Department of Mathematics

Dr. Christian Helanow, Iowa State University: "Numerical modeling of glacier sliding"

Jun 15, 2018 from 10:15 AM to 11:15 AM

WR 383 - Raum 306/307


Marine terminating glaciers account for the majority of the mass loss from Greenland and Antarctica, and are thus important to monitor since they impact e.g. the oceans and global sea-level rise. The deformation of glacial ice, which is essentially governed by the p-Stokes equations coupled to a free-surface kinematic condition, can only account for a minor part of the observed surface velocities in these fast-flowing glaciers. Thus the basal boundary conditions play a crucial role in accurately determining the future velocity increases of marine-terminating glaciers, in which sliding velocities often make up 80-90% of the total (surface) velocity.

Numerical models commonly use a fairly simple parametrized "law", relating the basal drag at the bed to the sliding speed in a one-to-one correspondence. Most often, the parameters in these relations are found via inverse modelling, using the observed surface velocity as an input. Hence, all the processes, possibly transient, that are dependent on the presence of substrate, water at the bed and bed topography are amalgamated in such a static parameter. A fundamental processed based understanding of how glaciers slide at the ice/bed interface is missing.

In this project we implement a numerical model that investigates how realistic bed topography, debris-rich ice and substrate affect the basal drag/sliding velocity relation. This will extend previous semi-analytical and numerical results regarding glacier sliding on simplified 2d beds.

The problem is a free-surface contact problem, where the evolution of the free surface corresponds to sub-glacial water filled cavities that grow due to the sliding velocity and water pressure. The contact line between cavity roof and bed is evaluated as a part of the free surface or as grounded to the bed depending on if the water pressure exceeds the normal component of the basal normal stress. The attempt is to solve this contact problem with the FEM software ElmerIce, which has been used extensively for glaciological applications, including the previous simpler 2d results. Currently, the scenario has been extended to 3d for simple hard beds. However, for more complicated geometry, the difficulties of using a kinematic free-surface, which can result in wave-like motion for initial guesses of geometry or highly distorted
elements, remains a challenge. Reaching a steady-state scenario has also proven to be difficult. Nevertheless, first results indicate that the relation between basal drag and sliding speed can be of double-valued nature, suggesting that in some cases rate-weakening drag occurs at the bed.


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