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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 three‐dimensional 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 …