Meteorological models were used to retrieve annual accumulation, runoff and surface mass balance on a 5 km x 5 km grid for the Greenland Ice Sheet for 1958-2003. We present the first such history that provides insight into seasonal and interannual variability, which should prove useful for those studying the ice sheet. Derived runoff was validated by means of a control model run and independent in situ data. Modelled accumulation has already been validated using shallow ice-core data. Surface mass balance (SMB) responds rapidly on a yearly basis to changing meteorological (surface air temperature and precipitation) forcing. There are distinct signals in runoff and SMB following three major volcanic eruptions. Runoff losses from the ice sheet were 264(±26) km3 yr-1 in 1961-90 and 372(±37) km3 yr-1 in 1998-2003. Significantly rising runoff since the 1990s has been partly offset by increased precipitation. Our best estimate of overall mass balance declined from 22(±51) km3 yr-1 in 1961-90 to -36(±59) km3 yr-1 in 1998-2003, which is not statistically significant. Additional dynamical factors that cause an acceleration of ice flow near the margins, and possible enhanced iceberg calving, may have led to a more negative mass balance in the past few years than suggested here. The implication is a significant and accelerating recent contribution from the ice sheet to global sea-level rise, with 0.15 mm yr-1 from declining SMB alone over the last six years.