Longitudinal Stresses and Basal Sliding: A Comparative Study

The main problems in understanding the dynamics of a marine-based ice sheet are (i) the role played by longitudinal deviatoric stresses, and (ii) basal sliding. Although several studies have been reported in which both processes are incorporated in an ice-sheet model (either a numerical or a theoretical model), it is not clear how they affect the model outcome.Following the recent analysis presented by Alley and Whillans (1984), however without neglecting the longitudinal-stress gradient along a flowline, an equation for the deviatoric stress is derived from the flow law and the equilibrium of forces. Incorporating this in a numerical model, together with an appropriate sliding relation, allows one to study the effect of (i) and (ii) on the behavior of the model ice sheet. This flowline model is compared with the Alley and Whillans model and with the earlier model of Budd and Jenssen (1975). In the latter model, longitudinal deviatoric stresses play a minor role and have very little effect on the model results. The two other models yield virtually the same results. This means that indeed the gradient of the deviatoric stress along a flowline may be neglected. In fact, the results suggest that only the longitudinal stress at the grounding line is important. Further inland, this stress becomes small and may safely be neglected without affecting the model results.As for basal sliding, two laws were applied to the models. The classical Weertman-type sliding relation, corrected for subglacial water pressure, has little effect on the shape of the model ice sheet; a similar decrease in ice-sheet size can be obtained by increasing the deformation constant in the flow law. On the other hand, the sliding relation as used by Budd et al. (1984) causes a large thinning near the grounding line which is greatly enhanced when longitudinal stresses are incorporated in the model. Together, these processes yield a concave surface profile as observed on West Antarctic ice streams.