In the accumulation zone of the Greenland ice sheet the annual accumulation rate may be determined through identification of the annual cycle in the isotopic climate signal and other parameters that exhibit seasonal variations. On an annual basis the accumulation rate in different Greenland ice cores is highly variable, and the degree of correlation between accumulation series from different ice cores is low. However, when using multiyear averages of the different accumulation records, the correlation increases significantly. A statistical model has been developed to estimate the common climate signal in the different accumulation records through optimization of the ratio between the variance of the common signal and of the residual. Using this model, a common Greenland accumulation record for the past 1800 years has been extracted. The record shows significant 11.9 years periodicity. A sharp transition to very dry conditions is found just before A. D. 1200, and very dry conditions during the 13th century together with dry and cold spells during the 14th century may have put extra strain on the Norse population in Greenland and may have contributed to their extinction. Accumulation rates gradually decrease from a distinct maximum in A. D. 1394 to very dry conditions in the late 17th century and thus reflect the Little Ice Age.