Skip to main content

Exact solutions to the thermomechanically coupled shallow-ice approximation: effective tools for verification

Buy Article:

$35.11 plus tax (Refund Policy)


We describe exact solutions to the thermomechanically coupled shallow-ice approximation in three spatial dimensions. Although artificially constructed, these solutions are very useful for testing numerical methods. In fact, they allow us to verify a finite-difference scheme, that is, to show that the results of our numerical scheme converge to the correct continuum values as the grid is refined in three dimensions. Comparison of numerical results with exact solutions has helped us to precisely quantify and understand some of the numerical errors we are making. Our verified numerical scheme shows the basal temperature spokes which arose in the EISMINT (European Ice Sheet Modelling INiTiative) II intercomparison (Payne and others, 2000). A careful analysis describes these warm spokes as numerical errors which occur when the derivative of the strain-heating term with respect to the temperature is large. On the other hand, the appearance of basal temperature spokes in a verified numerical scheme strongly suggests that they are a feature of the EISMINT II experiment F continuum problem. In fact, they are clear evidence of an unstable equilibrium point of the continuum problem. This paper is a sequel to Bueler and others (2005), which addresses exact solutions and verification in the isothermal case.

Document Type: Research Article


Publication date: July 1, 2007

More about this publication?
  • The Journal of Glaciology is published six times per year. It accepts submissions from any discipline related to the study of snow and ice. All articles are peer reviewed. The Journal is included in the ISI Science Citation Index.
  • Editorial Board
  • Information for Authors
  • ingentaconnect is not responsible for the content or availability of external websites

Access Key

Free Content
Free content
New Content
New content
Open Access Content
Open access content
Subscribed Content
Subscribed content
Free Trial Content
Free trial content
Cookie Policy
Cookie Policy
ingentaconnect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more