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Global patterns of declining temperature variability from the Last Glacial Maximum to the Holocene

A Corrigendum to this article was published on 15 March 2018

This article has been updated


Changes in climate variability are as important for society to address as are changes in mean climate1. Contrasting temperature variability during the Last Glacial Maximum and the Holocene can provide insights into the relationship between the mean state of the climate and its variability2,3. However, although glacial–interglacial changes in variability have been quantified for Greenland2, a global view remains elusive. Here we use a network of marine and terrestrial temperature proxies to show that temperature variability decreased globally by a factor of four as the climate warmed by 3–8 degrees Celsius from the Last Glacial Maximum (around 21,000 years ago) to the Holocene epoch (the past 11,500 years). This decrease had a clear zonal pattern, with little change in the tropics (by a factor of only 1.6–2.8) and greater change in the mid-latitudes of both hemispheres (by a factor of 3.3–14). By contrast, Greenland ice-core records show a reduction in temperature variability by a factor of 73, suggesting influences beyond local temperature or a decoupling of atmospheric and global surface temperature variability for Greenland. The overall pattern of reduced variability can be explained by changes in the meridional temperature gradient, a mechanism that points to further decreases in temperature variability in a warmer future.

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Figure 1: Proxy records for temperature.
Figure 2: Global LGM-to-Holocene change in variability and temperature gradient.
Figure 3: Latitudinal structure of LGM-to-Holocene variability and mean changes.

Change history

  • 14 March 2018

    Please see accompanying Corrigendum ( In this Letter, in the legend of Fig. 3, “Red and green shading” has been corrected to “Green and red shading”. In the Methods subsection ‘Potential effect of ecological adaption and bioturbational mixing on marine variance ratios’, the phrase “alkenone-based (nine sites) and the Mg/Ca of planktic foraminifera G. ruber (six sites)” has been corrected to “alkenone-based (eight sites) and the Mg/Ca of planktic foraminifera G. ruber (seven sites)”.


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This study was supported by the Initiative and Networking Fund of the Helmholtz Association grant no. VG-900NH. K.R. acknowledges funding by the German Science Foundation (DFG, code RE 3994/1-1). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 716092). We acknowledge P. Huybers, L. Sime, M. Holloway and T. Kunz for comments on the manuscript. We thank all original data contributors who made their proxy data available, and acknowledge the World Climate Research Programmes Working Group on Coupled Modelling, which is responsible for CMIP, and thank the climate modelling groups for producing and making available their model output. The US Department of Energy Programme for Climate Model Diagnosis and Intercomparison provided coordinating support for CMIP5 and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. The PMIP3 data archives are supported by CEA and CNRS.

Author information

Authors and Affiliations



K.R. and T.L. designed the research; T.M. established the ice database and signal-to-noise ratio correction. S.L.H. established the marine database. K.R. and T.L. developed the methodology. K.R. performed the data analysis and wrote the first draft of the manuscript. K.R., T.M., S.L.H. and T.L. contributed to the interpretation and to the preparation of the final manuscript.

Corresponding author

Correspondence to Kira Rehfeld.

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Competing interests

The authors declare no competing financial interests.

Additional information

Reviewer Information Nature thanks P. Ditlevsen 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 Figure 1 Zonal variability change pattern for different timescales and length requirements.

ad, Results for the estimated zonal-mean variance ratios based on the joint dataset are shown as a function of the timescale considered and the minimum number of data points in the time period: 500–1,000-year timescale with a minimum of 25 data points (a); 1,000–1,750-year timescale with a minimum of 25 data points (b); 650–2,000-year timescale with a minimum of 20 data points (c); and 500–1,750-year timescale with a minimum of 25 data points (d), which corresponds to the results shown in the main text. The number of records for each zonal-mean ratio is indicated by blue points. The total number of records varies depending on the timescale constraints. Error bars denote the 90% confidence intervals of the zonal mean.

Extended Data Figure 2 Temperature gradient versus variability change.

Scatter plot of the model-based equator-to-pole temperature gradient change at the proxy locations versus the variability change estimated from the proxy records. Filled circles correspond to ice-core records (red, Greenland; black, other) and filled diamonds to marine records. Error bars denote the 90% confidence interval of the estimated variance ratios. The data have a Spearman’s rank correlation coefficient of 0.43 (P ≤ 0.03, n = 28) when including the Greenland ice cores and of 0.35 (P ≤ 0.09, n = 25) when excluding them.

Extended Data Figure 3 Proxy- versus model-based variability change.

a, Zonal-mean LGM-to-Holocene variability change from the proxy compilations (red bars denote the joint estimate, orange points the separate estimate). b, Interannual to multidecadal zonal-mean variability change based on the PMIP3-CMIP5 simulations for the LGM and the pre-industrial period. c. Individual variability change at the proxy locations from the joint dataset. Error bars in a show the 90% confidence interval of the mean; error bars in c show the 90% confidence interval of the individual variance ratios.

Extended Data Figure 4 Raw periodograms of all records.

Thin blue lines show the spectra of the Holocene time slice; thin green lines show the spectra of the LGM time slice. Logarithmically smoothed spectra are given as thick lines with 90% confidence intervals as shading. Grey areas indicate the frequency response outside the bandwidth used for the timescale-dependent variance ratio estimate. x-axis scaling is in periods in years; y-axis scaling denotes power spectral density. Text insets give the time-slice variances for the LGM and the Holocene (‘Hol’) in K2; variance ratios for the records from the joint dataset are listed in Extended Data Table 2.

Extended Data Figure 5 Surrogate tests for the magnitude of variance change.

The magnitude of potential biases in the variance ratio estimates were derived using 1,000 realizations of power-law noise (slope β = 1) of constant variance on the original time axes of the records. Analyses for variability quantification were performed as for the primary analyses and described in Methods. a, Histogram of the bias of the variance ratio estimated from the surrogate data. The mean of the distribution (red line) is not significantly different from zero (c.i., confidence interval).b, Estimated zonal-mean ratios from the surrogate data. The individual surrogate zonal-mean ratios (black bars) are all close to 1 and show no latitudinal pattern, in contrast to the zonal-mean ratios from the proxy data (joint dataset, green bars). Error bars show the 90% confidence interval for the proxy data and ±2 times the standard error of the zonal mean for the surrogate data (n = 1,000).

Extended Data Figure 6 Effect of the Holocene signal-to-noise ratio of proxy records on the noise correction of the variance ratios estimated.

a, Noise correction as a function of the Holocene signal-to-noise ratio (SNR). The ratio of the true variance ratio to the estimated one, R/R′, is displayed for R′ = 0.5 and R′ = 5 (dashed lines) for a noise variance ratio of Fε = 1. The shaded area denotes the region where for R′ = 0.5, no R/R′ ≥ 0 exists. b, Test for the comparability of marine and Greenland ice-core variance ratios as a function of the signal-to-noise ratio. The expected value of R for the mean over all records of the joint dataset below 70° N is shown under the assumption of a wide range of signal-to-noise ratios (solid blue line), with uncertainty (dashed lines) of ±2 s.e.m. (n = 25). Within the realistic range of Holocene signal-to-noise ratios (shaded blue area, based on the published estimates listed in c), the noise-corrected global variance ratio (excluding Greenland) ranges from 1.7 to 11.4, which cannot be brought into agreement with the mean variance ratio of the Greenland ice cores (horizontal green line; shading denotes full uncertainty including the range of Greenland signal-to-noise ratios (c) used in the noise correction). c, Overview of published17,50,51,52 proxy signal-to-noise ratio estimates for the Holocene. Greenlandic and Antarctic estimates refer to δ18O. CI, confidence interval.

Extended Data Figure 7 Representativeness of the proxy data locations.

The centennial temperature variability in the TraCE-21K simulation, sampled at the proxy locations (black circles), the zonal-mean variability (green line) and the mean of the variability in the zonal box, either formed only from the variance at the proxy sites (blue) or formed using all grid points (red), are shown. The red vertical lines show the 90% quantiles from the mean of N random samples of the variance field, where N is the number of proxy sites in the zonal box. a, Results when sampling from the proxy locations of the separate dataset. b, Results when sampling from the joint dataset. In all cases the mean of the proxy sites is inside the distribution of random samples, which demonstrates that under the assumption of this variance field the proxy estimates are unbiased.

Extended Data Table 1 North Atlantic sea-ice variability ratios
Extended Data Table 2 Individual variability ratio estimates for all records from the joint dataset

Supplementary information

Supplementary Data

This spread sheet contains a README (Tab. 1), metadata information for all used proxy data (Tab. 2), references for the proxy data (Tab. 3) and the proxy data (Tabs 4-103). (XLS 2118 kb)

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Rehfeld, K., Münch, T., Ho, S. et al. Global patterns of declining temperature variability from the Last Glacial Maximum to the Holocene. Nature 554, 356–359 (2018).

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