Comparison of numerical schemes for the solution of the advective age equation in ice sheets



A one-dimensional model problem for the computation of the age field in ice sheets, which is of great importance for dating deep ice cores, is considered. The corresponding partial differential equation (PDE) is of purely advective (hyperbolic) type, which is notoriously difficult to solve numerically. By integrating the PDE over a space-time element in the sense of a finite-volume approach, a general difference equation is constructed from which a hierarchy of solution schemes can be derived. Iteration rules are given explicitly for central differences, first-, second- and third-order (QUICK) upstreaming as well as modified TVD Lax-Friedrichs schemes. The performance of these schemes in terms of convergence and accuracy is discussed. It turns out that second-order upstreaming and the modified TVD Lax-Friedrichs scheme with Minmod slope limiter are most suitable for numerical age computations in ice-sheet models.

Annals of Glaciology, 35, 487-494 (2002).

Last modified: 2008-09-08