Abstract
A number of improvements have been made to an existing two-dimensional ice-flow model applied to an alpine glacier. Analysis of the results of the existing model revealed several shortcomings. The first concerns the lack of mass conservation of the applied alternating-direction-implicit (ADI) scheme. A semi-implicit (SI) scheme is therefore proposed and the effects on mass conservation assessed by a comparison with the ADI scheme. The comparison is first carried out with a simple theoretical glacier for which the improvement is significant. Concerning the real case of Glacier de Saint-Sorlin, France, the initial deviation in mass conservation was much less pronounced such that the new scheme, although improving mass conservation, does not significantly change the modelled dynamics. However, other shortcomings that have a more profound impact on the modelling of glacier behaviour have been identified. The ice thickness may become negative over some gridpoints, leading to an inconsistency. The problem is partly resolved by incorporating extra checks on critical gridpoints at the glacier border. Finally, with the help of ice particle tracking, unrealistic ice settlement above the bergschrund has been identified as the main reason for spurious dynamic effects and has been corrected.
Highlights
Owing to their characteristic geometry, correct modelling of alpine-type glaciers usually requires three-dimensional (3-D) models in order to capture the specific features of their complex dynamics
To prevent unrealistic ice development over the upper part of the glacier, ice is not allowed to settle over points satisfying the following three conditions: (1) the point lies in the region above the bergschrund, (2) it was initially not glaciated and (3) the slope at that point is steeper than a certain threshold
Several shortcomings of a 2-D shallow ice approximation (SIA) ice-flow model applied to an alpine glacier have been identified and corresponding solutions proposed
Summary
Owing to their characteristic geometry, correct modelling of alpine-type glaciers usually requires three-dimensional (3-D) models in order to capture the specific features of their complex dynamics. A solution that incorporates systematic checks on the capability of peripheral points to provide ice to their neighbouring points partly solves this problem and contributes to better mass conservation Another inconsistency inherent in the old algorithm is the colonization of ice in the upper part of the glacier above the bergschrund, resulting in an overestimation of the local mass balance which affects the ice dynamics. The paper is organized as follows: after identifying the mass conservation problem, the main equations of the SIA model are presented and used to introduce the new semiimplicit (SI) scheme (section 2)
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