climate modelling simulations. We test this program by applying it to the modern Greenland Ice Sheet and Last Glacial Maximum Barents Sea ice sheet and demonstrate the optimal parameters that balance computational time and accuracy.

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