  Paleoclimate records are extremely rich sources of information about the past
history of the Earth system. Information theory, the branch of mathematics
capable of quantifying the degree to which the present is informed by the past,
provides a new means for studying these records. Here, we demonstrate that
estimates of the Shannon entropy rate of the water-isotope data from the West
Antarctica Ice Sheet (WAIS) Divide ice core, calculated using weighted
permutation entropy (WPE), can bring out valuable new information from this
record. We find that WPE correlates with accumulation, reveals possible
signatures of geothermal heating at the base of the core, and clearly brings
out laboratory and data-processing effects that are difficult to see in the raw
data. For example, the signatures of Dansgaard-Oeschger events in the
information record are small, suggesting that these abrupt warming events may
not represent significant changes in the climate system dynamics. While the
potential power of information theory in paleoclimatology problems is
significant, the associated methods require careful handling and well-dated,
high-resolution data. The WAIS Divide ice core is the first such record that
can support this kind of analysis. As more high-resolution records become
available, information theory will likely become a common forensic tool in
climate science.
