Surface runoff at the margin of the Greenland Ice Sheet (GrIS) drains to the ice-sheet bed, leading to enhanced summer ice flow. Ice velocities show a pattern of early summer acceleration followed by mid-summer deceleration due to evolution of the subglacial hydrology system in response to meltwater forcing. Modelling the integrated hydrological–ice dynamics system to reproduce measured velocities at the ice margin remains a key challenge for validating the present understanding of the system and constraining the impact of increasing surface runoff rates on dynamic ice mass loss from the GrIS. Here we show that a multi-component model incorporating supraglacial, subglacial, and ice dynamic components applied to a land-terminating catchment in western Greenland produces modelled velocities which are in reasonable agreement with those observed in GPS records for three melt seasons of varying melt intensities. This provides numerical support for the hypothesis that the subglacial system develops analogously to alpine glaciers and supports recent model formulations capturing the transition between distributed and channelized states. The model shows the growth of efficient conduit-based drainage up-glacier from the ice sheet margin, which develops more extensively, and further inland, as melt intensity increases. This suggests current trends of decadal-timescale slowdown of ice velocities in the ablation zone may continue in the near future. The model results also show a strong scaling between average summer velocities and melt season intensity, particularly in the upper ablation area. Assuming winter velocities are not impacted by channelization, our model suggests an upper bound of a 25% increase in annual surface velocities as surface melt increases to 4 ×  present levels.