scholarly journals Three-dimensional surface velocities of Storstrømmen glacier, Greenland, derived from radar interferometry and ice-sounding radar measurements

2003 ◽  
Vol 49 (165) ◽  
pp. 201-209 ◽  
Author(s):  
Niels Reeh ◽  
Johan Jacob Mohr ◽  
Søren Nørvang Madsen ◽  
Hans Oerter ◽  
Niels S. Gundestrup
Keyword(s):  
Steady State ◽  
Vertical Velocity ◽  
Three Dimensional ◽  
Greenland Ice Sheet ◽  
Mass Conservation ◽  
Ablation Rate ◽  
Radar Interferometry ◽  
Surface Velocity ◽  
Outlet Glacier ◽  
Dimensional Surface

AbstractNon-steady-state vertical velocities of up to 5 m a−1 exceed the vertical surface-parallel flow (SPF) components over much of the ablation area of Storstrømmen, a large outlet glacier from the East Greenland ice sheet. Neglecting a contribution to the vertical velocity of this magnitude results in substantial errors (up to 20%) also on the south–north component of horizontal velocities derived by satellite synthetic aperture radar interferometry (InSAR) measurements. In many glacier environments, the steady-state vertical velocity component required to balance the annual ablation rate is 5–10 m a−1 or more. This indicates that the SPF assumption may be problematic also for glaciers in steady state. Here we derive the three-dimensional surface velocity distribution of Storstrømmen by using the principle of mass conservation (MC) to combine InSAR measurements from ascending and descending satellite tracks with airborne ice-sounding radar measurement of ice thickness. The results are compared to InSAR velocities previously derived by using the SPF assumption, and to velocities obtained by in situ global positioning system (GPS) measurements. The velocities derived by using the MC principle are in better agreement with the GPS velocities than the previously calculated velocities derived with the SPF assumption.

Combining SAR interferometry and the equation of continuity to estimate the three-dimensional glacier surface-velocity vector

1999 ◽  
Vol 45 (151) ◽  
pp. 533-538 ◽  
Author(s):  
Niels Reeh ◽  
Søren Nørvang Madsen ◽  
Johan Jakob Mohr
Keyword(s):  
Steady State ◽  
Mass Balance ◽  
Vertical Velocity ◽  
Velocity Vector ◽  
Thickness Distribution ◽  
Vertical Surface ◽  
Horizontal Velocity ◽  
Sar Interferometry ◽  
Surface Velocity ◽  
Ice Thickness

AbstractUntil now, an assumption of surface-parallel glacier flow has been used to express the vertical velocity component in terms of the horizontal velocity vector, permitting all three velocity components to be determined from synthetic aperture radar interferometry. We discuss this assumption, which neglects the influence of the local mass balance and a possible contribution to the vertical velocity arising if the glacier is not in steady state. We find that the mass-balance contribution to the vertical surface velocity is not always negligible as compared to the surface-slope contribution. Moreover, the vertical velocity contribution arising if the ice sheet is not in steady state can be significant. We apply the principle of mass conservation to derive an equation relating the vertical surface velocity to the horizontal velocity vector. This equation, valid for both steady-state and non-steady-state conditions, depends on the ice-thickness distribution. Replacing the surface-parallel-flow assumption with a correct relationship between the surface velocity components requires knowledge of additional quantities such as surface mass balance or ice thickness.

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.

Combining SAR interferometry and the equation of continuity to estimate the three-dimensional glacier surface-velocity vector

1999 ◽  
Vol 45 (151) ◽  
pp. 533-538 ◽  
Author(s):  
Niels Reeh ◽  
Søren Nørvang Madsen ◽  
Johan Jakob Mohr
Keyword(s):  
Steady State ◽  
Mass Balance ◽  
Vertical Velocity ◽  
Velocity Vector ◽  
Thickness Distribution ◽  
Vertical Surface ◽  
Horizontal Velocity ◽  
Sar Interferometry ◽  
Surface Velocity ◽  
Ice Thickness

AbstractUntil now, an assumption of surface-parallel glacier flow has been used to express the vertical velocity component in terms of the horizontal velocity vector, permitting all three velocity components to be determined from synthetic aperture radar interferometry. We discuss this assumption, which neglects the influence of the local mass balance and a possible contribution to the vertical velocity arising if the glacier is not in steady state. We find that the mass-balance contribution to the vertical surface velocity is not always negligible as compared to the surface-slope contribution. Moreover, the vertical velocity contribution arising if the ice sheet is not in steady state can be significant. We apply the principle of mass conservation to derive an equation relating the vertical surface velocity to the horizontal velocity vector. This equation, valid for both steady-state and non-steady-state conditions, depends on the ice-thickness distribution. Replacing the surface-parallel-flow assumption with a correct relationship between the surface velocity components requires knowledge of additional quantities such as surface mass balance or ice thickness.

On Three-Dimensional Nonlinear Subharmonic Resonant Surface Waves in a Fluid: Part I—Theory

1988 ◽  
Vol 55 (1) ◽  
pp. 213-219 ◽  
Author(s):  
X. M. Gu ◽  
P. R. Sethna ◽  
A. Narain
Keyword(s):  
Surface Tension ◽  
Steady State ◽  
Energy Dissipation ◽  
Surface Waves ◽  
Three Dimensional ◽  
Critical Depth ◽  
Transient Phenomena ◽  
Vertical Excitation ◽  
Rectangular Container ◽  
Dimensional Surface

Three-dimensional surface waves in a rectangular container subjected to vertical excitation are studied. The analysis includes the effects of surface tension, energy dissipation, and critical depth. Both steady state and transient phenomena are discussed.

scholarly journals Transient evolution of basal drag during glacier slip

2021 ◽  
pp. 1-10
Author(s):  
Lucas K. Zoet ◽  
Neal R. Iverson ◽  
Lauren Andrews ◽  
Christian Helanow
Keyword(s):  
Steady State ◽  
Greenland Ice Sheet ◽  
Surface Velocity ◽  
Transient Effects ◽  
Steady State Condition ◽  
Drag Model ◽  
Lab Experiments ◽  
Transient Data ◽  
Bed Separation ◽  
Cavity Evolution

Abstract Glacier slip is usually described using steady-state sliding laws that relate drag, slip velocity and effective pressure, but where subglacial conditions vary rapidly transient effects may influence slip dynamics. Here we use results from a set of laboratory experiments to examine the transient response of glacier slip over a hard bed to velocity perturbations. The drag and cavity evolution from lab experiments are used to parameterize a rate-and-state drag model that is applied to observations of surface velocity and ice-bed separation from the Greenland ice sheet. The drag model successfully predicts observed lags between changes in ice-bed separation and sliding speed. These lags result from the time (or displacement) required for cavities to evolve from one steady-state condition to another. In comparing drag estimates resulting from applying rate-and-state and steady-state slip laws to transient data, we find the peaks in drag are out of phase. This suggests that in locations where subglacial conditions vary on timescales shorter than those needed for cavity adjustment transient slip processes control basal drag.

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 Influence of debris-rich basal ice on flow of a polar glacier

2014 ◽  
Vol 60 (223) ◽  
pp. 989-1006 ◽  
Author(s):  
Erin C. Pettit ◽  
Erin N. Whorton ◽  
Edwin D. Waddington ◽  
Ronald S. Sletten
Keyword(s):  
Low Temperatures ◽  
Ablation Rate ◽  
Surface Velocity ◽  
Inverse Theory ◽  
Limited Data ◽  
Outlet Glacier ◽  
Basal Ice ◽  
Glacier Ice ◽  
Glacier Flow ◽  
Taylor Glacier

AbstractAt Taylor Glacier, a cold-based outlet glacier of the East Antarctic ice sheet, observed surface speeds in the terminus region are 20 times greater than those predicted using Glen’s flow law for cold (–17°C), thin (100 m) ice. Rheological properties of the clean meteoric glacier ice and the underlying deformable debris-rich basal ice can be inferred from surface-velocity and ablation-rate profiles using inverse theory. Here, with limited data, we use a two-layer flowband model to examine two end-member assumptions about the basal-ice properties: (1) uniform softness with spatially variable thickness and (2) uniform thickness with spatially variable softness. We find that the basal ice contributes 85–98% to the observed surface velocity in the terminus region. We also find that the basal-ice layer must be 10–15 m thick and 20–40 times softer than clean Holocene-age glacier ice in order to match the observations. Because significant deformation occurs in the basal ice, our inverse problem is not sensitive to variations in the softness of the meteoric ice. Our results suggest that despite low temperatures, highly deformable basal ice may dominate flow of cold-based glaciers and rheologically distinct layers should be incorporated in models of polar-glacier flow.

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