A NUMERICAL STUDY OF THE VALIDITY OF SHALLOW ICE APPROXIMATIONS

• Main Authors: Josefin Ahlkrona, Nina Kirchner
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Subjects: Ice Sheet
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.640.2173; http://www.it.uu.se/research/publications/reports/2012-015/2012-015-nc.pdf

Improving numerical ice sheet models is a very active field of research. In part, this is be-cause ice sheet modelling has gained societal relevance in the context of predictions of future sea level rise. Ice sheet modelling is however also a challenging mathematical and computa-tional subject. Since the exact equations governing ice dynamics, the full Stokes equations, are computationally expensive to solve, approximations are crucially needed for many problems. Shallow ice approximations are a family of approximations derived by asymptotic expansion of the exact equations in terms of the aspect ratio, . Retaining only the zeroth order terms in this expansion yields the by far most frequently used approximation; the Shallow Ice Ap-proximation (SIA). Including terms up to second order yields the Second Order Shallow Ice Approximation (SOSIA), which is a so-called higher order model. Here, we study the validity and accuracy of shallow ice approximations beyond previous analyses of the SIA. We perform a detailed analysis of the assumptions behind shallow ice approximations, i.e. of the order of magnitude of field variables. We do this by using a numerical solution of the exact equations for ice flow over a sloping, undulating bed. We also construct analytical solutions for the