Constraints on the positions of ice-stream margins from linking thermomechanical behavior to subglacial hydrology

Evaluating the potential response of the West Antarctic ice streams to changing climatic conditions depends sensitively on the behavior of the shear margins, which play an important role in the force balance of active ice streams. Previous modeling efforts and field observations have raised the possibility of shear-induced melting in ice-stream margins, highlighting the potentially important role of hydrological processes for understanding margin stability. The goal of this paper is to couple the thermomechanical behavior of shear margins to the subglacial hydrology at the bed. An important component of our model is that we solve for the margin positions self-consistently instead of enforcing margin positions apriori.

Our 2D model represents a cross-section through the ice-stream margin perpendicular to the downstream flow direction. We assume that the ice flows over a bed consisting of Coulomb-plastic till. The position and extent of the ice stream is determined by where the shear stress at the bed attains the local and spatially variable yield stress. If the basal stress falls below the yield stress, the ice is assumed to lock to the bed. While a simplified variation of this model setup can be solved analytically, we adopt a numerical treatment to be able to incorporate a realistic ice rheology.

The mechanical, thermal and hydrological model are linked through melt water generation and flow: For a given yield stress at the bed, we compute the margin positions and the anti-plane strain in our mechanical model. The resulting shear heating is then used as a source term in the thermal model to estimate the extent of the temperate zone and amount of melt water produced in the ice. Assuming that the melt water rains down vertically to the bed, we estimate the pore pressure distribution, which in turn determines the yield stress, in our hydrological model. Changing hydrological conditions at the bed are thus intrinsically coupled to the mechanical and thermal properties of the margin and the margin position.