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Dynamic change at the marine-terminating margins of the Greenland Ice Sheet may be initiated by the ocean, particularly where subglacial runoff drives vigorous ice-marginal plumes and rapid submarine melting. Here we model submarine melt-driven undercutting of tidewater glacier termini, simulating a process which is key to understanding ice-ocean coupling. Where runoff emerges from broad subglacial channels we find that undercutting has only a weak impact on local submarine melt rate but increases total ablation by submarine melting due to the larger submerged ice surface area. Thus, the impact of melting is determined not only by the melt rate magnitude but also by the slope of the ice-ocean interface. We suggest that the most severe undercutting occurs at the maximum height in the fjord reached by the plume, likely promoting calving of ice above. It remains unclear, however, whether undercutting proceeds sufficiently rapidly to influence calving at Greenland's fastest-flowing glaciers.