AbstractOcean-driven melting of floating ice-shelves in the Amundsen Sea is currently the main process controlling Antarctica’s contribution to sea-level rise. Using a regional ocean model, we present a comprehensive suite of future projections of ice-shelf melting in the Amundsen Sea. We find that rapid ocean warming, at approximately triple the historical rate, is likely committed over the twenty-first century, with widespread increases in ice-shelf melting, including in regions crucial for ice-sheet stability. When internal climate variability is considered, there is no significant difference between mid-range emissions scenarios and the most ambitious targets of the Paris Agreement. These results suggest that mitigation of greenhouse gases now has limited power to prevent ocean warming that could lead to the collapse of the West Antarctic Ice Sheet.