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.
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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.
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.
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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.
The authors declare no competing interests.
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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).
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.
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.
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.
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.
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).
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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