Observed changes in the surface elevation of the Greenland Ice Sheet are caused by ice dynamics, basal elevation change, basal melt, surface mass balance (SMB) variability, and by compaction of the overlying firn. The last two contributions are quantified here using a firn model that includes compaction, meltwater percolation, and refreezing. The model is forced with surface mass fluxes and temperature from a regional climate model for the period 1960-2014. The model results agree with observations of surface density, density profiles from 62 firn cores, and altimetric observations from regions where ice-dynamical surface height changes are likely small. In areas with strong surface melt, the firn model overestimates density. We find that the firn layer in the high interior is generally thickening slowly (1-5 cm yr-1). In the percolation and ablation areas, firn and SMB processes account for a surface elevation lowering of up to 20-50 cm yr-1. Most of this firn-induced marginal thinning is caused by an increase in melt since the mid-1990s and partly compensated by an increase in the accumulation of fresh snow around most of the ice sheet. The total firn and ice volume change between 1980 and 2014 is estimated at -3295 ± 1030 km3 due to firn and SMB changes, corresponding to an ice-sheet average thinning of 1.96 ± 0.61 m. Most of this volume decrease occurred after 1995. The computed changes in surface elevation can be used to partition altimetrically observed volume change into surface mass balance and ice-dynamically related mass changes.