Clouds have been recognized to enhance surface melt on the Greenland Ice Sheet (GrIS). However, quantitative estimates of the effects of clouds on the GrIS melt area and ice-sheet-wide surface mass balance are still lacking. Here we assess the effects of clouds with a state-of-the-art regional climate model, conducting a numerical sensitivity test in which adiabatic atmospheric conditions as well as zero cloud water/ice amounts are assumed (i.e., clear-sky conditions), although the precipitation rate is the same as in the control all-sky simulation. By including or excluding clouds, we quantify time-integrated feedbacks for the first time. We find that clouds were responsible for a 3.1%, 0.3%, and 0.7% increase in surface melt extent (of the total GrIS area) in 2012, 2013, and 2014, respectively. During the same periods, clouds reduced solar heating and thus daily runoff by 1.6, 0.8, and 1.0 Gt day-1, respectively: clouds did not enhance surface mass loss. In the ablation areas, the presence of clouds results in a reduction of downward latent heat flux at the snow/ice surface so that much less energy is available for surface melt, which highlights the importance of indirect time-integrated feedbacks of cloud radiative effects.