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Probabilistic assessment of sea level during the last interglacial stage


With polar temperatures 3–5 °C warmer than today, the last interglacial stage (125 kyr ago) serves as a partial analogue for 1–2 °C global warming scenarios. Geological records from several sites indicate that local sea levels during the last interglacial were higher than today, but because local sea levels differ from global sea level, accurately reconstructing past global sea level requires an integrated analysis of globally distributed data sets. Here we present an extensive compilation of local sea level indicators and a statistical approach for estimating global sea level, local sea levels, ice sheet volumes and their associated uncertainties. We find a 95% probability that global sea level peaked at least 6.6 m higher than today during the last interglacial; it is likely (67% probability) to have exceeded 8.0 m but is unlikely (33% probability) to have exceeded 9.4 m. When global sea level was close to its current level (≥-10 m), the millennial average rate of global sea level rise is very likely to have exceeded 5.6 m kyr-1 but is unlikely to have exceeded 9.2 m kyr-1. Our analysis extends previous last interglacial sea level studies by integrating literature observations within a probabilistic framework that accounts for the physics of sea level change. The results highlight the long-term vulnerability of ice sheets to even relatively low levels of sustained global warming.

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Figure 1: Sites with at least one sea level observation in our database.
Figure 2: Localities at which LSL data exist in our database, for time slices through the LIG.
Figure 3: Schematic illustration of the process used in our statistical analysis.
Figure 4: Probability density plots of GSL and ice volume during the LIG.
Figure 5: Exceedance values calculated from the posterior probability distribution.

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  1. Jansen, E. et al. in Climate Change 2007: The Physical Science Basis (eds Solomon, S. et al. ) 433–498 (Cambridge Univ. Press, 2007)

    Google Scholar 

  2. Meehl, G. A. et al. in Climate Change 2007: The Physical Science Basis (eds Solomon, S. et al.) 747–845 (Cambridge Univ. Press, 2007)

    Google Scholar 

  3. Rahmstorf, S. A semi-empirical approach to projecting future sea-level rise. Science 315, 368–370 (2007)

    Article  CAS  ADS  Google Scholar 

  4. Grinsted, A., Moore, J. C. & Jevrejeva, S. Reconstructing sea level from paleo and projected temperatures 200 to 2100 AD. Clim. Dyn. 10.1007/s00382-008-0507-2 (published online 6 January 2009)

  5. Cuffey, K. M. & Marshall, S. J. Substantial contribution to sea-level rise during the last interglacial from the Greenland ice sheet. Nature 404, 591–594 (2000)

    Article  CAS  ADS  Google Scholar 

  6. Otto-Bliesner, B., Marshall, S., Overpeck, J., Miller, G. & Hu, A. Simulating Arctic climate warmth and icefield retreat in the Last Interglaciation. Science 311, 1751–1753 (2006)

    Article  CAS  ADS  Google Scholar 

  7. 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)

    Article  CAS  ADS  Google Scholar 

  8. Berger, A. & Loutre, M. F. Insolation values for the climate of the last 10 million years. Quat. Sci. Rev. 10, 297–317 (1991)

    Article  ADS  Google Scholar 

  9. Crowley, T. & Kim, K. Milankovitch forcing of the Last Interglacial sea level. Science 265, 1566–1568 (1994)

    Article  CAS  ADS  Google Scholar 

  10. Katsov, V. M. et al. in Arctic Climate Impact Assessment (eds Symon, C., Arris, L. & Heal, B.) Ch. 4, 99–150 (Cambridge Univ. Press, 2004)

    Google Scholar 

  11. Kaspar, F., Kühl, N., Cubasch, U. & Litt, T. A model-data comparison of European temperatures in the Eemian interglacial. Geophys. Res. Lett. 32 L11703 10.1029/2005GL022456 (2005)

    Article  ADS  Google Scholar 

  12. Lea, D. The 100,000-yr cycle in tropical SST, greenhouse forcing, and climate sensitivity. J. Clim. 17, 2170–2179 (2004)

    Article  ADS  Google Scholar 

  13. Weldeab, S., Lea, D., Schneider, R. & Andersen, N. 155,000 years of West African monsoon and ocean thermal evolution. Science 316, 1303–1307 (2007)

    Article  CAS  ADS  Google Scholar 

  14. Farrell, W. E. & Clark, J. A. On postglacial sea level. Geophys. J. R. Astron. Soc. 46, 647–667 (1976)

    Article  Google Scholar 

  15. Mitrovica, J. X. & Milne, G. A. On post-glacial sea level: I. General theory. Geophys. J. Int. 154, 253–267 (2003)

    Article  ADS  Google Scholar 

  16. Kendall, R., Mitrovica, J. & Milne, G. On post-glacial sea level – II. Numerical formulation and comparative results on spherically symmetric models. Geophys. J. Int. 161, 679–706 (2005)

    Article  ADS  Google Scholar 

  17. Yin, J., Schlesinger, M. E. & Stouffer, R. J. Model projections of rapid sea-level rise on the northeast coast of the United States. Nature Geosci. 2, 262–266 (2009)

    Article  CAS  ADS  Google Scholar 

  18. Mitrovica, J. X. & Milne, G. A. On the origin of late Holocene sea-level highstands within equatorial ocean basins. Quat. Sci. Rev. 21, 2179–2190 (2002)

    Article  ADS  Google Scholar 

  19. Lambeck, K. & Nakada, M. Constraints on the age and duration of the last interglacial period and on sea-level variations. Nature 357, 125–128 (1992)

    Article  ADS  Google Scholar 

  20. Lisiecki, L. E. & Raymo, M. E. A. Pliocene-Pleistocene stack of 57 globally distributed benthic δ18O records. Paleoceanography 20, 1–17 (2005)

    Google Scholar 

  21. Zagwijn, W. H. Sea-level changes in the Netherlands during the Eemian. Geol. Mijnb. 62, 437–450 (1983)

    Google Scholar 

  22. Rohling, E. J. et al. High rates of sea-level rise during the last interglacial period. Nature Geosci. 1, 38–42 (2008)

    Article  CAS  ADS  Google Scholar 

  23. Mitrovica, J., Wahr, J., Matsuyama, I. & Paulson, A. The rotational stability of an ice-age earth. Geophys. J. Int. 161, 491–506 (2005)

    Article  ADS  Google Scholar 

  24. Peltier, W. R. Global glacial isostasy and the surface of the ice-age Earth: the ICE-5G (VM2) model and GRACE. Annu. Rev. Earth Planet. Sci. 32, 111–149 (2004)

    Article  CAS  ADS  Google Scholar 

  25. Banerjee, S., Carlin, B. P. & Gelfand, A. E. Hierarchical Modeling and Analysis for Spatial Data (Chapman & Hall/CRC, 2003)

    Book  Google Scholar 

  26. Lighty, R. G., Macintyre, I. G. & Stuckenrath, R. Acropora palmata reef framework: a reliable indicator of sea level in the western Atlantic for the past 10,000 years. Coral Reefs 1, 125–130 (1982)

    Article  ADS  Google Scholar 

  27. Camoin, G. F., Ebren, P., Eisenhauer, A., Bard, E. & Faure, G. A 300,000-yr coral reef record of sea level changes, Mururoa atoll (Tuamotu archipelago, French Polynesia). Palaeogeogr. Palaeoclimatol. Palaeoecol. 175, 325–341 (2001)

    Article  Google Scholar 

  28. Rasmussen, C. & Williams, C. Gaussian Processes for Machine Learning (MIT Press, 2006)

    MATH  Google Scholar 

  29. Hastings, W. K. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97–109 (1970)

    Article  MathSciNet  Google Scholar 

  30. Muhs, D. R., Simmons, K. R. & Steinke, B. Timing and warmth of the Last Interglacial period: new U-series evidence from Hawaii and Bermuda and a new fossil compilation for North America. Quat. Sci. Rev. 21, 1355–1383 (2002)

    Article  ADS  Google Scholar 

  31. Overpeck, J. T. et al. Paleoclimatic evidence for future ice-sheet instability and rapid sea-level rise. Science 311, 1747–1750 (2006)

    Article  CAS  ADS  Google Scholar 

  32. Schellmann, G. & Radtke, U. A revised morpho- and chronostratigraphy of the Late and Middle Pleistocene coral reef terraces on Southern Barbados (West Indies). Earth Sci. Rev. 64, 157–187 (2004)

    Article  ADS  Google Scholar 

  33. Esat, T. M., McCulloch, M. T., Chappell, J., Pillans, B. & Omura, A. Rapid fluctuations in sea level recorded at Huon Peninsula during the penultimate glaciation. Science 283, 197–202 (1999)

    Article  CAS  Google Scholar 

  34. Carlson, A. E. et al. Rapid early Holocene deglaciation of the Laurentide ice sheet. Nature Geosci. 1, 620–624 (2008)

    Article  CAS  ADS  Google Scholar 

  35. Tamisiea, M. E., Mitrovica, J. X. & Davis, J. L. GRACE gravity data constrain ancient ice geometries and continental dynamics over Laurentia. Science 316, 881–883 (2007)

    Article  CAS  ADS  Google Scholar 

  36. Eisenhauer, A., Zhu, Z., Collins, L., Wyrwoll, K. & Eichstätter, R. The Last Interglacial sea level change: new evidence from the Abrolhos islands, West Australia. Int. J. Earth Sci. 85, 606–614 (1996)

    CAS  Google Scholar 

  37. Zhu, Z. R. et al. High-precision U-series dating of Last Interglacial events by mass spectrometry: Houtman Abrolhos Islands, western Australia. Earth Planet. Sci. Lett. 118, 281–293 (1993)

    Article  CAS  ADS  Google Scholar 

  38. Thompson, W. G. & Goldstein, S. L. Open-system coral ages reveal persistent suborbital sea-level cycles. Science 308, 401–405 (2005)

    Article  CAS  ADS  Google Scholar 

  39. Thomas, A. L. et al. Penultimate deglacial sea-level timing from uranium/thorium dating of Tahitian corals. Science 324, 1186–1189 (2009)

    Article  CAS  ADS  Google Scholar 

  40. Mitrovica, J. X. & Peltier, W. R. On postglacial geoid subsidence over the equatorial ocean. J. Geophys. Res. 96, 20053–20071 (1991)

    Article  ADS  Google Scholar 

  41. Peltier, W. R. The impulse response of a Maxwell Earth. Rev. Geophys. Space Phys. 12, 649–669 (1974)

    Article  ADS  Google Scholar 

  42. Wu, P. The Response of a Maxwell Earth to Applied Surface Mass Loads: Glacial Isostatic Adjustment. M.Sc. thesis, Univ. Toronto (1978)

    Google Scholar 

  43. Dziewonski, A. & Anderson, D. Preliminary reference Earth model. Phys. Earth Planet. Inter. 25, 297–356 (1981)

    Article  ADS  Google Scholar 

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We thank J. R. Stroud, L. D. Brown and B. McShane for statistical guidance, and M. Bender, B. Horton, D. Nychka and D. Peltier for comments. We also thank G. Spada for providing his SELEN sea level code, which we used for preliminary calculations incorporated in a previous version of the statistical model. Computing resources were substantially provided by the TIGRESS high performance computer centre at Princeton University, which is jointly supported by the Princeton Institute for Computational Science and Engineering and the Princeton University Office of Information Technology. R.E.K. was supported by a postdoctoral fellowship in the programme on Science, Technology, and Environmental Policy at the Woodrow Wilson School of Princeton University.

Author Contributions R.E.K. compiled the database, developed the statistical analysis method, and co-wrote the paper. F.J.S. contributed to the development of the statistical analysis method and co-wrote the paper. J.X.M. developed the physical sea level model and co-wrote the paper. A.C.M. contributed to the compilation of the database and co-wrote the paper. M.O. supervised the project and co-wrote the paper.

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Correspondence to Robert E. Kopp.

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Supplementary information

Supplementary Information

This file contains Supplementary Methods, a Supplementary Discussion, Supplementary References, Supplementary Tables 1-2 and Supplementary Figures 1-10 with Legends. Duplicated text that appeared on page 5 was deleted from this file on 04 August 2010. (PDF 791 kb)

Supplementary Table 1

This table describes the Last Interglacial sea level data points used in the analysis. Descriptions of the columns are provided in the worksheet entitled "Legend", while the data themselves are in the worksheet entitled "Database." (XLS 154 kb)

Supplementary Data

This zipped file contains 3 folders of Supplementary Data for Pre-processing, Processing and Post-processing. (ZIP 87 kb)

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Kopp, R., Simons, F., Mitrovica, J. et al. Probabilistic assessment of sea level during the last interglacial stage. Nature 462, 863–867 (2009).

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