scholarly journals Geometry and Dynamics of a Surge-type Glacier

1977 ◽  
Vol 18 (79) ◽  
pp. 181-194 ◽  
Author(s):  
R. Bindschadler ◽  
W. D. Harrison ◽  
C. F. Raymond ◽  
R. Crosson
Keyword(s):  
Steady State ◽  
Stress Distribution ◽  
Internal Stress ◽  
Ice Thickness ◽  
Surface Slope ◽  
Local Surface ◽  
Order Of Magnitude ◽  
Internal Deformation ◽  
Longitudinal Profiles ◽  
Similar Depth

AbstractMeasurement of geometry, motion, and mass balance from Variegated Glacier, Alaska portray conditions in this surge-type glacier close to the mid-point of its 20 year surge cycle. Comparison of longitudinal profiles of ice depth, surface slope, and surface speed indicate that the motion occurs largely by internal deformation assuming the ice deforms according to the experimental law of Glen. Surface speed is not noticeably affected by local surface slope on the scale of the ice thickness or smaller, but correlates well with slope determined on a longitudinal averaging scale about one order of magnitude larger than the ice depth. The rate of motion on Variegated Glacier agrees well with rates on non-surge type temperate glaciers which have similar depth and slope. Although the (low regime at the time of the measurements is apparently typical of temperate glaciers, a large discrepancy between the balance flux needed for steady state and the actual flux is indicative of a rapidly changing surface elevation profile and internal stress distribution.

scholarly journals Geometry and Dynamics of a Surge-type Glacier

1977 ◽  
Vol 18 (79) ◽  
pp. 181-194 ◽  
Author(s):  
R. Bindschadler ◽  
W. D. Harrison ◽  
C. F. Raymond ◽  
R. Crosson
Keyword(s):  
Steady State ◽  
Stress Distribution ◽  
Internal Stress ◽  
Ice Thickness ◽  
Surface Slope ◽  
Local Surface ◽  
Order Of Magnitude ◽  
Internal Deformation ◽  
Longitudinal Profiles ◽  
Similar Depth

AbstractMeasurement of geometry, motion, and mass balance from Variegated Glacier, Alaska portray conditions in this surge-type glacier close to the mid-point of its 20 year surge cycle. Comparison of longitudinal profiles of ice depth, surface slope, and surface speed indicate that the motion occurs largely by internal deformation assuming the ice deforms according to the experimental law of Glen. Surface speed is not noticeably affected by local surface slope on the scale of the ice thickness or smaller, but correlates well with slope determined on a longitudinal averaging scale about one order of magnitude larger than the ice depth. The rate of motion on Variegated Glacier agrees well with rates on non-surge type temperate glaciers which have similar depth and slope. Although the (low regime at the time of the measurements is apparently typical of temperate glaciers, a large discrepancy between the balance flux needed for steady state and the actual flux is indicative of a rapidly changing surface elevation profile and internal stress distribution.

scholarly journals Volume/area scaling of glaciers and ice caps and their longitudinal profiles

2016 ◽  
Vol 62 (235) ◽  
pp. 928-932 ◽  
Author(s):  
VALERIO FARAONI
Keyword(s):  
Differential Equations ◽  
Power Law ◽  
Empirical Data ◽  
Theoretical Models ◽  
Ice Thickness ◽  
Scaling Analysis ◽  
Surface Slope ◽  
Ice Caps ◽  
Longitudinal Profiles ◽  
Length Scaling

ABSTRACTEmpirical data on the volume/area scaling of glaciers and ice caps are compared with theoretical models of longitudinal glacier profiles. Ice caps are described well by theoretical solutions of the differential equations modeling longitudinal profiles, but glaciers for which the surface slope is approximated by the ice thickness divided by the length are not. A power-law profile recently derived analytically, reproduces exactly the thickness-length scaling, first predicted by scaling analysis for ice caps.

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 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.

Steady-State stress distributions in circumferentially notched bars subjected to creep

1982 ◽  
Vol 17 (3) ◽  
pp. 123-132 ◽  
Author(s):  
K D Al-Faddagh ◽  
R T Fenner ◽  
G A Webster
Keyword(s):  
Steady State ◽  
Stress Distribution ◽  
Stress Index ◽  
Stress Distributions ◽  
Computer Solution ◽  
Time Intervals ◽  
Throat Region ◽  
Intermediate Time ◽  
State Stress ◽  
Good Agreement

The paper describes a procedure, based on a finite element method, for calculating directly the steady-state stress distribution in circumferentially notched bars subjected to creep without the need for obtaining solutions at intermediate time intervals. Good agreement is obtained with relevant approximate plasticity solutions and with numerical calculations which approach the steady-state over a period of time from the initial elastic stress distribution. Also, the procedure is equally applicable to primary, secondary, and tertiary creep, provided the variables of stress and time are separable in the creep law. Results obtained for a range of notch geometries and values of the stress index, n, are reported. It is found for each profile that a region of approximately constant effective stress, σ, independent of n, is obtained which can be used to characterise the overall behaviour of the notch throat region when a steady-state is reached sufficiently early in life. An approximate method for estimating the maximum equivalent steady-state stress across the notch throat is also presented which does not require a computer solution.

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 Flow of Blue Glacier, Olympic Mountains, Washington, U.S.A.

1974 ◽  
Vol 13 (68) ◽  
pp. 187-212 ◽  
Author(s):  
Mark F. Meier ◽  
W. Barclay Kamb ◽  
Clarence R. Allen ◽  
Robert P. Sharp
Keyword(s):  
Maximum Velocity ◽  
Ice Thickness ◽  
Center Line ◽  
Surface Slope ◽  
Channel Narrowing ◽  
Olympic Mountains ◽  
Principal Axes ◽  
Flow Effects ◽  
Surface Ice ◽  
Longitudinal Extension

Velocity and strain-rate patterns in a small temperate valley glacier display flow effects of channel geometry, ice thickness, surface slope, and ablation. Surface velocities of 20–55 m/year show year-to-year fluctuations of 1.5–3 m/year. Transverse profiles of velocity have the form of a higher-order parabola modified by the effects of flow around a broad bend in the channel, which makes the velocity profile asymmetric, with maximum velocity displaced toward the outside of the bend. Marginal sliding rates are 5–22 m/year against bedrock and nil against debris. Velocity vectors diverge from the glacier center-line near the terminus, in response to surface ice loss, but converge toward it near the firn line because of channel narrowing. Plunge of the vectors gives an emergence flow component that falls short of balancing ice loss by about 1 m/year. Center-line velocities vary systematically with ice thickness and surface slope. In the upper half of the reach studied, effects of changing thickness and slope tend to compensate, and velocities are nearly constant; in the lower half, the effects are cumulative and velocities decrease progressively down-stream. Where the slope increases down-stream from 7° to 9°, reflecting a bedrock step, there is localized longitudinal extension of 0.03 year–1followed by compression of 0.08 year–1where the slope decreases. Marginal shear (up to 0.5 year–1) is strongly asymmetric due to flow around the bend: the stress center-line, where one of the principal axes becomes longitudinal, is displaced 150 m toward the inside of the bend. This effect is prominently visible in the crevasse pattern. Ice fluxes calculated independently by “laminar” flow theory and by continuity disagree in a way which shows that internal deformation of the ice is controlled not by local surface slope but by an effective slope that is nearly constant over the reach studied.

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