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The Greenland Ice Sheet is a substantial reservoir of almost 7 m of sea level equivalent, and on average, climate dictates 60% of its sea level contribution. Changes in ice discharge, driven by perturbations in outlet glacier ice dynamics, constitute the rest. Climate also affects ice discharge, since the flow of interior ice feeding the outlet glaciers evolves in response to surface changes over time. Here, using an ice sheet model and uncertainty quantification, we explore ice flow sensitivity to climate-driven changes in ice surface topography on multidecadal timescales. We find that changes in surface forcing near large outlet glaciers can influence region-wide ice flow. Improvements to climate products should be prioritized in these areas, especially in the Central West and Southeast. Results also suggest that over most of Greenland, surface forcing should be supplied at a spatial resolution of 21 km or finer to accurately simulate ice response to climate change.