| Summary: | Surface runoff from the Greenland ice sheet (GrIS) has dominated recent ice mass loss and is having significant impacts on sea-level rise under global warming. Here, we used two modified degree-day (DD) methods to estimate the runoff of the GrIS during 1950–2200 under the extensions of historical, RCP 4.5, and RCP 8.5 scenarios. Near-surface air temperature and snowfall were obtained from five Earth System Models. We applied new degree-day factors to best match the results of the surface energy and mass balance model, SEMIC, over the whole GrIS in a 21st century simulation. The relative misfits between tuned DD methods and SEMIC during 2050–2089 were 3% (RCP4.5) and 12% (RCP8.5), much smaller than the 30% difference between untuned DD methods and SEMIC. Equilibrium line altitude evolution, runoff-elevation feedback, and ice mask evolution were considered in the future simulations to 2200. The ensemble mean cumulative runoff increasing over the GrIS was equivalent to sea-level rises of 6 ± 2 cm (RCP4.5) and 9 ± 3 cm (RCP8.5) by 2100 relative to the period 1950–2005, and 13 ± 4 cm (RCP4.5) and 40 ± 5 cm (RCP8.5) by 2200. Runoff-elevation feedback produced runoff increases of 5 ± 2% (RCP4.5) and 6 ± 2% (RCP8.5) by 2100, and 12 ± 4% (RCP4.5) and 15 ± 5% (RCP8.5) by 2200. Two sensitivity experiments showed that increases of 150% or 200%, relative to the annual mean amount of snowfall in 2080–2100, in the post-2100 period would lead to 10% or 20% more runoff under RCP4.5 and 5% or 10% under RCP8.5 because faster ice margin retreat and ice sheet loss under RCP8.5 dominate snowfall increases and ice elevation feedbacks.
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