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Flow Modeling of Alpine and Rock Glaciers

The principal objective of the project is to improve the general understanding of the genesis and the mechanical behaviour of rock glaciers. In particular, hypotheses regarding the flow and the thermal structure of rock glaciers will be tested in a series of numerical experiments.

The two main aspects are: 1) investigating the length fluctuation of glaciers in general (alpine and rock glaciers) by a comparison of a zeroth-order with a full-system model; and 2) analysis of the detailed flow evolution of an advancing glacier front. The numerical model is a two-dimensional vertical plane-flow model which calculates the gravity driven transient evolution of an ice mass. The model includes all terms of the momentum equations, which are solved using a commercial finite-element program tailored for use in glaciology. With this numerical model the glacier geometry can be accurately followed through time for an advance or a retreat.

In a first series of numerical experiments the reaction of alpine glaciers to shifts in the equilibrium line altitude (ELA) is calculated. The full-system model is compared to a shallow ice approximation (SIA) model, widely used in glaciology, to investigate the significance of the differences in the results between the two models. The comparison shows that the rates of advance and retreat of the snout of typically-sized alpine glaciers are found to be insensitive to the details of the flow at the snout and to longitudinal stress gradients, even when the glaciers are far from steady-state. With a realistic mass-balance-altitude feedback only slight model-dependent changes in steady-state lengths are found. The model-dependent additional shifts in ELA needed for the SIA and the full-system models to produce identical changes in length are determined. Thus, a precise meaning is given to the relative importance of mass-balance and glacier dynamics in determining the transient response of alpine glaciers to changes in the ELA. For alpine glaciers these additional shifts in ELA are on the order of 10m, which is within the error range of ELA estimates. It follows that there is no need to include the effects of horizontal-stresses when calculating the reaction of alpine glaciers to climatic changes. Attention should focus on accurate determination of the mass-balance distribution and model tuning giving realistic ice-thickness distribution.

The advance of a glacier front over a sediment layer is calculated in a second series of numerical experiments. The rheology of the sediment is described by relating strain rate to the effective stress to the power of m. Experiments for an advancing glacier are undertaken for different sediment viscosities in the sediment layer. Three types of advances are obtained: 1) overriding, where the glacier overrides the sediment by ice deformation without deforming the sediment; 2) plug-flow, where the sediment is strongly deformed, the ice moves forward as a block and a bulge is built in front of the glacier; and 3) mixed-flow, where the glacier overrides the sediment and deforms it at the same time. An inverse depth-age relationship is obtained by a glacier advancing either by overriding or mixed-flow. The type and characteristic of an advance is unchanged when a nearly perfect plastic instead of a viscous sediment rheology is chosen. The model calculations imply that measurements of sediment thickness and sediment deformation which are taken close to the glacier front would significantly overestimate the average sediment thickness and displacement due to sediment deformation further upglacier.

Regarding rock glaciers we gain some insight about the simplifications that can be made to calculate the correct transient evolution and surface velocity field of a rock glacier having a large aspect ratio, large surface slope, or both. As for glaciers, the SIA model is appropriate for calculating the advance as well as the rate of advance of rock glaciers, whereas the full-system model is needed to calculate the exact evolution of rock glacier surface features such as its steep front and furrows and ridges.


Keywords: rock glacier; full-system flow model
Contacts: Dr. Gwendolyn Leysinger Vieli (now at Bristol Glaciology Centre, University of Bristol)
Dr. Hilmar G. Gudmundsson (now at British Antarctic Survey)
Commissioned by: ETH Research Grant TH-11/99-2
Publications: Leysinger Vieli, G. J.-M. C. and Gudmundsson, G. H. (2003):
Evolution of rock glaciers and alpine glaciers: A model-model approach. Proceedings of the 8th International Conference on Permafrost, Zurich, Switzerland.

Leysinger Vieli, G. J.-M. C., Gudmundsson, G. H. (2004). On estimating length fluctuations of glaciers caused by changes in climatic forcing. Journal of Geophysical Research, 109(F1), F01007, 10.1029/2003JF000027.

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