A hydrologically coupled flowband model of 'higher order' ice dynamics is used to explore perturbations in response to supraglacial water drainage and subglacial flooding. The subglacial drainage system includes interacting 'fast' and 'slow' drainage elements. The fast drainage system is assumed to be composed of ice-walled conduits and the slow system of a macroporous water sheet. Under high subglacial water pressures, flexure of the overlying ice is modelled using elastic beam theory. A regularized Coulomb friction law describes basal boundary conditions that enable hydrologically driven acceleration. We demonstrate the modelled interactions between hydrology and ice dynamics by means of three observationally inspired examples: (i) simulations of meltwater drainage at an Alpine-type glacier produce seasonal and diurnal variability, and exhibit drainage evolution characteristic of the so-called 'spring transition'; (ii) horizontal and vertical diurnal accelerations are modelled in response to summer meltwater input at a Greenlandtype outlet glacier; and (iii) short-lived perturbations to basal water pressure and ice-flow speed are modelled in response to the prescribed drainage of a supraglacial lake. Our model supports the suggestion that a channelized drainage system can form beneath the margins of the Greenland ice sheet, and may contribute to reducing the dynamic impact of floods derived from supraglacial lakes.

[1] The influence of hydrologic transience and heterogeneity on basal motion is an often-neglected aspect of numerical ice-flow models. We present a flow-band model of glacier dynamics with a Coulomb friction sliding law that is coupled to a model of the basal drainage system by means of subglacial water pressure. The ice-flow model contains "higher-order" stress gradients from the Stokes flow approximation originally conceived by Blatter (1995). The resulting system of nonlinear equations is solved using a modified Picard iteration that is shown to improve the rate of convergence. A parameterization of lateral shearing is included to account for the effects of threedimensional geometry. We find that lateral drag has a discernible effect on glacier speed even when glacier width exceeds glacier length. Variations in flow-band width are shown to have a greater influence on flow line speed than either different valley crosssectional shapes or the presence or absence of glacier sliding along valley walls. Modeled profiles of subglacial water pressure depart significantly from pressures prescribed as a uniform fraction of overburden, thus producing profiles of glacier sliding that are distinctly different from those that would be described by a sliding law controlled by overburden pressures. Simulations of hydraulically driven glacier acceleration highlight the value of including a representation of basal hydrology in models aiming for improved predictive capability of glacier dynamics.

Abstract. Glacier surges are a well-known example of an internal dynamic oscillation whose occurrence is not a direct response to the external climate forcing, but whose character (i.e. period, amplitude, mechanism) may depend on the glacier's environmental or climate setting. We examine the dynamics of a small (∼5 km 2 ) valley glacier in Yukon, Canada, where two previous surges have been photographically documented and an unusually slow surge is currently underway. To characterize the dynamics of the present surge, and to speculate on the future of this glacier, we employ a higher-order flowband model of ice dynamics with a regularized Coulomb-friction sliding law in both diagnostic and prognostic simulations. Diagnostic (force balance) calculations capture the measured ice-surface velocity profile only when non-zero basal water pressures are prescribed over the central region of the glacier, coincident with where evidence of the surge has been identified. This leads to sliding accounting for 50-100% of the total surface motion in this region. Prognostic simulations, where the glacier geometry evolves in response to a prescribed surface mass balance, reveal a significant role played by a bedrock ridge beneath the current equilibrium line of the glacier. Ice thickening occurs above the ridge in our simulations, until the net mass balance reaches sufficiently negative values. We suggest that the bedrock ridge may contribute to the propensity for surges in this glacier by promoting the development of the reservoir area during quiescence, and may permit surges to occur under more negative balance conditions than would otherwise be possible. Collectively, these results corroborate our interpretation of the current glacier flow regime as indicative of a slow surge that has been ongoing for some time, and support a relationship between surge incidence or character and the Correspondence to: G. E. Flowers (gflowers@sfu.ca) net mass balance. Our results also highlight the importance of glacier bed topography in controlling ice dynamics, as observed in many other glacier systems.