At high elevations of ice sheets, melting snow generally percolates and refreezes, so does not contribute to the shrinking of the ice sheet. Here, we systematically map the runoff area of the Greenland ice sheet, using surface rivers visible on satellite imagery. Between 1985 and 2020, the maximum runoff elevation rose by 58-329 metres, expanding the runoff area by 29% (-8%/+6%). Excess melt beyond the refreezing capacity of pores in snowfall has created near-impermeable ice slabs that sustain surface runoff even in cooler summers. We show that two surface mass balance models over-estimate the runoff area by 16-30%. Once restricted to our observed areas they indicate that 5-10% of recent runoff likely comes from the expanded runoff area. Runoff from higher elevations is sensitive to projected warming as further increases in the runoff limit will increase the runoff area disproportionately.