Flow Modelling of a Temperate Ice Cap: Vatnajökull, Iceland

In this project the flow dynamics and the stability of Vatnajökull ice cap in Iceland are analysed. Two types of models are used to model the flow and the evolution of the surface. A full system model is used on a small portion in the center of the ice cap to model how the ice flows into a surface depression created during glacier outburst flood that occurred in 1996. The full system model can be simplified with the Shallow Ice Approximation (SIA) which is valid if the thickness of the ice is much smaller than its length. The SIA model is used to compute the surface evolution of the whole ice cap. The SIA equations are solved with a finite difference method on a square grid.

The basis for the numerical modeling are the radio-echo sounding data of the bedrock topography of Vatnajökull, along with surface elevation and velocity of the ice, and mass balance measurements provided by Helgi Björnsson at the Science Institute, University of Iceland.

Several numerical schemes to solve the SIA equations are tested. It is shown that a commonly used method (alternating direction semi-implicit) is not mass conserving due to ice free points within the ice cap. It is necessary to use an upstream scheme to ensure mass conservation. All computations on Vatnajökull presented in the thesis are done with the upstream scheme.

Model computations with the SIA model forced with a regression model for the mass-balance distribution, including mass balance-elevation feed back, show that Vatnajökull ice cap can not be modeled with a constant ELA. Depending on the altitude of the ELA the ice cap either grows without bound or it settles to a steady state that is considerably smaller than the present ice cap. The ice cap is sensitive to the mass-balance forcing. Changes in the ELA that are within the range measured 1992-2000 cause large volume changes.

It is concluded that a critical size of an ice cap can occur where it is very sensitive to changes in mass balance input and can respond in an unstable manner by unlimited growth. Vatnajökull is presently close to this critical size. Ice caps that are smaller and glaciers resting on steep bedrock slopes are not as sensitive to mass balance changes.