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A First Step Toward Quantifying the Climate’s Information Production over the Last 68,000 Years

Part of the Lecture Notes in Computer Science book series (LNISA,volume 9897)


Paleoclimate records are extremely rich sources of information about the past history of the Earth system. We take an information-theoretic approach to analyzing data from the WAIS Divide ice core, the longest continuous and highest-resolution water isotope record yet recovered from Antarctica. We use weighted permutation entropy to calculate the Shannon entropy rate from these isotope measurements, which are proxies for a number of different climate variables, including the temperature at the time of deposition of the corresponding layer of the core. We find that the rate of information production in these measurements reveals issues with analysis instruments, even when those issues leave no visible traces in the raw data. These entropy calculations also allow us to identify a number of intervals in the data that may be of direct relevance to paleoclimate interpretation, and to form new conjectures about what is happening in those intervals—including periods of abrupt climate change.


  • Information Production
  • Storm Track
  • Moisture Source
  • Geothermal Heat
  • Permutation Entropy

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  1. 1.

    Since ice sheets preferentially collect \(^{16}\mathrm {O}\), while oceans preferentially collect \(^{18}\mathrm {O}\).

  2. 2.

    The accumulation data from the WDC has not yet been released publicly, so we cannot include a plot of it here, but there are some extremely interesting correspondences that we hope to be able to include in a few months, when we are allowed to share those data.



  2. Alley, R., et al.: Abrupt climate change. Science 299, 2005–2010 (2003)

    CrossRef  Google Scholar 

  3. Bandt, C., Pompe, B.: Permutation entropy: a natural complexity measure for time series. Phys. Rev. Lett. 88(17), 174102 (2002)

    CrossRef  Google Scholar 

  4. Bollt, E., Stanford, T., Lai, Y.C., Życzkowski, K.: What symbolic dynamics do we get with a misplaced partition?: on the validity of threshold crossings analysis of chaotic time-series. Physica D 154(3), 259–286 (2001)

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Buizert, C.: The WAIS divide deep ice core WD2014 chronology–Part 1: methane synchronization (6831 ka BP) and the gas age-ice age difference. Clim. Past 11, 153–173 (2015)

    CrossRef  Google Scholar 

  6. Cao, Y., Tung, W., Gao, J., Protopopescu, V., Hively, L.: Detecting dynamical changes in time series using the permutation entropy. Phys. Rev. E 70(4), 046217 (2004)

    CrossRef  MathSciNet  Google Scholar 

  7. Dakos, V., et al.: Slowing down as an early warning signal for abrupt climate change. Proc. Nat. Acad. Sci. 105(38), 14308–14312 (2008)

    CrossRef  Google Scholar 

  8. Dansgaard, W.: Stable isotopes in precipitation. Tellus 16, 436–447 (1964)

    CrossRef  Google Scholar 

  9. Dansgaard, W., et al.: Evidence for general instability of past climate from a 250-kyr ice-core record. Nature 364, 218–220 (1993)

    CrossRef  Google Scholar 

  10. Dansgaard, W., Johnsen, S., Clausen, H., Gundestrup, N.: Stable isotope glaciology. Medelelsser om Gronland 197, 1–53 (1973)

    Google Scholar 

  11. Dansgaard, W., White, J., Johnsen, S.: The abrupt termination of the younger Dryas climate event. Nature 339, 532–534 (1989)

    CrossRef  Google Scholar 

  12. Fadlallah, B., Chen, B., Keil, A., Príncipe, J.: Weighted-permutation entropy: a complexity measure for time series incorporating amplitude information. Phys. Rev. E 87(2), 022911 (2013)

    CrossRef  Google Scholar 

  13. Kraskov, A., Stögbauer, H., Grassberger, P.: Estimating mutual information. Phys. Rev. E 69(6), 066138 (2004)

    CrossRef  MathSciNet  Google Scholar 

  14. Lenton, T., et al.: Early warning of climate tipping points from critical slowing down: comparing methods to improve robustness. Philos. Trans. R. Soc. Lond. A: Math. Phy. Eng. Sci. 370(1962), 1185–1204 (2012)

    CrossRef  Google Scholar 

  15. Mantegna, R., Buldyrev, S., Goldberger, A., Havlin, S., Peng, C., Simons, M., Stanley, H.: Linguistic features of noncoding DNA sequences. Phys. Rev. Lett. 73(23), 3169–3172 (1994)

    CrossRef  MATH  Google Scholar 

  16. Petit, J., et al.: Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica. Nature 399, 429–436 (1999)

    CrossRef  Google Scholar 

  17. Scheffer, M., et al.: Early-warning signals for critical transitions. Nature 461, 53–59 (2009)

    CrossRef  Google Scholar 

  18. Schreiber, T.: Measuring information transfer. Phys. Rev. Lett. 85(2), 461–464 (2000)

    CrossRef  Google Scholar 

  19. Shannon, C.: Prediction and entropy of printed English. Bell Syst. Tech. J. 30(1), 50–64 (1951)

    CrossRef  MATH  Google Scholar 

  20. Sigl, M., et al.: The WAIS Divide deep ice core WD2014 chronology–part 2: Annual-layer counting (031 ka BP). Clim. Past 12, 769–786 (2016)

    CrossRef  Google Scholar 

  21. WAIS Divide Project Members: Onset of deglacial warming in west antarctica driven by local orbital forcing. Nature 500, 440–444 (2013)

    Google Scholar 

  22. WAIS Divide Project Members: Precise interpolar phasing of abrupt climate change during the last ice age. Nature 520, 661–665 (2015)

    CrossRef  Google Scholar 

  23. White, J., et al.: Abrupt impacts of climate change: Anticipating surprises. In: EGU General Assembly Conference Abstracts, vol. 16, p. 17028 (2014)

    Google Scholar 

  24. Winstrup, M., et al.: An automated approach for annual layer counting in ice cores. Clim. Past 8, 1881–1895 (2012)

    CrossRef  Google Scholar 

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Garland, J., Jones, T.R., Bradley, E., James, R.G., White, J.W.C. (2016). A First Step Toward Quantifying the Climate’s Information Production over the Last 68,000 Years. In: Boström, H., Knobbe, A., Soares, C., Papapetrou, P. (eds) Advances in Intelligent Data Analysis XV. IDA 2016. Lecture Notes in Computer Science(), vol 9897. Springer, Cham.

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