Abstract
During the Quaternary (the last 2.58 million years), Earth’s climate has fluctuated between glacials and interglacials, paced by external forcings and mediated by internal feedbacks. However, General Circulation Models (GCMs), essential for addressing the mechanisms associated with these fluctuations, require substantial computational resources, meaning they are unsuitable for exploring orbital-scale variability on million-year timescales. Here, we use a GCM to calibrate a faster statistical model, or emulator, and apply this to the Quaternary. We show a good agreement between the emulated climate and proxy data over the last 800,000 years, especially the timing of glacial-interglacial cycles. A series of sensitivity experiments allows us to identify the dominant components driving long-term climate change. The results show that a combination of the CO2 and ice sheet feedbacks provide the dominant contribution to the annual mean temperature signal, with the direct orbital radiative forcing playing only a minor role.
Similar content being viewed by others
Data availability
The data (used to create the results and figures in the main manuscript and Supplementary Information) generated in this study are too large to upload to a public repository; access can instead be obtained by contacting C.J.R.W. Likewise, all data required to train, build, optimise, test and run the emulator can be accessed by contacting C.J.R.W. and D.J.L., as there are too much gridded data to upload to a public repository.
Code availability
Code for the wrapper of the GP package, as well as the various scripts to display/visualise the data, is available from https://github.com/cwilliams2020-new/Pleistocene_emulator53. Please note, however, that the code provided here is not entirely stand-alone, because in order to run it would require all of the HadCM3 simulations used to train the emulator (see above). These data can be accessed by contacting C.J.R.W. and D.J.L.
References
Clark, P. U., Shakun, J. D., Rosenthal, Y., Köhler, P. & Bartlein, P. J. Global and regional temperature change over the past 4.5 million years. Science 383, 884–890 (2024).
Laskar, J. et al. A long-term numerical solution for the insolation quantities of the Earth. Astron. Astrophys. 428, 261–285 (2004).
Lisiecki, L. E. & Raymo, M. E. Plio-Pleistocene climate evolution: trends and transitions in glacial cycle dynamics. Quat. Sci. Rev. 26, 56–69 (2007).
Waters, C. N. et al. The Anthropocene is functionally and stratigraphically distinct from the Holocene. Science, 351, https://doi.org/10.1126/science.aad2622 (2016).
Past Interglacials Working Group of PAGES Interglacials of the last 800,000 years. Rev. Geophys. 54, 162–219 (2016).
Donohoe, A., Armour, K. C., Roe, G. H., Battisti, D. S. & Hahn, L. The partitioning of meridional heat transport from the last glacial maximum to CO2 quadrupling in coupled climate models. J. Clim. 33, 4141–4165 (2020).
Timmermann, A. et al. Modeling obliquity and CO2 effects on southern hemisphere climate during the Past 408 ka. J. Clim. 27, 1863–1875 (2014).
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).
Armstrong, E., Hopcroft, P. O. & Valdes, P. J. A simulated Northern Hemisphere terrestrial climate dataset for the past 60,000 years. Sci. Data 6, https://www.nature.com/articles/s41597-019-0277-1 (2019).
Ivanovic, R. F. et al. Transient climate simulations of the deglaciation 21-9 thousand years before present (version 1) - PMIP4 Core experiment design and boundary conditions. Geosci. Model Dev. 9, 2563–2587 (2016).
PalMod from the last interglacial to the Anthropocene - modelling a complete glacial cycle. https://www.palmod.de/home (Accessed 30/1/26) (2023).
Yun, K.-S. et al. A transient coupled general circulation model (CGCM) simulation of the past 3 million years. Clim. Past. 19, 1951–1974 (2023).
Timmermann, A. et al. Climate effects on archaic human habitats and species successions. Nature 604, 495–501 (2022).
Lorenz, S. & Lohmann, G. Acceleration technique for Milankovitch type forcing in a coupled atmosphere-ocean circulation model: method and application for the holocene. Clim. Dynam. 23, 727–743 (2004).
Stap, L. B., van de Wal, R. S. W., de Boer, B., Bintanja, R. & Lourens, L. J. Interaction of ice sheets and climate during the past 800 000 years. Clim. Past 10, 2135–2152 (2014).
Moseley, G. E., Edwards, R. L., Lord, N. S., Spötl, C. & Cheng, H. Speleothem record of mild and wet mid-Pleistocene climate in northeast Greenland. Sci. Adv. 7, 13 (2021).
Lord, N. S. et al. Emulation of long-term changes in global climate: Application to the mid-Pliocene and future. Clim. Past 13, 1539–1571 (2017).
Bounceur, N., Crucifix, M. & Wilkinson, R. D. Global sensitivity analysis of the climate-vegetation system to astronomical forcing: an emulator-based approach. Earth Syst. Dyn. 6, 205–224 (2015).
Van Breedam, J., Huybrechts, P. & Crucifix, M. A Gaussian process emulator for simulating ice sheet–climate interactions on a multi-million-year timescale: CLISEMv1.0. Geosci. Model Dev. 14, 6373–6401 (2021).
Johnson, J. S. et al. Evaluating uncertainty in convective cloud microphysics using statistical emulation. J. Adv. Model. Earth Syst. 7, 162–187 (2015).
Van de Wal, R. S. W., de Boer, B., Lourens, L. J., Köhler, P. & Bintanja, R. Reconstruction of a continuous high-resolution CO2 record over the past 20 million years. Clim. Past 7, 1459–1469 (2011).
Watterson, I. G., Bathols, J. & Heady, C. What influences the skill of climate models over the continents? bulletin of the american meteorological society. 95, https://doi.org/10.1175/BAMS-D-12-00136.1 (2014).
Lunt, D. J. et al. Multi-variate factorisation of numerical simulations. Geosci. Model Dev. 14, 4307–4317 (2021).
Singarayer, J. S. & Valdes, P. J. High-latitude climate sensitivity to ice-sheet forcing over the last 120 kyr. Quat. Sci. Rev. 29, 43–55 (2010).
He, F. et al. Northern Hemisphere forcing of Southern Hemisphere climate during the last deglaciation. Nature 494, 81–85 (2013).
Shi, X. et al. Unraveling the complexities of the Last Glacial Maximum climate: the role of individual boundary conditions and forcings. Clim. Past 19, 2157–2175 (2023).
Claquin, T. et al. Radiative forcing of climate by ice-age atmospheric dust. Clim. Dyn. 20, 193–202 (2003).
Gottwald, G. A. A model for Dansgaard–Oeschger events and millennial-scale abrupt climate change without external forcing. Clim. Dyn. 56, 227–243 (2021).
Romé, Y. M., Ivanovic, R. F., Gregoire, L. J., Sherriff-Tadano, S. & Valdes, P. J. Millennial-scale climate oscillations triggered by deglacial meltwater discharge in last glacial maximum simulations. Paleooceanogr. Palaeoclimatol. 37, e2022PA004451 (2022).
Li, L. et al. A 4-Ma record of thermal evolution in the tropical western Pacific and its implications on climate change. Earth Planet. Sci. Lett. 309, 10–20 (2011).
Herbert, T. D., Peterson, L. C., Lawrence, K. T. & Liu, Z. H. Tropical ocean temperatures over the past 3.5 million years. Science 328, 1530–1534 (2010).
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).
Schmidt, P., Lund, B., Naslund, J. O. & Fastook, J. Comparing a thermo-mechanical Weichselian Ice Sheet reconstruction to reconstructions based on the sea level equation: aspects of ice configurations and glacial isostatic adjustment. Solid Earth 5, 371–388 (2014).
Kug, J.-S. et al. Hysteresis of the intertropical convergence zone to CO2 forcing. Nat. Clim. Change 12, 47–53 (2022).
Valdes, P. J. et al. The BRIDGE HadCM3 family of climate models: HadCM3@Bristol v1.0. Geosci. Model Dev.https://doi.org/10.5194/gmd-2017-16 (2017).
Loutre, M. F. Paramètres orbitaux et cycles diurnes et saisonniers des insolations. (PhD thesis). Université catholique de Louvain, Louvain-la-Neuve, Belgium (1993).
Dowsett, H. J. et al. The PRISM4 (mid-Piacenzian) paleoenvironmental reconstruction. Clim. Past 12, 1519–1538 (2016).
Sacks, J., Welch, W. J., Mitchell, T. J. & Wynn, H. P. Design and analysis of computer experiments. Stat. Sci. 4, 409–423 (1989).
Kennedy, M. C. & O’Hagan, A. Predicting the output from a complex computer code when fast approximations are available. Biometrika 87, 1–13 (2000).
Oakley, J. & O’Hagan, A. Bayesian inference for the uncertainty distribution of computer model outputs. Biometrika 89, 769–784 (2002).
Wilkinson, R.D. Bayesian Calibration of Expensive Multivariate Computer Experiments. (2010).
Bereiter, B. et al. Revision of the EPICA Dome C CO2 record from 800 to 600 kyr before present. Geophys. Res. Lett. 42, 542–549 (2015).
Jouzel, J. et al. Orbital and millennial Antarctic climate variability over the past 800,000 years. Science 317, 793–796 (2007).
Spratt, R. M. & Lisiecki, L. E. A Late Pleistocene sea level stack. Clim. Past 12, 1079–1092 (2016).
de Boer, B., van de Wal, R. S. W., Bintanja, R., Lourens, L. J. & Tuenter, E. Cenozoic global ice-volume and temperature simulations with 1-D ice-sheet models forced by benthic δ18O records. Annal. Glaciol. 51, 23–33 (2010).
Cenozoic CO2 Proxy Integration Project (CenCO2PIP) Consortium Toward a Cenozoic history of atmospheric CO2. Science 382, 6675 (2023).
Wang, Y. J. et al. A high-resolution absolute-dated Late Pleistocene monsoon record from Hulu Cave, China. Science 294, 2345–2348 (2001).
Wang, Y. J. et al. Millennial- and orbital-scale changes in the East Asian monsoon over the past 224,000 years. Nature 451, 1090–1093 (2008).
Cheng, H. et al. The Asian monsoon over the past 640,000 years and ice age terminations. Nature 534, 640-+ (2016).
Chalk, T. B. et al. Causes of ice age intensification across the Mid-Pleistocene Transition. Earth Atmos. Planet. Sci. 114, 13114–13119 (2017).
Dyez, K. A., Hönisch, B. & Schmidt, G. A. Early Pleistocene obliquity-scale pCO2 variability at ~1.5 million years ago. Paleoceanogr. Paleoclimatol. 33, 1270–1291 (2018).
Martínez-Botí, M. et al. Plio-Pleistocene climate sensitivity evaluated using high-resolution CO2 records. Nature 518, 49–54 (2015).
Williams, C. J. R. et al. The relative role of direct orbital forcing versus CO2 and ice feedbacks on Quaternary climate. Zenodo https://doi.org/10.5281/zenodo.18496876 (2026).
Herbert, T. D. et al. Collapse of the california current during glacial maxima linked to climate change on land. Science 293, 71–76 (2001).
Dyez, K.A., Ravelo, A.C. & Mix, A.C. Evaluating drivers of Pleistocene eastern tropical Pacific sea surface temperature. Paleoceanogr. Paleoclimatol.https://doi.org/10.1002/2015PA002873 (2016).
Wara, M. W., Ravelo, A. C. & Delaney, M. L. Permanent El niño-like conditions during the pliocene warm period. Science 309, 758–761 (2005).
Hayward, B. W. et al. The effect of submerged plateaux on Pleistocene gyral circulation and sea-surface temperatures in the Southwest Pacific. Glob. Planet. Change 63, 309–316 (2008).
Acknowledgements
The work described in this paper was carried out in the framework of a project funded by Posiva Oy, SKB and KAERI, funding C.J.R.W., N.S.L. and A.T.K. C.J.R.W. was also partly supported by the NERC - NSFGEO grant NE/Y001443/1 (‘Pliocene Lessons for the Indian Ocean Dipole’, PLIOD). Some of the earlier development work was carried out in the framework of a project funded by R.W.M., D.J.L. and X.R. also acknowledge support from NERC grant NE/V01823X/1 (‘Solving the Oligocene icehouse conundrum’), and the NWS. C.J.R.W., D.J.L. and X.R. also acknowledge support from the TONIC grant (R102341-101). R.M.B. acknowledges support from NERC grant NE/L002531/1 (‘The Southampton Partnership for Innovative Training of Future Investigators Researching the Environment’, SPITFIRE). This work was carried out using the computational facilities of the Advanced Computing Research Centre, University of Bristol - http://www.bris.ac.uk/acrc/.
Author information
Authors and Affiliations
Contributions
C.J.R.W. conducted the emulator simulations, carried out the analysis, produced the figures, wrote the majority of the manuscript, and led the paper. N.S.L. initially set up the emulator and wrote some of the manuscript. A.T.K. provided technical assistance in running the emulator, and X.R. provided some of the figures. M.C. provided an earlier version of the emulator. D.A.R., A.K., M.T. and P.J.V. proofread the manuscript and provided edits. G.L.F., R.M.B. and E.L.M. provided the proxy reconstructions. D.J.L. contributed to some of the writing.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. A peer review file is available.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Williams, C.J.R., Lord, N.S., Kennedy-Asser, A.T. et al. The relative role of direct orbital forcing versus CO2 and ice feedbacks on Quaternary climate. Nat Commun (2026). https://doi.org/10.1038/s41467-026-70750-3
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s41467-026-70750-3
