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Glacial cooling and climate sensitivity revisited


The Last Glacial Maximum (LGM), one of the best studied palaeoclimatic intervals, offers an excellent opportunity to investigate how the climate system responds to changes in greenhouse gases and the cryosphere. Previous work has sought to constrain the magnitude and pattern of glacial cooling from palaeothermometers1,2, but the uneven distribution of the proxies, as well as their uncertainties, has challenged the construction of a full-field view of the LGM climate state. Here we combine a large collection of geochemical proxies for sea surface temperature with an isotope-enabled climate model ensemble to produce a field reconstruction of LGM temperatures using data assimilation. The reconstruction is validated with withheld proxies as well as independent ice core and speleothem δ18O measurements. Our assimilated product provides a constraint on global mean LGM cooling of −6.1 degrees Celsius (95 per cent confidence interval: −6.5 to −5.7 degrees Celsius). Given assumptions concerning the radiative forcing of greenhouse gases, ice sheets and mineral dust aerosols, this cooling translates to an equilibrium climate sensitivity of 3.4 degrees Celsius (2.4–4.5 degrees Celsius), a value that is higher than previous LGM-based estimates but consistent with the traditional consensus range of 2–4.5 degrees Celsius3,4.

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Fig. 1: Locations of geochemical SST proxies used for the LGM climate reconstruction.
Fig. 2: Global changes in temperature during the LGM derived from palaeoclimate data assimilation.
Fig. 3: Validation of the data assimilation with independent δ18Op data.
Fig. 4: LGM global temperature change and climate sensitivity derived from data assimilation.

Data availability

The LGM and LH proxy data are available as .csv files (including both raw proxy values and calibrated estimates of SST). We also provide a gridded 5° × 5° map of LGM–LH proxy anomalies in .netcdf format. The fields of the data assimilation product (SST, SAT, SSS, δ18O of seawater and δ18Op are also available in .netcdf format. Files are publicly available for download from PANGAEA ( and from GitHub ( Source data are provided with this paper.

Code availability

The data assimilation method used in this paper is publicly available as the Matlab code package DASH on GitHub ( The Bayesian forward models, BAYSPAR, BAYSPLINE, BAYFOX and BAYMAG are likewise publicly available on GitHub from The iCESM1.2 model code is available at


  1. 1.

    CLIMAP Project Members The surface of the Ice-Age Earth. Science 191, 1131–1137 (1976).

    ADS  Google Scholar 

  2. 2.

    MARGO Project Members Constraints on the magnitude and patterns of ocean cooling at the Last Glacial Maximum. Nat. Geosci. 2, 127–132 (2009).

    ADS  Google Scholar 

  3. 3.

    Charney, J. G. et al. Carbon Dioxide and Climate: A Scientific Assessment (National Academy of Sciences, 1979).

  4. 4.

    Knutti, R. & Hegerl, G. C. The equilibrium sensitivity of the Earth’s temperature to radiation changes. Nat. Geosci. 1, 735–743 (2008).

    CAS  ADS  Google Scholar 

  5. 5.

    Joussaume, S. & Taylor, K. Status of the Paleoclimate Modeling Intercomparison Project (PMIP) (WMO, 1995).

  6. 6.

    Braconnot, P. et al. Evaluation of climate models using palaeoclimatic data. Nat. Clim. Change 2, 417–424 (2012).

    ADS  Google Scholar 

  7. 7.

    Schmittner, A. et al. Climate sensitivity estimated from temperature reconstructions of the Last Glacial Maximum. Science 334, 1385–1388 (2011).

    CAS  ADS  Google Scholar 

  8. 8.

    Mix, A. C., Morey, A. E., Pisias, N. G. & Hostetler, S. W. Foraminiferal faunal estimates of paleotemperature: circumventing the no-analog problem yields cool ice age tropics. Paleoceanography 14, 350–359 (1999).

    ADS  Google Scholar 

  9. 9.

    Crowley, T. CLIMAP SSTs re-revisited. Clim. Dynam. 16, 241–255 (2000).

    ADS  Google Scholar 

  10. 10.

    Ballantyne, A., Lavine, M., Crowley, T., Liu, J. & Baker, P. Meta-analysis of tropical surface temperatures during the Last Glacial Maximum. Geophys. Res. Lett. 32, L05712 (2005).

    ADS  Google Scholar 

  11. 11.

    Telford, R., Li, C. & Kucera, M. Mismatch between the depth habitat of planktonic foraminifera and the calibration depth of SST transfer functions may bias reconstructions. Clim. Past 9, 859–870 (2013).

    Google Scholar 

  12. 12.

    Tierney, J. E. & Tingley, M. P. BAYSPLINE: a new calibration for the alkenone paleothermometer. Paleoceanogr. Paleoclimatol. 33, 281–301 (2018).

    Google Scholar 

  13. 13.

    Tierney, J. E., Malevich, S. B., Gray, W., Vetter, L. & Thirumalai, K. Bayesian calibration of the Mg/Ca paleothermometer in planktic foraminifera. Paleoceanogr. Paleoclimatol. 34, 2005–2030 (2019).

    Google Scholar 

  14. 14.

    Snyder, C. W. Evolution of global temperature over the past two million years. Nature 538, 226–228 (2016).

    CAS  ADS  Google Scholar 

  15. 15.

    Schneider von Deimling, T., Ganopolski, A., Held, H. & Rahmstorf, S. How cold was the Last Glacial Maximum? Geophys. Res. Lett. 33, L14709 (2006).

    ADS  Google Scholar 

  16. 16.

    Holden, P. B., Edwards, N., Oliver, K., Lenton, T. & Wilkinson, R. A probabilistic calibration of climate sensitivity and terrestrial carbon change in GENIE-1. Clim. Dynam. 35, 785–806 (2010).

    ADS  Google Scholar 

  17. 17.

    Shakun, J. D. et al. Global warming preceded by increasing carbon dioxide concentrations during the last deglaciation. Nature 484, 49–54 (2012).

    CAS  ADS  Google Scholar 

  18. 18.

    Annan, J. & Hargreaves, J. C. A new global reconstruction of temperature changes at the Last Glacial Maximum. Clim. Past 9, 367–376 (2013).

    Google Scholar 

  19. 19.

    Bereiter, B., Shackleton, S., Baggenstos, D., Kawamura, K. & Severinghaus, J. Mean global ocean temperatures during the last glacial transition. Nature 553, 39–44 (2018).

    CAS  ADS  Google Scholar 

  20. 20.

    Friedrich, T. & Timmermann, A. Using Late Pleistocene sea surface temperature reconstructions to constrain future greenhouse warming. Earth Planet. Sci. Lett. 530, 115911 (2020).

    CAS  Google Scholar 

  21. 21.

    Masson-Delmotte, V. et al. in Climate Change 2013: The Physical Science Basis (eds Stocker, T. F. et al.) 383–464 (IPCC, Cambridge Univ. Press, 2013).

  22. 22.

    Brady, E. et al. The connected isotopic water cycle in the Community Earth System Model Version 1. J. Adv. Model. Earth Syst. 11, 2547–2566 (2019).

    Google Scholar 

  23. 23.

    Tierney, J. E. & Tingley, M. P. A. Bayesian, spatially-varying calibration model for the TEX86 proxy. Geochim. Cosmochim. Acta 127, 83–106 (2014).

    CAS  ADS  Google Scholar 

  24. 24.

    Malevich, S. B., Vetter, L. & Tierney, J. E. Global core top calibration of δ18O in planktic foraminifera to sea surface temperature. Paleoceanogr. Paleoclimatol. 34, 1292–1315 (2019).

    Google Scholar 

  25. 25.

    Tardif, R. et al. Last millennium reanalysis with an expanded proxy database and seasonal proxy modeling. Clim. Past 15, 1251–1273 (2019).

    Google Scholar 

  26. 26.

    Gray, W. R. et al. Wind-driven evolution of the North Pacific subpolar gyre over the last deglaciation. Geophys. Res. Lett. 47, e2019GL086328 (2020).

    ADS  Google Scholar 

  27. 27.

    DiNezio, P. N. et al. Glacial changes in tropical climate amplified by the Indian Ocean. Sci. Adv. 4, eaat9658 (2018).

    PubMed  PubMed Central  ADS  Google Scholar 

  28. 28.

    Ford, H. L., Ravelo, A. C. & Polissar, P. J. Reduced El Niño–Southern Oscillation during the Last Glacial Maximum. Science 347, 255–258 (2015).

    CAS  ADS  Google Scholar 

  29. 29.

    Glushkova, O. Y. Geomorphological correlation of Late Pleistocene glacial complexes of Western and Eastern Beringia. Quat. Sci. Rev. 20, 405–417 (2001).

    ADS  Google Scholar 

  30. 30.

    Bartlein, P. J. et al. Pollen-based continental climate reconstructions at 6 and 21 ka: a global synthesis. Clim. Dynam. 37, 775–802 (2011).

    ADS  Google Scholar 

  31. 31.

    Roe, G. H. & Lindzen, R. S. The mutual interaction between continental-scale ice sheets and atmospheric stationary waves. J. Clim. 14, 1450–1465 (2001).

    ADS  Google Scholar 

  32. 32.

    Löfverström, M. & Liakka, J. On the limited ice intrusion in Alaska at the LGM. Geophys. Res. Lett. 43, 11030–11038 (2016).

    ADS  Google Scholar 

  33. 33.

    Hopcroft, P. O. & Valdes, P. J. How well do simulated Last Glacial Maximum tropical temperatures constrain equilibrium climate sensitivity? Geophys. Res. Lett. 42, 5533–5539 (2015).

    ADS  Google Scholar 

  34. 34.

    Porter, S. C. Snowline depression in the tropics during the Last Glaciation. Quat. Sci. Rev. 20, 1067–1091 (2000).

    ADS  Google Scholar 

  35. 35.

    Stute, M. et al. Cooling of tropical Brazil (5 °C) during the Last Glacial Maximum. Science 269, 379–383 (1995).

    CAS  ADS  Google Scholar 

  36. 36.

    Lea, D. W., Pak, D. K. & Spero, H. J. Climate impact of late Quaternary equatorial Pacific sea surface temperature variations. Science 289, 1719–1724 (2000).

    CAS  ADS  Google Scholar 

  37. 37.

    Masson-Delmotte, V. et al. EPICA Dome C record of glacial and interglacial intensities. Quat. Sci. Rev. 29, 113–128 (2010).

    ADS  Google Scholar 

  38. 38.

    Lee, J.-E., Fung, I., DePaolo, D. J. & Otto-Bliesner, B. Water isotopes during the Last Glacial Maximum: new general circulation model calculations. J. Geophys. Res. 113, D19109 (2008).

    ADS  Google Scholar 

  39. 39.

    Kurahashi-Nakamura, T., Paul, A. & Losch, M. Dynamical reconstruction of the global ocean state during the Last Glacial Maximum. Paleoceanography 32, 326–350 (2017).

    ADS  Google Scholar 

  40. 40.

    Amrhein, D. E., Wunsch, C., Marchal, O. & Forget, G. A global glacial ocean state estimate constrained by upper-ocean temperature proxies. J. Clim. 31, 8059–8079 (2018).

    ADS  Google Scholar 

  41. 41.

    Flato, G. et al. in Climate Change 2013: The Physical Science Basis (eds Stocker, T. F. et al.) 741–866 (IPCC, Cambridge Univ. Press, 2014).

  42. 42.

    PALAEOSENS Project Members Making sense of palaeoclimate sensitivity. Nature 491, 683–691 (2012); erratum 494, 130 (2013).

  43. 43.

    Prentice, I. C., Jolly, D. & Biome 6000 Participants Mid-Holocene and glacial-maximum vegetation geography of the northern continents and Africa. J. Biogeogr. 27, 507–519 (2000).

    Google Scholar 

  44. 44.

    Köhler, P. et al. What caused Earth’s temperature variations during the last 800,000 years? Data-based evidence on radiative forcing and constraints on climate sensitivity. Quat. Sci. Rev. 29, 129–145 (2010).

    ADS  Google Scholar 

  45. 45.

    Etminan, M., Myhre, G., Highwood, E. & Shine, K. Radiative forcing of carbon dioxide, methane, and nitrous oxide: a significant revision of the methane radiative forcing. Geophys. Res. Lett. 43, 12614–12623 (2016).

    CAS  ADS  Google Scholar 

  46. 46.

    Albani, S. et al. Aerosol-climate interactions during the Last Glacial Maximum. Curr. Clim. Change Rep. 4, 99–114 (2018).

    Google Scholar 

  47. 47.

    Shakun, J. D. Modest global-scale cooling despite extensive early Pleistocene ice sheets. Quat. Sci. Rev. 165, 25–30 (2017).

    ADS  Google Scholar 

  48. 48.

    Stap, L., Köhler, P. & Lohmann, G. Including the efficacy of land ice changes in deriving climate sensitivity from paleodata. Earth Syst. Dynam. 10, 333–345 (2019).

    ADS  Google Scholar 

  49. 49.

    Yoshimori, M., Yokohata, T. & Abe-Ouchi, A. A comparison of climate feedback strength between CO2 doubling and LGM experiments. J. Clim. 22, 3374–3395 (2009).

    ADS  Google Scholar 

  50. 50.

    Friedrich, T., Timmermann, A., Tigchelaar, M., Timm, O. E. & Ganopolski, A. Nonlinear climate sensitivity and its implications for future greenhouse warming. Sci. Adv. 2, e1501923 (2016).

    PubMed  PubMed Central  ADS  Google Scholar 

  51. 51.

    DiNezio, P. N. & Tierney, J. E. The effect of sea level on glacial Indo-Pacific climate. Nat. Geosci. 6, 485–491 (2013).

    CAS  ADS  Google Scholar 

  52. 52.

    Chan, D., Kent, E. C., Berry, D. I. & Huybers, P. Correcting datasets leads to more homogeneous early-twentieth-century sea surface warming. Nature 571, 393–397 (2019).

    CAS  ADS  Google Scholar 

  53. 53.

    Reimer, P. J. et al. IntCal13 and Marine13 radiocarbon age calibration curves 0–50,000 years cal BP. Radiocarbon 55, 1869–1887 (2013).

    CAS  Google Scholar 

  54. 54.

    Hurrell, J. W. et al. The community earth system model: a framework for collaborative research. Bull. Am. Meteorol. Soc. 94, 1339–1360 (2013).

    ADS  Google Scholar 

  55. 55.

    Kageyama, M. et al. The PMIP4 contribution to CMIP6–Part 4: scientific objectives and experimental design of the PMIP4-CMIP6 Last Glacial Maximum experiments and PMIP4 sensitivity experiments. Geosci. Model Dev. 10, 4035–4055 (2017).

    CAS  ADS  Google Scholar 

  56. 56.

    Peltier, W. R., Argus, D. F. & Drummond, R. Space geodesy constrains ice age terminal deglaciation: the global ICE-6G_C (VM5a) model. J. Geophys. Res. Solid Earth 120, 450–487 (2015).

    ADS  Google Scholar 

  57. 57.

    Lawrence, D. M. et al. Parameterization improvements and functional and structural advances in version 4 of the community land model. J. Adv. Model. Earth Syst. 3, M03001 (2011).

    Google Scholar 

  58. 58.

    Zhu, J. et al. Reduced ENSO variability at the LGM revealed by an isotope-enabled Earth system model. Geophys. Res. Lett. 44, 6984–6992 (2017).

    ADS  Google Scholar 

  59. 59.

    Gettelman, A., Kay, J. E. & Shell, K. M. The evolution of climate sensitivity and climate feedbacks in the Community Atmosphere Model. J. Clim. 25, 1453–1469 (2012).

    ADS  Google Scholar 

  60. 60.

    Zhu, J., Poulsen, C. J. & Tierney, J. E. Simulation of Eocene extreme warmth and high climate sensitivity through cloud feedbacks. Sci. Adv. 5, eeax1874 (2019).

    ADS  Google Scholar 

  61. 61.

    Richardson, A. D. et al. Climate change, phenology, and phenological control of vegetation feedbacks to the climate system. Agric. For. Meteorol. 169, 156–173 (2013).

    ADS  Google Scholar 

  62. 62.

    Meehl, G. A. et al. Effects of model resolution, physics, and coupling on Southern Hemisphere storm tracks in CESM1.3. Geophys. Res. Lett. 46, 12408–12416 (2019).

    ADS  Google Scholar 

  63. 63.

    Whitaker, J. S. & Hamill, T. M. Ensemble data assimilation without perturbed observations. Mon. Weath. Rev. 130, 1913–1924 (2002).

    ADS  Google Scholar 

  64. 64.

    Steiger, N. J., Hakim, G. J., Steig, E. J., Battisti, D. S. & Roe, G. H. Assimilation of time-averaged pseudoproxies for climate reconstruction. J. Clim. 27, 426–441 (2014).

    ADS  Google Scholar 

  65. 65.

    Hakim, G. J. et al. The last millennium climate reanalysis project: framework and first results. J. Geophys. Res. Atmos. 121, 6745–6764 (2016).

    ADS  Google Scholar 

  66. 66.

    Okazaki, A. & Yoshimura, K. Development and evaluation of a system of proxy data assimilation for paleoclimate reconstruction. Clim. Past 13, 379–393 (2017).

    Google Scholar 

  67. 67.

    Lauvset, S. K. et al. A new global interior ocean mapped climatology: the 1 × 1 GLODAP version 2. Earth Syst. Sci. Data 8, 325–340 (2016).

    ADS  Google Scholar 

  68. 68.

    Gray, W. R. & Evans, D. Nonthermal influences on Mg/Ca in planktonic foraminifera: a review of culture studies and application to the last glacial maximum. Paleoceanogr. Paleoclimatol. 34, 306–315 (2019).

    Google Scholar 

  69. 69.

    Houtekamer, P. L. & Mitchell, H. L. A sequential ensemble Kalman filter for atmospheric data assimilation. Mon. Weath. Rev. 129, 123–137 (2001).

    ADS  Google Scholar 

  70. 70.

    Gaspari, G. & Cohn, S. E. Construction of correlation functions in two and three dimensions. Q. J. R. Meteorol. Soc. 125, 723–757 (1999).

    ADS  Google Scholar 

  71. 71.

    Nash, J. E. & Sutcliffe, J. V. River flow forecasting through conceptual models part I—a discussion of principles. J. Hydrol. 10, 282–290 (1970).

    ADS  Google Scholar 

  72. 72.

    Werner, M. et al. Glacial–interglacial changes of H2 18O, HDO and deuterium excess—results from the fully coupled Earth System Model ECHAM5/MPI-OM. Geosci. Model Dev. 9, 647–670 (2016).

    CAS  ADS  Google Scholar 

  73. 73.

    Atsawawaranunt, K. et al. The SISAL database: a global resource to document oxygen and carbon isotope records from speleothems. Earth Syst. Sci. Data 10, 1687–1713 (2018).

    ADS  Google Scholar 

  74. 74.

    Comas-Bru, L. et al. Evaluating model outputs using integrated global speleothem records of climate change since the last glacial. Clim. Past 15, 1557–1579 (2019).

    Google Scholar 

  75. 75.

    Hamill, T. M. Interpretation of rank histograms for verifying ensemble forecasts. Mon. Weath. Rev. 129, 550–560 (2001).

    ADS  Google Scholar 

  76. 76.

    Danabasoglu, G. et al. The CCSM4 ocean component. J. Clim. 25, 1361–1389 (2012).

    ADS  Google Scholar 

  77. 77.

    Park, T.-W., Deng, Y., Cai, M., Jeong, J.-H. & Zhou, R. A dissection of the surface temperature biases in the Community Earth System Model. Clim. Dynam. 43, 2043–2059 (2014).

    ADS  Google Scholar 

  78. 78.

    Taylor, K. et al. Estimating shortwave radiative forcing and response in climate models. J. Clim. 20, 2530–2543 (2007).

    ADS  Google Scholar 

  79. 79.

    Braconnot, P. & Kageyama, M. Shortwave forcing and feedbacks in Last Glacial Maximum and Mid-Holocene PMIP3 simulations. Phil. Trans. R. Soc. A 373, 20140424 (2015).

    ADS  Google Scholar 

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We thank M. Fox and N. Rapp for assistance with compiling the proxy SST data and P. DiNezio for providing initial and boundary condition files for the CESM simulations. This research was supported by National Science Foundation grant numbers AGS-1602301 and AGS-1602223, and Heising-Simons Foundation grant number 2016-015. CESM computing resources ( were provided by the Climate Simulation Laboratory at NCAR’s Computational and Information Systems Laboratory, sponsored by the National Science Foundation and other agencies.

Author information




J.E.T. designed the study, conducted the data assimilation, analysed the results and led the writing of this paper. J.E.T. and S.B.M. compiled and quality-checked the proxy SST data. S.B.M. designed the proxy database and adapted BACON age modelling software to Python. J.K. wrote the DASH code used for the data assimilation, based on methods developed by G.J.H. J.Z. and C.J.P. planned and conducted the iCESM simulations. All authors contributed to the writing of this manuscript.

Corresponding author

Correspondence to Jessica E. Tierney.

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The authors declare no competing interests.

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Peer review information Nature thanks Bernhard Naafs and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Fig. 1 Comparison of model prior δ18Op with speleothem and ice core proxies.

a, Observed changes in ice core (Antarctica and Greenland) and speleothem LGM–LH δ18Op compared with the model prior ensemble. The R2 value is shown in the lower right corner. b, Spatial map of median changes in the δ18Op from the prior ensemble, overlain with LGM–LH ice core and speleothem observations (dots). Speleothem δ18O was converted from δ18O of calcite or aragonite to δ18Op (in ‰ VSMOW) before plotting (see Methods).

Source data

Extended Data Fig. 2 Assessment of model bias with rank histograms.

a, LGM, b, LH. The histograms are generally symmetrical, indicating little bias in the mean, but show a U shape that signals that the model prior may lack variability.

Source data

Extended Data Fig. 3 The impact of time averaging on the assimilation results.

ad, The 40-member ensembles of 5-yr (a), 10-yr (b), 25-yr (c) and 50-yr (d) averages were assimilated with the same set of proxy data. Spatial structures in the SST fields are largely similar. GSST and GMST values remain identical within uncertainty.

Source data

Extended Data Fig. 4 Data assimilation results for individual proxy types.

a, Assimilation-derived values for ΔGSST for all proxies combined (All), \({U}_{37}^{{K}^{{\prime} }}\), Mg/Ca and δ18O, respectively. Error bars represent the 95% CI. Lightest blue bounds show the range of the model ensemble prior. b, As in a, but for ΔGMST. ce, Locations for \({U}_{37}^{{K}^{{\prime} }}\) (c), Mg/Ca (d) and δ18O (e) data. Lighter blue circles are Holocene data points, darker blue circles are LGM data points.

Source data

Extended Data Table 1 Validation statistics associated with scaling the global estimate of the proxy variance (Rg)
Extended Data Table 2 Validation statistics associated with varying the cutoff radius of the covariance localization
Extended Data Table 3 Compilation of estimates of ΔRICE used for calculations of ECS

Source data

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Tierney, J.E., Zhu, J., King, J. et al. Glacial cooling and climate sensitivity revisited. Nature 584, 569–573 (2020).

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