Abstract
Last Glacial millennial-scale climate variability transitioned through distinct cold stadial and warm interstadial states. Here we use Earth system model simulations to demonstrate that nonlinear self-sustained climate oscillations appear spontaneously within a window of glacial-level atmospheric CO2 concentrations (~190–225 parts per million). Outside this window, the system remains in either quasi-stable cold low CO2 or warm high CO2 states, with infrequent and abrupt random transitions driven by noise. In the oscillatory regime, the time between climate transitions is governed by temporal variations in the state of the ocean, atmosphere and sea ice, with CO2 acting as a control on the relative rates of the internal forcing and feedback in the system. The Earth system model results map perfectly to a slow–fast dynamical systems model, where the fixed point of the system transitions into the oscillatory regime through a loss of stability at two critical tipping points, the window boundaries. The deterministic component of the oscillations is modified by a stochastic element associated with internal climate variability. Agreement between observations and the hierarchically disparate models suggests the existence of an internal stochastic climate oscillator, which tracks variations in atmospheric CO2 level through the glacial, acting in concert with noise-induced transitions.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Rent or buy this article
Prices vary by article type
from$1.95
to$39.95
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
Data availability
Decadal average time series data from the CCSM4 model simulations are available from the University of Copenhagen Electronic Research Data Archive (ERDA): https://sid.erda.dk/cgi-sid/ls.py?share_id=Fo2F7YWBmv. All other data are provided in the Supplementary Information.
Code availability
The head code repository for this manuscript is available on Github/Zenodo: https://doi.org/10.5281/zenodo.6372628. The simple model code (https://doi.org/10.5281/zenodo.6205127) can be viewed and run online at the following mybinder.org address: https://mybinder.org/v2/gh/guidov/scdom/main?filepath=index.ipynb.
References
Dansgaard, W. et al. Evidence for general instability of past climate from a 250-kyr ice-core record. Nature 364, 218–220 (1993).
Stocker, T. F. & Johnsen, S. J. A minimum thermodynamic model for the bipolar seesaw. Paleoceanogr. Paleoclimatol. 18, 1087 (2003).
Pedro, J. B. et al. Beyond the bipolar seesaw: toward a process understanding of interhemispheric coupling. Quat. Sci. Rev. 192, 27–46 (2018).
Thompson, A. F., Hines, S. K. & Adkins, J. F. A Southern Ocean mechanism for the interhemispheric coupling and phasing of the bipolar seesaw. J. Clim. 32, 4347–4365 (2019).
Dijkstra, H. A. Nonlinear Climate Dynamics (Cambridge Univ. Press, 2013).
Li, C. & Born, A. Coupled atmosphere–ice–ocean dynamics in Dansgaard–Oeschger events. Quat. Sci. Rev. 203, 1–20 (2019).
Ditlevsen, P. D., Kristensen, M. S. & Andersen, K. K. The recurrence time of Dansgaard–Oeschger events and limits on the possible periodic component. J. Clim. 18, 2594–2603 (2005).
Véez-Belchí, P., Alvarez, A., Colet, P., Tintoré, J. & Haney, R. L. Stochastic resonance in the thermohaline circulation. Geophys. Res. Lett. 28, 2053–2056 (2001).
Ganopolski, A. & Rahmstorf, S. Abrupt glacial climate changes due to stochastic resonance. Phys. Rev. Lett. 88, 038501 (2002).
Kleppin, H., Jochum, M., Otto-Bliesner, B., Shields, C. A. & Yeager, S. Stochastic atmospheric forcing as a cause of Greenland climate transitions. J. Clim. 28, 7741–7763 (2015).
Cessi, P. A simple box model of stochastically forced thermohaline flow. J. Phys. Ocean. 24, 1911–1920 (1994).
Timmermann, A., Gildor, H., Schulz, M. & Tziperman, E. Coherent resonant millennial-scale climate oscillations triggered by massive meltwater pulses. J. Clim. 16, 2569–2585 (2003).
Winton, M. & Sarachik, E. Thermohaline oscillations induced by strong steady salinity forcing of ocean general circulation models. J. Phys. Ocean. 23, 1389–1410 (1993).
Sévellec, F., Huck, T. & Ben Jelloul, M. On the mechanism of centennial thermohaline oscillations. J. Mar. Res. 64, 355–392 (2006).
Colin de Verdière, A. A simple model of millennial oscillations of the thermohaline circulation. J. Phys. Ocean. 37, 1142–1155 (2007).
Stommel, H. Thermohaline convection with two stable regimes of flow. Tellus 13, 224–230 (1961).
Berglund, N. & Gentz, B. Noise-Induced Phenomena in Slow–Fast Dynamical Systems: A Sample-Paths Approach (Springer, 2006).
Roberts, A. & Saha, R. Relaxation oscillations in an idealized ocean circulation model. Clim. Dyn. 48, 2123–2134 (2017).
Rial, J. & Saha, R. Modeling abrupt climate change as the interaction between sea ice extent and mean ocean temperature under orbital insolation forcing. Agu. Geophys. Mono. 193, 57–74 (2011).
Crucifix, M. Oscillators and relaxation phenomena in Pleistocene climate theory. Philos. Trans. R. Soc. A 370, 1140–1165 (2012).
Kwasniok, F. Analysis and modelling of glacial climate transitions using simple dynamical systems. Philos. Trans. R. Soc. A 371, 20110472 (2013).
Sima, A., Paul, A. & Schulz, M. The Younger Dryas—an intrinsic feature of late Pleistocene climate change at millennial timescales. Earth Planet. Sci. Lett. 222, 741–750 (2004).
Olsen, S. M., Shaffer, G. & Bjerrum, C. J. Ocean oxygen isotope constraints on mechanisms for millennial-scale climate variability. Paleoceanogr. Paleoclimatol. 20, PA1014 (2005).
Arzel, O., England, M. H., de Verdière, A. C. & Huck, T. Abrupt millennial variability and interdecadal-interstadial oscillations in a global coupled model: sensitivity to the background climate state. Clim. Dyn. 39, 259–275 (2012).
Peltier, W. R. & Vettoretti, G. Dansgaard-Oeschger oscillations predicted in a comprehensive model of glacial climate: a ‘kicked’ salt oscillator in the Atlantic. Geophys. Res. Lett. 41, 7306–7313 (2014).
Brown, N. & Galbraith, E. D. Hosed vs. unhosed: interruptions of the Atlantic Meridional Overturning Circulation in a global coupled model, with and without freshwater forcing. Clim. Past 12, 1663–1679 (2016).
Klockmann, M., Mikolajewicz, U. & Marotzke, J. Two AMOC states in response to decreasing greenhouse gas concentrations in the coupled climate model MPI-ESM. J. Clim. 31, 7969–7984 (2018).
Zhang, X., Lohmann, G., Knorr, G. & Purcell, C. Abrupt glacial climate shifts controlled by ice sheet changes. Nature 512, 290–294 (2014).
Zhang, X., Knorr, G., Lohmann, G. & Barker, S. Abrupt North Atlantic circulation changes in response to gradual CO2 forcing in a glacial climate state. Nat. Geosci. 10, 518–523 (2017).
Schulz, M., Berger, W. H., Sarnthein, M. & Grootes, P. M. Amplitude variations of 1,470-year climate oscillations during the last 100,000 years linked to fluctuations of continental ice mass. Geophys. Res. Lett. 26, 3385–3388 (1999).
Lohmann, J. & Ditlevsen, P. D. Random and externally controlled occurrences of Dansgaard–Oeschger events. Clim. Past 14, 609–617 (2018).
Bauska, T. K., Marcott, S. A. & Brook, E. J. Abrupt changes in the global carbon cycle during the last glacial period. Nat. Geosci. 14, 91–96 (2021).
Heinrich, H. Origin and consequences of cyclic ice rafting in the northeast Atlantic Ocean during the past 130,000 years. Quat. Res. 29, 142–152 (1988).
Gent, P. R. et al. The Community Climate System Model version 4. J. Clim. 24, 4973–4991 (2011).
Ohshima, K. I. et al. Antarctic bottom water production by intense sea-ice formation in the Cape Darnley polynya. Nat. Geosci. 6, 235–240 (2013).
Rasmussen, S. O. et al. A stratigraphic framework for abrupt climatic changes during the last glacial period based on three synchronized Greenland ice-core records: refining and extending the INTIMATE event stratigraphy. Quat. Sci. Rev. 106, 14–28 (2014).
Henry, L. G. et al. North Atlantic Ocean circulation and abrupt climate change during the last glaciation. Science 353, 470–474 (2016).
Rahmstorf, S. On the freshwater forcing and transport of the Atlantic thermohaline circulation. Clim. Dyn. 12, 799–811 (1996).
Jansen, M. F. & Nadeau, L.-P. A toy model for the response of the residual overturning circulation to surface warming. J. Phys. Ocean. 49, 1249–1268 (2019).
Lumpkin, R. & Speer, K. Global ocean meridional overturning. J. Phys. Ocean. 37, 2550–2562 (2007).
Nikurashin, M. & Vallis, G. A theory of the interhemispheric meridional overturning circulation and associated stratification. J. Phys. Ocean. 42, 1652–1667 (2012).
Marshall, J. & Speer, K. Closure of the meridional overturning circulation through Southern Ocean upwelling. Nat. Geosci. 5, 171–180 (2012).
Sun, S., Eisenman, I. & Stewart, A. L. Does Southern Ocean surface forcing shape the global ocean overturning circulation? Geophys. Res. Lett. 45, 2413–2423 (2018).
Boers, N., Ghil, M. & Rousseau, D.-D. Ocean circulation, ice shelf, and sea ice interactions explain Dansgaard–Oeschger cycles. Proc. Natl Acad. Sci. USA 115, E11005–E11014 (2018).
Drijfhout, S. S., Marshall, D. P. & Dijkstra, H. A. Ocean circulation and climate: a 21st century perspective. Int. Geophys. 103, 257–282 (2013).
Vettoretti, G. & Peltier, W. R. Fast physics and slow physics in the nonlinear Dansgaard–Oeschger relaxation oscillation. J. Clim. 31, 3423–3449 (2018).
Vettoretti, G. & Peltier, W. R. Thermohaline instability and the formation of glacial North Atlantic super polynyas at the onset of Dansgaard–Oeschger warming events. Geophys. Res. Lett. 43, 5336–5344 (2016).
Gowan, E. J. et al. A new global ice sheet reconstruction for the past 80,000 years. Nat. Commun. 12, 1199 (2021).
Klockmann, M., Mikolajewicz, U., Kleppin, H. & Marotzke, J. Coupling of the subpolar gyre and the overturning circulation during abrupt glacial climate transitions. Geophys. Res. Lett. 47, e2020GL090361 (2020).
Born, A. & Stocker, T. F. Two stable equilibria of the Atlantic subpolar gyre. J. Phys. Ocean. 44, 246–264 (2014).
Svensson, A. et al. Bipolar volcanic synchronization of abrupt climate change in Greenland and Antarctic ice cores during the last glacial period. Clim. Past 16, 1565–1580 (2020).
Schmittner, A., Green, J. A. M. & Wilmes, S.-B. Glacial ocean overturning intensified by tidal mixing in a global circulation model. Geophys. Res. Lett. 42, 4014–4022 (2015).
Gettelman, A. & Kay, J. E. The evolution of climate sensitivity and climate feedbacks in the community atmosphere model. J. Clim. 25, 1453–1469 (2012).
Danabasoglu, G. et al. The CCSM4 ocean component. J. Clim. 25, 1361–1389 (2012).
Lawrence, D. M. et al. The CCSM4 land simulation, 1850–2005: assessment of surface climate and new capabilities. J. Clim. 25, 2240–2260 (2012).
Jahn, A. et al. Late-twentieth-century simulation of Arctic sea ice and ocean properties in the CCSM4. J. Clim. 25, 1431–1452 (2012).
Argus, D. F., Peltier, W. R., Drummond, R. & Moore, A. W. The Antarctica component of post-glacial rebound model ICE-6G_C (VM5a) based on GPS positioning, exposure age dating of thicknesses, and relative sea level histories. Geophys. J. Int. 198, 537–563 (2014).
Peltier, W. R., Argus, D. F. & Drummond, R. Space geodesy constrains ice age terminal deglaciation: the global ICE-6G_C (VM5a) model: global glacial isostatic adjustment. J. Geophys. Res. 120, 450–487 (2015).
Pico, T., Birch, L., Weisenberg, J. & Mitrovica, J. Refining the Laurentide Ice Sheet at Marine Isotope Stage 3: a data-based approach combining glacial isostatic simulations with a dynamic ice model. Quat. Sci. Rev. 195, 171–179 (2018).
Dalton, A. S. et al. Was the Laurentide Ice Sheet significantly reduced during Marine Isotope Stage 3? Geology 47, 111–114 (2019).
Andres, H. J. & Tarasov, L. Towards understanding potential atmospheric contributions to abrupt climate changes: characterizing changes to the North Atlantic eddy-driven jet over the last deglaciation. Clim. Past 15, 1621–1646 (2019).
Vettoretti, G. & Peltier, W. R. Last glacial maximum ice sheet impacts on North Atlantic climate variability: the importance of the sea ice lid. Geo. Phys. Res. Lett. 40, 6378–6383 (2013).
Bryan, K. & Lewis, L. J. A water mass model of the world ocean. J. Geophys. Res. 84, 2503–2517 (1979).
Manabe, S. & Stouffer, R. J. Two stable equilibria of a coupled ocean-atmosphere model. J. Clim. 1, 841–866 (1988).
Jayne, S. R. The impact of abyssal mixing parameterizations in an ocean general circulation model. J. Phys. Ocean. 39, 1756–1775 (2009).
Danabasoglu, G., Large, W. G. & Briegleb, B. P. Climate impacts of parameterized Nordic Sea overflows. J. Geophys. Res. 115, C11005 (2010).
Shields, C. A. et al. The low-resolution CCSM4. J. Clim. 25, 3993–4014 (2012).
Orsi, A., Johnson, G. & Bullister, J. Circulation, mixing, and production of Antarctic bottom water. Prog. Ocean. 43, 55–109 (1999).
Wolfe, C. L. & Cessi, P. Multiple regimes and low-frequency variability in the quasi-adiabatic overturning circulation. J. Phys. Ocean. 45, 1690–1708 (2015).
FitzHugh, R. Mathematical models of threshold phenomena in the nerve membrane. Bull. Math. Biophys. 17, 257–278 (1955).
Nagumo, J., Arimoto, S. & Yoshizawa, S. An active pulse transmission line simulating nerve axon. Proc. IRE 50, 2061–2070 (1962).
Acknowledgements
This work is a result of the ChronoClimate project, funded by the Carlsberg Foundation, and the Tipping Points in the Earth System (TiPES) project, which received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 820970 (G.V.). S.O.R. received support from the Villum Investigator Project IceFlow (grant no. 16572). The computations were performed at the Danish Center for Climate Computing (DC3), and we thank its administrator, R. Nuterman, for support. This is TiPES contribution no. 90.
Author information
Authors and Affiliations
Contributions
G.V. conceived the study. G.V. designed and conducted the comprehensive glacial climate model simulations and developed the simple model. All authors contributed to the analysis. G.V. wrote the manuscript with contributions from all co-authors.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Nature Geoscience thanks Heather Andres, Andreas Born and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor(s): James Super, in collaboration with the Nature Geoscience team.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Extended data
Extended Data Fig. 1 Glacial model spinup to equilibrium.
a) Timeseries of global average ocean potential temperature (∘C) in four of the glacial CO2 experiments. b) Same as for temperature but for timeseries of salinity (practical salinity units), c) potential density anomaly (σ0: kg m−3) and d) ideal age (years).
Extended Data Fig. 2 Pre-Industrial control model validation.
a) Modern global average time-depth profile of ocean potential temperature differenced from observed (∘C) (see67 for observed data). b) Global average ocean potential temperature from the modern simulation. The modern observed value is also shown in purple c) Same as in a) but for salinity (practical salinity units). Global ocean overflow parameterizations66 have been turned off in the modern control simulation and a BL profile63 has been used for the vertical mixing.
Extended Data Fig. 3 Modern and Glacial ocean meridional overturning circulation.
a) Global zonal average overturning streamfunction (Sv) from the original NCAR CCSM4 simulation described in67. b) Global zonal average overturning streamfunction (Sv) from the modified CCSM4 pre-industrial control simulation (BL) used in this study. The same as in b) but for the glacial c) stadial and d) interstadial climate from a simulation with CO2=210 ppm. The maximum in NADW and AABW overturning streamfunctions (Sv) in the glacial climate are highlighted with white and yellow ellipses, respectively. These two points form the basis for the two degrees of freedom in our simple model.
Extended Data Fig. 5 Global thermocline salinity anomalies.
The stadial salinity anomaly of each the experiments with different levels of CO2 differenced from the ensemble mean of the four experiments. The average salinity in the top 1000 meters of the ocean in each experiment is averaged and then differenced from the ensemble mean average salinity in the top 1000 meters.
Extended Data Fig. 6 Global thermocline temperature anomalies.
The stadial temperature anomaly of each the experiments with different levels of CO2 differenced from the ensemble mean of the four experiments. The average temperature in the top 1000 meters of the ocean in each experiment is averaged and then differenced from the ensemble mean average temperature in the top 1000 meters.
Extended Data Fig. 7 Arctic and North Atlantic sea ice volume.
Sea-ice-volume variations in the a) Arctic box and the b) North Atlantic box (see Supplementary Materials for box areas) for each of the different CO2 simulations. The vertical lines span the range between minimum and maximum sea-ice volume for each simulation. The black dots represent the mean volume of sea-ice throughout the whole simulation. The sea-ice volume follows the characteristic pattern of a system with a fold bifurcation and a control parameter (the atmospheric CO2 concentration).
Supplementary information
Supplementary Information
Supplementary Figs. 1–12 and Discussion.
Rights and permissions
About this article
Cite this article
Vettoretti, G., Ditlevsen, P., Jochum, M. et al. Atmospheric CO2 control of spontaneous millennial-scale ice age climate oscillations. Nat. Geosci. 15, 300–306 (2022). https://doi.org/10.1038/s41561-022-00920-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41561-022-00920-7
This article is cited by
-
Simulating AMOC tipping driven by internal climate variability with a rare event algorithm
npj Climate and Atmospheric Science (2024)
-
Warning of a forthcoming collapse of the Atlantic meridional overturning circulation
Nature Communications (2023)
-
Impact of climatic oscillations on marlin catch rates of Taiwanese long-line vessels in the Indian Ocean
Scientific Reports (2023)
-
High-latitude precipitation as a driver of multicentennial variability of the AMOC in a climate model of intermediate complexity
Climate Dynamics (2023)
-
Identifying the mechanisms of DO-scale oscillations in a GCM: a salt oscillator triggered by the Laurentide ice sheet
Climate Dynamics (2023)