Introduction

Earth’s climate during the Oligocene epoch (~34 to 23 Ma) was poised in a unipolar (Antarctic) glacial state1, between the much warmer climate state2 of the early Cenozoic era, in which the continents were mostly ice-free, and the much colder climate state of the late Cenozoic2, when major ice sheets also waxed and waned in the Northern Hemisphere3. The Oligocene climate history began with the establishment of large sustained ice sheets on Antarctica at the Eocene–Oligocene Transition (~33.6 Ma ago)4,5, followed by the colder but highly variable Mid-Oligocene Glacial Interval (~28–26.3 Ma)6. A warming climate characterised the late Oligocene warming phase (LOW) between ~26.3 and 23.7 Ma6 that was abruptly terminated by a major transient glaciation at the Oligocene-Miocene Transition (OMT; ∼23.7–22.7 Ma ago; Fig. 1a)4,7. Thus, the long-term evolution of the Antarctic ice-sheet (AIS) across the Oligocene is now relatively well established4. Yet the astronomical pacemaker of the early Cenozoic AIS is debated. Ice-proximal sedimentological records are interpreted to indicate significant, recurring obliquity-paced AIS oscillations8,9,10,11 but stratigraphic age control in such archives is often challenging. Even in ice-distal pelagic marine sequences, where age control is typically stronger, the astronomical imprint on benthic foraminiferal oxygen isotope (δ18OBF) records is enigmatic with pronounced spatial and temporal variability in both the ~400- and 100-kyr eccentricity and 40-kyr obliquity cycles6,12,13,14,15. A further complicating observation is that δ18OBF-based ice-volume reconstructions for the AIS yield sharply conflicting conclusions over the size and stability of the AIS during the LOW interval. Using a δ18OBF record from Site 1264 (South Atlantic Ocean, Fig. 2a), ref. 6 inferred episodes of high-amplitude variability in δ18OBF requiring waxing and waning by at least ~85 to 110% of the present-day volume of the East Antarctic Ice Sheet (EAIS) on ~100-kyr timescales with a distinct overall ice-volume decrease from about 27 to 24 Ma (Fig. 2a). In contrast, a heavily glaciated Antarctic continent from 27.8 to 24.5 Ma with ice sheets approaching or exceeding their modern-size and no indications of significant ice-sheet disintegration is invoked based on a δ18OBF record from Maud Rise (Antarctica; Fig. 2a)16. One major source of uncertainty contributing to these conflicting interpretations of the Antarctic glaciation history during the late Oligocene6,16 is the undocumented contribution to these δ18OBF records of bottom-water temperature (BWT) versus ice-volume change4, highlighting the need for high-quality independent records of BWT to isolate the ice-volume signal from δ18OBF.

Fig. 1: Early Oligocene to Early Miocene oxygen-isotope data and orbital variability.
figure 1

a Oxygen isotope (δ18OBF) megasplice compilation40 spanning ~30–20 Ma. b Obliquity sensitivity (Sobl) determined as the ratio between the variance in the δ18OBF megasplice record and the La2004 obliquity solution21 (calculated following ref. 20). c Evolutive power spectra of δ18OBF megasplice compilation shown in (a) calculated following R-script of ref. 20 (red colours indicate maximum power, blue colours indicate minimum power). Red box indicates the study interval presented herein spanning ~25.94–25.78 Ma.

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Fig. 2: Antarctic climate evolution during the late Oligocene.
figure 2

a Late Oligocene (27–25 Ma) δ18OBF records (C. mundulus; in ‰ VPDB) of ODP Site 12646 (black) and Site 69016 (violet). Dashed lines indicate ice-free scenario and present-day-sized EAIS26 for Site 12646 and present-day sized AIS26 for Site 69016. b IODP Site U1406 δ18OBF record (in ‰ VPDB; C. mundulus has been normalised to O. umbonatus, Supplementary Note 2) (red) together with the orbital solution for obliquity (black)21. c IODP Site U1406 Mg/Ca-based BWT estimates (in °C; green). d IODP Site U1406 δ18Osw record (in ‰ SMOW; blue) with 5-pt smoother (dark blue line) and ±0.25 ‰ uncertainty resulting from Monte Carlo Simulations (grey envelop; Methods and Supplementary Information). Red bar and arrow indicate ice-volumes bigger than the modern continental ice-volume (i.e., EAIS) and, hence, the existence of marine-based ice-sheets. Vertical bars in (b) and (c) indicate the 1σ standard deviation associated with the individual Site U1406 proxy records. Study interval (~25.94–25.78 Ma) indicated by violet shading in (a). Shaded area in (d) represents the range between the size of the modern EAIS (~24.6 × 106 km3)26 and the modelled glacial ice-volume at the Oligocene-Miocene boundary (OMB, ~23 Ma ago)35.

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Here, we reconstruct changes in seawater δ18O (δ18Osw)—a proxy for continental ice-volume4—by determining Mg/Ca-derived BWT on the same samples as δ18OBF. Our approach (Methods and Supplementary Information) follows established protocols4,17. Our δ18Osw record comes from Integrated Ocean Drilling Programme (IODP) Site U1406 situated in the northwestern Atlantic Ocean (∼40 °N and 3814 m depth)18. Oligocene strata from Site U1406 comprise rapidly deposited (up to 3 cm/kyr in our study interval)19 sediment drift deposits. Our records are based on exquisitely well-preserved foraminifera (Supplementary Note 1) (δ18OBF: Cibicidoides mundulus and Oridorsalis umbonatus; Supplementary Fig. 1; Mg/Ca: O. umbonatus; Supplementary Fig. 2) and they are of high temporal resolution (600–1000 years) with an independent, astronomically-tuned age model19. Our focus, the late Oligocene, is an interval suggested to be strongly influenced by 400- and 100-kyr eccentricity cycles in δ18OBF6,12 and low obliquity sensitivity (Sobl)20 (Fig. 1b, c). The fidelity of our coupled δ18OBF-Mg/Ca measurements is high because (i) our records are unaffected by post-depositional diagenetic alteration (Supplementary Fig. 2) and sampling effects (Methods) and (ii) we used robust calibrations to calculate BWT and δ18Osw from our δ18OBF and Mg/Ca data (Methods and Supplementary Notes 3 and 4). Our calculations were made taking care to consider temporal variability in seawater chemistry, i.e., Mg/Casw, pH, and the past oxygen-isotope composition of the AIS (δ18Oice). Our δ18Osw reconstruction yields an average uncertainty of ±0.25‰ (Fig. 2d) based on calculated 95% probability intervals through Monte Carlo Simulations (Methods). Based on these analyses, we document substantial obliquity-paced ice-volume changes in Antarctica between ~25.94 and 25.78 Ma.

Results and discussion

Glacial-interglacial variability during the late Oligocene

Our δ18OBF record shows four well-pronounced sinusoidally shaped oscillations (hereafter, glacial-interglacial cycles) in δ18OBF between 1.8‰ and 2.7‰ (Fig. 2b). Spectral analysis of the record (Fig. 3) reveals a strong 40-kyr signal related to obliquity. Comparison to the astronomical solution for obliquity21 shows correspondence of high (low) δ18OBF values with low (high) obliquity (Fig. 2b), with a phase lag of 6.2 kyr (Fig. 3). This phase lag is similar to those reported (~6.5–8 kyr) between δ18OBF and Earth’s obliquity for the Pleistocene and late Pliocene22. Calculated BWTs also show obliquity-paced fluctuations (Figs. 2c  and 3) and vary by 2 to 3 °C over the study interval. Cooler BWTs (~4.5–6 °C) correspond to intervals of high δ18OBF while intervals of warmer BWTs (~6–8 °C; Fig. 2c) occur when δ18OBF is lower.

Fig. 3: Spectral analysis of the U1406 δ18OBF, BWT and δ18Osw records.
figure 3

REDFIT spectral analysis66 of our δ18OBF (a), BWT (b) and δ18Osw (c) records. Monte Carlo confidence intervals of 80% (light blue) and 90% (dark blue). d Blackman–Tukey cross-spectral phase estimate between the δ18OBF time series (at 95% significance) and the orbital solution for obliquity21 (converted to lag times in kyr). The signal at the obliquity frequency is highlighted with grey bars.

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Amplitude of δ18Osw fluctuations

Next, we use our Mg/Ca-based BWTs together with the δ18OBF time series to deconvolve the δ18Osw component of δ18OBF. The resulting δ18Osw record mimics the glacial-interglacial cyclicity of our δ18OBF record (Fig. 2b, d) and indicates obliquity-paced waxing and waning of late Oligocene land ice (in Antarctica). Glacials are characterised by higher δ18Osw (0 to 0.20‰) than interglacials (−0.25 to −0.55‰). The amplitude of glacial-interglacial change revealed by our δ18Osw record ranges from ~0.4 to ~0.6‰ (average of ~0.5‰) and is comparable to those determined for the late Oligocene in a less well resolved Mg/Ca record from the equatorial Pacific (0.4 to 0.6‰; ODP Site 1218)23. We estimated ice-volume from our δ18Osw record by assuming the mean isotopic composition of land ice (δ18Oice) was −42‰24,25 (Supplementary Fig. 4; Supplementary Notes 5 and 6) and inferring a modern AIS baseline for δ18Osw of 0‰ (SMOW), equivalent to ~26.9 million km3 (×106 km3) of ice26 with a growth of 3.8 × 106 km3 of ice per 0.1‰ change in δ18Osw6,27 (Supplementary Fig. 4). This approach yields interglacial ice-volume estimates of ~6–17 ± 9.5 × 106 km3 of ice (~22–65 % of the modern AIS) and glacial ice-volume estimates of ~27–34.5 ± 9.5 × 106 km3 of ice (~100–128 % of the modern AIS) and, on average, results in glacial-interglacial waxing and waning of ~19 ± 9.5 × 106 km3 of ice, equivalent to ice gain/loss of ~70%. Our higher-than-modern Antarctic ice-volume estimates for late Oligocene glacials cannot be explained by ice-sheet build-up in the Northern Hemisphere. While the sporadic presence of potential ice-rafted debris in the Greenland Sea and the Arctic Ocean28,29,30 has been used to infer the presence of Northern Hemisphere ice-sheets as early as the Eocene, modelling25 and proxy-based1,31 studies rule out the suggestion of extensive ice sheets in the Northern Hemisphere this early in the Cenozoic while leaving open the possibility that short-lived, isolated and small mountain glaciers existed there throughout most of the Cenozoic32,33. An Antarctic palaeotopographic reconstruction for the Oligocene-Miocene boundary (OMB, ca. 23 Ma) that incorporates physical processes including erosion, tectonics and isostatic feedback suggests a ~15% larger land area above sea-level than at the present-day34. Based on this OMB palaeotopography34, ice-sheet modelling experiments for the OMB35 suggest that Antarctica was able to support a glacial ice-sheet ~110% of its present volume (29.65 × 106 km3)35 with ice-sheet margins extending into the ocean. While some studies on the eastern Wilkes Land margin9,36,37 suggest temperate conditions during the late Oligocene, those data are of very low temporal resolution and therefore cannot be used to assess astronomically paced change. On the other hand, our estimates of AIS volume maxima for the late Oligocene glacials (~27–34.5 ± 9.5 × 106 km3) resonate well with the latest AIS model reconstructions showing larger than modern ice volumes for a cold climate OMB state35. Support for our interpretations is also provided by the presence of ice-rafted clasts in late Oligocene sections of the Polonez Cove Formation (King George Island, Antarctic Peninsula)38 suggesting that marine-based ice drained into the Weddell Sea and by evidence that marine-terminating glaciers extended periodically beyond the coast in the Ross Sea Embayment39 during our study interval.

Waxing and waning of the late Oligocene AIS

With fluctuations on the order of ~19 ± 9.5 × 106 km3 over individual obliquity cycles, our data suggest that the AIS was highly responsive to obliquity-dominated insolation forcing during this particular Oligocene time interval. Other records spanning our study interval imply a different picture. Ice-volume estimates from one record on Maud Rise16 imply a heavily glaciated Antarctic continent with only modest variability between intervals with an AIS slightly smaller than the present day to intervals with an AIS slightly larger than the present day (δ18OBF values between 2.3 and 3.1‰)26 (Fig. 2a). Another record of ice-volume estimates for our study interval6 suggests ice-volume fluctuations ranging between an almost ice-free state and an ice-volume smaller than the modern EAIS (∆ice-volume of 15–20 × 106 km3)26 (Fig. 2a). Our record, however, shows a glacial-interglacial structure with high amplitude change from the lower ice-volume estimates of ref. 6 (mainly during interglacials) to the higher ice-volume estimates of ref. 16 during glacials (Fig. 2a, d).

Ref. 20 determined δ18OBF obliquity sensitivity (Sobl) by dividing the obliquity variance in a δ18OBF ‘megasplice’ record40 by the variance of the numerical obliquity solution21 to detect a terrestrial versus marine-based AIS during the Oligo–Miocene. Because the marine-based portion of the AIS is considered susceptible to upwelling of warm deep water from the circum-Antarctic Southern Ocean onto the continental margin on obliquity timescales9,41, a marked increase in Sobl around 24.5 My ago was interpreted to indicate that the initiation of Antarctic ice sheets large enough to have been influenced in this way20. Orbitally-paced expansion of marine-based ice sheets from the OMT onwards is also suggested by a recent sea-surface temperature compilation from the Ross Sea42. Our new obliquity-paced δ18Osw record from Site U1406 reveals that major obliquity-paced Antarctic glacial-interglacial cycles occurred at least 1.5 My before the OMT.

Our estimates of interglacial ice-volume are markedly smaller than the present day EAIS26, strongly suggesting that these late Oligocene interglacial AISs were wholly land-based. However, while there are uncertainties associated with both our calculations and the land-ice capacity of Antarctica34,35, our ice-volume estimates suggest that, for three of the four glacials studied, the late Oligocene AIS was not only larger than the present day AIS26 but also in the same range as those modelled for the OMB which included floating ice shelves35 (Fig. 2d). This observation suggests that, during the obliquity-paced glacials that we document, the AIS advanced beyond the Antarctic coastline into marine environments introducing ocean-induced melting as a mechanism of obliquity-paced deglaciation earlier than previously proposed20,42. Our records show deglaciations resulting in reductions in size of the late Oligocene AIS to ~50% of its precursor maximum glacial volume, indicating vulnerability to both bottom-up (ocean) and top-down (atmospheric) warming (Fig. 2d).

Obliquity forcing of the late Oligocene AIS

The δ18Osw record from Site U1406 provides clear evidence of a highly dynamic cryosphere during the late Oligocene epoch between ~25.94 and 25.78 Ma and shows distinct cyclicity in the obliquity band (Fig. 3). We infer that high amplitude obliquity cycles21 drive the observed glacial-interglacial cyclicity of our δ18Osw data via predominantly obliquity-paced variability in deep-water circulation patterns across the Antarctic continental margin9,20. During obliquity maxima, westerly winds and the polar front are shifted polewards. Under these conditions, the associated Ekman transport (under influence of the Westerlies) promotes enhanced upwelling and advection of warm deep water from the circum-Antarctic Southern Ocean into grounding zones and ice-shelf cavities, causing ice melt and ice sheet retreat43,44. During glacials, when the angle of Earth’s tilt was decreased, westerly winds and surface oceanic fronts were positioned more equatorward, generating a more stratified ocean with reduced upwelling of warm water across the Antarctic shelf allowing ice sheets to grow and expand across the shelf9,20.

The strong imprint of obliquity on our records contradicts the suggestion of persistently low Sobl prior to 24.5 Ma that was reconstructed for our study interval using a composite δ18OBF record20 (Fig. 1b). Our results provide robust evidence to support the obliquity-paced glacial-interglacial facies changes that have been inferred in sediments of late Oligocene age (25.99 to 25.25 Ma) from off-shore the Wilkes Land margin (East Antarctica, IODP Site U1356)9. This is an important result because, while we can be confident that the Wilkes Land margin record reflects environmental changes influencing the size of the EAIS, our records quantify the overall size of the AIS involved and benefit from strong age control so we can now be sure of the astronomical pacemaker responsible.

Obliquity-paced δ18Osw fluctuations during unipolar and bipolar glaciated climate states

Our high-resolution δ18Osw record yields novel insight into the ice ages of the understudied early Cenozoic unipolar icehouse state. Obliquity-paced glacial-interglacial δ18Osw changes reported from the late Pliocene (~3.6–2.5 Ma; 0.34 to 0.55‰) as well as the early Pleistocene (~2.5–1.8 Ma; 0.4 to 0.6‰)45,46 show similar amplitude changes to those displayed in our late Oligocene record (average of ~0.5‰; Fig. 4). In contrast to the unipolar icehouse state of the late Oligocene, however, those Plio-Pleistocene changes were driven by the advance and retreat of ice-sheets in both the Southern17 and especially the Northern Hemisphere45,46. The two most important factors controlling global ice-volume on astronomical timescales are insolation and atmospheric CO2 concentrations25,47. Existing CO2 reconstructions for the late Oligocene (between 28.78 and 23.48 Ma) are sparse but display CO2 variations between ~410 and 730 ppmv48. These CO2 concentrations are significantly higher than those reported for the late Pliocene (450–250 ppmv) and early Pleistocene (360–250 ppmv)48,49, yet glacial-interglacial δ18Osw changes are similar (Fig. 4). Our new data and observations further demonstrate that the AIS was highly susceptible to melting driven by both bottom-up (ocean) and top-down (atmospheric) warming under warmer-than-present, high-CO2 conditions of the late Oligocene.

Fig. 4: Obliquity-paced δ18Osw fluctuations during unipolar and bipolar glaciated climate states.
figure 4

Comparison of amplitude changes in δ18Osw (∆δ18Osw) during the unipolar-glaciated late Oligocene (25.94–25.78 Ma; this study; dark grey), the late Pliocene (3.6–2.5 Ma) and the early Pleistocene (2.5–1.8 Ma) (yellow: ref. 45; light grey: ref. 46) under different radiative forcing conditions (atmospheric CO2 concentrations)48,49. Late Oligocene CO2 range from 28.78 to 23.48 Ma48.

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Materials and methods

Sample material and processing

Sediments retrieved from IODP Site U1406 (J-Anomaly Ridge, northwestern Atlantic Ocean19) yielded a largely complete upper Oligocene (Chattian) sequence as indicated by shipboard sedimentological, biostratigraphical (planktic foraminifera, calcareous nannoplankton, radiolaria), and magnetostratigraphical data19 and subsequent shore-based investigations using XRF core scanning48, magnetostratigraphy49, and dinoflagellate-cyst biostratigraphy50. The sampled core material consists of clay-rich drift sediments, characterised by brown to green nannofossil ooze19 and sedimentation rates of up to 3 cm/kyr19,49. Samples with a volume of ~20 cm3 were collected from 141.29 to 145.90 m revised CCSF-A (core composite depth below seafloor, method ‘A’), following the revised splice published by ref. 48. Sample ages were calculated using the astronomically tuned timescale of ref. 20, which was created by orbitally tuning the Site U1406 high-resolution XRF-based CaCO3 record to the astronomical solution for obliquity of ref. 22. We sampled at a spacing of 2–4 cm to generate a high-resolution, sub-orbital benthic foraminiferal oxygen isotope (δ18OBF) and Mg/Ca data set for the Late Oligocene between 25.78 and 25.94 Ma. After drying in an oven at 40 °C, samples were wet-sieved over a 63 µm sieve with deionized water. Subsequently, between 2 and 15 individuals of the benthic foraminiferal taxa Oridorsalis umbonatus or Cibicidoides mundulus were picked from the >125 µm fraction, weighted and isolated for geochemical analyses.

Foraminiferal preservation

The preservation of benthic foraminifera was determined via reflected light microscope and scanning electron microscope (SEM) imaging (Supplementary Fig. 2). The resulting images show that Late Oligocene tests from Site U1406 are of exceptional, glassy50 preservation (Supplementary Fig. 2) that allows the acquisition of high-quality geochemical data. In addition, information on potential susceptibility to dissolution of the sample material was obtained by studying the shell fragmentation index (FI, Supplementary Fig. 7). Results were plotted against CaCO3 (wt%) of the samples studied and indicate no correlation. Furthermore, U1406 FI values ≤10% (Supplementary Fig. 7) are significantly lower than those presented for studies from the Eocene51 and Pliocene52. We thus conclude that dissolution did not influence the benthic foraminiferal species used for geochemical analysis in this study.

Stable isotopes

Stable oxygen isotopes (δ18OBF) for Site U1406 were primarily derived from the benthic foraminiferal taxa Oridorsalis umbonatus and, where not abundant, substituted by analyses on Cibicidoides mundulus. Constant and predictable offsets from seawater equilibrium values make both species reliable and frequently used deep-sea stable isotope tracers53,54,55. For stable isotope analyses, ~20–80 µg of the sample material has been analysed using a ThermoFinnigan MAT253Plus gas source mass spectrometer equipped with a Thermo Fisher Scientific Kiel IV carbonate device at Heidelberg University. Values are reported relative to the Vienna Pee Dee Belemnite through the analysis of an in-house standard (Solnhofen limestone) calibrated to IAEA-603. The precision of the δ18OBF analyses is better than 0.06‰. Measured δ18OBF values of C. mundulus were adjusted to O. umbonatus values by adding 0.37‰ after calculating the average interspecies offset between C. mundulus and O. umbonatus (Supplementary Fig. 1). This isotopic correction factor applied to C. mundulus values is in close agreement with recent studies (0.4‰14, 0.34‰53) that infer rather similar offsets (Supplementary Note 2).

Trace-metal analysis and Mg/Ca-based bottom-water palaeothermometry

We performed trace-metal analysis (Mg/Ca, Mn/Ca, Fe/Ca) on specimens of the shallow infaunal dwelling benthic foraminifer O. umbonatus only (Supplementary Information). For Mg/Ca analysis, ~150–200 µg of test fragments were cleaned following the protocol of ref. 56. Following crushing, subsamples were cleaned for the removal of clays with Milli-Q ultrapure water (18.2 Ω) and methanol (CH4O, ROTISOLV ≥99.98%). Remaining organic material was removed by oxidative cleaning using 250 µl of an oxidising agent (120 µl of 30% H2O2 added to 12 ml of 0.1 M NaOH). Reductive cleaning that involves bathing the sample in a hot buffered solution of hydrazine was omitted because it has been shown to lower the Mg/Ca ratio by partial dissolution of foraminiferal calcite (see ref. 56,57 for detailed discussion). Thereafter, samples were visually inspected under a binocular microscope to remove large non-carbonate particles with a fine brush. Subsequently, a weak acid leach was applied to remove any re-adsorbed contaminants from the surface of the foraminifer tests by adding 250 µl of 0.001 M HNO3 after which samples were dissolved in trace metal pure 0.075 M HNO3 to a final volume of 500 µl. Samples were analysed using an Agilent Inductively Coupled Plasma-Optical Emission Spectrometer 720 at Heidelberg University. Reported Mg/Ca values were normalised relative to the ECRM 752-1 standard with a reference value of 3.762 mmol/mol58. To ensure instrumental precision, an internal consistency standard was monitored every 12 samples with a precision of ±0.03% (1σ). To assess the potential influence of contamination with clay, Fe-oxide or Mn-oxide coatings not removed during the Mg/Ca cleaning process, we also monitored Al, Fe and Mn contents during Mg/Ca analysis (Supplementary Note 3 and Supplementary Fig. 4).

BWTs based on Mg/Ca ratios of O. umbonatus were calculated using the species-specific, exponential calibration for O. umbonatus of ref. 59 because the range of Mg/Ca ratios observed at Site U1406 (1.09–1.92 mmol/mol) is only captured within the calibration range of this specific calibration (1.09–3.43 mmol/mol) than compared to other available calibrations (for a review see Table 2 of ref. 60). Furthermore, the chosen calibration covers a BWT range of 0.8 to 9.9 °C more appropriate than other calibrations60 for the late Oligocene interval which was overall warmer than the present day.

$${{{{{{\rm{Mg}}}}}}/{{{{{\rm{Ca}}}}}}}_{{{{{{\rm{c}}}}}}}^{{{{{{\rm{t}}}}}}={{{{{\rm{t}}}}}}}=\frac{{{{{{{\rm{Mg}}}}}}/{{{{{\rm{Ca}}}}}}}_{{{{{{\rm{sw}}}}}}}^{{{{{{\rm{t}}}}}}={{{{{\rm{t}}}}}}}}{{{{{{{\rm{Mg}}}}}}/{{{{{\rm{Ca}}}}}}}_{{{{{{\rm{sw}}}}}}}^{{{{{{\rm{t}}}}}}=0}}\times {{{{{\rm{B}}}}}}\,{{{\exp }}}^{{{{{{\rm{A}}}}}}\times {{{{{\rm{BWT}}}}}}}$$
(1)

where Mg/Cac is the Mg/Ca of the foraminiferal calcite, \({{{{{{\rm{Mg}}}}}}/{{{{{\rm{Ca}}}}}}}_{{{{{{\rm{sw}}}}}}}^{{{{{{\rm{t}}}}}}={{{{{\rm{t}}}}}}}\) is seawater Mg/Ca estimated for the Late Oligocene (3.6 mol/mol)61, and \({{{{{{\rm{Mg}}}}}}/{{{{{\rm{Ca}}}}}}}_{{{{{{\rm{sw}}}}}}}^{{{{{{\rm{t}}}}}}=0}\) is seawater Mg/Ca of the modern ocean (5.2 mol/mol)62, BWT is the bottom-water temperature in degrees Celsius, and A (0.114 ± 0.02) and B (1.008 ± 0.08) are species-specific constants for O. umbonatus59,63. Because this calibration is based on oxidative and reductive cleaning of foraminiferal tests, whereas only oxidative cleaning has been applied on foraminiferal tests in this thesis, measured Mg/Ca values were adjusted by reducing each value by 10%56.

Late Oligocene δ18Osw reconstruction

Coupled Mg/Ca-oxygen isotope measurements enable the δ18O paleotemperature equation to be solved for past δ18Osw (relative to the Standard Mean Ocean Water [SMOW]) by using the equation of ref. 64:

$${{{{{{\rm{\delta }}}}}}}^{18}{{{{{{\rm{O}}}}}}}_{{{{{{\rm{sw}}}}}}}=\frac{{{{{{\rm{BWT}}}}}}-16.9}{4.0}+{{{{{{\rm{\delta }}}}}}}^{18}{{{{{{\rm{O}}}}}}}_{{{{{{\rm{BF}}}}}}}$$
(2)

where T is the Mg/Ca-based BWT estimate, δ18OBF is the measured benthic foraminiferal oxygen isotope value, and δ18Osw is past seawater δ18O. We added 0.27‰ to our data to convert all values to SMOW. The uncertainty associated with our δ18Osw reconstruction from Site U1406 was determined through a Monte Carlo Simulation yielding 1σ probability intervals. The Monte Carlo Simulation relies on the assumption that the uncertainty in our δ18Osw record derives from errors associated with the δ18Osw reconstruction65 itself, the analytical precision of δ18OBF measurements (±0.06‰) and uncertainties in BWT estimates. The uncertainty in BWT estimates is based on the analytical precision of Mg/Ca measurements (±0.03 mmol/mol) and the error associated with the BWT calibration constants63. Individual data points were randomly sampled 14,000 times within their proxy uncertainties. The mean propagated uncertainty of the δ18Osw estimate is ±0.25‰.

Spectral analysis

We applied the REDFIT spectral analysis66 using the Paleontological Statistics Software Package (PAST)67. Before analysis, our δ18OBF, BWT, and δ18Osw records were linearly detrended. The δ18OBF time series was interpolated at 0.75 kyr, and BWT and δ18Osw were interpolated at 1 kyr. All three data sets (Fig. 3) show a distinct peak at the obliquity frequency. We applied Blackman–Tukey cross-spectral phase estimate between the δ18OBF and the orbital solution for obliquity21 using the AnalySeries software package version 2.0.868. Results were converted to lag times in kyr. Compared with the frequency modulation of obliquity, there is a relative lag of 6.2 kyr for δ18OBF (Fig. 3).