Light-absorbing impurities enhance snowmelt by boosting the absorption of solar energy. It is therefore important for coupled aerosol–climate and ice sheet models to include this effect, and yet most do not. We conduct several thousand simulations and develop a kernel and linear equations relating melt runoff on the Greenland Ice Sheet to the timing and amount of black carbon within precipitation and dry deposition, which can be used to extend the utility of state-of-the-art aerosol models.