Approximately half of Greenland's current annual mass loss is attributed to runoff from surface melt(1). At higher elevations, however, melt does not necessarily equal runoff, because meltwater can refreeze in the porous near-surface snow and firn2. Two recent studies suggest that all(3) or most(3,4) of Greenland's firn pore space is available for meltwater storage, making the firn an important buffer against contribution to sea level rise for decades to come(3). Here, we employ in situ observations and historical legacy data to demonstrate that surface runoff begins to dominate over meltwater storage well before firn pore space has been completely filled. Our observations frame the recent exceptional melt summers in 2010 and 2012 (refs 5,6), revealing significant changes in firn structure at different elevations caused by successive intensive melt events. In the upper regions (more than similar to 1,900m above sea level), firn has undergone substantial densification, while at lower elevations, where melt is most abundant, porous firn has lost most of its capability to retain meltwater. Here, the formation of near-surface ice layers renders deep pore space difficult to access, forcing meltwater to enter an efficient(7) surface discharge system and intensifying ice sheet mass loss earlier than previously suggested(3).