Concerted observational and modelling programmes are underway to determine the mass balance of the Greenland Ice Sheet, and therefore help predict its response to future climatic change. We give results of meteorological modelling based on ERA-40 reanalysis data from the European Centre for Medium Range Weather Forecasts (ECMWF). Our novel annual and seasonal surface-mass-balance history of the ice sheet for 1957-2003, is based on accumulation modelling and a new monthly melt-water runoff model by Janssens & Huybrechts (Huybrechts 2002). This yields valuable insights into the past and present state and variability of the Greenland ice mass and links with climate. Aspects of the validation of the new accumulation, runoff and SMB series are discussed. There was considerable interannual variability in snow accumulation, runoff and mass balance over the last 45 years. By comparing with long-term temperature, precipitation and accumulation records from the met. stations and ice cores, we discuss possible climatic factors forcing the ice in this period. We also derive sensitivity of the ice sheet to climatic forcing, based on real meteorological observations (ERA-40). Massive snow accumulation over south-east Greenland during winter 2002/03, well shown in our analysis, led to unprecedented thickening in recent NASA aircraft surveys. Is this recent thickening signal a sign of more extreme weather conditions over the Ice Sheet, more storminess and higher accumulation events, due to global warming?