Comparison of Numerical Schemes for the Solution of the Ice-Thickness Equation in a Dynamic/Thermodynamic Ice-Sheet Model

A general finite-difference marching scheme for the numerical solution of the ice-thickness equation in ice sheets is considered. From this scheme, a variety of explicit, ADI, implicit and over-implicit methods can be derived. These methods are compared for stability and accuracy within the dynamic/thermodynamic ice-sheet model SICOPOLIS for two different problems: (i) a simple axi-symmetric steady-state ice sheet which rests on a flat bedrock, and (ii) the time-dependent paleo-glaciation of the northern hemisphere. As expected, over-implicit methods turn out to be most stable. For the simple problem, all schemes provide a good accuracy, whereas for the northern hemisphere simulations, the accuracy of the over-implicit scheme is not satisfactory, so that the implicit technique without over-weighing appears favorable for this application.