Different parts of Antarctica receive different amounts of snowfall each year. In this paper we map the variations of the mean annual snow accumulation across the ice sheet. We also quantify the uncertainty in our estimates more objectively than has been possible for earlier maps. The new map is produced using observations from satellites and ground-based measurements. After a logarithmic transformation, these are combined using the geostatistical method of continuous-part universal kriging to give an estimate of the snow accumulation within each cell of a rectangular grid covering Antarctica. We also derive spatial averages over the major drainage systems of the ice sheet, along with their confidence intervals. We obtain a value of 143 ¿ 4 kg m-2 a-1 for the average rate of snow accumulation upon the grounded ice sheet of Antarctica.