Abstract Stable water isotopes from ice cores are a unique proxy for reconstructing polar climate variability. Their interpretation is, however, challenging due to the impact of depositional noise. Here, we analyze the centennial‐ to millennial‐scale isotope variability of the Greenland ice cores NGRIP, GRIP, and GISP2 to investigate how their coherent signal and local noise have evolved over the last 100,000 years. We show that the noise systematically depends on the climate state, with higher levels under colder temperatures and lower accumulation rates. Most of the noise originates from local stratigraphic disturbances, while additional noise variability only emerges in the Greenland stadials. The remaining climate signal variability is higher in the last glacial period compared to the Holocene, but does not systematically differ between stadials and interstadials. We show that, by considering systematic changes of noise, it is possible to achieve more accurate estimates of past climate variability. Plain Language Summary The stable water isotope composition of snow, accumulating on the ice sheets of Greenland and Antarctica, records surface temperatures. Ice cores therefore provide valuable information on the past climate and its variability. However, the archival process of snow is disturbed and irregular, for example, due to winds and dune formations at the snow surface and patchy snowfall. This introduces noise, which increases the variability represented in this climate archive. Here, we analyze three ice core records from Greenland and how their variability changed during the Holocene and the last glacial period. We show that there is systematically more noise in climate states with lower temperatures and less snowfall. In the Holocene and the warmer phases of the last glacial period (interstadials) most of the noise seems to originate from local disturbances of the snow surface. The actual regional climate variability was much lower in the Holocene than in the last glacial period, whereas it does not systematically differ between the cold and warm phases of the last glacial period. We show that, by acknowledging that noise in the isotope compositions can change over time, it is possible to get more accurate estimates of the past climate variability. Key Points Changes in Greenland centennial to millennial ice core isotope variability in the last glacial period can be attributed to noise levels The amount of noise systematically covaries with climate states and accumulation rates Most of it originates from local disturbances, likely related to the surface stratigraphy