The verification and significance of three approaches to longitudinal stresses in high–resolution models of glacier flow

With the purpose of improving the ice physics underpinning time–dependent glacier flowline models, three independent approaches for solving longitudinal stresses in glaciers are discussed and verified by application to Haut Glacier d’Arolla. To highlight any shortcomings, the reduced and much utilised driving stress approximation is also applied and compared. Modelled velocity patterns using the three full stress schemes exhibit consistency with one another and good coincidence with observed velocities for the 1991 summer melt season. Furthermore, these stress patterns indicate that longitudinal stresses are significant and of a similar order of magnitude as the basal shear stress components. However, the driving stress approximation yields erratic fluctuations in the stress and velocity fields which are neither realistic in terms of mass continuity nor agree with observations. Basal decoupling experiments indicate a complex relationship between basal velocity and englacial stresses with considerable dampening of any basal perturbation occurring as it is dissipated towards the surface and transferred throughout the ice mass. The driving stress approximation fails to account at all for any such coupling. Experiments to identify the length scale over which longitudinal effects operate indicate that they are significant even up to 10 ice thicknesses. The implication here is that longitudinal stresses play a significant role in determining glacier dynamics on length scales up to at least 2 km and that the predictive power of models of glacier flow based purely on the driving stress approximation is therefore subject to significant limitations. Inclusion of longitudinal stresses overcomes one of the main limitations imposed on such models and, given the potential ease of incorporation of the schemes described here, this deficiency may readily be resolved.