The objective is to demonstrate that spatially variable ice-surface roughness is an important, and so-far overlooked, component of melt processes in the Greenland Ice Sheet (GrIS), linking the analysis of spatial ice-surface roughness (SISR) derived from satellite laser altimeter data with a new regional energy balance model. Specific results are: (1) SISR can be calculated from ICESat Geoscience Laser Altimeter System (GLAS) data for the GrIS. (2) Seasonal and interannual changes of SISR are reflected in satellite-altimetry-based roughness maps, demonstrated for GLAS data. (3) Current regional climate models largely utilize roughness as a constant value in space and time. Here, we develop a new Regional Energy Balance Model (REBM) that is sensitive to SISR, using the same physical principles as the Integrated Forecasting System (IFS), constrained by climate fields of the Regional Atmospheric Climate Model (RACMO2). (4) A control study is carried out to ensure that REBM works correctly. (5) Melt energy of the GrIS calculated by REBM using SISR results in much higher melt values than predicted by regional climate models (RACMO2, IFS), which underestimate melting. (6) Application of the approach using REBM to the GrIS, driven by seasonally and interannually variable SISR, highlights regional and temporal differences in sensible heat flux and thus melt differences. In summary, SISR explains some of the discrepancy between observed and modeled melting in the GrIS. This study serves as a proof of concept for an approach that establishes mathematical and physical concepts for linking satellite altimeter measurements, SISR and energy balance modeling.