Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Concerns of assuming linearity in the reconstruction of thermal maxima

Matters Arising to this article was published on 27 July 2022

The Original Article was published on 27 January 2021

Your institute does not have access to this article

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: SAT method lacks skill in reconstructing simulated Holocene annual temperature.
Fig. 2: SAT method mutes thermal maxima.

Code availability

The R code for the performed analysis is deposited at


  1. Liu, Z. et al. The Holocene temperature conundrum. Proc. Natl Acad. Sci. USA 111, E3501–E3505 (2014).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  2. Marcott, S. A., Shakun, J. D., Clark, P. U. & Mix, A. C. A reconstruction of regional and global temperature for the past 11,300 years. Science 339, 1198–1201 (2013).

    ADS  CAS  Article  Google Scholar 

  3. Kaufman, D. et al. Holocene global mean surface temperature, a multi-method reconstruction approach. Sci. Data 7, 201 (2020).

    CAS  Article  Google Scholar 

  4. Bova, S., Rosenthal, Y., Liu, Z., Godad, S. P. & Yan, M. Seasonal origin of the thermal maxima at the Holocene and the last interglacial. Nature (2021).

  5. Galaasen, E. V. et al. Interglacial instability of North Atlantic Deep Water ventilation. Science 367, 1485–1489 (2020).

    ADS  CAS  Article  Google Scholar 

  6. Liu, Y. et al. A possible role of dust in resolving the Holocene temperature conundrum. Sci. Rep. 8, 4434 (2018).

    ADS  Article  Google Scholar 

  7. Laepple, T. & Lohmann, G. Seasonal cycle as template for climate variability on astronomical timescales. Paleoceanography 24, PA4201 (2009).

    ADS  Article  Google Scholar 

  8. Clement, A. C., Hall, A. & Broccoli, A. J. The importance of precessional signals in the tropical climate. Clim. Dyn. 22, 327–341 (2004).

    Article  Google Scholar 

  9. Erb, M. P., Jackson, C. S. & Broccoli, A. J. Using single-forcing GCM simulations to reconstruct and interpret quaternary climate change. J. Clim. 28, 9746–9767 (2015).

    ADS  Article  Google Scholar 

  10. Huybers, P. & Tziperman, E. Integrated summer insolation forcing and 40,000-year glacial cycles: the perspective from an ice-sheet/energy-balance model. Paleoceanography 23, PA1208 (2008).

  11. Milankovitch, M. Kanon der Erdbestrahlung und seine Andwendung auf das Eiszeitenproblem (Royal Serbian Academy, 1941).

  12. Wang, G. & Dillon, M. E. Recent geographic convergence in diurnal and annual temperature cycling flattens global thermal profiles. Nat. Clim. Change 4, 988–992 (2014).

    ADS  Article  Google Scholar 

  13. Lu, Z., Liu, Z., Chen, G. & Guan, J. Prominent precession band variance in ENSO intensity over the last 300,000 years. Geophys. Res. Lett. 46, 9786–9795 (2019).

    ADS  Article  Google Scholar 

  14. Rohling, E. J. et al. Asynchronous Antarctic and Greenland ice-volume contributions to the last interglacial sea-level highstand. Nat. Commun. 10, 5040 (2019).

    ADS  Article  Google Scholar 

  15. Nicholl, J. A. L. et al. A Laurentide outburst flooding event during the last interglacial period. Nat. Geosci. 5, 901–904 (2012).

    ADS  CAS  Article  Google Scholar 

  16. Benestad, R. E. Empirical-statistical downscaling in climate modeling. Eos 85, 417–422 (2004).

Download references


This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme Starting Grant SPACE (grant agreement number 716092). F.H. is supported by the University of Wisconsin-Madison Office of the Vice Chancellor for Research and Graduate Education with funding from the Wisconsin Alumni Research Foundation. We thank R. Hebert for discussions.

Author information

Authors and Affiliations



All authors collaborated on the design of the study, the interpretation of the results and writing the manuscript. T.L. led the study and performed the evaluation of the SAT method on the model simulations.

Corresponding author

Correspondence to T. Laepple.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Laepple, T., Shakun, J., He, F. et al. Concerns of assuming linearity in the reconstruction of thermal maxima. Nature 607, E12–E14 (2022).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing