The Annals of Applied Statistics

A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable?

Blakeley B. McShane and Abraham J. Wyner

Full-text: Open access

Abstract

Predicting historic temperatures based on tree rings, ice cores, and other natural proxies is a difficult endeavor. The relationship between proxies and temperature is weak and the number of proxies is far larger than the number of target data points. Furthermore, the data contain complex spatial and temporal dependence structures which are not easily captured with simple models.

In this paper, we assess the reliability of such reconstructions and their statistical significance against various null models. We find that the proxies do not predict temperature significantly better than random series generated independently of temperature. Furthermore, various model specifications that perform similarly at predicting temperature produce extremely different historical backcasts. Finally, the proxies seem unable to forecast the high levels of and sharp run-up in temperature in the 1990s either in-sample or from contiguous holdout blocks, thus casting doubt on their ability to predict such phenomena if in fact they occurred several hundred years ago.

We propose our own reconstruction of Northern Hemisphere average annual land temperature over the last millennium, assess its reliability, and compare it to those from the climate science literature. Our model provides a similar reconstruction but has much wider standard errors, reflecting the weak signal and large uncertainty encountered in this setting.

Article information

Source
Ann. Appl. Stat. Volume 5, Number 1 (2011), 5-44.

Dates
First available in Project Euclid: 21 March 2011

Permanent link to this document
http://projecteuclid.org/euclid.aoas/1300715170

Digital Object Identifier
doi:10.1214/10-AOAS398

Zentralblatt MATH identifier
05906786

Citation

McShane, Blakeley B.; Wyner, Abraham J. A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable?. Ann. Appl. Stat. 5 (2011), no. 1, 5--44. doi:10.1214/10-AOAS398. http://projecteuclid.org/euclid.aoas/1300715170.


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References

  • Amman, C. M., Joos, F., Otto-Bliesner, B. L. and Tomas, R. (2007). Solar influence on climate during the past millennium: Results from transient simulations with the NCAR climate system model. Proc. Natl. Acad. Sci. USA 104 3713–3718.
  • Ammann, C. and Wahl, E. (2007). The importance of the geophysical context in statistical evaluations of climate reconstruction procedures. Climatic Change 85 71–88.
  • BBC (2008). Earth: The Climate Wars. British Broadcasting Company, September 14.
  • Bradley, R. S. (1999). Paleoclimatology: Reconstructing Climates of the Quaternary, 2nd ed. Academic Press, San Diego.
  • Christiansen, B., Schmith, T. and Thejll, P. (2009). A surrogate emsemble study of climate reconstruction methods: Stochasticity and robustness. Journal of Climate 22 951–976.
  • Gore, A. (2006). An Inconvenient Truth. Lawrence Bender Productions.
  • Granger, C. W. J. and Newbold, P. (1974). Spurious regressions in econometrics. Journal of Econometrics 2 111–120.
  • Green, K. C., Armstrong, J. S. and Soon, W. (2009). Validity of climate change forecasting for public policy decision-making. International Journal of Forecasting 25 826–832.
  • Haslett, J., Whiley, M., Bhattacharya, S., Salter-Townshend, M., Wilson, S. P., Allen, J. R. M., Huntley, B. and Mitchell, F. J. G. (2006). Bayesian palaeoclimate reconstruction. J. Roy. Statist. Soc. Ser. A 169 395–438.
  • IPCC (2001). Climate Change 2001: The Scientific Basis. Cambridge Univ. Press, Cambridge.
  • IPCC (2007). Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change.
  • Johnson, K. (2009). Climate emails stoke debate. Wall Street Journal. November 23, page A3.
  • Johnson, K. and Naik, G. (2009). Lawmakers probe climate emails. Wall Street Journal. November 24, page A8.
  • Jolis, A. (2009). Revenge of the climate laymen. Wall Street Journal. November 18.
  • Ladurie, E. L. (1971). Times of Feast, Times of Famine: A History of Climate Since the Year 1000. Doubleday, New York.
  • Lamb, H. H. (1990). Climate: Past, Present and Future. Routledge, New York.
  • Lee, T., Zwiers, F. W. and Tsao, M. (2008). Evaluation of proxy-based millennial reconstruction methods. Climate Dynamics 31 263–281.
  • Li, B., Nychka, D. W. and Amman, C. M. (2007). The ‘hockey stick’ and the 1990s: A statistical perspective on reconstructing hemispheric temperatures. Tellus 59A 591–598.
  • Li, B., Nychka, D. W. and Amman, C. M. (2010). The value of multi-proxy reconstructin of past climate. J. Amer. Statist. Assoc. 105 883–895.
  • Luterbacher, J., Dieterich, D., Xoplaki, E., Grosjean, M. and Wanner, H. (2004). European seasonal and annual temperature variability, trends, and extremes since 1500. Science 202 1499–1503.
  • Mann, M. E. (2004). On smoothing potentially non-stationary climate time series. Geophysical Research Letters 31.
  • Mann, M. E. (2008). Smoothing of climate time series revisited. Geophysical Research Letters 35.
  • Mann, M. E., Bradley, R. E. and Hughes, M. K. (1998). Global-scale temperature patterns and climate forcing over the past six centuries. Nature 392 779–787.
  • Mann, M. E., Bradley, R. E. and Hughes, M. K. (1999). Northern hemisphere temperatures during the past millennium: Inferences, uncertainties, and limitations. Geophysical Research Letters 26 759–762.
  • Mann, M. E., Bradley, R. E. and Hughes, M. K. (2004). Corrigendum: Global-scale temperature patterns and climate forcing over the past six centuries. Nature 430 105.
  • Mann, M. E. and Rutherford, S. (2002). Climate reconstruction using pseudoproxies. Geophysical Research Letters 29 1501.
  • Mann, M. E., Rutherford, S., Wahl, E. and Ammann, C. (2005). Testing the fidelity of methods used in proxy-based reconstructions of past climate. Journal of Climate 18 4097–4107.
  • Mann, M. E., Rutherford, S., Wahl, E. and Ammann, C. (2007). Robustness of proxy-based climate field reconstruction methods. Journal of Geophysical Research 112.
  • Mann, M. E., Zhang, Z., Hughes, M. K., Bradley, R. S., Miller, S. K., Rutherford, S. and Ni, F. (2008). Proxy-based reconstructions of hemispheric and global surface temperature variations over the past two millenia. Proc. Natl. Acad. Sci. USA 105 13252–13257.
  • Matthes, F. E. (1939). Report of the committee on glaciers. Transactions of the American Geophysical Union 20 518–523.
  • McIntyre, S. and McKitrick, R. (2003). Corrections to the Mann et al. (1998) proxy base and northern hemispheric average temperature series. Energy and Environment 14 751–771.
  • McIntyre, S. and McKitrick, R. (2005a). Hockey sticks, principal components, and spurious significance. Geophysical Research Letters 32.
  • McIntyre, S. and McKitrick, R. (2005b). The M&M critique of the MBH98 and northern hemisphere climate index: Update and implications. Energy and Environment 16 69–100.
  • McIntyre, S. and McKitrick, R. (2005c). Reply to comment by Huybers on “Hockey sticks, principal components, and spurious significance.” Geophysical Research Letters 32 L20713.
  • McShane, B. B. and Wyner, A. J. (2011). Supplement to: “A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable?” DOI: 10.1214/10-AOAS398SUPP.
  • National Research Council (2006). Surface temperature reconstructions. National Academic Press, Washington, DC.
  • Phillips, P. C. B. (1986). Understanding spurious regressions in econometrics. J. Econometrics 33 311–340.
  • Rothstein, E. (2008). Apocalypse now, via diorama. The New York Times. October 17, page C27.
  • Rutherford, S., Mann, M. E., Osborn, T. J., Bradley, R. S., Briffa, K. R., Hughes, M. K. and Jones, P. D. (2005). Proxy-based northern hemispheric surface reconstructions: Sensitivity to method, predictor network, target season, and target domain. Journal of Climate 18 2308–2329.
  • Schneider, T. (2001). Analysis of incomplete climate data: Estimation of mean values and covariance matrices and imputation of missing values. Journal of Climate 14 853–871.
  • Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. J. Roy. Statist. Soc. Ser. B 58 267–288.
  • Tingley, M. and Huybers, P. (2010a). A Bayesian algorithm for reconstructing climate anomalies in space and time. Part I: Development and applications to paleoclimate reconstruction problems. Journal of Climate 23 2759–2781.
  • Tingley, M. and Huybers, P. (2010b). Bayesian algorithm for reconstructing climate anomalies in space and time. Part II: Comparison with the regularized expectation–maximization algorithm. Journal of Climate 23 2782–2800.
  • von Storch, H. E. and Zorita, E. (2005). Comment on “Hockey sticks, principal components, and spurious significance,” by S. McIntyre and R. McKitrick. Geophysical Research Letters 32.
  • von Storch, H. E., Zorita, E., Jones, J. M., Dimitriev, Y., Gonzalez-Rouco, F. and Tett, S. (2004). Reconstructing past climate from noisy data. Science 306 679–682.
  • von Storch, H. E., Zorita, E., Jones, J. M., Dimitriev, Y., Gonzalez-Rouco, F. and Tett, S. (2006). Response to comment on “Reconstructing past climate from noisy data.” Science 213 529.
  • Wahl, E. R. and Amman, C. M. (2006). Robustness of the Mann, Bradley, Hughes reconstruction of the Northern Hemisphere surface temperatures: Examination of criticisms based on the nature and processing of proxy climate evidence. Climatic Change 85 33–69.
  • Wahl, E. R., Ritson, D. M. and Amman, C. M. (2006). On “Reconstruction past climate from noisy data.” Science 312 592b.
  • Wegman, E. J. (2006). Response of Dr. Edward Wegman to questions posed by the honorable Bart Stupak in connection with testimony to the subcommittee on oversight and investigations. Available at http://www.uoguelph.ca/~ rmckitri/research/StupakResponse.pdf.
  • Wegman, E. J., Scott, D. W. and Said, Y. H. (2006). Ad Hoc committee report on the ‘hockey stick’ global climate reconstruction. Available at http://republicans.energycommerce.house.gov/108/home/07142006_Wegman_Report.pdf.
  • Wu, Y., Boos, D. D. and Stefanski, L. A. (2007). Controlling variable selection by the addition of pseudovariables. J. Amer. Statist. Assoc. 102 235–243.
  • Yule, G. U. (1926). Why do we sometimes get nonsense correlations between time series? A study in sampling and the nature of time series. J. Roy. Statist. Soc. 89 1–64.

Supplemental materials

  • Supplementary material: Code repository for “A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable?”. This repository archives all data and code used for “A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable?” In particular, it contains code to make all figures and tables featured in the paper.