Analysis of an Error Indicator used in Ice Sheet Modelling

Sammanfattning

The dynamics of large ice sheets, such as those covering Antarctica and Greenland, are crucial for predicting global sea level rise due to their vast freshwater reserves. This thesis investigates the accuracy of the ice sheet model ISCAL (Ice Sheet Approximation Levels method) compared to modelling using the full Stokes (FS) equations. Central to the ISCAL algorithm is the error indicator, which estimates the discrepancy between the Shallow Ice Approximation (SIA) and FS velocities. A deeper understanding of the error indicator is essential for accurately modeling ice sheet dynamics using the ISCAL method, and it could provide insights into improving the error indicator’s accuracy. The accuracy of the error indicator is analyzed through a theoretical investigation of the eigenvalues and the condition number of the matrices related to the finite element approximation of the FS equations. The main findings suggest that the accuracy of the error indicator depends on several factors, including the strain rates of the SIA and FS velocities, the critical shear rate, and constants related to the mesh size, domain, and shape regularity of the finite element mesh. These theoretical findings are then compared with the actual errors from simulations, focusing on variations in the critical shear rate. The numerical experiments did not show perfect alignment with the theoretical results, indicating that the upper bound for the accuracy of the error indicator may have been too generously estimated.