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.

Persistent 400,000-year variability of Antarctic ice volume and the carbon cycle is revealed throughout the Plio-Pleistocene


Marine sediment records from the Oligocene and Miocene reveal clear 400,000-year climate cycles related to variations in orbital eccentricity. These cycles are also observed in the Plio-Pleistocene records of the global carbon cycle. However, they are absent from the Late Pleistocene ice-age record over the past 1.5 million years. Here we present a simulation of global ice volume over the past 5 million years with a coupled system of four three-dimensional ice-sheet models. Our simulation shows that the 400,000-year long eccentricity cycles of Antarctica vary coherently with δ13C data during the Pleistocene, suggesting that they drove the long-term carbon cycle changes throughout the past 35 million years. The 400,000-year response of Antarctica was eventually suppressed by the dominant 100,000-year glacial cycles of the large ice sheets in the Northern Hemisphere.


There have been numerous efforts to explain climate variability during the Cenozoic era, the past 65 million years (Myr). The interactions between orbital forcing, temperature, the carbon cycle and glaciation at high latitudes seem to play important roles in determining the pacing of ice sheets, the variability of the surface-air temperature over the Earth and atmospheric CO2 concentrations (pCO2)1,2. For the past ~1 Myr, observations of pCO2 have shown that temperature and pCO2 vary coherently over glacial cycles3. However, the precise contribution of different components of the climate system to glacial–interglacial variability has yet to be resolved4. Although a clear link between changes in solar insolation and ice volume has been determined5,6, the exact causes and links with the pacing of the carbon cycle and the role of the ocean7 are not yet fully understood.

Ice sheets have been a significant part of the climate system since the transition from the Eocene to the Oligocene (~34 Myr ago). This transition has been identified in the marine sediment records of benthic oxygen isotopes (δ18O) as the initiation of Antarctic glaciation8, triggered by a decrease in pCO2 (ref. 9). During the Oligocene to Middle Miocene time interval, eccentricity cycles of 100,000-yr (100-kyr) and 400-kyr have been found in multiple marine sediment isotope records of carbon (δ13C) and oxygen (δ18O) isotopes and have been linked to changes in ice volume and the carbon cycle1,10,11,12. Over the past 5 Myr, oceanic carbon isotope records also reveal 400-kyr eccentricity cycles in the global carbon reservoir13. In contrast, the absence of the 400-kyr-long eccentricity signal in the Pleistocene ice-age records such as benthic δ18O data has raised the so-called ‘400-kyr problem’14. The benthic δ18O data are crucial in the interpretation of the long-term environmental changes as it reflects variations in global ice volume and deep-water temperature15.

Here we use a stacked record of benthic δ18O data16 (LR04) that represents a global averaged signal of climate variability for the Plio-Pleistocene (Fig. 1a). We use an inverse forward modelling approach to derive ice volume and temperature from the benthic δ18O data over the past 5 Myr. A Northern Hemisphere (NH) temperature anomaly is derived from the difference between modelled and observed benthic δ18O data (see Methods). This temperature anomaly is forwarded to four sophisticated three-dimensional (3D) ice-sheet-shelf models and a deep-water temperature parameterization17 to determine the temperature and ice-volume contributions to the benthic δ18O data. The modelled benthic δ18O data are calculated by minimizing the difference between the modelled and observed δ18O. The coupled system includes four ice-sheet-shelf models that simulate glaciation on Eurasia, North America, Greenland and Antarctica, thereby explicitly calculating all ice-volume contributions separately for the first time over the past 5 Myr. To investigate the disappearance of the 400-kyr-long eccentricity cycles in the benthic δ18O data, we analyse the ice-volume simulations and compare these with available proxy data. We show that the 400-kyr-long eccentricity cycles found in Antarctic ice volume, as a result of insolation-driven sub-shelf melting, can be linked to changes in the carbon cycle (δ13C) during the Plio-Pleistocene. The emergence of the large NH ice sheets, which are surface mass balance (SMB)-driven, suppresses the 400-kyr-long eccentricity signal in the benthic δ18O data.

Figure 1: Simulated variables and proxies with frequency wavelets.

(a) Forcing record of the inverse routine, the LR04 benthic δ18O stacked record16. (b) Wavelet analysis48 of LR04. (c) Simulated surface-air temperature anomaly (°C) over Antarctica and (d) wavelet analysis of temperature. (e) Simulated Antarctic ice volume (106 km3) and (f) wavelet analysis of ice volume. (g) Eastern equatorial Pacific Leg 138 benthic δ13C record13 and (h) wavelet analysis of δ13C. For b,d,f,h, the >95% confidence levels are indicated by the black lines, and horizontal dashed lines indicate the 41, 100 and 400 kyr frequencies. The light shading indicates possible distorted results due to edge effects of the time series. On the left, the total power spectrum with the 95% confidence level indicated by the dashed line.


Simulated climate variability over the past 5 Myr

As expected, the LR04 benthic δ18O stack16 shows a strong periodicity in the 41-kyr obliquity band and 100-kyr glacial periodicity during the past 1 Myr (Fig. 1a,b). The 400-kyr-long eccentricity cycles in benthic δ18O data are much less pronounced throughout the past 5 Myr (Fig. 1b). Reconstructed temperature (Fig. 1c,d) exhibits a similar periodic behaviour as the benthic δ18O data (Supplementary Fig. S1 and Supplementary Data 1). However, simulated Antarctic ice volume (Fig. 1e,f) does reveal a significant and persistent 400-kyr periodicity, responding to long eccentricity variability in the sub-ocean shelf melt (Supplementary Fig. S2b,d). In particular, the 400-kyr periodicity is found in ice discharge (Supplementary Fig. S2f). For the Antarctic ice sheet (AIS), it is the dominant frequency for the period from 4.2 to 3 Myr before present (Fig. 2b).

Figure 2: Power evolution in eccentricity and obliquity frequency bands.

For both panels, 400-kyr power is shown in black, 100-kyr power in red and 41-kyr power in blue. (a) Eustatic sea level. (b) Antarctic ice volume. The two vertical dashed lines indicate transitions from 400- to 41-kyr dominant frequencies (~2.9 Myr ago) and from 41- to 100-kyr (~0.9 Myr ago). Power evolution performed with AnalySeries49 using a moving window of 1 Myr with intermediate steps of 10 kyr and a Parzen window with 90% lags.

Coherent variability of ice volume and the carbon cycle

Carbon isotope records of both benthic and planktonic foraminiferal δ13C data reflect variability in the carbon cycle. For the past glacial cycles they vary out of phase with the benthic δ18O data7, whereas for long-term pacing δ13C and δ18O vary in phase1,10,11. Here we have analysed two records over the past 5 Myr, a stacked benthic δ13C record from the eastern equatorial Pacific (Leg 138)13 (Fig. 1g,h) and a stacked planktonic δ13C record from the Mediterranean13. Both sites reflect significant 400-kyr-long eccentricity power (Supplementary Fig. S3c,f).

In our simulations, the prominent frequency in both AIS volume and eustatic sea level (as calculated from ice-volume change of all four ice sheets) show a clear progression of dominant frequencies in the course of the past 5 Myr (Fig. 2). Notably, prior to inception of the NH ice sheets (~2.9 Myr ago) sea level and AIS variability are dominated by 400-kyr-long eccentricity variability. Around 3–3.5 Myr ago, we observe a short peak in 400-kyr periodicity in the LR04 stack and in the surface-air temperature variations (Fig. 1b,d). This has previously been observed and in fact coincides with a node in the 400-kyr power of eccentricity18. Following the glacial inception of the NH ice sheets (vertical dashed line in Fig. 2 at 2.9 Myr ago) the sea level progressed into obliquity paced glacial cycles (Fig. 2a). The NH ice sheets are predominantly influenced via the SMB that is controlled by local insolation and temperature acting on surface melt17. Accordingly, NH ice volume has been shown to be driven by obliquity variations19 and reflects the dominant obliquity periodicity as shown in the surface temperature (Fig. 1d and Supplementary Fig. S3b). The 100-kyr glacial cycles emerge from the NH ice sheets after the Mid-Pleistocene transition (0.9 Myr ago)20,21. At the same time, the large sea-level fluctuations drive grounding-line advance and retreat of the West AIS.

Most remarkable, our simulations show that 400-kyr-long eccentricity cycles are persistently present in the AIS ice volume (Fig. 2b) throughout the past 5 Myr. In contrast to the NH ice variations, AIS volume is primarily controlled by sub-shelf processes17,22. The sub-shelf melt is varied accordingly with surface temperatures and an insolation anomaly (Supplementary Figs S3,S4) to simulate retreat of the West AIS for several interglacial periods5,22,23. The 400-kyr-long eccentricity changes in the δ13C data from the Mediterranean and eastern Pacific vary coherently with our simulated AIS throughout the Plio-Pleistocene (Fig. 3). The δ13C data lag AIS ice volume with an average of 23.8±0.4 and 54.0±1.6 kyr, respectively (Fig. 4).

Figure 3: Simulated variables and proxies with 400-kyr components.

In all panels 400-kyr eccentricity is shown in light-blue shading in the background, 400-kyr filtered component is shown in black (right y axis). Horizontal dashed lines represent the PD values. (a) Simulated surface-air temperature anomaly in green. (b) Site 846 Sea Surface Temperature33 in red. (c) Simulated Antarctic Ice Sheet ice volume in orange. (d) Mediterranean stack planktonic δ13C data13 in grey. (e) Leg 138 benthic δ13C data13 in blue.

Figure 4: Cross-phase analysis of climate variables with eccentricity.

Lead (positive) and lag (negative) with respect to the 400-kyr filter of eccentricity. Surface-air temperature in green, Site 846 SSTs33 in red, Eustatic sea level in blue, AIS volume in orange, Mediterranean stack planktonic δ13C data13 in grey and Leg 138 benthic δ13C data13 in black, with the dashed line showing the apparent disappearance of 400-kyr cycles13.

Sensitivity experiments

We have performed eight runs with varying different model parameters as shown in Supplementary Table S1. All runs have the same basic settings and start 5.32 Myr ago and run to the present day (PD), using the full-time solution of the LR04 benthic δ18O stack16 (Supplementary Fig. S1). First, we have tested the values for the two enhancement factors, constraint by the range as given in Ma et al.24 Second, the mass balance constant Cabl (equation (4)) has been varied for five different sets of values.

Uncertainties in ice-flow parameters

The use of the shallow ice approximation (SIA) and shallow shelf approximation (SSA) to calculate ice velocities implies an underestimation of ice velocities on land and an overestimation of the velocities in ice shelves24. Hence, SIA/SSA ice-sheet-shelf models use enhancement factors to better reproduce ice-flow characteristics, changing ice rheology—that is, the flow parameter for sheet and shelf24,25. As has been described in Ma et al.24, a ratio of ESIA/ESSA between 5 and 10 is considered here. Results show the largest response to changes in the ESSA factor, for which we have tested values between 0.6 and 0.7 (Supplementary Table S1). Responses are largest for the AIS and Greenland ice sheet (GrIS) (Supplementary Table S2), a smaller ESSA factor resulted in a larger AIS during glacial maxima and a smaller GrIS during interglacials—that is, the ice sheets exhibit a greater dynamical response to changes in temperature and/or the sea level. For the Eurasian and North American ice sheets (EuIS and NaIS, respectively), the responses are smaller and are mainly influenced by changing the ESIA factor, which is varied between 4.5 and 5.5. The ranges of these variables correspond to the estimated values given by Ma et al.24 and are similar to those used in the Parallel Ice Sheet Model (PISM)25.

Mass balance uncertainties

The largest uncertainty in the SMB parameterizations is caused by the calculation of the surface ablation—that is, melt of ice, equation (4). Here we have run the model with five sets of parameters, varying the ablation constant Cabl (Supplementary Table S1). In agreement with other studies, a more negative value results in less ablation (reducing the approximate air temperature for which ice starts to melt)26. In this case, the NH ice sheets, which are mainly controlled by the SMB, show the largest response of about 5 m sea-level equivalent (Supplementary Table S2), whereas the AIS and GrIS show smaller differences of only a few metres.

Overall, these tests show that model results do show a consistent pattern of glacial–interglacial climate variability consistent with the benthic LR04 δ18O stack that is used to force the inverse method (Supplementary Fig. S1). In two previous studies with simplified ice-sheet models, but using the same inverse methodology, the uncertainty in model results on other parameterizations were already investigated27,28. Hence, in Supplementary Fig. S5 the 2σ uncertainty interval is shown, therefore accounting for uncertainties in the benthic δ18O data and model parameterizations of deep-ocean temperature and ice-sheet δ18O values.

Comparison with temperature proxies

In Supplementary Fig. S6a–c, we compare our reconstructed surface-air temperature anomaly with three proxy-based sea-surface temperature (SST) estimates from the North Atlantic, Equatorial Pacific and Southern Ocean, respectively. Note that we here compare a surface-air temperature anomaly, derived from a global stacked benthic δ18O record, whereas the SST data also include regional variability. The curves are plotted such that the data over the past ~1 Myr largely overlap each other. The overall trends and variability match quite well when compared with these independent proxy-based temperature estimates. All data show a clear overall cooling trend from about 3.5 to 1 Myr ago and strong (100-kyr) glacial–interglacial variability thereafter.

Second, we compare our modelled deep-water temperature with an independent reconstruction of deep-water temperature change from the Southern Ocean29. The latter is derived from a combination of benthic δ18O data and Mg/Ca proxy temperatures. In Supplementary Fig. S7a, we show that the benthic δ18O data compare very well with the LR04 benthic stack used in our study. Supplementary Fig. S7b shows the deep-water temperatures, except for the unusually low temperatures around 1.4 Myr ago, our output compares favourably with the proxy-derived estimates. Both data sets show similar values of glacial–interglacial temperature change.


Our results indicate that the absence of the 400-kyr-long eccentricity cycles during the Late Pleistocene glacial cycles (Fig. 1) can be ascribed to the dominant variability of the NH ice sheets since 2.9 Myr ago (Fig. 2a and Supplementary Fig. S3d), which obscure the 400-kyr variability of the AIS. As has previously been shown, NH ice volume is predominantly controlled through the SMB with the southern margin of the NH ice sheets terminating on land30. Henceforth, ice volume is determined by surface melt, induced by insolation and temperature variability17. Although NH ice volume also shows 400-kyr variability (Supplementary Fig. S3d), this is masked by the much stronger 41- and 100-kyr signals. In contrast, the AIS is mainly influenced by the sea-level change and oceanic melt/refreezing17,22. Recent studies have shown that sub-shelf melting is also an important contributor to current mass loss of the AIS31.

The long-term sub-shelf melt variability largely arises from the inclusion of the insolation anomaly (Δqj; equation (7)). We have included the insolation anomaly in line with previous studies to simulate retreat of the West AIS5,22. To test the importance of this hypothesis, we have performed a simulation that does not include the influence of insolation changes on sub-shelf melting (Supplementary Movie 1 and Supplementary Fig. S4b,c). The overall climate variability is preserved; however, as is clearly shown the simulated West AIS is not in accordance with observed retreat during several interglacial periods5,23. Moreover, the 400-kyr power in AIS ice volume is significantly reduced. As a result, the volume is mainly controlled by temperature and sea-level variations (Supplementary Figs S3,S8). Therefore, we can conclude that an insolation-driven process is required to explain the variability of Antarctic ice volume over the Plio-Pleistocene.

The connection between AIS variability and the carbon cycle prior to NH glacial inception has been established in the Miocene, for which similar long-term 400-kyr cycles are observed in both oxygen and carbon isotopes1,10,11. During this period, the dominant factor in benthic δ18O variability can be ascribed to the AIS12,28. Analysis of the benthic δ18O data has shown that 400-kyr-long eccentricity cycles exist in both simulated AIS volume and temperature12. Moreover, Miocene expansion of the AIS has been found to be paced by 400-kyr-long eccentricity cycles, prompting coherent fluctuations in δ13C and δ18O through the formation of intermediate and deep water32.

Our simulations reveal that during the past 5 Myr changes in the carbon cycle and in AIS volume vary coherently. Both processes could be driven by low-latitude climate variations, as revealed by the persistent 400-kyr periodicity in both SST from the eastern equatorial Pacific site 846 (ref. 33) and the Mediterranean stacked δ13C record (Fig. 3)13. Our simulated surface-air temperatures (albeit a weakening signal, Fig. 3a) and the eastern equatorial Pacific SSTs are leading AIS volume and δ13C variations (Fig. 4) in support of this hypothesis. This is in agreement with the lag of δ13C relative to ice volume as observed before in Miocene isotope data1,11.

Since eccentricity lags rather than leads long-term variability in temperature and AIS volume (Fig. 4), this could imply that the 400-kyr variability emerges from nonlinear processes within the climate system. This nonlinear behaviour is also revealed by the 500-kyr peaks in the benthic δ13C data13 during the past 1 Myr and the disappearance of 400-kyr cycles in the benthic δ18O data. For long-term changes, our analysis shows that surface-air temperatures rise in coherence with a reduction in AIS volume and lower δ13C. A possible mechanism for this relation is weathering, which could be ascribed to changes in the sea level and the waxing and waning of the AIS1. For the past 5 Myr, a coherent relationship has been identified between chemical weathering proxies and benthic δ13C data at orbital time scales, indicating that an increase in chemical weathering may result in lower δ13C and a pCO2 increase34. During the Pleistocene, however, sea-level changes are largely controlled by NH ice volume. Hence, the NH ice sheets presumably played a significant role on variability in weathering. Likewise, the marked increase in AIS volume at the Eocene–Oligocene transition has been linked to a drawdown in δ13C and weathering conditions as well35.

In conclusion, our simulations of ice volume over the past 5 Myr support previous theories that have been put forward on the overriding influence of the NH ice sheets after the Mid-Pleistocene transition on the δ13C spectral properties. We have shown for the first time that the long-term changes of Antarctica reveal the persistent interaction between ice sheets, the ocean and the carbon cycle. Notwithstanding, we present a qualitative interpretation and a more comprehensive case could be made when using a coupled system that includes both climate and carbon-cycle models. Our results do show that Antarctic ice volume and carbon-cycle dynamics vary coherently, which can now be traced back into the Miocene and allows for a new understanding of the ‘400-kyr problem’.


Calculating ice volume and temperature from benthic δ18O data

Benthic δ18O data are a proxy for global ice volume and deep-water temperature15. We use an inverse forward modelling approach to deduce ice volume and temperature from the LR04 benthic δ18O record16. Here we assume that deep-water temperatures and ice volume are related to changes in the surface-air temperature over the NH. The NH temperature anomaly drives the changes in ice volume over Eurasia and North America and controls deep-water formation36. The approach derives the NH temperature anomaly from the difference between the modelled and observed benthic δ18O data17. The ice-volume contribution follows from mass conservation of δ18O between the ocean and ice sheets17. Deep-water temperature anomalies are linearly related to the surface-air temperature anomaly36 and the contribution to benthic δ18O data follows from a palaeotemperature parameterization37. From this approach, we derive a continuous and self-consistent record of surface-air temperature, ice volume and benthic δ18O data (Supplementary Fig. S1a–c). This methodology has been applied in several studies that investigate ice-volume evolution during the late Cenozoic17,20,28,36. A full description of the approach can be read in de Boer et al.17

Simulating global ice volume

The NH temperature anomaly is forwarded to four 3D ice-sheet-shelf models and applied to the SMB fields. To allow for long million-year simulations, ice velocities are computed using approximate solutions of the stress balance for sheet and shelf flow, including a representation of the transition zone from sheet to shelf17. Surface and basal mass balance are accounted for by parameterizations that include changes in temperature and solar insolation. Subsequently, the total mass budget of the ice sheet is closed with ice discharge towards open water.

Ice fluxes and mass continuity

The ANICE ice-sheet-shelf model is based on the SIA for sheet flow on land38 and the SSA for ice streams and shelves39. Following the approach that has been put forward in the PISM40, the SSA velocities are used to determine sliding velocities and are added to the SIA velocities such that a smooth transition is obtained for ice-flow from sheet to shelf41. Both velocities are adjusted with an enhancement factor ESIA and ESSA, for which the default values are chosen to be 5.0 and 0.7, respectively, close to the values as used in PISM25, and within the range as determined in a recent study24. The mass continuity equation is given by:

with Hi being the ice thickness (in m), Q the ice flux (m2 per year) and B the mass balance (m per year), given by the SMB and sub-shelf melt or refreezing. The ice flux Q is divided in a diffusive (SIA) and SSA part as:

With the diffusivity D being the scalar part from the SIA velocity equation17, and Hs the surface elevation (in m). Velocities are calculated on the regular ice thickness grid points, from which the ice fluxes are determined in between grid points A and B (staggered) using a centred difference discretization:

In the SSA term, ice thickness Hi is chosen to be HiA if the average SSA velocity between point A and B is positive, if negative, Hi is chosen to be HiB. The rectangular grid size is 20 km for the GrIS and 40 km for the EuIS, NaIS and AIS. For each grid point, the fluxes towards the directly adjacent grid points are calculated as outgoing fluxes. To keep mass conserved, in case the mass balance is negative and larger than the available ice thickness at the grid point, the outgoing fluxes are set to zero and the mass balance is set equal to the available ice thickness. After the mass conservation check, the outgoing fluxes are reduced if the combined flux exceeds the sum of the available ice thickness and mass balance (either negative or positive) during that specific time step. The total mass balance of the ice sheet is conserved and per definition is calculated from the SMB (positive or negative), the sub-shelf mass balance (positive or negative) and ice discharge towards open ocean points (negative). Mass conservation over the entire domain is monitored and is negligible during the entire 5.32 Myr simulation.


For the SMB, the initial precipitation and temperature fields are taken from the ERA-40 Reanalysis data set42, using monthly averaged fields from 1971 to 2000. Accumulation over Greenland and Antarctica is adjusted according to changes in temperature, following the Clausius–Clapeyron relation17. A precipitation model has been used for the two large NH ice sheets to adjust the PD precipitation fields. The model includes orographic forcing of precipitation and changes in the moisture content, which are calculated from the 2-m surface-air temperature and the 850-hPa wind fields17. The melt rate (in m w.e. per year) is calculated from a parameterization that is based on PD mass balance observations and modelling results for Antarctica and Greenland and incorporates changes in temperature and insolation:

here Q is the monthly incoming shortwave radiation at the top of the atmosphere (W m−2), which is changed every 1,000 years43, 0.513 is an average value for the transmissivity of the atmosphere and α is the albedo of the surface. Furthermore, ρfw is the density of fresh water, L is the latent heat of fusion (both shown in Supplementary Table S3) and Δt is the time step of the melt model—that is, a month. The constant 10 (W m−2K−1) shows the dependence on the temperature, and Cabl is a constant that is set to −32 W m−2 for the AIS and the two NH ice sheets. For Greenland, this value is set to −40 W m−2. These values are chosen in such a way that after several glacial cycles the PD ice volume closely matches the current observations of ice volume, and the PD SMB patterns are in agreement with observations. The parameterization can only produce positive values—that is, melt of ice—and also accounts for the importance of changes in the solar insolation when calculating ablation44.

Sub-shelf melt or refreezing

The calculation of sub-shelf melt or refreezing in ANICE uses a combination of several parameterizations introducing glacial–interglacial changes and ice shelves that show close to PD extent22,25. For the GrIS model, ice shelves are considered negligible and are not taken into account. Underneath the ice shelves, the melt rate is based on heat transfer between the bottom of the ice and the ocean water25,45:

with the different parameters adopted from PISM25 and shown in Supplementary Table S3. Here ρw is the seawater density (kg m−3), cpO is the specific heat capacity of the ocean (J kg−1°C−1), γT is the thermal exchange velocity (m s−1), Fmelt the sub ice-shelf melt parameter (m s−1), L the Latent heat of fusion (J kg−1) and ρi the density of ice. Toc is the ocean-water temperature (°C) adjusted with a weighting function (equation (7)). The melt rate can have both positive and negative values, either leading to melting of ice shelves or (re)freezing of ocean water45. The freezing temperature of the saline ocean water (in °C) at the shelf base is calculated with:

with SO=35 psu being the average salinity of the ocean water and zb being the depth of the ice-shelf base (in m) calculated as: zb=−(ρiw)Hi. To simulate glacial–interglacial climate variability, the ocean temperature Toc in equation (5) is adjusted with a weighting function, including changes in temperature and a small influence of summer insolation22:

Here ΔT is the applied temperature anomaly relative to PD. Furthermore, Δqj is the summer insolation anomaly relative to PD, using the January 80 °S anomaly for the AIS, and the June 65°N anomaly (W m−2) for the large NH ice sheets. The ocean temperature is then adjusted for colder than PD periods, when 0≤wg<1, as:

and for warm periods, when 1≤wg≤2:

TCD, TPD and TWM indicate the cold, PD and warm values of the uniform ocean temperature as shown in Supplementary Table S3. These values are applied to the ice sheets as spatial uniform values and are based on values found in climate models and observations46,47.

Additional information

How to cite this article: de Boer, B. et al. Persistent 400,000-year variability of Antarctic ice volume and the carbon cycle is revealed throughout the Plio-Pleistocene. Nat. Commun. 5:2999 doi: 10.1038/ncomms3999 (2014).


  1. 1

    Pälike, H. et al. The heartbeat of the Oligocene climate system. Science 314, 1894–1898 (2006).

    ADS  Article  Google Scholar 

  2. 2

    PALEOSENS Project Members. Making sense of palaeoclimate sensitivity. Nature 491, 683–691 (2012).

  3. 3

    Siegenthaler, U. et al. Stable carbon cycle-climate relationship during the late Pleistocene. Science 310, 1313–1317 (2005).

    CAS  ADS  Article  Google Scholar 

  4. 4

    Köhler, P. et al. What caused Earth’s temperature variations during the last 800,000 years? Data-based evidence on radiative forcing and constraints on climate sensitivity. Quat. Sci. Rev. 29, 129–145 (2010).

    ADS  Article  Google Scholar 

  5. 5

    Naish, T. et al. Obliquity-paced Pliocene West Antarctic ice sheet oscillations. Nature 458, 322–328 (2009).

    CAS  ADS  Article  Google Scholar 

  6. 6

    Huybers, P. Combined obliquity and precession pacing of late Pleistocene deglaciations. Nature 480, 229–232 (2011).

    CAS  ADS  Article  Google Scholar 

  7. 7

    Sigman, D. M., Hain, M. P. & Haug, G. H. The polar ocean and glacial cycles in atmospheric CO2 concentration. Nature 466, 47–55 (2010).

    CAS  ADS  Article  Google Scholar 

  8. 8

    Coxall, H., Wilson, P., Pälike, H., Lear, C. & Backman, J. Rapid stepwise onset of Antarctic glaciation and deeper calcite compensation in the Pacific Ocean. Nature 433, 53–57 (2005).

    CAS  ADS  Article  Google Scholar 

  9. 9

    DeConto, R. M. & Pollard, D. Rapid Cenozoic glaciation of Antarctica triggered by declining atmospheric CO2 . Nature 421, 245–249 (2003).

    CAS  ADS  Article  Google Scholar 

  10. 10

    Zachos, J. C., Shackleton, N. J., Revenaugh, J. S., Pälike, H. & Flower, B. P. Climate response to orbital forcing across the Oligocene-Miocene boundary. Science 292, 274–278 (2001).

    CAS  ADS  Article  Google Scholar 

  11. 11

    Holbourn, A., Kuhnt, W., Schulz, M., Flores, J.-A. & Andersen, N. Orbitally-paced climate evolution during the middle Miocene ‘Monterey’ carbon-isotope excursion. Earth Planet. Sci. Lett. 261, 534–550 (2007).

    CAS  ADS  Article  Google Scholar 

  12. 12

    Liebrand, D. et al. Antarctic ice sheet and oceanographic response to eccentricity forcing during the early Miocene. Clim. Past 7, 869–880 (2011).

    Article  Google Scholar 

  13. 13

    Wang, P., Tian, J. & Lourens, L. J. Obscuring of long eccentricity cyclicity in Pleistocene oceanic carbon isotope records. Earth Planet. Sci. Lett. 290, 319–330 (2010).

    CAS  ADS  Article  Google Scholar 

  14. 14

    Imbrie, J. & Imbrie, J. Modeling the climatic response to orbital variations. Science 207, 943–953 (1980).

    CAS  ADS  Article  Google Scholar 

  15. 15

    Chappell, L. & Shackleton, N. J. Oxygen isotopes and sea level. Nature 324, 137–140 (1986).

    CAS  ADS  Article  Google Scholar 

  16. 16

    Lisiecki, L. & Raymo, M. A Pliocene stack of 57 globally distributed benthic δ18O records. Paleoceanography 20, PA1003 (2005).

    ADS  Google Scholar 

  17. 17

    de Boer, B., van de Wal, R. S. W., Lourens, L. J. & Bintanja, R. A continuous simulation of global ice volume over the past 1 million years with 3-D ice-sheet models. Clym. Dyn. 41, 1365–1384 (2013).

    Article  Google Scholar 

  18. 18

    Meyers, S. R. & Hinnov, L. A. Northern hemisphere glaciation and the evolution of Plio-Pleistocene climate noise. Paleoceanography 25, PA3207 (2010).

    ADS  Article  Google Scholar 

  19. 19

    Lourens, L. J. et al. Linear and non-linear response of late Neogene glacial cycles to obliquity forcing and implications for the Milankovitch theory. Quat. Sci. Rev. 29, 352–365 (2010).

    ADS  Article  Google Scholar 

  20. 20

    Bintanja, R. & Van de Wal, R. S. W. North American ice-sheet dynamics and the onset of 100,000-year glacial cycles. Nature 454, 869–872 (2008).

    CAS  ADS  Article  Google Scholar 

  21. 21

    Clark, P. U. et al. The middle Pleistocene transition: characteristics, mechanisms, and implications for long-term changes in atmospheric pCO2 . Quat. Sci. Rev. 25, 3150–3184 (2006).

    ADS  Article  Google Scholar 

  22. 22

    Pollard, D. & DeConto, R. M. Modelling West Antarctic ice sheet growth and collapse through the past five million years. Nature 458, 329–332 (2009).

    CAS  ADS  Article  Google Scholar 

  23. 23

    DeConto, R. M., Pollard, D. & Kowalewski, D. Modeling Antarctic ice sheet and climate variations during marine isotope stage 31. Glob. Planet. Change 88–89, 45–52 (2012).

    ADS  Article  Google Scholar 

  24. 24

    Ma, Y. et al. Enhancement factors for grounded ice and ice shelves inferred from an anisotropic ice-flow model. J. Glaciol. 56, 805–812 (2010).

    ADS  Article  Google Scholar 

  25. 25

    Martin, M. A. et al. The Potsdam Parallel Ice Sheet Model (PISM-PIK) –Part 2: Dynamic equilibrium simulation of the Antarctic ice sheet. Cryosphere 5, 727–740 (2011).

    ADS  Article  Google Scholar 

  26. 26

    Robinson, A., Calov, R. & Ganopolski, A. Greenland ice sheet model parameters constrained using simulations of the Eemian Interglacial. Clim. Past 7, 381–396 (2011).

    Article  Google Scholar 

  27. 27

    de Boer, B., van de Wal, R., Bintanja, R., Lourens, L. & Tuenter, E. Cenozoic global ice-volume and temperature simulations with 1-D ice-sheet models forced by benthic δ18O records. Ann. Glaciol. 51, 23–33 (2010).

    CAS  ADS  Article  Google Scholar 

  28. 28

    de Boer, B., van de Wal, R. S. W., Lourens, L. J. & Bintanja, R. Transient nature of the Earth’s climate and the implications for the interpretation of benthic δ18O records. Palaeogeogr. Palaeoclimatol. Palaeoecol. 335–336, 4–11 (2012).

    Article  Google Scholar 

  29. 29

    Elderfield, H. et al. Evolution of ocean temperature and ice volume through the Mid-Pleistocene climate transition. Science 337, 704–709 (2012).

    CAS  ADS  Article  Google Scholar 

  30. 30

    Ruddiman, W. F. Orbital changes and climate. Quat. Sci. Rev. 25, 3092–3112 (2006).

    ADS  Article  Google Scholar 

  31. 31

    Pritchard, H. D. et al. Antarctic ice-sheet loss driven by basal melting of ice shelves. Nature 484, 502–505 (2012).

    CAS  ADS  Article  Google Scholar 

  32. 32

    Holbourn, A., Kuhnt, W., Frank, M. & Haley, B. A. Changes in Pacific Ocean circulation following the Miocene onset of permanent Antarctic ice cover. Earth Planet. Sci. Lett. 365, 38–50 (2013).

    CAS  ADS  Article  Google Scholar 

  33. 33

    Herbert, T., Peterson, L., Lawrence, K. & Liu., Z. Tropical ocean temperatures over the past 3.5 Myr. Science 328, 1530–1534 (2010).

    CAS  ADS  Article  Google Scholar 

  34. 34

    Tian, J., Xie, X., Ma, W., Jin, H. & Wang, P. X-ray fluorescence core scanning records of chemical weathering and monsoon evolution over the past 5 Myr in the southern South China Sea. Paleoceanography 26, PA4202 (2011).

    ADS  Article  Google Scholar 

  35. 35

    Merico, A., Tyrrell, T. & Wilson, P. A. Eocene/Oligocene ocean de-acidification linked to Antarctic glaciation by sea-level fall. Nature 452, 979–982 (2008).

    CAS  ADS  Article  Google Scholar 

  36. 36

    Bintanja, R., Van de Wal, R. S. W. & Oerlemans, J. Modelled atmospheric temperatures and global sea level over the past million years. Nature 437, 125–128 (2005).

    CAS  ADS  Article  Google Scholar 

  37. 37

    Duplessy, J.-C., Labeyrie, L. & Waelbroeck, C. Constraints on the ocean oxygen isotopic enrichment between the Last Glacial Maximum and the Holocene: Paleoceanographic implications. Quat. Sci. Rev. 21, 315–330 (2002).

    ADS  Article  Google Scholar 

  38. 38

    Hutter, L. Theoretical Glaciology D. Reidel, Dordrecht (1983).

  39. 39

    Morland, L. W. Unconfined ice-shelf flow. inDynamics of the West Antarctic Ice Sheet (eds de Veen C. J. V., Oerlemans J. 99–116D. Reidel (1987).

  40. 40

    Winkelmann, R. et al. The Potsdam Parallel Ice Sheet Model (PISM-PIK) –Part 1: Model description. Cryosphere 5, 715–726 (2011).

    ADS  Article  Google Scholar 

  41. 41

    Bueler, E. & Brown, J. Shallow shelf approximation as a ‘sliding law’ in a thermomechanically coupled ice sheet model. J. Geophys. Res. 114, F03008 (2009).

    ADS  Article  Google Scholar 

  42. 42

    Uppala, S. M. et al. The ERA-40 re-analysis. Q. J. R. Meteorol. Soc. 131, 2961–3012 (2005).

    ADS  Article  Google Scholar 

  43. 43

    Laskar, J. et al. A long-term numerical solution for the insolation quantities of the Earth. Astron. Astrophys. 428, 261–285 (2004).

    ADS  Article  Google Scholar 

  44. 44

    van de Berg, W. J., van den Broeke, M., Ettema, J., van Meijgaard, E. & Kaspar, F. Significant contribution of insolation to Eemian melting of the Greenland ice sheet. Nat. Geosci. 4, 679–683 (2011).

    CAS  ADS  Article  Google Scholar 

  45. 45

    Beckmann, A. & Goosse, H. A parameterization of ice shelf-ocean interaction for climate models. Ocean Model. 5, 157–170 (2003).

    ADS  Article  Google Scholar 

  46. 46

    Braconnot, P. et al. Results of PMIP2 coupled simulations of the Mid-Holocene and Last Glacial Maximum - Part 1: experiments and large-scale features. Clim. Past 3, 261–277 (2007).

    Article  Google Scholar 

  47. 47

    Dowsett, H. J. et al. The PRISM3D paleoenvironmental reconstruction. Stratigraphy 7, 123–139 (2010).

    Google Scholar 

  48. 48

    Grinsted, A., Moore, J. C. & Jevrejeva, S. Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlin. Processes Geophys. 11, 561–566 (2004).

    ADS  Article  Google Scholar 

  49. 49

    Paillard, D., Labeyrie, L. & Yiou, P. Macintosh program performs time-series analysis. Eos Trans. AGU 77, 379 (1996).

    ADS  Article  Google Scholar 

Download references


This research was funded through the KNAW professorship of Johannes Oerlemans. Model runs were performed on the LISA Computer Cluster. We would like to thank SurfSARA Computing and Networking Services for their support.

Author information




B.d.B. performed the experiments, the analysis and wrote the manuscript. All authors contributed to the discussion of the results and implications and commented on the manuscript at all stages.

Corresponding author

Correspondence to B. de Boer.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Figures S1-S8, Supplementary Tables S1-S3 and Supplementary References (PDF 1665 kb)

Supplementary Data

Model output from the ANICE 3-D ice-sheet-shelf models over the past 5 million years. (XLSX 5544 kb)

Supplementary Movie 1

Antarctic ice sheet evolution over the past 5 Myr. The top left panel shows the default simulation, the top right panel shows the simulation without insolation changes in the oceanic sub-shelf melt. The left scale indicates surface topography, the right scale indicates the ice thickness of the floating ice shelves. Bottom panel shows AIS volume in meters sea-level equivalent for the run with insolation (orange) and the run without insolation (blue) over the entire 5 Myr period with a 4 kyr time step. (MOV 25428 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

de Boer, B., Lourens, L. & van de Wal, R. Persistent 400,000-year variability of Antarctic ice volume and the carbon cycle is revealed throughout the Plio-Pleistocene. Nat Commun 5, 2999 (2014).

Download citation

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