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


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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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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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