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Response of Blue Glacier to a Perturbation in Ice Thickness: Theory and Observation


Echelmeyer, Keith Alan (1983) Response of Blue Glacier to a Perturbation in Ice Thickness: Theory and Observation. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ZQHK-NA29.


A unique natural experiment has occurred on Mt. Olympus, Washington, in which the lower part of Blue Glacier has undergone a marked increase in ice thickness and a general decrease in surface slope. In response to this, the glacier flow velocities have increased considerably. The detailed study of the surface configuration and flow of the glacier during the period 1957-59, before the thickening (Meier, et al., 1974) provides a complete baseline against which the recent changes in geometry and surface velocity field are measured.

A detailed evaluation of the flow response to the changes in thickness and slope is made, testing for the existence of a quantitative observational relation among u, H, and α. A linear relation between the percentage ice thickness change and the percentage velocity increase is found. The slope of this response line is related to the exponent n in the flow law of ice, and the negative intercept represents an overall decrease in surface slope.

Detailed quantitative interpretations of the field measurements on the flow of Blue Glacier and its response to the change in surface configuration are made, using analytical and finite-element techniques.

A theoretical discussion of the effects of longitudinal stress gradients on the flow of an ice mass is given. This discussion leads to the development of an exponential Green's function which determines the effect of surface slope and ice thickness variations on the flow. This Green's function provides a weighting factor for longitudinal averaging of slope and thickness. The characteristic length scale up- and downglacier is dependent on the longitudinal strain-rate, the amount of basal sliding, and the flow-law parameters, being approximately three times the mean ice thickness. Application of this longitudinal averaging to the observed slope and thickness changes results in a marked decrease in deviations of the response data from a linear regression on the velocity changes, showing that longitudinal stress gradients are important.

A finite-element computer code for the calculation of flow of ice in channel cross sections of arbitrary shape, including transverse flow components, is developed. The model is applied to flow in channels of idealized parabolic cross-sectional shape to reveal the basic effects of channel shape and flow-law parameters on stress and velocity distribution. The stresses are found to be dependent on the flow-law parameters. Components of transverse flow within the cross section that develop in response to transverse convexity of the glacier surface were calculated. Comparison with observations shows that much of the splaying of the velocity vectors within an ablation zone can be attributed to flow driven by this convex surface.

Analytical models of the flow of a glacier in which the flow law parameters vary with position are developed. These models show that there is a nonuniqueness in flow-law parameters obtained from borehole deformation studies. Studies of the response of a glacier to a change in surface configuration can partially eliminate some of this ambiguity.

The theory and finite element calculations are extended to channels that follow a curving course in map view, which is necessary for application to Blue Glacier, since in the reach studied the glacier flows around a gently curving bend of 90°. Longitudinal channel curvature causes asymmetry in the stress and velocity distribution within a symmetric channel. The stress centerline is shifted toward the inside of the bend, while the position of the maximum velocity is usually shifted outward of the center for n ≥ 3. The effects of curvature are readily observable in the flow and crevassing of Blue Glacier.

The relation between perturbations in ice thickness and surface slope and the change in velocity is developed for arbitrary channels. Analytical and numerical results indicate that there is a linear relation between the changes in slope α, thickness H, and surface velocity u:

[Equation included in scanned thesis' abstract, pp. vii]

where Ψ is termed the response factor. For realistic channel geometries, Ψ is in the range 1/2 to 1. This factor represents the change in cross-sectional shape of an ice mass which accompanies a change in ice thickness within a given channel. The value of the stress exponent inferred from the observed flow response is significantly affected by this geometric factor, which is approximately equal to 0.82 for Blue Glacier. The slope of the response line implies that n = 4 for the flow of Blue Glacier when this response factor is taken into account.

Finite element models of flow and the flow response within the different cross sections of Blue Glacier (as determined by radio echo sounding) compare well with the observed velocity patterns and response to change in thickness if channel curvature is included. These results again imply a stress exponent of n = 4. The results also agree with the various field measurements which indicate that basal sliding contributes at most 10% to the overall motion of the glacier.

The results presented in this thesis represent the most detailed evaluation of the response of a glacier to perturbations in ice thickness and surface slope. They show that non-linear flow theory with n = 4 is applicable to a good approximation. The relationship between the flow velocity, slope, and thickness found in this work has direct application to the study of effects of climatic change on an ice mass.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Geophysics
Degree Grantor:California Institute of Technology
Division:Geological and Planetary Sciences
Major Option:Geophysics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Hager, Bradford
Thesis Committee:
  • Hager, Bradford H. (chair)
  • Ahrens, Thomas J.
  • Kamb, W. Barclay
  • Meier, Mark
  • Sharp, Robert P.
Defense Date:7 April 1983
Non-Caltech Author Email:kechel (AT)
Additional Information:Supplemental Files Information: Blue Glacier surface velocity: Supplement 1 from "Response of Blue Glacier to a Perturbation in Ice Thickness: Theory and Observation" (Thesis).
Funding AgencyGrant Number
Record Number:CaltechETD:etd-08242006-080724
Persistent URL:
Related URLs:
URLURL TypeDescription 1 in CaltechDATA: Blue Glacier surface velocity
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3214
Deposited By: Imported from ETD-db
Deposited On:29 Aug 2006
Last Modified:24 Sep 2020 00:52

Thesis Files

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PDF (Echelmeyer_ka_1983_plate_1.pdf) - Supplemental Material
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