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Satellite radar interferometry data reveals that the grounding line of Petermann Glacier, Greenland migrates by several kilometers during the tidal cycle, bringing pressurized, subsurface, warm ocean waters in regular contact with a large sector of grounded ice. We use the Massachusetts Institute of Technology general circulation model in two dimensions to calculate the ice melt rates as a function of grounding zone (GZ) length and ocean Thermal Forcing (TF). Ice melt rates are found to be higher in the GZ cavity than anywhere else in the ice shelf cavity. The melt rates increase sub‐linearly with the length of the GZ and ocean TF. The model results agree well with remote sensing estimates of ice melt. High basal ice melt rates in tidally flushed grounding zones imply that marine‐terminating glaciers are more sensitive to ocean TF than anticipated, which will increase their projected contribution to sea level rise. Plain Language Summary: The traditional view of ice melting in contact with ocean waters is that melt rates drop to zero at the grounding line, which is a semi‐fixed boundary at the junction between grounded ice and the ocean. In reality, the grounding line migrates by kilometers during the tidal cycle, more than 10 times beyond the range expected from hydrostatic equilibrium, which brings warm, saline water in rapid contact with broad sectors of grounded ice. We use an ocean model to calculate the melt rates caused by seawater intrusions. We find that the melt rates in the GZ are higher than anywhere else in the ice shelf cavity and increase as the GZ becomes wider and the ocean gets warmer. Ice melt in kilometer‐size grounding zones will reduce the basal resistance to flow and will increase the sensitivity of the glacier flow to ocean warming, hence projections of sea level rise from the glacier will go up. Key Points: First modeling of ice melt rates from seawater intrusions in the kilometer‐size grounding zone (GZ) of Petermann Glacier using an ocean modelModeled melt rates are highest in the GZ and increase linearly with GZ width and ocean thermal forcingHigh melt rates in kilometer‐size grounding zones imply a higher sensitivity of glaciers to ocean warming than anticipated [ABSTRACT FROM AUTHOR]