The Annals of Applied Statistics

Finding a consensus on credible features among several paleoclimate reconstructions

Panu Erästö, Lasse Holmström, Atte Korhola, and Jan Weckström

Full-text: Open access

Abstract

We propose a method to merge several paleoclimate time series into one that exhibits a consensus on the features of the individual times series. The paleoclimate time series can be noisy, nonuniformly sampled and the dates at which the paleoclimate is reconstructed can have errors. Bayesian inference is used to model the various sources of uncertainty and smoothing of the posterior distribution of the consensus is used to capture its credible features in different time scales. The technique is demonstrated by analyzing a collection of six Holocene temperature reconstructions from Finnish Lapland based on various biological proxies. Although the paper focuses on paleoclimate time series, the proposed method can be applied in other contexts where one seeks to infer features that are jointly supported by an ensemble of irregularly sampled noisy time series.

Article information

Source
Ann. Appl. Stat., Volume 6, Number 4 (2012), 1377-1405.

Dates
First available in Project Euclid: 27 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1356629044

Digital Object Identifier
doi:10.1214/12-AOAS540

Mathematical Reviews number (MathSciNet)
MR3058668

Zentralblatt MATH identifier
1257.62119

Keywords
Multiple time series Bayesian analysis scale space analysis paleoclimate temperature reconstruction

Citation

Erästö, Panu; Holmström, Lasse; Korhola, Atte; Weckström, Jan. Finding a consensus on credible features among several paleoclimate reconstructions. Ann. Appl. Stat. 6 (2012), no. 4, 1377--1405. doi:10.1214/12-AOAS540. https://projecteuclid.org/euclid.aoas/1356629044


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References

  • Alley, R. B., Mayewski, P. A., Sowers, T., Stuiver, M., Taylor, K. C. and Clark, P. U. (1997). Holocene climatic instability: A prominent, widespread event 8200 yr ago. Geology 25 483–486.
  • Ammann, C. M., Joos, F., Schimel, D. S., Otto-Bliesner, B. L. and Tomas, R. A. (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.
  • Auestad, B. H., Shumway, R. H., Tjøstheim, D. and Verosub, K. L. (2008). Linear and nonlinear alignment of time series with applications to varve chronologies. Environmetrics 19 409–427.
  • Berger, A. and Loutre, M. F. (1991). Insolation values for the climate of the last 10 million years. Quaternary Science Reviews 10 297–317.
  • Birks, H. J. B. (1995). Quantitative palaeoenvironmental reconstructions. In Statistical Modelling of Quaternary Science Data, Technical Guide 5 (D. Maddy and J. S. Brew, eds.) 161–254. Quaternary Research Association, Cambridge.
  • Birks, H. J. B., Heiri, O., Seppä, H. and Bjune, A. E. (2010). Strengths and weaknesses of quantitative climate reconstructions based on late-quaternary biological proxies. The Open Ecology Journal 3 68–110.
  • Blaauw, M. and Christen, J. A. (2005). Radiocarbon peat chronologies and environmental change. J. Roy. Statist. Soc. Ser. C 54 805–816.
  • Blaauw, M., Heuvelink, G. B. M., Mauquoy, D., Van Der Plicht, J. and Van Geel, B. (2003). A numerical approach to 14C wiggle-match dating of organic deposits: Best fits and confidence intervals. Quaternary Science Reviews 22 1485–1500.
  • Bond, G. et al. (1997). A pervasive millennial-scale cycle in North Atlantic Holocene and glacial climates. Science 278 1257–1266.
  • Bronk Ramsey, C. (2008). Deposition models for chronological records. Quaternary Science Reviews 27 42–60.
  • Brynjarsdóttir, J. and Berliner, L. M. (2011). Bayesian hierarchical modeling for temperature reconstruction from geothermal data. Ann. Appl. Stat. 5 1328–1359.
  • Chapin III, F. S. et al. (2000). Arctic and boreal ecosystems of western North America as components of the climate system. Global Change Biology 6 211–223.
  • Cressie, N. and Kornak, J. (2003). Spatial statistics in the presence of location error with an application to remote sensing of the environment. Statist. Sci. 18 436–456.
  • Davis, B. A. S., Brewer, S., Stevenson, A. C. and Guiot, J. (2003). The temperature of Europe during the Holocene reconstructed from pollen data. Quaternary Science Reviews 22 1701–1716.
  • Erästö, P. and Holmström, L. (2005). Bayesian multiscale smoothing for making inferences about features in scatterplots. J. Comput. Graph. Statist. 14 569–589.
  • Erästö, P. and Holmström, L. (2006). Prior selection and multiscale analysis in Bayesian temperature reconstruction based on species assemblages. Journal of Paleolimnology 36 69–80.
  • Erästö, P. and Holmström, L. (2007). Bayesian analysis of features in a scatter plot with dependent observations and errors in predictors. J. Stat. Comput. Simul. 77 421–431.
  • Erästö, P., Holmström, L., Korhola, A. and Weckström, J. (2011a). Supplement A to “Finding a consensus on credible features among several paleoclimate reconstructions.” DOI:10.1214/12-AOAS540SUPPA.
  • Erästö, P., Holmström, L., Korhola, A. and Weckström, J. (2011b). Supplement B to “Finding a consensus on credible features among several paleoclimate reconstructions.” DOI:10.1214/12-AOAS540SUPPB.
  • Fanshawe, T. R. and Diggle, P. J. (2011). Spatial prediction in the presence of positional error. Environmetrics 22 109–122.
  • Green, P. J. and Silverman, B. W. (1994). Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach. Monographs on Statistics and Applied Probability 58. Chapman & Hall, London.
  • Harsch, M. A., Hulme, P. E., McGlone, M. S. and Duncan, R. P. (2009). Are treelines advancing? A global meta-analysis of treeline response to climate warming. Ecol. Lett. 12 1040–1049.
  • Haslett, J. and Parnell, A. (2008). A simple monotone process with application to radiocarbon-dated depth chronologies. J. Roy. Statist. Soc. Ser. C 57 399–418.
  • 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.
  • Heegaard, E., Birks, H. J. B. and Telford, R. J. (2005). Relationships between calibrated ages and depth in stratigraphical sequences: Estimation procedure by mixed-effect regression. The Holocene 15 612–618.
  • Holmström, L. (2010a). BSiZer. Wiley Interdisciplinary Reviews: Computational Statistics 2 526–534.
  • Holmström, L. (2010b). Scale space methods. Wiley Interdisciplinary Reviews: Computational Statistics 2 150–159.
  • Holmström, L. and Erästö, P. (2001). Using the SiZer method in Holocene temperature reconstruction. Research Report A36, Rolf Nevanlinna Institute.
  • Holmström, L., Erästö, P., Weckström, J., Nyman, M. and Korhola, A. (2008). A Bayesian reconstruction of Holocene temperature variation in Northern Fennoscandia. In 2008 Joint Statistical Meetings, Abstract Book 256. Denver, CO.
  • Jansen, E. et al. (2007). Palaeoclimate. In Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor and H. L. Miller, eds.) 433–497. Cambridge Univ. Press, Cambridge.
  • Jones, P. D. et al. (2009). High-resolution palaeoclimatology of the last millennium: A review of current status and future prospects. The Holocene 19 3–49.
  • Kaplan, M. R. and Wolfe, A. P. (2006). Spatial and temporal variability of Holocene temperature in the North Atlantic region. Quaternary Research 65 223–231.
  • Kaufman, D. S. et al. (2004). Holocene thermal maximum in the western Arctic (0–180W). Quaternary Science Reviews 23 529–560.
  • Kaufman, D. S. et al. (2009). Recent warming reverses long-term arctic cooling. Science 325 1236–1239.
  • Knudsen, M. F., Riisager, P., Jacobsen, B. H., Muscheler, R., Snowball, I. and Seidenkrantz, M. S. (2009). Taking the pulse of the sun during the Holocene by joint analysis of 14C and 10Be. Geophysical Research Letters 36 L16701.
  • Korhola, A., Vasko, K., Toivonen, H. and Olander, H. (2002). Holocene temperature changes in northern Fennoscandia reconstructed from chironomids using Bayesian modelling. Quaternary Science Reviews 21 1841–1860.
  • Korhola, A., Weckström, J., Holmström, L. and Erästö, P. (2006). Reconstructing climate from palaeolimnological archives using multiple proxy indicators and sites simultaneously. In 10th International Paleolimnology Symposium. Abstract Volume: 94. Duluth, MI.
  • Kutzbach, L. E. (1981). Monsoon climate of the early Holocene: Climate experiment with the earth’s orbital parameters for 9000 years ago. Science 214 59–61.
  • Legrande, A. N. et al. (2006). Consistent simulations of multiple proxy responses to an abrupt climate change event. Proc. Natl. Acad. Sci. USA 103 837–842.
  • Li, B., Nychka, D. W. and Ammann, C. M. (2010). The value of multiproxy reconstruction of past climate. J. Amer. Statist. Assoc. 105 883–895.
  • Lindeberg, T. (1994). Scale–Space Theory in Computer Vision. Kluwer Academic Publishers, Dordrecht.
  • MacDonald, G. M. et al. (2000). Holocene treeline history and climate change across Northern Eurasia. Quaternary Research 53 302–311.
  • 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 millennia. Proc. Natl. Acad. Sci. USA 105 13252–13257.
  • Mayewski, P. A. et al. (2004). Holocene climate variability. Quaternary Research 62 243–255.
  • Nesje, A., Bakke, J., Dahl, S. O., Lie, Ø. and Matthews, J. A. (2008). Norwegian mountain glaciers in the past, present and future. Global and Planetary Change 60 10–27.
  • Renssen, H., Seppä, H., Heiri, O., Roche, D. M., Goosse, H. and Fichefet, T. (2009). The spatial and temporal complexity of the Holocene thermal maximum. Nature Geoscience 2 411–414.
  • Robert, C. P. and Casella, G. (2005). Monte Carlo Statistical Methods. Springer, New York.
  • Ruppert, D., Sheather, S. J. and Wand, M. P. (1995). An effective bandwidth selector for local least squares regression. J. Amer. Statist. Assoc. 90 1257–1270.
  • Salonen, S., Ilvonen, L., Seppä, H., Holmström, L., Telford, R. J., Gaidamavičius, A., Stančikaite, M. and Subetto, D. (2012). Comparing different calibration methods (WA/WA-PLS regression and Bayesian modelling) and different-sized calibration sets in pollen-based quantitative climate reconstruction. The Holocene 22 413–424.
  • Seidenkrantz, M. S., Aagaard-Sørensen, S., Sulsbrück, H., Kuijpers, A., Jensen, K. G. and Kunzendorf, H. (2007). Hydrography and climate of the last 4400 years in a SW Greenland fjord: Implications for Labrador Sea palaeoceanography. The Holocene 17 387–401.
  • Seppä, H. and Birks, H. J. B. (2001). July mean temperature and annual precipitation trends during the Holocene in the Fennoscandian tree-line area: Pollen-based climate reconstructions. The Holocene 11 527–539.
  • Seppä, H., Nyman, M., Korhola, A. and Weckström, J. (2002). Changes of treelines and alpine vegetation in relation to post-glacial climate dynamics in northern Fennoscandia based on pollen and chironomid records. Journal of Quaternary Science 17 287–301.
  • Telford, R. J., Heegaard, E. and Birks, H. J. B. (2004). All age–depth models are wrong: But how badly? Quaternary Science Reviews 23 1–5.
  • ter Braak, C. J. F. and Juggins, S. (1993). Weighted averaging partial least squares regression (WA-PLS): An improved method for reconstructing environmental variables from species assemblages. Hydrobiologia 269–270 485–502.
  • Tingley, P., Craigmile, P. F., Haran, M., Li, B., Mannshardt-Shamseldin, E. and Rajaratnam, B. (2012). Piecing together the past: Statistical insights into paleoclimatic reconstructions. Quaternary Science Reviews 35 1–22.
  • Toivonen, H. T. T., Mannila, H., Korhola, A. and Olander, H. (2001). Applying Bayesian statistics to organism-based environmental reconstruction. Ecological Applications 11 618–630.
  • Vasko, K., Toivonen, H. T. T. and Korhola, A. (2000). A Bayesian multinomial Gaussian response model for organism-based environmental reconstruction. Journal of Paleolimnology 24 243–250.
  • Weckström, J., Korhola, A., Erästö, P. and Holmström, L. (2006). Temperature patterns over the past eight centuries in Northern Fennoscandia inferred from sedimentary diatoms. Quaternary Research 66 78–86.

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