Increasing numerical stability of mountain valley glacier simulations: implementation and testing of free-surface stabilization in Elmer/Ice

Abstract. This paper concerns a numerical stabilization method for free-surface ice flow called the free-surface stabilization algorithm (FSSA). In the current study, the FSSA is implemented into the numerical ice-flow software Elmer/Ice and tested on synthetic two-dimensional (2D) glaciers, as well as on the real-world glacier of Midtre Lovénbreen, Svalbard. For the synthetic 2D cases it is found that the FSSA method increases the largest stable time-step size at least by a factor of ten for the case of a gently sloping ice surface (3°), and by at least a factor of five for cases of moderately to steeply inclined surfaces (6° to 12°) . Furthermore, the FSSA method increases the overall accuracy for all surface slopes. The largest stable time-step size is found to be smallest for the case of a low sloping surface, despite having overall smaller velocities. For Midtre Lovénbreen the FSSA method doubles the largest stable time-step size, however, the accuracy is in this case slightly lowered in the deeper parts of the glacier, while it increases near edges. The implication is that the non-FSSA method might be more accurate at predicting glacier thinning, while the FSSA method is more suitable for predicting future glacier extent. A possible application of the larger time-step sizes allowed for by the FSSA is for spin-up simulations, where relatively fast changing climate data can be incorporated on short time scales, while the slowly changing velocity field is updated over larger time scales.