Total surface accumulation (total snowfall minus total sublimation) on the Greenland Ice Sheet is estimated as 299 ¿ 23 kg m-2 yr-1 for an assumed 30-year span, the uncertainty being quoted as twice the standard error. The estimate is very similar to earlier estimates because it relies largely on the same compiled observations, but it is the first to be accompanied by formal error bars. An error model was developed for this purpose. It incorporates uncertainties due to measurement error, record length or span, and spatial bias in the distribution and density of the observations. Measurement errors, although dominant over large parts of the interior, make only a small contribution to uncertainty in the accumulation of the whole ice sheet. Time series of accumulation are shown to be stationary and independent, which means that the date of any given observation is of no importance when evaluating its uncertainty as an estimate of accumulation at any other date. However, as found earlier, the span of the observation is a leading contributor to uncertainty, and a means of placing short- and long-span measurements on an equal footing is developed. Spatial bias is the other leading contributor, to judge from modeling of the standard error of averages of pairs of observations as a function of their separation and from a map of the standard error of accumulation. The standard error of interpolated point estimates of accumulation is small where measurements are dense and well-distributed in the interior, but grows rapidly where measurements are more thinly or unevenly distributed. Estimates of accumulation are therefore most uncertain in the peripheral ablation zone. It is suggested that uncertainty in accumulation needs to be reduced by a factor of two or more if the measurements are to contribute reliably to explaining the observed sea level rise.