We take an information-theoretic approach to analyzing 68 thousand years of water isotope data from the WAIS Divide ice core, the longest continuous and highest-resolution record yet recovered from Antarctica. The water isotopes are primarily a proxy for local temperature at the time of snow deposition, but also contain information about broader atmospheric circulation patterns. Using a well defined depth-age scale, we apply weighted permutation entropy to calculate the Shannon entropy rate of the isotope measurements. We find that the rate of information production reveals differences in analytical techniques, even when those differences leave no visible traces in the raw data. The entropy calculations also allow us to identify a number of intervals in the data that may be of direct relevance to paleoclimate interpretation. To validate the results, we perform a number of tests, particularly whether the information production arises from climatic signals or post-processing of the ice after recovery from the drill site.
WPE measures the average rate at which new information -- unrelated to anything in the past -- is produced by the system that generated the time series. If that rate is very low, the current observation contains a lot of information about the past and the signal is perfectly predictable. If that rate is very high, all of the information in the observation is completely new: i.e., the past tells you nothing about the future.
A very interesting feature here is the large jump in WPE between 5–8 ka. As it turns out, an older instrument was used to analyze the ice in this region. The WPE results clearly show that that instrument introduced noise into the data: i.e., every measurement contains completely new information, unrelated to the previous ones. As can be seen from examination of the blue trace in the figure, that noise was not visually apparent in the d18O data itself, so the instrument issue was not detected immediately by the laboratory team.